High performance components of free -space optical and fiber -optic communications systems

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Content HIGH PERFORMANCE COMPONENTS OF FREE-SPACE OPTICAL AND FIBER-OPTIC COMMUNICATIONS SYSTEMS by Ryan Allan Stevenson A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) August 2005 Copyright 2005 Ryan Allan Stevenson Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3196898 Copyright 2005 by Stevenson, Ryan Allan All rights reserved. INFORMATION TO USERS The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. ® UMI UMI Microform 3196898 Copyright 2006 by ProQuest Information and Learning Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. ProQuest Information and Learning Company 300 North Zeeb Road P.O. Box 1346 Ann Arbor, Ml 48106-1346 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Dedication To my parents—• I can’t thank you enough Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgements I would first like to express my sincere gratitude to my thesis advisor, Professor P. Daniel Dapkus. Without his knowledge, experience, advice, and extraordinary patience, the completion of this thesis could not have been possible. Over the last five years I have come to understand that he is truly devoted to educating his students. Many of the personal lessons I have learned from him will prove to be just as important in my professional career as the technical ones. I would also like to express my appreciation to Dr. John O ’brien. He always made himself available to me to discuss technical issues, and the efforts he took in preparing his special topics classes made for an enriching graduate experience. I am thankful for all of his efforts in providing the photonics graduate students with some “depth.” The work presented here was a collaborative effort, thus I would like to thank my colleagues Sang Jun Choi and Yuanming Deng. Their hard work on maintaining the crystal growth reactors and on producing my epi-structures is greatly appreciated. I am also thankful for the support and friendship of the other members of my lab, Seung Jun Choi, Thiruvikraman Sadagopan, Dawei Ren, Qi Yang, Wei Zhou, Zhen Peng, Zhi-Jian Wei, and Lisandra Potaro. These are all very brilliant scientists with whom my interactions have benefited me greatly. I owe many thanks to some of the alumni of the compound semiconductor laboratory, namely Kostadin Djordjev, Aaron Bond, David (Chao-Kun) Lin, and iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Denis Tishinin. They all made time to show me device fabrication, clean room processing, and testing. I am indebted to them for this and for the numerous technical discussions that we engaged in. I am also very appreciative of Loring Smith and her hard work in getting my purchase orders processed quickly, dealing with pay roll issues, and making the business side of the lab run as smoothly as possible. I would like to thank Merrill Roragen. Without his efforts in maintaining the clean room and it’s equipment, this work would not have been possible. Lastly I would like to express my sincere appreciation to my wife, Summer, for her enduring love and support throughout the course of my time in graduate school. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents DEDICATION............................................................................................................................................ii ACKNOWLEDGEMENTS.................................................................................................................... iii LIST OF TABLES................................................................................................................................... vii LIST OF FIGURES................................................................................................................................viii ABSTRACT.............................................................................................................................................. xv CHAPTER 1: INTRODUCTION............................................................................................................ 1 1.1 F r e e Sp a c e O p t ic a l In t e r c o n n e c t s...........................................................................................................2 1.2 V e r t ic a l-C a v it y S u r f a c e-E m it t in g L a s e r s fo r F S O I ....................................................................4 1.3 In t e g r a t e d O p t ic s ............................................................................................................................................... 6 1.4 H y b r id v s. M o n o l it h ic In t e g r a t io n ........................................................................................................ 7 1.5 T h e sis O v e r v ie w a n d O u t l in e ...................................................................................................................... 9 CHAPTER 2: DESIGN OF VCSEL ARRAYS FOR FSOI............................................................. 12 2.1 O v e r v ie w o f V C S E L t e c h n o l o g y ............................................................................................................ 12 2.2 O pt ic a l C a v it y a n d M ir r o r D e s i g n ........................................................................................................17 2.2.1 Optical Cavity D esign ............................................................................................................................... 17 2.2.2 M irror D esig n .............................................................................................................................................. 18 2.3 O x id e a p e r t u r e pl a c e m e n t e f f e c t s ........................................................................................................ 29 2.4 A c t iv e r e g io n d e s ig n ...................................................................................................................................... 36 2.4.1 M aterials system selection........................................................................................................................37 2.4.2 Quantum well design................................................................................................................................. 38 2.5 D e v ic e o p tim iz a tio n .........................................................................................................................................43 2.6 S u m m a r y o f d e v ic e d e s ig n ...........................................................................................................................47 CHAPTER 3: HIGH-FREQUENCY VCSEL DESIGN....................................................................52 3.1 In t r in sic fr e q u e n c y p e r f o r m a n c e ......................................................................................................... 52 3.2 H ig h -f r e q u e n c y p a r a s it ic s..........................................................................................................................58 3.2.1 Parasitic R esistance...................................................................................................................................59 3.2.2 Parasitic C apacitance............................................................................................................................... 68 3.3 S u m m a r y o f h ig h -f r e q u e n c y d e s ig n ......................................................................................................73 CHAPTER 4: VCSEL FABRICATION AND PERFORMANCE................................................. 76 4.1 V C S E L E p it a x y ................................................................................................................................................76 4.1.1 M OCVD reactor se tu p .............................................................................................................................. 77 4.1.2 Crystal growth by M O C VD ..................................................................................................................... 79 4.2’ D B R AND CAVITY CALIBRATION.....................................................................................................................80 4.3 D e v ic e p r o c e s s in g .............................................................................................................................................83 4.3.1 Process overview ......................................................................................................................................... 83 4.3.2 Dry etching.................................................................................................................................................... 85 4.3.3 Wet o xid a tio n ............................................................................................................................................... 90 4.4 D e v ic e p e r f o r m a c e .......................................................................................................................................... 94 4.4.1 SiNx-isolated devices..................................................................................................................................94 4.4.2 Polyim ide-isolated V C SE L s....................................................................................................................96 4.4.3 Ion-im planted VCSELs........................................................................................................................... 103 4.5 V C S E L S u m m a r y ............................................................................................................................................. 105 CHAPTER 5: BAND GAP ENGINEERING WITH SELECTIVE AREA GROWTH...........107 V Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.1 SA G M e c h a n is m s............................................................................................................................................. 107 5.2 B r o a d -a r e a SA G l a s e r s .............................................................................................................................109 5.3 W a f e r p r e p a r a t io n fo r S A G .................................................................................................................... 111 5.4 SA G c h a r a c t e r iz a t io n ............................................................................................................................... 119 5.5 S u m m a r y o f S A G .............................................................................................................................................124 CHAPTER 6: MONOLITHIC PIC DESIGN WITH SAG............................................................ 127 6.1 E A M DESIGN........................................................................................................................................................ 127 6.1.1 Modeling the QCSE................................................................................................................... 128 6.1.2 EAM Optimization..................................................................................................................... 135 6.2 SO A D e s i g n ........................................................................................................................................................ 146 6.2.1 SAG Mask Pattern Design........................................................................................................ 146 6.2.2 Quantum Well Number..............................................................................................................147 6.2.3 SOA Length.................................................................................................................................149 6.3 S O A /E A M F a b r ic a t io n ................................. 151 6.3.1 Process Flow...............................................................................................................................151 6.3.2 Electroplating............................................................................................................................. 155 6.4 S O A /E A M PERFORMANCE RESULTS........................................................................................................... 156 6.4.1 Laser Performance.................................................................................................................... 157 6.4.2 Single-Pass Performance......................................................................................................... 159 6.4.3 Far Field Characterization.................................................................................. 164 6.5 D isc u s s io n a n d Su m m a r y ............................................................................................................................166 CHAPTER 7: ADIABATIC MODE EXPANSION.........................................................................170 7.1 O u t p u t f a c e t d e s ig n ......................................................................................................................................174 7.2 T a p e r d e s ig n ......................................................................................................................................................182 7.3 D e v ic e f a b r ic a t io n ........................................................................................................................................186 7.4 F a r f ie l d r e s u l t s ............................................................................................................................................189 7.5 Su m m a r y o f a d ia b a t ic m o d e e x p a n s io n ............................................................................................ 193 CHAPTER 8: SUMMARY AND FUTURE RESEARCH DIRECTIONS................................. 197 8.1 S u m m a r y o f h ig h -s p e e d , t o p-e m it t in g V C S E L s ............................................................................. 197 8.2 F u t u r e V C S E L r e s e a r c h d ir e c t io n s....................................................................................................199 8.3 S u m m a r y o f SA G a n d t h e in t e g r a t e d S O A /E A M /S S C ..............................................................200 8.4 F u t u r e SSC r e s e a r c h d ir e c t io n s...........................................................................................................202 BIBLIOGRAPHY.............................................. 205 APPENDIX A: NUMERICAL METHODS......................................................................................213 A1 T h e p r o p a g a t io n m a t r ix a l g o r it h m ................................................................................................... 213 A l .l Mathematical derivation........................................................................................................... 213 A1.2 Sample Matlab code................................................................................................................... 216 A2 T h e f i n i t e d i f f e r e n c e a l g o r i t h m ...........................................................................................................217 A2.1 Mathematical derivation........................................................................................................... 217 A2.2 Sample Matlab code...................................................................................................................219 APPENDIX B: DEVICE PROCESSING FOLLOWERS..............................................................221 vi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Tables T a b l e 2.1: P a r a m e t e r s u s e d t o c a l c u l a t e t h r e s h o l d c u r r e n t , c u r r e n t fo r I m W o u t p u t POWER, AND WALL-PLUG EFFICIENCY...................................................................................................................... 46 T a b l e 3.1 P r o t o n im p l a n t a t io n s c h e d u l e f o r b o n d pa d is o l a t io n ....................................................69 T a b le 6.1 I n t e g r a t e d SOA/EAM S t r a i n - s t a b l i l i z e d E p i - s t r u c t u r e ..............................................147 T a b le B 1.1 T o p -e m ittin g , S iN x - is o la te d VCSEL f o l l o w e r .................................................................222 T a b l e B 1.2 S O A /E A M /SSC p r o c e ss f o l l o w e r ..............................................................................................224 T a b l e B 1.3 InP B A la se r pr o c e ss f o l l o w e r ................................................................................................. 229 vii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. List of Figures F ig u r e 1.1 R e g im e s o f a ppl ic a t io n s f o r v a r io u s o p t ic a l in t e r c o n n e c t t e c h n o l o g ie s [8], T h e so l id l in e in d ic a t e s t h e n e c e s s a r y d a t a r a t e t o a c h ie v e 5 T b / s ..................................... 4 F ig u r e 1.2 F r e e -s pa c e o p t ic a l in t e r c o n n e c t c o n c e p t fo r m a ss iv e p a r a l l e l c o m m u n ic a t io n s b e t w e e n a d ja c e n t c o m p u t e r b o a r d s................................................................... 5 F ig u r e 1.3 S c h e m a tic o f b i - d i r e c t i o n a l b o a r d - t o - b o a r d c o m m u n ic a tio n s v ia FSOI..............6 F ig u r e 1.4 A s c h e m a tic o f a WDM tr a n s m i s s i o n s y s te m ........................................................................... 6 F ig u r e 2.1 VCSEL d e v ic e s t r u c t u r e s f o r o p t i c a l / e l e c t r i c a l c o n f in e m e n t: a ) e t c h e d - p o s t ; b ) d i e l e c t r i c a p e r t u r e ; c ) io n im p la n te d ; d ) b u r ie d h e t e r o s t r u c t u r e . T h e d i r e c t i o n o f c u r r e n t f l o w is i n d i c a te d b y t h e a r r o w s [1 1 ].............................................................................14 F ig u r e 2.2 A s c h e m a tic d ia g r a m o f a VCSEL c a v i t y ..................................................................................18 F ig u r e 2.3 A s c h e m a tic o f a DBR s h o w in g t h e s u c c e s s iv e c o h e r e n t r e f l e c t i o n s f r o m t h e h ig h - in d e x a n d lo w - in d e x l a y e r s . S m a l l r e f l e c t i o n s , r , f r o m e a c h l a y e r i n t e r f a c e ADD CONSTRUCTIVELY TO PRODUCE A LARGE NET REFLECTION, Rx...............................................19 F ig u r e 2.4 A t r a n s m i s s i o n m a t r i x r e p r e s e n t a t i o n f o r a DBR m i r r o r [3 5 ]...................................21 F ig u r e 2.5 P o w e r r e f l e c t a n c e o f a DBR m i r r o r v e r s u s p e rio d n u m b e r , m, f o r v a r i o u s h ig h / l o w r e f r a c t iv e in d e x c o n t r a st s a t t h e B r a g g w a v e l e n g t h ........................................ 23 F ig u r e 2.6 T h e r e f l e c t i v i t y s p e c tr u m c a l c u l a t e d f o r a 25 p e rio d A l 2G a .8A s/A l< )G a.i A s DBR USING t h e p r o p a g a t io n m a t r i x m e th o d . T h e in s e t s h o w s t h e p h a s e o f t h e r e f l e c t i o n ............................................................................................................................................................... 25 F ig u r e 2.7 T h e r e f l e c t i v i t y s p e c tr u m o f a c o m p l e te V C S E L c a v i t y w ith 20 p e r io d to p a n d b o t t o m A l 2G a .8A s / A l 9G a jA s DBRs........................................................................................................ 26 F ig u r e 2.8 T h e e l e c t r i c f i e l d a n d r e f r a c t i v e in d e x p r o f i l e o f a VCSEL c a v i t y w i t h a 20- p e r io d TOP DBR AND 40-PERIOD BOTTOM DBR........................................................................................ 27 F ig u r e 2.9 A VCSEL c a v i t y e f f e c t i v e - m i r r o r s c h e m a tic d e m o n s t r a t i n g s c a t t e r i n g l o s s FROM A NARROW APERTURE. THE DBRS ARE APPROXIMATED AS HARD MIRRORS AT A PENETRATION DEPTH LP E N FROM THE APERTURE...........................................................................................30 F ig u r e 2.10 VCSEL c a v i t y r e s o n a n t w a v e l e n g t h s h i f t s f o r o x id e a p e r t u r e p l a c e m e n t a t THE PEAK OR NULL IN THE STANDING WAVE ELECTRIC FIELD..................................................................32 F ig u r e 2.11 S c a t t e r in g lo ss c a l c u l a t io n s v e r su s a p e r t u r e ra d iu s fo r t h e o x id e a p e r t u r e PLACED AT THE PEAK AND NULL OF THE CAVITY STANDING WAVE....................................................... 33 viii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u r e 2.12 F a r -f ie l d a n g l e c a l c u l a t io n fo r t h e o x id e a p e r t u r e p l a c e d a t t h e p e a k o r NULL IN THE CAVITY STANDING WAVE FIELD. THE ARROWS INDICATE THE RANGE OF V - NUMBER FOR WHICH THE CALCULATION IS ACCURATE.............................................................................. 36 F ig u r e 2.13 G a in sp e c t r a a t 10 d e g r e e in c r e m e n t s fo r a n A lG a A s/G a A s q u a n t u m w e l l . T h e p e a k po s it io n is pl o t t e d v e r su s t e m p e r a t u r e in t h e in s e t.................................................40 F ig u r e 2.14 C o n t o u r lin es o f q u a n t u m w e l l t r a n s it io n w a v e l e n g t h v e r su s q u a n t u m WELL WIDTH AND AL MOLE FRACTION. THE DESIRED EMISSION IS 845NM.......................................41 F ig u r e 2.15 C o n d u c t io n b a n d b o u n d sta tes a n d w a v e fu n c t io n s fo r a n A l G a A s/G aA s QUANTUM WELL WITH AL MOLE-FRACTIONS OF 0.2 AND 0 .3 ..................................................................43 F ig u r e 2.16 Q u a n t u m w e l l n u m b e r o p t im iz a t io n .........................................................................................45 F ig u r e 2.17 B ias c u r r e n t a n d w a l l-p l u g e f f ic ie n c y v e r su s m ir r o r r e f l e c t iv it y f o r I m W o f o u t p u t p o w e r . N o t e t h a t t h e l e f t a x is is a l o g s c a l e ........................................................... 47 F ig u r e 3.1 F r e q u e n c y r e s p o n s e o f a V C S E L c a l c u l a t e d a s s u m in g t y p ic a l p a r a m e t e r s f o r a n A l 2G a .8A s/G aA s 80A q u a n t u m w e l l .................................................................................................53 F ig u r e 3.2 G a in a n d d if f e r e n t ia l g a in f o r a n A l 2G a .8A s/G aA s Q W .................................................55 F ig u r e 3.3 P a r a s it ic c ir c u it e l e m e n t s in a V C S E L s t r u c t u r e..............................................................59 F ig u r e 3.4 C ir c u l a r t e s t p a t t e r n s fo r d e t e r m in a t io n o f s pe c ific c o n t a c t r e s is t a n c e....... 61 F ig u r e 3.5 T r a n s m is s io n l in e m e a s u r e m e n t a n d f it t e d r e s u l t s..........................................................62 F ig u r e 3.6 V a l e n c e b a n d d ia g r a m s fo r a D B R s t r u c t u r e f o r : a ) M o d u l a t io n d o p in g WITHOUT GRADED INTERFACES; B) MODULATION DOING WITH GRADED INTERFACES; AND C) NEITHER DOPING NOR GRADED INTERFACES..................................................................................................64 F ig u r e 3.7 V C S E L s c h e m a t ic d is p l a y in g th e t h r e e r e g io n s o f c u r r e n t s p r e a d in g ................. 65 F ig u r e 3.8 C a l c u l a t e d a n d m e a s u r e d r e s is t a n c e d a t a ........................................................................... 67 F ig u r e 3.9 C a l c u l a t e d v a c a n c y d ist r ib u t io n s fo r in c r e a s in g im p l a n t a t io n e n e r g ie s f r o m 2 0 k eV t o 36 0 k eV . T h e in se t d ispl a y s t h e l o n g it u d in a l s t r a g g l e v e r s u s io n e n e r g y . ....................................................................................................................................................................................... 70 F ig u r e 3.10 C o m p a r is o n o f p o l y im id e a n d io n im p l a n t a t io n fo r b o n d p a d is o l a t io n .............72 F ig u r e 4.1 S c h e m a t ic d r a w in g o f a M O C V D r e a c t o r ...............................................................................77 F ig u r e 4.2 V C S E L c a v it y c a l ib r a t io n sh o w in g m e a s u r e d a n d c a l c u l a t e d r e f l e c t iv it y DATA (COURTESY Y. DENG)................................................................................................................................ 81 F ig u r e 4.3 A sc h e m a t ic o f t h e P l a s m a Q u e s t E C R d r y e t c h in g s y s t e m ...........................................85 ix Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u r e 4.4 SE M o f a V C S E L m e sa s u r f a c e a f t e r E C R e t c h in g w it h a 1000A S iN x m a s k a n d IMPROPER PHOTORESIST CLEANING. THE SURFACE LOOKS BLACK BECAUSE OF IT’S ROUGHNESS DUE TO MASK EROSION. THE STRAIGHT LINE FEATURES ARE PATTERN TRANSFERS FROM PHOTORESIST RESIDUE........................................................................................................................................... 88 F ig u r e 4.5 SE M o f a n e t c h e d V C S E L m e s a . T h e c o n t a c t r in g is s e e n o n t o p o f t h e m e s a . 89 F ig u r e 4.6 C h a r t r e c o r d e r o u t p u t d u r in g E C R e t c h in g o f a V C S E L s t r u c t u r e . E a c h PERIOD IN THE OSCILLATIONS CORRESPONDS TO ONE D B R PAIR........................................................... 89 F ig u r e 4.7 W e t o x id a t io n a p p a r a t u s...................................................................................................................90 F ig u r e 4.8 S c h e m a t ic o f w e t o x id a t io n m e c h a n is m s..................................................................................92 F ig u r e 4.9 A c o m p l e t e d t o p-e m it t in g V C S E L .................................................................................................94 F ig u r e 4.10 L I a n d IV d a t a f o r a 2|tm -a p e r t u r e t o p-e m it t in g V C S E L . T h e in se t s h o w s t h e l a s in g s p e c t r u m ...................................................................................................................................................95 F ig u r e 4.11 SE M o f a n e t c h e d V C S E L m e s a fo r p o l y im id e p a s s iv a t io n ..........................................96 F ig u r e 4.12 P o l y im id e spin s p e e d -t h ic k n e ss c a l ib r a t io n d a t a .............................................................97 F ig u r e 4.13 A c o m p l e t e d V C S E L w it h p o l y im id e p l a n a r iz a t io n ........................................................ 99 F ig u r e 4.14 F r e q u e n c y r e s p o n s e fo r a p o l y im id e- iso l a t e d d e v ic e w it h a n a p e r t u r e w id t h o f 6|tm a n d a t h r e s h o l d c u r r e n t o f 7 0 0 r A. T h e D C b ia s in c r e a s e s f r o m 1m A to 1.5m A a t 100pA in c r e m e n t s........................................................................................................................100 F ig u r e 4.15 M o d u l a t io n r e spo n se s fo r a 12|om a p e r t u r e, p o l y im id e-is o l a t e d d e v ic e ........ 102 F ig u r e 4.16 V C S E L w a fe r a f t e r m a s k in g fo r io n im p l a n t a t io n ........................................................103 F ig u r e 4.17 M o d u l a t io n r e s p o n s e s fo r a 6|tm a p e r t u r e, im p l a n t is o l a t e d d e v ic e ................104 F ig u r e 5.1 S c h e m a t ic o f SA G m e c h a n is m s......................................................................................................108 F ig u r e 5.2 C r o s s-s e c t io n a l SE M pic t u r e o f SA G m a t e r ia l s h o w in g t h e e f f e c t s o f g a s- PHASE DIFFUSION AND SURFACE MIGRATION...............................................................................................109 F ig u r e 5.3 A SE M im a g e o f a c o m p l e t e d SA G -B A d e v ic e ...................................................................... I l l F ig u r e 5.4 L I c u r v e s fo r B A la se r s fa b r ic a t e d f r o m t h e su r f a c e t r e a t m e n t e x p e r im e n t . O p t im u m r e su l t s a r e o b t a in e d w it h s a m p l e D .................................................................................115 F ig u r e 5.5 T h r e sh o l d c u r r e n t d e n s it y c o m p a r is o n b e t w e e n SA G -B A l a se r s w it h a n d w it h o u t a n In G aA s p r o t e c t io n l a y e r . T h e c a v it y l e n g t h fo r t h e E E L s is 1m m .....116 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u r e 5.6 T h r e s h o l d c u r r e n t d e n s itie s f o r SAG-BA l a s e r s w ith v a r i o u s s u r f a c e PREPARATION CHEMISTRIES.........................................................................................................................................117 F ig u r e 5.7 T h r e s h o l d c u r r e n t d e n s i ty c o m p a r is o n f o r i n t e r r u p t e d g r o w t h ......................... 119 F ig u r e 5.8 T h r e s h o l d c u r r e n t d e n s i ty a n d d i f f e r e n t i a l e f f ic i e n c y d a t a f o r s a m p le s in w h ic h t h e SiNx SAG m a s k w a s r e m o v e d w ith e i t h e r 1:10 BOE o r 49% HF a c i d 120 F ig u r e 5.9 S c h e m a tic o f t h e m a s k l a y o u t f o r t h e SAG c h a r a c t e r i z a t i o n e x p e r im e n t. ..121 F ig u r e 5.10 E n h a n c e m e n t r a t i o s f o r In P a n d In G a A s P v e r s u s SAG m a s k w i d t h ...................121 F ig u r e 5.11 SEM p ic t u r e s o f t h e q u a n tu m w e l l l a y e r s f o r d i f f e r e n t SAG m a s k w id th s FROM THE PLAIN REGION (NO GROWTH ENHANCEMENT) TO 50|TM................................................122 F ig u r e 5.12 W a v e l e n g t h s h i f t a n d t h r e s h o l d c u r r e n t d e n s i ty f o r SAG-BA l a s e r s v e r s u s SAG m a s k w i d t h ................................................................................................................................................ 123 F ig u r e 5.13 C L s c a n s t h r o u g h SAG a n d p la i n r e g i o n s f o r 10pM a n d 2 0|im SAG m a s k w i d t h s ......................................................................................................................................................................124 F ig u r e 6.1 T h e c a l c u l a t e d a b s o r p t i o n s p e c tr u m f o r a n In G a A s P q u a n tu m w e l l . T h e s p e c t r u m in c l u d e s t r a n s i t i o n s f r o m t h e h e a v y h o l e a n d l i g h t h o l e v a l e n c e b a n d s . ................................................................................................................................................................. 135 F ig u r e 6.2 T h e s q u a r e o f t h e e l e c t r o n - h o l e o v e r l a p i n t e g r a l f o r t h e CB-F1H1 a n d CB- LFU t r a n s i t i o n s . N o te t h a t t h e t w o d o n o t h a v e t h e s a m e d e p e n d e n c e o n e l e c t r i c FIELD..........................................................................................................................................................................136 F ig u r e 6.3 A c o n t o u r p l o t o f c o n t r a s t r a t i o a n d tr a n s m i s s i o n c h a n g e v e r s u s i n s e r t i o n LOSS AND THE M PARAMETER............................................................................................................................139 F ig u r e 6.4 O p t im iz a t io n o f in t r in sic l a y e r th ic k n e ss w it h r e s p e c t t o m o d u l a t io n BANDWIDTH AND ELECTRIC FIELD ACROSS THE INTRINSIC LAYER. THE ELECTRIC FIELD IS PLOTTED FOR DRIVE VOLTAGES OF 2-5 V .......................................................................................................140 F ig u r e 6.5 H e a v y h o l e e s c a p e t im e as a f u n c t io n o f a r se n ic c o m p o s it io n a n d b a r r ie r THICKNESS................................................................................................................................................................143 F ig u r e 6.6 A p l o t o f t h e p a r a m e t e r Aa/F2 v e r s u s q u a n tu m w e l l w id th a n d a r s e n i c c o m p o s it io n .......................................................................................................................................................... 145 F ig u r e 6.7 A p l o t o f t h e p a r a m e t e r M=Aa/a0 v e r s u s q u a n tu m w e l l w id th a n d a r s e n i c c o m p o s it io n .................................. 145 F ig u r e 6.8 L a s in g s p e c t r a f r o m t h e p la in , 10|im a n d 15|tm SAG m a s k p a t t e r n s ..................... 148 xi Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F ig u r e 6.9 C o m p a r is o n o f l o sse s a n d in t e r n a l e f f ic ie n c y fo r 6 a n d 8 q u a n t u m w e l l ACTIVE REGIONS.....................................................................................................................................................149 F ig u r e 6.10 I n t e r n a l e f f ic ie n c y , i n t e r n a l lo s s , a n d g a in f i t r e s u l t s f r o m t h e SAG-BA CAVITY LENGTH EXPERIMENT........................................................................................................................... 150 F ig u r e 6.11 G a in a n d c u r r e n t d e n s it y v a r ia t io n w it h pu m p in g c u r r e n t a n d a m p l if ie r LENGTH......................................................................................................................................................................152 F ig u r e 6.12 A s c h e m a t ic o f t h e d e v ic e l a y o u t............................................................................................153 F ig u r e 6.13 SEM p h o to o f t h e e t c h e d m e s a , lo o k i n g a t t h e j u n c t i o n b e tw e e n SAG a n d PLAIN REGIONS....................................................................................................................................................... 154 F ig u r e 6.14 A SEM c r o s s - s e c t i o n o f t h e c o m p le te d d e v ic e .................................................................155 F ig u r e 6.15 A s c h e m a t ic d r a w in g o f t h e e l e c t r o p l a t in g p r o c e s s...................................................157 F ig u r e 6.16 A n e l e c t r o p l a t e d b o n d p a d ......................................................................................................... 157 F ig u r e 6.17 Se c t io n -t o -Se c t io n IV m e a s u r e m e n t . T h e r e s is t a n c e is 9 k£2.................................. 158 F ig u r e 6.18 T h e p o w e r - c u r r e n t c h a r a c t e r i s t i c s o f a 10|im SAG SOA/EAM d e v ic e a t i n c r e a s i n g r e v e r s e b ia s o n t h e EAM. T h e i n s e t s h o w s a c a l c u l a t i o n o f t h e c h a n g e IN LOSS WITH INCREASING EAM REVERSE BIAS.........................................................................................159 F ig u r e 6.19 T h e L a s in g sp e c t r u m o f a 10|u .m SA G d e v ic e a t in c r e a s in g E A M r e v e r s e b ia s. 160 F ig u r e 6.20 A s c h e m a tic o f t h e w a v e g u id e m e a s u r e m e n t s e t u p ....................................................... 161 F ig u r e 6.21 SOA c h ip g a in a n d f i b e r - t o - f i b e r g a in m e a s u r e m e n t r e s u l t s ..................................163 F ig u r e 6.22 EAM a b s o r p tio n s p e c tr u m a n d a t t e n u a t i o n a t i n c r e a s i n g r e v e r s e b i a s 165 F ig u r e 6.23 F a r f i e l d r a d i a t i o n p a t t e r n s f o r t h e SOA/EAM d e v ic e . T h e 1/e2 h a l f - a n g l e s ARE 19° BY 50° IN THE HORIZONTAL AND VERTICAL DIRECTIONS.......................................................166 F ig u r e 7.1 T h r e e v a r i a n t s o f a l a t e r a l l y t a p e r e d w a v e g u id e m o d e e x p a n d e r : (a ) b u r ie d ; (B) VERTICALLY-COUPLED DILUTE WAVEGUIDE; (C) VERTICALLY-COUPLED SINGLE-CORE WAVEGUIDE............................................................................................................................................................. 173 F ig u r e 7.2 A s c h e m a tic l a y o u t o f t h e SOA/EAM d e v ic e w ith t h e p r o p o s e d m o d e e x p a n d e r STRUCTURE.............................................................................................................................................................. 174 F ig u r e 7.3 S c h e m a tic c r o s s - s e c t i o n o f t h e v e r t i c a l c o u p l e r m o d e e x p a n d e r . T h e m a r k e r s i n d i c a te d b y “E tc h - S t o p ,” “P a r t i a l e t c h - t h r u , ” a n d “E t c h - T h r u ” i n d i c a t e t h r e e d i f f e r e n t e t c h i n g sc h e m e s a s d is c u s s e d b e lo w (s e e f i g u r e 7.5 b e lo w ) ...............175 xii Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. F ig u r e 7.4 T h e v e r t ic a l c o u p l e r c r o s s-se c t io n a n d c o r r e s p o n d in g n e a r f ie l d m o d e PROFILES...................................................................................................................................................................176 F ig u r e 7.5 M o d a l in d e x c a l c u l a t i o n s v e r s u s t a p e r w id th f o r t h r e e d i f f e r e n t e t c h i n g c o n d itio n s . T h e d a s h e d li n e s r e p r e s e n t t h e m o d a l in d ic e s f o r t w o d i f f e r e n t p a s s iv e w a v e g u id e d e s ig n s . T h e i n t e r s e c t i o n o f t h e c u r v e s w ith t h e s e li n e s r e p r e s e n t s t h e p h a s e - m a tc h e d c o n d i t i o n ............................................................................................................................ 177 F ig u r e 7.6 M a x im u m f r a c t io n o f p o w e r c o u pl e d in t o t h e p a s s iv e w a v e g u id e v e r su s t a pe r w id t h . N e a r l y 100% p o w e r t r a n s f e r o c c u r s a t t h e p h a s e-m a t c h e d c o n d it io n . T h e po w e r c o u p l in g l e n g t h is r o u g h l y 63|XM............................................................................................ 179 F ig u r e 7.7 P o w e r t r a n s f e r c a l c u l a t io n s f o r v a r io u s spa c e r l a y e r t h ic k n e s s e s. T h e SOLID VERTICAL LINE REPRESENTS THE CUT-OFF POINT FOR THE ACTIVE WAVEGUIDE............... 181 F ig u r e 7.8 B P M c a l c u l a t io n s f o r a 2|tm spa c e r (l e f t) a n d a 0.5|i m sp a c e r (r ig h t )...............182 F ig u r e 7.9 S c h e m a t ic il l u s t r a t io n o f t h e l o c a l t a p e r l e n g t h s c a l e ........................................... 184 F ig u r e 7 .10 B PM c a l c u l a t io n f o r t h e 0.5|tm s p a c e r , 500|xm-l o n g t a p e r d e sig n a n d t h e c o r r e s p o n d in g po w e r in t h e a c t iv e a n d p a s s iv e w a v e g u id e s v e r su s p r o p a g a t io n DISTANCE. A SCHEMATIC OF THE TAPERED STRUCTURE IS ALSO SHOWN IN THE INTENSITY PLOT (LEFT)........................................................................................................................................................................ 186 F ig u r e 7.11 SEM o f a w e t - e t c h e d , t a p e r e d s t r u c t u r e s h o w in g m e c h a n i c a l d a m a g e t o t h e RIDGE WAVEGUIDE................................................................................................................................................187 F ig u r e 7.12 SEM p i c t u r e o f t h e t a p e r e d w a v e g u id e a f t e r ICP e tc h i n g . T h e p a s s iv e w a v e g u id e h a s n o t b e e n e t c h e d ...............................................................................................................188 F ig u r e 7.13 SEM p i c t u r e s h o w in g t h e d r y - e t c h i n t e r f a c e b e tw e e n t h e SOA a n d t a p e r e d s e c t io n s o f t h e d e v ic e ....................................................................................................................................190 F ig u r e 7.14 F a r fie l d m e a s u r e m e n t s fo r t h e v e r t ic a l l y -c o u pl e d m o d e e x p a n d e r s t r u c t u r e. T h e m e a s u r e m e n t s sh o w n a b o v e a r e fo r a 500|i m t a p e r , 0.5(im sp a c e r DEVICE......................................................................................................................................................................191 F ig u r e 7.15 A f i e l d e m is s io n SEM p i c t u r e o f t h e t a p e r e d w a v e g u id e f a c e t . T h e w a v e g u id e w id th a t t h e b a s e o f t h e a c t i v e w a v e g u id e is r o u g h l y 0.6|um. T h e BRIGHTER STRIPES INDICATE InGaAsP MATERIAL WHILE THE DARKER REGIONS INDICATE InP. T h e MATERIAL IN THE UPPER LEFT OF THE FIGURE IS HIGHLY-CHARGED POLYIMIDE.................. 192 F ig u r e 7.16 C a l c u l a t e d n e a r -f ie l d in t e n s it y pl o t s fo r t h e c o r r e c t l y -e t c h e d w a v e g u id e STRUCTURE (LEFT) AND THE OVER-ETCHED STRUCTURE (RIGHT). THE SUBSTRATE LEAKAGE IS CLEARLY OBSERVED IN THE OVER-ETCHED CASE.......................................................................................193 F ig u r e 8.1 S c h e m a tic o f a t u n n e l - j u n c t i o n VCSEL................................................................................ 201 xiii Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. F ig u r e 8.2 M o d e c r o s s - s e c t i o n s im u l a ti o n s o f a d i l u t e w a v e g u id e s t r u c t u r e . T h e m o d e IN THE ACTIVE WAVEGUIDE IS SHOWN ON THE LEFT. THE MODE IN THE PASSIVE WAVEGUIDE IS SHOWN ON THE RIGHT............................................................................................................... 205 F ig u r e A l . 1 S c h e m a tic o f a l a y e r e d d i e l e c t r i c s t r u c t u r e ................................................................215 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Abstract In this thesis the design, fabrication, and testing of high-performance components of future fiber-optic and free space optical communications systems are presented. The first part of this dissertation discusses the design and fabrication of high-speed, top-emitting, vertical-cavity surface-emitting lasers (VCSELs) for application with free space optical interconnects. Both ion implantation and polyimide planarization were investigated as methods of surface passivation to eliminate parasitic bond pad capacitance and increase the frequency bandwidth. Low-threshold, uniform, 20-by-20 arrays, with a 3dB frequency of up to 5GHz, were demonstrated. In the second part of this thesis the development of selective area growth (SAG) as a means of band gap engineering for fabricating photonic integrated circuits (PICs) is discussed. SAG is then applied specifically to the fabrication of a monolithic semiconductor optical amplifier (SOA) and an electroabsorption modulator (EAM). The photonic integrated circuit is then completed with the addition of a spot-size converter. The theory of design and fabrication for each of these issues is presented. Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Chapter 1: Introduction Historically, the trend in communications using electromagnetic radiation has been the use of ever-increasing frequencies. Radio, for example, started with kilometer wavelengths which were soon shortened to meters and then millimeters. With the advent of the laser, communications shifted towards lightwave frequencies using laser beams in air or guided through pipes with the help of lens guides [1]. Optical fiber presented a better type of light waveguide but initially suffered from high losses, which made them unattractive compared with established electromagnetic communications. With the first proposal of fused silica as a material for optical fiber by Kao in 1968 [1], losses in optical fiber decreased rapidly. Kao had measured losses in bulk fused silica on the order of tens of dB/km, which was followed by the report of silica fiber with a loss of 20dB/km by Corning Glass Works in 1970 [2], A decade later fiber losses of 0.2dB/km were reported at a wavelength of 1.55|im [3], which is near the theoretical limit [4]. With such low losses the transmission of lightwaves through optical fiber has become the dominant transmission technology for long-distance (tens to hundreds of kilometers) communications. As the need for bandwidth increases, multiplexing technologies such as dense wavelength division multiplexing (DWDM) are being used to send numerous data channels along a single fiber. Current systems can support up to 160 channels at a spacing of 50 or even 25 GHz intervals. 1 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. Since the widespread deployment of long-haul optical fiber optical interconnects, as a field, has experienced a continuous push into applications with shorter and shorter transmission distances. From long-haul transmission to chip- scale interconnects, optical interconnects now spans a length scale of about seven orders of magnitude [5], The push towards shorter distance is being driven by a mismatch between the exponential increase in silicon-chip speed and density and the metal-based interconnects that are needed to keep up that pace. Specifically, optics is being used to relieve the bandwidth bottleneck incurred with conventional bus transmission lines and wiring interconnects in standard computer and processor architecture. 1.1 Free Space Optical Interconnects Moore’s law dictates that transistor counts on a chip will double every 18 months. Today’s processors are operating at a few GHz, while the bus lines that connect the processor to memory run at a few hundred MHz. Bus lines connecting the processor to peripheral cards are slower yet (e.g. 66MHz for the 64 bit PCI bus). While schemes such as the utilization of different levels of high-speed cache memory improve performance, the slow bus speed ultimately limits aggregate data throughput. As silicon integrated circuit technology progresses towards higher clock frequencies, it is recognized that the main source of performance bottlenecks will occur with the electrical interconnects. According to the International Technology Roadmap fo r Semiconductors (ITRS) 2003 for the long term (2010 2 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. through 2018), “Traditional interconnect scaling will no longer satisfy performance requirements [6].” A solution to the above problem is being explored with optical interconnects. These interconnects can be fiber-optic ribbon cable or arrays, dielectric waveguides on a printed circuit board, or free space optical interconnects (FSOI). The advantages of optical over electrical interconnects are numerous, including larger bandwidth, lower cross-talk, immunity to electromagnetic interference, and the fact that power consumption is almost independent of propagation distance [7], In order to choose the appropriate optical interconnect technology one must understand the design requirements for off-chip interconnects. It is projected that by the year 2014 the off-chip bus will have a clock speed of 1.8 GHz and a width of 3000 high speed lines, with a total I/O capacity of 5 Tb/s. The on-chip clock speed is projected to reach 13.5 GHz [8], Using the total off-chip bandwidth as a constraint, the appropriate regimes of optical interconnect technology can be viewed, as shown in figure 1.1. In this figure the data rate per channel necessary to achieve 5 Tb/s is plotted as a function of the number of parallel channels. Using the on- and off-chip clock rates as boundaries it is apparent that solutions with a higher degree of parallelism must be implemented in order to have reasonable data rates. 1-D fiber ribbons and 2-D fiber arrays are not considered viable solutions because of their limited channel numbers and the fact that for the short distances considered, spacing is affected by the limited bending radius of the 3 Reproduced with permission ofthe copyright owner. Furiher reproduction prohibited without permission. fiber [8]. FSOI is thus seen as better choice here because massively parallel processing architectures can be built with FSOI in a relatively straightforward manner. 1 10 100 1000 10000 Fiber Array -10000 Fiber Ribbon FSOI ^ 1000- r 1000 On-chip Clock (13.5 Gb/s) >10 Off-chip clock (1.8 Gb/s) 1 10 10000 100 1000 Number of Channels Figure 1.1 Regimes of applications for various optical interconnect technologies [8]. The solid line indicates the necessary data rate to achieve 5 Tb/s. 1.2 Vertical-Cavity Surface-Emitting Lasers for FSOI One of the major requirements for FSOI is that it must be massively parallel; thus the optical transmitters and receivers must conform to this criterion. A light emitter that is well suited for this is the vertical cavity surface emitting laser (VCSEL). This type of semiconductor laser emits light perpendicular to the wafer surface, which makes it amenable to the fabrication of dense, two-dimensional arrays for massively parallel systems. VCSELs have many other qualities that make them attractive for FSOI, such as: 1) ultra-low threshold current; 2) high Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. electrical-to-optical energy conversion (“wall-plug”) efficiency; 3) narrow, circular beam shape; 4) single longitudinal mode; 5) high-frequency operation; 6) wafer- level fabrication and testing. For massively parallel chip-to-chip or board-to-board communications, processing architectures are envisioned in which dense VCSEL and detector arrays are flip-chip bonded to silicon circuitry. This is depicted in figure 1.2. VCSEL array Process Units Detector array Board-to-Board Optical Link Figure 1.2 Free-space optical interconnect concept for massive parallel communications between adjacent computer boards. VCSEL Array Microlens » E Array Fourier Lens Detector Array Si IC Figure 1.3 Schematic of bi-directional board-to-board communications via FSOI. 5 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. The optical beams of the lasers are directed to the corresponding detector elements through diffractive optical elements (DOEs) and Fourier lenses (figure 1.3). 1.3 Integrated Optics As mentioned above, the field of optical interconnects has dominated in long-haul transmission of information. DWDM networks are now shifting to all- optical designs, incorporating higher channel counts, higher transmission speeds, and larger-scale integration. Components of these systems will be expected to provide the listed features with a reduced footprint, and at lower costs. When examining cost factors, packaging currently accounts for nearly 60% of the cost of a fiber optic component [9]. Clearly the advantages of integrating several devices onto a single chip, and incurring this packaging cost only once, can be seen when comparing the cost of packaging several discrete components. This integration will also lead to footprint reduction when compared to utilizing discrete components in a fiber optic system. Transm itters R eceivers M ultiplexing D e-m ultiplexing Transm ission on fiber Figure 1.4 A schematic of a WDM transmission system Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. 1.4 Hybrid vs. Monolithic Integration The demands of functionality, cost and footprint are met by the photonic integrated circuit (PIC). This term refers to the subset of optoelectronic integrated circuits (OEICs) that focus mainly on the integration of optically interconnected, guided-wave, optoelectronic devices [10]. There are two main technologies for integration, hybrid and monolithic, each having its own advantages and disadvantages. Hybrid integration refers to a variety of techniques for combining devices of various different materials onto a chip. The most common usage refers to planar lightwave circuits (PLCs), in which a silica substrate is etched to form a network of passive waveguides. The silica substrate then becomes a subassembly for alignment and optical connection of discrete optoelectronic components, which are aligned and placed onto the subassembly by etched grooves [11-14], Advantages to the hybrid approach include being able to have a wide variety of devices from different materials systems incorporated into one circuit, each of which can be optimized separately. Also, the silica waveguides have near perfect mode matching to optical fiber [11]. A main disadvantage to PLCs is the strict tolerance on fabrication and alignment procedures [15]. The submicron alignment and fixation necessary is costly and tim e consum ing, although advanced techniques will mitigate this to a certain extent [14]. The bonds holding the various elements of the circuit together are also subject to failure due to vibration and thermal expansion. 7 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. There are two critical points to consider with hybrid integration. First, one of the most important issues in reducing cost and improving performance is to reduce the number of optical connections between devices. Hybrid integration, at the most basic level, still involves connecting discrete components, so fails to address this concern. Secondly, hybrid integration is not competitive in terms of reducing chip area. For example, a comparison of hybrid and monolithic transceivers shows that the chip area for a hybrid PLC ranges from 15-25 mm2 while a monolithic device ranges from 0.3-1.5 mm2 [16]. Monolithic integration is a much more attractive technique when trying to achieve integration, a reduction of optical interfaces between components, and miniaturization of chip area. The most viable monolithic integration technologies allow for simultaneous formation of the waveguides that connect the various optical components, so there are no optical alignment points as with hybrid integration. Another advantage is that monolithically integrated devices are fabricated using a linear sequence of processes using standard semiconductor processing, such as photolithography, dry/wet etching, etc. In terms of cost, the monolithic approach is ultimately cheaper in terms of mass production because batch processing can be used [17]. A major disadvantage of monolithic integration, for most implementations, is the fact that integration of many different optical functions on a single chip constitutes a compromise on the performance of each single element [15]. There 8 Reproduced with permission ofthe copyright owner. Further reproduction prohibited without permission. are, however, many types of devices, such as the one proposed here, where this is not an issue. 1.5 Thesis Overview and Outline In order for FSOI to be competitive with electrical interconnects, the light emitters must have very low power consumption. Thus, one of the main focuses in VCSEL research is to obtain ultra-low threshold current and high efficiency. Another main consideration is modulation speed. The first part of this thesis will document the efforts in making high-efficiency, high-speed VCSELs, and the challenges involved with putting these into a dense, uniform, 2-D array. The second part of this thesis will detail the development of the selective area growth (SAG) technique and demonstrate the viability of this method for making monolithic PICs. Secondly, it will be shown through the demonstration of an integrated semiconductor optical amplifier (SOA), electroabsorption modulator (EAM) and adiabatic mode expander (AME) that monolithic devices fabricated by SAG are competitive alternatives to hybrid circuits in terms of ease of fabrication, footprint, and functionality. The device mentioned above has been selected because it integrates components of commercial interest in the market today and has wide functionality. It can be used in a stand-alone configuration as a lossless EAM, where the SOA accounts for insertion loss, as an electroabsorption modulated laser (EML), or as a mode-locked laser in either an external cavity or monolithic configuration. 9 Reproduced with permission ofthe copyright owner. Furiher reproduction prohibited without permission. The remainder of this thesis will be organized as follows: Chapter 2 details VCSEL design and optimization; chapter 3 presents high-frequency VCSEL design issues; chapter 4 discusses VCSEL fabrication and performance results; chapter 5 introduces SAG mechanisms and SAG characterization; chapter 6 details PIC design, fabrication and results; chapter 7 presents the design, fabrication, and performance of the integrated adiabatic mode expander; chapter 8 summarizes the thesis and discusses future research directions. References 1. D. Marcuse, Principles o f Optical Fiber Measurement. Academic Press, San Francisco, Ch. 1, (1981). 2. F.D. Kapron, D.B. Keck, and R.D. Maurer, “Radiation losses in glass optical waveguides,” Appl. Phys. Lett., vol. 17, pp. 423-425 (1970). 3. T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita, “Ultimate low loss single-mode fibre at 1.55|im,” Electron. Lett., vol. 15, pp. 106-108 (1979). 4. T. Kimura, “Single-mode systems and components for longer wavelengths,” IEEE Trans. Circuits and Systems. Vol. CAS-26, no. 12, pp. 987-1010 (1979). 5. M. W. Haney, H. Theinpont, and T. Yoshimura, “Introduction to the issue on Optical Interconnects,” IEEE J. Select. Topics Quantum Electron., vol. 9, no. 2, p. 347, March- April (2003). 6. International Technology Roadmap fo r Semiconductors, 2003 ed, executive summary, pp. 16. 7. J.H. Collet, F. Caignet, F. Sellaye, and D. Litaize, “Performance constraints for onchip optical interconnects,” IEEE J. Select. Topics Quantum Electron., vol. 9, no. 2, pp. 425- 432, March-April (2003). 8. A.G. Kirk, D.V. Plant, M.H. Ayliffe, M. Chateauneuf, “Design rules for highly parallel free-space optical interconnects,” IEEE J. Select. Topics Quantum Electron., vol. 9, no. 2, pp. 531-547, March-April (2003). 9. O. Sezerman, G. Best, “Trends and Advances in Component Packaging.” Oz Optics Ltd. white paper, www.lightreading.com. (2003). 10. T.L. Koch, U. Koren, “Semiconductor Photonic Integrated Circuits,” IEEE J. Quantum Electron., vol. 27, no. 3, pp. 641-653, (1991). 11. M. Kawachi, “silica waveguides on silicon and their application to integrated-optic componenets,” Opt. Quantum Electron., vol. 22, pp. 391-416, (1990). 12. K. Kato, Y. Tohmori, “PLC Hybrid Integration Technology and Its Application to Photonic Components,” IEEE J. Select. Top. Quantum Electron., vol. 6, no. 1, pp. 4-13, (2000). 13. A. Himeno, K. Kato, T. Miya, “Silica-Based Planar Lightwave Circuits,” IEEE J. Select. Top. Quantum Electron., vol. 4, no. 6, pp. 913-924, (1998). 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14. S.J. Park, K.T. Jeong, S.H. Park, H.K. Sung, “A Novel Method for Fabrication of a PLC Platform for Hybrid Integration of an Optical Module by Passive Alignment,” IEEE Photon. Technol. Lett., vol. 14, no. 4, pp. 486-488, (2002). 15. E. Pennings, G.D. Khoe, M.K. Smit, T. Staring, “Integrated-Optic Versus Microoptic Devices for Fiber-Optic Telecommunication Systems: A Comparison,” IEEE J. Select. Top. Quantum Electron., vol. 2, no. 2, pp. 151-164, (1996). 16. R. Kaiser, H. Heidrich, “Optoelectronic/Photonic Integrated Circuits on InP between Technological Feasibility and Commercial Success,” IEICE Trans. Electron., vol. E85-C, no. 4, pp. 970-981,(2002). 17. R.G. Hunsperger, Integrated Optics: Theory and Technology, fifth ed., Springer, New York, (2002). 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 2: Design of VCSEL Arrays for FSOI 2.1 Overview of VCSEL technology The VCSEL was invented by Iga, et al. at the Tokyo Institute of Technology in 1979 [1, 2], and has since been the subject of intensive research throughout the world. The first devices could only operate under pulsed conditions at 77 K with a threshold current of roughly 860mA [1], From these humble beginnings VCSELs have proven to be one of the most efficient types of semiconductor lasers in the low power regime, with both ultra-low, micro-amp threshold currents [3, 4] and high wall-plug efficiencies having been demonstrated [5, 6 ], Like their edge-emitting counterparts, VCSELs are composed of two high- reflectivity mirrors separated by an optical cavity. One of the critical differences with VCSELs, however, is that the optical cavity is on the order of one wavelength long. This distinction is important for two reasons. First, the short cavity permits the device to emit with a single longitudinal mode. Secondly, the advantages of a microcavity are utilized. The volume of a true microcavity is small enough that only one optical mode exists, thus all of the spontaneous emission couples to the lasing mode (the theoretical threshold-less laser) [7], While VCSELs are not true microcavities in this sense (they are too large in the transverse direction) their small optical cavity volume does permit more efficient use of spontaneous emission, which improves their efficiency at lower power over edge-emitting lasers. 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Another consequence of a small optical cavity volume is that the per-pass gain of the optical mode through the active region is quite small— on the order of 1% [8]. This necessitates the use of high reflectivity mirrors of >99% reflectivity to reduce mirror loss. Indeed one of the reasons for the poor performance of the first VCSELs was the lossy and low-reflectivity metal mirror that was used [1], The distributed Bragg reflector (DBR) is the only type of mirror that can provide such high reflectivity, and was first incorporated into VCSELs in 1986 [9]. A DBR consists of multiple pairs of alternating high-refractive-index and low- refractive-index layers, each of which are a quarter-wavelength thick [10], For these thicknesses, the periodically modulated index of refraction leads to constructive interference and a large net reflection from the successive high/low index interfaces (the Bragg condition). High performance VCSELs utilize either monolithic, epitaxial DBRs or dielectric DBRs. DBRs placed above and below the quantum well (QW) active region and the QWs themselves define the optical and electrical confinement in the longitudinal (normal to the wafer surface) direction respectively; however, there must still be a mechanism of optical and carrier confinement in the transverse directions. Four basic VCSEL structures have evolved to implement transverse carrier/photon confinement. They are the etched mesa [12-16], proton implanted [18-21], buried heterostructure (BH) [22-27], and dielectric aperture structures [3-6, 28-32], Figure 2.1 illustrates these different implementations. 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The etched mesa structure is perhaps the simplest means of achieving lateral optical confinement. In a manner analogous to edge-emitter fabrication, a square or circular post is etched using either wet or dry techniques with the etch stopping just above the active region. The index step between the surrounding air and the post provides the optical confinement and the current is confined by the lateral dimensions of the post. Light Out Top Contact Top Contact P-DBR P-DBR Dielectric ^^-''-'Aperture QW Active Region QW Active Region N-DBR N-DBR n-lypo Substrate n-typc Substrate Bottom Contact Bottom Contact Light out (C) P roton B om bardm ent Epitaxial Regrowth Light O ut P-DBR Top Contact Top C ontact P-DBR N-DBR N-DBR n-type S u b stra te n-lype Substrate Bottom C ontact B ottom C ontact Light Out Figure 2.1 VCSEL device structures for optical/electrical confinement: a) etched-post; b) dielectric aperture; c) ion implanted; d) buried heterostructure. The direction of current flow is indicated by the arrows [11]. This design is subject to lateral current leakage, which has been estimated to account for roughly half of the threshold current of typical multiple quantum well VCSELs with diameters less than I Opm [17]. Furthermore, in order to get low 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. contact resistance the entire top surface of the post must be contacted, which restricts the device to bottom emission. With light emission using the GaAs/AlGaAs system the GaAs substrate is absorbing; thus strained InGaAs active regions operating around a wavelength of 980nm must be used. The proton-implanted structure has become a widely manufactured structure due to its simplicity, reproducibility, and the planarity of the wafer surface obtained with this technique. This embodiment relies on damaging the crystal lattice by H+ bombardment to make insulating regions, which then aperture the current. The implantation can either stop above the active region or go through it, although a shallow implant is preferred for reliability reasons and to reduce interface recombination [11], In the shallow implant case, the insulating regions do not provide an effective current aperture, allowing too much lateral current spreading. Furthermore, the proton-implanted structure is primarily a gain-guided structure, with no significant index guiding in the lateral dimension. The primary lateral index guiding mechanism is thermal lensing, which, under high-speed modulation conditions, can produce an unstable lateral mode [11]. The buried heterostructure VCSEL type is the most desired structure, because it combines all of the lateral confinement features, i.e. optical, current, and carrier confinem ent. In this em bodim ent, a small m esa is etched and insulating or current blocking layers are regrown over the mesa. The regrown layers should also have a larger band gap and lower index than the mirror layers so that they provide 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. lateral optical and carrier confinement. The regrown layers will also have better thermal conductivity than planarizing polymers such as polyimide or benzo- cyclobutene (BCB). This approach is technologically very difficult to implement. In the AlGaAs materials system regrowth on Al-containing layers is difficult due to surface oxides, and the slope of the sidewalls of the etched mesa must also be carefully controlled. Recent attempts still suffer from excess nonradiative recombination at the regrown interface [26], The dielectric-apertured VCSEL structure has been shown to have the best performance over the other types mentioned above, with records in both threshold current and wall-plug efficiency reported with this design [3-6], In this implementation, a layer with a high aluminum mole-fraction (usually AlAs or Al.98Ga.02As) is epitaxially grown just above the quantum wells. A mesa is then etched through this layer, and the wafer is placed in a high temperature steam. The aluminum layer is readily oxidized, and the oxidation proceeds laterally into the mesa. Narrow current apertures can be defined in this manner that allow for both current injection into a region smaller than the optical mode and the elimination of shunt currents between the p- and n-regions of the device. The oxide aperture also provides a lower-loss waveguide by reducing the optical scattering losses and diffraction losses [30-31, 33]. Due to its superior performance, the oxide-aperture VCSEL is the device of choice for high-performance light emitters for FSOI, and is the focus of this study. 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Achieving a low-threshold, high wall-plug efficiency, high frequency device for compatibility with FSOI requires careful design of the optical cavity, DBR reflectivity, oxide aperture placement and the multiple quantum well (MQW) active region. The next sections discuss these issues in detail. 2.2 Optical Cavity and Mirror Design 2.2,1 Optical Cavity Design In a VCSEL the optical cavity consists of the MQW active region bounded above and below by the DBR mirrors (see figure 2.2), with an AIx Gai_x As oxidation layer inserted just above the active region. Light emitted by the quantum wells undergoes multiple reflections off the top and bottom DBR mirrors and a standing wave pattern is established inside the cavity. In order for a field maximum to occur in the quantum wells (a prerequisite for optical gain), the MQW region thickness must be an integer multiple of a half-wavelength of the laser emission, which in this case is 850nm. A half-wavelength is not suitable for carrier confinement however, thus a 1 A , cavity is typically used. Furthermore, the MQW cavity should be sandwiched by lower index cladding layers so that the field peaks in the quantum wells. These layers form a separate confinement heterostructure (SCH) that confines the optical mode, whereas the quantum well heterostructure confines carriers. 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. T o p ___ DBR Oxidation Layer MQW Active Region and SCH / t t y ? - / : Bottom DBR Figure 2.2 A schematic diagram of a VCSEL cavity. 2.2.2 Mirror Design As mentioned above, the high mirror reflectivity required by the low per- pass gain of a VCSEL is achieved by utilizing DBR mirrors. As shown in figure 2.3, the DBR is a periodic dielectric stack with alternating layers of high-refractive- index and low-refractive-index where A is the period. The Bragg condition for coherent reflection is given by [34]: X m — = Kcosd (2 .1) 2 Thus, assuming normal incidence, the period must equal an integer multiple of half a wavelength. The difference in refractive index must also be taken into account so that the period is a half-wave optical thickness. The thickness of each high- or low- index layer must therefore be a quarter-wave optical thickness (QWOT): 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. L ,. A 4nL 4nu (2 .2 a) (2 .2b) In 2.2a and 2.2b, X is the free-space wavelength. Figure 2.3 A schematic of a DBR showing the successive coherent reflections from the high-index and low-index layers. Small reflections, r, from each layer interface add constructively to produce a large net reflection, RT. At each high/low or low/high interface there is a small reflection given by Fresnel reflection (assuming normal incidence): . _ n 2 ~ ni n 2 + n! (2.3) At each high/low reflection there is zero phase shift and at each low/high reflection there is a tt phase shift. As long as the layers are kept at a QWOT, the round trip phase change accumulated by propagating through the layers cancels the phase 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. change incurred by the low/high reflection. Thus, the individual high/low and low/high reflections interfere constructively, or in other words, the Bragg condition is satisfied. As light penetrates into the DBR stack, more and more small reflections add in phase to yield a large net reflection, Rt- Since the optical field must penetrate into the DBR stack for a large net reflection to occur, the number of high/low pairs must be determined so that the desired mirror reflectivity is achieved. Furthermore, the number of pairs will also depend on the difference in refractive index between the high-index and low-index layers. This problem can be solved numerically via a propagation matrix approach, but a numerical solution prevents an analytical understanding of the problem. Another approach based on transmission matrices given in Ref. 35 yields analytical results for which the dependence of DBR reflectivity on refractive index contrast and layer pair number can be seen. In the transmission matrix approach the DBR stack is modeled as a series of cascaded scattering junctions (figure 2.4). The reflectivity can be determined by matrix multiplying the individual components of the DBR, starting from the output and moving towards the input. For a uniform DBR in which there are only two refractive indices the matrix multiplication is simplified by the fact that each period is identical. Thus, once the transmission matrix (T-matrix) for a single period is found it can be multiplied by the number of periods to yield the T-matrix for the total structure. 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.4 A transmission matrix representation for a DBR mirror [35], To determine the T-matrix for a single period, four simple T-matrices must be multiplied together: 1) a high/low interface; 2 ) a propagation delay of length L]ow ; 2) a low/high interface; 4) a propagation delay of length Lhig h - These simple T-matrices can be grouped as (TiT2)(T3T4), which yields the T-matrix for one period. The simple T-matrices are given by: T, = - 1 r Kr ( e)Phr 0 o ~ jP ^itw (2.4a) (2.4b) T = - 3 t 1 - r -r 1 (2.4c) f giPhigii 0 ~ iP L iu X h (2.4d) Where r is determined from Eq. 2.2, t= V1 - r 2 from power conservation, and p is the propagation constant in the dielectric layers (assuming no loss or gain in the 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. material). Multiplying these matrices together yields the T-matrix for the first period: T = i r ( (je^+ - r 2e M r(e'^+ —e M ^ Y ~ I IJ " • • ' — £J " • I I Lf " ■ ■ — ' (2.5) r {e m - e 1K) {e~m - r 2e1 9 -) where ( j) ± =j3iLi±{32L2, which is either 0 or k at the Bragg wavelength. The T-matrix for the complete DBR is then given by: Tg T T -Mi M2 T T V 2 1 22 J (2.6) where m is the number of high/low pairs and Tn, T |2, T2i, and T22 are the matrix elements of the single-period T-matrix. At the Bragg frequency the total reflectivity is given by: rg = = m# « tanh(2mr), (2.7) 1gn A n where meff is the effective number of periods seen by the incident field. Equation 2.7 can be rewritten in terms of the refractive indices as: ‘ 1 + ( % /n t )2'" Equation 2.8 is restricted by the fact the Tg must be reciprocal, meaning that transmission through the DBR must be equal when light is incident from either side of the stack. This condition is not met in a real VCSEL structure, because on one side of the mirror is the optical cavity and on the other is the exit medium (usually air). The T-matrix formalism allows for easy modification of Eq. 2.8 to correct for 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. this inaccuracy; the index ratio of the incident and exit medium can be included as a factor multiplied by the high/low index ratio [36]: r _ ]- ( ninc/neJ(nH ^ L)2 m * i + (ninc/ n J ( n H/nL)2 m Eq. 2.9 thus yields the amplitude reflectivity of a DBR mirror at the Bragg wavelength including the effects of the incident and exit media. It should be noted that usually the power reflectivity is desired, thus lrgl 2 should be calculated. Reflectance Vs. Period Number 1.0 - CM o > 0.9- 0 .8 - £ O —- - n L /nH =0.7 — nL /nH =0.8 - A - n , / n =0.9 4 - > o V 0.7- O 0 .6 - C C 0.5- < D o C L 0.4- 0.3 0 10 15 25 5 20 Number of Periods Figure 2.5 Power reflectance of a DBR mirror versus period number, m, for various high/low refractive index contrasts at the Bragg wavelength. From Eq. 2.9 it can be seen that the DBR reflectivity depends on the high/low index contrast, as well as the number of mirror pairs. Figure 2.5 demonstrates the effects of these parameters on the reflectivity. For layers with lower contrast, more mirror pairs are necessary to achieve a high reflectivity. As 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the mirror periods decrease, the reflectance approaches that of the Fresnei reflection of the cavity/air interface (-32%). As the mirror periods increase, the reflectance asymptotically approaches 10 0%. As mentioned above, the optical field sees an effective number of mirror periods, meff. This is due to the fact that the forward-propagating wave is exponentially decaying as it propagates into the DBR because energy is being fed into the backwards-propagating wave. Thus there is an effective penetration depth, Lpen, at which the DBR mirror can be assumed to be a hard mirror. This penetration depth is given by: where for a large number of periods ( m — > oo); \ n . (2.11) in,, ~ — e . t t 2 nH+nL \ n H n L J The above approach can be used to compute the entire reflection spectrum of a DBR, however there are some drawbacks. For instance, a convenient simplification was possible based on the fact that one period of the DBR was identical to all the others. In practical VCSELs this is generally not the case. The DBRs in real devices have graded interfaces, thus the T-matrix for each pair plus the graded interfaces must be multiplied together. Furthermore dispersion must be taken into account. A convenient numerical method based on the propagation matrix approach can be implemented to yield more accurate results. This method is similar to the 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. transmission matrix method outlined above, but it is more straightforward to manipulate an arbitrary set of layers. The details of this numerical method are given in appendix A and the results are summarized below. DBR Reflectivity 1.0- R =99.81% ■100 ;> o.8- O 0) H — u cc a > 5 o a. Wavelength (jim) 0 . 6 - 0.4- 0 .2 - 0.0 0.7 0.8 0.9 1.0 Wavelength (p,m ) Figure 2.6 The reflectivity spectrum calculated for a 25 period A12 G a8 As/Al 9 Ga tAs DBR using the propagation matrix method. The inset shows the phase of the reflection. The above figure presents the reflectivity spectrum of a 25 period Al.2Ga.8As/Al.9Ga.1As DBR calculated by the propagation matrix method. Index dispersion has been taken into account through use of the model given by Afromowitz in Ref. 37. As can be seen from the figure, the reflectivity spectrum is characterized by a large reflection which is centered on the Bragg wavelength and encompassed by a stop band. The width of the stop band is given by [7]: 2 ^ragg^ AA, : s b 7Tn (2 .12) 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where neff is given by: n = 2 « S t ' 1 1 V' + — \ nH nL ) (2.13) From Eq. 2.12 it can be seen that the bandwidth of the stop band is determined by the index contrast between the high and low index layers. As the wavelength deviates from the Bragg condition, the reflections from the interfaces further into the grating return with increasing phase mismatch and destructive interference occurs. This causes the reflectivity to roll off, as can be seen in figure 2.6. The inset of the above figure shows the phase of the reflection, which is zero degrees at the Bragg wavelength and deviates sharply above and below the Bragg wavelength. VCSEL Cavity Reflectivity S pectrum 1.0 - > 0.8 - O 0) 0> 0 .6 - 0C 0 o CL 0.4- 0 .2 - 0 .0 - 0.75 0.80 0.85 0.90 0.95 Wavelength (|im) Figure 2.7 The reflectivity spectrum of a complete VCSEL cavity with 20 period top and bottom A12Ga gAs/Al 9 Ga jAs DBRs. 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Once a program is written to implement the propagation matrix method, any arbitrary refractive index structure can be calculated. Another useful calculation is to determine the resonant wavelength of the laser by simulating the entire VCSEL cavity (figure 2.7). This calculation can also yield the electric field in the cavity so that the confinement factor can be calculated (figure 2 .8). Figure 2.7 above shows the reflectivity spectrum for a VCSEL cavity with 20-period A12Ga.gAs/Al 9 GajAs top and bottom DBRs. The incident medium is air (n=l) and the both the cavity and exit media are GaAs. The resonant wavelength is at 850nm and is seen as the sharp dip at the center of the stop band. VCSEL Cavity Electric Field _]_____ i_____ I _____ i _____ L . D C 3.0 1.0 a) a > 2.6- T 3 £ 2.4- 4 6 Position (|im) Figure 2.8 The electric field and refractive index profile of a VCSEL cavity with a 20-period top DBR and 40-period bottom DBR. Figure 2.8 presents a calculation of the electric field in the VCSEL structure plotted on top of the refractive index profile. The same materials for the DBR were 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 014801000102010001020102010201000153020000530200304830020023530201234823535301020148 used, but in this case the top DBR has 20 periods and the bottom DBR has 40 periods. The concept of penetration depth can be observed more clearly from this figure as the electric field is seen to exponentially decay as it penetrates into the DBR. From the above analysis it is clear that the reflectivity of a DBR depends on the index contrast between layers and the number of mirror periods. Aside from these aspects, one must still choose the materials to be used for the high- and low- index layers. At first glance, it is obvious that the maximum contrast should be used so that the number of periods can be kept to a minimum. In the AlGaAs materials system this would lead to the use of GaAs/AlAs mirrors. GaAs, however, has a band gap lower in energy than the energy of a photon at 850nm. This means that a layer of GaAs will be absorbing and contribute to additional loss in the cavity. Thus, an additional design constraint is that the materials used in the DBRs must be transparent at the laser emission wavelength. For this reason Al.2Ga.gAs is used as the high-index layer. Secondly, if AlAs is used as the low-index material it will oxidize during the later wet-oxidation process. This oxide is an insulator and will prevent electrical conduction through the DBR. This can be circumvented by using intra-cavity contacts; however for the devices fabricated in this study, conduction through the DBRs is necessary. The addition of a few percent gallium is enough to slow the rate of oxidation considerably, thus a material composition of Al.93Ga.07As was used. 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The above analysis on DBRs can be used to calculate the period number and layer thicknesses once the desired reflectivity for the top and bottom DBRs is know. Further analysis is needed, however, to determine the exact mirror reflectivities that are needed to optimize performance issues such as threshold current, wall-plug efficiency, and frequency response. These issues are discussed in a later section. 2.3 Oxide aperture placement effects As mentioned above, the highest-performance VCSELs have used A10x apertures to provide lateral current confinement. Special attention must be paid, however, to where in the cavity this aperture is placed. Due to its low refractive index (-1.55) the AlOx layer can provide strong index confinement within the VCSEL cavity, but only in the localized region of the aperture; there is little lateral index confinement through the rest of the structure. For narrow apertures this leads to diffraction losses in the cavity because off-axis rays are scattered out of the cavity instead of coupling back into the gain region through the aperture opening (see figure 2.9 below) [30, 31]. Aperture placement also affects the far-field angle of the emitted radiation, which is an important consideration in terms of channel cross-talk for closely-spaced VCSEL and detector array elements. The scattering loss due to the oxide aperture can be calculated using the effective index model proposed by Hadley [38] combined with the analysis of Hegblom et al. for an unfolded cavity [39]. The effective index model can be used to determine the change in effective index of the cavity mode by considering the 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. effective index of a cold cavity (without the oxide aperture) and the change in cavity resonance wavelength presented by the addition of the oxide aperture: A n ff AA — *L = 1 — (2.14) n A core core Here nc o re is the effective index of the active region calculated from the overlap of the electric field in this region with the index profile, and the cold cavity resonance, Aam, is calculated as discussed above. The parameters AA and Ane ff are the change in cold cavity resonance and the effective index step across the boundary between the aperture opening and the AlOx region respectively. s c a tte r e d lig h t W No x id e a p e r tu r e h a rd m irro r L, p e n Figure 2.9 A VCSEL cavity effective-mirror schematic demonstrating scattering loss from a narrow aperture. The DBRs are approximated as hard mirrors at a penetration depth Lp en from the aperture. In the unfolded cavity model from Ref. 48, an approximate analytical formula is given for abrupt apertures based on Fresnel diffraction. It can be 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. assumed for convenience that the aperture is circularly symmetric; the scattering loss from the aperture is then given by: The effective index step above can be used to determine the phase shift, < j > n, introduced by the aperture from$, = koAneffLc, where k( ) is the free space wavenumber and Lc is the sum of the lengths of the core region and the penetration depths into the top and bottom DBRs. The Fresnel number, F, is given The above method can be used to calculate the scattering loss from the oxide aperture and compare the losses when the aperture is placed at different positions with respect to the cavity standing wave peak or null. First, the same calculation that was done for figure 2.7 was repeated with the oxide aperture placed at the peak and at the null of the cavity standing wave; figure 2 .1 0 shows the results. It can be seen from the figure that there is a much larger shift in the cavity resonance for the aperture placed at the peak as compared to the null. From the calculations, A/l for the null is 0.4nm while AA, for the peak is 7.2nm. The effective index step is calculated from Eq. 2.14 once the wavelength shifts are known. The scattering loss is then calculated from Eq. 2.15 as the aperture radius is varied. The results of the scattering loss calculations are shown in figure 2.11 below. a(%) = 2.28- ^ e * ° F p\3 0.206 (2.15) core c where a is the aperture radius. 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Cavity Resonance Shifts 1.0 > 0.9- > '5 O 0) < D tr 0.8 - 0.7- 0 .6 - T3 « 0.5- Cold Cavity R esonance Oxide at null Oxide at peak 0.840 0.845 0.850 0.855 Wavelength (|im) Figure 2.10 VCSEL cavity resonant wavelength shifts for oxide aperture placement at the peak or null in the standing wave electric field. The amount of loss incurred with the aperture at a standing wave peak is significantly greater than that incurred with the aperture at a null. This is due to the fact that with the aperture at a peak, there is strong lateral index guiding. However, the index guiding occurs only in the local region of the aperture; the rest of the VCSEL cavity is relatively unguided in the lateral direction. The result is diffraction from the aperture; the divergent light emitted from the aperture scatters out of the VCSEL cavity upon reflection from the DBR mirrors instead of focusing back into the narrow aperture region. Furthermore, the dependence of the loss on aperture size is much greater for the oxide-at-peak case compared to the oxide-at-null case. Again this is due to the strong lateral index guiding and the fact that as the aperture is narrowed the 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. diffraction is increased. The increased beam divergence results in more light being scattered out of the cavity, and thus, more loss is incurred. Oxide A perture Scattering L oss 0.050 Oxide at peak An =0.0289 0.045 k . U .V / - T V Q ) Q. 0.035- 0.040- 0.030- $ 0.025- ° 0.020- 0.015- " [jj 0.010- 03 0.005- Oxide at null An =0.0016 erf An o C O 0.000 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Oxide Aperture Radius (|im) Figure 2.11 Scattering loss calculations versus aperture radius for the oxide aperture placed at the peak and null of the cavity standing wave. The oxide-at-null case demonstrates less scattering loss and less dependence on aperture size simply because placing the aperture at a null in the cavity standing wave reduces it’s interaction with the field. Thus, the aperture presents a much weaker index guide to the field in this case, reducing the diffraction of the light through the aperture, and resulting in less scattering loss. This is an important result, especially with regards to FSOI, because uniformity between laser elements is critical. With less dependence of the scattering loss on aperture radius for the oxide-at-null case, variations in aperture 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. diameter due to non-uniformities in the oxidation process will have less effect on device performance. With regards to reducing overall modal loss, however, one might wonder which case is preferable. The strongly guided case restricts the mode’s lateral dimension more closely to the size of the aperture. Thus the mode is well confined to the same area of current flow so that it overlaps more with the pumped region of the quantum wells. This will result in less loss due to absorption in the unpumped regions. In the weakly guided case the mode’s lateral dimension spreads out and overlaps more of the unpumped region, which could potentially result in more absorption, and thus, increased loss. As was demonstrated conclusively by Bond et ai, however, devices fabricated with the aperture at a null have increased slope efficiency, lower threshold current, and a threshold current more insensitive to aperture radius than devices with the aperture at a peak. This is because there is enough lateral current spreading to pump a quantum well region which corresponds to the size of the mode. At aperture sizes below 2(im, however, the mode becomes unconfined and overlaps unpumped gain regions, thus increasing absorption loss [31]. The placement of the oxide aperture also has important implications for the far-field divergence angle of the device. As noted above, there is less diffraction from the oxide-at-null devices, thus they should have a lower far-field divergence. This is critical when considering dense arrays of VCSELs for FSOI. If the far-field 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. angle is too large, the emission from one VCSEL could be detected by the wrong detector in the corresponding detector array. The far-field angle can be calculated by approximating the VCSEL as a cylindrical waveguide. The V-number for the waveguide is then given by [40]: For 1.2<V<2.405 the fundamental HEn mode of a cylindrical waveguide can be approximated by a Gaussian beam with a mode radius given by: The 1/e far-field full angular spread for a Gaussian can then be approximated by Far-field angle calculations are shown below in figure 2.12 for the two different aperture placements (keeping in mind the limited range of V). The null position clearly has a smaller divergence angle with a weaker dependence on aperture size than the peak position. From the above analysis it is clear that the optimum position for the oxide aperture is at a null in the cavity standing wave pattern. This is especially true for FSOI applications due to the insensitivity of scattering losses and far-field angle on aperture radius. Non-uniformities that may arise during the oxidation process will (2.16) — = 0.65 + 1.619V~2+ 2.87V 6 (2.17) a [41]: (2.18) 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. not affect array uniformity. Overall device performance is also improved, and lower-threshold devices should result from placement of the aperture at the null. Far-Field Angle 45 40- O T 0) 0) _ 35- O) JL 30: V 25 20 - s 1 5 ^ O 10 - O xide-at-peak ixide-at-null il ■ (0 LL 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Aperture Radius Figure 2.12 Far-field angle calculation for the oxide aperture placed at the peak or null in the cavity standing wave field. The arrows indicate the range of V-number for which the calculation is accurate. 2.4 Active region design As was demonstrated in figure 2.7, the VCSEL cavity gives rise to a single longitudinal mode. It is therefore imperative that the optical gain spectrum of the active region be properly aligned with this mode. Thus, the objective in designing the active region is to optimize the quantum well and barrier materials, well and barrier thickness, and number of wells to yield a gain spectrum that is aligned with the cavity mode. Furthermore, both the cavity resonance and gain spectrum will shift with temperature; this must be accounted for to ensure efficient operation of 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the device [6 , 15, 42, 43], Lastly an efficient confinement structure must be designed to maximize overlap of the optical field with the quantum wells and to confine carriers. This will impact the well width as well as number of wells chosen. 2.4.1 Materials system selection The first step in designing the active region is to choose a materials system for the desired emission wavelength. The wavelength is constrained by the fact that low-cost Si and GaAs photodetectors which are to be used in FSOI must have good sensitivity. Si detectors have a peak responsitivity at 850nm, which has been chosen as the standard wavelength for FSOI for this reason [44], Furthermore, the band between 820nm and 860nm has been chosen as a standard for short-distance local area network (LAN) applications [6 ], Thus, for the purposes of this study, the VCSELs must emit around 850nm. Given that the emission wavelength must be 850nm, the active region is limited to the GaAs/AlGaAs materials system. This is disadvantageous in a way because this materials system is nearly lattice-matched across the entire composition range from GaAs to AlAs. Thus, strain can not be utilized to separate the quasi-fermi levels and lower the threshold current. Strained InGaAs active regions have been used to obtain the lowest threshold VCSELs [4]; unfortunately the emission wavelength is 980nm, which is not compatible with FSOI. 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2.4.2 Quantum well design As mentioned above, both the cavity resonance and the gain spectrum will shift with temperature as the VCSEL is driven to higher current levels. The gain spectrum of the device can be intentionally offset, however, so that at a desired current level (device temperature) the cavity mode and gain spectrum peak come into alignment [15, 42], This technique can be used to obtain minimum threshold currents, or in the case of this study, to maximize efficiency at a given power output. The design approach used for the quantum wells is to first estimate the temperature increase of the active region with drive current followed by estimation of the gain peak temperature shift and the cavity resonance temperature shift. The amount by which the gain peak should be offset can then be determined. The temperature increase of a VCSEL can be found from the total electrical power into the device compared to the total optical power out [35], This ratio is termed the conversion, or wall-plug efficiency, and is given by ijr =Pout/Pin. The power in is the product of the drive current and the voltage across the device and is expressed as: where Rs is the series resistance, Vd is the ideal diode voltage, and Vs is a current- independent series voltage. The power dissipated into the device as heat is the difference between the optical output power and the electrical drive power: (2.18) PD=Pin-Po=Pin(l->lc) (2.19) 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Using the thermal impedance of the device structure the temperature increase is An approximate expression for the thermal impedance of a VCSEL structure is given by [35]: where £ , is the thermal conductivity of the material and s is the device diameter, or in this case the oxide aperture diameter. For GaAs, £ , is 0.45 W/cm-C [35]. Using some typical numbers for the electrical power in and optical power out for the devices made in this study, the temperature increase in the device is in the range of 15 °C for pumping levels of a few times larger than threshold. Knowing the temperature increase, the cavity resonance wavelength shift and gain peak wavelength shift must be determined. From the literature, the variation of refractive index for an AlAs/GaAs DBR with temperature yields a wavelength red-shift of ~0.9A/°C [45], Therefore, the cavity resonance will shift by slightly more than 1 nm for the estimated increase in temperature. The primary mechanism leading to the red-shift in the gain spectrum is band-gap shrinkage. The dependence of band-gap on temperature is given by [46]: given by: AT = ZTPD (2.20) (2.22) 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where, for GaAs, Eg(0)=1.519, oc=5.405x"4, and p=204. The TE gain spectrum for an Al^Ga gAs/GaAs quantum well with LW =80A was calculated using the treatment in Ref. 47 and is plotted below at varying temperatures for the first- electron to first-heavy-hold transition (E1-HH1). The inset plots the peak gain position versus temperature with a slope of 3A/°C. This is in general agreement with experimental results from the literature [48], Gain Spectrum Vs. T em perature 2000 - T=300K 854 852 r* E o 1500- E ■ r j O .2 844 300 310 320 330 340 350 Tem perature (K) 1000- 500- T=350K 820 830 840 850 860 870 880 890 900 Wavelength (nm) Figure 2.13 Gain spectra at 10 degree increments for an AlGaAs/GaAs quantum well. The peak position is plotted versus temperature in the inset. From this calculation the peak of the gain spectrum will shift by approximately 4nm for the estimated temperature increase. Including the cavity shift as estimated above, the total wavelength shift that must be accounted for in the gain-offset is roughly 5nm. Thus, for optimum efficiency at higher pumping levels the gain spectrum peak should be designed for 845nm at room temperature. 40 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. From the above analysis, the design approach for the quantum wells and barriers is to first assume a well material of GaAs, and then vary both the well thickness, dw, and the A1 alloy composition in the barriers to yield the correct transition energy (wavelength). This will yield a range of values for dwan& A1 composition. Equations for the variation in effective mass and band gap versus A1 composition for Alx Ga[.x As are given by Adachi in Ref. 49, and are used in conjunction with a finite difference program (see Appendix A) to calculate the quantum well bound states and wave functions. The transition energy is then found from the E l and HH1 bound states. The transition wavelength is calculated by the 1 2398 formula X = — ------ , where X is in microns and Et is the E1-HH1 transition energy. E , AIGaAs/GaAs Quantum Well Transition Wavelength 100 0.850 .C T3 80- >.845 I.840 70- I.835 C 60- (0 3 o _ I.830 .0.82! .0.82! 0.10 0.15 0.20 0.25 0.30 0.35 0.40 B arrie r Al M ole F rac tio n Figure 2.14 Contour lines of quantum well transition wavelength versus quantum well width and Al mole fraction. The desired emission is 845nm. 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 2.14 above shows the results of the quantum well calculation as contour lines of different transition energies versus barrier Al mole fraction and quantum well width. The contour line corresponding to 0.845pm yields the barrier composition and well width that result in the desired transition wavelength. Some general considerations can restrict the range of values that must be considered for optimizing the quantum well parameters. At first glance it would seem that the widest possible well should be used to maximize the confinement factor. One must consider, however, that the Alx Gai_x As alloy goes through a transition between direct and indirect band-gap at -35% Al [50], At this composition the T, X, and L conduction-band valleys merge, yielding a deep level called the D-X center. This deep level acts as a carrier trap which degrades device performance; thus, barrier compositions should not exceed -30% aluminum. A second consideration is temperature sensitivity. With regards to barrier height, too low a barrier will result in poor thermal performance due to thermionic emission of carriers out of the wells [15]. Thus, barrier compositions are usually kept at or above 20% aluminum. Due to the above issues, the barrier aluminum composition is restricted to a range between 20% and 30%. Further consideration of the relationship between gain and well width/barrier height can help to determine the optimum quantum well parameters. It is desirable for the spacing between quantum well sub-bands to be large or even for the quantum well to have only one bound state. In this way, under normal injection levels, carriers will only populate the bound state which provides gain for 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the cavity mode. If there are two or more closely spaced sub-bands, the other sub bands will become populated and degrade quantum well performance [35]. Al 3 Ga ? As/GaAs 90A QW Si 0.80- 0.75- 0.70- 0 50 100 150 200 250 300 Position (Angstroms) > 0), > . O ) k - t o c in 0.95- 0 50 100 150 200 250 300 Position (Angstroms) Figure 2.15 Conduction band bound states and wavefunctions for an AlGaAs/GaAs quantum well with Al mole-fractions of 0.2 and 0.3. As shown in figure 2.15, the Al.2Ga.8As 80A well contains two bound states; however, the upper state is only 19.5meV from the top of the well. Thermal energy at room temperature is 25.9meV, therefore, carriers will not populate this energy level, but will instead be thermally scattered to the continuum states. The Al.3Ga.7As 90A well, on the other hand, has two well-confined states; thus, under carrier injection both levels can be populated. Optical gain produced from the upper level is not useful, however, because of the single longitudinal mode of the VCSEL cavity. Thus, the Al.2Ga.8As 80A well is a more efficient design. 2.5 Device optimization In order to minimize the threshold current and further optimize device performance, the number of quantum wells in the active region needs to be 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. determined, as well as the mirror reflectivity of the top and bottom DBRs. The optimum number of quantum wells can be determined by considering the dependence of threshold current on quantum well number [35]: j _ j. ( a ; + a m)IN J 'r t„ (2 23) Vi Here Nw is the number of wells, Vi is the volume of one well, B is the bimolecular recombination coefficient, Ntr is the transparency carrier density, T |, is the internal efficiency, oq is the internal loss, 0C m is the mirror loss, T i is the confinement factor for one well, and g0 is the gain coefficient from the two-parameter gain fit [35]: S = S > - § ~ (2-24) Equation 2.23 assumes that the confinement factor per well is constant regardless of the number of wells. In practice this is not true for a large number of wells because additional wells lie off the peak in the cavity standing wave. However, for a small number of wells this assumption is accurate. The optimum number of quantum wells is determined when equation 2.23 is minimized. A plot of threshold current versus number of wells is shown below in figure 2.16 using typical parameters for an 80A GaAs/Al^Ga.sAs quantum well (see table 2.1). The minimum can clearly be seen to occur at three quantum wells. In order to further optimize the device, the mirror reflectivity must be determined. The device configuration in this work is top-emitting; therefore, the bottom DBR will have a reflectivity close to 100%. For an Al.93Ga.07As/Al.2Ga.8As 44 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. stack with refractive indices of 2.9885 and 3.4124, respectively, the number of pairs required is 40 according to equation 2.9. Q uantum Well N um ber O ptim ization 550 _ 400- Q 350- ^ 300- O 4= </> d) v_ x: H 250- 200 - o —° 150 0 1 2 3 4 5 6 7 8 9 10 11 Number of Wells Figure 2.16 Quantum well number optimization. The reflectivity of the top DBR must now be determined. One cannot simply optimize threshold current versus mirror reflectivity, however; the result is 100% mirror reflectivity, which is of little use since no light will be emitted. Thus, the mirror reflectivity must be optimized with respect to the desired light output power so that the wall-plug efficiency is maximized. For FSOI applications, lmW of optical power is the design constraint. The task is thus to determine the mirror reflectivity of the top DBR that minimizes the drive current for lmW of optical power. 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 2.1: Parameters used to calculate threshold current, current for lmW output power, and wall- plug efficiency. 0.9 V! 2x1 O ' 1 3 cm3 B lxlO "10 cm3 /s N,r 2 .6x l 0 1 8 cm" 3 O C j 2 0 cm' 1 otm 25 cm' 1 r, 0 .0 2 go 1400 cm"1 R s 400£2 Vd 1.5V The total device drive current can be found from [35]: qP (a, + a ) 7 = — - J+It, (2.25) F Thhvam Here I* is that found from equation 2.23, P0 is the desired optical power, F is the fraction of total optical power coming out of the top mirror, h is Plank’s constant, and v is the frequency of the emitted light. Since the bottom mirror has a reflectivity close to 100%, F can be assumed to be 1. Equation 2.25 is plotted below in figure 2.17 along with a calculation of the wall-plug efficiency. As can be seen in the plot, at a mirror reflectivity of -99% the bias current for 1mA of output power (and consequently the wall-plug efficiency) is optimized. This reflectivity corresponds to 2 0 periods for the A l . 9 3 G a . 0 7 A s / A l . 2 G a . 8 A s DBR. 46 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Bias Current and Wall-Plug Efficiency for 1 mW Optical Power 0.40 0.35 0. 1 - 0.30 4 - * c 2 0.25 0.20 0.15 0.10 0.05 0.00 1E-3 -0.05 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 1.01 >* O c 0 ) 0 i t LU O ) 3 Q . 1 " ( 5 M irro r R e fle c tiv ity Figure 2.17 Bias current and wall-plug efficiency versus mirror reflectivity for lm W of output power. Note that the left axis is a log scale 2.6 Summary of device design Several aspects of VCSEL design have been considered, including the cavity and mirror design, oxide aperture placement, active region design, and optimization issues for the number of quantum wells and mirror reflectivity. It was determined that the optimum DBR design uses high-contrast layers to minimize the number of pairs needed. For the devices fabricated in this work with epitaxial AlGaAs mirrors the compositions were Al.93Ga.07As, with a refractive index of 2.9885, for the low-index layer, and Al.2Ga.8As, with a refractive index of 3.4124, for the high-index layer. 93% aluminum was chosen for the low-index layers due to consideration for the later wet-oxidation process, while 2 0 % aluminum was 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. chosen for the high-index layers so that the material is transparent to the 850nm emission from the active region. For the desired top-emission, the bottom DBR should have 40 periods to achieve nearly 100% reflectivity. Optimization of the wall-plug efficiency shows that the top DBR should have 20 periods to obtain a 99% reflectivity. An analysis of scattering loss from the oxide aperture was also done and it was shown that the optimum position for the oxide aperture is at a null in the cavity standing wave pattern. Positioning the oxide aperture here reduces scattering loss, but by reducing the interaction of the aperture with the field the device is also more insensitive to aperture size variations. This is an important consideration for obtaining high-uniformity VCSEL arrays. The GaAs/AlGaAs materials system was selected for 850nm emission, and the optimum quantum well design was shown to be an 80A GaAs quantum well with Al^Ga.gAs barriers. This design takes into account the temperature shift of the optical gain spectrum. It was also shown that the threshold current can be minimized by using 3 quantum wells in the active region. The design optimization discussed above was done to maximize wall-plug efficiency while obtaining low-threshold operation for continuous wave (CW) operation. 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Hull, “Fabrication and performance of selectively oxidized vertical-cavity lasers,” IEEE Photon. Technol. Lett., vol. 7, no. 11, pp. 1237-1239 (1995). 29. M.H. MacDougal, J. Geske, C.K. Lin, A.E. Bond, P.D. Dapkus, “Low resistance intracavity-contacted oxide-aperture VCSEL’s,” IEEE Photon. Technol. Lett., vol. 10, no. 1, pp. 9-11 (1998). 30. A.E. Bond, P.D. Dapkus, J.D. O ’Brien, “Aperture dependent loss analysis in vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett., vol. 11, no. 4, pp. 397-399 (1999). 31. A.E. Bond, P.D. Dapkus, J.D. O ’Brien, “Design of low-loss single-mode vertical-cavity surface-emitting lasers,” IEEEJ. Select. Topics Quantum Electron., vol. 5, no. 3, pp. 574- 580(1999). 32. C.K. Lin, P.D. Dapkus, “Uniform wafer-bonded oxide-confined bottom-emitting 850nm VCSEL arrays on sapphire substrates,” IEEE Photon. Technol. Lett., vol. 13, no. 4, pp. 263-265 (2001). 33. B.J. Thibeault, E.R. Hegblom, P.D. Floyd, R. Naone, Y. Akulova, and L.A. Coldren, “Reduced optical scattering loss in vertical-cavity lasers using a thin (300A) oxide aperture,” IEEE Photon. Technol. Lett., vol. 8, no. 5, pp. 593-595 (1996). 34. A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control o f Laser Radiation, Ch.6, John Wiley and Sons, New York (1984). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35. L.A. Coldren, S.W. Corzine, Diode Lasers and Photonic Integrated Circuits, John Wiley and Sons, New York (1995). 36. P. Yeh, Optical Waves in Layered Media, John Wiley and Sons, New York (1988). 37. M.A. Afromowitz, “Refractive index of Gai_xAlx As,” Solid State Comm., vol. 15, pp. 59-63 (1974). 38. G.R. Hadley, “Effective index model for vertical-cavity surface-emitting lasers,” Optics Lett., vol. 20, no. 13, pp. 1483-1485 (1995). 39. E.R. Hegblom, D.I. Babic, B.J. Thibeault, and L.A. Coldren, “Scattering losses from dielectric apertures in vertical-cavity lasers,” IEEE J. Select. Topics Quantum Electron., vol. 3, no. 2, pp. 379-389 (1997). 40. G.P. Agrawal, Fiber-Optic Communication Systems, 3rd ed., John Wiley and Sons, New York (2002). 41. A.E. Siegman, Lasers, University Science Books, Sausalito, CA (1986). 42. D.B. Young, et al., “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron, vol. 29, pp. 2013-2022 (1993). 43. B. Tell, F. Brown-Goebeler, R.E. Leibenguth, F.M. Baez, and Y.H. Lee, “Temperature dependence of GaAs-AlGaAs vertical cavity surface emitting lasers,” Appl. Phys. Lett., vol. 60, no. 6, pp. 683-685. 44. Chao-Kun Lin, “Wafer-bonded bottom-emitting 850nm VCSELs for short distance free- space optical interconnections,” Ph.D. thesis dissertation, pp. 5 (1999). 45. J.J. Dudley, D.L. Crawford, and J.E. Bowers, “Temperature dependence of the properties of DBR mirrors used in surface normal optoelectronic devices,” IEEE Photon Technol Lett., vol.4, no. 4, pp. 311-314 (1992). 46. S.M. Sze, Physics o f Semiconductor Devices, 2n d edition, John Wiley and Sons, New York, Ch. 1 (1981). 47. S.L. Chuang, Physics o f Optoelectronic Devices, John Wiley and Sons, New York (1995). 48. R.S. Geels, B.J. Thibeault, S.W. Corzine, J.W. Scott, and L.A. Coldren, “Design and characterization of In 2 Ga 8 As MQW vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron., vol. 29, no. 12, pp. 2977-2987 (1993). 49. S. Adachi, “GaAs, AlAs, and Alx Gai-x As material parameters for use in research and device applications,” J. Appl. Phys., vol. 58, no. 3, pp. R1-R29 (1985). 50. J. Singh, Physics o f Semiconductors and Their Heterostructures, McGraw-Hill, San Francisco (1993). 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 3: High-Frequency VCSEL Design 3.1 Intrinsic frequency performance In order for the bandwidth requirements of FSOI to be met, several VCSEL characteristics must be taken into account, some of which are intrinsic and others that are parasitic. The intrinsic frequency performance of a laser diode can best be understood by first considering the small-signal transfer function of a semiconductor laser [1]: H ( c q ) = 2 4 , (3-l) c o r -co + 1 coy Equation 3.1 is a two-pole transfer function where A is a multiplicative constant, y is a damping factor, co is the modulation frequency, and co r is the relaxation oscillation frequency. The oscillations occur as a result of coupling between the photon density and the carrier density, giving a response similar to that of an RLC tank circuit. The relaxation resonance frequency and damping factor are dependent on intrinsic device parameters as follows [1]: y , g . r „ , ( / - / , ) (32) qV fS r=8„S0+— (3.3) T,> Here vg is the group velocity, g0 is the differential gain, V is the cavity volume, e is the gain compression factor, S0 is the steady-state photon density, and T p is the photon lifetime in the cavity. The frequency response is plotted below for 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. increasing pumping levels. As the laser is biased higher the photon density increases; this increases the relaxation resonance frequency but increases the damping as well. As the photon density increases, the damping moves from underdamped to critically damped. If the device is biased too high, however, an overdamped condition will result, and the 3dB frequency will actually decrease. L aser Frequency R esponse CM - 2 - -4- ^3 X -3dB U) o -I 1.5*1 TH 3.0*1 TH 5.0*1 TH 2 0 * 1 TH - 10 - - 12 - -14- -1 6 -— 1E7 1E8 1E9 1E10 Log Frequency Figure 3.1 Frequency response of a VCSEL calculated assuming typical parameters for an Al 2 Ga 8 As/GaAs 80A quantum well. The 3dB bandwidth of the laser is f 3 d B ~ l.55fr [2]; thus, in order to maximize the bandwidth of the laser, the highest possible relaxation resonance frequency should be achieved. From Eq. 3.2 one can see that minimizing the threshold current, m axim izing the internal efficiency and confinem ent factor, and minimizing the cavity volume (thereby increasing the photon density) are key design points. 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. There is a trade-off between mirror reflectivity and cavity length, however, when considering photon lifetime, which should be minimized, and photon density, which should be maximized. It was demonstrated by Mar, et al., however, that the optimum design is a high mirror reflectivity with a short cavity [3]. In this way the threshold current is reduced while still maintaining a large photon density and small photon lifetime. Fortunately this condition exists naturally in a VCSEL cavity; therefore, these devices should be well suited to wide-bandwidth modulation in this regard. By combining equations 3.2 and 3.3 it can be seen that the damping depends on the resonance frequency as follows: r = K fr 2 + Z„ (3.4) 4 t t 2 p where K = — — 70 =goSo The K parameter, or K-factor, is a figure of merit that determines the maximum intrinsic bandwidth for a semiconductor laser by Fma = 2\f27r/K [1], The K-factor is directly proportional to the gain compression factor and inversely proportional to the differential gain. Since Fm a x scales inversely with K the K-factor should be minimized; thus, the differential gain should be maximized and the gain compression factor should be minimized. The differential gain deserves some attention because maximization of this parameter moves both fr and K in the right directions. The gain of a quantum well 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. as a function of carrier density can be approximated by a logarithmic function of the following form [2]: N + N. 1 S = g„ln (3.5) where N is the carrier density, Ntr is the transparency current density, and Ns is an empirical fitting parameter. The differential gain is then, dg/dN - g„/(N + Ns) . Typical numbers for an Al.2Ga.gAs/GaAs 80A QW are Ntr=2.6xl01 8 cm"3, Ns= l.lx l0 1 8 cm"3, and go =3000 cm"1 [2], Gain and Differential Gain 3500- 3000- O 2500- 2000 - 1500- O 1000 - 500- 2 4 6 8 10 E 0 CO 1 o T - X (0 0 w "J £ o 0) o Carrier Density (x101 8 cm'3 ) Figure 3.2 Gain and differential gain for an Al 2Ga.8 As/GaAs QW. Plots of the gain and differential gain are shown above in figure 3.2. It can be seen from the plots that the maximum differential gain occurs at transparency and decreases with increasing carrier injection. Thus, operating at a higher 55 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. differential gain means operating at a lower total material gain; this will result in increased threshold current and decreased fr. The optimum design for maximizing the differential gain is thus to operate as close to transparency as possible while still minimizing the threshold current. One way to increase the differential gain is to incorporate biaxial strain in the active region by using InGaAs quantum wells. Unfortunately FSOI applications can not tolerate the 980nm wavelength that is obtained with this materials system. Thus, strained active regions are not a viable design option for the devices in this work. Aside from maximizing the differential gain, minimizing damping mechanisms that lead to gain compression are equally as important with regards to device bandwidth. Gain compression is caused primarily by spectral hole burning and carrier heating, both of which are non-linear effects. Spectral hole burning is a saturation in gain at the lasing wavelength as the power in the lasing mode is increased. Physically, as the power in the lasing mode increases, the stimulated recombination rate increases to a point where it equals the carrier intraband relaxation time [4], At this point carrier relaxation limits the stimulated emission, resulting in gain saturation. Carrier heating also saturates the gain in the lasing mode, but works by increasing the carrier relaxation time. Carriers are heated through such processes as injection heating, recombination heating, and free carrier absorption heating [5]. In order for carriers to relax into the quantum well subbands and participate in 56 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. stimulated recombination they must give off the excess energy acquired from the above processes. This is done be emission of longitudinal optical (LO) phonons, a process that happens on a finite time scale. The more energy that carriers accumulate through the above heating processes, the longer it takes for those carriers to emit phonons. Typical time scales for carrier relaxation are a few picoseconds. The reduction in gain and differential gain due to spectral hole burning and carrier heating can be written as [6]: = (3.6) (1 + £S„) The gain compression factor, 8, takes into account the nonlinear effects discussed above and is typically in the range of 1.5xl0'1 7 cm3. One design approach for reducing the gain compression factor is p-doping the QW barrier layers in the active region [7, 8], P-type doping in the QW barriers simultaneously increases the differential gain and lowers the gain compression factor, thus increasing fr and reducing the K-factor. The gain compression factor is reduced because p-doping reduces the intraband relaxation time, thereby mitigating the effects of spectral hole burning and carrier heating. A critical issue with p-doping the active region, however, is localization of the p-doped region. During epitaxial growth, for example, the high growth temperatures can result in diffusion of the p-dopant. This will result in impurities in the QWs which will alter their band structure. Zinc was the p-dopant used for 57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the devices discussed here, and readily diffuses at standard growth temperatures. Thus, it was not possible to use a p-doped active region in these devices. Furthermore, doped active regions will suffer from increased free carrier absorption and, consequently, decreased differential efficiency and larger threshold currents. Thus, from a CW performance point of view, p-doping the QWs is not desirable either. 3.2 High-frequency parasitics In practice it is the device parasitics, rather than the intrinsic device performance, that limits maximum obtainable frequency response. These parasitics arise mainly from packaging such as bond pad capacitance and wire bond inductance, but can also result from poor carrier transport due to a badly designed active region or from excessive series resistance from the DBRs. Below is a device schematic showing the relevant parasitic circuit elements. The embodiment shown below employs a low-K dielectric, polyimide in this case, to reduce the bond pad capacitance. The combination of the bond wire inductance and bond pad capacitance can lead to a resonance in the frequency response if the wire bond is too long or if the bond pad capacitance is too high. Furthermore, a large bond pad capacitance in parallel with a large series resistance will result in a large RC time constant. This will produce a low-frequency roll-off in the modulation response and limit device bandwidth. Thus, it is imperative that the series resistance and bond pad capacitance be reduced as much as possible. 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Bond Wire Inductance Series Resistance Bond Pad Bond Pad Capacitance Polyimide ‘ it • l i 3C --------- Oxide Capacitance Series Resistance Figure 3.3 Parasitic circuit elements in a VCSEL structure 3.2.1 Parasitic Resistance The series resistance of the device is of critical importance because a large series resistance will result in a large RC time constant and increased operating temperature due to Joule heating. The heat produced by the power drop across the series resistance will contribute to shifting the gain spectrum, decreasing the wall- plug efficiency of the device, and increasing the gain compression factor. There are three main components to the series resistance: first, the contact resistance of the p-contact; second, the periodic potential barrier seen by carriers as they pass through the DBR layers; and third, the narrow oxide aperture that the current flows through. Not much can be done about the narrow current aperture; minimum threshold currents require that it be between 3-4 pm. The contact 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. resistance, however, can be lowered by appropriate doping and annealing conditions, and the resistance due to the DBRs can be reduced by modulation doping and graded interface techniques. In order to ensure that the contact resistance remains low the device structure is capped with a 100A, highly-doped, GaAs layer. The cap layer is required because it is difficult to achieve ohmic contact to AlGaAs. This cap layer must be kept thin because, for the devices fabricated in this study, light emits through the top of the device; GaAs is absorbing at 850nm, thus a thin layer must be used. The metal layers used for the p-contact are 300A of titanium, 500A of platinum, and 2000A of gold. The Ti/GaAs interface represents a Schottky contact that is ohmic as long as the GaAs contact layer is heavily doped. There is always a thin layer of oxide on the surface of the GaAs which will pin the Fermi level to 2 roughly Ec - — Er . A barrier thus exists between the metal and the semiconductor because of the surface states presented by the oxide layer. However, as long as the contact layer is heavily doped, this barrier will be thin enough so that carriers will readily tunnel through it. Thus, the doping in the GaAs contact layer is targeted at lxlO 1 9 cm'3. To check the contact resistance of the p-contact, a transmission line experiment was performed to determine the specific contact resistance of the Ti/Pt/Au-GaAs interface. Usually this experiment is performed using square test patterns; edge effects, however, can affect the accuracy unless mesa structures are 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. etched. A better method is to use circular test patterns so that edge effects can be neglected [9]. Figure 3.4 shows the test pattern used for the experiment. 650|j,m Figure 3.4 Circular test patterns for determination of specific contact resistance. The above pattern is lithographically defined on the contact surface, and the liftoff, the wafer is annealed at 400°C for 30sec. in a forming gas ambient environment using a rapid thermal annealer (RTA). The patterned is then probed, with one probe contacting the outer corner of the square pattern, and the other contacting one of the circular patterns. A constant current is injected and the voltage drop across the varying gap length, d, is measured for the various pattern sizes. The data is then fit to a transmission line model of the following form [9]: Here i0 is the injected current, AV is the voltage drop, Rs is the sheet resistance, and Lt is the transfer length. The specific contact resistance is calculated contact metals are evaporated at a starting pressure of 5x10"7 Torr. Following the U n ~ d Jj (3.7) 61 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. from Lj. = . In the test patterns used here, is 75jim, and d varies from 6 to 28(im. The voltage drop data is plotted below and fit to equation 3.7. 0, 0. 0. ^ o. > (? 0. 50 45 -( 40 35- 30- 25- 2 0 - 15- C ontact R esistan ce M easurem ent □ AV T ransm ission Line Fit Rs=273.16 Q/sq Rc=3.73x10'5 Q-cm2 5 10 15 20 25 30 Separation Distance (^m) Figure 3.5 Transmission line measurement and fitted results The results yield a sheet resistance of 273.16 Q/sq and a specific contact resistance of 3.73xl0’5 Q-cm2. The p-contact used in this device configuration has -5 2 an area of 1.2x10" cm . This yields a total contact resistance of 3.1 Q, which will be negligible compared to other sources of resistance. More significant contributors to the series resistance are the p-DBRs. As discussed in chapter 2, semiconductor layers with high refractive index contrast must be used in the DBRs to obtain large reflection coefficients with a minimum number of periods. This also means that the DBR layers will have large band gap differences that present energy barriers to electrons and holes. These potential 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. barriers can result in large resistances if not designed properly. This problem is most acute in the p-DBR due to the low mobility of holes compared to electrons. Solutions to this problem include modulation doping the DBRs and either linearly or parabolically grading the interfaces of the DBR layers [10-13]. In the device structure, a 180A, linearly graded layer was inserted between the Al.93Ga.07As and Al.2Ga.sAs layers in both the p- and n-DBRs. The graded layers at the standing-wave nulls were heavily doped to 5 x l0 1 8 cm'3, while the 1 8 -3 doping levels in the other layers are kept at -1x10 cm" . The doping in the first few pairs closest to the active region was reduced to 5 x l0 1 7 cm'3. This doping scheme was done to lower the heterojunction barrier height while minimizing losses due to free carrier absorption. The insertion of the grading layers also causes the reflectivity of the DBR to decrease slightly. This was accounted for by adding a few periods to the top and bottom DBR. Figure 3.7 below demonstrates the differences between DBR structures with doping but without graded interfaces (fig. 3.7a), doping and grading layers (fig. 3.7b), and neither doping nor graded interfaces (fig. 3.7c). In case c, the large offset between the high- and low-aluminum composition layers can be seen. Doping the layers, as in case a, decreases the overall offset, however there are still large spikes at the interfaces. Grading the interfaces between high and low aluminum composition layers (as in case b) eliminates the edge spikes, and results in a low-resistance DBR structure. 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.00 3.05 3.10 3.15 3.20 Position (nm) 3.25 2.95 3.00 3.05 3.10 3.15 3.20 3.25 3.30 Position (iim) -0.02 -0.04 -0.06 -0.08 O -0.16 LU -0.18 (c) -0.20 - 0.22 -0.24 3.00 3.05 3.10 3.15 3.20 3.25 Position (iim) Figure 3.6 Valence band diagrams for a DBR structure for: a) Modulation doping without graded interfaces; b) Modulation doing with graded interfaces; and c) neither doping nor graded interfaces Modulation doping and graded interfaces can reduce the DBR resistance to less than 10012. It is the current aperture and current spreading in the DBR, however, which contribute the majority of the series resistance to the device. The resistance introduced by the current aperture is primarily due to the narrow constriction that current must pass through. Furthermore, with the annular contacts used for these devices, there will be spreading resistance as the current moves towards the center of the etched mesa. The series resistance of the device will scale with the current aperture dimensions; thus, there will be an inherent trade-off between obtaining low threshold currents and high modulation speeds. Following the treatment of MacDougal, et al., the resistance due to lateral current spreading and constriction by the oxide aperture can be modeled and 64 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. compared to measured data [14]. The model breaks the device up into three sections: region A represents the contact resistance from injecting carriers into the semiconductor from the metal contact; region B represents the spreading resistance as the carriers move laterally from the contact to the aperture; region C represents the resistance seen as the carriers move through the oxide aperture (see figure 3.8). r 3 r 2 Ri h 1 -------- 1 i i i I C l B I A m m m wrnui m l Figure 3.7 VCSEL schematic displaying the three regions of current spreading. This model was developed for intra-cavity contacts where current was conducted primarily through a single p-GaAs layer. The model can be modified, however, to take into account conduction through the various DBR layers by defining vertical and lateral effective resistivities [15]: A = I(4 P ,)/i> , (3-8) i= l / i= 1 P i = H di / n ^ i 1 A ) (3-9) i= l / 1 = 1 Resistances for each region can be derived using Ohm’s law by assuming a voltage drop across the region and then calculating the current in the region. In 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. region A, the current density in the vertical direction in the metal layer is given by [14]: V -V O ) Jc(r) = ~ ---- — , (3-10) P c where pc is the specific contact resistance for the metal-semiconductor interface. Current traveling laterally is given by: / „ = ^ A (3. n ) P h d r where th is the thickness of the upper DBR and ph is the effective lateral resistance. Current continuity at the boundaries leads to a differential equation whose solutions are put in terms of Bessel functions: RA= ^ & - W U (3.12) Here Kv is the modified Bessel function of the second kind of order v, and 8a is the transfer length in region A. The resistance in region B can be found by directly integrating equation 3.11 and applying boundary conditions: R r = - ^ M n 2m h ( \ (3.13) V r3 J Lastly, the resistance in region C is found in a similar manner to region A, except that there is a more resistive semiconductor layer underneath, and that current first spreads laterally and then vertically. The solutions are presented as modified Bessel functions of the first kind: 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Rr p A 21 o {r! Sc) (3.14) 2nr3th I _ x { r l S c ) + h { r l S c ) Here 8c is the transfer length in region C. The transfer lengths are given by 3 A ~ V P P h / P h an^ & c ~ >/' P J i t h i P h ■ The above equations were solved for varying aperture width and fitted to measured data from the IV curves of fabricated devices. Linear fits were made of the IV curves within the corresponding linear regions of the light-current curves. Taking the series resistance at higher currents might have provided lower resistance values, but would not be accurate if the current were higher than the operating point of the device. VCSEL Series Resistance 1000 o Measured Data — Calculated 900- 800- ® 700- < 2 600- M 500- 400- 300- 200 0 2 4 6 8 10 12 Aperture diameter (pm) Figure 3.8 Calculated and measured resistance data. The above model for series resistance is lacking in that it does not account for resistance due to the heterointerfaces of the DBRs. Consequently, the curve generated by the calculations is offset from the measured resistance. By adding a 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. constant resistance that accounts for both the contact resistance and resistance due to the DBRs the calculation fits the measured data. Adding a constant resistance to account for contributions to the total resistance from the DBRs seems accurate since that resistance should not depend on aperture size. In the data presented above, a resistance of 25012 was added to the calculated curve, which resulted in a good data fit. 3.2.2 Parasitic Capacitance The large series resistance that is incurred by the narrow current aperture means that the bond pad capacitance must be reduced considerably so that the bandwidth of the device is not RC-limited. Two methods were undertaken to achieve this, the first being the use of polyimide and the second being proton bombardment. Polyimide is a low-K dielectric, the use of which is depicted in figure 3.3. It is supplied as a viscous polymer that can be applied to a wafer using spin-coating techniques. First a mesa is etched in the VCSEL epitaxial structure and the wafer is then coated with polyimide. An opening is etched through the polyimide so that the bond pad can make contact to the contact ring on the p-side of the device. By approximating the configuration of the bond pad, polyimide insulator, and ground plane as a parallel plate capacitor, the capacitance is given by C - K£r ) A /d . In this equation, A is the area of the bond pad, d is the thickness of the polyimide, k is the dielectric constant of the polyimide, and e0 is the 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. permittivity of free space. Etching depths for the YCSELs made in this work were typically ~5fim, which yielded bond pad capacitances in the range of 60-70fF for pad areas of 80x80|jm2. The RC-limited bandwidth can be determined from the 3dB roll-off incurred by the bond pad capacitance and series resistance by f 3 d B =1/2k RC . For the case of bond pads isolated by polyimide 3dB roll-off frequencies of 6 .6-5.7 GHz are expected for a series resistance of 400Q. The polyimide approach yields low capacitances but complicates the fabrication by the need to planarize the wafer after the deep mesa etching. The ion implantation technique is attractive because it maintains the planarity of the wafer. Furthermore, adhesion of the bond pads to the polyimide during subsequent wire bonding can be poor unless the pads are thicker than -5000A. The ion implantation technique allows for the bond pad to be evaporated directly to the semiconductor surface, thus improving adhesion. Table 3.1 Proton implantation schedule for bond pad isolation Implant # Energy Dose 1 20keV 2el4 cm"2 2 60keV 3el4 cm"2 3 lOOkeV 3el4 cm"2 4 140keV 3el4 cm"2 5 180keV 3el4 cm"2 6 220keV 5el4 cm"2 7 260keV 5el4 cm"2 8 300keV 5el4 cm'2 9 340keV 5el4 cm'2 10 360keV le l5 cm'2 69 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Bombarding the surface of the VCSEL epitaxial wafer with H+ protons creates vacancies in the crystal structure, yielding insulating regions in the implanted areas. By varying the ion dose and energy, sufficient isolation can be obtained between the bond pad and the ground plane to achieve low capacitance A freely available program, SRIM [10], was used to develop a ten step proton implantation sequence with increasing dosage and energy so that the crystal structure was semi-insulating up to a depth of ~3.5|im. SRIM, or the stopping and range of ions in matter, is a Monte Carlo simulation that calculates the penetration range and straggle of a given implant species at a given energy for a specified substrate material. Target V acancy Distribution 0.008- 20keV ^ 2 o o ° - o > f f 1500- O) £ 0.006- 1000- 0 50 100 150 200 250 300 350 Ion Energy (eV) « 0.004- 360keV 0 .002 - 0.000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Depth (|orn) Figure 3.9 Calculated vacancy distributions for increasing implantation energies from 20keV to 360keV. The inset displays the longitudinal straggle versus ion energy. 70 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The ion range follows a Gaussian distribution; therefore, the implantation scheme consists of increasing energies so that the range distributions at the various energies overlap. Furthermore, longitudinal and lateral straggle will serve to decrease the localized ion dose at higher energies, so the ion dose is increased as the energy increases. Channeling is also eliminated by tilting the wafer by 7 degrees during the implant. Figure 3.10 above depicts the ion distribution for the ten step implant procedure. With the ion implantation approach, bond pad capacitances of roughly 250fF were achieved. The RC-limited bandwidth for the capacitance obtained by ion implantation associated with a series resistance of 400Q is ~1.59GHz. Comparing this to the polyimide approach, polyimide is a better option for bond pad isolation. This is due to the fact that the dielectric constant of the semiconductor is much higher than that of the polyimide, and the implantation depths are somewhat shallower than the isolation depths that can be achieved with polyimide. Implantation depths could be increased by pursuing higher-energy implantation; however, MeV systems must be employed. As mentioned above, a trade-off exists between minimizing resistance with a large aperture diameter, and minimizing threshold current with a small aperture diameter. This can be analyzed based on the achievable bond pad capacitances of the two isolation methods using the resistance model discussed above. Figure 3.11 plots the parasitic, RC-limited bandwidth for both the polyimide and ion implantation techniques as a function of current aperture width. As can be seen 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. from the graph, even at large apertures the ion implantation approach is much more RC-limited than the polyimide approach. The analysis shows that the frequency performance is not expected to achieve more than 2GHz. Polyimide isolation, on the other hand, could potential yield modulation bandwidths of up to 10GHz. Bond Pad Isolation C om parison N £ 1E10- > o c a > 3 C T a > ■ o co 1E9 .........Polyimide Isolation -------Ion Implant Isolation s* * 4 / ' / ‘ / / --------------- 2 4 6 8 10 12 Aperture Width (pm) Figure 3.10 Comparison of polyimide and ion implantation for bond pad isolation. 3.3 Summary of high-frequency design In this chapter the aspects of high-frequency YCSEL design were discussed from the standpoint of both intrinsic and extrinsic limitations to device performance. By utilizing the short cavity and high mirror reflectivity of a VCSEL cavity, high photon densities, and therefore large relaxation oscillation frequencies can be achieved. One drawback, however, is the GaAs/AlGaAs active region that must be used for 850nm applications. The unavailability of strain as a degree of 72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. freedom for active region design means that the differential gain can not be altered from that which is inherently achieved with this material system. Extrinsic parameters such as parasitic bond pad capacitance and series resistance were also examined. By careful design of the DBR superlattice and by proper doping of the GaAs contact layer the heterojunction resistance and contact resistance can be minimized. Band pad capacitance can be reduced by isolation techniques such as polyimide planarization or proton implantation. It was found that the limiting factor for bandwidth, however, was the series resistance incurred by the narrow current aperture. This presents a trade-off between achieving low threshold current and high modulation speed. References 1. D. Tauber, and J.E. Bowers, “Dynamics of wide bandwidth semiconductor lasers,” International J. High Speed Electronics and Systems, vol. 8, no. 3, pp. 377-416 (1997). 2. L.A. Coldren, S.W. Corzine, Diode Lasers and Photonic Integrated Circuits, John Wiley and Sons, New York (1995). 3. A. Mar, P.A. Morton, J.E. Bowers, “Optimum facet reflectivity for high speed lasers,” Electron. Lett., vol. 26, no. 17, pp. 1382-1384 (1990). 4. G.P. Agrawal, “Gain nonlinearities in semiconductor lasers: theory and application to distributed feedback lasers,” IEEE J. Quantum Electron., vol. QE-23, no. 6, pp. 860-868 (1987). 5. C.Y. Tsai, C.Y. Tsai, R.M. Spencer, Y.H. Lo, L.F. Eastman, “Nonlinear gain coefficients in semiconductor lasers: effects of carrier heating,” IEEE J. Quantum Electron., vol. 32, no. 2, pp. 201-212 (1996). 6. G. Wang, R. Nagarajan, D. Tauber, and J. Bowers, “Reduction of damping in high-speed semiconductor lasers,” IEEE Photon. Technol. Lett., vol. 5, no. 6, pp. 642-645 (1993). 7. J.D. Ralston, S. Weisser, I. Esquivias, E.C. Larkins, J. Rosenzweig, P.J. Tasker, and J. Fleissner, “Control of differential gain, nonlinear gain, and damping factor for high-speed application of GaAs-based MQW lasers,” IEEE J. Quantum Electron., vol. 29, no. 6, pp. 1648-1659(1993). 8. N. Hatori, A. Mizutani, N. Nishiyama, A. Matsutani, T. Sakaguchi, F. Motomura, F. Koyama, and K. Iga, “An over 10-Gb/s transmission experiment using a p-type delta-doped 73 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. InGaAs-GaAs quantum-well vertical-cavity surface-emitting laser,” IEEE Photon. Technol. Lett., vol. 10, no. 2, pp. 194-196 (1998). 9. G.S. Marlow and M.B Das, “The effects of contact size and non-zero metal resistance on the determination of specific contact resistance,” Solid-State Electronics, vol. 25, no. 2, pp. 91-94 (1982). 10. R.S. Geels, S.W. Corzine, J.W. Scott, D.B. Young, and L.A. Coldren, “Low threshold planarized vertical-cavity surface-emitting lasers,” IEEE Photon. Technol. Lett., vol. 2, no. 4, pp. 234-236 (1990). 11. K. Tai, L. Yang, Y.H. Wang, J.D. Wynn, and A.Y. Cho, “Drastic reduction of series resistance in doped semiconductor distributed Bragg reflectors for surface-emitting lasers,” Appl. Phys. Lett., vol. 56, no. 25, pp. 2496-2498 (1990) 12. E.F. Schubert, L.W. Tu, G.J. Zydzik, R.F. Kopf, A. Benvenuti, and M.R. Pinto, “Elimination of heterojunction band discontinuities by modulation doping,” Appl. Phys. Lett., vol. 60, no. 4, pp. 466-468 (1992). 13. S.A. Chalmers, K.L. Lear, and K.P. Killeen, “Low resistance wavelength-reproducible p- type (Al,Ga)As distributed Bragg reflectors grown by molecular beam epitaxy,” Appl. Phys. Lett., vol. 62, no. 14, pp. 1585-1587 (1993). 14. M.H. MacDougal, J. Geske, C.K. Lin, A.E. Bond, P.D. Dapkus, “Low resistance intracavity-contacted oxide-aperture VCSEL’s,” IEEE Photon. Technol. Lett., vol. 10, no. l,p p . 9-11 (1998). 15. W. Nakwaski, M. Osinski, J. Cheng, “Spreading resistance in proton-implanted vertical- cavity surface-emitting diode lasers,” Appl. Phys. Lett., vol. 61, no. 26, pp. 3101-3103 (1992). 16. www.srim.org 74 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 4: VCSEL Fabrication and Performance This chapter will discuss in detail the steps necessary to realize high- performance, large-density VCSEL arrays. A critical step is the crystal growth calibration and control that must be performed to fabricate the DBRs. Another key issue is the uniformity of the wet oxidation process. These, along with other pertinent fabrication issues, will be discussed. Performance results for the polyimide-planarized and ion-implanted devices will also be presented. 4.1 VCSEL Epitaxy A VCSEL structure consists of more than 100 epilayers, each of whose thickness, doping, and composition must be carefully controlled. The DBRs are especially sensitive to thickness control, where variations in layer thickness of no more than 1 % can be tolerated. Only two epitaxial growth technologies are capable of this accuracy; molecular beam epitaxy (MBE) and metal-organic chemical vapor deposition (MOCVD). Of these two, MOCVD offers advantages in that growing graded layers for reduction of DBR resistance is more straightforward, and the growth rates are much faster. A complete VCSEL structure grown by MBE can take up to 8 hours to grow, whereas a VCSEL grown by MOCVD takes roughly half that time. Furthermore, compositional grading with MBE must be done by ramping the temperature of the effusion cells in the MBE apparatus; a process which is difficult to achieve and is not very reproducible [1], With MOCVD, mass flow controllers (MFCs) are used to control and ramp the flow rates of source 75 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. gases, resulting in a much more controlled compositional grading. Lastly, MOCVD is more scalable to commercial production because it does not depend on ultrahigh vacuum and the associated equipment, such as with MBE, and the throughput is higher because of the faster growth rates. The crystal structures for the devices fabricated in this study were grown by MOCVD. This growth technology was pioneered by Manasevit [2], and was later used by Dupuis and Dapkus in the fabrication of heterostructure devices such as high-efficiency solar cells and heterojunction lasers [3-5], The work of Dupuis and Dapkus clearly demonstrated MOCVD as a dominant epitaxial growth technology, capable of producing high-quality semiconductor films. MOCVD is now the epitaxial crystal growth technology of choice for a wide variety of commercial devices, such as lasers, light emitting diodes, heterojunction bipolar transistors, photodetectors, and solar cells. 4.1.1 MOCVD reactor setup A schematic of the low-pressure (0.1 atm) MOCVD system used in this work is shown below in figure 4.1. The three main components that comprise the system are the gas-handling mechanism, reaction chamber, and exhaust system. The gas handling system is composed of the group III, group V, and dopant sources, as well as the electronically-controlled MFCs for flow rate control and pneumatic valves in the inlet manifold. The group III sources are trimethyl gal Hum (TmGa) and trimethylaluminum (TmAl), and the group V source is arsine (AstE). The n-type dopant is silicon, and is supplied in the form of disilane (Si2H6). The p- 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. type dopant is zinc, and is supplied as the metal-organic (MO) diethylzinc (DeZn). Hydrogen is used as the carrier gas in this system, and is purified by a palladium diffusion purifier held at 375°C. The flow of hydrogen through the MO sources is controlled electronically via the MFCs. As the hydrogen passes through the bubbler the gas becomes saturated with the alkyl vapors from the MO source. These vapors are then transported to the reaction chamber via the hydrogen carrier gas. The arsine and disilane, on the other hand, are supplied to the reaction chamber directly from gas cylinders. MFCs Main H o C arrier DeZn Inlet M anifold TmGa TmAI P re s s u re C ontroller M etalorganic S o u rce B ubblers Q uartz R eacto r Purified RF Induction Coil T hrottle Valve - < 8 > - S cru b b e r G raphite S u s c e p to r E x h au st B aratron Pum p P article Filter T h erm o co u p le Figure 4.1 Schematic drawing of a MOCVD reactor. 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The reaction chamber itself is configured in a vertical geometry with a 2” SiC-coated graphite susceptor mounted inside a fused-quartz chamber with a gas inlet at the top. A showerhead is located at the inlet to distribute the injected source flows. The susceptor is heated through RF induction to temperatures in the range of 700°C-750°C with the temperature being monitored by a thermocouple. The susceptor is also attached to a motor so that it can be rotated during growth to improve uniformity in the gas distribution. At the exhaust side of the reactor, a pump combined with the throttle valve and baratron maintains a pressure of 76 Torr (0.1 atm) and pumps the excess reactants through a particle filter to the scrubber. The scrubber consists of a drum of activated carbon (charcoal) which removes the arsine and other toxic elements from the hydrogen carrier before the hydrogen is burned in a burn box. 4.1.2 Crystal growth by MOCVD With MOCVD, epitaxial layers are deposited on a semiconductor substrate that is placed on the reactor susceptor. As the carrier gas impinges on the heated substrate the vapors of the different alloy constituents undergo a pyrolysis reaction in which the individual constituents decompose to form the deposited layer and volatile reaction products [6]. A simple example is that of gallium arsenide (GaAs), in which a volatile MO compound and a gaseous hydride are reacting: (CH3)3 Ga + AsH3 -> ■ GaAs + 3CH4 (4.1) 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The growth of alloys such as AlGaAs is performed by mixing the vapors of the different alloy constituents in the appropriate vapor-phase ratio to form the desired composition. An equation for the ternary alloy Alx Gai_x As is expressed as: x(CH3)3Al + (l-jc)(C H 3)3 Ga + AsH3 — > Alx Ga,_xAs + 3CH4 (4.2) The vapor mixing is adjusted by controlling the flow rates of the constituent gases via the mass flow controllers. In the growth of a VCSEL structure, abrupt heterojunctions in the active region must be achieved, as well as compositionally graded heterojunctions in the DBRs. Abrupt heterojunctions are realized by interrupting the growth for a few seconds by shutting off the group III reactant and maintaining an arsenic overpressure. This is done to eliminate gas-phase dispersion [6 ], Compositional grading is achieved by varying the molar fraction of TmGa and TmAl simultaneously during the growth. This is done by ramping the flow rates of the TmGa and TmAl, respectively. 4.2 DBR and cavity calibration The crystal growth of 850nm VCSELs is complicated by the fact that the DBRs are ternary alloys; both thickness and composition of the epilayers must be controlled. Since the aluminum composition in the solid alloy does not exactly equal the mole fraction of the TmAl constituent in the gas phase, the actual composition and growth rate must be calibrated experimentally. 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In order to calibrate the AlGaAs composition and growth rate, first the growth rates of AlAs and GaAs were calibrated by growing DBR structures and fitting the measured reflectivity spectrum with theoretical simulations. A commercial software package, TFCalc, was used to perform the theoretical calculations and layer optimizations. The software compares the calculated and measured reflectivity spectrums and adjusts the refractive index and thickness of the GaAs and AlAs layers until a unique solution is found. The actual layer thicknesses and compositions were determined from the data fit. The AlAs and GaAs calibration discussed above is done to check the reactor condition and to ensure that growth rates have not changed. If the growth rates are found to have changed, then a detailed calibration of the Al.95Ga.05As/Al2G a 8As DBR is done. In order to do this, a DBR structure was grown using Al.95Ga.05As and Al.2Ga.8As layers. As before, the measured reflectivity can be compared to theoretical data to calibrate the thickness and composition of the AlGaAs layers. Corrections to growth time are then made according to changes in growth rate. Once this is done a DBR including the grading layers is done to check the optical thickness of the gradings and to adjust the Al.95Ga.05As and Al.2Ga.gAs layers once again to maintain a QWOT for each layer. Before an entire VCSEL structure is grown, cavity calibrations are performed to ensure that the cavity resonance is at the correct wavelength. In these runs, the desired VCSEL structure is grown with the 850nm active region, doping 80 Reproduced with permission of the copyright owner. Furiher reproduction prohibited without permission. schedule, and interface grading schedule as in the real device. In this case, however, fewer DBR pairs are used so that the cavity resonance can be resolved better in reflectivity measurements. By again fitting the reflectivity data to TFCalc simulations, adjustments to the Al.6Ga.4As SCH layer thicknesses can be made to tune the cavity resonance to 850nm. Following this calibration a full VCSEL structure is grown with the requisite number of DBR pairs. Figure 4.2 below shows a plot of the measured and calculated data for a VCSEL cavity. The resonance is slightly off of 850nm, indicating that some adjustment to the SCH layers is necessary. VCSEL Cavity Reflectivity o Measured Calculated 100 - 80- 60- > ^ 20 - 700 800 900 1000 Wavelength (nm) Figure 4.2 VCSEL cavity calibration showing measured and calculated reflectivity data (courtesy Y. Deng). 81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.3 Device processing 4.3.1 Process overview To begin the processing, the wafer was first cleaned by TCE, acetone, and methanol, followed by a deionized (DI) water rinse. This was done to remove contaminants from the wafer surface. Following this, the annular p-contact was defined lithographically using Clariant AZ5214 photoresist and an image reversal process. Image reversal was done so that the photoresist sidewall had an undercut profile, which makes the subsequent metal lift-off much easier. An oxygen plasma de-scum was performed to remove photoresist residues, followed by surface oxide removal in a HCkPEO 1:10 solution. The p-contact was evaporated in an Edwards electron-beam metal evaporator at a starting pressure of 5xl0 ~ 7 Torr. The p-contact consisted of Ti/Pt/Au with thicknesses of 300A/500A/2000A. The use of Ti requires a low vacuum pressure so that the Ti does not oxidize. Following the evaporation the metal was lifted off by soaking the wafer in acetone for a few seconds followed by another oxygen de-scum. A layer of SiNx was then deposited by chemical vapor deposition (CVD) to serve as a later dry-etch mask and to protect the p-contact from the later wet oxidation. A trench pattern was defined lithographically and transferred to the underlying SiNx layer by CF4 plasma in a reactive ion etching (RIE) system. The pattern consisted of 10 pm trenches and mesas that varied from 60|j.m to 6 6 |im in 82 Reproduced with permission of the copyright owner. Furiher reproduction prohibited without permission. 0.5 pm steps. With this pattern devices of thirteen different aperture sizes could be fabricated. Following the SiNx pattern transfer, the wafer was then rinsed in acetone and subjected to oxygen plasma to remove photoresist residues. The device mesa was then defined by dry-etching into the semiconductor. This etching electrically isolates one device from another in the array and exposes the AlAs layer for later wet oxidation. After dry etching the wafer is placed in methanol to prevent self-oxidation of the AlAs layer as it is transferred to the wet oxidation apparatus. The wet oxidation is carried out in an open tube quartz furnace at 425°C with a wet nitrogen steam flowing at 300sccm. The oxidation was carried out until the smallest mesa size was completely closed off so that the aperture sizes of the remaining mesas could be accurately determined. After the wet oxidation was complete about 50pm was lapped off of the substrate and a broad-area AuSn contact was electroplated to form the n-contact. The contacts were annealed in the RTA at 400°C for 30 seconds at a ramp rate of l°C/sec in a forming gas ambient. The ramp rate was slow so that the oxide layers would not crack, resulting in the upper DBR delaminating from the rest of the device mesa. Following the annealing a photoresist bridge was formed over the isolation trench using AZ4620 photoresist. The bridge allows probing pads to be deposited over the isolation trench to contact the p-contact ring. AZ4620 photoresist is used because it is extremely viscous and can fill in the deep trench. 50pm x 30pm 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. patterns were used to cover the isolation trench and overlap the device mesa. The photoresist was then hard-baked at 300°C in the RTA with a l°C/sec ramp rate in a nitrogen ambient. At this temperature the photoresist reflows and undertakes a rounded profile; there are no sharp edges which might cause fractures in the evaporated contact pad. The probing pad lift-off mask was then patterned using AZ4620 photoresist, the pad metals were evaporated, and the lift-off was done. 4.3.2 Dry etching The device mesas in this work were formed by dry-etching through the AlGaAs DBRs. This isolates one device from another in the array, and exposes the AlAs layer for wet oxidation. The tool that was used to do this was an electron cyclotron resonance (ECR) etching system. A diagram of the apparatus is shown below in figure 4.3. In this system, reactive gasses are injected into a high-vacuum chamber at the top. A microwave source is coupled in through the top as well, and ionizes the gases so that they form a plasma. The upper and lower magnets confine the plasma above the sample chuck. An RF source applies a bias across the sample chuck, which directs the ionized gas down to the sample surface. The microwave impedance is matched via the waveguide stub tuners positioned along the waveguide. The system is configured with a load lock so that pumping times are reduced, and with view ports so that laser reflectometry may be used to monitor the etching in situ. 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Microwave Power Supply Microwave Tuning S tu b s \ Ref Fwd G as Inlet M icrowave W aveguide U pper M agnet HeNe L aser P lasm a Si D etector LR View Port Sam ple C huck Load Lock Lower M agnet Throttle Valve k / y RF Pow er To Turbo Pum p Figure 4.3 A schematic of the PlasmaQuest ECR dry etching system. There are many process variables that can be adjusted so that smooth, vertical sidewalls are obtained at the etched surfaces. These include the microwave power, RF bias, upper and lower magnet currents, process pressure, process gases, and process gas flow rates. The numerous parameters give the operator several degrees of freedom in perfecting an etching recipe. The process chemistry used to etch the devices discussed here was a mixture of boron trichloride (BCI3 ) and argon (Ar). When converted to plasma, the BCI3 breaks down into chlorine and chemically attacks the exposed semiconductor 85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. surface, forming compounds of AICI3 and GaCl3 which then evaporate from the wafer surface [7], The Ar, on the other hand, acts as a milling agent, mechanically sputtering material from the surface of the semiconductor. The flow rate ratio of these two gases can yield either a rounded, undercut sidewall, or a straight sidewall. Another major factor influencing sidewall profile is the bias across the sample chuck. Higher biases will yield a more directional etching, and thus straighter sidewalls. Lower biases tend to give rounded, undercut sidewalls. Decreasing the process pressure will also improve the sidewall profile by decreasing the mean free path of ions in the plasma, thereby increasing the velocity at which they impact the semiconductor surface. In order to prepare a sample for dry etching, first a mask must be deposited and patterned so that the desired features are etched into the wafer. In this work photoresist patterns were transferred to a SiNx mask using C F 4 plasma in an RIF. system. Care must be taken to fully remove photoresist residues from the mask after pattern transferal. Furthermore, the mask will erode during the etching cycle, especially due to Ar milling. Thus, a thick-enough layer of SiNx must be deposited, -2000A in this case, so that the mask survives throughout the entire etch. In figure 4.4 below, a thin (~1000A) SiNx mask in which photoresist residues were not removed resulted in mask erosion and damage to the mesa surface. Photoresist residues left on the mask resulted in a pattern transfer to the mesa surface, leaving the lines as seen in the figure. 86 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4.4 SEM of a VCSEL mesa surface after ECR etching with a 1000A SiNx mask and improper photoresist cleaning. The surface looks black because of it’s roughness due to mask erosion. The straight line features are pattern transfers from photoresist residue. ECR conditions that resulted in smooth, vertical sidewalls were a microwave power of 300W, upper and lower magnet currents of 170 amps and 40 amps, respectively, process pressure of 5mTorr, DC bias of 100V, and BC^/Ar ratio of 25sccm/7sccm. Figure 4.5 below shows a SEM photo of a VCSEL mesa etched with these conditions. Smooth and vertical sidewalls are obtained. The rings at the base of the mesa are DBR layers that were not etched uniformly. The etching depth can be precisely controlled through laser reflectometry (LR). This apparatus consists of a 15mW HeNe laser which shines on the sample through a view port during the etching. The reflection is detected with a Si photodetector and the output current is monitored with a Kiethly picoammeter. The output of the ammeter is connected to a chart plotter, which records oscillations as the etching proceeds through the different DBR layers. One of these recordings is 87 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. displayed in figure 4.6 below. LR allows for precise etching depths to be achieved because each DBR pair is recorded as it is etched through. Figure 4.5 SEM of an etched VCSEL mesa. The contact ring is seen on top of the mesa. Bottom DBR \cli'o Region Top DBR i ! I I RtPi llllllll 1 i Start Figure 4.6 Chart recorder output during ECR etching of a VCSEL structure. Each period in the oscillations corresponds to one DBR pair. 88 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.3.3 Wet oxidation As discussed previously, an AlAs layer is placed at a null in the VCSEL cavity standing wave pattern in close proximity to the quantum well active region. A mesa in the VCSEL epitaxial structure is etched that exposes the edges of the AlAs layer. When this layer is exposed to moisture at high temperatures the AlAs oxidizes, with the oxidation front moving laterally from the edge towards the center of the mesa. Control of the oxidation process is critical for device uniformity, therefore, oxidation chemistry and reaction processes must be well-understood. The oxidation of AlAs binary material was first applied to the fabrication of GaAs MOS capacitors by Tsang [8], Oxidized high aluminum composition AlGaAs was later utilized by Dallesasse, et al. [9, 10], to fabricate oxide-defined, edge-emitting lasers and was first used in VCSELs by Huffaker, et al. [11]. The process essentially involves exposing the high aluminum composition layer to a wet nitrogen steam at high temperatures. A figure of the apparatus used for wet oxidation in this work is shown below. 3-way Valves UHPN. MFC 1 “ quartz tube Dl water bubbler Tube Furnace Figure 4.7 Wet oxidation apparatus. 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ultra-high-purity nitrogen is first bubbled through a round-bottom flask containing DI water held at 8 8 °C. The flow rate of nitrogen is controlled by an MFC at 300sccm. The wet nitrogen then proceeds through heated tubes to the oxidation furnace. The tubing is heated with thermal tape to prevent water condensation in the tubing. The three-way valves are in place so that the nitrogen stream can be switched away from the DI flask while still maintaining nitrogen flow through the oxidation furnace. The oxidation furnace is held at 425°C; this temperature produces oxidation rates of - 0 .7 jim/m in for 300A-thick AlAs layers. The oxidation rate is strongly dependent on nitrogen flow, furnace temperature and water vapor pressure. Therefore, the gas flow is controlled by an MFC, the furnace is stabilized to ±1°C and the bubbler is stabilized to ±0.1 °C to ensure a uniform process. The temperature of the furnace along the length of the tube is calibrated with a thermocouple, thus the exact position at which 425°C is maintained in the furnace is known. The wet oxidation reaction can be broken down into three distinct zones [12]: 1) Transport from the oxidizing gas to the outer surface of the mesa; 2) diffusion across the already-oxidized region; and 3) reaction at the interface between oxidized and unoxidized AlAs to form a new layer of AI2O3. The wet- oxidation reaction proceeds through the use of H+ from the water vapor as the oxidizing agent [13]. This is because the oxygen in the water is already in the -2 oxidation state. H+ oxidizes AlAs to form an AS2O3 intermediate while reducing its 90 Reproduced with permission of the copyright owner. Furiher reproduction prohibited without permission. oxidation number. The zero-valent H can then produce volatile As species by the reduction of the intermediate AS2O3 to As and/or AsH3. Oxide Layer \ ! Region - 1 1 , 1 t 1 ........ .. \ Water Vapor o - ^ ' R eactant Transport Figure 4.8 Schematic of wet oxidation mechanisms. Raman spectroscopy has confirmed the presence of As20 3 and As as intermediates in the wet oxidation process. Their presence can be explained by the following chemical reactions [13]: 2AlAs +6H20 ( g ) - 4 A120 3 + As20 3( 1 )+6H2 AG698 = -473kJ/mol (4.3) As20 3( 1 )+3H2 — > 2As+3HzO( g ) AG69 8 = -131kJ/mol (4.4) As20 3 ( I ) +6H - 4 2As+3H20 ( g ) AG6 9 8 = -1226kJ/mol (4.5) The Gibbs free energies for the above reactions are listed to the right of the equations, and are all energetically favorable. It is possible for elemental As to serve as the volatile species, but the reaction of H with As to produce AsH3 is also favorable (AG6 98=-471kJ/mol). Thus, AsH3 could also serve as a volatile species for removal of As from the oxidized film [13], In the wet oxidation of AlAs the mechanical stability of the film is a primary concern. It is possible, if the wrong conditions are used, for the oxidized 91 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. layer to delaminate from the DBR stack and for the upper DBR to pop off of the device during later contact annealing. One cause of this is the strain field that exists at the oxide terminus due to linear shrinkage (12-13%) of oxidized AlAs compared to un-oxidized AlAs [14]. This effect can be minimized by using thin AlAs layers so that the strain is insufficient to cause delamination. In this work, 300A layers were used. A second approach is to incorporate a small fraction of Ga into the oxidation layer. A linear shrinkage of 6.7% was reported for oxidized Al.98Ga.02As [14]. In the VCSELs made here, AlAs was used for uniformity reasons due to the difficulty in growing Al.98Ga.02As reproducibly. Oxidation studies have also shown that a two-step process in which the sample is held at a lower temperature after the oxidation is complete leads to improved mechanical stability of the film [7]. In this case, the oxidation is done at 420°C, and when finished, the wafer is pulled to a zone in the furnace that is held at 300°C. The wafer is left to anneal at this temperature for 10 minutes. It has been speculated that this annealing step allows for more complete removal of As20 3 from the lattice [7], This is because at the lower temperature, equation 4.3 no longer proceeds, while equations 4.4 and 4.5 continue. Thus, the As20 3 intermediary decomposes to As or AsH3 and is removed from the lattice, without any more As20 3 being produced. Annealing studies also show that for samples taken directly from the oxidation temperature to room temperature there is a great deal of cracking and delamination of the top DBR stack from the wafer. Samples that were oxidized under the two-step process do not show any cracking or 92 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. delamination [7], It is speculated that the delamination is caused by rapid evaporation of residual AS2O3 during high-temperature CVD or contact annealing steps that results in bubble formation in the crystal lattice. The two-step process eliminates the residual AS2O3 and eliminates the problem entirely. 4.4 Device performace 4.4.1 SiNx-isolated devices The first devices made in this study were fabricated as described above, with a dry-etched trench to form the device mesa. SiNx was deposited over the semiconductor areas between devices to electrically isolate the bond pads from the highly-doped GaAs contact layer. The SEM picture shown below depicts a completed device. Figure 4.9 A completed top-emitting VCSEL. The continuous wave (CW) light-current (LI) and current-voltage (IV) characteristics for a device with an aperture width of roughly 1.5pm are shown 93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. below. The threshold current for this device is ~180|iA with a turn-on voltage of ~3V. The turn-on voltage is somewhat higher than the photon energy due to the conduction through the DBR stacks. Even though modulation doping and graded interfaces reduce the heterobarriers significantly, a voltage barrier is still present. The lasing wavelength is very close to target at 850.6nm. The differential efficiency is 33% with a peak wall-plug efficiency of 8 %. The wall-plug efficiency is low due to the large series resistance (~810£2) that results from such a narrow current aperture. At higher pumping currents the LI curve rolls over; this is due to device heating and shifting of the gain spectrum away from the cavity resonance. 5 <D O ) ( B Top-Emitting VCSEL: LI and IV Data .0.5 0.4 0.3 0 > 0.2 0.0 2.5 0.0 2.0 0.5 1.5 844 8 46 848 8 50 852 8 54 856 Lasing S pectrum 0.0 0.5 1.0 1.5 2.0 Current (mA) 2.5 3.0 Figure 4.10 LI and IV data for a 2p.m-aperture top-emitting VCSEL. The inset shows the lasing spectrum . The SiNx-isolated device shown above is not suitable for high frequency operation. The series resistance is much too high, and the use of a thin layer of 94 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SiNx as isolation for the bond pad results in capacitances of ~5pF. This leads to a parasitic RC roll-off at roughly 40MHz. The polyimide and ion implantation processes developed to alleviate this problem will be discussed below. 4.4.2 Polyimide-isolated VCSELs In the polyimide-isolation process, a different etch-mask than that used to make the devices as shown in figure 4.9 was employed. As opposed to etching a trench around the VCSEL mesa, this mask allowed for the removal of all the surrounding semiconductor material so that it could be replaced by polyimide. This type of etching is depicted below in figure 4.11. Once the mesa is etched and the oxidation performed, the polyimide is coated over the surface and patterned to remove it from the top of the device mesa. Acc.V S p o t M agn D et WD I ---------------------------------1 20 pm 1 2 .Q k V 3 0 1500x S E 3 8.3 5244: 26rnin E tch /M esa M ask F igure 4.1 1 SEM o f an etched V C S E L m esa for polyim ide passivation. Hitachi-Dupont PI2611 polyimide was used for the passivation due to its viscosity and low dielectric constant. In order to realize polyimide-isolated devices 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. with a planar topology the process parameters for applying and patterning this type of polyimide had to be developed. This material is applied to a wafer by spin-coating, thus the first step in its use was to determine the speed-thickness relationship. First an adhesion promoter is applied to 1cm x 1cm sample wafers followed by the polyimide, which was spun at increasing rpms for lmin. and then cured. The curing process involves a soft- bake for 90 seconds at 120°C followed by the final curing. The final curing is carried out in an inert ambient environment (N2 in this case) at 350°C for 30min. The temperature must be ramped slowly (~10°C/min) up to the curing temperature to avoid bubble formation in the film. PI2611 Speed-Thickness Calibration ^ 4.6 £ 4.4 ^ 42 < 8 4.0 C 3.8 o “ 3.6 .£ h- £ 34 = 3.2 TJ 3.0 < D 3 2.8 ° 2.6 3.0 3.5 4.0 4.5 5.0 Spin RPM (x1000) Figure 4.12 Polyimide spin speed-thickness calibration data. After curing, the polyimide was coated with SiNx and then patterned with 100|iim wide trenches. The exposed polyimide was then dry-etched via RIE with 96 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. oxygen plasma, and a Dektak profilometer was used to measure the film thickness. The thickness data is plotted above in figure 4.12. The VCSEL mesas are nominally 5jim tall, thus from the curve shown above a spinning speed of 2500 rpm would provide an adequately thick coating. At lower spinning speeds, however, the edge-bead that results from the polymer viscosity is so large that the thickness uniformity across the 1cm x 1cm pieces is mined. A faster spinning speed is desirable to ensure film thickness uniformity, thus two coats at 5500 rpm were used. A 5min. extended soft-bake at 170°C is used after the first coat to ensure that bubble formation does not occur at the interface between the two layers. Due to its viscosity, the PI2611 polyimide does not leave a planar surface after spinning and curing. If this were the case, the polyimide could simply be etched back to expose the top of the VCSEL mesa. Instead the polyimide takes a rounded shape over the mesa because the film is a few microns thick in this area. A process was thus developed to etch back the polyimide from the mesa top and planarize the wafer surface. The process involved coating the wafer with a lower- viscosity material, which, in this case, was Clariant AZ5214 photoresist. This material fills in the low spots while remaining thin in the high spots over the mesa tops. An RIE etching chemistry was developed using a mixture of oxygen and carbon tetraflouride (CF4) so that the etch rates of the photoresist and the polyimide were equivalent. A design of experiments was performed that varied process power, pressure, and ratio of 0 2 and CF4. It was found that the optimum condition 97 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. for achieving similar etch rates between the photoresist and polyimide and for obtaining smooth surfaces was 80%:20% CF4/O2 at 200mT with 175W of RF power. An SEM picture of a completed polyimide sample is shown below in figure 4.13. Figure 4.13 A completed VCSEL with polyimide planarization. The polyimide planarization reduces the bond pad capacitance into the range of 60fF. With the parasitic capacitance reduced to this level, high-speed measurements were possible. The devices were mounted onto SMA connectors using conductive epoxy and a wire bond was connected between the bond pad of the device and the signal line of the connector. A bias-tee was used to mix a DC bias and an RF signal, the later of which was supplied through port 1 of a Hewlett- Packard 8510C vector network analyzer. The modulated light signal from the VCSEL was measured with a NewFocus high-speed photodetector, the output of which was connected to port 2 of the network analyzer. The S2i (forward 98 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. transmission) parameter, which gives the frequency response of the device, was then measured at increasing DC bias points. Frequency responses for a polyimide- isolated device with an aperture width of 6 |im are shown below in figure 4.14. VCSEL Frequency R esponse: Polyimide lsolated--d=6pm 1=1-1.5mA f =1.94-2.94GHz 3 a d (/) -55 0.4 0.8 1.2 1.6 2.0 2.4 2.8 Frequency (GHz) Figure 4.14 Frequency response for a polyimide-isolated device with an aperture width of 6pm and a threshold current of 700pA. The DC bias increases from 1mA to 1.5mA at lOOpA increments. The frequency response curves shown above show clearly the relaxation oscillation peak, which increases with DC bias, as expected. The curves were fit to the following transfer function to extract the relaxation resonance and damping frequencies [15]: 1 1 | W ) | =■ 1 + L f o 1- / \2 L \ f r j + (4.6) 99 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The transfer function shown in equation 4.6 has been modified from the form discussed in chapter 3 by the inclusion of the first term. This has been included to account for a third pole due to a parasitic RC roll-off with a frequency at f0. The rest of the transfer function is the same as that in equation 3.1, where fr is the relaxation oscillation frequency and y is the damping frequency. The curve fits are shown in figure 4.14 on top of the measured data. As was shown in equation 3.4, there is a linear relationship between the damping factor and the relaxation resonance frequency squared. By fitting the measured frequency responses to equation 4.6 and extracting the damping and resonance frequencies, a plot can be constructed of y vs. fr2. A linear fit to this data will yield the K-factor. The K-factor for this device was determined to be 1.0054x1 O '9 Hz'1 . The maximum 3dB bandwidth achievable with this K-factor is roughly 8.837GHz. This would be the maximum intrinsic bandwidth neglecting any parasitic effects at higher frequencies. This number is fairly low, indicating that the device is limited by the parasitic pole. As can be seen in the modulation responses, there is a lower frequency resonance which does not change with bias. Although it was not realized at the time of these measurements, this resonance is due to the bias-tee. The measurements would have been improved had the measurement been calibrated through the bias-tee instead of up to the bias tee. As it is, the parasitic roll-off frequency, f0, extracted from equation 4.6 is roughly 1.8GHz, which contributes to the somewhat low frequency response. 100 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In order to determine what effect the series resistance has on the modulation response of the polyimide-isolated VCSEL, a large aperture device was tested. This device had a roughly 12pm aperture width with a threshold current of 2.5mA. The modulation response curves are shown below along with transfer function fits. VCSEL Frequency R esponse: Polyimide lsolated--w=12pm C O "O cn o d) o * o CM f =975MHz- 3dB 2.845GHz 1=7-11mA 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 Frequency (GHz) Figure 4.15 Modulation responses for a 12pm aperture, polyimide-isolated device. The K-factor extracted from the curve fits to the data above is approximately 1.0095xl0’9 Hz’1 , which gives a maximum intrinsic bandwidth of 8.802GHz. In comparing the cases of the 6 pm and 12pm devices, the resonance peaks for the 6 pm device are lower in magnitude than for the 12pm device, most probably due to the higher series resistance damping the oscillations. As was discussed in chapter 3, however, it is desirable to minimize threshold in order to increase the relaxation oscillation frequency. For the 12p,m case, although the 101 Reproduced with permission of the copyright owner. Furiher reproduction prohibited without permission. series resistance is much lower, the increased threshold current prevents the device from achieving a high fr. For both devices, however it is the parasitic pole caused by the bias-tee that is limiting device bandwidth. 4.4.3 Ion-implanted VCSELs The implant-isolation process is very similar to the standard top-emitter discussed in section 4.4.1 in that the same trench mask pattern is used to define the mesa. After oxidation, however, a thick layer of photoresist is patterned over the device mesa to protect it from the implantation. Following implantation, the photoresist mask is removed, and the contact bridge and bond pad are completed. Below is shown an SEM picture of the device after implantation masking. The mask is approximately 25|itm thick (this thickness was recommended by the implantation company). Figure 4.16 VCSEL wafer after masking for ion implantation. 102 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The bond pad capacitance measured after implantation was roughly 185fF. The series resistance of this device was -300Q, which, with the bond pad capacitance, yields a parasitic pole at 2.868GHz. High frequency measurements were done on a device with an aperture of roughly 6 jlm and a threshold current of 750flA. In this measurement, however, a different bias-tee was used; the results are shown below in figure 4.17. VCSEL F requency R esponse: Im plant lsolated--w=6p.m -60 -65 W = 1-7-5-1 GHz -70- -3dB 3.2mA O -75- _l -80- 1.1mA CM -85 1 2 3 4 5 6 7 8 Frequency (GHz) Figure 4.17 Modulation responses for a 6pm aperture, implant isolated device. From figure 4.17 it is clear that the modulation bandwidth has been increased compared to the results of the polyimide isolated devices. Between the low and high bias points the bandwidth ranges between 1.7 and 5.1GHz. The data fits very well to equation 4.6; the extracted parasitic frequency pole lies at roughly 2.7GHz, which matches closely to the expected value from bond pad capacitance 103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. measurements. Furthermore, the K-factor determined from the linear fit of fr2 vs. y is about 3.535xlO' 10 Hz'1 , leading to a maximum bandwidth of roughly 25GHz. 4.5 VCSEL Summary The growth and fabrication of oxide-apertured, 850nm VCSELs have been discussed. Low-threshold and high efficiency operation was demonstrated for conventional top-emitters with SiNx bond pad isolation, and the limitations of this device topology to high-frequency performance were analyzed. Two methods of improving the frequency performance were discussed, those being polyimide isolation and ion implantation. While the polyimide-isolated device should have had better performance than the implant-isolated devices, a parasitic roll-off due to part of the measurement apparatus, the bias-tee, resulted in low bandwidth. The K- factor extracted from the implant-isolation measurements indicates a maximum intrinsic bandwidth of roughly 25GHz. In the cases of both polyimide-isolation and implant-isolation, low threshold and high-frequency operation are not simultaneously achievable. This is due to the large series resistance incurred by the narrow oxide current aperture. Further reduction in the series resistance by better doping control in the P-DBR through use of carbon doping, or through use of tunneling junctions to inject carriers, would result in some bandwidth improvement. Using a narrower mesa would also improve the spreading resistance. The narrow current constriction, however, presents a fundamental trade-off between low-threshold operation and high-frequency operation. 104 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. References 1. R.P. Schneider, Jr. and Y.H. Houng, “Epitaxy of vertical-cavity lasers," in Vertical-Cavity Surface-Emitting Lasers: Design, Fabrication, Characterization, and Applications, C. Wilmsen, H. Temkin, and L.A. Coldren, eds., Ch. 4, Cambridge University Press, New York (1999). 2. H. M. Manasevit, “Single-crystal gallium arsenide on insulating substrates,” Appl. Phys. Lett., vol. 12, no. 4, pp. 156-159 (1968). 3. R.D. Dupuis and P.D. Dapkus, “Room-temperature operation of Ga(1 .x )Alx As/GaAs double-heterostructure lasers grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett., vol. 31, no. 7, pp. 466-468 (1977). 4. R.D. Dupuis, P.D. Dapkus, N. Holohyak, Jr., E.A. Rezek, and R. Chin, “Room-temperature laser operation of quantum-well Ga(i_ x)Alx As laser diodes grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett., vol. 32, no. 5, pp. 295-297 (1978). 5. R.D. Dupuis, P.D. Dapkus, R.D. Yingling, and L.A. Moudy, “High-efficiency GaAlAs/GaAs heterostructure solar cells grown by metalorganic chemical vapor deposition,” Appl. Phys. Lett., vol. 31, no. 3, pp. 201-203 (1977). 6. J.J. Coleman, “Metalorganic chemical vapor deposition for optoelectronic devices,” Proc IEEE, vol. 85, no. 11, pp. 1715-1729 (1997). 7. A.E. Bond, Ph.D. dissertation (1999). 8. W.T. Tsang, “Self-terminating thermal oxidation of AlAs epilayers grown on GaAs by molecular beam epitaxy,” Appl. Phys. Lett., vol. 33, no. 5, pp. 426-429 (1978). 9. J.M. Dallesasse, N. Holonyak, Jr., A.R. Sugg, T.A. Richard, and N. El-Zein, “Hydrolyzation oxidation of Alx Gaj_xAs-AlAs-GaAs quantum well heterostructures and superlattices,” Appl. Phys. Lett., vol. 57, no. 26, pp. 2844-2846 (1990). 10. J.M. Dallesasse and N. Holonyak, Jr., “Native-oxide stripe-geometry AlxGa|_xAs-GaAs quantum well heterostructure lasers,” Appl. Phys. Lett., vol. 58, no. 4, pp. 394-396 (1991). 11. D.L. Huffaker, D.G. Deppe, K. Kumar, and T.J. Rogers, “Native-oxide defined ring contact for low threshold vertical-cavity lasers,” Appl. Phys. Lett., vol. 65, no. 1, pp. 97-99 (1994). 12. B. Koley, M. Daenais, R. Jin, J. Pham, G. Simonis, G. McLane, and D. Stone, “Kinetcis of growth of AlAs oxide in selectively oxidized vertical cavity surface emitting lasers,” J. Appl. Phys., vol. 82, no. 9, pp. 4586-4589. 13. C.I.H. Ashby, J.P. Sullivan, K.D. Choquette, K.M. Geib, and H.Q. Hou, “W et oxidation of AlGaAs: the role of hydrogen,” J. Appl. Phys., vol. 82, no. 6, pp. 3134-3136 (1997). 14. K.D. Choquette, et al., “Advances in selective wet oxidation of AlGaAs alloys,” IEEE J. Select. Topics Quantum Electron., vol. 3, no. 3, pp. 916-926 (1997). 15. B.J. Thibeault, K. Bertilsson, E.R. Hegblom, E. Strzelecka, P.D. Floyd, R. Naone, and L.A. Coldren, “High-speed characteristics of low-optical loss oxide-apertured vertical- cavity lasers,” IEEE Photon. Technol. Lett., vol. 9, pp. 11-13 (1997). 105 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 5: Band Gap Engineering with Selective Area Growth Photonic integrated circuits (PICs), as opposed to electronic integrated circuits, require that devices of widely different functionality be integrated onto a single chip. This means that regions of optical gain, absorption, and transparency must be incorporated into the circuit. As mentioned previously, the most advantageous techniques for fabricating PICs will incorporate these functions into a single waveguide so that optical interfaces are eliminated. In this case, all of the above functions must be performed with the same epitaxial material. In the design of PICs, a method must be devised for creating transparent and active (i.e. amplifying or absorbing) regions within the same material. When dealing with semiconductor optoelectronics, this means that a way must be found to selectively vary the band gap of the semiconductor across a wafer. Selective area growth (SAG) by MOCVD has proven to be a key technology in this respect, because it is an all-epitaxial technique in which localized band gap control can be achieved in a straightforward manner [1-4]. This chapter will introduce SAG and SAG mechanisms. Details of the development and experimental characterization of the SAG process will be given, along with a discussion of the usefulness of this technique for fabricating monolithic PICs. 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.1 SAG Mechanisms The growth rates of materials grown by MOCVD are determined by the gas phase concentration gradients of the different chemical species. It is this fact that makes SAG possible. By masking certain portions of the growth substrate with a dielectric (typically S i0 2 or SiNx ) on which crystal growth is inhibited, a concentration gradient is established by the buildup of unused material over the mask. The perturbation of the molecular flux due to this gradient is called gas- phase diffusion, and results in growth rate enhancement. In conjunction with the growth rate enhancement is a non-uniform composition change on the group III sub-lattice due to differences in diffusion lengths of the group III precursors (the group V sub-lattice is not significantly affected) [5], Gas-Phase Diffusion (001) Surface, Surface Migration (111)? Facet InP Substrate T / [110] [110] Figure 5.1 Schematic of SAG mechanisms. Thus, for an InGaAsP quantum well active region these effects result in wider wells with an increased indium content, yielding a band gap which is red- 107 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. shifted relative to the plain area (far from the dielectric mask) regions of the wafer. These band gap shifts can be easily controlled by adjusting the dielectric mask widths, the spacing between dielectric masks, or both. A second effect contributing to SAG is surface migration. For selectively grown stripes oriented in the [110] direction on (OOl)-oriented substrates (which applies to the work here) the stripe sidewalls are the (lll)B facets. These facets are known as no-growth facets, and precursors impinging on the dielectric mask and on the (lll)B facets will migrate to the (001) surface. Surface migration contributes to the growth enhancement of the SAG stripe only near the mask edges; for mask widths larger than 5|im, this effect is not significant [6 ], Figure 5.1 above demonstrates the gas-phase diffusion and surface migration effects. Figure 5.2 below shows a cross-sectional SEM picture of selectively grow material. The sharp peaks at the edges of the SAG region are a result of the surface migration effect. Surface migration + G as-phase diffusion G as-phase diffusion Figure 5.2 Cross-sectional SEM picture of SAG material showing the effects of gas-phase diffusion and surface migration. 108 Reproduced with permission of the copyright owner. Furiher reproduction prohibited without permission. 5.2 Broad-area SAG lasers In order to characterize certain aspects of the SAG process such as wavelength shift and strain build-up, and to evaluate various surface treatments and cleaning procedures, edge-emitting lasers (EELs) were fabricated from SAG material and compared. Performance metrics included threshold current density, internal efficiency, internal loss, and peak lasing wavelength. The EELs were fabricated by first defining a 10pm stripe mask using optical lithography in the region between SAG mask patterns. This was followed by an etch in H2S 0 4:H20 2:H20 (1:1:3@RT) for ~6 sec. to remove the InGaAs contact layer and a 30sec. etch in HC1:H20 (3:1) to remove the p-InP cladding layer. The cladding layer etch is terminated by an InGaAsP etch-stop layer located 500A above the first SCH layer. The HC1:H2 0 etch is a faceted etch, picking up the (2 1 1 ) crystal facet, thus there is a slight angle to the mesa sidewall after the etching. Following the wet etching, the photoresist mask was stripped off using acetone followed by a methanol rinse. Oxygen plasma ashing was then done to remove photoresist residues, followed by a lOsec. dip in buffered oxide etchant (BOE) to remove any surface oxides. A 1000A layer of SiNx was then deposited over the wafer to passivate the surfaces exposed by the wet etching. The next step in the EEL process was to define and evaporate the p-contact. A 7pm opening was defined with AZ5214 photoresist and an image reversal 109 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. process over the center of the 10|im mesa. A Ti/Pt/Au contact was then evaporated and the metals were lifted off using acetone. The p-contact on top of the mesa at this point in the process is nominally 7|im wide, which is too difficult to contact with electrical probes. A larger bond pad that is brought away from the device mesa was needed so that the devices could be probed adequately. To do this, a polyimide planarization step was employed using HD Microsystems PI2737 polyimide. This polyimide is a negative-tone, photo-expos able polyimide that planarizes the wafer surface so that a bond pad can be deposited over the device mesa. The SEM photo below shows a completed device with polyimide planarization. P-contact Etched Mesa Md'jn WL) ■ 1 -ih /x 1 n F > Figure 5.3 A SEM image of a completed SAG-BA device. Following the polyimide developing and curing, the bond pad was defined with AZ4620 photoresist and a Ti/Au contact was evaporated. Following the metal lift-off the substrate was lapped using 5|im alumina lapping compound to a 110 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. thickness of ~ 100|im. Following the lapping, a AuSn n-contact was electroplated onto the back of the wafer, and the contacts were annealed in the RTA at 430°C for 30sec. The final step in the process was to cleave the wafer into laser bars of different lengths and measure the bar lengths in an optical microscope. By measuring the LI curves for different EEL cavity lengths and obtaining the differentia] efficiency and threshold current from the LI curves, the internal efficiency and internal losses of the material can be extracted. The differential efficiency, internal efficiency, and internal loss are related by the following expression [7]: 1 1 a.L — =—■ + ......V ■ \ (fU) ^ n , lnp-1 [ r ) Here r|D is the differential efficiency, rji is the internal efficiency, o ci is the internal loss, and R is the mirror reflectivity (-32%). By plotting the inverse differential efficiency versus cavity length and fitting a straight line to the data, the y-intercept yields the inverse internal efficiency, and the slope yields the internal loss. For the various procedures that will be discussed below, the cavity-length-variation experiment was performed to extract the internal efficiency and internal losses of the material and evaluate the material quality. 5.3 Wafer preparation for SAG One of the drawbacks to SAG is that crystal growth must be performed on a wafer whose surface has undergone some processing. The risk of the wafer surface 111 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. being contaminated during the processing must be mitigated by stringent cleaning and surface treatment procedures. A large part of the development of SAG involved determining the appropriate surface cleaning and surface treatment procedures. The first chance for wafer contamination to occur is during the initial SiNx mask patterning before SAG. Photoresist residues can be difficult to remove, and various processes might damage the surface so that subsequent epi-layers have large defect densities. An experiment was performed in which InP wafers were cleaved into five pieces and various surface treatments were performed on each piece. The experimental protocol was as follows: 1) Sample A: reference sample; no treatment. 2) Sample B: sample surface was rinsed with DI water for 2 hours. 3) Sample C: A 1000A SiNx film was deposited, followed by spin-coating AZ5214 photoresist on the wafer. A high-energy UV exposure was performed, and the photoresist was removed with concentrated AZ400K developer. The SiNx was then stripped using 10:1 BOE for 3min. and the wafer surface was cleaned using HaSO^EhC^H^O (1:1:3@65C) for 20sec. followed by DI water rinsing for 2 hours. 4) Sample D: same as sample C, except that a 5min, high-power, RTE O2 plasm a ashing (PR F =100W, 200mT) was done to de-scum the photoresist residues. 112 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5) Sample E: same as sample C, except that the SiNx layer was removed with RIE CF4 plasma (100W, lOOmT) instead of BOE. This experiment simulated the various SAG pre-growth conditions used to pattern a wafer for SAG. In this experiment, however, the wafer surface was not patterned, thus SAG was not actually done. Following the surface treatments, a 1.49pm laser structure with four QWs was grown on each of the samples at the same time, and standard 65|im-wide BA EELs were fabricated for the evaluation. LI curves were measured in pulsed-mode operation with lps current pulses with a duty cycle of 1%. The results of the experiment are shown in figure 5.4 below. The LI curves for each sample are plotted against one another so that the differential efficiency and threshold current can be compared. The cavity lengths for the devices in this experiment are 1.5mm. By looking at the LI data for the different surface treatment samples, some conclusions can be drawn as to the effect of the different treatment parameters on device performance. First, it can be seen from the data that sample C has a much higher threshold current than sample D. This result indicates that residues exist after developing the photoresist and that the oxygen plasma de-scum of photoresist residues is extremely important. Second, sample E did not lase at all, indicating that using CF4 plasma to remove the SiNx somehow damages the surface of the wafer. Epi-layers grown on the CFHreated surface have a large enough defect density with a concomitantly large non-radiative recombination to prevent laser 113 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. operation. Thus, from the above experiment, it was found that BOE must be used to pattern the SiNx for SAG, and that an O2 plasma de-scum is required to produce high-quality SAG material. 60 50 40 E ■ — 1 30 3 — I § 20 Q . 10 0 #2937 - Samples Size L=1500 |im - Sample A - - Sample B - - Sample C - Sample D - - Sample E 0.0 0.2 0.4 0.6 0.8 1.0 Current [A] Figure 5.4 LI curves for BA lasers fabricated from the surface treatment experiment. Optimum results are obtained with sample D. In an effort to further protect the wafer surface from contamination during o SAG pre-growth processing, a lOOOA-thick sacrificial, lattice-matched InGaAs layer was grown on the InP wafer prior to SiNx deposition. Studies of surface recombination velocities have shown that the InP/In.53Ga.47As interface is of excellent quality, and the addition of the InGaAs protective layer should not degrade the InP surface [8], After growing the layer of In.53Ga.47As the SAG mask patterns were defined, and the InGaAs layer was removed with a solution of PESGpEEOaiKbO (1:1:3@RT) for ~6 sec., exposing the fresh InP surface underneath. SAG was then 114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. done following a 2 hour rinse in DI water, and SAG-BA EELs were fabricated once the growth was finished. C D CM E s z “3 900 800 700 600 500 400 300 200 100 InGaAs Protection Comparison Bare InP InGaAs Protective Layer 1 j I 1 10 20 30 40 Mask Width (pm) 50 Figure 5.5 Threshold current density comparison between SAG-BA lasers with and without an InGaAs protection layer. The cavity length for the EELs is 1mm. Figure 5.5 above compares the threshold current densities for EELs fabricated from InGaAs-protected and bare InP wafers at increasing SAG mask widths. From the data a slight improvement in threshold current density can be seen with the InGaAs-protected devices over the bare wafer. After the dielectric mask patterning, the wafer must be cleaned before it is grown on. The processing that is done to pattern the dielectric can leave a poor surface in terms of electronic quality. The electronic quality of the wafer surface must therefore be restored before crystal growth can be performed. It has been shown in GaAs that sulfide-based chemistries can restore surface quality, and that 115 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. with InP regrown in IngaAs, Br-based etching solution can restore surface quality [8], Surface Cleaning Comparison 1000 800 600 < 400 200 10 20 30 40 50 Mask Width (pm) Figure 5.6 Threshold current densities for SAG-BA lasers with various surface preparation chemistries. In order to determine the best surface preparation chemistry, an experiment was performed to compare sulfuric acid/peroxide solutions and HBr solutions. Three different solutions were tried: 1) H^SOpBhC^fbO 3:1:1; 2) H2S0 4 :H2 0 2:H20 5:1:1; and 3) HzSOpHzC^HzO 3:1:1 followed byHBr:H20 1:1. SAG-BA lasers were fabricated from wafers cleaned with the above solutions and the threshold current characteristics were compared, as shown in figure 5.6 above. The wafer cleaned with the sulfuric acid/peroxide solution with the 3:1:1 dilution shows the best performance over the other two, and was therefore the condition used in later SAG. The wafer cleaned with HBr shows much higher thresholds, 116 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and the wafer cleaned with the 5:1:1 dilution of sulfuric acid/peroxide, while showing intermediate thresholds, did not lase above mask widths of 25p.m. The fabrication of SAG devices requires the growth of a p-doped InP cladding layer and a p+ -doped InGaAs contact layer. These layers are grown after the QW and SCH layers. The dielectric mask must be removed before these layers are grown, however, because continued growth enhancement results in a very non- planar surface. Surface planarity is an important issue in device fabrication in terms of coating uniformity of photoresist and polyimide, and efforts must be taken to maintain a planar surface. With SAG, therefore, the growth is done in two steps, with the growth being interrupted so that the SiNx mask patterns can be removed. After the quantum wells are grown an undoped InP capping layer is grown, and crystal growth is terminated. Two issues that needed to be determined were how thick of a capping layer was needed and what mask-removal procedures could be used to obtain good devices. The first issue was explored by growing three samples, one was a laser structure grown in one step with no interruption, the second was an interrupted growth with a 300A InP capping layer, and the third was an interrupted growth with a 1000A InP capping layer. The results below in figure 5.7 show clearly that the 1 0 0 0A capping layer has an equivalent threshold current density to the single- step growth, while the 300A capping layer has a somewhat higher threshold current density. 117 ’ » Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Growth Interruption C om parison 700- 600- ® 500- "£ 400- S 300- X H 200 - 100 - Figure 5.7 Threshold current density comparison for interrupted growth. It is speculated that the thin InP capping layer does not protect the underlying active region from damage induced by the SiNx mask removal process. Furthermore, the thin capping layer may not adequately protect the active region from the thermal stress of heating the wafer to the growth temperature of 650°C. With regards to the second issue of mask removal procedures, it was already mentioned that removing SiNx with CF4 plasma leaves a poor growth surface. Thus, procedures using BOE and HF were investigated to see which one produced better devices. BA lasers were fabricated from two samples, one in which the SiNx was removed with 1:10 BOE, and the other in which the SiNx was removed with 49% HF acid. J_________ 1 _________ I _________1 _________ I _________ 1 _________ L • Interrupted Growth-Thin InP • ■ • Interrupted Growth-Thick InP . ♦ Continuous Growth • ♦ 5 • • 4 QWs ♦ : *'• • . * * + ■ . T----------------• --------------- 1 ----------------'----------------1 ----------------'----------------T 500 1000 1500 2000 Cavity Length (pm) 118 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 250 = 200 | CM E J s. + - » “ 9 150 100 50 ■ m ; • ■ § ■ BOE Etching « HF Etching : | • : % • ■ ■ ............................ • ■ ............................... . 500 1000 1500 2000 2500 Length (|xm) n BOE Etching • HF Etching H i =37.4% a = 10.13cm"1 nj=85.77% 500 1000 1500 2000 Length (m) Figure 5.8 Threshold current density and differential efficiency data for samples in which the SiNx SAG mask was removed with eitherl:10 BOE or 49% HF acid. Threshold current density is plotted in figure 5.8 above along with inverse differential efficiency for the two samples. The internal efficiency and internal losses are calculated from the differential efficiency data. The sample in which the SiNx was removed with BOE shows much better device performance than the sample that used HF, with an increase in internal efficiency of nearly 50%. 5.4 SAG characterization Several aspects of SAG effects on quantum well active regions must be known before monolithically integrated devices can be designed. Four main issues are the amount of growth rate enhancement achieved with a given mask geometry, the amount of wavelength shift for a given mask geometry, how long the band gap transition is between the SAG region and the plain region, and at what point the strain in the crystal increase to the point that it causes defects. 119 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Mask Separation •SA G . ■SiNx Mask Mask Width I i 1 P la in ____________________(J) l Figure 5.9 Schematic of the mask layout for the SAG characterization experiment. In order to characterize these issues, a mask was used to define the SAG regions that contained widths ranging from 10pm to 50pm with a constant separation of 15p.m. The individual SAG masks were on a 250pm pitch. A schematic of the mask geometry is shown above in figure 5.9. Enhancement Ratio for InP and InGaAsP 2.2 O - InP - * - InGaAsP (0 IT 2.0 C 1.8 0) | 1.6 o c « 1.4 .£ £ L U 15pm 1.2 1.0 0 10 20 30 40 50 Mask Width w (pm) Figure 5.10 Enhancement ratios for InP and InGaAsP versus SAG mask width. 120 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The growth rate enhancement was characterized using a SEM and a Dektak stylus profilometer. The enhancement ratios for InP and InGaAsP are plotted above in figure 5.10 versus SAG mask width. The growth rates for InP and InGaAsP materials increase by a factor of two for mask widths of 45pm. A cross- sectional SEM of the quantum well regions in the different SAG regions, all grown at the same time, depicts the growth rate enhancement in figure 5.11 below. Figure 5.11 SEM pictures of the quantum well layers for different SAG mask widths from the plain region (no growth enhancement) to 50ptn. In order for PICs to be designed, the amount of wavelength shift obtained versus SAG mask width must be calibrated. This was done by fabricating SAG- BA lasers from each SAG region and measuring the peak in the lasing spectrum. Figure 5.12 shows the linear shift in peak lasing wavelength as the SAG mask width increases. 121 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Wavelength Vs. SAG Mask Width Threshold Current Vs. SAG Mask Width 1580 ♦ 3000- i i * ^ 2500- d ) 2000- L = 4 9 0 fj.m 4 QW s CM c 0) 1500- % * (5 1480 1460- $ 1440- * 5 10 15 20 25 30 35 40 45 50 55 SAG Mask Width (nm) 04— — i ------ 1 ---------1 -------1 -------- 1 ------ '---------1 --------< r~ 10 20 30 40 50 SAG Mask Width (|xm) Figure 5.12 Wavelength shift and threshold current density for SAG-BA lasers versus SAG mask As mentioned above, with SAG there is an increase in indium composition as the SAG mask width increases, which, along with the increased layer thickness, red-shifts the band gap of the material. The increase in indium also increases the lattice constant of the crystal, which results in a build up of compressive strain in the SAG regions. There is a risk that if the SAG mask is too wide, and the concomitant compressive strain too large, then lattice dislocations will result, causing non-radiative recombination. If this were to happen the radiative efficiency of the material would be ruined. Evidence of SAG-induced strain effects can be seen in the threshold current data in figure 5.12, where threshold current density for the SAG-BA lasers is plotted versus SAG mask width. As can be seen from the data, the threshold current density is relatively constant up to SAG mask widths of 30pm. Beyond this there is a slight increase until 40pm, where there is then a dramatic increase in width. 122 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. threshold current density. It is speculated that the increase in threshold current is being caused by increases in lattice dislocations due to strain build-up. With mask patterns wider than 40pm catastrophic damage occurs. Another important consideration with SAG is the length of the transition in band gap between the SAG region and the plain region. This transition length will ultimately determine the density with which devices can be integrated onto a chip. In order to characterize the transition length, cathodoluminescence (CL) measurements were performed in which scans were taken through the SAG region and plain region along the direction of the SAG mask. 1560 1540 E 1520 £ 1500 U ) j j 1480 § B 1460 £ 1440 1420 -100 -80 -60 -40 -20 0 20 40 60 80 100 Position (pm) Figure 5.13 CL scans through SAG and plain regions for 10pm and 20pm SAG mask widths. The peak CL wavelength as a function of position is plotted above in figure 5.13 for 10pm and 20pm SAG mask patterns. Along the abscissa, 0pm corresponds to the edge of the SiNx mask pattern, with the negative side 123 CL Peak W avelength Vs. Position • 10um Mask Width m 20um Mask Width M M m * m 1 m m m m m m • I s s • £ * 5 • • • 1 . 1 . ................. • * • & * S V < i • at • _i_i_i _i _i_i , Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. corresponding to the SAG region, and the positive side corresponding to the un masked region. From the CL data one can see that the transition length for the 10pm and 20pm mask patterns extends beyond the SAG mask edge by about 35pm and 45pm respectively. There are two conclusions from this data, the first being that, depending on SAG mask width, the scale on which devices can be integrated is a few tens of microns. Secondly, some portion of the transition region will be absorbing to light generated in the SAG region. Thus, when designing a device, the p-contact must extend into the transition region to pump it to transparency. 5.4 Summary of SAG In this chapter gas-phase diffusion and surface migration were presented as the mechanisms responsible for SAG. Furthermore the efforts undertaken in developing the wafer preparation and growth steps for SAG were discussed. The major areas of importance were the removal of SiNx using BOE as opposed to CF4, the use of oxygen plasma to remove photoresist residues, sulfuric acid/peroxide/water cleaning with a 3:1:1 ratio, and the use of BOE as opposed to HF for the SiNx removal in preparation for the second growth. The characterization of SAG on quantum well active regions was also discussed, and the implications for device integration were explored. The wavelength shifts obtained with different SAG mask widths were calibrated, as well as the transition length in band gap from the SAG to the plain regions. 124 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. With regard to photonic integrated circuits, the studies that were performed on SAG have shown that, with the proper wafer preparation, threshold currents of SAG lasers are comparable to single-growth devices. The conclusion is that material quality does not suffer from the pre-growth processing and growth interruption as long as the proper measures are taken. From the threshold current data it was pointed out that strain levels in the material are acceptable up to mask widths of 35|im. The corresponding wavelength shift for mask patterns between 10|Ltm and 35fim is roughly 80nm, which is a suitably wide range for DWDM applications. Thus, the SAG technique produces a wide range in material band gap without sacrificing material quality. The only drawback, with regards to device integration, is that SAG produces rather long transition regions on the order of a few tens of microns in material band gap. References 1. Kostadin Djordjev, Sang-Jun Choi, Won-Jin Choi, Seung-June Choi, In Kim, and P. D. Dapkus,” Two-Segment Spectrally Inhomogeneous Traveling Wave Semiconductor Optical Amplifiers Applied to Spectral Equalization,” IEEE Photonic Technology Letters, Vol. 14, no. 5, pp. 603-605 (2002). 2. Ryan Stevenson, Sang-Jun Choi, Kostadin Djordjev, and P.D. Dapkus, “Semiconductor Optical Amplifier and Electroabsorption Modulator Monolithically Integrated via Selective Area Growth.” OSA Integrated Photonics Research Topical Meeting, Washington, DC. June, 2003, pp. 241-243. 3. Ryan Stevenson, Sang-Jun Choi, Kostadin Djordjev, and P.D. Dapkus, “Semiconductor Optical Amplifier and Electroabsorption Modulator Monolithically Integrated via Selective Area Growth.” TMS 45th Electronic Materials Conference, Salt Lake City, Utah. June, 2003, pp. 79. 4. Sang-Jun Choi, P. Daniel Dapkus, Kostadin Djordjev, Ryan Stevenson, “Experimental Studies and Modeling of Selective Area Growth of InP-Related Alloys by MOCVD.” TMS 45thElectronic Materials Conference, Salt Lake City, Utah. June, 2003, pp. 45. 5. Jonathan E. Greenspan, “Alloy composition dependence in selective area epitaxy on InP substrates,” Journal o f Crystal Growth, Vol. 236, pp. 273-280 (2002). 125 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6. J.E. Greenspan, C. Blaauw, B. Emmerstorfer, R.W. Glew, I. Shih, “Analysis of a Time- dependent Supply Mechanism in Selective Area Growth by MOCVD,” Journal o f Crystal Growth, vol. 248, pp. 405-410, (2003). 7. L.A. Coldren, S.W. Corzine, Diode Lasers and Photonic Integrated Circuits, John Wiley and Sons, New York (1995). 8. E. Yablonovitch, R. Bhat, C.E. Zah, T.J. Gmitter, and M.A. Koza, “Nearly ideal InP/In 5 3 Ga.47As heterojunction regrowth on chemically prepared In.53Ga.47As surfaces,” Appl. Phys. Lett., vol. 60, no. 3, pp. 371-373 (1992). 126 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 6: Monolithic PIC Design with SAG Band gap engineering via SAG allows for the monolithic integration of several types of devices including electroabsorption modulated lasers, two-section equalizers, extended cavity lasers, etc. The device implemented in this work consists of a semiconductor optical amplifier (SOA), electroabsorption modulator (EAM), and an adiabatic mode expander (AME). This device was chosen for its wide commercial applicability as well as for its versatility. It is possible to use this device in an insertion-lossless modulator configuration in which the SOA accounts for fiber-coupling and insertion losses, as well as an EML, or as a monolithic mode-locked laser. The task, with respect to SAG, in designing the SOA/EAM device involves determining the optimum detuning between SOA and EAM band gaps. This in turn determines the SAG mask patterns that will be used to fabricate the device. The design strategy used here is to begin with an optimization of the EAM, which will yield the desired detuning from the SOA band gap. The characterization of SAG given previously can then be used to place the SOA band gap where it is required. 6.1 EAM design The design of an EAM begins with modeling the fundamental physical process behind this type of device; the quantum confined Stark effect (QCSE). Accurate modeling of this phenomenon will yield the voltage-dependent absorption 127 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. coefficient for the device, which will be the basis for the device optimization routine. The QCSE modeling will include a calculation of the electron-hole (e-h) bound states and wavefunctions with applied reverse bias, the exciton binding energy, and the exciton linewidth. Once the QCSE modeling is done, the EAM design can be optimized with regards to waveguide design, absorption peak detuning, device length, and quantum well width, composition, number, and strain. An analysis of the effects of these parameters on key figures of merit will be given along with a routine for optimizing the above parameters. 6.1.1 Modeling the QCSE The quantum confined Stark effect (QCSE) describes the electric-field- dependent absorption in quantum well structures when the electric field is applied perpendicular to the epitaxial layers [1-3]. Due to the effective mass envelope function approximation, the problem of an electron-hole pair state reduces to that of a generalized hydrogen atom. The energy shift of the electron-hole pair with an applied electric field is therefore similar to the Stark shift of a hydrogen atom. The addition of a confining potential (the quantum well potential) leads to the moniker quantum confined Stark effect. The QCSE must be accurately modeled in order to calculate the voltage-dependent absorption of the modulator, which will be used later in optimization calculations. The first step in calculating the QCSE is to find the single-particle bound eigenstates and wave functions in the quantum wells at zero bias and with an 128 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. applied reverse bias. Several approaches have been suggested for this calculation, such as variational methods [4], an effective infinite well method [5], and a tunneling resonance method [2], The approach used here is an effective infinite well method in which the quantum well bound states at zero bias are calculated using a finite difference algorithm. An effective infinite well is then determined from the finite well eigenstates, and the finite difference algorithm is used again to solve for the effective infinite well eigenstates and eigenfunctions with an applied bias. Once this is done, the exciton binding energy must be calculated. Following [1], the exciton binding energy is given by Ee x h = (OI Hc h IO), where is chosen to be the separable w a v e fu n c tio n O ^ z ^ r) = (z( ,) x (z/;) x < p eh(r ). He h is the Hamiltonian of the electron-hole (e-h) pair and consists of two parts: 1) lowest energy electron wave function, h(zh) is the lowest energy hole wave function, and < / > eh{r) is a lS-like, two-dimensional hydrogenic wave function given by < p eh(r) = J — — e x . This wave function is the simplest that can be chosen, and \7 T A is a good approximation for quantum wells that are much thinner (~ 100A) than the three-dimensional exciton diameter (-300A) [2], the kinetic energy term, given b y ——, where mr is the in-plane reduced mass, 2 mr or and 2) the e-h Coulomb potential, given by 2 1 129 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The binding energy is then solved for variationally, with A as the variational parameter, and r as the relative position of the electron and hole. The energy of the lS-like exciton resonance is then given by Ee x = Ee z + Eh z + Eex h , where Ee z and Eh z are the electron and hole lowest eigenenergies. From [6 ], for a pure 2D exciton, A is equal to where ao is the exciton Bohr radius. The binding energy is given by -4Ry, where Ry is the exciton Rydberg energy. Thus, the exciton transition energy is equivalent to the electron-hole transition energy less the exciton binding energy. Once the exciton resonance energy is found, the absorption spectrum must be calculated. Following Ref. 6 , the absorption spectrum is found by summing the discrete and continuum absorption coefficients. The discrete absorption coefficient can be found by first assuming that there is no mixing between subbands. This assumption is valid if the subband energy difference is much greater than the exciton binding energy. With this assumption, each conduction band-valence band (CB-VB) transition (e.g. CB1-HH1) may be treated independently, and the absorption coefficient is given by: L x In this equation, x denotes the exciton quantum number (e.g. IS, 2S, etc.), nm is the CB-VB transition, I e ■ pc v I 2 is the dipole matrix element, and In m is the overlap integral between electron and hole wave functions. 130 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The continuum-state contribution to the absorption spectrum is found by making certain substitutions to the discrete spectrum. The sum over x becomes a sum over a continuum distribution of states kx and ky, the hydrogenic wave function ^ ( 7 = 0) gives a Sommerfeld enhancement factor, and the exciton binding energy is replaced by the in-plane kinetic energy. The continuum absorption coefficient is thus given by: a c(fiQ)) = C „ I I n m I 2 )dE tM (E t) I < // (()) I 2 S(Ex - hco) (6.2) TTri 1 -/ q Where I < ft* m(0) I 2U is the 2-D Sommerfeld enhancement factor l + e ’ r(a,i> p > 2k2 withkan = J E t /R ,E, = -------, and 2 Y = 2 Y Y = . M (Et) is the 2 m r " XX xh J continuum dipole matrix element, and M h is the bulk dipole matrix element. In the above analysis, when calculating the bound states in the conduction band and valence band quantum wells, the hole effective masses perpendicular to the quantum wells must be used. When calculating the reduced electron-hole mass, the in-plane hole effective masses must be used. In order to include band-mixing effects on the hole effective masses in a rigorous manner, the exact bandstructure must be calculated using a multiband model. Band-mixing at the band edge can be taken into account in an approximate way, however, through the following formulas [11]: 131 \ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 1 " h * m ±hh 1 1 ^ ^ (- l)" + 1+cos{rind *)1 "L/, mm nnd sin{nitd ) j ( - l )"+ 1 + cos(n7r6)~\ n7T0 s\n(n7rd) j (6.3) ^ f— l)"+ l +cos ( n . T r f l ) I ■ t r y Where n is the sub-band index and < 9 = (m±hh/m nh) . The above equations apply to an effective infinite well model, however the in-plane effective mass is not sensitive to the quantum well potential [12]. Thus, at the center of the Brillouin zone, equation 6.3 provides an accurate estimate of the hole effective mass with band-mixing effects in a finite quantum well. In the above equations for the discrete and continuous absorption coefficients, broadening mechanisms must be included so that the delta function can be replaced with some type of linewidth. Many different homogenous and inhomogenous broadening mechanisms have been proposed in the literature [2, 7- 9]. Homogenous mechanisms include lifetime broadening due to tunneling through the barriers and longitudinal-optical (LO) phonon interactions. Inhomogenous broadening includes effects from well width fluctuations, interface scattering in the heterostructures, and electric field variations from well to well due to background doping in the intrinsic region. If the barriers are of sufficient thickness to suppress tunneling, then the homogenous broadening can be described by LO phonon interactions only. The phonon broadening is proportional to the density of phonons, which is governed by Bose-Einstein statistics [7]: 132 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Also, if the quantum well region of the device has a sufficiently low background doping (~1016 cm"3, [3]) then electric field variations can be neglected. The inhomogeneous broadening due to well thickness variations and interface scattering can then be described as a Gaussian line shape with the FWHM given by [10]: r ( F ) = Qfd£ « (FW , (6.5) v ' aw where SW is the interface roughness in the growth direction, and a (<1) is a constant related to the interface roughness. The inhomogeneous broadening described here is dependent on the electric field, F. When a field is applied, the electron and hole probability densities concentrate towards opposite edges of the quantum wells; therefore, the heterostructure interfaces play a role in scattering the electron and hole. The LO phonon interaction, on the other hand, is field independent, because the LO phonon energy is much greater than the binding energy of the exciton. Any collision of an exciton with an LO phonon will therefore ionize the exciton, regardless of the electric field [7], The complete line width at room temperature is described by both LO phonons and inhomogeneity broadening, and is better described by a Gaussian 133 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. rather than a Lorentzian line shape [2]. For quaternary quantum wells such as InGaAsP quantum wells, however, alloy and interface scattering dominate the line broadening [ 11, 13]. V £ 18000 16000 c 14000 0) o 12000 E 0 ) o o 10000 8000 c o 6000 '• H Q. i_ 4000 O ( / > n 2000 < 0 Absorption Spectrum vs. Electric Field _j i i i i i i_ o 0 kV/cm □ 50 kV/cm a 100 kV/cm O 150 kV/cm 1.30 1.35 1.40 1.45 1.50 1.55 1.60 Wavelength (pm) Figure 6.1 The calculated absorption spectrum for an InGaAsP quantum well. The spectrum includes transitions from the heavy hole and light hole valence bands. The calculated absorption spectrum is shown in figure 6 .1 above for an 85A InGaAsP quantum well. The spectrum is characterized by sharp absorption peaks at the exciton transition energies (CB1-HH1 and CB1-LH1). As an electric field is applied the absorption edge shifts to longer wavelengths due to the shift in electron and hole bound state energy levels. The absorption peak also decreases in value because the electrons and holes are separated to opposite sides of the quantum well. This decreases their spatial overlap, which in turns yields a weaker oscillator strength. The oscillator strength 134 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. depends on the square of the overlap integral between electron and hole wavefunctions. This squared overlap integral versus electric field is plotted below in figure 6.2 for both CB1-HH1 and CB1-LH1 transitions. Electron-Hole Overlap Vs. Electric Field 1.0 - O CB1-HH1 □ CB1-LH1 0.9- 0.8 - . . 0.7- A 0 .6 - O ^ °'5i w 0.4- O J 0.3- 0 .2 - 0.1 0 20 40 60 80 100 120 140 Electric Field (kV/cm) Figure 6.2 The square of the electron-hole overlap integral for the CB-HH1 and CB-LH1 transitions. Note that the two do not have the same dependence on electric field. 6.1.2 EAM Optimization Once the exciton absorption spectrum has been accurately modeled, and the voltage-dependent absorption is known, calculations can be done to optimize the performance of the EAM. An EAM device consists of numerous variable parameters and many competing effects and trade-offs. For example, a large absorption coefficient can be had by increasing the number of quantum wells. More quantum wells will increase the active region thickness, however, and a larger drive voltage will be needed to shift the exciton spectrum. Alternatively, absorption can be increased by increasing the device length. Unfortunately 135 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. capacitance will also increase, and the device’s bandwidth will be reduced. It can be seen, therefore, that careful definition of figures of merit and optimization routines must be done to ensure that the device is fully optimized. The most important figures of merit are contrast ratio (CR), insertion loss a ( v ) - a ( 0 ) (IL), the power-bandwidth ratio P / Af , the ratio m = —-— , , , which is the or(0 ) ratio of absorption change to on-state absorption, and AT, which takes into account the trade-off between the transmittance in the on-state, and the CR [14]. It is useful to define AT and CR in terms of m and X = e{ ~a,m rL ), where T is the confinement factor of the waveguide, 0Con=0c(VO n), and L is the device length. Then CR, AT, and Pa c / A/ are given by [14]: CR = X~m (6 .6 ) AT = X ( \ - X m) (6.7) IL(dB) = -4.343 ln( A) (6 .8) Pac/A f = CAV2 =[ln(CR)£x] v r , f A a A VAF 1 j (6.9) Where C is the device capacitance, es is the dielectric constant, w is the device width, dj is the intrinsic region thickness, and AF = AV / di (assuming a uniform 136 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. field across the quantum wells). The parameter - ^ L is a waveguide parameter, and is a material parameter. .AF2 j The above figures of merit are interdependent and mutually constraining. It is not possible to optimize them simultaneously; therefore the general optimization routine consists of minimizing the power/bandwidth ratio while satisfying a given CR and IL. The integrated SO A, however, makes it possible to operate with zero insertion loss while using a smaller detuning of the signal wavelength from the exciton absorption peak. Inclusion of gain from the SOA section in the optimization routine will give more flexibility in the device design. The optimization challenge comes in relating the figures of merit described above to the material parameters. The advantage of the InGaAsP material system is that the quantum well width and material composition can be controlled Act independently. This allows ------- to be optimized at a given wavelength (i.e. V AF ) 1.55|J,m). Boundaries on the above design parameters can be determined by first considering constraints imposed by the required CR and IL. By plotting contour curves of CR and AT versus m and IL, the best operating point, given the specified CR and IL, is the intersection of the CR and AT curves. This plot is shown in figure 6.3 below. From the plot, a CR of 20dB with an insertion loss of 2dB constrains the design to quantum well structures that yield a relative change in 137 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. absorption, m, of greater than about 7, with a corresponding change in transmission of at least 0.6. As can be seen from the graph, acceptable designs are bounded on the left by the curves of constant CR. Contrast Ratio and Change in Transmission 30 cb Q - O 25 o 20 „8 a f l £ ,,x \ CR; Insertion Loss (dB) Figure 6.3 A contour plot of contrast ratio and transmission change versus insertion loss and the m parameter. Further boundaries on the design are found be examining equation 6.9. The power-bandwidth ratio is directly proportional to and inversely proportional to vAF 2 y . The first term is related to device geometry, while the second is dependent on quantum well structure. From the first term, the width is set by the requirements of having a single mode waveguide at roughly 2pm. Thus, the waveguide confinement factor should be maximized for a given device thickness. The maximum modulation speed will be determined by the device thickness and 138 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. device length. The junction capacitance in parallel with the source resistance (assumed to be 50Q) will create a low-pass filter which will limit device frequency performance (in a lumped-element configuration). The device bandwidth versus active region thickness is plotted below in figure 6.4 assuming a typical length of 150pm and a width of 2pm. It is also assumed that the electric field is completely uniform across the active region so that V = FcL . Intrinsic Layer Optimization E 550-] 500- 450- i . i , i 5V\ ____1 ______ i _ ...1 ______ ______ 1, o 400- 4V\ \ > 350- ■ D 300- 3V\ \ \ < D i l 250- - o 200- 2V\ ■ 5 150- - 0) 1 1 1 100- 50- 0- --------- 1 ----------1 ----------1 ---------- 1 ---------- 1 ---------- 1 — 1 1 1 • "1.......... 60 N o 50 <j M f T J 30 (0 m c 20 .2 1 5 10 -a o 0.1 0.2 0.3 0.4 0.5 0.6 Intrinsic Layer Thickness (pm) Figure 6.4 Optimization of intrinsic layer thickness with respect to modulation bandwidth and electric field across the intrinsic layer. The electric field is plotted for drive voltages of 2-5V. In the above figure it can be seen that to achieve a bandwidth of 40GHz (ignoring any parasitic capacitances) the active region should be thicker than about 0.45pm. At 2.5V the corresponding electric field is 55kV/cm. This value of electric field is somewhat low to achieve the necessary change in absorption. Realistically, an electric field on the order of lOOkV/cm is a reasonable value. This would require a drive voltage of between 4-5V for a length of 150pm. 139 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The above analysis determines the allowable intrinsic region thickness, but several other factors must be considered when designing the actual quantum well structures; specifically the thickness, strain, and composition for the quantum wells and barriers. These parameters affect not only the absorption spectrum but also the high-frequency performance and modulation efficiency as well. Starting with the barrier layers, it is advantageous to make them tensile strained to reduce the energy band offset. If parasitic capacitances are negligible then the speed of the modulator will depend on how quickly electrons and holes can escape from the active region of the device and get collected at the p and n- contacts. If there is a large energy discontinuity at the QW/barrier interface, then the escape of carriers out of the well can be impeded. This is more of a concern for the heavy holes, since they have a larger effective mass. Under high optical intensities, holes can “pile up” at the QW/barrier interface. The pile-up of holes at the interface will create a buildup of space charge and an electric field that will cancel out the applied electric field. This will allow more holes to pile up, saturating the absorption and decreasing the modulation response [15]. To mitigate carrier pile-up, the barriers should be tensile-strained. Tensile strain will decrease the band offset and increase the escape rate of holes from the QWs by increasing the thermal emission rate [16]. Tensile strain in the barrier is also needed to offset the compressive strain of the QW, thereby leaving a strain- compensated structure. Thinner barriers will also increase the hole escape rate via 140 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. tunneling. A faster hole escape rate will lead to an overall increase in the saturation intensity. The hole escape rate can be written as the sum of escape rates due to tunneling and thermionic emission as [15]: - = — + — (6.9) T t T E t T Here T te is the thermionic emission rate and uT is the tunneling escape rate. The escape rates due to tunneling and thermionic emission are given by [15]: 1 _ ruth - ( 2 L j 2 m hSE/f,) t t 2 Lw mw ' , r r \ ‘/ 2 f S E k„T k n T ’ (6.11) In the above equations, Lw is the well width, Lb is the barrier width, mw is the well in-plane effective mass, mb is the barrier effective mass, and 5E is the barrier height presented to the carriers. The escape time for heavy holes was calculated using the above equations as the barrier As composition and barrier thickness were varied. The strain was kept at -0.7% tensile so that the Ga composition was constrained. This strain is compatible with SAG (as discussed below). From figure 6.5 below it can be seen that the hole escape time will continue to decrease as both the barrier thickness and the As composition decrease. A combination of the two must be chosen, however, that does not minimize the conduction band offset too much, or the gain characteristics of the SOA will suffer. For this reason, a barrier thickness of 60A 141 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. and an As composition of 0.6 were chosen. This combination minimizes the hole escape time while maintaining a conduction band offset which is a few times room temperature energy. The corresponding band gap wavelength for the barrier composition and strain is 1,2 2 pm. 0.65 0) 100 o . < B O 1 0 50 LU .S i SO As Corr>Positj0n Figure 6.5 Heavy hole escape time as a function of arsenic composition and barrier thickness. Now that the barrier parameters have been chosen, the quantum well parameters can be optimized. The strategy is to vary the width and composition of the quantum well and calculate both Aot/a0 and Aoc/F2. The combination of well width and composition that maximizes Aa/F2 while satisfying the needed AaJa0 (from fig. 6.3) is the optimum design. As with the barrier, the first step in the QW optimization is to choose a reasonable value of compressive strain that is compatible with SAG. A good 142 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. number based on the literature and SAG effects is 0.8% compressive strain. The chosen strain now determines the gallium mole fraction as the arsenic mole fraction is varied. Next, the absorption spectrum at each arsenic mole fraction and well width point is calculated for applied electric fields ranging from OkV/cm to 150kV/cm. The maximum Aoc/F and the corresponding m=Aoc/a0 are then plotted versus arsenic mole fraction and well width. These plots are shown in figures 6 .6 and 6.7 below. From the figures the optimized quantum well structure is one that has a width of 85A with an arsenic composition of y=0.73. These parameters, combined with the barrier parameters given above, yield a transition wavelength of 1.49pm. This result indicates that the optimum detuning of the EAM absorption peak from the signal wavelength of 1.55|im is 60nm. Thus, SAG patterns must be chosen which can shift the wavelength from the plain region by 60nm. As discussed previously, SAG active regions become increasingly compressively strained due to increased thickness and increased indium. Thus, when designing the layer strain of the plain region, it is beneficial to have it tensile- strained overall. This will decrease the chance of creating misfit dislocations in the SAG region. Furthermore the quantum wells in EAM’s are typically compressively strained to improve speed and absorption. Consequently, the barriers should be tensile-strained to offset the strained quantum wells. 143 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 6.7 A plot of the parameter m =A a/a0 versus quantum well width and arsenic composition. 144 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A general rule of thumb for the stability of strained superlattices is [17]: X s> d‘ <10 (6.10) Where s; is the strain of the layer and dj is the thickness of the layer in angstroms. When this condition is met the overall strain of the superlattice is considered low enough so that defects are not created due to strain relaxation. When choosing the strain of the barriers and wells, equation 6.10 must be kept in mind. Furthermore, the increase in compressive strain with SAG must be considered. The challenge is in designing an active region that is stable in both the plain and SAG regions. With the mask patterns employed to obtain a 60nm shift between plain region and 15pm SAG regions, the growth rate enhancement is about R=1.33 with a strain enhancement of AS=+0.4%. The strain enhancement represents a worst-case estimate of the strain increase with 15pm SAG mask patterns. The following table outlines the proposed structure and the related strain issues. The structure contains a second SCH layer, which facilitate carrier sweep- out from the active region and increases the thickness to satisfy the capacitance requirements. In the plain region the total strain for an 8 QW active region is -9.92 which satisfies equation 6.10. The total expected strain in the 15pm SAG region is +5.159, which also satisfies equation 6.10. Therefor the active region should be stable in the plain region, and for the 15pm SAG region. 145 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table 6.1 Integrated SOA/EAM Strain-stablilized Epi-structure Parameter Plain region SAG region (expected) 8 x QW Sw +0.8 % + 1.2 % Lw 85 A 112 A 1.49 pm 1.55 pm 7 x Barriers sb -0.7 % -0.3 % Lb 60 A 83 A A b 1.22 pm 1.27 pm 2 x SCH1 SsCHI -0.5 % -0.1 % Lschi 660 A 875 A ^SCHl 1.22 pm 1.27 pm 2 x SCH2 SsCH 2 -0.3 % +0 .1% LsCH2 530 A 700 A ^SCH2 1.1 pm 1.16 pm Total ^tot -9.920 +5.159 di 0.3480 pm 0.4627 pm 6.2 SOA Design 6.2.1 SAG Mask Pattern Design While the active region of the SOA is determined in part by the EAM active region, it is still necessary to choose the proper SAG mask patterns that will place the peak in the SOA gain spectrum in coincidence with the signal wavelength (1.55pm). It has been observed that the SAG region wavelength shifts about 15nm for an increase in SAG mask pattern width of 5 microns. The shift from the plain region to the SAG region is determined, however, by the total surface area of the wafer that is covered by SiNx. This shift must be determined experimentally and will vary with changing mask patterns. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. For the mask set used for device fabrication, the lasing spectrum of lasers fabricated from the plain, 10pm, and 15pm SAG regions show that the wavelength from the plain up to the 10pm SAG region experiences a shift of 60nm, and an additional 15nm from the 10pm to 15pm SAG regions. Thus, with the plain region wavelength targeted at 1490nm, the 10pm SAG region lases at 1550nm, and the 15pm SAG region at 1565nm. The figure below shows the lasing spectra of lasers from each of these regions. SAG mask patterns of 10pm will thus yield the desired SOA gain peak. SOA Lasing Wavelength Plain Region -60- -70- -80- -90- ™ - 100 - O -1 1 0 - -120---- 1.45 1.50 1.55 1.60 1.65 Wavelength (pm) Figure 6.8 Lasing spectra from the plain, 10pm and 15pm SAG mask patterns. 6.2.2 Quantum Well Number Another aspect concerning the SOA section is the number of quantum wells to be used in the active region. From the perspective of the EAM it is desirable to have many quantum wells to increase the optical confinement factor. When 147 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. considering the SOA, however, more quantum wells means more free carriers being injected into the active region with a concomitant increase in loss due to free carrier absorption. Furthermore, the outer lying quantum wells that capture the most carriers also have a lower overlap with the optical mode, thereby lowering the gain. 6 QW Active Region 8 QW Active Region 9- s 0 ) 0.4 0.5 0.6 0.7 0.8 0.9 1.0 18- n.=33.2% a=48.5 cm' 16- 14- 1 2 - 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Length (mm) Length (mm) Figure 6.9 Comparison of losses and internal efficiency for 6 and 8 quantum well active regions. In order to determine the optimum number of quantum wells, active regions with six and eight quantum wells were grown, and BA lasers were fabricated. A cavity length variation experiment was performed to determine the losses and efficiency of the BA lasers. The results of this experiment are shown in figure 6.9 above. As can be seen from the graphs, the losses of the six quantum well active region were reduced by roughly 2 0 cm' 1 while the internal efficiency was improved by almost 10%. Thus, six quantum well active regions were chosen over eight quantum well active regions. 148 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 .2 .3 S O A L e n g t h In order to reduce the current density necessary to achieve the required gain from the SOA, the SOA length must be optimized. In order to perform the optimization, the material gain parameter, g0, and the transparency current density must be determined. This will allow for the use of the logarithmic gain model as described by [18]: In equation 6.11, J is the injected current density, JT r is the transparency current density, and T is modal overlap factor (-12% for this waveguide design). Both r g 0 and J tr can be determined by performing a SAG-BA cavity length variation experiment. The details of such an experiment were described previously in chapter five. Figure 6.10 Internal efficiency, internal loss, and gain fit results from the SAG-BA cavity length J \ rg = rg„in (6.11) 10(im SAG: Efficiency and Losses 10(±m SAG: Threshold Gain Fit a=8.62cm" 2.0 - 1.5- 4.5- 4.0- ri,=55.6% 1.0 40- 38- 36- 34- 32- 30- 28- 26- 24- 22 - 2 0 - 18- 400 600 800 1000 1200 1400 1600 380 400 420 440 460 480 500 520 540 560 Cavity Length (gm) J T H (A/cm2 ) experiment. 149 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 6.10 above shows the results of the inverse differential efficiency versus cavity length, and the threshold modal gain versus threshold current density for 10pm SAG-BA lasers. A linear fit of the inverse differential efficiency data yields the internal efficiency and internal losses. The internal loss number can then be used to compute the threshold modal gain at each laser cavity length by [18]: ^ S r n ~~ ^7 (6-12) In equation 6.12 a m is the mirror loss and is given by a m = (l/L )ln (l/R ) where R is the mirror power reflectivity. The threshold modal gain is then plotted against the threshold current density at each cavity length and fit to equation 6.11. This fit yields the transparency current density and the modal gain parameter. These two terms can then be used again with equation 6.11 to calculate the gain at various pumping current densities. One caveat to the above experiment is that the width of the BA lasers is only 10pm so that the laser stripe fits within the SAG mask pattern. Current spreading is therefore expected to lead to an underestimation of the actual threshold current density. The fitting parameters, Jtr and Tg0, are thus considered good estimations, but not perfectly accurate. The total gain in light intensity can be modeled by the simple exponential increase with length as I = I( ) ergL. In figure 6.11 below, the power gain and current density contour lines are plotted as a function of pumping current and SOA length. 150 Reproduced with permission of the copyright owner. Furiher reproduction prohibited without permission. Following the 20dB contour line, a minimum in pumping current occurs around an amplifier length of about 750|im. This is the optimum length for the SOA. Figure 6.11 Gain and current density variation with pumping current and amplifier length. 6.3 SOA/EAM Fabrication 6.3.1 Process Flow The analysis given above has determined the material structure for the active region of the device. In order to ensure optimized device performance, however, some consideration must also be given to the device topology. Poor device geometry can lead to unnecessarily high parasitics as well as low optical confinement. This section will briefly discuss certain aspects of the device SOA Length D esign C urrent Density 5000A/cmA 2, 4000A/cmA 2 3000A/cmA 2 2000A/cmA 2 20dB- 200 400 600 800 1000 1200 1400 Device Length (^m) 151 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. topology design and device fabrication. The detailed process flow is given in Appendix B. Figure 6.12 below shows the proposed device layout. The SOA is formed from the SAG region, and the EAM is formed from the plain region. A ridge waveguide is etched in between the SAG mask patterns, and runs through the SAG and plain regions. Electrical isolation between the two sections is achieved via an isolation trench etched into the waveguide. A p-contact runs along the top of the ridge. SiNx Mask SOA Isolation Trench EAM P-contact and Mesa Figure 6.12 A schematic of the device layout. The first step of the device process is the patterning of a 5pm stripe that runs through the SAG and plain regions. A sulphuric acid/hydrogen peroxide etch is used to etch through the top InGaAs contact layer, followed by an etch with H^POa/HBr to remove the top InP cladding layer. The viscosity of this etch is such that the reaction is diffusion-limited, producing an undercut profile along the [1 1 1] 152 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. crystal plane. This undercut is utilized to maintain a wide surface of 5|nm at the top of the mesa, while narrowing to about 2|im at the base. This is done so that a low contact resistance can be achieved at the p-contact on the one hand, but a narrower area is pumped at the active region on the other. The narrow waveguide at the base of the cladding is also needed to maintain a single-mode waveguide. Figure 6.13 below is a SEM photo of a cross section of the device after the cladding etch. A cc.V S p o t M agn W D 1 ------------------- 1 5 pm 1 6 .0 kV 2.1 5 0 0 0 x 1 4.8 # 1 5 3 3 : 10um S A G -M e s a T a p e r Figure 6.13 SEM photo of the etched mesa, looking at the junction between SAG and plain regions. After the mesa is etched, a Ti/Pt/Au p-contact is evaporated onto the top of the mesa, followed by planarizing the wafer surface with polyimide. The polyimide is used so that larger bond pads can be evaporated over the device mesa, as well as to serve as an insulating dielectric to eliminate parasitic bond pad capacitance. Once the polyimide planarization is complete the isolation trench is etched. This is done after the polyimide step so that the polyimide can protect the sidewall 153 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of the mesa. The isolation trench is fabricated by using the same sulphuric acid/hydrogen peroxide mixture to remove the InGaAs layer, followed by a HC1:H20 1:1 mixture to etch only a few thousand angstroms into the p-cladding. If the trench is etched too deep, scattering from the optical field may be introduced at the air/cladding interface. Care must therefore be taken to keep the etch shallow. Figure 6.14 A SEM cross section of the completed device. Following the isolation trench, the Ti/Au bond pads are evaporated. An additional electroplating step is performed here to increase the thickness of the bond pads for wire bonding. After the electroplating the wafer is lapped to ~ 100pm and a AuGe/Ni/Au n-contact is evaporated. The wafer is then annealed, cleaved into bars, and tested. Figure 6.14 above shows a cross section of the completed device. The polyimide dielectric surrounds the undercut mesa, with the p-contact visible on the mesa top. 154 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 .3 .2 E l e c t r o p l a t i n g In order to effectively wire bond to the bond pads, the thickness of the pads must be greater than 5000A. It is not feasible to evaporate this thick of a pad, therefore an electroplating process was developed to up-plate the pads with thick (~l|im ) gold. Figure 6.15 below is a schematic of the process. First, a seed layer consisting of Ti/Au (500A/1000A ) is evaporated after the bond pad lithography. It is important to use a thick photoresist for the lithography so that the sidewalls are sloped outward. This allows for a continuous connection of the seed layer over the entire wafer surface. Following the seed layer evaporation, a second lithography is done with a mask slightly smaller than the bond pad mask. This exposes an area only over the bond pads. A coating of photoresist is also applied to the back side of the wafer to isolate it from the electroplating solution. Once these processing steps are complete, the wafer is placed in a pure gold, potassium-cyanide-based electroplating solution (Technic, Inc.) at 65°C for about 5 minutes with a current density of 3A/ft2. Once the electroplating is complete, the wafer is placed in acetone to lift off the photoresist and extraneous metal. Figure 6.16 below is a SEM photo of an electroplated bond pad. With an up-plated thickness of roughly 2 pm, wire bonds to the pads would routinely satisfy pull tests up to 10 grams, with most of the failures occurring at the substrate bond, not at the bond pad. 155 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Electroplated G o ld •<— Photoresist < — Photoresist Figure 6.15 A schematic drawing of the electroplating process. ; -V ' ■ ■ H U ■ ■ M M Figure 6.16 An electroplated bond pad. 6.4 SOA/EAM Performance Results Several measurements were performed to characterize the performance of both the SOA and EAM. Since the device was designed to function in an external cavity, mode-locked laser configuration, the devices were first tested as lasers with 156 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. cleaved facets as mirrors. Following these measurements the device facets were AR-coated and the devices were tested as single-pass devices. 6.4.1 Laser Performance The device measurements conducted in the laser configuration consisted of measuring the SOA-to-EAM resistance, LI characteristics at varying EAM bias points, and optical spectrum measurements of the lasing spectrum at varying EAM bias points. Section-to-Section Resistance 0.3 0 . 2 - < £ 0.1 - 0.0 - -0.2 - -0.3 ■ 2 0 1 1 2 Voltage (V) Figure 6.17 Section-to-Section IV measurement. The resistance is 9kQ. Figure 6.17 above shows the results of a current-voltage measurement between the two sections of the device. The slope of the line yields the section-to- section resistance, which in this case is roughly 9kL>. Typical numbers for this 157 Reproduced with permission of the copyright owner. Furiher reproduction prohibited without permission. measurement fall in the range of 9-13kQ. This result shows that there is sufficient isolation between the SOA and EAM sections of the device. Following the isolation measurement the LI characteristics of the device were measured. This involved sweeping the forward pumping current of the SOA section at various reverse bias points on the EAM. The results of this measurement on a lOpm SAG device are show below in figure 6.18. The inset of the figure shows a calculation of the increase in internal loss, Aa, based on the increase in threshold current, at each EAM bias point. The internal loss increases exponentially, as predicted by the QCSE calculations. 10|im SAG: LI vs EAM Bias 0) s o CL EAM V oltage (V) ov ___ 2V 3V ------- 4V 5V (0 G a O o 20 40 60 80 100 C u rre n t (mA) Figure 6.18 The power-current characteristics of a 1 Oum SAG SOA/EAM device at increasing reverse bias on the EAM. The inset shows a calculation of the change in loss with increasing EAM reverse bias. The last characteristic measured in the laser configuration was a lasing spectrum measurement at increasing EAM reverse bias. The output light of the device was coupled into a multi-mode fiber, which was then connected to an 158 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. HP70951A optical spectrum analyzer. The peak in the lasing spectrum was then measured for each EAM bias point. Figure 6.19 below shows the measurement results for a 10pm SAG device. The total attenuation at 5V of reverse bias on the EAM is about -15dB. 10-^im SAG: Lasing Attenuation Vs. EAM Bias _ov - 3V - 5V -60- -80- - 1 1 0 - 1.50 1.55 1.60 W avelength (|xm) Figure 6.19 The Lasing spectrum of a 10|im SAG device at increasing EAM reverse bias. 6.4.2 Single-Pass Performance After characterizing the devices as lasers, the device facets were AR coated with a commercial multilayer dielectric film (Opticorp, Inc.). The reflectivity of the facets after coating was around 1 O ' . Once the device facets were coated, the device bars were mounted onto copper blades with conductive epoxy and positioned in a waveguide measurement setup. 159 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Fiber Holders With A R I o n c o r i P i h o r c XYZ Translation Stage □ □ □ □ □ □ □ □ Optical Spectrum Analyzer X Y 0 Translation Stage I/O Via GPIB Polarization Controller Tunable Laser Figure 6.20 A schematic of the waveguide measurement setup. The waveguide measurement setup is depicted in figure 6.20 above. It consists of a center translation stage with tilt control where the mounted device is fixed, two translation stages that hold the input and output optical fibers, a tunable laser and a polarization controller at the input, and an optical spectrum analyzer (OSA) at the output. Both the tunable laser and OSA are controlled with Labview software via GPIB. To conduct a measurement, the mounted devices were first fixed to the center translation stage. AR-coated, lensed fibers were then positioned, using the outer translation stages and fiber holders, to the input and output facets of the device. The output fiber was first aligned by biasing the SOA section of the device and maximizing the power through the fiber as measured on a power meter. The 160 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. input fiber was then aligned by tuning the tunable laser to the peak in the SOA gain spectrum and maximizing the photo-generated current in the SOA while it was unbiased. At the same time, the polarization controller was adjusted so that the input light was in the TE mode. Once the input and output fibers were aligned the chip gain, fiber-to-fiber gain, EAM absorption spectrum, and EAM attenuation were measured. For the gain measurements, the transparency current of the SOA had to be determined first. A method which relied upon producing a transient voltage across the p-i-n junction of the SOA was used to do this. The method consists of chopping the signal from the tunable laser before coupling it into the SOA. When the SOA is unbiased, it acts like a detector, and carriers are generated as photons are absorbed. A negative voltage appears across the junction in phase with the unchopped portion of the input signal. When the SOA is biased above transparency, carriers undergo recombination due to stimulated emission, and are thus depleted. The depletion of carriers produces a positive voltage across the junction of the SOA. Thus, the junction voltage signal shifts in phase by 180 degrees between the below- transparency and above-transparency conditions. The bias point at which this occurs is the transparency current of the material. This point can be found by monitoring the junction voltage signal with a lock-in amplifier as the bias on the SOA is increased. For the 10pm SAG devices fabricated in this work, the transparency current was around 10- 12mA. 161 Reproduced with permission of the copyright owner. Fudher reproduction prohibited without permission. After determining the SOA transparency bias point, the chip gain and fiber- to-fiber gain were measured. The chip gain measurement involved injecting a signal from the tunable laser and biasing the SOA to transparency. The signal is then measured at the output of the device using an optical spectrum analyzer. The relative increase in signal amplitude as the SOA is biased is the chip gain. The data from the chip gain measurement on a 10|im SAG device is shown below in figure 6.21 for a signal power of -12.5dBm. At an SOA bias of 90mA the chip gain is roughly 20dB. 10pm SAG: SOA Spectrum Vs. DC Bias 10pm SAG: Fiber to Fiber Gain m < l ) ~ o □ 'E o > n O ) o -55 -60 -65 -70 -75 -80 -85 -90 -95 -100 -105 -110 -115 -120 1 t / ...................... --------0m A ......... 12m A -------90m A • < i L y * ,48 1.50 1.52 1.54 1.56 1.58 1.60 C Q T J 15 10 5 0- C -5 o -10 o -15- V -20 Q -25 -30 s J.. ■ B * ■ r SI / / m ........ P =-12.5dBm O I s a / K Wavelength (pm) 20 40 60 80 Current (mA) 100 Figure 6.21 SOA chip gain and fiber-to-fiber gain measurement results. A more important parameter from a system point of view is the fiber-to- fiber gain. As opposed to chip gain, the fiber-to-fiber gain takes into account the coupling losses between the optical fiber and the semiconductor waveguide at the 162 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. input and output facets. The measurement is similar to the chip gain measurement, except that the absolute power at the output is measured relative to the input signal power. The data from this measurement is displayed in figure 6.21 above. lOdB of fiber-to-fiber gain is obtained at an SOA bias of 70mA. Following the gain measurements, the EAM was characterized, first by measuring the absorption spectrum, and second by measuring the attenuation characteristics. The absorption spectrum was found by measuring the photo generated current in the EAM as the wavelength of the tunable laser was swept. The data from this measurement is shown below in figure 6.22. From the figure it can be seen that the absorption peak occurs at 1495nm, which is very close to the 1490nm target. Thus, there is good spectral separation between the exciton absorption peak and the signal wavelength (1550nm). Furthermore, the absorption spectrum was observed to red-shift with applied reverse bias, in accordance with the QCSE theory. The EAM attenuation was characterized in a similar manner to the SOA gain. The SOA was biased to transparency, and a signal from the tunable laser was coupled into the device. The signal output was then measured as the EAM reverse bias was increased. The results of this measurement are shown in figure 6.22 below. An attenuation of -lOdB was achieved at a reverse bias of 5.5V. 163 Reproduced with permission of the copyright owner. Furiher reproduction prohibited without permission. Electro-Absorption Vs. Reverse Bias Modulator Static Attenuation 1480 1500 1520 1540 1560 Wavelength (nm) m ■ o ~ -6 T O I * 5 -to -12 \ \ \ % 0 1 2 3 4 5 6 7 8 Modulator Reverse Bias (Volts) Figure 6.22 EAM absorption spectrum and attenuation at increasing reverse bias. 6.4.3 Far Field Characterization The difference between the fiber-to-fiber gain result and the chip gain result shows that the facet coupling losses for the input and output facets is roughly 5dB/facet. When coupling to regular, cleaved single-mode fiber (SMF), this number jumps up to about lOdB/facet. Thus, there is a large amount of loss present in coupling from the fiber to the device. The reason for this is that the active region of the SOA/EAM device is designed to have a very tightly-confined optical mode so that the modal overlap factor is maximized. This improves both absorption in the EAM and gain in the SOA. Unfortunately, this tightly-confined mode has a large mismatch to the mode of the optical fiber. Furthermore, the tightly confined near-field mode in the SOA/EAM waveguide leads to a highly divergent output beam, which can increase the difficulty in coupling the device to external optics. 164 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In order to characterize the mode-mismatch problem, the far field divergence of the light beam emitted from the SOA/EAM facet was measured. The measured far field patterns for the SOA/EAM device are shown below in figure a 6.26. The 1/e half-angle points in the vertical and horizontal direction are 50° and 20° respectively. Thus, the beam is highly divergent, and extremely elliptical. Far Field: Parallel D irection Far Field: P e rp e n d icu la r D irection 1.2 Intensity G aussian Fit 1.0 - 1/e2 half angle: 19° 0 .8 - 0.6 - 0.4- 0 .2 - 0.0 -40 -20 0 20 40 1.2 - — Intensity ~ ■ Gaussian Fit 1.0 - 0 . 6 - C 0.4- 0 .2 - 1/e2 half angle: 50° 0 .0 - -40 -20 0 20 40 Angle (degrees) Angle (degrees) Figure 6.23 Far field radiation patterns for the SOA/EAM device. The 1/e2 half-angles are 19° by 50° in the horizontal and vertical directions. In order to improve the coupling of the device to SMF and to reduce the far field angle divergence, steps must be taken to transform the tightly-confined mode to a more weakly-confined mode. This will increase the dimensions of the guided mode’s near field, thereby improving matching to SMF. Furthermore, since the far field pattern is a Fourier transform of the near field pattern, a larger near field will result in reduced far field divergence angles. The methods employed to achieve this mode transformation are the subject of the next chapter. 165 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6.5 Discussion and Summary In this chapter the theoretical aspects of designing an integrated SOA and EAM were presented. The physical model of excitonic absorption and the QCSE was utilized to calculate the voltage-dependent absorption coefficient for a given quantum well active region. This absorption coefficient was then utilized in an optimization routine to find the best tradeoff between absorption peak detuning and applied electric field. The results from this calculation yielded a quantum well active region with a band gap wavelength of 1,49pm. One particularly important aspect of the active region design was strain compensation. The increase in compressive strain with SAG was discussed, as well as the need to make the active region in the plain section tensile-strained overall. In this way dislocations due to strain in the SAG regions can be avoided. An active region structure was also presented that met the strain stability requirements in both the plain region and 15pm SAG regions. Given that the optimum plain region band gap was calculated to be 1.49pm and that the signal wavelength is at 1,55pm, the amount of shift necessary between the plain and SAG regions is 60nm. This amount of shift can be achieved with a 10pm SAG mask pattern. Thus, the SOA section of the device should be fabricated from the 10pm SAG patterns. Optimization of the SOA also revealed the inherent tradeoffs when dealing with monolithically integrated PICs that share the same active region. It was found 166 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. that an 8 QW active region had too much internal loss as compared to a 6 QW active region, thus the 6 QW active region was selected. From the point of view of EAM absorption, however, 10 or 12 QWs would be desirable. Unfortunately, this would present too much loss in the SOA section of the device. Further optimization of the SOA was done with respect to the length of the SOA section. The material parameters of the SAG region were determined through a cavity length variation experiment with 1 0pm wide SAG-BA lasers. These parameters were then used to calculate the material gain and power gain as a function of SOA length and bias current. For a power gain of 20dB, the optimum length was found to be around 750pm. The transparency and gain characteristics of the SOA were measured in the single-pass condition. Some limitations of the material parameters determined using the SAG-BA cavity length experiment become apparent when comparing the measured transparency current to that calculated from the logarithmic gain fit. The transparency current calculated from the fit, for a 2pm wide mesa, is around 6 mA. The transparency current determined by the junction voltage transient method was roughly 12mA. Furthermore, 20dB of chip gain was attained around a pumping current of 90mA. According to the calculations shown in figure 6.11, 20dB of gain for an amplifier length of 750pm should have been achieved at about 15mA of pumping current. The discrepancies in transparency current and current to achieve 20dB of 167 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. gain are attributed to the inaccuracies generated by using a 1Opm wide laser stripe in the cavity length experiments. The performance aspects of the EAM were also measured in both the laser and single-pass configurations. In the laser configuration, since the optical field inside the laser cavity makes multiple round trips through the cavity, the EAM attenuation is enhanced compared to the single-pass case. In the laser configuration the EAM produced an attenuation of -15dB at -5V, while in the single-pass configuration the EAM achieved -lOdB of attenuation. The EAM, therefore, demonstrates decent performance in either configuration. When comparing the chip gain and fiber-to-fiber gain, the discrepancy was accounted for by facet coupling loss between the mode of the input and output optical fibers and the guided mode of the device waveguide. This loss amounted to roughly 5dB at each facet for a total coupling loss of ~10dB. This is a result of using a tightly-confined mode in the device waveguide to maximize the optical confinement factor. This also leads to a highly divergent far field pattern, with 1/e2 divergence angles of 20° by 50° in the horizontal and vertical directions respectively. References 1. D.A.B. Miller, D.S. Chemla, T.C. Damen, A.C. Gossard, W. Wiegmann, T.H. Wood, C.A. Burrus, “Band-edge Eiectroabsorption in Quantum Well Structures: The Quantum Confined Stark Effect,” Phys. Rev. Lett., vol. 53, no. 22, pp. 2173-2176, (1984). 168 Reproduced with permission of the copyright owner. Furiher reproduction prohibited without permission. 2. D.A.B. Miller, D.S. Chemla, T.C. Damen, A.C. Gossard, W. Wiegmann, T.H. Wood, C.A. Burrus, “Electric Field Dependence of Optical Absorption Near the Band Gap of Quantum- Well Structures,” Phys. Rev. B, vol. 32, no. 2, pp. 1043-1060, (1985). 3. S. Schmitt-Rink, D.S. Chemla, D.A.B. Miller, “Linear and Nonlinear Optical Properties of Semiconductor Quantum Wells,” Advances in Physics, vol. 38, no. 2, pp. 89-188, (1989). 4. G. Bastard, E.E. Mendez, L.L. Chang, L. Esaki, “Variational Calculations on a Quantum Well in an Electric Field,” Phys. Rev. B, vol. 28, no. 6, pp. 3241-3245, (1983). 5. M. Matsuura, T. Kamizato, “Subbands and Excitons in an Electric Field,” Phys. Rev. B, vol. 33, no. 12, pp. 8385-8389, (1986). 6. S.L. Chuang, Physics o f Optoelectronic Devices, John Wiley & Sons, Inc., New York, 1995. 7. P J . Stevens, M. Whitehead, G. Parry, K. Woodbridge, “Computer Modeling of the Electric Field Dependent Absorption Spectrum of Multiple Quantum Well Material,” IEEE J. Quantum Electron., vol. 24, no. 10, pp. 2007-2016, (1988). 8. J. Singh, K.K. Bajaj, S. Chaudhuri, “Theory of Photoluminescence Line shape Due to Interfacial Quality in Quantum Well Structures,” Appl. Phys. Lett., vol. 44, pp. 805-807, (1984). 9. J. Hegarty, M.D. Sturge, C. Weisbuch, A.C. Gossard, W. Weigmann, “Resonant Rayleigh Scattering from an Inhomogeneously Broadened Transition: A New Probe of the Homogeneous Linewidth,” Phys. Rev. Lett., vol. 49, no. 13, pp. 930-932, (1982). 10. F-Y. Juang, J. Singh, P.K. Bhattacharya, K. Bajema, R. Merlin, “Field-dependent Linewidths and Photoluminescence Energies in GaAs-AlGaAs Mutliquantum Well Modulators,” Appl. Phys. Lett., vol. 48, no. 19, pp. 1246-1248, (1986). 11. A. Bandyopadhyay and P.K. Basu, “Modeling of Excitonic Electrorefraction in InGaAsP Multiple Quantum W ells,” IEEE J. Quantum Electron., vol. 29, no. 11, pp. 2724-2730, (1993). 12. B.K. Ridely, “The In-Plane Effective Mass In Strained-Layer Quantum W ells,” J. Appl. Phys., vol. 68, no. 9, pp. 4667-4673, (1990). 13. A. Jaeger, G. Weiser, and P. Wiedemann, “Inhomogenous Exciton Broadening and Mean Free Path in Ini_x Gax AsyP|.y -rnP Heterostructures,” IEEE J. Select. Topics Quantum Electron., vol. 1, no. 4, pp. 1113-1118. 14. Mee K. Chin, William S.C. Chang, “Theoretical Design Optimization of Multiple- Quantum-Well Electroabsorption Waveguide Modulators,” IEEE J. Quantum Electron., vol. 29, no. 9, pp. 2476-2488 (1993). 15. A.M. Fox, D.A.B. Miller, B. Livescu, J.E. Cunningham, and W.Y. Jan, “Quantum Well Carrier Sweep Out: Relation to Electroabsorption and Exciton Saturation,” IEEE J. Quantum Electron., vol. 27, no. 10, pp. 2281-2295 (1991). 16. R. Sahara, K. Morito, and H. Soda, “Engineering of Barrier Band Structure for Electroabsorption MQW Modulators,” Electron. Lett., vol. 30, no. 9, pp. 698-699 (1994). 17. S.J. Choi, Personal communication. 18. L.A. Coldren, S.W. Corzine, Diode Lasers and Photonic Integrated Circuits, John Wiley and Sons, New York (1995). 169 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 7: Adiabatic Mode Expansion It was determined from the comparison of chip gain and fiber-to-fiber gain for the SOA/EAM device, that there is a coupling loss of roughly 5dB/facet to the lensed, AR-coated fibers that were used in the measurement. Power overlap calculations between the near field of the device waveguide and the near field of a cleaved single mode fiber (SMF) show even greater coupling loss; roughly lOdB/facet. Furthermore, the large divergence angles make it difficult to align the device to external optics in an external cavity configuration. Steps must therefore be taken to mitigate the coupling loss and narrow the beam. The coupling loss and beam divergence issues both stem from the tightly- confined mode in the SOA/EAM waveguide. The former results from poor overlap of the near field pattern of the dielectric waveguide with that of optical fiber. The latter results from the fact that the far field radiation pattern is a Fourier transform (from the Fraunhofer diffraction integral [1]) of the near field; a constricted near field thus results in a divergent far field. Since the constricted near field is the root cause of the coupling and divergence problems, a technique must be employed which transforms the near field mode to a more loosely-confined mode. It is essential that the mode in the SOA and EAM sections be tightly- confining to ensure optimized device performance. Thus, the mode transformation must occur in a separate section of the device. SAG is again utilized here so that the mode transformation can occur in a transparent region along the device 170 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. waveguide. Performing the mode expansion in a transparent region eliminates excessive loss due to absorption. Another consideration with respect to loss is that the mode transformation must occur adiabatically. A technique must be implemented that will allow for a continuous variation in the near field mode size, as opposed to an abrupt variation, as the optical field propagates along the waveguide. An abrupt variation would result in modal mismatch and power loss due to reflection and scattering. Furthermore, if the mode transformation occurs too rapidly, radiation modes can be excited, thus creating another source of power loss. Adiabatic mode expansion is typically achieved through the use of tapered waveguides [2, 3]. Various schemes have been implemented in vertical tapering geometries, lateral tapering geometries, or tapering in both directions, to squeeze the mode from a tightly confining waveguide and expand it to match the mode of SMF more closely. Common lateral implementations use a lithographically (photo- or e-beam) defined lateral taper, which is overgrown with a window material or vertically coupled to a passive waveguide. Vertical schemes use either selective area etching, SAG, or both and are either overgrown with a window material or are coupled to a passive waveguide. The most attractive implementation for this work is to use a laterally tapered active waveguide (figure 7.1), which is vertically coupled to a passive waveguide. This approach eliminates the need for complicated etching calibrations or re-growth, and can be achieved using standard optical lithography combined 171 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. with dry etch processes. An extensive literature survey found no clear performance advantage in terms of far field divergence angle or coupling loss to SMF for any one type of mode expander, therefore it would be best to use the simplest approach possible [4-23]. Figure 7.1 Three variants of a laterally tapered waveguide mode expander: (a) buried; (b) vertically- coupled dilute waveguide; (c) vertically-coupled single-core waveguide. The implementations depicted in figure 7.1 above show three variants of a lateral taper geometry. In case (a) the active waveguide is narrowed down to a tip and a window region is re-grown over the active waveguide. Case (b) and (c) both utilize a vertically-coupled geometry in which the active waveguide core is etched through and the waveguide is laterally tapered. The difference between (b) and (c) is the type of passive waveguide used. Case (b) uses a dilute ridge waveguide in which the high index waveguide core is distributed throughout the ridge waveguide, while case (c) utilizes a single-core ridge waveguide. Mode expander structures of type (b) and (c) are the simplest to implement because all of the waveguide geometries in the vertical direction are defined by the epitaxial crystal growth, while lateral geometries can be defined by standard optical ( a ) (b) (c) 172 Reproduced with permission of the copyright owner. Furiher reproduction prohibited without permission. photolithography. Furthermore, type (b) and (c) mode expanders do not require re growth, which can be a complicated endeavor. A schematic of the modified SOA/EAM device is shown below in figure 7.2. The SOA and EAM are in their original configuration, with the differences being that the active waveguide includes a taper on the other side of the SAG region, and that a wider, passive waveguide is also included. This implementation will be similar to that depicted in figure 7.1c. SiNx Masks Isolation Trench P-contact Passive W aveguide Tapered Active W aveguide EAM SOA Figure 7.2 A schematic layout of the SOA/EAM device with the proposed mode expander structure. In designing the laterally tapered mode expander two basic issues must be considered. First, the output facet geometry must be designed to yield the desired near field spot size and far field divergence angle. Second, the taper must be designed so that the mode transformation is adiabatic and that the coupling between upper and lower waveguides is optimized. The following sections will discuss these design issues in detail. 173 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7.1 Output facet design The design of the passive waveguide output facet geometry will determine the near field spot size and far field divergence for the expanded mode. Since the top cladding layer for the passive waveguide also serves as the spacer layer separating the active and passive waveguides, a coupling analysis must be done to determine the optimum spacer layer thickness. This in turn defines the upper cladding thickness for the passive waveguide. Once the upper cladding thickness is determined, the passive waveguide core can be optimized with regards to thickness and refractive index. Taper Width Active Waveguide Core InP Spacer Passive Waveguide Core Partial Etch-Thru Etch-Thru I i i P S ii ■Bill Inlll Figure 7.3 Schematic cross-section of the vertical coupler mode expander. The markers indicated by “Etch-Stop,” “Partial etch-thru,” and “Etch-Thru” indicate three different etching schemes as discussed below (see figure 7.5 below). Complete power transfer between the active and passive waveguides can only occur when the two guides are phase-matched. Thus, the first step in 174 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. optimizing the coupling is to determine at what point along the taper the phase matching occurs. To do this, a commercial software package (Olympios, C2V, Inc.) was used to calculate the electric field profiles and modal indices for the active waveguide at various taper widths and for certain passive waveguide designs. The two passive waveguide structures used in the simulation were a 1 0 0 0A core/0 .75pm spacer and a 1500A core/0 .5 pm spacer. Each of the spacer layers was 6 pm wide. The geometry is depicted in figure 7.3 above. Figure 7.4 below depicts the cross section of the device with the calculated mode profiles for the active and passive waveguides. CrossSection Figure 7.4 The vertical coupler cross-section and corresponding near field mode profiles. Figure 7.5 below shows the results of this calculation in which three different etching conditions were simulated. The first condition simulates stopping the etch above the active region, the second simulates etching half-way through the active region, and the third simulates etching completely through the active region. 175 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The two dashed lines in the figure indicate the modal indices for the two different passive waveguide designs. The point at which the effective index curves intersect the effective index of the passive guides represents the phase-matched condition. Modal Index Transformation 3.25-j 1 ■ i ■ i ■ i i i i i i 1 i '—r— i - ' T - i - ■ 3.24- . i □ □ □ □ X n □ ^ a A <D 1 3 3.23 □ □ □ A C 3 .2 2 - A Etch-stop 82 □ A _ > 3.21- A Partial Etch-thru O O O Etch-thru A O 3= 3 .20- ------------ PWG L U 3 .1 9 - /> o 0) A . ° f i r 3-176 TJ o 3 .18- /...\ 2 3 .17- A A - a - %=3-17 1 1 I 1 I 1 I 1 3 .1 6 - i ■ i i j i i i i i r - f 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Taper Width (pm) Figure 7.5 Modal index calculations versus taper width for three different etching conditions. The dashed lines represent the modal indices for two different passive waveguide designs. The intersection of the curves with these lines represents the phase-matched condition. From figure 7.5 it is clear that phase matching can only be achieved by etching at least partially through the active region. In this manner the presence of air on either side of the active waveguide core lowers the modal index enough so that it can match the modal index of the passive guide at some point along the taper. Stopping the etch above the active waveguide core does not permit enough change in modal index to match the passive waveguide. The etch-stop condition is thus an unacceptable design. The power coupling between active and passive waveguides is very sensitive to the phase-matched condition. This can be shown by calculating the 176 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. power transfer through a co-directional coupling analysis. The first step in the analysis is to solve for the coupling coefficients via the coupling integrals [24]: In these equations K1 2 and K 21 are the coupling coefficients for active/passive waveguide coupling and passive/active waveguide coupling respectively, k0 is the free space wave vector, (3 i and [T are the phase constants for the upper and lower waveguides, £1 and £2 represent the dielectric constant profiles of the upper and lower waveguides, and Ui and U2 are the transverse field profiles for the upper and lower waveguides. These integrals were solved numerically by using the electric field profiles and phase constants for the passive waveguide and for the active waveguide at decreasing widths as calculated with Olympios above. The field profiles and phase constants were used in conjunction with a Matlab program to calculate the coupling integrals over the core areas of the active and passive guides. Once the coupling integrals were solved, the power transfer could be calculated via [25]: (7.1) (7.2) (7.3) 177 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In equation 7.3 an average K = ^Kn Kn is defined for asymmetric waveguides and S = (/32- f t ) / ! is the codirectional detuning parameter [24]. From equation 7.3, the maximum power transfer is given by k2 / { k2 + 8 1) . The maximum power transfer for a 1000A core, 0.75pm spacer passive waveguide structure with a partially etched-thru active waveguide is shown below in figure 7.6. As can be deduced from the definition of the detuning parameter, maximum power transfer can only occur when p2=Pi, or, in other words, when phase- matching has been achieved. In Figure 7.5, phase-matching for the particular passive waveguide structure described above occurs at a taper width of roughly 0.9pm. At a taper width of 0.9pm in figure 7.6, roughly 99 percent of the power is coupled into the passive waveguide. Power Coupling Vs. Taper Width L =63|im PWG Core: 1000A Spacer: 0.75gm -e e- 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Active Waveguide Width (pm) Figure 7.6 Maximum fraction of power coupled into the passive waveguide versus taper width. Nearly 100% power transfer occurs at the phase-matched condition. The power coupling length is roughly 63 pm. 178 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Although nearly all the power in the active waveguide can be coupled to the passive waveguide, the key issue with regards to the spacer layer thickness is the coupling length. The power transfer occurs over a specific length due to the sinusoidal nature of equation 7.3. The critical point is that all of the power must be transferred from the active waveguide into the passive waveguide before the upper waveguide becomes cut off. As can be seen from figure 7.5, from the phase-matching point, the active waveguide only tapers another tenth of a micron before the modal index of the active waveguide approaches the refractive index of the InP cladding layers. Once the modal index in the active waveguide equals the refractive index of the cladding layers the mode in the active waveguide leaks out into the substrate. If some fraction of power remains in the active waveguide then this power will be lost due to substrate leakage. It is therefore imperative that the coupling length be short enough so that all of the power is coupled into the passive waveguide before the active waveguide is cut off. To determine the optimum spacer thickness which optimizes the coupling length, power transfer calculations were done with increasing spacer thickness. These calculations are shown in figure 7.7 above. In figure 7.7 several curves are plotted for spacer layers varying in thickness from 0.5pm to 2.0pm. These calculations were done assuming that the upper and lower waveguides were phase-matched. The vertical line represents the point along the taper in which the active waveguide becomes cut off. From figure 7.5, phase- 179 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. matching occurs at a taper width of roughly 1.3pm for the etch-thru case. The waveguide is then cut off at a taper width of roughly 1.2pm. This corresponds to a propagation distance of roughly 50p.m. Thus, only spacer thicknesses that result in coupling lengths of less than 50pm can be considered. Phase-Matched Power Coupling 0 L _ 0) O _l c o 5 o Q . *4— o c o « 3 o (0 0.9 0 . 6 - 0.3- 0.0 [ l 1. / / / i I j / / / / / I f / / ------- O.Sjim Spacer I / i f / i / / / / / 0.75pm Spacer / / 1pm Spacer - / / / / / 1,25pm Spacer - ■ W / y ------- 1.5pm Spacer ------- 1.75pm Spacer m ^ Cut-Off ------- 2pm Spacer 50 100 150 200 Propagation Distance (pm) Figure 7.7 Power transfer calculations for various spacer layer thicknesses. The solid vertical line represents the cut-off point for the active waveguide. As can be seen in figure 7.7, the 0.5pm spacer couples all of the power to the passive waveguide within a propagation distance of 50pm and a little more than 90% is coupled for the 0.75pm design. For a 2pm spacer, on the other hand, only about ten percent of the power is coupled to the passive waveguide before cut-off is reached. Thus, some 90 percent of the power is lost due to leakage into the substrate. Again, from figure 7.7, two designs considered acceptable are the 0.5pm and 0.75pm spacer thicknesses. 180 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The power transfer calculation was supported by a semi-vectorial beam propagation (BPM) calculation (using commercial software), which also showed that a great deal of power is lost due to substrate leakage in the 2 pm spacer design. This calculation is shown in figure 7.8 below. From this figure it is clear that for the 0.5pm spacer case, all of the power is coupled to the passive waveguide, while in the 2 pm spacer case, nearly all the power is lost due to substrate leakage. Figure 7.8 BPM calculations for a 2pm spacer (left) and a 0.5pm spacer (right). With the InP spacer thicknesses having been chosen, the final step in the facet design is to optimize the core layer refractive index and thickness to yield the desired near field pattern. There are not as many degrees of freedom, however, as it may seem. Combinations of refractive index and thickness serve to either increase or decrease the effective modal index of the passive waveguide. The most expanded near field occurs with a modal index that is closest to that of the cladding layers. In effect, to have the largest possible near field in the passive waveguide, 181 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the modal index should be as close to cut-off as possible while still maintaining a guided mode. Thus, in designing the output facet, a very low modal index structure was tried; this structure consisted of a 0.75pm spacer layer and a 1 0 0 0A core layer (n=3.35). This waveguide structure has a modal index of 3.17, and 1/e2 far field divergence angles of 10 degrees by 2 0 degrees in the horizontal and vertical directions, respectively. In addition to this structure a higher modal index waveguide was also implemented. This structure utilized a 0.5pm spacer layer and a 1500A core layer with a modal index of 3.176. The 1/e2 far field divergence angles of this waveguide structure are 10 degrees by 25 degrees in the horizontal and vertical directions, respectively. 7.2 Taper design In designing the taper the main consideration is that the modal index transformation happens in an adiabatic manner. If the taper occurs too fast, the fundamental guided mode can couple to local radiation modes or higher order guided local modes (including backwards traveling modes). Coupling to local modes would result in power loss from the fundamental guided mode. A design rule that ensures that the taper is adiabatic is given in Ref. 26 by Love, et al and is determined by considering local normal mode coupling. The basic principle for adiabaticity is a physical argument that the local taper length scale must be much greater than the coupling length between the fundamental mode and the dominant local coupling mode. In this way power loss from the 182 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. fundamental mode is negligible. Essentially this means that the taper angle must be kept very small. Figure 7.9 Schematic illustration of the local taper length scale. To find this angle a local taper length sealez, = d l 6 is defined, where w is the width of the local waveguide divided by 2 and 0 is the taper angle (see figure 7.9). The local coupling length between the fundamental and second local coupling modes is taken as the beat length between the two modes and is given by: Z b ~ a - a ' where (3 i and (3 2 are the propagation constants for the fundamental and second local mode, respectively. The conclusion from the above discussion is that for a waveguide taper to be approximately adiabatic z t must be much larger than Zb ( z t» Z b ) . Conversely, if the local taper length is smaller than the coupling length ( z t<Zb), then coupling between the fundamental mode and the second local coupling mode will not be negligible, resulting in power loss from the fundamental mode. The case where the local taper length equals the coupling length ( z t=Zb) provides an approximate 183 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. boundary between adiabatic and lossy tapers. Substituting for zt, the local taper angle can be solved for as: ^ d(R-fi2) f l= Hl! (7.5) 2 7 t As equation 7.5 would indicate, the taper angle should continuously vary as the taper width varies. This would result in an exponentially shaped taper, which is the most efficient type of adiabatic taper (in terms of taper length) [27-30], Physically, the mode dimensions in tapering from a width of 2pm to a width of 1.5pm do not change a great deal. Thus, the taper angle can be steeper in this region with the taper still being adiabatic. In the tapered region between widths of 1.5pm to 0.5pm, however, the mode dimensions change more rapidly, thus the taper angle must decrease to prevent power loss. While an exponential taper is the most efficient design, it is more difficult to fabricate. Expensive techniques must be used when making the photomasks so that the mask in the steep parts of the exponential taper is smooth. Furthermore, fabrication tolerances will be reduced with regards to photolithography and etching. A simplified approach, however, would be to use a single-step taper. Although inefficient with regards to taper length, the above issues pertaining to exponential tapers are not encountered. Typical dimensions for an adiabatic, single-step taper are a decrease in width from 2pm to 0.5pm over a length of 500pm [31]. This gives a taper angle of 0.086°. 184 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In order to characterize the power loss of the 500pm single-step taper design, BPM simulations were again performed, and power overlap integrals were calculated for the active and passive waveguides. This was done separately for the active and passive waveguides using the overlap of the propagated field with the fundamental mode of each waveguide. The power in the active waveguide and the power in the passive waveguide were then plotted versus propagation distance. The results of this calculation are shown in figure 7.10 below. Pow er Coupling 1.0 - < D § 0.8 - Q . T J N 0 6 - Active Guide Passive Guide 0.4- O z 0 .2 - 0.0 0 100 200 300 400 500 600 700 800 900 Propagation D istance (pm) Figure 7.10 BPM calculation for the 0.5p.m spacer, 500pm-long taper design and the corresponding power in the active and passive waveguides versus propagation distance. A schematic of the tapered structure is also shown in the intensity plot (left). As can be seen from the power coupling curves in figure 7.10, there is nearly 1 0 0% power transfer from the active waveguide to the passive waveguide for the 0.5pm spacer, 500pm -long taper design. The pow er in the active waveguide does not go all the way to zero because the evanescent tail of the passive waveguide mode overlaps the core of the active waveguide to a small 185 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. degree. Likewise, the initial power in the passive waveguide is not zero due to the evanescent tail of the active waveguide overlapping the passive waveguide core. 7.3 Device fabrication In order to fabricate the tapered waveguide structure, it was necessary to abandon the wet-etch technique. This was due to the need for vertical waveguide sidewalls, as well as to the fact that the inverse ridge waveguide structure was mechanically unstable. Figure 7.11 below demonstrates how fragile the undercut mesa is at the narrowest point in the taper. This figure shows a wet-etched, tapered ridge waveguide in which polyimide has been used to planarize the surface. When the polyimide is cured it contracts and, due to the location of the centroid of the trapezoidal structure, causes a large enough bending moment on the ridge structure to crack the mesa at its base. Figure 7.11 SEM of a wet-etched, tapered structure showing mechanical damage to the ridge waveguide. 186 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. In the above wet-etch approach the issue with mechanical stability is caused by the fact that the width of the mesa at the base is controlled by the angle achieved by the wet etch. This demands the use of an InP top cladding that is roughly 2.5pm thick. By switching to a dry-etch process, however, the cladding thickness can be reduced to lpm, the waveguide ridge can be narrowed to 2pm, and the ridge profile can be made vertical instead of undercut. This new geometry lowers the centroid of the ridge structure and mitigates the cracking problems that were discussed above. Figure 7.12 SEM picture of the tapered waveguide after ICP etching. The passive waveguide has not been etched. The tapered waveguide structures were thus dry-etched using a Surface Technology Systems (STS) inductively coupled plasma (ICP) dry etch system. The ICP system allows for much faster etching rates compared to an ECR system, and also offers less sidewall slope angle. A BCI3 chemistry was used for the ICP 187 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. etching with the following parameters: flow rate, lOsccm; pressure, 2mT; temperature, 165; coil/platen RF power, 300/150W. The dry etch was done in two steps, the first being etching the ridge waveguide down to the top of the active region. Because the top cladding is grown after removal of the SAG patterns, the first etch achieves the same depth in both the SAG and plain regions. The first etch is stopped above the active region so that in the SOA section of the device, where current is being injected, surface recombination and other deleterious effects that result from etching through the quantum wells will not be encountered. The second etch was done after masking over the waveguide in the SOA and EAM sections of the device. Thus, the etching continues only in the tapered section of the device. The mask used for the second etch has an angled interface so that the discontinuity at the dielectric interface between the SOA and tapered sections of the device will not generate reflections. Figure 7.12 above is an SEM photo of the dry-etched device. Figure 7.13 below is another SEM photo showing the interface between the SOA and tapered sections. Following the dry-etching steps, a 6 pm-wide SiNx stripe was patterned over the tapered waveguide. A wet etchant (HCkFEO 3:1) was then used to etch this pattern down to the passive waveguide core layer. This 6 pm-wide mesa provides the lateral guiding for the passive waveguide mode. Subsequent to the etching of the passive waveguide, the w afer was planarized with polyimide, followed by a p- metal contact (Ti/Pt/Au) on top of the active waveguide ridge. The isolation trenches were etched, and a p-metal bond pad (Ti/Au) was evaporated. The wafer 188 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. was then lapped and an n-contact (AuGe/Ni/Au) was evaporated. The contacts were annealed in the rapid thermal annealer, and the wafer was cleaved into device bars. Figure 7.13 SEM picture showing the dry-etch interface between the SOA and tapered sections of the device. 7.4 Far field results The tapered waveguide devices were measured as lasers in order to characterize the far field radiation patterns. Thus, antireflection coatings were not applied to the facets. Measuring the devices as lasers serves two purposes: 1) there is enough optical power to perform the far field measurement; 2 ) the losses of the various taper designs can be characterized by the differences in threshold current. After the devices were cleaved, they were mounted onto a testing fixture using indium solder. The fixture consists of a copper blade and a flange that allows an SMA connector to be bolted to the fixture. One end of a gold wire-bonding wire is then soldered to the connector and the other end is bonded to the device using a 189 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. wedge bonder. The fixture was then positioned in front of a GRIN-lens-collimated fiber attached to a two-axis (0,cf)) rotation stage. The far field radiation pattern was then measured by aligning the device to the center of the rotation hemisphere, and then measuring the optical power collected into the fiber as it was rotated around the facet of the device. The results of a far field measurement are shown below in figure 7.14 for a 500|im, single-step taper. In this figure, the horizontal 1/e2 half-angle measures approximately 10 degrees, with a symmetric profile. In the vertical direction, however, the profile is very asymmetric, and is characterized by intensity fluctuations on the substrate side of the pattern (negative angle). Horizontal FF Vertical FF 12 1 0 - c L. 0) I CL -60 -40 -20 0 20 40 60 12 1 0 - k. 0) 5 o CL -60 -40 -20 0 20 4 0 60 Angle (Degrees) Angle (Degrees) Figure 7.14 Far field measurements for the vertically-coupled mode expander structure. The measurements shown above are for a 500pm taper, 0.5pm spacer device. In the above far field results the horizontal profile matches the theoretical calculation very well. The vertical far field pattern, on the other hand, is both asymmetric and broader than what was expected from calculations. It is suspected 190 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. that this result is caused by a fabrication issue with regards to the second ICP etching step. This can be seen in figure 7.15 below. Figure 7.15 A field emission SEM picture of the tapered waveguide facet. The waveguide width at the base of the active waveguide is roughly 0.6|im. The brighter stripes indicate InGaAsP material while the darker regions indicate InP. The material in the upper left of the figure is highly-charged polyimide. In figure 7.15 the tapered waveguide facet is shown with a field emission SEM at 25,000x magnification. The bright, horizontal stripes are layers of InGaAsP, while the dark gray regions are InP. The bright area in the upper left of the figure is highly-charged polyimide (polyimide is an insulator). The lower most InGaAsP layer is the passive waveguide core. There is then a layer of InP separating the passive core from the quantum well region. The marker on the picture indicates that this separation is roughly 0.429pm. As can be seen from the picture, at the sidewall of the active waveguide the etch stopped just at the bottom edge of the quantum wells. Unfortunately, there is a foot or tail in the etching so that the etch was deeper away from the active waveguide. The marker on the 191 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. picture indicates that the InP spacer layer is only 0.230|Ltm thick in the area, where the target was 0.5p.m. This means that the spacer layer was over-etched by almost half its thickness. Mode cross sections were calculated to simulate this over-etched condition, the results of which are shown below in figure 7.16. The over-etched InP spacer layer results in a decrease of the modal index of the passive guide mode to the point where cut-off is reached and the passive guide mode leaks into the substrate. The calculated modal index for the over-etched case was 3.166 with a propagation loss of 2.03dB/cm. Passive Guide Correct Etch -< -3.0 - X [|jm] Passive Guide Over-Etch X [|jm] Figure 7.16 Calculated near-field intensity plots for the correctly-etched waveguide structure (left) and the over-etched structure (right). The substrate leakage is clearly observed in the over-etched case. The intensity fluctuations observed in the vertical far field pattern are therefore interference fringes between the leaky passive waveguide mode and the reflected light in the substrate. If the etching were corrected so that the passive 192 Reproduced with permission of the copyright owner. Fudher reproduction prohibited without permission. waveguide is not etched into, then the vertical far field pattern would also be corrected. 7.5 Summary of adiabatic mode expansion In this chapter the problem of modal mismatch between a tightly-confining, semiconductor waveguide mode and the mode of SMF was discussed. For the SOA/EAM devices fabricated in this work, this mismatch resulted in a coupling loss of roughly lOdB/facet. Tapered waveguide schemes were introduced as a solution to the coupling loss issue. The chapter then detailed the laterally-tapered, vertically-coupled waveguide scheme, and several design issues were investigated. The design was broken down into two areas; facet design and taper design. For the single-core, passive waveguide approach, the facet design was shown to be limited by the fact that the passive waveguide structure operates very close to cut-off. This fact, in turn, placed restrictions on acceptable InP spacer thicknesses so that power coupling was maximized. As was determined from the analysis given above, acceptable designs included passive waveguide structures with core/spacer layer thicknesses of 0.5ptm/ 1500A and 0.75(im/1000A. With regards to taper design, the conditions for adiabaticity were discussed and the length scale required to avoid coupling between the fundamental and local coupling modes was given. Although an exponential taper design would be the most efficient in terms of taper length, the mask design and subsequent processing would be more costly. Thus, a linear taper approach was used. In these mask 193 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. designs both single- and double-step taper designs were employed. For a single- step taper the adiabaticity requirements dictated the use of an extremely small taper angle (<0 .1°). The tapered waveguide fabrication was also described, including the need to switch from a wet-etched to a dry-etched approach. This switch was based on the mechanical instability of the wet-etched, reverse ridge waveguide at the taper tip. Thus, an ICP system was employed to fabricate the tapered waveguide, and a two- step etching sequence was developed. Following the discussion on fabrication, the far field characterization apparatus was described, and the far field results of a 500pxn-long, single-step taper were given. These results showed significant reduction in the horizontal far field (from 20° to 10°). The results in the vertical direction, however, showed intensity fluctuations on the substrate side of the device. This was related to a dry-etching issue and the fact that the InP spacer layer was being over-etched. Simulations show that the over-etched spacer layer results in an unconfined mode that leaks into the device substrate. It is therefore speculated that the intensity fringes seen in the vertical far field pattern are a result of reflections of the leaky mode off the bottom of the substrate, and interfering with the portion of the mode remaining in the passive waveguide core. 194 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. References 1. M. Bom and E. Wolf, Principles o f Optics- 7th ed., Cambridge University Press, New York (2002). 2. B. Mersali, “Optical-Mode Transformer: A III-V Circuit Enabler,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1321-1331 (1997). 3. I. Moerman, P.P. Van Daele, and P.M. Demeester, “A Review on Fabrication Technologies for the Monolithic Integration of Tapers with III-V Semiconductor Devices,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1308-1320 (1997). 4. V. Vusirikala, S.S. Saini, R.E. Bartolo, S. Agarwala, R.D. Whaley, F.G. Johnson, D.R. Stone, and M. Dagenais, “1.55-pm InGaAsP-InP Laser Arrays with Integrated-Mode Expanders Fabricated Using a Single Epitaxial Growth,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1332-1343 (1997). 5. H. Jeon, J.M. Verdiell, M. Ziari, and A. Mathur, “High-Power Low-Divergence Semiconductor Lasers for GaAs-Based 980-nm and InP-Based 1550-nm Applications,” IEEEJ. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1344-1350 (1997). 6. K. Kawano, M. Kohtoku, H. Okamoto, Y. Itaya, and M. Naganuma, “Coupling and Conversion Characteristics of Spot-Size-Converter Integrated Laser Diodes,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1351-1360 (1997). 7. G.A. Vawter, C.T. Sullivan, J.R. Wendt, R.E. Smith, H.Q. Hou, and J.F. Klem, “Tapered Rib Adiabatic Following Fiber Couplers in Etched GaAs materials for Monolithic Spot- Size Transformation,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1361-1371 (1997). 8. B. Hubner, et. al., “Laser Diodes with Integrated Spot-Size Transformer as Low-Cost Optical Transmission Elements for Telecommunications,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1372-1383 (1997). 9. H. Kobayashi, et. al., “Narrow-Beam Divergence 1.3-pm Multiple-Quantum-Well Laser Diodes with Monolithically Integrated Tapered Thickness Waveguide,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1384-1391 (1997). 10. H. Yamazaki, et. al., “1.3-pm Spot-Size-Converter Integrated Laser Diodes Fabricated by Narrow-Stripe Selective MOVPE,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1392-1398 (1997). 11. Y. Inaba, M. Kito, T. Nishikawa, M. Ishino, and Y. Matsui, “High-Temperature Operation of 1.3-pm Tapered-Active-Stripe Laser for Direct Coupling to Single-Mode Fiber,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1399-1404 (1997). 12. M. Aoki, et. al., “Reliable Wide-Temperature-Range Operation of 1.3pm Beam-Expander Integrated laser Diode for Passively Aligned Optical Modules, “ IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1405-1412 (1997). 13. A. Kasukawa, et. al., “Structural Dependence of 1.3-pm Narrow-Beam Lasers Fabricated by Selective MOCVD Growth,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1413-1420(1997). 14. C.H. Chen, et. al., “Semiconductor Optical Amplifier Array Coupled to Uncoated Flat-End Fibers with Integrated Beam Expanders and T i0 2 Antireflection Coatings,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1421-1428 (1997). 15. A. Lestra and J.Y. Emery, “Monolithic Integration of Spot-Size Converters with 1.3-pm Lasers and 1.55-pm Polarization Insensitive Semiconductor Optical Amplifiers,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1429-1440 (1997). 16. J.V. Collins, I.F. Lealman, A. Kelly, and C.W. Ford, “Passive Alignment of Second Generation Optoelectronic Devices,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, p p . 1441-1444 (1997). 195 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 17. G. Wenger, M. Schienle, J. Bellermann, B. Acklin, J. Muller, S. Eichinger, and G. Muller, “Self-Aligned Packaging of an 8x8 InGaAsP-InP Space Switch,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1445-1456 (1997). 18. X. Yan, M.L. Majsanovic, E.J. Skogen, D.J. Blumenthal, and L.A. Coldren, “Optical Mode Converter Integration With InP-InGaAsP Active and Passive Waveguides Using a Single Regrowth Process,” IEEE Photon. Technol. Lett., vol. 14, no. 9, pp. 1249-1251 (2002). 19. S.W. Ryu, S.B. Kim, J.S. Sim, and J. Kim, “1.55-p.m Spot-Size Converter Integrated Laser Diode With Conventional Buried-Heterostructure Laser Process,” IEEE Photon. Technol. Lett., vol. 15, no. 1, pp. 12-14 (2002). 20. D. Tishinin, K. Uppal, I. Kim, and P.D. Dapkus, “ 1,3pm Polarization Insensitive Amplifiers With Integrated-Mode Transformers,” IEEE Photon. Technol. Lett., vol. 9, no. 10, pp. 1337-1339 (1997). 21. K. Uppal, D. Tishinin, I. Kim, and P.D. Dapkus, “Study of 1.3-pm Tapered Waveguide SpotSize Transformers,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 3, pp. 975-979 (1997). 22. H. Bissessur, C. Graver, O. Le Gouezigou, G. Michaud, and F. Gaborit, “Ridge Laser with Spot-Size Converter in a Single Epitaxial Step for High Coupling Efficiency to Single- Mode Fibers,” IEEE Photon. Technol. Lett., vol. 10, no. 9, pp. 1235-1237 (1998). 23. H. Sato, M. Aoki, T. Tsuchiya, M. Komori, A. Taike, M. Takahashi, K. Uomi, and S. Tsuji, “Improved High-Temperature Characteristics in a Thickness-Tapered 1.3-pm Beam- Expander Integrated Ridge-Waveguide Laser,” IEEE Photon. Technol. Lett., vol. 10, no. 4, pp. 484-486. 24. L.A. Coldren, S.W. Corzine, Diode Lasers and Photonic Integrated Circuits, John Wiley and Sons, New York (1995). 25. A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control o f Laser Radiation, John Wiley and Sons, New York (1984). 26. J.D. Love, W.M. Henry, W.J. Stewart, R.J. Black, S. Lacroix, F. Gonthier, “Tapered Single-Mode Fibres and Devices Part I: Adiabaticity Criteria,” J. IEE Proceedings, vol. 138, no. 5, pp. 343-354 (1991). 27. P.V. Stedenkov, M.R. Gokhale, and S.R. Forrest, “Efficient Coupling in Integrated Twin- Waveguide Lasers Using Waveguide Tapers,” IEEE Photon. Technol. Lett., vol. 11, no. 9, pp. 1096-1098 (1999). 28. F. Xia, J.K. Thomson, M.R. Gokhale, P.V. Studenkov, J. Wei, W. Lin, and S.R. Forrest, “An Asymmetric Twin-Waveguide High-B and width Photodiode Using a Lateral Taper Coupler,” IEEE Photon. Technol. Lett., vol. 13, no. 8, pp. 845-847 (2001). 29. F. Xia, J. Wei, V. Menon, and S.R. Forrest, “Monolithic Integration of a Semiconductor Optical Amplifier and a High Bandwidth p-i-n Photodiode Using Asymmetric Twin- Waveguide Technology,” IEEE Photon. Technol. Lett., vol. 15, no. 3, pp. 452-454 (2003). 30. F. Xia, V.M. Menon, and S.R. Forrest, “Photonic Integration Using Asymmetric Twin- Waveguide (ATG) Technology: Part I-Concepts and Theory,” IEEE J. Select. Top. Quantum Electron., vol. 11, no. 1, pp. 17-29 (2005). 31. H. Bissessur, C. Graver, O. Le Gouezigou, G. Michaud, and F. Gaborit, “Ridge Laser with Spot-Size Converter in a Single Epitaxial Step for High Coupling Efficiency to Single- Mode Fibers,” IEEE Photon. Technol. Lett., vol. 10, no. 9, pp. 1235-1237 (1998). 196 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 8: Summary and Future Research Directions This thesis has discussed in detail various aspects of the design and fabrication of VCSELs for use in free-space optical interconnects and a monolithically integrated SOA/EAM/SSC for fiber-optic applications. This chapter will summarize the work done in both of these areas and discuss future research directions. 8.1 Summary of high-speed, top-emitting VCSELs In the discussion on high-speed, top-emitting VCSELs, the basic design principles as far as active region design, DBR design, and aperture placement effects were investigated. This was followed by an analysis of the trade-offs between wall plug efficiency, mirror reflectivity, threshold current and number of quantum wells. Two key ideas were presented in this section. First it was shown that, due to joule heating caused be excessive series resistance, the gain spectrum should be intentionally blue-shifted by about 5nm. This is to compensate for the temperature-induced red-shift in the gain spectrum incurred by the increased temperature. Second, in order to minimize loss in the VCSEL cavity and improve array uniformity, the oxide aperture should be placed at a null in the cavity standing wave. These topics were followed by an analysis of the extrinsic and intrinsic factors affecting high-speed operation of the devices. A parasitic circuit was discussed in which the bond pad capacitance in parallel with the large series 197 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. resistance comprised a low-pass filter that inhibited high-frequency operation. Two methods were investigated to eliminate the bond pad capacitance: polyimide planarization and ion implantation. The process development for each approach was given, as well as high-frequency performance for devices fabricated using each approach. The best high-speed performance achieved was from an ion-implanted VCSEL; the 3dB modulation frequency was 5.1GHz. The polyimide devices should have performed better due to a thicker insulating layer; however a measurement error (that went unnoticed at the time) obstructed the achievement of higher bandwidth. Although the measurements did not show it, polyimide should provide better bond pad isolation, due to its increased thickness and lower dielectric constant. The K-factor extracted from the ion-implantation measurements, however, indicated that the maximum intrinsic bandwidth was about 25GHz. The fundamental issue with regards to bandwidth limitations and high- efficiency VCSELs was uncovered through the dependence of series resistance on the oxide aperture. An analysis of series resistance determined that it was impossible to achieve low-threshold, high-frequency devices. The narrow oxide aperture needed to achieve low-threshold operation created an extremely large series resistance due to the narrow current constriction. The large series resistance in turn inhibited high-frequency perform ance. Thus, only a large-aperture device, with the concomitant large threshold current, can achieve high bandwidths. 198 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Even with the aperture widths obtained for the high-frequency measurements, the series resistance is several hundred ohms due to residual DBR resistance. Future VCSEL work should focus on eliminating the DBR resistance. 8.2 Future VCSEL research directions The series resistance issue mentioned above is one of the most critical issues to solve with VCSELs. Even though the DBRs have graded junctions with modulation doping, the resistance is still too large. Carbon doping would improve the series resistance, because one can achieve a more “delta-doped” structure than with zinc. Zinc readily diffuses so that the dopant does not remain at the hetero interface between DBR layers. Carbon would not diffuse, and would thus be better at reducing the barrier at the hetero-interface. Thus, one future research direction would be to incorporate carbon doping as a p-type dopant into the MOCVD growth cycle rather than zinc. Even carbon doping would not sufficiently eliminate the series resistance problem to the necessary degree. A novel technique that eliminates the p-type DBR altogether (and thus eliminates the DBR resistance issue altogether) is the tunnel-junction VCSEL. By stacking a highly-doped n+ layer on top of the p-side of the active region, a reverse-biased tunneling junction can be realized. When the tunnel junction is in reverse breakdown the voltage is essentially clamped at the breakdown voltage; very low resistances can therefore be obtained. A possible configuration of a tunnel-junction VCSEL is shown below in figure 8 .1. The p-type top DBR has now been replaced with an n-type DBR, which 199 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. offers a much lower resistance. Highly doped n- and p-layers have been added underneath the top n-DBR to form the tunnel junction. These tunnel junction layers can be placed at a null in the cavity standing wave to minimize absorption losses. Light Out Top Contact N-DBR QW Active Region N+P+ TJ Dielectric Aperture 2.1 ~ ’ ______ n s m y ■ ... ---------- ZSE 5E 5 n-type Substrate N-DBR Bottom Contact Figure 8.1 Schematic of a tunnel-junction VCSEL 8.3 Summary of SAG and the integrated SOA/EAM/SSC The second type of device discussed in this thesis was the monolithically integrated SOA/EAM/SSC. This device used SAG as a mechanism for varying the band gap of the MQW active region along the device waveguide. The mechanisms behind SAG were explained, and the various processing procedures required to get good regrowth and high-efficiency devices were described. The design of the integrated SOA/EAM was then developed; the approach being to focus on the optimization of the EAM active region. The excitonic 200 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. absorption spectrum was calculated and parameters such as quantum well composition and thickness, barrier composition and thickness, device length, and intrinsic region thickness were optimized. This analysis yielded the optimum detuning of the EAM absorption peak from the signal wavelength, which in turn determined the wavelength separation between SAG and plain regions. Strain compensation was also discussed, and a structure that was stable in both the plain and SAG regions was proposed. Following the EAM optimization an analysis of the SOA region was performed. The number of quantum wells, modal gain, and transparency current density were determined empirically through the use of SAG-BA lasers. These parameters were then used to optimize the SOA length in order to achieve maximum gain at a minimum pumping current density and length. After the device analysis was complete, details on fabrication and performance were given. The device mesas were wet-etched to achieve a reverse ridge waveguide profile, and planarized with polyimide. The bond pads were also up-plated with pure gold to improve wire bond strength. After facet cleaving, the devices were tested; first as lasers and then as single-pass devices with AR-coated facets. Parameters such as modulator attenuation, EAM absorption spectrum, chip gain, and fiber-to-fiber gain were measured. A comparison of the chip gain and fiber-to-fiber gain uncovered a major source of loss; coupling loss between the device facets and the input/output lensed fibers. This coupling loss was determined to be roughly 5dB/facet, and is caused 201 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. by the near-field mode mismatch between the optical fiber mode and the device waveguide mode. In order to solve the coupling loss problem a vertically-coupled, laterally- tapered mode expander structure was proposed. The theoretical design aspects of this structure were discussed in terms of co-directional power coupling and beam propagation. Device fabrication was also detailed, including the need to switch to a dry-etched structure. The far field of the expanded mode was measured, and the results were discussed. The horizontal far field profile was well-matched to calculations, with a divergence angle that was narrowed from 20° to 10° (1/e2 intensity point). The vertical far field profile, however, was broader than expected, and also exhibited intensity fluctuations on the substrate side of the device. These fluctuations were related to a fabrication issue; namely the passive waveguide cladding layer was over-etched. This caused the passive waveguide mode to become leaky. The intensity fluctuations were thus concluded to be interference fringes caused by light leaking into the substrate, reflecting off the bottom of the substrate, and interfering with the guided mode. 8.3 Future SSC research directions With regards to the single-core passive waveguide design, the over-etching issue needs to be corrected. The approach attempted in the above summary was an etch-thru structure (see figure 7.3). It is still possible, as shown by figure 7.5, to achieve phase-matching with a partial etch-thru structure. Thus, the over-etching 202 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. of the InP spacer layer can be solved by performing a more shallow etch. If the etch is stopped half-way through the quantum well region, then the etching tail should not extend into the InP spacer. Thus, the decrease in modal index of the passive guide should not be encountered and the mode should not become leaky. The fundamental difficulty with the single-core design, however, is that it operates very close to cut-off. The higher the modal index in the passive guide, the more confined the mode becomes. To obtain the largest near-field pattern, the passive waveguide must have an effective modal index that is very close to the cladding index. The use of a dilute waveguide structure, on the other hand, distributes the high-index core throughout a much larger structure, yielding a higher-index mode. Figure 8.2 below shows the facet cross section and computed mode profiles for the active and passive sections of a dilute waveguide structure. The dilute waveguide consists of 20 pairs of InGaAsP/InP layers. The InGaAsP layers are 150A thick, with a refractive index of 3.3575. The InP spacer layers have an index of 3.167 and a thickness of 1350A. The lower dilute waveguide is etched through 10 layer pairs and is 5(im wide. The calculation in this figure shows that the active waveguide mode is still well confined in the active waveguide, even with the presence of the higher index layers beneath it. The effective modal index for the active waveguide mode was 3.235. 203 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o Dilute Waveguide-Active Guide Mode Dilute Waveguide-Passive WG Mode 0.0 rf - 2.0 3, -4.0 - 6.0 -4.0 -2.0 0.0 2.0 4.0 -4.0 -2.0 0.0 2.0 4.0 X [jjm] X [pm] Figure 8.2 Mode cross section simulations of a dilute waveguide structure. The mode in the active waveguide is shown on the left. The mode in the passive waveguide is shown on the right. When the active waveguide has been narrowed to 0.5|im, the mode is confined to the dilute passive waveguide, with an effective index of 3.18. The far field profile calculated from this calculation shows 1/e2 half-angle divergences of 13.7°xl9°. 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Ebeling, “High performance oxide-confined GaAs VCSELs,” IEEE Select. Topics Quantum Electron., vol. 3, pp. 409-414 (1997). 135.G. Wenger, M. Schienle, J. Bellermann, B. Acklin, J. Muller, S. Eichinger, and G. Muller, “Self-Aligned Packaging of an 8x8 InGaAsP-InP Space Switch,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1445-1456 (1997). 136. Y.A. Wu, et al., “Single-transverse mode, low threshold current vertical-cavity surface- emitting laser,” IEEE Trans. Electron Devices, vol. 40, no. 11, pp. 2116-2117 (1993). 137.F. Xia, V.M. Menon, and S.R. Forrest, “Photonic Integration Using Asymmetric Twin- Waveguide (ATG) Technology: Part I-Concepts and Theory,” IEEE J. Select. Top. Quantum Electron., vol. 11, no. 1, pp. 17-29 (2005). 138.F. Xia, J. Wei, V. Menon, and S.R. Forrest, “Monolithic Integration of a Semiconductor Optical Amplifier and a High Bandwidth p-i-n Photodiode Using Asymmetric Twin- Waveguide Technology,” IEEE Photon. Technol. Lett., vol. 15, no. 3, pp. 452-454 (2003). 139.F. Xia, J.K. Thomson, M.R. Gokhale, P.V. Studenkov, J. Wei, W. Lin, and S.R. Forrest, “An Asymmetric Twin-Waveguide High-Bandwidth Photodiode Using a Lateral Taper Coupler,” IEEE Photon. Technol. Lett., vol. 13, no. 8, pp. 845-847 (2001). 140.H. Yamazaki, et. al., “ 1,3-|im Spot-Size-Converter Integrated Laser Diodes Fabricated by Narrow-Stripe Selective MOVPE,” IEEE J. Select. Top. Quantum Electron., vol. 3, no. 6, pp. 1392-1398 (1997). 141.X. Yan, M.L. Majsanovic, E.J. Skogen, D.J. Blumenthal, and L.A. Coldren, “Optical Mode Converter Integration With InP-InGaAsP Active and Passive Waveguides Using a Single Regrowth Process,” IEEE Photon. Technol. Lett., vol. 14, no. 9, pp. 1249-1251 (2002). 142.G.M. Yang, M.H. MacDougal, and P.D. Dapkus, “Ultralow threshold current vertical- cavity surface-emitting lasers obtained with selective oxidation,” Electron. Lett., vol. 31, pp. 886-888 (1995). 143. A. Yariv, P. Yeh, Optical Waves in Crystals: Propagation and Control o f Laser Radiation, Ch.6, John Wiley and Sons, New York (1984). 144.P. Yeh, Optical Waves in Layered Media, John Wiley and Sons, New York (1988). 145.D.B. Young, A. Kapila, J.W. Scott, V. Malhotra, and L.A. Coldren, “Reduced threshold vertical-cavity surface-emitting lasers,” Electron. Lett., vol. 30, no. 3, pp. 233-235 (1994). 146.D.B. Young, et al., “Enhanced performance of offset-gain high-barrier vertical-cavity surface-emitting lasers,” IEEE J. Quantum Electron, vol. 29, pp. 2013-2022 (1993). 147.D.B. Young, J.W. Scott, F.H. Peters, B.J. Thibeault, S.W. Corzine, M.G. Peters, S.L. Lee, L.A. Coldren, “High-power temperature-insensitive gain-offset InGaAs/GaAs vertical- cavity surface-emitting lasers,” IEEE Photon. Technol. Lett., vol. 5, no. 2, pp. 129-132 (1993). 212 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix A: Numerical Methods In VCSEL DBR design and in quantum well design two numerical algorithms were used to perform the calculations: 1) the propagation matrix method; and 2) the finite difference method. This appendix will describe the implementation of these two approaches. A l The propagation matrix algorithm A 1.1 Mathematical derivation The propagation matrix method (PMM) is a numerical technique that is, in general, used to solve systems of coupled differential equations. With regards to wave mechanics (specifically electromagnetic waves or Shrodinger particle wavefunctions), however, it has specific physically meaning with regards to transmission and reflection in periodic media. In periodic dielectric media (such as a DBR structure), the PMM can be used to solve for the reflection (or transmission) spectrum, as well as for cavity resonances and the electric field in a VCSEL cavity (see, for example, figures 2.6-2.8). Furthermore, the PMM can be used to solve for the bound states in a quantum well. The versatility and simplicity of the algorithm make it extremely useful for solving such problems, and will be outlined here [1], Figure A 1.1 below is a schematic depiction of a section of a DBR. The A and B coefficients represent the electric field amplitude of the forward and 213 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. backward traveling wave, respectively. For a TE-polarized wave the electric field can be written as: Ey =(A(z) + B{z))eim-k'x) (A 1.1) Equation A l.l is the sum of forward and backward electric field components. n. n 1 n2 n 3 <" o CM < "< a’2 a3 .... ----------- ^ B0 b ’0 B! B 1 b2 b 2 B3 .... Figure A l.l Schematic of a layered dielectric structure The field coefficients on either side of an interface are related through the boundary conditions, namely that Ex and Hy are continuous. This leads to the transmission matrix: D'2 = r hi 1 r 1 V 12 1 J (A1.2) Here ti2 and ri2 are the Fresnel transmission and reflection coefficients. These are given by: Ik . hi k + k Z 1 z2 z\ £ 2 _ k, + k y Z[ Z 2 (A1.3) (A 1.4) The transmission matrix relates the amplitude coefficients on either side of a dielectric interface. Now the amplitude coefficients on one end of a layer must be 214 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. related to the amplitude coefficients on the opposite end of the layer. This is done through a propagation matrix: Pa = ^ gikzn d a 0 0 (A1.5) Equation A 1.5 states that the field amplitude from one end of a layer to the other simply accumulates a phase change by propagating through the layer. The relation between incident field amplitude coefficients for adjacent layers can now be expressed as the multiplication of the transmission matrix and the propagation matrix. For a multilayer structure, the relation between the amplitude coefficients incident at the beginning of the structure to amplitude coefficients at the very end of the structure is given by the successive multiplication of the transmission and propagation matrices for each layer in the structure: B. M n M 12 B. \ M 2\ M 2 2 j (A1.6) (A1.7) i= i In calculating the reflectivity it is assumed that the wave is incident from the right. This yields boundary conditions of A0 =l and Bs=0. The reflectivity of the multilayer structure is then given by: R = V A Jb = o M 21 M, (Al .8) 215 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The successive matrix multiplications used in the PMM make it well suited to being solved with a computer. By discretizing the refractive index profile the reflectivity at a specific wavelength can be found. By sweeping the calculation over a range of wavelengths, the reflectivity spectrum can be found. If two DBR structures are included in the calculation with a cavity separating them, the resonant wavelength of the cavity can be solved for. Furthermore, the electric field in the cavity can be found by finding the field amplitude coefficients at each point in the dielectric structure and summing them. Examples of these calculations are given in figures 2.6-2.8. With regards to solving a quantum well problem, the essential features of the PMM are the same. The differences are purely cosmetic; instead of dielectric layers there are layers of varying potential energy and instead of an electromagnetic wave a particle has a Schrodinger wavefunction. In the quantum well case, there is a reflection or transmission in the particle wavefunction for a given energy barrier height. The transmission resonances yield the bound states in the quantum well, and the wavefunction can be found by summing the amplitude coefficients at each point in the energy profile (just like with the electric field in a dielectric cavity). A1.2 Sample Matlab code In this section a portion of Matlab code that was used to solve for the reflection and electric field of a VCSEL cavity is given. The code assumes that an appropriate refractive index profile has already been given. This section of code could be used as a subroutine where the refractive index profile is passed to it: 216 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. a / a / o / 0 / 0 / 0 / 0 / 0 / 0 / 0 / 0 / 0 / 0 / 0 / 0 / 0 / /© /o /o T o /o /o /o /o /o /o /o 7o /o /o 7o /o %calculate propagation matrix% %%%%%%%%%%%%%%%% i=sqrt(-1); M =eye(2); %initialize the matrix for m=1 :size(N ,2)-1 % setup up transm ission and propagation m atrices d (1 ,1 )=0.5*(1 +N(m+1 )/N(m)); d(1,2)=0.5*(1 -N(m+1 )/N(m)); d (2,1)= d (1,2); d(2,2)=d(1,1); p (1,1 )=exp(i*(2*pi*N(m+1 )/Lo)*h); p(1,2)=0; p(2,1)=0; p(2,2)=exp(-i*(2*pi*N(m+1)/Lo)*h); M=M*d*p; end r(j)=M(2,1)/M(1,1); field=[1 ;M(2,1 )/M (1,1)]; for m =1:size(N ,2)-1 d(1,1)=0.5*(1+N (m +1)/N (m )); d(1,2)=0.5*(1 -N(m+1 )/N(m)); d (2,1)= d (1,2); d(2,2)=d(1,1); p (1,1 )=exp(i*(2*pi*N(m+1 )/Lo)*h); p(1,2)=0; P(2,1)=0; p(2,2)=exp(-i*(2*pi*N(m+1)/Lo)*h); field=inv(d*p)*field; E(m)=real(field(1 )+field(2)); end O / O / O / O / O / O / O / O / O / O / O / O / O / O / 0 / O / 7 o 7 o / o /© / o 7 o / o / o / o 7 o / o / o 7 o 7 o / o / o A2 The finite difference algorithm A2.1 Mathematical derivation The finite difference method is a useful numerical method for solving second-order, partial differential equations. It can be applied to problems such as dielectric waveguides or quantum wells. The advantage to this approach over the PMM is that both the eigenvalues and eigenfunctions are obtained directly from the diagonalization of the secular equation. Considering the example of a quantum 217 %multiply successive m atrices together % calculate reflection coefficient % Caiculate initial field am plitude from reflection % solve for all other am plitude coefficients Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. well, the time-independent Schrodinger equation for a particle confined to a 1-D potential is given by [2]: ( n2 d 2 + V(x) y/(x) = Ey/(x) (A 1.9) 2 m dx The numerical solution to the above equation is obtained by first discretizing the potential, V(x), and the wavefunction, i|/(x). The first derivative of the discretized wavefunction in the finite-difference approximation is then: — y/(x) = ----- } — ------(A1.10) dx no Here h0 is the discretization step size in x. The second derivative is found from the second-order Taylor series expansion of the wavefunction [2, 3]: d 2 d - l y / i x d + y/ix^.) dx 1 h0 Substitution of equation Al.ll into A1.9 results in the matrix equation: Hi//(Xj) = -u\i/{xhl) + d] \i/{xj) - u h w (xj+ x') = Ey/ (x.) (A 1.12) Equation A 1.12 represents a symmetric, tri-diagonal Hamiltonian matrix where the diagonal elements are: d = h + V (A1.13) m h and the adjacent, off-diagonal elements are: Td 2 mh The Hamiltonian matrix can be expressed as a secular equation where: 218 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. o 0 s 1 S ' 1 1 1 ’ ¥x ’ — u2 (d, - E) -rq 0 ¥i e T)w = 0 - i q (d, - E) -u 4 ~aN_ [ (dA r_ j — E ) J ¥ N-x\ (A1.15) Here H is the Hamiltonian matrix and I is the identity matrix. The eigenfunctions and eigenvalues of equation A1.15 are found by diagonalizing the tri-diagonal matrix. Matlab is especially well suited for this due to it’s built in matrix functions. Equation A 1.15 can be solved for with an arbitrarily small step size (as long as the calculation time can be tolerated) and with an arbitrary potential profile. The finite difference method can also be used to calculate the eigenmodes and eigenfunctions of a dielectric waveguide (with appropriate substitutions) in either one or two dimensions. A2.2 Sample Matlab code In this section the routine for performing the finite difference calculation on a quantum well potential is given. Again, it is assumed that the potential profile has already been discretized and passed to this function, as well as an appropriate effective mass profile: %%%%%%%%%%%%%%%%%%% %%%%%%FD Routine%%%%%%% %%%%%%%%%%%%%%%%%%% % Calculation W indow N = size(V ,2)-1; % number of points ho=T/N; % step siz e num _sol=n; % number of solutions to look for 219 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. for i=2;size(x,2)-1 Dj(i-1 )=(V(i)*e)+c*((1/(m(i-1 )+m (i)))+(1/(m (i)+m (i+1)))); % diagonal matrix elem en ts end for i=2:size(x,2)-2 Uj(i-1)=-c*(1/(m(i+1)+m(i))); %off-diagonal matrix elem en ts end H=diag(Uj,1); % set up tri-diagonal matrix H =H+diag(Uj,-1); H=H+diag(Dj,0); %solve th e secu lar equation [phi,E]=eigs(H ,num _sol,'SM '); References 148.J.D. O ’brien, Electromagnetics fo r Semiconductor Photonics— Class Notes, pp. 452-458 (1999). 149.A.F.J. Levi, Applied Quantum Mechanics, Cambridge University Press, Cambridge, U.K. (2003). 150.L.A. Coldren and S.W. Corzine, Diode Lasers and Photonic Integrated Circuits, John Wiley and Sons, New York (1995). 220 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Appendix B: Device processing followers Table B l.l Top-emitting, SiNx-isolated VCSEL follower. Process Name Process Process Process Comments Description Action Parameters INring Contact • : .. . - . M S ; * , . Lithography Clean ICE. Ace. Melli. ( 'lean surface DI Rinse of organic Spin \/5214f«‘3krpm. eoiilaminants Spin 3 coalings bilge Wipe Swabs w/ aeelone Hake I20C InrdOsce. Expose H-rinn mask. Si lin.l Hake 120C for 1 miu. Mood Lxpo.se :7()m.l 1 Jcvelop A/.400K 1:4. 20sec. HR Doscuni RIE ()-. bOW. 20OmT. 30sec. M etal Evap HClill O 1:10 Hkec. Remove oxide li Dep 300A. 2A/see. l> l Dep 500A. 3A/see. An Dep 2->00.\. 5A/see. l.illnll Swabs w/ aeelone Mesa Etching SiNx Dep Clean Aee. Melli. DI I’IC V I) 40/20/M) 273C. 30W. 2(>min Lithography Spin HR 1X05 in 3krpin 1 dge Wipe Swabs w/ aeelone Bake 120C" lor 1 miu. 1 .xpose Trench mask. I50HI.I 1 )evelop MI-32 1. 45see. Inspeeiion No icsidue HR Desvum r ii; ().. b()W. dOOm l . 30see. SiNx Etch RIH. Lleli CL . m ow . IOO 111T. 1 111111. Inspeeiion No SiN\ residue PR Removal blood Exposure 'OOm.l Can NOT i Vvelop MI-32 1 . Inun-i-DI have any Inspection 1 .nsine 1 1 0 residue organic Cle.in Aee. Melli. DI residue! HR 1 tesouin RII-. ().. I20W. 1 V)mT. 2miii. DBR Etch I.CR Lie lung Run DBR.pic Stop etch 221 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. according to chart plotter Mellianol soak .... ' w m s s s m m Keep waler in Mieihanol until placed in oxidation lurnace Prevent self oxidation \\ eL0*xiriation ....................... Test oxidation Heat huhhler Ileal to SKC Ileal furnace Heat lo425C 1 low N. I el furnace siahili/e lor 1 hr. ( Kidaiion 'Omm Determine ( Kidaiion 45min Oxidation rate Main Oxidation Close off Observe Oxidation smallest mesa aperture w/ IR CCD Lapping Wax Mnuiiime ( 'heck thickness Suhslrale 1 .ap '1 Inn to 4.5 mils (.’lean TCI:. Aee. Melli Electroplate AuSn solution IDmA. l5-50sec. I )[ Rinse 1 min. Photoresist Bridge i . , . • • SiNx Removal Rll: l.leh c i :,. m ow . IDOmT. I min. SiNx Dep p e c y d 40/20/M) 275C. 'OW. lOuiin. Lithography Spin A/.4(i20(<' 5krpm Hake I20C. 2min 1 : xpose Bridge mask. lOiJniJ Develop A/.400K 1:4. 'inin. PR De.scum Rll-i ()■. 120W. |50inT. 2min. R'l A anneal '00C. 1 C/see. 30sec. mm -Pad Deposition Lithography Spin PR 1 x | it-- 5krpm Edge Wipe Swabs w/ aeelone Bake 1 20C for 1 min. Expose Ring opening mask. I50m.l Develop MF52I. 1 min-t-DI PR Descinn RIP. (K M)W. 200m l'. oOsee. SiNx Removal .. R1 1 ; l .leli Cl ,, m ow . lOiimT. lmin. PR Removal Mood 1 .xposure 300mJ 1 )e\elop Ml -121. Innn+DI 222 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Inspection Ensure no residue Glean Aee. Melli. 1)1 I’R Dcscum RIE ()-. I20W. 1 sOm 1 '. 2min. Metal Evap I’ .OE 1:10 dip lOsee. 1-1 )I rinse Ti deposition v)0A. 2A/see. An deposition 2000A. 5A/see. l.illolT Swabs w/ aeelone Anneal RTA anneal .GOG. aG/'sec. 3()sc. Table B 1.2 SOA/EAM/SSC process follower. Process Name Process Description Process Action Process Parameters Comments SAG Stripe I.itho • ' SiNx Dep Glean Aee. Melli. DI 11-0 I’l.GYI) ■ l;)/2(>/(i(> 275C, a lW. lOmin SiNx should be a blue- green color Lithography Spin PR 1 SOsfa akrpm Edge Wipe Swabs w/ acetone Hake l20C loi Imin. Expose S \(i Mask, 15(lni.l Align stripes to [110] direction 1 )e\elop MI G 1 . 1 min, DI Inspeeiion Ensure no residue I’R Descum RIE ().. (>OW , 200nfl. aOsec. SiNx Etch HOI: 1:10 dip ainin Observe color Inspeeiion ( ihser\e undercut PR Removal M ood Exposure 400m.l 1 )e\elop M IG 1. 1 niin+DI Inspeeiion I 'nsiiie no residue C lean \ee. Melli 1 )1 Rinse 1 min under riinnmc 1 )I water l’R Deseum ■ ■ 1 Rll. (K I20W, I50iiiT. 5 min. Pre-Growth Glean Acid Cleaning lLSOplTOel-LO v 1:1. tOsec, 27C DI Rinse (in m lh Room DI 2lu s undei Flush in same iimnme DI water beaker MOCVD............ Rinse C irow Epi-layers ll’A rinse. N2 dry 223 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. SiNx Dep Clean Acc, Meth, DI h 2 o p e c y d 40/20/60 275C, 30W, 30min Lithography Spin PR 1X1 3@5krpm Edge Wipe Swahs w/ acetone Bake I20C lor 2min. Expose 1 ■ .due head mask, OOni.l 1 Jevelop M F32I, lmin, DI 1 '.\pose 2um taper mask, 200mJ 1 )e\elop MF32I, 45sec. DI Rinse 1 inn under i mining DI H20 Inspection ( ihsei ve smooth p.niei ns PR Dcseum RII (),, 60W, loOmT, 30sec SiNx Etch RIE llleli Cl . I00W, 1 ^f>mT, 2min. Inspection 1 iisiuv no SiNx residue PR Removal Elood Exposure 3()()m.l Develop M E'21, lmin+DI Can NOT have any organic residue! Inspeeiion I nsure no residue Clean Aee. Meth, DI I’R Deseuni RII.O-, 120W, l5()mT, 2min. 1 )ekiak S.Nx iliickness ■ KiooA Record SiNx thickness. InGaAsP Etch ICP Etch M (AY. set -2:15 Stop etch according to chart plotter. Dekink Mesa height - 1 ,5pm Record etch time. SiNx Dep I T C Y D IO'2O/60, 275C, '0W. lOmin. Record SiNx color on top of mesa. ^ ^ , N ' Lithography Spin S 1 s 1 (<§>3krpm Swahs w/ acetone Bake 1 20C lor 2min. Expose S' ).\-Mask, 200H 1.I D e \e lo p M E'21 lmin+DI Inspeeiion ( iood litho PR Deseuni RIEO ., 60W, 224 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 200mT, 30sec. SiNx Etch HOE 1:10 dip -2:30 Record color 1 n-.pociinn Total removal PR Removal Flood Exposure 300mJ Develop MF321 lmin+DI ( 'lean Ace, Meth, DI PR Duscum RIE 0 2, 120W, 150mT, lmin. 1 lekluk Record SiNx thickness InGaAsP Etch ICP MQW. set ~45sec. Etch about 3500A 1 )ektak Mesa ~ 1.8pm Record mesa height SiNx Etch 151)1: 1:10 clip lOmin Remove all SiNx SiNx Dep PECVD 40/20/60, 275C, 30W, lOmin Deposit fresh SiNx Passive Mesa Elch " .? , > : Lithography Spin S1813@2.5krpm Edge Wipe Swabs w/ acetone Bake 120C for 2min. Expose 6pm stripe mask, 200mJ Develop MF321 lmin+DI Inspeeiion Good litho PR 1 )e sen m RIE 0 2, 60W, 200mT, 30sec. SiNx Etch RIE hi eh CF4, 200W, 150mT, 2min. Inspection Ensure no SiNx residue PR Removal blood Exposure 300mJ Develop MF321 lmin+DI ( lean Ace, Meth, DI PR De'cum R IE 0 2, 120W, 150mT, lmin. InP Etch 1 lt'l:l 1 f ) 3:1, ~10sec. +DI I lekiak Record PG Height SiNx Etch BOI: 1:10 dip 5min SiNx Dep PECVD 40/20/60, 275C, 30W, lOmin l*ul\iniiiii- ■ iiinu Lithography Spin PI2737@2.5krpm Soli Hake 60C-3min 90C-3min Expose 1 pm stripe mask, 150mJ Must have excellent contact 225 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Develop DE9040, lOsec. Agitate Rinse RI9180, 30sec. Inspeeiion Observe clean openings Polyimide l’ol\ imide Own 100C to 350C Ramp Curing @10C/min I’okim ide Oven 30min@350C Cure Residue Descuin 0 2, 100W, 200mT, 30sec. P-IIK't.d Cnlllael , . Lithography Spin AZ5214@3krpm Spin 3 coatings Edge Wipe Swabs w/ acetone liake 120C for 30sec. Expose P-contact mask, 80mJ Hake 120C for lm in 1 lood I .\pose 270mJ 1 )e\elop AZ400K 1:4 25- 30sec. DI Rinse lmin Inspeeiion Complete development I’R Dcsciun RIE 0 2, 60W, 200mT, 30sec. SiNx Etch RIE 1 :1 ell CF4, 200W, 150mT, 2min. HOF l:ld Dip 15 sec. Metal Evap 11 Dep 500A, 1 A/sec. I’l Dep 500A, 3A/sec. \u Dep 1000A, 3A/sec. Liftoff Aee \v/ swah Isolation Trenches Lithography Spin PR1813<ff5krpm Edge Wipe Swabs w/ acetone Hake 120C for 2min. Expose Trench mask, 200mJ Develop MF321, lmin, DI DI Rinse lmin. Inspection Complete development I’R 1 icscinn RIE 0 2, 60W, 200mT, 30sec. SiNx Etch RIE. I.ieh CF4, 200W, 150mT, 2min. InGaAs Etch 1 1 ■SO,:IIiO':l l.() 1:1:3, lOsec +DI Cool to 27C InP Etch IICIdLO 1:1, lOsec+DI PR Removal Clean V e. Meth, DI 226 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Lithography Spin AZ4620@4krpm Hake 120C for 30sec. 1 A p o s c P-pad mask, 400mJ 1 >C\dop AZ400K 1:4 3min. 1)1 R iiinc lmin Inspeeiion Complete development PR Deseuni RIE 0 2 ) 100W, 200mT, 30sec. Metal Evap 1 1 Dep 500A, lA/sec. \ll 1 )cp 1000A, 2.5A/sec. Electroplating s. Lithography Spin S1813@5krpm Hake 120C for lmin. Expose Electroplate mask, 250mJ 1 )evelop MF321, lmin. DI Rinse lmin Inspeeiion No residue I’R Deseuni RIE 0 2, 100W, 200mT, 30sec. Backside Isolation Spin S1813@5krpm Hake 120C for lmin. Electroplate 1’ure An Solution 65C, 3.23mA for lOmin. i.iiioir Ace w/ swabs N-Contact Deposition ■ a - . - ........... Lapping W ax Mounting Check thickness .Sulislinie 1 ap Thin to 4.5 mils Clean TCE, Ace, Meth Metal Evap A ntic Dep 1000A, 4A/sec. Ni Dep 500A, 3A/sec. An Dep 2000A, 5A/sec. Anneal RTA 435C, 1 C/sec, 30sec. ('leaving Scribing Mouni to Sticks Tape to glass I'ah slide Scribing Use diamond- tipped scriber breaking Remove from tab with vacuum tweezers. Use roller bar to break 227 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table B 1.3 InP BA laser process follower. Process Name Process Process Process Comments Description Action Parameters Mesa Etch Lithography Clean Ace. Melli. DI rinse Clean surface of organic Spin M S I 30' 5kipm contaminants Edge Wipe Six ahs \\7 aeelone Hake 120C lor 1 min Expose lOum ireneh mask. 15( )ni.l Pattern should be 60pm Shift Shill mask laicrullx In 70um stripe with 10pm Expose I5nm.l openings on D exelop M E C | I5seei-Dl either side PR Deseuni RIE. ().. m o w . 2()0mT, 50sce. InGaAs Etch H 'S O plI -O.iH-O 1:1:5. -5 see. Cool to 27C InP Etch IICEILO E l. - 15see. Rinse Runnimi DI PR Removal Clean Aee. Meth. DI I’R Deseuni R I E O .. I20W. 150m 1. 1 min. SiNx Dep P E C V D 40/20/60, 275C, 5()W. lOmin. Lithography Spin A / 5 2 141“ ^kipm Spin 5 coalings Edge Wipe Swabs \\7 aeelone Hake 1201 lor lOsee. Expose 50pm stripe mask. S(>iii.( Hake l2 0 C I 6 i limn Elood Expose 2’Mm.l Dexelop A / 4 0 0 K 1:4 25- 'Osee. DI Rinse 1 min Inspeeiion ( ’.miplele tlexelopmenl PR Deseuni RIE ().. 6 0 W. 200m l'. 50see. RIE. Elcli CE,. 20OW. 1 5()mT. 2mm. Metal Evap HUE EH) Dip 15 see. Ti Deposition 5(K)A. 2A/see. Pi Deposition S )0A . 3A/see. An Deposition 2u0O.\. 5 A/see. l.illoll Aee \ x ' sxxah V ( niitai'l D eposition 228 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Lapping Wax Minimim.' Check thickness Suhsiraie Lap Thin it' 1.5 mils <"lean TCI-:. Aee. Melli Metal Evap A ntic Dep 11)1 IDA. 4 A/see. Ni Dep 500A . .'A/see. All Dep 201 K)\. 5 A/sec. Anneal RTA 435C, 1 C/sec, .'Osee. Scribing Mount lo Siiekv 1 ape lo glass lab -lule Scribing I sc ili.nnoml- inpeil scribcr llieakmg R em ove Irom lab uilli \aeiimn Ivtee/eis. Lso rollei bar lo break 229 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

Asset Metadata

Creator Stevenson, Ryan Allan (author)

Core Title High performance components of free -space optical and fiber -optic communications systems

Contributor Digitized by ProQuest (provenance)

School Graduate School

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, electronics and electrical,OAI-PMH Harvest

Language English

Advisor Dapkus, P. Daniel (committee chair), O'Brien, John (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-458539

Unique identifier UC11336382

Identifier 3196898.pdf (filename),usctheses-c16-458539 (legacy record id)

Legacy Identifier 3196898.pdf

Dmrecord 458539

Document Type Dissertation

Rights Stevenson, Ryan Allan

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA