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Annealing Effect And Silicon-Site Distribution In Silicon-Doped Gallium-Arsenide

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Annealing Effect And Silicon-Site Distribution In Silicon-Doped Gallium-Arsenide

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Content ANNEALING E F F E C T AND S i-S IT E DISTRIBUTION IN S i-D O P E D GALLIUM ARSENIDE by Je n Kai Kung A D is s e rta tio n P r e s e n te d to the FA C U LTY OF TH E GRADUATE SCHOOL UNIVERSITY O F SOUTHERN CALIFORNIA In P a r ti a l F u lfillm e n t of the R e q u ire m e n ts fo r the D eg ree DOCTOR OF PHILOSO PHY (M a te ria ls Science) A u g u st 1973 INFORMATION TO USERS This material was produced from a microfilm copy of the original document. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the original submitted. The following explanation of techniques is provided to help you understand markings or patterns which may appear on this reproduction. 1. The sign or “target" for pages apparently lacking from the document photographed is “Missing Page(s)". If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting thru an image and duplicating adjacent pages to insure you complete continuity. 2. When an image on the film is obliterated with a large round black mark, it is an indication that the photographer suspected that the copy may have moved during exposure and thus cause a blurred image. You will find a good image of the page in the adjacent frame. 3. When a map, drawing or chart, etc., was part of the material being photographed the photographer followed a definite method in “sectioning" the material. It is customary to begin photoing at the upper left hand corner of a large sheet and to continue photoing from left to right in equal sections with a small overlap. If necessary, sectioning is continued again — beginning below the first row and continuing on until complete. 4. The majority of users indicate that the textual content is of greatest value, however, a somewhat higher quality reproduction could be made from “photographs" if essential to the understanding of the dissertation. Silver prints of "photographs" may be ordered at additional charge by writing the Order Department, giving the catalog number, title, author and specific pages you wish reproduced. 5. PLEASE NOTE: Some pages may have indistinct print. Filmed as received. Xerox University Microfilms 300 North Zeeb Road Ann Arbor, Michigan 48106 i. I 1 . 1 I 74-5868 I , KUNG, Jen Kai, 1941- { ANNEALING EFFECT AND SI-SITE DISTRIBUTION IN I SI-DOPED GALLIUM ARSENIDE. I \ University of Southern California, Ph.D., 1973 | Physics, solid state , University Microfilms, A X E R O X Company, Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED. UNIVERSITY O F SO U TH ERN CALIFORNIA TH E GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFORNIA 9 0 0 0 7 This dissertation, written by under the direction of his..... Dissertation Com mittee, and approved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillment of requirements of the degree of D O CTO R OF P H IL O SO P H Y J e n Kai Kung ? V n ^ f o < f - Dean Date August 1?73 DISSERTATION COMMITTEE Chairman A C K N O W LED G EM EN TS The au th o r is deeply g ra te fu l to P r o f e s s o r W. G. S p itz er for the guidance, invaluable ad v ice, e n c o u ra g e m e n t and helpful c r itic is m w hich he p ro v id e d throughout the c o u rs e of this p ro je c t. The c r itic a l read in g of the m a n u s c r ip t by P r o f e s s o r s J. M. W helan and M. H. H allo ra n is a p p re c ia te d . The au th o r w ish es to e x p re s s his thanks and a p p re c ia tio n to his wife, A gnes, fo r h e r a s s is ta n c e in p re p a rin g the in itia l m a n u s c rip t and fo r h e r u n d erstan d in g , p a tie n c e and e n c o u ra g e m e n t during the c o u rs e of this study. In this r e s p e c t, the au th o r is a lso g ra te fu l to his p a re n ts and fam ily. The au th o r should like to extend his s in c e re thanks to W. P . A llre d for p ro v id in g the advice and guidance in grow ing the GaAs c ry s ta ls u sed in th is w ork. The te c h n ic a l a s s is ta n c e of G. M u eller and J . E m e rs o n is a lso a p p re c ia te d . T he au th o r w ish e s to thank P r o f e s s o r s M. G ersh en zo n and W. H. S te ie r and th e ir students fo r using th e ir eq u ip m en t in doing the p h o to lu m in e sc en ce m e a s u re m e n t, and to P r o f e s s o r W. R. W ilcox fo r using his c r y s ta l grow th fa c ilitie s . T hanks a r e also due to A. K ahan, F . E u le r and L . B ou th illette of the A ir F o rc e C am b rid g e R e s e a r c h L a b o ra to rie s for doing the e le c tro n i r r a d i a tion; to D r. G. H. Schw uttke and K. B ra c k of IBM E a s t F is h k ill F a c ility fo r looking a t so m e of the s a m p le s w ith th e ir e le c tro n m ic ro s c o p e , to D r. M. E . L ev y and D. L . Howland for p re p a rin g the fig u res in this d is s e rta tio n ; and to V. G e ssfo rd fo r typing the d ra ft copy and the final copy of th is d is s e rta tio n . T his r e s e a r c h w o rk w as p a r tia lly su p p o rted by the N ational S cience F oundation r e s e a r c h c o n tra c t G K -25144 and by the Jo in t S e rv ic e s E le c tro n ic s P r o g r a m th ro u g h the A ir F o rc e Office of S cientific R e s e a rc h /A F S C under c o n tra c t F4462 0 -7 1 -C - 0067. F o r this s u p p o rt the au th o r is v e ry a p p re c ia tiv e . The au th o r is a lso g ra te fu l to the U n iv e rs ity fo r the opp o rtu n ity to do this r e s e a r c h . iii T A B L E O F C O N T EN TS P a g e A CK N O W LED G EM EN TS........................................................................................... ii LIST O F ILLU STR A TIO N S................................................................................... viii LIST O F T A B L E S .......................................................................................................x ii I. INTRODU CTIO N ................................................................................................ 1 II. CRYSTAL GROWTH...................................................................................... 5 II— I. H o rizo n ta l B rid g m a n T e c h n iq u e ................................................... 5 II-II. C z o c h ra lsk i T e c h n iq u e ...................................................................... 9 'II-III. F u rn a c e C o n s tru c tio n ........................................................................ 14 III. E X PE R IM E N T A L TECHNIQUE AND BACKGROUND 18 III-I. In tro d u c tio n .............................................................................................. 18 111-II. Sam ple P r e p a r a t io n ....................................................................... 18 A. Cutting fro m C ry s ta l In g o t................................................. 18 B. Sam ple S urface P o lish in g ...................................................... 19 C. T echniques fo r F r e e C a r r i e r C o m p e n sa tio n ................................................................................ 20 III-III. M e a s u re m e n t T e c h n iq u e .................................................................. 25 A. H all E ffec t-an d R e s is tiv ity M e a s u re m e n t . . . . . . 25 B. In fra re d S p e c tr o m e te r ............................................................. 26 C. In fra re d R efle c tiv ity M e a s u re m e n t ............................. 28 D. In fra re d T ra n s m is s io n M e a s u r e m e n t.......................... 29 E. P h o to lu m in esce n ce M e a s u re m e n t . ............................... 30 T A B L E O F C O N T E N T S (C ontinued) P ag e III-IV. B a c k g ro u n d ............................................................................................. 32 A. L o c a liz e d V ib ratio n al Mode M e a s u r e m e n t............. 33 B. Si-D oped G a A s......................................................................... 37 C. A nnealing E ffect of T e llu riu m -D o p e d G allium A r s e n id e .................................................................... 49 D. L a ttic e V acan cies G en eratio n Due to A nnealing of n -T y p e G a A s ............................................. 51 IV. IN FRA RED R E F L E C T IV IT Y M EA SU REM EN T AND F R E E CARRIER ABSORPTIO N O F N -T Y P E G aA s...................................................................................................................... 55 IV -I. In tro d u c tio n ............................................................................................ 55 IV -II. T h e o ry ....................................................................................................... 61 A. G e n e ra l E le c tro m a g n e tic T h e o ry B a c k g ro u n d ................................................................................... 61 B. D ru d e -Z e n e r T h e o r y ............................................................. 67 IV -III. M e a s u re m e n t T e c h n iq u e ................................................................. 70 IV -IV . D is c u s s io n ......................................................................................... 71 A. D eep R e fle c tiv ity M in im u m ............................................. 72 B. Shallow R eflectiv ity M in im u m -C la s s ic a l D ru d e -Z e n e r M o d e l ............................................................. 72 C. C o m p a riso n of D ru d e -Z e n e r C la s s ic a l E x p re s s io n W ith E x p e rim e n ta l R esu lts fo r n -ty p e G a A s ....................................................................... 76 D. C alcu latio n w ith M odified F r e e C a r r i e r D is p e rs io n R elatio n s B ased on P r e s e n t M e a s u r e m e n ts ............................................................................ 90 V ANNEALING STUDY O F Si-D O P E D G a A s . . . ........................... 101 V -I. In tro d u c tio n ............................................................................................. 101 v T A B L E O F C O N T E N T S (C ontinued) P ag e V-II. E x p e rim e n ta l M e th o d s ........................................................................ 104 A. A nnealing P r o c e d u r e ............................................................ 104 B. C a r r i e r C o n cen tratio n M e a s u r e m e n t...................... 107 C. P h o to lu m in e sc e n c e M e a s u r e m e n t...................................108 D. L o c a liz e d V ib ratio n al Mode M e a s u r e m e n t . 108 E. S u m m a ry of M e a s u r e m e n t s .......................................... I l l V-III. E x p e rim e n ta l R e s u lts ...................................................................... I l l A. Iso c h ro n a l A nnealing R e s u l t s ........................................ 112 B. Is o th e rm a l A nnealing R e s u l t s ........................................ 115 C. S u m m a ry of the E x p e rim e n ta l R e s u l t s ...................... 132 V -IV . G e n e ra l D is c u s s io n ...................................... 134 A. G e n e ra l A ssu m p tio n s and P re v io u s ly E s ta b lis h e d F a c t s .................................................................... 134 B. C a r r i e r C o n cen tratio n and Its R elatio n sh ip to D efect C o n c e n tra tio n fro m LVM M e a s u r e m e n t ................................................................................ 137 C. P ro p o s e d M odel fo r the A nnealing E f f e c t ...............140 D. D isc u s sio n of P h o to lu m in e sc e n c e M e a s u re m e n t R e s u l t ............................................................. 142 E. C o m p en satio n O b se rv e d By F r e e C a r r ie r A b so rp tio n and LVM M e a s u r e m e n t s ............................145 F . P o s s ib le O rig in of Changes in C o n cen tratio n s of S i- D e f e c ts ..............................................146 G. A d equacy of 1100°C/15 m in A nneal As S tartin g C o n d itio n ......................................................................154 V-V. C o n c lu s io n .............................................................................................. 155 v i T A B L E O F C O N T E N T S (C ontinued) P age VI. GaAs DOPED WITH Si AND SECOND D O P A N T .................. 157 V I-I. In tr o d u c tio n ......................................................................................... 157 VI-II. B ackground ............................................................................................ 157 VI-III. E x p e rim e n ta l R e su lts and D is c u s sio n ................................. 158 VI-IV. C o n c lu sio n ............................................................................................ 182 A PPE N D IX I. IN FL U E N C E O F R E F L E C T IV IT Y C O E FFIC IE N T IN CA LCULATING A BSORPTION C O E F F IC IE N T ...................................... 184 A PPE N D IX II. LITHIUM DIFFUSION O F S i-D O P E D GaAs AT T E M P E R A T U R E S BELOW 600°C ............................................................................. 188 L IT E R A T U R E C IT E D .......................................................................................... 196 v ii L IST O F IL L U ST R A T IO N S F ig u re N o. P a g e I I - 1 H o rizo n ta l B rid g m a n g alliu m a rs e n id e g ro w e r.................................................................................................... 7 II-2 T e m p e ra tu re p ro file of the h o riz o n ta l B rid g m a n fu rn a c e ........................................................................... 10 I I - 3 C z o c h ra lsk i liquid s e a l g alliu m a rs e n id e g ro w e r.................................................................................................... 12 / II-4 C ro s s se c tio n d ia g ra m of an annealing fu r n a c e .................................................................................................... 15 I I I - 1 C o m p a riso n of a b s o rp tio n s p e c tr a betw een two G aA s:Si s a m p le s c o m p e n sa te d by ?L i diffusion and 1 M eV e le c tr o n ir r a d ia tio n re s p e c tiv e ly . (A fter S p itz e r et al. 1969)........................ 24 III-2 S ch em atic d ia g ra m of a sa m p le fo r H all effect and r e s is tiv ity m e a s u r e m e n t s ................................ 27 III-3 S ch em atic d ia g ra m of p h o to lu m en scen c e m e a s u r e m e n t...................................................................................... 31 IV-1 R e fle c tiv ity s p e c tr a of four GaAs sa m p le s (A fter S p itz e r and W helan 1959)......................................... 58 IV-2 C a lib ra tio n cu rv e of c a r r i e r c o n c e n tra tio n v e rs u s the fre q u e n c y (and w avelength) of p la s m a edge re fle c tiv ity m in im u m of n -ty p e G aA s. (A fter O kada and Oku 1967)................................ 59 IV -3 R e fle c tiv ity s p e c tra of five G aA stSi s a m p le s ............. 60 IV -4 S ch em atic d ia g ra m of light b e a m p a s sin g th ro u g h an a b so rb in g m e d ia w ith th ic k n e ss d 64 IV -5 R efle c tiv ity as a function of w ith ^ = 1.................. 73 v iii L IST O F ILL U ST R A T IO N S (C ontinued) F ig u re No. P ag e V IV-6 - as a function of R b a s e d on V m m equations (4-46) and (4-47)................................................... 75 IV -7 F re q u e n c y dependence of extin ctio n co efficien t k of five G aA s:Si s a m p le s .............................. 78 IV-8 A b so rp tio n co efficien t a t v =1250 cm ^ as a function of c a r r i e r c o n c e n tra tio n of elev en GaAs s a m p le s .................................................................. 80 IV -9 F re q u e n c y dependence of five GaAs s a m p le s ................................................................................................. 86 I V -10 F re q u e n c y dependence of extin ctio n co efficien t of S am ples No. 5 and 6 of T able IV -II......................................................................................... 88 I V -11 F re q u e n c y dependence of nk of S am ples No. 5 and 6 of T able IV -II.................................................... 89 I V -12 F re q u e n c y dependence of e„, -e i fro m S am ples No. 1, 5 and 6 of T able IV -II....................... 91 - : V IV - 13 — 2 - as a function of R b a s e d on V m m equations (4-46) and (4 -5 4 )..................................................... 96 V - l R oom te m p e ra tu re c a r r i e r c o n c e n tra tio n ne> of heavily doped G aA s:Si and G aA s:T e sa m p le s a fte r e a c h is o c h ro n a l annealing s ta g e ....................................................................................................... 114 V-2 R oom te m p e ra tu re c a r r i e r c o n c e n tra tio n of a lig h tly S i-doped GaAs sam p le a f te r e a c h is o c h ro n a l annealing s ta g e ...................................................... 116 V -3 R oom te m p e ra tu re c a r r i e r c o n c e n tra tio n , n , d u rin g is o th e r m a l annealing of th re e heavily S i-doped GaAs sa m p le s a t 400, 600 and 750° C re s p e c tiv e ly ............................... 117 ix L IST O F ILL U ST R A T IO N S (C ontinued) F ig u re No. P ag e V -4 P e r c e n t re fle c tiv ity m e a s u re d a t ro o m te m p e r a tu r e as a function of freq u en cy , V, of the 600°C is o th e rm a lly annealed sa m p le in F ig . V -3 ..................................................................... 119 V -5 A b so rp tio n s p e c tra a t 77°K of two h eavily S i-doped GaAs sa m p le s w hich a r e a n n ea led a t 11 00°C /15 m in and 400°C/1178 h r re s p e c tiv e ly and co m p e n sa te d by 1 MeV e le c tro n ir r a d ia tio n ...................................................................... 123 V-6 A b so rp tio n s p e c tra at 77°K of two heavily S i-doped GaAs sa m p le s w hich a r e a n n ea led a t 1100°C/15 m in and 600°C/290. 5 h r re s p e c tiv e ly and co m p en sa ted by 1 M eV e le c tro n ir r a d ia tio n ...................................................................... 124 V -7 A b so rp tio n s p e c tra at 77°K of two h eavily S i-doped GaAs s a m p le s w hich a r e an n ea led a t 110 0 °C /15 m in and 750°C /320 hr re s p e c tiv e ly and co m p en sa ted by 1 M eV e le c tro n ir r a d i a ti o n ......................................................................... 125 V -b N o rm a liz e d in te g ra te d a b so rp tio n s tre n g th of th re e Si LVM bands a t 384 c m '^ , 393 c m " l , and 399 c m - - * - fro m fo u r h eav ily S i-doped GaAs s a m p le s w ith d iffe re n t an nealing h i s t o r i e s ........................................................................ 129 V -9 P h o to lu m in e sc e n c e s p e c tra a t 4. 2°K of four heavily S i-doped GaAs sa m p le s w ith d iffe re n t an n eal co n d itio n s...................................................... 130 V -10 F r e e c a r r i e r c o n ce n tratio n v e rs u s the d iffere n ce of in te g ra te d a b s o rp tio n stre n g th s betw een the 384 cm -1 and the 399 c m LVM b an d s of eig h t heavily S i-doped GaA s sa m p le s w ith d iffere n t an n ea l c o n d itio n s........................................... 1^9 V - l l R ad iativ e reco m b in atio n aicheme of h eavily S i-doped n -ty p e G aA s................................................................. 143 V-12 A b so rp tio n s p e c tra at 77°K of two S i-doped GaAs s a m p le s w hich a r e co m p e n sa te d by 1 MeV e le c tro n ir r a d ia tio n ..................................................... 147 x LIST O F IL L U ST R A T IO N S (C ontinued) F ig u re V I-1 VI-2 V I-3 VI-4 V I-5 VI-6 VI-7 No. P ag e A b so rp tio n s p e c tra a t 77°K of sa m p le s fro m ingots 1 and 2 of T ab le V I-II.................................. 162 P e a k a b so rp tio n co efficien t of the 384 cm " band v e rs u s th a t for the 399 c m - 1 b a n d ................................................................................ 163 A b so rp tio n s p e c tra of S i- and T e -d o p e d GaAs s a m p le s fro m ingots 3 and 4 of T ab le V I-II................................................................................. 165 A b so rp tio n s p e c tr a of Si- and Z n -d o p ed GaAs s a m p le s fro m ingots 6 and 7 of T ab le V I-II......................................................................................166 C o m p a riso n of the a b s o rp tio n s p e c tr a of &Li and ^ L i diffused sa m p le s fro m ingots 6 and 7 of T able V I-II............................................... 167 The ra tio of Si donor to Si a c c e p to r c o n c e n tra tio n s , Nj-j(Si)/N^(Si), a s a function of the F e r m i lev el e n e rg y in G aA s............................................................................ 177 The ra tio of Si donor to Si a c c e p to r c o n c e n tra tio n s , N ^ (S i)/N ^ (S i) , a s a function of the second dopant c o n c e n tra tio n in G a A s................................................................................................. 179 xx L IST O F T A B L E S T ab le No. P a g e III-1 M ajo r L o c a liz e d V ib ratio n al M ode of 28 GaAs: Si C o m p e n sa ted by L i o r C u ............................... 41 III-II S u m m a ry of A nnealing E ffects O b se rv ed in G a A s......................................................................... 53 IV -I S u m m a ry of A nnealing Condition and C a r r i e r C o n c e n tra tio n .......................................................... 79 IV -II R esu lts of R eflectiv ity M e a s u re m e n t - and C o m p a riso n of C alculated F r e e C a r r ie r E ffective M a ss w ith P re v io u s ly R ep o rted V a lu e ................................................................................ 85 IV -III R elatio n sh ip of P la s m a Edge R eflectiv ity M inim um Value and Its F re q u e n c y -A C o m p a riso n am ong C la ss ic a l, and Two E m p iric a l F r e e C a r r i e r A b so rp tio n E x p r e s s i o n s ........................................................................................ 98 IV -IV C o m p a riso n of C a r r i e r C o n cen tratio n D e te rm in e d fro m P la s m a Edge R eflectiv ity M e a s u re m e n t (C o rre c te d and U n c o rre c te d ) w ith th a t fro m H all E ffec t M e a s u r e m e n t..........................99 V -I M ass S p e c tro g ra p h ic A n aly sis of G a A s ........................ 113 V -II C o m p a riso n of F r e e C a r r i e r C o n cen tratio n V alues O btained fro m H all E ffect and In fra re d R e fle c tiv ity M e a s u r e m e n ts ................................. 120 V -III E le c tro n Irra d ia tio n F lu en c e U sed in O btaining E le c tr ic a l C o m p e n sa tio n ................................... 122 V -IV L is t of the In te g ra te d A b so rp tio n Band S tren g th of Si L o c a liz e d V ib ratio n al M o d e s ..................127 V -V L is t of L o c a liz e d V ib ratio n al M odes F r o m G aA s:Si C o m p en sated by 1 M eV E le c tro n I r r a d ia tio n .......................................................................................... 136 x ii LIST O F T A B L E S (C ontinued) T a b le N o. P a g e V I-I P e a k P o sitio n s of the L i- Z n and L i- T e LVM B an d s......................................................................... 159 V I-II L is t of D opants and Doping C o n cen tratio n s of GaAs C ry s ta l In g o ts .................................................................................................... 16 0 V I-III L is t of P e a k A b so rp tio n C oefficients (L ess B ackground) of T h re e Si LVM Bands and F r e e C a r r ie r C o n c e n tra tio n s ...........................172 V I-IV L is t of Si D onor to A c c e p to r C o n cen tratio n ND (Si) R atio ^ —(SiT an(^ Second Dopant A C o n cen tratio n in G a A s ................................................................ 180 A I-I A b so rp tio n C oefficient (a) C alcu lated F r o m R efle c tiv ity (R) and T ra n s m is s io n (T) C o e ffic ie n ts.............................................................................. 186 AI1-I L is t of L i D iffusion Condition and the F r e e C a r r i e r C o n cen tratio n B efo re and A fter The L i D iffusion P r o c e s s ............................................. 191 A II-II L is t of P e a k A b so rp tio n C oefficients (L ess B ackground) of LVM Bands in G aA s:Si A fter E le c tro n Irra d ia tio n - C o m p e n sa tio n ................................................................................... 193 C H A P T E R I INTRODUCTION The e x p e rim e n ta l w o rk p re s e n te d in this d is s e r ta tio n is a d etaile d study of so m e p ro p e rtie s of silic o n doped GaAs. M o st of the effects studied a r e re la te d to the a m p h o te ric n a tu re of Si as an im p u rity in G aA s. The effects o b s e rv e d and studied h e re include (1) a m a jo r change in both the e le c tr ic a l and in f r a r e d o p tical p ro p e rtie s of heavily S i-doped GaAs w hen the m a te r ia l is an n ealed at te m p e ra tu re s as low as 4 0 0 °C and (2) the ro le of o th e r e le c tric a lly activ e dopants in changing the Si site d is trib u - . tion in G aA s:Si. In the f i r s t study, the an n ea lin g -in d u ced changes in the c a r r i e r co n ce n tratio n , fre e c a r r i e r a b so rp tio n , in f r a r e d refle ctiv ity , lo c a liz e d v ib ra tio n a l m o d e s, and p h o to lu m i n e sc e n c e w e re m e a su re d , c o m p a re d , and used to deduce a m o d el for the b e h a v io r of the m a te r ia l. The second study d e m o n s tra te s th a t the re la tiv e c o n c e n tra tio n s of Si w hich is su b stitu tio n a l on e a c h of the two p o ssib le s u b -la ttic e s can be s u b sta n tia lly a lte r e d b y the p re s e n c e of o th e r donors o r a c c e p to rs . T he n -ty p e GaAs m a te r ia l is fre q u e n tly used to m a k e p - n junction in jectio n l a s e r d ev ices. D uring fa b ric a tio n of the device, the m a te r ia l is u su ally heated to an e le v a te d te m p e ra tu re and th u s, any an nealing effect can b e c o m e im p o rta n t in the p r o c e s s . 1 2 M o re o v e r, during o p e ra tio n of the in jectio n l a s e r s m ade of GaAs, d eg rad atio n effects a r e so m e tim e s o b se rv e d (K re s s e l and B y e r 1969), and the d eg rad a tio n w as found to be p ro p o rtio n a l to the injection c u rre n t density, w hich w ould in tu rn ca u se the junction te m p e ra tu re to in c re a s e . Thus the d e g ra d a tio n m a y be also re la te d to an annealing effect. In addition the an nealing effect is an in te re s tin g su b ject to in v e stig ate in te rm s of the fo rm a tio n and d istrib u tio n of im p u ritie s and la ttic e defects in the m a te ria l. Of p a rtic u la r in t e r e s t h e re is the an nealing effect in S i-doped GaAs w hich has not b een p re v io u sly re p o rte d in the lite r a tu r e . The o b s e rv a tio n in this d is s e rta tio n (and p u b licatio n s b a se d on it) a re b eliev ed to be the f ir s t re p o rts of this effect. S ilicon is an am p h o te ric im p u rity in GaAs (Kolm et al. 1957, R h o d erick 1959 and W helan et al. I960). It can su b stitu te on a G a -s ite , S i^ a , and is a donor. It can a lso su b stitu te on an A s -s ite , Si^_.a , and is an a c c e p to r. B eca u se of this a m p h o te ric n a tu re of Si in G aA s, a m e a s u re m e n t of the change of c a r r i e r co n c e n tra tio n d u rin g annealing w ill not yield enough in fo rm a tio n to analyze the an n ealin g effect and this is the r e a s o n for the m e a s u re m e n ts of a n u m b e r of p ro p e rtie s fo r the s a m e o r s im ila r s a m p le s. L o c a liz e d v ib ra tio n a l m o d es (LVM) a r e one of the m e a s u re m e n ts u sed to obtain additional in fo rm a tio n . B oth the S i^ a donor and S i ^ g a c c e p to r eac h give an in f r a r e d -a c tiv e LVM a b so rp tio n band and the bands have b een identified. (L o rim o r and S p itz er 1966, S p itz e r and A llre d 1968b). T he in te g ra te d a b so rp tio n s tre n g th of the LVM band is p ro p o rtio n a l to the im p u rity co n c e n tra tio n of th a t p a r tic u la r LVM band. Hence the c o n c e n tra tio n change of Si donors and a c c e p to rs as a re s u lt of annealing can be obtained. A lthough Si is an a m p h o te ric im p u rity in GaAs in that it can su b stitu te e ith e r a Ga s ite o r an As site , the Si p r e f e r s the Ga site and S i-doped GaAs grow n fro m the m e lt is alw ays n-type 19 -3 F o r a to tal Si c o n c e n tra tio n of 1 x 10 cm , the ra tio of c o n c e n tra tio n b etw ee n S i„ and S i. is a p p ro x im a te ly 3:1. H ow ever V jct J \ S b y adding a second im p u rity to the G aA srSi m a te r ia l, W helan e t al. ( I960) have found fro m a change of the c a r r i e r c o n c e n tra tion th at the S i-s ite d istrib u tio n c a n be v a rie d . In this d is s e rta tio n , this phonom enon is fu rth e r ex am in ed by using the LVM m e a s u r e m e n t to m e a s u r e d ire c tly the SiQa donor and S i^ g a c c e p to r co n c e n tra tio n s as a function of the doping le v el of a seco n d im p u rity . The second im p u rity can be e ith e r a n -ty p e or p -ty p e dopant. U su ally n -ty p e GaAs m a te r ia l has a v e ry deep re fle c tiv ity m in im u m (Rm ;$ 5%) n e a r the p la sm a edge. (S pitzer and W helan 1959). The fre q u e n c y of this re fle c tiv ity m in im u m is freq u en tly u sed to o btain the fre e c a r r i e r c o n c e n tra tio n of the sam p le. (Okada and Oku 1967). H ow ever in the p r e s e n t study, shallow re fle c tiv ity m in im a (^ 13%) a r e o b se rv e d in so m e of the sa m p le s. The re a s o n for the shallow R is studied and is found to be m re la te d to the p a r tia l co m p en sa tio n of the sa m p le . The a c c u ra c y of the c a r r i e r c o n c e n tra tio n obtained under this condition is also in v e stig a te d . 4 ; The o r d e r of p re s e n ta tio n in this d is s e rta tio n is b rie fly d e s c rib e d in the following. C h ap ter II d e s c rib e s the d iffere n t m eth o d s used in grow ing v ario u s GaAs m a te r ia ls fo r the p r e s e n t study. In this c h a p te r, the fu rn ace a rra n g e m e n t fo r the annealing and fo r the L i- s a tu r a tio n p r o c e s s e s a r e a lso d e s c rib e d . C h ap ter III is devoted to the d e s c rip tio n of the v a rio u s e x p e rim e n ta l tech n iq u es and the back g ro u n d of the p re v io u sly re p o rte d re s u lts w hich a r e re le v a n t to the p r e s e n t w ork. In C h ap ter IV, the shallow re fle c tiv ity m in im u m and its re la tio n sh ip to the fre e c a r r i e r a b so rp tio n is studied. C h ap ter V d e s c rib e s the annealing e ffect of h eav ily Si-doped GaAs and the re s u lts fro m v a rio u s e x p e rim e n ta l m e a s u re m e n ts of s a m p le s w ith d iffe re n t annealing conditions. A m odel to explain the annealing effect is a lso p r o - p o sed in this c h a p te r. F in a lly in C hapter VI, the S i-s ite d is trib u tio n in GaAs under the influence of e ith e r a n -ty p e o r a p -ty p e second dopant is studied. C H A P T E R II CRYSTAL GROWTH G allium a rs e n id e c ry s ta ls can be grow n by m an y d iffere n t m e th o d s, ju s t to nam e a few, th e re a re the C zo ch ra lsk i, B rid g m an , liq u id -p h a se epitaxy and v a p o r-p h a s e epitaxy m eth o d s. M o st of the GaAs c ry s ta ls u sed in this study a r e grow n in the la b o ra to rie s of the U n iv e rsity of S outhern C alifo rn ia w ith e ith e r the h o rizo n tal B rid g m a n o r C z o c h ra lsk i te ch n iq u es. T h e re fo re the d e s c rip tio n of the c r y s ta l grow th m ethods is r e s tr ic te d to th e se two te ch n iq u es. II— I- H o rizo n tal B rid g m an T echnique The b a s ic concept of the B rid g m a n m ethod is to s t a r t the grow th p r o c e s s w ith the w hole ch arg e m o lte n and then to solidify the ch arg e fro m one end. The conventional B rid g m a n m ethod u se s a c y lin d ric a l c ru c ib le w hich is lo w ered v e rtic a lly thro u g h a te m p e ra tu re g ra d ie n t. The h o riz o n ta l B rid g m a n m ethod has so m e slig h t m o d ificatio n s fro m the conventional B rid g m a n m ethod. The h o riz o n ta l B rid g m a n m ethod u ses a h o riz o n ta l c ru c ib le (boat), and the re la tiv e m otion betw een the c ru c ib le and the te m p e ra tu re g ra d ie n t is in the h o riz o n ta l d ire c tio n . In stead of m oving the b o at th ro u g h d iffe re n t te m p e ra tu re zones, the fu rn ace its e lf is m ounted on ra ils and is m oved re la tiv e to the c ru c ib le w hich is 5 held in a fixed p o sitio n . T his has the advantage th at the c ru c ib le re c e iv e s le s s v ib ra tio n in the grow ing p r o c e s s . A s shown in Fig. I I - 1, the fu rn a c e , w hich w as designed and co n stru cted by W. P. A llre d of the U n iv e rsity of S outhern C alifo rn ia, has four te m p e ra tu re zo n es. E ac h zone has its own te m p e ra tu re c o n tro l le r . T e m p e ra tu re sen sin g th e rm o c o u p le s of Zones 2, 3 and 4 a re b u ilt into the fu rn ace. The th e rm o co u p le of the Zone 1 c o n tro lle r is a s e p a ra te unit fro m the fu rn a c e . It is re lo c a te d a fte r ea c h loading so th at it is p la c e d n e a r the tip of one of the am poule b efo re the grow th is s ta r te d as show n in F ig. I I - 1. This a rra n g e m e n t is n e c e s s a r y b e c a u se the te m p e ra tu re at this end of the am poule is the lo w est in the e n tire am poule and thus this te m p e ra tu re d e te rm in e s the a r s e n ic p r e s s u r e in sid e the am poule. In p r e p a ra tio n fo r the g row th of a c ry s ta l, a high p u rity g alliu m and a r s e n ic a r e loaded into the am p o u le. The gallium is g e n e ra lly put into the b o a t in w hich the g alliu m a rs e n id e w ill be grow n. Any im p u rity th a t is to be p r e s e n t as a dopant in the ingot is added to the g alliu m a t this tim e . The boat is m ade of q u a rtz w ith a sand b la ste d s u rfa c e . The q u a rtz s y ste m w ill a u to m a tic a lly in tro d u ce Si as an im p u rity into the c ry s ta l. Hence, in the case that Si is not an intended dopant, a q u a rtz b o a t should not be u sed . Instead, boats m ad e fro m o th e r m a te r ia ls , such as v itrio u s carb o n , should be u sed and sh ield ed fro m the w all of the q u a rtz am poule w ith an a lu m in a tube. Silicon is used as a m a jo r dopant in this d is s e rta tio n and the Si doping le v e l is m u c h hig h er than the Si co n tam in atio n fro m the q u a rtz s y s te m . T h e re fo re , Alumina Tube End support Zone 1 Arsenic Windows Gallium U M DO OO OO OOO PO O Zone 2 ooooooooooo Zone 3 o o o o <yo o o oo Zone 4 O OOP o ooooooo f t : O O O O O ' O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O IE Furnace, Travel -Thermocouple to controller of Zone 1 F ig u re I I - 1 H orizo n tal B rid g m an galliu m a rs e n id e g ro w er. the Si con tam in atio n fro m the q u a rtz boat does not have a d v e rs e effect, and q u a rtz boats a r e used in all the grow th p r o c e s s e s . Once the m a te r ia ls a r e loaded into the am p o u le, the p r e s s u re in sid e the am poule is red u ced to = “2|-lm Hg w ith a com bination of m e c h a n ic a l and v a c so rb p u m p s. A t tim es w hen la rg e c h a rg e s a r e loaded into the am poule, it is n e c e s s a r y to b ack fill the am poule w ith in e rt gas during the pum ping p ro c e s s . The in e rt gas helps purge oxygen fro m the am p o u le. A fter the f i r s t evacu atio n , the am poule is filled ag ain w ith an in e rt gas and the g alliu m m e lt is h e a t-tre a te d n e a r 100° C to red u ce the w a te r contam in atio n . The in e rt gas p r e s s u r e in the am poule p re v e n ts the w a te r fro m b u rs tin g out of the g alliu m and c o n s e quently sp illin g the galliu m out of the b o at. A fte r the gallium m a te r ia l in the b o at is fre e fro m w a te r, the am poule is again pum ped down to = “ 2|im of Hg and seale d . W hen loading the am poule into the fu rn a c e , the b o at is p la ced in Zone 3, the m eltin g zone. In o r d e r to fa c ilita te lo catin g the p r o p e r p o sitio n for the am poule, fo u r 2 c m -d ia m e te r w indow s a r e in s ta lle d on top of the fu rn a c e and they a r e shown in F ig . II— 1. A s m entioned e a r lie r , the te m p e r a tu r e Zone 1 c o n tro ls the a r s e n ic p r e s s u r e in sid e the am p o u le. Zone 2 is the grow th zone w hich is m a in tain ed a t te m p e r a tu r e s 1100° C -1200° C. Zone 3 is the hot zone, o r the m e ltin g zone, w hich is kept at T> 1250° C. It is in Zone 3 that the g alliu m r e a c ts w ith a r s e n ic to fo rm g alliu m a rs e n id e . Zone 4 is u su a lly at T=“ 900° C, the p u rp o se of w hich is to keep the te m p e ra tu re p ro file of Zone 3 f ro m falling off too fa st. F ig u re II-2 show s the m e a s u r e d t e m p e r a tu r e p ro file of the fu rn a c e w hen it is not loaded. W hen the fu rn a c e is f i r s t tu rn ed on, Zone 1 te m p e ra tu re is g e n e ra lly s e t a t 500° C. W hen a ll the o th e r zones re a c h the d e s ire d te m p e r a tu re s , the te m p e ra tu re of Zone 1 is then in c re a s e d to 650° C. T his p ro c e d u re is e s s e n tia l b e c a u se if the te m p e r a tu r e of Zone 1 re a c h e s 650° C b e fo re the te m p e ra tu re of Zone 3 is above the m e ltin g te m p e ra tu re of g alliu m a rs e n id e , the a r s e n ic w ill not re a c t w ith gallium fa s t enough and the a r s e n ic p r e s s u r e w ill build up and ev en tu ally b re a k the q u a rtz am p o u le. To p re v e n t any a r s e n ic vapor fro m a c c id e n ta lly leaking into the la b o ra to ry , the e n tire fu rn ace is ho u sed in a la rg e fum e hood. A fter a ll the g alliu m has re a c te d w ith the a r s e n ic to fo rm g alliu m a rs e n id e , the fu rn a c e is slow ly pulled to one side so that the g alliu m a rs e n id e m e lt can g ra d u a lly e n te r into Zone 2 and solidify to fo rm a c r y s ta l. The fu rn ace is m ov ed by a m o to r w ith a red u ctio n g e a r a t a sp eed of = “ 0 .2 5 " p e r hour. Seeding is p o s s ib le w ith this technique. A seed is p la c e d a t the end of the b o at w hich is c lo s e r to the grow th zone. In o r d e r to obtain good seeding r e s u lts , p re v e n tiv e m e a s u r e s have to be taken to e n s u re that only a s m a ll p a r t of the seed is m e lte d d u rin g the re a c tio n p r o c e s s . M ost of the c ry s ta ls used fo r the p r e s e n t stu d ies a r e s e lf-s e e d e d . II— II. C z o c h ra lsk i T echnique In the C z o c h ra lsk i m ethod of grow th, c r y s ta ls a r e grow n 1500 1000 5 0 0 i — i— i— i— i — i— i— i — i— r WINDOW 18t I " 17^ - 10 w o o o 5" i l ^ 7 5 - GROWTH ZONE --------- CONTROLLER SETTING IO + 3 0 0 / 2 mV Pf -R h OPEN SLOT FOR PUTTING WINDOWS FURNACE BORE » 3 ^ 4 I" FURNACE DIMENSION SCHEMATIC DIAG. I I I I I I I I I I 1 T i — r i — r HOT ZONE CONTROLLER SETTING 10 + 542/ 2 mV PT-R h * MARKED ON FURNACE, each interval * l", for re lativ e position on fu rn a c e see in s e rt sc h e m a tic diog. J I I I I I I I 0 2 4 6 8 10 12 14 16 18 2 0 PO S IT IO N * F ig u re II-2 T e m p e ra tu re p ro file of the h o riz o n ta l B rid g m an fu rn ace. 2 2 2 4 11 fro m the m e lt by pulling. In p rin c ip le , this m eth o d has the advantage that is can p ro d u ce la rg e d is lo c a tio n -fre e c r y s ta ls . T his is b e c a u se the so lid -liq u id in te rfa c e is not in co n tact w ith a c ru c ib le and the ra d ia l te m p e ra tu re g ra d ie n ts can be kept sm a ll b y p ro p e r design of the c ru c ib le s y s te m . Since the heating is done freq u en tly by a R. F. (Radio F re q u e n c y ) h e a te r, the cru cib le used in this technique has to be ab le to couple w ith the R. F . coil. A c a rb o n c ru c ib le is g e n e ra lly used for this reaso n . Som e changes in the conventional C z o c h ra ls k i m ethod have b een in tro d u ced in this la b o ra to ry . T h ese m o d ific a tio n s, e s p e c ia lly the use of m o lte n as a se a l, w e re o rig in a lly conceived b y W. P . A llre d of the U n iv e rsity of Southern C a lifo r nia and a new c r y s ta l p u lle r d esig n is c u r r e n tly pending for paten t. A s shown in F ig . II-3, the new C z o c h ra lsk i p u lle r c o n sists of two a ll q u a rtz c h a m b e rs w hich a r e connected by a n a rro w q u a rtz neck. A q u a rtz rod is in s e r te d through the neck and a se e d is fa ste n e d to its end in the lo w er c h a m b e r. The o th e r end of the rod goes th ro u g h the u p p e r c h a m b e r and is connected to the pulling m o to r a t the top of the p u lle r. D uring the grow th p ro c e s s , this rod is f i r s t lo w ered so th at the seed touches the m e lt and it is su b se q u en tly pulled up a t a ra te = * jr to 1 ^ " p e r hour. A c r y s ta l is grow n fro m the m e lt by this p ro cess. It u su ally c r y s ta lliz e s w ith the sa m e o rie n ta tio n as the seed . D uring pulling, the rod is ro ta te d at =- 10 rp m in o r d e r to help ach iev e a u n ifo rm grow th. The fu rn a c e 2 of F ig . II-3 is heated to 650° C w hich keeps the a r s e n ic p a r ti a l p r e s s u r e in the low er SE A L GAS SUPPLY QUARTZ PULLROD VACUUM Bo0- FURNACE 1 WELD FURNACE 2 o / SEED CRUCIBLE ^ .IN D U C T IO N COILS 3 D GaAs MELT LIQUID SEAL GALLIUM A R SEN ID E GROWER F ig u re I I - 3 C z o c h ra ls k i liq u id s e a l g alliu m a rs e n id e g ro w e r 13 c h a m b e r a t = ? 1 a tm o s p h e re . T his e n s u re s the s to ic h io m e tric grow th of the galliu m a rs e n id e c ry s ta l. To p re v e n t the esc a p e of the a rs e n ic fro m the lo w er ch a m b e r, the u p p er c h a m b e r is p r e s s u r iz e d to 1 a tm w ith h eliu m gas and fu rn ace 1 is also heated to 650° C to keep the m o ^te n - The v is c o s ity of 3 m o lten ^ 2 ^ 3 *s (l u^te l a r ge 1 .6 x 10 g m /c m se c , E p p ler 1966), but it s till allow s the rod to m ove and ro ta te in the neck a r e a . At the sam e tim e the m o lten a c ts as a s e a l to keep the a r s e n ic v ap o r fro m escap in g the lo w er c h a m b e r. The p ro c e d u re to p r e p a r e the s y s te m for the grow th is as follow s: P u re g alliu m and a r s e n ic a r e loaded in the c ru c ib le to g e th er w ith a co n tro lled am o u n t of any dopant m a te r ia l th a t is to be in tro d u ced to the ingot. Solid is p la c e d n e a r the bottom of the upper c h a m b e r. The e n tire q u a rtz s y s te m is then fasten e d to the p u lle r and is connected to a pum p thro u g h the up p er c h a m b e r. The B^O^ m a te r ia l is h e a t- tr e a te d a f te r a good vacuum is obtained in both c h a m b e rs . H elium gas is back filled into th e se c h a m b e rs and fu rn a c e 1 is heated to a te m p e ra tu re = “ 900° C to m e lt the w hich then flows down to the neck. The h eliu m is su b seq u en tly pum ped out through the m o lten B2O3 to d riv e out any p o s sib le w a te r contam ination. A s m a ll am o u n t of heliu m gas is le ft in the lo w er c h a m b e r to keep the galliu m o r m o lten g alliu m a rs e n id e fro m sp illin g outside of the cru c ib le . The induction coils a r e now e n e rg iz e d and both fu rn a c e s 1 and 2 a r e kept at 650° C. A s the p r e s s u r e in the lo w e r c h a m b e r ris e s , h eliu m gas p r e s s u r e in the u p p e r c h a m b e r is a lso in c re a s e d . 14 : W hen all the g alliu m m a te r ia l re a c ts w ith a r s e n ic to fo rm m olten g alliu m a rs e n id e , the pulling p ro c e s s is c o m m e n c e d . The te m p e ra tu re of the c ru c ib le (hence the m o lte n g alliu m a rse n id e ) is m o n ito re d w ith a Si p h o to d e tecto r w hich is m ounted under the bottom of the lo w er c h a m b e r. The sig n al of this p h o to d etecto r goes to a te m p e ra tu re c o n tro lle r w hich in tu r n c o n tro ls the output of the g e n e ra to r. The C z o c h ra lsk i m ethod has the following ad vantages: (1) The g ro w e r can se e w hat has been grow n. (2) If the ingot is not s a tis fa c to ry it can be re m e lte d and grow n again, all in a single loading. (3) The siz e of the ingot can be co n tro lled during grow th. (4) The ro ta tio n of the p ulling rod helps to s tir the m e lt in the c ru c ib le w hich helps to m ak e an even d istrib u tio n of the dopant im p u rity . II-III. F u rn a c e C o n stru c tio n In so m e of the e x p e rim e n ts to be d e s c rib e d la te r , GaAs sa m p le s w e re h e a t- tr e a te d a t te m p e ra tu re s as high as 1100° C. U nder c e rta in conditions it is d e s ira b le to c o n tro l the a rs e n ic p a r tia l p r e s s u r e o v e r g alliu m a rs e n id e in an en clo sed am poule during the h e a t tre a tm e n t. T his can be a c h ie v e d by using two te m p e ra tu re zone fu rn ace. The sa m p le and a m e a s u re d quantity of e x c e ss a r s e n ic a r e se a le d in an ev ac u ated am p o u le. The p o sitio n of the am poule in the fu rn ace is su c h that the sam p le is lo c ated a t the d e s ire d te m p e ra tu re zone and the o th e r end of the am poule is m a in tain ed a t a d iffe re n t te m p e r a tu r e w hich determ inesj a p 2 4 Inconel Tube 2-1/16" ID, 2-3/8"0D h — 5"— H f t f t f t O O f t P .0 , 0 Q P 0 0 . 0 O A O f t f t f t f t C Kanthal A -l wire l- , C M TC TC, TC Vycor tube Alundum Core F ig u re II-4 C ro ss sectio n d ia g ra m of an annealing fu rn ace. 16 the p a r tia l p r e s s u r e of a r s e n ic in sid e the am poule. The following d e s c rib e s the p ro c e d u re s u sed in the c o n s tru c tio n of fu rn a c e s having a la rg e b o re and a m an ip u lab le te m p e ra tu re p ro file. To build a fu rn a c e , the o p eratin g te m p e ra tu re range is an im p o rta n t fa c to r w hich w ill affect the design. F o r annealing, the te m p e ra tu re is g e n e ra lly below 1100° C. A t this te m p e ra tu re , K anthal A - l w ire is p ro b ab ly the b e s t choice fo r fu rn a c e heating e le m e n ts. K anthal A - l m a te r ia l is an alloy containing A1 5 .5 , C r 22, Co 0 .5 , and the b alan ce being F e. The m a x im u m re c o m m e n d e d e le m e n t te m p e ra tu re in continuous use is 1375° C. F o r T < 1 1 0 0 ° C the K anthal A -l w ire should be v e ry d u rab le . The fu rn ace c ro s s sec tio n d ia g ra m is shown in the sc h e m a tic draw ing in Fig. II-4. The gauge 13 K anthal A -l w ire is wound on 2 ^ ” b o re 1 /4 " w all, A lundum (A ^O ^) tubing w ith a 1 /1 2 " groove and 6 tu rn s p e r inch. T h e re a r e te rm in a ls at both ends of the w inding. In addition, taps a r e e x tra c te d on the w inding a p p ro x im a te ly e v e ry two in c h e s. V a ria b le p ow er r e s i s to rs a r e connected betw een th e se taps a s show n in the fig u re. The c e n te r tap a lso s e rv e s as a th ird te rm in a l w hen the fu rn ace is o p e ra te d in a two te m p e ra tu re -z o n e m ode. T h e re a r e th re e te m p e ra tu re sen sin g th e rm o c o u p le s equally sp aced in the fu rn ace. F o r one te m p e ra tu re -z o n e m o d e, the c e n te r th e rm o co u p le ( T .C .2 ) sig n al is fed to the te m p e ra tu re c o n tro lle r. F o r two te m p e r a tu re -z o n e m ode o p eratio n , two te m p e ra tu re c o n tro lle rs a r e re q u ire d . The c e n te r th e rm o co u p le w hich is used in the o ne- te m p e ra tu re -z o n e m ode o p e ra tio n is d isco n n ec ted fro m the 17 c o n tro lle r and the sig n als fro m the o th e r two th e rm o c o u p le s a r e se n t to th e ir re s p e c tiv e te m p e ra tu re c o n tro lle r s . Since the h eating e le m e n t has one continuous w inding, only two pow er s o u rc e s can be connected to a fu rn a c e a t one tim e. This m e a n s th a t the fu rn ace can not be u sed fo r th re e -z o n e o p eratio n . The A lundum tube w ith the K anthal A -l w ire w inding is su p p o rted a t both ends b y a fib re fra x bed w ith 3 /8 " thick tr a n s i t p la te s . The fu rn ace has a c a se m ad e of a lu m in u m s h e e t p la te (A lclad 2 4 5 -T c A n -A -1 3 ). Two 5" long in co n el tubes a r e p la c e d in sid e the fu rn a c e c o re to co m p e n sa te the te m p e ra tu re fluctuations during o p e ra tio n . Inconel is a s p e c ia l a llo y w hich has a high sp ecific h e a t and a low th e rm a l conduction co efficien t at elevated te m p e r a tu re s . It can a lso be u sed a t te m p e r a tu r e s up to 2100° F (1150° C). A four foot long v y co r (or q u a rtz ) tube is then in s e rte d into the fu rn ace as the lining tube. V ycor tubing softens a t te m p e r a tu r e s above 900° C and the u se of a q u a rtz tube is re c o m m e n d e d fo r h ig h e r te m p e r a tu r e s . Two types of c o n tro lle rs a r e u sed to c o n tro l the fu rn ace te m p e r a tu r e . One is a s e lf-c o n ta in e d unit m ade b y E u ro th e rm L im ite d . The o th e r u s e s an A P I (A sse m b ly P ro d u c ts Inc. ) o n -o ff te m p e ra tu re c o n tro lle r w ith a p o w er p h a se co n tro l c irc u it and tr ia c unit. The c irc u it w as built in this la b o ra to ry . Both te m p e r a tu r e c o n tro lle rs use a c h r o m e l- a lu m e l type th e rm o co u p le input as the te m p e r a tu r e s e n s e r . C H A P T E R III E X P E R IM E N T A L TECHN IQ UE AND BACKGROUND III— I. In tro d u ctio n The e x p e rim e n ta l techniques w hich w e re u sed in the d iffere n t p h a se s of this d is s e rta tio n including the m eth o d s used fo r sa m p le p re p a ra tio n a r e b rie fly d e s c rib e d in this c h a p te r. In o rd e r to u n d erstan d the re s u lts of the p r e s e n t r e s e a r c h , som e b ack g ro u n d in fo rm a tio n of p re v io u s w o rk is n e c e s s a r y since the p rev io u s r e s u lts a r e freq u en tly quoted and c o m p a re d w ith the re s u lts obtained in the p r e s e n t w ork; th e re fo re a n outline of the b ack g ro u n d m a te r ia l is a lso p re s e n te d h e re . Ill-II. S am ple P r e p a r a tio n A. C utting fro m C ry s ta l Ingot T he GaAs sam p les used in this w o rk w e re o btained fro m c r y s ta l ingots grow n w ith the d e s ire d im p u rity co n c e n tra tio n s by one of the gro w th m eth o d s d e s c rib e d in C h ap ter II. The c ry s ta l ingot w as f i r s t slic e d into w a fe rs by using a silic o n c a rb id e o r diam ond cutting blad e on a w a fe rin g m a ch in e. The w a fe rs w e re g e n e ra lly 60 - 90 m il (0.1524 - 0.2286 cm ) in th ick n ess w ith the cutting plan e p e rp e n d ic u la r to the ingot axis so th a t the im p u rity co n c e n tra tio n in a given w afer w as re la tiv e ly u n ifo rm and w as le a s t affected by the se g re g a tio n effect of the im p u rity . E ac h w a fe r w as subdivided into a n u m b e r of individual sa m p le s 18 19 b y using a w ire saw w ith a 5 m il (0. 012 7 cm ) diam ond coated s te e l of B e -C u allo y w ire . A typical s iz e of the l a r g e r s u rfa c e w as 1 cm x 0. 5 cm . Sam ples w ith s m a lle r s iz e s w e re a lso p re p a r e d . B. Sam ple S u rface P o lish in g A m i r r o r - l i k e sam p le su rfa c e w as re q u ire d in m o s t of the o p tical m e a s u r e m e n ts . An o p tical q u ality sa m p le s u rfa c e w as e s s e n tia l to m in im iz e the s c a tte r e d lig h t lo s s . The po lish in g p ro c e d u re s ta r te d w ith a m e ta llu rg ic a l lapping of the sa m p le s u rfa c e b y using an a b ra s iv e s l u r r y (polishing com pound and w a te r) w ith p r o g r e s s iv e ly s m a lle r g rit s iz e s until the sa m p le w as w ithin a couple m ils of the d e s ire d th ic k n e ss. A 3200 m e s h p o lish in g com pound w as g e n e ra lly u sed in p re p a rin g the s u rfa c e for the final p o lish in g . The final polishing p r o c e s s can be done e ith e r m e ta llu rg ic a lly o r c h em ica lly . The m e ta llu rg ic a l final po lish in g step w as done w ith a L in d e-A , a A ^ O g s l u r r y (g rit s iz e « 0. 3(a ) on a silk polishing cloth o v e r a h a rd and fla t s u r face . The s a m p le s u se d in the m e a s u re m e n ts d e s c rib e d in C h a p te r VI w e re p o lish e d by using this m ethod. A ll the S i-doped GaAs s a m p le s u sed in the an nealing study (C hapter V) w e re p o l is h e d b y a ch e m ic a l p o lish in g m eth o d developed by Skolnik (1971). T his m eth o d u sed an etching solution w hich c o n siste d of 3 .1 gm of A C L 66 in 500 c. c. and d rip p ed slow ly on a fla t p o lish in g w heel c o v e re d w ith C o rfam b acked G eo scien ce P o lite x P ix cloth. The sa m p le w as held a g a in s t the w heel s u rfa c e by a sa m p le h o ld e r w hich w as a lso ro tatin g d u rin g the p o lish in g proP 20 c e d u re . The A C L 66 is a tra d e n am e u sed b y M onsanto C o r p o r ation for the [(m o n o trich lo ro ) te tr a - (m o n o p o tassiu m dichloro)] p e n ta iso c y a n u ra te com pound. D uring the polishing p r o c e s s of s a m p le s w hich w e re u sed for tra n s m is s io n m e a s u re m e n ts , a s m a ll w edge of a p p ro x im a te ly l t o 2 m ils a c r o s s a f“ 1 cm len g th of the sa m p le , w as in tro d u ced . The w edge e lim in a te d the in te rfe re n c e frin g es w h ich o th e rw is e would o c c u r in s p e c tr a l reg io n s of low ab so rp tio n . The th ick n ess of the sa m p le a fte r the p o lish in g p r o c e s s w as m e a s u r e d to the n e a r e s t 0. 1 m il. w ith a depth gauge. C. T echniques F o r F r e e C a r r i e r C o m p en satio n In the next sectio n , in f r a r e d tr a n s m is s io n m e a s u re m e n ts fo r lo c a liz e d v ib ra tio n a l m ode (LVM) stu d ie s of im p u ritie s in s e m ic o n d u c to rs w ill be d e sc rib e d . In GaAs m a te r ia l, m o s t of the in te re s tin g LVM bands of im p u ritie s o c c u r in the s p e c tra l reg io n betw een 340 c m * and 480 c m *. H ow ever, the fre e c a r r i e r a b s o rp tio n c ro s s sectio n in this reg io n is v e ry la rg e and w ill m a s k the LVM b an d s. H ence, the fre e c a r r i e r a b so rp tio n has to be e lim in a te d and this is u su ally done by in tro d u cin g a co m p en sa tin g sp e c ie s into the sa m p le . C om m only u sed tech n iq u es fo r e le c tr ic a l c o m p en sa tio n a r e by diffusing L i o r Cu fro m the s u rfa c e into the sam p le o r by e le c tro n irra d ia tio n . T h ese techniques w ill be b rie fly d e s c rib e d in the following. C l. L ith iu m D iffusion The m e c h a n is m for L i diffusion and co m p en sa tio n has b e e n d is c u s s e d b y L o rim o r (1966). L i diffuses by the in t e r s tit ia l- su b stitu tio n al m eth o d . (F u lle r and W o lfs tirn 1962, F u lle r and A lliso n 1964). L i is an a m p h o te ric im p u rity in GaAs and fo rm s b oth donor and a c c e p to r s p e c ie s . L i diffusion can co m p en sate both n -ty p e and p -ty p e s a m p le s . It is a lso s e lf-c o m p e n sa tin g w hen diffused • into undoped m a te r ia l and in this c a se the donor and a c c e p to r sp e c ie s a r e com p lex es of L i a to m s. (L evy 1973). It has b een o b se rv e d th a t L i diffusion into G aA s:Si a t t e m p e r a tu re s T s 800° C w ill cau se Si site tr a n s f e r in GaAs (S pitzer and A llre d 1968a) and hence a ll the L i diffusion p r o c e s s e s in this w ork w e re done a t T=700° C. T he p ro c e d u re fo r L i diffusion is as follow s: In itially L i is alloyed onto the GaAs sa m p le s u rfa c e s b y coating the sa m p le w ith a d is p e rs io n of L i in m in e r a l oil and heating it in an in e rt a tm o s p h e re (usually d ry arg o n ). The sa m p le is then p la ced in a Mo c ru c ib le filled w ith 80 m e s h SiC pow der to p re v e n t the s a m ple fro m touching the in n e r w all of the c ru c ib le . The lid of the c ru c ib le is then put on tightly and the w hole c ru c ib le loaded into a tube fu rn ace a t the d e s ire d diffusion te m p e ra tu re . The fu rn ace tube is continuously flushed w ith d ry a rg o n w hich is m a in ta in e d a t a slig h t o v e r p r e s s u r e . W hen the diffusion tim e is reac h ed , the c ru c ib le is p u sh ed out of the fu rn a c e b u t re m a in s inside the fu rn a c e lining tube w ith the d ry a rg o n flow ing. A fte r the crucible has cooled to n e a r room te m p e r a tu r e , the sa m p le is re m o v e d and w ash ed in w a te r. B ubbles a r e g e n e ra te d as e x c e ss L i re m a in in g on the sam p le su rfa c e s r e a c t w ith w a te r. This is a re lia b le ind icatio n of co m p en sa tio n by L i diffusion. A fte r the L i diffusion, 22 the sam p le is then lapped and p o lish e d acc o rd in g to the p ro c e d u re d e s c rib e d in the la s t sectio n . C2. Cu D iffusion Cu a lso d iffuses into GaAs s im ila r to L i diffusion by the in te r s titia l- s u b s titu tio n a l m ethod. (F u lle r and W helan 1958). Cu is a su b stitu tio n a l im p u rity , C u ^ a , in GaAs and is an a c c e p to r. T h e re fo re it c a n be u sed only to co m p e n sa te n -ty p e GaAs m a te r ia l. The diffusion p ro c e s s a lso has to be done c a re fu lly . At too low a te m p e r a tu r e , the Cu so lu b ility is in su fficien t to p ro v id e co m p e n sa tio n (Blanc e t a l . 1961). A t too high a te m p e r a tu re the Cu so lu b ility b e c o m e s too la rg e , thus over-com pensation o c c u rs and the sa m p le tu rn s out to be p -ty p e . The diffusion te m p e ra tu re g e n e ra lly used for Cu diffusion is b etw ee n 800° C - 900° C. The p ro c e d u re fo r Cu diffusion is s im ila r to th at of L i diffusion, ex ce p t th a t the diffusion w as c a r r i e d out fro m a s u rfa c e la y e r w hich is e le c tro p la te d on the sa m p le s u rfa c e s by using Cu(NOg)2 so lu tio n . The sa m p le is then se a le d in an ev acu ated q u a rtz am poule an d loaded into the fu rn a c e . The diffusion t e m p e r a tu r e and tim e have b een re p o rte d by L o r im o r (1966). F o r 18 -3 sa m p le s w ith c a r r i e r co n c e n tra tio n n e “* 10 cm " , the diffusion w as c a r r i e d out a t 800° C fo r 60 hours follow ed by 2 - ^ ho u rs a t 975° C and fin ally 3 hours a t 800° C. The 975° C tre a tm e n t would in s u re the u n ifo rm d istrib u tio n of Cu in the sa m p le . This tr e a tm e n t w as re c o m m e n d e d by P r o f e s s o r W helan (p riv ate 17 -3 co m m u n icatio n ). F o r s a m p le s w ith “ 5 x 10 cm diffusion 23 at 750° C fo r 18 hours yield a co m p e n sa te d sa m p le . B e c a u se of the high diffusion te m p e ra tu re and the p o s s i b ility of o v e r-c o m p e n s a tio n b y the Cu diffusion p r o c e s s , this m eth o d of c o m p e n sa tio n w as r a r e l y u sed in the p r e s e n t study. The d e s c rip tio n p re s e n te d h e re is for co m p le te n e ss of the d e s c rip tio n of e le c tr ic a l c o m p e n sa tio n m e th o d s. C3. E le c tro n Irra d ia tio n E le c tro n ir r a d ia tio n has b e e n u sed fo r c a r r i e r c o m p e n sa s tion in b oth n - and p -ty p e Si. (N ewm an and Sm ith 1968, A n g re s s e t al. 1965, F a n and R a m a d a s 1959). The e le c tro n ir r a d ia tio n m eth o d can a lso be u se d in n - and p -ty p e GaAs m a te r ia l to r e duce the c a r r i e r c o n c e n tra tio n (A u k erm an 1968). The n a tu re for the co m p en sa tio n m e c h a n is m is not w ell known. The irra d ia tio n p r o c e s s p re s u m a b ly g e n e ra te s la ttic e defects w hich w ill a c t as the co m p en sa tin g s p e c ie s. S p itz e r et al. (1969) have m ad e c o m p a r is o n b etw ee n the co m p e n sa tio n m ethods of the L i diffusion and e le c tr o n ir r a d ia tio n on G aA srSi s a m p le s . T h e ir IR a b so rp tio n m e a s u r e m e n t re s u lt is re p ro d u c e d in F ig u re II I - l w hich shows th a t ex ce p t for a w ide LVM band n e a r 369 cm *, the IR a b s o r p tion s p e c tr u m of the e le c tro n ir r a d ia te d sa m p le is s im p le r than th a t of the L i-d iffu se d sa m p le b e c a u se no L i re la te d LVM bands w ill b e in the e le c tro n ir r a d ia te d sa m p le s p e c tru m . A ll of the Si LVM bands betw een th e se two s a m p le s a r e in a g re e m e n t b oth in band s tre n g th and freq u en cy . T his r e s u lt s tro n g ly su g g e sts th at e le c tr o n ir r a d ia tio n is a p o te n tia lly s u p e rio r to L i diffusion as a c o m p e n sa tio n m eth o d . a ( c m '1 100- . 3 1 .3 (0 •• W CO p 80- Li - d if f u s e d elec tro n ir r a d ia te d 60 4 0 - 2 0 - 390 410 430 4 5 0 370 470 350 330 F ig u re III-1 C o m p a riso n of ab so rp tio n s p e c tra betw een two G aA s:Si sa m p le s co m pensated b y 7L i diffusion and 1 MeV e le c tro n irra d ia tio n resp e c tiv e ly . (A fter S p itzer e t al. 1969). ^ 25 The sa m p le s u sed in the p r e s e n t study w e re e le c tro n ir r a d ia te d a t A ir F o rc e C am b rid g e R e s e a r c h L a b o ra to rie s . The p ro c e d u re fo r e le c tro n co m p en sa tio n has b e e n d e s c rib e d by S p itz e r e t a l. (1969). The s a m p le s w e re e le c tr o n - ir r a d ia te d w ith 1-M eV e le c tro n s fro m a D y n am itro n e le c tro n a c c e le r a to r until th e re w as no m e a s u ra b le in fra re d fre e c a r r i e r a b s o rp tio n a t a fre q u e n c y n e a r 340 cm \ th e c o rre s p o n d in g fre e c a r r i e r con- 16 -3 c e n tra tio n is < 10 cm as e s tim a te d fro m d ata m e a s u re d by S p itz e r and W helan (1959)- D uring the e le c tro n irra d ia tio n p r o c e s s , the s a m p le s w e re m o u n ted on a co p p e r-c o o lin g fix tu re and s p ra y e d w ith liquid n itro g e n . T his p ro c e d u re kept the s a m ple te m p e r a tu r e below 100° K as m e a s u r e d b y a th e rm o co u p le in co n tact w ith the co p p e r-c o o lin g fix tu re w h e re the s a m p le s w e re m ounted. A fte rw a rd s the te m p e ra tu re w as g ra d u a lly ra is e d to ro o m te m p e r a tu r e . In the ann ealin g study of S i-d o p ed GaAs w hich w ill be d e s c rib e d in C h ap ter V, the e le c tro n ir r a d ia tio n w as chosen as the m e th o d of co m p en sa tio n . The r e a s o n is th a t d u rin g the L i diffusion p ro c e s s the sa m p le is held a t an elev ate d te m p e ra tu re w hich m ig h t in tro d u ce an u n c e rta in ad d itio n al an nealing effect. In the e le c tro n ir r a d ia tio n p r o c e s s , the sa m p le w as held a t a te m p e r a tu r e ^ 100° K. Ill-III. M e a s u re m e n t T echnique A. H all E ffec t and R e s is tiv ity M e a s u re m e n t T he sa m p le s u sed for H all effect and r e s is tiv ity m e a s u r e - m e n ts w ere u su ally re c ta n g u la r shaped. The sa m p le th ick n ess w as m u c h s m a lle r than its o th e r two d im e n sio n s. The c u r r e n t le a d s w e re connected a t the top arid b o tto m ends of the sa m p le as the w ire s la b elle d 1 in F ig. III-2. The c u r r e n t flow ed along the lo n g e st d im en sio n of the s a m p le . The H all p ro b e s w e re connected a t the m id d le of the sa m p le as the p ro b e s la b e lle d 2. The p a ir of p ro b e s la b e lle d 3 in the fig u re w as fo r the re s is tiv ity m e a s u re m e n t. To m ake ohm ic c o n ta c ts, the sa m p le w as f i r s t etched in a H F + HNOg (1:4) so lu tio n fo r a few seco n d s and then w ash ed tho ro u g h ly in deionized w a te r. A s m a ll am o u n t of indium w as th en alloyed by using a s m a ll g a s-o x y g e n to rc h on the sa m p le at e a c h of the d esig n ated p ro b e p o s itio n s. P ro b e w ire s w e re then s o ld e re d to e a c h indium dot by using an o rd in a ry so ld e rin g iro n . The sa m p le w as p la c e d in an e le c tro m a g n e t w ith the m a g n etic field s e t a t 5000 g a u ss. The m a g n e tic field w as tu rn e d off w hen r e s is tiv ity m e a s u r e m e n ts w e re being m a d e . F o r m e a s u r e m e n ts at 77° K, the sa m p le w as im m e r s e d in liquid n itro g en . B. In fra re d S p e c tro m e te r T he s p e c tr o m e te r u se d fo r the IR re fle c tiv ity and IR tr a n s m is s io n m e a s u r e m e n ts in the p r e s e n t w o rk has b een d e s c rib e d by L o r im o r (1966). The s p e c tr o m e te r c o n s is ts of a glo b ar s o u rc e , g ra tin g m o n o c h ro m a to r and a th e rm o c o u p le d e te c to r. The m o n o c h ro m a to r is a P e r k in - E l m e r M odel 2 10-B g ra tin g unit w hich u ses a s e t of six g ra tin g s b la z e d for f i r s t o r d e r w ith blaze w avelengths of 1.4|_im, 3. 75|im , 7. 5|im , 22.5|J.m, 30|am and 45|am. T h ese g ratin g s c o v e r a fre q u e n c y range fro m 200 c m * to 27 2 F ig u re III-2 S chem atic d ia g ra m of a sa m p le for Hall effect and r e s is tiv ity m e a s u r e m e n ts . 28 12,500 c m T h e re a r e eight m u lti- la y e r d ie le c tric t r a n s m i s sio n filte rs to e lim in a te h ig h e r o r d e r ra d ia tio n fro m the g ra tin g s. The sa m p le w as lo c a te d in a focal point of the lig h t b e a m on the ex it side of the m o n o c h ro m a to r. The s p e c tr o m e te r is desig n ed fo r single b e a m o p e ra tio n so the sam p le in -s a m p le out p ro c e d u re w as u sed . T he optics of the s p e c tr o m e te r a r e la id out su ch th a t b oth tr a n s m is s io n and re fle c tio n m e a s u re m e n ts m a y be m a d e by m aking only m in o r a d ju stm e n ts. The in cid en ce angle of the b e a m to the sam p le is = * 10° w hen the s p e c tr o m e te r is s e t up for r e flectiv ity m e a s u re m e n t. The change induced in the m e a s u re m e n t by using this angle r a th e r than n o rm a l in cid en ce is s m a ll, as d is c u s s e d in C h ap ter IV, S ection IV -II. T he e n tire s p e c tr o m e te r w as se a le d and p u rg e d w ith d ry n itro g e n gas b e fo re and d u rin g e a c h m e a s u re m e n t. T his p r o ced u re re d u c e s the w a te r vapor content in the s p e c tr o m e te r and thus re d u c e s the a b so rp tio n in the o p tical path. The w a te r vap o r a b s o rp tio n w as u sed to c a lib ra te the freq u en cy v e rs u s the m o n o c h ro m a to r se ttin g s (P y le r and A cq u ista 1955). The c a lib ra tio n is a c c u ra te and re p ro d u c ib le to 0 .5 cm The s p e c tr a l re so lu tio n fo r a ll m e a s u re m e n ts in this w o rk w as b e tte r than 0. 5 cm *. C. In fra re d R eflectiv ity M e a s u re m e n t T he sa m p le to be m e a s u r e d w as m ounted on a h o ld er to g e th e r w ith a f i r s t s u rfa c e a lu m in u m m i r r o r . T he c h e m ic a lly p o lish e d sa m p le s u rfa c e and the m i r r o r s u rfa c e w e re m ounted to w ard the in c id en t lig h t b e a m . The sa m p le h o ld e r w as p la ced in sid e the s p e c tr o m e te r in su ch a w ay th at it could m ove p e r p e n d ic u la r to the p ath of the light b e a m . Thus the re fle c te d ra d ia tio n fro m e ith e r the sa m p le o r the m i r r o r could be m e a s u re d . The re fle c tiv ity s p e c tru m of the sa m p le w as c a lc u la te d fro m the re fle c te d sig n al s tre n g th fro m the sa m p le and the m i r r o r a s su m in g the re fle c tiv ity of the m i r r o r is o for the e n tire fre q u e n c y ran g e. Only ro o m te m p e r a tu r e re fle c tiv ity w as m e a s u r e d . As m e n tio n ed in the la s t sectio n , the incidence angle of this s y s te m w as c lo se to = “10°. D. In fra re d T ra n s m is s io n M e a s u re m e n t In fra re d tr a n s m is s io n m e a s u re m e n ts w e re m a d e a t both ro o m te m p e r a tu r e and liquid n itro g e n te m p e r a tu r e . The sa m p le w as m o u n ted on a sa m p le h o ld e r in a liq u id n itro g e n te m p e ra tu re o p tic a l d ew ar, and the sa m p le c o v e re d one of the two p a ra lle l s lit openings on the h o ld e r. T he h o ld e r w as then a tta c h e d to the cold.-finger a t the b o tto m of the in n e r s te m of the d ew ar. The sa m p le w as m oved in and out of the b e a m by a co n tro lle d ro ck in g of the in n e r s te m . As the sa m p le w as m ov ed out of the b e a m , the open s lit of the sa m p le h o ld e r w as m oved into the b e a m and the in cid en t b e a m in te n sity could be m e a s u r e d . The tr a n s m is s io n a t n o rm a l in c id en ce , T , w as d e te rm in e d b y taking the ra tio of the ra d ia tio n in te n sity tra n s m itte d by the sa m p le to the in c id e n t lig h t in te n sity . F r o m the m e a s u r e d value of T, the a b s o rp tio n co efficien t, a , w as c a lc u la te d a s d is c u s s e d in Section III-IV . The ro o m te m p e r a tu r e tr a n s m is s io n m e a s u r e m e n t w as done by k eeping the c o ld -fin g e r of the d ew ar at ro o m te m p e r a tu r e . 30 T he s a m p le s u sed in th is m e a s u r e m e n t should have both fro n t and b a c k s u rfa c e s p o lish e d . T he th ic k n e ss of the sam p le w as g e n e ra lly betw een 10-20 m ils . O ccasio n a lly v e ry thin s a m p le s , x=“ 0 .5 m il, w e re re q u ire d to m e a s u r e la rg e a b so rp tio n c o e ffic ie n ts. (C hapter IV). E. P h o to lu m in e sc e n c e M e a s u re m e n t ❖ The e x p e rim e n ta l a r r a n g e m e n t for the p h o to lu m in e sc en ce m e a s u r e m e n ts is show n in F ig . III-3. The lig h t so u rc e w as a H e-N e l a s e r w ith an output p o w er ^ 30 mW tuned to the 6238 k lin e . The l a s e r lig h t b e a m re fle c te d fro m four f ir s t su rfa c e m i r r o r s and p a s s e d th ro u g h one filte r and one len s b e fo re it re a c h e d the sa m p le . The lig h t p o w er w as red u ce d by a lm o s t 50% w hen it re a c h e d the d ew ar w indow . T his red u ctio n w as m e a s u re d b y using a 6238 A p o w e r m e te r . The four f i r s t s u rfa c e m i r r o r s d ire c te d the 6238 k l a s e r lig h t b e a m so th a t it could c e n te r on the sa m p le . A C orning 1-75 f ilte r w as used to cu t off any p o s s i ble in f r a r e d ra d ia tio n fro m the l a s e r . A F L 75 m m lens w as u se d to focus the light on the sa m p le w hich w as im m e r s e d in liq u id h e liu m in sid e the d e w a r. The s iz e of the la s e r lig h t spot in c id e n t on the sa m p le s u rfa c e w as about 0 .5 m m in d ia m e te r. The lu m in e s c e n c e ra d ia tio n fro m the sa m p le w as c o lle c te d by a . F L 100 m m le n s and w as th en re fle c te d fro m a f ir s t s u rfa c e ❖ The H e-N e l a s e r w as b o rro w e d fro m P ro f. W. H. S te ie r. The m e a s u r e m e n ts w e re p e rfo rm e d in P ro f. G e rsh e n z o n 's la b o ra to ry . The a u th o r w ish e s to e x p re s s h is deep a p p re c ia tio n to th e se two p r o f e s s o r s and th e ir stu d en ts fo r th e ir kind a s s is ta n c e and under s tanding. Light beam elevation control M He-Ne laser f a $\ I J M M — first surface F , L , I L - lens M S mirror PAR l a N F - filter HR-8 Recorder L Sample in Dewar He Dewar 2 chopper I Detector Precision Lockin Amplifier Perkin-Elmer E -l Monochromator F ig u re III-3 S chem atic d ia g ra m of pho to lu m in escen ce m e a s u re m e n t. 32 m i r r o r w h ich changed the d ire c tio n of the lig h t p a s s a g e tow ard the m o n o c h ro m a to r. The lu m in e sc e n c e lig h t b e a m then p a s s e d th ro u g h e ith e r a C orning 2 -6 4 o r a C orning 3482 filte r . The C orning 2 -64 w as m o re effective in stopping the 6238 A lig h t fro m the l a s e r . The light w as then chopped a t 600 cps and focused on the e n tra n c e s lit of a P e r k in E lm e r E - l M o n o c h ro m a to r. This m o n o c h ro m a to r w as o p e ra te d in a double p a s s m ode and two g ra tin g s w e re u se d to co v er the s p e c tr a l ra n g e . Two d iffe re n t d e te c to rs w e re u sed w ith the choice of d e te c to r depending on the s p e c tru m ra n g e being m e a s u re d . The d e te c to rs w e re a RCA 7102 p h o to m u ltip lie r w ith a S - l re s p o n s e and a B a rn e s A -100B InAs p hotovoltaic d e te c to r. The sig n al fro m the d e te c to r w as then fed to a PA R H R -8 p re c is io n lo c k -in a m p lifie r and finally re c o rd e d on a L ee d s & N o rth ro p s tr ip c h a r t r e c o r d e r . The sig n al output w as c a lib ra te d by using a sta n d a rd lig h t s o u rc e . Due to vary in g fa c to rs su c h as the p ow er output of the l a s e r and the angle of the sa m p le v e rs u s the incom ing lig h t b e a m , only re la tiv e in te n sitie s could be obtained fro m each m e a s u re m e n t. Q uantitative in ten sity c o m p a riso n s betw een d iffe re n t m e a s u re m e n ts a r e n o t re lia b le . III-IV. B ack g ro u n d In this sectio n , the ap p licatio n of lo c a liz e d v ib ra tio n a l m o d e, s o m e tim e s c a lle d LVM , m e a s u re m e n ts to stu d y the im p u r itie s in GaAs is d is c u s s e d . Since the th e o re tic a l tre a tm e n t of LVM is w ell known and has b e e n rev ie w e d by L o r im o r ( 1966), S p itz e r ( 1971), N ew m an (1969)i E llio tt ( 1966) and M arad u d in (1966), 33 it w ill not be p re s e n te d h e re . H ow ever, the g e n e ra l back g ro u n d is im p o rta n t to u n d e rsta n d the re s u lts of the p r e s e n t w o rk and is s u m m a riz e d in this sectio n . The b ack g ro u n d includes previously- re p o rte d e x p e rim e n ta l re s u lts and p r o p e r tie s of G aA s:Si and G aA s:T e. A. L o c a liz e d V ib ratio n al M ode M e a s u re m e n t W hen a light im p u rity ato m is su b stitu te d fo r a h e a v ie r h o st ato m in an o th e rw is e p e rfe c t c ry s ta l, th e re m a y a r is e in fra re d activ e v ib ra tio n a l m o d es w ith fre q u e n c ie s hig h er than the top of the phonon s p e c tru m of the h o st c ry s ta l. The lig h t im p u rity has a high re so n a n c e freq u en cy w hich a c ts as a driving fo rce on the neig h b o rin g h o st a to m s cau sin g the la ttic e to o s c illa te a t a h ig h e r freq u en cy . T his fre q u e n c y is h ig h e r than the h ig h e st u n p e rtu rb e d n o rm a l m ode fre q u e n c y of the la ttic e and the v ib ra tio n a l am p litu d es of the a to m s in the c r y s ta l a r e lo c a liz e d in th a t they a r e a tten u ated a p p ro x im a te ly ex p o n en tially w ith d ista n c e fro m the im p u rity ato m . (M ontroll and P o tts 1955). Thus th e se high fre q u e n c y m o d e s a r e c a lle d lo c a liz e d v ib ra tio n a l m o d e s. The lo c a liz e d v ib ra tio n a l m ode fre q u e n c y depends on the m a s s d iffe r ence betw een the d efect and the h o s t a to m it re p la c e s and on changes in effective fo rce co n stan t coupling the im p u rity to the la ttic e . The atten u atio n length d e c r e a s e s and the fre q u e n c y of the m ode in c re a s e s w ith d e c re a sin g im p u rity m a s s a n d /o r an in c re a s in g effectiv e fo rc e constant. F re q u e n tly the lo c a liz e d v ib ra tio n a l m odds a r e in f r a r e d - activ e and they a r e o b se rv e d in the in f r a r e d a b s o rp tio n s p e c tru m 34 of the sa m p le . To obtain the a b s o rp tio n s p e c tru m , the in f r a r e d tr a n s m is s io n of the sam p le is m e a s u r e d and fro m the m e a s u re d tr a n s m is s io n , T, at a given freq u en cy , the c o rre sp o n d in g a b s o r p tion co efficien t a can be c a lc u la te d by usin g the following s ta n d a rd rela tio n sh ip : 1-R e w h ere T is the tr a n s m is s io n coefficient, R is the re fle c tiv ity coefficient, x is the th ic k n e ss of the sa m p le and a is the a b s o rp tio n coefficient. A ll the a b so rp tio n s p e c tr a of GaAs p re s e n te d h e re w e re c alcu la ted b y using equation (3-1) w ith R = 0 .3 0 . H ow ever, the value of R of GaAs is not a co n sta n t but a slow v ary in g function of the freq u en cy , V . In the fre q u e n c y ran g e of in te r e s t for the p r e s e n t w o rk the R value changes fro m 0.2 3 a t v = 333 c m * to 0 .2 8 a t v = 467 cm""*. (Seraphin and B en n ett 1967). T h e re fo re , one can q u estio n the a c c u ra c y of the a v alu es c a lc u la te d fro m equation (3-1) b y a ss u m in g a co n stan t value of R. H ow ever, the e s s e n tia l in fo rm a tio n fro m the a b so rp tio n s p e c tru m is the in te g ra te d a b s o rp tion band s tre n g th of the lo c a liz e d v ib ra tio n a l m ode, w hich is obtained by in te g ra tin g the a r e a u n d er an a b s o rp tio n band w ith the background a b s o rp tio n s u b s tra c te d . It is shown in A ppendix I th a t although the ab so lu te value of a changes by using d iffe re n t values of R in the calcu la tio n , the value of a given b y the a b s o r p tion band s tre n g th w ith the b ack g ro u n d a b s o rp tio n s u b stra c te d , 35 i . e . a a band a b ackground , re m a in s e s s e n tia lly the aam e value, independent of the R value. The exam ple in Appendix I shows th a t the m a x im u m e r r o r in c u rre d in calcu latin g the a b so rp tio n band s tre n g th by using R = 0 .3 0 in s te a d of 0.2 3 is le s s than 3%. This e r r o r is sm a ll c o m p a re d w ith the =- 5% lim it of the a c c u ra c y in m e a s u re m e n ts of the tra n s m is s io n . A study of the LVM yields in fo rm a tio n of the im m e d ia te en v iro n m en t of the im p u rity in the la ttic e . In addition, in fo rm a tion of c o n c e n tra tio n of the im p u rity can a lso be obtained fro m the LVM m e a s u re m e n t. D aw ber and E llio tt (1963 a ,b ) and E llio tt and D aw ber (1965) c a lc u la te d the a b so rp tio n due to the lo c al m ode fo r an isotopic su b stitu tio n al im p u rity in a cubic la ttic e and the ab so rp tio n coefficient a(U') is given by [N] |x(0)|2g(w) , (3-2) w h ere [N] is the im p u rity c o n c e n tra tio n , e is the sta tic c h arg e on the im p u rity , n is the re fra c tiv e index, A is the lo c al field c o rre c tio n fa c to r w hich is given by g(U>) is the line shape function w here 1, U) i s t h e a n g u l a r f r e q u e n c y a n d i s r e l a t e d t o v b y C D = 2 t t c v a n d lx(Q)| i s a c o r r e c t i o n f a c t o r to a c c o u n t f o r t h e f a c t t h a t t h e neig h b o rs of the im p u rity m a y contain p a r t of the kinetic e n e rg y . 36 The in te g ra te d a b so rp tio n is given by in te g ra tin g equation (3-2), J ^ a ( t o ) dm = [N] J*" |X (0)|2g(w )dw . (3-3) F o r a light im p u rity w ith m a s s M 1, the quantity |x ( 0 ) | M 1 a p p ro a c h e s 1 (D aw ber and E llio tt 1963a). U sing this condition p O O and Jo g(tt>) dC O = 1, equation (3-3) re d u c e s to J0 "a(W )du> = [N] . (3-4) E quation (3-4) show s th a t the in te g ra te d a b so rp tio n of the LVM band is p ro p o rtio n a l to the im p u rity co n ce n tratio n . L o rim o r, S p itz e r and W aldner (1966) re p o rte d m e a s u re m e n ts w hich d em o n s tr a te d the a p p ro x im a te lin e a r re la tio n sh ip betw een the a b so rp tio n co efficient, a , and the im p u rity co n c e n tra tio n fo r P and A1 in GaAs fo r o v e r a th re e o rd e r of m agnitude change in a . S im ila r re la tio n sh ip w as a lso o b se rv e d for B in Si (S pitzer and W aldner 1965) and Si in Ge (C osand and S p itz er 1971). An is o la te d su b stitu tio n a l im p u rity in III-V com pound la ttice has te tr a h e d r a l site s y m m e try (T^) and the lo c a l m ode has t h r e e fold d e g e n e ra c y . If the s u b stitu tio n a l im p u ritie s fo rm p a irs o r la r g e r co m p le x e s, the te tr a h e d r a l site s y m m e try is lo w e re d due to in te ra c tio n s betw een n eighboring im p u rity a to m s. H ence the th re e -fo ld d e g e n e ra c y is lifted, and a sp littin g of the d e g e n e ra te ab so rp tio n band m a y be ex p ected . T his is d is c u s s e d in the next se c tio n w hen (S i^ a ~ S i ^ g) p a irs fo rm in S i-doped GaAs in m e a s u ra b le co n c e n tra tio n . In addition, w hen the c o n c e n tra tio n of 20 -1 su b stitu tio n a l im p u rity ato m s b eco m e la rg e (> 10 cm ), they can no lo n g e r be re g a rd e d as n o n -in te ra c tin g s p e c ie s. In this c a se , b ro ad en in g of the fu n d am en tal LVM band m a y be o b s e rv e d (S pitzer 1967a). In g e n e ra l, fo r high im p u rity co n c e n tra tio n , the te tr a h e d r a l site s y m m e try b e c o m e s d isru p te d . T his m a y be ca u se d b y the p re s e n c e of vary in g in te rn a l s tr a in fields due to the p re s e n c e of im p u rity bond d is to rtio n s w hich le ad to changes in site p o te n tia l, o r by d ir e c t im p u rity -im p u rity in te ra c tio n s , o r by m ode coupling effects if the lo c a l m ode ex tends out s e v e r a l la ttic e sp a c in g s. T h ese effects can lo w e r the s y m m e try , sp lit the trip ly d e g e n e ra te lo c a l m ode and give the a p p e a ra n c e of line b ro ad en in g if the sp littin g is sm a ll. In C h ap ter V, so m e line bro ad en in g effects a r e o b se rv e d in the e x p e rim e n ta l r e s u lts . W hen no line bro ad en in g is o b s e rv e d , the ra tio of the in t e g ra te d a b s o rp tio n of two lo c a l m ode bands is equal to the ra tio of the p eak height of th e se two bands w hich is in tu rn the ra tio of the re s p e c tiv e im p u rity c o n c e n tra tio n s. If the line b ro ad en in g e x ists , the in te g ra te d a b so rp tio n m u s t be u se d to c o m p a re the , im p u rity c o n c e n tra tio n s . B. S i-doped GaAs In this sectio n , som e of the p re v io u s ly re p o rte d p ro p e rtie s of G aA s:Si a r e rev iew ed . The d is c u s s io n is r e s tr ic te d to those re s u lts w hich a r e re le v a n t to the p r e s e n t w ork. B l . B eh av io r of Si in S i-d o p ed GaAs Si is an a m p h o te ric im p u rity in G aA s. It s u b stitu te s on a Ga site , SiQa > as a donor, and on a As s ite as an a c c e p to r. The s o lu b ility lim it of Si in GaAs is =*0.5 ato m ic % o r =- 2 x 1(?^ 38 -3 cm (Kolm e t al. 1957). F o r low Si co n c e n tra tio n , [Si] = * ■ 17 -3 10 c m , the Si p r e f e r s the Ga site and b eh av es as a n o rm a l donor. The c a r r i e r c o n c e n tra tio n ng v e ry n e a rly equals [Si]. As the [Si] is in c re a s e d , the ng is not p ro p o rtio n a lly in c re a s e d . In 19 -3 floating zone m a te r ia l w ith [Si] > 10 cm , n is p r a c tic a lly [Si] 18 -3 independent a t 4 to 5 x 10 c m . T his dependence has been shown by W helan et al. (I960). S im ila r r e s u lts a r e obtained for b oth C z o c h ra lsk i and h o riz o n ta l B rid g m a n grow n c r y s ta ls . B2. L o c a liz e d V ib ratio n al Mode Study of C u- o r L i- d iffused GaAs: Si The m a s s of Si is lig h te r than e ith e r the Ga o r A s, hence b oth the S i^ a and S i^ g sp e c ie s should have lo c a liz e d v ib ra tio n a l m odes (LVM). W hen Si is an iso la te d su b stitu tio n a l im p u rity in the GaAs la ttic e i t has te tra h e d ra l point group s y m m e tr y and the th re e v ib ra tio n m o d es of the Si im p u rity w ill be d e g e n e ra te . T h e re fo re one in fra re d a b so rp tio n band is ex p ected for S i^ a and a n o th e r one fo r S i ^ g . The two sp e c ie s w ill have d iffe re n t f r e q u en cies b e c a u se of a slig h tly d iffe re n t m a s s d efec t, i . e . , the m a s s d efect is given by e = (Mg^-M)/M, w h e re M = m a s s of Ga o r A s, and a lso the d iffe re n t n e a r e s t n eig h b o rs in the two c a se s should influence the effective fo rce c o n sta n ts. The o b se rv e d 28 -1 -1 lo c a l m ode fre q u e n c y for ®*Qa *s v = c m a n ^ ^99 c m - 28 fo r S i. . (L o rim o r and S p itz e r 1966). A S 19 -3 In the c a se w hen the Si doping le v e l is high (> 10 cm ), two s m a ll LVM bands a r e a lso o b se rv e d . T h e se bands a r e a t 374 cm * and 378 c m * and a r e due to the S i_ d efec t w ith ^^Si Ga 39 29 and Si. The a b so rp tio n s tre n g th s of th e se S i^ a LVM bands ( i . e . , 384 c m \ 378 c m ^ and 374 c m a r e in good a g re e m e n t 28 29 w ith the n a tu ra l abundance of the iso to p e s Si (92.2% ), Si 30 (4. 7%) and Si (3. 1%). (T hom pson and N ew m an 1972). T h e se LVM bands w ere independently o b se rv e d h e re and a r e re p o rte d in C h a p te r V. In so m e c a s e s the silic o n im p u rity is not is o la te d fro m o th e r defects but is p a ire d w ith a n o th e r silic o n o r a n o th e r i m p u rity on a neighboring site . T h e re can be d iffe re n t re a s o n s for the e x iste n c e of th e se ion p a i r s . T h e re is evidence (Q u e isse r 1966; S p itz e r and A llre d 1968b) th a t a t high [Si], the (SiQa “S i ^ g) p a ir s tend to fo rm in c o n c e n tra tio n s w hich a r e la rg e c o m p a re d to th o se p re d ic te d b y ran d o m s ta tis tic s . Since the sa m p le s a r e s tro n g ly n -ty p e the re su ltin g fre e c a r r i e r a b so rp tio n m u s t be red u ce d b y the in tro d u ctio n of a n e le c tr ic a lly c o m p en sa tin g im p u rity . L ith iu m o r co p p er is diffused a t an elev ate d te m p e r a tu re to p ro d u c e the co m p en sa tio n . A fte r the diffusion, LVM bands have b een o b se rv e d and a r e a ttrib u te d to ( S i ^ - L i j - ^ ) o r (SiQa ~CuQa ) p a i r s . (S pitzer and A llre d 1968b). C le a rly , in th e se c a s e s , the silico n is no lo n g e r in a site w ith te tr a h e d r a l s y m m e try . F o r the ( S i ^ - L i ^ ) p a i r s w h e re the defect involves im p u ritie s on second n eig h b o r s ite s , a w eak coupling m o d el a p p e a rs to give re a so n a b le a g r e e m e n t w ith e x p e rim e n t (S pitzer and A llre d 1968b). The effect of one a to m is to a lte r the p o te n tia l a t the site of the o th e r im p u rity ato m . Since the n e a r e s t - 40 neighbor g alliu m s ite s a re along the < 110> d ire c tio n , w hich is not a s y m m e try ro ta tio n axis of the te tr a h e d r a l point group, the trip ly d e g e n e ra te S i^ a band w ill be s p lit into th re e bands w ith fre q u e n c ie s n e a rly independent of the lith iu m isotope. T h ese bands w ill be lo c a te d n e a r the SiQa fre q u e n c y of 384 c m ' l A sim p le p e rtu rb a tio n a rg u m e n t (L o rim o r and S p itz er 1967b) gives 3 V 2 = ^ S V .2 , (3-5) i= l 1 w h ere v is the fre q u e n c y of the trip ly d e g e n e ra te m ode and the V. values a r e the p e r tu r b e d fre q u e n c ie s . In the (Si_, - L i ^ ) 1 (jtcL V jtcL defect ca se th e re w ill a lso be th re e bands involving p r im a r ily lith iu m m o tio n . The fre q u e n c ie s of the p re d o m in a n tly silic o n m odes and those due to lith iu m a r e given in Table III-I. T he (®^Ga~^As^ defect m o re c o m p lica ted (Spitzer and A llre d 1968b; E llio tt and P feu ty 1967) in th a t the two im p u ritie s a r e stro n g ly coupled, and both a r e lig h t c o m p a re d to the a to m s they re p la c e . The p a ir axis is in a < 111 > d ire c tio n w hich is a th re e -fo ld ro ta tio n a x is, and the six v ib ra tio n a l m odes w ill c o n tain two se ts of doubly d e g e n e ra te m o d e s. T hus, th e re w ill be four fre q u e n c ie s , of w hich two a r e id e n tified in Table III-I. The th ird band a t 367 cm * is doubtful. Its ab so rp tio n stre n g th c o r r e la te d v e ry w ell w ith the s tre n g th of the 464 c m ^ band as if th e se two m o d e s w e re fro m the sa m e defect. Y et fro m a r e cent study (Leung e t a l . 1973), the 367 cm * band did shift to -1 30 30 28 357 cm " in S i-doped G aA s, b u t in Si and Si m ix ed is o to p e - doped GaAs s a m p le s the 367 cm * band did not show the m ix ed 41 T A B L E H I-I M AJOR LO C A LIZED VIBRATIONAL M ODE 7 fi O F GaAs: Si CO M PENSATED BY L i OR Cu Mode F re q u e n c y (Cm ) D efect Im p u rity L i L i Cu L i- la ttic e defects L i 321 365 379 352 389 406 L i Ga 438 447 454 470 480 487 SlG a-IjlGa SiG a "CuGa Si Ga Si Ga 374 379 405 374 379 405 374 376 399 Si Ga Si As S i_ -Si A Ga As Si Ga Si As SiG a -SiA 5 384 399 367(?) 393 464 384 399 3 67(?) 393 464 384 399 isotope ( S i- Si) p a ir band as did the o th e r two ban d s at 393 cm * and 464 cm *. Thus the id en tity of the 367 c m * band is in doubt and a q u estio n m a rk is p la c e d a f te r this band in T able III-I. The fo u rth m ode is e ith e r too s m a ll in a b so rp tio n to be o b se rv e d o r, as c a lc u la tio n in d ic a te s, it falls in a reg io n of la rg e a b s o rp tio n fro m the GaAs h o st la ttic e (S p itzer and A llre d 1968b). The lo catio n s of a ll bands o b s e rv e d in lith iu m - o r c o p p e r-d iffu se d , silico n -d o p ed GaAs a r e lis te d in T able III-I. F o r c o m p le te n e s s, the lo catio n of som e bands re la te d to lith iu m p a ire d w ith la ttic e defects in undoped GaAs is a lso given (Levy and S p itz e r 1968). T h ese la tte r bands a r e not re la te d to the silico n im p u rity but can o c c u r in all sa m p le s w hich a r e lith iu m - diffused and s a tu ra te d a t a su fficien tly high te m p e ra tu re (L o rim o r and S p itz e r 1966). No LVM band due to sin g le L i has e v e r b een o b se rv e d (Levy 1973). T h e re have b e e n a n u m b e r of e x p e rim e n ts w hich have s u g g ested th a t the d istrib u tio n of silic o n am ong the v a rio u s defects m e n tio n ed can be influenced by the p re s e n c e of o th e r im p u ritie s . Som e e le c tr ic a l and r a d io - t r a c e r m e a s u re m e n ts of s e le n iu m -p lu s - silic o n -d o p e d GaAs in d icated th a t the S e A d o n o rs could change J\ s [S i^ g] / [SiQa ] fro m a value < 1 to >1 (W helan e t al. I960). L o cal m ode m e a s u re m e n ts of a s u lp h u r-p lu s -s ilic o n -d o p e d sam p le (L o rim o r and S p itz e r 1966) show ed the S i. band a t 399 cm * to s be la r g e r than the S i^ a band a t 384 c m *. In s im ila r ly silic o n - doped sa m p le s but w ithout su lp h u r (Spitzer and A llre d 1968b), the 384 c m ” * band is 4 to 5 tim e s as stro n g as the 399 c m * band. 43 H ow ever, the bands in the su lp h u r-d o p e d sa m p le w e re s m a ll and clo se to som e v e ry la rg e L i-la ttic e d efect bands and the re s u lts w e re u n c e rta in . S p itz e r and A llre d (1968a) re p o rte d som e in te re s tin g effects on the Si site d istrib u tio n due to L i diffusion. T hey o b se rv e d fro m LV M m e a s u re m e n ts that the [ S i ^ ] / [S i^ g] w as d e c re a s e d b y an o r d e r of m agnitude and fro m > 1 to < 1 by L i diffusion a t 900° C c o m p a re d w ith th at a t 700° C. The to tal c o n c e n tra tio n of [S i^a ] + [S i^ g] re m a in e d unchanged. No lo ss of Si to com plex o r p a ir fo rm a tio n w as o b se rv e d and the site s y m m e try of the Si was te tr a h e d r a l b efo re and a fte r re d is trib u tio n . T his effect w as in te r p r e te d by the au th o rs to m e a n that Si can m ove fro m p r e do m in an tly Ga site s to p re d o m in a n tly As site s d u rin g a 900° C L i diffusion. M o re o v e r, c a r r i e r co n c e n tra tio n m e a s u re m e n ts m a d e by the a u th o rs in d icate d th a t this re d is trib u tio n of Si does not take p la ce during annealing at the s a m e te m p e ra tu re . B 3. L o c a liz e d V ib ratio n al M odes of G aAsrSi C o m p e n sa ted by E le c tro n Irra d ia tio n S p itz e r et a l . (1969) re p o rte d a c o m p a ris o n of the lo c a liz e d v ib ra tio n a l m odes in 1 MeV e le c tro n irra d ia tio n -c o m p e n s a te d and 7 L i d iffu sio n -c o m p e n sa te d GaAsrSi m a te r ia l. T h e ir r e s u lt is re p ro d u c e d in F ig . I l l - 1. T his fig u re shows th a t the s p e c tru m of the e le c tro n ir r a d ia te d sam p le is m u c h s im p le r than the L i- diffused one. A ll the ( S i ^ - L i ^ ) p a ir bands a r e a b s e n t in the e le c tro n ir r a d ia te d sa m p le . The b ro a d bands n e a r 445 c m ’ * and 458 c m show n in the s p e c tru m of e le c tro n ir r a d ia te d sam p le 44 : a r e due to m ultiphonon la ttic e a b s o rp tio n (S pitzer 1967b). The Si bands a r e a ll p r e s e n t and show no m e a s u ra b le change betw een the two co m p en sa tio n m e th o d s. This a g re e m e n t in d icates th a t the . e le c tro n irra d ia tio n p ro c e s s does not change the Si site d is tr ib u tion. The only new band in the e le c tro n ir r a d ia te d sam p le is a wide band n e a r 369 cm The o rig in of this band is not known. Leung et al. (1973) found th at this band shifted to 359 cm ^ w hen 30 28 Si iso to p e w as u sed as dopant in p la c e of Si. W hen a 50% 28 30 m ix ed isotope of Si and Si w as u sed as the dopant, no c ro s s band w as found in betw een 359 cm ^ and 369 cm * w hich s u g g e s t ed that this band w as p ro b a b ly not due to defects involving Si p a i r s . The sa m e r e s u lt w as u sed e a r l i e r in the d is c u s s io n of the id en tity of the 367 cm ^ band. H ow ever sin ce the 369 cm * band did show an isotope shift, this band m u s t be due to a defect a s s o c ia te d w ith Si. T h e re is so m e p o s sib ility th a t this defect m a y be a (SiQa “VQa ) com plex. T his p o s s ib ility is d isc u s se d in the next section. B4. C o rre la tio n B etw een C a r r i e r C o n cen tratio n and L o c a liz e d M odes in G aA s:Si S p itz e r and A llre d (1968b) show ed th at fo r S i-doped GaAs, the c a r r i e r c o n ce n tratio n , n e> w as p ro p o rtio n a l to the d ifferen ce in stre n g th s of 384 cm * and 399 c m * b an d s. Since the h a lf w idths of the bands w e re n e a rly equal, the band heights le s s back ground w e re u sed in the d e te rm in a tio n of the a b so rp tio n c ro s s sectio n . They found that -18 +2 A a / [defect] = (ot.384-0c399> ^ ne = ^ ' 3 x 10 cm ’ 45 w h ere A cc is the d iffere n ce in band heights of 384 cm * and 399 c m ’ ' b an d s. T his c r o s s se c tio n gave re a so n a b le a g re e m e n t betw een m e a s u r e d and e s tim a te d n fo r m o re than an o r d e r - o f - e m agnitude v a ria tio n in Ct^g^ an<* H ow ever, the Si co n cen tra tio n w hich accounted fo r the ( S iQ a '^ G a ^ o r (SiQa ~CuQa ) bands did not co n trib u te to the c a r r i e r co n ce n tratio n , though in the m o re h eavily doped sa m p le s th e se bands w e re la rg e . A p o ssib le ex p lan atio n for this d is c re p a n c y w as p ro p o se d by S p itz er and A llre d (1968b) who su g g ested that b e fo re L i diffusion, the h eav ily S i-doped GaAs m a te r ia l a lre a d y had so m e (®^Qa”^Ga^ d efec ts. C o n sid erin g the p o s sib ility th a t V q & could be an a c c e p to r (Munoz e t al. 1970), this p a ir could e ith e r be n e u tra l o r in the sa m e ch arg e sta te as the ( S i ^ - L i ^ ) s p e c ie s it b eco m es a fte r L i diffusion. A p h o to lu m in e sc en ce p e a k n e a r 1.2 eV w as a ttrib u te d to the (SiQa - VQa ) d efec t by W illiam s and B lack n all (1967). The elim in a tio n of ( S i ^ - L i ^ ) band in e le c tro n ir r a d ia te d sa m p le w ith no in c re a s e in the S i^ a band and the p h o to lu m in e sc en ce r e su lt s e e m e d to su p p o rt the a s s u m p tio n th a t the (®^Qa “^Ga^ defects did e x ist in the a s -g ro w n sa m p le . Since the 369 c m ^ lo c a liz e d m ode in e le c tro n ir r a d ia te d -c o m p e n s a te d sa m p le show ed a Si iso to p e sh ift, it w as not u n re a so n a b le to a s s u m e that this m ode is re la te d to (S*Ga”^Ga^ Pai r s * I* 1 C h ap ter V, a m o re ex ten siv e d is c u s s io n c o n ce rn in g this d efec t is given. E x p e rim e n ts w e re a lso d esig n ed to p o sitiv e ly id en tify this d efect, but they w e re u n su c c e ss fu l. An ex p lan atio n of th e se a tte m p ts is given in A ppendix II. 46 B5. P -T y p e Si-D oped GaAs S p itz e r and P a n is h (1969) m e a s u re d the lo c a liz e d v ib r a tional m o d es of L i-d iffu se d , p -ty p e S i-doped GaAs grow n a t a p p ro x im a te ly 800° to 850° C fro m a G a -ric h solution containing disso lv ed Si as the p r im a r y im p u rity . The a b so rp tio n coefficient of the Si_, donor band at 384 cm * w as h ig h e r than that of the u a a c c e p to r band at 399 c m If the SiQa and S i^ g sp e c ie s w e re the only donor and a c c e p to r sp e c ie s, the p -ty p e b eh av io r could not be explained. T h e re fo re the p -ty p e m a te r ia l m u s t have la rg e co n ce n tratio n s of som e o th e r a c c e p to r d e fe c ts. T his sp e c ie s has not b een identified. In C h ap ter V, an a c c e p to r s p e c ie s is found to e x is t in an n ealed GaAsrSi sam p les but no lo c a liz e d v ib ra tio n a l m ode is o b se rv e d fro m this defect. The p o ssib le connection betw een these two a c c e p to r sp e c ie s is sp e c u la te d upon in that c h ap ter. B 6. P h o to lu m in e sc e n c e Study of G aA s:Si T h e re a r e m a n y re p o rts of p h o to lu m in e sc en ce stu d ie s of G aA s:Si. W illiam s and B lack n all (1967) re p o rte d the o b se rv a tio n of th re e peaks a t 20° K in a G aA s:Si sa m p le w ith a c a r r i e r 16 -3 c o n c e n tra tio n of n g =• 6 x 10 cm . T h ese peaks w e re lo c ated a t 1.492 eV, =*1.2 eV and = “ 0. 98 eV. The 1.492 eV peak w as iden tified as a tra n s itio n fro m the conduction band to the Si a c c e p to r le v el. The 0. 98 eV p eak w as not identified, b u t w as sp ecu la ted as being re la te d to a d efec t com plex induced by Si. The p eak n e a r 1.2 eV w as a lso se e n in o th e r n -ty p e , m e lt-g ro w n 18 and flo a tin g -z o n e -g ro w n c r y s ta ls doped to a le v e l of 1 x 10 47 _3 d onors p e r cm o r g r e a te r w ith e ith e r group IV o r group VI im p u ritie s . H ow ever this peak is not o b s e rv e d in s in g le - c r y s ta l sa m p le s grow n fro m a Ga solution. (W illiam s 1968). The peak p o sitio n w as in the en e rg y ran g e 1.1 7 to 1.22 eV. The e m is sio n p eak e n e rg y a s s o c ia te d w ith the G roup IV im p u rity w as alw ays below th a t a s s o c ia te d w ith the G roup VI im p u rity . W illiam s (1968) id en tified this peak as due to tra n s itio n s fro m conduction band i edge to a d e fe c t w hich is p ro p o se d as a g a lliu m vacancy bound to a donor. In C h ap ter V, the o b se rv a tio n of both 1.2 eV and 0.9 8 eV peak s in the G aA s:Si s a m p le s a re re p o rte d and th e ir p o ssib le o rig in s a r e d isc u s se d . Two a c c e p to r le v els due to Si w e re found fro m p h o to lu m i n e sc e n c e m e a s u re m e n ts of e ith e r p -ty p e o r n -ty p e Si-doped GaAs p r e p a r e d by liq u id -p h a se epitaxy. (K re ss e l et a l . 1968, K re s s e l and N elso n 1969) T h ese a c c e p to r le v els w e re e stim a te d about = “ 30 m eV and = “ 90 m eV above the valence band. The p h o to lu m i n e sc e n c e peaks due to the tra n s itio n to th e se two a c c e p to r lev els w e re o b s e rv e d a t 1.44 eV and 1.3 8 eV a t 77° K in p -ty p e m a te r ia l. The tra n sitio n w as su g g ested to o rig in a te fro m a r a th e r n a r r o w e n e rg y ran g e below the conduction band (K re ss e l e t al. 1968). In n -ty p e m a te r ia l, th e se two p eak s w e re o b se rv e d a t =- 1.475 eV and = “ 1.435 eV a t 4 .2 ° K. At 77° K, only the tra n s itio n to the d e e p e r a c c e p to r le v e l w as o b s e rv e d . (K re s s e l and N elso n 1969). P ankove (1968) in his cath o d o lu m in escen ce study of n -ty p e G aA s, o b se rv e d th a t the e m is s io n p eak n e a r 1.5 eV m oved to h ig h e r values as the donor co n c e n tra tio n w as in- 48 c re a s e d . The e m is s io n peak shifted fro m 1.512 eV w ith ng = 4 x 10^ cm ^ t 0 1.537 eV w ith n = 6 .8 x 10*^ cm F o r a e 18 -3 S i-doped GaAs sam p le w ith n g = 3 x 10 c m ” , the p eak w as o b se rv e d at 1. 518 eV. Since the sh ift of the F e r m i le v e l p o s i tion due to the in c re a s in g ng w as la r g e r than the o b s e rv e d shift of the e m is sio n p eak p o sitio n , the e le c tro n s fo r the re c o m b in a tio n p ro c e s s could not o rig in a te fro m the conduction band n e a r the F e r m i le v e l. Thus the ra d ia tiv e p ro c e s s w as su g g ested by the au th o r to be a d o n o r-to -a c c e p to r tra n s itio n w ith the donor sta te s having m e rg e d w ith the conduction band below the F e r m i le v el. B7. A nnealing E ffect of G aA s:Si It is w ell known th a t n -ty p e GaAs b e c o m e s p -ty p e o r le ss n-ty p e as a r e s u lt of h e a t tre a tm e n t (Edm und I960, W ysocki I960). C opper is u su ally c o n sid e re d to be re sp o n s ib le fo r the change. Hwang (1968) re p o rte d th a t the c o n v e rsio n to p -ty p e took p la ce at te m p e r a tu r e s g r e a te r than 600° C in lig h tly S i-doped 16 -3 GaAs w ith a c a r r i e r c o n c e n tra tio n = “ 10 cm . He found th at fo r annealing te m p e ra tu re T ^ £ 870° C, co p p er con tam in atio n w as so lely re sp o n sib le fo r the c o n v ersio n . F o r T ^ s 9 0 0 ° C , in a d d i tio n to the Cu a c c e p to rs , an o th er shallow a c c e p to r lev el w hich gave a 1.49 eV p hotolum inescence p eak at 20° K w as o b se rv e d . It w as su g g ested by Hwang th a t this shallow a c c e p to r w as due to S i. w hich fo rm e d as a re s u lt of S i-s ite tra n s itio n during the A S annealing p r o c e s s . The Cu co n tam in atio n can be e x tra c te d fro m p -ty p e GaAs b y annealing in m o lte n KCN (Blanc and W e isb e rg 1964) and the sam p le w as found to be c o n v erted b ack to n -ty p e . 49 B 8. Ion -Im p lan tatio n of Si Into GaAs L o c a liz e d v ib ratio n al m ode a b so rp tio n of ion im p lan ted Si in GaAs has b een studied by Skolnik et al. (1972). The e s tim a te d 2 1 - 3 c o n c e n tra tio n of im p lan ted Si w as =” 1 x 1 0 cm . This is m u c h l a r g e r than the solu b ility lim it of Si in GaAs w hich is e s t i - 20 -3 m a te d to be 1 to 2 x 10 cm . (Kolm e t al. 1957). The im p lan ted sam p le at annealing te m p e ra tu re s T ^ £ 550° C show ed an in c re a s e of the in te g ra te d in te n sitie s of the lo c a liz e d v ib ra tio n a l m odes due to SiQa > S i ^ g and the n e a r e s t n eig h b o r ( S i ^ - S i ^ ) p a ir s . B etw een 550° and 600° C, the co n c e n tra tio n of S i^ a and S i. d e c re a s e d , w h e re a s the (Si— -S i. ) p a ir c o n c e n tra tio n r e - As v Ga A s' ^ m a in ed co n stan t. B etw een 600° C and 650° C, the S i^ a co n c e n tra tio n d e c re a s e d b u t th o se of the S i. and (Si— -S i. ) p a ir A S Vjrcl A S sp e c ie s in c re a s e d . F o r 650° C the s tre n g th of a ll th re e m odes in c re a s e d again. The an nealing of the S i^ a and S i ^ g bands fo r 600° C show ed evidence of a cy clic b eh av io r. C. A nnealing E ffect of T ellu riu m -D o p e d G allium A rse n id e Te is a lso a n-rtype dopant in G aA s. M any stu d ies on the annealing effects have b een re p o rte d and th e re fo re it is re a s o n - able to a tte m p t to co m p a re the re s u lts re p o rte d for G aA s:T e w ith the effects o b se rv e d in GaAsrSi. Some c o m p a ris o n s a r e m ade in C h ap ter V and th e re fo re w e p r e s e n t h e re so m e of the back g ro u n d in fo rm a tio n on the G aA srTe s y ste m . F u lle r and W o lfstirn (1963) studied annealing effects in h eav ily Te and Se-doped GaAs by using H a ll-e ffe c t m e a s u re m e n ts . They found th at w ith a doping 19 -3 le v e l of 10 c m , the sam p les show ed r e v e r s ib le te m p e ra tu re - 50 dependent changes in the fre e c a r r i e r co n c e n tra tio n o v e r the te m p e ra tu re ran g e 650° to 1100° C. The c a r r i e r c o n c e n tra tio n 19 -3 n g w as = “ 1 x 10 c m a fte r 1100° C annealing and d e c re a s e d to 18 - 3 =-2 x 10 cm a fte r 650° C annealing. They su g g ested th a t the d e c r e a s e of c a r r i e r c o n c e n tra tio n w as due to the donors reac tin g to fo rm m o lecu le s X (D ++ e ")« * D , (3-6) w h ere D re p r e s e n ts a group VI donor. G rish in a e t al. (1970) a lso re p o rte d a s im ila r annealing e ffect for h eavily T e-d o p e d GaAs by using H all effect m e a s u r e m e n ts . A fte r quenching a sa m p le fro m 1100° C to ro o m te m - 19 -3 p e r a tu r e , the c a r r i e r co n ce n tratio n w as ne = “ 1 .6 x 10 cm A nnealing red u ce d the c a r r i e r c o n c e n tra tio n , p a r tic u la r ly during the f ir s t 10 to 15 m in u te s. F o r the ann ealin g te m p e ra tu re range 700 to 800° C, a m onotonic d e c re a s e of the ro o m te m p e ra tu re c a r r i e r c o n c e n tra tio n w as o b se rv e d . T he c a r r i e r co n ce n tratio n 18 - 3 d e c re a s e d to = “ 3 x 10 c m a f te r a 50 h o u r an n ea l w ith no sig n ifican t fu rth e r change as the an nealing tim e i:s in c re a s e d . In the range fro m 900 to 1000° C, the c a r r i e r co n c e n tra tio n d e c r e a s e d in the f i r s t 25 to 30 m in u te s , and w as then followed by a 18 -3 sudden in c re a s e of A n = “ 2 x 10 c m " . A fter this sudden e in c re a s e , the c a r r i e r co n c e n tra tio n a g a in d e c re a s e d m o n o to n ically 18 - 3 to a sta b le value w ith ne= * 7 x 1 0 c m for 1000° C annealing 18 -3 and n e = “ 4 x 10 c m ” fo r 900° C annealing. F r o m the o b se rv e d changes in the c a r r i e r c o n c e n tra tio n and m o b ility , the a u th o rs 51 su g g ested that th e re w e re a t le a s t two d iffe re n t com plexes fo rm e d in G aA s:Te during annealing, b u t no sp ecific m o d els fo r these com p lex es w e re given. In the two stu d ies d e s c rib e d above, the m e a s u re m e n ts u sed w e re H all coefficient and e le c tr ic a l conductivity. Hwang (1969) studied the annealing of T e-d o p e d GaAs by using p h o to lu m i n escen c e m e a s u re m e n ts in addition to the H all effect and in fra re d re fle c tiv ity m in im u m m e a s u re m e n ts w hich w e re u sed to d e te rm in e the c a r r i e r co n cen tratio n . The sa m p le s w e re an n ealed a t 800° C for 3 h o u rs . F o r an in itia l c a r r i e r c o n c e n tra tio n below 2. 5 x 1 7 - 3 10 cm , no change in ng n o r in the in te g ra te d edge e m is s io n 17 in ten sity , I, w as o b se rv e d a fte r annealing. F o r ng> 2 .5 x 10 -3 cm , the annealing cau sed ng to d e c r e a s e . It w as o b s e rv e d that the d e c re a s e in ng w as ac c o m p a n ie d by a d e c re a s e in I. The edge e m is s io n in the p h o to lu m in e sc en ce is p re s u m a b ly due to tra n s itio n s fro m the conduction band to the valence band. The d e c re a s e in I a fte r annealing w as su g g e ste d by the au th o r as due to the c re a tio n of a c o n sid e ra b le n u m b e r of defects w hich could c ap tu re m o s t of the in jected holes. Hwang su g g ested th at the d efects fo rm e d during annealing w e re e ith e r p re c ip ita te s of Te ato m s o r com plexes involving T e ato m s in a g re e m e n t w ith the com plexes p ro p o se d by F u lle r and W o lfstirn (1963). D. L a ttic e V acan cies G e n e ra tio n Due To A nnealing Of n -T y p e GaAs P o tts and P e a r s o n (1966) found th a t the annealing of n -ty p e GaAs at 1000° C w ith an a r s e n ic o v e r p r e s s u r e d e p re s s e d the d e- 52 feet fo rm atio n w hich cau sed a m e a s u ra b le ex p an sio n in the la ttice co n stan t and id en tified the defects as a r s e n ic v a c a n c ie s. H a rris e t al. (1969) re p o rte d that S n-doped e p ita x ia l GaAs w a fe rs show ed 14 -3 a red u ctio n of Ang ^ 8 x 10 cm w ithin a depth of 2pm of -8 the sam p le s u rfa c e w hen they w e re h eated in v acu u m of 1 x 10 T o r r a t 600° C for 1 h o u r. The au th o rs in te rp re te d this change as a re s u lt of the fo rm a tio n of As v a c a n c ie s. The diffusion c o e f ficien t fo r A s v a c n a c ie s a t 600° C w as thus e s tim a te d to be -11 2 - 1 = “ 10 cm se c . M unoz e t a l. (1970) a lso found a c c e p to r form a tion a t the s u rfa c e of e ith e r n -ty p e o r p -ty p e liquid e p ita x ia l- grow n GaAs s a m p le s during annealing. In sa m p le s an n ea led a t 850° C for 30 m in u te s fo r A s^ p r e s s u r e s above 50 T o r r , the a c c e p to rs w e re a s s o c ia te d w ith Ga v a c a n c ie s and the o b se rv e d 16 -3 changes in c a r r i e r c o n c e n tra tio n w e re A ng =*2 x 10 cm . F o r A s^ p r e s s u r e s below 50 T o r r , the a c c e p to rs w e re a s s o c ia te d 17 -3 w ith A s v aca n cies w ith the o b s e rv e d A ne =“ 3 x 10 cm . The -12 2 diffusion coefficients a t 850° C w e re e s tim a te d to be 10 cm sec ^ for Ga v a c a n c ie s and 10 ^ c m ^ s e c * fo r A s v a c a n c ie s. T h ese v aca n cies w e re b eliev ed to be a lso re sp o n sib le for the th e rm a l co n v e rsio n of n -ty p e G aA s. (T oyam a 1969). The v ario u s effects of GaAs m a te r ia l d e s c rib e d in this se c tio n and in Section III-IV -B 7, III-IV -C a r e s u m m a riz e d in T able III-II. TA B LE III-H SUMMARY O F ANNEALING E F F E C T S OBSERVED IN GaAs M a te ria l n -ty p e floating - zone GaAs A nneal Condition T .= 1000°C , a rs e n ic A o v e rp re s s u re O b serv ed A nnealing E ffect D e c re a s e in expansion of la ttic e constant n -ty p e L P E GaAs :Sn T A =600°C in vacuum A D e c re a s e in n n -ty p e and p - T A=850°C, co n tro lled Change in su rfa c e type L P E GaAs A ^ ' ‘ ' ---------- p r e s s u r e c a r r i e r c o n ce n tra tion n -ty p e m e lt- grow n GaAs t a =650O c- 800O c’ As p r e s s u r e = 3 .4 T o r r C ry s ta l co n v erted to p -ty p e T e-d o p ed C z o c h ra lsk i GaAs Ta =700°C-1100°C in vacuum D e c re a se d in n € fo r Ta ^ 1000°C E xplanation R eduction of As m ono v acancie s F o rm a tio n of V . As w hich acts as a c c e p to rs A ccep to rs fo rm ed on su rfa c e w hich a re for P A >50 T o r r Ga A s^ ^ A s ^°r ^ A s .< 50 T o r r 4 F o rm a tio n of tja as a c c e p to rs F o rm a tio n of com plexes as a c c e p to rs R ep o rted By P o tts and P e a rs o n (1966 ) H a r r is et al. (1969) M unoz e t al. (1970) T oyam a (1969) G rish in a e t al. (1970) U 1 w TA B LE III-H Continued SUMMARY O F ANNEALING E F F E C T S OBSERVED IN GaAs M ate ria l T e - and S e- doped B rid g m an and floating zone GaAs A nneal Condition TA = 65 0oC - 1100°c , a r s e n ic o v e rp re s s u re O bserved A nnealing E ffect D e c re a s e d in n e fo r T A £l000°C A E xplanation F o rm a tio n of T e - (or Se-) com plexes o r p re c ip ita te s R ep o rted By F u lle r and W o lfstirn (1963) T e-d o p ed B rid g m an and C z o c h ra lsk i GaAs T . =800°C in A vacuum D e c re a s e in n and F o rm a tio n of T e - in te g ra te d pho^olum i- com plexes or n e sc e n c e edge p re c ip ita te s e m is sio n in te n sitie s Hwang (1969) Si-doped B rid g m an n -ty p e GaAs n -ty p e GaAs TA =600°C-1100°C in vacuum Ta =900°C-1000°C in vacuum C ry sta l converted to p-type C ry s ta l co n v erted to p -ty p e Cu contam ination to fo rm a c c e p to rs for T a < 870°C, Si site tra n s itio n to fo rm SiAg a c c e p to rs in addition to Cu contam ination for t a >900° c Cu contam ination and fo rm a c c e p to rs Hwang (1968) Edm und (I960) n -ty p e GaAs T a=800°C in A vacuum C ry s ta l co n v erted to p -ty p e Cu contam ination to fo rm a c c e p to rs W ysocki (I960) in C H A PTE R IV IN FRA RED R E F L E C T IV IT Y M EASU REM EN T AND F R E E CARRIER ABSORPTION O F N -T Y P E GaAs IV -I. Introduction The c a r r i e r c o n c e n tra tio n is an im p o rta n t p ro p e r ty of s e m i-c o n d u c to r m a te r ia l. The conventional m eth o d of d eterm in in g it is by using the H all effect m e a s u r e m e n t w hich g e n e ra lly r e q u ire s th at ohm ic co n tacts be m ad e to the sa m p le . The sam p le is u su ally b ro u g h t to an e lev ate d te m p e ra tu re and a foreign m a te r ia l is u sed fo r m aking the c o n tacts. T his p r o c e s s could in tro d u ce an n ealin g effects and s o m e tim e s even cau se the fo reig n m a te r ia ls to diffuse into the sa m p le and hence could change the p ro p e rty of the diffused p o rtio n of the sa m p le . In the p r e s e n t w ork, it is d e s ira b le to avoid m ak in g p h y sic a l co n tacts to the s a m p le . In p a r tic u la r the a n n e a lin g -e ffe c t study of GaAs in C h ap ter V re q u ire s th a t the c a r r i e r c o n c e n tra tio n of n -ty p e GaAs s a m p le s be m e a s u r e d during the c o u rse of annealing e x p e rim e n ts. Since the e x p e rim e n ts g e n e ra lly re q u ire fu rth e r annealing a t an e le v a te d te m p e ra tu re a fte r the c a r r i e r c o n c e n tra tio n m e a su re m e n ts, any fo reig n m a te r ia l w hich is le ft on the su rfa c e of the sam p le due to handling fo r a H all effect m e a s u r e m e n t is a p o ssib le so u rc e of co n tam in atio n . Of even m o re im p o rta n c e to the p r e s e n t 55 56 e x p e rim e n ts is th at the heating of the sa m p le to m ake th e se co n tacts w ill a lso p e rtu rb the annealing h is to ry of the sam p le and p e rh a p s m ak e the re s u lt u n re lia b le . T h e re fo re a m e a s u re m e n t m eth o d w hich e lim in a te s the above m en tio n ed fe a tu re s is highly d e s ir a b le . The use of re fle c tiv ity m e a s u re m e n ts to d e te rm in e the o p tical co n stan ts and the effective m a s s of the c a r r i e r s in s e m i c o n d u cto r m a te r ia ls is freq u en tly u sed sin ce the e a rly w o rk by W. G. S p itz e r and H. Y. F a n (1957). In p a r tic u la r , the fre q u e n cy of the re fle c tiv ity m in im u m n e a r the p la s m a edge can give an a c c u ra te m e a s u re m e n t of the c a r r i e r c o n c e n tra tio n (Kohl 1971, M oss et al. 1968, Oka da and Oku 1967, G o ld sm ith and O shinsky 1963).. This technique of m e a s u rin g c a r r i e r c o n c e n tra tio n has the advantage th at it is n o n d e stru c tiv e , needs no p h y sic a l contacts or p ro b e s and has a sim p lic ity in sam p le p re p a ra tio n . The sa m p le s need have only one su rfa c e p o lish e d to o p tical q u ality . D uring a s e r ie s of m e a s u re m e n ts , su ch as during the an nealing e x p e r i m e n ts m en tio n ed e a r l ie r , one has only to re fin is h the su rfa c e b efo re e a c h m e a s u re m e n t. F o r the re fle c tiv ity m e a s u r e m e n t the sa m p le can have any shape and d im e n sio n as long as the p o lish e d s u rfa c e is la rg e enough to give a q u a n titativ ely m e a s u ra b le r e flec tio n sig n al. S am ples w ith p o lish e d d im en sio n s of 0. 4 c m by 0 .2 cm have b een re a d ily m e a s u re d in the la b o ra to ry . U sually n-type GaAs w ith a c a r r i e r c o n c e n tra tio n ng S 1 0 ^ _3 c m has a v e ry pronounced p la s m a re fle c tiv ity edge w ith the re fle c tiv ity value a t the m in im u m being Rm ^ 5%. F ig u re IV -I 57 show s the typical re fle c tiv ity s p e c tra of a few n -ty p e GaAs s a m ples re p o rte d by S p itz er and W helan (1959). In this fig u re one can see th at eac h re fle c tiv ity cu rv e m in im u m is deep and the freq u en cy o r w avelength p o sitio n of the m in im u m can be lo c ated w ithin = “ 3%. Okada and Oku (1967) have p r e p a r e d a c a lib ra tio n cu rv e of the re fle c tiv ity m in im u m p o sitio n v e rs u s the c a r r i e r co n c e n tra tio n for n -ty p e GaAs. It is b a s e d on the e x p e rim e n ta lly obtained values fro m both re fle c tiv ity and H all effect m e a s u r e m e n ts including the data given in F ig u re IV -1. They have a lso shown th a t the e x p e rim e n ta l r e s u lts a g re e w ith the D ru d e -Z e n e r fre e c a r r i e r th e o ry (D -Z). The c a lib ra tio n c u rv e is re p ro d u c e d in F ig u re IV -2. The c a r r i e r co n c e n tra tio n of the s a m p le s in F ig u re IV-1 can be d e te rm in e d fro m the c a lib ra tio n c u rv e . In cluding the u n c e rta in ty of lo catin g the m in im u m p o sitio n , the c a r r i e r co n c e n tra tio n can be d e te rm in e d w ithin =- 6%. The c a lib ra tio n cu rv e shown in F ig u re IV -2 is obtained fro m e x p e rim e n ta l r e s u lts of s a m p le s w hich have a deep p la s m a edge re fle c tiv ity m in im u m (R-m ^ 5%). H ow ever, in so m e of the ann ealin g study re s u lts of C h ap ter V, the re fle c tiv ity m in im u m is quite shallow w ith values of Rm as la rg e a s =- 13% being o b s e rv e d T y p ical deep and shallow re fle c tiv ity m in im a r e s u lts fro m the annealing study of G aA s:Si a r e shown in F ig u re IV -3. N otice th a t the shallow m in im u m o c c u rs in the sa m e g e n e ra l s p e c tr a l re g io n as th o se deep m in im a c u rv e s shown in F ig u re IV -1. T h e re is , th e re fo re the b a s ic q u e stio n a s to the a c c u r a c y of the c a r r i e r co n c e n tra tio n d e te rm in e d fro m the re fle c tiv ity m e a s u r e - REFLECTIVITY R (%) FREQUENCY v (cm'1 ) 2000 1 0 0 0 700 500 400 300 SYMBOL SAMPLE 9 0 GoAs 8 0 7 0 6 0 5 0 3 0 20 20 24 28 32 3 6 8 1 2 1 6 4 W AVE LENGTH X (ft m) F ig u re IV-1 R eflectiv ity s p e c tr a of four GaAs S am ples (A fter S p itz e r and W helan 1959)- FREQUENCY V (cm '1 ) 2 0 0 0 1000 8 0 0 7 0 0 6 0 0 5 0 0 4 0 0 3 0 0 3 2 .19 1 0 ' 8 6 4 2 .18 1 0 ' 8 6 4 3 1 2 14 18 2 0 2 2 2 4 2 6 2 8 3 0 3 2 3 4 8 1 0 16 4 6 WAVE LENGTH X F ig u re IV-2 C alib ratio n c u rv e of c a r r i e r co n ce n tratio n v e rs u s the freq u en cy (and w avelength) of p la sm a edge re fle c tiv ity m in im u m of n -ty p e GaAs. (After Okada and Oku 1967). REFLECTIVITY R (%) G aA fS i 30 20 10 0 340 400 500 600 700 800 900 1100 1 0 0 0 FREQUENCY v (cm*1 ) F ig u re IV -3 R eflectiv ity s p e c tra of five GaAs:Si sa m p le s. The n u m b e r by eac h curve c o rre sp o n d s to the sam p le n u m b e r lis te d in Table IV -I. 61 m e n t w hen the re fle c tiv ity m in im u m value is not deep. M oss e t al. (1968) and Kohl (1971) have c o n sid e re d this p ro b le m and they have shown that the ra tio of the p la s m a freq u en cy , V , to P the re fle c tiv ity m in im u m freq u en cy , V , is a function of the value of the re fle c tiv ity m in im u m Since the p la s m a f re q u e n cy s q u a re d is p ro p o rtio n a l to the c a r r i e r co n ce n tratio n , the ra tio Vp/\>m in d ic a te s the a c c u ra c y of the m e a s u re m e n t. In th e ir d e riv a tio n s, th e se au th o rs have a s s u m e d th at both the r e a l and im a g in a ry p a rts of the d ie le c tric co n sta n t follow the D ru d e -Z e n e r e x p re s s io n . It w ill be shown h e re th a t for n -ty p e GaAs the r e a l p a r t of the d ie le c tric co n sta n t does follow this e x p re s s io n as v e rifie d b y e x p e rim e n t. H ow ever, the im a g in a ry p a r t does not. It is the p u rp o se of this stu d y to in v e stig a te the a c c u ra c y of using the re fle c tiv ity m e a s u r e m e n t to d e te rm in e the c a r r i e r c o n ce n tra-. tion of sa m p le s w ith a shallow re fle c tiv ity m in im u m . C o rre c tio n fa c to rs a r e c a lc u la te d w hich a r e b a s e d on the e x p e rim e n ta lly o btained b eh av io r of im a g in a ry p a r t of the d ie le c tric c o n stan t o r the ex tin ctio n coefficient. C o m p a riso n is also m a d e betw een our r e s u lts and those obtained by M oss e t al. (1968) b a s e d on full D ru d e -Z e n e r e x p re s s io n . IV -II. T h eo ry B efo re going into a d is c u s s io n of the D ru d e -Z e n e r th e o ry , le t us f ir s t re c a ll the g e n e ra liz e d b eh av io r of an e le c tro m a g n e tic w ave in a solid (Dixon, 1969). A. G en eral E le c tro m a g n e tic T h e o ry B ackground 62 The m a c ro s c o p ic b e h a v io r of an e le c tro m a g n e tic w ave in a so lid can be d e s c rib e d by M ax w ell's eq u atio n s. F o r a n o n m a g n e tic, hom ogeneous cubic c r y s ta l of d ie le c tric co n stan t e and conductivity ct, M ax w ell's equations can be w ritte n as follows: V • E = 0, V • H_ = 0, 1 3 H 1 3E V x E = - ^ , V x H = - ( e + 4 ttct E), (4-1) w h ere E is the e le c tr ic field, H the m a g n e tic field and c is the v elo city of light. By using the re la tio n sh ip V x V x A = V(V»A) - V^_A , (4-2) w h e re A is any v e c to r, we can get the w ave equation fro m e q u a tion (4-1) as , 2E - = 0. (4-3) c S t c A solution of equation (4-3) for a plane w ave tra v e lin g in the x d ire c tio n is E = E e " l W ( t “ v > . (4-4) — —o S ubstituting equation (4-4) into equation (4-3) gives the condition th a t 2 4 c . . 4t t c t „ , , ~ T = e + 1 — • < 4 ‘ 5) V The e le c tro m a g n e tic wave in a so lid is u su a lly d e s c rib e d in te rm s of a co m plex d ie le c tric c o n stan t e o r index of re fra c tio n N . T hey a r e defined as e = e 2 + ie 2 = (y) 2 , (4-6) N = n + ik = (e)^ , (4-7) 63 w h e re and a r e t^ ie r e a l a n d im a g in a ry p a rts of e, n is c alled the index of re fra c tio n , and k is the extinction coefficient. F r o m equations (4-5) to (4-7), one obtains the following r e la tio n ships f' e, = n^-k^ = e, (4-8) s 2 = 2nk = T T • < 4 - 91 S ubstituting for v in te rm s of n and k into equation (4-4), we get .. x(n+ik) . E = E ^ e ” ^ c ) (4-10) „ -iW (t - — x) x . = E e ' c e c E quation (4-10) d e s c rib e s an a tte n u a te d plane w ave. The in te n sity of the light b eam , I, is p ro p o rtio n a l to the m agnitude of the tim e a v e ra g e of the Poynting v e c to r S = E x H . The m agnitude of the P oynting v e c to r1 is given by |S| E • E * th e re fo re , |l| « |s | « E • E * = | e |2 . (4-11) As light p a s s e s an a b so rb in g m a te r ia l w ith th ic k n e ss, d, the light in te n sity a tte n u a te s. By using equations (4-10) and (4-11), the following e x p re s s io n can be o btained i n = u e ' a d = U e ' 2 ^ d ■ <4 - i 2 > w h ere [lo | is the in ten sity of the incom ing light and |jJ is the in te n sity a fte r the light has p a s s e d thro u g h the a b so rp tio n m a t e r ia l w ith th ick n ess d as shown in F ig u re IV -4. E quation (4-12) is known as L a m b e rt's law. The two p a r a lle l lin es in F ig u re IV -4 64 M II F ig u re IV -4 S ch em atic d ia g ra m of lig h t b e a m p a s s in g th ro u g h an a b so rb in g m e d ia w ith th ic k n e ss d. 65 do not r e p r e s e n t in te rfa c e s b u t r a th e r they sp ecify the th ick n ess "d" of the m a te r ia l. The light b e a m I and I in F ig u re IV -4 a r e in the sa m e m a te r ia l a s the shaded a r e a . T his draw ing is to illu s tr a te the e x p re s s io n of equation (4-12). If th e re a r e i n t e r face s, we should c o n s id e r the re fle c te d lig h t as w ell. The c o e f ficien t a is g e n e ra lly called the a b s o rp tio n co efficien t. F r o m equation (4-12) a can be e x p re s s e d as 2 us k 4tt k , a -ti\ a = — = — • (4“13) The e x p re s s io n for the re fle c tiv ity R of a lig h t b e a m a t n o rm a l incidence fro m the in te rfa c e betw een two m a te r ia ls w ith indexes of re fra c tio n and N2 can be d e riv e d by using the P oynting v e c to rs of the in c id en t light in te n sity Jjh and the re fle c te d lig h t in te n s ity as ■ - t , ' - ( # ) • ( # ) ’ ■ '— 1 1 — 1 — 1 C o n sid erin g the in te rfa c e b o u n d ary condition fo r the continuity of the ta n g e n tia l com ponents of E and H, the follow ing re la tio n sh ip is obtained E N .- N - (n -n ) + i(k. -k ) L = — = — i ------------i-----— (4-15) E. K i+ ^ 2 (nx+n2 ) + i(kj+k2 ) ’ ^ E quation (4-14) b e c o m e s ( n , - n 2 )2 + ( k r k 2 )2 R - ------------2------------------2” • (4-16) (nx+n2 ) + (kj+ k2 ) W hen the in c id en t lig h t b e a m is in vacuum , n j = 1, kj = 0, 66 : and th e se v alu es a r e a lso a good ap p ro x im a tio n in a ir. Then w ith th e se values equation (4-16) re d u c e s to the fa m ilia r fo rm . ( m - 1)2 + k 2 R = — o V * (4 ' 17> (n2 + i r + k2 The d ie le c tric co n stan t is so m e tim e s w ritte n as e = 1 + 4 t t x i (4 -1 8 ) w h e re X *s c a lle d the e le c tr ic s u sc e p tib ility o r p o la riz a b ility and is r e la te d to the p o la riz a tio n P by P = x E . (4-19) T h e re a r e th re e d is p e rs io n m e c h a n is m s w hich a r e of m a jo r s ig nificance in s e m ic o n d u c to rs: (1) bound e le c tro n s , (2 ) fre e c a r r i e r s and (3) the c r y s ta l la ttic e . If th e se m e c h a n ism s c o n tr i bute s im u lta n e o u sly b u t independently, equation (4-18) can be w ritte n in a m o re e x p lic it fo rm e = 1 + 4 t t (Xb e +Xf c +XL ) , (4 — 2 0 ) j w h ere X^e is the e le c tric s u sc e p tib ility due to bound e le c tro n s , X£c is the e le c tric s u sc e p tib ility due to fre e c a r r i e r s , and X k is the e le c tric s u sc e p tib ility due to c r y s ta l la ttic e . Since we a r e in te re s te d in the in f r a r e d s p e c tr a reg io n w h e re the fre e c a r r i e r d is p e rs io n m e c h a n is m d o m in a te s, equation (4-20) can be w ritte n as e = £„ + 4 t t x f<j , (4-21) w h ere e » = 1 + 4TT* be + 4 " X l • 67 : U sually the la ttic e p o la riz a tio n is negligible and the re p r e s e n ts the bound e le c tro n co n trib u tio n w hich is r e a l and n e a r ly f r e - quency independent. B. D ru d e -Z e n e r T h eo ry The D rude Z e n e r c la s s ic a l th e o ry of fre e c a r r i e r d is p e r sion can be d e s c rib e d as follow s: C o n sid e r a fre e c a r r i e r of effective m a s s m and ch arg e e w hich is d isp la c e d by an am ount x a s a r e s u lt of in te ra c tio n w ith the e le c tro m a g n e tic field E . A ss u m e a dam ping fo rc e is p r e s e n t w hich is p ro p o rtio n a l to the m a s s and th e v elo city of the c a r r i e r . The equation of m otion can be w ritte n a s : * * * dx . m — ~— + m ' r -57 — = e E e =eE, (4-22) dt2 dt - o - w h ere F is the co efficien t of the dam ping fo rc e . The solution to equation (4-22) is e E x = - — j --------------- . (4-23) m (tel +iT ) Since P = 7 1 e x , w h ere 7 1 is the c o n c e n tra tio n of d ip o les, one obtains P . n * 2 i : - f c * W(W+iF) m F r o m equation (4-19), we have 2 * fc “ ^ + iT ) ’ (4-24); m T h e re fo re , the total d is p e rs io n is 68 ; 4n??e2 1 , . 4rr7?e2 T e = e» * T T Z + 1 ------5--------?— Z • (4 “25) m U + r m W « + r F r o m equations (4-6), 4-8) and (4-9), we get the re la tio n sh ip s 2 , 2 _ 4 t e 2 s 2 = 2nk = - 2, • < 4 -2 7 > m U ) (M +T ) The c a r r i e r dam ping co efficien t T is s o m e tim e s w ritte n as T = ~ > w h ere T is called the c a r r i e r s c a tte rin g re la x a tio n tim e . Sub stitu tin g T for F , equations (4-26) and (4-27) b eco m e . 2 , 2 4ttTie2 T 2 j n - k = 5----------- 2^ " ’ (4-28) m l+tt> t 2 _oi _4TT?(e T , A 02 * ' 2 2 . ‘ (4-29) m (1+C0 T )« The above e x p re s s io n s a r e b a s e d on the a s su m p tio n that the c a r r i e r s c a tte rin g can be r e p re s e n te d by an e n e rg y -in d e p e n d e n t 2 dam ping co efficient. In s p e c tr a l reg io n w h ere (w t ) > > 1 the equations (4-28) and (4-29) can be sim p lifie d and b eco m e useful. The re fle c tiv ity m in im u m is fre q u e n tly lo c ated in this region. The sim p lifie d fo rm of equations (4-28) and (4-29) a re e x = n2 -k2 = ew - . (4-30) m (ti e2 = 2nk = 4n7? J . (4-31) m u) t F o r a lo s s le s s m a te r ia l, k=0 and hence e2 =®‘ F r o m equation (4-30) one has The p la s m a freq u en cy , v , is defined as the freq u en cy a t w hich P e^ = 0 and is given by 4TT7?e2 2 / 0 _ x 2 4t t7 ? e2 , A * 0 = eoo * 2 o r = (2ttcv) = H r ’ (4-33) m 40 * s m p 0 0 w h ere the w ave n u m b e r v is com m o n ly u sed in in fra re d m e a s u r e m e n ts as a unit fo r freq u en cy . F r o m equation (4-17), fo r ^ = 0 (ideal c a se ), the re fle c tiv ity b e c o m e s , (n - l )2 R = — (n2+1)2 ' C le a rly , if r ^ l , R has its m in im u m value, w hich is z e ro . The fre q u e n c y V , w hen R=Rm , is o « 2 Vm = " ----------------- 2" • < 4 ' 34> ( e B - 1 ) m ttc C o m p arin g equations (4-33) and (4-34), the ra tio betw een v and P v is m v_ \ 2 _ e -1 “ — ------ • (4-35) m ' o o T h e re fo re the ra tio of v /v is uniquely defined in the c a se p m ' # 2 w h ere ^£=0. A lthough the value of m in Vp is a function of the fre e c a r r i e r c o n c e n tra tio n (Okada and Oku, 1967), n e v e r th e le s s th e re is s till a one to one c o rre s p o n d e n c e betw een the value of v m and the c a r r i e r c o n c e n tra tio n , as can be se e n in equation (4-34). H ence the c a r r i e r c o n c e n tra tio n can be c a lc u la te d fro m 70 ; \>m b y usin g the p r o p e r value of m . F o r a l o s s y m a t e r i a l k d o e s n o t e q u a l z e r o a n d a n e x - 2 p re s s io n for (Vp / Vrr] can be d e riv e d . A ssu m e the n^ and k^ values a r e known a t re fle c tiv ity m in im u m and c a lle d ant^ k2m> w h ere F r o m equations (4-28) and (4-29) we can obtain _2 ,2 _ 4 tt 71 eZ T2 n2m " 2m e» " * . 2 2 » (4-36) m 1 +00 T m Z”2mk2m = Z* 2,--- • <4-37' m ( l + « T a) ' m m By com bining equation (4-33) w ith the above two equations, we can g et the e x p re s s io n / V \ 2 / to \ 2 e - n 2 + k 2 4 n ? k 2 P - ( E. I = — “IE 2m + 2m 2m f4-38> 2 2 W hen (cu T ) 5>1, the e x p re s s io n for (v /v ) can be obtained ' m ' p m d ire c tly fro m equation (4-36). The re s u lt is the s a m e as shown in .equation (4-38) e x c e p t th at the second te r m on the rig h t hand sid e of this equation v a n ish e s . IV-in. M e a s u re m e n t T echnique T he re fle c tiv ity m e a s u re m e n ts w e re m a d e b y usin g a single b e a m s p e c tr o m e te r w ith a P e r k in - E l m e r M odel 210 g ratin g m o n o c h ro m a to r. The p ro c e d u re w as d e s c rib e d in Section III-III-C . As m en tio n ed in th a t sectio n , the in cidence angle to e ith e r the sa m p le o r the m i r r o r w as c lo se to = “ 10° . The re fle c tiv ity value m e a s u re d w ith this incidence angle is v e r y clo se to the n o rm a l 71 incidence re s u lt. F r o m the d e riv a tio n s given by L o n g h u rst (1967) o r M oss (1959), it can be shown th a t if the re fle c tiv ity value is R = 28.8% for 0=0° then R = 28.75% for 0 = 10°, w hich a s s u m e s n = 11 and k = 0. N e a r the p la s m a edge re fle c tiv ity m in im u m , n = 1, k = 0, the value of re fle c tiv ity m in im u m R is R = 0% ’ 7 m m for 0=0° and Rm = 0.6% fo r 0 = 10°. The fre q u e n c y of r e flec tiv ity m in im u m re m a in s the sa m e p o sitio n betw een 0 = 0° and 0 = 10°. T h e re fo re , although the in c id en ce angle u sed in the m e a s u re m e n ts w as 10°, the n o rm a l in cid en ce fo rm u la tio n is u sed in the calcu la tio n and d is c u s s io n , sin ce the e r r o r in c u rr e d by this a p p ro x im a tio n is v e ry s m a ll. IV -IV . D is c u s sio n T h e re a r e two m a jo r points of c o n c e rn w hich m u s t be d is c u s s e d . In sa m p le s w hich have s m a ll values fo r R-m » b u t ./> w h e re n k does not follow equation (4-29), can one s till use equation (4-35) to d e te rm in e Vp and hence the c a r r i e r den sity ? Secondly, fo r n -ty p e GaAs sa m p le w hich h as a sh allo w m in im u m in its re fle c tiv ity c u rv e , w hat is the re la tio n s h ip b etw ee n V p / v m and R . In o r d e r to a d d re s s the second poin t it w ill be n e c e s - m s a r y to p r e s e n t so m e a b s o rp tio n m e a s u r e m e n ts w hich w ill be used t to e s ta b lis h an e m p iric a l law to su b stitu te for eq u atio n (4-29). 2 2 It w ill a lso be d e m o n s tra te d th a t n -k does follow equation (4-28) and gives re a s o n a b le v a lu e s for the effectiv e m a s s fo r the shallow m in im u m c a s e . C o n sid e r the c a s e of in fra re d re fle c tiv ity a t the a i r to 72 : se m ic o n d u c to r in te rfa c e w hich is the a c tu a l e x p e rim e n ta l situation. The value of n^ = l and k^=0 is a good a p p ro x im a tio n fo r a ir. T h e re fo re eq u atio n (4-17) is u sed in the e x p re s s io n fo r the r e flectiv ity . We now c o n sid e r two c a s e s . A. D eep R eflectiv ity M inim um N e a r the plasm a edge re fle c tiv ity m in im u m the value of jx, is c lo se to 1. E quation (4-17) shows th a t the re fle c tiv ity m i n i m u m value is a m o n o to n ically in c re a s in g function of This rela tio n sh ip is shown in F ig u re IV -5. T h e re fo re fo r a deep re fle c tiv ity m in im u m ( i . e . , R ^ 5%), the values a r e 0 .4 6 . 2 W ith th e se k- v a lu e s, the value of (v / v ) c a lc u la te d fro m 2 ' p m ' equation (4-38) a ss u m in g em = 1 1 .0 , is w ithin 4.5% of the value c a lc u la te d fro m the id e al c a se for k2 =0. H ence fo r su ch s m a ll values of k2 , the id eal c a se of k2=0 is a good ap p ro x im atio n . The e x p re s s io n s of (4-34) and (4-35) w ill hold in this c a se . It m e a n s th a t for a deep re fle c tiv ity m in im u m the freq u en cy of the m in im u m s q u a re d is p ro p o rtio n a l to the c a r r i e r co n cen tratio n . In this s p e c ia l c a se the fo rm of £2 is u n im p o rta n t sin ce it is s m a ll and \> m is d e te rm in e d c o m p le te ly by the e ^ equation (4-32). T his d is c u s s io n explains why O kada and Oku (1967) w e re able to obtain the a c c u r a te c a lib ra tio n cu rv e for c a r r i e r c o n ce n tratio n v e rs u s v m show n in F ig u re IV -2. B. Shallow R eflectiv ity M in im u m -C la s s ic a l D ru d e -Z e n e r M odel W hen the value of the p la s m a edge re fle c tiv ity m in im u m is la rg e (S 10%), it is called a sh allo w m in im u m . This la rg e REFLECTIVITY R (%) 20 (r^-1) ♦ k. 1 5 10 5 0 03 1.0 k 2 F ig u re IV -5 R eflectiv ity as a function of w ith n^ 74 value is m a in ly due to an in c re a s e in a b s o rp tio n fo r the sam p le. The value of Rm > the re fle c tiv ity m in im u m , can v a ry o v er a w ide ran g e. The ra tio of the p la s m a freq u en cy , to v m a c tu a lly b eco m es a function of the value of R ^ * M oss e t al. (1968) and Kohl (1971) have c a lc u la te d the re la tio n sh ip betw een the ra tio V / v and R b a s e d on the D -Z c la s s ic a l th e o ry . The c a lc u la - p m m 7 tion of M o ss et al. (1968) is outlined h e re . By using equations (4-17), (4-28) and (4-29) the re la tio n betw een and k2m> the values of n and k a t the re fle c tiv ity m in im u m , can be obtained (assu m in g n^ = l) and is (4 . 39) . 2 ., 2 .2 ... 4 0 _ o o 4n_ (3n0 -k0 -1 )k0 . 2 /e 2 , , . 2 w 2 .. 2m ' 2m 2m 2m k0 (5n„ + 3g -2) = (e -n 0 )(n0 - 1 ) -------------------------= -----=----------. 2m ' 2m < ® ' ' ® 2m ' v 2m , 2 . 2 .2 (e -n_ +k0 ) ' 0 0 2m 2m As w ill be shown, the seco n d te r m on the rig h t-h a n d side of equation (4-39) is a s m a ll c o r r e c tio n w hich b e c o m e s negligible in 2 the a p p ro x im atio n (wt) 1 w hich gives a d ir e c t re la tio n s h ip for 2 2 k^m and n2m > n am ely , 7 (e - m )(m - 1) k? = V — . (4-40) 2 m 5n? +3e -2 2m 0 0 F r o m equation (4-40), fo r e v e ry given value of c o r r e s “ ponding value of k2m can be calcu la ted . F r o m anc^ ^ 2 m ’ the c o rre sp o n d in g v alu es of R and v /v can be found b y using m p m j o equations (4-17) and (4-38). C u rv es re la tin g the valu es of Rm and V p /v m can be plo tted and a r e r e p o tte d by M oss et a l. (1968) and Kohl (1971). The cu rv e la b e lle d . " c la s s ic a l" in F ig u re IV -6 is ca lc u la te d by M oss e t al. (1968) b y using this m eth o d w ith 0.9 CLASSICAL 0.8 y= 3 y= 4 0.7 0 5 10 1 5 20 25 F ig u re IV-6 — ^ a s a function of R b a se d on equations (4-46) and (4-47). The cu rv e m lab elled " c la s s ic a l" is a fte r M oss e t a l. (1968). 76 e = 11. 0. C O C. C o m p a riso n of D ru d e -Z e n e r C la s s ic a l E x p re s s io n W ith E x p e rim e n ta l R e su lts F o r n -ty p e GaAs C l. C o m p a riso n of the A b so rp tio n C oefficient and V alues F ro m the p rev io u s e x p e rim e n ta l r e s u lts , it w as found that the a b so rp tio n of n -ty p e GaAs does not follow the D ru d e -Z e n e r c la s s ic a l e x p re s s io n s . The c la s s ic a l e x p re s s io n p re d ic ts that _2 the a b so rp tio n co efficien t a , should be p ro p o rtio n a l to V . T his is only tru e in the low fre q u e n c y re g io n , v < 200 c m - *, as o b se rv e d in the e x p e rim e n ta l r e s u lts (P erk o w itz 1971 and Sobotta 1970). D um ke (1961) and Haga and K im u ra (1963) have pointed out th a t in the freq u en cy reg io n kT?> ti ^ , the quantum and c la s s ic a l e x p re s sio n s for the a b so rp tio n coefficient b eco m es equal. T h ese c r it e r ia w e re used by P e rk o w itz (1969) to show th a t the fre e c a r r i e r a b so rp tio n in n -ty p e GaAs should show a n e a rly c la s s ic a l b eh av io r fo r fre q u e n c ie s below 200 c m *, c a r r i e r con- 17 -3 c e n tra tio n s below 1 x 10 c m , and te m p e ra tu re s betw een 77° 17 and 300° K. H ow ever, fo r c a r r i e r co n c e n tra tio n s above 1 x 10 _3 cm , the freq u en cy v m a t the p la s m a edge re fle c tiv ity m in im u m is h ig h e r th an 300 c m * and in this fre q u e n c y re g io n the k T » ^ C 0 c r ite r io n is no lo n g e r tru e , even a t 300° K. T h e re fo re the —z c la s s ic a l e x p re s s io n is not ex p ec ted to hold. In stead of a “ V " , _3 the a b s o r p tio n co e ffic ie n t a. is found to be p ro p o rtio n a l to v -1 -3 for v > 300 cm . The a “ V re la tio n s h ip has b een re p o rte d by m an y in v e s tig a to rs including S p itz e r and W helan (1959) M ilvidskii 77 e t al. (1966), V akuienko and L is its a (1967) and R o s h e rs k a y a and • -3 Fistul* (1968). The a “ V dependence is a lso o b se rv e d in the p r e s e n t w o rk for annealed., s a m p le s w ith shallow m in im a . F ig u re IV -7 show s the re s u lt of five G aA srSi s a m p le s w hich have b een a n n ea led at d ifferen t te m p e r a tu r e s . The annealing condition and c a r r i e r c o n c e n tra tio n fo r the s a m p le s show n in F ig u re IV -7 a r e lis te d in Table IV-I. The re fle c tiv ity c u rv e s of these and e q u i v alen t sam p les have b een shown e a r l i e r in F ig u re IV -3. The th r e e low er te m p e ra tu re a n n ea led sa m p le s show shallow m in im a w ith R , g e n e ra lly n e a r 13%, w hile the two high te m p e ra tu re m ^ an n ealed sam p les show deep m in im a w ith R m values < 5%. A ll -4 th e se sa m p le s have a k « v b e h a v io r as can be se e n in F ig u re -4 IV -7, w h e re k is the extin ctio n coefficient. A ka v is the same _ 3 a s a “ V sin ce a = 4tt kv . Haga and K im u ra (1964) have a t t r i - _3 b u te d the a K v b eh av io r to a la rg e co n trib u tio n fro m ionized -3 3 im p u ritie s w hich have a fre q u e n c y dependence of a “ V . A n -ty p e sa m p le w ith a shallow re fle c tiv ity m in im u m a l w ays has a la r g e r th an u su al fre e c a r r i e r a b s o rp tio n c ro ss- se c tio n . This fe a tu re can be d e m o n stra te d b y co m p arin g a b s o r p tion co efficien ts of sa m p le s w ith shallow m in im a to th o se w ith deep m in im a . S p itz er and W helan (1959) Have m e a s u re d the a b s o rp tio n co efficien t as a function of c a r r i e r c o n c e n tra tio n for n -ty p e GaAs s a m p le s w ith deep re fle c tiv ity m in im a . T h e ir r e s u lts , m e a s u r e d a t X = 8p m ( v =1250 c m ’ \ a r e re p ro d u c e d as c ir c le s in F ig u re IV -8 . T hese d ata points show th a t the a b s o r p tion in c re a s e s m o re rap id ly than the c a r r i e r co n ce n tratio n . A s T A B L E IV -I SUMMARY O F ANNEALING CONDITION AND CARRIER CONCENTRATION Sam ple No. D opant Sam ple I. D . A nnealing Condition 1 Si W A -9 9 -H a 1100° C /1 5 m in 2 Si W A -99-10a 600° C /290. 5 h r +1100° C /15 m in 3 Si W A -9 9 -H c 750° C /320 h r 4 Si W A -9 9 -H b 600° C /2 9 0 . 5 hr 5. Si W A -99-10b 400° C /1178 h r 6 Te 232B A s grow n a Se M e a s u re d b y S p itz e r ------ b Se and W helan (1959) ------ C a r r ie r C o n cen tratio n (c m “3) (fro m H all effect m e a su re m e n t) 8.0 x 10 8.0 x 10 1.9 x 10 1. 5 x 10 1 .5 x 10 2.8 x 10 5 .4 x 10 1.1 x 10 18 18 18 18 18 18 18 18 absorption coefficient a (cm '1 ) 4 2 4 2 I02 8 4 2 10 8 4 2 1 . 0 J8 8 id9 2 i? 2 4 8 10 4 4 2 10 carrier concentration [nj (cm'3) F ig u re IV-8 A b so rp tio n coefficient at v = 1250 c m as a function of c a r r i e r c o n c e n tra tio n of eleven GaAs sam ples;. D ata shown a s c irc le s a r e a f te r S p itz e r and W helan (1959). 81 w ill be show n sh o rtly , this is due to the co n trib u tio n fro m the ionized im p u rity s c a tte rin g w hich is not a lin e a r function of c a r r i e r , co n ce n tratio n . In F ig u re IV -8, we a lso p lotted the ab so rp tio n co efficien ts fro m the five sa m p le s shown in F ig u re IV -7, and one T e-d o p ed sam p le m e a s u r e d h e re and ca lle d No. 6. R ecall th a t sa m p le s No. 1, 2 and 6 have deep re fle c tiv ity m inim a, and' sa m p le s No. 3, 4, and 5 have shallow re fle c tiv ity m in im a . It is c le a rly seen fro m F ig u re IV-8 th a t the data points of the th re e s a m p le s w ith shallow re fle c tiv ity m in im a do lie above the dashed cu rv e w hich shows the n o rm a l a b so rp tio n value. The ab so rp tio n co efficien ts fro m Samples No. 1, 2 and 6 a r e in a g r e e m e n t w ith the re s u lts of S p itz er and W helan. (1959b H ence, it is d e m o n stra te d th a t the s a m p le s w ith shallow re fle c tiv ity m in im a do have a l a r g e r than u su al fre e c a r r i e r a b so rp tio n c r o s s sectio n . T he fre e c a r r i e r ab so rp tio n in se m ic o n d u c to r m a te r ia l g e n e ra lly co m es fro m two m a jo r c o n trib u tio n s, that due to la ttic e s c a tte rin g and th a t due to ionized im p u rity s c a tte rin g . (Haga and K im u ra 1964). lb fa c ilita te o u r d is c u s s io n , the fre e c a r r i e r a b so rp tio n co efficien t of n-type GaAs a t a given freq u en ce is w ritte n in the fo r m ° f c = a L + a I = A L n e + B Ine NI ’ (4 ~41) w h ere n is the fre e c a r r i e r co n ce n tratio n , e N j is the ionized im p u rity c o n ce n tratio n , Aj^ is the coefficient fo r the la ttic e s c a tte rin g t e r m and 82 B j is the coefficient fo r the ionized im p u rity s c a tte rin g te rm . F o r sa m p le s w ith little o r no co m p en satio n , the values of n g and Nj a re a p p ro x im a te ly equal. T h e re fo re , equation (4-41) can be w ritte n as a fc = A L n e + B In e - (4“42) The above equation shows that the co n trib u tio n fro m the ionized im p u rity s c a tte rin g to the ab so rp tio n is p ro p o rtio n a l to the second pow er of the c a r r i e r co n ce n tratio n . T his is the re a s o n th a t the a b so rp tio n in c re a s e s m o re rap id ly than the c a r r i e r co n cen tratio n , as is shown by the dashed cu rv e in F ig u re IV -8 . F o r a sam p le w ith p a r tia l co m p en satio n , the c a r r i e r c o n c e n tra tio n is given b y the d ifferen ce of the donor c o n c e n tra tio n Nj-j and the a c c e p to r co n ce n tratio n N ^ , ne = Nd - N a . (4-43) H ow ever, the ionized im p u rity c o n c e n tra tio n Nj. is now given by N j = Nd +N a = ne + 2NA . (4-44) The fre e c a r r i e r a b so rp tio n a.£c of the sa m p le w ith p a r tia l c o m p e n sa tio n can be obtained by su b stitu tin g equations (4-43) and (4-44) into equation (4-41). a £c = A L (ND -NA> + B I(ND -NA )< ND +NA ) , (4-45) = A T n +BT n + 2B .n N . . L e I e I e A If the ng values in equation (4-42) and (4-45) a r e equal, c le a r ly the a b so rp tio n of the co m p en sa ted sa m p le is la r g e r than th a t of 83 j the sa m p le w ith no co m p en satio n . The d iffere n ce of th e se two ab so rp tio n coefficients is given by the th ird te r m on the rig h t- hand side of equation (4-45), w hich is p ro p o rtio n a l to the p ro d u c t o f c a r r i e r c o n c e n tra tio n and the c o n c e n tra tio n of the co m p en satin g c e n t e r s . A s w ill be show n in C h ap ter V, the c a r r i e r co n ce n tratio n in th e se sa m p le s w ith shallow m in im a has b een p a rtia lly c o m p e n sa te d as a re s u lt of annealing. T h e re m u s t be a la rg e c o n c e n tra tio n of c o m p en sa tin g c e n te rs in th e se sa m p le s . B a se d on the d is c u s s io n follow ing equation (4-45), we can conclude that the higher than u su a l a b so rp tio n c r o s s se c tio n of th e se s a m p le s is indeed re la te d to the p re s e n c e of the co m p en sa ted c e n te rs in th e se an n ealed s a m p le s . Since a. o r k does not follow the freq u en cy dependence p re d ic te d by the c la s s ic a l th eo ry , the d e riv a tio n of the i n t e r r e l a tion b etw ee n v /v and R w hich is b a s e d on the c la s s ic a l p m m th eo ry b e c o m e s q u estio n ab le. In o rd e r to d e te rm in e the a c c u ra c y of the c a r r i e r c o n c e n tra tio n obtained fro m the re fle c tiv ity m e a s u re m e n t m eth o d w hen the p la sm a edge re fle c tiv ity m in im u m is shallow , the dependence of v / V on the value of R h as to be r p m m re -e x a m in e d w ith the fre e c a r r i e r ab so rp tio n re la tio n given by the _3 e x p e rim e n t. H ow ever, the r e p o rts of a “ V b e h a v io r in the lite r a tu r e a r e all in the fre q u e n c y reg io n v > V . No in fo rm a tio n is av ailab le for s a m p le s w ith v ® " V . T h e re fo re m e a s u re m e n ts m have to be m a d e on a sa m p le w ith shallow re fle c tiv ity m in im u m to o b se rv e the fre e c a r r i e r d is p e rs io n re la tio n s in the fre q u e n c y 84 ; reg io n n e a r v m S e v e ra l GaAs:Si sam p les have been m e a s u r e d and the m e a s u re d k values as a function of freq u en cy of five s a m p le s have b e e n shown in F ig u re IV -7. In the following d isc u ssio n , the r e su lts of two of th e se s a m p le s w ill be ex am in ed in d etail. They a re Samples No. 1 (W A -9 9 -H a ) and No. 5 (W A -99-10b) of F ig u re IV -7. T h e ir re s u lts a r e c o n sid e re d re p re s e n ta tiv e of the g e n e ra l b eh av io r of the G aA s:Si s a m p le s . Sam ple W A - 9 9 - lla has a deep re fle c tiv ity m in im u m w ith R -m < 5% and Sam ple W A -99-10b has a shallow m in im u m w ith R = “ 13%. In addition to th e se two s a m - m p ie s , a T e-d o p e d GaAs sa m p le (232B) w hich is S am ple No. 6 in F ig u re IV -8, is a lso m e a s u re d . This th ird sa m p le has a deep m in im u m w ith Rm = “ 4%. The an nealing h isto ry , c a r r i e r c o n c e n tra tio n and re fle c tiv ity m e a s u re m e n t data of th e se th re e sa m p le s a re lis te d in T ab les IV -I and IV -II. The value of the a b so rp tio n coefficient of the th re e s a m p le s, No. 1, 5 and 6 a r e plo tted as a function of freq u en cy in F ig u re IV -9 to g e th e r w ith the re s u lts of two s a m p le s m e a s u re d by S p itz e r and W helan (1959) and la b eled as (a) and (b). The c a r r i e r co n ce n tratio n of th e se sa m p le s a r e lis te d in T ab le IV -I. _3 A ll the lin e s show a a “ V b eh av io r except th a t of S am ple No. 6 n e a r the freq u en cy of the re fle c tiv ity m in im u m , V , w h e re it _3 d ev iates fro m V.. tow ard a h ig h e r p o w er dependence. The r e a son fo r this b e h a v io r is not un d ersto o d , b u t it m a y be due to the in a c c u ra c y of the m e a s u re m e n t b eca u se of the high ab so rp tio n coefficient. T A B L E IV -II RESU LTS O F R E F L E C T IV IT Y M EA SU REM EN T AND COMPARISON O F CA LCU LA TED F R E E CARRIER E F F E C T IV E MASS W ITH PREVIOUSLY R E P O R T E D VALUE Sam ple R eflectiv ity E ffective M ass No._________ M e a s u re m e n t____________________________________ V R C alcu lated in P re v io u s ly m m this study rep o rted ^ 1 940 c m 4.5% 0.088 m o 0.091 m o 5 450 c m * 13% 0.085 m o 0 .076 m o 6 594 c m -1 3.7% 0 .074 m o 0.078 m o + P ill e r (1966) a b s o rp tio n coefficient a (cm"1 ) N o.5 No.6 N o .l FREQUENCY V (cm"') F ig u re IV -9 F re q u e n c y dependence of five GaAs s a m p le s . S am ples (a) and (b) a r e a f te r S p itz e r and W helan (1959). 87 B y using equations (4-13) and (4-17) w ith the a and the re fle c tiv ity data, values of n and k a t eac h given freq u en cy of S am ples No. 5 and No. 6 w ere calcu lated . The k and nk values fro m the calcu latio n a r e plo tted as a function of freq u en cy in Figures IV -10 and IV-11 re sp e c tiv e ly . Note that in F ig u re I V - 10, -4 the k cu rv e of Sam ple No. 5 (W A -99-10b) follows v dependence even to v vm reg io n w hile th at of Sam ple No. 6 (232B) follows the sa m e fre q u e n c y dependence ex cep t n e a r v = “ V m reg io n it fo l low s an ev en s te e p e r slope. F ig u re IV-11 show s th a t the nk _4 lin es of th e se two sa m p le s a re close to a v dependence. N e a r V =“ V , the nk value fo r Sam ple No. 6 se e m s to follow the sam e slope a t h ig h e r freq u en cy reg io n but the nk slope of Sam ple No. 5 _3 d ev iates to w ard v dependence a t fre q u e n c y v n e a r v . C2. C o m p a riso n of B etw een D ru d e -Z e n e r C la s s ic a l E x p re s s io n and E x p e rim e n ta l R esu lts In this section, the c la s s ic a l D ru d e -Z e n e r e x p re s s io n fo r Sj as given by equation (4-28) is c o m p a re d to the e x p e rim e n ta l r e s u lts in o r d e r to d e te rm in e w h e th e r the D -Z e x p re s s io n for is obeyed in n -ty p e GaAs m a te r ia l w hich has e ith e r shallow re fle c tiv ity m in im u m o r deep re fle c tiv ity m in im u m . A s m en tio n ed in the la s t sectio n , fro m the m e a s u re d a b s o rp tio n co efficien t and re fle c tiv ity v alu es, n and k values can be c a lc u la te d b y using equations (4-13) and (4-17). F r o m the n 2 2 and k values the quan tity - gj = e - ( n - k ) can be com puted and 2 plo tted v e rs u s frequency. If (OPT) : » 1 then the data points fro m _2 this p lo t should follow V dependence as equation (4-30) p r e d ic ts . 88 SYMBOL SAMPLE NO. I/'4 1 dependence k dependence 1 0 * ' FREQUENCY v (cm*1 ) F ig u re I V -10 F re q u e n c y dependence of extinction coefficient of S a m p le s No. 5 and 6 of T ab le IV-II. 4 nk 10 V* d ep en d en ce d e p e n d e n c e •2 SYMBOL SAMPLE NO 5 6 \ _L _L I 10 4 8 10 2 FREQUENCY V (cm*1 ) 8 10 F ig u re IV-11 F re q u e n c y dependence of nk of S am ples 5 and 6 of T ab le IV-H. F u r th e r m o re , the effective m a s s of the fre e c a r r i e r s can be c a lc u la te d fro m equation (4-30) by using the fre e c a r r i e r co n ce n tra tio n value d e te rm in e d fro m H all effect m e a s u re m e n ts . The c a lc u la te d effective m a s s can b e checked w ith the p re v io u sly re p o rte d v a lu e s. Such a te s t has b een p e rfo rm e d on the sam e th re e s a m p le s used in the la s t sectio n , nam ely, Sam ples No. 1 (WA-99-1 la ), No. 5 (W A -99-10b) and No. 6 (232B). The -e 1 v e rs u s V c u rv e s of th e se sam p les a r e p lotted in F ig u re IV -12. This fig u re c le a rly shows th at a ll th re e lines have close to the _2 p re d ic te d V dependence. The fre e c a r r i e r effective m a s s of th e se sa m p le s has b een c alcu la ted and lis te d in Table IV -II. The ra tio of effective m a s s to fre e e le c tro n m a s s —— of the th re e m o s a m p le s is 0.088 (W A -9 9 -U a ), 0.085 (W A -99-10b) and 0.074 (232B). T hey a re in re a s o n a b le a g re e m e n t w ith the p re v io u sly re p o rte d values (F ille r 1966) of —— = 0. 091, 0. 076 and 0. 078 o re s p e c tiv e ly as show n in T able IV -II. T h e re fo re equation (4-28) of the c la s s ic a l e x p re s s io n is valid fo r sa m p le s w ith shallow re fle c tiv ity m in im u m as w ell as the deep m in im u m . D. C alcu latio n W ith M odified F r e e C a r r ie r D isp e rsio n R elations B a se d on P r e s e n t M e a s u re m e n ts F r o m the d is c u ss io n in the la s t two se c tio n s , it is c le a r th a t the r e a l p a r t of the d ie le c tric co n sta n t as show n in equation (4-28) a g re e s w ith the e x p e rim e n ta l r e s u lts . But the im a g in a ry p a r t of the d ie le c tric co n stan t as shown in equation (4-29) does not a g re e w ith the e x p e rim e n ta l re s u lts in the freq u en cy reg io n of in te re s t. To find the re la tio n betw een v /v and R , equation p m m 91 15 10 9 8 \ 6 7 6 5 4 3 V DEPENDENCE 2 700 300 400 500 1000 1500 FREQUENCY v (cnrf*) F ig u re I V - 12 F re q u e n c y dependence of - e ^ fro m S am ples No. 1, 5 and 6 of T ab le IV -H . The lines draw n th ro u g h d ata points a r e of slope - 2 . (4-28) can s till be used , but a m odified e x p re s s io n has to re p la c e .4 equation (4-29). The k « v dependence in the fre q u e n c y reg io n V > v has b een e s ta b lish e d . F u r th e r m o re , F ig u re IV -10 shows m ° -4 the k follows a V dependence even n e a r V m fo r Sam ple No. 5 (W A -99-10b) w hich has a shallow re fle c tiv ity m in im u m 13%). _4 T h e re fo re a k “ v is used and we w ill ex am in e the effect of this a ssu m p tio n . T he m odified fre e c a r r i e r d is p e rs io n e x p re s s io n can be w ritte n w h e re the f i r s t equation is the sa m e as equation (4-28), 2 ,2 _ A n -k = e s - —2--------5“ ’ (4-46) U) + T w here A = 4lT . u> = 2 tt cv . m Instead of equation (4-29), we in tro d u ce the re la tio n k2 = B tt> " Y , (4-47) w h ere y is a v a ria b le and B is a co n stan t w hich is independent of Oi. S ubstitution of equation (4-47) into equation (4-46) gives n^ = ew + B2 W “2Y - A t 2 /(U)2t 2 + 1) . (4-48) 2 If (U>T) » 1, equation (4-48) b eco m es n2 = e# + B 2w "2Iv -A o )"2 . (4-49) Substituting equations (4-47) and (4-49) into eq u atio n (4-17) one obtains 93 1+R The q u an tity ^ ^ ■ has a m a x im u m w hen R has a m in im u m . H ence, 1+R d 1-R = 0 w hen = 0. dW dO) D ifferen tiatin g equation (4-50) w ith re s p e c t to (ti and a fte r a few m a n ip u la tio n s, we get 0 = - < " L +kL +"i><-v fcL +A“ ' 2 >+2nL < - ^ kL +A" ' 2 > • < 4 - 51> -2 2 2 R eca llin g th at AoJ = e m ^ 2 , ^hen e(l uati on (4-46) b e c o m e s 0 = < n r nL )(ec o -4 m >fkL t 3n2m-V - 2n2m +<1-'V!)nl + e . 3 +< 1- ^ )fc2m- (4-52) 2 As the value is le s s than 1 in the s p e c tr a l reg io n of in te r e s t, 4 the te r m of k2m is v e ry s m a ll and can be n eg lecte d . T h e re fo re equation (4-52) b e c o m e s / 2 2 w 2 \ k2 _ 2m ~ n l ^e °° ~n2m 2m “ 2 . 1 , 2 (3y " )n2m ( _Y )nl +e» H e re the s u b s c rip t m is u sed on n2m and k2m b e c a u se this e q u a tion is tru e only a t freq u en cy of the re fle c tiv ity m in im u m . A ssu m in g n^ and _ Y values a r e known, one can c alcu la te the k2m value for e v e ry given va^ue- Such a c a lc u la tio n has been c a r r i e d out for g alliu m a rs e n id e w ith = 11.0 and n^ = 1 fo r the values of y = 2 a n d V = F r o m the valu es of the re la tio n s h ip betw een v /v and R is obtained. The re s u lts a r e r p m m plo tted in F ig u re IV -6. In usin g equation (4-38) to c a lc u la te the V p /v m value shown in F ig u re I V -6, the seco n d t e r m on the rig h t 94 hand side of equation (4-38) w as n eg lected due to the a p p ro x i- 2 m a tio n (WT ) 1 w hich w as u sed in the d e riv a tio n of equation (4-49). The effect of this a p p ro x im a tio n is to m ak e ^ p /v m s m a lle r and as w ill be se e n this w ill c a u se us to o v e re s tim a te the e r r o r in the c a r r i e r co n c e n tra tio n obtained fro m the cu rv e of F ig u re IV-E. T he r e s u lt of the T e-d o p e d GaAs S am ple No. 6 shows a d iffe re n t fre q u e n c y dependence of k n e a r as can seen in F ig u re IV -10. H ow ever, the re fle c tiv ity m in im u m 3.8% is quite deep for this sa m p le , hence the dev iatio n of V p/vm fro m 0% is s m a ll re g a r d le s s of the freq u en cy dependence of k w hich is used. In this c a se the e r r o r found in c a r r i e r co n c e n tra tio n fro m the freq u en cy of re fle c tiv ity m in im u m is a lso sm all. N e v e rth e le s s , it is s till in te re s tin g to d e te rm in e the dependence of v /v on R for s a m p le s w ith this kind of b e h a v io r. F r o m p m m v -4 F ig u re IV -11, the nk p ro d u c t s e e m s to follow a v dependence. T h e re fo re , in ste a d of equation (4-47), we use the e x p re s s io n nk = C w "6 (4-54) C om bining equations (4-46) and (4-54) and following the sa m e d e riv a tio n p ro c e d u re , we have (6 - 3)k2 m - t ( 3 6 - 4)n2 m - ( 6 - 1)nl +3e J k2 m + {e * 4 ^ = 0 ‘ (4-55) 2 T his eq u atio n can be so lv ed ex ac tly fo r U sually, in the 4 s p e c tr a l reg io n of in te r e s t, the kj* te r m is v e ry s m a ll and can 2 be n eg lecte d . The solution fo r k2m is It is of in te r e s t to note th a t fo r 6=3 (c la s s ic a l e x p re ss io n ), 4 the k te r m in equation (4-55) v a n ish e s. This v e rifie s the s ta t e m e n t u sed in obtaining equation (4-40) fro m equation (4-39). The re su ltin g e x p re s s io n has ex ac tly the sa m e fo rm as re p o rte d by M oss e t a l . (1968 ). F r o m equation (4-56) by taking 6 values to 3 and 4, and known values of > a s e t of v a^ues a * - re fle c tiv ity m in im u m c a n be obtained. F r o m th e se m and k£m v alu es, the re la tio n sh ip betw een v /v and R can be calcu la ted . The c p m m re s u lts a r e p lo tted in F ig u re IV -13 w ith the c u rv e s given fo r R ^15%. F o r R >15% the U > t value w ill be le s s than 3 (Moss m m m ' 2 e t al. 1968), and the (COT) » 1 condition u sed fo r the calcu latio n c e a se s to be valid. The c u rv e s la b e lle d " c la s s ic a l" w as re p o rte d by M oss et al. (1968) w hich should be id e n tic a l w ith the 6=3 ca lc u la tio n in the p r e s e n t w ork. As shown in this fig u re, it d ev iates fro m the c alcu la ted 6=3 c u rv e . T his deviation is due to the a p p ro x im atio n u sed in calcu la tin g V p /v m fro m equation (4-38) 2 w hich u se s the condition (tt)T) >> 1. T h e re fo re , the deviation of the V p /v m ra tio c o m p a re d w ith the ra tio a t Rm =0 i-n this fig u re is o v e re s tim a te d . F o r ex am p le, the deviation is 3% betw een 6=3 and the c la s s ic a l cu rv e a t R =12.5% as shown in F ig u re m IV -13. F r o m F ig u re s IV-6 and IV -13 the p e rc e n ta g e change in V p /v m a t hig h er Rm values c o m p a rin g to the value of V p /v ^ 1 .0 m 0, 9 - 0 . 8 - CLASSICAL 8 = 4 - 10 15 'm F ig u re IV -13 — as a function of R b a s e d on equations (4-46) and (4-54). v m The curve lab elled " c la s s ic a l" is a fte r M oss e t al. (1968). vO O' 97 : a t 9% i-s com puted, including the c la s s ic a l r e s u lt fro m M oss e t al. (1968). The re s u lts a r e show n in the fo rm of v° /v and --------- m m a re lis te d in T able IV-III. The is the fre q u e n c y a t r e f le c tiv ity m in im u m w hen Rm =0%. F o r the m odified d is p e rs io n e x p r e s - - Y sion of k=Bu) , as Rm value in c r e a s e s , the h ig h e st deviation of V / v is given by Y =4 cu rv e . It is in te re s tin g that fo r s m a ll p m 0 values of R m * the m odified d is p e rs io n e x p re s s io n shows le s s deviation of v for R < 9%. In the c ase of y =3, the e m p iric a l m m e x p re s s io n shows le s s deviation than the c la s s ic a l e x p re s s io n p r e d icts for Rm < 12.5%. F o r R m =12.5% , w ith y =4, the value of V° /v is 91.3% as liste d in T ab le IV -III. T his deviation of v m m m cau ses an e r r o r of up to 18% in determ ining^ c a r r i e r co n c e n tra tio n fro m the c a lib ra tio n cu rv e. The r e s u lts of calcu latio n s w e re te s te d as follow s: a s e rie s of s a m p le s w e re m e a s u r e d to d e te rm in e R and v . F ro m c m m the c a lib ra tio n c u rv e s of y =4 in F ig u re IV-6 and 6=4 in F ig u re IV -13 the v w as c o r r e c te d to its value w hen R =0 and this m m c o r r e c te d \>m w as used w ith the cu rv e of F ig u re IV-2 to give ne » The re s u lts a r e given in Table IV -IV in w hich the ng obtained as d e s c rib e d a r e c o m p a re d w ith H all data for the sa m e s a m p le s . The re p ro d u c ib ility of the H all data is e s tim a te d to be ± 10%. E xcept fo r Sam ple No. 3 all ng v alu es fro m the H all effect and Vm w ithout any c o rre c tio n a g re e w ithin 15% and in m o s t c a se s w ithin 10%. W hen v is c o r r e c te d w ith the Y =4 cu rv e and u sed m to obtain ng the c o m p a ris o n w ith the H all values is n o t s u b s ta n tia lly im p ro v ed . The values fo r only two of the 14 s a m p le s TA B L E IV-HI RELATIO NSHIP OF PLASMA EDGE R E F L E C T IV IT Y MINIMUM VALUE AND ITS FREQUENCY - A COMPARISON AMONG CLASSICAL, AND TWO EM PIRICA L F R E E CARRIER ABSORPTION EXPRESSIONS R m C la s s ic a l v M oss r et al. v° /v -- m m k= v , -6 nk<= v V=3 6=3 6=4 V / v p m v° /v m m V /v p m Y_4 v° /v. m m V /v p m V'° N m m V /v p m “ 0. 0% 2.5% 5.0% 7.5% 10. 0% 12. 5% 15.0% 0.954 0. 944 0.933 0. 921 0. 905 0. 885 0. 865 1. 000 0. 990 0. 978 0. 965 0. 949 0. 928 0. 907 0.954 0. 949 0. 943 0. 933 0. 917 0. 890 0. 855 1. 000 0. 9-94 0. 988 0. 978 0. 961 0.933 0. 896 0.954 0. 948 0. 940 0. 926 0. 902 0.871 0. 829 1. 000 0. 994 0.985 0. 971 0. 945 0.913 0. 869 0.954 0. 940 0.924 0. 906 0.884 0.856 0. 819 1. 000 0. 985 0. 969 0. 950 0. 927 0. 897 0. 858 0. 954 0. 939 0.923 0. 902 0. 870 0.825 0. 806 1. 000 0. 984 0.968 0. 945 0. 912 0.865 0.845 V° / v m ---------- --------- in m ^ ^ is the freq u en cy of Rm w hen Rm =0%. TA B L E IV-IV COMPARISON O F CARRIER CONCENTRATION DETERM IN ED FROM PLASMA EDGE R E FL E C T IV IT Y M EASUREM ENT (CORRECTED AND UNCORRECTED) WITH THAT FRO M HALL E F F E C T M EASUREM ENT n ( in e ' units of in 18 “3. 10 c m ) % D eviation C o m p ared w ith H all effi Sam ple No. R m v (cm " m fro m m e a s u re d v m U n c o rre c te d C o rre c te d C o rre c te d ) b y y =4 by 6=4 fro m H all effect (fcio%) W ith m e a su re d Vm C o rre c te d by y=4 1 4.5% 940 8 . 1 8. 0 7 .8 8. 0 +1. 3% 0. 0% 2 4.9% 940 8. 1 8. 0 7 .8 8. 0 +1. 3% 0. 0% 3 12.5% 542 2 .3 1. 8 1.8 1 .9 +21. 0% -5. 3% 4 13.7% 465 1. 7 1. 3 1.2 1. 5 +13. 0% -13. 0% 5 13.0% 450 1.6 1. 3 1.2 1. 5 +6. 7% -13. 0% 6 3.7% 594 3 .0 2 . 8 2 .7 2 . 8 +7. 1% 0. 0% 7 5.7% 677 3 .9 3. 8 3. 7 4 .4 - 11. 0% -14. 0% 8 13. 1% 470 1. 7 1 .4 1.3 1. 5 +13. 0% - 6. 7% 9 4.8% 949 8 .7 8. 1 8.0 8 .4 +3. 6% -3. 6% 10 4.7% 926 8.0 7 .9 7 .7 8. 5 -5. 9% -7. 1% 11 12.4% 460 1. 7 1 .4 1.3 1 .9 -10. 5% -26. 3% 12 11.4% 530 2.2 1. 9 1.8 2. 3 -4. 3% -17.4% a 1. 0% 770 5 .4 5 .4 5 .4 5 .4 0. 0% 0. 0% b 0. 6% 400 1.2 1.2 1.2 1. 1 +9. 1% +9. 1% 100 d is a g re e by m o re than 15% w hile the m a jo rity a r e again w ithin a 10% a g re e m e n t. It a p p e a rs th a t the m e a s u r e d V m is a re lia b le m eth o d of d e te rm in in g ng w ithin the sta te d e r r o r s fo r both deep and shallow m in im u m (Rm £ 15%) sa m p le s and th a t ap p licatio n of the c alcu la ted c o rre c tio n s does not n e c e s s a r i ly im p ro v e the re lia b ility . In s u m m a ry , this c h a p te r has d e m o n stra te d the fe a sib ility of using the in fra re d re fle c tiv ity m e a s u r e m e n t to d e te rm in e the c a r r i e r c o n c e n tra tio n of n -ty p e G aA s. F o r s a m p le s w hich have a shallow re fle c tiv ity m in im u m value, the a c c u ra c y of the in fra re d p la s m a edge m e a s u r e m e n t in d e te rm in in g the fre e c a r r i e r c o n c e n tra tio n has b een d is c u s s e d . The shallow re fle c tiv ity m in im u m is shown to be ca u se d by an e x ce p tio n a lly la rg e a b s o rp tio n coefficient fo r the sa m p le . The la rg e a b so rp tio n is p re s u m a b ly cau sed by co m p en satin g im p u rity s p e c ie s. C H A PTE R V ANNEALING STUDY O F Si-D O PE D GaAs V -I. Introduction The effect of an nealing on n -ty p e GaAs has b een studied b y m a n y r e s e a r c h e r s (G rish in a et al. 1970, M unoz et al. 1970, H a r r is e t a l. 1969, T o y am a 1969, Hwang 1968, P o tts and P e a r s o n 1966, F u lle r and W o lfstirn 1963, E dm und I960, and W ysocki I960). In g e n e ra l, the c a r r i e r co n ce n tratio n d e c r e a s e s as a function of annealing tim e and finally re a c h e s an a p p a re n t e q u ili b r iu m (G rish in a e t al. 1970, F u lle r and W o lfstirn 1963) value and s o m e tim e s the lig h tly doped m a te r ia l changes to p -ty p e (T oyam a 1969, Hwang 1968, E dm und I960 and W ysocki 1960). A b r ie f re v ie w of the p rev io u s an n ealin g e x p e rim e n ts has been p re s e n te d e a r l i e r in C h ap ter III, Section IV, p a r tic u la r ly in su b se c tio n s B7, C l and D. M ost of the p re v io u s stu d ies w e re e ith e r of lightly 17 -3 doped n -ty p e GaAs w ith in itia l c a r r i e r c o n c e n tra tio n n g< 10 cm (T oyam a 1969, Hwang 1968, E dm und I960 and W ysocki I960) o r of GaAs h eav ily doped w ith Te or Se w ith the doping le v e l in the 1 9 - 3 o r d e r of 10 cm (G rish in a e t a l . 1970, F u lle r and W o lfstirn 1963). No rep o rt- has b e e n m a d e on an annealing study of m o d e ra te ly to h eavily S i-doped GaAs m a te r ia l w ith doping le v e l 17 20 -3 of 10 to 10 c m . It is the p u rp o se of this p r e s e n t study, 101 l o i th ro u g h a s y ste m a tic in v e stig atio n of H all effect, lo c a liz e d v ib r a tional m o d e, fre e c a r r i e r ab so rp tio n , p la s m a re fle c tiv ity and ph o to lu m in e sc en ce m e a s u re m e n ts , to p r e s e n t an in te g ra te d p ic tu re of the annealing effects that take p la ce in S i-doped G aA s. The annealing b e h a v io r is d is c u sse d in te rm s of the b eh av io r of those individual d efec t sp e c ie s w hich have b een identified. Silicon is an a m p h o te ric im p u rity in GaAs sin ce it can be e ith e r a donor o r an a c c e p to r depending on w hich su b lattic e site it s u b stitu te s . (Kolm et a l . 1957, R h o d erick 1959. and W helan e t a l . I960) Any a tte m p t to a p p ro a c h the annealing p ro b le m by studying only the changes of c a r r i e r co n ce n tratio n is not lik e ly to yield a valid p ic tu re . T h e re fo re m ethods such as those u sed in annealing stu d ies of G aA s:T e by G rish in a et al. (1970) and F u lle r and W o lfstirn (1963) as d e s c rib e d in Section III-IV -C , if applied to the c a s e of S i-doped GaAs, would im m e d ia te ly be su sp e c t b e c a u se of the d iffe re n t po in t defects of Si w hich a r e known to be p re s e n t. The change of c a r r i e r c o n c e n tra tio n as a function of annealing is one p ie ce of im p o rta n t in fo rm atio n , but we need to m e a s u re o th e r p r o p e r tie s and put the in fo rm atio n to g e th e r in one p ic tu re to have a m e an in g fu l sta te m e n t. In o r d e r to u n d e rsta n d the b eh a v io r of the s y ste m , w hen changes of c a r r i e r c o n c e n tra tio n o c c u r, in fo rm a tion of the following type would be d e s ira b le : (1) Do the Si donor c o n ce n tratio n , [Si-Qa L and the Si a c c e p to r co n ce n tratio n , [S i^ g] change as a re s u lt of annealing? (2) If the Si donor and a c c e p to r co n ce n tratio n s do change, in w hat w ay do the changes o c c u r? Is th e re sig n ifican t Si site 103 tr a n s f e r fro m Ga site s to As s ite s ? (3) Does the su b stitu tio n al Si p a ir w ith so m e o th e r la ttic e defect to fo rm new com plexes? (4) A re th e re new donor o r a c c e p to r sp e c ie s in addition to the S i^ a and S i ^ g being g e n e ra te d during an n ealin g , and if so, a t w hat annealing te m p e ra tu re a r e th e se sp e c ie s g en era ted ? In o r d e r to a n sw e r questions su ch as th e se , s e v e ra l d iffere n t m e a s u re m e n ts have to be m ade. The Si ato m s in GaAs give d istin ctiv e lo c a liz e d v ib ra tio n a l m odes w hich can give in fo rm atio n about the e x iste n c e and the c o n c e n tra tio n of the differen t Si sp e c ie s in G aA s. The b ack g ro u n d in fo rm a tio n of S i-doped GaAs including the lo c a liz e d m ode m e a s u re m e n t has b e e n d e sc rib e d in Section III-IV -B and w ill not be re p e a te d h e re . The lo c a liz e d v ib ra tio n a l m ode m e a s u re m e n t has the cap ab ility to a n sw e r q u estio n (1) above and p o s s ib ly the o th e r qu estio n s r a is e d if the com plex g e n e ra te d during annealing has an in fra re d -a c tiv e lo c a liz e d v ib ra tio n a l m o d e. Not all defects give lo c a liz e d v ib ra tio n a l m o d e s. A s d is c u s s e d in S ection III-IV -A , if the d efec t m a s s is h e a v ie r than the h o st a to m it re p la c e s o r if the fo rce co n stan t betw een the d efec t and the h o st la ttic e is s u ffi ciently red u ce d , no lo c a liz e d m ode due to this d efec t m a y be o b se rv e d . T his is the re a s o n th at Te in GaAs does not give lo c a liz e d m o d es. P h o to lu m in e sc e n c e m e a s u re m e n ts can give valu ab le in fo rm a tion about defect sp e c ie s in the host m a te r ia l if th e re e x ists ra d ia tiv e tra n s itio n s through the e n e rg y le v e ls of the d efec ts. 104 P h o to lu m in e sc e n c e m e a s u re m e n ts of S i-doped GaAs a r e known to show peaks due to the defect s p e c ie s . W illiam s and B lacknall (1967) o b s e rv e d p h o to lu m in e sc en ce peaks n e a r 1 .2 eV and 0 .9 8 eV w hile K r e s s e l et al. (1968) and K r e s s e l and N elso n (1969) used p h o to lu m in e sc en ce m e a s u re m e n ts to d e te c t two a c c e p to r levels and have a ttrib u te d th e m to the p re s e n c e of Si a c c e p to rs . Hence the p h o to lu m in e sc en ce m e a s u re m e n ts can be u se d as an aid to the lo c a liz e d v ib ra tio n a l m ode m e a s u r e m e n t to a n s w e r the q u e s tions r a is e d e a r l ie r . F o r m o re d etaile d d e s c rip tio n of the back g ro u n d in fo rm a tio n about p h o to lu m in e sc en ce m e a s u re m e n ts in S i-doped G aAs, the r e a d e r is r e f e r r e d to Section III-IV -B 6. V -II. E x p e rim e n ta l M ethods In the la s t sectio n , the m e a s u re m e n ts u sed to study the annealing effect w e re d e s c rib e d . T hese m e a s u re m e n ts a r e the H all effect o r in fra re d p la sm a edge re fle c tiv ity to d e te rm in e the c a r r i e r c o n c e n tra tio n , p h o to lu m in e sc en ce to d e te c t the d efect le v e ls and lo c a liz e d v ib ra tio n a l m ode in f r a r e d a b so rp tio n to d etect the Si donor and a c c e p to r im p u rity c o n c e n tra tio n s. In the follow ing su b se c tio n s, the o r d e r , p ro c e d u re and the s ta te of the sam p le fo r eac h m e a s u r e m e n t w ill be d is c u s se d . F r e e c a r r i e r a b s o r p tion m e a s u re m e n ts w e re a lso m a d e w ith the a n n ea led sam p les u se d in this study. The r e s u lts w e re p re s e n te d and d isc u ss e d in C h ap ter IV and a r e not re p e a te d h e re . A. A nnealing P ro c e d u re Ingots of n -ty p e , S i-doped GaAs w e re grow n b y both the 105 h o riz o n ta l B rid g m a n and C z o c h ra ls k i m e th o d s. The s ta rtin g m a te r ia l u sed in the h o riz o n ta l B rid g m a n m ethod w as p u re Ga and A s e le m e n ta l m a te r ia l w ith the Si dopant added to the Ga w hich w as in a b o a t m ade of q u a rtz . The ingot w as s e lf-s e e d e d during g row th and w as not a single c r y s ta l. The s ta rtin g m a te r ia l u se d in the C z o c h ra lsk i m eth o d w as p r e - r e a c t e d GaAs grow n by the h o riz o n ta l B rid g m a n m ethod. The GaAs w as m e lte d in a v itrio u s c a rb o n c ru c ib le and pulled w ith a GaAs seed o rie n te d in the (1 1 1 ) d ire c tio n . H ow ever, the r e s u lte d ingot w as p o ly c ry s ta llin e w ith ty p ic a l g ra in d im en sio n s of s e v e r a l m m s . F o r a d e ta ile d d e s c rip tio n of th e se c r y s ta l grow th m eth o d s the r e a d e r is r e f e r r e d to C h ap ter II. S am p les w e re cu t fro m w a fe rs w hich w e re in tu rn cu t fro m the ingot w ith the cutting plane p e rp e n d ic u la r to the ingot a x is. T his cutting p ro c e d u re is to m in im iz e the v a ria tio n of dopant c o n c e n tra tio n in a w a fe r due to the s e g re g a tio n effect during c r y s ta l grow th. S am ples w e re an n ealed e ith e r iso c h ro n a lly or is o th e rm a lly in ev ac u ated and se a le d s ilic a am p o u les. P r i o r to sealin g , the am poule and the s a m p le w e re w ash ed in 25% KCN aqueous solution and rin s e d w ith deionized w a te r to p re v e n t p o s sib le Cu co n tam in atio n . G e n e ra lly , the f i r s t step w as to e s ta b lis h a com m on th e rm a l b ack g ro u n d fo r a ll s a m p le s by h e a t ing for 15 m in u tes n e a r 1100°C and quenching to ro o m t e m p e r a tu r e b y im m e rs in g the w hole am poule in ethylene glycol. The sa m p le does re a c h th e rm a l e q u ilib riu m in the 1100°C /15 m in 106 annealing tr e a tm e n t as judged b y the c a r r i e r co n c e n tra tio n sin ce fu rth e r annealing for up to 3 h r at 1100° C p ro d u c e s no fu rth e r change in n g . H e re a fte r, u n less sp ecified to the c o n tra ry , the sa m p le a f te r the 1100° C /15 m in h e a t tr e a tm e n t is called the s ta rtin g sa m p le and to be d istin g u ish ed fro m the sam p le b efo re the 1100° C /15 m in an n eal, w hich is c a lle d the a s -g ro w n sa m p le . In the is o c h ro n a l annealing, a sa m p le w as h eated to the an nealing te m p e ra tu re , T ^ , and held at fo r two h o u rs . The sa m p le w as then quenched to ro o m te m p e r a tu r e , its c a r r i e r c o n c e n tra tio n m e a s u re d , se a le d in a new am p o u le, an nealed a t the n e x t te m p e ra tu re fo r two h o u rs, etc. T he volum e of the am poule 3 w as ab o u t 3 c m and u n le ss o th e rw ise in d ic a te d , no e x c e ss a r s e n ic w as added. M e a s u re m e n ts w e re m a d e betw een annealing ste p s and a f te r re m o v a l of a t le a s t a two m il th ick n ess of m a te r ia l fro m the la rg e a r e a s u rfa c e s b y lapping and ch e m ic a l p o lish in g . The e s tim a te d a r s e n ic lo ss fro m the sa m p le s u rfa c e to e s ta b lis h the a r s e n ic p a r tia l p r e s s u r e in sid e the am poule at the an n ealin g te m p e ra tu re can be e x p re s s e d in te rm s of effective th ic k n e ss of the sa m p le s u rfa c e w hich lo s s e s a r s e n ic . A t 1100°C, _ 3 the effective th ic k n e ss is = “ 2 .4 x 10 m il, a t 600°C , the effective th ic k n e ss is = ■ 6 .2 4 x 10 m il. T h e re fo re , if the a r s e n ic lo ss is confined to the s u rfa c e the two m il th ic k n e ss rem o v e d fro m the sa m p le is th ick enough to rem o v e the d am ag ed s u rfa c e la y e r. F u r th e r m o r e , e x p e rim e n ts in d icate th a t re m o v a l of m o re m a te r ia l fro m the s u rfa c e a fte r the two m il th ic k n e ss of m a te r ia l has b e e n re m o v e d does not change the m e a s u r e d ng . 107 The is o th e rm a l annealing follow ed the sa m e g e n e ra l p ro c e d u re as the iso c h ro n a l annealing, ex ce p t the tim e in te rv a ls betw een c a r r i e r c o n c e n tra tio n m e a s u re m e n ts v a rie d . The tim e in te rv a l betw een m e a s u re m e n ts w as 15 m in in the f i r s t h our and g rad u ally in c re a s e d to lo n g e r tim e s . F o r re a so n s to be m ade c le a r , the te m p e ra tu re s ch osen for the is o th e rm a l annealings w e re 400°C, 600°C and 750°C. B. C a r r i e r C o n cen tratio n M e a s u re m e n t The c a r r i e r c o n c e n tra tio n w as m e a s u r e d by using both an in f r a r e d p la s m a re fle c tiv ity m e a s u r e m e n t and a H all effect m e a s u re m e n t. S ection IV -I in d icate d th at the d e s ira b ility of avoiding the fre q u e n t u se of H all effect m e a s u re m e n ts during the an nealing p ro c e s s b e c a u se of the p o s sib ility of co n tam in atio n and effect of heating the sa m p le to m ake H all p ro b e contacts w hich m ig h t in tro d u ce a sig n ific a n t p e rtu rb a tio n of the annealing h is to ry of the sa m p le . T h e re fo re , p la sm a edge re fle c tiv ity m e a s u re m e n ts w e re u sed e x c lu siv e ly to m e a s u r e the c a r r i e r co n c e n tra tio n during the annealing p r o c e s s . Only a t the la s t stag e of the is o th e rm a l annealing p ro c e s s w h e re no fu rth e r ann ealin g w as sch ed u led w e re b o th H all effect and p la s m a edge re fle c tiv ity m e a s u re m e n ts m ad e. T he eq u ip m en t u sed and e x p e rim e n ta l a r r a n g e m e n t for the H all effect and in f r a r e d re fle c tiv ity m e a s u re m e n ts have b een d e sc rib e d in S ections III-III-A and III-III-C , re s p e c tiv e ly . The ch e m ic a l polishing m eth o d u sed in sa m p le s u rfa c e p re p a ra tio n for the re fle c tiv ity m e a s u r e m e n t has b een d is c u s s e d in Section IH-II-B. The in f r a r e d p la s m a edge re fle c tiv ity has been d is c u s s e d ex ten - 108 siv ely in C hapter IV fo r s a m p le s w ith shallow as w ell as deep re fle c tiv ity m in im a . C. P h o to lu m in esce n ce M e a s u re m e n t A fter the la s t stag e of is o th e rm a l an n eal and the H all effect and in f r a r e d p la sm a re fle c tiv ity m e a s u re m e n ts w e re m a d e, the p h o to lu m in e sc en ce s p e c tr a fro m the v ario u s s a m p le s w ere m e a s u re d . Two of the s ta rtin g sa m p le s w e re a lso m e a s u re d . The m e a s u re m e n ts w e re m a d e w ith the sa m p le im m e rs e d in liquid h eliu m (4.2°K ). The e x p e rim e n ta l p ro c e d u re and the equipm ent u sed w e re d e s c rib e d in S ection III-III-E . Only lu m in e sc e n c e fro m the fro n t su rfa c e was m e a s u re d . Since the p e n e tra tio n depth of the la s e r light so u rc e is quite shallow (=* 2|im ), the s u rfa c e co n dition of the sa m p le is v e ry im p o rta n t. Two m ethods of s u rfa c e p re p a ra tio n w e re used. The f i r s t was the sam e as the s u rfa c e p re p a ra tio n of the re fle c tiv ity m e a s u re m e n t, i . e . , c h e m ic a l polishing by using A CL 66 aqueous solution. This ch e m ic a l polishing m eth o d has b e e n d e s c rib e d in d etail in S ection III-II-B . The o th e r m eth o d w as by etching the sa m p le s u rfa c e w ith a m ix tu re of H F and HNO.j(l:4) fo r a few seconds and then w ashing in deionized w a te r. T his etching p ro c e d u re re m o v e s s u rfa c e dam age fro m the sa m p le . The p h o to lu m in e sc en ce s p e c tr a obtained fro m th e se two d iffe re n t tre a te d sa m p le s u rfa c e s w e re e s s e n tia lly id e n tica l. As w as a lso d is c u s s e d in S ection III-IH -E , only re la tiv e lu m in e sc e n c e in te n s itie s could be obtained fro m th e se m e a s u r e m e n ts . D. L o c a liz e d V ib ratio n al M ode M e a s u re m e n t 109 To obtain s p e c tr a of the lo c aliz ed v ib ra tio n a l m odes of a sa m p le , the in fra re d tr a n s m is s io n is m e a s u re d . The freq u en cy reg io n of in te r e s t is known to be fro m 350 cm ^ to 470 cm T his reg io n has a v e ry high background ab so rp tio n fro m fre e c a r r i e r s w hich m a sk s the lo c a liz e d v ib ra tio n a l m ode s p e c tru m . The fre e c a r r i e r a b s o rp tio n has to be quenched and this is g e n e ra lly done by using one of the m eth o d s of e le c tr ic a l co m p en sa tio n as d e s c rib e d in Section III-II-C . F o r the p r e s e n t study, the e le c tro n ir r a d ia tio n m eth o d w as ch o sen to obtain e le c tr ic a l co m p en sa tio n for the s a m p le s . T his m ethod has the advantage th a t the s a m p le is kept at low te m p e ra tu re (T< 100°K) during the ir r a d ia tio n p r o c e s s and the sa m p le te m p e r a tu r e is not b ro u g h t above ro o m te m p e ra tu re in the e n tire p ro c e s s . T h e re fo re , no above ro o m te m p e ra tu re p e rtu rb a tio n is in tro d u ced to the annealing h is to ry of the s a m p le . T his is not the c a se fo r the o th e r c o m p en sa tio n m eth o d s su ch as L i diffusion o r Cu diffusion. 1 In th e se m ethods the diffusion p r o c e s s has to be held a t t e m p e r a tu r e s h ig h e r than 600°C, thus m ak in g the annealing h is to ry of the sa m p le u n c e rta in . The sa m p le s w e re e le c tro n ir r a d ia te d w ith a 1 MeV e le c tro n b e a m and a fluence n e c e s s a r y to co m p en sate them . 18 18 - 2 T y p ical flu en ces w e re betw een 0. 5 x 10 and 3. 6 x 10 e /c m p e r sid e, the values depending upon the in itia l c a r r i e r c o n c e n tra - The e le c tro n ir r a d ia tio n w as p e rfo rm e d by F . E u le r and L. B outhillette of the A ir F o rc e C am b rid g e R e s e a rc h L a b o ra to ry , B edford, M a s s. The au th o r w ish es to e x p re s s his a p p re c ia tio n for th e ir help. 110 tio n s. The in fra re d tr a n s m is s io n w as then m e a s u re d a fte r this irra d ia tio n -c o m p e n s a tio n p r o c e s s . B e c a u se of the n e c e s s ity to in tro d u ce the co m p en sa tio n step , the lo c a liz e d v ib ra tio n a l m ode (LVM) m e a s u r e m e n t w as m a d e a fte r a ll the o th e r m e a s u re m e n ts w e re p e rfo rm e d . T he in fra re d a b s o rp tio n s p e c tru m w hich shows the LVM bands of e a c h sa m p le is c a lc u la te d fro m the m e a s u re d in fra re d tr a n s m is s io n s p e c tru m . The m e a s u re m e n ts w e re done a t 77°K. The e x p e rim e n ta l a rra n g e m e n t fo r the in fra re d tra n s m is s io n m e a s u r e m e n t has been d e s c rib e d in S ection III-III-D , and the a b s o rp tio n co efficien t a is c a lc u la te d as d e s c rib e d in Section m -IV -A . In S i-doped GaAs s a m p le s w hich a r e e ith e r L i diffused or e le c tro n ir r a d ia te d (w ithout p r io r annealing) to o btain e le c tric a l co m p en sa tio n show the sa m e linew idths fo r the 399 cm * and 384 c m * b an d s. (Spitzer and A llre d 1968b, S p itz e r e t al. 1969) As m e n tio n ed e a r l i e r (Section III-IV -B 4), a b s o rp tio n band peak heights a r e freq u en tly u sed as a m e a s u r e of the in te g ra te d ab so rp tio n . H ow ever, in the p r e s e n t m e a s u re m e n ts of a , it is found th a t the bandw idth a s w ell as p eak height of the LVM bands a r e a function of annealing and th e re fo re a ll stre n g th s should be m e a s u r e d fro m the in te g ra te d a b so rp tio n . L a rg e e r r o r s w ill be in c u rre d if only the p e a k height is u sed fo r c o m p a riso n s betw een the s a m p le s . The in te g ra te d band s tre n g th w as obtained by using a p le n im e te r to m e a s u r e the a r e a under the band fro m a p lotted a b s o rp tio n s p e c tru m w ith the b ack g ro u n d a b s o rp tio n s u b s tra c te d . I l l The m e a s u re d value w as then c a lib ra te d to give the d im en sio n of -2 -1 "1 cm " [a (cm " ) x v (c m )]. E . S u m m a ry of M e a s u re m e n ts . In the above four se c tio n s, the m e a s u re m e n ts u sed in the p r e s e n t study have b een d e s c rib e d . The following is a listin g of th e se m e a s u re m e n ts in the o r d e r th a t eac h w as m e a s u re d in the p r e s e n t study. The state of the sa m p le a t eac h m e a s u re m e n t is a lso given. (1) In fra re d p la sm a edge re fle c tiv ity m e a s u r e m e n t w as p e rfo rm e d during the annealing p r o c e s s . The sam p le had one s u rfa c e ch e m ic a lly p o lish e d w ith A C L 66 m ethod. (Section III-IIB) (2) H all E ffect m e a s u re m e n ts w e re p e rfo rm e d a fte r the la s t stag e of the is o th e rm a l anneal. (3) P h o to lu m in esce n ce m e a s u re m e n ts w e re m ade a fte r the c a r r i e r co n ce n tratio n of the sa m p le had been m e a s u re d . (4) L o ca liz ed v ib ra tio n a l m ode m e a s u re m e n ts w e re m ade a fte r the p h o to lu m in escen ce and a f te r e le c tr ic a l co m p en satio n . V -III. E x p e rim e n ta l R esu lts T he m a te r ia l used is h eav ily S i-doped G aA s. B ased on the dopant added to the m e lt d u rin g grow th and the m e a s u r e d se g re g a tio n coefficient (Skolnik et al. 1971; W illa rd so n and A llre d 1966) the to tal Si co n ce n tratio n , fSi], n e a r the fro n t end of two 19 -3 ingots is 4 x 10 cm . A sa m p le fro m a C z o c h ra ls k i grow n ingot (W ACZ-99) w as an aly zed b y a m a s s sp e c tro g ra p h ic 112 ❖ m eth o d , and the r e s u lts a r e show n in T able V -I. T he re s u lts 19 -3 show th a t [Si] = 3 .4 x 10 c m , c lo se to the intended doping le v el. M o st of the annealing r e s u lts w e re obtained fro m a h o r i zontal B rid g m a n grow n ingot. H ow ever, s a m p le s fro m the C z o c h ra lsk i grow n ingot w e re also an n ea led and m e a s u re m e n ts gave v e ry s im ila r r e s u lts . A. Iso c h ro n a l A nnealing R e su lts The iso c h ro n a l annealing r e s u lts of two h eavily doped n-type GaAs sa m p le s a r e show n in F ig u re V -I. As in d icated p re v io u sly , the ng v alu es w e re obtained fro m the in f r a r e d p la s m a re fle c tiv ity m e a s u r e m e n t by using the c a lib ra tio n cu rv e in F ig u re IV-2 w hich re la te s n g to the fre q u e n c y of the re fle c tiv ity m in im u m . One of 19 -3 the sa m p le s is S i-doped and has [Si] =- 4 x 10 cm , w hile the 19 -3 o th e r is a T e-d o p e d sa m p le w ith [Te] = “ 1 x 10 c m . As shown in the fig u re, the 1100° C /15 m in h e a t tr e a tm e n t cau sed the c a r r i e r co n c e n tra tio n in both sa m p le s to in c re a s e . S ubsequent an n ealin g s fo r 2 ho u rs a t e a c h annealing te m p e r a tu r e fro m 300°C to 900°C w e re p e rfo rm e d . The an n ealin g cu rv e fo r the S i-doped sa m p le has two e a s ily d istin g u ish e d te m p e ra tu re reg io n s. The c a r r i e r c o n c e n tra tio n n show s su b sta n tia l d e c r e a s e s for 400°C^ e T£ 700°C, a te m p e r a tu r e ran g e in w hich the T e-d o p e d m a te r ia l has little change for s im ila r annealing tim e . M o re o v e r, the n g changes in G aA s:Si on F ig u re V - l a r e fully as la rg e as any The m a s s s p e c tro g ra p h ic a n a ly sis w as done by D. C. W a lte rs a t B a tte lle Colum bus L a b o r a to r ie s , C olum bus, Ohio 43201, su p p o rted b y the A dvanced R e s e a r c h P r o je c ts A gency, A RPA O rd e r N u m b er 1628, G ra n t No. DAHC 15-72-G 7. 113 T A B L E V -I MASS SPEC TR O G R A PH IC ANALYSIS1 " O F GaAs (Ingot W A C Z-99) E le m e n t C o n cen tratio n (ppmw) E le m e n t C o n cen tratio n (ppm w ) Li < 0. 003 Cd < 0. 05 Be < 0. 03 In < 0. 1 B 0. 2 Sn 0.5 F < 0. 1 Sb < 0. 05 Na (a) Te < 0. 05 Mg < 0. 03 I < 0. 02 Al fS 1 Cs < 0. 02 Si 300 Ba < 0. 5 P 0. 01 L a < 0. 1 S < 0. 2 Ce < 1 Cl 0. 2 P r < 0. 1 K 0. 1 Nd < 0. 1 Ca 0. 02 Sm < 0.2 Sc < 0. 1 Eu < 0.2 Ti < 0. 02 Gd < 0.2 V < 0. 02 Tb < 0.2 C r 0. 02 Dy < 0. 1 Mn < 0. 03 Ho < 0. 03 Fe 0. 2 E r < 0. 1 Co < 0. 03 T m < 0. 03 Ni < 0. 05 Yb < 0. 1 Cu 0. 05 Lu < 0.0 3 - Zn 0. 05 Hf < 0. 1 Ge < 0. 3 Ta < 1 Se < 0. 3 W < 0. 1 B r < 0. 3 Re < 0. 05 Rb < 0. 2 Os < 0. 1 S r < 0. 5 Ir < 0. 05 Y < 0. 1 P t < 0. 3 Z r < 0. 1 Au < 0.2 Nb < 0. 05 Hg < 0. 1 Mo < 0. 2 Tl < 0. 1 Ru < 0. 05 Pb 0.2 Rh < 1 B i < 0. 03 P d < 0. 2 Th < 0. 05 Ag < 0 . 1 U < 0 . 1 (a) In te rfe re n c e fro m Ga. M e a su re d a t B a tte lle Colum bus Labo r a t o r i e s , C olum bus Ohio 43201, S upported by the A dvanced R e s e a r c h P ro je c ts A gency, G ran t No. DAHC 15-72-G 7. xIO 18 9 114 8 to I E o n > c . 6 5 4 3 / \ G a A s : Si \ h * G a A s : Te L P re -A n n e al 1100 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 i i i i___ i i____i i____i i_ _ i i i 3 0 0 4 5 0 5 5 0 6 5 0 7 5 0 8 5 0 1100 ° C / 2 H R S ------------------* 1 t kin — I ° C /I5 m in ° C /I5 m in F ig u re V - l R oom te m p e ra tu re c a r r i e r co n c e n tra tio n , n , of h eav ily doped G aA s:Si and G aA s:T e sa m p le s a f te r e a c h is o c h ro n a l annealing stag e. 115 re p o rte d fo r T e - o r S e-doped m a te r ia l (G rishina e t a l. 1970, F u lle r and W o lfstirn 1963) as d e s c rib e d in Section III-IV -C . A fte r the 900°C/2 h r anneal, the sam p les w e re an n ea led a t 1100°C fo r 15 m in u te s. A s shown in F ig u re V - l, this anneal b ro u g h t the c a r r i e r co n c e n tra tio n of the G aA s:Si sam p le b ack to the o rig in a l s ta rtin g value. F o r the G aA s:T e sa m p le , the n g also in c re a s e d b u t w as so m ew h at below the s ta rtin g value. F ig u re V-2 show s the changes for is o c h ro n a l annealing of 17 a m o re lig h tly S i-doped sa m p le . In this sam p le n ^ 6 x 10 _3 c m and n g show s e s s e n tia lly no change w ith an annealing h is to ry s im ila r to th a t of F ig u re V - l. B. Is o th e rm a l A nnealing R e su lts A n u m b e r of m e a s u re m e n ts w e re m ade on is o th e rm a lly annealed s a m p le s . In o r d e r to m ak e the p re s e n ta tio n c le a r, the re s u lts a r e p re s e n te d in su b se c tio n s. B l. C a r r i e r C o n cen tratio n M e a s u re m e n t T he c a r r i e r co n ce n tratio n s m e a s u r e d during the is o th e rm a l annealing p r o c e s s of th re e sa m p le s a r e plo tted as a function of annealing tim e in F ig u re V -3. T h ese s a m p le s w e re an n ealed at 400°C, 6 0 0 °C and 750°C. A ll th re e s a m p le s w e re taken fro m neig h b o rin g w afers cu t fro m a h o riz o n ta l B rid g m a n ingot (Ingot 19 -3 W A -99) w ith [Si]®* 4 x 10 c m . R e c a ll that the sa m p le s w e re f i r s t a n n ea led at 1100°C fo r 15 m in u tes and quenched to ro o m te m p e ra tu re to e s ta b lis h a com m on th e rm a l b ack g ro u n d and the re s u ltin g ng fo r e a c h sa m p le is show n as the s ta rtin g value for the is o th e rm a l annealing. The ng values w e re d e te rm in e d by 116 ? * 6 1 0 - a Z e a t 4 • o e o u 10 IT GaAs • Si — — Hall — o - ------ -o Rsflsctlvity - i i i i i ANNEAL 300 450 600 800 ANNEAL CONDITION ( *C/2Hrs) F ig u re V-2 R oom te m p e ra tu re c a r r i e r co n c e n tra tio n of a lig h tly S i-doped GaAs sa m p le a f te r eac h iso c h ro n a l annealing sta g e . [njtcrrf3) 400°C ANNEAL 600°C ANNEAL 75 0°C ANNEAL I 2 3 4 5 1 0 20 30 40 50 100 150 200 400 600 800 1 2 0 0 ANNEALING TIME (hours) F ig u re V -3 R oom te m p e ra tu re c a r r i e r co n cen tratio n , n , during is o th e rm a l annealing of th re e heavily Si-doped GaAs sam p les a t %00, 600 and 750° C, re sp e c tiv e ly . 118 j by in fra re d p la s m a re fle c tiv ity m e a s u r e m e n t and e x am p les of the re fle c tiv ity data fo r the 600°C annealed sam p le a r e shown in F ig u re V -4. The n u m b e r on eac h re fle c tiv ity c u rv e r e la te s to the c o rre s p o n d in g ly n u m b e re d point of F ig u re V -3. The r e f le c tiv ity c u rv e s fo r the o th e r two annealing te m p e ra tu re s a r e s im ila r to th o se shown in F ig u re V -4. H all effect m e a s u re m e n ts w e re ma. m ad e on th e se s a m p le s a t the m a x im u m annealing tim e for each of the cu rv es on F ig u re V -3, and a lso m a d e on neighboring s a m p le s in a tim e eq u al z e ro condition (sta rtin g condition). A c o m p a riso n of the n g m e a s u re d fro m the re fle c tiv ity m in im u m and n fro m the H all m e a s u r e m e n t is given in T able V -II. The n e e values obtained fro m th e se two m ethods a r e w ithin 10% of ea c h a o th e r. The a g re e m e n t is re g a rd e d as s a tis fa c to ry and w as c o n sid e re d f u rth e r in the a n a ly sis in C h ap ter IV. In F ig u re V -3 , the 600°C and 750°C th e rm a l an n eals a p p e a r to have re a c h e d e q u ilib riu m w hile the 400°C sam p le show s s ig n ifi cant changes fo r the lo n g e st tim e s u sed . The 400° C eq u ilib riu m value for n g a p p e a rs to be below th a t fo r the 600°C an n ealed sa m p le . The e q u ilib riu m ng in c re a s e s w ith h ig h e r is o th e rm a l annealing te m p e ra tu re as w as o b se rv e d (G rish in a e t al. 1970) for T e-d o p ed s a m p le s . The is o th e r m a l annealing c u rv e s shown in F ig u re V -3 a r e re p ro d u c ib le in th a t o th e r sa m p le s fro m the sa m e p o rtio n of the ingot have e s s e n tia lly id e n tic a l re s u lts and o th e r s a m p le s w ith s im ila r Si doping le v e ls also have s im ila r effects. T he annealing effects a r e c o m p lete ly r e v e r s ib le . T h re e ANNEALING AT 600 °C 50 Annealing time 0 hrs. Omin, 40 30 30 30 30 30 30 30 20 179 290 1 1 0 0 800 i/(cnrf') 900 1000 600 700 500 400 F ig u re V -4 P e rc e n t re fle c tiv ity m e a s u re d a t ro o m te m p e ra tu re as a function of frequency, v , of the 600°C is o th e rm a lly an n ealed sam p le in F ig u re V -3. The n u m b e rs in c irc le s c o rre sp o n d to those shown in F ig u re V -3. 120 T A B L E V -II COMPARISON O F F R E E CARRIER CONCENTRATION VALUES OBTAINED FRO M HALL E F F E C T AND IN FRA RED R E F L E C T IV IT Y M EASUREM ENTS A nnealing n e fro m n e fro m H all C ondition R eflectivity; M e a s u re m e n t effect M e a s u re m e n t Shown in F ig. V -3i (cm ) (c m - ) 1 8.3 x 1018 8. 5 x 1018 7 1 .7 x 1018 1 .5 x 1018 A 2 .3 x 1018 1 .9 x 1018 B 1.5 x 1018 1 .5 x 1018 121 s a m p le s w e re re p e a te d ly cycled betw een 1100°C/15 m in and 60 0 °C /tim e > 20 h r s . One sam p le w as cycled betw een th e se two annealing s ta te s six tim e s . The ng values and the fo rm of the re fle c tiv ity c u rv e s of a ll th e se sa m p le s w e re quite re p ro d u c ib le and the sa m e as th o se shown on the fig u re s. Is o th e rm a l an n ealin g s w e re also p e rfo rm e d a t 600°C and 750°C w ith ad d itio n al a r s e n ic added in o r d e r to m a in ta in inside the am poule an A s p r e s s u r e of a p p ro x im a te ly 2 /3 and 1 a t m o s p h e re re s p e c tiv e ly a s s u m in g the do m in ate a r s e n ic v a p o r sp e c ie s to be A s^ . A t 600°C this p r e s s u r e is a p p ro x im a te ly the e q u ili b riu m value for a r s e n ic v ap o r o v er p u re a r s e n ic (solid). The n g m e a s u re d w e re the s a m e as those shown in F ig u re V -3 w h ere no a r s e n ic w as added. B2. R e su lts of L o c a liz e d V ib ratio n al Mode (LVM) M e a s u re m e n ts The LVM m e a s u re m e n ts w e re m ad e a fte r the p h o to lu m i n escen c e m e a s u re m e n t, b u t fo r convenience w ill be p re s e n te d h e re . The sa m p le s used in the LVM m e a s u r e m e n t w e re an n ea led w ith the lo n g e st ann ealin g tim e s u sed , su ch as (A), (B) and (7) in F ig u re V -3. A couple of s ta rtin g sa m p le s w e re a lso m e a s u re d . The e le c tro n : ir r a d ia tio n fluence u sed fo r c o m p e n sa tio n of e a c h sa m p le is lis te d in T able V -III. T he a b s o rp tio n s p e c tr a of th e se s a m p le s a r e p lo tted in F ig u re s V -5 th ro u g h V -7. E a c h figure shows a co m p o site plot of the re s u lts of two s a m p le s , one of w hich is a s ta rtin g sa m p le , i . e . , 1100°C/15 m in annealing, and one is a low te m p e ra tu re TA B L E V -IH E L EC TR O N IRRADIATION F L U E N C E USED IN OBTAINING E L E C T R IC A L COMPENSATION n (cm ) e ' E le c tro n F luence 2 e le c tro n /c m /s id e 300°K 77°K Side 1 Side 2 W A -99-4B 750°C /320 h r 1.9 x i o 18 1.9 X i o 18 5. 0 X 1017 5. 0 X i o 17 W A -99-6B 1100bC /15 m in 9 .4 x i o 18 9 .4 X 1018 3. 0 X 1018 3. 0 X 1018 W A -99-10A W A -99-10B 600°C/290. 5 h r +1100°C/15 m in 400°C/1178 h r 8 . 0 x 1. 5 x 1018 i o 18 8 .9 1. 6 X X 1018 i o 18 4 .2 1. 6 X X i o 18 i o 18 4. 3 9 .2 X X i o 18 i o 17 W A -99-11A 1100°C/15 m in 8 , 0 x i o 18 8 .9 X i o 18 3. 6 X i o 18 3. 6 X 1018 W A -99-11B 600°C /290.5 h r 1. 5 x i o 18 1. 5 X i o 18 1. 6 X i o 18 9. 3 X i o 17 E le c tro n e n erg y = 1 MeV 14 -1 E le c tro n flux = 1 .4 to 1.9 x 10 cm sec (22 to 30 nA /<cm ) 120 GaAs =Si Compensated by electron irradiation 77°K — IIOO°C/l5min ANNEAL — +— 400°C/II78 HR ANNEAL 100 120 80 rioo 60 40 80 This scale 20 60 40 This scale -g 20 V 450 410 430 390 FREQUENCY v (cm"') 370 F ig u re V -5 A b so rp tio n s p e c tra a t 77°K of two heavily Si-doped GaAs sam p les w hich a re annealed a t 1100°C/15 m in and 400°C/1178 h r re sp e c tiv e ly and com p en sated b y 1 M eV e le c tro n irra d ia tio n . The v e rtic a l sc a le of the 1100°C/15 m in sam ple is shifted up 40 c m “ to avoid overlapping of s p e c tra . ab so rp tio n coefficient a (cm-1 120 100 80 60 40 20 0 F ig u re V -6 A b so rp tio n s p e c tra a t 77°K of two heavily Si-doped GaAs sa m p le s w hich a re annealed a t 1100°C/15 m in and 600°C/290. 5 h r re s p e c tiv e ly and co m pensated by 1 M eV e le c tro n irra d ia tio n . The 1100°C/15 m in sam p le is not the sam e sam p le as shown in F ig u re V -5. I I I G aA s = Si Com pensated by electron irradiation 77°K 1 100 °C/15 m in ANNEAL 600°C/290.5HR ANNEAL This scale This scale 370 380 390 FREQUENCY v (cm *1 ) 400 124 120 GaAs = S i Compensated by electron irradiation 77°K —« — IIOO°C/l5min ANNEAL — 750°C/320HR ANNEAL 100 120 80 60 100 This scale 40 a 80 20 60 40 This scale a. 380 FREQUENCY i/(crn') 390 400 410 370 F ig u re V -7 A b so rp tio n s p e c tra at 77°K of two h eavily Si-doped GaAs sa m p le s w hich a re annealed a t 1100°C/15 m in and 750°C/320 h r re s p e c tiv e ly and co m pensated by 1 M eV e le c tro n irra d ia tio n . The 1100° C /15 m in is not the sam e sam p le as shown in e ith e r F ig u re V -5 o r F ig u re V - 6. 125 126 is o th e rm a lly an n ealed s a m p le . The two s a m p le s in eac h fig u re a r e e ith e r fro m the sa m e w a fe r o r fro m neig h b o rin g w a fe rs . The a b so rp tio n co efficien t s c a le of the s ta rtin g sa m p le in a ll of th e se fig u re s has b een shifted to avoid o v erla p p in g of the two s p e c tra . A ll the points show n in th e se fig u re s a r e m e a s u r e d and c a lc u la te d data p o in ts. A ll the bands o b s e rv e d in F ig u re s V -5 th ro u g h V-.7 have b e e n id e n tified p re v io u s ly and have b e e n d e s c rib e d in Sections III-IV -B 2 and III-IV -B 3. F ig u re V -5 c o v e rs a fre q u e n c y ra n g e up to 470 c m F ig u re s V -6 and V -7 stop a t 410 cm "* sin ce the (^ 1 _ i only LV M band b etw een 410 and 470 cm is at 464 cm and its s tre n g th is known to be p ro p o rtio n a l to the band a t 393 cm It is se e n fro m th e se fig u re s th a t th e re a r e d iffere n ces in both p e a k heights and bandw idths fo r the v a rio u s an nealing s ta te s . The in te g ra te d s tre n g th s of the m a jo r Si LVM bands shown in F ig u r e s ' V-Si to V -7 a r e lis te d in Table V-IV. Note th at the 367 c m ^ and 369 cm ^ bands w e re not m e a s u r e d . T h ese two bands a r e lo c a te d clo se to g e th e r and the 369 c m ^ band is a lso v e ry b ro a d w hich m a k e s the d e te rm in a tio n of the s e p a ra te stre n g th s of th e se two bands v e ry d ifficult. A s s ta te d e a r l i e r in this sectio n , d iffe re n t s ta rtin g s a m p le s (1100°C/15 m in) w ere u se d in F ig u re s V -5 th ro u g h V -7. H ence the in te g ra te d a b s o rp tio n band s tre n g th s of th e se s ta rtin g s a m p le s a r e not p r e c is e ly the sa m e , h o w ev er, the values a r e w ithin 10% of each o th e r. In o r d e r to fa c ilita te the c o m p a ris o n of the bands betw een the s a m p le s , the in te g ra te d band s tre n g th s of the two s ta rtin g s a m p le s shown in F ig u re s V -6 TA B LE V -W LIST O F TH E INTEG RA TED ABSORPTION BAND STRENGTH OF Si LO CA LIZED VIBRATIONAL MODES Sam ple F ig u re w h ere the A nnealing In teg ra ted A bsorption Band I. D. S p ectru m of the Condition s tre n g th (c m “2) Sam ple is plotted 384 cm ^ 393 c m - '* ' 399 c m W A -99-4B VI-7 750°C /320 h r 183. 1 50. 65 89. 61 W A -99-6B VI-7 1100°C/15 m in 224. 8 41.57 90. 62 W A -99-10A VI-5 600°C /290.5 h r +1100°C/15 m in 212. 1 44.92 95. 84 W A -99-10B VI-5 4 0 0 °C /1178 h r 126. 2 56.10 99.89 W A -9 9 -H A V I-6 110 0°C /15 m in 210. 8 4 4 .5 7 82. 13 W A -9 9 -H B V I-6 600°C /290.5 hr 143. 7 83. 14 7 3 6 63 A ll sam p les w e re e le c tric a l co m p en sated by 1 MeV e le c tro n irra d ia tio n 128 and V -7 a r e n o rm a liz e d to the s ta rtin g sa m p le shown in F ig u re V -5. The sa m e n o rm a liz a tio n fa c to rs a r e u sed to n o rm a liz e the in te g ra te d a b so rp tio n band stre n g th s of the 600°C /290. 5 h r and the 750°C/32 0 h r an n ealed s a m p le s . The re s u ltin g in te g ra te d a b so rp tio n s tre n g th of th e s e sa m p le s a fte r this n o rm a liz a tio n p ro c e d u re is plo tted in F ig u re V -8 w hich shows the in te g ra te d a b s o rp tio n s tre n g th of the 384 c m \ 393 c m ^ and 399 c m - ^ bands fro m the four s a m p le s . B 3. R esu lts of P h o to lu m in e sc e n c e M e a su re m e n ts P r i o r to e le c tro n ir r a d ia tio n to p ro d u c e e le c tr ic a l c o m p e n sa tio n p h o to lu m in e sc e n c e m e a s u re m e n ts w e re m ade in s e v e r a l c a s e s , and the r e s u lts of th e se m e a s u re m e n ts a t 4 .2 ° K for four s a m p le s a re show n in the c o m p o site plot in F ig u re V -9. A s was m en tio n ed in S ection III-III-E , only re la tiv e lu m in e s c e n c e in te n sity w as o btained fro m this m e a s u re m e n t. T h e re fo re , quantitative in te n sity c o m p a ris o n s betw een s p e c tr a of d iffe re n t s a m p le s a r e not sig n ifican t. The an n ealin g conditions of the four s a m p le s of F ig u re V -9 a r e : (1) s ta rtin g sa m p le (1100°C/15 m in), (2) 4 0 0 °C /1178 h r, (3) 600°C/290. 5 h r and (4) 750°C /320 h r. The p h o to lu m in e sc en ce p eak s a r e o b s e rv e d in th e se s a m p le s n e a r the follow ing photon e n e rg ie s : (1) 1.5 eV (2) 1.2 eV (3) 1.15 eV (4) 0. 98 eV. The follow ing is a c o m p a ris o n b etw ee n the sa m p le s a n n ea led a t d iffe re n t te m p e r a tu r e s in te r m s of the p h o to lu m in e s cence p e a k s. (1) 1.5 eV P e a k T his p eak is o b s e rv e d in the 1100°C/15 m in annealed 25r- xIO 20 - 10- 5 - O 1 — F ig u re V - ANNEAL TEMPERATURE o 400°C /II78 HR * 6 0 0 °C /290.5 HR □ 750°C/ 3 2 0 HR • II00°C/ 15 min □ o A © _ l___________ I ___________ I ______ 384 393 t 399 V (cm") 8 N o rm a liz e d in te g ra te d a b so rp tio n s tre n g th of th re e Si LVM bands a t 384 c m - *, '3#3 cm " and 399 c m - * fro m four h eav ily S i-doped GaAs sa m p le s w ith d iffe re n t annealing h is to r ie s . 40 20 0 60 40 20 0 60 40 20 0 60 40 20 0 II00°C/ 1 5 min ANNEAL GaAs = Si 4.2°K l T — i-------- r 400°C /1178 HR ANNEAL 600°C /290.5 HR “ ANNEAL r 750°C /320 HR 1.2 1.3 1.4 1.5 1.6 0.7 0.8 0.9 1.0 l.l PHOTON ENERGY, eV V -9 P h o to lu m in esce n ce s p e c tra a t 4 . 2°K of four 1 S i-d o p e d GaAs sa m p le s w ith d iffe re n t an n eal c o n d itio n s. ....................131 s ta rtin g sa m p le , but not in s a m p le s an n ealed a t lo w er t e m p e r a tu r e s . T his p eak e n e rg y is clo se to the band gap e n e rg y of GaAs a t 4.2°K (1.52 eV). (2) 1.2 eV P e a k T his peak w as o b se rv e d in the 1100°C/15 m in s ta rtin g sa m p le . It is quite lik e ly th a t this p eak and the 1. 15 eV peak o b se rv e d in the low te m p e ra tu re an n ea led sa m p le s a r e a c tu a lly fro m the sa m e ra d ia tiv e tra n s itio n . The d iffere n t p eak e n e rg ie s m a y be in tro d u c e d a rtific ia lly by the d iffe re n t d e te c to rs u sed in the m e a s u r e m e n ts . The lu m in e sc e n c e s p e c tru m of the s ta rtin g sa m p le (1100°C/15 m in ) w as m e a s u r e d w ith a RCA 7102 p h o to m u ltip lie r. The s e n sitiv ity of the s p e c tra l re s p o n se of the RCA 7102 p h o to m u ltip lie r n e a r the 1.2 eV reg io n d e c re a s e s rap id ly w ith d e c re a sin g photon e n erg y . A s m a ll e r r o r in the m e a s u r e m e n t o r in the c a lib ra tio n of the re s p o n s e cu rv e w ill cau se a sig n ifican t sh ift of p eak en erg y . The o th e r th re e s p e c tr a in F ig u re V -9 w e re m e a s u r e d w ith an InAs photovoltaic d e te c to r in the photon e n e rg y ran g e below 1.3 eV. T he s e n sitiv ity of the InAs d e te c to r s p e c tra l re s p o n s e cu rv e does not have a stro n g e n e rg y dependence n e a r 1 .2 eV. T h e re should be little sh ift of the p eak e n e rg y fro m the c a lib ra tio n c alcu la tio n p ro c e d u re , but th e re could be a c a lib ra tio n e r r o r betw een the InAs d e te c to r and the RCA 7102 p h o to m u ltip lie r. Hence it is p o s sib le th a t the d iffe re n t peak e n e rg ie s of the 1.2 eV and the 1.15 eV lu m in e s cence bands a r e a rtific ia l. The d iffe re n t p eak e n e rg y m a y be also due to the b ro ad en in g of the re c o m b in a tio n c e n te r e n e rg y 132 le v el. T his c a n happen w hen the co n c e n tra tio n of re c o m b in a tio n c e n te r in c r e a s e s as a re s u lt of annealing a t lo w er te m p e r a tu r e s . T h e re fo re in the d isc u s sio n sectio n , th e se two p h o to lu m in e sc en ce peaks w ill be tre a te d a s due to the sa m e ra d ia tiv e tra n sitio n . (3) 1. 15 eV P e a k T his p eak w as o b se rv e d in a ll the low te m p e ra tu re a n n e a l ed s a m p le s . A s m en tio n ed above, this peak is tre a te d a s due to the sa m e tr a n s itio n as the 1.2 eV peak w hich is o b s e rv e d in the s ta rtin g sa m p le . (4) 0 .9 8 eV P e a k T his p eak w as o b s e rv e d in the 6 0 0 °C /2 9 0 .5 h r and the 750°C /320 h r an n ea led s a m p le s . It w as a b s e n t in the 400°C /1178 h r an n ea led sa m p le as w ell as in the s ta rtin g sa m p le . As shown in F ig u re V -9, this p e a k has c o m p a ra b le in te n s ity as the 1.15 eV p eak in the 600°C/290. 5 h r an n e a le d sa m p le . The lu m in e sc e n c e s p e c tru m of the 750°C /320 h r an n ea led sa m p le shows that the 0 .9 8 eV p eak has b e c o m e do m in an t and the 1.15 eV p eak show s only a s a sh o u ld er. Since it is n o t p o ssib le to c o m p a re in te n s i tie s b etw ee n d iffe re n t m e a s u r e m e n ts , we do not know w h eth er the change betw een the 600°C and 750°C an n ealed sa m p le s is due to an in c re a s e in the 0 .9 8 eV band, a d e c re a s e in the 1.15 eV band o r both. C. S u m m a ry of the E x p e rim e n ta l R e su lts T he im p o rta n t p o in ts of the an nealing effects of h eav ily S i-doped GaAs o b s e rv e d in this study a r e s u m m a riz e d in the following list: 133 (1) In the is o c h ro n a l annealing fo r 2 h r in te rv a ls , the c a r r i e r c o n c e n tra tio n n g begins to d e c r e a s e a t 4 0 0 °C, continues d e c re a sin g up to T = 600°C. A bove T = 600°C, the n g s ta r ts to in c re a s e . (2) A nnealing of a sam p le a t 1100°C fo r 15 m in u tes p ro d u c e s th e rm a l e q u ilib riu m in the se n se th a t a lo n g e r annealing tim e does not change the ng value. (3) The an n ealin g effect is c o m p lete ly re v e rs ib le betw een 1100°C/15 m in and the lo w er te m p e r a tu r e s . (4) The 1100°C/15 m in an n eal e r a s e s the s a m p le 's p re v io u s an n ea lin g h is to ry . (5) The is o th e r m a l annealing e q u ilib riu m value of n g b e c o m e s l a r g e r as the an nealing te m p e ra tu re b eco m es h ig h er. C hanges in ng as la rg e as a fa c to r of 6 a r e o b se rv e d . 17 -3 (6 ) L ig h tly S i-doped GaAs, w h e re n = * • 6 x 10 cm , does not show the an n ealin g effect. (7) The in te g ra te d s tre n g th of the ab so rp tio n band a t 384 cm * d e c r e a s e s due to low te m p e r a tu r e an n ealin g . The d e c re a s e is in v e rs e ly re la te d to the annealing te m p e ra tu re . (8 ) The in te g ra te d s tre n g th of the a b so rp tio n band a t 399 c m * does not change sig n ifican tly during annealing. (9) The in te g ra te d a b s o rp tio n s tre n g th of the band a t 393 c m ^ in c re a s e s slig h tly a fte r annealing a t e ith e r 400°C /1178 h r o r 750°C /320 h r, b u t in c re a s e s to a lm o s t tw ice the o rig in a l value a fte r an nealing a t 6 0 0 °C /2 9 0 .5 h r. (10) Only the s ta rtin g sa m p le ( i.e . annealed a t 1100°C /15 134 m in) show s a 1.5 eV p h o to lu m in escen ce peak. (11) T he s ta rtin g sam p le shows a p h o to lu m in e sc en ce p eak n e a r 1.2 eV. A ll the lo w er te m p e ra tu re an n ea led sam p les show a lu m in e sc e n c e p eak n e a r 1. 15 eV. T h e re a r e re a s o n s to b elieve th a t th e s e p eak s a r e fro m the sa m e re c o m b in a tio n c e n te rs . (12) A new p h o to lu m in escen ce p eak n e a r 0.98 eV is o b s e rv e d only fo r s a m p le s an n ea led a t 600°C and 750° C. The in te n sity of the 0 .9 8 eV p eak re la tiv e to the one at 1. 15 eV grow s w hen the an nealing te m p e ra tu re is in c re a s e d fro m 600° to 7 5 0 °C. V-IV. G e n e ra l D isc u ssio n In this sectio n , the re s u lts p re s e n te d in the p rev io u s sec tio n a r e d is c u s s e d and ex am in ed in o r d e r to find a suitable m o d e l fo r the an n ea lin g effect. The e x p e rim e n ts also su g g est so m e sp ecu la tio n s w hich can a lso be u sed to su p p lem en t the m o d el but w ith so m e c le a r ly sta te d lim ita tio n s. F i r s t it is helpful to li s t the a ss u m p tio n s and p re v io u sly e s ta b lis h e d facts w hich w ill be u sed in the d is c u s s io n and also to in d icate the valid ity of each assu m p tio n . A. G e n e ra l A ssu m p tio n s and P re v io u sly E s ta b lis h e d F a c ts (1) The co n c e n tra tio n of ea c h d e fe c t s p e c ie s is p ro p o rtio n a l to the in te g ra te d a b s o rp tio n s tre n g th of the LVM due to th at p a r tic u la r d efec t s p e c ie s . T his re la tio n has b een v e rifie d both th e o re tic a lly and e x p e rim e n ta lly (see Section III-IV -A ). (2) The 1 M eV e le c tro n ir r a d ia tio n p ro c e s s a t low t e m p e r a tu r e (T < 1 0 0 °K ) u sed to obtain e le c tr ic a l co m p en sa tio n of the 135 ! sam p le does not change the Si site d istrib u tio n in the sa m p le . The in te g ra te d a b so rp tio n s tre n g th of the LVM bands due to the d iffe re n t Si sp e c ie s a fte r the sam p le having b een e le c tro n irra d ia tio n -c o m p e n s a te d is a n in d icatio n of the c o n c e n tra tio n of the v ario u s Si sp e c ie s in the sa m p le b efo re the e le c tro n irra d ia tio n . T his a ssu m p tio n w as v e rifie d b y S p itz e r et al. (1969)(see S ection III-II-C 3). (3) S u b stitu tio n al Si of m a s s 28 on Ga s ite , S i ^ , is a donor and has a LVM freq u en cy a t 384 cm S ubstitutional Si on As site , S i^ g , is an a c c e p to r w ith a LVM freq u en cy a t 399 cm The n e a r e s t n eig h b o r p a ir is e le c tric a lly n e u - and gives LVM a b so rp tio n bands a t 393 and 464 cm T hese id en tificatio n s w e re v e rifie d by L o rim o r and S p itz e r (1966), S p itz e r and A llre d (1968b) and Leung et a l . (1973)(see Section III-IV -B 2) The band fre q u e n c ie s and re sp o n sib le defects a r e su m m a riz e d in T able V-V. (4) The LVM in f r a r e d a b s o rp tio n c r o s s se c tio n of the S i^ a and S i^ g sp e c ie s a r e a p p ro x im a te ly equal. T his a ss u m p tio n w as v e rifie d b y c alcu la tin g the c a r r i e r co n c e n tra tio n fro m the d iffe re n c e of the a b so rp tio n s tre n g th of 384 cm ^ and 399 c m ^ bands a ss u m in g equal a b s o rp tio n c r o s s sectio n s and the re s u lt a g re e d v e ry w ell w ith the ng value obtained fro m H all effect m e a s u re m e n t (S pitzer and A llre d 1968b). Silicon site tr a n s f e r e x p e rim e n ts a lso show ed th a t w hen S i^ a -» S i^ g , the lo ss of a b s o r p tion in the 384 c m ^ band eq u aled the gain in a b s o rp tio n in the 399 c m - ^ band (see Section III-IV -B 2). T A B L E V -'V LIST O F LO C A LIZED VIBRATIONAL MODES FROM G aA s:Si CO M PEN SA TED BY 1 M eV E L E C T R O N IRRADIATION LVM A b so rp tio n D efect band fre q u e n c y (cm ) 28* O a 29SiGa 378 30 S L 373 (_ra 28Si 399 As 28 _28 393 ( Ga A s 464 Unknown 369 367 137 B. C a r r i e r C o n cen tratio n and Its R elatio n sh ip To D efect C o n cen tratio n F r o m LVM M e a s u re m e n t B eca u se of the linew idth as w ell as the p e a k height change a fte r the sa m p le s have been an n ealed , the in te g ra te d ab so rp tio n v alu es of the th re e m a jo r Si LVM bands a r e u sed to m e a s u re the change of Si d efec t co n c e n tra tio n s. The in te g ra te d a b so rp tio n values of th o se Si bands shown in F ig u re s V-5 th ro u g h V-7 a r e tab u late d in Table V -IV . T h ese values w e re n o rm a liz e d as p re v io u s ly d e s c rib e d and u sed to p ro d u c e F ig u re V - 8. The re a s o n fo r the linew idth change o b s e rv e d on the 384 c m * band is not known. P o s s ib le re a s o n s fo r line b ro ad en in g sta te d in S ection III-IV -A can not give a s a tis fa c to ry explanation in the p r e s e n t c a se . T h ese explanations would a lso re q u ire that the sa m e type of change be o b s e rv e d on the o th e r Si LVM bands su ch as the 393 c m * o r 399 c m * b an d s. H ow ever, e s s e n tia lly no linew idth change w as o b se rv e d on th e se b an d s. It is in te re s tin g to note th a t the change of linew idth of the 384 cm * band is so m ew h at re la te d to the c o n c e n tra tio n of the S i^ a s p e c ie s. The lo w e r the [ S i ^ ] (400°C/1178 h r annealed sa m p le ), the n a r r o w e r linew idth. In F ig u re V - 8, the in te g ra te d a b so rp tio n s tre n g th of the S i ^ g a c c e p to r band a t 399 cm * show s little change a s a re s u lt of an n ealin g . On the o th e r hand, the c o n c e n tra tio n of the S i^ a donor sp e c ie s does d e c re a s e a fte r low te m p e r a tu r e annealing as in d icated in this fig u re by the d e c re a s in g in te g ra te d a b s o rp tio n of the 384 c m * band. The la r g e s t d e c re a s e o c c u rs a f te r the 4 0 0 °C 1 3 8 j /1178 h r anneal. The re su ltin g s tre n g th of the 384 cm ^ band is only about 57% of the s ta rtin g sa m p le (1100°C /15 m in ). The d e c re a s e b eco m es s m a lle r as the annealing te m p e r a tu r e beco m es h ig h e r. H ow ever, even a fte r the 750°C /320 h r an n eal the s tre n g th of the 384 c m * band d e c re a s e s to 77% of the s ta rtin g value. T his change is s till la rg e w hen c o m p a re d to th at fo r the 399 c m * band. T h ese re s u lts im m e d ia te ly ru le out the p o s s i b ility of the s ite tr a n s f e r of Si a to m s fro m Ga to A s s ite s w hich could ca u se the c a r r i e r c o n c e n tra tio n to d e c r e a s e . It is r a th e r the d e c re a s e of the [ S i ^ ] donor sp e c ie s alone w hich co n trib u tes to the d rop of ng . F ig u re V -10 shows the d iffere n ce of the in te g ra te d a b s o r p tion s tre n g th s betw een the 384 c m ^ and the 399 c m * b an d s, i»e. , A=J> 3g4 adv - J * 3^g a-d v , v e rs u s the fre e c a r r i e r co n ce n tratio n of sa m p le s a fte r being an n ealed a t d iffe re n t te m p e r a tu r e s . The value of A is p ro p o rtio n a l to the d iffe re n c e betw een the Si donor and a c c e p to r co n c e n tra tio n s. If the S i^ a and S i^ g a r e the only donor and a c c e p to r sp e c ie s in th e s e s a m p le s , then A should be p ro p o rtio n a l to the c a r r i e r co n c e n tra tio n of e a c h sa m p le . Hence the data points fro m d iffe re n t sa m p le s show n on F ig u re V -10 should be clo se to a s tra ig h t lin e w hich in te rc e p ts the poin t a t n e = 0 and A = 0 . F ig u re V -10 show s th at the s ta rtin g sa m p le s (1100°C /15 m in), the a s -g ro w n sa m p le and the 4 0 0 °C /1 1 7 8 h r an n ealed sa m p le s a r e a ll quite clo se to the d ash ed line w hich in te r s e c ts the o rig in . Thus in th e se sa m p le s the S i^ a and S i^ g a r e indeed the only donor and a c c e p to r sp e c ie s n eeded to d e te r - F ig u re I B xIO T 8 - 'e u ^ 7 I 6 c r . UJ o z o o ^ - X UJ O E £ E < J > O ^ UJ UJ tr 1---------1 ---------1 ---------1 ---------1 ---------1 ---------1 --------- r ^ r IIOO°C/l5mirr ANNEAL / / 600°C /290.5H R + IIO O °C /l5m in— o / o ANNEAL / / / IICX)°C/l5m in ANNEAL H / / / / / / / 400°C /II78 HR' ANNEA^ / / / c As grown NO ANNEAL 6 0 0 °C /2 9 0 .5 HR ANNEAL '750°C /320H R ANNEAL X X 4 0 6 0 100 fCLcfl/ - [CLdV (cm-2) *384 cm " •'■xoarm- 120 V -10 F r e e c a r r i e r co n cen tratio n v e rs u s the d ifferen ce of in te g ra te d ab so rp tio n stre n g th s betw een the 384 c m - ^ and the 399 c m - ^ LVM bands of eight heavily Si-doped GaAs sa m p le s w ith d iffe re n t anneal conditions. 140 1 m in e the c a r r i e r c o n ce n tratio n . The d ata points w hich do not lie c lo se to the d a sh e d lin e a r e fro m the 6 0 0 °C /2 9 0 .5 h r and 750°C/32 0 h r a n n ea led s a m p le s . T hese data points lie f a r below the dashed line d e m o n stra tin g that for th e se two s a m p le s , the ng should be h ig h e r than th e ir m e a s u re d v alu es if only c o n sid e rin g the c a r r i e r s fro m SiQa (donor) and S i^ g(a cc ep to r) s p e c ie s . Hence th e re m u s t be ad d itio n al a c c e p to r sp e c ie s g e n e ra te d in th e se sa m p le s during annealing, and th e se sp e c ie s a c t as co m p en satin g c e n te rs w hich red u ce the c a r r i e r c o n c e n tra tio n . The c o n c e n tra tio n of th e se ad d itio n al a c c e p to r s p e c ie s can be roughly e s tim a te d fro m F ig u re V -10 b y m e a s u rin g the d iffere n ce in c a r r i e r c o n c e n tra tio n betw een the d ash ed line and the data point. T h e r e fore fo r the 600°C /290. 5 h r sa m p le , the c o n c e n tra tio n of the 18 -3 additional co m p en sa tin g c e n te rs is = “ 3 x 10 c m , and for the 18 -3 750°C /320 h r sa m p le , the c o n c e n tra tio n is 4 x 10 cm " . A fter a su b se q u en t 1100°C/15 m in an n eal, th e se c o m p en sa tin g c e n te rs d is a p p e a re d and the c a r r i e r c o n c e n tra tio n w as ag ain only p r o p o r tional to the d iffere n ce of [SiQa ] donor and [S i^ g ] a c c e p to r species. T his r e s u lt is shown in F ig u re V -10 by the r e s u lt of a sam p le w hich w as an n ea led at 600°C/290. 5 h r and an n ea led a g ain a t 1100°C /15 m in . T his re s u lt w ill be cited la te r to d e m o n stra te the re v e r s ib ility of the annealing effect. C. P ro p o se d M odel F o r The A nnealing E ffect The h eavily S i-doped GaAs m a te r ia l h as the h ig h e st c a r r i e r c o n c e n tra tio n n g a fte r 1100°C/15 m in annealing. A t this annealing stag e, the m a jo r donor and a c c e p to r sp e c ie s a r e the S i^ a and 141 S i^ g> re sp e c tiv e ly . The c a r r i e r co n c e n tra tio n n g is p ro p o rtio n a l to the d ifferen ce of the Si donor and a c c e p to r c o n c e n tra tio n s. A fte r being an n ealed a t lo w er te m p e r a tu r e s , the c a r r i e r c o n ce n tra tio n n g of the sam p le has u su ally d e c re a s e d to le s s than 25% o f the o rig in a l value. D ifferen t m e c h a n is m s a re re s p o n s ib le for the d e c re a s e of n . e (1) At 400°C an n ealin g the m e c h a n is m is th at the donor c o n c e n tra tio n [S i^a ] d e c re a s e s w hile the a c c e p to r c o n c e n tra tio n [S i^ g] re m a in s n e a rly unchanged. The S i^ a and S i ^ g sp ecie s a r e s till the m a jo r d onors and a c c e p to rs a fte r this annealing. Thus the d e c re a s e of n g is d ire c tly re la te d to the d e c re a s e of [SiQa ] donor c o n ce n tratio n . (2) At 600°C and 750°C a n n ea lin g s, in addition to the d e c re a s in g [SiQa ] m e c h a n is m ju s t m entioned, a new a c c e p to r sp e ic e s is g e n e ra te d as a r e s u lt of annealing. The c o n c e n tra tio n of this new a c c e p to r sp e c ie s is h ig h e r in the 750°C an nealing than fro m the 600°C annealing. C o n v e rse ly , the d e c r e a s e of [S i^ a ] is lo w er in the 750°C an n ealed sa m p le than in the 600°C an n ealed sa m p le . The new a c c e p to r sp e c ie s a c t as co m p en satin g c e n te rs w hich is p a rtia lly re s p o n s ib le fo r the d e c re a s e of n g . Thus the ng of the s a m p le s a f te r annealing is p ro p o rtio n a l to the d iffere n ce b etw ee n the co n c e n tra tio n of the d o n o rs, [SiQa J. to the c o n c e n tra tio n s of the two types of a c c e p to rs . ( i . e . , [Si. ] + the A s new a c c e p to r). The effects of the above m en tio n ed two m e c h a n is m s a re re v e r s ib le . The annealing effects can be e r a s e d b y r e - a n n e a l the 142 sa m p le a t 1100°C/15 m in and the [S i^a ] is r e s to r e d to th e s ta rtin g value w hile the new a c c e p to r sp ecie s is re m o v e d . By an nealing the sam p le again a t lo w er te m p e ra tu re s the s a m e annealing effect w ill be o b se rv e d . D. D isc u ssio n of P h o to lu m in esce n ce M e a s u re m e n t R e su lt A re co m b in atio n sch em e is illu s tra te d in F ig u re V - l l in o rd e r to fa c ilita te the d isc u ss io n of the p h o to lu m in e sc en ce re s u lt. This fig u re show s fo u r p o ssib le ra d ia tiv e tra n s itio n s w hich a re re sp o n sib le for the lu m in e sc e n c e peak s o b se rv e d . As w as d i s c u sse d in S ection III-IV -B 6, all re c o m b in a tio n tra n s itio n s in this d e g e n e ra te n -ty p e GaAs p ro b a b ly o rig in a te fro m donor sta te s m e rg e d w ith the conduction band so m ew h at below the F e r m i le v e l (Pankove 1968). T ra n s itio n n u m b e r 1 is re s p o n s ib le for the 1.5 eV p eak w hich is p ro b ab ly due to the tra n s itio n to an a c c e p to r le v e l (A c e n te rs ), p re s u m a b ly S i. w hich is a p p ro x im a te ly 0. 03 A S eV above the v alen ce band. The b re a d th of this p eak m a y be due to the b ro a d e n e d S i ^ g a c c e p to r le v el since the [S i^ g] is e s tim a te d 18 -3 to be = * ■ 5 x 10 cm " fro m LVM re s u lt. The d is a p p e a ra n c e of the 1. 5 eV p eak in the lo w er te m p e ra tu re an n ealed sa m p le s m a y be due to the co m p etitio n betw een tra n s itio n 1 and the o th e r p r o c e s s e s . F o r ex am p le, if the re c o m b in a tio n ra te thro u g h the B c e n te rs is h ig h e r than th a t of the A c e n te rs , then the 1. 5 eV p eak can be quenched w hen the B c e n te r co n c e n tra tio n is in c re a s e d . A s d e s c rib e d in Section V -III-B 3, th e 1.2 eV and 1.15 eV peaks a r e b elie v e d to o rig in a te fro m the s a m e ra d ia tiv e tra n s itio n . The tra n s itio n 2 and 3 shown in F ig u re V - l l a r e the sa m e p r o - 143 CONDUCTION BAND eV 0 .5 4 0 .3 7 0 .3 2 eV VALENCE BAND 0 .0 3 F ig u re V - l l R adiative re c o m b in a tio n sc h e m e of h eav ily Si-doped n -ty p e G aA s. 144 c e s s . The re c o m b in a tio n c e n te r B for this p ro c e s s w as su g g ested b y W illiam s and B lack n all (1967) and W illiam s (1968)(see S ection III-IV -B 6) as a g alliu m v aca n cy -S i donor com plex (SiQa - VQa ). The sh ift of the p eak e n e rg y fro m 1.2 eV to 1.15 eV is p o ssib ly due to the b ro ad en in g of the B c e n te r e n e rg y level cau sed by the in c re a s e of the B c e n te r c o n ce n tratio n a fte r low te m p e ra tu re annealing (Section V -III-B 3). T his s e e m s to su p p o rt the p ro p o se d m odel since the d e c re a s e of [ S i ^ ] can be cau sed b y the in c re a s e of the (^^Ga"^Ga^ concent r a tion (B c e n te r). An in c re a s e of the B c e n te r c o n ce n tratio n m a y be a lso re sp o n sib le for the quenching of the 1. 5 eV peak. The (S^Ga"^Ga^ com plex -will be d is c u s s e d fu rth e r in S ection V -IV -F w hich follow s. T ra n s itio n 4 in F ig u re V - l l gives the 0.9 8 eV peak. This p eak is o b se rv e d only in the 600°C /290. 5 h r and 750° C /320 hr sa m p le s w hich a lso have a la rg e co n c e n tra tio n of co m p en satin g a c c e p to r c e n te rs as sta te d in the p ro p o se d m o d el. F u r th e r m o re , the hig h er c o n c e n tra tio n of the co m p en satin g a c c e p to r c e n te rs in the 750°C/320 h r sa m p le se e m s to coincide w ith the h ig h e r 0 .9 8 eV p eak in te n sity c o m p a re d w ith the 1.15 eV peak fro m the p h o to lu m in escen ce m e a s u re m e n t. Since this 0.9 8 eV p eak follows the sam e p a tte rn s as the o b se rv e d LVM and n g re s u lt p ro p o se d in the m o d el, it is a ttra c tiv e to p o stu la te th a t the 0 .9 8 eV re>r com bination c e n te r C is re la te d to the e x tra co m p en satin g a c c e p to r c e n te r g e n e ra te d during annealing. The 0 .9 8 eV p eak w as only o b se rv e d by W illiam s and B la ck n all (1967) and w as sp ecu la ted as due to tra n s itio n to d efec t com plex c e n te rs induced by Si (Section III-IV -B 6). In the p r e s e n t study, we a r e able to identify the c e n te rs as co m p en satin g a c c e p to r sp ecie s and this id en tificatio n s e e m s to su p p o rt the p ro p o se d annealing m od el. The p h o to lu m in e sc en ce peak s shown in F ig u re V- 9 a r e in g e n e ra l quite b ro a d . The p o ssib le explanation of the b ro a d 1. 5 eV p eak has b een d is c u s s e d e a r l ie r . The b roadening of the o th e r lu m in e sc e n c e peaks is p ro b ab ly due to the bro ad en in g of the re c o m b in a tio n c e n te r s ta te s . In p re v io u s ly re p o rte d stu d ie s (K re ss e l and N elson 1969, K r e s s e l e t al. 1968. W illiam s and B lacknall 1967), s u b sta n tia l b ro ad en in g of the p h o to lu m in e sc en ce peaks fro m d eep -ly in g im p u rity sta te s w e re o b s e rv e d in b oth n - o r p - type GaAs w ith an im p u rity doping le v el ranging fro m 17 -3 19 -3 10 c m to 10 cm . The b ro ad en in g effect of d eep -ly in g bands of im p u rity sta te s h as b e e n stu d ied th e o re tic a lly by M organ (1965) and is show n to be re la te d to the fluctuations in the lo c a l Coulorrb p o te n tial. A w ide lu m in e sc e n c e line is expected fro m a reg io n having a high ch arg e den sity and a la rg s c re e n in g length. In the p r e s e n t study, the s a m p le s a r e h eav ily doped w ith Si ([Si]=” 4 x 1 9 - 3 10 c m ) and a lso have a high le v e l of co m p en satio n . The lo c a l Coulom b p o te n tial should have m a jo r fluctuations w hich r e s u lt in b ro ad en in g of the p h o to lu m in e sc en ce p eak s. E . C o m p en satio n O b se rv ed B y F r e e C a r r i e r A b so rp tio n And LVM M e a s u re m e n ts In C h ap ter IV, we have d e m o n stra te d th at the an nealed h eav ily S i-doped GaAs sa m p le s u se d in the p r e s e n t study have a h ig h e r than n o rm a l fre e c a r r i e r a b so rp tio n c r o s s sectio n as shovai in F ig u re IV - 8 . The high fre e c a r r i e r a b s o rp tio n c ro s s sectio n w as a ttrib u te d to the la rg e co n trib u tio n fro m the im p u rity s c a tte rin g p r o c e s s in the annealed sa m p le s w h ich have la rg e co n c e n tra tio n of co m p en sa tin g c e n te rs . This h eav ily co m p en sa ted n a tu re of the an n ea led sa m p le s can be s e e n fro m the LVM s p e c tr a of th e se sa m p le s. In F ig u re V -12, the a b s o rp tio n s p e c tr u m of the 400°C/1178 h r sam p le shown in F ig u re V -5 is c o m p a re d w ith the s p e c tru m of a n o th e r S i-doped sa m p le m e a s u r e d by S p itz e r e t al. (1969). This sa m p le w as not an n ealed but w as co n tam in a ted by A l as can be se e n fro m the stro n g A l band at 362 cm Since Al is a n is o e le c tro n ic im p u rity in G aAs, it does n o t affect the e le c tr ic a l p r o p e r ty of the sa m p le and hence the p r e s e n t d is c u s s io n is not affected by it e ith e r. B oth sa m p le s shown in F ig u re V-12 a r e co m p e n sa te d by s im ila r e le c tro n i r r a diation p r o c e s s e s . Note th a t the 384 c m ^ and 399 c m * bands of the unannealed sam p le a r e m u c h s m a l le r th an th o se of the 400°C /1178 h r an n ealed sam p le although the n g of the unannealed 18 - 3 sa m p le is 3 x 10 c m o r about tw ice the ng value of the an n ealed sam p le. Thus it is c le a r ly in d icativ e th a t the annealed sa m p le is indeed h eav ily c o m p en sa ted . In the p ro p o se d m o d el fo r the an nealing effect, both m e c h a n is m s would c a u se the sa m p le to b eco m e m o re c o m p e n sa te d th an the s ta rtin g sa m p le . Since a high le v el of co m p en sa tio n is a lso found in the fre e c a r r i e r a b s o rp tio n and LVM m e a s u r e m e n ts , th e se r e s u lts do not c o n tra d ic t the m o d el. F . P o s sib le O rig in of C hanges In C o n cen tratio n s of coaffictant • (cnT*) 147 90 GaAs* Si Compensated by electron irradiation 77*K ■ ■ ■ » ■ ■ [nj*3xic/® cm"3 (After Spitzer eta/.) no anneal — (nj* 1.5x10" 70 crrf° 400*0/1170 hr. annealing 60 50 40 30 20 350 370 390 410 FREQUENCY 430 (cm'1 ) 450 470 F ig u re V-12 A b so rp tio n s p e c tra a t 77°K of two S i-doped GaAs sa m p le s w hich a r e co m p e n sa te d by 1 MeV e le c tro n irra d ia tio n . The 4 0 0°C /1178 h r an n ea led sam p le has a h ig h e r Si doping le v e l than the o th e r sa m p le . T he s p e c tru m of the sa m p le w ith no an n eal is a f te r S p itz e r e t al. (1969). S i-D efects F I . D efects for the A nnealing M odel The f ir s t m e c h a n is m of the an n ealin g m o d e l p ro p o se d in S ection V -IV -C re q u ire s th a t the TSiQa ] d e c re a s e s during a n n e a l ing. P o s s ib ilitie s fo r this d e c re a s e can b e: (1) The S i^ a sp e c ie s fo rm p re c ip ita te s o r m ove to the ex istin g Si p re c ip ita te s . (2) The S i^ a donor a s s o c ia te s w ith a n o th e r defect to fo rm a n e u tra l com plex. In o r d e r to in v e stig a te th e se p o s s ib ilitie s , we have to obtain in fo rm a tio n co n ce rn in g the diffusivity of Si in GaAs a t th e se annealing te m p e r a tu r e s . To o u r know ledge, the d iffusivity of Si in GaAs has not b e e n re p o rte d in the li te r a tu r e . In o r d e r to obtain a rough e s tim a tio n of the p o s sib le diffusion c o efficien t of Si in G aA s, one can look to the known diffusion co efficien t of o th e r s im ila r i m p u ritie s in G aA s. K endall (1968) has re p o rte d the diffusion co efficien t of s e v e r a l im p u ritie s in G aA s. By ex tra p o latin g th e se -17 2 diffusion coefficients to T=600°C, the values a r e = * • 1 x 10 cm / - 1 8 2 - 1 8 2 sec fo r Sn, = “ 8 x 10” cm /s e c for Mg and “ 1 x 10 c m /s e c for Zn. A ssu m in g the diffusion co efficien t of Si to be c lo se to -17 2 th a t of Sn and Mg, the value is = * 10 cm /s e c a t 600°C. If e x tra p o la te d to 400°C, the diffusion co efficien t is a p p ro x im a te ly 1 0 " ^ c m ^ / s e c . Thus w hile annealing at 400°C fo r 1178 h r, the diffusion len g th of Si a to m is only a p p ro x im a te ly one la ttic e -8 constant o r 6 x 10 cm . W ith a diffusion len g th this sh o rt, Si ato m s should not be able to fo rm p re c ip ita te s a t 400° C. H ence the f ir s t p o s s ib ility sta te d above is unlikely to be re sp o n sib le for 149 I the annealing effect. T he second p o ssib ility th a t S i^ a a s s o c ia te s w ith an o th er defect to fo rm a n e u tra l p a ir is p ro b a b ly the p ro c e s s re sp o n sib le for the annealing effect. The d efec t w hich p a ir s w ith the S i^ a could be a la ttic e vacancy. One m u s t be cautious in accepting a v aca n cy m odel, sin ce th e re is little d ir e c t in fo rm atio n s u p p o rt ing the e x isten ce of a sig n ifican t vacan cy c o n c e n tra tio n in GaAs a t ro o m te m p e ra tu re . H ow ever, the p a ir p o s s ib ility is su p p o rted by the following c o n sid e ra tio n s: (1) As d e s c rib e d in Section III-IV -D , the diffusion -11 2 co efficien t of an a r s e n ic v acan cy a t 600°C is = “ 10 c m /s e c -1 0 2 (H a rris e t a l . 1969) and a t 850°C it is 10 c m /s e c . (Munoz et a l . 1970). The diffusion co efficien t of a Ga vacan cy is e s ti - -12 2 m a te d to be 10 cm /s e c at 850°C. (Munoz e t al. 1970). F r o m th e se v alu es, the diffusion co efficien t a t 4 0 0 °C is e s tim a te d to be =-10 ^ c m ^ / s e c fo r V ^ g and =*10 ^ c m ^ / s e c for H ence a t 400°C, the V q can m ig ra te = “ 100 la ttic e co n stan ts in one h o u r, w hile V ^ g sp e c ie s can diffuse = “ 1000 la ttic e constants in the sa m e tim e . Thus it is p o ssib le fo r la ttic e v aca n cies to m ove th ro u g h the GaAs la ttic e and p a ir w ith the S i^ a donor to fo rm co m p lex es during annealing. (2) L a ttic e v a ca n cies have been id en tified as a c c e p to r sp e c ie s. (S pitzer and A llre d 1968a, M unoz e t a l. 1970). H ence the S i^ a donor is co m p e n sa te d by the v aca n cy to w hich it p a i r s . Thus the c a r r i e r co n ce n tratio n of the sa m p le is d e c re a s e d th ro u g h this p r o c e s s . 150 (3) The Si in the (SiQa “V acancy) p a ir is no lo n g e r in a site of te tr a h e d r a l s y m m e try and hence the a b so rp tio n fro m these Si c e n te rs is re m o v e d fro m the iso la te d S i„ lo c a liz e d v ib ra tio n a l u a m ode band. T his explains the d e c re a s e of the SiGa lo c a l m ode a b so rp tio n a fte r the annealing a t lo w er te m p e r a tu r e s . (4) As su g g ested in S ection V -IV -D 1 above, the la ttic e v acan cy that p a irs w ith the SiGa donor is p ro b ab ly a Ga vacancy. The p re s e n c e of the (SiQa -VG a) com plex in S i-doped GaAs was a lso p ro p o s e d by S p itz er and A llre d (1968b) to explain w hy the Si c o n c e n tra tio n acco u n ted for by the ( S i ^ - L i ^ , ) LVM bands do not co n trib u te to the c a r r i e r co n ce n tratio n (Section III-IV -B 4). It a p p e a r s t h a t t h e (®^Qa " ^ Q a ^ P a ’-r s P e c i e s c o u l d b e re sp o n sib le for the 369 c m - * LVM band. T his band is alw ays la r g e r in the lo w e r te m p e ra tu re an n ea led s a m p le s than in the s ta rtin g sam p le as can be se e n in F ig u re s V -5 through V -7 w hich is also the tre n d of the (SiG a ~VG a) concentra tio n acc o rd in g to the m o d el. F u r th e r m o re , the 369 cm * band show ed a Si isotope shift, hence it is a s s o c ia te d w ith a com plex involving Si. (Leung 28 30 e t al. 1973). M o re o v e r, the fact th a t only the Si and Si bands a r e o b s e rv e d in sa m p le s doped w ith both iso to p e s in d icate s th a t th e re is only one Si in eac h defect of the s p e c ie s . The 369 c m - * band m u s t be the h ig h e st in fra re d activ e LVM band of the (SiG a -V G a ) p a ir sin ce no o th e r band is o b s e rv e d w hich can be re la te d to this defect. The re a s o n th a t it is a t a su b sta n tia lly lo w er fre q u e n c y than the 384 c m * (SiG a) band m a y be due to the softening of the fo rc e co n stan t of the SiGa a fte r it p a irs w ith the The vacan cy u se d to fo rm the (SiQa -V acancy) p a ir s m a y com e fro m s o u rc e s w ithin the sam p le su ch as d islo c a tio n s, or they m a y be g e n e ra te d at the sam p le s u rfa c e and su b seq u en tly diffuse into the sa m p le during annealing. H ow ever, the diffusion length of the v aca n cies (8 . 4|am fo r V ^ g and 0 .8 |im for V ^ a at 600°C for 20 h o u rs) is m u ch le s s than the th ick n ess of the s u r face la y e r (=^50. 8(jm) re m o v e d a fte r ea c h anneal. A lso, the s a m e annealing effect w as o b s e rv e d w hen additional a r s e n ic was added to the am poule to keep P A “ I a tm during the an n eal. a s 4 (Section V -III-B l). T h e re fo re the vacan cy sp e c ie s a r e p ro b a b ly not fro m the s u rfa c e of the sa m p le b u t r a th e r they o rig in a te fro m s o u rc e s w ithin the sa m p le . The (SiQa - VQa ) d efec t is ju s t one p o s sib le d efec t th a t can be g e n e ra te d during an n ealin g . T h e re a r e o th e r p o s s ib le s t r u c tu re s w hich could fit the p ro p o se d m o d el. The (®^Ga”^Ga^ com plex should not be re g a rd e d as a definite explanation but r a th e r as one of the p o s sib le w ays to illu s tr a te the f i r s t m e c h a n is m of the p ro p o se d ann ealin g m odel. The c o m p en sa tin g a c c e p to r s p e c ie s for the second m e c h a n is m of the m o d e l is not id en tified b e c a u se of th e la ck of in fo rm a tio n . T h ese sp e c ie s do not have LVM b ands, at le a s t not in the freq u en cy reg io n fro m v = 360 cm ^ to v = 1940 cm T hey m a y 1 be re la te d to the 0 .9 8 eV p h o to lu m in e sc en ce and hence could be Si com plex c e n te rs induced by the an n ealin g (Section 152 S p itz er and P a n is h (1969) have found th a t fo r p -ty p e Si- doped GaAs the S i^ a LVM band s tre n g th is h ig h e r than th a t of S i. (Section III-IV -B 5). T h e re fo re a la rg e c o n c e n tra tio n of x \ S a c c e p to r sp e c ie s m u s t p r e s e n t in the m a te r ia l. Since this p -ty p e m a te r ia l w as grow n in a te m p e ra tu re ran g e (800 to 850°C) w hich is clo se to one of the annealing te m p e ra tu re s in the p r e s e n t study, one m ig h t sp ecu la te th at the a c c e p to r s p e c ie s in this m a te r ia l is re la te d to the com pensating c e n te rs o b s e rv e d in the p r e s e n t study. H ow ever, b eca u se of the deep e n e rg y lev el (=-0.54 eV above the valence band) a s s o c ia te d w ith the c o m p e n sating sp e c ie s o b se rv e d in the p r e s e n t study, th ey can not be the sa m e a c c e p to r sp e c ie s re sp o n sib le fo r the p -ty p e G aA s:Si s a m - 17 -3 p ie s . F o r ex am p le, fo r a hole co n ce n tratio n of 5 x 10 cm a t 300°K, th e c o n c e n tra tio n of the deep lying a c c e p to r should be 2 _3 = -2 .4 x 10 cm , w hich is u n re a lis tic . F 2. The Change of (®’'Ga " S i^ s ) P a ir C o n c e n tra tio n F ig u re V -8 shows the change of in te g ra te d a b s o rp tio n stre n g th of the 393 c m ^ LVM band as a function of annealing. Since the co n c e n tra tio n of the defect sp e c ie s is p ro p o rtio n a l to the in te g ra te d a b s o rp tio n s tre n g th of the c o rre s p o n d in g LVM (Section III-IV -A ), this fig u re also in d icate s the change of (Sij-,a - S i ^ g) p a ir c o n ce n tratio n . A fter an nealing a t 60 0 °C /2 9 0 . 5 h r, the (Si_ -S i. ) p a ir co n c e n tra tio n in c re a s e s to a lm o s t tw ice A S the o rig in a l value. Since S i^ g shows little change a f te r this annealing, it is a p p a re n t th a t the in c re a s e of the (LSi q -S i^ ) p a ir 153 co n c e n tra tio n is not a t the expense of the iso la te d S i^ g s p e c ie s . The Si u sed to fo rm the ( S i ^ - S i ^ ) p a irs m u s t com e fro m an o th e r s o u rc e in the sa m p le , p o ssib le Si p re c ip ita te s . The 19 -3 sa m p le is h eav ily doped w ith [Si]=“ 4 x 10 cm , and it is p o s s i ble th a t Si m ic r o - p r e c ip ita te s e x is t in the sa m p le . F r o m the e s tim a tio n of the Si diffusion co efficien t m ade in the p rev io u s sectio n , the diffusion len g th of Si at 600°C for 290. 5 h r is a p p ro x im a te ly 3 x 10 ^cm , w hich is about 50 la ttic e co n stan ts (1 la ttic e co n stan t = 5 .6 a ) . This d ista n c e m a y be la rg e enough for the Si a to m s to m ig ra te aw ay fro m the p re c ip ita te s and fo rm (Si(-,a - S i ^ s ) p a irs w hich show the 393 c m ’ ^ LVM band. Leung e t al. (1973) c alcu la ted the s p a c ia l atten u atio n of the am plitude of the (Si_, -S i. ) LVM band and found th a t the am p litu d e d im in ish es to le s s than 1% in a seco n d neig h b o r p o sitio n fro m the (SiQa - S i^g) p a ir and thus th e re can be a high d en sity of p a irs and they m a y s till be n o n -in te ra c tin g . T he in te g ra te d a b so rp tio n s tre n g th of the 393 c m ” * band did not in c r e a s e su b sta n tia lly a fte r the 400°C and 7 5 0 °C a n n ea ls. The re a s o n fo r the 400°C r e s u lt m a y be a lim ita tio n fro m the Si diffusion length. As e s tim a te d in the p re v io u s sectio n , the diffu sion le n g th at the 400°C anneal for 1178 h o u rs is a p p ro x im a te ly -8 6 x 10” c m o r one la ttic e c o n stan t. T hus, the fo rm a tio n of (Si£.a ~ S i^ g) p a ir defects fro m Si p re c ip ita te s is c u rta ile d by the sh o rt Si diffusion length a t this te m p e r a tu r e . Follow ing the sa m e m eth o d of e stim a tio n , the Si diffusion co efficien t in GaAs a t -14 2 750°C is a p p ro x im a te ly 10 cm / s e c . The Si diffusion length 154 -5 3 for a 320 hour an n ea l a t 750°C is = “ 11 x 10 cm o r = “ 2 x 10 la ttic e c o n sta n ts. H ence the s m a ll in c re a s e of the (Si-, -S i. ) ' Ga A s 7 p a ir c o n c e n tra tio n a t 750°C an nealing is p ro b a b ly not lim ite d by Si diffusion. It m a y be due to the co m p etitio n b etw een the fo rm atio n of the p a ir band and som e o th e r Si induced com plex su ch as the co m p en satin g a c c e p to r s p e c ie s w hich have b een d isc u ss e d in the p re v io u s sectio n . It has to be e m p h a siz e d th at the foregoing q u alitativ e d is c u s s io n is b a s e d on a rough e s tim a tio n of the diffusion c o e ffi cie n t of Si in G aA s. The a c c u ra c y of this e s tim a tio n is unknown and the co n clu sio n should not be tak en too s e rio u s ly . H ow ever, sin ce the evidence in d ic a te s th a t th e (SiQa _S i ^ g) p a ir is a n e u tra l defect in GaAs, it should not affect the change of ng in any d ir e c t m a n n e r. H ence, in the p re v io u s d is c u s sio n s of the annealing effects in te r m s of the change in n , the (Si_, -S i. ) p a ir co n ce n - 6 vjfcl J \ S tra tio n w as not c o n s id e re d . G. A dequacy of 1100°C/15 m in A nneal A s S tartin g Condition In a ll the an n ealin g s tu d ie s, the 1100° C /1 5 m in an n eal follow ed by a fa s t quench to ro o m te m p e r a tu r e w as u sed to obtain the sta rtin g condition fo r e a c h s a m p le . T he adequacy of using this tre a tm e n t is c o n s id e re d in the following: (1) The an nealing effects of ng a r e c o m p le te ly re v e rs ib le betw een 1100°C/15 m in and low te m p e ra tu re an n ea ls (Section V - III-B 1). (2) The an n ea l at 1100°C for 15 m in has re a c h e d e q u ili 155 b r iu m as f a r as the ne value is co n c e rn e d . E x p e rim e n ts have shown th at fu rth e r annealing a t 1100°C up to 3 h o u rs does not change the n g value of the sa m p le . (3) The re v e r s ib ility betw een 1100°C/15 m in and low te m p e ra tu re an n ea l ( e .g ., 600°C /290. 5 hr) is also o b se rv e d in eac h of the p rin c ip a l Si LVM b an d s. F ig u re V -10 shows that a sa m p le , a fte r annealing a t 600°C /290. 5 h r followed by a 1100°C / 15 m in tre a tm e n t re c o v e rs both the n value and the d ifferen ce e in the co n ce n tratio n betw een S i^ ^ and S i ^ g s p e c ie s. The re s u lt is even m o r e s trik in g fro m the d ata shown in T able V -IV . Note th a t the in te g ra te d a b s o rp tio n of the Si LVM bands a r e n e a rly the sa m e fo r a ll th re e sa m p le s w ith a la s t annealing step of 1100°C /15 m in . One of th e se s a m p le s w as p re v io u sly an n ealed a t 600°C for 2 9 0 .5 h r and the Si LVM bands s tre n g th s a fte r this an n eal w e re quite d iffe re n t as can be se e n fro m the re s u lt of the 600°C /290. 5 h r an n ea led sa m p le . Thus the Si donor and a c c e p to r co n c e n tra tio n s a r e e a c h fixed by the 1100°C/15 m in tre a tm e n t as w ell as the n value. e F r o m the above d isc u ssio n , it is a p p a re n t that the 1100°C / 15 m in an n ea l does re m o v e the effects of any fo r m e r annealing. C onsequently the use of this tre a tm e n t to e s ta b lis h a com m on th e r m a l b ack g ro u n d as the s ta rtin g condition a p p e a rs ju stified . V -V . C onclusion In this c h a p te r, we have p re s e n te d the an nealing effect of h eav ily S i-doped GaAs in te rm s of th e change of fre e c a r r i e r 156 ; co n c e n tra tio n n e - The annealing effect is fu rth e r in v e stig a te d by m e a n s of lo c a liz e d v ib ra tio n a l m ode m e a s u re m e n t and p h o to lu m i n esc e n c e m e a s u re m e n t. F r o m the re s u lts of th e se m e a s u re m e n ts, a m odel is p ro p o se d w hich su g g ests th a t th e re a re two m e c h a n r is m s re s p o n s ib le for the d e c re a s e of the c a r r i e r co n ce n tratio n during low te m p e r a tu r e annealing. The f i r s t m e c h a n is m is the d e c re a s e of S i^ a donor co n ce n tratio n p re s u m a b ly by fo rm in g a defect com plex. T his m e c h a n is m is re sp o n sib le fo r the a n n e a l- ine effect a t 4 0 0 °C and is also p a rtia lly re sp o n sib le fo r the d e c re a s e of ng a f te r 600°C and 750°C an n e a ls. At th e se h ig h er annealing te m p e r a tu r e s , a second m e c h a n is m w hich b e c o m e s sig n ifican t is the g e n e ra tio n of a new co m p en satin g a c c e p to r. The an n ealin g induced changes in defect sp ecie s can be re m o v e d if the sa m p le is su b se q u en tly an n ealed a t 1100°C for 15 m in. Thus the annealing effect is capable of cycling betw een 1100°C and low te m p e r a tu r e a n n e a ls. T his cyclic annealing effect w as a lso o b s e rv e d in the an n ealin g study of Si io n -im p la n te d GaAs. (See S ection III-IV -B 8). C H A PTE R VI GaAs D OPED WITH Si AND SECOND DOPANT V I-I. Introduction G allium a rs e n id e w hich is grow n fro m a sto c h io m e tric m e lt and doped w ith silico n is alw ays a n n -ty p e d s e m ic o n d u c to r. H ow ever, it is known (W helan e t al. I960; K olm et al. 1957) that 19 -3 a t Si co n ce n tratio n of [Si] >10 cm , the c a r r i e r co n ce n tratio n n g is s u b sta n tia lly le s s than [Si]. The d iffe re n c e b etw ee ^ t-h e values of ng and [Si] is re la te d to the a m p h o te ric n a tu re of Si in GaAs. T h e re have b een s e v e r a l stu d ies o£ the in f r a r e d a b so rp tio n a s s o c ia te d w ith lo c a liz e d v ib ra tio n a l m odes of im p u ritie s in s e m i c o n d u cto rs. In p a r tic u la r , th re e of th e se stu d ie s (L o rim o r and S p itz e r 1966; S p itz er and A llre d 1968a; S p itz e r and A llre d 1968b) have d ealt w ith Si im p u ritie s in G aA s. It w as found th a t one could c o r r e la te m a n y of the o b se rv e d a b so rp tio n bands w ith the p re s e n c e of d iffere n t poin t defects involving Si (Section III-IV -B 2). By using this id en tificatio n the p r e s e n t c h a p te r shows the in v e s ti gation of the site d istrib u tio n of Si u n d er the influence of the o th e r im p u ritie s , sp ec ific a lly te llu riu m , zinc and m a n g n e se . VI-II. B ackground T h e re has b een c o n sid e ra b le p r o g r e s s in the u n d erstan d in g 157 158 of the lo c a liz e d v ib ra tio n a l m ode (h e re a fte r called LVM) a b s o r p tion in S i-doped GaAs. B e c a u se of the im p o rta n c e of p rev io u s stu d ies for the in te rp re ta tio n of the p r e s e n t r e s u lts , a b r ie f rev ie w is w a rra n te d . A rev ie w is given in S ection III-IV -B 2 and w ill not be re p e a te d h e re . In the re s u lts to be p re s e n te d la te r , the LVM bands due to (L i-T e) and (L i-Z n) p a irs a r e o b se rv e d . The re p o rte d LVM freq u en cies due to th e se p a irs a r e u sed to identify the bands and the a b so rp tio n stre n g th s a r e u se d to m ake e s tim a te s of the defect c o n c e n tra tio n s. The LVM fre q u e n c ie s due to (L i-T e) p a irs have b een re p o rte d by H ayes (1965) and by L o rim o r and S p itz e r (1967a). The (L i-Z n) p a ir LVM fre q u e n c ie s w e re re p o rte d by L o rim o r and S p itz er (1967b). T h ese fre q u e n c ie s a r e lis te d in T able V I-I for future re fe re n c e . The LVM of the (L i-Z n ) p a ir as w ell as the (L i-T e) p a ir a r e p r im a r ily due to L i m o tio n sin ce the bands showed n e a rly the full L i-is o to p e shift. VI-III. E x p e rim e n ta l R e su lts and D isc u ssio n T able V I-II lis ts n in eteen ingots of GaAs w ith e s tim a te s of the doping le v e ls an ticip a ted n e a r the seed end on the b a sis of the im p u ritie s added and p ublished d istrib u tio n co efficien ts (W illardson and A llre d 1966). S am ples w e re taken fro m ea c h in got and diffused w ith L i. In som e c a s e s s a m p le s w e re taken fro m both the seed end and n e a r the b a c k end of the ingot. The te m p e ra tu re of diffusion w as T (j=700°C in o r d e r to avoid the site re d is trib u tio n o b se rv e d (S pitzer and A llre d 1968a) for T(ja 8 0 0 °C . 159 T A B L E V I-I PE A K POSITIONS O F TH E L i- Z n AND L i-T e LVM BANDS L i- Z n P e a k P o s itio n (c m - *) L i-iso to p e ^ L i ^*Li Shift (cm *) 405 433 28 378 404 26 361 385 24 340 361 21 L i- T e 475 391 510 419 35 28 160 T A B L E V I-II LIST OF DOPANTS AND DOPING CONCENTRATIONS O F GaAs CRYSTAL INGOTS Ingot D opants Doping C o n cen tratio n s N um ber 1 Si [Si]= 2 X 10I 8c m ' 3 2 Si [Si]= 2 X 1019c m "3 3 Si, •Te [Si]=l X i n 18 " 3 10 cm , [Te]=5 X i n 18 - 3 10 cm 4 Si, Te [Si]=7 X i n 18 " 3 10 cm , [Te]=5 X i — ' o H — * 0 0 n 3 I U > 5 Si, Z n [Si]=6 X i n 18 - 3 10 cm , [Zn]=l X m 18 -3 10 cm 6 Si, Zn [Si] =6 X 1018c m “3, [Zn]=3 X 1018c m " 3 7 Si, Zn [Si]=6 X 1019c m ' 3, [Zn]=3 X 1019c m "3 8 Si [Si]=l X 1019c m “3 9 Si, Z n [Si] =1 X 10l 9c m " 3, [Zn] = l X i n 18 -3 10 c m 10 Si, Z n [Si]=l X 1019c m " 3, [Zn]=3 X i n 18 “3 10 cm 11 Si, Zn [Si]=l X 1019c m “3, [Z n ]=6 X 1018c m “3 12 Si, Zn [Si]=l X 1019 cm ” 3, [Zn]=l X 1019c m " 3 13 Si, Z n [Si]=l X 1019c m “3, [Zn]=3 X 1019c m “ 3 14 Si, Mn [Si]=l X 1019c m " 3, [Mn]=l X i n 18 “3 10 c m 15 Si, Mn [Si] =1 X 10l 9c m ' 3, [Mn]=6 X 1018c m " 3 16 Si, Mn [Si]=l X 1019c m " 3, [Mn]=3 X 1019c m ' 3 17 Si, T e [Si] =1 X 1019c m “3, [T e ]=6 X 1018c m ' 3 18 Si, T e [Si] =1 X 1019c m ' 3 , [Te]=l X 1019c m "3 19 Si, Te [Si]=l X 10l 9c m " 3, [Te]=3 X 1019c m " 3 161 The diffusion w as done fro m a s u rfa c e a llo y p h ase w hile in an arg o n a tm o s p h e re . The m ethod of diffusion has been d is c u s s e d in S ection III-II-C 1. S am ples fro m the S i-doped ingots 1 and 2 w e re L i-d iffu se d and the in fra re d a b so rp tio n m e a s u r e d a t liquid n itro g e n t e m p e r a tu re is given in F ig. V I-1. A lso shown fo r c o m p a riso n is the m e a s u re d a b so rp tio n cu rv e for p u re G aAs. The c u rv e s show the s p e c tra l reg io n containing m o s t of the lo c a l m ode bands w hich a re la b e lle d w ith the re la te d d efect. A lthough, as in d icated in Table V I-I, som e bands o c c u r a t v > 4 3 0 c m \ th ey have b een shown in p rev io u s m e a s u re m e n ts (L o rim o r and S p itz e r 1966; S p itz e r and A llre d 1968b) and w ill not be of m a jo r im p o rta n c e for the p r e s e n t w ork. The c r o s s e s of F ig u re VI-2 show, on a lo g -lo g g rap h , the p eak a b so rp tio n co efficien t a for the SiQa band at 384 c m ^ p lo tted a g a in st a fo r the S i^ g band at 399 c m The data a re ta k en fro m a n u m b e r of S i-doped s a m p le s w hich a r e all diffused w ith L i a t T ^ 800°C. M ost of th e se sa m p le s w e re m e a s u r e d as p a r t of an e a r l i e r stu d y (S pitzer and A llre d 1968b). The re a s o n th a t the p eak a b so rp tio n c o efficien t in ste a d of the in te g ra te d a b so rp tio n s tre n g th is u sed h e re is b e c a u se the lin e -w id th of the LVM bands does not change in L i-c o m p e n s a te d s a m p le s . H ence the peak ab so rp tio n co efficien t of a LVM band is p ro p o rtio n a l to the co n ce n tratio n of the re s p e c tiv e im p u rity s p e c ie s . It should be em p h a siz e d th at Si is the only m a jo r dopant in th e se s a m p le s . The a b so rp tio n of sa m p le s fro m ingots 3 and 4, w hich a r e Cl-UJD) X> 162 90 80 70 60 50 40 30 20 10 to _ 5 r> .JP .JP to to to Inqot Pure Inqot I 350 370 390 4 1 0 430 to (cm-1) F ig u re VI-1 A b so rp tio n s p e c tr a a t 77°K of s a m p le s fro m ingots 1 and 2 of Table V I-II. The sa m p le s w e re ^L i diffused a t 700°C fo r 24 h o u rs. 163 500 ( 12) ro * 1 0 5 0 100 a n ( 3 9 9 cm ) F ig u re V I-2 P e a k a b so rp tio n co efficien t of th e 384 cm band v e rs u s th a t fo r the 399 c m " ' band. X , * r S i-doped sa m p le s ; O : S i- and T e-d o p e d sa m p le s ; • : S i- and Z n-doped sa m p le s ; a : S i- and M n-doped s a m p le s. The n u m b e rs in d icate the ingot of T able VI-II. A ll sa m p le s a r e L i diffused. 164 7 doped w ith silico n plus te llu riu m and diffused w ith L i is shown in F ig u re V I-3. C o m p a riso n w ith F ig u re V I - 1 shows s e v e ra l new fe a tu re s . The bands n e a r 475 cm * and 391 cm "* a r e due to (Li,, - T e . ) and have b een p re v io u s ly studied (L o rim o r and A S S p itz e r 1967b). The band at 379 cm * is la rg e ly a L i-la ttic e defect band and show s a la rg e lith iu m isotope shift, i. e. , 379 c m *-» 406 c m ^ w hen ^Li-» ^L i. The bands a t 464 and 393 cm ^ in the sam p le fro m ingot 4 a r e the (SiQa - S i ^ g) bands m en tio n ed e a r l i e r and liste d in T able V I-I. A p rin c ip a l d ifferen ce betw een the s a m p le s of F ig u re VI-3 and F ig u re V I-1 is the changes in the re la tiv e stre n g th s of the S i^ a and S i^ g bands at 384 and 399 cm The a b s o rp tio n peak values le s s back g ro u n d fo r th ese bands of the Si plus Te s a m p le s a re shown as c irc le s on F ig u re VI-2 and l a b elled w ith the ingot n u m b e r. The effect of the te llu riu m has been to su b sta n tia lly enhance the fra c tio n of the [Si] w hich re s id e s on As s ite s . T he m o s t in te re s tin g re s u lts w e re obtained fro m sa m p le s ta k en fro m ingots w hich w e re doped w ith silic o n plus zinc. F ig u re V I-4 show s the ab so rp tio n for s e v e r a l sam p les diffused 7 w ith L i. F ig u re V I-5 show s, for e a c h of two ingots, a c o m p a r iso n of two sa m p le s taken fro m a d ja c e n t w a fe rs and diffused w ith 1 6 /L i and L i re s p e c tiv e ly . M any of the (L i-Z n) bands liste d in T able V I-I a r e o b se rv e d in F ig u re s V I-4 and V I-5 and a r e tak en into acco u n t in so m e of the qu an titativ e d is c u s sio n w hich follow s. The S i. a c c e p to r band a t 399 c m * is o b s e rv e d in the A S lig h tly zinc o r m a n ag n e se -d o p e d ingots. T his band b e c o m e s v e ry o f C c m * 0 165 © o in to o U LO _ cn . j p in in o in Ingot 4 Ingot 3 350 490 390 410 450 470 370 co (cnrO F ig u re V I-3 A b so rp tio n s p e c tr a of S i- and T e -d o p e d GaAs s a m p le s fro m ingots 3 and 4 of T able V I-II. (,-u iO ) X > 166 400 350 300 250 200 Ingot 7 (seed end) Ingot 6 (back end) 1 0 0 Ingot 6 f (seed end) I I . 470 490 410 430 450 oo CcnH) 350 370 390 F ig u re V I-4 A b s o rp tio n s p e c tr a o f S i- and Z n -d o p e d G aAs s a m p le s f ro m in g o ts 6 an d 7 of T ab le V I-II. 500 400 300 200 1 00 Ingot 7 Ingot 6 / W 450 470 390 410 430 350 370 oo fair1 ) 6 7 F ig u re V I-5 C o m p a riso n of the ab so rp tio n s p e c tra of L i and L i diffused sam p les fro m ingots 6 and 7 of T able VI-II. 167; 168 s m a ll w hen the doping le v el of Zn o r M n is in c re a s e d . W ithin e x p e rim e n ta l a c c u ra c y this band is to tally a b se n t in s a m p le s fro m ingots 6, 7, 13 and 16. F ig u re V I-4 show s the a b so rp tio n s p e c tra of ingots 6 and 7. T h e re is no d etecta b le 399 c m * band in the s p e c tra . A lso note fro m F ig u re s V I-4 and VI-5 that (SiQa - S i ^ g) p a ir bands a r e to ta lly ab se n t (at 464 and 393 c m *) in the h eavily z in c-d o p ed ingots. M o re o v e r, s e v e ra l of the s a m p le s show the a p p e a ra n c e of th re e new bands of a p p ro x im a te ly equal s tre n g th . T hese bands a r e at 395, = “382, and 378 c m ” *. The 378 c m * band r e q u ire s so m e d isc u ssio n . In F ig u re VI-5, the band a t 378 cm * could involve co n trib u tio n s fro m th re e a b so rp tio n bands seen in p rev io u s w ork. In GaAs w ith (^Li-Zn), th e re is a band a t 378 cm *, but it should be equal in 7 -1 stre n g th to the ( L i-Z n ) band a t 405 cm . T h e re is also a 7 -1 ( L i-la ttic e ) d efec t band a t 379 cm w hich could be contributing. 7 7 H ow ever, b oth the ( L i-la ttic e ) and the ( L i-Z n ) bands sh ift to — 1 6 7 6 n e a r 405 c m ” if L i is used . C o m p a ris o n of the L i and L i s a m p le s of ingot 7 in F ig u re VI-5 show s little change in the 378 c m ” * band. The rem a in in g p re v io u s ly known co n trib u tio n to the a b s o rp tio n n e a r 378 cm * com es fro m a 379 cm * silic o n m ode for ( S i ^ - L i ^ ) defect (see T able IH -I). H ow ever, th is c o n trib u tion should only be a s la rg e as the m u c h w e a k e r band a t 374 c m ^ (see F ig u re V I-5, ingot 7). T h e re fo re , we have the re s u lt th a t m o s t of the s tre n g th of the 378 cm * band of ingot 7, F ig u re V I-5 cannot be acc o u n ted for in te rm s of any of the p re v io u s ly known d efec ts. 169. The enhanced s tre n g th of the 378 cm "* band o c c u rs only in those c a se s w h ere the 395 and 382 c m 1 bands a r e a lso o b se rv e d . The th re e new bands do not show any lith iu m iso to p e shift, and th ey o c c u r only in s a m p le s w ith both la rg e [SiQa J and [Z n^^]. It is re a s o n a b le to a s s u m e that th ese new bands a r is e fro m (Si,, - Z n „ ) defects w h ere the silico n and zinc a r e on n e a r e s t - Ga Ga neighboring g alliu m s ite s (second neighbor p o sitio n s). F o r such a p a ir, the p rin c ip a l ax is is ( 110) and, as d is c u s s e d fo r (SiQa ~ L i ^ ) , in S ection III-IV -B 2 the th re e -fo ld d e g e n e ra c y of the te tr a h e d r a l p o te n tial w ill be c o m p lete ly lifted. Since the m a s s , M(Zn) = 65, is c lo se to the M(Ga)=70 w hich it re p la c e s , we expect to see only th re e silic o n m odes s p lit in fre q u e n c y about the S i^ a band. A p p licatio n of the freq u en cy ru le (equation (3-5)) given p re v io u s ly yields T his r e s u lt is in good a g re e m e n t w ith the 384 c m value fo r the Si_. band. The c o n c e n tra tio n of ( S i ^ - Z n ^ ) m a y be cru d ely e s tim a te d as follows: It is a s s u m e d that the to ta l a b s o rp tio n c ro s s se c tio n for the (Si-, -Z n n ) bands is the s a m e as th a t fo r the S i_ band, Ga Ga Ga i . e . , the only effect of the zinc has b e e n to lift the d e g e n e ra c y of Si,, but the to ta l a b so rp tio n p e r c e n tre is unchanged. Then V = [4 { (395)2 + (382)2 + (378)2 }] 384. 5 c m " 1 3 (6 - 1 ) -1 Ga [SiGa"ZnGaJ a 395+ a 382 + a '378 a 384 (6 - 2 ) The p rim e on Ct^^g is to sp ecify th at the o th e r s o u rc e s of a b s o r p - 170 tion a t that freq u en cy have b e e n a lre a d y s u b tra c te d . F r o m other stu d ie s (S pitzer and A llre d 1968b) it is known that the a b so rp tio n c ro s s se c tio n for the 384 cm * band is given by a 3S4 ^ [ ^ c a ] ! ^‘ -18 2 7 .3 x 10" cm . Thus [ S i ^ - Z n ^ ] for the ingot 7 s a m p le s of F ig u re VI-5 is = “ 3 x l O ^ c m ^ and [SiQa ] 4 x l O ^ c m The 19 -3 to tal silic o n c o n c e n tra tio n of “ 7 x 10 cm w hich c o m p a re s 19 -3 fav o rab ly w ith the doping e s tim a te of = * ■ 6 x 10 cm given in Table V I-II. The to ta l zinc c o n c e n tra tio n of ingot 7 is 4 x 19 -3 10 cm . This co n ce n tratio n includes b oth [Z n ^ a -SiQ a ] = ” 3 x 19 -3 19 -3 10 c m and [ Z n ^ - L i ^ ] = “ 1 x 10 cm as e s tim a te d fro m the 405 c m * and 361 cm ^ bands and p re v io u s p u b lish ed (L o rim o r and S p itz e r 1967b) a v e rs u s [ Z n ^ - L i ^ ] d ata. A gain the to tal [Zn] is re g a rd e d as in re a so n a b le a g re e m e n t w ith the e s tim a te of 19 -3 3 x 10 c m given in Table V I-II. It m a y a lso be noted th at if the Z n ^ a and S i^ a w e re ra n d o m ly d istrib u te d on the galliu m sub- 17 18 -3 la ttic e then the [ Z n ^ - S i ^ ] w ould be 10 to 10 c m fo r these s a m p le s . T his c o n c e n tra tio n is su b sta n tia lly s m a lle r than the e s t i m a te given above w hich in d ic a te s th a t the p a irin g e n e rg y p lays a sig n ifican t ro le in d e te rm in in g the [ Z n ^ - ^ - S i^ ] p a ir concentrations. T he m e a s u re m e n ts of s a m p le s tak en fro m s ilic o n -p lu s -z in c ingots have b een u sed to obtain the points given by solid dots on F ig u re V I-2. R e c a ll th a t in som e of th e se s a m p le s no detectab le band w as o b s e rv e d a t 399 cm \ and thus the a rro w s indicate th a t the points have b een p la c e d a t e s tim a te s fo r the m a x im u m p o s sib le values fo r a (399 c m *). The c o r r e c t value is p ro b ab ly P su b sta n tia lly s m a lle r . The points in d icate th a t fo r ingots 6, 7, 171 13 and 16 the [S i^ g] has b een d e c re a s e d by a t le a s t one o r d e r of m a g n itu d e, and a m o re r e a lis tic e s tim a te gives a p p ro x im a te ly two o r d e r s of m agnitude fo r a given ("Si^. ]. In o r d e r to ob tain som e s e m i-q u a n tita tiv e r e s u lts , a s e r ie s of GaAs ingots w e re grow n b y the h o rizo n tal B rid g m a n m ethod. T h ese ingots a r e liste d as ingot 8 and 19 in Table V I-II. As shown in this table, th e se ingots have the sa m e Si doping lev el 19 - 3 ([Si]=“ 1 x 1 0 cm ) n e a r the fro n t end. D ifferen t co n cen tratio n s of a second dopant w e re in tro d u ced . The doping le v els w e re c o n tro lle d by adding to the m e lt an am ount of each dopant m a te r ia l w hich w as c alcu la ted fro m the re p o rte d s e g re g a tio n co efficient. (W illardson and A llre d 1966). The a b s o rp tio n s p e c tra of s a m p le s cu t fro m the fro n t end of th e se ingots and L i-c o m p e n s a te d w e re m e a s u r e d . Since th e se s p e c tra a r e v e ry s im ila r to those shown in F ig u re s V I-1, V I-3 and V I-4, they w ill not be shown h e re . In stead , the a b so rp tio n co efficien ts of m a jo r Si lo c a liz e d v ib r a tional m o d es w ith the b ack g ro u n d su b tra c te d a r e liste d in T able V I-III. The peak a b so rp tio n coefficients fo r 384 cm * and 399 c m - '* ' bands liste d in this T able a r e a lso p lo tted in F ig u re VI-2. Since the se g re g a tio n co efficien t is m u c h le s s than 1 for each of the im p u ritie s c o n sid e re d , the doping lev el n e a r the b ack end of the ingot is a rap id ly changing function of p o sitio n and th e re fo re su sc e p tib le to c o n sid e ra b le e r r o r . H ence the r e s u lts fro m the s a m p le s fro m the b ack end of the ingots a r e not u sed to obtain q u an titativ e in fo rm atio n and only the re s u lts fro m the fro n t end o f ea c h ingot a r e lis te d in T able VI-III. The fre e c a r r i e r 172 TA B L E V I-III LIST O F PE A K ABSORPTION C O E FF IC IE N T S (LESS BACKGROUND) O F T H R E E Si LVM BANDS AND F R E E CARRIER CONCENTRATIONS Ingot F r e e C a r r i e r LVM P e a k A b so rp tio n N u m b er C o n cen tratio n C o efficien t o ( c m ^ j P 384cm * 393cm 1 399cm 1 8 4.1 X 1018 30. 2 5. 7 10. 4 9 3.1 X 1018 32. 4 3. 3 . 6. 8 10 2.3 X io18 35. 4 3. 0 5. 5 11 9.8 X io17 56. 0 3.8 5. 2 12 2.6 X * 0 0 H o H 51. 4 + ND 1. 3 13 1.6 X 1019 64. 1 + ND +ND 14 3. 1 X io18 47. 5 5.5 9. 6 15 6.7 X io17 84. 0 6. 0 6. 6 16 2. 1 X 1 o18 * 62. 8 + ND +ND 17 3 .3 X io18 33. 0 3.9 10. 8 18 2.4 5.8 X X io18 io18** 26. 1 3. 5 15. 1 19 2.2 7. 3 X X io18 io18** 22. 1 4.7 35. 6 rP -ty p e fre e c a r r i e r s , the o th e r c o n c e n tra tio n s a r e a ll fo r n -ty p e fre e c a r r i e r s . ^V alues a fte r 1100°C/15 m in an n eal. + ND = none detectab le 173 c o n c e n tra tio n n e a r the fro n t end of ea c h ingot fro m the H all effect m e a s u r e m e n t is a lso lis te d in this T ab le. F o r the s a m p le s m e a s u r e d h e re the lin e w idths of the Si LVM bands a r e indep en d en t of defect c o n ce n tratio n . H ence the p e a k a b s o rp tio n co efficien t of a LVM band is p ro p o rtio n a l to the in te g ra te d a b so rp tio n of th at band w hich is in tu rn p ro p o rtio n a l to the c o n c e n tra tio n of the d e fe c t s p e c ie s. F r o m p re v io u s w ork (S pitzer and A llre d 1968b) on L i-c o m p e n s a te d G aA s:Si as w ell a s the p r e s e n t m e a s u re m e n ts it is known that the line w idths of the 384 c m Viand 399 c m - * LVM bands a r e n e a rly the sam e. The a b s o rp tio n c r o s s sectio n s given by the p e a k ab so rp tio n co efficien t divided by the d efec t c o n c e n tra tio n a r e a lso the sam e. Thus the ratio of the m e a s u r e d p eak a b so rp tio n coefficients of the 384 cm * (S^Ga) and 399 c m * (S i^ g) bands gives N jj(S i)/N ^(S i) w hich is lis te d in T able V I-IV . Since no 399 c m - * band w as o b s e rv e d in ingots 13 and 16, the ra tio fo r th e se c a s e s w as e s tim a te d a s > 100. T his table show s the change of N jj(Si)/N ^(Si) as the c o n c e n tra tio n of second dopant v a rie s w hile the to tal Si c o n c e n tra tio n is co n stan t. W ithout the second dopant as in ingot 8 , the ra tio is c lo se to 3. W hen a p -ty p e seco n d dopant is added, the ra tio in c re a s e s w ith an in c re a s in g doping le v el. W hen an n -ty p e second dopant, su ch as Te, is added, the ra tio d e c r e a s e s as the doping le v e l in c r e a s e s . L ongini and G reen e (1956) have shown fro m th e rm o d y n a m ic a rg u m e n ts th a t the ra tio N j^(Si)/N ^(Si) should v a ry w ith the F e r m i 174 le v e l as (6-3) w h ere Is the in trin s ic F e r m i lev el e n e rg y a t the te m p e ra tu re T and (N ~ (S i)/N A (Si)). is the lim itin g ra tio of Si donor to a c c e p to r U A 1 c o n c e n tra tio n as the to ta l [Si] a p p ro a c h e s z e ro . C alculations b a se d on equation (6-3) have been c a r r i e d out to c o m p a re the p re d ic te d Si b e h a v io r w ith the e x p e rim e n ta l r e s u lts obtained fro m the p r e s e n t study. The b a s ic a ssu m p tio n s used in the calcu latio n s w e re (1) the Si a to m s occupy the Ga and A s s u b -la ttic e s ite s and a ct as to ta lly ionized, sin g ly c h a rg e d d o n o rs and a c c e p to rs , r e s pectiv ely ; (2) the su m of the Si donor and a c c e p to r co n ce n tratio n s u sed is eq u al to the total Si co n ce n tratio n ; (3) the second dopant ato m s a r e ran d o m ly d is trib u te d on the p r o p e r su b la ttic e site s; (4) the donors and a c c e p to rs a r e in e q u ilib riu m a t a te m p e ra tu re slig h tly below the m e ltin g point of GaAs (1513°K) T his e q u ili b r iu m te m p e ra tu re is a s s u m e d to be 1500°K in the calcu latio n ; (5) the site d istrib u tio n of Si a to m s re m a in s the sa m e a fte r cooling fro m 1500°K and is not s u b sta n tia lly a lte r e d b y the s u b s e q u en t L i diffusion. Some of th e se a s su m p tio n s a r e the sa m e as th o se u sed by W helan e t al. (I960). The f i r s t and second assu m p tio n s s ta te th a t [Si] = NA (Si) + ND (Si) = 1 x 1019c m "3 (6S-4) F r o m the n e u tra lity condition, we have n e " p h = N D(Si) ' NA (Si) " B> (6-5) 175 w h e re n is the e le c tro n co n cen tratio n , e is the hole co n c e n tra tio n , and B is the c o n c e n tra tio n of the second dopant, p o sitiv e fo r a p -ty p e dopant and neg ativ e fo r an n -ty p e dopant. The n g and p ^ a r e re la te d to the F e r m i le v e l e n e rg y E p by the following re la tio n s ne = N ^ l n ) p h = n v f | ( P ) /2 T T m ;k T \^ / e - E „ \ w h e re is the e le c tro n d e n sity of s ta te s effective m a s s in the conduction band, m ^ is the hole d e n sity of s ta te s effective m a s s in the v a len ce band, k is B o ltz m a n n 's co n stan t, h is P la n c k 's c o n s ta n t, E c is the e n e rg y of the conduction band- E ^ is the e n e rg y of the v alen ce band, and F ^ ( n ) is the F e r m i - D i r a c in te g ra l w hich is equal to r 0 0 2tt L Jo l+exp(e - p ) The v alu es of p a r a m e te r s used in the calcu la tio n w e re the e n e rg y gap E (eV) = l. 522 - 5 .8 x 10_4T2 /(T +300), (P a n ish and C asey 1969), O m =0.08 m and m. =0. 4 m , w h e re m is the fre e e le c tro n m a s s , e o h o o 176 V alues fo r m e of 0. 07 m o to 0. 09 m Q have b een re p o rte d (P ille r 1966) depending on the e le c tro n c o n ce n tratio n . This v a ria tio n in m e has little effect on the calcu latio n . The d e p e n dence of m ^ on hole c o n c e n tra tio n is quite s m a ll (R heinlander 1973) and the is a p p ro x im a te ly 0 .4 Two s im ila r calcu latio n s have b een p e rfo rm e d . The f ir s t c a lc u la tio n w as b a s e d on the m e a s u r e d c a r r i e r d en sity . E quation (6-3) w as u sed to c a lc u la te the N j^(Si)/N ^(Si) for a s s u m e d values of E p . The (Np(Si)/N^(Si))^ value used in the com putation w as o btained fro m equation (6-3) by using (a) the m e a s u re d value of Nj-)(S i)/N ^(S i) = 3 fro m the singly S i-doped ingot 8, and (b) the E p value w hich w as c a lc u la te d by equating the m e a s u r e d ro o m J 1 te m p e ra tu re c a r r i e r c o n c e n tra tio n of ingot 8 to the d iffere n ce n e ~p^ a t 1500° K. The (Nj-j(Si)/N^ (Si))^ value thus c alcu la ted is 92. 1. The re s u lt of the. c a lc u la te d N j^(Si)/N ^(Si) is show n by the s tra ig h t line in F ig. V I-6. T he m e a s u r e d v alu es of Nj-j(Si)/ N .(S i) a r e also p lo tted in th is fig u re w ith the ingot n u m b e rs by the data p o in ts. In this c a lc u la tio n the doping le v e ls a r e n o t u s e d F o r sa m p le s w hich have p -ty p e second dopants, the m e a s u re d points show the p re d ic te d b eh a v io r although they tend to fall below the c a lc u la te d line. The th re e sa m p le s having the n -ty p e second dopant and shown by the open c ir c le s n ex t to the ingot n u m b e rs in F ig . V I-6 do not have the p re d ic te d b e h a v io r. The s o u rc e s of e r r o r include a ± 10% u n c e rta in ty in the m e a s u r e d c a r r i e r co n c e n tra tio n and in a c c u ra c ie s in the peak a b so rp tio n co efficien t m e a s u re m e n t, p a r tic u la r ly fo r the 399 c m * band w hen it is s m a ll 177 100 ( 1 3 ) ( 1 6 ) calcu lated 5 0 (1 2)* (1 5 ) ND(Si) ( 1 8 ) o : [Si]=1*io cm _ Second Dopant Zn • M n a T e ° ( I 9 ) o ♦ O - 0.2 0 - 0 . 4 0.2 0 .4 E F- ER (eV) F ig u re V I-6 The ra tio of Si donor to Si' a c c e p to r c o n c e n tra tio n s, N j^(Si)/N ^(Si), a s a function of the F e r m i le v e l e n e rg y E p - E p . in G aA s. Ep^ is the in trin s ic F e r m i le v e l e n e rg y . 178 as in the c a s e s w h e re N _ (S i)/N . (Si) is > 10. F o r ex am p le, the JL/ r i " * “ * of the 399 cm ^ band of ingot 12 is only 1.3 c m The sa m p le has to be sufficiently thin (x = 0. 038 cm ) th at the a = 5 1 .4 cm ^ of the 384 cm 3 band can be m e a s u re d . With P this th ick n ess the 399 cm band p ro d u c e d a to tal change of 2.3% ± 1.0% in the m e a s u r e d tr a n s m is s io n . H ow ever, th e se e r r o r s can not ac c o u n t fo r the d is c re p a n c ie s betw een the calcu la ted and m e a s u r e d v a lu e s. The second c a lc u la tio n gives the re la tio n sh ip betw een the N ^ (S i)/N ^ (S i) and B. The n g and p ^ can be c a lc u la te d fro m a s s u m e d v alu es of E^, and hence equation (6-5) gives N ^ - N ^ - B . F o r the sa m e a s s u m e d E -,, N „ ( S i) /N . (Si) is c a lc u la te d fro m equa- J? JJ A tion (6-3) su b je c t to (N ^(Si)/N ^(Si))^= 147. 8 w h ich gives N ^ (S i)/ NA (Si) = 3 w hen ND (Si) + NA (Si) = 1 x 1019c m ' 3 and B=0. Thus for any a s s u m e d E p , c a lc u la te d v alu es of N ^(S i), NA (Si) and B a r e obtained su b je c t to equation (6-4). Note th a t in this c a lc u la tion, the m e a s u r e d n values a r e not u sed , and this acco u n ts for e the d iffe re n t (N ^(S i)/N A (Si))j em ployed in the two calcu la tio n s. If (N _.(Si)/N . (Si)). = 147.8 w as u sed to com pute the line shown in JJ A X F ig. V I-6, it would c a u se a shift of 0. 03 eV to the rig h t. In o r d e r to c o m p a re the data w ith the second calcu latio n , the c alcu la ted c u rv e s fo r the dependence of N p (S i)/N A (Si) on the second dopant c o n c e n tra tio n B a r e show n in F ig . V I-7. The m e a s u re d v alu es of Nj-j(Si)/NA (Si) fro m LVM e x p e rim e n ts w ith the B values fro m T able V I-IV a r e a lso shown in F ig . V I-7. T h e re is re a so n a b le a g re e m e n t betw een the c a lc u la te d and the m e a s u re d 179 100 113) 116) Total [Si] = 1 x 1019 cm-3 Second Dopant Calculated 50 • (12) Zn Mn Measured (1 0 1 • (14) 0.5 0.2 Second Dopant Concentration (cm"'*) F ig u re V I-7 The ra tio of Si donor to Si a c c e p to r c o n c e n tra tio n s, N n (S i)/N A (Si), as a function of the second dopant co n c e n tra tio n in GaAs. T A B L E VI-IV LIST O F Si DONOR TO A C C E PT O R CONCENTRATION RATIO N (Si) A T /g . ' - AND SECOND DOPANT CONCENTRATION IN GaAs C o n cen tratio n of Np(Si) Ingot N u m b er Second D opant (cm ~ 8 ) N ^(Si) 8 3. 0 9 [Zn] - 1 X 0 0 o H 4. 8 10 [Zn] = 3 x 1018 6 .4 11 [Zn] = 6 x io 18 10. 8 12 [Zn] = 1 X io 19 39. 5 13 [Zn] = 3 x i o 19 > 100. 0 14 [Mn] = 1 X i o 18 4 .9 15 [Mn] = 6 x i o 18 12. 7 16 [Mn] = 3 x i o 19 >100. 0 17 [Te] = 6 x i o 18 2. 9 18 [Te] = 1 X i o 19 1. 7 19 [Te] = 3 x i o 19 0. 6 N ote: T o tal Si c o n c e n tra tio n in ea c h ingot is a 19 -3 co n stan t. = 1 x 10 cm ) values fo r the p -ty p e second dopant (Zn o r Mn). A s in F ig . V I-6 the re s u lts a r e p o o r w hen T e is the second dopant. T h e re a r e s e v e ra l fa c to rs and u n c e rta in tie s w hich w ill affect the e x p e rim e n ta l re s u lts and a n a ly se s ju s t d e s c rib e d . T h ese fa c to rs include the following: (1) W hile the d etaile d b e h a v io r of Te is lik ely to be co m p lica ted in the p r e s e n t c a s e , it is w ell known th a t in singly 19 -3 T e -d o p e d GaAs w h e re [Te] =-1 x 10 cm th e re is a su b sta n tia l annealing effect (M itchell et al. 1971, F u lle r and W o lfstirn 1963) and n g< [Te]. Some of the T e ato m s m a y fo rm co m p lex es, p re c ip ita te s o r be a t off la ttic e - s ite p o sitio n s and thus not be activ e d o n o rs. In o r d e r to d e te rm in e w h e th e r this annealing e f fe c t could be re s p o n s ib le fo r the p o o r a g re e m e n t in F ig. V I-6 the ng of ingots 18 and 19 w e re r e m e a s u r e d a fte r annealing at 1100°C/15 m in and quenching to ro o m te m p e ra tu re . T his t r e a t m e n t is known to rem o v e som e of the T e -a n n e a lin g effect and the new n g a r e given in T able VI-III. W ith th e se new ng values the m e a s u r e d p oints m ove to the rig h t as in d icate d by the a rro w s in F ig . VI- 6 and the a g re e m e n t w ith the calcu la tio n is now v e ry good C o m p a riso n w ith F ig u re VI-7 in d ic a te s th a t a s u b sta n tia l fra c tio n of the [Te] s till does not a c t as d o n o rs. (2) It has b een e sta b lis h e d in C h ap ter V th a t th e re a r e s u b s ta n tia l annealing effects in h eavily doped GaA s:Si and t h e r e fo re , the a ss u m p tio n that N ^ (S i)/N ^ (S i) is given by the 1500°K e q u ilib riu m value m a y be in e r r o r . A nnealing e x p e rim e n ts d e s c rib e d in C h ap ter V have shown th a t Nj-j(Si)/N^(Si) can be 182 d e c re a s e d as m u ch as a fa c to r of 2 by annealing a t te m p e ra tu re s as low as 673°K. The annealing effect is c o m p lica ted b y the fact th at the sa m p le s had to be co m p e n sa te d b y L i diffusion n e a r 973°K b efo re the LVM bands could be m e a s u re d . (3) The se g re g a tio n coefficients u sed in calcu la tin g the Si and second dopant c o n c e n tra tio n s w e re b a s e d on values fo r sin g ly - doped GaAs w hich m a y be in e r r o r w hen la rg e c o n c e n tra tio n s of two d iffe re n t dopants a r e sim u lta n e o u sly in tro d u ced . (4) N ot a ll Si ato m s a r e SiGa of S i ^ g . P a ir s a r e fo rm e d including SiG a-SiA g , S iG a-Z n G a, SiQ a - L iGa and p ro b a b ly S iQ a - M nGa> The p a irin g e n e rg ie s have n o t b e e n ta k en into acco u n t in the th e rm o d y n am ic calculation. In view of the c ru d ity of the a ss u m p tio n s used in the c alcu latio n s and u n c e rta in tie s in the m e a s u r e d v a lu e s, the a g r e e m e n t betw een the calcu la tio n s and the m e a s u r e m e n ts a r e re g a rd e d a s quite s a tis fa c to ry . The q u a lita tiv e dependence of the Si site d istrib u tio n upon o th e r dopants is e sta b lis h e d and . the L ongini and G reen e equation does s e m i-q u a n tita tiv e ly p r e d ic t the o b se rv e d b eh av io r. VI-IV. C onclusion In this ch a p te r, the influence of S i-s ite d istrib u tio n in GaAs by adding a seco n d dopant is stu d ied . The a c tu a l change of the co n ce n tratio n s of Si donor (SiG a) v e rs u s Si a c c e p to r (SiA g) sp e c ie s can be d e te rm in e d b y in f r a r e d lo c a liz e d v ib ra tio n a l m ode m e a s u re m e n t. It is found th a t by adding donor im p u rity as the second dopant, the ra tio of Si donor to Si a c c e p to r c o n c e n tra tio n w ill be d e c re a s e d . On the o th e r hand, by adding a c c e p to r im p u rity as the second dopant, the ra tio w ill be in c re a s e d , effect can be explained by the F e r m i level effect. 183 This A PPE N D IX I IN FL U E N C E OF R E F L E C T IV IT Y C O E F F IC IE N T IN CALCULATING A BSORPTION C O E FF IC IE N T In C h ap ter III, S ection III-IV -A , the m eth o d of calcu latin g the a b so rp tio n coefficient a fro m the m e a s u r e d in f r a r e d t r a n s m is s io n c o efficien t T has b een d e sc rib e d . The re la tio n sh ip b etw ee n a. and T a t a given freq u en cy is given in eq u atio n (3-1) w hich is re p e a te d h e re . (1 -R )2 e " a x T = *■ ■ ■ ~V ?------- , (A l-1 ) 1 - R e w h e re R is the re fle c tiv ity co efficien t and x is the th ic k n e ss of the sa m p le . F o r the a b so rp tio n co efficien t calcu la tio n s using equation (A l-1), the R value has b e e n a s s u m e d to be independent of fre q u e n c y and equal to 0 .3 0 for G aA s. T his a s su m p tio n is in c o r r e c t in th at R is known to be a function of freq u en cy . F o r e x a m p le , in the fre q u e n c y reg io n of in te r e s t to the p r e s e n t study, the R values of GaAs in c re a s e s slow ly fro m 0 .2 3 a t v = 333cm ^ to 0 .2 8 a t V = 467 c m '* '. (S eraphin and B en n ett 1967). T h e re fo re , it is n e c e s s a r y to d e te rm in e the e r r o r m ade in calcu la tin g a fro m T w ith the in c o r r e c t re fle c tiv ity co efficien t value. T he a b s o rp tio n co efficien t a c a n be obtained fro m equation (A l-1 ) and has the following e x p re s s io n 184 185 ( l-R )2 v 2 ] * 2T ’ (A 1-2) The e x p re s s io n is c o m p lica ted in th a t an y a n a ly tic a l m eth o d to find the deviation of a at a given T by v ary in g the R value re s u lts in a v e ry co m p lica ted fo rm w hich is not v e ry useful. The d e viation of a can be c le a rly illu s tra te d b y using n u m e ric a l values of R and T to calcu late the value of a and then c o m p a re them w ith ea c h o th e r. Such a calcu la tio n has b een c a r r ie d out and the r e s u lt is shown in T able A I-I. T his table shows th a t for a given value of tra n s m is s io n co efficien t T, the co rre sp o n d in g v alu es of a b so rp tio n co efficien t n as the re fle c tiv ity co efficien t R v a r ie s , a s su m in g sa m p le th ic k n e ss x is unity. The a. value calcu la ted w ith R=0. 30 is alw ays s m a lle r than the a value c a lc u la te d w ith R< 0. 30. The p e rc e n ta g e deviation of a b etw een the values c a l culated by using R < 0 .3 0 and R=0. 30 in c re a s e s as the t r a n s m i s sio n T in c r e a s e s . F o r ex am p le, the dev iatio n of a betw een R=0. 28 and R=0. 30 a t T=0. 01 is =“ 1.52% w hile a t T = 0 .4 0 is = * • 13. 3%. The deviation of a b etw ee n R = 0.23 and R = 0.30 a t T=0. 01 is ^4.65%! w hile a t T = 0 .4 0 is = “ 38. 1%. H ence the p e rc e n ta g e e r r o r in c a lc u la ting a a t a given freq u en cy by using a c o n stan t R value of 0. 30 in ste a d of the c o r r e c t R value a t th a t freq u en cy can be as la rg e a s 38% even though the d iffere n ce of the a value its e lf changes v e ry little a s T values in c re a s e fro m 0. 01 to 0 .4 0 w hich is show n in the la s t two colum ns of T able A I-I. T he im p o rta n t q u estio n in the p r e s e n t w o rk how ever is not the e r r o r in the value of a but r a th e r the e r r o r in the a v alu es T A B L E A I-I ABSORPTION C O E FFIC IE N T (a) CA LCU LA TED FROM R E FL E C T IV IT Y (R) AND TRANSMISSION (T) CO EFFIC IEN TS (A ssum e Sam ple T h ick n ess x = l. 0) a a a Aa Aa T (R=0. 23) (R=0. 28) (R=0. 30) (R=0. 23)-(R=0. 30) (R=0. 28)-(R=0. 30) 0. 01 4. 08 3 .95 3. 89 0. 19 0 .06 0. 10 1. 78 1.65 1. 59 0. 19 0.06 0. 20 1. 09 0 .9 6 0. 91 0. 18 0. 05 0. 30 0. 69 0.57 0. 52 0. 17 0.05 0. 40 0. 42 0. 30 0.26 0. 16 0. 04 187: w hich d e te rm in e an a b so rp tio n band su ch as in the LVM m e a s u r e m e n ts . In this c a s e the cu .= a a , , , w h e re band m e a s u r e d b ack g ro u n d a . , . v alu es a r e u su ally obtained fro m a p u re sam p le w ith - b ack g ro u n d 1 r r out the LVM band o r sm oothly e x tra p o la tin g a c r o s s the b a s e of the band. In a , , the e r r o r s a r e indeed sm a ll. C o n sid e r a band fre q u e n c y w h e re T(band) = 0 .1 0 and T (background) = 0 .4 0 then a band va^ues 1*09, 1.08 and 1.07 a r e obtained fro m Table A I-I for R = 0 .2 3 , 0.2 8 and 0 .3 0 , re s p e c tiv e ly . F o r bands such th a t the tr a n s m is s io n changes is by 20% o r m o re w ith r e s p e c t to the back g ro u n d , w hich is the c a se in the p r e s e n t w o rk , the e r r o r in ^ due to using an in c o r r e c t R is le s s than = “ 3% and can be n eg lecte d . A PPEN D IX II LITHIUM DIFFUSION O F S i-D O P E D GaAs A T TE M PE R A T U R E S BELOW 600° C S p itz e r and A llre d (1968b) have found fro m the LVM study of L i-d iffu se d G aA s:Si sa m p le s th a t the in itia l fre e c a r r i e r concen tra tio n ( i . e . , b efo re the L i diffusion p ro c e s s ) of a sam p le is p ro p o rtio n a l to the d iffere n ce in the a b so rp tio n s tre n g th of 384 c m - * (S i^ a ) and 399 c m * (S i^ g ) LVM b an d s. The SiQa sp e c ie s w hich p a ir w ith L i ato m s do not s e e m to co n trib u te to the fre e c a r r i e r c o n c e n tra tio n b e fo re the L i diffusion p ro c e s s even though in so m e c a s e s the LVM band s tre n g th s fro m SiQa of (SiQ -L iQ ) p a i r s a r e quite la rg e (about o n e -h a lf to o n e -th ird the s tre n g th of the 384 c m * band). One p o ssib le ex p lan atio n fo r this fa c t is th a t p r i o r to the L i diffusion, so m e of the S i ^ s p e c ie s a r e air- re a d y in the fo rm of (S^Qa "^Ga^ Pa i r s * Since Vq & is b eliev ed to be an a c c e p to r (Munoz et al. 1970), the ( ^ G a ^ G a ^ Pa ^r s can e ith e r be n e u tra l o r in the sa m e ch a rg e s ta te a s the ( S i ^ - L i ^ ) p a i r s a f te r the L i diffusion p r o c e s s , w hich a r e fo rm e d by L ii + < SiG a- V Ga> * < SiG a- L i Ga>' < A 2 -1 > H ence, only the iso la te d S i^ a donors co n trib u te to the fre e c a r r i e r c o n c e n tra tio n p r i o r to the L i diffusion. T he S i^ a sp e c ie s in the (SiQa - Vq &) p a irs do n o t contribute to n e< The (SiG a- ^Ga^ Pa *r fo rm a tio n w as a lso p ro p o se d in C h ap ter V to p lay a ro le in the 188 189! annealing effect and the id e n tificatio n of this p a ir se e m e d to be su p p o rted by the r e s u lt of p h o to lu m in e sc en ce m e a su re m e n t. H ow ever, th e re is s till no d ir e c t e x p e rim e n ta l evidence as to the fo rm a tio n of ( S i ^ - L i ^ ) p a ir s by in c o rp o ra tin g L i ato m s w ith the ( S i ^ - V ^ ) p a irs during L i diffusion p r o c e s s . One e x p e rim e n t w hich could p o s sib ly p ro v id e the evidence m en tio n ed above would be to diffuse L i into G aA s:Si s a m p le s a t low te m p e ra tu re (400°C=s 600°C). A t th e se low te m p e ra tu re s the L i a to m s can diffuse into the GaAs (F u lle r and W o lfstirn 1962) and hopefully so m e of the L i a to m s w ill occupy the V ^ a of the ex istin g (SiQa _VQa ) sp e c ie s and thus fo rm ( S i ^ - L i ^ ) p a ir s as d e s c rib e d by the p r o c e s s of equation (A l-1 ). The th e rm a l g e n e r a tion of vacan cy sp e c ie s by the lo s s of e ith e r Ga o r As fro m the sam p le s u rfa c e d u rin g L i diffusion p r o c e s s is m in im iz e d at th ese low diffusion te m p e ra tu re s b e c a u se the eq u ilib riu m p a r tia l p r e s s u r e of e ith e r Ga o r As o v e r GaAs is v e ry low a t th e se te m p e r a tu r e s (A rth u r 1967). F r o m e x tra p o la tio n of A r th u r 's -18 re s u lt, the p a r tia l p r e s s u r e s a r e : P . =1.6 x 10 a tm , j \ s 2 P . =6.3 x 10- ^ a t m , P ^ =6.3 x l O ^ a t m a t 400°C; A s^ Ga P . =10- ^ a t m , P . =5 x 1 0 ~ ^ a t m , P _ =4 x 10 ^ a t m at 500°C; A S a a v_t3. 11 1 C IK and P . =10" a tm , P . =5 x 10” a tm , P _ =5 x 10 a tm a t x \ S ^ ^ wcL 600°C. T h e re fo re , the s tre n g th of the ( S i ^ - L i ^ ) bands in a sa m p le co m p en sa ted at T> 600°C c o m p a re d to one co m p en sa ted a t T = 400 to 600°C should give in fo rm a tio n on w h e th e r the (SiQa ~ V-, ) defects a r e th e rm a lly g e n e ra te d o r fro z e n in a t o r n e a r U Ta grow th te m p e ra tu re . A t th e se low te m p e r a tu r e s (400° ^ T j- j^600°C ), 190 the Li diffusion p r o c e s s is g e n e ra lly unable to e le c tr ic a lly c o m p en sate the sa m p le . H ence, 1 M eV e le c tro n ir r a d ia tio n p r o c e s s w ill b e u sed to obtain e le c tr ic a l c o m p e n sa tio n a fte r the L i diffusion p r o c e s s . The r e s u lt of LVM m e a s u r e m e n t should show the lo c al m o d es fro m the (Si_ - L i_ ) p a ir s if the re a c tio n G a G a d e s c rib e d in equation (A2-1) does o c c u r d u rin g L i diffusion p ro c e s s . T his r e s u lt w ill a lso show that the (SiQa -VQa ) sp e c ie s do e x ist in the s ta rtin g sam p le. To c a r r y out the p ro p o s e d e x p e rim e n t, fo u r sa m p le s fro m a d ja c e n t s lic e s of a G aA s:Si ingot w e re used. The ingot had a 19 -3 doping le v e l of Si^* 1 x 10 c m n e a r the fro n t end. T h re e of 7 the sa m p le s w e re s u rfa c e alloyed w ith L i and one each diffused a t 400°C, 500°C and 600°C, a c c o rd in g to the p ro c e d u re d e s c rib e d in S ection III-II-C 1 . The m in im u m diffusion tim e a t e a c h te m p e r a tu r e w as e s tim a te d fro m the diffusion co efficien t of L i in GaAs re p o rte d by F u lle r and W o lfstirn (1962) and by a s su m in g the th ic k n e ss of the sam p le to be 0.2 3 cm . The m in im u m diffu sion tim e s a r e 240 h r a t 400°C, 96 h r a t 500°C and 48 h r a t 600°C. The a c tu a l diffusion tim e s u sed fo r 400°C and 600° C w e re lo n g e r than the above e s tim a te s . The L i diffusion conditions of the sa m p le s a r e lis te d in T able A II-I. T he fre e c a r r i e r c o n c e n tra tio n s of th e se sa m p le s b e fo re and a fte r the L i diffusion a re a lso lis te d in this T ab le. Note th a t the ng of S am p les N os. 2, 3 and 4 b e fo re L i diffusion w e re not m e a s u r e d b u t w e re a s s u m e d to have the sam e value as S a m p le No. 1 s in c e th e se sa m p le s w e re ob tain ed fro m ad ja c e n t w a fe rs of the ingot. The d e c r e a s e TA B L E A ll-I LIST O F L i DIFFUSION CONDITION AND T H E F R E E CARRIER CONCENTRATION B E F O R E AND A F T E R TH E L i DIFFUSION PRO CESS F r e e C a r r i e r C o n cen tratio n * * 7 S am ple L i D iffusion B efo re A fte r N u m b er Condition 7 L i diffusion ^L i diffusion 1 N ot diffused . , l n 18 -3 4. 3 x 10 cm 18 -3 4 .3 x 10 cm 2 400° C /717 h r a i i r»^8 -3 4. 3 x 10 cm 3 .2 x lO ^ c m " ^ 3 500°C /96 h r i i n 18 - 3 4. 3 x 10 cm _ _ . n18 -3 3 .2 x 10 cm 4 600°C /100 h r . , iri18 -3 4. 3 x 10 cm 17 -3 3. 0 x 10 cm * F r e e c a r r i e r c o n c e n tra tio n s w e re d e te rm in e d by m e a s u rin g the fre q u e n c y of p la s m a -e d g e re fle c tiv ity m in im u m as d e s c rib e d in C h a p te r IV. The values of S am ple No. 2, 3, 4, b e fo re L i diffusion w e re not m e a s u r e d b u t a s s u m e d to be the sa m e as Sam ple No. 1 sin ce a ll the s a m p le s w e re ta k en fro m a d ja c e n t w a fe rs . 192 in n a fte r L i diffusion w ith T_.< 600°C m a y be a lso re la te d to e D the annealing effect d e s c rib e d in C h ap ter V. A fte r the L i diffusion p ro c e s s , only Sam ple No. 4 w as tr a n s p a r e n t betw een v = 470 cm * and v = 330 c m *, a ll o th er sa m p le s w e re opaque in this freq u en cy reg io n . The LVM s p e c tru m of Sam ple No. 4 w as m e a s u re d and found to be s im ila r to th a t show n in F ig . V I - 1 except th a t it has a hig h er back g ro u n d a b s o rp tio n (a |3a c ] < .groun(j= “ 27 cm ^). H ow ever, the th re e LVM bands due to S i ^ in ( S i ^ - L i ^ ) p a ir s w e re c le a rly o b s e rv e d at -1 7 Q 3n 374, 379 and 405 cm . Since Si_ and Si,_ also have LVM G a G a bands n e a r 379 c m ^ and 374 cm , it s e e m s th at the 405 cm band is a good in d ic a tio n of the e x iste n c e of the (S*Qa “k iQ a ) p airs. The p eak a b s o rp tio n co efficien t of these bands w ith background a b s o rp tio n s u b tra c te d , to g e th e r w ith th at of the m a jo r Si bands a t 384 cm *(Si£a ), 399 c m ~ * (S i^ s ) and 393 c m *(SiQa " S i^ s ) a r e lis te d in T able A II-II. A fte r the Li diffusion p ro c e s s , the s a m p le s w e re then sen t to A ir F o r c e C am b rid g e R e s e a r c h L a b o ra to rie s fo r e le c tro n i r r a - d ia tio n -c o m p e n sa tio n . T he e le c tro n ir r a d ia tio n p ro c e d u re has b e e n d e s c rib e d in S ection III-H -C 3. The e le c tro n fluence re c e iv e d 18 2 b y e a c h sa m p le w as the sa m e , 2 x 10 /c m on one side and 18 2 1.3 x 10 /c m on the o th e r sid e. A fte r the ir ra d ia tio n , all sa m p le s w e re found to be tr a n s p a r e n t in the in f r a r e d freq u en cy a . The e le c tro n ir r a d ia tio n w as p e rfo rm e d by F . E u le r and L. B o u th illette a t the A F C R L , B edford, M a ss. The au th o r w ish es to e x p re s s his a p p re c ia tio n for this effo rt. 193 T A B L E A II-H LIST O F P E A K ABSORPTION C O E FFIC IE N T S (LESS BACKGROUND) O F LVM BANDS IN GaAsrSi A F T E R E L E C T R O N IRRADIA TION- COM PENSATION’ + LVM F re q u e n c y P e a k A b so rp tio n C oefficient a (cm ) -1 p (cm )___________________________________________________________________ Sam ple Sam ple Sam ple Sam ple No. 4 No. 1 No. 2 No. 3 A fter A fte r A fte r A fter B efo re E le c tro n E le c tro n E le c tro n E le c tro n E le c tro n Irra d ia tio n Irra d ia tio n Irra d ia tio n Irra d ia tio n Irra d ia tio n 405 3. 5 5 .2 399 4 .9 5. 3 7 .3 8. 9 9 .4 393 4. 4 5 .6 9 .2 8. 3 10. 4 384 47. 1 41. 1 34. 6 44. 6 37. 7 379" 2. 3 2.1 2 .6 8. 8 8. 3 374 0. 6 1.1 1.0 7. 6 7 .4 369 4 .2 5. 0 6. 5 ^ T he b e fo re e le c tro n ir r a d ia tio n values a r e a lso lis te d fo r S am ple No. 4. • f c 2Q LVM of Si.Qa a lso o c c u r n e a r this freq u en cy . ❖ ❖ 28 LVM of Si_. also o ccu r n e a r this freq u en cy . 194 reg io n of in te r e s t, n a m e ly v = 470 cm * to v = 330 c m The LVM w e re m e a s u r e d fro m th e se s a m p le s and the peak a b so rp tio n coefficients of the m a jo r LVM bands a r e lis te d in Table A II-II. The s p e c tr a of s a m p le s 1, 2 and 3 w e re s im ila r to th o se shown in C h a p te r V, F ig s. V -5 th ro u g h V -7; no ( S i ^ - L i ^ ) n o r any o th e r L i - r e la t e d LVM band w as o b se rv e d in th e se sa m p le s. On the o th e r hand, Sam ple No. 4 a f te r the e le c tro n irra d ia tio n p r o c e s s s till show ed the ( S i ^ - L i ^ ) p a ir b ands. H ow ever this sa m p le w as s h a tte re d during the e le c tro n ir r a d ia tio n p r o c e s s and only a s m a ll p ie c e w as av a ila b le fo r LVM m e a s u re m e n t a fte r the irra d ia tio n . B e c a u se of the s m a ll size of the av ailab le sa m p le , the s ig n a l-to -n o is e ra tio of the LVM m e a s u re m e n t w as d r a s tic a lly d e c re a s e d , thus the r e s u lt is p ro b a b ly b e s t fo r giving q u alitativ e r a th e r than q u an titativ e in fo rm a tio n . The LVM s p e c tru m of this sa m p le se e m e d to show a v e ry w eak 369 cm ^ band a s c o m p a re d to the o th e r s a m p le s . T his would su p p o rt the sp e c u la tio n m ad e in C h ap ter V and a lso by S p itz er et al. (1969), th a t the ( ^ G a _^Ga^ Pa *r *s P r °b a b ly re la te d to the 369 c m * band. Since no (Si„ -Li_, ) p a ir LVM bands w e re o b se rv e d in u a Ga th e se low te m p e r a tu r e 500°C), L i-d iffu se d sa m p le s, the q u estio n as to w h e th e r equation (A2-1) p re v a ils during L i d iffu sio n p r o c e s s re m a in e d u n an sw ered . The n ex t lo g ical step s e e m s to find o u t w h e th e r the L i did diffuse into the GaAs s a m p le s a t th e se low te m p e r a tu r e s . Thus a ll s a m p le s , including Sam ple No. 4 w e re se n t to P a c ific S p e c tro c h e m ic a l L a b o ra to ry , Inc. (PSL) fo r flam e s p e c tro p h o to m e tric a n a ly sis to d e te rm in e the L i content. T he r e s u lt show ed th a t no d etecta b le tr a c e of L i w as found in any of th e se s a m p le s , including Sam ple No. 4. The lim it of L i d etectio n w as given by P S L as 0. 005%. T his is 18 -3 eq u iv alen t to =*2.5 x 10 c m ” , w hich is c lo se to the solu b ility lim it of L i in GaAs as re p o rte d by F u lle r and W o lfstirn (1962) 18 -3 a t 600°C (3 .6 x 10 cm ) and h ig h e r than the lim it a t 500° C (1.5 x l O ^ c m and 400°C (3.7 x l O ^ c m ^). T his a n a ly sis . a g a in did n o t p ro v id e co n clu siv e a n s w e rs to o u r e x p e rim e n ta l r e s u l t s . In s u m m a ry , a low te m p e r a tu r e L i diffusion e x p e rim e n t w as p ro p o s e d to p ro d u ce d ir e c t evidence of the e x iste n c e of (SiQa ~VQa ) p a ir s p e c ie s in the p r e - L i- d if f u s e d sa m p le and a lso to v e rify the p r o c e s s s ta te d in equation (A 2-1). 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Advisor Spitzer, William G. (committee chair), Halloran, Michael H. (committee member), Whelan, James M. (committee member)

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