University of Southern California Dissertations and Theses

Photonic crystal nanocavity lasers for integration

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Photonic crystal nanocavity lasers for integration

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Content PHOTONICCRYSTAL NANOCAVITYLASERS FOR INTEGRATION by LingLu A Dissertation Presented to the FACULTYOFTHE USC GRADUATESCHOOL UNIVERSITYOF SOUTHERNCALIFORNIA InPartialFulfillmentof the Requirements for theDegree DOCTOR OFPHILOSOPHY (ELECTRICALENGINEERING) May 2010 Copyright 2010 Ling Lu Dedication Tomyparents ii Acknowledgments I would like to thank my thesis adviser, Prof. John O’Brien, for having me in the group that one will never regret in joining. I am grateful to his support, patience and the freedom he provided for my research. His knowledge and insights as a researcher, his enthusiasm and excellence in teaching and his kindness and integrity as a person make him a unique young professor to work for. I also want to express my gratitude to Prof. P. Daniel Dapkus,Stephan Haas,William Steier, Alan Willner and Michelle Povinelli for the time they spent on my qualifyingand defense exams andtheir advice on myresearch andjob hunt. I acknowledge all the student members in our group: Jiang-Rong Cao intro- duced me to the group and has always been responsive to all my questions after hegraduated;Min-HsiungShih,TianYangandStephanFarrelltrainedmereally wellinthecleanroom;Tianencouragedmetofurtherinvestigatetheedge-emitter ideaonwhichIgotmyfirstpublication;AndrewStapletonandMahmoodBagheri helped me alot withdevice characterization;WanKuangandAdamMock taught me 3D FDTD and how their codes work; The collaboration with Adam is fruitful; Cheol-Woo Kim, Roshanak Shafiiha, Nan-Kyung Suh, Hooman Akhavan, Ray- mond Sarkissian, Ashkan Seyedi and Aaron Friesz have been great colleagues to work with. Thankyouall, guys! iii I appreciate our collaboration and close relationship with members of Prof. Dapkus’ group who not only provided high-quality InGaAsP quantum well sam- ples but also shared their expertise with us. The successful device fabrication wouldnotbepossiblewithoutthededicatedmanagementoftheUSCcleanroomby Merrill Roragen andDong-Hai Zhu. The construction of the measurement setups became much easier with the parts made by Kan Lee and John Whited in the engineering machine shop. All the paralleled 3D FDTD calculations were done on the computer clusters maintained by the USC center for High Performance Computing andCommunications (HPCC). I thank USC Physics department for offering me the teaching assistantship for my first two years at USC. The research in this thesis was funded by various agentsincludingDARPA,NSF andDOE. iv TableofContents Dedication ii Acknowledgments iii ListofTables viii ListofFigures ix Abstract xvi Chapter1: Introduction 1 1.1 Electrical injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Continuous-waveoperation atroom temperature andabove. . . . . 2 1.3 Sufficientin-planeoutput power . . . . . . . . . . . . . . . . . . . . . 3 1.4 Highmodulation bandwidthandlow noise . . . . . . . . . . . . . . . 3 1.5 Integrationplatform . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Chapter 2: High peak output power from edge-emitting photonic crystalnanocavitylasers 5 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Device fabricationandcharacterization . . . . . . . . . . . . . . . . . 6 2.3 120μWfrom double-heterostructure edge-emitters . . . . . . . . . . 8 2.4 Estimationof laser efficiencies . . . . . . . . . . . . . . . . . . . . . . 10 2.5 230μWfrom L3edge-emitters . . . . . . . . . . . . . . . . . . . . . . 12 2.6 540μWfrom finite-waveguideedge-emitters . . . . . . . . . . . . . . 15 2.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Chapter3: Quantumwellintermixing 20 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2 Overview of different approaches . . . . . . . . . . . . . . . . . . . . . 21 3.2.1 Dielectric capping . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2.2 Implantationapproach. . . . . . . . . . . . . . . . . . . . . . . 23 3.2.3 Laser-inducedapproach . . . . . . . . . . . . . . . . . . . . . . 24 3.2.4 Performance ofQWI . . . . . . . . . . . . . . . . . . . . . . . . 24 3.3 Dielectric capping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 v 3.4 Thermalrapid annealing . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.5 Ionimplantation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.5.1 Ionspecies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.5.2 Incidentangle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.5.3 Substratetemperature . . . . . . . . . . . . . . . . . . . . . . . 35 3.5.4 Ionenergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.5.5 Dose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.5.6 Ionflux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.5.7 Annealingtemperature andtime . . . . . . . . . . . . . . . . 39 Chapter4: Double-heterostructurephotoniccrystalnanocavitylasers with lower thresholds and higher slope efficiencies obtained by quantumwellintermixing 40 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.2 Device fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 4.3 Resultsof quantumwell intermixing. . . . . . . . . . . . . . . . . . . 44 4.4 Improvement inlaser thresholds andslope efficiencies . . . . . . . . 46 4.5 Estimationof laser qualityfactors . . . . . . . . . . . . . . . . . . . . 48 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Chapter 5: Monolithic integration of photonic crystal nanocavity laserandwaveguidebyquantumwellintermixing 50 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 5.2 Choices of thecavity andtheintegration platform. . . . . . . . . . . 51 5.3 Cavity-waveguidecouplingin frequency . . . . . . . . . . . . . . . . . 52 5.4 Cavity-waveguidecouplingin space . . . . . . . . . . . . . . . . . . . 53 5.5 Directional emission from waveguide facet . . . . . . . . . . . . . . . 55 Chapter 6: Gain compression and thermal analysis of a sapphire- bondedphotoniccrystalmicrocavitylaser 57 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 6.2 Measurement of wavelengthshift. . . . . . . . . . . . . . . . . . . . . 58 6.3 Modeling of wavelength shift . . . . . . . . . . . . . . . . . . . . . . . 61 6.4 3DFDTDsimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 6.5 Resultsof datafitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 6.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Chapter 7: Spacegroup analysis of two-dimensional photonic crys- talwaveguides 66 7.1 Frieze groups: the space groups of2D PhCwaveguides. . . . . . . . 67 7.2 Symmorphic space groupof Type A PhCwaveguides . . . . . . . . . 68 7.3 Non-symmorphic spacegroup of Type B PhCwaveguides . . . . . . 71 References 77 vi AppendixA:PhotoniccrystalsurfacemodesinΓ−Mdirection 89 AppendixB:Digitalimageprocessinginnano-fabrication 94 B.1 Quantificationof fabricationimperfections . . . . . . . . . . . . . . . 94 B.2 Sub-pixelalignment inelectron-beam-lithography . . . . . . . . . . 96 B.2.1 Correlation technique . . . . . . . . . . . . . . . . . . . . . . . 96 B.2.2 Barkersequences andarrays . . . . . . . . . . . . . . . . . . . 98 B.2.3 Aperfect binaryarray . . . . . . . . . . . . . . . . . . . . . . . 99 B.2.4 Sub-pixelresolution . . . . . . . . . . . . . . . . . . . . . . . . 101 B.2.5 Implementation andcalibration . . . . . . . . . . . . . . . . . 101 AppendixC:Devicefabricationprocedures 108 vii ListofTables 3.1 Three types ofdielectric films availablein USCcleanroom. . . . . . 26 3.2 Listofimplantationparametersandtheirvalueschosentointermix the QW in Fig. 3.4. I sent this table to Leonard Kroko, Inc. in Tustin,CA to get the implantationdone. . . . . . . . . . . . . . . . . 34 4.1 LasercharacteristicsofthreePhCDHlasersofdifferentgainstripe widths(g=4,3,and2μm)withtheirnon-intermixedreferencesnamed (g=∞). Their lattice constants (a 1 ) are 420nm. The ratio is calcu- lated usingdatafrom g=4,3,2over datafrom g=∞in the table. r/a 1 is computed throughtop-view SEM images usinganedge detection routine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 7.1 Charactertableof C 2v point group. . . . . . . . . . . . . . . . . . . . . 69 7.2 Charactertableof C 1h point group. . . . . . . . . . . . . . . . . . . . . 70 7.3 Charactertableof the factorgroup of F k=0 2mg /T na . . . . . . . . . . . . . 72 7.4 CharactertableofthefactorgroupofF 2mg /T 2na . Thetwo-dimensional irreducible representation (K) is also shown in the unity matrix form. [Cra74] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 B.1 Statisticsofthe281air-holesdefinedintheSEM imageinFig. B.1. “r” is the radius of the air hole. “a” is the lattice constant, where “ax” are the horizontal ones in cyan and “ay” are the vertical ones inyellow shownin Fig. B.1b) . . . . . . . . . . . . . . . . . . . . . . . 96 B.2 Table of all Barker sequences found. It is conjectured that no more of them exists. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 B.3 TheBEWITCHbeam-writingcommand andits parameters. . . . . 101 viii ListofFigures 2.1 (a1) and (a2) are SEM images of the diced facet along the wrong direction after HCl undercut. Lower half of the edge-emission will be blocked in this case. (b1) and (b2) are SEM images of the diced facetalongthe right direction after HCl undercut. . . . . . . . . . . 7 2.2 (a) Top view SEM image of a fabricated PhC DH cavity with five PhCcladding periods onthe left. . . . . . . . . . . . . . . . . . . . . . 8 2.3 TheexperimentalsetupusedtocharacterizethePhCedge-emitting nanocavitylasers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4 (Color) (a) L-L curves of No. 4, 5 and 6 devices. (b) Threshold and lasing wavelength behaviors versus device numbers. (c) Las- ingspectrum of the No. 5laser. . . . . . . . . . . . . . . . . . . . . . . 10 2.5 (Color) Mode profile of the No. 5 edge-emitter, calculated by 3D FDTDusingthestructureinformationfromitstop-viewSEMimage. (a) Intensity plot of the vertical magnetic field (H z ) distribution in x-y plane at the center of the membrane. (b) H z field profile in the x-zplane throughthecenter ofits waveguide core. Indexprofiles of thedeviceareoutlinedinbothplotsingray. (CourtesyofAdamMock) 11 2.6 (Color) (a) Top view SEM image of a fabricated PhC L3 cavity with fivePCcladdingperiodsonthefacetside(number5device). (b)L-L curves of number 4, 5, 6, 7 and 8 devices. (c) Threshold and lasing wavelength behaviors versus device numbers. (d) Lasing spectrum of thenumber 5laser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.7 (Color) (a) Top view SEM image of a fabricated 10-period-long PhC finite-WG cavity (number 10 device). (b) L-L curves of number 8, 9 and10devices. (c)Lasingspectra of thenumber 8,9and10lasers. 16 ix 2.8 (Color) Mode profile of the number 5 L3 edge-emitter. (a) Intensity plot of the vertical magnetic field (H z ) distribution in x-y plane at the center of the membrane. (b) H z field profile in the x-z plane through the center of its defect. Index profiles of the device are outlined ingrayin bothplots. . . . . . . . . . . . . . . . . . . . . . . . 17 2.9 (Color) Mode profile of the number 10 finite-WG edge-emitter. (a) Intensity plot of the vertical magnetic field (H z ) distribution in x-y plane at the center of the membrane. (b) H z field profile in the x-z planethroughthecenterofitswaveguidecore. Indexprofilesofthe device are outlined in grayinboth plots. . . . . . . . . . . . . . . . . 18 3.1 Illustration of how QWI works. a) Atomic arrangement of a reg- ular and an intermixed QW. b) The corresponding conduction and valence bandedges and the energy levels of the confined electrons andholes. c)Thecorrespondingphotoluminescence(PL)oftheQWs. The PL peak of the intermixed QW is blueshifted with respect to that of the original QW, same as the absorption peak. At the wave- length region in pink, it experiences gain or loss from the original QW (black curve) but are transparent to the intermixed QW (blue curve). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Illustrationof themethod ofthe dielectric cappingapproachfor QWI. 22 3.3 Illustrationof themethod of the implantationapproach for QWI. . 23 3.4 Illustration of the epitaxy structure of QW sample (#1433). The drawingis to scale inthe vertical direction. . . . . . . . . . . . . . . . 25 3.5 ShiftsofQWPLpeaksafterthermalannealingwithdifferentdielec- tric cappingfilms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.6 Spatial scans of PL peaks across the trench/stripe patterns after 4 minutes RTA anneal at 800 ◦ C. (a) E-beam SiO 2 is on top of the MPDG SiN x trench. (b) MPDG SiN x is on top of the E-beam SiO 2 stripe. Foreachsample,amicroscopeimageofthesamplesurfaceis presented;TwoCCDimagesshowtherelativepositionbetweenthe pump spot ( 2μm) and the stripe pattern at the transition region. Wavelength shifts of two control samples are plotted, which are capped with 150nm singlefilms of SiN x or SiO 2 . . . . . . . . . . . . 28 x 3.7 Performance of SiN x -on-SiO 2 -stripe samples annealed at different temperatures for different time. Micro-PL spectra were taken at three area on the sample: underneath SiN x , underneath the 10μm strips and underneath a large area of SiO 2 (larger than 50μm in size). Every data point is the average of a few measurements at equivalentplacesonthesample; theerror baristhestandarddevi- ation. Amicroscope imageofoneannealedsamplesurfaceisshown onthe right.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.8 WavelengthshiftunderneaththeSiO 2 stripesisnotuniformacross thesamplewhiletheblueshiftunderneathSiN x isuniform. ThePL separation is non-uniform. (a) Microscope image of the annealed sample surface. (b) Microscope image of the annealed sample sur- faceafter removing the cappingfilms. Thepositions of thePL mea- surement along the SiO 2 stripe regions are labeled with numbers. ThepositionsoflargePLseparations(>50nm)aredenotedinolive. ThepositionsofsmallPLseparations(<50nm)aredenotedincyan. (c) The PL spectra at different locations (on the stripe and off the strip) compared to the original QW PL. The two PL curves of olive andcyancolor were taken at two different positions on the sample; their colors correspond to the color of the position labels in (b). (d) Thetableof wavelength separationat positions labeled in(b). . . . 31 3.9 Amicroscope imageoftheannealedInPsurfacewhenthedielectric capswere removed. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3.10 SEM images of the annealed InP surfaces underneath dielectric films. (a) Surface underneath MPDG SiNx. (b) Surface containing the region that was covered by the SiO 2 stripe. (c) and (d) The cor- responding regions in(a)and(b)after HCl wet-etch which removes theInPcap layer atthe surface. . . . . . . . . . . . . . . . . . . . . . 32 3.11 The top view of zinc-blend lattice is illustrated to show the chan- neling effect. The surface normal is along <100> direction. There arefiveunit-cellsdrawninthisdirection. (a)Sampleisflatwithout tilting. (b)Sample isslightly tilted. . . . . . . . . . . . . . . . . . . . 35 3.12 Ion depth versus the energy of P + ions in pure InP. The epitaxy of the QW is overlaid for comparison. The data points are calculated bySRIM [ZZB05]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3.13 Simulation results of the ion trajectories, spatial distribution and the created vacancy density in the 60 nm InP cap. The data is cal- culatedbySRIM using10,00010KeVP + ions. . . . . . . . . . . . . . 37 xi 3.14 Simulationresultsoftheiontrajectories andspatialdistributionin SiN x andSiO 2 . ThedataiscalculatedbySRIMusing10,00010KeV P + ions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.15 Ion dose is varied when all the other parameters were kept the same. The sample was 7 ◦ titled away from surface normal and the substratewaskept at200 ◦ C.PLblueshiftsandintensitiesareplot- ted. Thedose of choice is1E15. . . . . . . . . . . . . . . . . . . . . . . 38 3.16 PL blueshifts of implanted sample annealed under different tem- peratures andtime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.1 Schematic illustration of anintermixed DH cavity. . . . . . . . . . . 41 4.2 (color) (a)Top view SEM image of a fabricated intermixed PhC DH cavity. Its QW active region (g) after intermixing is illustrated on top. (b)H z field component of theDH high-Qmode atthemid-plane ofthemembranecalculatedby3DFDTD(CourtesyofAdamMock). Air holes are outlined in gray and the perturbed center defect lat- tices are indarker gray. Inbothfigures,a 2 is 5% larger thana 1 . . . 43 4.3 (color) PL spectra taken at different regions on the QW sample. (a)PLspectraofion-implantedandion-freeQWregionsafteranneal- ing, compared with PL of an as-grown QW reference sample under the same experimental condition. (b)PL taken at the transition regions of gainstripes withdifferent width. . . . . . . . . . . . . . . 45 4.4 (color) Light-in-light-out (L-L) curves of the PhC DH lasers with 2μm gain stripe and the corresponding non-intermixed reference. Theirlasingspectra are shownasinset. . . . . . . . . . . . . . . . . . 46 5.1 Schematic illustration of a PhC DH cavity coupled to an adjacent waveguide. Quantumwellintermixingisdonetoremovetheoptical absorption except the gain stripe region in pink. The DH cavity is 60 ◦ tilted away from the horizontal waveguide next to it in order for the DH mode tail to overlap the single line defect waveguide and achieve optimal coupling. The perturbed lattice constant (a’) is drawn in black and the rest PhC has a lattice constant of a, which is5% smaller thana’in ourdesign. . . . . . . . . . . . . . . . . . . . 51 xii 5.2 Dispersion relation of a regular W1 PhC waveguide. The resonant frequencies of the DH nanocavity with different defect waveguide width (w) are plotted as lines. The waveguide modes are plotted in red lines. The filled gray area is PhC cladding modes. The filled yellow areaare inside the lightcone. . . . . . . . . . . . . . . . . . . . 53 5.3 H z field component of the DH mode at the center of the membrane. NinedifferentWGstartingpointsarelabeledfrom1to9. Theinter- faces between semiconductor and air are outlined in gray. The cen- tralperturbed lattice (5%increase) region is outlined inlighter gray. 53 5.4 3D FDTD calculations of different cavity-WG coupling geometries. The Q factors of the DH mode and the coupling efficiency into the WGare plotted versusWG startingpositions. . . . . . . . . . . . . . 54 5.5 H z field profiles of thecoupling configurationof couplingposition 5. (a)Fielddistributioninthex-yplaneatthecenterofthemembrane. (b) Field distribution in the x-z plane through the WG center. The interfaces between semiconductor and air are outlined in gray. The central perturbed lattice (5% increase) region is outlined in lighter gray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 6.1 (a), (b) SEM images showing a melted InGaAsP membrane PhC device after being pumped bya few milli-watts of CW power at 850 nmunder room temperature. . . . . . . . . . . . . . . . . . . . . . . . 58 6.2 SEM image of afabricatedD4 cavityon asapphire substrate. . . . 58 6.3 (Color) (a)Wavelengthv.s. pumping power of the same lasing mode under different duty cycles. L-L curve under CW condition is also included. (b) CW lasing spectra under various pumping levels and thephotoluminescence (PL)of gainmaterial atlow bias.. . . . . . . 59 6.4 Illustrationof the“RC circuit" thermal model. . . . . . . . . . . . . . 61 6.5 (Color) H z field component of the lasing mode calculated by 3D FDTD. (a) field distribution in x-y plane at the mid-plane of the membrane. (b)fielddistributioninthex-zplanethroughthecenter of thecavity. Theair hole andmembrane edges are outlined in gray. 63 6.6 (Color) (a) Experimental wavelength data fitted by our model. (b) Carrier densityand temperature behaviorsas aresult of thefit. . . 64 xiii 7.1 ThesevenFriezegroups[Mir99]. F 11g andF 2mg arenon-symmorphic groupscontainingglide reflections. The rest are symmorphic. . . . 68 7.2 Illustrationof atype A PhCwaveguide andits symmetry operations. 69 7.3 Thedispersiondiagramoftheair-cladmembranetypeAwaveguide (CourtesyofAdamMock). Therepresentationsareassignedaccord- ingto the H z field component of the waveguide mode profiles. . . . 70 7.4 Illustrationof atype B waveguide andits symmetry operators. . . . 71 7.5 Thedispersiondiagramoftheair-cladmembranetypeBwaveguide whose defect core width is narrowed down to 0.8 of its original size (CourtesyofAdamMock). Therepresentationsareassignedaccord- ingto the H z field component of the waveguide mode profiles. . . . 75 7.6 Thedispersion diagrams for six PhCwaveguides with different lat- tice shift. A lattice shift of 0.0a corresponds to a type A waveguide. The PhC lattice on the two sides of the waveguide core are shifted along the defect direction until 0.5a which corresponds to a type B waveguide. (Courtesyof Adam Mock) . . . . . . . . . . . . . . . . . . 76 A.1 Illustrationof the facet termination parameterτ alongΓ−M direc- tion in the triangular lattice. The PhC lattice is terminated on the rightandis infiniteon the rightandvertically. . . . . . . . . . . . . 90 A.2 Dispersion relation of a triangular lattice PhC folded along differ- ent periodic directions. (a) Folded PhC dispersion alongΓ−M. (b) Folded dispersion alongΓ−K. W1 waveguide modes are plotted in red. Inbothplots,theshadedgrayareaarebulkPhCmodesandthe yellow area is above the light line. Figure (a) and (b) are vertically aligned. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 A.3 (a)SurfacemodedispersionrelationsalongΓ−Mdirectionwithdif- ferent termination parameters. (b) W1 waveguide dispersion rela- tion along Γ−K direction. The guided transmission band (under- neath the light line) of the main WG mode is highlighted in light purple. Figure (a)and(b)sharethe same y-axis. . . . . . . . . . . . 91 A.4 H z field profiles of the surface modes at bandedge with different termination parameters. The interfaces between semicondutor and airare outlined in gray. . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 A.5 Surface mode frequencies versus the termination parameter (τ) at theBrillouin zone boundary(1× π p 3a ) alongΓ−M direction. . . . . . 93 xiv B.1 (a) A top view SEM image of triangular PhC lattice patterned on a silicon membrane. Courtesy of Stephen Farrell. (b) Illustration of theanalysis. Thedetectedair-semiconductorinterfacesareoutlined in green. The centers-of-mass of the air-holes are labeled by red crosses. The lattice points are connected by yellow lines vertically andbycyanlinesinotherdirections. (c)Theclosedobjectsarefilled with white color. (d) The equivalent radii of the closed objects are color-coded byhow much theydeviate from theaverage values. . . 95 B.2 Theauto-correlations of the three longest Barkersequences. . . . . 99 B.3 (a) The 2D binary pattern patched from Barker sequence of length 11. (b) The auto-correlation of (a). The highest peak has a value of 121andthe second peak hasa valueof 46. 121/46=2.6304. . . . . . 99 B.4 (a)A6×6perfectbinaryarray. (b)Theaperiodicauto-correlationof (a). The highest peak has a value of 36 and the second peak has a valueof 7. 36/7=5.1429. . . . . . . . . . . . . . . . . . . . . . . . . . . 100 B.5 Calibration data. (a) The SEM image obtained from the frame- grabber. Thesizeoftheperfect-6markeris30×30μm. (b)Thecorre- lation calculated from (a). (c) Find the offsets from the real pattern center. (d) The collected offset data after the 1st and 2nd calibra- tion. (e) and (f) The linearly fitted conversion function between the pixels andvolts at10KeV,WD=10mm, 500×andYOFF=1.35. . . . 104 B.6 Examplesshowing therobustnessof the correlation technique. . . . 105 B.7 Examplesshowing theflexibility of the correlation technique. . . . 106 B.8 A microscope image showing devices patterned through the silicon nitridemasklayerontopoftheQWs. Thecentersofthecavitiesare aligned inside the vertical gain strip, which can be seen from the slight color difference. This strip is 3μm wide. The e-beam writing window is a250μmsquare. . . . . . . . . . . . . . . . . . . . . . . . . 107 xv Abstract Thegoaloftheworkthroughoutthisthesisistodeveloptwo-dimensionalphotonic crystal micro/nanocavity lasers to meet all the five requirements for practical on- chipsources. Theyare1)electricalinjection,2)continuous-waveoperationatroom temperature and above, 3) sufficient in-plane output power, 4) high modulation bandwidthandlow noise and5)anintegration platform. Chapter 1discussed the fiverequirements. Chapter2workedoutthethirdrequirement: sufficientlaseroutputpowerwas collected underpulsed operations. Chapter 3 picked quantum well intermixing as a solution to the fifth require- ment andworked out thefabrication. Chapter 4 worked out the fifth requirement by integrating photonic crystal nanocavitylaser with theintermixing approach. Chapter 5 worked out a high-performance laser-waveguide coupling design usingthe intermixingplatform. Chapter 6 obtained the gain compression factor and thermal resistance of a room-temperature continuous-wavelaseron sapphire. Gaincompression is alim- iting factor for modulation bandwidth in the fourth requirement; thermal resis- tanceis the key parameter for the second requirement. xvi Chapter7analyzedthesymmetrypropertiesintwo-dimensionalphotoniccrys- talwaveguides. ThisanalysisexplainsthemodesinTypeBphotoniccrystalstruc- turewhichmayleadtohigh-quality-factoron-substratedesignsthatcanfulfillall the requirements. AppendixAcalculatedthesurfacestatesintheΓ−Mdirectionofthetriangular photonic crystal lattice in the membrane structure. The understanding of the surface modes is helpful to the design of lattice termination at device junctions andboundaries. AppendixBshowedtheapplicationofdigitalimageprocessinginnano-fabrication. Fabrication imperfections can be quantified by analyzing the SEM images. Sub- pixel alignment is achieved in electron-beam-lithography using correlation tech- niques. Appendix C summarized the fabricationrecipes. xvii Chapter1 Introduction Two-dimensional (2D) photonic crystal (PhC) semiconductor bandgap lasers are miniature laser sources. The light confinement is achieved in-plane by the pho- tonic bandgap and vertically by total internal reflection. These resonators are referred to as microcavities or nanocavities depending on their mode volumes. Theopticalgainisprovidedbysemiconductormaterialssuchasquantumwellsor quantumdots. Theseminiaturelasersareexcellentcandidatesforon-chipsourcesofphotonic integrated circuits. First, PhC bandgap defect-mode cavities have mode volumes on the order of wavelength cubed (λ/n) 3 , where λ is the lasing wavelength in free spaceandnistherefractiveindexofthesemiconductormaterial. Second,thetwo dimensional pattern offers a large number of degrees of freedom for engineering andoptimizing the local fields with sub-wavelengthdetails. The following subsections describe five practical requirements for an on-chip laser. 1.1 Electricalinjection The first 2D PhC defect-mode laser was demonstrated to operate at pulsed condi- tionunder143kelvinin1999[PLS + 99]. Thefirstinjectionversionwasreportedto lase in a pulsed mode at room temperature in 2004 [PKK + 04, PKS + 05, SJY + 07]. The current was conducted through the thin membrane and a sub-μmpost at the center of the cavity. This structure has a high electrical resistance (2.2kΩ); the air-clad membrane has ahigh thermal resistance. There hasbeen much research 1 effortsinelectricalpumping[CT06,MNMK09,TCBC06,Zho06,FBG + 08,CBM06, HYLL07, LLD + 07, CST + 03, MN09, KEL + 08, LGC09]. Unfortunately, this is the only demonstration in electrical injection so far and it is less likely this structure canfulfillthe following two requirements (RTCW andpower) at thesame time. 1.2 Continuous-waveoperationatroomtempera- tureandabove The first room-temerature (RT) continuous-wave (CW) 2D PhC microcavity laser was made on an Al 2 O 3 substrate oxidized from an AlAs layer in 2000 [HRS + 00]. Smaller devices were later demonstrated using sapphire (Al 2 O 3 crystal) substrates through direct-wafer-bonding [CKW + 05, SKY + 06, SBM + 07, SYL + 09,SMB + 07]. Thesubstrateservesasalow-refractive-indexopticalcladding and a heat sink at the same time. The asymmetric cladding increases the optical losses: in-planelossincreasesbecauseoftheTE-TMcouplingandtheverticalloss into the substrate increases through reduced total-internal-reflection. Those on- substratecavities thushave avery limited qualityfactor, which makes it difficult to fulfill thefollowing power requirement. Very recently, researchers haveshown thatmembrane devices, though having a thermal resistance ∼1000K/mW, can reach RT CW thresholds without much heating[NKB07,KNB08,NIW + 06,NIKA08,NIKA07,TNG + 09,MAP + 09]. Thisis achievedbyloweringthelaserthresholdstotheμWrange. Butitisnotlikelythat membrane type lasers can be biased much above thresholds to output sufficient CW power. 2 1.3 Sufficientin-planeoutputpower This power requirement is two-fold: magnitude and direction. Sufficient power level is needed for an on-chip photo-detector to operate at high speed and low bit- error rate (BER). This requires a high bias and a thermal solution. The advance- mentofthedetector technologymayrelaxtheseconstraints. Thestate-of-artGer- manium/Silicon avalanche photo-detector in Ref. [KLM + 09] requires 1.5 μW to operate at 10 Gb/s with 10 −12 BER. Considering the loss in modulators, filters, waveguide (bends) and other components, 10 dB more power (15 μW) might be needed from the laser ateach wavelength. Planer light-wave circuits prefer in-plane emitters over vertical emitters. 2D PhC lasers are genetically vertical emitters due to the loose optical confine- ment in the out-of-plane direction. The direction of optical emission/loss can be controlled starting with a high Q cavity (>> 10 4 ). This can currently only be realized with a membrane structure in which the index contrast is maximized [LMY + 09,LMH + 09]. 1.4 Highmodulationbandwidthandlownoise In order to transmit data, lasers can be modulated directly or integrated with a modulator. The direct-modulation speed is limited by the relaxation oscilla- tion frequency which increases as the laser is biased further above threshold. In most cases, the frequency response of a QW laser is damped by gain compression [LLTW09,LMB + 09]andcannotreachthebandwidthoftherelaxationoscillation. A laserhasintensitynoise(RIN)andphasenoise (linewidth) originatingfrom spontaneousemission. Theyareboth detrimental to thecommunication system. It has been shown that 2D PhC microcavity lasers have direct-modulation bandwidthabove10GHz[BSW + 06]and linewidth below 1GHz [BSC + 09]. 3 1.5 Integrationplatform Besides the performance, integratability of a device is equally important for its application. BasedonQWgainmaterials,aregrowthapproachwasdemonstrated to integrate 2D PhC lasers [NWB08, WB06, WB08]. Quantum well intermixing has also been shown to be a potentially much better solution to PhC nanocavity lasers [LMB + 08]. Today, all of the requirements have only been realized individually. The diffi- culties lie in the simultaneous fulfillment of the first three requirements. A high Q cavity designed on a substrate that will provide a viable solution: a conduct- ing substrate can conduct current for electrical injection; a thermally-conductive substratecanalleviatetheheatingproblem inRTCWoperation; thehighquality factor also provides freedom in engineering the laser emission. But this cavity design hasnot been found[ZJSR08]. 4 Chapter2 Highpeakoutputpowerfrom edge-emittingphotoniccrystal nanocavitylasers Asanattempttocollectmorein-planeemissionpoweroutofwavelengthsizetwo- dimensional photonic crystaldefect lasers,edge-emitting photonic crystaldouble- heterostructure nanocavity QW membrane lasers were fabricated by shortening the number of cladding periods on one side. 120μW peak output power was col- lected from the facet of the single mode laser at room temperature. The esti- mated differential quantum efficiency (η d ) is 7%. To improve the laser far-field and collect more power, L3 cavity and finite-waveguide cavity laser arrays are fabricated. Peak power levels of 230 μW and 540μW were collected from L3 and finite-waveguideedge-emittersandtheirdifferentialquantumefficienciesare11% and27%,respectively, still limited bytheir collection efficiencies in free space. 2.1 Introduction The physical size of semiconductor lasers has been shrinking down to the wave- length[PLS + 99]oreven sub-wavelengthscale[HOS + 07],whichgreatlyincreases the potential for dense photonic integration. But the laser output power scales with its mode volume. As one of the smallest lasers that is capable of electrical injection [PKK + 04] and CW operation at room temperature [HRS + 00, CKW + 05, 5 BSW + 06, SKY + 06, SBM + 07, NIW + 06, NKB07], two-dimensional (2D) photonic crystal(PhC)defectlasershavenotbeenshowntohavesufficientcollectedoutput power(>50μW)forcurrenton-chipopticalreceiverstooperateathighbandwidth (10GHz)andlowbit-error-rate(10 −12 )[KSS + 07],andmorepowerisalsopreferred for having more functionalities on chip. In addition, most 2D PhC defect lasers emitverticallyinsteadofin-planewhichisthepreferreddirectionforplanarlight- wave circuits. Their dominant out-of-plane loss has always been a bottleneck in engineering the direction of laser emission. Recently, the double-heterostructure (DH)cavity[SNAA05,MLO08]wasrealizedon2DPhCmembraneswithaquality factor(Q)ofmorethan100,000andmodevolumeassmallas∼(λ/n) 3 . Thiscavity’s ultra-highQgivesustheluxuryto intentionallyincrease thein-planeoptical loss by orders of magnitude so that it is much greater than its vertical loss and still be able to achieve lasing [NWB08]. This was done by shortening the waveguide cladding on one side of the cavity, following up on the previous demonstration by Yang et al. [YMO + 07] in which a DH nanocavity laser was demonstrated to edge-emit into a planar integrated photonic crystal waveguide. We expect that thisapproachwillresultinasingle-sidededge-emitter withthepotentialforhigh collection efficiency at the output facet without going to a larger mode volume structure [WB08]. 2.2 Devicefabricationandcharacterization To demonstrate this idea, DH cavities with an InGaAsP QW active region were fabricated in which each cavity had a different number of photonic crystal peri- ods cladding one side of the central heterostructure. Their waveguide cores were alignedalongthe<011>directionona(100)InPsubstrateinordertoopenupthe facetfrometchstopplanesinthefinalHClundercut[CLC + 02]. Thisisillustrated in Fig. 2.1. Fabrication of these devices followed the same procedures as in Ref. 6 [SKM + 06] with the addition that the sample was diced very near the end of the cavities inorder to facilitate the collection of the edge-emitted laser radiation. (a1) (a2) (b1) (b2) Figure 2.1: (a1) and (a2) are SEM images of the diced facet along the wrong direction after HCl undercut. Lower half of the edge-emission will be blocked in thiscase. (b1)and(b2)areSEMimagesofthedicedfacetalongtherightdirection after HCl undercut. Figure 2.2 is an SEM image of the No. 5 device where the device number rep- resents the number of cladding periods on the facet side of the heterostructure. All devices have14cladding periods on theother side and14periods inthedirec- tionperpendiculartothewaveguideexcepttheheterostructureregionwheremore periods wereaddedtoeaseidentification. Thelatticeconstantis441nmalongthe waveguide core only in the heterostructure region and 420nm everywhere else. Ther/a (radiusover lattice constant)valueis 0.306. 7 5μm Figure2.2: (a)TopviewSEM imageofafabricatedPhCDHcavitywithfivePhC cladding periods on theleft. These cavities were optically pumped byan 852nmdiode laser at normal inci- dence through a 100× IR-corrected objective lens at 21 ◦ C substrate temperature. The pulse durationwas 8nswith 0.1%dutycycle. Thesize of the pump spot over- lappingthefield-confiningheterostructureregionwasabout2μmindiameter. The output power was collected from the facet by a 60× AR-coated aspheric lens with 0.65 numerical aperture (N.A.) and detected by an InGaAs photodiode. A piece of double-side-polished Si wafer was used as a filter to verify that light from the pumping laser was not collected. The measurement setup is illustrated in Fig. 2.3. 2.3 120μW from double-heterostructure edge- emitters Light-in-light-out(L-L)curvesofNo. 4,5and6lasersareshowninFig. 2.4(a). No. 4 cavity is the device lasing with the least number of facet cladding periods. The trends of their lasing wavelengths and thresholds are plotted in Fig. 2.4(b). As 8 Si filter 100X N.A. 0.5 852nm Pump laser beam 8ns pulse width 0.1% duty cycle pump spot ~2µm 60X N.A. 0.65 Substrate Temperature 20~21 C InGaAs detector 10mm Figure 2.3: The experimental setup used to characterize the PhC edge-emitting nanocavitylasers. the number of cladding periods decreases, lasing wavelength blueshifts since the average index of the mode decreases. Both their thresholds and slope efficiencies increase due to the increasing optical loss towards the facets when more PhC mirror periods are removed. No. 4 and 5 devices output similar powers of 120μW at the highest pumping level. No. 5 laser has a lower threshold and its lasing spectrum is shown inFig. 2.4(c). To the best of our knowledge, this 120μW peak output power is much higher thanthatofanyotherPhCdefectmodelaserreported todate[LYM + 07,NWB08]. This number is edge-emitted power from a single cavity of small mode volume under single mode operation at room temperature. No optimization was done to engineer thefarfield or improve the coupling,andnodisordering wasdone to the cladding mirror to reduce the QW absorptionloss [LMB + 08]. 9 0246 8101214 0 20 40 60 80 100 120 Output Peak Power (μW) 21°C No.4 No.5 No.6 Incident Peak Power (mW) 01234 1.31.4 1.51.6 Intensity (a.u.) Wavelength (μm) P incident =13mW 45 6 0.8 1.0 1.2 Threshold P incident (mW) Device Number 1500 1504 1508 1512 Wavelength (nm) (c) (b) Absorbed Peak Power (mW) (a) Figure 2.4: (Color) (a) L-L curves of No. 4, 5 and 6 devices. (b) Threshold and lasing wavelength behaviors versus device numbers. (c) Lasing spectrum of the No. 5laser. 2.4 Estimationoflaserefficiencies Thethree-dimensionalfinite-differencetime-domain(3DFDTD)methodwasused to model the No. 5 device. The dielectric structure in calculation is directly taken from the top view SEM image in Fig. 2.2 using an edge-detection algorithm, in order to get an estimation of the passive quality factor (Q passive ) of the fabricated device. Theresultis4,000forQ passive andthemodeprofilesareplotted inFig. 2.5 10 which clearly shows a dominant facet-emission. To calculate the radiated power, atime-averageofoneoscillationperiodofthePoyntingvectorsisperformed. Inte- grating the averaged Poynting vectors over a conical area set by the N.A. of the collecting lens and dividing it by the integral over a closed surface containing the whole DH mode, we get18%for collection efficiency(η collection ). x y x z |H z | 0.1 1 10 100 (a) (b) Figure2.5: (Color)ModeprofileoftheNo. 5edge-emitter,calculatedby3DFDTD using the structure information from its top-view SEM image. (a) Intensity plot of the vertical magnetic field (H z ) distribution in x-y plane at the center of the membrane. (b)H z fieldprofileinthex-zplanethroughthecenterofitswaveguide core. Index profiles of the device are outlined in both plots in gray. (Courtesy of Adam Mock) The differential quantum efficiency (η d ) [CC95] of the No. 5 device at low pumping level is 7%, calculated by dividing the collected photon number by the total number of electrons injected in the semiconductor slab. η d is defined as the number of photons collected per electrons injected (through optical pumping) abovethreshold. η d is expressed as 11 η d =η collection η internal α passive α passive +α absorption , (2.1) whereα passive andα absorption are passive optical loss of the resonator andopti- cal absorption loss from the QW in the mirror region where carrier density is belowtransparency. Theratiobetweenthesetwolosstermscanbedetermined by their corresponding Q values (which is inversely proportional to loss). From Ref. [LMB + 08],wehaveanequivalentQ absorption of5,600forDHlaseratitsthreshold, which gives a value of 60% for the α passive /(α passive +α absorption ) term using the Q passive result from 3D FDTD. The internal quantum efficiency (η internal ) is taken to be 80% [MD96], which is the fraction of the absorbedcarrier being captured by the QWs. Then the only unknownterm η collection in Eq. 2.1can be extracted to be 15%,whichagrees well withthe calculated numberabove. There is plenty of room to improve η d . A well engineered facet termination [KAS + 04, WB08] and cavity-waveguide coupling [KLSN04, FWE + 07, YMO + 07, NWB08] increased η collection ; photo-pumping at a longer wavelength to reduce device heating due to phonon relaxation; and quantum well intermixing (QWI) hasalreadybeendemonstratedtobeabletoeliminatemostoftheabsorptionloss, leading to both increased slope efficiency and lower threshold [LMB + 08]. A 80% η collection and our intermixing result can improve the η d to be 43% and a power level approaching1mW. 2.5 230μWfromL3edge-emitters DH and L3 [ASAN06] high quality factor (Q) nanocavities are excellent choices for designing small-footprint in-plane lasers for their low out-of-plane losses (Q out-of-plane >100,000)andtiny mode volumes (∼(λ/n) 3 ). Bydecreasing the num- ber of cladding periods on one side, we experimentally increase their in-plane 12 losses to surpass the out-of-plane loss. For the L3 cavity, we choose to open up its PhC mirrors in the direction in which the high-Q mode is most extended in space, which is 30 degrees awayfrom the line defect direction. Thisis anattempt toobtainamoredirectionalemissionpatterninthefarfield,sothatthecollection efficiencycanbeimproved. Thisapproachisalsoinaccordancewiththeoptimiza- tion result in the cavity-WG coupling design [FWE + 07]. It’s worth pointing out that we can equally start with DH as the resonant cavity and expect similar or even better performance, since DH cavity has a very similar mode pattern and a higherpassive Q compared to the L3structure. The fabrication and measurement setup are the same as those in Ref. [LMY + 09]. The sample substrate is in thermal contact with a thermoelectric cooler set to be 20∼21 ◦ C. An array of devices was made in which the number of photoniccrystalperiodsbetweenthedefectcavityandoutputportwasvaried. Fig- ure 2.6(a) is a scanning electron microscope (SEM) image of the number 5 device where the device number represents the number of cladding periods on the facet side of the defect. The lattice constant is 410 nm and the r/a (radius over lattice constant) value is 0.29. Light-in-light-out (L-L) curves of the laser array, rang- ing from device number 4 to number 8, are plotted in Fig. 2.6(b). The trends of their lasing wavelengths and thresholds are shown in Fig. 2.6(c). As the number of cladding periods decreases, the lasing wavelength blueshifts since the average index of the mode decreases. Both the thresholds and slope efficiencies increase duetotheincreasingopticallosstowardthefacetswhenmorePhCmirrorperiods are removed. The number 4 cavity is the device lasing with the least number of facet cladding periods. The highest peak power (230 μW) was collected from the number 5 laser. This lasing spectrum is shownin Fig. 2.6(d). The estimated η d is 11%. 13 5μm ° Figure 2.6: (Color) (a) Top view SEM image of a fabricated PhC L3 cavity with five PC cladding periods on the facet side (number 5 device). (b) L-L curves of number 4, 5, 6, 7 and 8 devices. (c) Threshold and lasing wavelength behaviors versusdevice numbers. (d)Lasingspectrum of the number5 laser. 14 2.6 540μWfromfinite-waveguideedge-emitters Recent studies have shown that a PhC single-line-defect WG laser might be an efficient edge-emitter with reasonable footprint [ZRX + 08, WB08, RH07]. We also fabricated an array of single-line finite-WG cavities with different defect lengths. Figure 2.7(a) shows an SEM image of the number 10 device with 410 nm lattice constant and 0.30 r/a, where the device number represents the number of defect periods of the finite-WG cavity. L-L curves of the number 8, 9, and 10 lasers are plotted in Fig. 2.7(b) and their lasing spectra are plotted in Fig. 2.7(c). Cavities shorter than 8 periods did not lase and cavities longer than 10 periods suffered from multimode-lasing. The number 10 laser, having the lowest threshold and highestslope efficiency, output540μWin peakpower. Theestimatedη d is 27%. 2.7 Discussion Three-dimensional finite-difference-time-domain (3D FDTD) calculations were done to study these two devices further using the same methodology described in Ref. [LMY + 09]. Structural information used in the simulation of the L3 cav- ity was directly obtained from the top view SEM image in Fig. 2.6(a) through edge-detection. The r/a of the PhC lattice shown in Fig. 2.7(a)is uniform, but the completestructuralinformationofthefinite-WGcavitycouldn’tbeextractedfrom this top view SEM image due to the reflection of the electron beam off the under- neathsubstrateontherighthalfofthedevice. Thusaperfectlatticewasdrawnin the calculation. PassiveQ and collection efficiencies were evaluatedfor these two cavities. The numerical aperture (N.A. = 0.65) used for calculating the collection efficiencies is the same as that of the collection lens in the experiment. The L3 cavity is shown to have a passive Q of 3,500 and 17% of its optical power can be collected intheexperiment; thefinite-WGcavityhasa1,600passiveQanda35% 15 5μm ° Figure 2.7: (Color) (a) Top view SEM image of a fabricated 10-period-long PhC finite-WGcavity(number10device). (b)L-Lcurvesofnumber8,9and10devices. (c) Lasingspectra of the number8,9and10lasers. 16 x y x z |H z | 10 0 10 1 10 2 10 3 (a) (b) Figure 2.8: (Color) Mode profile of the number 5 L3 edge-emitter. (a) Intensity plot of the vertical magnetic field (H z ) distribution in x-y plane at the center of themembrane. (b)H z fieldprofileinthex-zplanethroughthecenterofitsdefect. Indexprofiles of thedevice are outlined in grayinbothplots. collection efficiency. The difference in collection efficiency explains the difference in collected power levels. The mode profiles are shown in Fig. 2.8 and Fig. 2.9. They indicate that both laser modes couple to the surface modes [RAM + 93] existing at the device facets where the photonic crystal lattice is terminated. Theycarrypower away from the laser and, for the finite-WG cavity, the amount of power flowing alongthe facet is about 6% each in the up and down directions. However, the surface waves might bealsoresponsibleforthedirectionalemissionpatternin-plane(x-yplane)inFig. 2.9(a),which isaninteresting direction to collimate thelaser beamemitting from asub-wavelengthaperture [MGVMM04,KAS + 04, YBF + 08]. 17 x y x z |H z | 10 0 10 1 10 2 10 3 (a) (b) Figure 2.9: (Color) Mode profile of the number 10 finite-WG edge-emitter. (a) Intensity plot of the vertical magnetic field (H z ) distribution in x-y plane at the center of the membrane. (b) H z field profile in the x-z plane through the center of its waveguide core. Indexprofiles of the device areoutlined ingrayin bothplots. For our 2D PhC membrane structures, the collimation can only be achieved in-plane. Along the z direction, the 240 nm thick membrane diffracts the beam in wide angles and limits the collection efficiency as in the case of the No. 10 finite-WG laser. Though we have demonstrated high peak power edge-emitters by collecting laser radiation in free space from the device facets, this is not the end goal. In the integrated form enabled by quantum well intermixing (QWI) [LMB + 08] or regrowth [WB08, NWB08], the laser power will be coupled into an adjacentWGin-plane. Thiscouplingefficiencycanbeengineeredtobeabove90% while maintaining a reasonable cavity Q (a few thousand)for low threshold oper- ation [KLSN04, YMO + 07, FWE + 07, WB08, NWB08]. We might expect to obtain 18 1.4 mW of peak power coupled into the waveguide and η d of 70%, inferred from the finite-WGdata. 2.8 Conclusion Ourresultsshowthatsmalllaserscanpotentiallybeasefficientaslargeonesand can provide sufficient in-plane output power for on-chip communications if their temperatures are kept low. We believe these results are promising for nanocavity laser applications toward on-chip sources andsingle photon emitters aswell. 19 Chapter3 Quantumwellintermixing 3.1 Introduction Monolithic integration of optoelectronic devices is a key to realizing low-cost highly-functional photonic integrated circuits. The ability to modify the bandgap energy across a single substrate is a key requirement for monolithic integration. There are six integration platforms [Col08] based on quantum well (QW) epitaxy which is currently the most mature active material technology. They are verti- cal twin-guide, butt-joint regrowth, selective area growth, offset quantum wells, dual quantum wells and quantum well intermixing. All of the six platforms have been used in commercial products. The first five platforms are all challenging for growth. The selective area growth method needs a mask for growth and the remaining four need regrowth. The quantum well intermixing [Li00, Li98] method, providing a postgrowth modification of the bandedge of multiple QWs, is thus a simple way compared to other five methods listed. It is worth noting that gainmaterialsoflowerdimensions,suchasquantumwireandquantumdots,can be intermixed the same way. The intermixing process of a QW is illustrated in Fig. 3.1. High temperature promotestheinterdiffusionofatomsinthecoreandbarrierregionfollowingFick’s laws of diffusion. The well becomes wider and shallower, so do the confined elec- tron and hole states. The corresponding intermixed absorption peak blueshiftsin wavelength. This process can be done in selected areas on the same wafer with different amountof blueshifts. 20 AlGaAs GaAs AlGaAs V V V V V I I I V Al Ga I I Inters al s Vacancies Conduc on band edge Valence band edge λ λ 1.3 1.4 1.5 1.6 Intensity (a.u.) W avelength (µm ) As-grow n Q W Interm ixed Q W Photoluminescence (a) (b) (c) Figure 3.1: Illustration of how QWI works. a) Atomic arrangement of a regular and an intermixed QW. b) The corresponding conduction and valence bandedges and the energy levels of the confined electrons and holes. c) The correspond- ing photoluminescence (PL) of the QWs. The PL peak of the intermixed QW is blueshifted with respect to that of the original QW, same as the absorption peak. Atthewavelengthregioninpink,itexperiencesgainorlossfromtheoriginalQW (blackcurve) butaretransparentto the intermixed QW (bluecurve). 3.2 Overviewofdifferentapproaches In this section, different approaches of QWI are summarized and divided into three categories: dielectric capping, implantation and laser-induced approaches. Selected areas are treated differently to enhance the local diffusion coefficients. Thisisdonebygeneratingpointdefectsinallthreeapproaches. Subsequentrapid 21 thermal annealing (RTA) at 600 ◦ ∼ 800 ◦ is used for the interdiffusion to happen. A lower processing temperature is alwaysdesired. 3.2.1 Dielectriccapping InP substrate InP cap 100nm SiO2 100nm SiNx Figure3.2: Illustrationofthemethodofthedielectric cappingapproachforQWI. At high temperature, dielectric films, deposited on the semiconductor surface, can generate point defects in the material beneath. The out-diffusion of Ga from the epilayer into the dielectric layers leads to the Ga vacancy concentration at the surface [KNK89]. Those vacancies propagate and increase the interdiffusion rates. Dielectric films deposited with different methods or different conditions are foundto havedifferent abilities in defect-generation. Some enhanceit, others suppressit. QWsofvariousbandgapscanberealizedbyannealingauniformQW sample covered with different dielectric films. One successful realization of this approach is described in Ref. [MKH + 98]. Films that suppress defect-generation are usually used to protect the sample surface and prevent group V desorption during high temperature processes. The problem of film cracking at high temperature due to the stress buildup between 22 layers needs to be solved. This stress field, originated from the different thermal expansion coefficients, can be designed, by the capping layer structure, to guide the point-defects to diffuseanisotropically. 3.2.2 Implantationapproach InP cap InP substrate SiNx Ion Implantation Figure3.3: Illustrationof the method of theimplantation approach for QWI. Accelerated ions incident on the sample surface generate point defects dis- tributed around the penetration depth beneath the surface. The spatial varia- tion can be achieved by patterning the surface with ion-stopping films of differ- ent thicknesses. The implantation can be done either by an ion implanter or an plasma process (Ar gas) [DM05]. Low annealing temperature of 600 ◦ C (for 2 minutes) isreported for the Arplasma approach. Theionimplantationapproachismoreflexiblethanthedielectriccappingone. The density and the depth of the point-defects can be controlled while, for dielec- triccapping,thedefectsallstartatthesurface. Charbonneau[CKP + 98]explained this approach in detail; Skogen [SRM + 05] introduced a sacrificial layer that can be etched away to stop the intermixing and reduced absorption coefficients in the intermixed region; Aimez [ABB + 02] featuredthe usageof low-energy ions. 23 3.2.3 Laser-inducedapproach Inthedemonstratedlaser-inducedQWIapproach[OOG04],aQ-switchedNd:YAG laser with nanosecond pulse widths and 10Hz repetition rate is used to irradiate the sample. The absorptionof high-energypulses produces transient heatingand cause bond-breakingand lattice disruption. The generated point-defects enhance thediffusionrateduringthesubsequenthigh-temperatureannealing. Metalcoat- ings are patterned to reflect the laser light away from the region QWs need to be preserved. Low annealingtemperature of 625 ◦ C (for 2minutes) is reported. 3.2.4 PerformanceofQWI Annealing temperature, surface morphology, uniformity and repeatability are important criteria in choosing a QWI approach. The performance of QWI can be evaluated from the maximal wavelength separation, minimum propagation loss and spatial resolution. For InGaAsP QWs at 1.5 μm, the reported number from the above references are summarized here. The maximal wavelength separation, notthepureblue-shiftbeforeandafterannealing,achievedonthesamewaferare around80∼90nm(46meV);Theminimumpropagationlossmeasuredvariesfrom 1.6∼4.1 cm −1 ; The spatial resolution is 2.4∼3 μm. It is worth noting that, using QWI, quantum wires and boxes can be fabricated, where electrons are shallowly bounded by10∼15meV (Chapter10of Ref. [Li00]). It is easier to intermix a QW of larger core-barrier bandgapenergy difference. It is easier to intermix a QW of thinner core. The strain of the QW is a secondary effect in QWI. 24 3.3 Dielectriccapping In this section, the trials of dielectric capping approach are summarized. The epitaxial structure of the QW sample (#1433) is shown in Fig. 3.4. It was grown at650 ◦ C byMOCVD in Dr. Dapkus’group atUSC. InP substrate 60nm InP cap 57.3nm top waveguide In 0.74 Ga 0.26 As 0.538 P 0.462 (λ=1.25nm) 57.3nm top waveguide In 0.74 Ga 0.26 As 0.538 P 0.462 (λ=1.25nm) 18.6nm barrier In 0.75 Ga 0.25 As 0.538 P 0.462 (λ=1.25nm) four 9.8nm quantum well compressive strain(0.6%) In 0.74 Ga 0.26 As 0.745 P 0.255 (λ=1.55nm) Figure3.4: IllustrationoftheepitaxystructureofQWsample(#1433). Thedraw- ingis to scale in thevertical direction. The dielectric capping approach requires findingtwo films: one that enhances theintermixing;onethatsuppressesit. Itisalwaysdesiredtohavealargerdiffer- enceinwavelengthblueshifts. Silicon oxide (SiO 2 )andsilicon nitride (SiN x )films are common choices for these purposes. PECVD grown SiN x and electron-beam evaporatedSiO 2 areavailableinUSCcleanroom. TwotypesofPECVDSiN x films are used by MicroPhotonic Devices Group (MPDG) and Compound Semiconduc- tor Laboratory (CSL) as dry-etch masks for their processes. All three films and their deposition conditions are tabulated in Table 3.1. MPDG SiN x is grown at higher RF power, higher pressure and a higher flow-rate ratio between ammonia (NH 3 ) to silane (SiH 4 ) with ahigher growth rate (70nm thick for 5min) thanthe CSL SiN x (100 nm thick for 10 min). It was reported (Ref. [CLH + 94, CHS + 98] and the chapter 11 of Ref. [Li00]) the higher RF power and higher NH 3 flow rate 25 results in a SiN x film of higher trapping density for Ga atom out-diffusion, which is considered the mainreason for cappinginduced QWI. Table3.1: Three types of dielectric films availablein USCcleanroom. Films Methods 1 SiO 2 E-beam evaporation (rate of 4Å/s) of silicon oxidepurchasedfromAlfaAesar(item#43736). Gas flow (max- iumis100sccm) RFPower Pressure Temperature SiH 4 NH 3 N 2 2 SiN x (MPDG) 100W 0.8Torr 275 ◦ C 12% 60% 62% 3 SiN x (CSL) 30W 0.44Torr 275 ◦ C 40% 20% 60% The dielectric films are deposited on the surfaces of QW samples; the samples are annealed in a Rapid Thermal Annealer (RTA) in a nitrogen gas environment for two minutes; photo-luminescence (PL) is measured at room-temperature at low photo-pumpingcondition (∼40μW,continuouswave). Theresultsof thewave- length blue-shifts are plotted in Fig. 3.5. A bare QW sample serves as a refer- ence. Fig. 3.5shows thatSiO 2 suppresses blue-shift andMPDG SiN x enhancesit with an activation temperature above 750 ◦ C. The combination of these two films is a good candidate for selective-area QWI. The CSL SiN x has a slightly larger blueshift in wavelength and a lower PL intensity compared to the e-beam evapo- rated SiO 2 film. Selective-areaQWIcanberealizedbydepositinge-beamSiO 2 andMPDGSiN x ondifferent areasofaQWsample. There aretwowaystorealize this. Eitherfilm can be deposited first; pattern it with photo-lithography and wet etch; cover the sample with the other film. The results of the two deposition orders are shown in Fig. 3.6. The trench structure data in Fig. 3.6(a) doesn’t match what one may expect from single film results. The SiN x doesn’t seems to induce the same 26 600 700 800 -60 -40 -20 0 QW Thermal Stability PL Shift (nm) Temperature ( o C) 2min anneal in RTA Bare SiO2 (300nm Evaporation) SiNx (300nm PECVD MPDG) Figure3.5: Shifts of QW PLpeaks after thermal annealingwithdifferent dielec- tric capping films. amount of Ga out-diffusion when the SiO 2 layer covers on top. The large blue- shifts localized at the edge of the trench may be attributed to the strain fields induced by the dielectric patterns at high temperature. On the other hand, the desired intermixing result is obtained if the SiO 2 is deposited first, as shown in Fig. 3.6(b). More samples were fabricated with SiN x on top of SiO 2 stripes. Photo-resist doesn’t stick on the e-beam evaporated SiO 2 surface. This was solved by growing a thin layer of PECVD SiN x on top of the SiO 2 surface as an adhesion layer. To findthebestannealingcondition,sampleswereannealedinRTAat750 ◦ C,800 ◦ C and 850 ◦ C for 1 to 8 minutes. The results are summarized in Fig. 3.7. The diffusion coefficient(D) has an Arrhenius type temperature dependence: D(T)= D 0 exp(−T a /T), where T a is the activation temperature. The diffusion length L= p Dt, where t is the annealing time. The blue-shift underneath SiN x at 850 ◦ C 27 (a) 9 18 (b) 8 17 Figure 3.6: Spatial scans of PL peaks across the trench/stripe patterns after 4 minutesRTAannealat800 ◦ C.(a)E-beamSiO 2 isontopoftheMPDGSiN x trench. (b)MPDGSiN x isontopoftheE-beamSiO 2 stripe. Foreachsample,amicroscope image of the sample surface is presented; Two CCD images show the relative position between the pump spot ( 2μm) and the stripe pattern at the transition region. Wavelength shifts of two control samples are plotted, which are capped with 150nm singlefilms of SiN x or SiO 2 . 28 saturates at 200 nm. The difference in blueshifts underneath SiO 2 strips and large areasis becauseof thelateral diffusion dueto thediffusion isotropy. 750°C 4min ° ° ° Figure 3.7: Performance of SiN x -on-SiO 2 -stripe samples annealed at different temperaturesfordifferenttime. Micro-PLspectraweretakenatthreeareaonthe sample: underneath SiN x , underneath the 10μm strips and underneath a large area of SiO 2 (larger than 50μm in size). Every data point is the average of a few measurements at equivalent places on the sample; the error bar is the standard deviation. A microscope image of one annealed sample surface is shown on the right. The surface morphology after thermal annealing is a significant problem for this dielectric capping approach. Pinholes of μm size were everywhere in the annealed 300 nm MPDG SiN x films. This is shown in the upper right image in Fig. 3.6(a). The pinholes were mostly gone when the film thickness was thinned to 150nm as can be seen in the upper right image in Fig. 3.6(b). But the solution is not veryrepeatable: pinholes showed up againin Fig. 3.7. The bubbles along the SiO 2 strips, shown in Fig. 3.6(b) and Fig. 3.7, make it almostimpossibletomakedevicesonthestrips. ItriedtofixitbyvaryingtheSiN x growth condition. The chamber pressure was varied while the other parameters 29 were kept the same. The bubbles can be removed this way, but the InP surface was still not good enough for photonic crystal devices. A microscope image of the annealed InP surface after removing all the dielectrics is presented in Fig. 3.9. The obviousblacktraces alongthe stripe patternsareμm-size surfacecracks due to the thermal stress at the interfaces of the two films during high-temperature annealing. All these surface-defects issues can be improved but not completely solved in a reliable way in the USC cleanroom; the QW epitaxy structure doesn’t have a thick enough sacrificial layer (only 60 nm) to remove the defected surface resulting from the high activation temperature. The PL scans across the stripes reveals, in Fig. 3.8, the non-uniform PL separations on-and-off the strips. For these reasons, I abandoned the dielectric capping approach and switched to the implantation one. SEM images are taken on the areas that don’t have any notable defects seen under the microscope; they are shown in Fig. 3.10. The surface voids under the SiN x , shown in Fig. 3.10(a),of diameter below 100 nm are evidence of the vacan- cies created from the out-diffusionor decomposition process. 3.4 Thermalrapidannealing The importance of the annealing step in QWI is worth a separate section. All of the QWI approaches rely on the annealing step to activate the diffusion. The diffusion coefficient depends exponentially on temperature. Selective area QWI requires large difference in diffusion coefficients on the same sample; the higher the temperature, the larger the difference will be between the areas of different treatment. A rapid thermal annealer sends the sample to the set temperature with a heating rate above 10 ◦ C/s. This is used to minimize the time the sample spends atlower temperature awayfrom the optimal one. 30 4 10 11 12 13 14 15 16 17 18 19 20 21 9 5 6 7 8 PL sepera!on >50nm <50nm (a) (b) 1.1 1.2 1.3 1.4 1.5 1.6 0 20 40 60 80 12min 500mT MPDG SiNx 850C 100s PL intensity (a.u.) Wavelength( m) blueshift: -65nm -119nm -166nm Wavelengthseparation 4 102nm 13 70nm 5 69nm 14 85nm 6 44nm 15 80nm 7 38nm 16 47nm 8 43nm 17 20nm 9 114nm 18 51nm 10 57nm 19 81nm 11 32nm 20 101nm 12 37nm 21 103nm (c) (d) Figure 3.8: Wavelength shift underneath the SiO 2 stripes is not uniform across the sample while the blueshift underneath SiN x is uniform. The PL separation is non-uniform. (a) Microscope image of the annealed sample surface. (b) Micro- scopeimageoftheannealedsamplesurfaceafterremovingthecappingfilms. The positions of the PL measurement along the SiO 2 stripe regions are labeled with numbers. ThepositionsoflargePLseparations(>50nm)aredenotedinolive. The positionsofsmallPLseparations(<50nm)aredenotedincyan. (c)ThePLspectra atdifferent locations(onthestripe andoffthestrip)compared to theoriginalQW PL.ThetwoPLcurvesofoliveandcyancolorweretakenattwodifferentpositions on the sample; their colors correspond to the color of the position labels in (b). (d) Thetable of wavelengthseparation atpositions labeled in (b). The MOCVD growth temperature for the QW sample in Fig. 3.4 is 650 ◦ C; decomposition(lossofphosphorus)ofInPsurfacestartsataround400 ◦ C[BSA90]; the temperature limit for CMOS backend processes is 400 ◦ C [FMC + 06]. A lower 31 Figure 3.9: A microscope image of the annealed InP surface when the dielectric capswere removed. (a) (b) (c) (d) Figure 3.10: SEM images of the annealed InP surfaces underneath dielectric films. (a)SurfaceunderneathMPDG SiNx. (b)Surfacecontainingtheregion that was covered by the SiO 2 stripe. (c) and (d) The corresponding regions in (a) and (b)after HCl wet-etch which removes theInPcap layer atthe surface. activation temperature for QWI gives better surface morphology and better com- patibility withother processes. Here are some of my observations withthe RTA process. 32 - E-beam evaporated SiO 2 film protects the InP surface from decomposition athightemperature (800 ◦ C)in aN 2 environment in RTA. - Decreasingthefilmthicknesstoaround100nmpreventsthecrackingofthe film during annealing. A thicker film contains more strain because of the difference in thermal expansion coefficients between the substrate and the film, when the temperature is much higher than the film deposition tem- perature. If the film is deposited on a non-flat surface that has pre-defined structures,crackingoccurs at theinterfaces. - Flipping the sample on a polished Si sample was found to yield much bet- ter surface morphology than leaving the sample face-up in a nitrogen envi- ronment in the RTA. The contact pressure from gravity helps even when a protective dielectric film is present. Another polished Si wafer covers the backsideoftheInPsampletoprotectthebacksurfaceandincreasethepres- sure at the lower interface. This configuration looks like the InP sample is sandwiched bytwo silicon wafers. - The DC bias in a plasma process accelerates ions and implants them into the sample. Avoiding any plasma processes before the high temperature annealingis agood idea. 3.5 Ionimplantation I tried to intermix the QWs by implanting argon ions through both ion-beam- etching (IBE) and inductively coupled plasma (ICP). No enhancement in PL blueshiftwere foundafter annealing. In this section, the parameter space of the implantation approach using an ion-implanter is discussed, how they are determined and their influence on the performance of QWI.Thecomplete parameters are listed in Table3.2. 33 Parameters values 1 Ionspecies P + 2 Incidentangle 7 ◦ 3 Substratetemperature 200 ◦ C 4 Ionenergy 10KeV 5 Dose 1E15 cm −2 6 Ionflux 100 nA/cm 2 Time 26.7minutes Table 3.2: List of implantation parameters and their values chosen to intermix the QW in Fig. 3.4. I sent this table to Leonard Kroko, Inc. in Tustin, CA to get the implantationdone. 3.5.1 Ionspecies There aretwo reasonsto choose phosphorusions (P + ). First, impurities aredetri- mental to the quality of QWs. P + is an alien atom for InP material system. Sec- ond, the material composition differs in phosphorus concentration between the QWs andthebarriers,shown inFig. 3.4. 3.5.2 Incidentangle When the ions are accelerated along the surface normal of a <110> InP sample, they see channels everywhere between the atoms. For a perfect lattice, the chan- nels are open all the way to the back-side of the sample. Ions, in this case, can penetratedeepintothesamplewithoutscatteringandcreatingdefects. Thischan- neling effect, illustrated in Fig. 3.11, makes it difficult to predict the scattering events andthe ions are not efficient in creatingdefects thathelp the intermixing. The samples are thus tilted 7 ◦ away from surface normal during implantation to avoid channeling. 34 <100> lted away from <100> (a) (b) Figure3.11: Thetop viewofzinc-blendlattice isillustratedto showthechannel- ing effect. The surface normal is along <100> direction. There are five unit-cells drawn in this direction. (a) Sample is flat without tilting. (b) Sample is slightly tilted. 3.5.3 Substratetemperature The substrate temperature during implantation changes the defect production and recovering rates. An optimal substrate temperature happens around 200 ◦ C for intermixing InPbasedQWs. 3.5.4 Ionenergy The energy of the ions determines the depth and distribution of the defects cre- ated. The sacrificiallayer just above the QWs would be the bestplace to generate the defects; this avoids the direct damage of the QWs. The Stopping and Range of Ionsin Matter (SRIM, http://www.srim.org/)is free software thatsimulates the implantationprocessaccurately. TheionpenetrationdepthisplottedinFig. 3.12. 10 KeV is chosen as the P + energy and the detailed statistics data is shown in Fig. 3.13. Thescatteringeventsdon’toccurbeyondthe60nmInPcap. Inorder to know what mask can stop 10 KeV P + ions, the ion distribution is also calculated 35 InPSubstrate 0 50 100 150 200 250 300 350 0 50 100 150 200 250 300 350 IonEnergy (keV) IonD epth (nm) P + inInP Figure 3.12: Ion depth versus the energy of P + ions in pure InP. The epitaxy of the QW is overlaid for comparison. The data points are calculated by SRIM [ZZB05]. inside the SiN x and SiO 2 dielectric films. 30 nm SiN x or 40 nm SiO 2 is sufficient to stop the 10KeV P + ions. 3.5.5 Dose Dose has a unit of (number of ions)/cm 2 . It is the density of implanted ions. The higher the dose, the higher the defect density will be, thusmore intermixing. But one has to make sure the peak vacancy density will be lower than the atomic density of the crystal to avoid creating an amorphous layer. An incident ion with higher energy creates more defects. The choice of implant dose depends on the implant energy. Figure 3.13 shows the peak vacancy density is 0.5 /ion/Å = 5E7 /ion/cm. The 3D peak vacancy density is dose×5E7 /ion/cm and this should be less than the atomic density in the crystal which is 5E22cm −3 . Based on this estimation, The upper limit of the dose is 1E15 cm −2 for 10KeV P + implantation in InP. 36 Figure 3.13: Simulation results of the ion trajectories, spatial distribution and thecreatedvacancydensityinthe60nmInPcap. ThedataiscalculatedbySRIM using10,00010KeVP + ions. In order to find the optimal dose, three different doses were varied around 1E15. PL blueshift andintensities are compared and plotted in Fig. 3.15. Dose of 1E15 cm −2 produced thelargest blueshiftandthe highestintensity. 3.5.6 Ionflux IonfluxorcurrentdensityhasaunitofnA/cm 2 . Itistherateoftheimplantation. A high current density will cause heating of the sample surface and affect the dynamics of self-healing during implantation. A low rate increases the operation 37 (a) (b) Figure3.14: Simulation results of the ion trajectories and spatialdistribution in SiN x and SiO 2 . Thedatais calculatedby SRIM using10,00010KeVP + ions. 1E14 1E15 1E16 0 25 50 75 100 0.00 0.25 0.50 0.75 1.00 Dose test 10KeV P + , flux=100nA/cm 2 700C 4min RTA Anneal Normalized intensity Blue shift (nm) Implant dose (cm -2 ) Figure3.15: Iondoseisvariedwhenalltheotherparameterswerekeptthesame. Thesamplewas7 ◦ titledawayfromsurfacenormalandthesubstratewaskeptat 200 ◦ C.PLblueshiftsandintensities are plotted. The dose of choice is 1E15. 38 time and the operation charges. It takes 26.7 minutes to implant a dose of 1E15 ata currentdensity of 100 nA/cm 2 . 3.5.7 Annealingtemperatureandtime UsingtheparametersdeterminedaboveandsummarizedinTable3.2,theanneal- ing condition are tested by varying the temperatures and time. Figure 3.16 plots the results. 0 2 4 6 8 0 40 80 120 160 200 Dose = 1E15cm -2 800C 700C Anneal with SiO2 Cap Blueshift (nm) Anneal time (min) Dose = 1E14cm -2 800C 700C Figure3.16: PLblueshiftsofimplantedsampleannealedunderdifferenttemper- aturesandtime. 39 Chapter4 Double-heterostructurephotonic crystalnanocavitylaserswith lowerthresholdsandhigherslope efficienciesobtainedbyquantum wellintermixing In order to reduce the optical absorption loss, an array of double-heterostructure photonic crystal microcavity lasers was fabricated in which much of the photonic crystal mirror region was disordered by quantum well intermixing. In charac- terizing these devices, we obtained more than a factor of two increase in slope efficiencies and more than 20% reduction in threshold pump powers compared to devices thatwere not intermixed. 4.1 Introduction Two-dimensional photonic crystal (PhC) microcavity lasers [PLS + 99, PKK + 04] wouldbeamorepromisingsourcecandidateforphotonicintegratedcircuits(PIC) if they were capable of higher output powers and higher output slope efficiencies. Photonic crystal lasers have typically suffered from an absorption loss due to the 40 active medium (quantumwells or quantumdots) inthe mirror regions of the cav- itywherecarrierdensityisbelowtransparency. Thethresholdgain(g threshold )and slope efficiency(η slope )are expressed as: Γg threshold =α total =α passive +α absorption , (4.1) η slope =η collection η internal α passive α passive +α absorption . (4.2) whereΓistheconfinementfactorandα total isthetotalopticallosswhichconsists of not only loss of a passive resonator but also absorption loss. By reducing this absorptionterm(α absorption )inEq. 4.1and4.2,wecandecreasethelaserthreshold andincrease the slope efficiency atthe same time. QW active region intermixed QW intermixed QW perturbed lattice Figure4.1: Schematic illustration of anintermixed DH cavity. We haverecently demonstratedoptically-pumped pulsedoutputpowers ofone hundred micro-watts in edge-emitting double-heterostructure (DH) microcavities [YMO + 07,LYM + 07]. Thesedevices couldbeimproved iftheabsorptionduetothe quantum wells in the mirror regions was eliminated. In this demonstration we reduce or eliminate this loss by blue-shifting the quantum well absorption peak inthemirrorregionusingquantumwellintermixing(QWI).Figure4.1illustrates the device we have in mind. The intermixing was accomplished using the ion implantation approach[ABB + 02, CKP + 98, SRM + 05]. 41 4.2 Devicefabrication DH [MLO08, SNAA05] photonic crystal lasers were formed in a 240nm thick InGaAsP active waveguide capped by a 60nm InP layer grown by MOCVD on a (100) InP substrate. The active region contains four compressively strained InGaAsP QWs. A 400nm thick silicon nitride (SiN x ) layer was first deposited on the sample and a 35nm thick nickel film of stripe patterns was evaporated on it through lift-off. A wet-etch of the SiN x followed by removing the nickel film left nitridestripeswithdifferentwidths. Theresultingnitridestripewidthswere1,2, 3, and 4 microns. They masked the active regions so that the central areas of the laser cavities would not be disordered. Thena 1×10 15 cm −2 dose of 10keV P+ ions were implanted. Duringimplantationthe sample wastilted 7 ◦ awayfrom surface normal. Other conditions were a 200 ◦ C substrate temperature and a 100nA/cm 2 current density. The P+ ions stop inside the 60nmInP capin regions where there wasnonitridelayerandgetcompletelyblockedbytheSiN x stripes[ZZB05]. Next, the SiN x stripes were removed and a 100nm thick e-beam evaporated SiO 2 film was deposited on the sample at a rate of 4Å per second. This was done to protect the surface from decomposition in the subsequent high temperature annealing, which was done at 700 ◦ C for 4 minutes in a nitrogen gas environment in a rapid thermal annealer (RTA). During this anneal, defects inside the InP cap created byimplantation propagate down andintermix thefour QWs below. The SiO 2 film wasthenremovedandtheintermixedsamplewasreadyforpatterningPhCmicro- cavities. The resonant cavity fabrication followed the same procedures as in Ref. [SKM + 06] with the addition that during the e-beam lithography step the devices were aligned with respect to nickel alignment marks defined and protected from thebeginningoftheprocessing. Thealignmentwasaccomplishedwithbetterthan 0.5μm accuracy. A final HCl wet etch removed the top InP cap and undercut the QW membrane to form an air bridge. For comparison, every lithography window 42 had an identical array of cavities written in an area that was protected by SiN x , thushavingno intermixing. g=2μm a 2 a 1 a 1 H z (a) (b) -600 -400 -200 0 200 400 600 a 2 a 1 a 1 x y Figure 4.2: (color) (a)Top view SEM image of a fabricated intermixed PhC DH cavity. Its QW active region (g) after intermixing is illustrated on top. (b)H z field component of the DH high-Q mode at the mid-plane of the membrane calculated by 3D FDTD (Courtesy of Adam Mock). Air holes are outlined in gray and the perturbedcenterdefect latticesareindarkergray. Inbothfigures,a 2 is5%larger thana 1 . Figure 4.2(a) shows the top view of a finished PhC DH cavity. The lattice constant in the waveguide cladding region, a 1 , is 420nm and the lattice constant in the center perturbed area, a 2 , is 5% larger along the waveguide direction only. 43 The hole radius to lattice constant ratio, r/a 1 , is approximately 0.31. The upper section of Fig. 4.2(a) indicates the region (g) that was protected by the nitride mask and not subsequently intermixed. This two micron stripe indicated in the figurerunsperpendicular to the waveguideaxis ofthe DH resonantcavity. Thefieldprofileofthehigh-QDHmodeisshowninFig. 4.2(b). Apassivequal- ityfactor (Q)of 265,000isobtained from three-dimensional (3D)finite-difference- time-domain (FDTD) calculation. The details of the modeling is reported else- where [MLO08]. Fig. 4.2(a) and (b) shows that most of the field intensity is still within the gain stripe (g) while the QW region overlapping the tail of the mode was intermixed. 4.3 Resultsofquantumwellintermixing Photoluminescence (PL) measurements were first done to check the intermix- ing results and the resulting spectra are plotted in Fig. 4.3(a). In the regions where the sample surface was exposed during ion implantation, the PL peak is blue-shifted about 90nm with respect to the area where ions were blocked by the SiN x . The PL intensity in the intermixed area is also eight times smaller. This is attributed to defects introduced into the QW along with the intermixing. This 90nm PL shift provides a window in wavelength in the 1.55μm band for lasers to operate with only a narrow active region inside the cavities. It is worth noticing that the PL in the ion-free region hasno obvious blue-shiftingandits intensity is slightly higher compared to the PL of as-grown QW. This is attributed to defects formed duringgrowth beingannealedaway. PL in Fig. 4.3(b) was taken close to the interfaces of the gain stripes with different widths, so that both peaks can be identified at the same time. The peak separation decreases as the stripe widths narrows because the lateral diffusion 44 Intensity (a.u.) Intensity (a.u.) QW Photoluminescence Intensity (a.u.) Ion-free As-grown Ion-implanted 90nm 1.3 1.4 1.5 1.6 Stripe width 2µm 1µm 3µm Wavelength (μm) 4µm Figure4.3: (color)PLspectratakenatdifferentregionsontheQWsample. (a)PL spectra of ion-implanted andion-free QW regions after annealing,compared with PL of an as-grown QW reference sample under the same experimental condition. (b)PLtakenatthe transitionregions of gainstripes with different width. of the defects blueshifts the QW in the ion-free stripes and ultimately limits the spatialresolution, which is about2μmin our process. 45 4.4 Improvement in laser thresholds and slope efficiencies These PhC DH cavity pairs (intermixed and non-intermixed) were optically pumpedbyan850nmdiodelaseratnormalincidencethrougha100×IR-corrected objective lens at a substrate temperature of 20 ◦ C. The pulse duration was 8ns under a 0.1% duty cycle and the pump spot size was about 2μm in diameter. Deviceswithgainwidths,g,of4,3and2μmalllase. Duringthemeasurement,the overlap of the pump spot with the field-confining center region of the DH cavities was optimized while the collection setup was not adjusted. Lasing spectra and input-output characteristics of one device pair (g=2μm) are plotted in Fig. 4.4. Lasercharacteristics of three pairsof devices aretabulatedin Table. 4.1. 0.0 0.5 1.0 1.5 2.0 0.0 0.2 0.4 0.6 1.50 1.52 1.54 1 10 100 Pincident=1.22mW Intensity (a.u.) λ (μm) 2μm gain stripe not intermixed Peak Absorbed Power (mW) Intensity (a.u.) Peak Incident Power (mW) slope ratio = 2.37 threshold ratio= 0.63 Figure4.4: (color)Light-in-light-out(L-L)curvesofthePhCDHlaserswith2μm gain stripe and the corresponding non-intermixed reference. Their lasing spectra are shownasinset. 46 Table 4.1: Laser characteristics of three PhC DH lasers of different gain stripe widths (g=4, 3, and 2μm) with their non-intermixed references named (g=∞). Their lattice constants (a 1 ) are 420nm. The ratio is calculated using data from g=4,3,2over data from g=∞ in the table. r/a 1 is computed through top-view SEM images usinganedge detection routine. g r/a 1 λ(nm) threshold threshold slope (μm) P incident (mW) ratio ratio 4 0.310 1527.73 0.22 0.80 2.79 ∞ 0.315 1519.34 0.28 3 0.302 1539.25 0.19 0.77 2.90 ∞ 0.307 1531.84 0.25 2 0.309 1528.60 0.18 0.63 2.37 ∞ 0.313 1523.21 0.30 The comparisons from all three pairs of lasers in Table 4.1. show consistently more than a factor of two increase in the slope efficiencies and a decrease in the threshold pump powers by 20∼37%. All six lasers operate in the wavelength region where the intermixed QW areas are transparent. The slight differences in lasing wavelengths are caused by the slight differences in r/a 1 from device to device. Thisdifferenceinr/a 1 wasverifiedinSEMimagestakenofthecavitiesand is attributed the fact that the two cavity types (disordered and non-disordered) were written atdifferent positions inthe field of view duringe-beam lithography. The data collected indicates that by disordering the gain material around the cavity mode, the absorption loss from the gain material can be reduced. The greater than a factor of 2 increase in slope efficiencies indicates that more than halfofthetotallosswaseliminatedbythisdisordering. Itisstilltruethatabsorp- tion loss in thevertical stripe direction still exists. 47 4.5 Estimationoflaserqualityfactors To estimate the quality factor (Q) from our laser thresholds, we apply a simple model described in Ref. [SKY + 06] to the lasing data of g=3μm laser and its non- disordered pair. We assume an averaged gain region of around 3μm in diameter at the center of the cavities where carriers are uniformly distributed, this leads to an 80% in-plane confinement factor (Γ xy ). 40% of the incident power (P incident ) is calculated to be absorbed by the slab and an 80% internal quantum efficiency (η internal ) [MD96] is used. The result gives device Q of 5,200 and 15,000 for the non-intermixed and intermixed lasers at their lasing thresholds. This improve- ment of about 8,000 in Q is due to the reduced absorption loss in the mirror cladding by QW intermixing. The mode energy that overlaps the intermixed QW regionis0.019ofthetotalenergyofthemode,evaluatedfromthecalculatedmode profiles. AninternalQWabsorptioncoefficientof1,100cm −1 isextractedfromthis data,whichagreeswiththereported value[ZKH + 89]. Byimportingthestructure information from the top view SEM image into 3D FDTD calculation, we get a passive device Q of 75,200. This implies equivalent quality factors of 5,600 and 18,700leftforabsorptionlossinthenon-intermixedandintermixedlasersattheir thresholds. 4.6 Conclusion In summary, we demonstrated PhC DH microcavity QW membrane lasers with a significantly reduced absorption loss using a quantum well intermixing tech- nique to disorder the mirror regions. The slope efficiencies of these disordered devices increased by more than a factor of two and the threshold pump powers were reduced by 20% or more. We believe this result is promising for monolithic 48 integration of PhC microcavity lasers with passive devices and suggests an inter- esting route towards better performance of PhCmicrocavity lasers. Instead of a stripe of QW gain region, we can also make it a square or rect- angularshape, so thatalmost all the absorptionloss canbe removed at threshold andmorethantentimesofincreaseinslopefficiencymightbeobtained. But,bear in mind, all the significant amount of improvement in slope and threshold we got herereliesonthefactthatabsorptionlossdominatesthetotallossfortheselasers (passiveQÀabsorptionQ).Thisisnottrueforcavitieswithintentionallylowered passive Qfor edge-emittion or in-planecoupling. 49 Chapter5 Monolithicintegrationofphotonic crystalnanocavitylaserand waveguidebyquantumwell intermixing Inchapter 2, it was shownthatthe double-heterostructure (DH) nanocavitylaser isanefficienthigh-peak-powerin-planeedge-emitter. Inchapter4,ahigh-spatial- resolution(<2μm)quantumwellintermixing(QWI)processisdevelopedandinte- grated with the DH nanocavity lasers. The obvious extension will be integrating the photonic crystal (PhC) laser with PhC waveguide using the QWI platform, which will be thetarget for this chapter. 5.1 Introduction Twodimensionalphotoniccrystal(PhC)defect-typelasersarecurrentlythesmall- est lasers that are capable of electrical injection, room-temperature continuous wave operation, sufficient in-plane peak power (>500μW) and high modulation bandwidth (10GHz). In this paper, we propose to use quantum well intermixing 50 as the integration platform suitable for these nanocavity lasers; provide cavity- waveguide coupling designs of more than 90% coupling efficiencies and high cav- ityqualityfactors(Qwellabove10 3 )atthesametime;thewaveguidefacetisalso engineered to haveahighlydirectional emission pattern for power collection. 5.2 Choicesofthecavityandtheintegrationplat- form W gain stripe a’ a intermixed region Figure 5.1: Schematic illustration of a PhC DH cavity coupled to an adjacent waveguide. Quantum well intermixing is done to remove the optical absorption except the gain stripe region in pink. The DH cavity is 60 ◦ tilted away from the horizontalwaveguidenexttoitinorder fortheDHmode tailtooverlapthesingle line defect waveguide and achieve optimal coupling. The perturbed lattice con- stant (a’) is drawn in black and the rest PhC has a lattice constant of a, which is 5%smaller thana’ inour design. In order to have the most efficient cavity-waveguide coupling, one wants to start with a cavity with a passive Q as high as possible, then increase the opti- cal loss by channeling all the optical power into the adjacent waveguide. PhC 51 double-heterostructure (DH) nanocavity is the cavity of choice for its high Q and small mode volume. Using DH membrane nanocavity, we have already demon- strated high peak power edge-emitting lasers [YMO + 07, LMY + 09] and improve- mentinlaserperformancebyremovingtheopticalabsorptionlossusingquantum well intermixing(QWI)[LMB + 08]. QWIisamore suitablemonolithic integration platform for PhC nanocavity lasers over the previous used regrowth approach [NWB08, WB08]. The regrowth method suffers from difficulties in the second growth such as abrupt hetero-interfaces and low spatial resolution. Figure 5.1 illustrates the proposed integration scheme. The gain stripe containing original QWs goes through the center of the cavity, where the high-Q mode is confined, to supply optical gain. TheQWs inthe rest of the areaare intermixed. 5.3 Cavity-waveguidecouplinginfrequency The cavity-waveguide coupling occurs in both frequency and space. Figure 5.2 plots the frequency lineup between the DH cavity and a single-line-defect (W1) WG. A regular DH cavity, w=1.00( p 3a), has its high-Q resonant mode frequency bounded just below the bandedge of the WG dispersion, thus the coupling will not happen. Squeezing the cavity width (w) pushes the resonant frequency up intotheguidingbandoftheWG.Whenw=0.90( p 3a),thecouplinghappensatthe linear range of the WG dispersion. In this chapter, we squeeze the width to be w=0.95( p 3a) so that the farfield from the WG exit can be easily engineered to be highlydirectional,whichisdesiredforpowercollectionduringlabdemonstration. The coupling is not sensitive to these slight changes in the cavity width. This flexible tuning of the DH cavity frequency in this design is an advantage over otherproposeddesigns,whichinvolvethemodificationoftheWGinordertoalign the frequenciestogether. 52 0.0 0.2 0.4 0.6 0.8 1.0 0.24 0.26 0.28 0.30 0.32 0.34 0.24 0.26 0.28 0.30 0.32 0.34 Cavity frequency w=0.90 w=0.95 w=1.00 Waveguide dispersion Frequency (a/ ) Wavevector (2 /a) Figure 5.2: Dispersion relation of a regular W1 PhC waveguide. The resonant frequencies of the DH nanocavity with different defect waveguide width (w) are plotted as lines. The waveguide modes are plotted in red lines. The filled gray areais PhCcladding modes. The filled yellow areaare inside the lightcone. 5.4 Cavity-waveguidecouplinginspace 1 2 3 4 6 5 7 9 8 1E2 1E1 1E0 x y |H z | Figure 5.3: H z field component of the DH mode at the center of the membrane. NinedifferentWGstartingpointsarelabeled from1to9. Theinterfacesbetween semiconductor and air are outlined in gray. The central perturbed lattice (5% increase) region is outlined inlighter gray. 53 1 2 3 4 5 6 7 10 3 10 4 10 5 Q Q Q Q Q Q Q Quality factor (Q) Position label 0.5 0.6 0.7 0.8 0.9 1.0 Coupling efficiency ( ) Figure 5.4: 3D FDTD calculations of different cavity-WG coupling geometries. The Q factors of the DH mode and the coupling efficiency into the WG are plotted versusWG startingpositions. Spatial placement of the WG with respect the cavityneeds to be optimized for thecouplingefficiencybetweenthem. Thepreviousstudiesshowthattheoptimal coupling takes place when the WG approaches the cavity in the direction where thecavitymode is mostlyextended inspace [FWE + 07,KLSN04,NWB08]. InFig. 5.3, the DH mode profile is plotted in a log scale and nine candidate positions for the starting point of the WG are labeled. The performance of coupling is numer- ically evaluated for all nine positions using three-dimensional finite-difference- time-domain (3DFDTD) method. The coupling efficiencies andthe corresponding Q values are plotted in Fig. 5.4. As the WG approaching the field maximum of the cavity mode, optical loss into the WG increases and cavity Q decreases. The difficultyinthecouplingdesignliesinthesimultaneousrealizationofhighcavity- WG coupling efficiency and high cavity Q values. Figure 5.4 shows high coupling efficiency (above 90%) and high cavity Q (well above 1,000) for coupling position at 4, 5, 6 and 7. The cavity Q values of position 8 and 9 are below 1,000 and the 54 resonancesareburiedamongthesurroundingones inthecalculatedspectra. The performance of our designsurpassesthe previously reported ones andcanstill be improved by a more detailed engineering of the joint region between the cavity andWG. 5.5 Directionalemissionfromwaveguidefacet 10E0 10E1 10E2 10E3 x z (b) |H z | x y (a) Figure 5.5: H z field profiles of the coupling configuration of coupling position 5. (a) Field distribution in the x-y plane at the center of the membrane. (b) Field distributioninthex-zplanethroughtheWGcenter. Theinterfacesbetweensemi- conductorandairareoutlinedingray. Thecentralperturbedlattice(5%increase) region is outlined in lighter gray. 55 DirectionalemissionoutofaPhCWGhasrecentlybeensubjecttoheavyinves- tigation, which is very important for in-and-out coupling of PhC devices. Tak- ing advantage of the surface modes at waveguide termination is an interesting approach to obtain a far-field of low divergence; but this approach works in a very narrow bandwidth and are extremely sensitive to the surface termination [KAS + 04, MGVMM04]. Building on 2D ideas in Ref. [Kur09], we enlarge the waveguide core at the exit. The field inside interferes and emits directionally. 3D calculations verify that it works for the membrane structure with a larger band- width andis robustwith respect to facettermination. Figure 5.5 shows the field profile of the cavity-WG geometry of coupling posi- tion 5 with a directional farfield. Using a lens whose numerical aperture is 0.65, thecouplingorcollectionefficiencyfromthecavitytothelensisabout38%. Thisis evenhigherthanourbestreportednumber[LMH + 09]. Thisnumberisboundedby thecoupling efficiencybetween thecavity-WGandissolely limited bythediffrac- tioninthedirectionperpendiculartothemembraneasshowninFig. 5.5(b). Com- pared to our previous experimental results [LMH + 09], more than 1mW of peak power is expected to be coupled into the WG with quantum differential efficiency above70%. 56 Chapter6 Gaincompressionandthermal analysisofasapphire-bonded photoniccrystalmicrocavitylaser Gain compression factor and thermal properties of a photonic crystal microcavity laserbondedonasapphiresubstrateareextractedbyanalyzingwavelengthshifts under different duty cycles. A high thermal resistance of 43K/mW and a gain compression factor of 1.2×10 −16 cm 3 are obtained. 6.1 Introduction A room temperature (RT) two-dimensional photonic crystal (PhC) microcavity laserwith highmodulation bandwidthis agood on-chipsource candidatefor pho- tonic integrated circuits. However, poor heat dissipation prevents most of those lasers from RT continuous wave (CW) operation [HRS + 00, NKB07]. (Fig. 6.1 are SEM images showing a melted InGaAsP membrane PhC device after being pumped by a few milli-watts of CW power at 850 nm under room temperature.) In addition, gain compression is a very important factor in high speed lasers [LLTW09]. Gain compression is well known to damp the relaxation oscillations and limit a laser’s bandwidth. The introduction of a sapphire substrate allowed our PhC microcavity lasers to operate under RT CW conditions [CKW + 05] and achieve a direct modulation bandwidth of more than 10GHz [BSW + 06, BSC + 08]. 57 In this paper, we extract coefficients related to the thermal properties and gain compression factorbyanalyzingthewavelengthshiftsundervariousdutycycles. (a) (b) Figure 6.1: (a), (b) SEM images showing a melted InGaAsP membrane PhC device after being pumped by a few milli-watts of CW power at 850 nm under room temperature. 6.2 Measurementofwavelengthshift 1.0kV 3.4mm x20.0K 20° lt 2.00μm Figure6.2: SEM imageof a fabricatedD4cavityon asapphire substrate. Figure 6.2 is a scanning electron microscope (SEM) image showing a finished device patterned on a 240nm thick InGaAsP membrane bonded on a sapphire substrate. These cavities were formed by removing four periods of air holes in a hexagonal shape (D4 cavity) in the otherwise perfect trigonal PhC lattice. The 58 × × × × × × (a) (b) Figure 6.3: (Color) (a) Wavelength v.s. pumping power of the same lasing mode under different duty cycles. L-L curve under CW condition is also included. (b) CWlasingspectra under variouspumpinglevels andthe photoluminescence (PL) of gainmaterial atlow bias. membrane waveguide was grown by metal-organic chemical vapor deposition. It contains four 0.6% compressively strained 10nm thick InGaAsP quantum wells (QWs),whoseemissionwavelengthisnear1.55μm,and20nmthickInGaAsPbar- rier layers between the QWs, whose emission wavelength is 1.25μm[MD96]. The 59 fabricationprocesses, characterization setup are detailed in the previous publica- tions [CKW + 05, SKY + 06]. An 852nmdiode laser is used to pump the device with about 2μm spot size. Its pulse width (t 1 ) was fixed at 8ns. A cavity with 390nm lattice constant and 0.355 hole radius to lattice constant ratio was used in this studyandallthe measurements were done ata21 ◦ C substratetemperature. The wavelength is monitored in an optical spectrum analyzer with 0.1nm resolution bandwidth. The CW light-in-light-out(L-L) curve in Fig. 6.3(a)starts to roll over at about fourtimestheCWthreshold. Theblueandredshiftsoftheresonantwavelengths, illustrated in Fig. 6.3(a), as a function of pump power are a result of increas- ing carrier density and increasing device temperature which move the refractive index in opposite directions. Processes such as thermal expansion [LCC + 02] and thermal strain induced index change [JvDvEW98] are negligible compared to the two mentioned. Below threshold, the increase of carrier density is dominant and the wavelengths blueshifts; above threshold, the wavelength shifts from carrier density and device temperature are comparable. The laser redshifts under CW condition and blueshifts under pulsed conditions, since device heating is allevi- ated as the duty cycle decreases. For the same reason, laser threshold decreases with thedecrease of dutycycle. Theexistenceoftheblueshiftabovethresholdisasignthatthecarrierdensity is not clamped and is modeled through gain compression. This can be verified by the growing intensity of spontaneous emission with increasingpump power away from the lasing wavelength above threshold shown in Fig. 6.3(b). Low intensity PLof the QW is alsoplotted for comparison. 60 6.3 Modelingofwavelengthshift In order to quantify the contribution to the wavelength shift from both tempera- ture (T)and carrier density (N)in Eq. 6.1 Δλ=(∂λ/∂n)[(∂n/∂T)ΔT+(∂n/∂N)ΔN], (6.1) the device heatingwas modeled analogouslyto anRC circuit andthe carrier den- sityismodeledusingthephenomenologicalparameter(ε),knownasthegaincom- pression factor. Here n is the refractive index of the semiconductor slab. The coefficients ∂n/∂T (2.5×10 −4◦ C −1 ) and ∂n/∂N (−1.63×10 −20 cm 3 ) can be found in Ref. [CCK08] and [Web94], respectively. ∂λ/∂n is estimated through numerical modeling insection 6.4. 0 t 1 t T 0 T’ qR th Time Temperature T 1 τ C τ D Hea ng pulse (Duty cycle=t 1 /t) Figure6.4: Illustrationof the “RC circuit" thermal model. Figure 6.4 illustrates our analytical thermal model. The device temperature is "charged" and "discharged" with time constants (τ C ) and (τ D ) by the heating pulse qR th ,whereR th isthethermalresistanceand q istheheatfluxfrom photo- pumping. It is assumed that all non-radiative recombination contributes to heat. The radiative efficiency is estimated to be 64% below threshold and 95% above threshold [LMY + 09]. The average temperature increase canthus be expressed in Eq. 6.2 as a function of absorbed pumping power and duty cycles (dc) at steady state when T 0 equals T 0 . 61 ΔT average =qR th [1+(τ C /t 1 ) 1−e (1/dc−1)(t 1 /τ D ) e (1/dc−1)(t 1 /τ D ) −e (−t 1 /τ C ) (1−e −t 1 /τ C )] (6.2) The increase of the carrier density above threshold can be found by equating QW gain (g) to the total optical loss which was assumed to be a constant above thresholdforalldutycycles. TheQWgainasafunctionofcarrierdensityandpho- ton density(N p ) is expressed as g(N,N p )=g 0 ln(N/N transparency )/(1+εN p ). Thus ΔN slab = f QW ΔN QW = f QW [N threshold (e εN p ln(N threshold /N transparency ) −1)], (6.3) where f QW is a conversion factor from QW carrier density to the averaged carrier density in the semiconductor slab. Since the carrier density inside the QWs are higherthanthatinthe barriers, f QW is less than1. Equations6.1-6.3withtheassumptionsofconstantN threshold andεforallduty cyclescompleteourmodel. τ C ,τ D ,R th ,εand f QW canthusbedeterminedbyfitting all fivecurves of wavelengthdatain Fig. 6.3(a)simultaneously. 6.4 3DFDTDsimulation Thethree-dimensionalfinite-difference-time-domain(3DFDTD)methodwasused to model the electromagnetic field in this cavity. Mode identification was carried outthesamewayasthatinRef. [SBM + 07]. Themid-planefielddistributionofthe lasingmode is plotted inFig. 6.5. The passivequalityfactor (Q)is1,732,which is in reasonable agreement with the estimated Q value (1,250) from threshold car- rier density [SKY + 06, LMB + 08] considering the imperfections in fabrication and 62 x y (a) H z -40 0 40 80 (b) x z Sapphire (n=1.74) Air Figure6.5: (Color)H z fieldcomponentofthelasingmodecalculatedby3DFDTD. (a) field distribution in x-y plane at the mid-plane of the membrane. (b) field distribution in the x-z plane through the center of the cavity. The air hole and membrane edges are outlined in gray. optical absorption loss [LMB + 08]. The mode volume is evaluated to be 17.8(λ/n) 3 [PLS + 99],wherenis3.4inthecalculation. Inordertoobtain∂λ/∂nforthismode, we varied, in the simulation, the refractive index of the slab at the center region ofthecavity. Thediameterofthisregionis3μm. Bymonitoring thelinearshiftof the resonantpeak withthe changeof the index,we get210nmfor∂λ/∂n. 63 ° (a) (b) Figure 6.6: (Color) (a) Experimental wavelength data fitted by our model. (b) Carrier density andtemperature behaviorsasaresult of the fit. 6.5 Resultsofdatafitting Our model provides a good fit to the experimental wavelength data as shown in Fig. 6.6(a). Figure6.6(b)plots,accordingtothefit,bothcarrierdensityanddevice temperatureasafunctionofpumppowerforalldutycycles. WhentheCWpump- ing level exceeds four times the CW threshold where the CW L-L curve is begin- ningtorollover,therateofblueshiftismuchfasterthanwhatthemodelpredicts. This indicates a different mechanism responsible for the rapid growth of carrier 64 density at about 32 ◦ C above room temperature and is likely due to the increase of nonradiative recombination rates and the decrease of QW gain with the rise of laser temperature. The standard deviation of the fit, excluding this high CW bias region, is 0.1nm. The results of the total number of five fitting parameters are listed in Fig. 6.6(a). A very high thermal resistance of 43K/mW is obtained due to localized heating and insufficient heat dissipation. The gain compression factor of 1.2×10 −16 cm 3 agrees very well with the reported and predicted values for strained QWlasers [WTA92,SYY + 93,GDG + 95]. 6.6 Conclusion We measured, under variousduty cycles, thewavelength behaviorsof asapphire- bonded RT CW QW PhC microcavity laser. Changesin carrier density and device temperature from photo-pumping are responsible for the wavelength shifts. We modeled carrier density above threshold with gain compression factor and device temperature through an RC circuit analogy. Fitting the data using our model provides boththermal properties andgaincompression factor of the laser. In much of the literature, it is a common practice to get thermal resistance of a laser from its wavelength shift above threshold [SMB + 07, SYL + 09]. This is valid if, above threshold, carrier density clamps at the threshold value, which means there is no gain compression. This is also a good approximation, when the thermalresistanceissolargethattheindexchangefromgaincompressioncanbe neglected. 65 Chapter7 Spacegroupanalysisof two-dimensionalphotoniccrystal waveguides In this appendix, we will analyze the two-dimensional photonic crystal (PhC) waveguides using space groups. This study is motivated by the fact that the waveguide dispersion curves are always double-degenerate at the Brillouin edge [Ben96,KO04], which canbepredicted bygrouptheory. Two-dimensional (2D) PhC slab waveguides are important building blocks for photonicintegratedcircuitsfortheircompactsize,lithographictunabilityandlow bending-loss and so on. The 2D PhC patterns make it compatible with the layer- by-layer fabrication process for planer lightwave circuits. They’re also attrac- tive for generating slow light and enhancing light-matter interactions. But the spacesymmetryofthe2DPhCwaveguideshavenotbeensystematicallyexplored. Group theory [Tin64] has been used in PhC research to understand and classify the modes [Sak05, ON04, KCY + 05, KL03]. The previous literature, however, all focusedonthepointgroupswhicharesubgroupsofthespacegroups. Inthischap- ter,we’llexaminethesymmetrypropertiesoftwo-dimensionalPhCwaveguidesin thecontextofspacegroupsandespeciallythenon-symmorphicspacegroupofthe type B waveguide. 66 7.1 Frieze groups: the space groups of 2D PhC waveguides Space groups [BG90], consisting of point groups and translation groups, can be described by the Seitz operator {R|t} defined by a point operation R followed by a translation t. Itoperates onanarbitraryposition vector r as{R|t}r=Rr+t. Fora Bravais lattice, its space group involves all the translations of the lattice vectors thatare linear combinations of the primitive lattice vectors. But this space group mayalsoinvolveatranslation(τ)smallerthanaprimitive latticetranslationcou- pledwitharotationorreflection. Theseoperationsareknownas“screwrotations” and “glide reflections”. A space group is “non-symmorphic” if it contains screw or glide operations, otherwise it’s “symmorphic”. A screw rotation, whose transla- tion is parallel to the rotation axis, does not exist when space-dimension is lower than three. Glide reflection is the only “non-symmorphic operation” in the two- dimensional (2D)space group. Crystallographic space groups of 3D lattices have 73 symmorphic groups and 157 non-symmorphic groups. 2D space groups, also named wallpaper group, has 13symmorphicgroupsand4non-symmorphicgroups. Spacegroupof2Dpatterns containing only 1D translation, named Frieze groups, have 5 symmorphic groups and 2 symmorphic group. The space groups of 2D PhC waveguides are Frieze groups. InFig. 7.1,thetotalnumberofsevenFriezegroupsarelabeledandillustrated using simple examples [Mir99]. The symbols for the group starts with “F” as in Frieze. The number “1” and “2” refers to the rotation operator C 1 and C 2 . “m” indicatestheexistenceofamirroroperationand“g”meansaglideoperation. The spacegroupoftypeAwaveguideisF 2mm (symmorphicgroup)andthespacegroup of type B waveguide is F 2mg (non-symmorphic group). 67 F 1 F 11m F 2 F 1m F 2mm F 11g F 2mg Figure7.1: ThesevenFriezegroups[Mir99]. F 11g andF 2mg arenon-symmorphic groups containingglide reflections. Therest are symmorphic. Inthefollowingtwosections,wewillanalyzethetypeAandtypeBPhCwaveg- uides using the Frieze groups F 2mm and F 2mg . We choose to work on these two group because they’re the symmorphic and non-symmorphic Frieze groups of the highestsymmetry. TheremainingfiveFriezegroupscanbeconstructedbyremov- ing one or two symmetry operations from them. The results can be applied to 2D PhCslabstructures withtop and bottom claddings. 7.2 Symmorphic space group of Type A PhC waveguides The symmorphic space group of the dielectric structure of the type A PhC waveg- uide F 2mm is isomorphic to the direct-product (⊗) of a translation group and a point group (T na ⊗C 2v ). The translation group T na ={E|na} is Abelian and has onlyone-dimensionalrepresentationswhicharejustcomplexnumbers. Sowecan always analyzethe point groups alone for symmorphic space groups. In the Seitz operator, E is aunityoperator, n isanarbitraryintegerand a isthelatticevector 68 σ x σ y Type A 0 x y C 2 a Figure7.2: Illustration of atype A PhCwaveguideand itssymmetry operations. illustratedinFig. 7.2. ThepointgroupisC 2v =(E,C 2 ,σ x ,σ y )asillustratedinFig. 7.2,whereσ isthe reflection operator. The point group of wavevectors (k), also known as the “little group", consists of point group elements that transform k into itself or an equivalent point that is connected by reciprocal lattice vectors. It is denoted as G k and is a subgroup of the point group. In the case of type A waveguide, G k is a subgroup of C 2v . At theBrillouin zonecenter andedge,G k=0 =G k=π/a =C 2v . For “general" k points insidetheBrillouinzone,thepointgroupisG 0<k<π/a =C 2v =(E,σ y ). Thecharacter table of the point group C 2v and C 1h is shown in Table 7.1 and Table 7.2. Their compatibility relation is evident from the eigenvalues of the σ y operation. The dispersion curves of the type A waveguide are assigned to the representations in the character tables in Fig. 7.3, according to the H z field components of the waveguidemodes. Theseeigenmodesareirreduciblerepresentationsofthegroup. Table7.1: Charactertable of C 2v point group. C 2v (2mm) E C 2 σ x σ y A 1 1 1 1 1 A 2 1 1 -1 -1 B 1 1 -1 1 -1 B 2 1 -1 -1 1 69 Table7.2: Charactertableof C 1h point group. C 1h (m) E σ y A 1 1 B 1 -1 B 2 A 1 B 2 B 1 A 2 A B 1 A A B B Figure 7.3: The dispersion diagram of the air-clad membrane type A waveguide (Courtesy of Adam Mock). The representations are assigned according to the H z field component of thewaveguide mode profiles. Becauseall therepresentations ofC 2v areone-dimensional, thereis nodegen- eracy imposed by symmetry. The crossing of waveguide modes “A” and “B” in the middle of the TEbandgapis accidental. 70 m g Type B 0 x y c a Figure7.4: Illustrationof a type Bwaveguide andits symmetry operators. 7.3 Non-symmorphic space group of Type B PhC waveguides The symmetry operations of type B waveguide illustrated in Fig. 7.4 are e, c, m and g,where e = {E|0}, c = {C 2 |0}, m = {σ x |a/2}, g = {σ y |a/2}. (7.1) The coordinate origin is choosen at the center of the C 2 rotation, so it is quarter- lattice-constantshiftedawayfromalatticepointalongthexdirectionatthecenter ofthedefectregion. Themirroroperationσ x isthusnotwithrespecttothevertical line throughthe origin. The g operator is the glide reflection. Being different from the type A case, these non-translation operations (e,c,m,g) do not form a group due to the existence of the glide operation. For example, g 2 ={E|a} becomes a pure translation. So we couldn’t express the non- symmorphic group asthe direct-product of atranslationgroup anda point group. 71 Furthermore, the translation group, T na ={E|na}, has an infinite number of ele- ments. Fortunately,itisaninvariantsubgroup(normaldivisor),andwecandivide itout. Theresultingfactorgroupcanbeanalyzedwithafinitenumberofelements andis homomorphic to the original space group[Her42]. At k = 0, the whole translation group T na = {E|na} is the normal divisor, since e k×na = e 0×na =1. The factor group F 2mg /T na =(eT na ,cT na ,mT na ,gT na )= ({E|na},{C 2 |na},{σ x |a/2+na},{σ y |a/2+na})wheretheelementsofthefactorgroup arecosetsofthenormaldivisor. Thisfactorgroupisisomorphictothepointgroup C 2v andthecharactertableislistedinTable7.3. TherepresentationsinTable7.3 are all one-dimensional. Therefore one expects the type B waveguide bands to be nondegenerate at k=0. Table7.3: Charactertableof the factor groupof F k=0 2mg /T na . F k=0 2mg /T na eT na cT na mT na gT na Γ 1 1 1 1 1 Γ 2 1 1 -1 -1 Γ 3 1 -1 1 -1 Γ 4 1 -1 -1 1 At k=π/a, the translation group T 2na ={E|2na} is the normal divisor, since e k×2na = e π/a×2na =1. Then the factor group F 2mg /T 2na =(e 0 ,e 0 ,c 0 ,c 0 ,m 0 ,m 0 ,g 0 ,g 0 ) [Hei60,Fal66]. It haseight elements andtheyare 72 e 0 = {E|2na}, e 0 = {E|a+2na}, c 0 = {C 2 |2na}, c 0 = {C 2 |a+2na}, m 0 = {σ x |a/2+2na}, m 0 = {σ x |a/2+a+2na}, g 0 = {σ y |a/2+2na}, g 0 = {σ y |a/2+a+2na}. (7.2) This factor group is isomorphic to the point group C 4v and the character is shownin Table7.4. There arefour one-dimensional representations andone two- dimensional representations. For a Bloch wave representation at Brillouin zone boundary(k=π/a),onelatticevector{E|a}translationchangestherepresentation by a minus sign (e k×a = e π/a×a =−1). The only representation that changes the sign for the characters between e 0 ={E|2na} and e 0 ={E|a+2na} is K, the two- dimensional one. K is thenthe onlycompatible representation at k=π/a. Table7.4: Charactertableofthefactorgroupof F 2mg /T 2na . Thetwo-dimensional irreducible representation (K) isalso shownin the unitymatrixform. [Cra74] F 2mg /T 2na e 0 e 0 c 0 ,c 0 m 0 ,m 0 g 0 ,g 0 1 1 1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 1 -1 -1 1 K 2 -2 0 0 0 µ 1 0 0 1 ¶ µ -1 0 0 -1 ¶ µ i 0 0 -i ¶ µ 0 1 -1 0 ¶ µ 0 i i 0 ¶ 73 Since K is a 2D representation, it explains the double-degeneracy of all the typeBwaveguidedispersionsattheBrillouinzoneboundary. This“bandssticking together" effect is associated with the glide reflection symmetry that makes the space group non-symmorphic. The dispersion curves of the type B waveguide are assigned with representa- tions in the character tables in Fig. 7.5, according to the H z field components of thewaveguidemodes. TherepresentationforageneralpointintheBrillouinzone is trivial andnotlabeled. The 2-by-2unity matrix irreducible representation of K at the bottom of table 7.4revealstherelationbetweenthereal-spacefielddistributionsofthetwodegen- eratemodeatBrillouinzoneedge. Theoperators(m,m 0 )and(g,g 0 )transformone mode to the other withonly extra phasefactors (-1or i)while the dielectric struc- ture remains the same after these operations. This implies they share the same frequencyandare, thus,degenerate atthe Brillouin zoneboundary. At last,thewaveguide dispersions of six different PhCwaveguidesare plotted in Fig. 7.6. 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High efficiency operation of butt joint line-defect-waveguide micro- laser in two-dimensional photonic crystal slab. App. Phys. Lett., 93(8):081109,2008. 87 [Zho06] Weidong Zhou. Encapsulation for efficient electrical injection of photonic crystal defect mode surface-emitting lasers. Applied PhysicsLetters,88(5):051106,2006. [ZZB05] J.F. Ziegler, M. D.Ziegler,and J.P.Biersack. SRIM-2003,2005. [ZKH + 89] E. Zielinski, F. Keppler, S. Hausser, M. H. Pilkuhn, R. Sauer, and W.T.Tsang.Opticalgainandlossprocessesingainasinpmqwlaser structures. IEEEJ.QuantumElectron.,25(6):1407–1416,1989. 88 AppendixA Photoniccrystalsurfacemodesin Γ−Mdirection The assumption of infinite periodicity is only in theoretical models. At the inter- face where the lattice stops, there exists surface states [MBRJ91, RAM + 93]. This study is motivated by the surface wave existing at the facets of the edge-emitting lasers inChapter 2. In a photonic crystal of triangular lattice, the high symmetry points in the reciprical space are Γ, M and K. Surface waves along Γ−K direction has been alreadystudiedinanumberofpapers[YKK + 04,CTP06,LHHL09],butadetailed calculation of the surface modes along theΓ−M direction has not been reported. Γ−M is the direction most PhC waveguides are terminated because it is perpen- dicular to regular PhC waveguides alongΓ−M. Experimental study of PhC crys- tal devices always involve light coupling via waveguide facets along the Γ−M direction; and the surface states have a significant influence on both coupling efficiencies [DBdS + 06] and collection efficiencies [MGVMM04, KAS + 04]. In this appendix,thesurfacestatespropertieswillbecalculationfortheair-claddedsemi- conductor membrane by3D FDTD. As shown in Fig. A.1, we can terminate the 2D PhC lattice on the right and the air holes in the other directions repeat forever. Surface modes in this case are modes bounded from both left and right sides. On the right, it’s confined by total-internal-reflection between semiconductor and air interface; on the left, it’s confined by the photonic band gap. Thus, the surface modes is similar to PhC 89 0 1 2 3 Γ Κ Μ τ FigureA.1: IllustrationofthefacetterminationparameterτalongΓ−Mdirection inthetriangularlattice. ThePhClatticeisterminatedontherightandisinfinite on theright andvertically. waveguide modes [KCL + 07] and their properties can be engineered by modifying the surfacegeometries. One of the simplest terminations is to terminate the semiconductor with a straightlineatdifferentpositionsofthelatticeillustratedinFig. A.1. Theparam- eter τ is used to specify the position of the termination which is consistent with the notation in the previous literatures [YKK + 04, LHHL09] but has some differ- ences. When terminating inside an infinite lattice, τ only needs to vary from 0 to 1 due the periodicity of the lattice. Here I have extended τ to 3 by filling the air holes beyond τ=1, so that τ is also meaningful to be extended beyond 1. The only redundant region is τ=[1,1−2r/a] which is still the same as the region of τ=[0,1−2r/a],when r<a/2. Figure A.2 plots the bandstructures alongΓ−M (Fig. A.2(a)) and Γ−K (Fig. A.2(b)) directions. The period inΓ−M direction is sqrt(3)a so the Brillouin zone is shorter than that in Γ−K direction. There is very limited space under the lightline inside the bandgap in Fig. A.2(a). A regular W1 waveguide dispersions are included in Fig. A.2(b). 90 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 0.0 0.1 0.2 0.3 0.4 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.1 0.2 0.3 0.4 (b) Frequency (a/ ) K Wavevector ( /a) M Frequency (a/ ) Wavevector ( / 3a) (a) FigureA.2: Dispersion relation of a triangularlattice PhCfolded alongdifferent periodic directions. (a) Folded PhC dispersion alongΓ−M. (b) Folded dispersion along Γ−K. W1 waveguide modes are plotted in red. In both plots, the shaded gray area are bulk PhC modes and the yellow area is above the light line. Figure (a)and(b)are vertically aligned. 0.7 0.8 0.9 1.0 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.8 0.6 0.4 0.2 0.0 0.22 0.24 0.26 0.28 0.30 0.32 0.34 (b) K Frequency (a/ ) Wavevector ( /a) (a) =1.0 =2.0 =3.0 M Frequency (a/ ) Wavevector ( / 3a) FigureA.3: (a) Surface mode dispersion relations alongΓ−M direction with dif- ferent termination parameters. (b) W1 waveguide dispersion relation alongΓ−K direction. The guided transmission band (underneath the light line) of the main WG mode is highlightedinlight purple. Figure (a)and(b)sharethe same y-axis. Azoomed-inversionofFig. A.2isshowninFig. A.3. Surfacemodedispersions ofdifferentterminationparameters(τ=1,2and3)areplottedinFig. A.3(a). There 91 are two guided surface modes when τ is equal to 3 while there is only one mode inside bandgapfor τ= 1 and 2. In Fig. A.3(b) The transmission bandwidth of the mainwaveguide mode is highlighted. The mode profiles of the surfacemodes at Brillouin zone boundaryare plotted in Fig. A.4. They all localized at the interface bewteen PhC lattice and air. Hz field components are plotted on the whole calculation domain which is one period intheΓ−Mdirection. SincethelengthsofthelatticeperiodsalongΓ−MandΓ−K differ byafactorof p 3whichisnotaninteger,nonuniformCartesiangrid isused in samplingthe geometry [KKO07]. 300 200 100 0 -100 -200 -300 -400 -500 -600 -700 40 30 20 10 0 -10 -20 -30 -40 500 0 -500 -1000 3 2 1 0 -1 -2 -3 τ=1.0 β=/√3a a/λ 0 =0.280 τ=2.0 β=/√3a a/λ 0 =0.270 τ=3.0 β=/√3a a/λ 0 =0.260 τ=3.0 β=/√3a a/λ 0 =0.282 H z H z H z H z FigureA.4: H z field profiles of the surface modes atbandedge with different ter- mination parameters. The interfaces between semicondutor and air are outlined in gray. 92 In order to know how the modes evolve with the termination parameterτ, the modefrequenciesatBrillouinzoneboundaryareplottedwiththechangeofτfrom 0to 3 inFig. A.5. 0 1 2 3 0.22 0.24 0.26 0.28 0.30 0.32 0.34 W1 waveguide transmission band Light cone Dielctric band Air band = a Frequency (a/ ) Figure A.5: Surface mode frequencies versus the termination parameter (τ) at the Brillouin zoneboundary(1× π p 3a ) alongΓ−M direction. 93 AppendixB Digitalimageprocessingin nano-fabrication B.1 Quantificationoffabricationimperfections Improvements in the fabrication can be made only if the imperfections can be evaluated. SEM images are one of the most common ways to check the quality of the fabrication. This section shows how the imperfections in the fabricated PhC lattice canbe quantifiedbyanalyzingthetop-view SEM images of the device. 1. Take a top-view image. The x-y ratio in the SEM can be checked by mea- suringthesameobjectagainafterphysicallyrotatingtheobjectby90 ◦ . The brightnessandcontrastshouldnotbetunedmuchawayfromtheautomated values when saving an image: radius-over-lattice-constant value changes with brightness and contrast. This could be understood by looking at the histogramsof the images. 2. Edge detection. After cropping the information bar in the image if it exists, theedge-detectionalgorithmofCanny’smethodisusedtofindthemaximum localgradientofthegray-scaleSEMimage. Themaximumshouldhappenat thesemiconductor-airinterfaces;athresholdcanbedefinedwiththeCanny algorithm to filter out thelow-contrast objects. 3. Select the closed objects. If all the pixels at the peripheries of a air-hole are detected, this object is closed and well-defined. Closed objects are filled; the 94 (a) (b) +3% +2% +1% 0% -1% -2% -3% (c) (d) Figure B.1: (a) A top view SEM image of triangular PhC lattice patterned on a silicon membrane. Courtesy of Stephen Farrell. (b) Illustration of the analysis. The detected air-semiconductor interfaces are outlined in green. The centers-of- mass of the air-holes are labeled by red crosses. The lattice points are connected by yellow lines vertically and by cyan lines in other directions. (c) The closed objectsarefilledwithwhitecolor. (d)Theequivalentradiioftheclosedobjectsare color-coded byhow much they deviate from the averagevalues. open ones are removed along with the partial holes close to the boundaries of the image. 4. Analyze the structure. The radius of every air-hole is calculated from the area. The lattice points are defined by the centers-of-mass of the holes. In order to find all the lattice constants,all non-repeating pairs are connected. All the lengths are sorted and they increase in steps like a, 2a, 3a and so on. The ratio of the neighboring lengths are compared to a threshold value 95 between1and2tofindthefirsttransitionpointfromato2a. Lengthsabove thispoint are deleted. The datainTableB.1canthenbe obtained. Parameter Averagevalue Standarddeviation r/a 0.295 2.548% a 64.856pixels (429.0nm) 2.19% ax 65.476pixels (433.1nm) 1.91% angleof ax 29.069 ◦ ay 63.627pixels ( 420.9nm) 1.28% angleof ay 88.660 ◦ ax/ay 1.029 0.569% r 19.130pixels (126.5nm) 1.31% Eccentricity 0.319 0.1724% Table B.1: Statistics of the 281 air-holes defined in the SEM image in Fig. B.1. “r” is the radius of the air hole. “a” is the lattice constant, where “ax” are the horizontal ones in cyan and “ay” are the vertical ones in yellow shown in Fig. B.1b) B.2 Sub-pixel alignment in electron-beam- lithography Accuratealignmentinelectron-beam-lithography(EBL)isindispensablefornano- scale device fabrication. Correlation technique has been recognized as one of the best alignment methods for its high immunity to noise, poor contrast and mark imperfection. B.2.1 Correlationtechnique The purpose of the alignment is to determine the position of a known mark and exposenewpatternssomedistanceawayfromit. Correlationisacommonmethod to evaluate the similarity between two patterns. Equation B.1 defines the dis- crete correlation function between two 2D functions f(i,j) and w(i,j). Corr(x,y) 96 is called auto-correlation when f and w are thesame functionand iscalled cross- correlation otherwise. The correlation function peaks at the position that two patterns are best matched. This can be understood by writing the correlation as part of the least square function of f and w in equation B.2. When the difference betweenthetwopatterns(f andw)areminimized,theircorrelationismaximized. Corr(x,y)= i=M X i=1 j=N X j=1 f(i,j)w(i+x,j+y) (B.1) LS(x,y)= i=M X i=1 j=N X j=1 f(i,j)−w(i+x,j+y)) 2 = i=M X i=1 j=N X j=1 f(i,j) 2 −2f(i,j)w(i+x,j+y)+w(i+x,j+y) 2 =constant−2Corr(x,y) (B.2) In e-beam alignment, an SEM image of the sample containing the alignment mark is cross-correlated to an ideal mark image. The coordination of the mark is determined by the correlation maximum. The fabricated alignment mark has imperfectionsorevenpartialdamage. Dependingonthematerialandthewaythe markisdefinedonthesample,thecontrastandthenoiseleveloftheSEMvaries. As aresult, afalsemaximum may showup. The shape of the correlation function is pattern dependent. A good alignment mark for the correlation method should have a high side-lobe suppression ratio and a sharp peak. The ideal auto-correlation function will have minimal ampli- tude everywhere when the patternis not alignedwith itself. 97 B.2.2 Barkersequencesandarrays Binary sequences and arrays whose out-of-phase aperiodic auto-correlations are collectively small are particularly useful in digital communication systems espe- cially synchronization. The finding of the optimal binary patterns is an engineer- ingproblemaswellasamathematicalone. ThissearchwasstartedbyBarkerfor one-dimensional binary sequences [Bar53]. The Barker’s sequence is a string of a i =±1 of length l≥2 such that| P l−x j=1 a j a j+x |≤1, for all 1≤x<l. All the known Barker’s sequences are listed in Table ??. It is conjectured that no more of them exists. The auto-correlations of the three longest Barker sequences are plotted in Fig. ??. Length Codes 2 +1 -1 +1 +1 3 +1+1 -1 4 +1+1 -1+1 +1 +1+1 -1 5 +1 +1+1 -1+1 7 +1 +1+1 -1-1+1-1 11 +1 +1+1 -1-1-1+1 -1-1+1-1 13 +1+1 +1+1+1 -1-1+1 +1-1+1-1 +1 TableB.2: Table of all Barker sequences found. It is conjectured that no more of them exists. As2Dpatternsareneededinthealignment,theEBLcommunityusespatched Barker sequences of length 11 in 2D [HJA81, BK90, AHL04]. The construction andauto-correlation of this patternare shownin Fig. B.3 This patched pattern is certainly not an optimized one havingminimum side- lobecorrelation. Two-dimensionalbinaryarrayssatisfyingtheBarkercriteriaare called Barker arrays. Unfortunately, it has been recently proved [DJK + ] that an s×t Barkerarraywith s,t>1 existsonly when s=t=2,    1 1 1 −1    98 −10 −5 0 5 10 −2 0 2 4 6 8 10 12 14 Auto−correla on of Barker sequences 7 11 13 FigureB.2: Theauto-correlations of the three longest Barkersequences. ++ + -- - + - - + - + ++ + - - ++++ + - + ++ + - - ++++ + - + ++ + - - ++++ + - - ++ + -- -- --- - - ++ + -- -- --- - - -- -- - - + - - + - + ++++ + - + - - + - - -- -- - - + - - + - - -- -- - - + - - + - + ++++ + - + - - + - - -- -- --- -- - - −10 0 10 −10 0 10 0 50 100 Auto−correla on (a) (b) Figure B.3: (a) The 2D binary pattern patched from Barker sequence of length 11. (b) The auto-correlation of (a). The highest peak has a value of 121 and the second peak hasavalueof 46. 121/46=2.6304. which was conjectured in 1989 [AS89]; the conjecture that there are no Barker arrayshavingmore thantwo dimensions was alsoproved [JP07]. B.2.3 Aperfectbinaryarray Barkersequencesandarraysare definedbytheir aperiodic auto-correlation func- tion. If this is relaxed to be periodic auto-correlation function, binary arrays can 99 be found whose out-of-phase values are all zero. For a binary array f(i,j) with size N x by N y , this condition is express as P N x i=1 P N y j=1 f(i,j)f(i+x,j+y)=0 for all x and y, where i+x and j+y are calculated mod of N x and N y respectively. They arecalledperfect binaryarrays[BA90]. Thoughtheperfect correlationproperties can only be achieved when the pattern is periodic which is not realistic in EBL, the perfect arrays still have low out-of-phase side-lobes for aperiodic correlation functions. Perfect arraysare thus potentially good alignment patterns, especially the squareperfect arrayswho yields equalaccuracyinbothdimensions. Ihaveusedoneofthe6×6perfectarrays. Thisperfect6arrayanditsaperiodic auto-correlation are shownin Fig. B.4. - +++ + - + - ++ + - + + - + + - ++ + - + - +++ + - - -- -- - + −5 0 5 −5 0 5 0 10 20 30 40 Auto−correla on (a) (b) Figure B.4: (a) A 6×6 perfect binary array. (b) The aperiodic auto-correlation of (a). The highest peak has a value of 36 and the second peak has a value of 7. 36/7=5.1429. The search of the optimal EBL pattern, based on correlation techniques, is an interesting question that has not yet been explored. Except the correlation properties, the figures of merit may involve pattern dimension, feature size, sur- vivability and so on. This perfect 6 pattern serves as an alternative to the 2D Barker 11pattern. 100 B.2.4 Sub-pixelresolution Theword pixel here meansthe pixel of thedigitalgray-scaleSEM image contain- ing the alignment mark at certain magnification. The so-called least-significant- bit (LSB) or minimum beam step is the minimal size the SEM window is dis- cretized by the D/A card, which is the resolution limit of the instrument. Each dimension of the SEM window usuallyhas∼10 3 pixels and2 16 LSBs. Sub-pixel alignment means the error of alignment is less than one pixel, whichvariesinrealdimensions withtheSEMwindow size(magnification). Since the correlation peak is represented by one pixel, sub-pixel resolution cannot be achieved without interpolation. First [BK90] and second order polynomials have been used[AHL04]. B.2.5 Implementationandcalibration The alignment was performed by Philips XL30 SEM and a software package named BEWITCH (BEam Writing InTegrated Control Handler). The bewitch command does beam-writing is explained in Table??. XOFF and YOFF are used for alignment in translationand THETA canpotentially be used for alignment in rotation. WriteRaw(hRaw,SPEED,XSCALE, YSCALE, XOFF, YOFF, THETA,XSTOP, YSTOP) Parameter Description hRaw the loaded raw file SPEED writing speed of unit[points per second], controls dose andwriting time XSCALE unitless scalingfactor inx,default valueis 1 YSCALE unitless scalingfactor iny, defaultvalue is∼1.33333 XOFF offset voltage in x YOFF offset voltage in y THETA rotation angleof the patternsin the rawfile XSTOP where the beamstops, inx, afterthe writing YSTOP where the beamstops, iny, afterthe writing TableB.3: TheBEWITCHbeam-writing command andits parameters. 101 The alignment procedures are as follows. After locating the writing area and the alignment mark on the SEM screen with good signal-to-noise ratio, the SEM image is obtained by the frame-grabber installed to cross-correlate with an ideal alignmentmarkimagetogetthecorrelationfunction. Thesetwodigitalgray-scale images have pixel values range from 0 (black) to the maximal value (white). This dataisscaledto-1to1toconformtothebinaryarrayrequirement. Afast-Fourier- transform isused to speed upthe calculationof the correlation. The obtainedcor- relationdataarrayistheninterpolatedtofindthepeakwithsub-pixelresolution. ThepeakfoundinthecoordinatesoftheSEMimageneedstobeconvertedtovolt- agesandbepassedtothe(XOFF,YOFF)forBEWITCH.Thisconversionhastobe calibrated,which is discussed later inthis subsection. Alignment in 2D requires both translation and rotation. Only one alignment mark is needed for translation; multiple alignment marks are need for rota- tion. unfortunately,rotationalalignmentcouldn’tbedonewithoutrewritingsome BEWITCH codes. 1 volt in Philips XL30represents different beam movements in xandydirections. IfthedrawingisdoneinAUTOCADassumingasquarewindow from-5voltto5voltsinbothdirections,theBEWITCHparameters(XOFF,YOFF) cannot be (1,1). The value of YOFF has to be∼1.33333. This could be seen from the SEM image it saves. The tiff image is 712×484, the resolution in x and y directions are 267/9 and 242/9 respectively. So the ratio of x and y dimensions the image represents is 712×242 484×267 = 4 3 . BEWITCH does the scaling before rotation of THETA. This distorts the pattern. In order to use the THETA parameter for rotational alignment in this system, the order must be reversed in BEWITCH. Thelackofrotationalalignmentatthispointrequiresmanualanglealignmentof the sample andlimits theaccuracyof the one-mark translationalalignment. 102 As stated above, calibration is done to find the coordination conversion from the SEM image to the voltage. The procedures are illustrated in Fig. B.5. Fig- ure B.5(c) shows a processed high resolution SEM image of one the alignment result. Thegoalistobringthecenterofthecircle,wherethebeamstoppedduring lithography, to the center of the pattern, which is indicated by the red cross. The distance between them is smaller after each calibration, until it saturates to the limit. Thealignmenterrorafterthe2ndcalibrationisclosetothislimit. Asshown in Fig. B.5(d), the standard deviations of the alignment error in x and y are 132 nm and 282 nm. The frame-grabber discretizes the 250 μm window (500×) into a 640×480 digital image. Each pixel represents ∼400 nm in size. The fact that the alignment error is less than the pixel size implies the realization of sub-pixel resolution. Figure B.6 are examples to show the robustness of the correlation technique. Even when the marks were partially damaged or distorted, the correlation peak is still well abovethe noise level andgives reliable results. FigureB.7areexamplestoshowtheflexibilityofthecorrelationtechnique. In Fig. B.7(a),thefabricatedalignmentmarkturnsouttobebrightonlyattheedges of the pattern. This failed the correlation matching as shown in Fig. B.7(b)using the ideal mark image in Fig. B.7(b1). By changing this image to Fig. B.7(c1), which resembles the fabricated mark better, the real correlation peak showed up again. Figure B.8 is a microscope image showing patterned devices with their cavity centers aligned inside the 3μm-wide gainstripe. 103 (a) (b) -3 -2 -1 0 1 -2 -1 0 1 2 Y offset (um) X offset (um) 2nd 1st Standard deviation X = 132nm Y = 282nm Calibration results (c) (d) 200 400 600 -4 -2 0 2 4 data points line fit X_Volts X_Pixel X_Volts = 5.09598-0.01477*X_Pixel 100 200 300 400 -4 -2 0 2 4 data points line fit Y_ Volts Y_Pixel Y_Volts = -3.74246+0.01534*Y_Pixel (e) (f) Figure B.5: Calibration data. (a) The SEM image obtained from the frame- grabber. The size of the perfect-6 marker is 30×30μm. (b) The correlation cal- culatedfrom(a). (c)Findtheoffsetsfromtherealpatterncenter. (d)Thecollected offset data after the 1st and 2nd calibration. (e) and (f) The linearly fitted con- version function between the pixels and volts at 10KeV, WD=10mm, 500× and YOFF=1.35. 104 (a1) (a2) (a3) (b1) (b2) (b3) (c1) (c2) (c3) FigureB.6: Examples showingthe robustnessof the correlation technique. 105 (a) (b1) (b2) (b3) (c1) (c2) (c3) FigureB.7: Examples showingthe flexibility of thecorrelation technique. 106 Figure B.8: A microscope image showing devices patterned through the silicon nitride mask layer on top of the QWs. The centers of the cavities are aligned inside the vertical gain strip, which can be seen from the slight color difference. Thisstrip is 3μm wide. The e-beam writingwindow isa 250μmsquare. 107 AppendixC Devicefabricationprocedures MicroPhotonic Devices Group MOCVD Aligner Wet bench FESEM Metal evaporator Dielectric evaporator RTA Dicing saw PECVD/RIE E-beam lithography ECR/RIE ICP Spinner Lapping Furnace RIBE PECVD Wafer bonding 108 check crystal direction for undercut:sample backside has flat ellipse patterns WG direction must be perpendicular to the flat ellipse, Otherwise the facet will be blocked. to be patterned by PL and BOE; (CSL SiNx etches too slow in BOE) color: yellow-green-red-green (center -> edge) ~400nm(left room for cleanning latter); (100nm enough for stopping 10keV ions) 0. Acetone, hotbake at 120C >2min 1. Spin AZ 5214, 4k 30s; edge removal 2. Prebake 120C 30s 3. 70mJ, (405nm,10mw/cm2=[B:259, A:322]) 4. bake 120C 1min 5. Blank exposure 210mJ 6. AZ400k (1:4) for 25s O2 in Asher 100w/200mT/20s Evaporate Nickel 35nm; 1A/s Acetone lift off Acetone soak + 5seconds ultrasonic O2 in Asher 100w/200mT/30s 0. Acetone, hotbake at 120C >2min; set hot plate to 110C 1. AP405 @5k 30s; S1813 @5k 30s; Edge Removal 2. Soft bak @110C for 1min ( 3~ 5 min for fine features, but harder to remove) 3. 405nm detector, [PAPER+RAINBOW] 4. Exposure for 120~150mJ (140mJ) 5. MF 321 developer (watch with eyes), (1~2min) O2 in Asher 100w/200mT/30s 7:1 BOE Wet Etch MPDG 4~5min, this defines the strip width, watch it. Nickel etchant TFG 1~3min, @50C (our hot plate setting 2), watch the marks. Remove PR & Clean Sample Acetone, ultrasonic(<1min) O2 in Asher 100w/200mT/30s Send for Kroko Implantation Energy=10keV; Dose=1E15cm-1; Sepecies=P+; tilt=7degree; Temp.=200C; Current = 100nA/cm2; [Time=26.7min] Alignner Cover marks S1813 Photolithography, develop 5min to clean the whole surface. O2 in Asher 100w/200mT/20s 7:1 BOE wet etch 3min37seconds Remove PR & Clean Sample Acetone, ultrasonic(<1min) O2 in Asher 100w/200mT/30s NO MATTER WHAT SURFACE SHOULD BE CLEAN FOR ANNEAL! Evaporate 100nm SiO2 Anneal Cover, 4A/s; surface crack during anealling using 1A/s. thicker film will cause more cracking. RTA Aneal 700C, 4min, in Si sandwitch NO ULTRASONIC after anneal, pads are weak Remove SiO2 by BOE(10:1) 40S for Annealed, much faster than MPDG SiNx Aligner Stripe Pattern Cover perpendicular S1813 Photolithography (AZ5214 doesn't stick on SiNx) rotation Knob[CW] -> sample[CCW] 30min MPDG SiNx (Ion Stopper) Lift-Off Au Align Marks & stripes [PAPER cusions the sample; Contact until RAINBOW shows for most of the sample area.] PHOTOLUMINESCENCE TEST 109 surface treatment Acetone, methanol, water 100w(355)/800mT, SiH4/NH3/N2 =12/60/62 =(141/773/800) 275C, growth rate: 70nm/5min Spin PMMA for a perfect surface, gental corner scratch will help the focus. 5% PMMA, 3.5K 45s; wipe backside for flatness and baking residues >2min 180C prebake; >10min for sapphire substrate. go to smallest mag. before turning on the beam 1. 10kV, focus, set z=WD=10mm, align sample 2. I_hole=20pA, SpotSize~3.1 3. Stigma on Ref., fine focus on sample 4. set to 500x, write, I(writing)~16.4pA PC skip = _20.raw; speed = 160K~110K for 0.3 r/a, (r/a=0.18 in AutoCAD) Open skip = _60.raw; speed ~ 35K develop 40s in 1:3 MIBK:IPA, 30s in IPA ECR CF4 [CF4_Udisk.PRC] >250s, 10mT (mannual, valve = ~352); [290sec for 11min CSL SiNx] CF4=28.7 sccm, 500watts Remove PMMA Acetone 15min, Ultrasonic O2 in Asher 100w/200mT/2min CH4/H2/Ar setting: X/20/15, valve position~60 flow: x/16.7/12.4 sccm; optimal CH4 flow rate (x) is always changing. increase X when etch rate decrease; decrease X if too much polymer. 77.10mT, Temp.=27C, 500watts Spin PMMA blade = ZH05, lower side smooth Z=0.40~0.42mm clean PMMA Acetone + O2 Asher 2min, too much PMMA Remove SiNx mask BOE or HF, 1min HCl:H2O 4:1, Temp=0C, ice-water bath & spinner wait 20min to reach equilibrium 1. 40ml HCl fist to revent bottle flip, then 10ml H2O 2. have H2O rinse bottle ready 3. Lower the fume hood door Cleave, use needle probes gental left once, gental right once, until it breaks Mount 180C 1hour 1. 4K 30s 2. 120C, 30s, prebake 3. 200mJ exposure (405nm) 4. Az400K (4:1), observe (~1min) defocus and keep it moving during exposure 15kV, I<5nA, 300X, spotsize~6.8, 8min alternative mask: CSL growth rate 10nm/min 30w(111)/440mT(lower-the-better); 40/20/60=(515/247/773) reexposure 150X -> 150nA*min, I<10nA ECR CH4 [INP-CH4.PRC, step 2] 850sec etches 1 Ӵ m in pure InP; the well-etched big open THE END Dice on brown tape on blue tape AZ5214 positive way Undercut [9min] Ebeam Use the golden stage; I_hole means the current going though the hole in the stage. PECVD 5min MPDG SiNx green/yellow 110

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Lu, Ling (author)

Core Title Photonic crystal nanocavity lasers for integration

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 01/21/2010

Defense Date 01/11/2010

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

Tag OAI-PMH Harvest,photonic crystal,photonic integration,quantum well intermixing,semiconductor laser

Language English

Contributor Electronically uploaded by the author (provenance)

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

Creator Email lely_lu@hotmail.com,lingl@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m2808

Unique identifier UC1178084

Identifier etd-Lu-3450 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-288665 (legacy record id),usctheses-m2808 (legacy record id)

Legacy Identifier etd-Lu-3450.pdf

Dmrecord 288665

Document Type Dissertation

Rights Lu, Ling

Type texts

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

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu