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Cathodoluminescence studies of the influence of strain relaxation on the optical properties of InGaAs/GaAs quantum heterostructures

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Cathodoluminescence studies of the influence of strain relaxation on the optical properties of InGaAs/GaAs quantum heterostructures

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Content CATHODOLUMINESCENCE STUDIES OF THE INFLUENCE OF STRAIN RELAXATION ON THE OPTICAL PROPERTIES OF INGAAS/GAAS QUANTUM HETEROSTRUCTURES Copyright 1996 by Karthikeyan Rammohan A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Materials Science) December, 1996 Karthikeyan Rammohan R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES. CALIFORNIA 90007 This dissertation, written by K arth ik eyan Rammohan under the direction of kXs Dissertation Committee, and a-pproved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillment of re quirements for the degree of DOCTOR OF PHILOSOPHY Dean of Crat Studies Date November 20, 1996 DISSERTATION COMMITTEE R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . to my parents R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Acknowledgments I would like to give my greatest thanks to my thesis advisor. Prof. Dan Rich, for his financial and moral support throughout the period of my studies. His objective insights and wisdom, and the friendly working environment he fosters, help inspire the self-motivation one needs to perform innovative research. I was very fortunate to have a gifted set o f colleagues, including Hsin-Tah Lin and Yongkang Tang. I am thankful to them not only for their contributions during the - course of this work but also for their friendship. I would also like to thank Prof. Anupam Madhukar and his student K.C. Rajkumar, Prof. Karen Kavanaugh and her student R.S. Goldman, Prof. M. Goorsky and his student M. Meshkinpour, Prof. Dan Dapkus and his student M. Macdougal for productive collaborations. I would also like to thank Karthik Ananth, Suresh Subramaniam, and R. Ganesh for their contributions of companionship and levity. Last but not the least, I would like to thank my wife, Latha, for providing me moral support through many trials and tribulations I have experienced over the last couple of years. Finally, I would like to thank all the other people inside and outside the group who helped make my sojourn in graduate school a fruitful and memorable one. iii R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . TABLE OF CONTENTS D edication.............................................................................................................................................ii Acknowledgments..............................................................................................................................iii List o f Figures....................................................................................................................................vii List o f T ab les..................................................................................................................................... xv A bstract.............................................................................................................................................. xvi C H A P T E R I. IN T R O D U C T IO N ................................................................................................. 1 C H A P T E R II. EX PER IM EN TA L T E C H N IQ U E S............................................................... 9 n.A . C athodoluminescence.......................................................................................................9 II. A. 1. Interaction o f electrons with solids............................................................................12 II.B. Formation of CL signal.................................................................................................. 16 II.C. S patial and spectral resolution of cathodoluminescence technique .... 20 II.D. T he JEOL 840A SEM-CL sy stem..................................................................................21 II.D .1.JEO L 840-A SEM ......................................................................................................... 21 n.D.2. Sample holder................................................................................................................24 II.E. CL COLLECTION S Y S T E M ..................................................................................................... 25 II.F. D etectors............................................................................................................................. 26 References.................................................................................................................................... 28 C H A P T E R IH . IN FLU EN C E O F M ISFIT D ISL O C A T IO N S ON T H E O P T IC A L P R O P E R T IE S O F InxG a,.xAs/GaAs H E T E R O ST R U C T U R E S AND Q U A N TU M W E L L S ...............................................................................................................................................29 LH.A. Introduction................. 29 m .B . Strained layer epita x y.................................................................................................30 m .B.1. Critical Thickness........................................................................................................32 m .C . Effect of misfit dislocations on spatial variations in strain in In xGa i. xA s/G aA s(001) heterostructure.......................................................................................... 35 ffl.C .l. Experimental Details....................................................................................................35 ffl.C.2. Results and D iscussion...............................................................................................35 ni.D . Influence of misfit dislocations on therm al quenching of luminescence in In x G a i- x A s/G aA s multiple quantum w el l s..................................................................45 iv R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . m .D .l. Experimental details...........................................................................................45 HI.D.2. Results and Discussion.......................................................................................46 m.E. Effect of interface defect formation on the carrier diffusion and LU M IN ESCEN CE IN lN 0. 2GA0. 8AS/ALxGAuxAS Q U A N TU M W ELLS....................................... 56 ID.E.1. Experimental Details........................................................................................... 58 m.E.2 . RESULTS AND DISCUSSION........................................................................61 III.E.2.a. Evaluation o f the average strain relaxation in the HEMT samples 61 III.E.2.b. Local CL energy and polarization variations in close proximity to dislocations...................................................................................................................70 III.E.2.C. CL temperature dependence and spatial variations in the activation energy.............................................................................................................................78 III.E.2.d. Spatial variations in the carrier diffusion length...................................... 8 8 IILF. CONCLUSIONS....................................................................................................... 96 References......................................................................................................................... 98 CHAPTER IV. INFLUENCE OF SUBSTRATE MISORIENTATION ON THE OPTICAL PROPERTIES OF Inx G a,.x As FILMS GROWN ON GaAs(OOl) 103 IV.A. Introduction.........................................................................................................103 IV.B. Experimental details.......................................................................................... 105 IV.B.l. Effect of strain on band structure of heterostructures.....................................106 IV.C. R esults and Discussion....................................................................................... 1 10 IV.C. 1. InGaAs films grown on GaAs(001) substrates misoriented towards (011). 110 IV.C.2. Correlation between LPCL and CLWI............................................................116 IV.D. InGaAs films grown on GaAs(001 ) substrates misoriented towards {1 1 1 } .................................................................................................................................. 118 IV.D. 1. Correlation of LPCL with CLW I.................................................................. 124 IV.D.2. Analysis of anisotropic strain relaxation........................................................ 128 IV.D.3. Defect-induced Long-wavelength Emission.................................................. 132 IV.E. Conclusion............................................................................................................. 137 References.......................................................................................................................138 CHAPTER V. EFFECT OF RAPID THERMAL ANNEALING ON STRAINED INGAAS/GAAS QUANTUM W ELLS BONDED TO UNPATTERNED AND PATTERNED SILICON VIA AN EPITAXIAL LIFT-OFF TECHNIQUE............140 V.A. Introduction...........................................................................................................140 V.B. Epitaxial lift-off....................................................................................................141 V.B.l. ELO film separation and handling.................................................................... 143 V.B.2. ELO film bonding...............................................................................................144 V.C. Processing of Silicon.............................................................................................145 V.C.l. Standard cleaning................................................................................................145 V.C.2. Photolithography.................................................................................................145 v R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . V.C.3. Silicon nitride deposition.................................................................................... 146 V.C.4. Etching o f silicon nitride......................................................................................147 V.C.5. Etching o f Silicon dioxide.................................................................................. 147 V.D. Rapid thermal annealing (R T A )...............................................................................148 V.E. EXPERIMENTAL DETAILS.................................................................................... 148 V.F. RESULTS AND DISCUSSION................................................................................. 149 V.F.l. Modeling o f RTA effect on the CL peak positioa............................................154 V.G. CONCLUSIONS.......................................................................................................... 160 References................................................................................................................................... 161 CHAPTER VI. CONCLUSIONS AND POSSIBILITIES FOR FUTURE W O R K .......................................................................................................................................163 APPENDIX A ...........................................................................................................................166 APPENDIX B ...........................................................................................................................177 vi R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . LIST OF FIGURES Fig. 2-1 Schematic representation of the variety of signals due to electron beam interaction with solid....................................................................................1 0 Fig. 2-2 The electron beam range, Re, for Si and GaAs as a function of the electron beam energy calculated from Everhart -Hoff model...................................14 Fig. 2-3 Depth-dose curves for GaAs..........................................................................15 Fig. 2-4 Schematic diagram of radiative transitions between the conduction band (Ec), the valence band (Ev) and exciton ( E e ) , donor ( E d ) and acceptor ( E a ) levels in a semiconductor......................................................................19 Fig. 2-5 Schematic representation of the JEOL 840A CL system at USC.............. 22 Fig. 2-6 Schematic representation of cryo stage and light collection system..........23 Fig. 3-1 Schematic representation of strained layer epitaxy depicting in (a) lattice matched films, (b) coherent films, and in (c) incoherent films................ 31 Fig. 3-2 CL wavelength imaging in (a) and local spectra in (b) for two different positions. A scale showing the mapping of wavelengths of peak CL intensity into shades of gray is shown in (a). The blue- and red-shifted local spectra in (b) were obtained from the spatial positions labeled B ad R, respectively, with arrows in (a)............................................................... 41 Fig. 3-3 Monochromatic linearly polarized CL images for the same region shown in Fig. 3-2(a) at A . = 956 nm. The polarization detection conditions of E ±[110] and Ej|[l 10] are shown in (a) and (b), respectively. The ratio image of log (Ij/I||) is showing (c), revealing the pm-scale polarization anisotropy....................................................................................................... 42 Fig. 3-4 Plan-view TEM showing two different regions of the Ino.15Gao.85As/Ino.20Gao.80As interface which exhibits different dislocation densities and strain relaxation along both <110> directions in (a) and (b) .43 Fig. 3-5 Histogram of the CL wavelength imaging, CLWI, and Ix/Iy ratio for a line scan along the [110]. The spatial correlation of regions with a red shift and an increased polarization anisotropy (regions of nearly uniaxial vii with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ith out p erm issio n . compressive stress) and regions with blue shift and a reduced polarization anisotropy (regions of nearly biaxial compressive stress) is observed.... 44 Figure 3-6 Temperature dependence of CL intensity for sample D18. The data labeled A corresponds to CL integrated intensity, Im qw, measured while the electron beam was scanning a 128 pm x 94 pm region. The data labeled B and D correspond to the intensity obtained from bright and dark regions, respectively, shown in Fig. 3-7 (a). The solid lines are linear fits to the data........................................................................................................48 Fig. 3-7 Monochromatic CL images (at T = 8 6 K) obtained at 955 nm for sample D18. The activation energy (in meV) image of Eai obtained in the intermediate temperature range (86-150 K) for the same regions shown in (a) is shown in (b). The activation energy image of obtained in the high-temperature range (150-250 K) is shown in (c). A scale showing the mapping of the activation energies is shown below each image............... 49 Fig. 3-8 Monochromatic CL images (at T = 8 6 K) obtained at 960 nm for sample D38. The activation energy (in meV) image of Eai obtained in the intermediate temperature range (86-150 K) for the same regions shown in (a) is shown in (b). The activation energy image of E^ obtained in the high-temperature range (150-250 K) is shown in (c). A scale showing the mapping of the activation energies is shown below each image............... 50 Fig. 3-9 Monochromatic CL images (at T = 8 6 K) obtained at 948 nm for sample D179. The activation energy (in meV) image of Eai obtained in the intermediate temperature range (86-150 K) for the same regions shown in (a) is shown in (b). The activation energy image of E^ obtained in the high-temperature range (150-250 K) is shown in (c). A scale showing the mapping of the activation energies is shown below each image............... 51 Fig. 3-10 Stack plot of CL intensity, activation energies Eai and Ea2 for an arbitrary line scan done along the (110) direction for sample D38. The spatial correlation of regions showing decreased luminescence efficiency, higher Eai, and lower E^ (indicated by dotted lines) and increased luminescence efficiency, lower Eai, and higher E^ (indicated by solid lines) is observed.......................................................................................................... 52 Fig. 3-11 Schematic diagram of the HEMT sample structure showing the ambipolar diffusion experiment...................................................................................... 59 viii R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithou t p erm issio n . Fig. 3-12 Stack plot of spatially integrated CL spectra at room temperature for all HEMT samples...............................................................................................65 Fig. 3-13 Self-consistent-field calculation of the band profile for the Ino.2Gao.8As HEMT sample (channel thickness of 150 A) showing the el and hhl wavefunctions and Fermi-level position...................................................... 66 Fig. 3-14 Self-consistent-field calculation of the maximum electric field Fm in the Ino.2Gao.8As channel and the change in the el-hhl transition energy vs electron concentration n« at room temperature............................................ 67 Fig. 3-15 Plots of theoretical el-hhl luminescence energy position vs the Ino.2Gao.8As QW width for (i) fully strained, (ii) fully relaxed, (iii) uniaxially strained, and (iv) partially relaxed strain (squares) conditions using data in Table 3-2. The experimental CL peak positions from Fig. 3- 12 are shown as dots. Calculations of el-hhl vs the QW width are also shown for fully strained Ino.21Gao.79As QW, to illustrate the effect of In composition variation.....................................................................................6 8 Fig. 3-16 (a) CL Intensity and (b) CLWI images of the same regions in the Ino.2Gao.8As HEMT sample with 150 A channel thickness........................73 Fig. 3-17 (a) CL Intensity and (b) CLWI images o f the same regions in the Ino.2Gao.8As HEMT sample with 185 A channel thickness........................74 Fig. 3-18 Line scan analysis for an arbitrary [110]-oriented line for the images of Fig. 3-16 (150 A Ino.2Gao.8As channel width) showing CL intensity and CLWI correlations. Dashed and solid lines are used to show correlations between a reduced CL intensity (DLDs) and a blue shift in the el-hhl transition energy..............................................................................................75 Fig. 3-19 Line scan analysis for an arbitrary [110]-oriented line for the images of Fig. 3-17 (185 A Ino.2Gao.8As channel width) showing CL intensity and CLWI correlations. Dashed and solid lines are used to show correlations between a reduced CL intensity (DLDs) and a blue shift in the el-hhl transition energy..............................................................................................76 Fig. 3-20 CL imaging of the 150 A Ino.2Gao.8As HEMT sample showing (a) spectrally integrated CL images for the el-hhl emission, (b) LPCL ratio images, (c) activation energy Eai images for the Ino^GaosAs QW luminescence, monochromatic CL images for GaAs/AlojsGao 7 5 A S MQW ix R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . at (d) T = 87 K and (e) 180 K, and (f) activation energy E& images for the GaAs/ Alo.25Gao.75As MQW emission......................................................... 79 Fig. 3-21 Fig. 3-22 Fig. 3-23 Fig. 3-24 Fig. 3-25 Fig. 3-26 Fig. 3-27 CL imaging o f the 185 A In0. 2Ga0.sAs FIEMT sample showing (a) spectrally integrated CL images for the el-hhl emission, (b) LPCL IJI\\ ratio images, (c) activation energy Eai images for the In0. 2Gao.sAs QW luminescence, monochromatic CL images for GaAs/Alo.25Gao 75AS MQW at (d) T = 87 K and (e) 180 K, and (f) activation energy Ea2 images for the GaAs/ Alo.25Gao.75As MQW emission......................................................... 80 Line scan analysis for an arbitrary [110]-oriented line for the images of Fig. 3-21 (185 A Ino^Gao.sAs channel width showing (a) the CL intensity for the el-hhl emission, GaAsMlo.25Gao.75As MQW emission intensity at (b) T = 180 K and (c) t = 87 k, (d) LPCL IJI\\ ratio, and activation energies (e) Ea2 and (f) Eai............................................................................ 81 Calculation of the el-hhl IL II\\ emission ratio an LuuGaosAs QW transition energy vs si 10 for a fixed Siio = 0.0141 at room temperature. 82 CL intensity vs 1000/T for the same local bright (B) and dark regions (D) in the In0. 2Gao.sAs el-hhl and GaAs/Alo.2sGao 7 5 A S MQW monochromatic CL images. The solid lines running through the curves are fit of Eq. 3-6 to the data to determine the activation energies Eai and Ea2 for the In0. 2Ga0.sAs QW and GaAsM.lo.25Gao.75As MQW luminescence, respectively............................................................................83 CL intensity vs beam position x for different line scans (labeled a-d) parallel to the [1 1 0 ] dislocation line direction near and between dislocations for the 150 A In0. 2Ga0.sAs HEMT samples.............................. 90 CL intensity vs beam position x for different line scans (labeled a-d) parallel to the [1 1 0 ] dislocation line direction near and between dislocations for the 185 A Ino^Gao.sAs HEMT samples.............................. 91 CL intensity and diffusion length plot vs distance along [110] (perpendicular to dislocation direction) for various temperatures for the 150 A sample. The dashed and solid vertical lines show the spatial correlation between DLD positions and a reduced diffusion length 92 x R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . F ig . 3 -2 8 Fig. 3-29 Fig. 3-30 Fig. 4-1 Fig. 4-2 Fig. 4-3 Fig. 4-4 Fig. 4-5 CL intensity and diffusion length plot vs distance along [110] (perpendicular to dislocation direction) for various temperatures for the 185 A sample. The dashed and solid vertical lines show the spatial correlation between DLD positions and a reduced diffusion length 93 Diffusion length vs temperature for various bright (a and b) and dark (c and d) regions in the 150 A sample..............................................................94 Diffusion length vs temperature for various bright (a and b) and dark (c and d) regions in the 185 A sample..............................................................95 Calculated intensity ratio (I±/I||) of luminescence with EJL[110] polarization to that with E||[ 110], |cll0i.m |2- and |c* 10j.hh |2 versus aj/tTn for In0. 06Ga0. 94As. The 110 superscripts are used to emphasize that the | J. m,) basis wavefunctions are in the [110] representation here. The || and _ L subscripts denote parallel and perpendicular to the [1 1 0 ] direction, respectively................................................................................................... 108 Spatially averaged polarized CL spectra obtained for Ino.o 6Gao 94AS films grown on both the nominally flat and misoriented GaAs(001) substrate, where E j_ and E y refer to electric field vector E perpendicular and parallel to [1 1 0 ]..........................................................................................................I ll The CLWI, the integrated CL intensity, and the LPCL images in (a), (b). and (c), respectively for the Ino.06Gao.94As film grown on the flat substrate. A scale showing mapping of wavelengths of peak CL intensity is shown in (a)...............................................................................................113 The CLWI. the integrated CL intensity, and the LPCL images in (a), (b), and (c), respectively for the In0. 06Ga0. 94As film grown on the substrate misoriented towards (011). A scale showing mapping of wavelengths of peak CL intensity is shown in (a)..............................................................114 Histogram of CLWI, integrated CL intensity and LPCL Ij/I|| ratio for an arbitrary line scan done along the [lfO] for the sample grown on the substrate misoriented towards (011). The spatial correlation of regions showing redshifit, a decreased luminescence efficiency, and enhanced polarization (indicated by dashed vertical lines) and regions of blueshift, increased luminescence efficiency and no polarization (indicated by dotted vertical lines) is observed...............................................................115 xi R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . F ig. 4 -6 Fig. 4-7 Fig. 4-8 Fig. 4-9 Fig. 4-10 Fig. 4-11 Fig. 4-12 Fig. 4-13 CLWI, the integrated CL intensity, and LPCL images in (a), (b). and (c), respectively for the Ino.13Gao.g7As film grown on the substrate misoriented 2° towards (111)A. A scale showing mapping of wavelengths of peak CL intensity is shown in (a). The LPCL image in (c) is displayed at X = 929 nm..................................................................................................................1 2 0 CLWI, the integrated CL intensity, and LPCL images in (a), (b). and (c), respectively for the Ino.13Gao.g7As film grown on the substrate misoriented 2° towards (111)A. A scale showing mapping of wavelengths of peak CL intensity is shown in (a). The LPCL image in (c) is displayed at X = 929 nm..................................................................................................................1 2 1 Local CL (solid line) and LPCL spectra for the (111 )A misoriented sample along the dashed line indicated in Fig. 4-6(b). The distance. Ax. along the dashed line from point A is indicated. The LPCL spectra were acquired under Ex (dashed line) and E || (dotted fine) polarizer orientations, where the electric field subscripts denote perpendicular and parallel to [ 1 1 0 ], respectively....................................................................................... 1 2 2 Spatially averaged LPCL spectra over the (111 )A and (111 )B misoriented samples. The sampled regions correspond to the same 128 x 94 pm2 regions shown in Figs. 4-6 and 4-7. Ex and E|| refer to electric field vector R perpendicular and parallel to [110]........................................................ 123 Histograms of CLWI, integrated CL intensity and LPCL I||/Ix ratio for an arbitrary line scan along [110] for the samples grown on the (111 )A misoriented substrate...................................................................................125 Histograms of CLWI, integrated CL intensity and LPCL I||/Ix ratio for an arbitrary line scan along [110] for the samples grown on the (111 )A misoriented substrate...................................................................................126 View of {111} slip planes for a (001) substrate misoriented an angle 6 towards (111)A. the geometry of the Burgers vector 1-4 are shown for a [1 1 0 ]-oriented a dislocation....................................................................... 130 Monochromatic CL images at X = 929 nm (a) and X = 1060 nm (b) showing a region containing long-wavelength emission for ( 1 1 1 )A misoriented sample...................................................................................... 133 xii R ep ro d u ced w ith p erm issio n o f th e cop yright ow n er. Further reproduction prohibited w ithou t p erm issio n . Fig. 4-14 Local CL spectra taken along the line A-B as shown in Fig. 8(b). The distance, Ax, along this line is shown................................................134 Fig. 4-15 Histograms o f the CL imaging at X = 929 nm and X = 1060 nm along an arbitrary [110]- oriented line.............................................................. 135 Fig. 5-1 Schematic diagram showing the epitaxial lift-off process................ 142 Fig. 5-2 Variation of the CL peak energy and linewidth in the InoiGao gAs/GaAs QW films on Si as a function of the annealing temperature............151 Fig. 5-3 CL spectra of the Ino.2Gao.8As/GaAs QW for various anneal times at 775° C............................................................................................................ 152 Fig. 5-4 Plot of the temporal evolution of the CL peak energy and linewidth at temperatures of 725, 750, 775 and 800° C. respectively. The solid lines represent the fits to the theoretical model..........................................153 Fig. 5-5 Plot of the interdiffusion constant Din as a function o f annealing temperature........................................................................................... 158 Fig. 5-6 Monochromatic image of Ino.2Gao.8As QW ELO bonded to patterned Si surrogate substrate consisting of 5 pm mesas annealed at 750° C for 45 seconds.................................................................................................. 159 Fig. A-l Schematic diagram of band structure near zone center for zinc-blende structure (a) without strain and (c) with compressive biaxial strain. Panels (b) and (d) show constant energy surfaces for |3/2 ± 3/2) and [3/2 ± 3/2) bands without strain and with strain, respectively............................ 172 Fig. B-l Schematic representation of a piecewise constant potential profile consisting ofN-layers.......................................................................... 178 xiii R ep r o d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithou t p erm issio n . LIST OF TABLES Table 3.1 Table 3.2 Table A.l Table A.2 Effective barrier heights, E b c a n d E b v for re-emission out of quantum well Linear dislocation densities along the [110] and [110] directions for various Ino.2Gao.8As channel thickness Important parameters at 0 K The notation of bands under consideration R ep ro d u ced with p erm issio n o f th e cop yright ow n er. Further reproduction prohibited w ithout p erm issio n . K. Rammohan Prof- Dan Rich Cathodoluminescence studies of the influence of strain relaxation on optical properties of InGaAs/GaAs quantum heterostructures Strained-layer quantum wells and heterostructures of Inx Ga(.x As grown epitaxially on GaAs have attracted considerable attention because of their promise for novel photonic device applications. High contrast modulators, for example, are key elements required for optical computing and communications. We have examined the influence of strain relaxation on the excitonic recombination, polarization anisotropy and ambipoiar diffusion in Inx Gai.x As quantum wells and heterostructures using various cathodoluminescence (CL) techniques. The presence of misfit dislocations resulted in a reduction in luminescence efficiency accompanied by changes in the excitonic luminescence energy and the polarization anisotropy. The spatial variation in excitonic peak energy was mapped via cathodoluminescence wavelength imaging (CLWI). The polarization properties of luminescence were studied using linearly polarized cathodoluminescence (LPCL) imaging and spectroscopy. A strain-induced modification o f the luminescence energy and polarization anisotropy was measured near misfit dislocations. The polarization anisotropy observed was found to correlate with the spectral shifts in the peak positions of excitonic luminescence. The influence of misfit dislocations and point defects associated with strain relaxation on the thermal quenching of luminescence was investigated, and the spatial variation in activation energies was examined. The influence of misfit dislocations on the ambipoiar diffusion of excess carriers in Inx Gai,x As/Alx Gai.x As high-electron mobility transistors was examined utilizing a novel CL-based diffusion experiment. We observe that misfit dislocations and point defects act as barriers for carrier transport. We have utilized the epitaxial lift-off (ELO) technique to achieve monolithic integration between InGaAs/GaAs quantum wells and Si. We observed that the ELO technique does not degrade the optical properties of the QW films after bonding. We examined the thermal stability of ELO bonded films by annealing ELO bonded films to very high temperatures. No peeling of films were observed and the optical properties did not degrade when subjected to temperatures as high as 600° C. Beyond 700° C, Ga-In interdiffusion was observed at the QW interface resulting in a shift in QW excitonic peak energy. We have modeled this diffusion process and also extracted the activation energy for interdiffusion. ELO films bonded to patterned Si substrates show a lateral variation in peak energy which could be utilized for the fabrication of nanostructures in ELO films. XV R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . C h a p t e r I INTRODUCTION The advent of layer by layer growth techniques such as molecular beam epitaxy1 and metalorganic chemical vapor deposition has opened the horizon for the fabrication of quantum confined structures and for the realization of new classes of heterojunction devices. In 1974 the effects of quantum confinement were demonstrated in two basic experiments: Esaki and Chang reported the oscillatory behavior of perpendicular differential conductance due to resonant tunneling across potential barriers, 2 and the optical measurements of Dingle3 showed directly the quantization of energy levels in quantum wells; a realization of the well known elementary example of quantization in a one dimensional square well given in quantum mechanics textbooks. Studies of ultrathin semiconductor structures have, since then, proliferated at an explosive rate. To date, heterostructures have been used to study transport and optical properties in one-, two-, and three-dimensionally confined structures revealing a variety of new phenomena. The electronic properties in one-dimensionally confined structures fall under the categories of heterojunctions, quantum wells, and superlattices which have been exploited for a variety of semiconductor devices ranging from transistors and tunneling diodes to opto-electronic devices such as lasers, detectors and light l R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ith out p erm issio n . modulators. Devices such as separate-confinement-heterostructure quantum well lasers4 combine optical confinement, carrier confinement and quantum confinement in a single device. Most of the III-V heterostructure devices which have been fabricated until recently are made of lattice matched semiconductors based on binary or ternary compounds that contain Ga and A1 (such as AlGaAs on GaAs. AlGaSb on GaSb) and on lattice matched InP and Ino.53Gao.47As materials. In recent years, there has been a growing interest in the lattice mismatched heterostructure materials for their distinctive features. This dissertation undertakes studies on the influence of defects on the optical properties of strained and partially relaxed quantum well structures. Our studies of lattice mismatched materials, and in particular, the strained InGaAs/GaAs combination are motivated by: I) The strain in lattice mismatched materials modifies the electronic structure in the materials. In InGaAs layers under biaxial compressive strain, the heavy hole and the light hole energy bands are reversed in the biaxial (x-y) plane relative to dispersion along the growth (z) direction. As a consequence, an enhanced mobility and lower density of states is possible. An integrated circuit that contains both n-channel and p-channel FETs would benefit from this because the characteristics of both FETs would be more similar. A QW laser benefits from this because a smaller DOS means a lower threshold current for room temperature operation. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 2) Lattice mismatched materials also enrich the selection of materials used to induce band and refractive index discontinuities in devices. The band discontinuity defines the potential wells that give rise to the quantum confinement effects. Devices such as lasers, light modulators, resonant tunneling diodes (RTD), and field effect transistors (FET) benefit from these wider selections. Lattice mismatched materials extend the working wavelength of optical devices. InGaAs/GaAs multiple quantum well (MQW) light modulators that work in the transparent region of the GaAs substrate are a typical example. In this dissertation we intend to address issues in three major categories: (1) the materials related issues, and in particular the influence o f strain induced defects on the optical quality of InGaAs/GaAs(001) quantum wells suitable for light modulator and detector applications, and (2 ) the issues relating to control of strain induced defects utilizing substrate misorientation (3) integration o f dissimilar lattice mismatched materials via a novel technique known as epitaxial lift-off technique (ELO). The influence of defects on the optical quality is one of the most important issues in the application of lattice mismatched materials. In lattice mismatched materials, strain relaxation occurs via the formation of misfit dislocations. The presence of increasing strain with increasing In content results in limiting the thickness of the Inx Gai.x As layer for a specific In composition, beyond which strain induced structural defects begin to seriously compromise the material properties. Early works treat this subject within the macroscopic continuum thermodynamic ground state theories which have led to the R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . concept of a critical thickness5-6 for the occurrence of a lattice mismatch induced formation of misfit dislocations. The presence of misfit dislocations causes the electronic band levels to fluctuate in close proximity to defects. It also results in an anisotropic relaxation in strain which will affect the polarization properties o f the material. The point defects and the dislocations present in the material affect the carrier transport in the material by presenting a barrier to the movement of carriers. It also affects the luminescence efficiency of the materials by increasing the density of non-radiative recombination centers at higher temperatures. In order to perform a comprehensive study of the influence of defects on the optical quality of the material, we have employed the use o f novel CL imaging and spectroscopy techniques. We have examined the influence of misfit dislocations on the anisotropic strain relaxation resulting in local fluctuations in energy levels accompanied by a polarization anisotropy. We have also examined the influence of defects on carrier transport properties and on the temperature dependence of luminescence efficiency. The feasibility of tailoring the optical polarization properties of the InxGai.x As/GaAs system for future photonics applications by choosing suitable substrate orientations is examined via linearly polarized CL imaging and spectroscopy technique. 7 The final issue we are going to address relates to the monolithic integration of InxGai.x As/GaAs quantum well heterostructures to Si substrate via an epitaxial lift-off o technique. The hybridization of Ul-V/Si materials is important in the realization of opto electronic integrated circuits (OEIC) which find many applications in broadband and 4 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . coherent optical communication networks and in optical recording. Although impressive advances have occurred in achieving high quality GaAs via heteroepitaxial growth on Si. the GaAs film grown by this process generally exhibits poor optical and electrical properties which is insufficient for device applications.7'9 The problems encountered with heteroepitaxial growth have stimulated different research groups to investigate alternate routes in achieving monolithic integration of dissimilar crystalline materials. Epitaxial lift-off (ELO) was developed by Yablonovitch et al.8 in 1987 in which ELO films bond to a surrogate substrate primarily by van der Waals forces. These studies have been extended by several other researchers who have integrated GaAs MESFETs on Si and other quasi arbitrary surrogate substrates. 10*12 The important issues which need to be examined prior to utilizing this technique on a large scale are: 1. Individual device performance characteristics such as optical quality, speed, and temperature sensitivity. 2. Issues associated with realizing a large array of devices on Si substrate. 3. Issues regarding manufacturability, yield, long term reliability and resistance to thermal cycling. Our efforts in this dissertation focus on the optical quality of the ELO bonded films and also the reliability of these films to thermal cycling. We have examined the influence of ELO processing on the optical properties of Inx Gai.x As quantum well films bonded to Si(OOl) via ELO. We have also studied the effect of thermal processing on the optical quality of ELO bonded films to both planar and patterned Si substrates. 5 R ep ro d u ced w ith p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . This dissertation is organized as follows: In chapter II, we list in detail the experimental background of this work such as the low-temperature cathodoluminescence (CL) setup and optical collection systems, which were designed and implemented at USC, and CL detectors. We provide a basic description of the equipment, experimental processes and principles. We also discuss the application and analysis of optical characterization in this chapter. In chapter E H , we discuss the influence of misfit dislocations on the optical properties on InGaAs/GaAs heterostructures. We report on the influence of misfit dislocations on the spatial variation in excitonic peak energy, and the associated strain relaxation via polarization measurements. We study the temperature dependence of luminescence efficiency. Finally, we examine the interplay between strain relaxation, optical properties, and transport properties in Ino.2Gao.8As/AlxGai.x As QW samples, designed for HEMTS. In chapter IV, we address the issue of polarization anisotropy induced by asymmetric distribution of misfit dislocations in InGaAs heterostructures grown on GaAs(OOl). We study the effect of substrate misorientation on the anisotropic strain relaxation and excitonic polarization properties of InGaAs/GaAs heterostructures suitable for light modulators applications. In chapter V, we address the issue of integration of InGaAs/GaAs QW structures with Si. We discuss in detail the thermal stability of these devices when subjected to very R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . high annealing temperatures. We estimate the interdiffusion coefficient of In/Ga in these structures and the associated activation energy for interdiffusion.. In chapter VI, we provide our conclusions and point out some useful future directions. References 1. A.Y. Cho and J.R. Arthur, Proc. Solid State Chem. 10, 157 (1975). 2. L. Esaki, and L.L. Chang, Phys. Rev. Lett. 33,495 (1974). 3. R. Dingle, W. Wiegmann, and C.H. Henry, Phys. Rev. Lett. 33, 827 (1974). 4. W.T. Tsang, Appl. Phys. Lett. 39, 134(1984); ibid. 40, 217 (1982). 5. F.C. Frank and J.H. Van der Merwe, Proc. Roy. Soc. London, A198. 216 (1949). 6 . J.W. Matthews and A.E. Blakeslee, J. Cryst. Growth, 27, 118 (1974); ibid. J. Cryst. Growth 29,273 (1975); ibid. J. Crsyt. Growth 32,265 (1976). 7. D.H. Rich, A. Ksendzov, R.W. Terhune, F.J. Grunthaner, B.A. Wilson. H. Shen. M. Dutta, S.M. Vernon, and T.M. Dixon, Phys. Rev. B 43, 6836 (1991). 8 . E. Yablonovitch, T. Gmitter, J. Harbison, and R. Bhat, Appl. Phys. Lett. 51. 2222 (1987). 9. Y. Tang, D.H. Rich, E.H. Lingunis, and N.M. Haegel, J. Appl. Phys. 76, 3032 (1994). 10.1 . Pollentier, C. Brys, P. Demeester, P. Van Daele, and L. Martens, Electron. Lett. 29, 201 (1990). 7 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 11.1. Pollentier. P. Demeester. A. Ackaert, L. Buydens, P. Van Daele. and R. Baets. Electron. Lett. 26,103 (1990). 12. W.K. Chan, A. Yi-Yan, and T. Gmitter, IEEE Jour. Quant. Elect. 27. 717 (1991). 8 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithou t p erm issio n . C h a p t e r II EXPERIMENTAL TECHNIQUES II.A.Cathodoluminescence The continuing progress in solid-state electronics directed toward further miniaturization of electronic devices presents a great challenge from the characterization point of view. It is now feasible to generate patterns on a sub-micron scale, and there is ongoing discussion on the feasibility of ultra-submicron level electronic devices. Hence it is essential to develop microcharacterization tools to investigate these devices. One technique which offers great versatility as a characterization tool is cathodoluminescence (CL). Cathodoluminescence is the emission of light as a result of electron bombardment. This phenomenon, first reported in the middle of last century led to the discovery of the electron and the determination of its charge to mass ratio e/m. 1 In an electron probe instrument, electron irradiation of a solid results in a variety of useful signals. A schematic representation of the interaction of electron beam with solid is given in Fig. 2-1. Primary electrons may be backscattered from the specimen with little or no energy loss. Some primary electrons, which are absorbed into the bulk material, will dissipate energy as characteristic x-rays; the generation of electron-hole pairs will result in the emission of photons in the ultraviolet, visible and infrared spectral 9 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . Primary electron beam Backscattered electrons Secondary electrons Cathodoluminescence Auger electrons X-rays Inelastically scattered * electrons Elastically scattered electrons Unscattered electrons Fig. 2-1 Schematic representation of the variety of signals due to electron beam interaction with solid. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . ranges (cathodoluminescence); transmitted electrons may be scattered elastically or inelastically. All these processes lead to the formation of signals that can be used in characterization of the structural, chemical and electronic properties of the material. CL analysis can be performed in a simple high-vacuum chamber with an electron beam source and optical windows. However, one drawback with this simple setup is the inability to study spatial variations across the sample owing to the lack of scanning ability of the electron beam. Scanning electron microscopes on the other hand are well suited for microcharacterization owing to the high spatial resolution which can be achieved with them. In general, CL analysis performed in a scanning electron microscope can be divided into two categories: i) microscopy and ii) spectroscopy. In microscopy, luminescence images or maps of regions of interest can be acquired; while in spectroscopy mode a spectrum corresponding to a selected area of the sample can be obtained. The three main advantages which have motivated further development of the CL technique are: 1) CL is the only non-contactless technique (in electron probe instruments) that provides the ability to characterize the optical and electronic properties of luminescent materials with a high spatial resolution. 2) With increasing interest in fabrication o f light emitting optoelectronic devices, there is a greater need for development of characterization tools to study the emission properties of these materials. 11 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 3) CL technique can detect impurities as low as 1014 atoms cm'J which is several orders of magnitude smaller than X-ray technique. II.A.1. Interaction of electrons with solids Electron beam interaction with solids, electron energy dissipation and creation of carriers in solids are of great importance for the CL analysis of solids. Electrons interacting with solids undergo both elastic and inelastic scattering mechanisms. The elastic scattering of electrons by the nuclei of atoms, which are partially screened by the bound electrons, can be analyzed using Rutherford model and the total scattering cross section is given by f z l 2 4 K f T ' 1 \ E + mac~ I e J S (S + \) ^ E + 2 m0 c2 j where Z is the atomic number of the scattering atom, E is the energy of the electron in kV, and S is a screening parameter. This model is fairly accurate for low electron energies from about 20 to 50 keV for solids with low to intermediate atomic numbers. Inelastic scattering can be described by the Bethe expression for the mean rate of energy loss per segment of distance S traveled in the solid as where e is the electronic charge, Na is Avogadro’s number, p is the density, A is the atomic weight, E is the mean electron energy, and J is the mean ionization potential. (2.2) 12 R ep ro d u ced with p erm issio n o f th e copyright ow ner. Further reproduction prohibited w ithout p erm issio n . The incident electron undergoes a series of elastic and inelastic scattering events in the material. As a result of these scattering events within the material, the original trajectories of the electrons are randomized. The range of the electron penetration is a function of the electron beam energy £*, K ~ (k /p ) E° (2.3) where p is the density of he material, k depends on the atomic number of the material and is also a function of the the energy, a depends on the atomic number of the material and on the beam energy Eb} The total length of an individual electron can be obtained from Eqs. 2.1 and 2.2 and is known as the Bethe range. The effective depth to which energy dissipation extends is known as the Gruen, electron beam, or penetration range and is defined by Eq. 2.3. Figure 2-2 shows the comparison of the electron penetration range calculated according to Everhart-Hoff formula for Si and GaAs. Everhart and Hoff have estimated the total generation volume in a material and is given as2 Re = (0.0398/p) E l 75 (pm) (2-4) where p is in g/cm3, Eb is in keV. The shape of the generation volume depends on the atomic number, varying from a pear shape for a low atomic number material, through a spherical shape for 15 < Z < 40, to a hemispherical for larger atomic numbers. One of the fundamental differences between CL and photoluminescence (PL) is that, whereas a photon can generate only one electron-hole pair, one high energy electron, can generate R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 15 10 5 GaAs 0 0 10 20 30 40 E-beam energy (keV) Fig. 2-2. The electron beam range, R«, for Si and GaAs as a function of the electron beam energy calculated from Everhart -Hoff model. R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . GaAs 5keV 20 E 3 . > < D j*. 10keV N 5 U J ■o 40keV 35keV 15keV \ 20keV 25ke' 30keV 0 1 2 3 4 5 Depth (pm) Fig. 2-3. Depth-dose curves for GaAs R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . thousands of electron-hole pairs. The generation factor(i.e.. the number of electron-hole pairs generated per incident beam electron) is given by G = Eb (1 - y) / E; (2-5) where Eb is the electron beam energy, E, is the energy required for the formation of an electron-hole pair, i.e. ionization energy, and y represents the fractional electron beam energy loss due to backscattered electrons. The local generation rate of carriers is g (r, z) = < g> G Ib / e (2.6) where directions in Fig. 3-2(a). These streaks correlate with the orientation and position of dark line defects (DLDs) of this sample, as observed in the LPCL images of Figs. 3- 3(a) and 3-3(b). DLDs are typically observed in the monochromatic CL imaging of partially relaxed InGaAs films grown on GaAs. 18 The LPCL images of Figs. 3-3(a) and 36 R ep ro d u ced w ith p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . 3-3(b) were taken with the polarizer rotated to detect emission of light with E-L[l 10] and E||[l 10] detection orientations at a wavelength of 956 nm (1296 meV). where E is the electric field of light. In order to emphasize polarization variations in luminescence, the ratio of these images is displayed in Fig. 3-3(c). The pixels in the ratio image at a (x.y) position are represented as log[Ii(x,y)/I||(x,y)], where L and In are the pixel intensities under E -L [110] and E || [110] detection orientations, normalized to a 256 level greyscale. The bright and dark regions in Fig. 3-3(c) correspond to intensity ratios. Ix /Ij i - of -0.9 and -0.6, respectively. The average value of Ij/I|| is 0.83, as measured from integrated LPCL spectra taken while the electron beam is rapidly scanning the entire region shown in Fig. 3-3(c). It is our hypothesis that the presence o f dark and light streaks (i.e., a non-uniform intensity) in Fig. 3-3(c), running parallel to the DLDs in Figs. 3-3(a) and 3-3(b), reveals a polarization anisotropy caused by pm-scale variations in strain. The strain-induced splitting of the heavy-hole (hh) and light hole(lh) valence bands at k= 0 can be studied by examining the polarization and energy dependence of the luminescence. 1619 We have discussed the effect of strain on the band structure in Appendix A. The energy change, AE, of the excitonic luminescence involving the j = 3/2 valence bands induced by the strain is given by the following solution of the orbital strain Hamiltonian for k=0; 19 R ep r o d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . )±jj4 c /2 s l +b 2 [ls: )" + 362(^„ - e yy)' . (3-3) where Sxx Eyy Ezz (E110 E | |0 ) / 2, S X y (E l 10 ' El io ) / 2, and Sjrz -2 Sxx C 12 / CI j. Elio and Euo are the strains along [110] and [110] directions, respectively. The constant a is the hydrostatic deformation potential; b and d are uniaxial deformation potentials associated with strains of tetragonal and rhombohedral symmetries, respectively, which remove the degeneracy of the bands as indicated by the ± sign, Cn and C 12 are elastic constants; these constants for Inx Gai-x As are found by interpolating between values for GaAs and InAs given in table A. 1,20 We have examined the Ino.15Gao.85As/Ino.20Gao.80As interface with plan-view TEM, as shown in Fig. 3-4. The misfit dislocation distribution, most of which are of the 60° type,21-22 was examined at several different regions of the interface. Figures 3-4(a) and 3-4(b) show linear misfit dislocation densities of 6.1 x 104 and 8.0 x 104 cm' 1 along [110] and 6.5 x 104 and 1.3 x 105 along [110], respectively. For 60° misfit dislocations, an average strain relaxation of 0 .0 2 % occurs for linear dislocation density of 1 x 1 0 4 cm' 1.22 The resulting in-plane strains, si 10 and suo, in the Ino.20Gao.80As film relative to a relaxed Ino.15Gao.85As film are 0.219% and 0.227%, respectively, in Fig. 3-4(a) and 0.189% and 0.091% in Fig. 3-4(b). Application of Eq. 3-3 gives a AE of 19.3 ± 7.4 and 12.1 ±5.1 me V for the regions of Fig. 3-4(a) and 3-4(b), respectively; the center of the 38 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . strain-split bands is separated by -7 meV. It is therefore, evident that regions of isotropic and anisotropic relaxation are both found in this sample. The regions of Figs. 3-4(a) and 3-4(b) represent typical variations sampled with TEM. The CL images represent a sampling over a much larger area, thereby enabling measurements of variations in transition energy [as, e.g., the -19 me V shift seen in the CL spectra o f Fig. 3-2(b)] which are greater than those estimated from the TEM analysis and Eq. 3-3. For an in-plane biaxial stress (resulting in sx y = 0)), no polarization of either hh- or Ih-excitonic emissions is expected for emission normal to the (001) surface plane. For a pure uniaxial stress along the [ 1 1 0 ] direction, mixing of hh and Ih characters in the strain-split bands is negligible, and hh (lh) excitonic emission normal to the (0 0 1 ) surface plane is totally (partially) linearly polarized perpendicular (parallel) to [ 1 1 0 ] . 19 Since the interface exhibits varying degrees o f relaxation along both <110> directions, there will be varying degrees of mixing of hh and lh characters in the strain split bands, leading to only a partial linear polarization for excitation emission. The regions of uniform bright and dark contrast in Fig. 3-3(c) indicate variations from nearly biaxial to uniaxial compressive stress, respectively, as the system relaxes preferentially along the [110] direction. Such anisotropic relaxation would create regions of quasiuniaxial stress which are observed to run along both <110> directions in Fig. 3-3(c). The bright streaks in Fig. 3-3(c) indicate regions where the intensity ratio Ij/I||, is closest to unity, revealing regions closest to biaxial stress. The dark streaks, likewise, run along both .<110> directions, yield minima of Ix/I||, and reveal regions closest to the uniaxial stress. 39 R ep r o d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . A further correlation of the CLWI image of Fig. 3-2(a) with the LPCL image of Fig. 3-3(c) is shown with a peak wavelength and Ix/I|| ratio versus distance histogram in Fig. 3-5, taken along an arbitrary [110]-oriented line. The histogram shows that the blue- and red-shifted regions in CLWI correspond to the regions of reduced and enhanced- polarization anisotropy [bright and dark regions in Fig. 3-3(c)], respectively, in the LPCL imaging. This correlation confirms that the spatial variation in emission wavelengths, as shown in Fig. 3-2(a), is caused primarily by variations in in-plane strain as opposed to composition which would not yield a polarization anisotropy. The regions of anisotropic relaxation (quasiuniaxial) correspond to regions of primarily enhanced relaxation along [ 1 1 0 ] which results in a red-shifted luminescence that is spatially correlated with a polarization anisotropy, as observed in Fig. 3-5. R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 947 951 955 959 963 Unm) T = 87 K RED (0 BLUE 5 k - 4 - » CO c < D c _l O 900 925 950 975 1000 Wavelength (nm) Fig. 3-2. CL wavelength imaging in (a) and local spectra in (b) for two different positions. A scale showing the mapping of wavelengths of peak CL intensity into shades of gray is shown in (a). The blue- and red-shifted local spectra in (b) were obtained from the spatial positions labeled B ad R, respectively, with arrows in (a). 41 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Fig. 3-3. Monochromatic linearly polarized CL images for the same region shown in Fig. 3-2(a) at X = 956 nm. The polarization detection conditions of E J_[l 10] and E||[l 10] are shown in (a) and (b), respectively. The ratio image of log (Ij/I||) is showing (c), revealing the pm-scale polarization anisotropy. 42 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithou t p erm issio n . Fig. 3-4. Plan-view TEM showing two different regions of the In0.15Ga0.85As/In0.20Ga0.80As interface which exhibits different dislocation densities and strain relaxation along both < 1 1 0 > directions in (a) and (b). 43 R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . 970 [1 T O ] scan . T = 87 K 965 CLW I 1 960 < < 955 950 0.9 0.8 H 0.7 - LPCL 0.6 0 20 40 80 100 120 60 Distance (nm) Fig. 3-5. Histogram of the CL wavelength imaging, CLWI, and Ij./I|| ratio for a line scan along the [110]. The spatial correlation of regions with a red shift and an increased polarization anisotropy (regions of nearly uniaxial compressive stress) and regions with blue shift and a reduced polarization anisotropy (regions of nearly biaxial compressive stress) is observed. 44 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . III.D.Influence o f m isfit dislocations on therm al quenching o f lum inescence in InxG ai.xA s/G aA s m ultiple quantum w ells The temperature dependence of luminescence in quantum wells and superlattices has been investigated previously, 23-24 however little work that addresses the effects of thermal quenching of luminescence by misfit dislocations has been reported. Thermal quenching of luminescence in QWs has been interpreted in several ways by different authors, and has been attributed to thermal dissociation of excitons and thermally activated nonradiative recombination,25 or due to thermal emission of carriers out of the QWs, resulting in a reduction of luminescence intensity at higher temperatures.26 In this section, the influence of misfit dislocations and point defects associated with strain relaxation on the thermal quenching of luminescence is examined. The activation energy associated with the thermal quenching of luminescence vary spatially in close proximity to defects, and we have utilized a new approach which uses spatially resolved CL to image these activation energies. III.D.l.Experimental details Multiple-quantum-well (MQW) samples were grown by molecular beam epitaxy using standard In, Ga, and As solid sources. The samples designated D38 and D18 consist of 144 periods of 65 A Ino.21Gao.79As MQWs with barrier thicknesses of 115 A and 400 A, respectively. In sample D 179, a 65 A MQW structure having 1 0 0 and 1230 A barriers with 14 periods (28 QWs) were grown. The samples were investigated with 45 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . scanning CL microscopy. An electron beam current of -7 nA and beam energy of 20 keV were used to probe the samples. CL spectra and images were recorded for various different temperatures between 8 6 and 250 K. III.D.2.Results and Discussion The temperature dependence of the electron-to-heavy-hole excitonic luminescence intensity for sample D18 is shown in Fig. 3-6 for temperatures between 8 6 and 250 K. The data labeled A correspond to the integrated CL spectral intensity, Im q w . measured while the electron beam was scanning a 128 pm x 94 pm region. The C L' intensity reduced by about two orders of magnitude as the temperature increased from 8 6 to 250 K. From Fig. 3-6, it is evident that there exists two temperature ranges which show an Arrenhius behavior. This behavior indicated the presence of two different thermally activated processes responsible for the reduction in luminescence intensity. The activation energies for both cases are obtained from the straight line portions of the log I m q w v s . 1/T plots; activation energies of -227 and -79 meV are obtained in the temperature ranges of 86-150 K and 150-250 K, respectively. In order to study local variations in the activation energy, we performed CL imaging of the MQW excitonic luminescence at various different temperatures between 8 6 and 250 K. A scanning area of 128 pm x 94 pm was discretized into 640 x 480 pixels. CL studies enable a mapping of local changes in activation energies on the scale of -1 pm in GaAs, as the resolution is limited by the minority-carrier diffusion and the size of 46 R ep ro d u ced w ith p erm issio n o f th e cop yright ow n er. Further reproduction prohibited w ithout p erm issio n . the peak-shaped excitation volume. The activation energy (Ea) was determined at all spatial (x,y) positions; gray-scale images representing the activation energies are shown in Figs. 3-7, 3-8 and 3-9. In order to determine Ea at each pixel position, 14 images were obtained for various fixed temperatures between 8 6 and 250 K. The slopes were determined separately for the two temperature ranges observed in Fig. 3-6 using a least- squares fitting at each (x,y) position. The monochromatic CL images obtained at 8 6 K for samples D18, D38, and D 179 are shown in Figs. 3-7(a), 3-8(a), and 3-9(a), respectively. Figures 3-7(b), 3-8(b), and 3-9(b) represent a spatial mapping of the activation energies for the same regions shown in Figs. 3-7(a), 3-8(a), and 3-9(a), respectively, for the intermediate temperature range (86-150 K). Figures 3-7(c), 3-8(c), and 3-9(c) represent a spatial mapping of the activation energies obtained in the high temperature range (150-250 K). The mapping of Ea into a gray-scale representation is shown by the gray bar indicating the activation energy scale. Plots of log I m q w v s . 1/T for sample D18 are shown in Fig. 3-6 for two arbitrary local regions, labeled B and D (for bright and dark regions). Long streaks of constant gray shade are seen to run along the high symmetry < 1 10> directions in Figs. 3- 7, 3-8 and 3-9 in both monochromatic and activation energy CL images. In monochromatic CL imaging, dislocations appear as dark line defects (DLDs) as a result of a localized reduction of luminescence efficiency due to an enhanced nonradiative * IS recombination. Comparing Figs. 3-7(a) and 3-7(b), we observe that regions containing 47 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithou t p erm issio n . 250 (0 'c 3 _d (0 160 T (K) 125 100 86 10 4 6 8 10 12 Fig. 3-6 Temperature dependence of CL intensity for sample D18. The data labeled A corresponds to CL integrated intensity, Im q w , measured while the electron beam was scanning a 128 mm x 94 mm region. The data labeled B and D correspond to the intensity obtained from bright and dark regions, respectively, shown in Fig. 3-7 (a). The solid lines are linear fits to the data. 48 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 38meV llOmeV Fig. 3-7. Monochromatic CL images (at T = 8 6 K) obtained at 955 nm for sample D18. The activation energy (in meV) image of Eai obtained in the intermediate temperature range (86-150 K) for the same regions shown in (a) is shown in (b). The activation energy image o f Ea2 obtained in the high-temperature range (150-250 K) is shown in (c). A scale showing the mapping of the activation energies is shown below each image. 49 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ith out p erm issio n . TomeV Fig. 3-8. Monochromatic CL images (at T = 8 6 K) obtained at 960 nm for sample D38. The activation energy (in meV) image of Eai obtained in the intermediate temperature range (86-150 K) for the same regions shown in (a) is shown in (b). The activation energy image of Ea2 obtained in the high-temperature range (150-250 K) is shown in (c). A scale showing the mapping of the activation energies is shown below each image. 50 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . 40meV 190 meV Fig. 3-9 Monochromatic CL images (at T = 8 6 K) obtained at 948 nm for sample D179. The activation energy (in meV) image o f Eai obtained in the intermediate temperature range (86-150 K) for the same regions shown in (a) is shown in (b). The activation energy image of Ea2 obtained in the high-temperature range (150-250 K) is shown in (c). A scale showing the mapping of the activation energies is shown below each image. 51 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ith out p erm issio n . 5 E CM (0 L U 250 CO c 3 (0 c _l O 34 (0 32 L U 0 60 80 20 40 Distance (|im) Fig. 3-10. Stack plot of CL intensity, activation energies Eai and Ea2 for an arbitrary line scan done along the (110) direction for sample D38. The spatial correlation of regions showing decreased luminescence efficiency, higher Eai, and lower E^ (indicated by dotted lines) and increased luminescence efficiency, lower Eai, and higher E ^ (indicated by solid lines) is observed. 52 R ep r o d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . misfit dislocations (dark regions) show a lower activation energy than regions absent of DLDs [bright regions in Fig. 3-7(a)]. However, in the high temperature range [Fig. 3- 7(c)], there is a reversal of contrast as compared to Fig. 3-7(a), i.e., the bright regions in Fig.3-7(a) exhibit a lower activation energy while the dark regions (DLDs) exhibit a higher activation energy. In order to further illustrate the spatial correlation existing between sets of images for a given sample, we show stack plots for sample D38 in Fig. 3-10, corresponding to images in Figs. 3-8(a), 3-8(b), and 3-8(c). The luminescence intensity, and the activation energies for the intermediate (Eai) and high-temperature range (Ea2) are plotted as a function of the distance along an arbitrary <110>-oriented line. The activation energy Eai ranges from -23 to 38 meV for all three samples. Prior to the capture of electrons and holes into the QWs, free carriers which have thermalized down to the band edges must diffuse along the GaAs barriers. A recent study showed that the activation energy for ambipolar diffusive transport, Ed, in a nipi-doped Ino.2Gao.8As/GaAs MQW structure possessing similar barrier and MQW thicknesses has a lower limit of -29 meV.2 7 It is plausible that the same defects which impede ambipolar diffusion also serve as nonradiative recombination centers. Thus, once sufficient thermal energy is attained to surmount the defect-induced barriers, the mobile carriers also become more susceptible to nonradiative recombination at these same centers before capture in the QWs, thereby explaining similar values of Eai and Ed- Likewise, it is also possible that ionization of free and bound excitons in the QWs, prior to radiative 53 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . recombination, also contributes to the decrease in I m q w in the intermediate temperature range since defects in the QWs should also exhibit similar thermal barriers. The binding energy of the exciton is -7 meV, requiring additional thermal activation over defect- induced barriers in the QWs prior to nonradiative recombination. For the intermediate temperature range (86-150 K), the bright regions in samples D179 and D38 exhibit a smaller activation energy Eai than that of dark regions (DLDs) while the bright regions in sample D18 exhibit a larger activation energy than the dark regions. Consistent with the above description, we expect that diffusing carriers in the GaAs barriers o f dark regions will experience an enhanced probability for nonradiative recombination prior to their capture in the InGaAs QWs. The bright regions which contain a reduced density of defects (i.e., density of misfit dislocations and point defects) in all three samples exhibit similar activation energies (26-33 meV). The decrease [as shown in Fig. 3-7(c)] or the increase {as shown in Figs. 3-8(c) and 3-9(c)] in activation energies of dark regions as compared to the bright regions is evidently due to a change in the distribution o f defects (both in density and type) in the dark regions caused by the differences in the GaAs barrier thickness between samples. Prior studies by Hillmer et 28 al. have shown that the 2D carrier mobilities remain nearly constant between 80 and 150 K and 2D carrier difTUsivity increases by a factor of less than 2 between 80 and 150 K. The excitation volume of a 20 keV electron limits the spatial resolution to ~1.5 pm in GaAs.2 9 Thus, small changes in carrier diffusion length with temperature will negligibly affect the local changes in activation energy that are observed here. 54 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithou t p erm issio n . The activation energy is most likely a result of re-emission of carriers which have been captured in the QWs since Eai varies from -65 to -130 meV. for all three samples, and is close to the electron and hole barrier heights (ground state to unbound state) for Ino.2Gao.8As/GaAs MQW’s.3 0 A similar re-emission of captured carriers has previously been observed in AlGaAs/GaAs MQW systems.2 6 For a region which contains misfit dislocations, the local reduction in strain results in a lowering of the band gap and an increase in the effective barrier height for electrons (E b c ) and holes (E b v ) as compared to the effective barrier height for electrons and holes in a bright region exhibiting a larger local strain. It is possible that the enhanced activation energy exhibited by the DLDs in Figs. 3-7(a) and 3-9(a) is due to the larger barrier heights for carrier re-emission exhibited in the partially relaxed regions. The limiting cases for the QW barrier heights are shown in Table 3-1, as calculated with a standard transfer matrix method which is explained in detail in Appendix B.3 0 The barrier heights for the partially relaxed regions will be intermediate to the fully strained and relaxed cases. In the high- temperature range (150-250 K), the barrier regions exhibit a lower activation energy than the dark regions in samples D18 and D179, which is consistent with the lower effective barrier height for electron and holes listed in Table 3.1 in a quantum well subject to a larger strain. The converse is true for D38, which exhibits a higher activation energy near bright regions (away from DLDs). The nonradiative recombination that gives rise to DLDs is a result o f recombination at cores of misfit dislocation and point defects in the t f i vicinity of the dislocations. 55 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Table 3-1. The effective barrier heights, E b c and E b v for re-emission out o f the quantum well. These heights are calculated as E b c = AEc - Eei and E b v = AEv - Ehhi, where AEc and AEv are the conduction- and valence band offsets between Ino.2 iGao 79AS and GaAs. and Ed and Ehhi denote the calculated first electron and heavy-hole subband energy. E bc E b v (meV) (meV) Fully strained 1 1 1 58 Fully relaxed 159 80 It is possible that D38, which has the smallest average GaAs barrier layer thickness of all the samples, may contain the largest average point defect density. This enhanced defect density could act to reduce the activation energy for nonradiative recombination near the DLDs, in competition with the opposite tendency for a higher activation barrier caused by a greater strain relaxation. Thus, the behavior of the activation energies near DLDs reflects the extent to which both (i) strain relaxation and (ii) defect centers will influence the thermal re-emission of carriers from the QWs. III.E.EfTect o f interface defect form ation on the carrier diffusion and lum inescence in In0jG a 0.8As/AlxG ai.x As quantum wells High-electron mobility transistors (HEMTs) are utilized as switches or amplifiers in the 10 - 100 GHz range.31' 35 Electronic transport in these carriers is carried out via a high-mobility two-dimensional electron gas (2DEG). This 2DEG is formed at the interface of the large-band gap AlGaAs barrier layer material and an undoped smaller 56 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . band-gap InGaAs channel layer. If the channel layer is sufficiently thin, the lattice mismatch between InGaAs and AlGaAs is accommodated by elastic strain and the HEMT is called pseudomorphic HEMT. The transport properties depend on the conduction-band discontinuity between the channel layer and the barrier layer, and hence a larger In content would result in superior performance.j6 However increasing the In content results in an increase in the strain in the material. Once the critical thickness is exceeded the strain relaxation proceeds via the formation of misfit dislocations at the interface. In this section, we examine the interplay between strain relaxation, optical properties, and transport properties in Ino.2Gao.8As/Alx Ga|.x As QW samples, designed for HEMTS. We have examined the samples with CL techniques similar to those discussed in the previous two sections: the spatial variation in excitonic peak energy and polarization anisotropy, and thermal quenching of luminescence by misfit dislocations. In addition to these studies, we have also examined the change in the ambipolar diffusion length of carriers parallel to and in close proximity to misfit dislocations using a CL- based diffusion experiment. The changes in diffusion length are measured in varying proximity to DLDs, and correlation with the CL intensity, activation energy, polarization anisotropy, and luminescence energy are established. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . III.E.l.Experimental Details Six HEMT devices were grown by molecular-beam epitaxy3 7 -4 0 . Each sample consisted of the following layers (in order from substrate to the surface) grown on semi-insulating GaAs (001) substrates: a 1750-A thick GaAs undoped buffer layer: a GaAs/Alo.2sGao.75As MQW (-42-A- thick QWs); a 3000-A-thick undoped GaAs buffer; an Ino.2Gao.8As QW (channel) varying in thickness from 75 to 300 A; a 530 A layer of Alo.25Gao.75As, containing a 5-doped Si layer (-5 x 1012 cm'2 ) within about 30 A of the channel; and a 50-A thick undoped GaAs cap. These samples were previously analyzed with transmission electron microscopy (TEM), triple axis x-ray diffraction (XRD), and Hall measurements to establish a relation between degradation of device performance and the formation of <110>- oriented misfit dislocations.37-38 That study established that the onset of the substantial device degradation occurred when misfit dislocations formed along both (110) directions. High resolution XRD further showed that the average In composition x in the sample varied from 0.203 < x <0.214. Scanning monochromatic CL, panchromatic CL. CLWI, and LPCL were performed with a modified JEOL 840-A scanning electron microscope. An electron- beam energy of 12keV with varying beam currents from 0.1 to 10 nA was used to probe the samples. The temperature of the samples were varied between 87 and 300 K, for the various CL measurements. CLWI and LPCL measurements were performed to study the spatial variation in CL peak wavelength energy and the polarization ratio. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . e-Beam Ellipsoidal Mirror [110] 50 A GaAs cap 530 A L 259a 0.75A s barrier Carrier 5-doped Si generation QW GaAs/AlGaAs MQW region 3000 A GaAs barrier GaAs (001) substrate Fig. 3-11. Schematic diagram of the HEMT sample structure showing the ambipolar diffusion experiment. 59 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . The ambipolar diffusion lengths were measured using an approach illustrated in Fig. 3-11. The HEMT samples were coated with a 800-A- thick Ag mask over part of the sample. The Ag film had lateral dimensions of 100 x 100 pm2 , and the edges of these squares were oriented along the (110) directions. The e-beam energy of 12 keV was sufficiently large so that -80% of the beam penetrated the Ag film and generated electrons and holes in the region just below the mask.2 9 The Ag mask prevented light from radiative recombination in the generation region just below the mask from being detected by the CL collection system; however, luminescence from carriers which diffused along the [110] direction (as shown in Fig. 3-11) and recombined just beyond the edge of the mask was detected. By simultaneously scanning the e-beam toward the edge of the mask and recording the integrated intensity of excitonic luminescence coming from the Ino.2Gao.8As channel as a function of x, the distance from the mask edge, we have measured the ambipolar diffusion length, Ld, of carriers in the channel. From a simple diffusion model, the CL intensity is proportional to exp(-x/Lo), as first demonstrated by Zarem et a f x for transport in GaAs/Alx Gai.x As heterostructures using a similar CL experiment. Our diffusion length was performed for various line scans parallel to and in varying proximity to the DLDs in the samples with 150 and 185 A Ino.2Gao.8As channel thickness. Owing to the formation of an orthogonal network of dislocations for channel thickness greater than 185 A, we did not attempt this diffusion experiment in samples with thicker Ino.2Gao.8As channels. A nonexponential dependence 60 R ep ro d u ced with p erm issio n o f th e copyright ow ner. Further reproduction prohibited w ithout p erm issio n . of the CL intensity would be expected for an e-beam crossing misfit dislocations in this situation, thus requiring more elaborate means to extract the diffusion lengths. HI.E.2.RESULTS AND DISCUSSION \\\.E.2.a.Evaluation o f the average strain relaxation in the HEMT samples An anisotropy was observed in the density of (110>- oriented, where dislocations first form along [110] and continue to have a greater density along this direction as the channel thickness increases. The two types of 60° dislocations are chemically inequivalent, owing to the difference in termination of the extra half-plane which, e.g., in the type-I (shuffle) set has a Ga and As termination, respectively, for the unreconstructed a ([110] line direction) and p ([110] line direction) dislocation cores. For a nonvicinal GaAs(OOl), substrate (i.e. normally no misorientation) it is well established that for single thin Inx Gai.x As (x < 0.2) films grown on GaAs(OOl), a dislocations are the first to form in relaxing the strain.2 2 -4 2 This has previously been attributed to the different levels of stress required to nucleate a and p dislocations and the differences in a and Pdislocation propagation velocities on nonvicinal GaAs(OOl) substrates.4 3 -4 4 Assuming a predominance of 60°-type misfit dislocations in these samples, the average strain relaxation along a (110) direction is 0.02% for a linear dislocation density (LDD) of lxlO4 cm'1 2 2 . The maximum in-plane strain of 1.41% in the Ino.iGao.gAs channel is 61 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . therefore reduced in proportion to the orthogonal LDD. The average [110]- and [110]- oriented LDD and resulting in-plane strains, Si 10 and eno, are shown in Table 3-2 for the HEMT samples with various InojGao.sAs channel thickness. Table 3-2. Linear dislocation densities (LDD) along the [110] and [110] directions for the various Ino.2Gao.8As channel thickness. The calculated eno and eno strains for each sample are shown. Channel thickness (A) [110] LDD (cm'1 ) [lfO] LDD (cm'1 ) si 10 £110 75 < 1 x 10' < l" x 101 0.014129 0.014129 150 3 x 103 < 1 x 102 0.014068 0.014127 185 5 x 103 4.4 x 102 0.014027 0.014120 205 1.7 xlO 4 5.5 x 102 0.013785 0.014117 250 4 x 104 1.8 x 103 0.013313 0.014092 300 1.16 x 105 2.5 x 103 0.011769 0.014078 The linear dislocation densities were obtained from a combination of CL imaging and plan-view TEM. For CL imaging of DLD’s, a maximum area o f -0.4 x 0.4 mm2 limited by the field of view of the ellipsoidal mirror was used to determine the LDD. In order to evaluate the average strain relaxation in the Ino.2Gao.8As HEMT samples, we have examined spatially integrated CL spectra of these samples at room temperature, as shown in Fig. 3-12. An area of 128 x 94 pm2 was scanned during the acquisition of these spectra. The energy of the peak position is found to decrease from 1.217 to 1.179 62 R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . eV as the channel thickness is increased from 150 to 300 A. The first confined electron to heavy-hole (el-hhl) transition energy was calculated as a function of the channel thickness for the case of (i) fully biaxially strained (pseudomorphic), (ii) uniaxially strained, (iii) fully relaxed, and (iv) partially relaxed Ino.2Gao.8As channels. The purpose of the top Alo.2sGao.75As barrier is to increase the confinement energy for electrons, thereby effectively increasing the electron density in the channel. The resulting asymmetrical QW structure (with a 150 A width) subject to an electric field created by the ionized 5-doped Si layer is shown in Fig. 3-13. The electron and hole envelope wave-function calculations were performed with a transfer-matrix method (TMM) technique using a self-consistency field approximation that includes Hartree term3 0 -4 5 '47. Ail occupied confined electron states, as determined by the Fermi-level position, were used in calculating the field as a function of the position in the channel. A similar method was employed to calculate the field self-consistently in a nipi-doped Ino.2Gao.8As MQW structure, as discussed in Ref. 30. The wave functions and potentials were calculated self-consistently using Airy functions in the TMM by discretizing the potential into discrete linear field regions with -5 A widths. The use of narrower widths only negligibly affected the calculated electron and hole eigenstates. The conduction to valence-band offset ratios (AEC / AEJ at both interfaces of the Inx Ga|. 63 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . x As QW were taken as linear interpolations between 70/30 and 60/40 for GaAs/ Inx Gai. x As and GaAs/Aly Gai.y As interfaces, respectively.4 8 The results of a calculation showing the band diagram, ground state electron and hole wave functions and Fermi level for the pseudomorphic case is shown in Fig. 3-13. The ground-state electron and heavy hole wave functions are shown superimposed on the calculated band profile in Fig. 3-13. The maximum electric field Fm in the Ino.2Gao.8As channel (for a 150 A width) and the el-hhl transition energy versus the electron concentration in the channel ne at room temperature is shown in Fig. 3-14. The maximum field in the channel occurs at the Alo.25Gao.75As/ Ino.2Gao gAs interface, resulting in Stark shifts of the confined electron and hole states. The field-induced Stark shift decreases from a reduced electron concentration in the channel and Si 5-doping concentration, resulting in a larger el-hhl transition energy as ne decreases (as shown in Fig. 3-14). The strain-induced change in the Ino.2Gao.8As band edges were calculated using the 4 x 4 Luttinger-Kohn and Pikus-Bir Hamiltonian for a general in-plane strain £110 * £iTo, referred to the (110) dislocation directions as discussed in Appendix A. The strain- induced energy change AE of the band gap involving the j = 3/2 valence bands is obtained by a solution of the orbital-strain Hamiltonian and is given in Eq. 3-3. The low symmetry for a eno * Sno strain in the Ino.2Gao.8As channel required the use o f the Luttinger-Kohn Hamiltonian to determine the Ino.2Gao.8As effective mass of 64 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . In0 2G 3 q 8A s Channel thickness (A) - T = 296 K 300 250 (O ■ 4 — » c =3 (0 205 >* 4-4 to c V 4 > 4 c O 185 150 900 1000 1100 Wavelength (nm) Fig. 3-12. Stack plot of spatially integrated CL spectra at room temperature for all HEMT samples. 65 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 0.0 - 0.2 -0.4 > < D hh1 ■ >* D) o 0.0 L U - 0.2 Pseudomorphic -0.4 -100 0 100 200 Distance (A) Fig. 3-13. Self-consistent-field calculation o f the band profile for the Ino.2Gao.8As HEMT sample (channel thickness of 150 A) showing the el and hhl wavefimctions and Fermi- level position. 66 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 0 > -20 -60 -80 Pseudomorphic 0 2 1 3 4 5 6 5 4 E o to O 2 E u_ 1 0 ne (x 101 2 cm'2) Fig. 3-14. Self-consistent-field calculation of the maximum electric field Fm in the Ino.2Gao.8As channel and the change in the el-hhl transition energy vs electron concentration at room temperature. 67 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . 1.35 > < D L U T = 296 K Pseudomorphic Uniaxial strain Fully relaxed 1.30 1.25 Pseudomorphic 1.20 — G L 1.15 i 1.10 X X X X » X X X 100 200 300 QW thickness (A) 400 Fig. 3-15. Plots of theoretical el-hhl luminescence energy position vs the In0. 2Ga0.sAs QW width for (i) fully strained, (ii) fully relaxed, (iii) uniaxially strained, and (iv) partially relaxed strain (squares) conditions using data in Table 3-2. The experimental CL peak positions from Fig. 3-12 are shown as dots. Calculations of el-hhl vs the QW width are also shown for frilly strained Ino.21Gao.79As QW, to illustrate the effect of In composition variation. 68 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithou t p erm issio n . holes along the [001] growth directions. Standard hole masses and band gaps are used for AlxGai.x As.The Luttinger parameters are taken as a linearization, again, between the values for InAs and GaAs.4 9 The effective masses and strain-modified barrier heights were then used in the TMM calculation to calculate the el-hhl transition energies for (i) the pseudomorphic case (sno = Eno, = 0.0141), (ii) the uniaxial strain condition (£no= 0 and Eno = 0.0141), (iii) the fully relaxed case (si io = eilo= 0) and (iv) the partially relaxed case with general strain values, £no and £uo, as obtained from the measured dislocation densities shown in Table 3-2 for each channel thickness. The results are shown in Fig. 3-15 as solid lines, medium dashed lines, long- dashed lines, and squares for cases (i)-(iv), respectively. The experimental el-hhl peak energies (dots) are found to lie closest to the theoretical curve for the pseudomorphic case ( e i io = Eno = 0.0141). The deviation between the experimental peak positions and pseudomorphic calculation increases as the channel thickness increases, consistent with an increased strain relaxation of the Ino.2Gao.8As channel. The use of the measured strains of the Table 3-2 resulted in a better agreement between the experimental and calculated el-hhl transition energies, as shown in Fig. 3-15. The CL imaging and plan-view TEM revealed an increase in the dislocation density with increasing channel thickness as shown in 69 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . Table 3-2. It is apparent that even for the case of the largest channel width of 300 A. the largest dislocation density yields a strain of eno ~ 0.0118, and the film is still -84% strained in the [110] direction. Therefore, the TMM calculations, when incorporating the observed strain relaxation, explain the salient features of the CL peak energies for varying channel thicknesses. Further, the deviation between the experiment and calculations for the partially relaxed case (dots and squares, respectively, in Fig. 3-15) is likely due to a variation in the In composition x. A calculation of the el-hhl energy for a fully strained Ino.21Gao.79As QW (short-dashed lines) is shown in Fig. 3-15, indicating a - 1 0 meV decrease in the calculated el-hhl energy will occur for cases (i) and (iv) above if x = 0 .2 1 is used instead of x = 0 . 2 0 in these calculations. ///.£. 2.6 .Local CL energy and polarization variations in close proximity to dislocations In the previous section, we have established that there are significant energy and polarization variations in the optical transitions in close proximity to misfit dislocations, in addition to the non-radiative behavior of DLDs. The previous systems examined were partially relaxed InxGai.x As/GaAs films which had linear dislocation densities greater than ~ lx l0 4 cm' 1 or one dislocation per pm. Since the carrier diffusion length is ~lpm, defect densities greater than ~ lx l0 4 cm' 1 result in DLDs that are composed of bunches of dislocations, which cannot be resolved individually with conventional CL imaging. Bunches of dislocations that are formed with very narrow dislocation spacings can result 70 R ep ro d u ced w ith p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ith out p erm issio n . in nearly complete strain relaxation along one ( 1 1 0 ) direction with a partial strain remaining in the orthogonal direction. This can further result in a quasi-uniaxial stress leading to a large l\\/1± polarization anisotropy and a reduction in the excitonic transition energy, as previously reported. 50' 52 We have pursued a similar analysis here for the case of dislocations separated by a length by on average greater than the carrier diffusion length, so as to examine the effects of isolated dislocations. Figures 3-16 and 3-17 show (a) CL intensity and (b) CLWI images of samples with 150 and 185 A channel thicknesses, respectively. The gray scale represents the wavelength position A .m of the peak CL intensity. A particularly striking feature is observed in the CLWI images. The wavelength of emission is found to decrease near the DLD position, showing a blue shift correlated with a defect-induced CL intensity reduction. Figures 3-18 and 3-19 each show a line scan analysis for an arbitrary line scan taken perpendicular to the [1 1 0 ] dislocation direction and illustrate a one-to-one correlation between the blue shift and the DLD position. A maximum increase of ~5 and ~10 meV is seen at the DLD centers for the 150 and 180 A samples, respectively, in Figs. 3-16 - 3-19. This behavior appears contradictory to the previously observed red shift measured near DLD positions in Inx Gai.x As samples exhibiting a greater strain relaxation and greater dislocation-induced reductions in the eno strain.50' 32 This apparent discrepancy is, however, explained by the influence of the dislocations and associated point defects on the electron density in the channel. It is our hypothesis that 71 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . these defects create localized deep levels and traps that reduce the effective electron density in the channel near DLDs. thereby simultaneously reducing the field in the channel. The reduction in both the electron density and field will concomitantly reduce the Stark shift, thereby resulting in a local increase in the el-hhl emission energy. A similar behavior was observed for defect-induced reductions in the electric field and Stark shifts for nipi-doped Ino.2Gao.8As/GaAs MQWs.3 0 The larger blue shift in the el-hhl transition energies for the 185 A sample (Figs. 3-17 and 3-19) is evidently due to the enhanced dislocation density. Dislocation bunching and an enhanced point defect density are more prevalent for larger Ino.2Gao.8As channel thicknesses, which should result in a greater local depletion of the electron density in the channel. The local strain relaxation appears to minimally effect the el-hhl transition energy. As shown in Fig. 3-15, the curve for a uniaxial strain condition is -50 meV lower than that for the pseudomorphic case. A defect-induced reduction in the quantum confined Stark effect could also cause a blue shift of -50 me V in the el-hhl transition energy, as seen from Fig. 3-15. That is, strain relaxation and defect-induced reductions in the field cause the el-hhl energy to shift in opposite directions, thereby possibly masking the effects caused by strain relaxation. However, from the CL polarization results discussed below, we show that the average strain tensor within the - 1 pm carrier diffusion length near DLD’s is still well described by a biaxial strain with eno - silo, for the 150 and 185 A samples analyzed in Figs. 3-16-3-19. 72 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . (a ) C L (b)CLWl f t 963 964 9g5 n m Fig. 3-16. (a) CL Intensi ty and (b) C L W I i m ages o f the H E M T sam pl e w i th 150 A channel thi ckness. 73 produced wa hpermte. onof^ C0Pyright owner. Further reproduction prohibited w 'drou^pemiission. 966 968 970 972 974 976 nm Fig. 3-17. (a) CL Intensity and (b) CLWI images of the same regions in the Ino.2Gao.8As HEMT sample with 185 A channel thickness. 74 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 966 lnnoGanaAs 150 A channel T= 87 K 964 962 960 >> 100 0 0 20 1 0 0 120 40 60 80 Distance (fim) Fig. 3-18. Line scan analysis for an arbitrary [110]-oriented line for the images of Fig. 3- 16 (150 A Ino.2Gao.8As channel width) showing CL intensity and CLWI correlations. Dashed and solid lines are used to show correlations between a reduced CL intensity (DLDs) and a blue shift in the el-hhl transition energy. 75 R ep ro d u ced with p erm issio n o f th e copyright ow ner. Further reproduction prohibited w ithout p erm issio n . 980 T = 87 K lnn oGan pAs, 185 A channel 976 972 968 c 200 0 25 50 75 100 125 Distance (jim) Fig. 3-19. Line scan analysis for an arbitrary [110]-oriented line for the images of Fig. 3- 17 (185 A Ino.2Gao.8As channel width) showing CL intensity and CLWI correlations. Dashed and solid lines are used to show correlations between a reduced CL intensity (DLDs) and a blue shift in the el-hhl transition energy. 76 R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . Linearly polarized monochromatic CL images were taken with the polarizer rotated to detect emission of light with E±[110] and E|| [110] detection orientations at wavelengths of 962 and 972nm for the 150 and 185 A samples, respectively. In order to emphasize the polarization variations, the ratio of these images is displayed in Figs. 3-20 and 3-21. The pixels in the ratio image at a (x, y) position are presented as log[L (x. y) / I I I (*, y)]- where Ix and I|| are the pixel intensities under with EJL[110] and E|| [110] detection orientations. The bright and dark bands present in the LPCL ratio images exhibit a local polarization anisotropy, which indicates the presence of pm-scale variations in eno. These bands correlate with the peaks and dips in the CL intensity image, as shown in the line scan analysis of Fig. 3-22 for the 185 A sample. The maximum polarization anisotropies (minimum ratios) are Ix / In « 0.995 and Ix / I y = 0.85 for the 150 and 185 A samples, respectively. The spatially averaged Ix / In ratios for the LPCL images of Figs. 3-20(b) and 3-21(b) are 0.98 and 0.95, respectively. From the four-band k.p calculation, we have calculated Ix / Iy using the dipole approximation in Fermi’s golden rule, i.e., IM n a I ( ue /Ex. n. p !uh ) f 1, where u h is the wave function of the uppermost hole state, and p is the linear momentum operator. Both u e and u h include the envelope functions and zone-center Bloch functions for the s- and p- type conduction- and valence-band states, respectively. The polarization ratio was calculated for a fixed euo = 0.0141 and variable Eno. to simulate the effect of a transition from uniaxial to biaxial (pseudomorphic) strain. The results are shown in Fig. 3-23 for the 150 77 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ith out p erm issio n . and 185 A samples, where we also show the calculated el-hhl transition energy as a function of Z\io- From the measured average polarization anisotropy ratios above and the calculation in Fig. 3-23, the estimated values for eno are 0.0138 and 0.0132 (i.e. 98% and 94% strained) for the 150 and 185 A samples, respectively. This is in reasonable agreement with the low strain relaxation and eno values observed in Table 3-2 from the linear dislocation densities for these samples. These results contrast with the situation previously studied for highly relaxed InxGai.x As samples with dislocation densities greater than - 1x10s cm'1 , where dislocation bunching lead to a quasiuniaxial strain and a larger polarization anisotropy.5 0 '5 2 Thus, for individual dislocations studied here, within the minority carrier diffusion length of ~1 pm, the presence of dislocations with densities less than -IxlO 4 leads to a measured luminescence behavior still well described by a biaxial strain, ei io » euo. III.E.2.C.CL temperature dependence and spatial variations in the activation energy The integrated CL intensity It o f the el-hhl transition in the Ino.2Gao.8As channel and the excitonic luminescence of the GaAs / Alo.25Gao.75As MQW was measured as a function of temperature for selected local regions in close proximity to and away from dislocations, labeled D and B, respectively to denote dark and bright regions in the Ino.2Gao.8As CL imaging. The results are shown in Fig. 3-24 for both the 150 and 185 A 78 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithou t p erm issio n . (a) CL (InojGao gA s) T = 87 K (d) CL (GaAs/AIGaAs MQW) T = 87 K, X = 776 nm (b) LPCL lo g it (Ino^Gao gA s) u. 40 6 8 96 124 152 180 meV (c) Eal (Ino^jao gA s) (e) CL (GaAs/AIGaAs MQW) T = 180 K, X= 794 nm 50 ?2 U 36 5i meV (f) Ea2 (GaAs/AIGaAs MQW) Fig. 3-20. CL imaging of the 150 A In0. 2Ga0.sAs HEMT sample showing (a) spectrally integrated CL images for the el-hhl emission, (b) LPCL IJI\\ ratio images, (c) activation energy Eai images for the In0. 2Ga0.sAs QW luminescence, monochromatic CL images for GaAs/Alo.25Gao.7sAs MQW at (d) T = 87 K and (e) 180 K, and (f) activation energy Ea2 images for the GaAs/ Alo.25Gao.75As MQW emission. 79 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . (a) CL (InojGaogAs) T = 87 K (b) LPCL log J l (Ino^Gao gA s) Ix (d) CL (GaAs/AIGaAs MQW) T = 87 K, A= 776 ran (e) CL (GaAs/AIGaAs MQW) T = 180 K, X= 794 ran 40 6 8 96 124 152 180 meV (c) Eai (tao^jao gA s) 5 o 1 2 £ T 36 38 (f) Ea2 (GaAs/AIGaAs MQW) 4° meV Fig. 3-21. CL imaging of the 185 A Ino.2Gao.8As HEMT sample showing (a) spectrally integrated CL images for the el-hhl emission, (b) LPCL IJI\\ ratio images, (c) activation energy Eai images for the Ino.2Gao.8As QW luminescence, monochromatic CL images for GaAs/Alo.25Gao.75As MQW at (d) T = 87 K and (e) 180 K, and (f) activation energy E^ images for the GaAs/ Alo.25Gao.75As MQW emission. 80 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . lnnoGanaA s. 185 A channel 240 c 160 = > an C fl ® 120 >» CO c (D c i 2 o r _i o 80 - H 0.9 ~ 0.8 g 39 — 36 l u ” 33 > 150 g 120 in 36 90 0 18 54 72 Distance (|im) Fig. 3-22. Line scan analysis for an arbitrary [110]-oriented line for the images of Fig. 3- 21 (185 A Ino.2Gao.8As channel width showing (a) the CL intensity for the el-hhl emission, GaAs/Alo.25Gao.75As MQW emission intensity at (b) T = 180 K and (c) t = 87 k, (d) LPCL 1J1\\ ratio, and activation energies (e) Ea2 and (f) Eai. 81 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ith out p erm issio n . 1.0 0.8 0.6 - h0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 6,10 (X10'2) Fig. 3-23. Calculation of the el-hhl 7i II\\ emission ratio an In0. 2Ga0.sAs QW transition energy vs euo for a fixed suo = 0.0141 at room temperature. 82 T = 296 K QW width (A) 150 185 1 1.22 1.20 > < D ■ C .c 1.18 L U 1.16 R ep r o d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . Temperature (K) 250 200 160 130 100 ln02Ga08As, 150 A channel 10000 1000 100 GaAs/AIGaAs MQW D ***** GaAs/AiGaAs MQW B ***** lnnoGan Q As B ooooo 4 6 8 10 1000/T (fC1) Fig. 3-24. CL intensity vs 1000/T for the same local bright (B) and dark regions (D) in the In0. 2Gao.gAs el-hhl and GaAsZAlo.25Gao.75As MQW monochromatic CL images. The solid lines running through the curves are fit of Eq. 3-6 to the data to determine the activation energies Eai and Ea2 for the In0. 2Ga0.gAs QW and GaAs/Alo.25Gao.7sAs MQW luminescence, respectively. 83 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . samples in a log It v s . 1000/T plot. The CL intensities reduce as the temperature increases from 87 to 250K. This reduction corresponds to the increase of thermally activated nonradiative recombination, which causes an Arrhenius dependence in the high-temperature range. In previous reports of the temperature-dependent luminescence efficiency,2 3 - 2 4 - 5 3 the linear region of the Arrhenius behavior in the high-temperature range was characterized by one or two thermally activated nonradiative recombination processes. We use the following fitting equation for the temperature dependence of the Ino.2Gao.8As QW CL intensity: I t = R t|, ( 3 -4 ) where q=I / (I + R nr / Rr ) is the quantum efficiency,5 4 -5 5 R is a coefficient which depends on the generation rate of the electron-hole pairs and the relative weights of monomolecular recombination and bimolecular recombination,5 4 Rr is the radiative recombination rate which is assumed to be temperature independent, and Rnr represents the rate for nonradiative recombination and is assumed to have the following temperature dependence: Rnr = Rnrl RnrO exp(-Ea / kT), ( 3 -5 ) where R ^ and Ea are the temperature-independent prefactor and the thermal activation energy,5 3 -5 4 respectively, and Rnri is the rate for nonthermally activated nonradiative recombination (i.e., independent of temperature). The temperature dependent exponential term is due to the enhancement of the capture cross section of nonradiative recombination centers as seen by carriers as the temperature increases. The model of Eq. 84 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 3-5 is motivated by the existence of DLDs in the CL imaging at the lowest temperatures, indicating that there are nonradiative channels which are independent of any thermal activation. Therefore, 0 I ----------- -------------- (3-6) 1 + (3 exp(- Ea / kT) where 0 = R / (1 +Rnri/ Rr) and P = R nro / (Rnri + Rr) are independent of temperature and depend on the density of nonthermally and thermally activated nonradiative recombination centers. At the low-temperature limit, r| saturates since thermally activated nonradiative recombination vanishes and It = 0. The spatial variation in Q therefore accounts for the difference in It , the el-hhl emission intensity, when T < 100 K.. as shown in Figs. 3-20, 3-21 and 3-24. The solid lines in Fig. 3-24 show a fit of Eq. 3-6 to the experimental CL data for the el-hhl transition at the corresponding B (bright) and D (dark) regions. The activation energies Eai. were determined for each pixel position by fitting all 640 x 480 pixel intensity values for the monochromatic CL images of the el- hhl transition taken at 12 different temperatures. The results o f Eai for each (x,y) position are shown in Figs. 3-20(c) and 3-21(c), for the 150 and 185 A sample. For the luminescence originating from the GaAs/ Alo.25Gao.75As MQW. I b , a low- temperature saturation of its intensity was not reached for the 87 K minimum in this study (as shown in Fig. 3-24). We have also fit the CL images of I b , taken at 12 different temperatures, with the model of Eqs. 3.4-3.6 , obtaining the activation energy, £ 32, for the GaAs/ Alo.25Gao.75As MQW excitonic luminescence. The results of two fits are shown by 85 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . the solid lines in the log plot of Fig. 3-24 for the same regions, B and D, as indicated for the el-hhl Ino.2Gao.8As luminescence. We further observe a change in the relative intensity of the GaAs/ Alo.25Gao.75As MQW emission near features which correspond to DLDs in the CL imaging of the el-hhl Ino.2Gao.8As Q W emission. At T = 180 K, for both the 150 and 185 A samples, the imaging of the GaAs/ Alo.2sGao 75As MQW emission [Figs. 3-20( e) and 3-21(e)] results in DLDs which correlate, one to one, with that of the el-hhl imaging, as also shown in the line scan data of Fig. 3-22. As the temperature is lowered, a reversal in the relative intensity of the GaAs/ Alo.25Gao.75As MQW emission occurs near defects, resulting in bright lines in the CL images, as shown in Figs. 3-20(d) and 3-21(d). This striking contrast reversal is also illustrated in the line scan analysis of Figs. 3-22(b) and 3-22( c). That is, high temperature DLDs in the GaAs/ Alo.25Gao.75As MQW emission become bright line defects (BLDs) at lower temperatures. The activation energy for this emission E^ increases near these defects, as indicated by the imaging and line scan analysis. This is in contrast to the decrease in Eai near DLDs. This behavior reflects salient differences in the thermal activation of carriers which are in close proximity, but on opposite sides, o f the Ino.2Gao.8As/GaAs interface. The Eai energy represents the activation energy for thermal reemission of carriers out of the Ino.2Gao.8As QW, as has been observed for similar QW and MQW systems.2 3 '2 6 Once out of the Ino.2Gao.8As QW, the carriers can be recaptured by the QW, recombine in the GaAs barrier, or diffuse to the GaAs/Alo.2sGao.75As MQW where recombination can occur. An extremely weak GaAs near-band-edge luminescence was detected relative to 86 R ep ro d u ced with p erm issio n o f th e copyright ow ner. Further reproduction prohibited w ithout p erm issio n . emissions from the Ino.2Gao.8As QW and GaAs/ Alo.25Gao.7sAs MQW, indicating the very low impurity concentration and high quality of the GaAs barrier layer. Carriers which are generated in the GaAs barrier will then primarily diffuse to the underlying GaAs/Alo.2sGao.75As MQW or Ino.2Gao.8As QW. where a high carrier capture rate in these layers is expected, owing to quantum capture. The 3000 A thickness of the GaAs barrier is less than the -lp m ambipolar diffusion length for high-quality and low- impurity GaAs, thereby enabling the GaAs barrier to serve as a conduit for efficient transport of electrons and holes to and from the GaAs/ Alo.2sGao 75AS MQW and Ino.2Gao.8As QW. The defects created by the misfit dislocations further introduce other recombination channels for carriers in the Ino.2Gao.8As QW. These defects enhance the probability for thermally assisted nonradiative recombination for carriers already residing in the Ino.2Gao.8As QW, thereby resulting in a decrease in Eai near DLDs. The analysis in Figs. 3-20( c), 3-21( c), and 3-22(f) shows that there is a maximum decrease in Eai of -60 and -80 meV near DLDs for the 150 and 185 A samples. The greater reduction in Eai for the 185 A sample reflects the enhanced defect density. For carriers, recombining in the GaAs/Alo.25Gao.7sAs MQW, the misfit dislocations, likewise, introduce additional thermally assisted nonradiative channels which are accessible at higher temperatures. These channels may compete with carrier capture by the In0. 2Ga0.sAs QW and subsequent radiative recombination. However, at lower temperatures, carrier capture by these defects is substantially reduced and 87 R ep ro d u ced w ith p erm issio n o f th e cop yright ow n er. Further reproduction prohibited w ithout p erm issio n . simultaneously results in a reduced transfer of carriers from the GaAs/Alo.asGao 75AS MQW to the Ino.2Gao.8As QW at defect sites, thereby resulting in a local increase of E^. These defect sites also appear to act as a barrier to transport into the Ino.2Gao.8As QW at low temperatures, thereby enhancing the relative the GaAs/Alo.2sGao.75As MQW emission near dislocations and resulting in BLDs correlated with the Ino.2Gao.8As QW DLDs. The spatially averaged values of Ea2 [from Figs. 3-20(f) and 3-21(f)] are 32.3 and 35.3 me V for the 150 and 185 A samples. The larger value in the latter sample again likely reflects the larger relaxation-induced defect density in that sample. III.E.2.d.Spatial variations in the carrier diffusion length The diffusion length experiment was performed by scanning the e-beam along the [110] direction (parallel to the DLDs) and recording the intensity of the el-hhl luminescence as a function of the distance x from the mask edge (as illustrated in Fig. 3- 1 1 ). Typical scans are shown for the 150 and 185 A Ino.2Gao.8As samples at four different regions in each sample, labeled a-d, in Figs. 3-25 and 3-26, respectively. These regions are further identified in the CL line scan analysis of Figs. 3-27 and 3-28, which show the Ino.2Gao.8As QW luminescence intensity versus distance (bottom scan) along [110] (i.e. perpendicular to the dislocation line direction). The dips in the CL intensity scan, again, represent the DLDs, while c and d are near the center o f DLDs. From Figs. 3-25 and 3- 26, it is apparent that a reduction in CL intensity at these regions is also accompanied by 88 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . a greater negative slope, resulting in a smaller ambipolar diffusion length. This correlation is illustrated in Figs. 3-27 and 3-28 for several diffusion length measurements performed in varying proximity to DLDs at different temperatures. For both samples, regions near and far from the DLDs correspond to regions of smaller and larger diffusion lengths, respectively. A wide variation in Lp is observed from about 0.5 to 3 pm in Figs. 3-29 and 3-30, showing that defect regions can substantially influence the transport. No clear systematic variations in Lp with temperature are observed. From previous Hall measurements of these samples, the In0. 2Gao.sAs channel contains a large electron concentration of -3 x 1012 cm' 2 at 77 K. 3 7 J8 The Lp measured here therefore reflects the diffusion of the minority carriers, i.e., holes. This hole diffusion length will involve an interplay between local changes in mobility pp , and minority-carrier recombination lifetime t p as Lp= (Dp t p)l/2, where pp and Dp are related by the Einstein relation pp = eDp/kT.56 The presence of defects will evidently reduce both pp and t p as a result of enhanced scattering near defects and introduction of nonradiative recombination channels. As discussed in Sec III.E.2.a, the enhanced defect density near dislocations is expected to locally reduce the electric field. The reduction in the field is also expected to result in a decrease in xp since the electron and hole envelope wave- function overlap will also increase with a decrease in the field [see Fig. 3-13]. However, without a quantitative measurement of the lifetime and its variations we refrain from attempting to deconvolve Lp into separate pp and t p terms here. R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . 150 A channel 10000 c 3 C D 1000 CO c Q ) c _l o 100 0 2 1 3 4 5 6 Distance (p.m) Fig. 3-25. CL intensity vs beam position x for different line scans (labeled a-d) parallel to the [110] dislocation line direction near and between dislocations for the 150 A Ino.2Gao.8As HEMT samples. 90 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . 10000 (0 c 3 1000 (0 (0 c d ) 100 ■ 4 - > c O 0 1 2 3 4 5 Distance (jim) Fig. 3-26. CL intensity vs beam position x for different line scans (labeled a-d) parallel to the [1 1 0 ] dislocation line direction near and between dislocations for the 185 A Ino^Gao.gAs HEMT samples. 91 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . Temp. (K) ln02Ga0 8 As, 150 A channel 0 5 10 15 20 25 Distance (pm) Fig. 3-27. CL intensity and diffusion length plot vs distance along [110] (perpendicular to dislocation direction) for various temperatures for the 150 A sample. The dashed and solid vertical lines show the spatial correlation between DLD positions and a reduced diffusion length. 92 R ep ro d u ced with p erm issio n o f th e cop yright ow n er. Further reproduction prohibited w ithout p erm issio n . iTemp. (K) 240 ln02Ga08As, 185 A channel-j E n. o c a) — I c o CO 3 aU ^ y rrr 0.4 : CO ‘c 3 xi 2 0 0 c 0) 1 0 0 c _ l 0 o 0 10 15 20 Distance (pm) 25 Fig. 3-28. CL intensity and diffusion length plot vs distance along [110] (perpendicular to dislocation direction) for various temperatures for the 185 A sample. The dashed and solid vertical lines show the spatial correlation between DLD positions and a reduced diffusion length. 93 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 3.5 lnnoGanoAs, 150 A channel 3.0 E 2.5 n sz 4 -> O) c < D _l 2.0 c o (0 3 b 0.5 1 0 0 150 200 250 Temperature (K) Fig. 3-29. Diffusion length vs temperature for various bright (a and b) and dark (c and d) regions in the 150 A sample. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 2.5 ln02Ga08As, 185 A channel 2.0 E = L x: O) c < D c I.u o 'to si 5 0.5 0.0 1 0 0 150 200 250 Temperature (K) Fig. 3-30. Diffusion length vs temperature for various bright (a and b) and dark (c and d) regions in the 185 A sample. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . IILF.CONCLUSIONS In this chapter, we first examined the strain relaxation of compositionally step- graded Inx Gai.x As/GaAs layers using LPCL, CLWI, and TEM. We observed local pm- scale variations in compressive stress ranging from nearly uniaxial to biaxial, resulting in a marked polarization anisotropy concomitant with a variation in luminescence transition energy. We then studied the temperature dependence of CL intensity from Ino.21Gao.79As/GaAs multiple quantum wells. Using a new CL imaging analysis, we observed local variations in the activation energies associated with thermal quenching caused by local fluctuations in the band edge near misfit dislocations and point defects. A pronounced decrease in CL intensity occurs in both the bright and dark regions above 150 K. The magnitude of the activation energies observed for the temperatures above 150 K indicates that this decrease is probably due to the thermal re-emission of electrons and holes from the quantum wells. The latter part of the chapter was devoted to the study of the fundamental optical and transport properties of partially relaxed In0. 2Ga0.gAs HEMT samples. We studied the excitonic luminescence polarization and wavelength, thermally activated nonradiative recombination, and carrier diffusion near individual dislocations. The dislocations and DLD network were found well separated on a pm scale and oriented primarily along one of the <110> directions. A plan-view TEM and CL imaging analysis was used to determine the dislocation densities for samples with Ino.2Gao.8As channel thickness below and well beyond the critical thickness. Theoretical calculations using a four band 96 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . k.p and TMM were used to calculate the band profile and eigenstates of the HEMT sample. CL wavelength imaging showed a striking blue shift of -5 and -10 meV in the 150 and 185 A samples, respectively, contrary to a red shift observed in samples examined previously. We hypothesized that a defect-induced reduction in the field occurs and leads to a reduced Stark shift of the electron and hole eigenstates. A small polarization anisotropy was observed, consistent with the level of strain relaxation in each sample and theoretical calculations of the polarization ratio. The temperature dependence of luminescence was examined and we observed spatial variations in activation energies which correlate with DLDs. These defects were found to lower the activation energy for thermal reemission of carriers from the Ino.2Gao.8As QW and increase the activation energy for carrier transfer into the Ino.2Gao.8As QW from the underlying GaAs barrier and GaAs/Alo.25Gao.7sAs MQW. The ambipolar diffusion length of carriers in the Ino.2Ga.8As QW was quantified with a noncontact optical diffusion length measurement which utilized a one dimensional line scan during monochromatic CL detection and a Ag mask which covered part of the sample. The diffusion length of holes parallel to the dislocation line direction were found to decrease by as much as a factor of -5 in close proximity to DLDs, thereby revealing that an important transport parameter is deleteriously affected by the dislocation formation. This study revealed that the optical and transport properties of Inx Gai.x As HEMTs are linked on a pm scale and are both intimately tied to the presence of misfit dislocations and dark line defects which form during strain relaxation. 97 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . References 1. L.D. Nguyen, D.C. Radulescu, M.C. Foisy, J. Tasker, and L.F. Eastman. IEEE Trans. Electron Devices ED-36, 833 (1989). 2. T.J. Drummond, W. Kopp, R. Fischer, H. Morkoc, R.E. Thome, and A.Y. Cho. J. Appl. Phys. 53, 1238 (1982). 3. R. Fischer, T.J. Drummond, J. Klem, W. Kopp, T.S. Henderson, D. Perrachione, and H. Morkoc, IEEE. Trans. Electron Devices ED-31. 1028 (1984). 4. J.W. Matthews and A.E. Blakeslee, J. Cryst. Growth. 27, 118 (1974). 5. F.R.N. Nabarro, Proc. Roy. Soc. A175, 519 (1940). 6 . F.C. Frank, and J.H. Van der Merwe, Proc. Roy. Soc. A198,205 (1949a) 7. F.C. Frank, and J.H. Van der Merwe, Proc. Roy. Soc. A198, 216 (1949b) 8 . F.C. Frank, and J.H. Van der Merwe, Proc. Roy. Soc. A200. 200 (1949c) 9. J.W. Matthews, and A.E. Blakeslee, J. Cryst. Growth. 27,118 (1974). 10. J.W. Matthews, and A.E. Blakeslee, J. Cryst. Growth. 32,265 (1976). 11. J.W. Matthews, and A.E. Blakeslee, J. Vac. Sci. Technol. 14, 989 (1977). 12. R. People, and J.C. Bean, Appl. Phys. Lett. 47, 322 (1985). 13. P.G. Orders, and B.F. Usher, Appl. Phys. Lett, 50, 980 (1987). 14. T.G. Anderson, Z.G. Chen, V.D. Kulakovski, A. Uddin and J.T. Vallin, Appl. Phys. Lett. 51, 752 (1987). 98 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 15. J. Zou, DJ.H. Cockayne, and B.F. Usher. J. Appl. Phys. 73, 619 (1993). 16. D.H. Rich, A. Ksendzov, R.W. Terhune, F.J. Grunthaner, B.A. Wilson. H. Shen, M. Dutta, S.M. Vernon, and T.M. Dixon, Phys. Rev. B 43. 6836 (1991). 17. M. Grundmann, J. Christen, D. Bimberg, A. Hashimoto, T. Fukunaga, and N. Watanabe, Appl. Phys. Lett. 58,2090 (1992). 18. D.H. Rich, T. George, W.T. Pike, J. Maseijian, F.J. Grunthaner, and A. Larsson, J. Appl. Phy. 72, 5834 (1992). 19. F.H. Poliak and M. Cardona, Phys. Rev. 172, 816 (1968). 20. S. Adachi, J. Appl. Phys. 53, 8775 (1982). 21. J.C.P. Chang, J. Chen, J.M. Fernandez, H.H. Wieder, and K.L. Kavanaugh, Appl. Phys. Lett. 62, 1129 (1992). 22. K.L. Kavanaugh, M.A. Capano, L.W. Hobbs, J.C. Barbour. P.M.J. Maree. W. SchafF, J.W. Mayer, D. Petit, J.M. Woodall, J.A. Stroscio, and R.M. Feenstra, J. Appl. Phys. 64,4843 (1988). 23. D. Bimberg, J. Christen, A. Steckenbom, G. Weimann. and W. Schlapp, J. Lumin. 30, 562(1985). 24. K. Uno, K. Hirano, S. Noda, and A. Sakaki, Proceedings o f the 19th International Symposium on GaAs and Related Compounds (IOP, Bristol. 1993), 241. 25. D.S. Jiang, H. Jung, and K. Ploog, J. Appl. Phys. 64, 1371 (1988). 99 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 26. U. Jahn, J. Menninger. R. Hey, and H.T. Grahn, Appl. Phys. Lett. 64. 730 (1994). 27. D.H. Rich, K. Rammohan. Y. tang, H.T. Lin. J. Maseijian, F.J. Grunthaner. A. Larsson, and S.I. Borenstain, Appl. Phys. Lett. 64. 730 (1994). 28. H. Hillmer, A. Forchel, S. Hansmann, M. Morohashi, E. Lopez, H.P. Meier, and K. Ploog, Phys. Rev. B 39, 10901 (1989). 29. T.E. Everhart and P.H. Hoff, J. Appl. Phys. 42. 5837 (1971). 30. D.H. Rich, H.T. Lin, and A. Larsson, J. Appl. Phys. 77, 6557 (1995). 31. P.M. Solomon and H. Morkoc, IEEE Trans. Electron. Devices ED-31, 1015 (1984). 32. T.J. Drummond, W.T. Masselink, and H. Morkoc. Proc. IEEE 74. 773 (1986). 33. Special issue on heterojunction field-effect transistors, IEEE Trans. Electron Devices ED-33, No. 5 (1986). 34. M. Abe, T. Mimura, N. Kobayashi, M. Suzuki, M. Kosugi, M. Nakayama. K. Odani, and I. Hanyu, IEEE Trans. Electron Devices 36, 2021 (1989). 35. A. Fischer-Colbrie, J.N. Miller, S.S. Laderman, S.J. Rosner, and R. Hull. J. Vac. Sci. Technol. B 6,620 (1988). 36. A.A. Ketterson, W.T. Masselink, J.S. Gedymin, J. Klem, C-K. Peng, W.F. Kopp, H. Morkoc, and K.R. Gleason, IEEE Trans. Electron Devices ED-33. 564(1986). 100 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . 37. M. Meshkinpour, M.S. Goorsky, G. Chu. D.C. Streit, T.R. Block, and M. Wojtowicz, Appl. Phys. Lett. 6 6 , 748 (1995). 38. M. Meshkinpour, M.S. Goorsky, D.C. Streit, T.R. Block, M. Wojtowicz. K. Rammohan. and D.H. Rich, Mater. Res. Soc. Symp. Proc. 340,327 (1994). 39. D.C. Streit, K.L. Tan, R.M. Dia, J.K.. Liu, A.C. Han, and J.R. Velebir. IEEE Electron Device Lett. EDL-9, 621 (1988). 40. M. Meshkinpour, M.S. Goorsky, G. Chu, D.C. Streit. T.R. Block, and M. Wojtowicz, Mater. Res. Soc. Symp. Proc. 378, 783 (1995). 41. H.A. Zarem. P.C. Sercel. J.A. Lebens. L.E. Eng, A. Yariv, and K.J. Vahala. Appl. Phys. Lett. 55, 1647 (1989). 42. E.A. Fitzgerald, G.P. Watson, R.E. Proano, D.G. Ast, P.D. Kirchner, G.D. Petit, and J.M. Woodall, J. Appl. Phys. 65, 2220 (1989). 43. T. George, E.R. Weber, S. Nozaki, T. Yamada. M. Konagai, and K. Takahashi. Appl. Phys. Lett. 59, 60 (1991). 44. I. Yonenaga and K. Sumino, J. Appl. Phys. 65, 85 (1989). 45. D.C. Hutchings, Appl. Phys. Lett. 55, 1082 (1989). 46. D. Campi and C. Alibert, Appl. Phys. Lett. 55.454 (1989). 47. S.I. Borenstain, I. Grave, A. Larsson, D.H. Rich, B. Jonsson, I. Andersson, J. Westin, and T. Andersson, Phys. Rev. B 43,9320 (1991). 48. G. Ji, D. Huang, U.K. Reddy, H. Unlu, T.S. Henderson, and H. Morkoc, J. Vac. Sci. Technol. B 5, 1346 (1987). 101 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 49. S.L. Chuang, Phys. Rev. B 43, 9649 (1991). 50. K. Rammohan. D.H. Rich, R.S. Goldman, and K.L. Kavanaugh. Appl. Phys. Lett. 6 6 , 871 (1995). 51. K. Rammohan, Y. Tang, D.H. Rich, R.S. Goldman. H.H. Wieder. and K.L. Kavanaugh, Phys. Rev. B 51, 5033 (1995). 52. D.H. Rich. K. Rammohan, Y. Tang, H.T. Lin. R.S. Goldman. H.H. Wieder. and K.L. Kavanaugh, J. Vac. Sci. Technol. B 13, 1766 (1995). 53. J.D. Lambkin, L. Considine, S. Walsh. G.M. O’Connor. C.J. Mcdonagh. and T.J. Glynn. Appl. Phys. Lett. 65, 73 (1994). 54. B.G. Yacobi and D.B. Holt, J. Appl. Phys. 59, R1 (1986). 55. J.I. Pankove, Optical processes in Semiconductors (Dover. New York. 1971). p. 166. 56. See, for example, N.W. Ashcroft and N.D. Mermin, Solid State Physics (Saunders College, Philadelphia, 1976), pp. 602-605. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . C h a p t e r I V INFLUENCE OF SUBSTRATE MISORIENTATION ON THE OPTICAL PROPERTIES OF Inx Ga,_x As FILMS GROWN ON GaAs(OOl) rV.A.Introduction Strain relaxation in lattice-mismatched semiconductor epilayers occurs via the formation of misfit dislocations. In the previous chapter, we have studied the effect of misfit dislocations on the electrical and optical properties of Inx Gai_x As quantum wells and heterostructures. In addition to influencing the local carrier recombination rate, the fluctuation in the strain fields associated with misfit dislocations influence the energy of the InxGaj.x As excitonic luminescence and induce polarization effects. In order to obtain high quality epitaxial strained films of Inx Gai.x As on GaAs to enable fabrication of high quality electronic devices such as high electron mobility transistors, and MISFETS and optical devices such as lasers, detectors and light modulators, we need to examine the factors which to affect the optical and electrical properties of these epitaxial films. One of the factors that influence the structural, optical and electronic properties of strained InxGai.x As films pertains to the starting quality of the GaAs substrate. One such factor is the misorientation of the GaAs substrate. Substrate misorientation is found to induce R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . asymmetry in the formation of <110>-oriented 60° misfit dislocations in Inx Gai. xAs/GaAs films during strain relaxation. 1' 3 Even on a nonvicinal (no misorientation) substrate, the chemical inequivalence of orthogonal a and p dislocations, induces a preferred relaxation direction during growth of Inx Gai.xAs on GaAs(001).4 '5Anisotropic electrical properties of these materials observed along the orthogonal < 1 1 0 > directions.6 ' o have been attributed to the asymmetric strain relaxation. This asymmetry in strain relaxation will result in a polarization anisotropy in excitonic luminescence similar to what was observed in InGaAs/GaAs quantum wells in the previous chapter. In this chapter, we have examined the influence of substrate misorientation on the optical properties of Inx Gai-x As thin films grown on GaAs(OOl) substrate which are misoriented towards (Oil) and {111} directions. We first examine the optical properties of Inx Gai.x As films grown on nominally flat GaAs(OOl) substrate. Next with a view towards tailoring the optical polarization properties for future photonics applications, we proceed to compare these results with similar films grown on GaAs(OOl) substrates misoriented 2 ± 0.05° towards the nearest (Oil) plane. We also examine the variations in strain relaxation and associated excitonic polarization variations in these two films. We examine the polarization properties caused by an anisotropic distribution of misfit dislocations in Inx Gai.x As films grown on GaAs(OOl) substrates misoriented towards {1 1 1 } planes. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . rV.B.Experimental details The samples examined in this study were grown by solid source molecular-beam epitaxy. The samples were grown at UCSD and structural characterization via TEM and X-ray crystallography was also performed at UCSD. Details of the preparation and structural characterization have been described elsewhere. 1 They consisted of 280-nm- Si-doped (Nd a 1017 cm'3) In0. 06Ga0. 94As on 500-nm-undoped GaAs buffers grown simultaneously on semi-insulating (OOl)-oriented GaAs substrates (a) nominally flat (0.05°) and (b) misoriented 2 ± 0.05° towards the nearest (Oil) plane. A second set of samples consisting of 300 nm-Si doped Ino.13Gao.g7As on 500 nm undoped GaAs buffers were grown simultaneously on semi-insulating (001 )-oriented GaAs substrates misoriented towards (111) A and (111) B planes, each terminated with single Ga and As bonds, respectively. Scanning monochromatic cathodoluminescence (CL), CL wavelength imaging (CLWI), and linearly polarized CL (LPCL) were performed with a modified JEOL 840A scanning electron microscope. A rotatable linear polarizer was mounted in vacuo to perform polarization measurements.9 ' 10 An electron beam with a 15-keV beam energy was used to probe the sample, and beam currents ranging from 1-50 nA were used to probe the samples which were cooled to 87 K. In order to study in detail the local variations in strain, we performed CLWI and LPCL imaging on all four samples. In CLWI imaging the wavelength, A .m , at which the R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . intensity of luminescence is a maximum is mapped as a function of the spatial (x. y) position, and a gray-scale image representing these wavelengths is generated. A scanning area of 128 x 94 pm2 is discretized in this study. The mapping of A .m into a gray-scale representation is shown by the gray-bar key indicating the wavelength scale. In order to understand the nature of relaxation and the polarization properties of these films, we have performed LPCL imaging and spectroscopy. LPCL spectra was recorded with the polarizer rotated to detect emission of light, with E X [110] and E || [110], respectively. In order to emphasize the polarization variations, we have generated ratio images. The pixels in the ratio image at a (x,y) position are represented as logioPi(x,y) / 1 || (x,y)], where Ij. and I|| are the pixel intensities under E X [110] and E || [110}] detection orientations, normalized to a 256 level gray scale. IV.B.l.Effect of strain on band structure of heterostructures The strain-induced splitting of the heavy-hole (hh;mj = ± 3/2) and light-hole(lh; mj = 1 4 ) valence bands at k= 0 can be examined by studying the polarization and energy dependence of the luminescence.9,10’12 For a general biaxial stress (cr) in the (001) plane, which contains two orthogonal stress components an and ctx (as referred to [110], a diagonalization of the orbital-strain Hamiltonian enables a determination of the set of uppermost J = 3/2 strain-split valence-band wave functions,Uj. 12 In the [110] representation of | J, m j> , these normalized wave functions are given by R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . where i = 1 and 2 represent the highest and lowest bands, respectively. The coefficients c,.hh and cU h are given by where the parameters 77 and £ are represented in terms of the elastic compliance constants Sn. S 12 and S44, the uniaxial deformation potentials b and d. and the in-plane stress components C T || and ctx: The elastic compliance constants and deformation potentials for Inx Gai.x As are approximated well by interpolating between the corresponding values for pure GaAs and InAs listed in table 2.3; these constants are given by b = -l.7-0.lx, d= -4.55 + 0.95x (in eV), and S,, = (1.176 + 0.769x) 10*1 2 , S,2 = (-0.365 - 0.32x) 10*1 2 , and S44 = (1.684 + 0.84lx)10'1 2 (in cm2 /dyne), where x = 0.06 in this study.1 3 * 1 5 (4.2) Cljih ~ C\J h 'C2Jh C ljih (4.3) 107 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . 0.06 0.94 0.8 0.8 0.6 H 0.4 0.4 0.2 0.2 l.hh 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 oo ‘5 £ Fig. 4-1. Calculated intensity ratio (I±/I||) of luminescence with EJ_[110] polarization to that with E||[l 10], |cU0 |jh|2, and |c110i.hh |2 versus <Ji/an for In0. 06Gao.94As. The 110 superscripts are used to emphasize that the |J, mj) basis wavefunctions are in the [110] representation here. The || and _ L subscripts denote parallel and perpendicular to the [110] direction, respectively. 108 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . Interband optical transitions involving the hh and Ih states exhibit polarization selection rules which depend on the strain sensor, deformation potentials and orientation of the electric field, E, of light emitted or absorbed. 12 For a [110]-oriented pure uniaxial compressive stress (i.e., Ol = 0), very little mixing of the hh and Ih bands occurs, as Eq. 4.2 yields cu,h = 0.045, when = 0. The excitonic emission associated with the lh valence band is the lowest-energy transition and is partially linearly polarized parallel to [110]. The ratio o f oscillator strengths o f luminescence with E [110] polarization to that with E [110], Ii / 1 ||, for the lowest-energy transition in the strain split bands is given by where the calculation uses the dipole approximation in Fermi’s golden rule, i.e. Ii,n o c Ku<:|Ei.,||-p|U|)|2, where U c is the conduction-band wave function and p is the linear momentum operator. For pure uniaxial stress (c tj. = 0) the calculated value of L / I y is 0.29. We note that for a material in which there is no mixing of hh and lh characters in the valence bands (cijh = 1 and C |,h h = 0), Eq. 4.4 yields ideally T / Ij = 0.25. The calculated values for Ij. / Iy, |cu,h|2, and |ci,ih|2 versus in the [ 1 1 0 ] representation are shown in Fig. 4-1. For an in-plane biaxial compressive stress with a i = cry , no polarization of the hh or lh excitonic emissions is expected as seen in Fig. 4-1, and the valence band associated with the lowest optical transition energy has a pure hh character when the wave functions are transformed to the [0 0 1 ] representation. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . IV.C.Results and Discussion IV.C.l.InGaAs films grown on GaAs(OOl) substrates misoriented towards (Oil). Figure 4-2 shows spatially averaged LPCL spectra of the bulk Ino.06Gao.94As excitonic luminescence obtained from both samples. It is evident from both spectra that the misoriented substrate exhibits a greater degree of polarization anisotropy as compared to the flat substrate. The values of Ii / Ig are 0.926 and 0.877 for the sample grown on the flat and the misoriented substrate, respectively, where I is the integrated intensity and then subscript refers to its electric field orientation. X-ray rocking curve (XRC) measurements performed at UCSD showed that the sample grown on nominally flat substrate relaxed 13 ± 1 and 12 ± 1 % in the [110] and [110] directions, respectively, isotropic relaxation to within the experimental error. The sample grown on the misoriented substrate relaxed 8 ± 1 and 2 0 ± 1 % in the [1 1 0 ] and [110] directions, respectively resulting in distinct anisotropy. The average relaxation in the Inx Gai.x As film on the misoriented sample (14 ± 1%) is only slightly larger than that on the flat substrate (12.5 ± 1%). Thus, the estimated average dislocation density in the nominally flat sample was 2.5 ±0.1 x 104 cm' 1 along both < 1 10> directions. Or the case of misoriented substrate, the estimated dislocation densities were 1.8 ± 0.1 and 4.5 ± 0.2 x 1 0 4 cm' 1 in the [ 1 1 0 ] and [ 1 1 0 ] directions, respectively. 110 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . T = 87 lnnneGano„As/GaAs c 3 C O > 4 -4—> '(/) c < D -4—1 c O 800 820 840 860 880 900 X (nm) Fig. 4-2. Spatially averaged polarized CL spectra obtained for Ino.06Gao.94As films grown on both the nominally flat and misoriented GaAs(OOl) substrate, where Ex and Ej refer to electric field vector E perpendicular and parallel to [110]. R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . The increased deviation of Ix / I y from unity for the sample grown on the misoriented substrate as compared to the sample grown on the flat substrate is indicative of the greater level of anisotropic strain relaxation associated with the misorientation. Further, the luminescence intensity is highest when E || [110], which indicates the presence of quasiuniaxial compressive stress along the [I10]direction. This also corresponds to a greater relaxation along the [lfO] direction, which is in agreement with the strain relaxation symmetry determined by XRC. Figures 4-3(a) and 4-4(a) show the CLWI micrographs of the nominally flat and the sample misoriented towards (Oil) direction, respectively. Figures 4-3(b), and 4-4(b). show spectrally-integrated CL intensity micrographs from the same region (panchromatic for the 860 < A . < 874 nm range). Long streaks of a constant gray shade can be seen in the CLWI micrographs, which correlate in position and orientation with the DLDs in the integrated CL intensity images. The reduction in the luminescence effect is due to the presence of nonradiative recombination centers, likely caused by the presence of misfit dislocation cores and point defects left in the wake of dislocation propagation. 16 Figures 4-3(c) and 4-4(c) show monochromatic LPCL images for the samples grown on the flat and misoriented substrates, respectively. Images were taken with the polarizer rotated to detect emission of light with E x [1 1 0 ] and E||[l 1 0 ] detection orientations at a wavelength of 869 nm (1426 meV). In order to emphasize the polarization variations, the ratio of these images is displayed in Figs. 4-3(c) and 4-4(c). R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . Fig. 4-3. The CLWI, the integrated CL intensity, and the LPCL images in (a), (b), and (c), respectively for the Ino.06Gao.94As film grown on the flat substrate. A scale showing mapping of wavelengths of peak CL intensity is shown in (a). 1 1 3 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . Fig. 4-4. The CLWI, the integrated CL intensity, and the LPCL images in (a), (b), and (c), respectively for the Ino.06Gao.94As film grown on the substrate misoriented towards (011). A scale showing mapping of wavelengths of peak CL intensity is shown in (a). R ep r o d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 872 T = 87 K (011) Misoriented Substrate [110] Line Scan 870 - 868 866 0.9 0.8 0.7 100 0 20 60 80 40 Distance (pm) Fig. 4-5. Histogram of CLWI, integrated CL intensity and LPCL Ij/I|| ratio for an arbitrary line scan done along the [ 1 1 0 ] for the sample grown on the substrate misoriented towards (011). The spatial correlation of regions showing redshift, a decreased luminescence efficiency, and enhanced polarization (indicated by dashed vertical lines) and regions of blueshift, increased luminescence efficiency and no polarization (indicated by dotted vertical lines) is observed. 115 R ep ro d u ced w ith p erm issio n o f th e cop yright ow n er. Further reproduction prohibited w ithout p erm issio n . The bright and the dark bands present in the LPCL ratio images clearly exhibit the local polarization anisotropy, which indicates the presence of pm-scale variations in strain. A distinct asymmetry in the CLWI, spectrally integrated, and the LPCL images is observed in Fig 4-4 for the misoriented substrate, in which a greater density of DLD, constant- wavelength and polarization ratio streaks is observed along the [110] direction. This asymmetry is markedly reduced in Fig. 4-3 for the flat substrate, consistent with the XRC results. IV.C.2.CorreIation between LPCL and CLWI Figure 4-5 shows the correlation existing between the CLWI image, the integrated CL image, and the LPCL images for the misoriented substrate. The results for the flat substrate are qualitatively similar, and are not shown here. Peak wavelength (A .m ). luminescence intensity and I _ l / Iy ratios are plotted as a function of the distance taken along an arbitrary [110]-oriented line. The histogram shows that the blueshifted and the redshifted regions correspond to the regions of enhanced and reduced luminescence efficiency [bright and dark regions in Figs. 4-3(b) and 4-4(b)]. Regions o f reduced luminescence efficiency are due to an enhanced nonradiative recombination near misfit dislocation cores. The material has also relaxed in the regions near dislocations, resulting in a change in the band gap, i.e., a reduction in compressive stress has resulted in a redshift seen in the CLWI imaging. In the regions of enhanced luminescence, where R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . there are very few dislocations, little relaxation has occurred, resulting in higher biaxial compressive stress, which gives rise to a relative blueshift. Our hypothesis that the blueshift and redshift seen in CLWI imaging is due to variation in strain and not due to alloy variation, is supported by the correlation between the CLWI and LPCL images, as evident from the histogram analysis. In Fig. 4-5, the histograms show that regions of enhanced and reduced luminescence efficiency correspond to regions of reduced and enhanced polarization anisotropy, and also correspond to regions of blueshift and redshift in the CLWI image, respectively. In the regions of high misfit dislocation density, i.e., reduced luminescence efficiency, the material is preferably relaxed in a direction perpendicular to the dislocation line direction, resulting in a deviation from an ideal biaxial stress with cti = cry, and this causes a polarization anisotropy (L. / Iy <1). In the regions of low dislocation density (high luminescence efficiency) very little relaxation has occurred, thus resulting in minimal deviation from biaxial stress with L . / Iy «1. Regions which show an enhanced polarization anisotropy correspond to regions which exhibit a redshift in the CLWI images. This further indicates that a local reduction stress occurs along [110], which leads to a [110]-oriented quasiuniaxial stress that is consistent with the lh polarization selection rules previously discussed. The minimum polarization ratios (Ij. / Iy) are, however, greater than the theoretical value of 0.29 for pure uniaxial stress, as shown in Fig. 4-1. This is explained with the R ep r o d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . help of a model where the strain component perpendicular to the DLD’s is not completely relaxed and a quasiuniaxial stress with a dominant longitudinal component. O T ||, parallel to the DLDs is present such that O n » ox. The presence of a quasiuniaxial stress as opposed to a pure uniaxial stress (c t x = 0) results in a considerable mixing of the hh and lh characters in the strain-split band (see Fig. 4-1), which causes the polarization ratios to deviate from theoretically predicted values for a x = 0. IV.D.InGaAs films grown on GaAs(OOl) substrates m isoriented towards {111} Figures 4-6 (a) and 4-7 (a) show CLWI images for the Ino.13Gao.87As films grown on the GaAs(OOl) substrates misoriented towards (111)A and (111)B, respectively. The mapping of Xm into a gray-scale representation is shown by the gray-bar key indicating the wavelength scale. Figures 4-6 (b) and 4-7 (b) show spectrally-integrated CL intensity micrographs for the same regions. Similar to the CL monochromatic images shown in the previous section, we see long streaks of a constant gray-shade can be seen in Figs. 4- 6(a) and 4-7(a) which correlate in position and orientation with the DLD’s in the integrated CL intensity images. The spectrally integrated images of Figs. 4-6(b) and 4- 7(b) represent a spatial mapping of the excitonic luminescence efficiency, which is lowest in the regions of the DLDs. An asymmetry in DLD density is observed in the R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . image of Fig. 1(b), with large dark bands oriented along the [110] direction. A stack plot of local spectra along an arbitrary [110]-oriented line [indicated with a dashed line and showing endpoints labeled A and B in Fig. 4-7(b)] is shown in Fig. 4-8. The distance Ax along this line where the electron beam was fixed is indicated. It is apparent that the peak position of the CL spectra varies with Ax. In the CLWI image of Fig. 4-6 (a), the regions corresponding to the dark lines appear as blue-shifted (towards shorter wavelengths) long bands along [110]. This relative blue-shift is indicative of a higher-compressive biaxial stress relative to red-shifted bands which run predominantly along [ifO]. This asymmetry is reversed in the CLWI image of Fig. 4-7(a) for the (ill )B misorientation, where the principal DLD and CLWI banding direction is along [110]. Thus, the CLWI asymmetry is clearly linked to the choice of substrate misorientation. In order to further understand the nature of the relaxation, we have performed LPCL imaging and spectroscopy over these same regions. Figures 4-6 (c) and 4-7 (c) show monochromatic LPCL images of log [In (x,y) / Ii (x,y)] at X =929 nm. A series of local LPCL spectra corresponding to each of the unpolarized local spectra are shown in Fig. 4-8. The spectra were taken under the two polarization orientations, with E J_ [110] and E || [110], as indicated in the figure. In order to asses the overall average relaxation over the total regions imaged in Figs. 4-7 and 4-8, we show, in Fig. 4-9, spatially- integrated LPCL spectra over these same regions of the (111)A and (111 )B misoriented samples. It is evident from both spectra that the GaAs(OOl) substrate misoriented 119 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . Fig. 4-6. CLWI, the integrated CL intensity, and LPCL images in (a), (b), and (c), respectively for the Ino.13Gao.87As film grown on the substrate misoriented 2 ° towards (111)A. A scale showing mapping of wavelengths of peak CL intensity is shown in (a). The LPCL image in (c) is displayed at k = 929 nm. R ep ro d u ced w ith p erm issio n o f th e cop yrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 921 Fig. 4-7. CLWI, the integrated CL intensity, and LPCL images in (a), (b), and (c), respectively for the Ino.13Gao.87As film grown on the substrate misoriented 2 ° towards (111)A. A scale showing mapping of wavelengths of peak CL intensity is shown in (a). The LPCL image in (c) is displayed at X = 929 nm. I R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . (001)-^(111)A Unpolarized T = 87 K AX (pm) 0(A) 13.6 ( /> c 3 25.4 C O V >* . 4—» (0 c 0) c 31.6 O 46.3 51.4 (B) 880 900 920 940 960 980 1000 Xm (nm) Fig. 4-8. Local CL (solid line) and LPCL spectra for the (111)A misoriented sample along the dashed line indicated in Fig. 4-6(b). The distance, Ax, along the dashed line from point A is indicated. The LPCL spectra were acquired under E i (dashed line) and E|| (dotted line) polarizer orientations, where the electric field subscripts denote perpendicular and parallel to [110], respectively. 122 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . T = 87 K c = J CD >* 3j c < D c (001) 880 900 920 940 960 980 1000 X (nm) Fig. 4-9. Spatially averaged LPCL spectra over the (111)A and (111)B misoriented samples. The sampled regions correspond to the same 128 x 94 pm2 regions shown in Figs. 4-6 and 4-7. Ex and E|| refer to electric field vector R perpendicular and parallel to [110]. 123 R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . towards (111)A exhibits a greater degree of polarization anisotropy as compared to the one misoriented towards (111)B. The values of I|| / Ij. are 0.85 and 0.99 for the samples grown on the (111)A and (lll)B misoriented substrates, respectively, where I is the integrated intensity and the subscript refers to its electric field orientation. The reduction of the polarization anisotropy for the (111)B misorientation reflects a change in the preferential direction for the initial relaxation which evidently depends on the substrate misorientation. The spatially-integrated LPCL spectra for the (111 )B-misoriented sample are shifted ~5nm towards longer-wavelengths relative to the spectra for the (111)A- misoriented sample in Fig. 4-9, consistent with the greater average strain relaxation in the (111 )B sample as measured in XRC. Based on the theory detailed in the beginning of this chapter and in Appendix A, we can conclude that the polarization anisotropies are consistent with quasi-uniaxial stresses along [110] and [110] for the (111)A and (111 )B misoriented samples, respectively, with the (111)A having a larger average stress. The term quasi-uniaxial connotates <ti * ctj with the larger stress component defining the uniaxial direction. The reduction of the total polarization anisotropy for the (111 )B misorientation (see Fig. 4-9) is also consistent with the reduction in the strain asymmetry measured in XRC. IV.D.l.Correlation of LPCL with CLWI It is apparent from the images of Figs. 4-6 and 4-7 that the blue and red-shifted regions correspond to regions of smaller and larger polarization anisotropies, 124 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 936 [110] Line Scan T = 87 K 932 928 ^ 924 920 0.8 125 25 75 100 0 50 Distance (|im) Fig. 4-10. Histograms of CLWI, integrated CL intensity and LPCL I||/Ix ratio for an arbitrary line scan along [110] for the samples grown on the (111)A misoriented substrate. R ep ro d u ced with p erm issio n o f th e copyright ow ner. Further reproduction prohibited w ithout p erm issio n . 936 [110] Line Scan' T = 87 K ;(0 0 1 )-^ (1 1 1 )B E S 932 E 928 (0 c 3 (0 c _J O H 125 25 100 0 50 75 Distance (|im) Fig. 4-11. Histograms of CLWI, integrated CL intensity and LPCL I||/Ij. ratio for an arbitrary line scan along [110] for the samples grown on the (111)A misoriented substrate. R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . respectively, for both these samples. The local LPCL spectra of Fig. 4-8 show an example of a CL spectrum (at Ax=13.6 m) which shows a reduced polarization anisotropy associated with a blue-shift. Histograms along an arbitrary [110]-oriented line of Figs. 4-6 and 4-7 are shown in Figs. 4-10 and 4-11, respectively, revealing the spatial correlation between energy shift and polarization. The dashed and dotted vertical lines, respectively, illustrate the correlation between regions of enhanced red-shift with decreased I||/Ix and enhanced blue-shift with increased I||/Ix. The increase in polarization anisotropy (Ij|/Ij. <1) indicates an enhancement in the quasi-uniaxial character of the stress which is largest for the red-shifted regions in both samples. The region of Fig. 4-6 shows a preferential DLD line direction along [110], while the region of Fig. 4-7 shows slightly greater DLD densities with a line direction along [110]. In Fig. 4-6. the red- shifted regions indicate regions of greater relaxation along [110], with misfit dislocations occurring preferentially along [110] (i.e., a dislocations). A particularly striking feature of the data for the (111)A misorientation is the reduction in luminescence efficiency (from the spectrally integrated CL data of Figs. 4-6 and 4-10) near regions of enhanced compressive stress (blue-shifted regions). Regions of blue-shift in Fig. 4-6 show a reduced luminescence efficiency despite a reduction in total strain relaxation. The converse, however, is true for the (lll)B misorientation which shows an increase in luminescence efficiency near regions of blue-shift, as seen in Figs. 4-7 and 4-11. In both these cases the relative blue-shifts reflects a greater average biaxial stress and 127 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithou t p erm issio n . corresponds to a reduced polarization anisotropy. Some blue-shifted regions of Figs. 4-6 and 4-10 show a reversal in the polarization anisotropy where I|| / Ix >1. This can only happen if the direction of quasi-uniaxial stress changes direction. It is possible that a large decrease in the [110]-oriented a dislocations relative to the [110]-oriented p dislocations will induce a quasi-uniaxial stress along [110], despite having a greater average density of a dislocations throughout the sample. rV.D.2.Analysis of anisotropic strain relaxation The above observed features represent the complex nature of the strain relaxation and may relate to the differences in carrier combination rates associated with a ([1 f0] line direction) and p ([110] line direction) dislocation cores and point defects associated with these dislocations. These two types of 60° dislocations are chemically inequivalent, owing to the difference in termination of the extra half-plane which, e.g.. in the type-I (shuffle) set has a Ga and As termination, respectively, for the unreconstructed a and P dislocation cores. For a nonvicinal GaAs (001) substrate (i.e., nominally no misorientation) it is well established that for a single thin Inx Gai.x As (x < 0.2) films grown on GaAs (001), a dislocations are the first to form in relaxing the strain.4 '5 This has previously been attributed to the different levels of stress required to generate a and R ep ro d u ced with p erm issio n o f th e copyright ow ner. Further reproduction prohibited w ithout p erm issio n . P dislocations and the differences in a and P dislocation propagation velocities on nonvicinal GaAs(OOl) substrates.1 7 ,1 8 The asymmetries found in the XRC and CL data can be understood by considering the influence of the GaAs(OOl) miscuts towards (111)A and (111)B on the stress experienced by the relevant {111} slip systems of 60° a and p dislocations. Consider the geometry of a [110] oriented dislocation, as shown in Fig. 4-12. The two possible {111} glide planes for this dislocation. ( I ll) and (111), intersect the (001) plane at an angle 0 = 54.7°. The four possible Burger vectors for this dislocation are 14[101], '/2[011], ‘ /2 [011], and 1 /2( 101], and are labeled 1-4, respectively, in Fig. 4-12. The strain relaxation by a given misfit dislocation is in proportion to the magnitude of the Burgers vector component perpendicular to the dislocation projected onto the interface plane. For the positive misfit angle 5 depicted in the figure, Burgers vectors 1 and 2 will have larger perpendicular components projected onto the interface compared to that for Burgers vectors 3 and 4. Therefore, Burgers vectors 1 and 2 will have a slightly greater driving force formation than that of 3 and 4. The tilt component of Burgers vectors 1 and 2 is toward the interface, and this tendency for formation of a preferential Burgers vector set has previously been used to explain the direction of epilayer tilt in strained heterostructure systems with vicinal substrates.1 9 ,2 0 For a (111)A misorientation angle 5 (5 = 2° in this study), the (111) and (111) planes make angles of 0 - 8 and 0 + 5. 129 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . ^ \e V InGaAs/GaAs Interface Fig. 4-12. View of {111} slip planes for a (001) substrate misoriented an angle 5 towards (111)A. The geometry of the Burgers vector 1-4 are shown for a [110]-oriented a dislocation. 130 R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . respectively, with the Ino.13Gao.87As/GaAs interface. During the initial phase of Ino.13Gao.87As growth, the film will be under a homogeneous biaxial stress ax = an = a. The differences in the strain relaxation between our two samples can now be explained by considering differences in the shear stress on {1 1 1 } slip systems with substrate misorientation angle 5 since the glide force per unit length is proportional to the shear stress. These differences in glide force caused by the misorientation will then be in competition with inherent differences in a and P dislocation formation energies which are already present in nonvicinal strained systems. For a (111 )A miscut. as depicted in Fig. 4-12, the shear stress, ti, on the slip system for an a dislocation defined by the (111) glide plane and Burgers vector 1 (l A [101]) is 2 1 The formation o f [110] oriented dislocations (P-type) will involve glide on (111) and (1 1]). The resulting shear stress, 1 2, on this slip system for the (111)A misorientation of Fig. 4-12 is For small 8, x\ > xz, and the driving force for a dislocations is further enhanced for the (111)A miscut. This would explain the large anisotropic relaxation seen in XRC and CL (4.5) 11) planes. The relevant slip system for glide on (11 l)invoives Burgers vector 2 (X A[0\ _ — \ 2 x _L r: ' V6V $ S ^ 2 sin £ cos J / (4.6) 131 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . imaging which indicates a greater density of a dislocations compared to ( 3 dislocations. For the miscut towards (111)B, the converse is true by the same arguments leading up to Eqs. (4.5) and (4.6), and the formation of { 3 dislocations will now become more favorable due to the enhanced stress on a (111)B slip plane. This greater shear stress will still be in competition with a reduced inherent a dislocation formation energy, which minimizes the resulting dislocation and strain relaxation anisotropy in the (111 )B miscut orientation. Thus, this simple model qualitatively explains the anisotropic strain relaxation and concomitant excitonic polarization properties. IV.D.3.Defect-induced Long-wavelength Emission Some small isolated regions o f the (111)A misoriented sample were found to exhibit long-wavelength emission in the 1000 < X <1100 nm range. Such emission was not found on the (111 )B misoriented substrate or on the samples grown on (011) misoriented substrate. The region previously studied for (111)A in Fig. 4-6 also showed no detectable emission in the 1000 to 1100 nm range. Monochromatic CL images for A=929 nm and X =1060 nm are shown in Figs. 4-13(a) and 4-13(b), respectively, for a different region of the (111)A misoriented sample. A stack plot of local CL spectra is shown in Fig. 4-14. The electron beam was positioned along the line shown in Fig. 4- 13(b) and the position of each of the spectra relative to the starting point A are shown. The images showing DLD’s in Fig. 4-13(a) and 4-13(b), appear similar. A histogram R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . Fig. 4-13. Monochromatic CL images at X = 929 nm (a) and k = 1060 nm (b) showing region containing long-wavelength emission for (111)A misoriented sample. R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithou t p erm issio n . T = 87 K - (001)-^(111)A AX (|im) 0(A) C O 3.1 c 3 X I k_ C O 18.3 CO c 0 c 30.8 _i O 36.8 49.2 64.2 (B) 900 1000 1100 1200 (nm) Fig. 4-14. Local CL spectra taken along the line A-B as shown in Fig. 8(b). The distance. Ax, along this line is shown. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . C L Intensity (arb.units) T = 87 K (0 0 1 )-^ (111 )A X = 929 nm 0 25 50 75 100 125 Distance (nm) Fig. 4-15. Histograms of the CL imaging at X = 929 nm and X = 1060 nm along an arbitrary [110]- oriented line. R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . over a [110]-oriented line, as shown in Fig. 4-15, reveals that there is, for the most part, a correlation in the excitonic and long-wavelength peak intensities. That is, where excitonic emission is weak, a reduced long-wavelength emission is also observed. It is evident then that the reduction in the excitonic luminescence efficiency is due to carriers recombining by other recombination channels, both radiative at longer wavelengths and nonradiative in character. Previous studies have shown that an enhancement of the dislocation density can lead to long-wavelength emission.1 6 The overall image contrast in Fig. 4 -13(b) is determined by a competition of long-wavelength channels with nonradiative sources. The histograms of Fig. 4-15, show regions where peaks and dips in excitonic luminescence efficiency correspond with peaks and dips, respectively, in long- wavelength emission (dashed vertical lines). We observe some regions where there exists an anti-correlation between the occurrence of peaks and dips in 929 and 1060 nm histograms (dotted vertical lines). Again, the complexity of the strain relaxation may lead to regions of dislocations bunching and generation of point defects which have significantly long-wavelength radiative recombination rates compared to the nonradiative recombination rate near dislocations which appears to dominate for recombination of excess carriers in most InxGai.x As/GaAs thin film systems that lead to DLDs.1 6 Similarly, previous studies of defect-induced long-wavelength emission in Ino.2Gao.8As/GaAs multiple quantum well showed that competing nonradiative channels lead to spatially correlated DLDs at both the quantum well e-hh excitonic transition energy and the subgap emissions.1 6 136 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . IV.E.ConcIusion In summary, we have studied extensively the influence o f substrate misorientation on the optical properties of Inx Gai.x As films grown on GaAs(OOI) substrates. Spectrally-integrated CL, monochromatic CL, LPCL and CLWI imaging were used to study the spatial variations of optical properties. We have shown the existence of local variations in compressive stress ranging from biaxial with an = ax to quasiuniaxial with G||» ax, resulting in a marked polarization anisotropy concomitant with a variation in luminescence transition energy. We observed that the substrates tilted towards (Oil) and (111)A showed an enhanced anisotropy in misfit dislocation density, i.e. the density of [110]-oriented (a) dislocations was found to be greater than [110]-oriented P dislocations, giving rise to a net polarization anisotropy. The polarization anisotropy was reduced for growth on (111)B misoriented sample, consistent with XRC measurements. A model has been developed that discusses the changes in stress on <110> {111} slip systems caused by the substrate offcut and also on the change in the misfit dislocation anisotropy between the (111 )B and (111 )A misorientations. These results show that the polarization and relaxation anisotropy of InxGa|.x As can be tailored with a suitable choice of the misorientation for the starting GaAs (001) substrate. R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . References 1. R.S. Goldman, H.H. Wieder, K.L. Kavanaugh, K. Rammohan, D.H. Rich, Appl. Phys. Lett, 65, 1424 (1994). 2. Z. Liliental-Weber, Y. Chen, P. Wemer, N. Zakharov, W. Swider. and J. Washburn, J. Vac. Sci. Technol. B 11, 1379 (1993). 3. D. Morris, Q. Sun, C. Lacelle, A.P. Roth, J.L. Brebner, M. Simard-Normandin, and K. Rajan, J. Appl. Phys. 71,2321 (1992). 4. K.L. Kavanaugh, M.A. Capano, L.W. Hobbs, J.C. Barbour, P.M.J. Maree. W. Schaff, J.W. Mayer, D. Petit, J.M. Woodall, J.A. Stroscio. and R.M. Feenstra. J. Appl. Phys. 64,4843 (1988). 5. E.A. Fitzgerald, G.P. Watson, R.E. Proano, D.G. Ast, P.D. Kirchner. G.D. Petit, and J.M. Woodall, J. Appl. Phys. 65, 2220 (1989). 6. J.J. Duga, J. Appl. Phys. 33, 169 (1962). 7. J. Chen, J.M. Fernandez, and H.H. Wieder, in Mechanisms o f Heteroepitaxial Growth, edited by M.F. Chisholm, R. Hull, L.J. Schowaiter, and E.J. Garrison. MRS Symposia Proceedings No. 263 (Materials Research Society, Pittsburgh. 1992), p. 377. 8. T. Schweizer, K. Kohler, W. Rothemund, and P. Ganser, Appl. Phys. Lett. 59, 2736(1991). 9. D.H. Rich, A. Ksendzov, R.W. Terhune, F.J. Grunthaner, B.A. Wilson, H. Shen. M. Dutta, S.M. Vemon, and T.M. Dixon, Phys. Rev. B 43, 6836 (1991). 138 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 10. Y. Tang, D.H. Rich, E.H. Lingunis, N.M. Haegel, J. Appl. Phys. 76. 3032 (1994). 11. M. Grundmann, J. Christen, D. Bimberg, A. Hashimoto, T. Fukunaga, and N. Watanabe, Appl. Phys. Lett. 58,2090 (1991). 12. F.H. Poliak and M. Cardona, Phys. Rev. 172, 816 (1968). 13. S. Adachi, J. Appl. Phys. 53, 8775 (1982). 14. S. Niki, C.L. Lin, S.C. Chang, and H.H. Wieder, Appl. Phys. Lett. 55. 1339 (1989). 15. V. Swaminathan and A.T. Macrander, Materials Aspects o f GaAs and InP Based Structures (Prentice-Hall, Englewood Cliffs, NJ, 1991), pp. 21-25. 16. D.H. Rich, T. George, W.T. Pike, J. Maseijian, F.J. Grunthaner, and A. Larsson, J. Appl. Phys. 72, 5834 (1992). 17. T. George, E.R. Weber, S. Nozaki. T. Yamada. M. Konagai, and K. Takahashi. Appl. Phys. Lett. 59,60 (1991). 18. I. Yonenaga and K. Sumino, J. Appl. Phys. 65, 85 (1989). 19. K.L. Kavanaugh, R.S. Goldman, and J.C.P. Chang, Mat. Res. Soc. Proc. 340. 552 (1994). 20. J.E. Ayers, S.K. Ghandhi, and L.J. Schowalter, J. Cryst. Growth 113, 430 (1991). 21. For a calculation of stress on <110>{ 111} slip systems see e.g., J.P. Hirth and J. Lothe, Theory o f Dislocations, 2n d Ed., Ch. 9 (Krieger, Malabar, Florida, 1992). R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . C h a p t e r V EFFECT OF RAPID THERMAL ANNEALING ON STRAINED INGAAS/GAAS QUANTUM WELLS BONDED TO UNPATTERNED AND PATTERNED SILICON VIA EPITAXIAL LIFT-OFF TECHNIQUE V.A.Introduction In recent years, there has been an increasing interest in the integration of HI-V and Si technologies. The hybridization of ID-V/Si materials is important in the realization of opto-electronic integrated circuits (OEIC) which finds many applications in broadband and coherent optical communication networks and in optical recording. Although impressive advances have occurred in achieving high quality GaAs via heteroepitaxial growth on Si. the GaAs films grown by this technique have exhibited poor optical and electrical properties which make them unsuitable for device applications.1 '2 The problems encountered with heteroepitaxial growth have stimulated different research groups to investigate alternate routes in achieving monolithic integration of dissimilar crystalline materials. One technique which has exhibited considerable amount of success in achieving integration of dissimilar materials is the epitaxial lift-off (ELO) technique.3 This 140 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . technique makes use selective removal of a very thin sacrificial AlAs layer between the substrate and the active layer. After lift-off. the layer structures are bonded to arbitrary substrates. Based on the extensive work performed so far, it is clear that this technique does not suffer from the problems encountered in heteroepitaxial growth.4' 7 However, it is still not clear as to whether the optical properties of these films are affected by this technique and also the reliability of these devices, in terms of their ability to withstand thermal shock, thermal cycling, and high temperature conditions.8 V.B.Epitaxial lift-off Epitaxial lift-off (ELO) (then called peeled film technology) was first reported by Konagai et al9 in 1978 and it showed the possibility of grafting GaAs solar cells onto an A1 plate. Interest in thin film grafting techniques has increased rapidly recently, mainly due to difficulties in heteroepitaxial growth, the new approach for epitaxial lift-off proposed by Yablonovitch,3 and the interesting results obtained with bond and etchback silicon on insulator (BESOI) technology. 10 The basic steps of ELO is shown in figure VI-1. The first step is to grow the active layer on a GaAs substrate with an intermediate AlAs lift-off layer. The film is now covered with a thick layer of black wax. The next step is the lift-off of the layer or device structure using a selective etchant for AlAs. The devices can either be pre-processed prior to lift-off or can be processed after lift-off is performed. After the lift-off is done, one can graft the thin films onto a surrogate substrate if it is sufficiently flat. The major 141 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . 65 A ln0 2Ga0 8As QW \ AIA 0.4) is used in the structure. If we do need to lift-of devices containing AlGaAs with low A 1 composition, we need to take special precautions to protect the layer structure from HF solution. 11 The thickness of the AlAs lift-off layer is about 500 A and the undercutting speed is about 0.3 mm/hr. It is very important to use thin AlAs layers and a low HF concentration, because the hydrogen produced during the etching process can form gas bubbles, resulting in cracks in the layer structure and the blocking of the etching channel. The black wax used on top of the ELO film plays a very important role in the epitaxial lift-off process. The stress induced by black wax is important to bow the epilayer structure, providing a channel of enhanced diffusion for the etching process. The black wax (typically 200 pm to 300 pm thick) also provides sufficiently rigid carrier for thin films. The deposition of black was (Apeizon W) is done by melting a small quantity R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . o f wax at about 80° C and applying it to the sample surface. The wax is then reflowed at a higher temperature (typically about 100° C) so that we obtain a smooth film. V.B.2.ELO film bonding One of the major problems with ELO is the mechanical adhesion of the thin films to the new host substrate. The different requirements for the bonding process are : low' defect density, low-temperature processing, strong bonding, and no degradation of the layer structure or device compatibility with the new host substrate. Strong electrical and thermal contact between the grafted film and the original substrate is another requirement. One method which satisfies most of the requirements is the Van der Waals bonding procedure. The released surface of the wax coated film is squeezed to the surrogate substrate in a pure deionized water medium. After drying, for about one day under a small weight, a close-contact bonding occurs at low temperature. After bonding is complete, wax is removed by dissolving it in a solution of trichloroethane (TCE). Additional bonding strength is achieved by baking the sample at a temperature of 150° C for 1 0 minutes. An important issue in the bonding procedure used is the number of defects introduced in the bonding of the ELO film. In the case of the non-optimized procedure we observe a large density of defects which are bubbles formed between the substrate and the ELO film. This is most probably due to dust particles trapped on the back side of the ELO films during the transfer from the original substrate to the new host substrate. 144 R ep r o d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . These bubbles have to be avoided since they are a place of localized stress, a barrier for heat dissipation and nucleation point for further release of the film during temperature cycling. The bubble density can be improved by a factor of 100 to below 100 cm' 2 by using the optimized “underwater processing” procedure developed by Demeester et al. 8 In this technique one dilutes the HF etchant continuously by adding fresh DI water. The ELO film is transferred and bonded without leaving the water, because crossing the water surface leads to a large number of dust particles on the back side of the ELO film. V .C .Processing o f Silicon V.C.l.Standard cleaning The silicon samples covered with a 3500 A thin layer of Si02 were first chemically cleaned by degreasing in solvents. Boiling trichloroethane for 15 minutes, acetone for 5 minutes, and methanol for 5 minutes were used in this order to clean the surface of any residue. The solvent cleaning was followed by rinsing in deionized (DI) water (resistivity > 18 MQ-cm) and blow drying ultra high pure-Ni gas. This procedure is referred to as the standard cleaning procedure. V.C.2.Photolithography A positive photoresist (PPR) based process was used. The steps were: i) Spin coat the samples with Hoechst AZ 5214 PPR at 4000 rpm for 30 sec. 145 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ith out p erm issio n . ii) The PPR coated wafers were soft baked in an oven at 90° C for 30 minutes to release residual solvents in the PPR. The photoresist thickness at the end of this bake was determined to be 1.3 to 1.4 pm depending upon the age of the resist. iii) The lithography was done using a Karl-Suss mask aligner (model MJB 3) using chrome plates. The exposure to UV light was done at a power setting of 6 mW/cm2 for about 6 sec. iv) The PPR pattern was developed in Hoechst AZ 400 K (1:4) developer for about 30 sec. One of the problems encountered during etching of Si0 2 using photoresist as a mask was that the etchant eroded the edges of the photoresist which in turn resulted in a widening of the linewidths. In order to avoid this problem we deposited Six Ny on top of Si0 2 prior to depositing PPR, and used Six Ny as the masking material. V.C.3.Silicon nitride deposition Silicon nitride was used as a masking material for preferential etching of SiC^. The oxidized wafers were cleaned by the standard cleaning procedure and were loaded into the PECVD chamber. Silicon nitride was deposited in a Plasma Technology model DPM80M reactor. The gases used are S1H4 (2% in N2), NH3 (5% in N2) and ultra high purity-N2. The substrate temperature during deposition was fixed at 325° C. The flow rates of the gases were SiR* : 120 seem, NH3 :10 seem, and N 2 :255 seem. The RF frequency was fixed at 13.6 MHz. The RF power was fixed at 30 W. With the above 146 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ith out p erm issio n . condition a deposition rate of - 1 0 0 A/min was achieved. Deposition was performed for 1 0 minutes to obtain a total thickness o f 900 A. V.C.4.Etching of silicon nitride The wafers with Six Ny encapsulation were cleaned using standard cleaning procedure and through use of photolithography windows were opened in the photoresist. Silicon nitride was selectively etched by reactive ion etching (RIE) using a mixture of carbon tetrafluoride and oxygen (CF4/ 5% O2) form the exposed area. Wafers were loaded into the RIE chamber and the chamber was pumped down to a few milli torr pressure. Then CF4/O2 was introduced into the chamber and the chamber pressure was set to 150 millitorr. The plasma power was set to 100 W. The etching was done at these conditions for 30 seconds to remove all the silicon nitride in the exposed regions. V.C.5.Etching of Silicon dioxide The photoresist was removed by dissolving it in a solution of n-butyl acetate prior to etching of S iC > 2. The samples were then immersed in a solution of buffered oxide etch (BOE 7:1) to remove the SiC>2 in the region not covered by Six Ny. This etchant selectively etches SiC>2 but does not attack Six Ny. After immersing in the solution for 3.5 minutes all the Si02 was removed. The Six Ny was then remove by reactive ion etching. The final wafer thus contains SiC >2 mesas on top of Si. R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . V.D .R apid therm al annealing (RTA) The rapid thermal annealing equipment used in this study is an AG Associates, model Heat Pulse 610. The samples were place close to the thermocouple on a 3 inch silicon substrate which has a thickness of 300 pm. The thermocouple is embedded in the silicon substrate wafer. Samples were placed closed to the thermocouple in order to reduce the effect of temperature variation away from the thermocouple. The rate of rise of temperature was around 1° C/s and rate of fall was also 1° C/s down to room temperature. The stability of the temperature at the maximum desired temperature was around ± 3° C. Before the start of the temperature ramp-up there was a 3 minute purge of the system with UHP-N2 and annealing was performed in a reducing atmosphere of forming gas (Ar + H2) to minimize oxidation of the sample during high temperature operation. Samples were placed face-up on silicon and no GaAs wafers were used to prevent outgassing of As from the surface of the samples. V .E.EX PER IM EN TA L DETAILS The sample studied was grown by metalorganic chemical vapor deposition (MOCVD) on a GaAs(OOl) substrate. Starting from the GaAs substrate, the sample consists of a 500 A AlAs buffer layer, a 2100 A GaAs buffer layer, a 65 A Ino.20Gao.80As QW, and a 100 A GaAs capping layer. The original sample was cleaved into several small pieces and each individual piece was bonded to a planar Si substrate via epitaxial lift-off technique. 148 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . Rapid thermal annealing was performed at four different temperatures of 725. 750, 775 and 800° C for varying anneal times between 15 seconds to 5 minutes. Rapid thermal annealing was performed in a reducing atmosphere of forming gas to minimize oxidation of the sample during the high temperature operation. The anneals for consecutive time intervals at each temperature was carried out on the same sample to avoid scatter due to material variations. Anneals at different temperature were carried out on different samples. All samples were examined using cathodoluminescence imaging and microscopy. Cathodoluminescence measurements were performed with a modified JEOL 840-A scanning electron microscope.1 The light collected was dispersed by a 0.275m spectrograph and detected with a liquid-nitrogen cooled Si array CCD detector. CL spectra were obtained with a spectral resolution of 0.3 nm. An electron beam energy of 8 kV and a beam current of 2 nA was used to probe the samples. The temperature of the sample was maintained at 85 K for CL measurements. V.F.RESULTS AND D ISC U SSIO N The variation in the CL peak energy shift, AE, and the full width at half maximum (FWHM) as a function of annealing temperature is shown in Fig. 5-2 for samples annealed for 15 seconds. The energy position of CL spectra remains the same (i.e.. AE * 0) up to an annealing temperature of 700° C. Above that temperature, the peak moves rapidly to higher energies. The blue-shift in the CL peak position, as seen in Fig. 5-2 implies a 149 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . significant change in the QW confining potentials. As Ga and In interdiffusion smoothes out the initially abrupt Ino^Gao.gAs/GaAs quantum well interface, the band-gap increases, shifting the confined states to a higher energy. Similar results have been observed for pseudomorphic InGaAs/GaAs high electron mobility structures1 2 and high hole mobility transistors after thermal annealing.1 3 From Fig. 5-2, we also observe that the CL linewidth decreases as we increase the annealing temperature. The interface quality and the defects present in the unannealed sample could result in an initially large increase in CL linewidth. We suggest that on annealing, the interface roughness decreases and the defect density reduces, resulting in the observed reduction in linewidth. In Fig. 5-3 we have plotted , as an example, the CL emission from the sample annealed at 775° C for various anneal times. The CL peak moves progressively to higher energies with increasing anneal time. The CL linewidth decreases gradually as the anneal time increases for each annealing temperature as shown in Fig. 5-4. Also in Fig. 5-4 we have plotted the CL emission energies as a function of time for five different anneal temperatures. At temperatures between 600-700° C we observe no change in CL peak energy, luminescence intensity, or line width after annealing for more than 7 minutes. This indicates that mixing has not occurred and there is no catastrophic failure in these ELO films. We also observe no evidence of the films lifting off from the surrogate Si substrate for all temperatures reported in this paper. R ep ro d u ced with p erm issio n of th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . 60 _ 50 40 ~ 30 LLi Q 20 10 0 > < D £ 11 sz -4 —» ■g $ < D 10 _c _l O 9 720 730 740 750 760 770 780 790 800 Temperature ( °C) ,n0 2^ a0 8As/^ aAs on Si(001). 15 sec. RTA _ Fig. 5-2. Variation of the CL peak energy and linewidth in the Ino.2Ga0.sAs/GaAs QW films on Si as a function of the annealing temperature. R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . C L Intensity (arb. units) InGaAs/GaAs QW annealed at 775° C Anneal time (secs) 240 150 60 0.5 0.0 840 860 880 900 920 940 960 Wavelength (nm) Fig. 5-3. CL spectra of the Ino.2Gao.8As/GaAs QW for various anneal times at 775° C. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . ~o O o 1.44 1-42 & © 1.40 © 1.38 725° C 1 750° C 775° C 1.36 1.34 800° C - 0 50 100 150 200 250 300 350 400 450 Time (sec) Fig. 5-4. Plot of the temporal evolution of the CL peak energy and linewidth at temperatures of 725, 750, 775 and 800° C, respectively. The solid lines represent the fits to the theoretical model. 153 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . V.F.l.M odeling o f RTA effect on the CL peak position In order to have a better understanding of the nature of interdiffusion at the interfaces between the InGaAs QW and GaAs barriers, a model is developed that relates the observed changes in excitonic luminescence peak energy to interdiffusion through changes in electron and hole confinement potential induced by spatial variation in the In composition. It utilizes the model developed and explained in Appendix B for the calculation of exciton transition energy for highly strained quantum wells via transfer matrix method. In order to incorporate the interdiffusion-induced change in the composition profile of the barriers and QW layers, the confinement potential is made dependent on the In compositional profile. We assume the interdiffusion process involves an isotropic diffusion of In and Ga with a diffusion coefficient independent of Ga concentration. The system can be characterized by a single diffusion coefficient (D) for both Ga and In. The assumption of one-dimensional diffusion from an initially abrupt interface into a semi-infinite solid is used here.1 4 According to this model, the composition of the diffusing species, x, as a function of the distance from the reference point (z) and the diffusion time (t) can be derived as: (5.1) 154 R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . where xa represents the composition of the diffiisant far from the interface at time t = 0. 2fD t represent the diffusion distance, and is assumed to be small relative to the length of the system. If the diffusion occurs in two directions, as in our case, namely In diffuses out from the well to both barriers, and Ga fills into the well from both barriers, we must redefine the origin of the diffusion as the center of the well (z = 0), and therefore z in equation 5.1 is replaced with z + h for one half of the well (i.e. z > h) and z - h for the other half, where h is the half-width of the well in the as grown structure. Hence, the solution for the semi-infinite case Eq. 5-1 becomes: i+ r \ z ijDt. forz >h (5.2) and with, erf (z) = -erf (-z), Eq. 5.1 forz < h becomes; 1 \2 4 m . for z < h (5.3) Combination of Eqs. 5.2 and 5.3 describes the spatial profile of In composition in this interdiffusion process for the entire QW region as; { \ c(x) = — erf h + x + erf (5.4) in which ca represents the concentration of In in the well at time t = 0, h is the half-width of the quantum well, Di„ is the interdiffusion constant, t is the annealing time, and x is the distance from the center of the QW. The confined electron and hole energies were calculated by solving the Schrodinger equation for a quantum well with these graded 155 R ep r o d u ced w ith p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . interfaces using a transfer matrix method.1 2 The effects of strain and composition on the effective masses, band gap, band offsets, and heavy hole-to-light hole band splitting were taken into account in these calculations.1 5 The exciton transition energy (AEei-hi) was calculated using the following relationships AEei.hi =EC-Ev (5.5) where Ec is the lowest confined energy level of the conduction band and Ev is the first confined energy level at the top of the valence band (heavy holes). These confined energies were calculated by solving the Schrodinger equation in the context of effective mass approximation with the inclusion of strain effect on the effective mass and with the following composition and strain dependent profiles: s(x) (5.6) 'ii ' for the conduction band composition dependent energy profile and, C - C '“ II '“'IZ Vlv ) = - 2 a(v){x) C, [^(x) + b II ' ' '-I I C, e(x) (5.7) for the valence band potential energy profile. In Eqs. 5.3 and 5.4, Cn = Cn(x) and C 12 = Ci2(x) are the composition dependent components of he stiffness tensor, alc,(x) and a(v )(x) are the composition dependent deformation potentials for the conduction and valence bands, respectively and b = b(x) is another composition dependent deformation 156 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . potential. e(x) is the composition dependent strain tensor, in which its components for a compressively strained layer are defined as: (2 CI21 a(x) — a(GaAs) = a n d £ = = - (5.8) In Eq. (5-8) a(x) is the composition dependent lattice constant of the strained Inx Gai.x As well and a(GaAs) is the lattice constant of GaAs. The composition dependence of the above mentioned parameters are obtained by linear interpolation between the values of InAs and GaAs listed in table A. 1 in Appendix A. The theoretical curves of the CL emission energy (solid lines in Fig. 5-4)) were obtained by using the interdiffusion constant D/„ as the only fitting parameter in these calculations, and D/„ is therefore determined unambiguously. Interdiffusion constants of 2.563 x 10'1 6 , 7.2 x 10'1 6 , 1.45 x 10'1 5 , and 4.1 x 10'1 5 were obtained for 725, 750. 775 and 800° C respectively. The theoretically calculated values of D/n are plotted as a function of the T 1 in the semi-logarithmic plot of Fig. 5-5 from which an activation energy of 3.303 eV is obtained. The Arrenhius-type behavior observed in Fig. 5-5 supports strongly this interdiffusion model. We have performed similar rapid thermal annealing experiments on Ino.2Gao.8As/GaAs quantum well films bonded to patterned Si substrates. The surrogate Si substrate is patterned prior to bonding and consists of 5 pm SiC>2 squares on Si separated by a distance of 5 pm. Fig. 5-6 shows monochromatic CL image obtained from the ELO bonded In0. 2Ga0.sAs/GaAs quantum wells which have been annealed at 750° C for 45 157 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . Temperature ( °C) 800 775 750 725 100 0.925 0.950 0.975 1.000 1000/T (K " 1) Fig. 5-5. Plot of the interdiffusion constant Di„ as a function of annealing temperature. R ep ro d u ced with p erm issio n o f th e copyright ow ner. Further reproduction prohibited w ithout p erm issio n . Fig. 5-6. Monochromatic image of In0. 2Ga0.sAs QW ELO bonded to patterned Si surrogate substrate consisting of 5 |rm mesas annealed at 750° C for 45 seconds. R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithou t p erm issio n . seconds. From Fig. 5-6, we observe that there is a spatial variation in the luminescence peak energy from the two regions. The film resting on the square mesas exhibit an reduced blue-shift as compared to the film between the mesas. The exact reason for this lateral variation is not clear. This lateral band gap modulation could have potential implications in creating reduced dimensionality structures in ELO films. Further detailed investigations are necessary to ascertain the cause for the spatial variation in peak energy. V.G.CONCLUSIONS In summary, we have investigated the effect of rapid thermal annealing in the temperature range of 600-800° C on the optical properties o f strained Ino.2Gao.8As/GaAs QW films bonded to Si(001) substrates via ELO. We have observed that ELO films are stable for the thermal cycling employed in this study with no apparent peeling of the films from the Si substrate. We have also demonstrated that these structures are stable under normal device processing conditions (-600° C). At higher annealing temperatures, we observe the intermixing of In and Ga atoms, resulting in a blue shift in the CL peak energy. We have determined the Ga/In interdiffusion constant, £>/„, for various annealing temperatures, thereby enabling the determination of the activation energy for interdiffusion at the Ino.2Gao.8As/GaAs interface. ELO films bonded to patterned Si substrates show a spatial variation in luminescence peak energy. This phenomenon could have potential implications in the fabrication of reduced dimensionality structures in these films. 160 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . References 1. D.H. Rich, A. Ksendzov, R.W. Terhune, F.J. Grunthaner, B.A. Wilson, H. Shen. M. Dutta, S.M. Vernon, and T.M. Dixon, Phys. Rev. B 43 6836 (1991). 2. Y. Tang, D.H. Rich, E.H. Lingunis, and N.M. Haegel, J. Appl. Phys 76 3032 (1994). 3. E. Yablonovitch, T. Gmitter, J. Harbison, and R. Bhat, Appl. Phys. Lett 51, 2222 (1987). 4. I. Pollentier, P. Demeester, A. Ackaert, L. Buydens, P. Van Daele and R. Baets, Electron. Lett. 26, 103 (1990). 5. I. Pollentier, C. Brys, P. Demeester, P. Van Daele and L. Martens. Electron. Lett. 29, 201 (1990). 6. W.K. Chan, A. Yi-Yan, and T. Gmitter, IEEE Jour. Quant. Elect. 27,717 (1991). 7. E. Yablonovitch, K. Kash, T.J. Gmitter, L.T. Florez, J.P. Harbison, and E. Colas. Electron. Lett. 25, 171 (1989). 8. P. Demeester, I Pollentier, P.De Dobbelaere, C. Brys and P. Van Daele. Semicon. Sci. 9. M. Konagai, M. Sugimoto, and T. Takahashi, J. Crystal Growth 45,277 (1978). 10. W.P. Maszara, J. Electrochem. Soc. 138,341 (1991). 11.1. Pollentier, L. Buydens, P. Van Daele, and P. Demeester, IEEE Photon. Technol. Lett. 3,115(1991). 12. D.C. Streit, W.L. Jones, L.P. Sadwick, C.W. Ki, and R.J. Hwu, Appl. Phys. Lett. 58 2273 (1991). 161 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . 13. W. Gillin, Y.S. Tang, N.J. Whitehead, K.P. Homewood, B.J. Sealy, M.T. Emery, and C.R. Whitehouse, Appl. Phys. Lett. 56 1116 (1990). 14. P. Shewmon, in Diffusion in Solids, 2nd ed. TMS publication, Warrendale. Pennsylvania, 208 (1989). 15. D.H. Rich, H.T. Lin, and A. Larsson, J. Appl. Phys. 77,6557 (1995). R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . C h a p t e r V I CONCLUSIONS AND POSSIBILITIES FOR FUTURE WORK The specific conclusions derived from the studies on the optical properties of InGaAs/GaAs system, the influence of defects on local variations, the viability of epitaxial lift-off technique and the studies on thermal processing of ELO films were presented in chapters IV through VI. Here we present some general conclusions derived from the research carried out in this dissertation. We have systematically studied the optical properties o f the InGaAs system. We have studied the influence of defects such as misfit dislocations on the local variation in band gaps, and also have studied the polarization anisotropy created by the anisotropic distribution of misfit dislocations. Upon comparing CL, TEM and XRC results, we have shown that substrate misorientation plays a critical role in the distribution of misfit dislocations in these samples. We have also explored this substrate misorientation as a way of trying to control the polarization properties of partially relaxed InGaAs films. For obtaining monolithic integration of HI-V materials with Si to achieve monolithic integration essential for realization of opto-electronic integrated circuits, we have examined the viability of the epitaxial lift-off technique. We have examined the optical properties of films prior to lift-off and after lift-off and have observed no R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . deterioration in the optical or structural quality of ELO films. We have examined the effect of high temperature thermal processing on these films in order to evaluate the thermal stability of devices fabricated via ELO technique. A model was developed which related the change in excitonic peak transition energy with the interdiffusion at the interface, and thus were able to extract the interdiffusion coefficients of Ga/In. Further, we have also estimated the activation energy for interdiffusion. The scope for future work, we believe, falls into two categories: extensions of the present study and studies of new issues, some uncovered during the course of this work. As an extension of the present study, room exists to continue the present work by studying the influence of misfit dislocations on material properties such as carrier lifetime. The availability of state of the art equipment to perform time-resolved cathodoluminescence opens up new avenues to further study the interplay between strain relaxation and the corresponding influence of carrier lifetime. It should also be possible to evaluate the substrate misorientation as a way of achieving suitably relaxed buffer layer films on top of which the active layer could be grown with very little defects. This technique could enable us to grown thick high indium composition films which are essential for the realization of high quality InGaAs/GaAs light modulators. The epitaxial lift-off technique has shown very promising results and needs to be evaluated as a way of creating nanostrcutures via annealing. In our preliminary studies, we were able to observe lateral variation in peak energy caused by a lateral variation in 164 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm ission . In interdiffusion. It would be a very interesting experiment to see if we can control the level of interdiffusion and create similar variations on a nanoscale. 165 R ep ro d u ced w ith p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . A p p en d ix A Effect of strain on band structure of heterostructures The valence band electronic structure will be described based on the model proposed by Luttinger.1 - 2 Luttinger used as a basis the top 6 valence bands, |3/2. 3/2), |3/2, 1/2), |3/2, -1/2), [3/2, -3/2), |l/2, 1/2) and |l/2, -1/2). The contributions of all other bands (including s-like conduction bands) are taken into account using the second order perturbation. The Hamiltonian can be written in the form given below using the notation of Chan, Sanders and Tin;3 H(k) = where ’ S + T L M 0 - l/ S -■Ji m r S - T 0 M ■ J i t ■fiiiL (h * ] M ’ 0 S - T L VV2 r yJlT U m J 0 M" r S + T ■ J i m - L ’/ J i - l’/ S ■JlT VV2 L J i m ’ S -A 0 -Ji m ’ f i l l L ’ ■JlT - l/ J i 0 S - A 5 hi i H + k; + k; ) 7 III 1 H u + ky - 2k ;) (A.l) (A.2) L = 2-J3y,(kx - ft,)*., M^-^nikl-k^ + lSrjKk, 166 R ep r o d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . Y i , Y 2 , and y 3 are the Luttinger parameters, and D is the spin-orbit splitting. In this Hamiltonian matrix, the energy for the heavy hole at k = 0 is chosen as zero. Values of Y i , Y 2> and Y 3 for InAs, GaAs and AlAs are listed in table A.I. For the behavior of the valence band near the Brillouin zone center, since L, M and Q are significantly smaller than A when k is small, the effective mass of the heavy hole and the light hole band can be obtained by solving the upper left 4 x 4 Hamiltonian matrix. H (k) = Jr_ 2m .. S + T L M 0 L' S - T 0 M M ' 0 S - T - L 0 A 4' - L ' S + T (A.3) This leads to the dispersion relation4 -5 E(k) = - Ak1 ± ^ B 2k*+C2(k2k ;+ k 2k; + k;k: )] (A.4) where + denotes the heavy hole band and - denotes the light hole band. A, B and C are related to the Luttinger parameters by Y i =-A Y 2 = (-1/2) B Y 3 = -(1/6)[3C2 + 9B2 ]i/2 (A.5) The effect of strain can be incorporated into the kp calculation by introducing into the Hamiltonian a strain dependent term-the Pikus-Bir hamiltonian,4 167 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . Table A.l Important parameters at 0 K InAs GaAs AlAs Eo(eV)a 0.42 1.52 3.06 A (eV)a 0.38 0.34 0.28 Yia 19.67 7.65 4.04 Y 2 a 8.37 2.41 0.78 Y 3° 9.29 8.68 1.57 a (eV)b 5.79 8.68 7.96 b (eV)b -1.8 -1.7 -1.5 d (eV)b -3.6 -4.55 -3.4 C 11 (xlO1 1 dyn/cm2 )b 11.88 14.12 12.02 CI2(x l0 1 1 dyn/cm2)b 5.38 6.253 5.70 C44(x l 0 ‘* dyn/cm2) * 5 5.94 7.047 5.89 a) P. Lawaetz, Phys. Rev. B 4,3460 (1971). b) S. Adachi, J. Appl. Phys. 53, 8775 (1982). 168 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . (A.6) where ctJ denotes the components of the strain tensor, L the angular momentum operator, c.p. denotes cyclic permutations with respect to the rectangular coordinates x. y z and {} indicates the symmetrized product of {LxLy} = (LxLy + LyL,)!2. The parameter a is the hydrostatic pressure deformation potential. The parameters b and d are the uniaxial deformation potentials for tetragonal and rhombohedral symmetry, respectively, and are both zero for the s-like conduction band. The total Hamiltonian is thus. where the Hs.o. denotes for the spin-orbit Hamiltonian in the absence of strain. At the Brillouin zone center (k = 0), it is possible to construct the conduction band and valence band Hamiltonian separately. For a biaxial strain s along [100] and [010] directions, we have9 where Ca and Cn are components of the stiffness tensor. The Hamiltonian is written in the form, H = Hs.o. + He (A.7) 6a = -(2Ci2/Cii)S (A.8) 169 R ep ro d u ced with p erm issio n of th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . where 8 E = - 2 a lc)( —1 C'2 V (SEj;1 = - 2 a 'v|f-i-' -~ C|- 2 v C, i y II ' \ SEt =3 b C, | + 2C1 2 (A. 10) It is possible to diagonalize the 6 x 6 valence band Hamiltonian into two degenerate 3 x 3 matrices written in the order of |3/2,3/2>, |3/2,1/2) and 1 1/2,1/2) HV' = & h' 0 1 0 0 8 H ^ - - 8 E t V2 0 — 5Et V2 8Et 8H( h v ) - A (A.l 1) By diagonalizing Eq. A.9, we obtain. 170 R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . E — E i = E — SE u — -S E r c v2 £ H ^ T 2 (A. 12) Ee - Evi = Eg - 8E h + (A + ^SE t ) - A2 - |A<5Er + (<5E r )2 2 where v2, vl and v3 denote heavy hole, light hole and split-off bands, respectively, and the conduction band, and the heavy hole, light hole and split-off bands without [panel (a)] and with [panel (c)] the presence of strain. The direction of the shift in each band corresponds to the case of biaxial compressive strain along [100] and [010] direction. the light hole bands and reflects the contribution of the hydrostatic term in the Pikus-Bir Hamiltonian. The splitting between the heavy hole and the light hole reflects the tetragonal term since the rhombohedral term is zero in this case. The tetragonal term also causes the mixing between the heavy hole, light hole and split-off bands at the T point. The presence of strain in semiconductor materials also introduces a strain- induced anisotropy of luminescence. Interband optical transitions involving the 8E=SE(‘] - 8 E { " (A.13) v '-II ' The values of a, b and d are listed in table A.I. Fig. A-l shows the schematic behavior of The dashed line in panel (c) corresponds to the ‘average’ position of the heavy hole and 171 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . ll/2 ,± l/2 > (a) No Strain (c) Compressive Strain Heavy Hole !3/2Jb3/2> (b) (d) Fig. A-l Schematic diagram of band structure near zone center for zinc-blende structure (a) without strain and (c) with compressive biaxial strain. Panels (b) and (d) show constant energy surfaces for | 3/2, ±3/2) and | 3/2, ±3/2) bands without strain and with strain, respectively.2 172 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . hh and Ih states exhibit polarization selection rules which depend on the strain tensor, deformation potentials and orientation of the electric field, E, of light emitted or conduction bands and the six highest valence bands. It also gives the orbital angular momentum L, lz and the spin S, S z components that form the total angular momentum J. jz states. The T point energy of these bands are also given. For a general biaxial stress (cr) in the (001) plane, which contains two orthogonal stress components c t u and (as referred to [110], a diagonalization of the orbital-strain Hamiltonian enables a determination of the set of uppermost J = 3/2 strain-split valence-band wave functions,Uj.4 In the [110] representation of | J, m j> . these normalized wave functions are where i = I and 2 represent the highest and lowest bands, respectively. The coefficients cM and cU h are given by absorbed.4 Table A.2 shows other frequently used notations for the two lowest given by (A. 14) 7 (A. 15) C 2Jih ~ C \Jh>C 2Jh ~ C \ M 173 R ep r o d u ced w ith p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . where the parameters r|and £ are represented in terms of the elastic compliance constants Sii, S 12 and S44, the uniaxial deformation potentials b and d, and the in-plane stress components on and a±: a. 1 + - ^ d - g 54 4 1 - ^ 1 + + T d s “ (A.1 6) The elastic compliance constants and deformation potentials for Inx Gai.x As are approximated well by interpolating between the corresponding values for pure GaAs and InAs listed in table A.I. Using the dipole approximation in Fermi’s golden rule, i.e. T,u °c KuclExj-plu,)!2, where u« is the conduction-band wave function and p is the linear momentum operator, we can calculate the ratio of the oscillator strengths of luminescence with E _ L [110] polarization to that with E || [110], for the lowest-energy transition in the strain split bands. 174 R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithou t p erm issio n . Table A.2 The notations of bands under consideration Name limj) ‘ T im Group Notation E(k = 0) conduction band i i ) 2 '2 / |St> - - - ) 2 ' 2/ |S 4-> heavy hole (v2) 2 2 ^ 2 ’ 2/ 1 . 1 ) 2 ' 2/ r6 E0 light hole (vl) 2 4 2 '2 / 2 - 4 2' 2/ Tg 0 spin split-off (v3) I I \ 2 '2 / 2 ’ 2/ - ^ ( 2 r - , r ) t ) + ^ z i ) r7 -A R ep ro d u ced with p erm issio n o f th e copyright ow n er. Further reproduction prohibited w ithout p erm issio n . R eferences 1. J.M. Luttinger and W. Kohn, Phys. Rev. 97, 869 (1955). 2. J.M. Luttinger, Phys. Rev. 102, 1030 (1956). 3. Y.C. Chang, G. D. Sanders and D.Z.Y. Ting, Exciton in confined system. (Proceedings of the International meeting), editors. R. Del Sole, A. D’Andrea, and A. Lapiccirella, Spring-Verlog, Berlin, 1988. 4. F.H. Poliak and M. Cardona, Phyr B **'' 172. 816 (1968). R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . A p p en d ix B Calculation o f energy levels and w ave functions using transfer m atrix m ethod (TM M ) In this dissertation, we have used an algorithm based on the transfer matrix method to numerically solve the Schrodinger equation in quantum well structures.1 '2 In order to discretize the problem, we consider a piecewise constant profile, as shown in Fig. B-l where we have a total of N layers, starting with layer No. 0 (for -oo < x < x0) to layer No. N-l ( for x > *n-2)- In each of these layers both the potential Vj and the effective mass m / are assumed to have a constant value. Our problem is now to solve the one dimensional Schrodinger equation in each layer for a given potential profile. Within each layer the wave functions can be expressed as exponential functions according to Euler’s formulas and we write for the wavefimction in layer number j as T ;(x)= A, .e p‘ix) +B, .e~p’< 1 ) (B.l) where p/x) is a complex function, given by fr0 .x U = o) i r , • ( * - * , . , ) u > 0) <B2) The unknown complex constants Aj and B} are to be determined by the boundary conditions for the wave functions. The variable r, is related to the eigenvalue E by the expression 177 R ep ro d u ced with p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n . * N - l Distance, (x) Fig. B-l. Schematic representation of a piecewise constant potential profile consisting of N-layers. 178 R ep ro d u ced with p erm issio n o f th e cop yright ow ner. Further reproduction prohibited w ithout p erm issio n . 18x2 ■ m' T, (£ ) = /. ~ y ~jT -(E-V,) (B-3) If E < Vp then T y is real and negative, otherwise it is complex. The boundary conditions for the wavefunctions at the border between 2 layers can be written as ( according to Fig. B-l the x-coordinate at the boundary between layer j and j -1 has the value Xj.\) (B.4) \ d \ i 1 d r I The total wavefunction for the system is now given by summing the wavefunctions. Tj in all individual layers together. It should be noted however that the process of discretizing with each piece assumed to have a constant effective mass and potential values, implies that the wavefunctions given in Eq. B.l are only valid within each layer and not at the very boundary points. However, this does not in any way restrict the generality of the numerical method presented here. Applying the boundary conditions in Eq. B.4 to Eq. B.l. it is possible to derive an expression that relates the A and B constants in layer J + 1 to the constants in layer j in the following way: r a , ,i [A 1 j * i = M • i . b j+ j A 179 R ep ro d u ced with p erm issio n o f th e copyright ow ner. Further reproduction prohibited w ithout p erm issio n . where Mj is a 2 x 2 matrix. By repeatedly applying Eq. B.5, we can find a relation between A and B coefficients in the outermost layers (B.6) a u a n -^o 1 ^22 B0 Further, the wave fimctions should be bound in space, i.e. they should be zero in amplitude when x tends to plus or minus infinity. The eigenenergy E can be obtained by applying the condition By dividing the potential into several layers with a constant potential profile within each layer it is now possible to solve the one-dimensional Schrodinger equation for an arbitrary potential profile. We have implemented an algorithm for solving Eq. B.8 and is solved using a 486-based PC. The algorithm is explained in detail in the Ph.D. thesis of H.T. Lin. R eferences 1. D.C. Hutchings, Appl. Phys. Lett. 55,454 (1989). 2. D. Campi and C. Alibert, Appl. Phys. Lett. 55,454 (1989). CX22(E) = 0. (B .7 ) 180 R ep ro d u ced with p erm issio n o f th e copyrigh t ow n er. Further reproduction prohibited w ithout p erm issio n . INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type o f computer printer. The quality o f this reproduction is dependent upon the quality o f the copy subm itted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. 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UMI Number: 9720281 UMI Microform 9720281 Copyright 1997, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 R ep ro d u ced w ith p erm issio n o f th e copyrigh t ow ner. Further reproduction prohibited w ithout p erm issio n .

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Asset Metadata

Creator Rammohan, Karthikeyan (author)

Core Title Cathodoluminescence studies of the influence of strain relaxation on the optical properties of InGaAs/GaAs quantum heterostructures

School Graduate School

Degree Doctor of Philosophy

Degree Program Materials Science

Degree Conferral Date 1996-12

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

Tag engineering, materials science,OAI-PMH Harvest,physics, condensed matter

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Rich, Daniel (committee chair), Dapkus, Daniel (committee member), Goorsky, M. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c17-251881

Unique identifier UC11352823

Identifier 9720281.pdf (filename),usctheses-c17-251881 (legacy record id)

Legacy Identifier 9720281-0.pdf

Dmrecord 251881

Document Type Dissertation

Rights Rammohan, Karthikeyan

Type texts

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

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

Repository Name University of Southern California Digital Library

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