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Optical and electronic properties of GaAsBi alloys for device applications Masnadi Shirazi Nejad, Mostafa 2015

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   Optical and Electronic Properties of GaAsBi Alloys for Device Applications by Mostafa Masnadi Shirazi Nejad  B.Sc., Sharif University of Technology, 2007 M.Sc., The University of British Columbia, 2010  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY  in   The Faculty of Graduate and Postdoctoral Studies (Electrical and Computer Engineering)  The University of British Columbia   (Vancouver)  August 2015  © Mostafa Masnadi Shirazi Nejad, 2015    ii  Abstract GaAs1-x Bix  is a new III-V semiconductor alloy that  shows promise for many optoelectronic applications. In this thesis, several characterization techniques were used to explore the properties of molecular beam epitaxy grown GaAs 1-x Bix  alloys in a wide range of Bi-content. The fundamental bandgap and the optical absorption coefficient of pseudomorphic GaAs1-x Bix /GaAs films are studied by op tical transmission and photoluminescence spectroscopies. All GaAs1-x Bix  films (0≤ x ≤17.8%) show direct optic al bandgaps. The bandgap (Eg) decreases strongly with increasing Bi-content, reaching 0.52 eV (~2.4 µm) at 17.8% Bi. At Eg <1.06 eV, GaAs 1-x Bix  has the least lattice mismatch from GaAs of any ternary GaAs alloy, including GaAsN, for a given bandgap. Below the GaAs 1-x Bix  bandgap, exponential ab sorption tails are observed with Urbach energies 3-6× larger th an that of bulk GaAs. The electrical conductivity and Hall transport measurements on nominally undoped GaAs1-x Bix  films with 0<x ≤21.5% Bi reveal an exponential incr ease in p-type conductivity and a monotonic decrease in hole mobility with increasing Bi-content . From temperature dependent electrical measurements, this behavior is found to be associated with an increase in the density of states in the valence band of GaAs1-x Bix  alloys and the presence of Bi-induced acceptor states above the valence band.  A few optoelectronic devi ce applications of GaAs1-x Bix  alloys are also examined in this thesis. The photovoltaic response of single junction dilute GaAs1−x Bix  p+/n diodes were investigated for the first time. W ith the introduction of Bi into GaAs, the spectral response is shown to expand to longer wavelengths than in GaAs. Based on theoretical modeling, the minority carrier lifetimes in unoptimized bismide material are found to be significantly shorter than the standard grown GaAs, resulting in low collecti on efficiency in solar cell devices.  Furthermore, a systematic analysis is carried out to investigate the influence of rapid thermal annealing on the terahertz emission from bismide based photoconductive switches. Notable enhancement in terms of terahertz emission amplitude and bandwidth are demonstrated from annealed GaAs1-x Bix substrates. The optimum thermal annealing was found at 670 °C and 1 min duration. We found that GaAs 1-x Bix can perform better than conventional low temperature GaAs in generating the terahertz radiation.        iii  Preface  Some of the work presented in this thesis was carried out in collaboration with other graduate students. Therefore, my contributions are specifically declared in the beginning of each chapter. By the time of submitting this thesis, the following research papers related to the thesis have been published:    R. B. Lewis, M. Masnadi-Sh irazi and T. Tiedje, “Growth of high Bi concentration GaAs1-x Bix  by molecular beam epitaxy”, Appl. Phys. Lett., 101(8):082112, (2012). (Part of Chapter 2)  M. Masnadi-Shirazi, R. B. Lewis, V. Bahrami- Yekta, T. Tiedje, M. Chicoine, P. Servati, “Bandgap and optical absorption edge of GaAs 1− x Bix  alloys with 0< x< 17.8%”, J. Appl. Phys. 116, 223506 (2014). (A version of Chapter 3)  B. Heshmat, M. Masnadi‐Shirazi, R. B. Lewis, J. Zha ng, T. Tiedje, R. Gordon, T. E. Darcie, “Enhanced Terahertz Ba ndwidth and Power from GaAsBi ‐based Sources”, Adv. Optical Mater. 1 (10), 714–719 (2013). (Part of Chapter 6)  For the first paper, R. B. Lewis was the lead inve stigator and performed and analyzed most of the experiments. My role was to assist R. B. Lewi s with the MBE growth of some samples and with RHEED, HR-XRD and SEM character izations of samples. I was i nvolved in data analysis and reviewing the draft of the paper. T. Tiedje was the rese arch supervisor of this work.  I was the lead investigator, responsible for the experiment al design, data collection, analysis and manuscript composition of the second paper. R. B. Lewis and V. Bahrami-Yekta assisted by providing samples for this study. M. Chicoine performed Rutherford Backscattering Spectroscopy (RBS) experiments on the samples. Th e RBS data were analy zed by M. Chicoine, R. B. Lewis and me. The manuscript was edited by a ll the authors. T. Tiedje and P. Servati were the research supervisors of this work.  For the third paper, B. Heshmat was the ma in investigator and performed all the THz experiments. My role was to provide samples for these measurements. The samples were grown jointly by me and R.B. Lewis. All post-growth sa mple characterization (e.g. x-ray diffraction, PL, SEM) and sample preparation (e.g. thermal annealing and acid etching) and part of the  iv  photolithography process of the devices were carried out by me. I wa s involved in analysis of the results and editing the draft of the paper. This work was supervised by T. Darcie, T. Tiedje and R. Gordon.   The author was also involved in several presenta tions at international conferences and technical workshops:   M. Masnadi-Shirazi, R. B. Lewis, B. Heshmat,  V. Bahrami-Yekta, T. Tiedje, T. E. Darcie, P. Servati, “Optical and Electronic Tr ansport Properties of MBE Grown GaAs 1-x Bix  (0 < x < 22%)”, Material Research Society (MRS ) Spring meeting, Symposium FF, paper No. FF1.04, San Francisco, USA, April 2013. (Oral Presentation)  B. Heshmat, M. Masnadi-Shirazi, R. B. Le wis, T. Tiedje, T. E. Darcie, "Dual THz emissions of GaAsBi for THz photoconductive switching." CLEO : QELS_Fundamental Science, pp. JTh2A-51. Optical Society of Am erica, June 2013. (Poster Presentation)  R. B. Lewis, M. Masnadi-Shirazi, V. Bahram i-Yekta, T. Tiedje, ”MBE growth of GaAsBi: effect of growth conditions on Bi incorpor ation”, 3rd International Workshop on Bismuth-Containing Semiconductors, Victoria, Canada, July 2012. (Oral Presentation)  M. Masnadi-Shirazi, R.B. Lewis, D.A. B eaton, T. Tiedje, “Surface Reconstructions in GaAs1−x Bix  Alloys”, 1st International Works hop on Bismuth-Containing Semiconductors, Ann Arbor, USA, July 2010. (Oral Presentation)  During my PhD. studies, I also collaborated on several other projects related to the III-V material research and molecular beam epitaxy technology that led to additional refereed publications. These papers, which are not the main focus of this thesis, are cited in the text when referred.  It should be noted that in Chapter 5, solar performance tests were carried out by Zenan Jiang at the UBC flexible electronics and energy lab (U BC-FEEL). My contribution was in designing the experiments, providing samples and initial motiv ation, as well as carrying out the device modeling and the analysis of the results.    v  Table of Contents Abstract ...................................................................................................................... . . . . . . . . . . . . . . . . . . . . ii  Preface ....................................................................................................................... . . . . . . . . . . . . . . . . . . . . iii  Table of Contents ............................................................................................................. ............. v  List of Tables ................................................................................................................ . . . . . . . . . . . . . . viii  List of Figures ............................................................................................................... . . . . . . . . . . . . . . . . ix  Acknowledgements ......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii  Dedication .................................................................................................................... . . . . . . . . . . . . . . xvii  C HAPTER 1  Introduction ............................................................................................................... 1  C HAPTER 2  Structural characterization of low temperature grown GaAs and GaAs 1-x Bix  alloys........... ............................................................................................................. ....................... 9  2.1. Contributions................................................................................................................... 9 2.2. Crystal growth by molecular beam epitaxy .................................................................. 10 2.3. Ex-situ characterization techniques .............................................................................. 14 2.3.1. High resolution x-ray diffraction .............................................................................. 14 2.3.2. Photoluminescence ................................................................................................... 17  2.3.3. Scanning electron microscopy .................................................................................. 18 2.3.4. Atomic force microscopy .......................................................................................... 18 2.4. MBE growth and properties of  low temperature GaAs ................................................ 19 2.5. MBE growth and surf ace properties of GaAs1-x Bix  alloys ............................................ 24 2.5.1. Surface droplet formation during growth of GaAs 1-x Bix alloys ................................ 28 2.5.2. Etching the GaAs1-x Bix surface droplets ................................................................... 33 C HAPTER 3  Bandgap and optical absorption edge of GaAs 1-x Bix  alloys with 0<x< 17.8% ... 37   vi  3.1. Contributions............................................................................................................. .... 37 3.2. Introduction ............................................................................................................. ...... 38 3.3. Sample preparation .......................................................................................................  39 3.4. Experimental setup........................................................................................................  39 3.5. Results and discussion .................................................................................................. 41 3.5.1. Structural characterization ........................................................................................ 41 3.5.2. Optical absorption and emission ............................................................................... 46 3.6. Conclusion ............................................................................................................... ..... 54 C HAPTER 4  Electronic transport properties of GaAs1-x Bix alloys ........................................... 56  4.1. Contributions............................................................................................................. .... 56 4.2. Introduction ............................................................................................................. ...... 57 4.3. Conductivity and Hall mobility using Van der Pauw method ...................................... 58 4.4. Sample fabrication and experimental setup .................................................................. 61 4.5. Results and discussion .................................................................................................. 62 4.5.1. Room temperature electrical transport ...................................................................... 64 4.5.2. Temperature dependence of conductivity and hole mobility .................................... 68 4.5.3. Variable range hopping in GaAs 1-x Bix  alloys ........................................................... 70 4.6. Conclusion ............................................................................................................... ..... 73 C HAPTER 5  Photovoltaic response of GaAs and dilute GaAs 1-x Bix p+/n solar cells ......... . . . . . . 7 4  5.1. Contributions................................................................................................................. 74 5.2. Motivation ..................................................................................................................... 75 5.3. Experimental section .....................................................................................................  76 5.3.1. Device fabrication .....................................................................................................  76 5.3.2. Device characterisation setups .................................................................................. 80 5.4. Results and discussion .................................................................................................. 80 5.4.1. Device performance .................................................................................................. 80   vii  5.4.2. Solar response simulation ......................................................................................... 87 5.5. Conclusion .................................................................................................................... 94 C HAPTER 6  Terahertz emission from GaAs 1-x Bix  based photoconductive switches ......... . . . . . 9 5  6.1. Contributions............................................................................................................. .... 95 6.2. Terahertz radiation ...................................................................................................... .. 96 6.3. THz pulse source using phot oconductive material ....................................................... 97 6.4. Experimental section .....................................................................................................  99 6.4.1. Sample preparations .................................................................................................. 9 9 6.4.2. THz emission and detection using heterodyne setup .............................................. 100 6.5. Results and discussion ................................................................................................ 10 1 6.6. Conclusion ............................................................................................................... ... 109 C HAPTER 7  Conclusions ............................................................................................................ 110  7.1. Future work .............................................................................................................. ... 112 Bibliography .................................................................................................................. ............ 114  Appendix A Photocurrent and spectral respo nse of p+/n junction solar cell ...................... 124          viii  List of Tables Table 1-1: Atomic properties of elements  of interest from group III and V. .................................. 3 Table 2-1: Surface droplet comparison for GaAs 1-x Bix  samples grown at 265 ºC growth temperature and Bi:Ga BEPR of 0.35 below and above stoichiometric As 2:Ga BEPR. Energy-dispersive X-ray (EDX) spectroscopy measurements confirm droplet composition................................................................................................................................................ 30 Table 2-2: Surface droplet comparison for GaAs 1-x Bix  samples grown under similar conditions at 220-30 ºC growth temperature and Bi:Ga BEPR  of ~0.5 below and above stoichiometric As2:Ga BEPR. Energy-dispersive X-ray (EDX) spectroscopy measurements confirm droplet composition. .......................................................................................................................... 31 Table 2-3: Growth conditions of several droplet-free MBE grown GaAs 1-x Bix  samples. ............ 32 Table 4-1: Initial electrical tran sport measurements of several thin and thick GaAsBi films. ..... 63 Table 4-2: Sample details and calculated Mott’s and conductivity parameters from Eq. (4-8) and Eq. (4-9). .................................................................................................................... ........... 72 Table 5-1: Specifications of GaAs an d GaAsBi p+/n grown samples. ......................................... 78 Table 5-2: Extracted photovoltaic performance parameters from the I-V experiments. .............. 83 Table 5-3: Experimental and cal culated photocurrent for GaAs and GaAsBi p+/n devices. ....... 94 Table 6-1: Specificati on of MBE grown GaAs 1-x Bix  and LT-GaAs films.................................. 100         ix  List of Figures Figure 1-1: Schematic view of  the band structure of GaAs1-x Nx  and GaAs1-x Bix  alloys. The abbreviations are: CB: conduction band, HH: heavy hole band, LH: light hole band, SO: split off band and Δo: spin-orbit splitting energy. The bandga p in nitrides is reduced due to the resonance of the N 2s state and NN2 dimer state with the conduction band minimum while in bismides, the Bi 6p resonance with  the valence band maximum, reduces the bandgap. Figure originally published in [11]. ......................................................................... 3 Figure 1-2: Bandgap energy as a fu nction of lattice constant for III-V semiconductors. The blue and red solid lines are the experi mentally verified data for GaAs1-x Bix  and GaAs1-x Nx  alloys, respectively [6], [12]. The dash ed line correspond to density functional theory results for GaAs1-x Bix  [9], in which the values are shifted to match the room temperature bandgap of GaAs. ...................................................................................................................................... 5 Figure 2-1: AFM image of the surface of 1 μm thick GaAs film grown at low substrate temperature (Tsub=250 ºC, As 2:Ga flux ratio=3.6, excess As=0.6%). The surface RMS roughness is ~0.61 nm. ........................................................................................................ . 20 Figure 2-2:  (a) (004) θ-2 θ HR-XRD scans of an as-grown an d annealed 900 nm thick LT-GaAs film grown at 240 °C subs trate temperature with As 2:Ga flux ratio of 5.3. (b) Plots of the HR-XRD (004) peak separation (proportional to point defect density) as a function of the annealing time at different anneal temperatures for several LT-GaAs films. ....................... 21 Figure 2-3: GaAs lattice mismat ch and the corresponding density of incorporated As antisites as a function of MBE growth temper ature, at a nearly fixed As 2:Ga flux ratio. ....................... 23 Figure 2-4: Room temperature PL spectra of 1 µm thick GaAs film s grown at different substrate temperatures. ......................................................................................................................... 24 Figure 2-5: Surface reconstruction maps  for (a) GaAs (001) and (b) GaAs1-x Bix  (001) for substrate temperatures of 250 to 425 °C and As 2:Ga flux ratio of 0 to 3. The growing GaAs 1-x Bix  surface has an incident Bi BEP of 3×10 -9  torr. Figure originally published in [31]. .... 27 Figure 2-6: Bi conten t as a function of As2:Ga BEPR at three different growth temperatures. The Bi:Ga BEPRs were fixed at 0.47, 0.35, and 0.09 for 220–230 °C, 265 °C, and 330 °C substrate temperatures respectively. Based on the discussion in section 2.2, the green dash line indicates the place of stoichiometric grow th condition (i.e. unity As:Ga atomic ratio).  x  Surface reconstruction patterns were al so monitored while changing the As 2:Ga BEPR at 265 °C growth temperature. Figure is reproduced from Ref. [37]. ...................................... 27 Figure 2-7: SEM image of the su rface of two droplet-free MBE grown GaAsBi films with 1.0% and 5.8% Bi content. The specification and the details of the growth conditions of these films are summarized in Table 2-3. Both film s were grown above the stoichiometric As 2:Ga flux ratio. The inset in the second image is a blow-up of small features on the surface of 5.8% Bi film. These small features appear to be nano scale pin holes, which could indicate the start of Bi droplet nucleation on the surface. The shadow pa ttern in the top figure is due to a difference in exposure to the incident electron beam. ................................................... 32 Figure 2-8: SEM images of the surface of GaAs0.86 Bi0.14  film (a) before and (b) after etching the droplets with HCl:H 2O solution. This sample was grown at 250 ºC substrate temperature with As 2:Ga BEPR of 1.5 (i.e. in Ga-rich conditions). ......................................................... 35 Figure 2-9: SEM image of the surf ace of two high Bi content films after etching the droplets with HCl:H 2O solution. The visible surface roughness is due to non-uniform growth around the droplets. Both layers were gr own in Ga-rich conditions. ..................................................... 35 Figure 2-10: (a) AFM image of the surface of 2.5% Bi film af ter etching the droplets with HCl:H 2O solution. (b) AFM 3D height profile from  a vacant place of one etched droplet on the surface of a 2.5% Bi, 100 nm thick film. The base of the droplet is ~35 nm below the flat surface. The sample was gr own in Ga-rich conditions. .................................................. 36 Figure 3-1: Schematic of the optical transmission spectroscopy setup. ....................................... 40 Figure 3-2: (004) θ–2θ HRXRD scans of GaAs 1−x Bix  films on GaAs. Scans are offset vertically for clarity. The composition and thickness of the layers are determined from dynamical simulations. The sample with 9.7% Bi a nd no thickness fringes showed composition variation in the growth direction in RBS. Th e inset shows the measured strained out-of-plane lattice parameter (red squares) and co rresponding relaxed lat tice parameter (black circles) assuming a Poisson ratio of 0.31, as a function of the RBS Bi content. The GaBi lattice parameter is indicated from the extra polation of the best fit (solid line). Figure originally published in [58]. ................................................................................................. . 42 Figure 3-3: (224) RSM of several pseudomorphic GaAs1−x Bix  films on GaAs substrates. The horizontal and vertical scales are the in-pla ne and out-of plane reciprocal space vectors ( qx [220],  qz [004]). The upper peak is from the GaAs s ubstrate and the lower peak is from the  xi  GaAs1−x Bix  films. RSM’s of 14.2% and 9.7% Bi cont ent films correspond to the samples (b) and (c) in Figure 3-2. The Bi content and the thickness of the layers obtained from dynamical simulations of the (004) HRXRD scans are: (I) 5.0%, 100 nm (II) graded 9.7%, thickness not determined (III) 14.2% , 53 nm (IV) 19.4%, 40-60 nm. .................................. 43 Figure 3-4: RBS spectra (dot s) and SIMNRA simulations (red lines) for several GaAs1−x Bix  films on GaAs. Spectra are offset vertically for clarity. The peak near 1.9 MeV for each spectrum corresponds to backscattering from Bi atoms in the GaAs 1−x Bix  layer. The large step near 1.6 MeV corresponds to backscattering from Ga and As atoms in the layer and substrate. The labels (a,b,c) correspond to the matching samples in Figs. 2, 4 and 5. For spectrum (c), a simulation with three layers gives a better f it than a single layer. The Bi composition and layer thickness of GaAs 1−x Bix  films obtained from SIMNRA are shown in this figure. The Bi composition and layer thickness obtained fr om the dynamical simulations of the (004) HRXRD scans on the same samples are: (from bottom to top) (1) 3.7%, 255 nm (2) 9.7%, thickness not determined (3 ) 14.2%, 53 nm (4) 17.3%, 33 nm (5) 19.2%, ~40-60 nm. RBS measurements were performed by M. Chicoine at  Université de Montréal. Figure originally published in [58]. ............................................................................................................ ...... 45 Figure 3-5: Room temperature optical transmission spectra of several GaAs1-x Bix /GaAs heterostructures divided by the GaAs substrate transmission spectrum (TGaAsBi/TGaAs). The labels correspond with the samples in Figure 3-2 and Figure 3-4. Figure originally published in [58]. ...................................................................................................................... ............. 47 Figure 3-6: Absorption coefficient α and (b) α2 vs. photon energy for several GaAs1-x Bix  films and for a 350 µm thick semi-insulating GaAs subs trate. The dashed line is calculated from GaAs extinction coefficient data in Ref. [66]. Eg of each layer is estimated from linear fits to α2 from α2=2×10 7 cm-2  to α2=1.0-1.7×10 8  cm-2 extrapolated to zero absorption (solid lines in (b)). The location of the bandgap in each layer is shown with ve rtical solid dashes in figure (a). The absorption coefficient of the graded 9.7% layer is calculat ed by considering two thicknesses: (I) RBS total thickness of 8% and 10% Bi-containing layers (95nm) and (II) RBS thickness of the 10% layer only (24nm). The Urbach parameters, E0, are determined from exponential fits below the bandgaps (sol id lines in a). The inset summarizes the measured values of E0 as a function of the Bi content at room temperature. Figure originally published in [58]. ............................................................................................................ ...... 49  xii  Figure 3-7: Room temperature photoluminescence spectra of GaAs1-x Bix /GaAs layers and a semi-insulating GaAs substrate. The Bi cont ent and the thickness of  each layer are shown on top of each spectrum. The scale factors indicated are the multiplication factors that used to normalize (divide) the spectra to the intensity of the GaAs substrate. Figure originally published in [58]. ............................................................................................................ ...... 52 Figure 3-8: Compositional dependence of the GaAs 1-x Bix  bandgap, from optical absorption and PL measurements. The solid line is a fit to the absorption data using a Bi concentration dependent bowing coefficient as discussed in the text. PL data and a fit function from Lu et al. [12] along with a DFT calculation  [9], shifted to match the room temperature Eg of GaAs, are shown for comparison. The inset shows Eg as a function of lattice mismatch for bandgap lowering ternary alloys with Sb  [19], In  [20], N [6] and Bi (this work) on GaAs substrates. The range of fits for GaAsBi and GaAsN are shown for experimentally measured compositions (i.e. max 18% Bi and 5% N conten t). Figure originally published in [58]. .... 53 Figure 4-1: Schematic of sample structure and the configuration for the Hall mobility measurements. The dark regions show th e surface Ti/Pt/Au Ohmic contacts. ..................... 59 Figure 4-2: Conductivity and Hall mobility testi ng setup with iron-core electromagnet. ............ 62 Figure 4-3: Proposed band diagram for GaAsBi/GaAs heterostructure. The Fermi level is pinned at the surface near the valence band due to high surface Bi concentration. At the GaAsBi/GaAs interface, the Fermi level is pinne d due to presence of Bi induced states. The diagram is to scale for 10% Bi concentration. ...................................................................... 64 Figure 4-4: Compositional dependence of room te mperature electrical conductivity of nominally un-doped GaAs 1-x Bix films. The dashed line shows the exponential fit to the data. The square data points are from Ref. [81]. The estim ated systematic measurement uncertainty is ~30% for all of the data, which is sm aller than the sample variability. ................................ 65 Figure 4-5: Compositional dependence of fr ee-hole concentration in un-doped GaAs 1-x Bix  films as obtained from I-V analysis of V H acquired at fixed magnetic fi eld (filled circles) and at variable magnetic field (open circles) at room temperature. The dashed line indicates the exponential fit to the filled circle data. Re d square data are from Ref. [81] and were obtained at 250 K temperature. The estimated systematic measurement uncertainty is ~30% for all of the data, which is smalle r than the sample variability. .......................................... 66  xiii  Figure 4-6: Hole mobility as a func tion of Bi content in un-doped GaAs 1-x Bix  films, as well as p-GaAs doped with carbon grown at conventional (T sub= 550 ºC, As 2:Ga BEPR=6) and unconventional (Tsub= 330 ºC, As 2:Ga BEPR=3) growth conditions. Literature mobility data of un-doped GaAs 1-x Bix  films (red squares) [81] and carbon doped p-GaAs 1-x Bix  films (blue triangle) [80] are also shown for comparison. ...................................................................... 67 Figure 4-7: Temperature depe ndence of the hole concentration in high Bi content GaAs1-x Bix  films. Data from Ref. [81] (red squares) for 10.6% Bi film is shown for comparison. Solid lines are exponential fits to the data, showi ng nearly a constant characteristic activation energy of ~27-32 meV. Inset shows the y-inte rcept (infinite temperature) for the hole concentration fits in the main figure as a function of Bi content. ......................................... 69 Figure 4-8: Hole mobility as a function of temperature for three high Bi content GaAs1-x Bix  films. ..................................................................................................................................... 69 Figure 4-9: Electrical conductiv ity as a function of (a) T-1/4  and (b) T-1 for un-doped GaAs 1-x Bix films. The lines in (a) are the exponential fit functions to th e low temperature parts of the experimental data and yield σ0 and T0 in Eq. (4-8). The lines in (b) are calculated from Eq. (4-9) with the parameters  listed in Table 4-2. ....................................................................... 71 Figure 5-1: Standard solar irradiance spect ra in space (AM0) and terrestrial (AM1.5G) environments. The green colored area show s the extended spectral range that can be absorbed by GaAs1-x Bix  alloys. ............................................................................................. 76 Figure 5-2: Layer structure of p+/n solar cell und er AM1.5G incident light. The top electrode is semi-transparent Au thin film. The cross sectional drawing is not to scale. ........................ 77 Figure 5-3: (a) Transmission spectrum of 10 nm Au deposited on a glass substrate (black solid line). Dashed lines show the calculated tran smission spectra at different thickness of Au. Based on the calculations, the thickness of the deposited Au film is estimated to be 7 nm (b) Simulated transmission spectrum of 7 nm Au on GaAs substrate. The average transmission is ~ 0.53 in 400-1000 nm spectral window. .......................................................................... 79 Figure 5-4: J-V behavior  of GaAs and GaAsBi p+/n diodes in the dark (das h lines) and under AM 1.5G illumination (solid lines). The measurements were performed by Zenan Jiang in UBC-FEEL lab................................................................................................................... ... 82 Figure 5-5: (a) External quantum efficiency (EQE) spectra of GaAs and GaAsBi p+/n diodes at zero bias at room temperature. With increa sed Bi content, the EQE expands to longer  xiv  wavelengths. The dashed curves are calculated from a p/n junction model that is described in section 5.4.2 (b) EQE and photoluminescence (PL)  spectra of p+/n devices near the band edge. The data are normalized to the peak va lue. The EQE measurements were performed by Zenan Jiang in UBC-FEEL lab. ....................................................................................... 86 Figure 5-6: Absorption coefficien t data used as an input parameter in the solar response calculations. The absorption coefficient of GaAs is calculated from the extinction coefficient data in Ref. [66]. The absorpti on coefficient of GaAsBi is calculated from ellipsometry measurements. The GaAsBi sample was prepared in our lab and the ellipsometry measurements was performed by R. Synowicki from J.A. Woollam Company................................................................................................................................................ 88 Figure 5-7: Experimental EQE (red dots) and calculated (dash lines) quantum efficiencies for the standard grown GaAs cell (r2321). Different va lues of the front (a) and back (b) surface recombination velocities are shown to re produce the experiment al results. Minority lifetimes of doped GaAs layers are found from Refs. [96], [97] and used as constants for these simulations. .................................................................................................................. 89 Figure 5-8: Experimental EQE (re d dots) and model (dash lines) qua ntum efficiencies for GaAs devices. Minority carrier lifetimes (τn and τp) were varied recipro cally to reproduce the experimental results. Sn (front) = Sp (back) = 10 7 cm/s were used for these simulations. .... 91 Figure 5-9: Experimental EQE (red dots) and model (dash lines) quantum efficiencies for GaAsBi devices. Minority carrier lifetimes (τn and τp) were varied reciprocally to reproduce the experimental results. Sn (front) = Sp (back) = 10 7 cm/s were used for these simulations................................................................................................................................................ 92 Figure 5-10: Extracted electron a nd hole minority carrier lifetimes as a function of Bi content from device simulations. ....................................................................................................... 93 Figure 6-1: Terahertz band in th e electromagnetic spectrum. ...................................................... 97 Figure 6-2: (a) Schematic of the heterodyne TH z emission and detection setup. Abbreviations are: MR = Mirror, BS = Beam splitter, DL = Delay line, L= Lens, Tx = THz transmitting PCA, Rx = THz receiving PCA, and fs laser = femtosecond Ti-Sapphire pulse laser. The shaded area in the ellipse is enlarged in (b). Silicon lenses are used at the back of the PCAs to focus the THz beam. (b) 3D schematic di agram of THz pulse emission from a GaAsBi PC dipole antenna excited by a femtosecond laser pulse. .................................................... 99  xv  Figure 6-3: Room temperature PL  spectra of a 2.2% Bi film at  different thermal annealing temperatures. The Inset shows the PL peak intensity improvement for 2.2% and 3.0% Bi films as a function of the anneal temperatures. The PL improvement ratio is the ratio of the PL peak intensity of each layer to the as-grown PL peak intensity. ................................... 102 Figure 6-4: (a) THz pulse emitted from a dipol e PCA on: LT-GaAs, commercial device, 3% GaAsBi and 2.2% GaAsBi. The signals are measured in the same condition with a commercial PCA at the receiver. The signals are separated horizontally for clarity. (b) Signal amplitude spectrum (10log10 |F (I))|) is in dB. The de tector noise level is about − 80 dB. The measurements were performed by B. Heshmat at UVIC-OSTL lab. Figure is reproduced from Ref. [113]. ............................................................................................... 103  Figure 6-5: Measured THz signal for GaAsBi and LT-GaAs samples as a function of annealing temperature. The data points are all obtained at 1 min annealing time with the exception of the two points indicated. The dashed lines with  points show the amplitude of the higher bandwidth (HBW) peak. The measurements were performed by B. Heshmat at UVIC-OSTL lab. Figure is reproduced from Ref. [113]. ......................................................................... 105 Figure 6-6: Temporal profile of  the emitted THz pulse from 2.2% GaAsBi sample with 1, 10, 20 minutes of annealing at 500°C. The measur ements were performed by B. Heshmat at UVIC-OSTL lab. Figure original ly published in [113]. ..................................................... 106 Figure 6-7: OOCR for 2.2% GaAsBi and LT-GaAs as a func tion of the annealing temperature. The effect of the annealing time for three devices at 500 °C anneal temperature is also shown. The green square shows the OOCR for a commercial LT-GaAs device that believed to be annealed at 600 °C. Inset shows the dark  current of the same samples in the main figure as a function of the annealing temperature. All the measurements were done at 10 V bias voltage and 17 mW averag e optical power. The measurements were performed by B. Heshmat at UVIC-OSTL lab. This Figure is reproduced from Ref. [113]. ........................ 107 Figure 6-8: Net photocurrent at  different annealing conditions for 2.2% GaAsBi and LT-GaAs PCAs. GaAsBi and LT-GaAs s how different behavior as  a function of annealing temperature. All the measurements were done  at 10 V bias voltage and 17 mW average optical power. The measurements were performed by B. Heshmat at UVIC-OSTL lab. This Figure is reproduced from Ref. [113]. ................................................................................ 108  xvi  Figure A-1: (a) p+/n solar cell under illumination. (b) Carrier generation rate as a function of distance at short and long wavelengths. .............................................................................. 125                      xvii  Acknowledgements    I would like to acknowledge everyone  who had a share in helping me in the course of my studies in Canada. I would like to express my sincere gr atitude to my outstanding and kind supervisors, Dr. Thomas Tiedje and Dr. Peyman Servati, for their inspiration, guidance and continuous support during my Ph.D. studies. I consider myself privileged for having the opportunity to work with them. My special thanks to all of my lab mates in UBC and UVIC for their friendship, assistance and support throughout this work in the past fe w years. I would like to thank Dr. Lucas Chrostowski for generously allowing us to use his equipment through this work. I also want to thank Mr. Robert Fichtner from UVIC-ECE departme nt for helping me in setting up the apparatus for electrical transport experiments.  These years in Canada would ha ve never been this precious without great friends and a graceful community. My sincere thanks to all of  my friends in Canada and outside for the unforgettable memories and their help and friendships. Most importantly, this work is dedicated to my wonderful parents fo r all their love and support during my life. I always felt them near me, even though they were  living far away from here. And my thanks to my dear brothers , Mohammad Sadegh and Amir Hossain for their encouragement and good company throughout my journey.     Dedication   xviii      TO MY Family for their endless love and support                1  C hapter 1   Introduction    It is hard to imagine today’s world without semiconductors. Sinc e the first practical device, a transistor, in the mid-20 th century, the astonishing benefit of semiconductor materials has made a revolution in the electronics industry. These special materials are present in every electronic device that we use nowadays such as computers, TV s, smart phones, kitchen appliances, medical equipment and many other devices. Due to the conti nuous request for faster, sm aller, more efficient and lower power consumption electronic devi ces, research on exploring new semiconductor materials has been growing steadily. As a result, a close synergy between success in electronic technology and the advancement in the scientific knowledge of nove l materials has been created. In this regard, experimental materials growth techniques such as molecular beam epitaxy have a significant role in the creation and investigation of new metastab le semiconductor materials which do not exist freely in nature. Among the many semiconductor materials available today, the group III-V compound semiconductors are important for optoelectronics applications due to their direct bandgaps. These include advanced materials for solid state lasers, light emitting diodes (LEDs), solar cells, photodetectors and high frequency transistors used in telecommunication devices. In particular, GaAs is one of the most important III-V co mpound semiconductors which has been studied comprehensively over the past 50 years. GaAs has a number of key propertie s that make it and its alloys unique for diverse range of device app lications. First, GaAs is a direct bandgap semiconductor, allowing for effici ent generation and detection of light. It has a higher electron mobility than silicon (~8500 vs. ~1400 cm 2 V-1  s-1  at 300K), making transistors that function at higher frequencies. Due to its re latively large bandgap, GaAs devices have less noise than silicon devices, especially at high frequenc ies. In solar cells, GaAs and its alloys are the most efficient semiconductor materials [1]. Finally, due to the f act that GaAs can conveniently be alloyed with  2  other group III (Al, In) and group V (P, Sb) elements, a wide range of bandgap energies with a diverse range of electronic properties can be engineered. Over the years ternary and quaternary III-V all oys with the above mentioned elements have been explored. As these elements produce a weak  perturbation to the GaAs host band structure, the properties of their alloys generally follow simple, often linea r, relationships between their binary end members. In recent years, several new group III (B a nd Tl) and V (N and Bi) elements have been investigated in alloys with GaAs [2]–[8 ]. In particular, alloys with N and Bi, GaAs 1-x Nx  and GaAs1-x Bix , have received considerable attention as these two material systems exhibit parallel properties. The N atom has a smaller atomic radius than As, and introduces tensile strain in GaAs, while Bi atoms are larger and introduce co mpressive strain. In addition, N is highly electronegative, whereas Bi has low electronegativity. Both elem ents produce large perturbations in the GaAs host band structure which results in a similar change in electronic and optical properties with a relatively low alloy content, as  discussed below. Atomic properties of group III and V elements of interest are compared in Table 1-1. Bi is the heaviest non-radioactive element in the periodic table, and unusually for the heavy elements, it is non-toxic.  From the band structure point of view, GaAs 1-x Bix  can be considered complementary to GaAs1-x Nx . The relative energy levels of Ga, As and Bi valence orbitals suggests that the Bi 6p orbitals are resonant with the valence band maxi mum (VBM) of GaAs, as shown schematically in Figure 1-1 [9]. In the case of GaAs 1-x Nx , the opposite situation is found, where the N 2s orbital is resonant with the GaAs conducti on band minimum (CBM) [10], [11] . In both alloy systems, the resonant interaction results in a relatively large reduction of the bandgap energy with a large bandgap bowing effect for low alloy concentrations  [6], [9], [12]. Thus, the bandgap of dilute nitrides is primarily reduced by lowering the CBM, whereas the bandgap of bismides is reduced by the increase in the VBM energy, as illustrated in Figure 1-1. The resonant interaction can be understood as being due to the fact that the 2s state of N is significantly lower than that of the 4s of As; thus , N generates a potential trap for the electrons in CBM state. Similarly, because the 6p state of Bi is  substantially higher than that of the 4p of As, Bi is likely to generate a potential trap for the holes in VBM state [13]. Thus N alloying strongly affects the electron mobility whereas Bi allo ying is expected to affect the hole mobility.  3  Table 1-1: Atomic properties of elements of interest from group III and V. Element Atomic number Electron configuration Atomic weight Covalent radius (nm) Electronegativity (Pauling’s scale) Ga 31 [Ar] 3d 10 4s 2 4p 1 69.72 0.122 1.81 N 7 [He] 2s 2 2p3  14.00 0.071 3.04 As 33 [Ar] 3d 10 4s 2 4p 3  74.92 0.119 2.18 Bi 83 [Xe] 4f 14 5d10 6s 2 6p 3  208.98 0.148 2.02     Figure 1-1: Schematic view of the band structure of GaAs 1-x Nx  and GaAs1-x Bix  alloys. The abbreviations are: CB: conduction band, HH: heavy hole band, LH: light hole band, SO: split off band and Δo: spin-orbit splitting energy. The bandgap in nitrides is reduced due to the resonance of the N 2s state and NN2 dimer state with the conduction band minimum while in bismides, the Bi 6p resonance with the valence band maximum, reduces the bandgap. Figure originally published in [11].     4  Similar to nitrides, the extension of the GaAs family of semiconductors to alloys with Bi is a relatively new development. The first GaAs 1-x Bix  alloy was synthesized by K. Oe et al. in 1998 where 2% Bi incorporation was obtained by usin g metal organic vapor phase epitaxy (MOVPE) method [8]. Molecular beam epitaxy (MBE) growth of GaAs 1-x Bix  alloys was first reported 5 years later in our group at UBC and in Japan [7], [14]. Due to the larg e atomic size and low electro-negativity of Bi compared with As, the growth conditions of GaAs 1-x Bix  alloys were found to be rather different than the standard growth co nditions of GaAs. In particular low growth temperatures and low As:Ga flux ratios on the threshold of having an As-shortage, favour Bi incorporation [7], [15]. However, these condition s also favour formation of metallic Bi and Ga droplets on the surface which makes the growth pro cess of this material challenging [16]. Using the above mentioned conditions, a Bi content of up to ~11% was achieved before the current study [15], [17]. GaAs1-x Bix  has a number of appealing properties, both from a materials science point of view and for its potential applications. Incorporati on of a small amount of Bi into the GaAs lattice causes a large reduction in the bandgap, ~83 meV/ %Bi for Bi concentrations up to few percent [18]. This reduction is much larger than the eff ect of In and Sb (11 meV/% In, 19 meV/% Sb) [19], [20] and only lower than the eff ect of N alloying (125 meV/% N in 0 ≤ x ≤2% range) [6]. To illuminate this appealing property, Figure 1-2 s hows the bandgap energy versus lattice constant for bandgap-reducing III-V semiconductors having a lattice constant betw een 5.4 Å to 6.5 Å. The lines connecting the two points co rrespond to the ternary alloy betw een the two end members. The blue and red solid lines are fits to experimental data for GaAs 1-x Bix  and GaAs1-x Nx  alloys, respectively [6], [12] and the dashed line is fr om the first principles calculations for GaAs1-x Bix  [9]. The end GaBi compound has never been synt hesized and is predicted to have a negative bandgap of -1.45 eV [9]. From the trend of Bi alloying, it is clear that GaAs1-x Bix  reduces the bandgap with the least change in the lattice cons tant of any of the traditional GaAs alloying elements, In and Sb or N. This shows the potentia l of bismide alloys to engineer a wide range of bandgaps (0< Eg <1.42 eV) on GaAs substrates with le ss strain than any other III-V alloy.  5   Figure 1-2: Bandgap energy as a function of lattice constant for III-V semiconductors. The blue and red solid lines are the experimentally verified data for GaAs 1-x Bix  and GaAs1-x Nx  alloys, respectively [6], [12]. The dashed line correspond to density functional theory results for GaAs1-x Bix  [9], in which the values are shifted to match the room temperature bandgap of GaAs.   In fact, the ability to grow high quality long wavelength (i.e. small Eg) material on GaAs substrates is of great interest for applications in optical devices such as solid state lasers. These lasers are useful for fiber-optics communications , as light signals at wavelengths of 1.30 to 1.55 μm have the least transmission losses in silica based optical fibers. These wavelengths correspond to 0.8 to 0.95 eV bandgaps which can be reached with 7.5-10% Bi incorporation. The solar cell industry would also like semiconduc tor materials with tunable bandga ps to improve the efficiency of multi-junction solar cells. One example is the lattice matched triple-junction In 0.49 Ga0.51P / GaAs / Ge solar cell with the sequence of 1.90/1.42/0.67 eV  band gaps [1]. Its efficiency could be increased by adding a fourth junction at 1 eV band gap. This bandgap can be achieved on GaAs with ~ 6% Bi alloying.   6  Although low growth temperatures are need ed to achieve Bi incorporation, GaAs1-x Bix  films have shown a strong and broad photolumin escence (PL) spectrum in the infrared (~ λ> 900 nm). An example of GaAs 1-x Bix  PL emission and the PL dependence on Bi composition is shown in Chapter 3 at Figure 3-7. This broadband emission suggests that Bi related localized states (e.g. Bi clusters) form in the grown films or the Bi composition varies throughout the film thickness. In principle, the localized states can trap photogenerated carriers, preventing them from diffusing to non-radiative recombination centers, which could re sult in strong broad PL emission from this material. This optical property makes the GaAs 1-x Bix  alloys a potential candidate for low coherence light sources (e.g. in superluminescent diodes). Infrared low cohere nce light sources are used in a medical imaging technique known as optical c oherence tomography (OCT). OCT system uses interferometry of low coherence light to produ ce three-dimensional images of body tissues which typically have a millimeter depth, with micron re solution. It is noteworthy that the strong electroluminescence emission has been also demonstrated from dilute GaAs1-x Bix  light emitting diodes [21]. Recently room temperat ure lasing at the wavelength of ∼9 47 nm has also been obtained from electrically pumped GaAs1-x Bix  quantum well laser struct ure having 2.2% Bi [22]. GaAs1-x Bix  films are found to have several other properties of interest for device applications. Similar to low temperature grown GaAs, strong terahertz (THz) emission has been demonstrated from low temperature grown dilute GaAs 1-x Bix  based photoconductive devices [17], [23], [24]. These successe s indicate that GaAs1-x Bix  alloys have ultrafast (i.e. sub-picosecond) electron trapping times and high electron mobility, making bismides competitive with the current commercial THz materials. One advantage of GaAs1-x Bix  alloys relative to low temperature GaAs (LT-GaAs) is its reduced bandgap, which can allow GaAs 1-x Bix  THz photoconductive devices to be pumped with longer than 1 μm emission wavelengths using femtosecond diode and fiber coupled lasers. These lasers are generally more compact and cost effective than the Ti:Sapphire laser that is commonly used for exc itation of LT-GaAs photoconductive devices.  As show in Figure 1-1, the ba ndgap reduction in bismide alloys is mainly due to the movement of the heavy and light hole bands. Howe ver, the position of the split off (SO) band is found to not change significantly, resulting in a huge increase in the spin orbit splitting energy (Δo) [25]. This makes GaAs 1-x Bix  a unique material for possible app lications in spintronics. At x>10% Bi the energy splitting of the split off band exceeds the bandgap ( Δo ≥ Eg) [26]. This feature in the  7  band structure could suppress an important Auger recombination channel and improve the performance of semiconductor lasers having Bi-containing active layers. As GaAs1-x Bix  alloy is a developing new III-V semiconductor, many aspects of this material system are still unknown. In this regard, th e purpose of this thesis is to investigate the growth process and to explore the properties of this new alloy. Par ticular attention has been paid in this study to investigate the effect of growth  parameters on the Bi incorporation amount and on the quality of the grown films. Several characterization techniques were used in this thesis to explore the structural, optical a nd electronic properties of GaAs1-x Bix  alloy in a wide range of Bi concentration. Moreover, a few potential opt oelectronic device applications of GaAs1-x Bix  alloys are examined in this work through experi mental and theoretical investigations. This thesis is organized into 7 chapters. The current chapter presents the motivation and objectives of this work. A more specific introduction and literature review are given in each of the experimental chapters. Chapter 2 describes the ma terial growth by molecular beam epitaxy (MBE), the technique used to grow samples in this thesis. A description of MBE in-situ and ex-situ characterization techniques that were used in this  work is given in this chapter. In addition, the MBE growth of low temperature GaAs and GaAs 1-x Bix  epitaxial films is discussed in this chapter. In chapter 3, the op tical properties (e.g. bandgap and absorption edge) of MBE grown GaAs 1-x Bix alloys in a wide range of Bi contents (0 ≤ x ≤17.8%) are investigated by  optical transmission and photoluminescence spectroscopies. Structural characterization of GaAs1-x Bix  epitaxial films with 0<x ≤19.4% on GaAs substrates is also  discussed in this chapter. Chapter 4 covers electronic transport properties in nominally undoped GaAs1-x Bix  films with 0<x ≤21.5% Bi content. As Bi primarily affects the valence band of GaAs, the effect of Bi alloying on electronic transport of holes is explored in this chapter. In chapte r 5 the fabrication and the photovoltaic operation of dilute GaAs1-x Bix  p+/n solar diodes are investigated for the first time. The experimental results were also modeled employing the theoretical co ncept of diffusion and drift of photogenerated carriers. An analysis of the model reveals information about the minority carrier lifetimes in bismide materials. In Chapter 6, a systematic analys is is carried out to investigate the influence of rapid thermal annealing on the THz emission from bismide photoconductive devices. Notable enhancement in terms of THz emission amplitude and bandwidth are demonstrated from annealed GaAs1-x Bix substrates. Our results suggest that GaAs1-x Bix  is a promising candidate material for  8  improving the THz output power of the photoconductiv e switches. Finally, chapter 7 presents a summary of the contributions and conclusion of this work and also comments on possible future work.                     9  C hapter 2   Structural characterization of low temperature grown GaAs and GaAs 1-x Bix  alloys   The following chapter describes material growth by molecular beam epitaxy (MBE), the technique used to grow samples in this thesis. First, de tails of the MBE system and the sample growth procedure are discussed. Next, the MBE in-situ  and ex-situ characterization methods are introduced which were carried out during growth  and on the grown films respectively. Then the MBE growth of low temperature GaAs and GaAsBi epitaxial films and the initial characterization of the grown structures are discussed. The obser vation of droplet formation and the method to grow droplet-free GaAsBi ar e discussed at the end.   2.1.  Contributions As MBE is a complex material growth system, a significant amount of knowledge, experience and techniques are required for its daily operation. Th e MBE system that was used to grow samples for this thesis was operated a nd maintained continuously by fellow students R.B. Lewis and V. Bahrami-Yekta, and the author. The samples discu ssed in this thesis we re grown by the above fellow students and the author in a joint project on III-V bismide materials. The majority of the samples (~80%) were grown by R.B. Lewis, some times with the assistance of the author. The remaining portion of the samples were grown by  the author (~10%) an d by V. Bahrami-Yekta (~10%). Most of the x-ray diffraction, scanni ng electron microscopy imaging, optical spectroscopy and all the atomic force microscopy measurements discussed in this chapter were collected and  10  analyzed by the author. Moreover, the author studied the process of droplet formation and investigated the conditions for having droplet-free GaAs 1-x Bix  films.   2 . 2 .  Crystal growth by molecular beam epitaxy  Molecular beam epitaxy (MBE) is a technique for growing single crystals of a wide variety of materials with high purity and low defect dens ity. In the MBE process, beams of atoms or molecules are thermally evaporated from pure source materials on to a heated substrate under ultra-high vacuum (UHV). The base pressure inside the MBE chamber is typically on the order of 10-10  torr which means that the mean free path of resi dual gas molecules is several hundred kilometers. The evaporated atoms from the effusion cells have a higher pressure but they also do not interact with each other and form a directed beam towa rd the substrate. During growth of Arsenic compounds, the base pressure is increased to typically 10-6 -10 -8  torr which still allows a long collision free beam path. As a result, the probability of impurity incorporation during the MBE growth, particularly of oxygen and/or water, is ex tremely low due to the low partial pressure of these gases. By the use of mechanical shutters, MBE offers sub-monolayer control over the layer thickness, allowing growth from sub-nanometer thin  films to several micrometers bulk films. Due to the fact that surface atoms are much more mobile than atoms in the bulk, MBE growth is typically done at well below the melting point of the bulk material s. For example, MBE growth of GaAs is typically done at about half the bulk melti ng point or lower (T~650 ºC). This low growth temperature minimizes the number of thermodynamically activated defects and vacancies in the grown films and provides an oppor tunity to form metastable compounds that could not be synthesized in bulk form in quasi equilibrium grow th conditions. As a result, MBE is an important tool for research on novel materials as well as  an established method for mass production of electronic and optical devices. Samples discussed in this thesis were grow n in a VG-V80H molecular beam epitaxy reactor equipped with standard thermal Knudsen effusion cells for Ga, In, Si, Al and Bi. A valved two zone thermal cracker source was used to produce arsenic dimers (As 2). Arsenic tetramers (As4 ) can also be produced by reducing the cracking zone  temperature. Source materials are arranged in a circular pattern, where each is directed toward  the substrate position. The purity of Ga, As, Bi,  11  Al in our MBE system are: 99.999999% [8 N], 99.999995% [7N5], 99.9999% [6N] and 99.9999% [6N], respectively. The molecular flux of each cell is controlled by the cell temperature. Except As, electromagnetic or pneumatic shutters were us ed to open and close the molecular beam fluxes at a given time. As flux  is controlled manually by the cracker micrometer valve position. These shutters operated in a fraction of a second which is normally much s horter than the time needed to grow one monolayer (ML). In addition, the MB E system was connected to an external CBr 4  gas-injection system (Varian mass flow controller ) as a carbon p-type dopant source. The CBr 4  molecule cracks on the heated substrate surface and the bromine is then pumped away by the vacuum system. A Si effusion cell was used as  a source for n-dopant. The temperature of the substrate was monitored using optical bandgap thermometry with an accuracy of 5°C [27]. Due to thermal radiation of hot effusion cells and the substrate heater in the MBE, it is conventional to cool the MBE system with liquid nitrogen (LN 2) in the MBE cryo-shroud.  This leads to high consumption of LN2 and contributes to the high cost of operating an MBE system. To reduce this cost, since 2010 a novel closed-cycle cooling set up was implemented in our MBE system to replace LN2. In this method, LN2 was replaced with Dow Chemical Syltherm XLT heat transfer fluid, which is composed of dimethyl polysiloxane with a freezing point of -111ºC. The fluid is cooled to near -80°C with an ultra- low temperature recirculating chiller, RC311-FTS system. This new method is described in detail el sewhere [28]–[30]. This is a new concept that has a potential broad impact on the MBE community. Most of the layers discussed in this thesis were grown with the system configured for cooling with the chiller.  This MBE system is equipped with reflec tion high-energy electr on diffraction (RHEED) which is used for in -situ monitoring and measurement of surface structures during the growth of epitaxial films. In this technique, a focused be am of high energy electrons (5–20 KeV) strikes a crystalline sample at a glancing angle (~ 1 − 3 °). This small incidence angle limits the beam penetration depth to a few monolayer s of material and only the electrons in the top layer of sample are scattered elastically (1-2 MLs). From the RH EED perspective, the electron diffraction behaves as though it were diffraction from a two-dimensi onal crystal. Considering the elastic scattering between the incident and diffracted wave vectors, ห݇పሬሬሬԦห ൌ ห݇௙ሬሬሬሬԦห, the diffraction condition is satisfied when the scattering vector, ∆݇ሬሬሬሬԦ, matches a reciprocal lattice vector: ∆݇ ൌ ݇௙ሬሬሬሬԦ െ ݇పሬሬሬԦ. In reciprocal space, a two-dimensional array of surface atoms can be  visualized as infinitely long vertical lines  12  named reciprocal lattice rods (or Bragg rods). Therefore wherev er these rods cross the Ewald sphere, the condition for constructive interference of scattered electron beams is satisfied and a diffraction pattern is created. This diffraction pattern can be detected with a phosphor screen placed on the opposite side of the MBE chamber to the RHEED electron gun.  When a bulk crystal is terminated at a surfac e, reorganization of the surface structure is necessary to minimize the surface energy associated with dangling bonds. This reorganization can form a crystal structure with a new lattice period icity on the surface, which is referred as “surface reconstruction”. As a result, extra diffraction s pots/streaks will appear in the RHEED pattern. Examples of RHEED patterns duri ng MBE growth of GaAs and GaAs 1-x Bix  can be found elsewhere [31]–[33]. In this work, the RHEED experiments were done with a Staib phos phorescent screen and Staib electron gun operating at 15keV energy,  a high sensitivity CCD camera and EE2010 software. Films were grown on 350±25 μm thick, one side polished, (001)  oriented semi-insulating (SI) GaAs substrates with a maximum ± 0.5º o ffcut. Before each growth, the substrate was thermally degassed for at least one hour at 3 00-400 ºC temperature in the MBE preparation chamber. Once loaded into the growth chamber, each  substrate is initially heated to about 610 ºC for 10 minutes under As2 overpressure to remove the native surface oxide layer. RHEED was used to detect when the su rface oxide is removed. This thermal desorption process tends to leave micron size pits on the surface [ 34]. The substrate temperature is then ramped down to 550-580 °C to smooth the pitted surface by growing a 300-600 nm thick GaAs buffer layer at a rate of 1.0 μm/h . Following the GaAs buffer growth, desired epi-la yers were deposited on the substrates at a specified growth conditions. To ensure a uniform film deposition, the samples were always rotated at moderate speeds (∼0.5 Hz) during growth. Depending on the experiment, some samples we re subject to a post-growth annealing treatment, either in the MBE growth chamber or in an external rapid thermal annealing system (RTA). The RTA uses a 400 Watt halogen reflective  light bulb to achieve the heating. The RTA chamber is evacuated down to 10 −6 Torr and a thermocouple attached to the copper substrate measures the temperature. Samples that were an nealed at high temperatures (i.e. T>500 ºC) were  13  in contact with a SI-GaAs wafer to protect the surf ace from As loss. After annealing, samples were cooled down to room temperature (RT) under the nitrogen atmosphere. Our MBE is equipped with a retractable Baya rd-Alpert-type ion ga uge for measurements of the beam equivalent pressure (BEP) of each mo lecular source. The ion gauge is located inside the MBE deposition chamber. BEP values are measured in units of pressure as this gauge is factory calibrated for N2 gas at 300K. The relative relationship between the ion gauge BEP readings and molecular beam fluxes is [35]:  ܬ௫ܬ௬ ൌ௫ܲ௬ܲߟ௬ߟ௫ ቆ௫ܶܯ௬௬ܶܯ௫ቇଵ/ଶ (2-1) where Ji represents the flux of substance i ; Pi is the BEP and Ti and Mi represent the absolute temperature and the molecular mass of material i. The ηi is the ion gauge sensitivity coefficient which has been approximated by [35]:   ߟ௜ ൌ 0.6ܼ௜14 ൅ 0.4 (2-2)   Zi is the atomic number of element i. By using the above equation the ion gauge sensitivity coefficients for Ga and Al are ηGa =1.74, ηAl =0.96. In the case of complex molecules like As 2 and As4 , Eq. (2-2) may result in significant error. Th e direct quartz crystal monitoring (QCM) and ion gauge measurements for As2 and As4  were done by Preobrazhenskii et al. [35], showing ηAs2 = 4.0 and ηAs4 =6.8. Bi is known to evaporate as a combina tion of monomers and dimers in nearly equal amounts [36] and there are no report s of the ionization efficiencies of these species. Thus, we did not attempt to convert the Bi BEP into Bi flux.  The absolute values of the Ga flux can be f ound from the growth rate; for example in this study the Ga growth rate is inferred from x-ra y diffraction measurements (see section 2.3.1) on a test structure or from RHEED intensity oscillations during the growth of GaAs and GaAs 1-x Bix   14  [31], [32]. By knowing the Ga flux, the flux of othe r species can be calculated from the BEPs using Eqs. (2-1) and (2-2).  At typical MBE conditions for GaAs growth (As 2 cracker temperature at 1000 °C and Ga cell at 950 °C), Eq. (2-1) shows that As 2:Ga flux ratio of 0.5 (stoichiometric GaAs) takes place at As2:Ga BEP ratio (BEPR) of 1.7 [35]. Experimenta lly finding this ratio is important as this condition is needed for the growth of GaAs 1-x Bix  alloys (see Section 2.5). In our MBE system with the use of RHEED and laser light scattering techniques, the stoichiometric growth condition was found at As2:Ga BEPR of 2.2±0.2 [30]. A larger value of BEPR  (2.2 > 1.7) pos sibly could suggest that the sticking coefficient (fraction of adsorb atoms on the surface) for As2 is less than 1 in our MBE system, which would shift the data to higher BEPR [30], [37] . A larger value of stoichiometric BEPR could also arise from the systematic errors in the measurements of the beam equivalent pressure of mol ecular fluxes by the ion gauge.  2 . 3 .  Ex-situ characterization techniques In addition to the above in-situ measurements during MBE growth of ep i-layers, the following analysis techniques were used frequently after growth to characterize th e grown samples. Other techniques used in this thesis, are ex plained in detail in the next chapters.  2.3.1.  High resolution x-ray diffraction High resolution x-ray diffraction (HR-XRD) is the prim ary tool to characterize the structure of the grown films. By measuring HR-XRD, one can obt ain information about the crystal structure, lattice mismatch and strain, layer compositions and thicknesses. The position of a given peak in a typical θ−2θ HR-XRD scan determines the condition fo r constructive interference of diffracted x-rays, which described by Bragg’s law:  sin ߠ஻ ൌ ݊2݀ߣ௛௞௟ (2-3) 15                                                                                            Here λ is the wavelength of the x-rays, n is an integer and θB is the diffraction angle of the x-ray beam from the hkl plane of the atoms. dhkl is the spacing between the { hkl } planes , which for the cubic crystals with lattice constant a is :  ݀௛௞௟ ൌ ௔√௛మା௞మା௟మ As the lattice constant, and the corresponding plane spacing dhkl, of the grown epitaxial film is different from the substrate, the Bragg condition will be sati sfied at two different angles. Thus HR-XRD θ−2θ spectra will show two diffracted peaks, one co rresponding to the substrate and the other for the grown film. In th is case, the differential form of Eq. (2-3)  relates the peak-splitting, ∆ߠ஻, to the change in plane spacing, ∆݀௛௞௟ :   ∆ߠ஻ ൌ െ∆݀௛௞௟݀௛௞௟ tan ߠ஻ (2-4) where ߳௛௞௟ ൌ ∆ௗ೓ೖ೗ௗ೓ೖ೗  is defined as the misfit strain of { hkl } planes. The lattice mismatch between film and substrate is also defined by:   ߳௙ ൌ ܽ௙ െ ܽ௦ܽ௦  (2-5) where ܽ௙ and ܽ ௦ are the film and substrate relaxed lattice parameters. In the case of pseudomorphic growth in the (001) direction with  no relaxation on GaAs substrates, ሺܽ௙ሾ110ሿ ൌ ܽ௙ሾ11ത0ሿ ൌܽீ௔஺௦ሻ, the lattice mismatch (߳௙ሻ can be written in term of the mi sfit strain of {001} planes as [38]:  ߳௙ ൌ ܽ௙ െ ܽீ௔஺௦ܽீ௔஺௦ ൌ ൬1 െ ߥ1 ൅ ߭൰ ߳ሾ଴଴ଵሿ (2-6)             16  where ν is the Poisson ratio of the grown film and ߳ሾ଴଴ଵሿ ൌ ௔ሾబబభሿି௔೑௔೑ . Once the growth direction misfit strain is known, then Vegard ’s law [39] can be used to determine the film composition. For a ternary alloy like GaAs 1-x Bix , Vegard’s law proposes a linear cha nge of the lattice parameter with composition between the lattice paramete rs of the end binary compounds (e.g. aGaAs and aGaBi). This relation in the case of GaAs1-x Bix  relaxed lattice parameter is:   ܽ௙ ൌ ሺ1 െ ݔሻܽீ௔஺௦ ൅ ீܽݔ௔஻௜ (2-7) Now by combining Eqs. (2-6) and (2-7), the Bi composition is:  ݔ ൌ ߳௙߳ ൌܽ௙ െ ܽீ௔஺௦ܽீ௔஻௜ െ ܽீ௔஺௦ ൌ ൬1 െ ߥ1 ൅ ߭൰߳ሾ଴଴ଵሿ߳  (2-8) where ߳ ൌ ௔ಸೌಳ೔ି௔ಸೌಲೞ௔ಸೌಲೞ  is the lattice mismatch between the end binary compounds. In addition to composition information, the film thickness can also be determined by HR-XRD measurements. The observation of Pendellö sung fringes, intensity oscillations due to interference between the diffracted x-ray beams from the bottom and top of the film, is an indication of uniform composition, un-relaxed films, and sharp in terfaces. After measuring the Pendellösung fringe peak separation, 	Δߠ௉, the film thickness can be determined from the following [38]:   ݐ ൌ 2ߣΔߠ௉ cos ߠ஻ (2-9)  In this work HR-XRD measurements we re performed with a Bruker D8 Discover diffractometer at UVIC. The x-rays are produced from the Kα1 transition of copper (λ=0.154051 nm), and are monochromated with a Göbel mirror an d a Ge crystal channel- cut for two asymmetric  17  (004) reflections. This results in a highly collimat ed x-ray beam with mi nimum beam divergence of ~16 arcsec. The x-ray collimated beam has a rectangular footprint of several mm2 on the sample surface. The diffracted x-ray is dete cted by x-ray counter detector th rough either a pair of computer controlled motorized slits or a 3-boun ce Ge analyzer crystal. Typically θ−2θ HR-XRD scans were performed over a range of 1 – 3 °  using step sizes of 0.001º  with counting integr ation time of 1-10 seconds per step. The (004) θ-2θ scans and (224) reciprocal space maps (RSMs) were recorded to measure the in-plane and out-of-plane lattice cons tants, layer thicknesses  and degree of film relaxation. The (004) scans were dynamically simu lated using LEPTOS software to determine the composition and layer thickness. Ve gard’s law, GaBi lattice para meter of 6.33 Å [7] and Poisson ratio of 0.31 (same as GaAs) were the input assu mptions for the dynamical simulation in LEPTOS. HR-XRD thicknesses are also compared to the estimated thickness from the growth rate and growth time.  2.3.2.  Photoluminescence Luminescence is the emission of optical radiation when a system  decays from a high energy level (excited state) to a low energy leve l. Different types of luminescence are classified by the different method of initial excitation. In the case of photoluminescence (PL) in semiconductors, the excitation is with an optical s ource where the photons excite el ectrons from the valence band to the conduction band, creating electron-hole pairs. Depending on the intensity of incident photons, the density of excited electron-hole pairs will ch ange. These pairs can either recombine radiatively by emitting photons or non-radiativ ely through defect, surface or Auger recombination. Therefore the spectrum of the emitted photons (PL) gives valuable information about the electronic properties of materials, such as the optical bandgap and the defect density.  As electron-hole pairs are likely to recombin e from the band edges in semiconductors, the PL emission peak can identify the optical band gap. The high energy side of the PL emission spectrum is due to the thermal excitation of el ectrons and holes into higher levels above the conduction and valence band minima. The shape of this tail for relatively high temperatures (T >100 K) can be modeled by a Boltzmann distribution with kBT characteristic energy width. The  18  low energy side of the PL emission spectra can also  rise due to the Urbach edge where the electron and hole pairs are recombined in shallow states in the ba ndgap [40], [41].  In this study, samples were excited by 20 ns pulses at 532 nm from a diode-pumped frequency doubled Nd:YLF laser at room temper ature for PL measurements. The average power of the laser was 1.5 mW, at a repetition rate  of 2 kHz and peak power density of 10 5 W/cm 2. The PL was dispersed using a Spect raPro-300i spectrograph and then  detected by a liquid nitrogen-cooled InGaAs array detector. PL spectra were corrected for spectrometer throughput and the relative PL efficiencies were calibrated using a p-doped GaAs re ference sample. All wavelength dependent spectra ݂ሺߣሻ	are converted from wavelength to photon energy using the following transformation [42]:  ݃ሺܧሻ ൌ ݂ ൬݄ܿܧ ൰݄ܿܧଶ (2-10) 2.3.3.  Scanning electron microscopy  Build-up of metallic Ga-Bi droplet s on the surface of growing GaAs 1-x Bix  film is problematic and undesirable. Therefore, study is needed to understand the process of droplet formation on the surface and also to see the possibility of growing droplet-free GaAs 1-x Bix  films. In this regard, the surfaces of the grown GaAs 1-x Bix  films were studied using a scanning electron microscope (SEM). SEM Images were recorded at UVIC’s advanced microscopy facili ty using a Hitachi S-4800 cold field emission SEM. The SEM was operated with  an accelerating voltage of 1 kV, giving a resolution as small as 1.4 nm. This system is e quipped with two secondar y electron detectors, a ring-type YAG backscatting detector and a Bruker Quantax EDX system fo r energy-dispersive x-ray spectroscopy (EDX).   2.3.4.  Atomic force microscopy  The surface morphology of the grown samples is probed using a Digital Instruments Multimode Atomic Force Microscope (AFM) with a vertical resolution of fractions of a nanometer. The  19  samples were scanned in the tapping mode with a Si 3 N4  tip having a 10-30 nm radius loaded on the Si cantilever. AFM gives high resolution 3D space images of the film’s surface.  2 . 4 .  MBE growth and properties of low temperature GaAs Molecular beam epitaxy is particularly well studied for the growth of GaAs and its ternary and quaternary substitutional alloys (e.g. Ga x In1-x As, Alx Ga1-x As, GaAs1-x Sbx  and Gax In1-x AsyP1-y ). As formation of stoichiometric GaAs is thermodynamically preferred and stable for a wide range of temperatures and beam fluxes, the MBE growth of  GaAs crystals with low defect density is relatively accessible. High quality GaAs crystal films can be grow n in MBE at a temperature of about half the melting point of GaAs, 500-650 °C, with high As 2 or As4  overpressure which results in (2×4) RHEED surface reconstruction. Under thes e conditions, every Ga atom that impinges on the surface will remain and have enough thermal ener gy to find a lattice site while the excess As not bonded to Ga will evaporate from the surface [43] . Thus the growth rate is just determined by the Ga flux.  The diffusion length of Ga adatoms along the surface is determined by the substrate temperature, growth rate and the roughness of th e starting surface. A higher substrate temperature and lower growth rate will allow Ga adatoms to migrate further on the surface before a monolayer grows. In the case of GaAs  growth in the (001) di rection, due to the difference in step densities (roughness) along ሾ110ሿ and ሾ11ത0ሿ lateral directions, Ga adatom diffusion is anisotropic. The diffusion length along the ሾ110ሿ and ሾ11ത0ሿ directions are found to be about 1 and 8 µm at 560 ºC, respectively at As4  BEPs of 3-8×10 -6  torr. The difference in these diffusion lengths at low temperatures is expected to be larger (e.g. ~2 nm along ሾ110ሿ while ~200 nm along ሾ11ത0ሿ at 300 ºC) [44], [45]. This indi cates that under the standard high temperature grow th, Ga adatom diffusion is nearly 2-dimensional while at low temperatures  Ga adatom diffusion occurs much more readily in the ሾ11ത0ሿ direction. As an example, Figure 2-1 shows the surface morphology of 1 µm thick GaAs (001) buffer layer grown by MBE at low temperature of 250 ºC. An asymmetric surface pattern consisting of atomic steps elongated along the ሾ11ത0ሿ crystal direction is observed. Growth of GaAs at temperatures lower than  400 °C under As-rich conditions, results in non-stoichiometric composition, in which excess As in corporates into the GaAs matrix in the form  20  of point defects. Arsenic antisite (AsGa) and Ga vacancies (VGa) are the common point defects, although a low concentration of As interstitials (Asi) is also observed in low temperature grown GaAs (LT-GaAs) materials [43], [46] , [47].  A high concentration of As Ga defects of up to 1020 cm-3  in the form of neutral and positive charge states, ሾீݏܣ௔଴ ሿ and ሾீݏܣ௔ା ሿ were identified by near-infrared absorption (NIRA), and magnetic circular dichroism of absorption (MCDA) measurements on LT-GaAs layers grown at 200°C [4 6]. This high density of incorporated defects changes the properties of the grown GaAs, however the GaAs host matrix is reported to be single crystal down to substrate temperatur es as low as 140°C [43], [48].      Figure 2-1: AFM image of the surface of 1 μm thick GaAs film grown at low substrate temperature (T sub=250 ºC, As2:Ga flux ratio=3.6, excess As=0.6%). The surface RMS roughness is ~0.61 nm.  21   Figure 2-2:  (a) (004) θ-2 θ HR-XRD scans of an as-grown and annealed 900 nm thick LT-GaAs film grown at 240 °C substrate temperature with As 2:Ga flux ratio of 5.3. (b) Plots of the HR-XRD (004) peak separation (proportional to point defect density) as a function of the annealing time at different anneal temperatures for several LT-GaAs films.   As a result of the point defect incorporation, the lattice constant of LT-Ga As is larger than the GaAs substrate. The x-ray diffraction measurem ents may be used to estimate the change in lattice constant, which is proportion al to the density of defects. The black curve in Figure 2-2(a) shows the (004) θ-2θ HR-XRD scan for an as-grown LT-GaAs  epilayer on a GaAs (001) substrate. This film was grown by MBE at a low substrate temperature of 240 °C with As 2:Ga flux ratio of 5.3. The sharp peak corresponds to the GaAs buffer and substrate layers and the split off peak on the left corresponds to the LT-GaAs film with larg er lattice parameter. The peak separation in this curve corresponds to 0.06%  lattice mismatch to GaAs. Based on the Liu et al. calibration curve between the lattice mismatch and the density of As antisites [46], we can estimate a concentration of 5×10 19  cm-3  AsGa defects for this sample. Although this film contains a high density of point defects, clear pendellösung fringes are observed. This result indicates that the epitaxial growth of GaAs with smooth and sharp interfaces  is possible at low temperatures.  Most of the strain in LT-GaAs  is relaxed with modest post- growth thermal annealing, e.g. 600°C for 10 min or 700°C for 30 sec [43] , [49]. Figure 2-2(a) shows the (004) θ-2θ HR-XRD scans of two LT-GaAs epilayers (two pieces of the same as-grown sample), that were annealed at 500 °C and 600 °C for 10 min in RTA under comp arable conditions. As shown, the x-ray double  22  peak of the as-grown LT-GaAs turned into a si ngle diffraction peak at an annealing temperature of 500 °C with a shoulder at the lower angle side formed by a small lattice mismatch between the LT-GaAs and GaAs substrates. This shoulder can also be relaxed with higher temperature annealing (i.e. 600 °C), and the x-ray diffraction FWHM decreases as the annealing temperature rises. This indicates complete recovery in lattice mismatch occurs at an annealing temperature of around 600 °C. The recovery of the lattice constant is  associated with a decr ease in point defects as As antisites diffuse and merge into As clusters with high temperature annea ling.  In this process, the presence of Ga vacancies (VGa) is proposed to enhance the diffusion of As antisites [43], [46], [50].  Figure 2-2(b) demonstrates the recovery behavi or of the lattice mismatch of several LT-GaAs films as a function of annealing time for different anneal temperatures. For any given annealing temperature, the point defect concentration will decrease as the duration of the anneal increases. As expected, at higher anneal temperat ures, a faster recovery of lattice mismatch is obtained; for example similar lattice mismatch ca n be obtained at 700 °C for 20 sec or at 400 °C for 45 min.  With increasing growth temperature, the lat tice mismatch between the LT-GaAs epilayers and the GaAs substrate decreases. This is demonstrated in Figure 2-3 where a series of LT-GaAs layers were grown at a fixed As 2:Ga flux ratio but at different s ubstrate temperatures. As shown, nearly a linear relation between the lattice mism atch and the growth temperature is obtained. Therefore, during the MBE growth process, the amount of excess As  can be set by controlling the substrate temperature. The As2:Ga flux ratio also influences the amount of excess As incorporation in LT-GaAs. As an example, Figure 2-3 shows thr ee LT-GaAs layers grown with nearly 3× higher As2:Ga flux ratio (red data points). These layers s how ~20% increase in lattice mismatch and a higher density of incorporated defects. As annealed LT-GaAs is a common photoconduc tion material, such grown samples (i.e. samples in Figure 2-2 and Figure 2-3) were used for fabricati on of THz photoconductive switches (see Chapter 6 for details).   23    Figure 2-3: GaAs lattice mismatch and the corresponding density of incorporated As antisites as a function of MBE growth temperature, at a nearly fixed As 2:Ga flux ratio.   The high concentration of point defects in LT- GaAs has a significant effect on the optical activity and electronic transport properties of GaAs. Figure 2-4 presen ts room temperature photoluminescence (PL) spectra of several GaAs layers gown at fixed As 2:Ga flux ratio but at different growth temperat ures. As shown, GaAs has an infrar ed band to band emission at 869 nm. Its intensity decreases at lower growth temp eratures. Below ~300°C, LT-GaAs material is observed to be optically "dead". Th is behavior is attributed to an increase in the density of point defects that act as recombination and trapping centers. It is noteworthy to mention that no PL is observed from the 250°C sample in Figure 2-4 that  is also annealed in RTA at 500 and 600°C. The electrical resistivity (ρ) of LT-GaAs films in Figure 2-2( a) are measured with a 4 probe I-V setup. The as-grown LT-GaAs  shows a resistivity of 12 Ω.cm, while the annealed films show a resistivity of ~10 6  Ω.cm at room temperature. In comparison to semi-insulating (SI) GaAs substrates (i.e. ρ>107 Ω.cm), the low resistivity of as-grown LT-GaAs is associated with hopping conduction between the defect states, due to the high concentration of point defects [43]. By merging As antisites into the As clusters with high temperat ure annealing, the hopping conduction will be decreased and resulted in pinning the Fe rmi level at the midgap. Thus, the LT-GaAs turns semi-insulating, similar to the SI-GaAs substrates. It is noteworthy to men tion that the electrical resistivity (ρ) of SI-GaAs substrate is hi gh due to the presence of native As antisites in the midgap, associated with high temper ature bulk crystal growth.  24   Figure 2-4: Room temperature PL spectra of 1 µm thick GaAs films grown at different substrate temperatures.   2 . 5 .  MBE growth and surface properties of GaAs 1-x Bix  alloys Growth of the heavy metal III–V alloy GaAs 1-x Bix  is far less known than GaAs. Due to the large difference in the atomic size and the electronic structure of Bi relative to As and Ga, Bi has a strong tendency to surface segregate rather than incorporate under standard GaAs growth conditions. The same phenomenon is also present in the case of In and Sb, but they do not surface segregate as strongly as Bi and continue to incorporate at low leve ls under standard GaAs growth conditions. This behavior makes Bi an ideal surfactant, enhancing surface diffusion and in some cases enhancing the incorporation of other species [51], [52]. To get Bi to incorporate into GaAs, it is known that an As:Ga flux ratio cl ose to unity (V/III stoichiometric regime) and a substrate temperature below 400 ºC are requir ed [7], [15], [31]. This results  in a narrow growth window for GaAs1-x Bix  alloy films. By using these unconventional growth conditions, Bi incorporation of up to 11% was reported, before the current study [12].   25  The most difficult aspect of the growth proce ss is the control of the As flux, which must be maintained close to the stoichiometric V/III ratio with high accuracy in order to achieve high Bi content. At high As2:Ga flux ratios, As displaces Bi bonded to Ga on the surface and inhibits Bi incorporation. This condition at low temperatur es can result in excess Bi on the surface and the formation of Bi droplets. Too low an As 2:Ga flux ratio will lead to  excess Ga on the surface and formation of metallic Ga and Bi droplets. Therefore, the As pressure is a critical parameter in growth of GaAs 1-x Bix  alloys. The author has found previously that the As pressure can be set with reference to the surface reconstructions that are present at the growth temper ature of interest [31], [32]. In the presence of a Bi flux, a (2×1) surface reconstructi on is observed under conditions of near-stoichiometric As 2:Ga flux ratio. No such surface phase exis ts in the absence of Bi flux. This reconstruction has been explored  by Laukkanen et al. by STM showi ng (2×1) is a me tallic surface, having 2 pairs of Bi dimers [53]. It is found that  the growth with the (2 ×1) surface reconstruction produces films with high Bi incorporation, shar p interfaces and strong photoluminescence [31]. A surface reconstruction map obtained from in-situ  RHEED observations as a function of As2:Ga flux ratio and temperature is given in Figure 2-5 [31].  According to the above discussion, the Bi content of MBE-grown GaAs 1-x Bix  films depends on three growth parameters: As 2:Ga flux ratio, Bi:Ga flux ratio and the growth temperature. In this regard, the effect of growth parameters on th e Bi incorporation and the process of surface droplet formation was investigated by R.B.  Lewis and the author with use of in-situ ion gauge beam flux measurements, RHEED and elas tic light scattering, and ex-situ HR-XRD and SEM [37]. In this study, R.B. Lewis had the lead role in the growth of GaAs 1-x Bix  samples. The author assisted with the MBE growth of a few samples and with RHEED, HR-XRD and SEM characterizations and in analyzing the data.  Figure 2-6 shows the depende nce of Bi content on As2:Ga beam equivalent pressure ratio (BEPR) for samples grown at substrate temper atures of 220–230 ºC, 265 ºC and 330 ºC, with Bi:Ga BEPRs of 0.47, 0.35, and 0.09, respectively. The 330 ºC samples were grown at 1.0 µm/h while the other samples were grown at 0.13 µm/h. The three data sets show similar behavior. Below an As 2:Ga BEPR of 2.25, the Bi inco rporation is saturated, and further lowering of the As2:Ga ratio does not result in an increase of Bi incorporation. For BEPRs between 2.25 and 3.6, the Bi content decreases strongly with increasing As 2:Ga BEPR. Above an As 2:Ga BEPR of 4.5,  26  no Bi incorporation was detected with x-ray diffraction (<0.1% det ection limit). Interestingly, the As2:Ga BEPR of 2.25 corresponds to the unity As:Ga atom ic ratio (stoichiometric growth), as mentioned earlier in section 2.2 for the growth of  GaAs in our MBE system. This result indicates that the Bi incorporation has a strong dependence on group V/III stoich iometry of the growing film.  Figure 2-6 also shows the relative position of th e surface reconstructions recorded for     265 ºC samples, showing good agreement with the surface reconstruction map in Figure 2-5. The (2×1) and (2×3) surface reconstruc tion phases were observed to be  consistent with having Bi incorporation, while no Bi incorporation was observed at (1×3) surface phase. As shown in Figure 2-5, the As-rich (1×3) surface phase is the common phase for both GaAs and GaAs1-x Bix  at low temperatures. This observation suggests th at under (1×3) surface reco nstruction, the high As flux can push away the adsorbed Bi atoms from the surface of the growing film and inhibits the Bi incorporation. Bi incorporation in Figure 2-6 was found to increas e with decreasing temperature, with the lowest growth temperature of 220-230 ºC resulting in nearly 20% Bi. This is a new world record for Bi incorporation, about double the previously reported value in Ref. [12]. Solid curves in Figure 2-6 are from the growth model develo ped by R.B. Lewis [37] and show good agreement with experimental data.   The structural quality, la ttice constant and Bi composition of the grown GaAs 1-x Bix  films were studied using HR-XRD. The (004) θ-2θ HR-XRD scans for several GaAs 1-x Bix  films on GaAs substrates used for optical characterizations, are discussed in detail in the next chapter, section 3.5.1. In each (004) HR-XRD curve (see Figure 3-2) , increasing the Bi content of the grown film increases the lattice constant and shifts the GaAs1-x Bix  split off peak to lower diffraction angles. The (004) scans were dynamically simulate d using LEPTOS software to determine the Bi content and the thickness of the films.  Every 300 arcsec spacing between the GaAs 1-x Bix  film and substrate (004) HR-XRD peaks i ndicates ~1% Bi incorporation. Mo reover, x-ray reciprocal space maps (RSM) of the (224) off-axis peaks of several GaAs 1-x Bix  films were recorded to measure the in-plane and out-of-plane lattice constants and the degree of relaxation (See Figure 3-3 and the related discussion for more details). RSM measurements show that the grown GaAs 1-x Bix  films are coherently strained to the GaAs substrates.  27   Figure 2-5: Surface reconstruction maps for (a) GaAs (001) and (b) GaAs1-x Bix  (001) for substrate temperatures of 250 to 425 °C and As 2:Ga flux ratio of 0 to 3. The growing GaAs 1-x Bix  surface has an incident Bi BEP of 3×10 -9  torr. Figure originally published in [31].   Figure 2-6: Bi content as a function of As2:Ga BEPR at three different growth temperatures. The Bi:Ga BEPRs were fixed at 0.47, 0.35, and 0.09 for 220–230 °C, 265 °C, and 330 °C substrate temperatures respectively. Based on the discussion in section 2.2, the green dash line indicates the place of stoichiometric growth condition (i.e. unity As:Ga atomic ratio). Surface reconstruction patterns were also monitored while changing the As 2:Ga BEPR at 265 °C growth temperature. Figure is reproduced from Ref. [37].    28  2.5.1.  Surface droplet formation during growth of GaAs 1-x Bix alloys  Metallic droplets on the surface of growing fi lms are undesirable because they create surface roughness and cause local variations in the amount of Bi coverage and hence the local composition. In addition, droplets leave behind non-uniformities in  the film thickness, since droplets prevent As atoms from reaching the surface so that GaAs does not grow underneath the droplets. From the device application point of view, surface droplets are also undesirable, as metallic droplets can screen the surface carriers and act like recombination centers or electrically short the device at the surface. Therefore a significant challenge in growth of GaAs 1-x Bix alloys is to find a way to suppress the formation of metallic Bi and Ga droplets. Ideally the Bi flux will exactly match the Bi incorporation rate plus the evaporation rate, otherwise droplets will form. The low growth temperature of GaAs1-x Bix  (T <400 ºC) means that the evaporation rate of Bi is low, so control of Bi flux is required. In addition, below the unity As 2:Ga flux ratio excess Ga will form Ga droplets on the surface. To reach this ideal situation, careful control of both group V As and Bi fluxes is important. Table 2-1 and Table 2-2 compare the surfaces  of films grown under similar conditions below and above the stoichiometric As 2:Ga flux ratio. These samples correspond to the 220–230 ºC and 265 ºC growth temperatur e data points in Figure 2-6 whic h were grown below and near the melting points of Bi (271.5ºC). Ther efore, the Bi droplet phase is likely not changed after the growth when samples cooled down. At low As 2:Ga flux ratios (Ga-rich regime), phase-separated submicron size Ga and Bi metallic droplets are apparent, as shown in Table 2-1 and Table 2-2. The Ga-Bi droplets at higher growth temperature are shown to be more homogeneous and better phase separated. The formation of Ga-Bi composite droplet s is likely due to the limited presence of As on the Ga terminated surface during growth. Theref ore instead of As, group V surface sites are filled by the Bi atoms and since Ga and Bi are immiscible [16], [54], phase-separated Ga-Bi droplets will form. This result s uggests that the Ga-Ga and/or Bi -Bi bonding is stronger than Ga-Bi bonding.  At the stoichiometric As2:Ga threshold in Table 2-1, smalle r size phase-separated droplets are observed. At an above stoichiometric flux ratio (As -rich regime), pure Bi droplets with much smaller size (nanoscale) and higher density are observed on the surface. This suggests that under As rich conditions, Bi incorporation in the GaAs1-x Bix  film is saturated and additional Bi flux is  29  taken up by Bi droplets on the surface. At high As flux in this region (~As 2:Ga BEPR ≥ 4.5), no Bi incorporation is observed and an SEM study shows that the incoming Bi flux accumulates into Bi nano-droplets or evaporates. This is  likely due to the fact that high As flux displaces Bi bonded to Ga on the surface and inhibits Bi incorporation. As is apparent in Table 2-1 and Table 2-2, with increase in As2:Ga BEPR, the surface mobility of droplets is significantly reduced, resulting in formation of localized Bi nano- droplets in As-rich conditions.  By careful control of the Bi flux in the As-rich condition, it is possible to grow GaAs 1-x Bix  films without Bi droplets (droplet-free). Using this method, we have achieved the growth of droplet-free samples with up to 5.8% Bi content. Figure 2-6 show s an SEM image of the surface of two droplet-free GaAs 1-x Bix  films with 1.0% and 5.8% Bi cont ents. These films were grown in As rich conditions at As2:Ga BEPR of 3.4 and 2.6 respectivel y. The droplet-free 5.8% Bi sample in this figure has the same grow th temperature as samples in Table 2-1, but with ~70% less Bi:Ga BEPR. This reduction in Bi:Ga flux can be regulate d by lowering the temperature of the Bi effusion cell. The small features on the surface of this sample appear to be nano scale pin holes (Figure 2-6 inset), which could indicate the start of Bi dropl et nucleation on the surface. These features may also exist due to the initial contamination on the su rface of the wafer. This result suggests that As-rich conditions with low Bi flux (minimal to just have Bi incorporation) are required for growth of droplet-free GaAs 1-x Bix  films.  Table 2-3 summarizes the specificati ons of several droplet-free GaAs 1-x Bix  films, grown in As-rich conditions, showing that droplet-free thic k films (e.g. 450 nm) or droplet-free films grown at low temperatures (e.g. T=215 ºC) are possible. It  should be noted that the control of Bi droplets at low growth temperatures, such as 215 ºC, is mo re difficult as the Bi evaporation rate is low.  High Bi incorporation requires low growth te mperatures. At low growth temperature as shown in Figure 2-6 Bi conten t has a steep dependence on surface stoichiometry (i.e. As2:Ga flux ratio). These conditions illustrate the difficulty of obtaining droplet-free hi gh Bi-content films.     30  Table 2-1: Surface droplet comparison for GaAs1-x Bix  samples grown at 265 ºC growth temperature and Bi:Ga BEPR of 0.35 below and above stoichiometric As 2:Ga BEPR. Energy-dispersive X-ray (EDX) spectroscopy measurements confirm droplet composition.  SEM Image (1 µm scale bar) Bi % As2 :Ga BEPR Growth time (min)   11.5   1.3  Ga-rich   20   11.4   2.2  Near Stoichiometric   17   2.8   3.3  As-rich   17   0   5.1  As-rich   17  Bi Bi Bi Ga Bi  31  Table 2-2: Surface droplet comparison for GaAs1-x Bix  samples grown under similar conditions at 220-30 ºC growth temperature and Bi:Ga BEPR of ~0.5 below and above stoichiometric As 2:Ga BEPR. Energy-dispersive X-ray (EDX) spectroscopy measurements confirm droplet composition.  SEM Image (1 µm scale bar) Bi % As2 :Ga BEPR Growth time (min)   15.9   0.8  Ga-rich   15   13.6   2.5  As-rich   15   0   4.6  As-rich   15       Bi Bi Ga Bi  32  Table 2-3: Growth conditions of several droplet-free MBE grown GaAs 1-x Bix  samples. Bi% Thickness (nm) Growth Temperature (°C) As2 :Ga BEPR Bi:Ga BEPR Surface Reconstruction 1.0 240 330 3.4 0.02  2×1 2.2 450 330 3.1 0.07 2×1 4.3 250 215 2.2 0.1 1×1 or 2×1 5.5 200 265 2.6 0.1 1×3 or 2×3 5.8 54 267 2.5 0.1 2×1   Figure 2-7: SEM image of the surface of two droplet-free MBE grown GaAsBi films with 1.0% and 5.8% Bi content. The specification and the details of the growth conditions of these films are summarized in Table 2-3. Both films were grown above the stoichiometric As 2:Ga flux ratio. The inset in the second imag e is a blow-up of small features on the surface of 5.8% Bi film. These small feat ures appear to be nano scale pin holes, which could indicate the start of Bi droplet nucleation on the surface. The shadow pattern in the t op figure is due to a difference in exposure to the incident electron beam.  33  2.5.2.  Etching the GaAs 1-x Bix surface droplets  As described above, Ga and Bi droplets on the surface of grown GaAs 1-x Bix  film are undesirable. The droplets can be selectively removed using mineral acids. Hydrochloric acid is commonly used for cleaning the surface of GaAs wafe rs, as this acid attacks the native oxides of GaAs but leaves the GaAs untouched. In this study samples covered with droplets were wet etched using HCl:H 2O solution (1:4 ratio) for 2 min, which removes both Ga  and Bi droplets. Concentrated sulfuric acid (H2SO4 , 96 %) was also used but it sele ctively etches Bi and not Ga.  To assess whether the droplets a ffect the film composition, (004) θ-2θ HR-XRD measurements were carried out on several GaAs 1-x Bix  samples that were heavily covered with droplets, before and after the HCl:H 2O etch. No significant change in Bi content or change in thickness is observed, although sharper and more dis tinct thickness fringes were observed for the etched samples. The GaAs1-x Bix  films heavily covered with dr oplets have optically scattering surfaces. Etching with HCl:H 2O solution significantly reduces the amount of light scattered from the sample surface.   Removal of droplets was confirmed by SEM a nd AFM measurements. Figure 2-8 compares SEM images of the surface of a 14% Bi f ilm before and after etching with HCl:H 2O solution. As this sample was grown in Ga-rich conditions, Ga-Bi phase-separated droplets formed on its surface. Dipping this sample for 2 min in HCl:H 2O solution completely removes the droplets. Figure 2-9 shows the surface morphology of two othe r high Bi content films after a similar etch process. Both of these films were also grown in the Ga-rich condition and had Ga-Bi surface droplets. These etched layers show surface roughne ss in the form of tail shapes due to non-uniform growth around the droplets. The tail shape rough ness is possibly formed during the MBE growth as the material underneath the Ga side of the phase-separated droplet grow fa ster than the Bi side. As a result, the solid layers grown on the Ga side  causes the liquid droplets to move on the surface and creates the tail shaped surface structures. It is noteworthy that we coul d not find any tail shape surface roughness for samples having Bi droplets only (i.e. samples in As-rich conditions). Therefore, the tail shapes are believed to be the signature feature of bi-metallic Ga-Bi droplets. Figure 2-10 (a) shows AFM image of the surface of a 100 nm, 2.5% Bi film after etching the droplets with HCl:H 2O solution. This sample was also grow n in Ga-rich conditions. Similar to  34  the SEM results, vacant places of the etched droplets and the tail shape surface structures around the droplets are observed. AFM 3D profile from a vacant place of one etched droplet is shown in Figure 2-10 (b). The droplet dept h is ~35 nm, below the flat su rface. This result suggests not surprisingly, that the Ga-Bi dropl ets prevent the growth of GaAs 1-x Bix  underneath the droplets.              35   Figure 2-8: SEM images of the surface of GaAs0.86 Bi0.14  film (a) before and (b) after etching the droplets with HCl:H 2O solution. This sample was grown at 250 ºC substrate temperature with As 2:Ga BEPR of 1.5 (i.e. in Ga-rich conditions).      Figure 2-9: SEM image of the surface of two high Bi conten t films after etching the droplets with HCl:H 2O solution. The visible surface roughness is due to non-uniform growth around the droplets. Both layers were grown in Ga-rich conditions.   36   Figure 2-10 : (a) AFM image of the surface of 2.5% Bi film after etching the droplets with HCl:H 2O solution. (b) AFM 3D height profile from a vacant place of one etched droplet on the surface of a 2.5% Bi, 100 nm thick film. The base of the droplet is ~35 nm below the flat su rface. The sample was grown in Ga-rich conditions.  37  C hapter 3   Bandgap and optical absorption edge of GaAs1-x Bix  alloys with 0<x<17.8%   Alloying of GaAs with Bi has a profound effect on the properties of this compound, most notably in the reduction of the optical bandgap. The composition dependence of fundamental bandgap and other optical properties such as optical constants, absorption coefficient and recombination centers in bismide material are not well  known especially in  the high concentration region. Here we investigate the optical properties of MBE grown GaAs 1-x Bix alloys with 0 ≤ x ≤17.8% by optical transmission and photoluminescence spectroscopies. The lattice constant and Bi content of GaAs1-x Bix  films with 0<x ≤19.4% are studied using high resoluti on x-ray diffraction and Rutherford backscattering spectroscopy.  3.1.  Contributions The majority of the samples discussed in this chapter (~90%) were grown by R.B. Lewis, sometimes with the assistance of the author. About  10% of the samples were grown by the author. I set up the optical absorption setup in the MBE lab and performed all of the optical measurements and data analysis. Most of the x-ray diffraction and scanning el ectron microscopy imaging were collected and analyzed by the author. Rutherford backscattering (RBS) meas urements were carried out by M. Chicoine at the Université de Montréal.    38  3 . 2 .  Introduction Bismuth-containing III-V semiconduc ting alloys have attracted attention due to the large bandgap (Eg) reduction observed with incorp oration of small amounts of Bi, allowing the wavelength range for GaAs-based devices which absorb and em it infrared light to be extended. In GaAs 1-x Bix  the bandgap reduction is ~83 meV/% at low Bi concentrations (x ≤5%) [12], [18], whic h is much larger than the effect of In and Sb (11 meV/% In, 19 meV/ % Sb) [19], [20] and only  lower than the effect of N alloying (125 meV/% N in 0 ≤ x ≤2% range) [6]. Photoluminescence with emission wavelength up to 1.44 µm has previously been observed in GaAs 1-x Bix  alloys with x ≤10.6% Bi [12]. As a result of growth challenges, until recen tly the incorporation of high amounts of Bi (~ x>12%) into GaAs 1-x Bix  films had not been achieved. Since highly crystalline GaAs1−x Bix  alloys with Bi contents up to 22% have been successfully grown on GaAs substr ates in our lab [37], nearly double the highest previously reported Bi content [12] , [15], [55], one of th e most important question is: what is the optical bandgap of these new non- dilute alloys? Material with the expected low bandgap (~ Eg ≤0.8 eV) is desirable for optoelectronic applications in the near and mid-infrared spectral range. Light sources emitting in the mid-infrared (MIR ) wavelengths (2-5 µm) are technologically important due to their potential applications in telecommunications and molecular spectroscopy. Optical communication can be achieved in the 2-2.5 µm and 3.5-5 µm bands as the atmosphere has high transparency for these wavelengths. Mol ecular spectroscopy with a high resolution can also be possible as many common gases and organic molecules have strong absorption lines associated with vibrational and rotational motions in MIR wavelengths, for example: NH 3  (2.1 µm), HF (2.5 µm), CH 4  (2.35 µm and 3.3 µm) and CO (2.3 µm  and 4.6 µm) [56]. Therefore, the MIR emitters/detectors offer rich potential for gas detection and air pollution monitoring especially in the industrial process environments. In addition, efficient high-power MIR semiconductor lasers are useful for soft-tissue laser surgery [56], [57].   To address the above question, we used  room temperature optical transmission spectroscopy to measure the fundamental optical bandgap and absorption coefficient of thin, pseudomorphic GaAs1-x Bix  films on GaAs substrates. These measurements reveal the composition dependence of Eg in this previously unexplor ed composition range. Moreover, the structural quality, lattice constant and Bi composition of the GaAs 1-x Bix  layers are studied using high resolution x-ray diffraction (HRXRD) and Rutherfo rd backscattering spectroscopy (RBS). RBS is  39  an excellent method for determinatio n of Bi content, due to the large mass of Bi relative to Ga and As.  3 . 3 .  Sample preparation A set of nominally undoped GaAs1-x Bix  layers (0<x ≤19.4%) were grown on 350 μm thick single-side polished semi-insulating (S I) GaAs (001) substrates in a VG-V80H MBE reactor. During operation, the MBE shroud was cooled to ~ -80°C w ith a polysiloxane heat transfer fluid, instead of conventional liquid nitrogen co oling [28], [29]. Each sample consists of a 300-500 nm GaAs buffer layer, followed by a GaAs 1-x Bix  layer grown at low temperatures (220°C<T sub<360°C). The growth conditions of part of th e samples are shown in Figure 2- 6. Layers with x>10% Bi were grown at low temperatures (220°C<T sub<250°C) at or below the stoichiometric As 2:Ga flux ratio (i.e. Ga-rich conditions). The thic kness of the layers was gradually decreased from 450 to 20 nm with increasing Bi content, to avoid strain rela xation and also to minimi ze surface roughening due to build-up of Ga-Bi droplets on the surface. Layers covered with metallic droplets were subsequently etched in an HCl:H 2O solution (1:4 ratio) for 2 min to remove the droplets. This greatly reduced the light scattered from the sample surface during the measurements. Removing the droplets by etching caused a ~2× increase in the photolumin escence (PL) emission in the case of the 10.5% Bi sample that was heavily covere d with surface droplets. Removal of the surface droplets was confirmed by scanning electron micros copy (SEM). As an example, Figure 2-9 shows the surface morphology of 17.3% and 14.2% Bi sample s (layers (a) and (b) in Figure 3-2) after etching the droplets. We note that  etched layers with x>9% Bi  showed surface roughness in SEM due to non-uniform grow th around the droplets.  3 . 4 .  Experimental setup Optical transmission measurements were pe rformed at room temperature on the GaAs1-x Bix /GaAs heterostructures with 0 ≤ x ≤17.8% and on a GaAs reference substrate with the same thickness. Figure 3-1 shows the schematic of  the optical transmission spectroscopy setup. In this experiment, white light from a halogen bulb wa s chopped at 200 Hz and focused on the entry slit of a Oriel   40   Figure 3-1: Schematic of the optical transmission spectroscopy setup.   Cornerstone 260 monochromator. The samples were illuminated at normal incidence with monochromatic light and the transmitted light was detected using un-cooled 1×1 mm Ge (800-1750 nm) and 3×3 mm PbS (1000-2800 nm) photodetector s, connected to a lock-in amplifier, and a combination of optical long-pass filters. In th is experiment, the unpolishe d back surface of the substrate wafer was placed close to the detector to maximize the collectio n of transmitted specular and scattered light. The transmission spectra of the GaAs1-x Bix  layer was isolated  by dividing the spectra of the GaAs1-x Bix /GaAs heterostructure by that of  the GaAs reference sample (TGaAsBi/TGaAs). The GaAs1-x Bix  sample and a reference substrate were measured right after each other to minimize any possible drift in optical power. The bandgap and optical absorption coefficient are obtained from the resulting spectra. Samples with up to 10.5% Bi content were also excited with a 532 nm 20 ns pulsed diode-pumped solid state laser at room temperature for photoluminescence (PL) measurements.  Unsuccessful attempts were made to measure the PL emission from high Bi content GaAs 1-x Bix  samples (i.e. x>11%) with the above-mentioned PbS photodetector. PL could not be detected, as the high Bi content samples are relatively thin (d≤70 nm) and they were grown at low temperatures and not optimized for the PL emission. In addition, the un-cooled PbS photodetector is not ideal for PL experiments as it has a rela tively low sensitivity at room temperature. RBS measurements were performed on the GaAs 1-x Bix /GaAs samples with up to 19.4% Bi content using 2 MeV alpha particles. The detector was placed at a s cattering angle of 170° and the  41  sample was tilted ~7° from the surface normal to minimize channeling effects. The compositions and layer thicknesses were obtained by simulating the RBS spectra using the SIMNRA software. RBS measurements were carried out by M. Chicoine at Université de Montréal.  High resolution x-ray diffraction (HRXRD) meas urements were performed with a Bruker D8 Discover diffractometer. The (004) θ-2θ scans and (224) reciprocal space maps (RSMs) were recorded to measure the in-plane and out-of-plan e lattice constants, layer thicknesses and degree of relaxation in the GaAs 1-x Bix  films. The (004) scans were dy namically simulated using LEPTOS software.  3 . 5 .  Results and discussion 3.5.1.  Structural characterization  Figure 3-2 shows (004) θ-2θ HRXRD scans for several GaAs 1-x Bix  films on GaAs substrates used for optical transmission and PL experiments. In each rocking curve, the sharp peak corresponds to the GaAs buffer and substrate layers and the split off peak on the left  corresponds to the GaAs1-x Bix  layer. As expected, increasing the Bi content of  the epilayer increases the lattice constant and shifts the split off peak to lower diffraction angles . With the exception of th e 9.7% Bi sample (layer c), which is discussed below, θ-2θ scans show pendellösung fr inges, indicating good film uniformity and sharp interfaces. The composition and thickness of each film in this figure was determined by simulating the curves using LEPTOS assuming a pseudomorphic growth and employing the relationship between  the lattice parameter and Bi content obtained from HRXRD and RBS measurements, as discussed below. Figure 3-3 shows the x-ray reci procal space maps (RSM) of the (224) off-axis peaks of GaAs1-x Bix  films with 5.0%, 9.7%, 14.2% and 19.4% Bi  contents. The RSM’s of 14.2% and 9.7% Bi films correspond to the samples (b) and (c) in Figure 3-2. In each RSM map, the upper peak is from the GaAs buffer and substrate layers and the lower peak is from the GaAs 1-x Bix  film. The in-plane component of the film peak, qx, exactly matches the substrat e to within the measurement error, indicating that these films are coherently strained (pseudomorphic) to the GaAs substrates. This is in spite of the fact that the 14.2% and 19.4% GaAs 1-x Bix  films have large (1.7% and 2.3%)  42   Figure 3-2:  (004) θ–2θ HRXRD scans of GaAs 1− x Bix  films on GaAs. Scans are offset vertically for clarity. The composition and thickness of the layers are determined from  dynamical simulations. The sample with 9.7% Bi and no thickness fringes showed composition variation in the growth direction in RBS. The inset shows the measured strained out-of-plane lattice parameter (red squares) and correspondin g relaxed lattice parameter (black circles) assuming a Poisson ratio of 0.31, as a function of the RBS Bi cont ent. The GaBi lattice parameter is indicated from the extrapolation of the best fit (solid lin e). Figure originally published in [58].  lattice mismatches with the GaAs substrate. Ba sed on the Matthews-Blakeslee (M-B) criteria for epitaxial growth with no relaxation through the misf it dislocations formation [59], the above lattice mismatches correspond to critical layer thickne sses of 5.2 nm and 3.5 nm, respectively. These critical thicknesses are about 10× smaller than the actual thickness of thes e films. The reason for this deviation is that the M-B theory of the critical layer thickness is based upon equilibrium considerations while the MBE gr owth happens under conditions far from equilibrium. In the MBE growth of low temperature materials such as bi smides, the thermal energy available on the growing  43   Figure 3-3:  (224) RSM of several pseudomorphic GaAs 1− x Bix  films on GaAs substrates. The horizontal and vertical scales are the in-plane and out-of  plane reciprocal space vectors (qx [220],  qz [004]). The upper peak is from the GaAs substrate and the lower peak is from the GaAs 1− x Bix  films. RSM’s of 14.2% and 9.7% Bi content films correspond to the samples (b) and (c) in Figure 3-2. The Bi content an d the thickness of the layers obtained from dynamical simulations of the (004) HRXRD scans are: (I) 5.0%, 100 nm  (II) graded 9.7%, thickness not determined (III) 14.2%, 53 nm (IV) 19.4%, 40-60 nm.   surface is low. As a result, the nucleation of disl ocations is kinetically limited during the growth and it is possible to grow epitaxial layers with no relaxation, much thicker than M-B limit. In particular the above mentioned 14.2% and 19.4% Bi films were gr own at low temperatures of  44  250°C, 220°C. Pendellösung fringes are also seen be tween the film and substrate peaks in RSM’s of 5.0% and 14.2% Bi samples, indicating sm ooth interfaces and uniform compositions.  The angular separation between substrate and th e split off x-ray peaks indicates the lattice constant of the Bi containing layer, but since the lattice constant of GaBi is unknown, the Bi content cannot be obtained from the (004) HR-XRD  measurements alone. Therefore, Bi content was also measured on sel ected pseudomorphic GaAs1-x Bix /GaAs samples by Rutherford backscattering (RBS) experiments. Figure 3-4 presents RBS spectra together with simulations for several samples. The peak near 1.9 MeV in each sp ectrum corresponds to backscattering from Bi atoms in the GaAs1−x Bix  layer. The large step near 1.6 MeV is due to backscattering from Ga and As atoms. The height of the Bi peak reflects the Bi content, while the width is proportional to the layer thickness. The peak shape can be used to  determine the uniformity of the Bi composition. For thin layers that do not result in flat-top peak s, the Bi content is determined by fitting the shape of the peak. In the thin sample limit, the RBS pe ak measures the product of the Bi content and the film thickness. The uncertainty in the Bi content determined by RBS of the thick 4% sample is 4.0±0.1%. The thinner, high Bi content layers have  larger uncertainties: for example 18.6±3% and 16.6±2.5% in the case of samples (a) and (b) in Figure 3-4. For sample (c), a three layer simulation gives a better fit than a single layer, suggesting the Bi content is not uniform over the layer thickness. This sample corres ponds to the 9.7% film in Figur e 3-2, which has a broad (004) HRXRD scan with no pendellösung fringes.  In the case of pseudomorphic growth in the (001) direction on GaAs substrate (ܽ∥ ൌܽீ௔஺௦), the relaxed lattice parameter, ܽ௙, of GaAs1-x Bix  films can be calculated from the Eq. (2-6) as:   ܽ௙ ൌ ܽீ௔஺௦ ൅ ሺܽୄ െ ܽீ௔஺௦ሻ ൬1 െ 1ߥ ൅ ߥ൰ (3-1) Here, ν is the Poisson ratio and ܽୄ is the GaAs1-x Bix  pseudomorphic out-of-plane lattice parameter which can be obtained from (004) HRXRD.  Since the Poisson ratio of both GaAs1-x Bix  and the GaBi compounds is unknown, in this study the Poisson ratio is assumed to be the same as that of GaAs (ν(100) = 0.31) [60], [61]. This assumption is valid for dilute GaAs 1-x Bix  alloys, but might cause error for high Bi content films, as the effect of Bi alloying on the elastic constants of  45   Figure 3-4: RBS spectra (dots) and SIMNRA simulations (red lines) for several GaAs1− x Bix  films on GaAs. Spectra are offset vertically for clarity. The peak near 1.9 MeV for each spectrum corres ponds to backscattering from Bi atoms in the GaAs1− x Bix  layer. The large step near 1.6 MeV corresponds to backscattering from Ga and As atoms in the layer and substrate. The labels (a,b,c) correspond to the matching samples in Figs. 2, 4 and 5. For spectrum (c), a simulation with three layers gives a better fit than a single layer. The Bi composition and layer thickness of GaAs 1− x Bix  films obtained from SIMNRA are shown in this figure. The Bi composition and layer thickness obtained from the dynamical simulations of the (004) HRXRD scans on the same samples are: (from bottom to top) (1) 3.7%, 255 nm (2) 9.7%, thickness not determined (3) 14.2%, 53 nm (4) 17.3%, 33 nm (5) 19.2%, ~40-60 nm. RBS measurements were performed by M. Chicoine at Université de Montréal. Figure originally published in [58].  GaAs1-x Bix  could be significant. The calculated pseudomorphic and free standing lattice parameters (ܽୄ, ܽ௙ሻ of GaAs1-x Bix  layers with 0 ≤ x ≤19.4% are shown as a f unction of Bi content in the inset of Figure 3-2. The la ttice parameters were measured  from (004) HRXRD scans while the Bi contents were determined from RBS. Fitting a line to the relaxed data and assuming Vegard’s law and that the layers are pseudomorphi c, and then extrapolati ng to 100% Bi yields a  46  GaBi relaxed lattice constant of 6.33 ± 0.05 Å, in  agreement with the ear lier reported result of 6.33± 0.06 Å obtained from si milar experiments on GaAs 1-x Bix  /GaAs films with much lower Bi concentrations (up to 3.1% Bi) [7].  This result is also in good agreement with the value of 6.328 Å obtained from density functional theory calculations [9]. The uncertainty in the lattice constant is the statistical error in the fit to the data and does not include systematic errors. The GaBi lattice constant of 6.33 ± 0.05 Å determined here is larger  than other reported values, also obtained by extrapolation of RBS and HRXRD da ta, namely: 6.272± 0.005 Å from GaSb 1-x Bix /GaSb films with up to 9.6% Bi [62], and 6.23 Å from GaAs 1-x Bix  /GaAs films with up to 4.8% Bi [63]. The reason for the difference in the various experimental measuremen ts is not known. A different choice of Poisson ratio makes a small difference. In Ref. [63] a Poisson ratio of 0.334 was used instead of 0.31. If we had used 0.334, the GaBi lat tice constant would have been 6.30 Å rather than 6.33 Å. In Ref. [62] the host compound was Ga Sb not GaAs, with a different set of elastic constants. The extrapolated GaBi lattice cons tant is used in the LEPTOS dynamical diffraction model to determine the Bi composition and layer thickness of each pseudomorphic film in Figure 3-2 as noted above. The GaAs1-x Bix  lattice constant could in principle be subject to systematic errors associated with excess As incorporation. As  shown in section 2.4, the excess As incorporates in GaAs host matrix at low growth temperatures and that this e ffect increases the lattice constant. Under standard As-rich growth conditions at  220 ºC (the lowest GaAs 1-x Bix  growth temperatures used in our study), the compressive strain due to the excess As would be comparable to that for 0.3% Bi incorporation. However, excess As incorporation is  substantially reduced for growth at or below stoichiometric As:Ga flux ratios [64], which is the case for the GaAs 1-x Bix  layers in this work. Therefore excess As incorporation is not expected to induce signifi cant compressive strain in the GaAs1-x Bix  films discussed here.  3.5.2.  Optical absorption and emission Figure 3-5 shows the normalized transmission spectra ( TGaAsBi/TGaAs) of several GaAs1-x Bix  films. For photon energies below the GaAs bandgap, 1.42 eV, the GaAs 1-x Bix  layer partially absorbs the incident light. The absorption edge is strongly red-shifted toward lo wer photon energies with increasing Bi content. At low photon energies below the GaAs 1-x Bix  absorption edge, the epilayers  47   Figure 3-5:  Room temperature optical transmission spectra of several GaAs1-x Bix /GaAs heterostructures divided by the GaAs substrate transmission spectrum (TGaAsBi/TGaAs). The labels correspond with the samples in Figure 3-2 and Figure 3-4. Figure originally published in [58].  show maximum transmissivity near unity, indicati ng that there is weak sub-gap absorption and the refractive index of the layers is similar to that of the GaAs substrate. Although the refractive index of GaAs1-x Bix  increases slightly with Bi content [65], the effect on the reflectivity is smaller than the measurement error. To confirm this observation, the change in reflectivity between a thin GaAs1-x Bix /GaAs heterostructure and a GaAs  substrate is calculated from the optical constant data in Ref. [65]. This calculation shows that the reflectivity of a thin 50 nm 7.5% Bi layer on GaAs deviates by ~ 0.5% from GaAs in the 0.2-0.8 eV range. Despite the excellent interface quality in most samples, no interference fringes are observed in the spectra, due to the small difference between the refractive indices of substrate and th e epilayer. Therefore multiple reflections within the GaAs1-x Bix  layer are neglected and the absorption coefficient, α, can be well approximated by:  ߙሺܧሻ ൌ െ 1݀ ln ൬ܶீ ௔஺௦஻௜ܶீ ௔஺௦ ൰ (3-2)                                                              48  where d is the layer thickness and E is the photon energy. Below the bandgaps, the transmission spectra show small offsets (~ ±0.7%) from unity, likely due to differences in surface scattering caused by differences in sample roughness. The offsets measured below the bandgap are subtracted from each transmission spectrum in Figure 3-5, an d the resulting spectra are used to derive α from Eq.(3-2), as shown in Figure 3-6 (a). The experi mental data is not accurate enough to determine the absorption below about 100 cm -1 . Figure 3-6 (a) also shows the absorption coefficient of a 350 µm thick semi-insulating GaAs re ference substrate. For this sample, absorption values above ~ 200 cm-1  are omitted as they have low signal levels . The GaAs absorption coefficient is also calculated from literature values of the extinction coefficient [66], ߙ ൌ 4ߣ/ߢߨ, and is shown for comparison. For a direct bandgap semiconductor, parabolic band theory predicts an abrupt absorption edge with the form ߙሺܧሻ ൌ ܣඥܧ െ ܧ௚ above the band tail [67], where A is a constant. Therefore, a plot of α2 vs. photon energy should demonstrate a linear relation and provide an estimate of Eg from the x-intercept. The square of the abso rption coefficient is plotted for selected GaAs1-x Bix  layers in Figure 3-6 (b). For most of the samples, α2 is approximately lin ear with photon energy with similar slopes up to α2~10 8  cm-2 . This supports the notion that GaAs1-x Bix  has a direct optical bandgap up to at least 18% Bi. Band tails are visi ble at low absorption, re sulting in a deviation from the linear behavior. The bandgaps are obtained by least square fitting the straight lines to the absorption curves from α2=2×10 7 cm-2  (below this the band tails dominate) to α2=1.0 - 1.7×10 8  cm-2 , and then extrapolating these linear fits to zero (solid lines). The samples with high Bi contents of 17.3% and 14.2% show bandgaps of 0.55±0.04 and 0.66±0.02 eV, respectively.  The sample with 9.7% Bi shows more than  one absorption slope due to composition variations in the growth direc tion. These variations also show up in the RBS and HRXRD results (layer c in Figure 3-2 and Figure 3- 4). Both RBS and HRXRD indicate that this film has Bi content above 8%. The RBS data can be fitted with three sub-layers: (1) 4.8% Bi, 24 nm (2) 8% Bi, 71 nm and (3) 10% Bi, 24 nm. If the total thickness of the 8% and 10% Bi layers (95 nm) is used in the calculation of the absorption coefficient we obtain  curve I in Figure 3-6 (b). The slope of the absorption spectrum is anomalously low in this case. The low energy absorption is controlled by the high Bi content portion of the film, which is thinner than the assumed value. If we repeat the calculation of the absorption spectrum using the RBS value for the thickness of the high Bi content component only (24 nm), we obtain curve II in Figur e 3-6 (b). The slope of this curve is better  49   Figure 3-6: Absorption coefficient α and (b) α2 vs. photon energy for several GaAs1-x Bix  films and for a 350 µm thick semi-insulating GaAs substrate. The dashed line is calcula ted from GaAs extinction coefficient data in Ref. [66]. Eg of each layer is estimated from linear fits to α2 from α2=2×10 7 cm-2  to α2=1.0-1.7×10 8  cm-2 extrapolated to zero absorption (solid lines in (b)). The location of the bandgap in each layer is shown with vertical solid dashes in figure (a). The absorption coefficient of the graded 9.7% layer is calculated by considering two thicknesses: (I) RBS total thickness of 8% and 10% Bi-containing layers (95nm) and (II) RBS thickness of the 10% layer only (24nm). The Urbach parameters, E0, are determined from exponential fits below the bandgaps (solid lines in a). The inset summarizes the measured values of E0 as a function of the Bi content at room temperature. Figure originally published in [58].   aligned with the other samples. In the region below the bandgap, the absorpti on coefficient decreases exponentially with decreasing photon energy as shown in Figure 3-6 (a ). The width of the expone ntial tail or Urbach  50  energy, is often taken as a meas ure of the structural qualit y of crystalline and amorphous semiconductors [40], [41]. The optical absorption in the Urbach region can be described by:   ߙሺܧ, ܶሻ ൌ ߙ௚exp ൬ܧ െ ܧ௚ܧ଴ሺܶሻ ൰ (3-3)                                                                  where Eg is the bandgap energy, αg is the value of the absorption coefficient at the bandgap and E0 is the characteristic energy of the exponential absorption edge (Urbach energy). The parameter ܧ଴ሺܶሻ is composed of a thermal phonon interaction component and a temperature independent structural disorder component [40], [41], [68].  As shown by the solid lines in Figure 3- 6 (a), the Urbach energy of the GaAs 1-x Bix  layers is determined from exponential fits below the bandgaps. The inset shows the measured values of E0 as a function of Bi content. E0 increases linearly from 24 to  40 meV as Bi content increases from 1 to 5.5%. However, the higher Bi content samples (x>9%) show a constant E0 of 25 meV. Anomalous changes in the nature of the shallow electronic defects have been observed in other measurements for the same range Bi concentration near 5%, which we  summarize here. In magnetic field dependent photoluminescence experi ments Pettinari et al. [69] found that the exciton reduced mass increased w ith Bi concentration up to about 3% then decreased above 6%. Far-infrared photoinduced absorpti on measurements as a function of magnetic field, also by Pettinari, showed that above 5.6% Bi, Bi-relate d acceptor states are no longer present [70]. The intensity and linewidth of photoluminescence in GaAs 1-x Bix  were observed to peak at ~5% Bi  [12], [69]. A defect contribution was observe d in the linewidth of PL from GaAs 1-x Bix /GaAs quantum wells for x=3.5% but there was no defect contributi on to the linewidth for x= 6% [71]. Bi short range ordering was observed for x=2.4% but this ordering vanished for x>5.4% Bi [72]. These properties reveal a complex evolution of  the band edge states in dilute GaAs1-x Bix  alloys with increasing Bi concentration. The increase in E0 at low Bi concentrations may be due to the formation of localized states above the valence band associated with Bi dimers or larger clusters  [12], [69], [73]. The s ubsequent decrease in E0 at high Bi concentrations could then be considered as a transition from an alloy dominated by disorder associated with Bi to a more conventional III-V semiconductor alloy, once the Bi-associat ed localized states merge into a band  [69] or get overtaken by extended band states at higher Bi  concentrations, as the valence band moves up.  51  The resulting E0 values are 3-6 times larger than the Urbach energy for bulk GaAs, E0 =7.7 meV, indicating that the addition of Bi to GaAs, broadens the band edge. The results obtained here are consistent with other published data, fo r example the 7.5 meV reported earlier for GaAs   [68 ], the 25-27 meV observed for undoped GaAs 1-x Bix  films with 0.7 ≤ x ≤2.2% [74],  the 21-24 meV observed in GaAs0.94 Bi0.06 /GaAs diodes [75] and ~ 30 meV reported for a GaAs 0.95 Bi0.05 quantum well structure  [73].  Figure 3-7  shows room temperature PL spectra for the GaAs 1−xBix/GaAs layers with up to 10.5% Bi content. The highest energy peak in  each spectrum corresponds to the band edge emission which shifts to lower energy with increas ing Bi content, as exp ected. In thick layers (d>200 nm), a lower energy emission peak between 1.10 eV to  1.21 eV is also observed. This peak is believed to correspond to emission from defect states in the bandgap. It should be noted that the low energy emission is not generally  observed in thin samples (~ d<50 nm) grown under the same conditions. In thin samples, the electron-hole pa irs have a reduced diffusion length, making it more difficult for carriers to find the isolated deep levels associated with defect states. It is noteworthy that sub-bandgap PL emission with peaks at ~1.1  eV is also reported from ~2.5% Bi films with 100 and 280 nm thicknesses [76].  The PL peak intensity of thin GaAs 1-x Bix layers are also shown in  Figure 3-7, relative to the intensity of a bulk semi-insul ating GaAs reference substrate. Strong luminescence is observed from thin GaAs1-x Bix layers with up to 5.7% Bi content.  The 10.5% Bi layer shows weak PL emission, however this sample is thinner than the other layers and was grown at a lower substrate temperature (260 °C). Other layers in this figure were grown at 300-350 °C. In general GaAs1−xBix layers show broader PL emission than bulk GaAs  (~ 0.1 eV vs. 0.03 eV FWHM). This is likely due to the distribution of localized levels close to the band edge associated with Bi clusters [77]. The room temperature bandgaps of GaAs1-x Bix  alloys (0≤ x ≤17.8%) obtained from absorption edge measurements as well as from the PL peak position (0≤ x ≤10.5%) are shown in Figure 3-8. PL data from Lu  et al. [12] and density  functional theory (DFT) [9] calculations are also presented for comparison. The DFT curve is shifted downward to match the room temperature GaAs bandgap energy of 1.42 eV. The experimental results in this figure are for pseudomorphic films under in-plane compressive stress, while th e DFT calculations are for unstrained material. The Eg acquired from PL experiments is at a lower energy than the Eg acquired from the optical   52   Figure 3-7: Room temperature photoluminescence spectra of GaAs1-x Bix /GaAs layers and a semi-insulating GaAs substrate. The Bi content and the thickness of each layer are shown on top of each spectrum. The scale factors indicated are the multiplication factors that used to normalize (divide) the spectra to the intensity of the GaAs substrate. Figure originally published in [58].   absorption experiment due to the PL emission ta king place below the bandgap in the tail states. The composition dependence of Eg in III-V semiconductor al loys is commonly described by interpolation between the binary end compounds  using a quadratic equation. For the ternary GaAs1-x Bix  the interpolation formula is as follows:   ீܧ௔஺௦భషೣ஻௜ೣ ൌ ீܧݔ௔஻௜ ൅ ሺ1 െ ݔሻீܧ௔஺௦ െ ܾݔሺ1 െ ݔሻ (3-4) where b is the bowing parameter and EGaBi and EGaAs are the bandgap energies of GaBi and GaAs, respectively. As EGaBi is unknown, there are two fitting parameters, EGaBi and b, in the above equation. For most III-V alloys, a constant bowing parameter is suffi cient to fit experimental data. However, in the case of highly mismatched alloys, such as GaAsN, GaAsBi and InAlN, a composition-dependent bowing parameter has been used  [6], [12], [78]. In  the case of GaAs1−xBix   53   Figure 3-8:  Compositional dependence of the GaAs1-x Bix  bandgap, from optical absorption and PL measurements. The solid line is a fit to the absorption data using a Bi concentration dependent bowing coefficient as discussed in the text. PL data and a fit function from Lu et al. [12] along with a DFT calculation  [9], shifted to match the room temperature Eg of GaAs, are shown for comparison. The inset shows Eg as a function of lattice mismatch for bandgap lowering ternary alloys with Sb  [19], In  [20], N [6] and Bi (this work) on GaAs substrates. The range of fits for GaAsBi and GaAsN are shown fo r experimentally measured compositions (i.e . max 18% Bi and 5% N content). Figure originally published in [58].  alloy, Lu et al. [12]  showed that PL data can fit well w ith a bowing paramete r that decreases monotonically with increasing Bi content, of the form:  ܾሺݔሻ ൌ 1ߙ ൅ 5-3) ݔߚ)  54  The relation is analogous to that used earlier for InAlN alloys [78]. This relation is  found to provide a good fit to our experimental absorption data. Fr om the expression for the composition dependent bowing parameter in Eq. (3-5), a best fit to the absorption data is obtained with EGaBi= -1.60 eV, α=5.63 and β =7.34. This fit is shown as the solid line in  Figure 3-8. An earlier fit to lower Bi concentration samples by Lu et al. [12] using the same equation found the following different fitting parameters: EGaBi = -0.36 eV, α= 9.5 and β=10.4. The fit from Lu et al. is plotted in Figure 3-8 as a dotted line. This curve does not fit the bandgap of the high Bi concentration samples with x>10% in Figure 3-8. As a result, the Lu et al. fit predicts a zero bandgap at [Bi] = 64% whereas the new fit to samples with Bi concentrations up to 17.8% predicts a zero bandgap at [Bi] = 35%. Since the new fit in this work is based on data  for samples with higher Bi concentration, the extrapolation to zero bandgap is sh orter, and the zero bandgap point is therefore expected to be more reliable, nevertheless being an extrapolatio n it is difficult to determine the accuracy of the inferred zero bandgap point.  The inset in Figure 3-8 compar es the dependence of the bandgap on lattice mismatch for bandgap lowering ternary alloys with Sb  [19], In  [20], N [6] and Bi (this work) on GaAs substrates. The GaAsBi curve is taken from the fit to the optical absorption bandgap in the main figure. The range of fits for GaAsBi and GaAsN are shown for experimental ly tested concentrations (i.e. max 18% Bi and 5% N content).  Below ~1.06 eV (x ≥ 5.5% Bi), GaAsBi has th e least lattice mismatch from GaAs of any alloy, including GaAsN, for a given bandgap. This unmatched bandgap reduction makes GaAsBi appealing for extending the wavelength of  optoelectronics devices on GaAs substrates as well as substrates with larger  lattice parameter like InP, beyond what traditional alloying elements offer.   3 . 6 .  Conclusion The composition dependence of the bandgap of pseudomorphic GaAs1-x Bix  layers (0≤ x ≤17.8%) on GaAs substrates has been measured with optical transmission and PL spectroscopies. All samples show direct bandgaps. The bandgap energy decreases with increasing Bi content, reaching Eg=0.52 eV at 17.8% Bi. The absorption coeffici ent below the bandgap reveals exponential band tails with 3-6× larger Urbach energy than that of bulk GaAs. The Urbach parameter is found to  55  increase from 24 to 40 meV with increasing Bi in the 1%<x< 5.5% range; at higher concentrations x> 9%, it remains constant at about 25 meV. Th is dependence on Bi content is consistent with literature reports of changes in the nature of the shallow el ectronic defects near x~5%. The relationship between lattice constant and Bi c ontent has been measured by RBS and HRXRD up to 19.4% Bi. Below Eg ~1.06 eV, GaAs 1-x Bix  has less mismatch to GaAs than any other ternary GaAs alloy, including GaAsN, for a given bandgap. The strong bandgap reduction per unit strain in GaAs1-x Bix  alloys shows promise for extending th e wavelength range of devices on GaAs, beyond what other III-V alloys offer. Extrapolating our results, GaAs 1-x Bix  lattice matched to InP is expected to have a bandgap of ~ 0.1 eV or ~10 µm.             56  C hapter 4   Electronic transport properties of GaAs1-x Bix alloys  The following chapter covers th e electronic transport characterizations in nominally undoped GaAs1-x Bix  films with 0<x ≤21.5% Bi content. As Bi primary affects the valence band of GaAs, the effect of Bi alloying on electronic transport of holes is of interest. Room temperature conductivity and Hall transport measurements reveal a nearly exponential increase in p-type conductivity and a monotonic decrease in hole mobility with increasing Bi-content. The temperature dependence measurements on several GaAs1-x Bix  samples suggest that at low temperatures (T≲150 K), the hole conduction is governed by a variable-range-hopping mechanism in shallow localized states above the valence band.  4.1.  Contributions The majority of the samples discussed in this chapter (~70%) were grown by R.B. Lewis, sometimes with the assistance of the author. Th e remaining portion of the samples were grown by V. Bahrami-Yekta (~20%) and by author (~10%). Mo st of the post-growth sample preparations including wet etching, fabrication of metal contacts and making the Hall samples were carried out by the author. Others were carried out by V. Bahrami-Yekta. I designed and set up the new experimental Hall setup using an electromagnet and performed all the measurements and data analysis.    57  4 . 2 .  Introduction The large difference in atomic orbital energies of Bi, (Xe) 4f 14 5d106s 26p 3 , compared to As, (Ar) 3d 104s 24p 3 , lead to a perturbation of the GaAs host band structure parameters such as the bandgap energy. Early theoretical band structure calculations predicted that Bi 6p level(s) form a bound state at ~180 meV above the GaAs valence band maximum (VBM) [9]. A mo re recent theoretical calculation indicated that the Bi 6p state is locate d ~80 meV below the GaAs VBM, nearly resonate with the top of the valence band [13]. To our k nowledge the location of the isolated Bi energy level in GaAs is unknown experimentally, alth ough  experimental evidence of bound states has been reported and attributed to the formation of Bi cluster states [77]. As  a result, introducing Bi in GaAs could generate a hole trap near the VBM, and could result in stronger scattering of holes than electrons. Therefore one might expect that the hole mobility will decrease with Bi alloying. The opposite behavior might be expected for electr ons in dilute nitrides where electron traps are expected near the conduction band minimum (CBM). Despite numerous studies on structural and optical properties of dilute GaAs1–x Bix , the electronic transport properties of this material are not well known. Previous study on n-type dilute GaAs1–x Bix has shown that the Bi incorporation doe s not significantly degrade the electron mobility (µe) for at least x ≤1.2%, although at higher Bi  concentrations (1.6 ≤ x ≤2.5%) some degradation of the electron mobility was observed, although with cons iderable scatter in the data [79]. The first experimental studies of the effects of Bi on the hole mobility ( µh) have been reported in our group by Hall transport measurements on p-type (C-doped) GaAs 1–x Bix  samples of up to 5.5% Bi [80] and later by Pettinari et. al on un-doped GaAs 1–x Bix  samples (x ≤ 10.6%) [81]. This work has revealed a general decrease of the hole mobility following Bi incorporation. On the other hand, Pettinari et. al reported p-type hole conductivity in undoped GaAs 1–x Bix  alloys and suggested that the hole mobility might start to increase above 8.5% Bi, due to band formation in Bi impurity and cluster levels at high Bi concentrations. The behavior of µh in high Bi content materials (x ≥10%) as well as the influence of Bi  on the concentration of free-hole ( p) is still not clear.  As shown in the previous chapter, high Bi content GaAs 1–x Bix  alloys have low energy bandgaps (Eg≤0.8 eV) and have great potential for use in device applications such as high-efficiency solar cells, spintronics or infrared optoelectronic devices. Therefore understanding the electronic transport properties of this new semiconduc tor alloy is crucial. In this regard, we used  58  electrical conductivity and Hall mobility to understand the effect of Bi incorporation on the transport properties of undoped GaAs1–x Bix  films over a wide range of Bi concentrations (0<x ≤21.5%). Both room temperature and low temper ature measurements are discussed in this chapter. These measurements reveal the transport properties of bismide alloys in a previously unexplored composition range.   4 . 3 .  Conductivity and Hall mobility using Van der Pauw method When an electric field ܧሬԦ is applied across a piece of semiconductor, the free carriers in the material respond to the electric field by moving with an  average velocity called the drift velocity	ݒௗሬሬሬሬሬԦ. The carrier mobility is the proportionality constant between the drift velocity and the applied electric field and indicates how fast the carriers are responding to the electric field:   ݒௗሬሬሬሬԦ ൌ ܧߤሬԦ (4-1)   As both sides of the above equation can be  expressed in terms of current density, ܬԦ ൌ ܧߪሬԦ ൌ ݒ݊ݍௗሬሬሬሬԦ, the carrier mobility becomes:  where ߪ is the electrical conductivity, ݊ is the concentration of majority carriers and ݍ is the fundamental unit of charge. Using the four-probe technique (van der Pauw method), both ߪ and ݊ can be obtained from the resistivity and Hall effect measurements on a thin, flat sample having an arbitrary shape [82]. The measur ements require four small Ohmic contacts to be placed around the edge of the sample. In this study, square shape sa mples with small corner-side contacts are used, as shown schematically in Figure 4-1.  ߤ ൌ ݊ݍߪ (4-2)    59   Figure 4-1: Schematic of sample structure and the configuration for the Hall mobility measurements. The dark regions show the surface Ti/Pt/Au Ohmic contacts.   In the four-probe technique the current s ource and voltage measurement contacts are separated. For example to perform the resistivity measurement, the current is applied to the two adjacent contacts (e.g. contacts 1 and 2 in Figure 4-1)  and the voltage is measured across the other adjacent contacts (e.g. contacts 3 and 4, V 34 ). From these two values , a resistance can be found from an Ohm's law; for example R 12, 34  = V 34 /I 12. With the change in the polarity of the current, the opposite resistance R21,43  can also be achieved. Repeating the same procedure for R43,12 and R34,21  , the average horizontal resistance is:  Similarly the vertical resistance is:  ܴு ൌ ܴଵଶ,ଷସ ൅ ܴଶଵ,ସଷ ൅ ܴସଷ,ଵଶ ൅ ܴଷସ,ଶଵ4  (4-3)   ܴ௏ ൌ ܴଵସ,ଶଷ ൅ ܴସଵ,ଷଶ ൅ ܴଶଷ,ଵସ ൅ ܴଷଶ,ସଵ4  (4-4)    60  From measurements of the horizontal and vertical resistance, the sheet resistance (ܴ௦) and the electrical conductivity (ߪ ൌ ଵோೞௗሻ of a sample with thickness d could then be determined by the van der Pauw equation [82]:  This function does not have a closed-form analytic  expression and must be solved numerically. In order to find the carrier concentration, the sample is placed in a magnetic field and the current applied to opposite side contacts (e.g. to I24+ in Figure 4-1) and the voltage measured across the others (e.g. V13+ ). The positive sign in the subscript show s the direction of the magnetic field. A similar measurement with the opposite magnetic field direction yields the partial Hall voltage:  By repeating the Hall measurements for all of the other contacts, the sheet carrier density can be found from:  where the sign of the voltage sum (Hall voltage) indicates the type of the majority carriers (electrons or holes). By knowing the sheet carrier  density from Eq. (4-7) and the thickness of the film (d), the film carrier concentration can be calculated from: ݊ ൌ ݊௦/݀. In this study, electrical conductivity, carrier type, concentration and mobility were calculated using Eqs. (4-2), (4-5) and (4-7).  ݁ିగோಹ/ோೞ ൅ ݁ିగோೇ/ோೞ ൌ 1 (4-5)   ଵܸଷு ൌ ଵܸଷା െ ଵܸଷି (4-6)   ݊௦	ݎ݋	݌௦	ሺܿ݉ିଶሻ ൌ ݍܤܫ	ሺ ଵܸଷு ൅ ଷܸଵு ൅ ଶܸସு ൅ ସܸଶுሻ ൌܤܫݍ ுܸ  (4-7)    61  4 . 4 .  Sample fabrication and experimental setup  A set of nominally undoped GaAs1-x Bix (0<x ≤21.5%) films were grown on 350 μm thick SI-GaAs (001) substrates in a VG-V80 MBE reactor. Duri ng operation, the MBE shroud was cooled to ~ -80°C with a polysiloxane heat transfer fluid [ 28], [29]. Each sample consists of a 300-500 nm GaAs buffer layer, followed by a GaAs 1-x Bix  epilayer grown at low temperatures (200<T sub<300°C). The thickness of the layers was gra dually decreased from 500 to 15 nm with increasing Bi content, to avoid strain relaxa tion and also to minimize surface roughening due to build-up of Ga-Bi droplets on the surface. After growth, layers cove red with metallic droplets were wet etched using HCl:H 2O solution (1:4 ratio) for 2 min to re move the surface oxide and metallic droplets. As shown in Figure 4-1, samples were cleaved into 7.5×7.5 mm squares and then using a shadow-mask technique, four corner Ti/Pt/A u contacts (50/100/200 nm ) were deposited by electron beam evaporation. This metal contact is shown to have a very low resistivity and be non-rectifying (Ohmic) on p-doped GaAs [83]. Contacts we re annealed for 30 sec at 450 °C to improve conductivity and diffusion into the films. Annealed contacts were  then wire bonded via silver conductive epoxy.  Room temperature Hall effect measurements were performed using an iron-core electromagnet. Figure 4-2 shows th e experimental setup that I desi gned for this work. The direct current of up to 12 A was produced from thr ee phase alternating power which allows the electromagnet to yield a constant magnetic field of up to 1.4 Tesl a. The Hall transport measurements were carried out e ither as a function of the longitudinal current (I) at fixed B (1.4 T) or as a function of B at fixed I. A Keith ley 220 current source and Keithley 197A voltmeter were used for the current-voltage measurements. All measurements were performed in the dark. Samples for the cryostat measurements were  mounted on thin copper plates using GE varnish adhesive. Copper was chosen for its hi gh thermal conductivity. The temperature dependent conductivity and Hall measurement were performed in a Advanced Research Systems closed-cycle He cryostat in the temperature range of 50 to 300 K and with the use of a B=0.27 T permanent magnet. The sample in the cryostat was shielded thermally and optically from the ambient environment using aluminum foil. The temperature of the sample was monitored using two calibrated diode thermometers; one was placed clos e to the sample at the sample mount and the other placed on the cryostat cold head.  62   Figure 4-2: Conductivity and Hall mobility testing setup with iron-core electromagnet.  4 . 5 .  Results and discussion In covalent semiconductors, it is typical to assume that the Fermi energy is pinned at mid gap at the surface. At the epilayer/substrate interface, the film Fermi energy needs to align with the substrate Fermi energy. These assumptions result in band bending and the formation of depletion widths at the surface ( ݀௦ሻ and the substrate interface ሺ݀௜ሻ	of the epilayer [84]. Therefore to correctly estimate the electrical properties in Eqs. (4-5) and (4-7 ), these widths need to be subtracted from the epilayer thickness, ݀ ൌ ݀௧௢௧ െ ݀௦ െ ݀௜. To examine whether it is necessary or not to subtract the depletion widt hs from the film thickness of GaAs 1-x Bix  alloys, as shown in Table 4-1, electrical transport measurements we re carried out on several ~10% and 14% undoped GaAs1-x Bix  pair samples, one thin and one thick to expl ore the effect of the surface depletion layer. Two thin ~5% Bi samples are also shown in this Table. Based on Eqs. (4-5) and (4-7), the sheet resistance (ܴ௦) and sheet carrier density (݊௦ሻ	were calculated for each sample. Moreover, bulk carrier density and the surface depletion width were  also calculated from the thickness of each layer and listed in Table 4-1. The depletion widths are calculated from the abrupt depletion edge approximation at the surface as described elsewhere [84]. As ܴ௦ and ݊௦	are not dependent on the  63  film thickness, we expect a larger sheet resistivity and smaller sheet carrier concentration in thin samples than thick ones. Nevertheless, no systematic difference in the sheet resistance and sheet carrier concentration of the pair thin and thick samples were observed. Contrary to expectation, the thin samples in our study also show slightly hi gher bulk carrier densities than the thick samples.  One interpretation of this result is that the depletion width is relatively small due to the presence of a high density of localized states [12], [69], [73], [85] in the bandgap of the GaAs 1-x Bix  alloys. Moreover, at the surface of the GaAs1-x Bix  epilayer, the Bi concentration is higher than in the bulk due to the tendency of Bi to surface segr egate. This results in the formation of a strongly p-type surface layer which induces  the band bending at the surface, similar to Figure 4-3 diagram. The strong p-type conduc tivity in high Bi concentration alloys is illustrated in Figure 4-5. From the conductivity data we conclude  that the p-type conductivity at  the surface is due to the high surface Bi concentration pins the surface Fermi level near the valence band.  In this case the surface band-bending will be small and the depletion width correspondingly thin. The band diagram in Figure 4-3 implies a higher density of accumulated holes at the surface for the thin samples and a higher bulk carrier densit y in thin samples, as is observed experimentally.  A narrow depletion width is also expected to form at the GaAs 1-x Bix /GaAs interface, since the MBE grown GaAs buffer layer has a low density of states  in the bandgap relative to the GaAs1-x Bix  epilayer.   Table 4-1: Initial electrical transport measuremen ts of several thin and thick GaAsBi films. Bi (%) Thickness (nm) Sheet resistance, Rs (Ω / □) Sheet carrier density (cm-2 ) Bulk carrier )3-density (cm Surface depletion width (nm)* 5.7 54 9.8×10 7 1.3×10 9  2.4×10 14  778 4.2 500 2.2×10 8  6.2×10 8  1.3×10 13  1925 9.6 25 4.5×10 6  5.1×10 11 2.0×10 17 43 10 91 2.3×10 6  1.2×10 11 1.3×10 16  146 9.7 120 3.7×10 6  7.5×10 11 6.3×10 16  72 13.5 15 7.4×10 5 2.6×10 12 1.7×10 18  18 14.0  75 1.1×10 5 1.3×10 12 1.7×10 17 45 *Barrier height of ߶஻ ൌ ா೒ଶ௤ is considered for calculation of depletion width.  64   Figure 4-3: Proposed band diagram for GaAsBi/GaAs heterostructure. The Fermi level is pinned at the surface near the valence band due to high surface Bi concentration. At the GaAsBi/GaAs interface, the Fermi level is pinned due to presence of Bi induced states. The diagram is to scale for 10% Bi concentration.   4.5.1.  Room temperature electrical transport  Figure 4-4 demonstrates the room temperature (T=293 K) conductivity ( σ) as a function of Bi content at B=0 T for the GaAs 1-x Bix epiliayers. The data reveal a nearly exponential increase in conductivity with increasing x up to ~22% Bi. Su ch a significant increase in conductance of nominally undoped films is unexpected and suggests that high concentrations of Bi creates donors or acceptors in GaAs. The electrical conductivity of GaAsBi epilayers are much larger than the conductance of semi-insulating GaAs ( σGaAs <10 -7  Ω -1 cm-1 ). Conductivity data from the Pettinari et. al study on un-doped GaAs 1–x Bix  films at 300 K and 250 K temper atures are also presented in this figure [81]. The 250 K results and the 300K data in 8<x<11% Bi  range show ge neral agreement with our data at 293 K temperature, although si gnificant higher conductivity were reported at 300 K temperature in low Bi contents [81].  As described in section 4.3, the Hall voltage (V H) was acquired for each sample from two different experiments: as a functio n of the longitudinal current (I) at fixed B (1.4 T) or as a function of B at fixed I. In both confi gurations, a linear dependence of VH on I and B was observed. The sign of VH shows p-type hole conductivity in all nominally un-doped GaAs 1-x Bix  samples. Figure 4-5 shows the compositi onal dependence of the free hole concentration at room   65   Figure 4-4: Compositional dependence of room temperature electrical conductivity of nominally un-doped GaAs 1-x Bix films. The dashed line shows the exponential fit to the data. The square data points are from Ref. [81]. The estimated systematic measurement uncertainty is ~30% for a ll of the data, which is smaller than the sample variability.  temperature, calculated from the Eq. (4-7) for fi xed and variable magnetic field. For most of the samples, similar values of hole concentration are found from both experiments. This measurement reveals that the free hole concentration in nominally un-doped GaAs 1-x Bix increases exponentially with Bi concentration with p=2.2×10 19  cm-3 at 21.5% Bi. Data from the Pe ttinari et. al study at 250 K temperature is also presented in  Figure 4-5, following the similar trend with Bi concentrations [81]. One explanation for the increase in carrier  concentration is the existence of a Bi-induced acceptor level in GaAs1-x Bix  close to the valence band. The results in sections 4.5.2 and 4.4.3, show that the effective density of states at the valence band of GaAs1-x Bix also changes with Bi alloying.     66   Figure 4-5: Compositional dependence of free-hole concentration in un-doped GaAs 1-x Bix  films as obtained from I-V analysis of VH acquired at fixed magnetic field (filled circles) and at variable magnetic field (open circles) at room temperature. The dashed line indicates the exponential fit to the filled circle data. Red square data are from Ref. [81] and were obtained at 250 K temperature. The estimated sy stematic measurement uncertainty is ~30% for all of the data, which is smaller than the sample variability.  The Hall mobility of holes as a function of x, obtained from Eq. (4-2), is shown in Figure 4-6 for V H at fixed and variable magnetic field. In general, the hole mobility decreases monotonically with increasing Bi-conte nt, reaching a low value of ~2 cm 2V-1 s-1  at 21.5% Bi. At high Bi concentrations the mobility data has more scatter due to variability of the mobility in different grown samples and measurement uncer tainty. The low values of Hall voltage (V H) at high Bi concentrations make the measurements more uncertain. Similar measurements at higher magnetic field (B) are desirable, as VH increases with B which reduces the experimental uncertainty. Considering data from Figure 4-5 and Figure 4-6, the hole mobility in GaAs 1-x Bix follows the relation ߤ ൌ ఓ೚ଵାሺ௣/௣೚ሻഀ, with these parameters: µo =263 cm2V-1 s-1 , po=1.7×10 13  cm-3   67   Figure 4-6: Hole mobility as a function of Bi content in un-doped GaAs 1-x Bix  films, as well as p-GaAs doped with carbon grown at conventional (T sub= 550 ºC, As 2:Ga BEPR=6) and unconventional (T sub= 330 ºC, As 2:Ga BEPR=3) growth conditions. Literature mobility data of un-doped GaAs 1-x Bix  films (red squares) [81] and carbon doped p-GaAs1-x Bix  films (blue triangle) [80] are also shown for comparison.    and α =0.39. A similar relation was found previously for p-doped GaAs [86]. Literature mobility of un-doped (red squares) [81] and carbon doped (blue triangle) [80] GaAs 1-x Bix  films are also presented in Figure 4-6, showing ge neral agreement with our data for low Bi concentrations. The mobility data in Figure 4-6 does not support the s uggestion by Pettinari et. al [81] that the hole mobility increases for x>8% due to energy band tran sport in the presence of high densities of Bi clusters. In this study, two identical 500nm thick p-GaAs films doped with carbon to ~2×10 17 cm-3  level were also grown at conventional (T sub= 550 ºC, As 2:Ga BEPR=6) and unconventional (T sub= 330 ºC, As 2:Ga BEPR=3) growth conditions. As shown in Figure 4-6, p-GaAs growth at low temperature similar to the bismide growth condi tions, has a ~2.6× reduction in the hole mobility,  68  likely due to presence of more scattering centers su ch as point defects for low temperature growth. As the GaAs1-x Bix  films discussed in this work were grown at lower temp eratures (200-270°C) than the two p-GaAs films and demonstrate m obilities comparable to high temperature GaAs samples, we can conclude that the reduction in hole mobility in the GaAs1−x Bix  alloys is uniquely due to the incorporation of Bi and not to changes in the structure or the unconventional growth conditions.  4.5.2.  Temperature dependence of conductivity and hole mobility Temperature dependent conductivity and Hall measurements were carried out on several GaAs1−x Bix  samples. Figure 4-7 shows the temperatur e dependence of the hole concentration of three high Bi content films in the 65-300 K temp erature range. A nearly exponential temperature dependence is observed with the ch aracteristic activation energy of ΔE~29-32 meV. A similar activation energy (ΔE=26.8 meV) is also reported by Pettinar i et al. [81] from measurements on an un-doped 10.6% Bi sample (red data in Figure 4-7). This behavior suggests that Bi induces shallow acceptor levels near the valence band of hi gh Bi content materials. Based on the expression for the hole concentration, ݌ ൌ ௏ܰexp ቀെ ∆ா௞ಳ்ቁ, the characteristic activation energy (∆ܧሻ indicates the location of the Fermi level relative to the valence band. It is noteworthy that ΔE~29-32 meV activation energy of the shallow ac ceptor states is in good agreement with the 24-40 meV Urbach band tail parameter previously discussed in section 3.5.2. The inset in Figure 4-7 shows the hole concentr ation at infinite temperature (y-intercept) in the main figure as a function of Bi content. The y-intercept has a near ly exponential increase with Bi composition and is proportio nal to the hole effective density of states in the valence band ሺ ௏ܰሻ. This suggests that ௏ܰ of high Bi content materials increases with Bi incorporation. Figure 4-8 shows the calculated hole mobility as a function of temperature for 13.5, 17.6 and 21.5% Bi films (previously discussed samples in Figure 4-7). The mobilities for these films are observed to be low and have a weak temperature dependence. Below 150 K the hole mobility is observed to increase. This behavior suggests that phonon (ߤ௣௛ ൌ αܶିଵ.ହሻ and temperature independent Bi alloy related scattering are the dominant scattering mechanisms in high Bi content  69  films in the 75-300 K temperature range [87]. Similar weak temperature dependence of hole mobility in the 100-300 K temperature range was also  reported by Beaton et al. [80] from p-doped GaAs1-x Bix  films with 0.9 ≤ x ≤ 5.5 %. In particular, Beaton et  al. found that a 5.5% Bi sample exhibited near zero temperature dependen ce in the 75-300 K temperature range [80].    Figure 4-7: Temperature dependence of the hole concentration in high Bi content GaAs1-x Bix  films. Data from Ref. [81] (red squares) for 10.6% Bi film is shown for compar ison. Solid lines are exponential fits to the data, showing nearly a constant characteristic activation energy of ~27-32 meV. Inset sh ows the y-intercept (infinite temperature) for the hole concentration fits in the main figure as a function of Bi content.   Figure 4-8:  Hole mobility as a function of temperature for three high Bi content GaAs1-x Bix  films.  70  4.5.3.  Variable range hopping in GaAs 1-x Bix  alloys Temperature dependent Van der Pauw c onductivity measurements on several GaAs1-x Bix  alloys are presented in Figure 4-9. The electrical cond uctivity decreases exponen tially with temperature and at lower temperatures (T ≲150 K), deviation from the exponentia l behavior is observed. Such deviation could be the signature of hopping conduction of holes in tail states or localized states above the valence band. Mott variable range hopping (VRH) theory describes the low temperature behavior of the conductivity in strongly disordered systems where st ates are localized. In particular VRH is observed in highly doped and lightly doped compensated crystalline semiconductors. Assuming a relatively constant density of localized states in the vicinity of the Fermi level, the VRH conduction is characterized by a temperature variation as follows [88]:    here ߪ଴ is the hopping conduction prefactor which in general is defined as: ߪ଴ ൌ 2݁ଶݎ௜௝ଶ݃ߛሺܧ௙ሻ, where ݎ௜௝ is the distance between localized state i and j, ߛ is the hopping rate of carriers between the states and the ݃ሺܧ௙ሻ is the density of states at the Fermi level [88]. The exponent factor ଴ܶ is defined by: ଴ܶ ൌ ఈ௚ሺா೑ሻ௞ಳ௔ಳయ 	, where kB is Boltzmann’s constant, 	ܽ஻ is the effective Bohr radius which is assumed to be equivalent  to the localization radius for states near the Fermi level and α is a unit less constant calculated to be ~18 [89]. The parameter ଴ܶ is inversely proportional to the density of centers participating in hopping conduction.  Considering the VRH conductance at low te mperatures, and the typical form of conductivity for an extrinsic semiconductor at higher temperatures, ߪ௘௫ ൌ ߪ௖݁షሺಶಷషಶೇሻ಼೅ , the total conductance can be written as a su m of the two conductance channels:  ߪ௜ ൌ ߪ଴݁ିቀ బ்் ቁభ/ర (4-8) ߪሺܶሻ ൌ ߪ௜ ൅ ߪ௘௫ ൌ ߪ଴݁ିቀ బ்் ቁభర ൅ ߪ௖݁ିሺாಷିாೇሻ௄்  (4-9)  71   Figure 4-9: Electrical conductivity as a function of (a) T-1/4  and (b) T-1 for un-doped GaAs 1-x Bix films. The lines in (a) are the exponential fit functions to the low temper ature parts of the experimental data and yield σ0 and T0 in Eq. (4-8). The lines in (b) are calculated from Eq. (4-9) with the parameters listed in Table 4-2.   There are four free parameters in the above equation ( ߪ଴, ଴ܶ, ߪ௖, ܧி െ ܧ௏ሻ. To correctly evaluate these parameters, first the conductivity data is plotted vs. T-1/4  in Figure 4-9 (a), showing good agreement with Eq. (4-8) at T ≲ 150 K for all films. Fitting the exponential functions to the low temperature part of the experiment al data in Figure 4-9 (a) yields ߪ଴, ଴ܶ parameters. Then, the experimental data are plotted vs. T -1 to find the other two paramete rs. Figure 4-9 (b) shows the conductivity data and the fit functions. Equation (4-9) provides a good f it to the experimental data.  The fitting parameters are listed in Table 4-2. With the exception of the 18.7% Bi sample, the ଴ܶ parameter is shown to be near ly constant for all of the GaAs1-x Bix samples, with an average value of ~6200 K. This suggests that the density  of localized states near the Fermi level participating in hopping conduction is nearly constant and independent of Bi alloy concentration. The hopping conduction parameter, ߪ଴, increases strongly with incr easing Bi-content. As shown earlier in Eq. (4-8), ߪ଴ parameter has a linear dependence on the hopping rate of carriers (ߛሻ. Thus, the increase in ߪ଴ could originate from the high sensitivity of the hopping rate of carriers to small changes in the density of Bi-induced localized states near the Fermi level. The hopping rate involves tunneling of carriers between the neighboring local ized states, which depends  72   Table 4-2:  Sample details and calculated Mott’s and conductivity parameters from Eq. (4-8) and Eq. (4-9).  Bi% p (cm-3) T0 (K) σ0 ( Ω-1  cm -1 )  Ef - Ev (meV)  σc ( Ω-1  cm -1 )  5.8 2.4×10 14  6079 0.0008 115 0.1 9.7 7.0×10 16  6126 0.01 47 0.2 13.5 1.0×10 18  5755 1.1 45 2.0 17.6 4.5×10 18  6150 3.0 38 3.7 18.7 1.5×10 19  3164 5.7 34 4.0 21.5 2.2×10 19  6560 4.5 38 12.5  exponentially on the separation of the states. Table 4-2 also presents the Bi composition de pendence of the other two fitting parameters: ܧி െ ܧ௏ and ߪ௖. With the exception of the 5.8% Bi  sample, the Fermi energy parameter,	ܧி െ ܧ௏, of high Bi content GaAs1-x Bix  is nearly constant at 34-47 meV above the valence band. Within the experimental and fitting errors, the infe rred Fermi energy parameters are close to ΔE~29-32 meV activation energy that previously obtained in section 4.5.2 from th e temperature dependence of the hole concentration measurements on high Bi content films. A higher value for the Fermi energy, 115 meV, is estimated for the 5.8%  Bi sample. Similar anomalous behavior in the density of shallow electronic defects, e.g. Urbach parameter, have been observed in other measurements for Bi concentrations near 5%, wh ich are summarized in section 3.5.2 and might be related to the higher value of the Fermi level for the 5.8% Bi sample. Like ߪ଴, the ߪ௖ parameter also grows with increasi ng Bi content. This behavior of ߪ௖ suggests that the effective density of states in the valence band ሺ ௏ܰሻ for GaAs1-x Bix  alloys increases with Bi alloying, since the hole mob ility shows only a weak dependence on Bi content in the relevant concentration range (see Figure 4-6). This inte rpretation can be understood more easily by the following equation, showing explicitly  the parameters that depend on Bi content:  ߪሺݔሻ ൌ ߪ௖ሺݔሻ݁ିሺாಷିாೇሻ௄் ൌ ݊ߤݍሺݔሻ ൌ ߤݍ ௏ܰሺݔሻ݁ିሺாಷିாೇሻ௄்  (4-10) 73   Based on the Bi compositional dependence shown in Eq. (4-10), the increase in the room temperature conductivity and hole concentration for high Bi concentrations discussed in section 4.5.1 is mainly associated with the increase in  the density of states at the valence band edge of GaAs1-x Bix  alloys.   4 . 6 .  Conclusion We have measured the p-type hole conductivity in nominally un-doped GaAs 1-x Bix  epilayers for a wide range of Bi-content (0<x ≤21.5%). Room temperature c onductivity and hall transport measurements (B up to 1.4 tesla)  reveal an exponen tial increase in p-t ype conductivity with increasing Bi-content, where σ ~10 Ω -1 cm-1  and p=2.2×10 19  cm-3  at 21.5% Bi. The hole mobility decreases monotonically with increasing Bi-content to ~2 cm 2V-1 s-1  at 21.5%. The reduction in mobility associated with Bi incorporation and is not due to changes in the structure or unconventional growth conditions for GaAs. The incr ease in carrier concentration with Bi-content is believed to be due to the existence of Bi  related acceptor levels. Temperature dependent measurements show that the Fermi level pinned at ~30-47 meV above the valence band in high Bi content films (10<x<21.5%). In a ddition, these measurements reveal that the effective density of states in the valence band increases with Bi incorporat ion. At low temperatures (T ≲150 K), the electrical conductivity is found to be govern by variable-r ange-hopping conduction in shallow localized states.      74  C hapter 5   Photovoltaic response of GaAs and dilute GaAs1-x Bix p+/n solar cells    The following chapter discusses the fabr ication and operation of dilute GaAs1-x Bix  photovoltaic devices under one sun illumination. These results are also compared to similar measurements on conventional and unconventional (low temperatur e and low As) grown GaAs based solar cells. The photo-absorption and emission spectral response of devices were explored in this chapter. The experimental results were modeled employing the theoretical concept of diffusion and drift of photogenerated carriers in a similar p+/n structure. An analysis of the model reveals information about the lifetime of photo carriers in GaAs and GaAs1-x Bix  alloys.   5.1.  Contributions  Samples characterized in this chapter were gr own by R.B. Lewis. The author helped with calibration of the MBE dopant sources prior to the growth of the samples. All post-growth sample preparations including metal contact deposition, photolithography fabrication and wet etching the devices were carried out by the author. The pho tolithography photo masks were designed by the author and A. Jooshesh from the optical system s and technology lab (OSTL) at the university of Victoria. The initial I-V characteristic test a nd photoluminescence experime nts were performed by the author. Solar performance tests were carried ou t by Zenan Jiang at the U BC flexible electronics and energy lab (UBC-FEEL). My contribution wa s in designing the experiments, providing samples and initial motivation, as well as carrying out the device modeling and the analysis of the results.    75  5 . 2 .  Motivation Solar radiation is a clean and free energy source for generation of electricity. Figure 5-1 presents the standard irradiance spectra of sun in space (AM0) and at global terrestrial (AM1.5G) environments. These radiation spectra have an integrated power density of 1367 W/m 2 and ~1000 W/m 2 respectively. One requirement for engineering an  efficient solar cell is to employ materials that can absorb photons in the solar spectral range, namely from 300 to 2500 nm. The III-V compound semiconductors cover most of the solar spectral range and in fact they are demonstrated to be among the most efficient solar materials [1], [90]. In particular, the large decrease in optical bandgap with Bi incorporation (e .g. see Chapter 3), makes GaAs 1-x Bix  alloy a potential solar material that can absorb infrared radiation below the bandgap of GaAs (λ> 870 nm). This potential advantage of bismide alloys over GaAs is illustrated by the green color in Figure 5-1.  Semiconductors with tunable bandgaps can be used to improve the efficiency of multi-junction solar cells. For instance, the efficiency of lattice matched triple-junction In0.49 Ga0.51P/GaAs/Ge solar cells with the sequen ce of 1.90/1.42/0.67 eV band gaps, could be increased by adding a fourth junction with a 1 eV band gap [1].  Currently the dilute nitride materials (e.g. GaAsN, GaInNAs) are strong candidates for this purpose. However, nitrogen (N) incorporation degrades the material quality and th e growth of high quality dilute nitride materials on GaAs or Ge substrates is challenging [13], [91]. Based on the results in Chapter 3, the 1 eV bandgap can also be achieved with 6.5% Bi incorporation. In fact, there is a potential advantage in using GaAs1−x Bix  instead of GaAs1−x Nx , since the electron mobility is found to significantly decrease with N alloying (e.g. ~20× reduction with  1% N incorporation) while no degradation in electron mobility is observed up to 1.2% Bi all oying [79], [92]. The co-allo ying approach of N and Bi, GaAs1−x −yNx Biy, is also promising for having GaAs or Ge lattice matched 1 eV junction. The GaAs1−x Bix  alloy has already been used as the active region in optoelectronic devices such as lasers [22], [9 3] and light emitting diodes [21], [75], however to date, no investigation has been reported yet on the solar response of a photovoltaic cell having a GaAs1−x Bix  active layer. In this regard, single junction GaAs and dilute GaAs1−x Bix  based p+/n solar diodes grown by MBE were investigated to examine the effect of Bi  for the first time. This study could open up the possibilities for using GaAs1−x Bix  material in photovoltaic applications.   76   Figure 5-1: Standard solar irradiance spectra in space (AM0) and terrestrial (AM1.5G) environments. The green colored area shows the extended spectra l range that can be absorbed by GaAs1-x Bix  alloys.   5 . 3 .  Experimental section 5.3.1.  Device fabrication  Epitaxial p+/n junction diodes were grown by MB E on Si-doped GaAs (001) substrates. Figure 5-2 illustrates the typical layer structure of the bismide p+/n cell in the solar test setup. In the growth process, the MBE shroud was cooled to ~ -80°C with  a polysiloxane heat tran sfer fluid [28], [29]. Ga-type effusion cells were used for Ga and Bi, and an As cracker was used for As 2. A solid Si source and CBr4  source were used as n and p type dopants, respectively. The heavily n-doped GaAs buffer layer and capping p+ GaAs layers were grown at standard conditions (substrate temperature of 580 °C, As:Ga flux ratio of 6) while the bismide layers were grown at lower temperature (Tsub=330 °C) and at As:Ga flux ratio of ~2. The Bi flux was varied to yield different alloy compositions while maintaining the same grow th rate as buffer growths (i.e. ~1 µm/h). In this way abrupt GaAs 1x Bix /GaAs interfaces were formed. For comparison, pure GaAs structures were also grown: one GaAs in the same growth conditions as the GaAs 1x Bix  layers but with no Bi flux, and another GaAs structur e at standard growth conditions  (high temperature and As-rich  77   Figure 5-2:  Layer structure of p+/n solar cell under AM1.5G incident light. The top electrode is semi-transparent Au thin film. The cross sectional drawing is not to scale.   environment). The thickness of the layers and the Bi  content of the structures were determined by the growth rate and the high resolution x-ray diffraction (HRXRD) measurements. The net donor concentration in the n-doped laye r was determined by Mooney et al . from the capacitance-voltage (C-V) measurements on separate pieces of the sa me samples [85]. The acceptor concentration in the p+ layer was determined from resistivity-Hall measurements on calibration p-GaAs 1x Bix  and p-GaAs samples. Table 5-1 summarizes th e specification of the grown structures. After growth, large area N i/AuGe/Au (25/100/200 nm) Ohmic contact were deposited by electron beam evaporation on the back side of th e Si-doped substrates. On  the front side, 10 nm Au in a pattern as shown in Figure 5-2 was de posited using standard photolithography procedures. Samples were mesa etched in H 2SO4 :H 2O2:H 2O (4:1:5 volume ratio) Piranha solution to isolate the devices. The devices were etched through the p+/n interface into the n+ GaAs buffer layer, typically ~2 µm.   78  To identify the transmission of the top metal contact layer, optical transmission measurements were conducted on a 10 nm Au/g lass substrate. Figure 5-3 (a) shows the experimental transmission spectrum (solid line) as well as the simulated spectra (dashed lines) for 7, 10 and 13 nm of Au on SiO 2 substrates1. Although the simulated curves were not exactly matched to our experimental data, the average tran smission level of the deposited Au film is shown to have more agreement with 7 nm thick Au calc ulated curve. Therefore, it is inferred that the thickness of the deposited Au film is thinner th an 10 nm. As the transmission of Au/GaAs is important to estimate the optical power that tran smitted into the solar cell active layers, the 7 nm thick Au is used to simulate the transmission  spectrum of Au/GaAs substrate, as shown in Figure 5-3 (b). The average transmission in 400-1000 nm spectral window is found to be near 0.53. Thus, the optical power density of AM1.5G incide nt light transmitted through the top metal contact into the p+/n diode struct ure is estimated to be Pd ~53 mW/cm 2 in this work.   Table 5-1:  Specifications of GaAs and GaAsBi p+/n grown samples.  Sample No. Bi (%) Growth temp. (ºC) Estimated bandgap (eV) *** *  N D  (cm -3 ) *   N A   (cm -3 ) n layer thickness (nm) p+ layer thickness (nm) r2321 0 580 1.42 9×10 16  3×10 18  1000 500 r2336 **  0 330 1.42 2×10 17 3×10 18  580 500 r2331 0.3 330 1.40 6×10 16  3×10 18  595 82 + 416 ***  r2337 0.7 330 1.36 4×10 16  3×10 18  595 82 + 416 ***  r2346 1.1 330 1.33 5×10 16  3×10 18  595 82 + 416 ***  * N D values were obtained from the C-V measurements [85]. ** This sample is grown at conditions similar to GaAsBi p+/n samples but without Bi flux. ***  Thickness of top p+ GaAs layer. **** The bandgap values were estimated from the fit to the optical absorption data discussed in section 3.5.2.                                                  1 The simulations were performed using a freeware online tool for optical thin-films calculations [117].  79   Figure 5-3: (a) Transmission spectrum of 10 nm Au deposited on a glass substrate (black solid line). Dashed lines show the calculated transmission spectra at different thickn ess of Au. Based on the calculations, the thickness of the deposited Au film is estimated to be 7 nm (b) Simulated transmission spectrum of 7 nm Au on GaAs substrate. The average transmission is ~ 0.53 in 400-1000 nm spectral window.      To characterize each device as shown in Figure 5-2, the large pad side of the front contact was covered with silver conductive paint and then a wire bond was made to the back Ni/AuGe/Au contact. The top patterned contact was exam ined by the optical microscope and only the transparent areas were counted as the active area. In this regard, the area of silver painted pad was also not considered.    80  5.3.2.  Device characterisation setups For measuring the photovoltaic (PV) performance of devices, the fabricated devices were placed in front of a 150 W Xenon lamp (Newport Co.), passing through a AM1.5G filter at room temperature. The total optical power density was ~100 mW/cm 2. The devices were connected to a computer-controlled Keithley 2400 source meter,  for the current–voltag e (I–V) measurements. The external quantum efficiency (EQE) was obtaine d at zero bias using monochromatic light from a monochromator (Cornerstone 130, Newport C o.) in the 400-1100 nm spectral range and by measuring the current and voltage of the device. The quantum efficiency is not measured below ~400 nm as the power of AM1.5 light source is very low at thes e wavelengths. These measurements were carried out by Zenan Jiang at UBC flexible  electronics and energy lab (UBC-FEEL).  In the above experiments as s hown in Figure 5-2, the light source was grea ter than the size of the p+/n cell, therefore the incident light c ould also generate carriers out of the device active area in the n+ GaAs buffer substrate. As the di ffusion length of minority carriers in highly doped GaAs are generally much shorter than the thickness of the substrate, e.g. Lp < 3 µm for 3×10 18  cm-3  n+ GaAs [94], it is expected that generated carriers more than 3 µm from the contact do not contribute to the photo-current as  they recombine before they can diffuse to the junction. Samples were also excited with a 532 nm 20 ns pulsed diode-pumped solid state laser at room temperature for photoluminescence (PL) measurements. The average power of the laser was 1.5 mW, at a repetition rate of 2 kHz and peak power density of 10 5 W/cm 2 with a spot size on the sample of ~3 mm. The PL was dispersed using a SpectraPro-300i spectrograph and then detected by a liquid nitrogen-cooled InGaAs array detector.   5 . 4 .  Results and discussion 5.4.1.  Device performance Figure 5-4 presents the current density vs. voltage (J -V) characteristic curves of fabricated devices in the dark (dashed lines) and AM 1.5G (solid lines) conditions. All GaAs and GaAs1x Bix  diodes show photovoltaic (PV) operation under illumina tion. Relatively large reverse dark leakage  81  currents are observed for most of the samples. The leakage current is increa sed by the fact that the whole area of each device, including the Au cont act pad and the area covered by silver paint, contributed to the dark current , while only the exposed Au area contribute to the photo current. The performance parameters of each cell, such as dark current density ( JDark), open circuit voltage (Voc) and short circuit current density (JSC), are extracted from J-V measurements and listed in Table 5-2. Based on these parameters, the fill factor ( FF) and the power conversion efficiency ( η) are calculated from the following equations [90]:    where ܬ௠ and ௠ܸ are quantities for the maximum power output and Pd is the incident optical power density that transmitted to the p+/n junction whic h as mentioned earlier, is estimated to be ~53 mW/cm 2 in this work. For an ideal diode, the open circuit voltage (Voc) is defined by:   where IL and Is are the photocurrent and the reverse saturation current, respectively. The Voc decreases with increasing reverse saturation current. A similar relation is observed experimentally in Table 5-2. Generally, the fill factor and power conversion effici ency values are lower than we expected.  The unconventional low As, low temperature grown GaAs  diode (r2336) gives much higher reverse dark current than the conventiona l grown diode (r2321), as shown in Table 5-2. The high level of dark current lowers the open circui t voltage and also the pow er conversion efficiency of the r2336 device. This increase in dark cu rrent with unconventional growth conditions is expected as the incorporation of As Ga defects in GaAs increases at lower growth temperature [43]. For this reason, in the unconventional grown GaAs cell photo- carriers recombine on the AsGa ܨܨ ൌ ܬ௠ ௠ܸܬ௦௖ ௢ܸ௖  			ߟ ൌ ௠ܲ௜ܲ௡ൌ ܬܨܨ௦௖ ௢ܸ௖ௗܲ (5-1) ௢ܸ௖ ൌ ݇ܶݍ ln ൬ܫ௅ܫௌ ൅ 1൰ ൎ݇ܶݍ ln ൬ܫ௅ܫௌ൰ (5-2)    82  defects before they can diffuse out of the device. These observation reveal that unconventional low temperature GaAs is not a suitable material  for photovoltaic applications. Nevertheless, all GaAs1x Bix  devices grown under the same unconventi onal conditions demonstrate much lower dark current and higher open circuit voltage than  sample r2336. This indicates that by introducing Bi in GaAs at unconventional growth conditions, fe wer defects are incorpor ated into the growing film. In fact, a similar conclusion was also repo rted by Mooney et al. from deep level transient spectroscopy (DLTS) on the same p+/n samples [85] . The DLTS measurements demonstrated that the incorporation of Bi suppresses the formation of electron traps with activation energy of 0.40 eV by more than a factor of 20 compared to GaAs grown under the same conditions [85].       Figure 5-4: J-V behavior of GaAs and GaAsBi p+/n diodes in the dark (dash lines) and under AM 1.5G illumination (solid lines). The measurements were performed by  Zenan Jiang in UBC-FEEL lab.     83  Table 5-2 : Extracted photovoltaic performance parameters from the I-V experiments.  Sample No. Bi (%) Growth temp. (ºC) J Dark  at -1 V (mA/cm 2 ) V OC  (V) J SC  (mA/cm 2 ) Fill factor      (%) PCE   η (%) r2321 0 580 44.4 0.40 27.6 26.5 5.8 r2336 0 330 > 360* 0.19 8.8 26.7 0.9 r2331 0.3 330 29.0 0.53 20.0 29.4 5.9 r2337 0.7 330 0.9 0.59 12.0 45.0 6.0 r2346 1.1 330 6.8 0.47 9.0 35.5 2.8 *the current meter is over-limit.  As shown in Table 5-2, the GaAs 1x Bix  diodes demonstrate photovoltaic performance comparable to the standard grown GaAs cell. Ge nerally, larger open circuit voltage with lower reverse dark current and higher fill factor (~30-45%) were observed from GaAs 1x Bix  cells than GaAs ones. Although most of the diodes investigated in this study were show n to have a high dark current in the absence of light, the 0.7% Bi (r2337) device gives low dark current, with near ideal diode performance. Thus, it is more reliable to count on the PV performance of this device than others. The 0.7% Bi cell demonstr ates the largest open circuit (Voc=0.59 V), fill factor ( FF= 45.0%) and the power conversion efficiency ( η=6.0%) among our samples.  In general, GaAs1-x Bix  samples show lower short circuit current ( Jsc) than for GaAs. The low photocurrent (i.e. Jsc) could originate from the short diffusion lengths of the carriers and/or high recombination rate of carriers at the surfaces. As a result, the PV performance parameters of our devices are lower than the highest reported values from similar GaAs p+/n layer structures under AM 1.5G spectrum: Voc~1.0 V, Jsc= 23.2 mA/cm 2 , FF=79.7% and  η = 18.4% [1], [95].  It should be noted that the above mentioned device was grown on a large area polycrystalline  Ge substrate, and the layer structure was optimized for maximum Voc.  To investigate the performance of GaAs1x Bix  solar cells further, the spectral external quantum efficiency (EQE) and PL measurements were performed. The EQE of solar devices at zero bias are shown in Figure 5-5 (a). The EQE is calculated from the ratio of the number of charge carriers collected by the solar cell to the number of photons at a given energy shining on the device.  84  In general, values of EQE up to ~0.45 are observed from GaAs and GaAs 1x Bix  cells. However, the measured EQE at wavelengths above the ba ndgaps are lower than our expectation, possibly due to the high surface recombination rates and/or  short diffusions lengths of the photo carriers. The high front surface recombination could contribute in the EQE at short wavelengths, e.g. 400-600 nm in Figure 5-5 (a), and the back surface r ecombination and low diffu sion in the body of the cell could result in lowering the EQE at longer wavelengths. The GaAs cells demonstrate non-zero quantum efficiency up to thei r absorption bandgaps, namely λ< ~890 nm. Below the GaAs band edge, the quantum efficiency is zero, as expect ed. With the introduction of Bi into GaAs, a non-zero EQE below the GaAs bandedge is obtained, indi cating that the photon absorption and carrier generation have taken place in GaAs 1x Bix  alloys at longer wavelength s than that in GaAs. The spectral EQE is shown to expand to the infrared w ith increasing Bi content. The current collected with incident photon energies be low the GaAs band edge gives 1.2%, 2.1% and 2.9% of the total photo current, respectively, for 0.3%, 0.7% and 1. 1% Bi samples. This confirms that GaAs 1x Bix  alloys extend the photovoltaic ope ration of solar cells to longer wa velengths than in the case of GaAs.   The standard grown GaAs solar cell (r2321) is efficient at capturing carriers generated by light with the wavelength of 600 nm to near the GaAs band edge (~850 nm) with EQE reaching ~0.45. In comparison, the low temperature low As  grown GaAs cell (r 2336) shows ~3× lower EQE. This supports the idea that low temperature grown GaAs is not an efficient material for photovoltaic applications. Nevertheless, the unconventional grown GaAs 1x Bix  devices exhibit better EQE response than the low temperature GaAs (r2336), reaching a maximum EQE of 0.35 for the 0.7% Bi sample. In general, similar EQE response shape is observed for the unconventional grown GaAs and GaAs 1x Bix  solar devices with best quant um efficiency in the 500-700 nm wavelength range. The EQE response shape is diffe rent from the EQE of standard GaAs. The standard GaAs displays an abrupt EQE transition near the band edge, while the unconventional grown devices show much broader EQE transitions near the band edge.  This effect can be seen better in Figure 5-5 (b) where normalized EQE sp ectra are plotted near the bandgap wavelengths.  The 0.7% Bi sample demonstrates a higher EQ E response than the other samples in the 400-500 nm wavelength range. It is surprising to s ee such behavior, as the absorption length for generating the carriers is relatively short at these wavelengths (~ l <100 nm). The reason for this  85  observation could be a lower front surface recombination velocity (Sn). In fact, based on the theoretical calculations in the next section, we have estimated Sn = 6 ×10 5 cm/s for 0.7% Bi sample while other samples have higher values: Sn =10 6 -10 7 cm/s.  Figure 5-5 (b) also presents photoluminescen ce (PL) spectra for each p+/n device. The highest PL peak in each spectrum corresponds to th e band edge emission which shifts to longer wavelengths with increasing Bi content, as expe cted. The PL emission peak for each sample is observed to match well with EQE transitions at  the band edges, indicating the position of the bandgaps. These bandgaps are also close to the estimated values indicated in Table 5-1. Similar to what is seen from PL experiments in section 3.5.2, a longer wavelength PL  emission peak in the 950-1100 nm range (corresponding to 1.12-1.30 eV) is  also observed from these thick GaAs 1x Bix  p+/n samples. This shoulder emission is belie ved to correspond to emission from the radiative defect states in the bandgap. The dashed curves in Figure 5-5 are a theoretical model which is discussed in the following section.  86   Figure 5-5: (a) External quantum efficiency (EQE) spectra of GaAs  and GaAsBi p+/n diodes at zero bias at room temperature. With increased Bi content, the EQE expands to longer wavelengths. The dashed curves are calculated from a p/n junction model that is described in section 5.4.2 (b) EQE and photoluminescence (PL) spectra of p+/n devices near the band edge. The data are normalized to the peak value. The EQE measurements were performed by Zenan Jiang in UBC-FEEL lab.   87  5.4.2.  Solar response simulation  To investigate the physical origin of the solar performance observed in the tested devices, the quantum efficiency is estimated theoretically usi ng a simple 1D steady-state continuity model for photocurrent generation in the front p+ layer, depletion region a nd the substrate n layer of our devices. This model is a well-known approach to estimate the performance of ideal p-n junction solar diodes under low-injection conditions and is  sufficiently accurate to predict the overall photovoltaic operation of practical solar cells [90] . The derivation of the model is explained in Appendix A. In this work, the quantum efficiency  and the photocurrent of the cells are calculated from Eqs. (A-16) and (A-18) respectively, and compar ed to the experimental results in the previous section. These calculations provide a better understanding of the carrier collection properties in GaAs and GaAsBi based materials such as the lifetime of the minority carriers and the interface recombination velocities.  To evaluate the total generated photocurrent, the partial photo current in the front p+ layer, depletion regions, and the substrate n layer are calculated based on Eqs. (A-10), (A-13) and (A-14) at each wavelength, respectively. The photo absorption in each of these layer is taken into account. Figure 5-6 shows the absorption coefficients  data for GaAs and dilute 1.1% GaAs 1-x Bix  that are used as input parameters in our model. As the bandgap of the GaAsBi devices depends on the Bi content of the films, the absorption coefficient near the band edge is shifted to match the bandgap of the layer. Moreover, since the diffusion length of carriers in highly doped GaAs are generally much shorter than the thickness of the substrate, e.g. Lp < 3 µm for 3×10 18  cm-3  n+ GaAs [94], it is expected that most of the genera ted carriers in this region do not contribute to the photo-current as they recombine before they can diffuse through the thick substrate back to the junction. Thus, the photocurrent generation in the n+ GaAs substrate is neglected.  The baseline material doping and the layer thicknesses used in this study are given in Table 5-1. To calculate the di ffusion length of the minority carriers in the doped layers, µn =2000 cm2/Vs and µp =200 cm 2/Vs were chosen. These mobility values were obtained from Hall measurements on the same GaAs doping calibration samples and are in approximate agreement with reported values in the literatures [87]. Based on Eqs. (A-10), (A-13) and (A-14), there are four free parameters in this model: front and back surface recombination velocities ( Sn and Sp) and the minority carrier lifetimes in p+ and n regions ( τn and τp). Each of these parameter has a  88  fingerprint in the spectral response of the solar cell as shown below. Therefore, it is necessary to vary these parameters systematically to correctly simulate the expe rimental EQE data of GaAs and GaAsBi devices.          Figure 5-6: Absorption coefficient data used as an input parameter in the solar response calculations. The absorption coefficient of GaAs is calculated from the extinction coefficient data in Re f. [66]. The absorption coefficient of GaAsBi is calculated from ellipsometry measurements. The GaAsBi sample was prepared in our lab and the ellipsometry measurements was performed by R. Synowicki from J.A. Woollam Company.     89   Figure 5-7: Experimental EQE (red dots) and calculated (dash lin es) quantum efficiencies for the standard grown GaAs cell (r2321). Different values of  the front (a) and back (b) surface recombination velocities are shown to reproduce the experimental results. Minority lifetimes of dop ed GaAs layers are found from Refs. [96], [97] and used as constants for these simulations.   Figure 5-7 shows the experimental EQE spect ra of the standard grown GaAs sample (r2321) together with the simulate d quantum efficiency curves calcu lated from Eq. (A-16). In this calculation, typical values of minority lifetimes in high temperature grown GaAs, τn =10 -10  at Na~3×10 18  cm-3  and τp =10 -8  sec at Nd~10 17 cm-3  [96], [97], were assumed as input parameters for the calculation. The front and the back surface re combination velocities are varied to fit the experimental data. As shown in Figure 5-7, a good fit with the literature  reported lifetimes is possible. As the back contact of  our devices is considered as an ideal Ohmic contact for GaAs, therefore the surface recombination velocity at the back, Sp, is infinite, collecting all the carriers. However with the practical Ohmic contact, Sp will not be infinite, but very large. Therefore, as an initial guess in our model we  choose the large value of 107 cm/s, for Sp. Then as shown in Figure 5-7 (a), the front surface recombination,  Sn, is varied and fitted to the experimental EQE data. A relatively good fit is obtained with Sn~7×10 6  cm/s. It is noteworthy that in general, similar large surface recombination velocities (106 –10 7 cm/s) are reported for the un-passivated (free surface) of doped GaAs [98]. Next by knowing the Sn value, the experimental data is fitted again  90  by varying only the back contac t surface recombination velocity, Sp (Figure 5-7 (b)). As expected,  the long wavelength response (most sensitive to the body of the cell) is influenced with having less effect than changing the Sn parameter. Relatively good fits to the experimental data are obtained when Sp > 10 5 cm/s. With similar procedures and us ing typical GaAs lifetimes (τn =10 -10 sec, τp =10 -8  sec), we have attempted to simulate the EQE spectra of other low temperature grown samples. Reasonable fits were not achieved, indicating that  the minority carrier lifetimes in low temperature grown GaAs and GaAs1-x Bix  alloys are different than the standard grown GaAs. Thus the minority lifetimes parameters were also considered as fitting parame ters in this work. Figur e 5-8 and Figure 5-9 show the experimental EQE (red dots) and the model cal culated (dash lines) quantum efficiencies for GaAs and GaAsBi devices while vary ing the minority carrier lifetimes (τn and τp).  The carrier lifetimes were varied, vary one parameter at a ti me, to reproduce the experimental results. Similar to the results in Figure 5-7 and the literature reports [98], fixed surface recombination velocities of Sn (front) =  Sp (back)= 10 7 cm/s  were used as an initial guess for these simulations. Unlike the effect of the surface recombination velocities, the shape of the spectral response is generally untouched by varying τn. Relatively good fits to the experimental data are attained with lifetimes much lower than that of typical GaAs lifetimes. Th e range of lifetimes that gives the best fits are indicated in each plot. To ensure the reliability of the inferred lifetimes, the surface recombination velocities are varied afterward. In general for all the samples, best fits are obtained with 6×10 5< Sn <10 7 cm/s and Sp >10 5 cm/s. It is noteworthy that similar to the results in Figure 5-7 (b), no change in spectral response is observed by varying 105< Sp<10 10 cm/s for all the samples.       91   Figure 5-8: Experimental EQE (red dots) and model (dash lines) quantum efficiencies for GaAs devices. Minority carrier lifetimes (τn and τp) were varied reciprocally to reproduce the experimental results. Sn (front) = Sp (back) = 107 cm/s were used for these simulations.    92   Figure 5-9: Experimental EQE (red dots) and model (dash lines) quantum efficiencies for GaAsBi devices. Minority carrier lifetimes (τn and τp) were varied reciprocally to reproduce the experimental results. Sn (front) = Sp (back) = 10 7 cm/s were used for these simulations.   93    Figure 5-10: Extracted electron and hole minority ca rrier lifetimes as a function of Bi content from device simulations.  Figure 5-10 presents the extracte d minority lifetimes as a function of Bi content, obtained from the device simulations. Low temper ature grown GaAs shows ~10× and ~10 2-10 3 ×  smaller electron and hole lifetimes than standard grown Ga As. This reduction in carrier lifetimes could be due to an increase in non-radiative recombinati on centers such as As antisites at low growth temperatures. Similar results were reported by Ito et al. [96], as th ey found that the electron lifetime in heavily p-doped GaAs decrease d significantly by lowering the gr owth temperature. As shown in Figure 5-10, much lower electron lifetimes (10-13 < τn <10 -12  sec) are estimated for dilute GaAs1-x Bix  alloys. The reason for such low lifetimes is  unknown although the incor poration of Bi might introduce non-radiative el ectron traps. As long minority carrier diffusion lengths are needed for photovoltaic and photodetector devices, this result suggests that unconventionally grown GaAs and GaAs1-x Bix  alloys are less competitive materials than standard grown GaAs.    The best estimated quantum efficiency from our calculations are shown by the dashed lines for each sample in Figure 5-5 (a). Based on th ese spectral responses and using the AM 1.5G photon flux density, the total photocurrent density ( JL) is estimated using Eq. (A-18). Table 5-3 summarizes the calculated and the experimental  photocurrent densities of each device. The measured and calculated current densities are comparable although some deviations are observed.  94  The JL of GaAs1-x Bix  samples are lower than the JL of the standard GaAs sample (r2321), due to the much lower minority carrier lifetimes.  Table 5-3:  Experimental and calculated photocurrent for GaAs and GaAsBi p+/n devices. Sample No. Bi (%) Experiment       J L  (mA/cm 2 ) Simulation        J L (mA/cm 2 )  r2321 0   27.6 22 r2336 0 8.8 7.3 r2331 0.3 20.0 15 r2337 0.7 12.0 16.3 r2346 1.1 9.0 11  5 . 5 .  Conclusion In this study, the photovoltaic response of single junction dilute GaAs1−x Bix  (0<x<1.1%) p+/n diodes were investigated under one sun illuminati on for the first time. Similar device structures were fabricated with GaAs films grown under st andard conditions (580°C substrate temperature, As:Ga flux ratio of 6) and under the conditions used to grow th e Bi alloys (330°C substrate temperature, As:Ga flux ratio of 2). The sta ndard grown GaAs cell shows better photovoltaic performance than the GaAs cell grown at low temperature. The spectral responses of GaAs1−x Bix  devices were measured and the photovoltaic re sponse was observed to extend up to ~1000 nm wavelength with 1.1% Bi alloying. The experimental results were fi tted with a theoretical model in order to determine the effect of Bi on minority carrier lifetime in n and p-type Bi alloys. An analysis of the model reveals that the minority lifetimes in GaAs1x Bix  alloys are extremely short, 0.1< τe<0.5 psec and 0.5< τh<5 psec, resulting in low collecti on efficiency. The lifetimes showed only a weak dependence on Bi concentration and we re found to be lower than the minority carrier lifetimes in standard grown GaAs (3×10 -11 < τe<10 -10  sec and 10-9 < τh<10 -7  sec).    95  C hapter 6   Terahertz emission from  GaAs1-x Bix  based photoconductive switches   Semiconductor materials with ultrafast carrier r ecombination are important for applications in photoconductive emitters and detectors of pulsed terahertz (THz) radiation activated by femtosecond lasers. These sources can be used in THz time-domain spectroscopy systems. Low temperature MBE grown GaAs 1-x Bix  semiconductors are used in this study to fabricate THz photoconductive switches. We repor t enhanced THz frequency ra diation from annealed GaAs1-x Bix  based devices. The effect of rapid thermal annealing on the THz bandwidth and power emission of GaAs1-x Bix  photoconductive devices is investigated in this chapter. The results are compared to conventional low temperature grow n GaAs (LT-GaAs) devices which are well known for having ultra-short carrier lifetimes.    6 . 1 .  Contributions Samples discussed in this chapter were grown jointly by the author and R.B. Lewis. All post-growth sample characterization (e.g. x-ray di ffraction, PL, SEM) and sample preparation (e.g. thermal annealing and acid etching) were perf ormed by the author. Photolithography fabrication of near 40% of the THz devices was carried out  by the author. Others were performed by B. Heshmat. THz radiation measurements of devices were carried out by B. Heshmat at the optical systems and technology lab (OSTL) at the University of Victoria. The author was involved in analysis of the results.     96  6 . 2 .  Terahertz radiation Terahertz (THz) radiation is electromagnetic radiation between infrared and millimeter waves in the 100 GHz to 10 THz frequency range (Figure 6-1) . These frequencies are considered too high from an electronics perspective and too low from an optics viewpoint. This part of the electromagnetic spectrum was called the “THz gap” because it was the least explored region in the electromagnetic spectrum mainly due to the difficulties involved in making efficient and compact THz sources and detectors [99]. However, the TH z field has gone through major progress in the last 20 years due to the advent of femtosecond lasers and the fabrication of materials with ultra-short carrier lifetimes. As a result, optical techniques such as TH z spectroscopy have recently been introduced. In addition, high power THz sources su ch as quantum cascade lasers have recently become available. These advancements are rapidly diminishing the THz gap between the optics and electronics. THz waves can be implemented in many applic ations and techniques such as spectroscopy, imaging, remote sensing and short range communications. Like microwave radiation, THz radiation is non-ionizing and can penetrate into a wide variety of non-conducting ob jects such as cloth, paper, cardboard, wood, plasti c, paints and many ceramic materials [85]. This radiation cannot penetrate into liqui d water or metals as the THz radia tion is absorbed or reflected. Many biological compounds and small molecules (e.g. H2O, O2, SO2, CO, HCl, HNO3 ) have rotational and vibrational modes in the THz frequency range  [99], [100]. This means THz radiation will interact with the molecules and results in characteristic absorption peaks in the THz frequency region. Thus, many materials can be characterized with use of THz waves based on their intrinsic properties. It is noteworthy to mention that ma ny explosive materials (e .g. TNT, RDX and HMX) and illegal drugs (e.g. cocaine, heroin and morphine) also have distinctive absorption features in the THz region arising from the combination of inter- and intra- molecular vibrations [101]–[103]. Hence, THz radiation can be useful in security screening of packages.       97   Figure 6-1: Terahertz band in the electromagnetic spectrum.  6 . 3 .  T H z pulse source using photoconductive material Among the many mechanisms available for generation and detection of THz radiation, an optoelectronic approach using ultrafast pulsed excitation of a phot oconductive material is quite popular. In this method, a micro-antenna structure (typically a dipole antenna) is fabricated on a short lifetime (ultra-fast) photoconductive semiconductor materi al. Then by employing an ultrafast laser with pulse width < 1 ps, the photoconducti ve semiconductor is excited above its bandgap, creating excess electron and hole pair s in the material. As the antenna is biased with an external DC voltage, the generated photocarriers are accelerated towards the ante nna electrodes. This creates a short current pulse with a sub-picosec ond rise time. Thus, the antenna dipole moment changes rapidly and results in pulsed emission of THz radiation. This method is typically called photoconductive switching and leads to the genera tion of broadband THz radiation at room temperature. A schematic diagram of a THz pulse emission system is shown in Figure 6-2 (b).  Photoconductive switches were first demonstr ated by Auston et al. in 1975 [104] as a means to switch an electrical path in Si transm ission-lines with the use of optical pulses. The concept gradually became widespread as faster ma terials enabled switching speeds that could not be realized with conventional electronics. Sw itches fabricated on GaAs substrates enabled switching in the GHz frequency range [105]. Low- temperature grown GaAs (LT-GaAs) substrates increased the bandwidth into the THz range [106], making LT-GaAs p hotoconductive switches into one of the common sources for THz wave generation.  Today, photoconductive antennas (PCAs) are becoming widespread as THz sources for different applications including imaging and spectroscopy [99], [1 03], [107]. Along with  98  commercialization of these applications, the demand for more efficient PCAs has increased. Therefore, ongoing research focuses on increasing the output power a nd bandwidth of these devices. Unique material propertie s, such as ultrashort electron trapping time, high mobility and high dark resistivity, and high thermal and el ectrical breakdown are the key parameters for increasing the THz output pow er and bandwidth of photoconduc tive materials. Among these properties, mobility and carrier lifetime are the two main factors in  determining the efficiency of the PCA. Mobility mainly increases the amplitude of the radiation and carrier lifetime affects the THz bandwidth [108]. In this regard, thermal ann ealing is used to optimise the above mentioned parameters of photoconductive LT-GaAs [43], [ 49], [99]. In addition, from the antenna perspective, recent works have used nanostructu res in the gap of the antenna to improve the efficiency of the LT-GaAs  PCAs [109], [110].  Like annealed low temperature grown Ga As, low temperature grown dilute GaAs 1-x Bix  also demonstrates ultrafast electron trapping times with  high dark resistivity and high electron mobility, making these materials advantageous for generation and detection of THz radiation in PCAs [23]. One advantage of GaAs1-x Bix  alloys compared with LT-GaAs is  its reduced bandgap, which allows GaAs1-x Bix  PCAs to be pumped with longer than 1 μm wavelengths using femtosecond solid state and fiber-coupled lasers. These lasers are more compact and cost effective than the Ti:Sapphire laser that is commonly used for excitati on of LT-GaAs PCAs. Wavelengths above 1 μm can also be reached with InGaAs alloys, however attempts to grow low temperature InGaAs have achieved limited success because the shortest carrier lifetimes are only ~2 ps [111] and, most importantly, the material has low dark resistivity, which is a serious obstacle for applications in photoconductive switches.  Although THz operation from GaAs1-x Bix  based PCA have been demonstrated in the literature [23], [112], the optimized anneali ng conditions for maximum THz output power have not yet been identified. In this regard, a systematic analysis is carried out to investigate the influence of rapid thermal annealing on the THz bandwidth and the output power of GaAs 1-x Bix  PCA. The performance of annealed GaAs1-x Bix  PCAs is also compared to the performance of our MBE grown LT-GaAs PCAs that have been ann ealed under the same conditions. Our results are compared to the performance of a commercial LT-GaAs-based PCA.    99   Figure 6-2:  (a) Schematic of the heterodyne THz emission and detection setup. Abbreviations are: MR = Mirror, BS = Beam splitter, DL = Delay line, L= Lens, Tx = THz transmitting PCA, Rx = THz receiving PCA, and fs laser = femtosecond Ti-Sapphire pulse laser. The shaded  area in the ellipse is enlarged in (b). Silicon lenses are used at the back of the PCAs to focus the THz beam. (b) 3D schematic diagram of TH z pulse emission from a GaAsBi PC dipole antenna excited by a femtosecond laser pulse.   6 . 4 .  Experimental section 6.4.1.  Sample preparations For this study, two dilute GaAs 1-x Bix films with 2.2% and 3.0% Bi content were grown by MBE on semi-insulating GaAs (001) substrates under comparable growth conditions. The thickness of the 2.2% and 3.0% Bi films were 330 nm and 90 nm, respectively. Moreover, a 900 nm thick low temperature GaAs (LT-GaAs) sample was also grown under As-rich conditions for comparison. The growth conditions of these samples are given in Table 6-1. In addition to these samples, a commercial PCA device (BATOP PCA- 800nm) is used as a referen ce in this study. The structure  100  of the commercial device is 1 µm LT-GaAs/SI-GaAs substrate that is annealed at 600 °C and have ~0.25 ps carrier lifetime. The thickness, Bi conten t and the amount of excess As were determined by high resolution x-ray diffracti on (HR-XRD) measurements. The grown samples were cleaved into ~5×5 mm pieces and annealed under comp arable conditions for different times and temperatures in a rapid thermal annealing (RTA) chamber that was evacuated to ~10 −6 Torr. The as-grown and annealed samples were used to  fabricate THz photoconductive switches. The micro-antenna dipole structures (20 µm dipole with 5-6 µm center gap, 5 µm width, and 100 nm Au/5 nm Ti thickness) were fabricated on each samp le by photolithography. It should be noted that the commercial LT-GaAs device used in this study (BATOP PCA-800nm) also has a 20 µm dipole antenna with 5µm center gap and 10 µm width, with back-mounted silicon lens and surface antireflection coating.   Table 6-1: Specification of MBE grown GaAs 1-x Bix  and LT-GaAs films. Sample Type Bi (%) Growth Temp. (°C) As:Ga BEP Bi:Ga BEP Thickness (nm) GaAsBi 2.2 365 2.2 0.06 330 GaAsBi 3.0 360 1.9 0.06 90 LT-GaAs      (0.5% excess As) 0 240 12.0 - 900  6.4.2.  T H z emission and detection using heterodyne setup  In order to investigate the THz emission from the fabricated PCAs, we used a heterodyne THz setup as shown in Figure 6-2 (a). The transmitte r and receiver PCAs are pumped by a 810 nm Ti-Sapphire laser with 30 fs pulses at an 80 MHz repetition rate . A retroreflector is translated along a precision stage to vary the phase of the generated THz pulse. When the incident THz pulse overlaps with the optical excitation pulse in the THz-rece iving PCA, a small current is induced in the receiver and measured by a lock-in amplifier.  The temporal profile of the generated current is recorded as the relative phase between THz pulse and the incident optical pulse is scanned. Such  101  a setup is typically called time domain THz spectroscopy (TDTS) and can be used to characterise chemical and biological samples.  In this study, all the transmitter PCA dipoles we re biased with 20 V and the incident optical power on each chip was 17 mW. A commercial  PCA (BATOP PCA-40–05–10–800-a) is used as a reference in the detector side and the distances in the setup are kept constant for all the tests. This is necessary for a fair comparison between the em issions of different transmitters. In addition for optimizing the sensitivity of the setup, the THz signal is first measured with another similar commercial PCA switch and then our fabricated PCAs were tested. These measurements were carried out by B. Heshmat at the optical systems and technology lab (OSTL) at the University of Victoria. The as-grown and annealed GaAs 1-x Bix  samples were also excited with a 532 nm 20 ns pulsed diode-pumped solid state laser at room temperature for photoluminescence (PL) measurements. The average power of the laser was 1.5 mW, at a repetition ra te of 2 kHz and peak power density of 10 5 W/cm 2. The PL was dispersed using a Spect raPro-300i spectrograph and then detected by a liquid nitrogen-c ooled InGaAs array detector.   6 . 5 .  Results and discussion Figure 6-3 presents the room temperature PL  spectra of as-grown and annealed GaAs 1-x Bix  samples with 2.2% Bi content that were  used as photoconductive substrates in this work. For annealing temperatures of 500 °C and 600 °C, the bismid e PL intensity increases by 1.2× and 2.3× in comparison to the as-grown PL, while the PL peak wavelength remained relatively unchanged. This indicates that the luminescence of the GaAs1-x Bix  alloy could be improved with moderate thermal annealing. However, the PL intensity is observed to degrade significantly at higher annealing temperatures of 670 °C and 700 °C. Hence, 600 °C is near the optimum annealing temperature for maximum PL intensity. Similar behaviour was also observed in the 3.0% GaAs 1-x Bix  sample. Figure 6-3 Inset summarizes the PL p eak intensity improvement for these films as a function of the anneal temperatures. The PL intensity could possibly improve due to the removal of As and Ga related defects and vacancies by thermal annealing that originated during the growth at low temperatures. However GaAs 1-x Bix  alloys could also undergo changes in their properties  102   Figure 6-3: Room temperature PL spectra of a 2.2% Bi film at  different thermal annealing temperatures. The Inset shows the PL peak intensity improvement for 2.2% and 3.0%  Bi films as a function of the anneal temperatures. The PL improvement ratio is the ratio of the PL peak intensity of each layer to the as-grown PL peak intensity.     with thermal annealing which ev entually results in a significant reduction in their PL emission. Our result suggests that the recombination lifetime in dilute GaAs1-x Bix  decreases with 600-700 °C rapid thermal annealing possibly due to phase separation and formation of Bi or As clusters. To further investigate the PL behaviour, we tested the THz em ission of these photoconductive materials in the heterodyne setup.  The temporal profiles of the emitted signals for four distinct samples are shown in Figure 6-4 (a). The THz emission of these samples are optimized with rapid thermal annealing, as discussed below in Figure 6-5. We found notable, c onsistent dual emission peaks from our MBE grown samples. The first peak has higher freque ncy components (sub-picosecond peak to peak time) and is usually small, and the second peak is larger in amplitude but has lower frequency components. In general, the GaAs1-x Bix  PCAs show higher amplitude  emission peaks with higher bandwidths than the LT-GaAs PCAs. The initial high-frequency peak in GaAs 1-x Bix  samples is more intense and sharper than the LT-GaAs sample, indicating that GaAs 1-x Bix  can notably enhance the hyper-THz range frequencies. On th e other hand, the second emission peak of GaAs 1-x Bix  PCAs has much lower frequency components th an the LT-GaAs PCAs. This suggests that  103   Figure 6-4: (a) THz pulse emitted from a dipole PCA on: LT-GaAs, commercial device, 3% GaAsBi and 2.2% GaAsBi. The signals are measured in the same condition with a commercial PCA at th e receiver. The signals are separated horizontally for clarity. (b) Signal amplitude spectrum (10log10 |F (I))|) is in dB. The detector noise level is about −80 dB. The measurements were performed by  B. Heshmat at UVIC-OSTL lab. Figure is reproduced from Ref. [113].   GaAs1-x Bix  can possibly improve the THz radiation in two distinct low and high THz frequency ranges. As the 2.2% Bi sample is thicker (330 nm ) than 3.0% Bi sample (90 nm), higher emission signals (~93% and 50% increase in the peak to peak  amplitude of the first and second peaks) with broader temporal responses are observed from the 2.2% Bi sample than from the 3.0% Bi one. The increase in the amplitude of the peaks is smalle r than the change in the thickness of these two samples. This difference is not due to the differences in excess carrier generation in these two samples since the penetration depth of the laser excitation at 810 nm wavelength is ~1 µm, larger than the thickness of both sample s. The area under the first and second emission peaks of 2.2% Bi is calculated to be ~3.0× and ~2.8× larger th an the area under the peaks of 3.0% Bi sample, respectively. This ratio is closer to the ratio of the thicknesses of these two samples, suggesting that carriers with long lifetimes could contribute more to the current pulse of the 2.2% Bi sample. Moreover, as 3.0% Bi sample is thinner that th e 2.2% Bi one, larger portion of photo carriers can be trapped and recombined at the surface, contributing in a faster THz emission response.  Figure 6-4 (b) shows the Fourier spectrum of th e detected signal in decibel (dB). Compared to the commercial LT-GaAs-based PCA, the spectrum of the GaAs 1-x Bix  samples are notably  104  enhanced in the hyper-THz range  due to the sharp primary peaks. The cut-off to the ~ − 80 dB noise level is increased by about 0.5 and 0.75 THz for 3.0 and 2.2% GaAs 1-x Bix PCAs, respectively.  At first glance one might think that the secondary peak is ge nerated by the GaAs substrate beneath the GaAs1-x Bix  films. This is unlikely as the GaAs substrate underneath the GaAs 1-x Bix  layer should have much longer carrier lifetimes than picosecond range (τ>100 ps) [43]. Moreover, there are smaller tails following the main pulses th at are more likely to be generated by long lifetime carriers in the GaAs substrate (see Figure 6-4 (a)). A reflection of THz radiation from the silicon lens on the back of the PCA device or from GaAsBi/GaAs interface is improbable, as the second peak is much larger in amp litude compared to the first peak.  The dual emission behavior could be related to the electron dynamics in GaAs1-x Bix . In fact, a dual exponential photocarrier decay rate w ith short (few picosecond) and long (25-30 ps) time constants was previously reported for dilute GaAs 1-x Bix alloys from optically pumped THz transmission measurements. The dual rates were inferred as short carrier-trapping and longer trap-emptying times [17]. Unlike LT-GaAs [43], [49], [114] , [115], the dependenci es of carrier lifetime on the growth conditions and annealing have not been explored for GaAs 1-x Bix alloys. Previous studies have noted that the carrier lifetime is measured to be a few picoseconds for samples with over 600 °C annealing temp erature [17], [116].  Figure 6-5 shows the peak-to-peak amplitude of the emitted THz pulse as a function of annealing temperature, as measured with the heterodyne setup. The THz emission amplitude of both GaAs1-x Bix  and LT-GaAs samples is notably enhan ced with 1 min thermal annealing. This enhancement in THz emission amplitude is observed to be more significant at annealing temperatures above 600 °C. The 2.2% GaAs 1-x Bix  shows a peak at around 670 °C, 1 min annealing conditions. The 3% GaAs 1-x Bix  follows the same pattern. This behavior indicates that carrier recombination centers increase in dilute GaAs1-x Bix  alloys with increasing annealing temperature. The same conclusion can be drawn from the PL st udies on the same samples shown in Figure 6-3. Figure 6-3 shows that both GaAs 1-x Bix  samples have a maximum PL peak intensity improvement at 600 °C annealing temperature and at higher annealing temperatures the PL intensity falls off. These observations confirm that the recombination lifetime in dilute GaAs1-x Bix  alloys decreases with thermal annealing above 600 °C. The increas e in both the THz emission and the PL with annealing at 600 °C is due to the improvement in local ordering of material (removal of antisites  105   Figure 6-5: Measured THz signal for GaAsBi and LT-GaAs samples as a function of annealing temperature. The data points are all obtained at 1 min annealing time with the ex ception of the two points indicated. The dashed lines with points show the amplitude of the higher bandwidth (HBW) peak. The measurements were performed by  B. Heshmat at UVIC-OSTL lab. Figure is reproduced from Ref. [113].   and vacancies), which enhances the carrier mob ility. However, at higher temperatures due to formation of recombination and trap centers in the material (e.g. As and Bi clusters), PL intensity falls off while THz emission is increasing. The p eak-to-peak amplitude of the higher bandwidth (HBW) peak is also shown in Figure 6-5 (dashe d lines). Both the high and low bandwidth peaks show similar behavior with resp ect to annealing temperature. The results show notable enhancement in THz emission in GaAs 1-x Bix compared to our LT-GaAs based devices. This enhancement is such that the 670°C GaAs 1-x Bix sample shows higher THz emission than that of the optimized commercial LT-GaAs device. This is a remarkable result in light of the fact that the GaAs1-x Bix is much thinner than the commercial device, and doesn’t have antireflection coatings.    106   Figure 6-6: Temporal profile of the emitted THz pulse from 2.2% Ga AsBi sample with 1, 10, 20 minutes of annealing at 500°C. The measurements were performed by  B. Heshmat at UVIC-OSTL lab. Figure originally published in [113].  As shown by the three points in the elliptical  area for 500 °C annealing in Figure 6-5, the annealing time also affects the amplitude of the THz radiation. The temporal profile of the emitted THz pulse from the 2.2% GaAs 1-x Bix sample with 1, 10, 20 minutes annealing time at 500 °C are shown in Figure 6-6. Along with peak-to-peak am plitude variation, we found that the bandwidth of emission is notably reduced for longer annealing times. Therefore, a short annealing time such as 1 min is the best choice for wide THz bandw idth. As shown in Figure 6-6, the smaller high bandwidth peak of 2.2% PCA disappears with  the 10 minute annealing and the pulse is significantly distorted with 20 mi nutes of annealing time. This indicates that the lifetime of the photogenerated carriers are significantly affected by the annealing time. A key factor in the electrical efficiency of an  optical switch is the ratio between dark and photo current (Iphoto/I dark ) or On-Off Current Ratio  (OOCR). The photocurrent or “On” current is the total average DC current measured when the in frared laser light is illuminating the gap of the PCA and the dark current or “Off” current is th e current measured when there is no illumination. Figure 6-7 shows the OOCR me asurements for 2.2% GaAs 1-x Bix and LT-GaAs samples. In general, the GaAs1-x Bix  samples demonstrate the opposite OOCR trend with annealing temperatures to LT-GaAs devices. It is noticed that at lower annealing temperatures the GaAs 1-x Bix OOCR is superior to LT-GaAs. As shown in Figure 6- 7 inset, this behavior is mainly attributed   107   Figure 6-7: OOCR for 2.2% GaAsBi and LT-GaAs as a function of  the annealing temperature. The effect of the annealing time for three devices at 500 °C anneal temperature is also shown.  The green square shows the OOCR for a commercial LT-GaAs device that believed to be annealed at  600 °C. Inset shows the dark current of the same samples in the main figure as a function of the annealing temperature. All the measurements were done at 10 V bias voltage and 17 mW average optical power. The measurements were performed by  B. Heshmat at UVIC-OSTL lab. This Figure is reproduced from Ref. [113].   to the much lower dark current observed from GaAs 1-x Bix  than LT-GaAs samples at low annealing temperatures. The low dark current  is significant for THz switching applications as the leakage current increases the power consumption of the switch and limits the bias voltage that can be applied to the PCA switch. Figure 6-7 shows a d ecreasing trend with incr ease in the annealing temperature and a minimum at 670 °C for the GaAs 1-x Bix OOCR. The OOCR of three 2.2% GaAs 1-x Bix devices annealed at different times (1, 10, 20 min) at 500 °C are also shown in Figure 6-7, demonstrating the decreasing trend of OOCR with increasing annealing time. As shown in the inset of this figure, this trend is mainly due to the increase in the dark current of the PCA switch   108   Figure 6-8: Net photocurrent at different annealing conditions for 2.2% GaAsBi and LT-GaAs PCAs. GaAsBi and LT-GaAs show different behavior as a function of anneali ng temperature. All the measurements were done at 10 V bias voltage and 17 mW average optical power. The measurements were performed by  B. Heshmat at UVIC-OSTL lab. This Figure is reproduced from Ref. [113].  with increasing annealing time.  The dark current indirectly affects the pe rformance of the device by pushing the dipole antenna structures closer to their current breakdown limit. As l ong as the dark current does not cause device malfunctioning, the emission amplitude of these dipoles is only influenced by the net photocurrent (Iphoto-I dark ). The measured net photocurrent is depicted in Figure 6-8, showing higher average DC photocurrent form GaAs1-x Bix  than LT-GaAs samples under continuous pulsed illumination. This result could show that the photocarrier lifetime in GaAs 1-x Bix  is larger than that in LT-GaAs. In addition, th e electron mobility in GaAs1-x Bix  could be higher than LT-GaAs which could result in a higher photocurrent.   109  Similar to the results in Figure 6-7, Figure 6-8 also shows an opposing trend for the LT-GaAs and the GaAs1-x Bix materials. When GaAs 1-x Bix has a maximum in net photocurrent, LT-GaAs shows a minimum. The results are also compared to a commercial device that shows a slightly improved OOCR and net photocurrent compared to our LT-GaAs samples. This is expected due to the antireflection coating on th e commercial device that enhances the optical coupling efficiency of the gap by ~33% at 810 nm laser excitation wavelength.  Figure 6-7 and Figure 6-8 results indicate that the effect of annealing on the photocurrent and OOCR’s in GaAs 1-x Bix and LT-GaAs are rather differe nt. At the optimum annealing temperatures, the OOCR’s of both GaAs 1-x Bix and LT-GaAs are similar, however GaAs 1-x Bix shows much higher level of photocurrent. Th is suggests that a PCA made on the GaAs1-x Bix substrate can have a higher efficiency (more photocurrent for the same optical power and bias voltage) compared to LT-GaAs.  6 . 6 .  Conclusion Terahertz photoconductive switches are im portant devices for THz wave generation.  In comparison to other methods for generating of THz radiation, photoconductive switches suffer from low THz output power. In this work, c onventional LT-GaAs photoconductive switches are compared with dilute GaAs 1-x Bix devices whose performance is optimized by rapid thermal annealing. Notable enhancement in THz emission amplitude and bandwidth are obtained from annealed GaAs1-x Bix substrates. A maximum THz emission from GaAs 1-x Bix was found for annealing at 670 °C for 1 min. Th e highest THz emission in GaAs1-x Bix is consistent with highest net DC photocurrent. We observed a s uperior On-Off current ratio for GaAs 1-x Bix samples in comparison to the LT-GaAs devices . Our results suggest that GaAs1-x Bix  is a promising material for improved photoconductive THz switches.    110  C hapter 7   Conclusions    GaAs1-x Bix  is a new III-V semiconductor alloy that  shows promise for many optoelectronic applications including infrared light emitters and detectors, lasers, solar cells, terahertz photoconductive switches and spintronic devices. The unusual large band gap reduction and the formation of in-gap Bi cluster states associated with Bi alloying are the unique features of this alloy. GaAs1-x Bix  epitaxial films can be grown at low temperatures with low degree of relaxation on readily available substrates such as GaAs and InP. This alloy is an alternative to the InGaAsN quaternary alloys and offers potential for long er wavelength device applications on common III-V substrates. In this thesis, we have explored  the growth process and optical and electrical properties of this new alloy. At the time of the undertaking of this thesis, epitaxial GaAs 1-x Bix  layers with high Bi c oncentrations (10<x<22% Bi) were successfully grown in our lab. Understanding the properties of these non-dilute alloys are essential. Several characterization techniques were used in this th esis to explore the structural, op tical and electronic properties of GaAs1-x Bix  alloy in a wide range of Bi concentra tion. Moreover, potential optoelectronic device application of GaAs1-x Bix  alloys in solar cells and terahertz emitters are explored in this thesis through experimental and theo retical investigations.  A systematic study is carried out to investigate the effect of the GaAs1-x Bix  growth parameters on the Bi incorporation and the formation of surface droplets. The Bi incorporation is found to be sensitive to the surface stoichiometry (i.e. As2:Ga flux ratio) of the growing films. The Bi incorporation rapidly increases as the As2:Ga flux ratio is lowered to unity and saturates for lower flux ratios. At an above stoichiometric fl ux ratio (As-rich condition) , As displaces Bi bonded to Ga on the surface and inhibits Bi incorporation. This leads to excess Bi on the surface and the formation of Bi droplets under same growth cond itions. Below the stoichiometric flux ratio (Ga-rich condition), due to the limited presence of As, the excess Ga accumulates on the surface and  111  results in formation of phase-separated metallic Ga-Bi droplets. This suggests that Ga-Ga and/or Bi-Bi bonding is stronger than Ga-Bi bonding. Unde r As-rich conditions with low flux of Bi (minimal to just have Bi incorporation), the growth of  droplet-free GaAs 1-x Bix  films is demonstrated. The optical bandgap and absorption edge of pseudomorphic GaAs1-x Bix  films on GaAs substrates have been studied for a wide range of Bi contents (0 ≤x ≤17.8%) with optical transmission and PL spectroscopies. All samples show direct bandgaps. The relation between the Bi composition and the bandgap is obtained in a previously unexplored alloy composition range. A small bandgap of 0.52 eV (~2.4 µm) is demonstr ated for 17.8% Bi film. To our knowledge, no other ternary GaAs alloy with such a low bandgap can be gr own pseudomorphically on a GaAs substrate. Below Eg ~1.06 eV, we have  verified experimentally that GaAs 1-x Bix  has less mismatch to GaAs than any other ternary GaAs alloy, including GaAsN, for a given bandgap. This strong bandgap reduction shows promise for extending the wavelength range of optical devices on GaAs, beyond what other III-V alloys offer.  The electrical transport measurements on nominally undoped GaAs1-x Bix  films with 0<x ≤21.5% Bi content reveal an exponential incr ease in p-type conductivity and a monotonic decrease in hole mobility with increasing Bi-content, where p=2.2×10 19  cm-3  and µp ~2 cm 2V-1 s-1  at 21.5% Bi. Based on temperature dependent meas urements, the increase in p-type conductivity with Bi incorporation is found to be  associated with an increase in density of states in the valence band of GaAs1-x Bix  alloys and the presence of Bi related acceptor states. Temperature dependent measurements also show that the Fermi level is located at ~30-47 meV above the valence band in high Bi content films (10<x<21.5%). The photovoltaic response of dilute GaAs1−x Bix  (0<x<1.1%) p+/n diode s was investigated for the first time. Photovoltaic operation is observed from all GaAs1−x Bix  cells. With the introduction of Bi into GaAs, the response expand s to longer wavelengths than in GaAs. Based on theoretical modeling, the minority carrier lifetimes in unoptimized bismide material were found to be shorter than those in standard grown GaAs, resulting in low collection efficiency in solar cell devices. Terahertz photoconductive switches are technol ogically important devices for generating the broadband THz radiation. In this work, low temperature grown GaAs 1-x Bix  semiconductors are  112  used to fabricate THz photoconductive switches. A syst ematic analysis is carried out to investigate the influence of rapid thermal annealing on the THz emission from bismide photoconductive switches. Notable enhancement in terms of  THz emission amplitude and bandwidth is demonstrated from annealed GaAs1-x Bix substrates. We found that GaAs 1-x Bix performs better than conventional LT-GaAs in generating the TH z radiation. Our results suggest that GaAs1-x Bix  is a promising material for improving the THz output power from photoconductive switches.  7 . 1 .  Future work As GaAs1-x Bix is a new semiconductor alloy, many issues re lating the growth process of this alloy have not been resolved. A significant challenge in growth of this alloy is to find a way to suppress the formation of metallic droplets. In this regard, a reproducible growth method for controlling the surface droplets while retaining the Bi incor poration above 10% is essential for further development of high Bi content alloys. Applying innovative MBE growth techniques such as pulsing the As and Bi molecular sources could be helpful in achieving this purpose.  In this thesis, room temperature optical absorption were measured for high Bi content films (x>10%), although no photoluminescence (PL) emissi on was detected as these films were grown at extremely low temperatures (T < 250°C) and were relatively thin (d ≤70 nm). Work is needed to optimise the growth conditions of high Bi cont ent films for PL emission. In addition, a more systematic PL study (e.g. low temperature and in tensity dependence measurements) is needed to examine the emission properties of  these new non-dilute alloys.  In terms of applications, fabrication of high quality p-n junction diodes is essential to correctly evaluate the photovoltaic operation of GaAs1-x Bix material. This is of great importance in demonstrating the maximum conversion efficiency  of bismide alloys for solar cell applications. The fact that many of our p+/n diodes show hi gh dark current also need s further investigation. Improvement to the performance of the tested device could be made by: optimizing the thicknesses and doping levels of the layers; improving the structure design and the growth process; optimizing the contact design and also the use of the surface passivation. 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Page break    124  Appendix A                                     Photocurrent and spectral response of p+/n junction solar cell   In this section we derive the photocurrent and the spectral response for a single p-n junction solar cell which could serve as a reference model for all solar cells. The basics of this model is briefly covered below, although more details can be fou nd in section 13.9.3 of Ref. [90]. As devices used for analysis in Chapter 5 were p+/n devices, here we assumed an abrupt p+ /n structure. Figure A-1 (a) shows the typical schematic of the p+/n structure under illumination. As the density of acceptors in the p+ layer is much larger  than density of donors in the n layer, NA> > ND, nearly an abrupt one-sided junction is formed with deple tion region extending in to the n layer. Constant doping is also assumed on either side of the junction. When monochroma tic light of wavelength λ is incident on the front surface, photons are absorbed and carriers are generated at a distance x from the semiconductor surface, at the following rate:   where ߙሺߣሻ is the absorption coefficient, Фሺߣሻ is the number of incident photons per unit area per unit time per unit bandwidth, and ܴሺߣሻ is the fraction of the photons reflected from the surface. All of the common semiconductors have higher absorption coefficient at short wavelengths, therefore the generation rate is dependent on the wavelength of the incident photons. As a result at short wavelengths, most of the electron hole pair s are generates in the vicinity of the surface while at long wavelengths, the electron hole pairs ar e generated far into the device. This difference in the generation rate of the carriers at short and long wavelengths is shown in Figure A-1 (b). Depending on the wavelength of the incident phot on, the carrier generation and recombination ܩሺߣ, ݔሻ ൌ ߙሺߣሻФሺߣሻ൫1 െ ܴሺߣሻ൯expሺെߙሺߣሻݔሻ (A-1)  125   Figure A-1:  (a) p+/n solar cell under illumination. (b) Carrier genera tion rate as a function of distance at short and long wavelengths.     (~ Δn/ τ) can take place in three region s of the device: the top p+ re gion, the depletion region of the junction, and in the un-depleted n region. The photoge nerated carriers in the un-depleted p+ and n regions are collected by diffusion while in the depletion region the carriers are collected by a drift process. Under low-injection c ondition, the one-dimensional steady-state continuity equation for the generated electrons in the p+ layer is:    where ݊௣ െ ݊௣௢ is the density of excess electrons in the p+ layer that have a recombination lifetime of ߬ ௡. In addition,  ܬ௡ is the collected current density of the electrons at every segment of the device. Similarly for the holes in the n layer we have:    ܩ௡ െ ൬݊௣ െ ݊௣௢߬௡ ൰ ൅1ݍ݀ܬ௡݀ݔ ൌ 0 (A-2)  126   In the above equations, the current de nsities can also be obtained from:   For the front p+ side of the junction, combining Eqs. (A-1), (A-2) and (A -4) yields the following expression:   The general solution to this equation is:    where ݈௡ ൌ ඥܦ௡߬௡ is the diffusion length of minority electrons and ܥଵ, ܥଶ are constants. This equation have two boundary conditions. One at the surface with recombination velocity ܵ௡ :   ܩ௣ െ ቆ݌௡ െ ݌௡௢߬௣ ቇ െ1ݍ݀ܬ௣݀ݔ ൌ 0 (A-3) ܬ௡ ൌ ݊ߤݍ௣ࣟ ൅ ܦݍ௡ ൬݀݊௣݀ݔ ൰ (A-4) ܬ௣ ൌ ݌ߤݍ௡ࣟ െ ܦݍ௣ ൬݀݌௡݀ݔ ൰ (A-5) ܦ௡ ݀ଶ݊௣݀ݔଶ ൅ ߙФሺ1 െ ܴሻeିఈ௫ െ ൬݊௣ െ ݊௣௢߬௡ ൰ ൌ 0 (A-6) ݊௣ െ ݊௣௢ ൌ ܥଵ cos ݄ ൬݈ݔ௡൰ ൅ ܥଶ sin ݄ ൬ݔ݈௡൰ െߙФሺ1 െ ܴሻ߬௡ߙଶ݈௡ଶ െ 1 eିఈ௫ (A-7) ܦ௡ ݀ሺ݊௣ െ ݊௣௢ሻ݀ݔ ൌ ܵ௡൫݊௣ െ ݊௣௢൯ ܽݐ ݔ ൌ 0 (A-8)  127  and the other at the edge of the depletion region where the excess carrier density is small due to the high electric field in the depletion region:   By using the above boundary conditions in Eq. (A-7), the electron density can be solved and results in following electron photocurrent density at the depletion edge of p+ layer [90]:   This photocurrent could be collected by the metal contact on the front side of the p+/n junction at a given wavelength. To find the hole photocurrent gene rated in the n substrate layer, Eqs. (A-1), (A-3) and (A-5) are used with the following boundary conditions:   where ܵ௣ is the recombination velocity of holes at the back surface of the cell. Similar to the p+ layer calculation, by using the above boundary conditions the hole photocurrent at the depletion edge, ݔ ൌ ݔ௝ ൅ ஽ܹ, is:     ݊௣ െ ݊௣௢ ൎ 0 ܽݐ ݔ ൌ ݔ௝ (A-9) ܬ௡ ൌ ܦݍ௡ ቆ݀݊௣݀ݔ ቇ௫ೕൌ ቀߙݍФሺ1 െ ܴሻ݈௡/൫ߙଶ݈௡ଶ െ 1൯ቁ൮൬ܵ௡݈௡ܦ௡ ൅ ݈ߙ௡൰ െ eିఈ௫ೕ ൬ܵ௡݈௡ܦ௡ cos ݄ ൬ݔ௝݈௡൰ ൅ sin ݄ ൬ݔ௝݈௡൰൰൬ܵ௡݈௡ܦ௡ ൰ sin ݄ ൬ݔ௝݈௡൰ ൅ cos ݄ ൬ݔ௝݈௡൰െ ݈ߙ௡eିఈ௫ೕ൲																			 (A-10) ݌௡ െ ݌௡௢ ൎ 0	 ܽݐ ݔ ൌ ݔ௝ ൅ ஽ܹ (A-11) െܦ௣ ݀ሺ݌௡ െ ݌௡௢ሻ݀ݔ ൌ ܵ௣ሺ݌௡ െ ݌௡௢ሻ ܽݐ ݔ ൌ ܪ (A-12)  128   where ܪᇱ ൌ ܪ െ ሺݔ௝ ൅ ஽ܹሻ is the width of n layer region.  In addition to the p+ and n ne utral regions, some photocurrent is generated within the depletion region. Due to the high electric field inside the depletion region, the generated carriers are mostly accelerated out of the depletion region before they can recombine. The quantum efficiency in this region is near 100% and th e photocurrent per unit bandw idth is equal to the number of photons absorbed:   As a result, the generated photocurrent density at a given waveleng th in the p+/n junction cell is the sum of Eqs. (A-10), (A-13) and (A-14):    The spectral response is defined as this sum divided by ݍФ for externally observed response (ESR) or by ݍФሺ1 െ ܴሻ for internal response (ISR):     The ܴܵܧሺߣሻ is corresponded to the external quantum efficiency (EQE) of a solar cell as the photocurrent is only divided to the number of the incident photons. It should be noted that the ܬ௣ ൌ െܦݍ௣ ൬݀݌௡݀ݔ ൰௫ೕାௐವ ൌ െቆߙݍФሺ1 െ ܴሻ݈௣൫ߙଶ݈௣ଶ െ 1൯ቇ eିఈ൫௫ೕାௐವ൯.ۉ݈ߙۇ௣ െ൬ܵ௣݈௣ܦ௣ ൰ ൬cos ݄ ൬ܪ′݈௣ ൰ െ eିఈுᇲ൰ ൅ sin ݄ ൬ܪ′݈௣൰ ൅ ݈ߙ௣eିఈுᇲ൬ܵ௣݈௣ܦ௣ ൰ sin ݄ ൬ܪ′݈௣൰ ൅ cos ݄ ൬ܪ′݈௣ ൰ یۊ																			 (A-13) ܬௗ௥ ൌ ݍФሺ1 െ ܴሻeିఈ௫ೕሺ1 െ eିఈௐವሻ (A-14)ܬ௅ሺߣሻ ൌ ܬ௡ሺߣሻ ൅ ܬ௣ሺߣሻ ൅ ܬௗ௥ሺߣሻ (A-15)ܴܵܧሺߣሻ ൌ ܬ௅ሺߣሻݍФ ൌܬ௡ሺߣሻ ൅ ܬ௣ሺߣሻ ൅ ܬௗ௥ሺߣሻݍФ  (A-16) 129  spectral response calculated here is different than the spectral responsivety,	࣬ሺߣሻ, which is the ratio of the photocurrent to the power of the incident photons. Th ese two quantities can be related by the following equation:   Once the spectral response is known, the total phot ocurrent density can be obtained from the following equation:   ࣬ሺߣሻ ൌ ݄ܿߣݍ ܴܵܧሺߣሻ (A-17)ܬ௅ ൌ ݍන Фሺߣሻܴܵܧሺߣሻఒ೘଴݀ߣ (A-18)

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