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Epitaxial growth of dilute nitride-arsenide compound semiconductors by molecular beam epitaxy Adamcyk, Martin 2002

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E P I T A X I A L G R O W T H OF D I L U T E NITRIDE-ARSENIDE C O M P O U N D S E M I C O N D U C T O R S B Y M O L E C U L A R B E A M E P I T A X Y by Martin Adamcyk B.Sc.(Engineering Physics) Ecole Polytechnique de Montreal 1996 A THESIS S U B M I T T E D IN P A R T I A L F U F I L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E OF Doctor of Philosophy in T H E F A C U L T Y OF G R A D U A T E STUDIES (Department of Physics and Astronomy) We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y OF BRITISH C O L U M B I A April 2002 © Martin Adamcyk 2002 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department The University of British Columbia Vancouver, Canada DE-6 (2/88) 11 Abstract IriyGax-yAsi-ajNx containing a small amount of nitrogen (x<0.05) is a new nar-row bandgap semiconductor alloy that has advantageous properties for the fabrication of optoelectronic devices. In this thesis, we seek to improve the material quality of InGaAsN and GaAsN by studying how the epitaxial growth conditions affect both the structural and electronic properties of the alloy. We describe a novel RF plasma source based on a helical resonator design that was developed for the incorporation of nitrogen into GaAsN and In-GaAsN thin films grown by molecular beam epitaxy. The plasma source is equipped with a baffle apparatus that decreases the ion content of the flux. We show how the structural and electronic properties of InGaAsN epilayers depend on the growth conditions. In situ light scattering measurements and atomic force microscopy show that a faceted surface morphol-ogy occurs when growth conditions increase adatom surface diffusion: slow growth rate, high substrate temperature and high V/III ratio. Large nitrogen concentrations also favour the faceted growth mode. The residual strain in relaxed InGaAsN films is found to be higher than in InGaAs epilayers having the same lattice mismatch. In situ substrate curvature measurements were used to monitor the strain state of. the sample in real time during the growth. Ex situ transmission electron microscopy and x-ray diffraction measurements agree Ill with the residual strain determined with the in situ monitor. These characterization results also indicate that threading dislocation glide is slower in InGaAsN than in InGaAs. Finally, we find that the electronic properties of InGaAsN are generally degraded with increasing nitrogen content. However, by choosing appropriate growth conditions, we demonstrate InGaAsN quantum wells with room temperature photoluminescence efficiencies that are comparable to InGaAs structures. These photoluminescence results may be related to the faceting transition that was observed during GaAsN growth. In contrast with the findings of other groups, rapid thermal anneals only moderately improve the photoluminescence in-tensity and line shape of InGaAsN single quantum wells. We observe peak intensity gains on the order of 2 after one minute anneals at 785°C. Hall measurements indicate that the electron mobility of Si-doped GaAsN is inversely proportional to the nitrogen content. We conclude that nitrogen-related neutral impurity scattering is the limiting factor in the elec-tron mobility of GaAsN. The use of Bi as a surfactant during growth is shown to improve the surface morphology of GaAsN epilayers and the photoluminescence properties of InGaAsN single quantum wells. This work provides insight into some of the key issues that must be taken into account in the growth of dilute nitrides. iv Contents Abstract ii List of Tables vi List of Figures vii Acknowledgements xiii 1 Introduction 1 2 Radio frequency plasma source 6 2.1 Molecular nitrogen dissociation by plasma discharge 6 2.2 RF helical resonator plasma source design 7 2.2.1 General description of the helical resonator 8 2.2.2 Lumped element transmission line model 10 2.2.3 Plasma source configuration 17 2.3 Plasma source characterization 20 2.3.1 Optical emission spectroscopy 20 2.3.2 In vacuo characterization 23 3 Growth, structure and composition of GaAsN films 29 3.1 Growth of GaAs by molecular beam epitaxy 29 3.1.1 Effect of the As 2 flux 31 3.2 Determination of the composition of GaAsi_ xN;r 34 3.2.1 Secondary ion mass spectroscopy 35 3.2.2 x-ray diffraction 36 3.3 Nitrogen incorporation in GaAsN 38 3.3.1 Thermally cracked ammonia 39 3.3.2 RF plasma source 40 3.4 Light scattering experimental setup 44 3.5 GaAsN Surface morphology 45 3.6 Other effects on GaAsN surface morphology 56 3.6.1 Bi surfactant 56 V 3.6.2 Indium 58 3.7 Summary 60 4 Strain Relaxation 61 4.1 Basic concepts of thin film strain relaxation 61 4.1.1 Definitions 61 4.1.2 Dislocations and strain relaxation 64 4.2 In situ substrate curvature measurement 66 4.3 Comparison of strain relaxation in InGaAs and InGaAsN 70 4.3.1 InGaAs strain relaxation 70 4.3.2 Effect of nitrogen on strain relaxation 72 4.4 Brittle strain relaxation in GaAsN 77 5 Optical and electronic properties 82 5.1 Photoluminescence 82 5.1.1 Bulk GaAsN 82 5.1.2 InGaAsN single quantum wells 85 5.2 Charge carrier mobility 95 6 Conclusions 102 Bibliography 106 A Bandgap Bowing: two level model 114 vi List of Tables 2.1 Dependence of the ion content in the plasma source's effluent on the number of baffles present at the output of the plasma source. The gas pressure was approximately 80 mTorr, the excitation frequency was 185 MHz and the applied power was 50W 28 3.1 Lattice constant, a, and elastic stiffness constants, Cy, of GaAs and zinc blende GaN : 37 3.2 Change in nitrogen content, x, as a function of As2 flux and the substrate temperature. The subscripts "high" and "low" refer to the magnitude of the As2 flux. 7 is the exponent of the arsenic flux dependence of the nitrogen content 44 4.1 Results extracted from substrate curvature measurements carried out on In-GaAs and InGaAsN films. R! is the maximum relaxation rate, p' is the maximum rate of change of the dislocation density. 74 4.2 Comparison of I n x G a i - x A s / G a A s critical thickness (hc) results measured by different research groups using various in situ measurement techniques. . . 75 4.3 Summary of XRD, T E M and substrate curvature data comparing the strain state of InGaAs and InGaAsN samples grown at two different substrate tem-peratures. R is the relaxation coefficient, / is the lattice mismatch, and p is the dislocation density. (XRD and T E M data courtesy of the Alexey Kovesh-nikov and Victoria Fink respectively, Department of Physics, Simon Fraser University, Burnaby (B.C.)) 76 5.1 Peak photoluminescence intensity of In0.3Gao.7As0.994N0.006 (nominal) quan-tum wells grown at different substrate temperatures and different V/III ra-tios. The emission wavelength is in the 1215 to 1255 nm range 88 5.2 Summary of the effect of one minute rapid thermal anneals on the pho-toluminescence of In^Gai-yAsi-ajNx single quantum wells. / is the peak photoluminescence intensity of the as grown material and G is the peak pho-toluminescence intensity gain of the annealed material 95 vii List of Figures 1.1 The curved solid lines give the bandgap of the ternary alloys, GaNzAsi-a: and In^Gai-^As as a function of lattice constant. The bowing parameter is 14.2 eV and 0.43 eV for GaAsN and InGaAs respectively. The solid ver-tical line gives the bandgap of the Ina^Gai-a^Asi-xNa; alloy which has a lattice constant equal to that of GaAs. The solid horizontal line indicates the technologically important 0.96 eV (1.3 yum) bandgap energy. 3 2.1 Schematic representation of a helical RF resonator. One end of the helix is shorted to the shield of the transmission line whereas the other is left open circuited. RF power is provided by directly connecting the supply to one of the turns of the coil 9 2.2 Schematic representation of the helical resonator. The RF tap connects to the inner conductor of the transmission line, dividing it into two sections, one short circuited, the other open circuited 10 2.3 Typical equivalent circuit used to model an infinitesimal section of transmis-sion line. The model consists of lumped elements 11 2.4 Computed frequency dependence of the reflection coefficient associated with a lossy helical resonator, b is a dimensionless propagation constant which is proportional to the excitation frequency. The attenuation factor, a, was set to 0.05 and assumed to be independent of the excitation frequency. 13 2.5 Calculated quality factor, Q, and frequency shift, Ab/b, of the first harmonic of the helical resonator as a function of the dimensionless loss parameter, a. 14 2.6 Calculated position of the RF tap, x, required to achieve resonance as a function of the dimensionless loss parameter, a. The shaded area indicates the range of loss parameters where the resonance is washed out. It is only in this region where the minimum reflection coefficient, p, is non-zero 16 2.7 Reflection coefficient, p, of the RF plasma source as a function of the ex-citation frequency with the coupling loop in three different positions along the coil. Measurements were performed using a network analyzer on the unloaded resonator 16 2.8 Schematic representation of the RF plasma source designed for the M B E growth of GaAsN 18 viii 2.9 Cross-sectional view of the three-stage baffle that terminates the P B N dis-charge tube of the RF plasma source. Top: front view of each baffle stage. . 19 2.10 Optical emission spectrum from nitrogen plasmas confined in a 8 mm diam-eter tube. The excitation frequency was 70 MHz and the applied power was approximately 50W. Both spectra are normalized to the atomic emission intensity at 746.8 nm. The spectrum is a complex superposition of lumines-cence which is due to rotational, vibrational and electronic energy transitions in the species present in the plasma 21 2.11 Intensity ratio of the optical emission at two different wavelengths, one cor-responding to an atomic transition, the other corresponding to a molecular transition. The excitation frequency was 70 MHz and the applied power was approximately 50W 22 2.12 Schematic of the RF plasma source inserted in the UHV test chamber. . . . 24 2.13 A M U 14 signal measured as a function of time with a mass spectrometer. The plasma was cycled on and off during the measurement. The A M U 14 signal is proportional to the sum of the molecular and atomic nitrogen in the effluent 25 2.14 Fraction of nitrogen atoms present the in the flux emitted from the plasma source inferred from the mass 28 signal of a mass spectrometer. The applied power was approximately 50W 26 2.15 Atomic nitrogen flux emitted from the RF plasma source as a function of the discharge pressure. The applied power was approximately 50W 27 3.1 2 fj,m A F M images taken from homoepitaxial GaAs thin films grown under identical conditions except for the As2 flux. The growth temperature was 555°C and the growth rate was 10.4 nm/min. Both images have a 2 nm greyscale. ( a ) The V/III ratio is 1 and the rms roughness is 0.28 nm. ( b ) The V/III ratio is 2.8 and the rms roughness is 0.20 nm. The white arrow is oriented along the [OlT] crystal direction 32 3.2 Power spectral density contours taken from the PSD computed with 5x5 /xm A F M images of the samples shown in Figure 3.1. The value of the PSD along the contours is 5 nm 4 34 3.3 SIMS depth profile carried out on a typical G a A s i _ x N x / G a A s epitaxial thin film (x = 1.4%). The concentration of boron and nitrogen is measured throughout the film. The sample surface is located at 0 \xm on the horizontal axis, the substrate-buffer layer interface is located at approximately 0.6 fim. (Data courtesy of Rick Streater, Nortel Networks, Ottawa (Canada)). . . . 35 3.4 Typical 004 rocking curves obtained from GaAsi_xNa; epitaxial thin films grown on GaAs. Curves for three different compositions are plotted. The data are vertically offset for clarity. The nitrogen content is indicated next to each curve 37 ix 3.5 Nitrogen content of G a A s i - ^ N ^ films as a function of 004 X R D peak splitting. The x-rays used for the measurement had a wavelength of 1.5405 A. The nitrogen content was determined by secondary ion mass spectroscopy. The calculation relies on the elastic parameters of the ternary alloy being a linear interpolation of the elastic constants of GaAs and GaN 38 3.6 Nitrogen content in GaAsN thin films grown under fixed growth conditions except for the substrate temperature. The concentration is referenced to the nitrogen content at 450°C. The solid line is a fit to the data with a 2.1 eV activation energy for nitrogen desorption 41 3.7 Asymmetric 115 x-ray diffraction reciprocal space map of a heterostruc-ture consisting of a GaAso.9906No.0094 and a GaAso.99i6No.oo84 layer grown on GaAs at a substrate temperature of 500°C. The two diffraction peaks are highlighted with vertical arrows. The difference in nitrogen content between both GaAsN layers is due to an increase in the As2 flux by a factor of 1.6. Each contour corresponds to a factor of 2 change in the diffracted inten-sity. The origin of the axes is set at the GaAs diffraction peak, q x = -0.250' A - 1 and qz = 0.884 A - 1 . (Data courtesy of Marlene Jeffries, Department of Physics, Simon Fraser University, Burnaby (B.C.)) 43 3.8 Schematic representation of the experimental setup for in situ UV elastic light scattering measurements 44 3.9 Light scattering measured at a spatial frequency of 41 fxm~l during the growth of 1.8% GaAsN for two different runs carried out at a substrate tem-perature of 500° C but with different As2 overpressures. The insert shows on a log scale the data taken from the sample grown with a high As2 flux with the background scattering from the buffer layer subtracted 46 3.10 Scanning electron microscope image of a rough GaAsN thin film grown on GaAs. The substrate temperature was 502°C and the nitrogen content was 1.4%. The viewing angles with respect to the sample normal were 45° (a) and 90° (b) 47 3.11 Digital camera image of quarter 2" wafer after the growth of GaAsN without sample rotation. A rough three dimensional growth took place on a part of the wafer 48 3.12 Relative Ga flux as a function of position on the wafer for a stationary sample and a rotating sample. Percentages are relative to the Ga flux at the center of the wafer. The zone highlighted in grey indicates the ± 1.5% range. . . 50 3.13 Diagram showing the boundary between smooth and faceted GaAsN films grown on GaAs. The position of each marker indicates the composition and growth temperature of the GaAsN epilayer. The films indicated by the square and round markers designate faceted and smooth surface morphologies respectively. 51 X 3.14 2x2 fim A F M images of three GaAso.9sNo.02 (nominal) samples grown with the same nitrogen flux and different substrate temperatures and arsenic fluxes, (a) Tsub = 500°C, As 2 BEP = 7 .6x l0 - 6 Torr, the rms roughness is 24.0 nm. (b) Tsub = 500°C, As 2 BEP = 1.5 x l O - 6 Torr, the rms roughness is 1.2 nm. (c) Tsub = 460°C, As 2 BEP = 1.5 x l O - 6 Torr, the rms roughness is 1.3 nm. The white arrow is oriented along the [Oil] crystal direction. . . 52 3.15 Symmetric 004 x-ray diffraction 6 — 26 measurements taken from the rough and smooth areas on the same sample. The nitrogen content of the film was 1.2% and 1.4% on the 2D and 3D regions of the sample respectively. The growth temperature was 500°C. The orientation of the incident x-ray beam with respect to the crystal axes is indicated in the legend 54 3.16 Asymmetric 115 x-ray diffraction reciprocal space map of a smooth 2D GaAso.9s9No.011 epilayer grown at a substrate temperature of 500°C. Each contour corre-sponds to a factor of 4 change in the diffracted intensity. The origin of the axes is set at the GaAs diffraction peak, = -0.250 A - 1 and qz = 0.884 A - 1 . (Data courtesy of Marlene Jeffries, Department of Physics, Simon Eraser Uni-versity, Burnaby (B.C.)) 55 3.17 2x2 jum A F M images of GaAso.996No.004 samples grown one after the other in the same conditions except for the presence of a Bi flux, (a) No Bi flux, the rms roughness is 1.14 nm (b) The Bi BEP is 1 .8xl0 - 5 mBar, rms roughness is 0.10 nm. The substrate temperature was 460°C and the As/Ga ratio was approximately 1. The arrows indicate the [OlT] crystal direction. . . . . . . 57 3.18 Light scattering measured at a spatial frequency of 41 ^ m _ 1 during the growth of GaAs, Ino.04Gao.96As, GaAso.99No.01 and In6.04Gao.96Aso.99No.01 layers. The solid horizontal lines at the top of the graph indicate the time intervals over which the In and N fluxes are impinging on the surface. The Ga flux is turned on throughout the growth. The substrate temperature was 500°C 59 4.1 Section of a cubic crystal showing a dislocation having thread and misfit segments 62 4.2 Illustration of a cubic cell showing the orientation of the Burgers vector for a 60° screw-edge dislocation. The dislocation line is aligned with [011]. The Burgers vector makes an angle of 60° with both the dislocation line, [011], and the direction along which the dislocation relieves strain, [Oil] 63 4.3 Illustration of the various steps involved in the strain relaxation process. . . 65 4.4 Schematic representation of a substrate on which a strained epilayer is de-posited, (a) The substrate is infinitely rigid and the epilayer accomodates all of the elastic deformation due to coherency stress, (b) The substrate has elasticity and is curved in order to relieve a fraction of the stress in the film. 66 4.5 Illustration of the strain profile in a compressively strained heterostructure. The magnitude of the effect of the substrate elasticity on the strain profile is greatly exaggerated for illustrative purposes 4.6 Schematic representation of the experimental setup used to measure the sub-strate curvature in situ 4.7 Spot spacing as a function of film thickness for a set of three Ino.osGao.92 As/GaAs growths carried out under exactly the same conditions except for the total epilayer thickness. The amount of relaxation, R, as measured by X R D is indicated for each data set along with the film thickness, h. The substrate temperature was 450°C. The samples were rotated during growth. The data are offset for clarity. 71 4.8 Relative spot spacing measured as a function of film thickness for Ino.osGao.92 As and Ino.12Gao.88Aso.99No.01 runs carried out at 400°C and 450°C. The data are offset for clarity. 72 4.9 Relaxation coefficient as a function of thickness for InGaAs(N) epilayers each having a lattice mismatch of 0.62%. The growth temperature was 450°C. . 73 4.10 27 x 27 fim A F M image of a 600 nm thick strain relaxed GaAso.9s5No.015 epilayer (/ = -0.3%). The RMS roughness of the image is 1.5 nm. The arrow is aligned along the [Oil] crystal direction. 78 4.11 Dark field image of a strain relaxed GaAs0.9s4N0.0i6 hi™ grown at 460°C. The greyscale of the image is inverted. The wafer is illuminated with a bright white light which impinges on the sample at grazing incidence in the direction indicated by the arrow. The sample is imaged from the top. Each panel shows the same sample oriented differently so that the incident light is aligned with [Oil] (a) and [011] (b) 79 4.12 (a) Bright-field transmission electron microscopy image, g=(400), taken from a <011> cross section of a 300±30 nm thick GaAs0.97sN0.022/GaAs film. A crack is seen to propagate from the surface through the interface into the substrate. The position of the interface is indicated by a horizontal white line. The surface roughness amplitude is about 5 nm. (Data courstesy of Victoria Fink, Department of Physics, Simon Fraser University, Burnaby (B.C.)). (b) Illustration of "T"-shaped crack in a tensile strained film. . . . 80 5.1 Photoluminescence data taken at a temperature of 4.2K from 2D and 3D GaAsN films grown at 500°C. The data are offset for clarity. (Data courtesy of Denis Karaiskaj, Department of Physics, Simon Fraser University (Burn-aby B.C.)) 83 5.2 Photoluminescence data taken at a temperature of 4.2K from two GaAso.993No.007 (nominal) samples grown at a substrate temperature of 540°C under differ-ent As2 overpressures. (Data courtesy of Denis Karaiskaj, Department of Physics, Simon Fraser University (Burnaby B.C.)) 84 5.3 Room temperature photoluminescece spectra taken from as grown Ino.isGao.ssAsi-a; single quantum wells. Each spectrum is normalized to the Ino.15Gao.85As peak intensity. The nitrogen content of the epilayers, the F W H M and the Urbach slope, E 0 , of the luminescence are given in the legend. The growth temperature was 445°C and the V/III ratio was 4 86 5.4 Map of the peak photoluminescence intensity as a function of the lateral position on the wafer, x = 0 mm corresponds to the edge of the wafer, x = 12 mm corresponds to the middle of the wafer. For each data set, the photoluminescence data is normalized to the intensity recorded at x = 0. . . 89 Xll 5.5 Room temperature photoluminescence spectra taken from as grown Ino.15Gao.85 As and Ino.15Gao.85Aso.993No.007 single quantum wells grown in the same condi-tions except for the magnitude of the Bi flux. The Bi flux is quantified by the Bi cell temperature as indicated in the legends. The growth temperature was 450°C and the V/III ratio was 4. Each spectra is normalized to the peak intensity of the InGaAs SQW grown with no Bi flux 91 5.6 Room temperature photoluminescence spectra taken from an In0.3Gao.7As0.994N0.006 (nominal) single quantum well. The spectra were taken from a different piece of the same wafer. Each sample was annealed for one minute at the temper-ature indicated in the legend 93 5.7 Room temperature electron mobility of silicon-doped GaAsi-zNr samples determined using Hall effect measurements. The growth temperature was 460°C. The horizontal dotted line indicates the mobility of a GaAs sam-ple grown under the same conditions. The Si impurity concentration was 6 x l 0 1 7 c m - 3 96 5.8 Charge carrier mobility as a function of nitrogen content for GaAsN and InGaAsN. The GaAsN data has been corrected for phonon scattering as described in the text. The InGaAsN data is taken from the work of Kurtz et al. [68] and Robinson et al. [69] 98 5.9 Carrier concentration of silicon-doped GaAsi-xNr samples determined us-ing Hall effect measurements. The growth temperature was 460°C. The Si impurity concentration was 6 x l 0 1 7 c m - 3 100 A . l GaAsN conduction band diagram showing the E + and E_ levels which are due to the anticrossing of the GaAs conduction band and the localized nitrogen state. The calculation was carried out using values consistent with those used by Shan et al.[72] for the calculation of InGaAsN energies at the T point. . 115 Xlll Acknowledgements This work could not have been done without the help of a large group of people. I would like to take this opportunity to thank them all for their hard work, which was much appreciated. In particular, I would like to thank M . Jeffries, V. Fink, A. Koveshnikov, A. Chahboun, S. Francoeur, J. Ramsey, D. Karaiskaj and M . Thewalt for their experimental contributions. I would like to thank Mario Beaudoin and Tom Pinnington who both taught me how to grow M B E films. I would like to thank Karen Kavanagh and Itzhak Kelson for all the time they spent with me sharing their knowledge and experiences. I would also like to thank Anders Ballestad, Eric Nodwell, Ben Ruck, Jens Schmid, Eric Strohm and Sebastien Tixier for helping me with carrying out my work and for providing insight that was useful in understanding many of my results. Not only did these people contribute intellectually to my work, but, through their good natured and often very humorous personalities, they made the lab into a tremendously fun place to work. I would like to thank Jim MacKenzie for all the time he spent with me designing the plasma source and fixing things I broke. We could not keep things running without him. I would like to mention David Jez who always had a solution to my computer/instrumentation problems. I would like to thank Tom Tiedje for taking me into his group. No matter how many things were going on around him, Tom was xiv always available to spend time with me to talk about my project or just about any other subject I was trying to deal with. I would like to thank my parents and my brother for all the support they have given me throughout my life. I also thank my new found family who has been very encouraging these past years. Finally, I would like to thank my wife, Catherine Lai, who unconditionally supported me and helped me in many different ways during my degree. 1 Chapter 1 Introduction In order to increase the bandwidth accessible to individual internet users, the optical part of the network must be brought as close as possible to the subscriber. Having a high-capacity optical fiber directly connected to the home of the subscriber would require low cost high performance emitters in order to optically relay information from the home up to the network. Present day laser technology is prohibitively expensive for this application. In 1996, Kondow[l] demonstrated that In^Gai-yAsi-zNa; (x < 0.05) grown on GaAs is a new narrow bandgap semiconductor alloy that possesses many advantages for use in the active region of long wavelength telecommunications lasers emitting at 1.3 /zm, the wavelength at which dispersion is minimal in single mode optical fiber. The high conduction band offset between InGaAsN and GaAs ensures good electron confinement in the quantum well, which means that temperature variations have less of an impact on the electron population in the well. The threshold current, hhreshold, of an InGaAsN laser is therefore less temperature sensitive. Several research groups have reported InGaAsN lasers 2 T with characteristic temperatures, T 0 , above 100K (Ithreshoid ~ eTo)[2][3]. This is sufficient to operate the laser without a thermoelectric cooler: a significant cost reduction. Because InGaAsN is epitaxially grown on GaAs, the alloy takes advantage of the many benefits of the substrate material. When compared to InP, GaAs is more robust, substantially cheaper and available in large diameter wafers. The current industry standard wafer diameter is 6" for GaAs whereas 4" InP is just beginning to become available. In addition to these cost-saving features, GaAs has many physical properties that are advantageous for the fabrication of electronic and optoelectronic devices. GaAs is compatible with the growth of AlGaAs at any composition. Relative to InAlGaAs/InAlAs alloys lattice matched to InP, GaAs/AlGaAs multilayers grown on GaAs have a high refractive index contrast and a high thermal conductivity, which are beneficial for Bragg reflectors used in vertical cavity surface emitting lasers (VCSELs). Also, buried AlAs layers can be selectively oxidized. This makes possible the fabrication of device structures containing buried oxides which are useful for current and light confinement. Presently, several companies such as Infineon and Cielo are developing InGaAsN based 1.3 ^m VCSELs[4]. InGaAsN also has certain disadvantages. The alloy must contain around 1% ni-trogen in order to achieve a bandgap of 0.95 eV (A=1.3 /xm). However, the addition of nitrogen degrades the electronic properties of the semiconductor such as the luminescence efficiency and the electron mobility. Currently, dilute nitrides are not well understood. It is therefore unclear if the degradation of the electronic properties of InGaAsN with increasing nitrogen content is truly intrinsic to the material or can be controlled with a suitable choice of the growth conditions. 3 > <D Q . CO CD •o C CO 4 h 3 h 2 h GaN InGaAs GaAsN O Data GaAs InAs -\2 0.3 0) < CD, CD 0.4 £ 0.5 0.6 0.8 1.1 TP 3 10 4.0 4.5 5.0 5.5 6.0 6.5 Lattice parameter (A ) Figure 1.1: The curved solid lines give the bandgap of the ternary alloys, GaN^Asi-a; and I%Gai_ y As as a function of lattice constant. The bowing parameter is 14.2 eV and 0.43 eV for GaAsN and InGaAs respectively. The solid vertical line gives the bandgap of the InszGai-sjrAsi-xNa; alloy which has a lattice constant equal to that of GaAs. The solid horizontal line indicates the technologically important 0.96 eV (1.3 fim) bandgap energy. Figure 1.1 gives the lattice parameter dependence of the bandgap of In^Gai-yAs and GaAsi-rcNx, which are subsets of the In^Gai-^Asi-xNx materials system. The circular markers in Figure 1.1 are data taken from a variety of sources in the literature[5][6][7][8]. Each curve was calculated by fitting the data to the following expression for the bandgap, E*B = xEf + (1 - x)E% - bx(l ~ x) where the superscripts A and B designate the constituents of the alloy, x is the compo-sition and b is the bowing parameter. Measured values of the bandgap are only available 4 for compositions where relatively thick layers of the alloy can be epitaxially grown on a substrate. Hence, in the case of the GaAsN curve, all the data points are close to the GaAs end member. As seen in Figure 1.1, GaN is a wide bandgap semiconductor which has a bandgap in the violet region of the visible spectrum. One might expect that incorporating small quantities of nitrogen into GaAs would result in an alloy having a larger bandgap than GaAs. However, this is not the case. For small nitrogen concentrations, the interaction of the nitrogen impurity states with the GaAs conduction band actually results in a lowering of the bandgap (see Appendix A). Figure 1.1 shows that the difference in the bowing parameter between GaAsN and InGaAs is quite striking. Up to now, GaAsN in the intermediate composition range has not been successfully synthesized. Since the lattice parameter of GaN is smaller than that of GaAs, GaAsN alloys grown on GaAs are under tensile strain which limits the thickness with which epilayers of this material can be grown without cracks or dislocations. Also, the large lattice mismatch between GaN and GaAs can result in phase separation of GaAsN which will severely degrade the material properties[9][10][ll]. Presumably, non-equilibrium growth conditions are necessary for the synthesis of these alloys. The addition of In to the GaAsN alloy results in a further lowering of the bandgap as well as a compensation of the nitrogen-induced strain due to the large size of In atoms. As shown in Figure 1.1, it is therefore feasible to engineer materials having a bandgap in the 1.3-1.55 /xm wavelength range which are either lattice matched to GaAs or pseudomorphically strained. 5 The objective of the present work is to improve the material quality of dilute nitride-arsenides by better understanding the growth process. In Chapter 2, the char-acterization of a radio-frequency plasma source fabricated specifically for the purpose of incorporating nitrogen into InGaAsN is discussed. Several features of the plasma source were designed in order to improve upon commercially available sources. Chapter 3 describes how the nitrogen incorporation and the surface morphology of the epilayers are controlled by the growth conditions. In Chapter 4, the effect of nitrogen on strain relaxation is dis-cussed. The structural properties studied in these two chapters have a strong impact on the electronic and optical properties of the material, which are described in Chapter 5. 6 Chapter 2 Radio frequency plasma source In this chapter, we discuss the design and performance of the radio-frequency (RF) plasma source that was developed for the incorporation of nitrogen into GaAs epitaxial thin films. To begin, we will review some of the early work done on plasma-assisted incorporation of nitrogen into compound semiconductors grown by molecular beam epitaxy (MBE). 2.1 Molecular nitrogen dissociation by plasma discharge Gaseous nitrogen is non-toxic and non-flammable. It is also easily pumped in a ultra high vacuum (UHV) environment. The nitrogen molecule does not contain any ad-ditional elements which may act as detrimental impurities. However, due to the strong 28 eV binding energy of the nitrogen molecule [12], thermal cracking is not compatible with the thermal stability of known refractory materials. Therefore, another method must be employed to sufficiently activate molecular nitrogen in order to achieve appreciable incorpo-ration of nitrogen into GaAs. The generation of a nitrogen plasma is an attractive solution 7 to this problem. The output of a nitrogen plasma is commonly referred to as "active nitrogen" and has several different constituents: ions, atoms and molecules (all of which can be in an excited state). By establishing a flux of active nitrogen on the growing semiconductor's surface, nitrogen can incorporate into the crystal matrix. As of yet, it is unclear if the incorporation of nitrogen in GaAsN is mainly due to nitrogen atoms or to excited-state nitrogen molecules. In the case of GaN, excited-state molecules have been proven to play an important role in the crystal growth[12]. Also, energetic ions contained in the source's effluent tend to create defects in the crystal lattice. In the context of molecular beam epitaxy, the earliest use of an RF plasma source in conjunction with nitrogen was for p-type doping of the II-VI compound semiconductor ZnSe[13][14][15]. In this system, nitrogen acts as an acceptor. At high concentrations, dopant compensation limits the maximum carrier concentration in the material. Experi-ments show that the material quality of p-type ZnSe is improved when the energetic ions contained in the plasma source's flux are removed by using a pair of electrostatic deflector plates[13]. Other work on the growth of GaN using RF-assisted M B E shows that the elec-tron mobility is 2.5 times greater for material grown with metastable nitrogen molecules rather than atomic nitrogen [12]. 2.2 RF helical resonator plasma source design. Commercially available plasma sources typically function only in a narrow window of operating parameters. This contributes to one of the principal disadvantages of traditional 8 inductively coupled plasma sources: the difficulty of reliably striking and maintaining the plasma under a variety of power and pressure conditions. In order for one to grow precisely engineered epitaxial structures, one must have excellent control over the on/off state of each source in the M B E growth chamber. For this reason, high quality-factor RF resonators are an attractive solution for coupling power into the plasma. Prior to the ignition of the plasma, the RF resonator creates large electromagnetic fields in the volume containing the discharge. For a range of pressures, the plasma can therefore be rapidly started by simply turning on the RF power. Also, traditional inductively coupled plasma sources require a matching box in order to ensure maximum power transmission to the plasma. The matching box transforms the impedance of the coil coupled to the plasma to match the impedance of the RF power supply. Typically, RF matching boxes are expensive, have three different tuning parameters and dissipate power. In the following paragraphs, we will describe the helical resonator and explain the physics behind its operation. 2.2.1 General description of the helical resonator A length of transmission line can be made into a resonant circuit simply by shorting one end and leaving the other end open circuited. By exciting the section of transmission line with an RF field whose quarter wavelength corresponds to the length of the line, a resonant standing wave will be created. Conventional coaxial lines can be made into resonators using this scheme. However, the wavelength is on the order of 10 m for frequencies at which high power generators are available at reasonable cost. Therefore, the size of the required coaxial line is prohibitively long. The helical resonator was initially developed as a solution to this problem[16] and has proven to be an excellent method for coupling RF power to 9 Figure 2.1: Schematic representation of a helical RF resonator. One end of the helix is shorted to the shield of the transmission line whereas the other is left open circuited. RF power is provided by directly connecting the supply to one of the turns of the coil. plasmas[17][18][19]. A schematic of the helical resonator is given in Figure 2.1. The helical resonator is analogous to a conventional coaxial line except for the fact that the inner conductor is wound into a coil whose axis is parallel to that of the shield. As shown in Figure 2.1, one end of the coil is shorted to the shield of the transmission line whereas the other end is left open-circuited. RF power is coupled to the resonator by connecting one of the coil's turns to an RF power supply. As we shall see later in this chapter, depending on the position of the tap along the length of the resonator, the resonance can be optimized. Because of its geometry, the helical resonator is well suited for plasma generation in an M B E system. The field distribution inside the resonator is quite complex, since both the electric and the magnetic fields have axial, radial and azimuthal components[20]. The axial electric field which is generated by the voltage difference between the short circuited and open circuited 10 Closed circuit Open circuit Shield RF generator Figure 2.2: Schematic representation of the helical resonator. The RF tap connects to the inner conductor of the transmission line, dividing it into two sections, one short circuited, the other open circuited. ends of the resonator drives the discharge. Electrons are accelerated along the length of the discharge tube thereby ionizing molecules and increasing the electron density in the plasma. The axial magnetic field confines the electrons away from the walls of the discharge tube. 2.2.2 Lumped element transmission line model Using standard transmission line theory, we can develop an intuitive understanding of how the helical resonator works. Figure 2.2 schematically represents the helical resonator. The RF power supply is connected to two distinct transmission lines in parallel which are respectively terminated with a short circuit and an open circuit. To model the transmission line, we consider the standard lumped element equivalent circuital] shown in Figure 2.3. 11 l(z,t) RAz LAz l(z+Az,t) a + A M M A M ^ o + V(z,t) CAz V(z+Az,t) o o Az Figure 2.3: Typical equivalent circuit used to model an infinitesimal section of transmission line. The model consists of lumped elements. In Figure 2.3, L is the self inductance in the inner conductor of the transmission line whereas C is the capacitance between the inner conductor and ground. R is a resistance that represents losses in the transmission line. These losses can be caused by a variety of phenomena, including power absorption by the plasma discharge. The units of these quantities are expressed per unit length (i.e. R is in 0,/m). A transmission line will reflect a certain amount of power depending on the impedance of the termination relative to the characteristic impedance of the line. The reflection coefficient is defined by the following expression: where Za is the characteristic impedance of the line which is determined by the lumped elements shown in Figure 2.3 and ZL is the impedance of the terminating load. The reflec-P = ZL + Z0 (2.1) 12 tion coefficient, p, quantifies the amplitude and the phase of the reflected voltage wave with respect to the incident voltage wave. As we shall see in the following paragraphs, when resonance is achieved, p approaches zero and the incident power is entirely absorbed by the load. When an ideal transmission line (R = 0) of length / is terminated with a load with impedance ZL, the impedance measured at the input is given by r 7 / 1 s _ r 7 ZL +jZ0 tan (pi) Z { l ) - Z o Z 0 + jZLtan((3l) ( 2 - 2 ) where j3 is the propagation constant of the electromagnetic waves that are guided within the transmission line. By inspection of Equation 2.2, we find the following expressions for the input impedance of short circuited (Zsc) and open circuited (Zoc) transmission lines: Zsc = jZ0tan(J3l) (2.3) Zoc = -jZocot(0l) (2.4) These equations highlight a fundamental result of transmission line theory. If the wavelength is such that / < A/4, a short circuited transmission line will act as an inductor whereas an open circuited line will act as a capacitor. For A/4 < I < A/2, the situation is reversed. In our case, this result gives an intuitive picture with which we may understand the system of interest: each arm of the helical resonator is analogous to one element of a parallel LC circuit. The equivalent impedance, Zeg, of the circuit is then given by: - L - + (2.5) 7 7 7 ^eq ^sc *-<oc By extending this way of thinking to the lossy transmission line, we can compute the impedance of the helical resonator. In this case, the equations that describe the system 13 — x Is — 0.144 - 0.049 i| I I I I f I 1/4 1/2 3/4 1 5/4 3/2 7/4 2 b / 7i Figure 2.4: Computed frequency dependence of the reflection coefficient associated with a lossy helical resonator, b is a dimensionless propagation constant which is proportional to the excitation frequency. The attenuation factor, a, was set to 0.05 and assumed to be independent of the excitation frequency. are the following: Zsc = Z0tanh(7Z) (2.6) Zoc = Z 0 coth( 7 /) (2.7) where j = a+j(3 (2.8) In these equations, 7 is the complex propagation constant of the electromagnetic waves guided by the transmission line. The reader should notice that, in the case of lossy trans-mission lines, hyperbolic functions are used. Therefore, the complex part of 7 describes the propagation of the wave along the line and the real part quantifies the losses in the line, which are proportional to the magnitude of the distributed resistance shown in Figure 2.3. For simplicity, we will set the characteristic impedance of the line equal to one and 14 o 1000 6 ' 1 1 1 1 1 1 1 | 1 I I I 1 " i : • • • • -100 -D • • -10 • • Q • • • Ab/b • a? 1 • • • i 1111ii i i i i i 111 i i i i i v-2 x-3 >-4 2 4 6 2 4 6 2 4 6 0.001 0.01 0.1 1 CT CT Figure 2.5: Calculated quality factor, Q, and frequency shift, Ab/b, of the first harmonic of the helical resonator as a function of the dimensionless loss parameter, a. write the impedances in terms of a dimensionless propagation constant b = f3L which is proportional to the excitation frequency. We then model the behaviour of the helical res-onator by considering the reflection coefficient due to a load consisting of Zeq as expressed in Equations 2.5, 2.6 and 2.7. The position of the RF tap is now expressed as a fraction of the total helical resonator length as illustrated in Figure 2.2. Figure 2.4 shows the cal-culated frequency dependence of the reflection coefficient. These results show that the Q of the resonance depends on the position of the RF tap. Figure 2.4 also shows that, for a particular position of the RF tap and a particular value of the loss, the use of higher harmonics can yield better matching. The reflection coefficient also changes significantly depending on the magnitude of the losses, which are represented in the model by the dis-tributed resistor. The impedance matching condition of the first harmonic of the resonator has been calculated for a range of losses. Figure 2.5 shows the calculated Q of the resonator as a function of a dimensionless loss parameter, a = aL. These results show that the Q of 15 the resonator is essentially inversely proportional to the magnitude of the losses. Figure 2.5 also shows that the resonance frequency shifts by less than 3% over the entire range of loss parameters. Therefore, the tuning of the helical resonator is essentially one dimensional. Figure 2.6 shows that by tuning both the excitation frequency and the tap position, zero reflection can be achieved over a range of losses spanning three orders of magnitude. The reflection coefficient only becomes greater than 1 0 - 4 when the losses are sufficiently large to completely wash out the resonance. Figure 2.6 also shows that the entire interval of possible RF tap positions must be covered in order to achieve resonance over a wide range of losses. Figure 2.7 gives a network analyzer measurement of the reflection coefficient of the helical resonator as a function of frequency. The results are qualitatively similar to those shown in Figure 2.4. Depending on which harmonic was being excited and the tap position, the measured Q of the unloaded resonator ranged between 150 and 475. The Q measured with a Bird "Thruline" wattmeter drops to the 10 to 50 range when the plasma is ignited thereby indicating that most of the power is dissipated in the plasma. The model presented here provides a good description of the frequency dependent impedance of the helical resonator. Quantitatively determining the various parameters in the model would require measuring the impedance of the resonator with the plasma ignited, which is not possible with the network analyzer. Such a detailed electrical characterization of the source is not the object of the present work. However, the change in Q of the loaded and unloaded resonators can be compared to the calculations given in Figure 2.5. According to these results, turning on the plasma increases the losses by a factor of approximately 40. 16 Figure 2.6: Calculated position of the RF tap, x, required to achieve resonance as a func-tion of the dimensionless loss parameter, a. The shaded area indicates the range of loss parameters where the resonance is washed out. It is only in this region where the minimum reflection coefficient, p, is non-zero. Excitation frequency ( MHz ) Figure 2.7: Reflection coefficient, p, of the RF plasma source as a function of the excitation frequency with the coupling loop in three different positions along the coil. Measurements were performed using a network analyzer on the unloaded resonator. 17 2.2.3 Plasma source configuration Figure 2.8 gives a schematic representation of the RF plasma source designed for the growth of GaAsN. The helical resonator is mounted on a 4.5" conflat flange. Nitrogen gas is fed into the pyrolitic boron nitride (PBN) discharge tube via a stainless steel line which is welded onto the flange. Because an inert dielectric material must be used in the discharge area, a P B N tube replaces the stainless steel inside the RF shield. The Q of the resonator is the same whether the discharge tube is composed of quartz or PBN. Quartz is not used in the plasma source because of the possibility of contaminating the GaAsN with oxygen. RF power is coupled into the resonator by using a two-turn inductor that is concentric with the helical resonator. Because the coupling mechanism is physically detached from the resonator, it becomes possible to maximize the power transmitted to the discharge by moving the coupling loop along the axis of the resonator. This is analogous to changing the value of "x" in the model that was previously discussed. One should note that the model does not take into account the coupling between the RF power supply and the resonator coil. A UHV-compatible coaxial line connects the coupling loop to a feedthrough mounted on a 1.3" conflat miniflange which is attached to the main flange. The plasma source is terminated with a baffle in order to minimize the ion content in the exiting flux. As previously mentioned, a low ion flux is known to be important in order to fabricate high quality material. The baffle neutralizes most of the ions through wall collisions. Atomic nitrogen is very long lived and can survive many collisions with non-metallic surfaces without recombining into molecular nitrogen. However, ions rapidly lose their charge after coming into contact with a surface. Figure 2.9 shows an expanded 18 Nitrogen in I 4.5" conflat flange Coupling loop Figure 2.8: Schematic representation of the RF plasma source designed for the M B E growth of GaAsN. view of the baffle as it was implemented in the plasma source. Gas molecules that exit from the discharge tube have no direct line of sight to the sample due to the presence of the baffle. Several wall collisions are necessary in order for a gas molecule to find its way out of the discharge tube. The dimensions of the downstream baffle stages were chosen in order to minimize the effect on the total conductance of the aperture, which is limited by the first baffle stage. We have also studied the effects of placing electrostatic deflector plates at the exit of a plasma source. The field created by a large potential on the electrostatic deflector plates steers charged species out of the reactive nitrogen flux and away from the sample surface or causes them to collide with the deflector plate. However, this solution has several drawbacks. We find that it is difficult to adjust the electrostatic field in order to totally eliminate ions from the flux, possibly because secondary ions are produced in wall collisions. 19 • / / / / / / / / / / / / / / / / _ '////. ////// 7-7*/ ///// Figure 2.9: Cross-sectional view of the three-stage baffle that terminates the P B N discharge tube of the RF plasma source. Top: front view of each baffle stage. Also, contamination could result from sputtering the metallic deflector plate. Energetic neutrals are not affected by the deflector plates and are free to damage the crystal. In the case of the baffle, energetic neutrals thermalize through collisions with the baffle. Finally, the baffle is easy to implement since it is simply comprised of machined P B N discs which are held into the P B N tube by a press fit. Deflector plates on the other hand require additional electrical feedthroughs and a high voltage power supply. Measurements of the composition of the output gas from the plasma source will be discussed in the following sections. 20 2.3 Plasma source characterization 2.3.1 Optical emission spectroscopy By measuring the spectrum of the light emitted by a glow discharge, one can identify the chemical species that are present in the plasma. Optical techniques do not easily provide absolute measurements of the concentrations of the various constituents in the plasma. However, in this section, we will show that the emission spectrum of the plasma can be a useful tool in optimizing the design of a plasma discharge. We will begin by describing the basic features that are present in the optical spectrum emitted by our plasma source. Figure 2.10 gives a typical optical emission spectrum observed from a nitrogen plasma excited by the helical resonator. A fiber bundle placed in front of the window shown in Figure 2.8 couples the emitted light into a grating monochromator. The intensity of the monochromatized light is measured with a Hamamatsu R955 photomultiplier tube. The section of the spectrum shown in Figure 2.10 corresponds to an electronic transition between the first two excited electonic states of the nitrogen molecule. These states are designated in spectroscopic terms by B3Hg (second excited state) and A 3 E+ (first excited state) [22]. Al l of the structure that is observed in Figure 2.10, is the product of simultaneous vibrational and rotational transitions that cause a slight shift in the overall energy of the electronic transition. In addition to the lines resulting from vibrational and rotational transitions, there is a strong triplet of lines that occur at wavelengths of 742.4, 744.2 and 746.8 nm. These lines correspond to the 3s AP-3p 4 S° atomic transitions[23]. From this spectrum alone, we can conclude that both atomic and molecular nitrogen are present in the 21 T 730 735 740 745 750 X (nm) Figure 2.10: Optical emission spectrum from nitrogen plasmas confined in a 8 mm diameter tube. The excitation frequency was 70 MHz and the applied power was approximately 50W. Both spectra are normalized to the atomic emission intensity at 746.8 nm. The spectrum is a complex superposition of luminescence which is due to rotational, vibrational and electronic energy transitions in the species present in the plasma. discharge. However, this cannot be taken as a direct measure of the amount of each species that is present since the emission intensities are not a simple function of the concentration of the species present in the plasma. Also, the way the species are extracted from the source can affect the state of the gas. We can optimize the geometry of the discharge by maximizing the intensity of the atomic emission relative to the molecular emission. The ratio of the intensities measured at a wavelength of 746.8 nm (atomic transition) and a wavelength of 775.3 nm (molecular transition) is plotted in Figure 2.11. This data shows that the atomic optical emission 22 c CD g to CD i_ Z J o o E o 'E o •1 1 I - i — i — r — i — | 1 — r , ~' _ • i i_ - • 20 mTorr --O 10 mTorr • -£K Slope = -2 . "l 1 1 i i i i I . . . . i i" 4 5 6 7 8 9 10 Tube diameter (mm) Figure 2.11: Intensity ratio of the optical emission at two different wavelengths, one corre-sponding to an atomic transition, the other corresponding to a molecular transition. The excitation frequency was 70 MHz and the applied power was approximately 50W. grows quadratically with respect to the molecular emission as the discharge tube diameter is decreased. Optical emission efficiencies depend on a number of factors. Therefore, one must be careful not to misinterpret the data in Figure 2.11. One interpretation is that by decreasing the volume of the discharge at a constant applied power, the energy density in the plasma is increased thereby favouring the dissociation of nitrogen molecules into atoms. At a constant length, the volume of the discharge tube is proportional to the area of its cross section. The -2 slope of the data in Figure 2.11 shows that the emission ratio is inversely proportional to the square of the tube diameter which tends to support the energy density argument. Therefore, a smaller discharge tube is preferable in order to maximize the molecular dissociation. Also, Figure 2.11 shows that an increase in the discharge pressure by 23 a factor of two proportionally decreases the atomic/molecular emission ratio. This further supports the argument that the power dissipated per molecule in the plasma determines the dissociation. Similar results where obtained by Merel et al. using a combination of NO titration and optical spectroscopy [24]. However, striking a plasma reliably becomes difficult when the tube diameter is small because the increased surf ace/volume ratio of the tube tends to favour the absorption of the electrons which sustain the discharge. Considering all the above mentioned data, 8 mm was selected as the optimal tube inner diameter. Al l of the following work (plasma source characterization as well as growth experiments) was carried out using a plasma source with an 8 mm diameter, 150 mm long discharge tube. 2.3.2 In vacuo characterization By placing the RF plasma source in a separate ultra high vacuum chamber, we were able to determine the composition of the flux produced by the discharge. Experiments with retarding grids show that the plasma discharge produces ions with energies up to several hundred eV. Ion damage is well known to have a deleterious effect on the electronic properties of IH-V semiconductors. Therefore, it is of interest to suppress these energetic species. Figure 2.12 gives a schematic of how the plasma source is inserted into the UHV test chamber along with the gas handling system necessary to supply nitrogen gas to the plasma. Semiconductor process grade nitrogen gas (99.9999% pure) is injected into the discharge tube via a leak valve. The pressure in the discharge is measured by a bakeable Pirani gauge placed just upstream of the discharge tube. A turbomolecular pump is connected to the discharge tube via a throttle valve. By actuating the throttle valve, the pressure in the discharge tube can be adjusted to the desired value. The use of the turbomolecular 24 RGA or Faraday cup UHV chamber L \ \ Nitrogen in Figure 2.12: Schematic of the RF plasma source inserted in the UHV test chamber. pump has several advantages. The incorporation of impurities due to outgassing from the walls of the gas-handling system is minimized by maintaining a high flow of nitrogen. The turbo pump also can be used to evacuate the nitrogen gas handling system. This facilitates changing the gas bottle without venting the growth chamber. Using a Stanford Research "RGA 200" mass spectrometer, we have measured the relative amplitude of the mass 14 signal ( N + or Ng"4") with respect to the mass 28 signal (N2 ). When the plasma is ignited, the ratio, 7, of the two signal intensities departs from the normal cracking pattern of nitrogen[25] thereby indicating that molecules are being dissociated into atoms. Figure 2.13 shows the mass 14 signal of the mass spectrometer as a function of time. The plasma source was cycled on and off during the measurement. The 25 12 I 1 1 1 1 1 r 0 1 1 1 1 1 1 1 0 40 80 120 Time (seconds) Figure 2.13: A M U 14 signal measured as a function of time with a mass spectrometer. The plasma was cycled on and off during the measurement. The A M U 14 signal is proportional to the sum of the molecular and atomic nitrogen in the effluent. background level in the measurement is simply due to molecular nitrogen which has a mass 14 component in its cracking pattern. When the plasma is turned on, the nitrogen atoms produced in the plasma increase the mass 14 signal. The data in Figure 2.13 also shows that the plasma source starts reliably. The growth of InGaAsN quantum wells requires a nitrogen flux for a brief period of time on the order of 30 seconds. Conventional non-resonant plasma sources are usually turned on during the growth of cladding layers (before the growth of the quantum well) in order for the source to stabilize. In this case, an effusion cell shutter is usually used to prevent the nitrogen flux from reaching the sample or an argon carrier gas is used to sustain the discharge when the nitrogen gas flow is turned off. However, because of the long lifetime of atomic nitrogen, the shutter is not 100% efficient and some nitrogen 26 c g +-« co 'o o c/> w 0 i i i | 1 r — O 220 MHz • 70 MHz _ Q a o_ o o J A A A ± _ l 10 4 6 8 100 Pressure (mTorr) 4 6 8 1000 Figure 2.14: Fraction of nitrogen atoms present the in the flux emitted from the plasma source inferred from the mass 28 signal of a mass spectrometer. The applied power was approximately 50W. does incorporate into the layers adjacent to the quantum well. Being able to reliably ignite the plasma on demand improves the abruptness of the heterostructures. The ionization cross-sections for molecular and atomic nitrogen are almost identical [26]. If the atom density is small compared to the molecule density and if the density of excited state molecules is small or if the excited state ionization efficiency is the same as for ground state molecules, then the dissociation is given by the following expression: Ton T o / / M [N2] (2.9) where 7 is the ratio of the mass 14 and mass 28 signals, the subscripts designate the on/off state of the plasma source. [N] and [JVjj] are the atomic and molecular nitrogen concentra-tions respectively. Figure 2.14 shows the amount of dissociation that was achieved using the plasma source. At lower discharge tube pressures, the decreased number of gas phase collisions results in a larger electron mean free path. This, in turn, causes larger electron 27 Z5 CO _ D <+-C CD O ) O i_ —^• 'c o "E o 5c 1000 10 I 1 1 1 — l — T T T | 1 c o 220MHz O : • 70MHz o A o A o A n ° A Po°° -1 - ? O €> A - A * i A * I ^ I • i i i i i 1 i i i i 10 3 4 5 6 100 Pressure (mTorr) 3 4 5 6 Figure 2.15: Atomic nitrogen flux emitted from the RF plasma source as a function of the discharge pressure. The applied power was approximately 50W. energies and more ionization. Hence, a higher molecular nitrogen dissociation is observed at lower pressures. By exciting the higher harmonics of the helical resonator, we found that the dissociation initially increases with the excitation frequency and eventually saturates. This is consistent with the findings of Merel et al. [24] who studied the frequency depen-dence of nitrogen dissociation using a RF surface wave plasma source. Because the plasma source is resonant, only a discrete set of frequencies could be accessed during our study. It is found that the second resonance frequency of the plasma source yielded the best results. Figure 2.15 shows that the atomic nitrogen flux is linearly dependent on the discharge pres-sure for pressures above 40 mTorr. This is convenient for adjusting the nitrogen content in GaAsN epilayers. At lower pressures, the nitrogen flux is independent of pressure. Operat-ing the source in this regime could prevent slight variations in gas pressure from affecting the composition of the film. However, in the present configuration of the plasma source, the conductance of the discharge tube is not sufficient for the growth of GaAso.99No.01 at 28 # of baffles Ion current (nA) 1 2600 2 45 3 0.6 Table 2.1: Dependence of the ion content in the plasma source's effluent on the number of baffles present at the output of the plasma source. The gas pressure was approximately 80 mTorr, the excitation frequency was 185 MHz and the applied power was 50W. standard growth rates using low discharge tube pressures. The conductance of the aperture could be modified in order to operate the plasma source at lower pressures and maintain a sufficient nitrogen flux. Finally, the ion content of the plasma source's effluent was determined using a Faraday cup. Table 2.1 gives the ion current measured by the Faraday cup as a function of the number of baffle stages that are inserted into the P B N discharge tube. The data in Table 2.1 shows that three baffle stages decrease the number of ions in the source's effluent by a factor of 4500. The nitrogen dissociation measured with the mass spectrum analyzer was unchanged by the baffles. Other similar measurements with electrostatic deflector plates instead of baffles showed that the deflectors reduced the ion content by more than a hundred. Three baffle stages were employed for ion suppression in the plasma-assisted growth experiments that will be described in the following chapters. 29 Chapter 3 Growth, structure and composition of GaAsN films Although only small amounts of nitrogen are incorporated into the material, the epitaxy of high quality GaAsN requires very different growth conditions than those used for GaAs. This chapter will describe how the growth conditions affect the structural properties of MBE-grown GaAsN. To begin, we will review standard GaAs growth conditions. 3.1 Growth of GaAs by molecular beam epitaxy The epitaxial growth of III-V semiconducting crystals by M B E takes place under group V-rich conditions. Because the group V element has a larger vapour pressure than the group III element, an excess of the group V is supplied to the surface of the crystal during growth. The growth rate is therefore controlled by the arrival of the group III element. During growth, the surface is populated with mobile group III atoms that are produced by 30 the incoming flux. The substrate temperature, the growth rate and the step density affect how far a group III atom diffuses on the surface. Higher substrate temperatures increase the surface diffusion and usually result in smoother films. GaAs growth by M B E is typically carried out at a substrate temperature in the 400°C to 620°C range. The best quality material is grown at the higher end of the range. At even higher temperatures, gallium atoms begin desorbing from the surface. Films grown below 400°C are non-stoichiometric. Excess arsenic is incorporated in interstitial sites thereby degrading the material's properties. Because the symmetry of the crystal at the surface is different from that of the bulk, depending on the growth conditions, the atoms on the growing GaAs surface adopt one of a variety of different surface reconstructions in order to minimize the energy of the surface. The periodicity of each surface reconstruction is often different from that of the bulk. Because M B E is carried out under ultra high vaccuum, the surface reconstruction can be probed in situ using reflection high energy electron diffraction (RHEED). Under optimum GaAs growth conditions, the surface is in the arsenic terminated 2x4 reconstruction. For this reconstruction, the surface unit cell's lattice constant is twice the bulk lattice parameter along [Oil] and four times the bulk lattice parameter along [Oil]. At a constant growth temperature, decreasing the AS2 flux eventually causes the surface to be terminated by Ga atoms. A 4x2 surface reconstruction is then observed. A l x l surface reconstruction occurs in the intermediate regime where the arsenic flux is approximately equal to the Ga flux. The amount of arsenic required to maintain a 1 x 1 surface reconstruction depends on the substrate temperature because the As2 sticking coefficient is thermally activated. It is believed that the l x l RHEED pattern is in fact due to a random distribution of domains 31 that are either 2x4 or 4x2 reconstructed. In this work, we shall define the ratio of group V to group III atom fluxes (V/III ratio) as being equal to one when the arsenic flux is at its lowest possible level under which a stable 2x4 reconstruction is maintained for a given substrate temperature. Under these conditions, the arsenic flux is in fact slightly larger than the Ga flux. Nevertheless, we will adopt the convention that V/III = 1 just before the surface reconstruction changes from 2x4 to l x l . This is a more reliable reference point, especially for growths carried out at substrate temperatures in the 400°C to 500°C range where the RHEED pattern is not as clear as for higher temperature growth. Group III atoms are produced using Knudsen effusion cells. Arsenic is supplied to the growth front by using a bulk sublimation source equipped with a valved high tempera-ture cracker. Polycrystalline arsenic lumps typically held at 400°C sublime in the form of AS4 tetramers. The arsenic flux is then passed through a hot zone held at 960°C that cracks a majority of the AS4 into As 2 . The use of As 2 has been shown to improve the electronic and structural properties of epitaxial GaAs [27]. Because the bulk heater has a large thermal mass and responds slowly to temperature changes, a valve at the end of the arsenic source controls the magnitude of the output flux in a precise and reproducible manner. The flux emitted from an effusion cell is measured using a retractable ion gauge placed in the sample position. The reading of the gauge when the shutter is opened is proportional to the flux and is termed "beam equivalent pressure" (BEP). 3.1.1 Effect of the As 2 flux The magnitude of the arsenic overpressure during growth has a strong effect on the surface morphology of GaAs thin films grown by MBE. Figure 3.1 gives atomic force 32 Figure 3.1: 2 pm A F M images taken from homoepitaxial GaAs thin films grown under identical conditions except for the As2 flux. The growth temperature was 555°C and the growth rate was 10.4 nm/min. Both images have a 2 nm greyscale. ( a ) The V/ I I I ratio is 1 and the rms roughness is 0.28 nm. ( b ) The V/III ratio is 2.8 and the rms roughness is 0.20 nm. The white arrow is oriented along the [Oil] crystal direction. microscope (AFM) images of the surface of two GaAs homoepitaxial thin films grown under the same conditions except for the magnitude of the arsenic flux. The surface was main-tained in the arsenic terminated 2x4 reconstruction in both cases. These images show that the ratio of the incoming group V and group III fluxes has a dramatic effect on the surface morphology. The most striking difference between these two images is in the anisotropy of the surface roughness. At low As2 flux, the surface diffusion is highly anisotropic. Elongated atomically flat terraces are primarily aligned along the [OlT] direction. Along [Oil], step bunches separate atomically flat terraces. However, along [Oil], only single atomic steps separate terraces. At a higher flux, the surface roughness becomes much more isotropic with wider terraces. A statistical analysis of the A F M images in Figure 3.1 gives a quan-33 titative measure of the amount of anisotropy in the surface roughness of these epilayers. The power spectral density (PSD) of a square surface of lateral extent L is given by the following expression: where h(x,y) is the surface height distribution. Intuitively, the PSD can be thought of as being a measure of roughness as a function of lateral length scale on the surface. The quantity q represents the spatial frequency of the surface height fluctuations. It is related to a real space length scale I in the plane of the surface by q = 2ir/l. Figure 3.2 gives contours of equal power taken from the PSD computed from A F M images of both samples shown in Figure 3.1. A change in the V/III ratio from 1 to 2.8 induces a change in the aspect ratio of the 5 nm 4 PSD contours from 3.6 to 1.1 respectively. Our interpretation of these results is the following: as the arsenic flux increases, the surface diffusion changes from ID to 2D. This results in an increased number of sites being visited by the diffusing group III atom which increases the smoothing rate of rough surfaces. On the 2x4 reconstruction of GaAs, arsenic dimers form rows that are aligned along [Oil]. Presumably, there exists an interaction between the diffusing Ga adatom and the dimer rows which can be weakened by increasing the As 2 flux thereby assisting lateral hopping. These results are consistent with the work of LaBella et al. who observed a similar increase in Ga surface diffusion on GaAs with increasing AS4 overpressure, using M B E and scanning tunneling microscopy[28][29]. Additionally, our findings agree with the work of Pinnington et al, who showed that indium diffusion on GaAs increased with As 2 overpressure [30]. (3.1) 34 -100 0 100 q [001] ( ^ m ) Figure 3.2: Power spectral density contours taken from the PSD computed with 5x5 yum A F M images of the samples shown in Figure 3.1. The value of the PSD along the contours is 5 nm 4. 3.2 Determination of the composition of GaAsi_ xN x The simplest way of measuring the nitrogen content of the GaAsN films is to use x-ray diffraction (XRD). XRD is attractive because it is a non-destructive method for measuring epitaxial thin film compositions. However, in order for this measurement to be accurate, the epilayer must have a thickness on the order of a few hundred nanometers. For a novel material such as GaAsN, where the relation between the nitrogen content and the lattice constant is unknown, the XRD measurements must be calibrated. Secondary ion mass spectroscopy experiments were carried out for this purpose. 35 10 Depth ( um ) Figure 3.3: SIMS depth profile carried out on a typical GaAsi-xN^/GaAs epitaxial thin film (x = 1.4%). The concentration of boron and nitrogen is measured throughout the film. The sample surface is located at 0 /xm on the horizontal axis, the substrate-buffer layer interface is located at approximately 0.6 /xm. (Data courtesy of Rick Streater, Nortel Networks, Ottawa (Canada)). 3.2.1 Secondary ion mass spectroscopy Secondary ion mass spectroscopy (SIMS) measurements performed at Nortel Net-works were used to determine the composition of the first films that were grown at UBC. The SIMS system was calibrated by measuring the nitrogen content in a GaAs wafer which had a known dose of nitrogen implanted in it. A typical SIMS depth profile is shown in Figure 3.3. The SIMS measurements revealed the presence of nitrogen and boron in the samples. The boron found in the epitaxial layer (from 0 to 0.4 /xm) is attributed to the sputtering of the P B N tube that contains the plasma discharge. Boron can also be found 36 in the substrate (from 0.6 /xm and on). This is a residue from the liquid encapsulant used during the Czochralski growth of the GaAs boule used to fabricate the wafer. Because boron is an isoelectronic impurity that is much more dilute than the nitrogen present in the film, we do not expect it to have any detrimental effects on the material properties. Other more common impurities such as carbon and oxygen were also monitored and were found to have concentrations below 10 1 6 cm - 3 which was the detection limit of the SIMS for these elements. 3.2.2 x-ray diffraction Typical 004 x-ray diffraction measurements taken from GaAsN thin films having various compositions are given in Figure 3.4. The x-ray diffractometer had a Bede go-niometer and a Rigaku rotating anode x-ray generator. The x-rays were produced by the K a i transition of copper (A = 1.5405 A). The sharp Pendellosung fringes observed on both sides of the epilayer peak are an indication of abrupt interfaces and a smooth surface. The growth conditions under which these types of films are obtained are further discussed in the following sections. If the layers are coherently strained, the displacement of the epilayer diffraction peak with nitrogen content corresponds to the elastic deformation of the thin film's lattice due to uniform biaxial strain generated by the forced registry of the film's atoms with that of the substrate. For lack of better information, we assume that the elastic properties of the alloy can be determined by linearly interpolating from the end constituents (GaN and GaAs). We can then determine a theoretical calibration for the X R D measure-ments. Table 3.1 summarizes the elastic parameters that are used to compute the distortion of the heteroepitaxial crystal lattice[31][32]. The computation was carried out using com-37 0 (arcsec) Figure 3.4: Typical 004 rocking curves obtained from G a A s i - z N r epitaxial thin films grown on GaAs. Curves for three different compositions are plotted. The data are vertically offset for clarity. The nitrogen content is indicated next to each curve. mercial x-ray diffraction simulation software. Assuming that there is no relaxation, a value of 526" was obtained for the splitting between the GaAs substrate peak and the diffraction peak of a GaAso.99No.01 epilayer. Figure 3.5 compares the results of SIMS measurements with X R D data. The SIMS data agrees within experimental uncertainly with the predicted XRD compositions. The main cause of error in this SIMS analysis is the non-uniformity in the composition of the samples. A more thorough SIMS study carried out at the University Compound a (A) Cu(GPa) C12 (GPa) C44 (GPa) GaAs 5.6535 118.41 53.72 59.12 GaN 4.50 296 154 206 Table 3.1: Lattice constant, a, and elastic stiffness constants, dj, of GaAs and zinc blende GaN. 38 T , , , 1 . -j Peak splitting ( arcsec ) Figure 3.5: Nitrogen content of G a A s i _ x N a ; films as a function of 004 XRD peak splitting. The x-rays used for the measurement had a wavelength of 1.5405 A. The nitrogen content was determined by secondary ion mass spectroscopy. The calculation relies on the elastic parameters of the ternary alloy being a linear interpolation of the elastic constants of GaAs and GaN. of California at San Diego found a peak splitting of 515" per percent nitrogen incorporated which is equal within experimental error to our results. In the rest of this work, we shall de-termine the nitrogen content of our films using a peak splitting of 526" per percent nitrogen incorporated. 3.3 Nitrogen incorporation in GaAsN The incorporation of nitrogen into GaAsN alloys requires growth conditions that are different from the ones that are usually found to yield optimal GaAs films. Two nitrogen 39 sources were explored for the growth of GaAsN: thermal cracking of ammonia on the growth surface, and active nitrogen produced in a plasma source. 3.3.1 Thermally cracked ammonia The simplest way to decompose a molecule is to thermally crack it on the substrate, which is maintained at a high temperature during growth. In this case, the only necessary piece of hardware is a gas feed which allows the gaseous precursor to be introduced in controlled amounts into the growth chamber. For the growth of GaN by metal organic chemical vapour deposition (MOCVD), ammonia (NH3) is the nitrogen precursor of choice. Ammonia is known to dissociate on con-tact with surfaces maintained at temperatures exceeding 800°C, which is a typical growth temperature for GaN[33]. However, GaAs growth temperatures are usually below 620°C. Otherwise, the material will decompose by preferential desorption of the group V con-stituent. Prior to the development of the RF plasma source, several growths were attempted using ammonia. A constant flux of ammonia was difficult to establish on the sample be-cause the liquid nitrogen-filled cryo shroud would radiatively cool the ammonia feed line thereby freezing the gas. No GaAsN-related x-ray diffraction peak was measured from sam-ples grown at a substrate temperature of 600°C with an ammonia background pressure of 2.7xl0~6 mBar. Other growths were attempted using a hot tungsten filament to crack the ammonia before it impinged on the substrate. SIMS measurements carried out at Nortel Networks on the samples grown with ammonia did not measure any nitrogen above the de-tection limit of 5xl0 1 7 c m - 3 . This result is due to the fact that, at this growth temperature, 40 thermal cracking is inefficient or nitrogen sticking is low, or both. When used in the M B E environment, ammonia is known to cause group III source materials to creep out of their crucibles. Also, ammonia is pumped very effectively by the cryo shroud. Once the growth experiments were finished and the cryo shroud was allowed to warm up to room temperature, ammonia desorption from the shroud resulted in a large pressure rise in the growth chamber. The current pumping system on the chamber was not able to manage such a large gas load. This resulted in a growth chamber pressure in the 10~4 mBar range. Our inability to incorporate nitrogen into GaAs, along with the other problems associated with using ammonia in MBE, prompted us to discontinue our efforts to grow dilute nitrides using ammonia. Dimethyl-hydrazine (DMHy) [(CHa^lN^Ha] is another candidate for use as a ni-trogen precursor. DMHy is an unstable molecule and dissociates at temperatures in excess of 130°C[34]. Many groups have reported on the growth of GaAsN using DMHy[34] [35]. However, the presence of methyl groups in the DMHy leads to carbon contamination in the films. Hydrogen also incorporates into the films and tends to passivate acceptor impuri-ties thereby limiting the maximum carrier concentration in p-type GaAsN. Also, DMHy is highly explosive. These reasons are sufficient motivation for finding another precursor for the growth of GaAsN. 3.3.2 R F plasma source At usual growth temperatures, the growth rate of GaAsN is controlled by the arrival of group III elements on the surface. Therefore, keeping the nitrogen flux and the substrate temperature constant, the nitrogen content in the film is inversely proportional 41 400 450 500 550 600 Substrate temperature ( °C ) Figure 3.6: Nitrogen content in GaAsN thin films grown under fixed growth conditions except for the substrate temperature. The concentration is referenced to the nitrogen content at 450°C. The solid line is a fit to the data with a 2.1 eV activation energy for nitrogen desorption. to the growth rate. Taking into account the total gas flux produced by the plasma source during the growth and the plasma-induced molecular dissociation (see Figure 2.14), the main contributor to nitrogen incorporation in our experiments seems to be atomic nitrogen emitted from the plasma source. Furthermore, as seen in Figure 3.6, the desorption of nitrogen is thermally activated with an activation energy of 2.1 eV. For comparison, the data of Gotthold et al. is also presented[36]. At a substrate temperature of 600°C, very little nitrogen incorporates into the film. This result is surprising since GaN can be heated up to 1000°C without loss of nitrogen[37]. Desorption mass spectroscopy (DMS) indicates that nitrogen and arsenic react at the substrate and form volatile AsN molecules that carry 42 away a fraction of the impinging nitrogen flux. No GaN signal was observed by DMS during GaAsN growth above the background partial pressure which was 7 x l 0 - 1 2 Torr. The AsN DMS signal was monitored for different substrate temperatures. Because the measured activation energy for AsN production is only 0.3 eV, these measurements are not able to account for all of the nitrogen loss at high temperatures. Other temperature activated processes must also come into play. Since nitrogen is a group V element, one might expect there to be a competi-tion between arsenic and nitrogen for incorporation into GaAsN. Figure 3.7 gives an x-ray diffraction reciprocal space map of a GaAsN film grown at a substrate temperature of 500°C. Midway through the growth of this sample, the As2 flux was increased by a factor of 1.6. The vertical arrows in Figure 3.7 highlight the diffraction peaks associated with the two different GaAsN compositions that resulted from changing the As2 flux. This x-ray data indicates that the film grown with a high As2 flux has 11% less nitrogen. If we assume that the arsenic flux is greater than the nitrogen flux and that both group V elements have equal sticking coefficients, the nitrogen content in the film, [TV], can be expressed in the following way: ^ ^ FN + FAS FAS ^ ^ where F designates a flux of the element identified by the subscript. However, we find that the nitrogen content is less sensitive to the arsenic flux than what is predicted by Equation 3.2. In order to quantify this effect, we use the following empirical relationship for the dependence of the nitrogen content on the arsenic flux: [N] = (3-3) 43 1.0 0.5 X CT < 0.0 R 0.5 h -1.0x10 -3 0 1 2 3x10 -3 Aq z ( A ) Figure 3.7: Asymmetric 115 x-ray diffraction reciprocal space map of a heterostructure consisting of a GaAso.ggo6No.oo94 a n d a GaAs0.99i6N0.0084 layer grown on GaAs at a substrate temperature of 500°C. The two diffraction peaks are highlighted with vertical arrows. The difference in nitrogen content between both GaAsN layers is due to an increase in the As 2 flux by a factor of 1.6. Each contour corresponds to a factor of 2 change in the diffracted intensity. The origin of the axes is set at the GaAs diffraction peak, = -0.250 A - 1 and qz = 0.884 A - 1 . (Data courtesy of Marlene Jeffries, Department of Physics, Simon Eraser University, Burnaby (B.C.)) where 7 < 1. Table 3.2 compares the effect of the As 2 flux at two different growth temper-atures. The results show that the nitrogen incorporation is slightly more sensitive to the As 2 flux at higher temperatures. This could be due to several effects such as the change in N and As 2 sticking or a higher AsN production. A more thorough investigation of the effect of the As 2 flux on the nitrogen incorporation would be useful. From a practical perspective these results greatly simplify the growth of GaAsN: the nitrogen content can be controlled without precise control over the As 2 flux. 44 A S 2 high/low X-high/xiow 7 460°C 4.3 0.77 0.18 500°C 1.6 0.89 0.25 Table 3.2: Change in nitrogen content, x, as a function of As 2 flux and the substrate temperature. The subscripts "high" and "low" refer to the magnitude of the As 2 flux. 7 is the exponent of the arsenic flux dependence of the nitrogen content. GaAs substrate MBE growth chamber Figure 3.8: Schematic representation of the experimental setup for in situ U V elastic light scattering measurements. 3.4 Light scattering experimental setup In situ light scattering measurements were used during the GaAsN crystal growth in order to monitor the surface roughness in real time. Elastic ultra-violet light scattering has proven to be a powerful technique for real time measurement of the evolution of surface roughness of epitaxial thin films during MBE [38]. In the present work, we provide an introduction to light scattering in order to ensure that the measurements that will be presented later are clear. A more detailed description of the UV light scattering setup and 45 its application to M B E can be found elsewhere[30]. The experimental setup is schematically represented in Figure 3.8. For simplicity, the scattering experiment is described in the "in plane" geometry (i.e. the incident and scattered light rays are in the plane that contains the sample normal). UV light generated by a 100W Hg arc lamp is directed towards the sample at an angle of incidence #j. The incident wavelength is 254 nm. Because of the sample's mirror-like finish, most of the light is reflected specularly from the GaAs sample. However, more light is scattered in off-specular directions as the sample develops roughness. By placing a photomultiplier tube on one of the viewports on the MBE, we can collect scattered light at a fixed angle 6S. The light scattering signal is proportional to the PSD (see Equation 3.1) of the surface roughness at a spatial frequency q defined by the scattering geometry and the wavelength of the incident radiation. In the geometry described in Figure 3.8, q is given by the following expression: 27T g = y ( s i n 0 i - s i n 0 a ) (3.4) where A is the wavelength of the incident light. In Figure 3.8, the scattered light is detected at a backscattering angle so as to maximize the in-plane spatial frequency to which the measurement is sensitive. For our scattering geometry, the scattered light depends on surface roughness with a spatial frequency of 41 / m i - 1 , or equivalently, to a length scale of 154 nm, during growth. 3.5 GaAsN Surface morphology The surface morphology of GaAsN is much more sensitive to growth conditions than that of GaAs, as we will see through the light scattering measurements discussed below. 46 CO "E =$. T — CO & w c 53 "O 8 3.0x10"3 2.5 2.0 1.5 1.0 0.5 0.0 ' i I I . I 10-3 _ ' I ' 1 !••'!_ | 10"5 - | 10"7_ / w>\if * * • S S1 i | | 1 2 0 2 4 ! As 2 BEP (mBar) j 3.3 x 10"6 j 10.0 x 10"6 T i 10 20 30 Time (min ) 40 Figure 3.9: Light scattering measured at a spatial frequency of 41 /xm" 1 during the growth of 1.8% GaAsN for two different runs carried out at a substrate temperature of 500°C but with different As 2 overpressures. The insert shows on a log scale the data taken from the sample grown with a high As 2 flux with the background scattering from the buffer layer subtracted. We now focus on two GaAsN growths carried out under different As 2 overpressures and at a substrate temperature of 500° C. We label the sample grown at high A s 2 pressure (BEP = lO.OxlO - 6 mBar) as H and the sample grown at low As 2 pressure (BEP = 3.3xl0 - 6 mBar) as L. The epilayer thicknesses for samples H and L are 40 nm and 350 nm respectively. The nitrogen flux was the same during the growth of both films. The nitrogen content of sample H is 1.8% as measured by x-ray diffraction. Figure 3.9 compares the light scattering signal measured at 41 /^m _ 1 during the growth of samples H and L. The time axis is shifted so that t=0 corresponds to the time at which the plasma is ignited, or in other words the start 47 " - J i (a) f A •4 / / jf * M * Mm (b) 700 nm Figure 3.10: Scanning electron microscope image of a rough GaAsN thin film grown on GaAs. The substrate temperature was 502°C and the nitrogen content was 1.4%. The viewing angles with respect to the sample normal were 45° (a) and 90° (b). of the nitrogen alloy deposition. The insert in Figure 3.9 shows the light scattering data for the sample that roughens (H) . The background scattering from the GaAs buffer layer was subtracted from the data in order to distinguish the scattering associated with the growth of the GaAsN layer. The insert in Figure 3.9 shows that sample H , which was grown at high arsenic flux, began to roughen immediately after the ignition of the plasma. We will refer to this phenomenon as 3D growth. The sample grown at low arsenic flux (L) showed only a slight roughening and the sample surface retained a mirror-like appearance. As we will see later, a small amplitude roughness can also develop in the 2D growth regime even though the surface is smooth to the eye. An SEM image taken from a nominally 300 nm thick GaAsN film grown under 48 Figure 3.11: Digital camera image of quarter 2" wafer after the growth of GaAsN without sample rotation. A rough three dimensional growth took place on a part of the wafer. the same conditions as sample H is shown in Figure 3.10. The surface of the crystal is rough and has pyramid shaped pits whose depth is on the order of the film thickness, which suggests 3D growth. Figure 3.10b gives a cross section view of the sample and shows that the sidewalls of the pits are smooth. Analyzing several images similar to Figure 3.10b taken from the same sample, we found that the sloped sidewalls make an average angle of 52° with the [UO] crystal direction. This is consistent with the formation of {111} facets during the growth for which we would expect facets oriented at 54° with respect to [Oil]. Figure 3.11 gives a picture of a quarter 2" GaAs wafer after a GaAsN growth during which the substrate was not rotated. The substrate temperature for this growth was 495°C and the nominal nitrogen concentration was 1.1%. One can clearly see that the surface morphology of the wafer is not uniform. A sharp border separates rough and smooth regions on the wafer. As was previously discussed, this two-region surface morphology is 49 not necessarily found on all samples and its appearance depends on the growth conditions. The border has an arc shape which indicates that the roughness might be related to the distribution of the flux emitted by one of the Knudsen cells. On the V G V80H M B E system, the focus of the sources is behind the sample. Due to this misalignment, when using Knudsen cells that employ straight-walled crucibles, the sample uniformity is only good if the substrate is rotated during growth. The Ga flux uniformity was measured by growing a 2 nm Ino.04Gao.96As layer capped with 300 nm of GaAs. During the growth, the sample was not rotated. Symmetric [004] x-ray diffraction measurements were carried out on this sample. The embedded InGaAs layer generates interference fringes that are related to the cap layer thickness. The thickness of the buried InGaAs layer is negligible compared to that of the cap. By taking such measurements in different areas of the wafer, the uniformity of the Ga flux can be quantified. The result is shown in Figure 3.12. Because the growth rate is controlled by the group III fluxes, this result directly translates into a ±20% non-uniformity in the nitrogen content of a film grown on a stationnary sample. Although, the Ga flux on the surface varies slowly as a function of position, the transition between smooth and rough growth happens abruptly, as is demonstrated by the sharp border between rough and smooth regions on the sample seen in Figure 3.11. This behaviour is similar to a phase transition. Various growth experiments have been carried out that highlight this effect. The transition from 2D to 3D growth is also observed as a function of nitrogen content and growth temperature. High growth temperatures and high nitrogen contents favour 3D growth. Figure 3.13 maps out the growth temperature and nitrogen content at which the 50 _30 I l l l l l I -10 -5 0 5 10 Lateral position on wafer ( mm ) Figure 3.12: Relative Ga flux as a function of position on the wafer for a stationary sample and a rotating sample. Percentages are relative to the Ga flux at the center of the wafer. The zone highlighted in grey indicates the ±1 .5% range. faceting transition occurs. Growth runs carried out under two different As 2 overpressures are shown. The studied As 2 beam equivalent pressures were 3.3 x l O - 6 and 10.0 x l O - 6 mBar. The square symbols indicate samples that exhibited 3D growth and the circular symbols indicate 2D growth. The solid line in Figure 3.13 is a fit of an Arrhenius function to the border between the smooth and faceted films for the high As 2 overpressure growth conditions. The fitted curve has an activation energy of 0.62 eV. The 2D/3D transition also depends sensitively on the growth rate of the film. Slower growth rates tend to push the epitaxy process nearer to equilibrium and therefore favour roughening. Al l of the samples grown in the 2D regime had a mirror-like surface morphology when visually compared to the faceted material. However, a more careful look at these films 51 Figure 3.13: Diagram showing the boundary between smooth and faceted GaAsN films grown on GaAs. The position of each marker indicates the composition and growth tem-perature of the GaAsN epilayer. The films indicated by the square and round markers designate faceted and smooth surface morphologies respectively. shows that there is an intermediate regime in which surface roughness develops but only at the nanoscale. As we saw in the first section of this chapter, the arsenic flux dramatically affects the surface diffusion. Higher arsenic fluxes reduce the asymmetry in the surface diffusion. Figure 3.14 gives several A F M images that are taken from samples grown with the same nitrogen flux but with different substrate temperatures and As 2 overpressure. These images show that a wide variety of surface morphologies can be obtained from GaAsN thin films. Figure 3.14(a) gives a view of the microscopic features in the rough 3D growth. Figure 3.14(b) is an A F M image of a GaAsN film which was grown in the 2D regime in 52 Figure 3.14: 2x2 /xm A F M images of three GaAso.98No.02 (nominal) samples grown with the same nitrogen flux and different substrate temperatures and arsenic fluxes, (a) Tsuo = 500°C, As 2 BEP = 7 . 6 x l 0 - 6 Torr, the rms roughness is 24.0 nm. (b) Tsub = 500°C, As 2 BEP = 1.5 x l O - 6 Torr, the rms roughness is 1.2 nm. (c) Tsub = 460°C, As 2 BEP = 1.5xlO - 6 Torr, the rms roughness is 1.3 nm. The white arrow is oriented along the [Oil] crystal direction. 53 conditions similar to sample L in Figure 3.9. However, the film still possesses a small amplitude roughness with a faceted structure. The lateral dimension of these roughness features is surprisingly regular and oriented. This type of surface morphology has also been observed in MOCVD-grown GaAsN films[35]. Finally, Figure 3.14(c) shows a GaAsN film with no faceted features. The low spatial frequency features in this image are due to the residual roughness that is caused by the incomplete smoothing of the oxide desorption pits. The high frequency atomic scale roughness seen in Figure 3.14(c) is caused by quenching the substrate temperature immediately after the growth. At the end of the growth, if the sample had been annealed under an arsenic flux, this surface roughness would smooth out resulting in atomically flat terraces. Given that the 3D growth mode is favoured by high nitrogen content, high arsenic flux and high growth temperature (both high temperature and high arsenic favour high surface diffusion), it is tempting to interpret the rough growth mode as a sign of GaN/GaAs phase separation. One would expect phase separation to be favoured by the parameters mentioned above. However, x-ray diffraction, transmission electron microscopy, and Raman scattering measurements[39] failed to detect any GaN phases in the GaAsN films. Figure 3.15 gives 004 x-ray diffraction 9 — 29 measurements taken from the rough and smooth areas on the sample shown in Figure 3.11. In this geometry, the x-ray scans measure the lattice constant perpendicular to the sample surface, a^p. Pendellosung fringes are clearly visible in the XRD data measured from the smooth area on the sample thereby indicating abrupt interfaces. For the x-ray scan taken from the 3D material along the [Oil] crystal direction, the epilayer peak is split into two. Such a feature has been observed in all 3D samples with 54 G (arcsec) Figure 3.15: Symmetric 004 x-ray diffraction 6 — 26 measurements taken from the rough and smooth areas on the same sample. The nitrogen content of the film was 1.2% and 1.4% on the 2D and 3D regions of the sample respectively. The growth temperature was 500°C. The orientation of the incident x-ray beam with respect to the crystal axes is indicated in the legend. varying degrees of intensity. The data does not allow us to determine if the non-uniformity in &perp is due to inhomogeneity in the composition or due to strain relaxation. Figure 3.15 shows that the corresponding a^p for both 3D GaAsN diffraction peaks is always smaller than the bulk lattice parameter of GaAso.986No.oi4) 5.6374 A. Figure 3.16 shows a 115 x-ray diffraction reciprocal space map of a GaAso.989No.011 epilayer grown at a substrate temperature of 500°C in the smooth 2D regime. The width of the epilayer diffraction peak along the direction is the same as that of the substrate thereby indicating that the strain in the epilayer is rather uniform across the sample. The 55 1.0 0.5 h i < X < o.o ^Ife -0.5 - --1.0x10 -3 0 1 2 3 4x10 -3 Aq z ( A ) Figure 3.16: Asymmetric 115 x-ray diffraction reciprocal space map of a smooth 2D GaAso.989No.011 epilayer grown at a substrate temperature of 500°C. Each contour cor-responds to a factor of 4 change in the diffracted intensity. The origin of the axes is set at the GaAs diffraction peak, qx = -0.250 A - 1 and = 0.884 A - 1 . (Data courtesy of Marlene Jeffries, Department of Physics, Simon Fraser University, Burnaby (B.C.)) lateral non-uniformity of the sample is therefore lower than the resolution of the instrument, 3 x l 0 - 5 A - 1 which corresponds to a lateral length scale of 3.3 pm. In the light of these results, we propose that the films are metastable. Nitrogen lowers the energy of the {111} surfaces with respect to the {100} surfaces, thereby inducing the formation of {111} facets when the growth conditions favour equilibrium. This results in a faceted surface morphology as well as a non-uniformity in either the composition or the relaxation. Photoluminescence data in Chapter 5 will further clarify this question. 56 3.6 Other effects on GaAsN surface morphology 3.6.1 Bi surfactant During growth, it is possible to modify the surface of GaAsN by exposing the film to a flux of a third variety of atoms ("surfactant") that do not incorporate into the material. Although the resulting material has the same composition as an epilayer grown without the surfactant, its properties could, in principle, be different because the presence of the surfactant atoms on the surface modifies the growth process. The surfactant can affect the surface reconstruction of the crystal, the surface diffusion of the adatoms and the incorporation of detrimental impurities. Several elements have been shown to exhibit a surfactant effect during M B E growth of GaAs. Lavoie et al. showed that In can enhance Ga surface diffusion during GaAs growth at a substrate temperature of 600°C[40]. In the case of InGaAsN, it could be hoped that a surfactant could eliminate nitrogen-induced defects. Yang et al. used Sb as a surfactant during the growth of InGaAsN quantum wells[41]. These authors showed that the photoluminescence efficiency of InGaAsNSb quantum wells is increased by as much as 5 times. In order to minimize strain energy, elements such as Bi and In which cause com-pressive strain in the epilayer tend to surface segregate rather than incorporate into the film. Bi has been used as a solvent for improving the growth of GaAs by liquid phase epitaxy[42]. In this case, small (~1018cm~3) quantities of Bi were incorporated into the GaAs. However, the electronic properties of the GaAs were not found to be degraded by the presence of Bi . Also, Bi is non-toxic. Al l of these factors indicate that Bi could be a good candidate as a surfactant during the growth of GaAsN. Bi has been used as a surfactant for the growth 57 Figure 3.17: 2x2 A F M images of GaAso.996No.004 samples grown one after the other in the same conditions except for the presence of a Bi flux, (a) No Bi flux, the rms roughness is 1.14 nm (b) The Bi BEP is 1.8xlO - 5 mBar, rms roughness is 0.10 nm. The substrate temperature was 460°C and the As/Ga ratio was approximately 1. The arrows indicate the [OlT] crystal direction. of InGaAs/GaAs by M B E and was found to improve photoluminescence efficiency of multi quantum well structures [43]. Figure 3.17 shows A F M images of GaAso.996No.004 samples grown at 460°C with varying fluxes of Bi . The surface morphology is dramatically modified by the presence of the surfactant. The surface roughness of the epilayer grown with Bi is an order of magnitude smaller than that of the standard epilayer. Figure 3.17(b) shows that the Bi flux has promoted a step-flow growth mode that results in large atomically flat terraces aligned along the [Oil] crystal direction and propagating along [OlT]. Along the [Oil] crystal direction, a high density of steps is present on the surface grown without Bi (Figure 3.17(a)). Possibly, Bi eliminates the barrier which normally impedes adatom diffusion along [Oil]. This is a 58 remarkable result since step-flow growth of GaAs normally requires growth temperatures around 600°C. X-ray diffraction measurements and SIMS measurements indicate that Bi incor-poration does not exceed 2 x l 0 1 7 c m - 3 (the detection limit was 6 x l 0 1 6 c m - 3 ) for growths carried out at a substrate temperature of 420°C. SIMS and low temperature PL measure-ments indicate that Bi incorporation is lower at higher growth temperatures[44]. We have achieved Bi concentrations ranging from 10 1 8 to 10 2 0 cm - 3 with the Bi cell temperature maintained between 300°C and 550°C at a growth temperature of 375°C. The higher levels of Bi incorporation were difficult to reproduce. As we mentioned earlier, In also can be used as a surfactant during the growth of GaAs. In the following, we shall see how the presence of In on the surface affects the growth of GaAsN. 3.6.2 Indium The experimental conditions under which the growth of GaAsN is smooth have been established in the preceeding sections. However, for the growth of InGaAsN lattice matched to GaAs, it is not certain that the same conditions will result in smooth films. Figure 3.18 shows light scattering data taken during the growth of a heterostructure con-sisting of GaAs, InGaAs, GaAsN and InGaAsN layers. The light scattering data shows that, in these experimental conditions, the growth of both InGaAs and GaAsN is smooth. However, simultaneous fluxes of In and N cause the surface to roughen in the same way as was observed for 3D GaAsN (see Figure 3.9). We interpret this to be caused by the higher surface mobility of indium atoms, which may also facilitate the surface diffusion of 59 In N 8 0 0 1 | 1 1 1 1 , 1 190 195 200 205 210 215 220 225 Time ( min ) Figure 3.18: Light scattering measured at a spatial frequency of 41 jimr1 during the growth of GaAs, Ino.04Gao.96As, GaAso.99No.01 and Ino.04Gao.96Aso.99No.01 layers. The solid hor-izontal lines at the top of the graph indicate the time intervals over which the In and N fluxes are impinging on the surface. The Ga flux is turned on throughout the growth. The substrate temperature was 500°C. Ga adatoms. Because the magnitude of the strain is lower in the InGaAsN than in the GaAsN or the InGaAs, this result indicates that the transition to the 3D growth regime is not strain-related. Interestingly, Figure 3.18 shows that the roughening continues after the closure of the In shutter at 219 minutes. Once the faceting transition is initiated, the In flux is no longer required to maintain the roughening. The In flux simply lowers the acti-vation barrier which exists betwen the 2D and 3D GaAsN growth regimes. Due to surface segregation, it is also possible that some In remains on the surface after the In flux is turned off thereby maintaining the 3D GaAsN growth regime. 60 3.7 Summary We find that, a careful choice of growth conditions results in the growth of smooth GaAsN thin films. Growth conditions which increase adatom surface diffusion such as high substrate temperature and high As 2 flux tend to favour the formation of a faceted sur-face morphology. The growth experiments described in the following chapters are therefore carried out in the 400°C to 470°C substrate temperature range where 3D growth is gener-ally avoided. At these temperatures, the incorporation of nitrogen into GaAsN is mainly dependent on the growth rate. The As 2 flux only weakly affects the composition of the films. 61 Chapter 4 Strain Relaxation The bulk lattice constant of alloys used in heteroepitaxial thin films is typically different from that of the substrate material on which they are grown. Because the epitaxial process forces the atoms in the thin film to register with the substrate lattice, the epilayer lattice is deformed. Elastic strain energy therefore builds up in the material during growth. Eventually, the film reaches a critical thickness, / i c , above which it becomes energetically favourable to form strain-relieving dislocations in the crystal. In this chapter, we discuss strain relaxation in GaAsN and InGaAsN thin films. In particular, we compare strain relaxation in nitride and non-nitride material. 4.1 Basic concepts of thin film strain relaxation 4.1.1 Definitions We will begin our treatment of strain relaxation by defining certain key concepts. A more thorough treatment of strain relaxation in MBE-grown thin films can be found in 62 [100] [001] \ Xi [010] 60° screw-edge misfit segment Epilayer-substrate interface \ Pure-screw threading segment Figure 4.1: Section of a cubic crystal showing a dislocation having thread and misfit segments. reference [45]. The lattice mismatch, / , between the epilayer and the substrate is defined by the following expression: where aB is the bulk lattice constant of the film and asub is the substrate lattice constant. aB depends on the composition of the film. The lattice mismatch corresponds to the initial misfit strain in the film before any relaxation occurs. Dislocations are defects in the crystal structure that relieve strain. Dislocations are characterized by a Burgers vector and a dislocation line. The Burgers vector quantifies the magnitude and direction of the perturbation in the crystal lattice which is associated with the dislocation. The dislocation line describes where the disorder in the crystal lattice has propagated. A dislocation can be composed of many segments each having a different orientation with respect to the Burgers vector. Because the displacement of the atoms in / = (4.1) ^sub 63 [100] Figure 4.2: Illustration of a cubic cell showing the orientation of the Burgers vector for a 60° screw-edge dislocation. The dislocation line is aligned with [Oil]. The Burgers vector makes an angle of 60° with both the dislocation line, [Oil], and the direction along which the dislocation relieves strain, [OlT]. the lattice associated with a single dislocation must be conserved along its entire length, each segment of a dislocation has the same Burgers vector. It is impossible for a single dislocation to terminate anywhere except at a free surface. Dislocations may also form closed loops or two dislocations having equal but opposite Burgers vectors can annihilate one another. In order for a dislocation to relieve coherency strain, the dislocation line of one or more of its segments must be contained at the interface between the epilayer and the substrate. Additionally, in order to relieve misfit strain, the Burgers vector of this dislocation segment must have a component that is perpendicular to the dislocation line and that is contained within the plane of the interface. Dislocation segments which have dislocation lines contained in the interface are referred to as "misfits" whereas dislocation segments that do not are referred to as "threads". Figure 4.1 illustrates a dislocation having 64 three different segments. In the rest of this chapter, we will use the term "dislocation" when referring to a "dislocation segment". An "edge" dislocation has its Burgers vector perpendicular to the dislocation line, while a "screw" dislocation has its Burgers vector parallel to the dislocation line. Misfit edge dislocations relieve a maximum amount of coherency strain whereas misfit screw dislocations do not relieve strain at all. Because the slip planes in III-V semiconductors are the close packed {111} planes, it is energetically favourable to form composite misfit dislocations that have a Burgers vector contained in a {111} plane. These dislocations have both screw and edge components to their Burgers vector and are therefore less efficient at relieving strain than pure-edge dislocations. Figure 4.2 shows the orientation of the Burgers vector associated with a 60° screw-edge dislocation. 4.1.2 Dislocations and strain relaxation Once misfit dislocations are present at the epilayer /substrate interface, the strain in the film along a particular crystal direction is described by the following expression: e = / - PrmsfitH (4-2) where e is the epilayer strain, pmisfit is the linear misfit dislocation density and fry is the pro-jection of the Burgers vector onto a line perpendicular to the dislocation line and contained in the interface. For a mixed screw-edge dislocation in a zinc blende crystal, fry = a/(2\/2) where a is the lattice constant of the thin film. In order to relieve strain, a threading dislocation must be forced to glide along the interface thereby laying down an increasingly long misfit dislocation segment. Any process which tends to inhibit dislocation glide also 65 Primary relaxation: Substrate threading dislocation Dislocation glide Misfit segment Epilayer Substrate Secondary relaxation: Dislocation nucleation Dislocation glide Misfit segment Dislocation pinning Epilayer Substrate Figure 4.3: Illustration of the various steps involved in the strain relaxation process. inhibits strain relaxation. We will describe strain relaxation in terms of two processes. The various phenomena that come into play are illustrated in Figure 4.3. Initially, strain relaxation proceeds through the glide of threading dislocations al-ready present in the substrate material prior to growth. We will refer to this as the primary relaxation process. A three-dimensional view of a threading dislocation after it has glided at the interface is shown in Figure 4.1. Once all the substrate threading dislocations have reached the extremities of the crystal, no further relaxation can occur until new threading dislocations are nucleated. The secondary dislocation process shown in Figure 4.3 corre-66 Epilayer 7 Substrate (a) (b) r Figure 4.4: Schematic representation of a substrate on which a strained epilayer is de-posited, (a) The substrate is infinitely rigid and the epilayer accomodates all of the elastic deformation due to coherency stress, (b) The substrate has elasticity and is curved in order to relieve a fraction of the stress in the film. sponds to the nucleation and glide of new threading dislocations originating at the surface of the crystal. Dislocation sources can also be found at the epilayer/buffer layer interface (not shown in Figure 4.3). Figure 4.3 also illustrates a defect which pins threading disloca-tions thereby impeding dislocation glide and strain relaxation. The reader should note that dislocation pinning can also occur during the primary relaxation process. 4.2 In situ substrate curvature measurement Dislocation formation is not the only process by which coherency strain can be relieved in an epitaxial layer. One alternative way for the film to relax the strain energy that builds up during growth is by deforming the substrate. Figure 4.4(a) schematically shows a compressively strained epilayer deposited on an infinitely rigid substrate. Assuming that no dislocations are present in the film, all of the strain is in the epilayer as illustrated in Figure 67 c "co 1— CO 0.6 0.4 0.2 0.0 -0.2 1 1 ' 1 Net pla i | . . i | i i i | i i i Infinitely rigid substrate j — - Elastic substrate itral ne ^ - Epilayer i Substrate -i i i i i i i i i i i i i 0 20 40 60 Thickness (a.u.) 80 100 Figure 4.5: Illustration of the strain profile in a compressively strained heterostructure. The magnitude of the effect of the substrate elasticity on the strain profile is greatly exaggerated for illustrative purposes. 4.5. However, if the substrate is allowed to possess some elasticity, it will bend in response to the stress in the epilayer as shown in Figure 4.4(b). The substrate deformation is quantified by the radius of curvature of the wafer. Figure 4.5 further illustrates the situation. When the wafer is curved, the substrate material is in tension at the epilayer/substrate interface, for a compressively strained heterostructure. This tensile stress decreases as one moves deeper into the substrate. At a particular depth, the strain vanishes. This position is commonly referred to as the "neutral plane". Below the neutral plane, the substrate is in compression. At a fixed epilayer thickness, the substrate curvature is determined by the equilibrium between the total stress in the film and in the substrate, which drive the curvature in different directions. Because of the thickness difference between the substrate 68 and the epilayer, the amount of strain relaxed in the epilayer is quite small. The reader should therefore note that the magnitude of the effect of the curvature on the strain is greatly exaggerated in Figure 4.5 in order to illustrate the phenomenon. In reality, the strain relief generated by the substrate curvature is on the order of 10~4% of the lattice mismatch. Stoney described the curvature of the substrate in terms of the stress inside the film[46]. Assuming that the film is much thinner than the substrate, the following expression describes the strain state of the sample: h  M ^ (A <X\ °fhf = -fyT (4-3) where the subscripts / and s designate the film and the substrate respectively, a is the stress, h is the thickness, M is the biaxial Young's modulus and r is the radius of curvature of the wafer. In the case of uniform biaxial stress, a = Mfe, where e is the misfit strain in the film. Equation 4.3 shows that the product of the film stress and the film thickness is inversely proportional to the radius of curvature of the sample. Figure 4.6 illustrates the experimental setup used to measure substrate curvature in situ during M B E growth. An A r + ion laser beam is split using a transmission grating. Two of the diffracted orders are collimated with a lens into two nearly parallel beams (deviation < 0.0005 rad) that impinge on the sample surface. The specularly reflected laser beams are imaged on a screen positioned three meters away from the substrate. The spot positions are then recorded using a CCD camera interfaced with a personal computer. Post-growth analysis of the images taken with the CCD camera yield the spot spacing as a function of time during growth. The spot spacing is related to the radius of curvature of 69 Computer CCD camera GaAs substrate MBE growth chamber Parallel A r laser beams Figure 4.6: Schematic representation of the experimental setup used to measure the sub-strate curvature in situ. the sample by the following expresssion which results from simple geometry: 6d 2L (4.4) d rcos(#) where d is the initial spot spacing, 6d is the change in spot spacing, L is the distance between the screen and the sample and 9 is the angle of incidence of the laser with respect to the sample normal. Combining equations 4.3 and 4.4, we obtain the following relation: (4.5) 8d — - (X (Tftlf d Therefore, the initial slope of the spot spacing data plotted as a function of the film thickness is proportional to the coherent stress inside the film. Once the critical thickness is reached, the stress in the film changes and so does the time dependence of the spot spacing data. In the V G V80H M B E system, the lateral layer uniformity is poor (±15%) unless the sample 70 is rotated (±1.5%) (see Chapter 3). We have found that this non-uniformity impedes the run-to-run reproducibility of the curvature data when the substrate is not rotated. Wobble in the substrate rotation results in a large motion of the spots. When imaging the spots on a screen, the field of view of the CCD camera can be adjusted in order to capture the spots at all times during substrate rotation. This is not possible if the spots are imaged directly on the CCD array. 4.3 Comparison of strain relaxation in InGaAs and InGaAsN 4.3.1 InGaAs strain relaxation We begin our study of strain relaxation by examining the case of InGaAs/GaAs heteroepitaxy. Figure 4.7 gives substrate curvature data taken during Ino.osGao.92As growths carried out under exactly the same conditions except for the final film thickness. The noise in the data is mainly due to wobble in the substrate rotation. Al l three data sets show an initially linear increase in the spot spacing which corresponds to coherent epitaxial growth. The spot spacing begins to deviate from this initial slope at the end of the growth of the 338 nm thick sample. The longest growth has a prominent feature in the 300 nm to 400 nm thickness interval. An x-ray diffraction study was carried out on these samples after growth. Symmet-ric (004) 6-20 rocking curves were measured with the plane of incidence aligned along [011] and [OlT] and 180° rotations of each. In this way, the amount of tilt and its axial direction in the relaxed epilayers were determined and used to correct the subsequent asymmetric scans. In order to measure the in-plane lattice constant, asymmetric (224) x-ray diffraction 71 Film thickness ( nm ) Figure 4.7: Spot spacing as a function of film thickness for a set of three Ino.08Gao.92As/GaAs growths carried out under exactly the same conditions except for the total epilayer thickness. The amount of relaxation, R, as measured by XRD is indicated for each data set along with the film thickness, h. The substrate temperature was 450°C. The samples were rotated during growth. The data are offset for clarity. rocking curves were carried out in the glancing exit and the glancing incidence geometries with the incident x-rays aligned along [Oil] and [OlTj. By combining the data from all eight XRD measurements, we were able to determine the strain state of the sample using Vegard's law for estimation of the elastic properties of the films. The XRD results summarized in Figure 4.7 show that only samples having thicknesses in excess of approximately 200 nm possess any appreciable relaxation. 72 T3 C O 0.4h 0.3 h 0.1 0.2 InGaAsN InGaAs 0.0 200 400 Film thickness ( nm ) 600 Figure 4.8: Relative spot spacing measured as a function of film thickness for Ino.osGao.92 As and Ino.12Gao.88Aso.99No.01 runs carried out at 400°C and 450°C. The data are offset for clarity. 4.3.2 Effect of nitrogen on strain relaxation In order to quantify how the presence of nitrogen affects strain relaxation, we compare the behavior of In0.0sGao.92As and Ino.12Gao.8sAso.99No.01 epilayers whose compo-sitions were chosen such that both alloys had approximately the same lattice mismatch. In order to obtain equal lattice mismatches for the nitride and non-nitride alloys, the Ga and N fluxes were adjusted while keeping the In flux constant. Therefore, the alloys were grown at different growth rates (14.8 nm/min for InGaAs and 10.6 nm/min for InGaAsN). Al l other growth conditions were kept constant. Ino.osGao.92As and Ino.12Gao.8sAso.99No.01 films grown at 400°C and 450°C. As in the pre-Figure 4.8 shows the relative spot spacing as a function of film thickness for 73 c o "•+-» CD X 0 5 CD or 100 80 h 60 R • ' 1 ; ' N 0 . 1 2 ^ A 0 . 8 8 ^ S 0 . 9 9 ^ 0 . 0 1 ' N 0 . 0 8 ^ A 0 . 9 2 ^ S 200 400 Film thickness ( nm ) 600 Figure 4.9: Relaxation coefficient as a function of thickness for InGaAs(N) epilayers each having a lattice mismatch of 0.62%. The growth temperature was 450°C. vious measurements, the initial linear increase in the spot spacing corresponds to coherent growth. The decrease of the spot spacing to a relatively constant value corresponds to con-tinuing strain relaxation. For each material system, the substrate temperature had little effect on the data. However, there is a marked difference between the InGaAs and the InGaAsN. The larger decrease in the spot spacing indicates that the residual strain in the InGaAs is smaller than in the InGaAsN. Further data analysis is required to quantify the residual strain in the films. The substrate curvature data can be converted into a relaxation coefficient, R, by applying the following transformation: R = 1 _ E urn j mill (4.6) 74 R! Pmis fit material ( ° C ) (nm-1) (nm"*) InGaAs 450 9.8xl0~ 3 3.0xl0- 4 InGaAsN 450 2.6xl0~ a 0.8 x l O - 4 InGaAs 400 7.3xl0- a 2.3xl0- 4 InGaAsN 400 2.3xl0~ 3 0.7xl0- 4 Table 4.1: Results extracted from substrate curvature measurements carried out on InGaAs and InGaAsN films. R' is the maximum relaxation rate, p' is the maximum rate of change of the dislocation density. where rrii is the slope of the initial linear increase in spot spacing. Figure 4.9 gives the results for in situ measurements of the evolution of the strain in an Ino.08Gao.92As and in an Ino.12Gao.88Aso.99No.01 epilayer. Figure 4.9 shows that, at the end of the growths, the InGaAsN sample possesses 25% more residual strain. Also, the InGaAs film relaxes much more abruptly than does the InGaAsN film. The slower changes in the InGaAsN curvature data indicate that the strain relaxation is impeded. The rate of change of the relaxation can be related to the misfit dislocation density. By combining equations 4.2 and 4.6 and then differentiating with respect to the film thickness, we obtain the following result: R'=jP'misfit (4-7) where / denotes a derivative with respect to the film thickness. The solid black lines in Figure 4.9 are tangents to the data where the rate of relaxation is maximal. Table 4.1 gives the measured rate of relaxation determined by the in situ measurement. The rate of relaxation is on average 3.5 times larger for InGaAs than for InGaAsN. The difference in the rate of relaxation is even larger when the growth rates are taken into account. Because of the noise caused by the substrate wobble during sample rotation, vari-ous kinks in the data render the measurement of the critical thickness imprecise. In Figure 75 author technique T s ub(°C) x(%) h c (nm) this work substrate 400 8 300 curvature 450 8 300 Beresford et al. substrate curvature 443 18 110 Pinnington et al. laser light 490 8.4 120 scattering 452 18 100 515 18 45 Table 4.2: Comparison of InxGai_a;As/GaAs critical thickness (hc) results measured by different research groups using various in situ measurement techniques. 4.9, the onset of relaxation appears to occur at a thickness of approximately 300 nm for both InGaAs and InGaAsN. The substrate curvature data is not sensitive enough to deter-mine whether there is a difference in critical thickness between InGaAs and InGaAsN. In the case of Ino.osGao.92As, we find that the critical thickness determined by the substrate curvature measurement is larger than the thickness at which the first dislocations occur. In Figure 4.7, a 213 nm thick film was found to be 0.4% relaxed. Therefore, the thickness at which the first dislocations nucleate is less than what is measured by substrate curvature. As a comparison, InGaAs critical thickness results from this work and from other groups are compared in Table 4.2. The critical thicknesses were determined using various in situ measurement techniques. Taking into account the difference in sample composition, the results of Beresford[47] and of Pinnington[48] are consistent with our findings. Because of the high noise level at low relaxation, the substrate curvature measurement is less sensitive to the primary relaxation process. The curvature measurement actually probes the onset of dislocation nucleation and multiplication (secondary relaxation). Symmetric (004) and asymmetric (224) x-ray 6-29 scans were carried out on this set of samples[49]. The results are summarized in Table 4.3. The XRD measurements 76 XRD In situ T E M material Tsub R / R Pmis fit Pthread R ( ° C ) (%) (%) (%) ( cm"1 ) ( cm-* ) (%) InGaAs 450 67 0.620 68 1.4xl0 5 0.3xlO e 45 InGaAsN 450 53 0.613 50 l . l x l O 5 2.0xlO e 36 InGaAs 400 67 0.600 65 1.3xl0 5 2.5 x10 s 40 InGaAsN 400 54 0.634 54 l.OxlO 5 8.5xl0 e 32 Table 4.3: Summary of XRD, T E M and substrate curvature data comparing the strain state of InGaAs and InGaAsN samples grown at two different substrate temperatures. R is the relaxation coefficient, / is the lattice mismatch, and p is the dislocation density. (XRD and T E M data courtesy of the Alexey Koveshnikov and Victoria Fink respectively, Department of Physics, Simon Fraser University, Burnaby (B.C.)) show that the four samples have a lattice mismatch of 0.62 ± 0.02%. Also, the relaxation determined with the in situ curvature measurement agrees remarkably well with the XRD-determined relaxation. Both methods show that there is approximately 25% more relaxation in the InGaAs than in the InGaAsN independently of the substrate temperature. Bright-field plan-view T E M images (g=(220)) were taken of all four samples [50]. The measured misfit and threading dislocation densities for InGaAs and InGaAsN are given in Table 4.3. As was measured by XRD and substrate curvature, the T E M data confirms that the misfit dislocation density is approximately 25% lower in the nitride. By assuming that all the misfit dislocations in the material are 60° mixed screw-edge dislocations, we can estimate the relaxation coefficient from the T E M data. Table 4.3 shows that, compared to XRD, T E M underestimates the relaxation by 60%. Possibly, the small area probed by the T E M does not provide enough statistics in order to yield results comparable to the X R D or to the substrate curvature measurements. Interestingly, the InGaAsN films have a higher thread density than the InGaAs epilayers. We interpret the larger thread density in the nitride material to be an indication 77 of slower dislocation glide. Because existing threads glide more slowly in the nitride, new threads must be nucleated in order to relieve the strain in the material which has not been relaxed by the glide of existing threads. The substrate temperature dependence of the thread density is also consistent with this picture. Both epilayers grown at 400°C had more threading dislocations in them compared to the same film grown at 450°C. This indicates that dislocation glide is slower at lower temperatures, as expected. We attribute the slower rate of strain relaxation to the presence of nitrogen inter-stitials in the InGaAsN epilayers and/or to the higher nitrogen bond strengths associated with substitutional nitrogen. For example, the cohesive energy per bond is 1.63eV for Ga-As and 2.24eV for Ga-N[51]. Both of these factors will slow down dislocation glide processes thereby impeding the formation of dislocations. Dilute nitrides are known to possess a large quantity of nitrogen interstitials that can be removed from the sample upon annealing[52]. The removal of these interstitials is thought to be one of the causes for the improvement in the optical quality of annealed InGaAsN quantum wells. This phenomenon would be anal-ogous to the pinning of dislocations by interstitial carbon atoms in steel, thereby hardening the material. 4.4 Brittle strain relaxation in GaAsN Because GaAsN grown on GaAs is under tensile stress, one might expect its strain relaxation to behave in a different way than the compressively strained InGaAsN we exam-ined in the preceeding section. In this section, we will briefly review strain relaxation in GaAsN. In particular, we shall see that tensile stress can also be relieved by crack formation 78 Figure 4.10: 27 x 27 /mi A F M image of a 600 nm thick strain relaxed GaAso.9s5No.015 epilayer ( / = -0.3%). The RMS roughness of the image is 1.5 nm. The arrow is aligned along the [Oil] crystal direction. in these films. Figure 4.10 gives an A F M image of a strain relaxed GaAso.9s5No.015 epilayer grown to a total thickness of 600 nm at a substrate temperature of 480°C. An orthogonal array of linear features can be seen in the surface roughness. This is a "crosshatch" pattern typically seen in the case of strain relaxed epilayers such as InGaAs/GaAs. The surface roughness develops because the strain field generated by misfit dislocations modifies the surface chemical potential felt by the adatoms thereby biasing the surface diffusion[30]. The observed surface roughness therefore indicates that there is an array of orthogonal misfit dislocations at the epilayer/buffer interface. Plan-view T E M images confirm that the formation of 60° misfit dislocations identical to those found in InGaAs/GaAs occurs in GaAsN. Also, the entire image shown in Figure 4.10 is traversed by a deep trench in the material that we interpret to be a crack. The crack is a result of the tensile stress in the GaAsN. The absence of material accumulation around the top of the crack indicates that 79 Figure 4.11: Dark field image of a strain relaxed GaAs0.9s4N0.0i6 film grown at 460°C. The greyscale of the image is inverted. The wafer is illuminated with a bright white light which impinges on the sample at grazing incidence in the direction indicated by the arrow. The sample is imaged from the top. Each panel shows the same sample oriented differently so that the incident light is aligned with [OlT] (a) and [Oil] (b). it must have occured after the growth had been completed. Figure 4.11 gives a dark field CCD camera image of a cracked GaAsN sample. By illuminating the sample at grazing incidence, surface roughness features are highlighted. The image shows that cracks propagate only along the [OlT] crystal direction. This has been found to be always the case for samples having a lattice mismatch around -0.4%. The cracks propagate along the entire length of the wafer. In Figure 4.11, the non-uniform intensity distribution of the light on the wafer highlights the crack segments in the middle of the sample. At a lattice mismatch of -0.3%, the cracks in GaAsN did not always occur. However, no obvious trends in the growth conditions could be correlated to crack formation. A bright-field T E M image (g=(004)) of a crack observed in cross section from a 300 nm thick 2.2% GaAsN film is shown in Figure 4.12. Assuming Vegard's law, the lattice mismatch in the sample was -0.45%. The interface between the GaAsN layer and the GaAs buffer layer is not visible in the T E M image in Figure 4.12(a). Although clear Pendellosung 80 Figure 4.12: (a) Bright-field transmission electron microscopy image, g=(400), taken from a <011> cross section of a 300±30 nm thick GaAso.978No.022/GaAs film. A crack is seen to propagate from the surface through the interface into the substrate. The position of the interface is indicated by a horizontal white line. The surface roughness amplitude is about 5 nm. (Data courstesy of Victoria Fink, Department of Physics, Simon Fraser University, Burnaby (B.C.)). (b) Illustration of "T"-shaped crack in a tensile strained film. fringes are normally visible in x-ray diffraction on coherently strained samples, fringes were not present in scans taken from this sample. It is possible that Pendellosung fringes are absent because of the crack-related local non-uniformities in the strain which are seen in the contrast of the T E M image given in Figure 4.12(a), and/or because of the 5 nm amplitude in the surface roughness of the sample. Therefore, we could not directly measure the thickness of the cracked sample using x-rays. However, based on the nominal growth rate of the sample determined by x-ray diffraction on calibration runs, we conclude that the cracks penetrate through the interface with the substrate as indicated in Figure 4.12(a). The large uncertainty in the film thickness is due to the fact that the substrate was not rotated during this growth. The change in direction of the crack in the substrate is consistent with the 81 fracture surface switching from a {011} plane to a {111} plane. A similar change in crack propagation direction has been observed in 2% tensile strained InGaAs/InP by Wu[53]. Figure 4.12(b) shows an exagerated illustration of the deformation of a tensile strained film in the vicinity of a "T"-shaped crack. Because the film is free to contract in the vicinity of the crack, a bending moment tends to peel the film away from the substrate. A similar vertical stress parallel to the crack is believed to be responsible for the change in fracture surface that we observe in GaAsN. In tensile strained InGaAs/InP samples, cracks form along the [Oil] direction rather than along [Oil] as in our samples. The disorder in the ternary alloy is on the group III sublattice for InGaAs and on the group V sublattice for GaAsN. Therefore, it is possible that the asymmetry in the crack orientation is related to the different nucleation characteristics of a and (3 dislocations which are chemically different because they occur on group III and group V sublattices respectively[54]. Similar cracks have been observed in tensile strained GaPN/GaP[55], InGaAs/InP[53] and AlGaN/GaN[56] films. Hearne et a/.[56] have observed crack formation during the growth of AlGaN/GaN heterostructures having tensile strain in the 0.5% range which is similar to the strain in our GaAso.97sNo.022 sample. The absence of changes in the surface profile due to deposited material around the open end of the crack shown in Figures 4.10 and 4.12(a) suggests that the cracks formed after the growth was completed and possibly during the cool down for these samples. 82 Chapter 5 Optical and electronic properties Because of the strong effect of nitrogen on the bandstructure of InGaAsN, the electronic properties of the material are highly dependent on the nitrogen concentration. In this chapter, we will discuss experimental results on the optical and electronic properties of dilute nitride alloys and correlate them with the growth conditions. 5.1 Photoluminescence 5.1.1 Bulk GaAsN Photoluminescence measurements were carried out on bulk GaAsN samples using a Bomem spectrometer equipped with a liquid nitrogen cooled Ge detector. An A r + ion laser was used to optically pump the sample. The incident power was 100 mW. The pump laser was mechanically chopped and the photodetector output signal was measured using a Stanford Research lock-in amplifier. The data was normalized with the response of the Ge detector. Figure 5.1 shows low temperature photoluminescence measurements taken 83 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Photon energy ( eV ) Figure 5.1: Photoluminescence data taken at a temperature of 4.2K from 2D and 3D GaAsN films grown at 500°C. The data are offset for clarity. (Data courtesy of Denis Karaiskaj, Department of Physics, Simon Fraser University (Burnaby B.C.)) from smooth 2D and faceted 3D GaAsN samples as described in Chapter 3. The broad luminescence seen around 0.85 eV is observed in all bulk GaAsN samples at low temper-ature and is presumably caused by nitrogen-induced defects in the crystal lattice such as nitrogen interstitials, nitrogen antisites or arsenic antisites. The peak observed at higher energies corresponds to the band edge luminescence. The band edge luminescence from the 3D material is much broader than that of the 2D GaAsN thereby indicating the presence of additional defects and/or variations in composition or relaxation. The photoluminescence peak intensity of the 2D GaAsN is approximately 4.5 times that of the 3D material, an-84 25 CO w c CD _ l Q_ 20 151 10 5| 0 A s 2 BEP = 3.3 x 10"6 mBar 10.0 x10"6 mBar 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Photon energy ( eV ) Figure 5.2: Photoluminescence data taken at a temperature of 4.2K from two GaAso.993No.007 (nominal) samples grown at a substrate temperature of 540°C under differ-ent As2 overpressures. (Data courtesy of Denis Karaiskaj, Department of Physics, Simon Fraser University (Burnaby B.C.)) other indication of an increased defect density in the rough epilayers. Also, a shoulder is observed on the high energy side of the main photoluminescence peak of the 3D material. This is consistent with a compositional non-uniformity in the sample, as observed by x-ray diffraction in Figure 3.15. The photoluminescence of bulk 2D GaAsN was found to be sensitive to the As2 overpressure during the growth. Figure 5.2 shows low temperature PL spectra from two GaAso.993No.007 films grown at 540°C with different As2 pressures. Although the As2 over-85 pressures were different during these two growths, both films were grown in the smooth 2D regime. The intensity of the defect luminescence in the far-infrared region of the spectrum is similar for both samples. However, the band-to-band luminescence is ten times stronger for the film grown at higher As 2 overpressure. The full width at half maximum of the band-to-band luminescence is about 62 meV for both samples. This indicates that, within the 2D growth regime, high As 2 fluxes are required in order to maximize photoluminescence efficiency. 5.1.2 InGaAsN single quantum wells Room temperature photoluminescence experiments were carried out on InGaAsN single quantum wells using a frequency-doubled Q-switched Nd:YLF laser emitting at a wavelength of 523 nm. The pump power was approximately 5 mW. The luminescence was collected by placing an optical fiber bundle approximately 4 mm away from the sample. An Aries FF250 spectrometer was used to monochromatize the collected light, which was then detected using a liquid nitrogen cooled InGaAs photodetector. The pump laser was mechanically chopped and the photodetector output signal was measured using a Stanford Research lock-in amplifier. Al l of the single quantum well samples discussed in the following pages had the following structure: 300 nm GaAs buffer layer, 5.5 nm InGaAsN quantum well and 235 nm GaAs cap. The first 100 nm of the buffer layer were grown at 590°C and at a V/III ratio of 4. The substrate temperature was lowered to the quantum well growth temperature during the final 200 nm of the buffer layer. If required, the V/III ratio was modified during this time as well. After the quantum well growth, 9 nm of GaAs were deposited at the quantum well 86 1000 1100 1200 1300 X ( nm ) Figure 5.3: Room temperature photoluminescece spectra taken from as grown Ino . i5Gao .85Asi_ x N x single quantum wells. Each spectrum is normalized to the Ino.15Gao.85As peak intensity. The nitrogen content of the epilayers, the F W H M and the Urbach slope, E 0 , of the luminescence are given in the legend. The growth temperature was 445°C and the V/III ratio was 4. growth temperature before ramping the substrate temperature to 590° C for the remainder of the cap layer growth. At no time was the growth interrupted. The substrate was rotated throughout the quantum well and cap layer growth in order to maximize the thickness and composition uniformity. Figure 5.3 shows photoluminescence spectra taken from Ino.isGao.ssAsi-xNc quan-tum well samples having various nitrogen contents. As expected, the wavelength of the peak intensity is red shifted as the nitrogen content is increased. Also, increasing the nitrogen content results in a drop in the intensity and an increase in the line width. Nitrogen is 87 presumed to introduce defects in the material which increases the density of non-radiative recombination centers. We expect the slope of the exponential tail on the low energy side of the photoluminescence peak to be equal to the Urbach parameter, E 0 , which quantifies the disorder in the material. As indicated in the legend of Figure 5.3, the Urbach parameter measured in this way, increases with the nitrogen content. This might be due to inhomo-geneities in the composition of the well caused by nitrogen clustering. Strohm measured an Urbach parameter of approximately 11 meV for bulk layers of undoped GaAso.99No.01 using photoconductivity[57]. It is possible that added disorder on the group III sublattice introduced by the presence of indium in the quantum well could account for the higher Urbach parameter (15.5 meV) that we observed in the Ino.15Gao.85Aso.993No.007-Growth conditions Typical growth temperatures for InGaAs quantum wells are in the 480°C to 520°C range. Lower temperatures usually result in non-optimal photoluminescence characteristics because of excess incorporation of impurities and/or group V elements. In the case of In-GaAsN, the optimal growth temperatures are well below those used for InGaAs. Table 5.1 shows that low substrate temperatures and high As 2 fluxes tend to improve the photolu-minescence of InGaAsN single quantum wells. These results can be interpreted in terms of the faceting transition that was observed in GaAsN. In Chapter 3, we found that an In flux also favours the rough 3D growth regime (see Figure 3.18). It was hypothesized that this is due to the larger surface diffusion of In atoms. The decreased photoluminescence intensity of the samples grown at high temperature may be associated with the faceting transition which is promoted by the In flux. However, 88 Tsub (°C) V/III PL intensity (a.u.) 430 4 0.41 430 1 < 0.005 460 4 0.03 460 1 < 0.005 Table 5.1: Peak photoluminescence intensity of Ino.3Gao.7Aso.994No.006 (nominal) quantum wells grown at different substrate temperatures and different V/III ratios. The emission wavelength is in the 1215 to 1255 nm range. because the quantum well structures are thin (5.5 nm) and because of the 235 nm GaAs cap layer, it is difficult to determine with certainty whether the quantum well growth occured in the 3D regime or not. Due to the manual operation of the plasma source, the RHEED could not be monitored during the growth of the quantum well. Table 5.1 shows that the quantum well grown at the lower substrate temperature has the higher photoluminescenece intensity, in agreement with the principles for smooth nitride growth determined in Chapter 3. Table 5.1 also shows that samples grown at low V/III flux ratios had the weakest photoluminescence intensities. In Chapter 3, high A S 2 fluxes were found to favour the 3D growth regime. However, if the growth is carried out in the 2D regime, we observed that bulk GaAsN photoluminescence intensity increases with the As2 flux (see Figure 5.2). Combining both bulk epilayers and quantum well structures, our conclusions on the effect of the V/III ratio are based on about eight samples. Harris et al. also reported that high As2 overpressures are required for the growth of GaAsN having good photoluminescence efficiency[58]. We therefore propose that the best photoluminescence efficiencies are obtained when the samples are grown at low substrate temperatures and high V/III ratios without triggering the faceting transition. Plan-view T E M images show that InGaAs grown at low temperatures with a low 89 430°C 455°C - '430°C 450°C 445°C sub 984 nm 1143 nm 1218 nm 1244 nm 1272 nm In 15% 20% 30% 23% 30% N 0% 0.65% 0.6% 1.7% 0.6% 0 4 8 12 x ( mm ) Figure 5.4: Map of the peak photoluminescence intensity as a function of the lateral position on the wafer, x = 0 mm corresponds to the edge of the wafer, x = 12 mm corresponds to the middle of the wafer. For each data set, the photoluminescence data is normalized to the intensity recorded at x = 0. As2 flux have a high concentration of defects. Since group Ill-rich growth conditions lead to degraded material properties, the growth process becomes sensitive to the magnitude of the As2 flux when using a unity V/III ratio. For a fixed effusion cell temperature, source depletion results in the gradual decrease of the flux over time. It is therefore possible that the weak PL observed for samples grown at low V/III ratio (see Table 5.1) is caused by an arsenic deficiency during the growth, which is due to an unintentional variation of the arsenic charge. We find that the photoluminescence of InGaAsN single quantum wells is sensitive to the substrate temperature at which the samples were grown. Figure 5.4 gives the intensity of the photoluminescence of InGaAsN single quantum wells as a function of the lateral 90 position on the wafer. For each sample, the photoluminescence intensity was normalized to the intensity measured at the edge of the wafer. Because the semi-insulating GaAs substrate is held at its edges during growth, there is a non-uniformity in the substrate temperature across the wafer. Although the temperature variation is not known exactly, we expect the center of the wafer to be approximately 10°C hotter than the edge[59]. The emission wavelength of the samples is uniform across the wafer within ±3nm thereby indicating that the composition of the quantum wells is macroscopically rather uniform. However, Figure 5.4 shows that the intensity of the luminescence varies significantly across the wafer. In the case of InGaAs, the intensity is maximal at the center of the wafer. This is to be expected since the optimal growth of InGaAs quantum wells usually takes place at temperatures in the 480 to 520°C range. InGaAsN has higher photoluminescence intensities at the edges thereby indicating that the optimal growth temperature for InGaAsN quantum wells is below 430°C in our M B E growth system. Figure 5.4 also shows that the growth temperature sensitivity of the quantum well emission intensity increases with the wavelength (i.e. high nitrogen and indium content). From the perimeter to the center of the wafer, the peak photoluminescence intensity varies by a factor of 2.7 at a wavelength of 1272 nm. Effect of a Bi surfactant In Chapter 3, we found that the use of a Bi surfactant was an effective way to enhance the surface morphology of GaAsN (see Figure 3.17). Therefore, the application of a Bi flux during growth was examined as a way to improve the quality of the InGaAsN quan-tum well structures. Figure 5.5 shows the photoluminescence spectra of several InGaAsN single quantum wells grown under exactly the same conditions except for the magnitude of 91 900 950 1000 1050 1100 1150 1200 X ( nm ) Figure 5.5: Room temperature photoluminescence spectra taken from as grown Ino.15Gao.85As and In0.15Ga0.85As0.993N0.007 single quantum wells grown in the same con-ditions except for the magnitude of the Bi flux. The Bi flux is quantified by the Bi cell temperature as indicated in the legends. The growth temperature was 450°C and the V/III ratio was 4. Each spectra is normalized to the peak intensity of the InGaAs SQW grown with no Bi flux. the Bi flux which was applied throughout the growth of the entire structure. The surfactant significantly improves the peak luminescence intensity of both InGaAs and InGaAsN quan-tum wells. The improvement is larger for the InGaAsN than for the InGaAs. Presumably, the surfactant eliminates certain nitrogen-related non-radiative recombination centers. The luminescence intensity of the InGaAsN grown with Bi is even found to surpass that of the reference InGaAs quantum well. The width of the luminescence is determined by the com-position and strain uniformity of the quantum well. Figure 5.5 shows that the line width of the luminescence is essentially unchanged by the surfactant for both alloys. This indicates that the amplitude of the roughness of the quantum wells grown without a Bi flux is not 92 sufficient to broaden the luminescence. Therefore, the smoothing due to the surfactant has no effect on the photoluminescence line width. Compositional inhomogeneity due to nitrogen clustering could be the cause for the broad InGaAsN luminescence with respect to InGaAs. In this scenario, the surfactant does not appear to inhibit nitrogen clustering. In the light of this data, it could be that the low step density during Bi-assisted growth modifies the nitrogen incorporation in a way that improves the luminescence effi-ciency. It is possible that substitutional nitrogen incorporation on an arsenic site is favoured by the presence of Bi on the surface thereby decreasing the number of nitrogen interstitials and/or arsenic anti-sites. Pillai-er. al. proposed that the improvement of the luminescence of InGaAs quantum wells grown with a Bi flux is due to decreased impurity incorporation on the Bi-terminated surface[43]. Unintentional impurities could come from residual gases such as water vapour present in the growth chamber or contaminants in the N2 feed gas (below 1 ppm). Water is particularly difficult to completely eliminate from our growth chamber even after baking for several days at 200°C. Assuming a unity nitrogen sticking coefficient, the atomic nitrogen which incorporates into the film (~102 0cm~3) represents a few percent of the total molecular nitrogen flux which means that the density of impurities related to the feed gas is 104 times smaller than the nitrogen concentration. Therefore, the impurity density could reach 10 1 6 cm - 3 levels. The absence of the nitrogen feed gas during InGaAs growth could explain why the Bi-related improvement of the photoluminescence for the InGaAs quantum wells is not as great as for the InGaAsN wells. A purifier could be added to the gas handling system of the plasma source in order to minimize impurities. 93 Z3 CO co 0.8 -0.6 -2 0 4 a. 0.2 0.0 - as grown - 715°C - 775°C - 820°C 1100 1150 1200 X ( nm ) 1250 1300 Figure 5.6: Room temperature photoluminescence spectra taken from an In0.3Gao.7As0.994N0.006 (nominal) single quantum well. The spectra were taken from a different piece of the same wafer. Each sample was annealed for one minute at the temperature indicated in the legend. Rapid thermal anneal The effects of one minute ex situ rapid thermal anneals carried out at temperatures in the 700°C to 850°C range were also explored. Figure 5.6 shows room temperature photoluminescence spectra taken from an InGaAsN single quantum well which has been annealed at various temperatures. During the anneal, nitrogen gas was flowed through the oven and the samples were proximity capped with a bare GaAs wafer. The nitrogen purge was initiated ten minutes prior to the anneal and was left on for half an hour after the anneal. The rapid thermal anneals were found to improve the photoluminescence efficiency of InGaAsN quantum wells. Figure 5.6 shows that the the emission wavelength is blue shifted by the anneal. This is believed to be due to quantum well intermixing[60]. The high temperature of the anneal allows the constituents of the heterostucture to interdiffuse. Both 94 In and N could diffuse away from the quantum well thereby increasing the bandgap of the material. Quantum well intermixing is normally enhanced by the presence of point defects in the crystal lattice. These defects can be induced by capping the sample with silica prior to the anneal[61] or they can be "grown in" by using a low substrate temperature during the growth[62]. It is possible that nitrogen-induced crystal defects could result in increased quantum well intermixing. L i et al. found that In0.2Gao.sAs quantum wells in which no intentional defects were introduced did not exhibit any measurable intermixing for RTAs carried out in the 700°C to 800°C temperature range[61]. The magnitude of the improvement in the photoluminescence efficiency varied from sample to sample. We define the photoluminescence intensity gain, G, in the following way: G = If± (5.1) 0 where IRTA and IQ are the peak photoluminescence intensities of the annealed and as grown samples. Table 5.2 gives a summary of the change in the photoluminescence of the annealed quantum wells. Because of machine-dependent issues that are different from one M B E to another, an absolute comparison of the PL efficiency of our samples with those grown by other groups is not possible. Therefore, in order to compare our results with those found in the literature, we use the relative intensity of the InGaAsN PL with respect to that of InGaAs samples grown in our system. Other groups have observed that anneals carried out at similar temperatures result in substantially larger improvements in peak photoluminescence intensity (factors of 10-20) and stronger blue shifts (42 meV on average) [60] [63] [64]. The reduced sensitivity of our material to anneals might be due to the baffle apparatus on the plasma source which suppresses ions and energetic neutrals from V 95 anneal temperature as grown 715°C 785°C 820°C x(%) y(%) T s u b (°C) I (a.u.) A (nm) G A (nm) G A (nm) G A (nm) 0.6 30 432 0.05 1272 3.6 1253 3.9 1239 1.2 1235 0.8 30 430 0.03 1255 3.1 1228 2.2 1204 1.5 1193 0.6 30 430 0.41 1218 1.4 1208 1.7 1197 1.2 1193 2.1 15 445 0.31 1180 1.7 1171 4.0 1144 0.65 20 445 1.80 1143 1.2 1114 1.7 1121 1.9 1119 0.7 15 445 1.56 1094 1.3 1091 2.2 1078 0.7 15 450 1.69 1063 1.3 1061 1.6 1053 Table 5.2: Summary of the effect of one minute rapid thermal anneals on the photolumines-cence of In^Gai-^Asi-zNa; single quantum wells. 7. is the peak photoluminescence intensity of the as grown material and G is the peak photoluminescence intensity gain of the annealed material. the nitrogen flux. Therefore, the density of non-radiative recombination centers and point defects could possibly be lower in our material. 5.2 Charge carrier mobility Because of the resonant nitrogen state above the bottom of the conduction band, one might expect the electron mobility of GaAsN to be strongly dependent on the nitrogen content (see Appendix A and references therein). Figure 5.7 shows the composition de-pendence of the electron mobility of n-type G a A s i - z N r . Every sample nominally has the same concentration of Si impurities which was evaluated using SIMS[44]. As expected, the electron mobility drops rapidly with increasing nitrogen. Figure 5.7 also shows that both rapid thermal anneals and the use of a B i surfactant during growth do not significantly affect the electron mobility. As opposed to the photoluminescence efficiency of InGaAsN, the low electron mobility of GaAsN appears to be an intrinsic property of the material and cannot be improved through optimization of the growth or by post-growth treatments. 96 co > NJ E o 5 i — i — i i i i 11 —1 1 1 1 4 3 A as grown o • 1 min. 770°C RTA o as grown with Bi 1000 A -6 5 4 -3 2 • 100 . i i i i i i i 1 1 1 1 1 1 1 1 1 > 4 6 8 0.001 2 4 6 8 2 0.01 Figure 5.7: Room temperature electron mobility of silicon-doped G a A s i _ x N x samples deter-mined using Hall effect measurements. The growth temperature was 460°C. The horizontal dotted line indicates the mobility of a GaAs sample grown under the same conditions. The Si impurity concentration was 6 x l 0 1 7 c m - 3 . It was proposed by Mascarenhas that Bi incorporation in GaAsN might improve the material properties[65]. His idea was that Bi and N might cluster together thereby reducing the nitrogen-induced perturbation in the conduction band due to lattice strain. This effect would be analogous to the faster fall off of the potential induced by a dipole compared to the potential induced by a monopole. As described in Chapter 3, Bi does not incorporate into GaAsN at typical growth temperatures. At present, we have not yet successfully grown GaAsNBi. For the as grown GaAsN mobility data shown in Figure 5.7, the decrease in mo-bility approximately follows a 1/x trend for nitrogen concentrations ranging from 0.07% 97 to 0.6%. This suggests that scattering by neutral nitrogen atoms is the dominant scatter-ing mechanism. Because the intrinsic mobility of GaAs at room temperature is limited by phonon scattering and therefore is not infinite, the total electron mobility which we are measuring is given by Matthiessens's rule: 1 1 +-5- (5.2) f-tot ^GaAs Vimp where /x t o t is the total electron mobility, n-GaAs1S the mobility of n-type GaAs (2950 cm 2/V-s) at the dopant concentration we are considering (6x l0 1 7 cm - 3 ) and nimp is the impurity scattering limited electron mobility. Figure 5.8 shows / X j m p , the GaAsN electron mobility limited by impurity scattering obtained from Equation 5.2. Data measured by other groups on InGaAsN has also been added to the graph in order to extend the nitrogen concentration range. Using the Drude model for conductivity, we can express the electron mobility limited by neutral impurity scattering in the following way: where e is the electron charge, r is the relaxation time and m* is the electron effective mass. The relaxation time is related to the mean free path of the charge carrier and its thermal velocity which is given by: vth = \ l ^ r (5-4) m* where k is the Boltzmann constant and T is the temperature. Assuming nitrogen-related neutral impurity scattering, the scattering length is then given by: 98 co > E o 1000 100 8h 6 . . . . I uelectron • l n 3 x G a i - 3 x A s i - x N x (other work) A GaAs 1 . X N X (this work) uhole ° l n 3 x G a l - 3 x A s 1 - x N x ( ° t h e r w o r k ) 4 6 8 0.001 - I l _ 4 6 8 0.01 Figure 5.8: Charge carrier mobility as a function of nitrogen content for GaAsN and In-GaAsN. The GaAsN data has been corrected for phonon scattering as described in the text. The InGaAsN data is taken from the work of Kurtz et al.[Q8] and Robinson et al.[69}. where a is the nitrogen scattering cross section and NN is the nitrogen concentration. The following expression for the neutral impurity scattering limited mobility is obtained by combining Equations 5.3, 5.4 and 5.5: t^imp m p oNNy/ZkTm* (5.6) A value of 2 .3x l0 _ 1 4 cm 2 is obtained for a by fitting a 1/x function to the GaAsN mobility data shown in Figure 5.8. Since the composition range of interest is relatively small and \xirnp only depends on the square root of m*, the effective mass was assumed to be independent of the nitrogen concentration and equal to 0.075. This is the linearly interpolated effective mass for GaAso.99sNo.002, which was determined using the data in reference [66]. The radius 99 associated with the neutral impurity scattering cross section (a — nr2), 8.6 A, compares well with the radius of the spherical volume of GaAso.99No.01 which is occupied by a single nitrogen atom, 8.2 A. The overlap between scattering cross sections could therefore be the explanation for the apparent leveling off of the mobility for concentrations in the 0.6 to 2% range which is shown in Figure 5.8. These results agree with the conclusions of Zhang et al. who found that the upper limit for the concentration at which nitrogen forms an impurity band is below 1%[67], The hole mobilities measured by Kurtz and Robinson[68][69] also seem to follow a 1/x trend. However, the electron and hole mobilities are offset with respect to one another. Assuming that the light hole effective mass for GaAsN is the same as for GaAs, this indicates that the nitrogen-related scattering cross section is approximately 1.3xl0- 1 4 cm 2 for holes. Figure 5.9 gives the carrier concentration determined using resistivity measure-ments carried out on the same set of samples as in Figure 5.7. The decrease of the carrier density with increasing nitrogen concentration is an indication that the nitride has a large concentration of traps situated in the bandgap. For an energy level, E x , the Fermi-Dirac distribution function, f x , is given by: •k = 1 + ge(Ex-Ef)/kT (5-7) where E j is the Fermi level and g is the degeneracy factor. For a donor state, g is equal to 1/2. Because the nature of the nitrogen-related defects is not exactly known, we will assume that g is equal to 1 for the traps. The net charge, N ~ , on a discrete energy level E x is given by: N ~ = N x f x (5.8) 100 3.5 A As grown A 770°C RTA O As grown with Bi 3.0 A 0.0 -3 0 2 4 6 8 10x10 x Figure 5.9: Carrier concentration of silicon-doped GaAsi_a;N x samples determined using Hall effect measurements. The growth temperature was 460°C. The Si impurity concentra-tion was 6xl0 1 7 cm~ 3 . where Nx is the density of states at the energy Ex. For GaAsN doped with a donor impurity, the total number of excess electrons in the material is equal to the number of donors. Ther-mal equilibrium governs how these carriers are then distributed over the conduction band, the impurity states and the nitrogen induced trap levels. Therefore, charge conservation requires that: where the subscripts d and t designate the donors and traps respectively and n is the charge carrier concentration in the conduction band which is determined using resistivity Nd = Ndfd + Ntft + n (5.9) 101 measurements. The charge carrier density in the conduction band is given by: n = Nce-(Ec-Ef)/kT ( 5 1 0 ) where Ec is the conduction band energy and Nc is the effective density of states in the conduction band which is 4.7xl0 1 7 cm~ 3 for GaAs at room temperature. This result is valid for non-degenerate semiconductors (i.e. Ec — Ef > SkT). In these calculations, all energies are referenced to the bottom of the conduction band. Therefore, measuring n also gives the Fermi level which then allows us to determine the number of charge carriers on the impurities and on the traps. Kaplar et al. identified several traps in GaAsN using deep level transient spectroscopy[70]. These authors concluded that a trap lying 0.36 eV below the conduction band was the dominant electron trap. We use this value for the energy of the traps in order to evaluate their number. For each value of the carrier concentration in the conduction band, we can solve Equation 5.9 for the density of traps. The calculated trap density is found to vary linearly with the nitrogen concentration and is shown in Figure 5.9. We find that 5.3xl0 1 7cm~ 3 traps are created in the material per percent nitrogen incorporated. At the doping level in our samples, traps situated more than 0.2 eV below the conduction band are all occupied by a charge carrier. Therefore, the energy of the trap does not affect its occupancy, as long as it is deeper than 0.2 eV. As in the case of the mobility, rapid thermal anneals and Bi-assisted growth had no effect on the carrier concentration. 102 Chapter 6 Conclusions InGaAsN-based electronic and optoelectronic devices have the potential for tremen-dous impact on compound semiconductor technology. InGaAsN has many advantages that could allow it to replace InGaAsP for lasers emitting at 1.3 /xm: low cost substrate mate-rial, compatibility with high index contrast GaAs/AlGaAs multilayers and high conduction band offset. Currently, several companies are developing low cost InGaAsN vertical cavity surface emitting lasers at 1.3 //m for 10 Gbps applications. These devices could potentially make "fiber to the home" economically feasible. InGaAsN could also have an impact on other important technologies such as multijunction solar cells, where a 1 eV bandgap is needed. This work demonstrates the advantages of a novel plasma source for the production of atomic nitrogen during the growth of dilute III-V-nitride compound semiconductors by molecular beam epitaxy. The plasma source relies on a RF resonator design and has several attractive features for the growth of nitrides: reliable plasma ignition, multiple excitation 103 frequencies, broad operating pressure range and wide power range. Also, a P B N baffle placed at the output of the plasma source was demonstrated to decrease the ion content of the nitrogen flux by a factor of 4500 without affecting the atomic nitrogen concentration (4 to 8% of the molecular nitrogen flux at an excitation frequency of 220MHz). To our knowledge, this is the first time that such a baffle apparatus has been used for M B E . This simple ion suppression scheme could significantly improve M B E process quality. Using this plasma source, optimum growth conditions for GaAsN and InGaAsN thin films were established. A faceted surface morphology was found to occur at high nitrogen content and under growth conditions that increase adatom surface diffusion: slow growth rate, high substrate temperature and high V/III ratio. The transition between smooth 2D growth and rough 3D growth is abrupt, similar to a phase transition. We propose that the faceting transition occurs because the surface energy of {111} GaAsN crystal planes is lowered with respect to that of the (100) growth surface under conditions that favour surface diffusion. The residual strain in relaxed InGaAsN films was found to be higher than in InGaAs epilayers having the same lattice mismatch. The slower strain relaxation in the nitride could be useful for improving the yield of highly strained device structures. In situ substrate curvature measurements were used to monitor the strain state of the sample in real time during the growth. The final strain state of the samples as determined by substrate curvature measurements agrees well with ex situ x-ray diffraction and transmission electron microscopy measurements. The combined in situ and ex situ results indicate that threading dislocation glide is slower in InGaAsN than in InGaAs. This was attributed to the higher 104 Ga-N bond strength and/or to the presence of nitrogen interstitials in the crystal lattice. Because strain relaxation appears to behave differently for InGaAsN and InGaAs, it would be interesting to improve the sensitivity of the substrate curvature measurement system in order to more acurately determine the critical thickness and to monitor the strain relaxation of InGaAsN quantum well structures. We demonstrated the growth of InGaAsN quantum wells with photoluminescence efficiencies that are comparable to InGaAs structures. In contrast with the findings of other groups, rapid thermal anneals only moderately improve the PL intensity and line shape of InGaAsN single quantum wells. We observe peak intensity gains on the order of 2 whereas many report factors of 10 to 20. The electronic properties of GaAsN films are degraded with increasing nitrogen content. Ex situ rapid thermal anneals had no effect on the charge carrier concentration or the electron mobility of Si-doped GaAsN. The 1/x dependence of the electron mobility of GaAs i -xNi indicates that nitrogen-related neutral impurity scattering is the limiting factor in the mobility. A comparison of the quality of GaAsN grown with and without the baffle on the plasma source is left for future work. This would determine the extent to which ion damage limits the properties of dilute nitrides grown by plasma-assisted MBE. We have used Bi as a surfactant during the growth of GaAsN and InGaAsN for the first time. We showed that the Bi surfactant improves the surface morphology of GaAsN epilayers. Surfactant-assisted growth of InGaAsN single quantum wells was found to result in material with increased photoluminescence efficiency by as much as a factor of 3. This is a significant improvement of the material quality which could translate into high performance 105 devices. Also, a fabrication cost reduction could be achieved through the removal of the ex situ anneal processing step which is currently required for InGaAsN lasers. Several issues related to Bi-assisted M B E growth could be investigated. The surfactant might prevent the faceting transition which would allow dilute nitrides to be grown at higher temperatures and higher As 2 fluxes, which might be expected to improve the quality of epitaxial material. The Bi surfactant could also be extended to the AlGaAs system which normally suffers from oxygen contamination due to the high reactivity of A l . A Bi-terminated growth surface could inhibit this oxidation thereby improving AlGaAs material quality. Finally, by using substrate temperatures where Bi incorporates into GaAs, we could attempt the growth of GaAsNBi with the objective of verifying the assertions of Mascarenhas[65] who predicted improved electronic properties for this materials system. The material quality of InGaAsN depends sensitively on the growth conditions. This work provides insight into some of the key issues that must be taken into account in the growth of dilute nitrides thereby bringing us one step closer to realizing the full potential of this promising material system. 106 Bibliography [1] M . Kondow, K. Uomi, A. Niwa, T. Kitatani, S. Watahiki, and Y . Yazawa. Jpn. J. Appl. Phys., 35(2B):1273-1275, 1996. [2] T. Kitatani, K. Nakahara, M . Kondow, K. Uomi, and T. Tanaka. Jpn. J. Appl. Phys., 39(2A):L86-L87, 2000. [3] A. Mercuta, S. Bouchoule, F. Alexander, I. Sagnes, J. Decobert, and A. Ougazzaden. Elect. 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Kurtz. Phys. Rev. Lett, 82(6):1221-1224, 1999. [73] T. Mattila, S.H. Wei, and A. Zunger. Phys. Rev. B, 60(16):R11245-R11248, 1999. 114 Appendix A Bandgap Bowing: two level model As shown in Chapter 5, both the electron mobility and the charge carrier concentra-tion of Si-doped GaAsN depend strongly on the nitrogen concentration. Also, experimental results show that 97% of the change in the bandgap of GaAsN is taken up by the conduc-tion band offset[71]. These results indicate that nitrogen incorporation strongly affects the conduction band of GaAsN. In the following, we will use the two level model developed by Shan et al. to explain the nature of the GaAsN bandgap bowing[72]. Figure A . l shows the GaAs conduction band calculated in the parabolic band approximation. An s-like resonant state which lies above the delocalized GaAs conduction band minimum is introduced by the addition of nitrogen to the material. Because the nitrogen state is localized in real space, it is delocalized in k-space as shown in Figure A . l . The interation between the GaAs conduction band and the nitrogen state leads to the following eigenvalue problem: E C - E Vint Vint EN — E - 0 (A.1) 115 Figure A . l : GaAsN conduction band diagram showing the E+ and E_ levels which are due to the anticrossing of the GaAs conduction band and the localized nitrogen state. The calculation was carried out using values consistent with those used by Shan et al. [72] for the calculation of InGaAsN energies at the T point. Where E is the resulting GaAsN conduction band, Ec is the GaAs conduction band, EN is the energy of the localized nitrogen state and Vint is the matrix element which describes the interaction between £jv and Ec- The anticrossing interaction between the localized nitrogen states and the extended GaAs states results in a splitting of the GaAs conduction band into two non-parabolic bands, E+ and E _ . Equation A . l can be solved for E which gives the following result: EN + EC± J(EN-EcY + Wlt E± = £ (A.2) The result of the calculation is given in Figure A . l . Setting Vint equal to 0.26 eV results in a conduction band shift of about 140 meV which is consistent with the bandgap of GaAso.99No.01- Shan et al. used this model to successfully explain the features they observed in pressure dependent photoreflectance experiments carried out on InGaAsN samples. In 116 these experiments, Vint was used as a fitting parameter. Shan found that the magnitude of Vint increases with the nitrogen concentration, as one would expect. Mattila et al.[73] pointed out that it is difficult to determine with certainty the microscopic identity of the two levels used in the model. These authors also state that calcu-lations based on first principles without the use of fitting parameters are a more conclusive way of explaining the composition dependance of the bandgap of dilute nitrides. However, such calculations are quite involved and their explanation is outside the scope of this work. 

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