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Surface reconstructions during growth of GaAs₁-xBix alloys Masnadi Shirazi Nejad, Mostafa 2010

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Surface Reconstructions During Growth of GaAs1-xBix Alloys by Mostafa Masnadi Shirazi Nejad B.Sc., Sharif University of Technology, 2007  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER of SCIENCE in  The Faculty of Graduate Studies (Physics)  The University of British Columbia (Vancouver)  April, 2010 © Mostafa Masnadi Shirazi Nejad, 2010  Abstract GaAs1-xBix is an exciting new semiconductor alloy with numerous promising applications. Incorporation of Bi into GaAs allows for a large reduction of the GaAs bandgap per percent incorporation (7x greater than In, with modest increase in lattice size) and shows strong photoluminescence (PL) and low material degradation associated with Bi. This will allow for longer wavelength devices to be grown on GaAs substrates, than is currently possible with pseudomorphic InGaAs on GaAs. Since Bi has a strong tendency for surface segregation, the molecular beam epitaxy (MBE) growth of GaAs1xBix  is challenging. To achieve Bi incorporation, this alloy requires unconventional MBE  growth conditions such as a low substrate temperature and low As overpressure. The low As:Ga flux ratio also makes Ga and Bi droplet formation a problem. Therefore careful control of growth parameters, especially the As:Ga flux ratio is necessary. In this regard reflection high-energy electron diffraction (RHEED) is used as a crucial tool in locating the optimum growth conditions. The surface reconstruction phase map of GaAs1-xBix is explored in this study as a function of growth temperature and As:Ga ratio. For comparison, the phase map of GaAs, at low temperatures is also obtained. It is observed that the (1×3), (2×3), (2×4) surface phases are common between GaAs and GaAs1-xBix but due to the presence of Bi, a new (2×1) reconstruction appears in the case of GaAs1-xBix. This new reconstruction is observed for various Bi fluxes, showing the evolution of this phase with substrate temperature and As:Ga flux ratio. In addition, the emissivity of the (2×1) surface was found to be lower than for the other As-rich reconstructed surfaces (e.g. (1×3) and (2×3) surfaces) which suggests that the (2×1) surface phase is metallic. Throughout this work, several GaAs1-xBix films were grown with (1×3) and (2×1) reconstructions at different substrate temperatures. Each film is characterized using highresolution x-ray diffraction (XRD), photoluminescence spectra (PL) and atomic force microscopy (AFM). Superior crystal quality, higher Bi incorporation and higher intensity PL was observed for GaAs1-xBix samples grown on (2×1) surfaces, relative to samples grown on (1×3) surfaces.  ii  Table of Contents Abstract ............................................................................................................................. ii Table of Contents ............................................................................................................. iii List of Tables .................................................................................................................... iv List of Figures.................................................................................................................... v Acknowledgements ........................................................................................................... x Dedication ......................................................................................................................... xi Chapter 1  Introduction................................................................................................. 1  Chapter 2  Theory of Surface Structures .................................................................... 5  2.1.  Relaxation and Reconstruction ........................................................................... 5  2.2.  Notation of Surface Reconstruction.................................................................... 7  2.3.  The Electron Counting Model ............................................................................ 9  2.4.  Measurement of Surface Reconstruction .......................................................... 13  Chapter 3  RHEED Surface Analysis of GaAs and GaAs(1-x)Bix ............................. 17  3.1.  Molecular Beam Epitaxy Growth of GaAs Based Compounds........................ 17  3.2.  RHEED Intensity Oscillation............................................................................ 19  3.3.  Surface Phase Diagram ..................................................................................... 23  3.4.  RHEED Observation of Metallic (2×1) Surface............................................... 35  Chapter 4  Growth and Properties of the GaAs(1-x)Bix Alloys ................................. 38  4.1.  Growth Procedure ............................................................................................. 38  4.2.  Ex-situ Characterization.................................................................................... 41  4.2.1.  High Resolution X-ray Diffraction ........................................................... 41  4.2.2.  Photoluminescence ................................................................................... 44  4.2.3.  Atomic Force Microscopy ........................................................................ 48  Chapter 5  Conclusion ................................................................................................. 50  Bibliography ................................................................................................................... 52 Appendix A.  RHEED Screen Fabrication ................................................................ 58  Appendix B.  Numerical Calculation of Bismide Infrared Absorption .................. 62  iii  List of Tables  Table 3-1 : Activation energy for surface reconstruction phase transitions on GaAs(001) surfaces. .......................................................................................................................... 26 Table 4-1: Summary of grown bismide samples. . .......................................................... 41 Table 4-2: Summary of growth conditions for bismide samples. ................................... 41 Table A-1: Summary of two different kinds of RHEED screen made on the four inch lead glass plate and tested in the MBE chamber. ................................................................... 59 Table B-1: Optical properties of GaAs and bismuth at λmax=4.3 μm from references [42,43]. ……………………………………………………………………………….…66  iv  List of Figures  Figure 1-1 Schematic view of the band structure for the GaAs , GaAs1-xNx and GaAs1xBix  where x=0.03. The bandgap in nitride reduced due to the resonance of  the N 2s state and the conduction band minimum (CBM) energy level while in bismide, the Bi 6p resonance with the valance band maximum (VBM). . 3 Figure 2-1 Schematic illustrations of surface atom rearrangements for (a) normal relaxation of topmost atomic layer with surface lattice spacing of α d ; (b) lateral relaxation of topmost atomic layer with lateral shift β d ; (c) surface reconstruction with missing row of atoms; (d) the atomic model of GaAs(001) α (2 × 4) surface reconstruction with missing rows of Ga and As. ...................................................................................................................... 7 Figure 2-2 Atomic model for (a) the bonds and dangling bonds, both filled (shaded) and empty (open), of GaAs- (2 × N ) surface where N periodicity arises from missing dimers; (b) Bi/GaAs- (2 × 1) reconstruction with Bi dimers on top proposed in [21,22]. The Bi-dangling bonds on this structure are half filled. .................................................................................................................... 10 Figure 2-3 Ewald sphere construction and diffraction geometry of RHEED. Intensity maxima of Laue zones (L0, L1, etc.) on the phosphor screen correspond to projected intersections of the Ewald sphere with the reciprocal rods. The specular reflection is located at the intersection of the zero order Laue zone with the (00) reciprocal lattice rod. ........................................................... 15  v  Figure 2-4 RHEED patterns of (a) (2 × 1) and (b) (1 × 3) Bi-stabilized reconstruction along [01 1 ] and [011] azimuths  during the growth of GaAs(1-x)Bix at 300 ° C. ..... 16  Figure 3-1 RHEED oscillations observed during growth of GaAs at 560°C with and without the Bi pre-deposition. These oscillations measured along the [0 11] azimuth when the GaAs surface reconstruction was (2×4). Both growths were carried out under identical conditions and the growths started by opening a gallium shutter. In the second oscillation, bismuth shutter was opened before opening a gallium shutter and remained open during the growth. ...................................................................................................... 20 Figure 3-2 RHEED oscillation of GaAs(1-x)Bix films at substrate temperatures 290°C and 360°C. Each growth started by first opening the bismuth shutter and then the gallium shutter. The RHEED intensity is measured along the [0 11] azimuth. The bismide surface had a (1x3) reconstruction. The composition of each film was measured later with X-Ray Diffraction (XRD). ............ 21 Figure 3-3 Surface phase diagram of GaAs(001) at low substrate temperatures (LTGaAs) and at low growth rate (0.1 μm/h). The surface reconstructions are plotted as a function of substrate temperature and the As2:Ga flux ratio expressed by the beam equivalent pressure (BEP) ratio. Data points and the different phases are shown by the filled colored circles and the shaded areas. Fits to the phase transition boundaries are shown by dashed lines. 25 Figure 3-4 Surface phase diagram of GaAs(1-x)Bix at low substrate temperatures (LTGaAs) and at low growth rate (0.1 μm/h). The arsenic BEP varies from 4×10-8 to 7×10-7 torr and the bismuth BEP is constant at 3×10-9 torr. This  vi  phase diagram transforms to the phase diagram of GaAs(001) above 400°C as no bismuth incorporates into the growing film. The starting point of the GaAs(001) phase diagram is shown by dashed lines. Data points and the different phases are shown by the colored circles and the shaded areas. .. 28 Figure 3-5 The phase diagram of the (2×1) phase for four different bismuth beam fluxes. The observed (2×1) phases shown by the shaded areas. The bismuth fluxes are labeled in each figure and they correspond to bismuth cell temperatures of 425˚C, 450˚C, 475˚C, and 500˚C. The growth rate in all of the phase diagrams is 0.1 μm/h. ................................................................................ 31 Figure 3-6 (a) The As2:Ga BEP ratio versus the bismuth flux for the (2×1) surface phase. The observed growth condition is shown with bar lines and the fitted line to the middle point in each growth condition is given by a dashed line. (b) The upper temperature limit of the (2×1) phase (Tmax) versus the bismuth flux. These fluxes correspond to bismuth cell temperatures of 425˚C, 450˚C, 475˚C, and 500˚C. The arsenic BEP flux varies from 4×10-8 to 7×10-7 torr and the growth rate is 0.1 μm/h. ............................................................... 32 Figure 3-7 (a) shows a measurement of RHEED specular intensity as the arsenic valve is closed. The RHEED intensity dropped fast and metallic droplets started to form on the surface when the As2 BEP reached 2×10-8 torr. The reconstruction during the growth was constant (2×1) and at each point on the diagram, bismide material was grown for at least 15 min. (b) A photographic image of the droplets after the growth. On average, the droplet size is in the one micron range. .................................................... 34  vii  Figure 3-8 The effect of different bismuth surface reconstructes on the temperature of the substrate. The initial substrate temperature is around 400˚C and the power of the substrate heater is not changed during the experiment. The growth has been done under the bismuth flux of 7.0×10-9 torr. The occasional large scatter in data points is obvious and is caused by noise or pick up in the optical bandgap thermometry. .................................................................. 37 Figure 4-1 Effect of growth interruption of GaAs on (a) the specular RHEED intensity and on (b) RHEED patterns along [0 11] azimuth at substrate temperature near 380˚C. It is observed that by closing a gallium shutter, the intensity of specular RHEED streaky lines increased by 35%. In addition, the reconstruction lines become much brighter and both the first and second Laue zones (shown by white arrows) appeared on the RHEED screen. .... 40 Figure 4-2 [004] X-ray rocking curves of GaAs(1-x)Bix(001) epilayers at (a) 300˚C, (b) 350˚C, and (c) 400˚C substrate temperatures. Blue figures show samples grown with a (2×1) reconstruction while the red figures show samples grown with a (1×3) reconstruction. Fit to r2169 data set is shown with dash line. ........................................................................................................... 43 Figure 4-3 Room temperature photoluminescence of growm samples at (a) 300˚C, (b) 350˚C, and (c) 400˚C substrate temperatures. Samples are pumped with a 532 nm diode pumped frequency doubled YLF laser. Blue figures show samples grown with a (2×1) reconstruction while the red figures show samples grown with a (1×3) reconstruction. All PL measurements have the  viii  same integration times (10 sec) and the relative PL efficiency was calibrated using a p-GaAs reference sample. ............................................ 46 Figure 4-4 Room temperature photoluminescence from p-GaAs reference samples used for PL calibrations. In comparison with Figure 4-3, the emission peak of the first p-GaAs reference sample is 12% higher but the emission peak of the second p-GaAs reference sample is nearly halved. .................................. 47 Figure 4-5 1×1 μm and 5×5 μm AFM images of r2138 and r2139 samples. These samples were grown at 300˚C substrate temperature with (1×3) and (2×1) reconstruction. The bismuth concentration in  r2138 was 2.3% and in  r2139, it was about 5.0%. The z scale is 2 nm in all the images. ............. 49 Figure A-1 (a) Variation of resistivity and the transmission of 75 nm ITO on glass as a function of post baking substrate temperature. Transmission measured by using the neutral density filters (ND) from a green laser at wavelength λ=532 nm; (b) Images of a conductive mirror-like ITO film just after the deposition via e-beam evaporation (before the post baking) and yellowish transparent ITO film after the baking in air up to 400 ˚C on the hot plate. 60 Figure B-1 The schematic illustration of the thermal radiation between the heater and the substrate at two different thicknesses d and d+Δd. ……………………….61 Figure B-2 The schematic illustration the optical reflection and transmission from (a) GaAs/Vacuum interface when Δd=0 (two medium) (b) GaAs/Bi and Bi/Vacuum interfaces when Δd≠0 (three medium). The Fresnel amplitudes of reflection and transmission are labled by r and t. ……………………...63  ix  Acknowledgements  I would not have completed this thesis without the significant help of many great people who have made my life at UBC a pleasant and productive experience. First and foremost, I would like to express my sincere gratitude to my supervisor, Dr. Tom Tiedje for his inspiration, guidance and continuous support during my M.Sc. study. I consider myself very fortunate for having the opportunity to work with him. Many thanks to my cosupervisor, Nicholas Ingle for his valuable comments and suggestions on the content of this research. My special thanks to Dan Beaton and Ryan Lewis for their tremendous leadership and support throughout this work. I would like to thank them for teaching me how to work and grow with the MBE. Thanks to the rest of the MBE group for their help and support during my stay in the lab; Mike Whitwick, Xianfeng Lu, Raveen Kumaran, Scott Webster, Wei Li and Shown Penson. And my special thanks to Jim Mackenzie who knows the MBE better than anyone else and helped me a lot on making the RHEED screens. Most importantly, this work is dedicated to my wonderful parents for all their love and support during my life. They have been my main motivation throughout my studies. I always felt them near me, even though they were living far away from here. And my thanks to my dear younger brothers, Mohammad Sadegh and Amir Hossain for their encouragement and good company during this work.  x  Dedication  TO MY PARENTS  xi  Chapter 1 Introduction  With the invention of the transistor by Shockley, Bardeen, and Brattain in the mid-20th century, the astonishing usefulness of semiconductors was recognized and they became the heart of the electronics industry. Due to the continued need for faster, more efficient, higher density, and lower power consumption electronic devices, research on exploring new semiconductor materials has been growing steadily. Therefore there has been a close synergy between the success in electronic technology and the scientific knowledge of novel materials. In this regard, epitaxial growth methods such as molecular beam epitaxy (MBE) play an important role in the creation and investigation of new metastable materials which do not exist in nature. The  group  III-V  semiconductor  materials  are  undoubtedly  the  most  technologically important compound semiconductors. The direct bandgap of most of this class of materials means that they are ideally suited for optoelectronic devices such as light emitting diodes (LEDs), diode lasers, solar cells, and transistors used in telecommunication devices. The basic foundation among all the III-V semiconductor materials is GaAs which has been studied comprehensively over the past 40 years. GaAs has a high electron mobility (~ 8500 cm2 V-1 s-1 at 300K), allowing transistors to function at frequencies higher than 250GHz. Unlike silicon, GaAs relatively is insensitive to heat and has a higher breakdown voltage (~4×105 Vcm-1) therefore these properties recommend GaAs for high power devices. In addition, due to the fact that GaAs can easily be alloyed with other III-V elements (e.g. Al, In, N, P, Sb), a wide range of bandgap energies can be engineered. This is one of the key properties of GaAs which is used extensively in quantum wells devices. In general, the bandgap for most of the semiconductor alloys GaAs1-xXx is defined by,  1  Chapter 1. Introduction  Eg = xEgGaX + (1 − x) EgGaAs − bx(1 − x)  (1-1)  where b, the coefficient of the quadratic term, is known as the bowing parameter. In recent years two new group V elements have been alloyed with GaAs. Nitrogen is one of them which can incorporate completely to form GaN. This compound has a wide bandgap of 3.4 eV. It is quite amazing that dilute nitride GaAs1-xNx (0 ≤x≤ 5 %) is found to have a smaller bandgap than GaAs at 1.42 eV. Based on equation (1-1), this means that the dilute nitride has a giant bandgap bowing parameter. In this regard, U. Tisch et al. showed that every 1% nitrogen incorporation reduces the bandgap by the anomalously large amount of 0.2 eV which is much higher than other group V elements [1]. Since this discovery, diluted GaAs1-xNx is commonly used to reduce the bandgap in long wavelength devices [2]. However, despite the success of dilute nitrides from a bandgap engineering point of view, between GaAs1-xNx and GaAs, this alloying causes a significant amount of defects associated with nitrogen [3]. This limits the useful applications of the grown film. Also it is difficult to reduce the bandgap beyond a narrow range because of large lattice strain. One way to correct this lattice mismatch is to introduce indium where at a 3:1 ratio of indium to nitrogen, the mismatch disappears. Another way to improve the crystal quality of dilute nitrides is to introduce a surfactant during growth as discussed in reference [3]. Recently, bismuth, the heaviest non-radioactive element in the periodic table, has been alloyed with GaAs. Due to the large atomic size of bismuth in comparison to gallium and arsenic, this element hardly incorporates into the lattice under usual growth conditions and has a tendency to surface segregate. The first GaAs1-xBix alloy was reported by K. Oe et al. in 1998 where 2% bismuth incorporation was observed in metal organic vapor phase epitaxy (MOVPE) growth [4]. MBE growth of bismides was observed 5 years later [5,6,7]. Similar to the effect of nitrogen in GaAs1-xNx, bismuth was also found to reduce the bandgap of GaAs by a large amount namely 88 meV per percent bismuth [8]. This is eight times greater than the effect of indium on the bandgap. Furthermore, bismuth does not have the same density of defects associated with it as  2  Chapter 1. Introduction  Figure 1-1 : Schematic view of the band structure for the GaAs , GaAs1-xNx and GaAs1-xBix where x=0.03. The bandgap in nitrides reduced due to the resonance of the N 2s state and the conduction band minimum (CBM) energy level while in bismides, the Bi 6p resonance with the valance band maximum (VBM).  nitrogen; therefore bismuth is more effective in bandgap reduction. It is observed that these two ternary alloys, GaAs1-xNx and GaAs1-xBix, are complementary in the way that the bandgap is reduced. In the nitrides the energy of the conduction band is reduced whereas in the bismide the energy of the valence band is increased. This kind of behavior in nitrides is due the resonance interaction between the nitrogen 2s energy level and the conduction band minimum (CBM) [9,10], while in bismides, the bismuth 6p energy level is resonant with valence band maximum (VBM). The resonance interaction can be understood due to the fact that the 2s state of N is significantly lower than that of the 4s of As; thus, N generates a potential trap for the electron in the CBM state. Similarly, because the 6p state of Bi is substantially higher than that of the 4p of As, Bi is likely to generate a potential trap for the hole in the VBM state [10]. Thus nitrogen alloying strongly affects the electron mobility whereas bismuth alloying is expected to affect the hole mobility. A schematic comparison of band structure for these two materials is presented in Figure 1-1 when the incorporation of nitrogen and bismuth are 3 percent.  3  Chapter 1. Introduction From the optical point of view, the GaAs1-xBix alloy has been shown to have a broad photoluminescence (PL) spectrum in the infrared (~ λ> 900 nm), depending on the Bi concentration. This broadband spectrum suggests that the bismuth can form clusters that the composition of the material varies throughout the film thickness. The broad emission spectrum makes the bismides a potential candidate for low coherence light sources. Low coherence light sources are used extensively in a medical imaging technique known as optical coherence tomography (OCT). OCT system uses a Michelson interferometer to produce three-dimensional images of body tissues which usually have a depth resolution of 1-15μm. Another possible optical application of bismide alloys is in high efficiency solar cells. Throughout this work, we are seeking to improve the growth condition of GaAs1xBix  alloy by using the reflection high energy electron diffraction (RHEED). RHEED is a  technique used to characterize the surface of crystalline materials. This thesis is ordered in the following way: Chapter 2 reviews the basic concepts of RHEED and surface reconstructions. This chapter also provides a general introduction to the electron counting model (ECM) for GaAs(001) and GaAs1-xBix(001). Possible reconstructions are presented in this chapter. In Chapter 3, first we describe the procedure used to grow GaAs(001) and GaAs1-xBix(001) films. Then, the experimental RHEED observations, including RHEED oscillations and RHEED phase maps are presented. In chapter 4, different properties of grown bismide samples are compared for different surface reconstructions during growth. A discussion of the experimental results is presented in Chapter 5.  4  Chapter 2 Theory of Surface Structures  2.1. Relaxation and Reconstruction The III-V compound semiconductors are characterized by tetrahedral (i.e. sp3 hybrids) covalent bonding of different group elements where the atoms are coordinated periodically in a bulk crystal. When a bulk crystal is terminated at a surface, dangling bonds are formed. Each dangling bond is a broken covalent bond with one un-paired electron. This lack of electron pairing makes the dangling bonds unstable and the surface can minimize its free energy by moving or rebonding the surface atoms. As a result, a crystal structure with a new periodicity can form on the surface. This makes the surface crystal structure different from the bulk structure of the material and the surface can have different electronic and optical properties. In the thermodynamic equilibrium state of a system which contains N particles at fixed temperature T and pressure p, the surface free energy is given by the Helmholtz free energy [11], F = U − TS  (2.1)  where U is the internal energy and the entropy S comes from the Legendre transformation. Therefore based on this equation, the surface can minimize its free energy through two different methods. Relaxation and reconstruction is one method, where the surface free energy is lowered due to a decrease in the internal energy U. In this method, a new periodicity of atoms will form on the surface. The other method is roughening, where the surface minimizes its free energy through increasing the entropy S. In this  5  Chapter 2. Theory of Surface Structures method, nanoscale structures such as islands or pits form on the surface as the entropy of the surface increases [12]. Relaxation refers to the displacement of the position of surface atoms relative to the bulk positions without changing the surface periodicity. Figure 2-1(a) shows an example of the first type of relaxation where the surface layers move in a direction normal to the surface plane. This normal relaxation results in smaller lattice spacing  α d where the d is the bulk lattice spacing and 0 < α ≤ 1 . Figure 2-1(b) shows another type of relaxation where the topmost atomic layers have a lateral shift relative to the bulk layers. In this relaxation, the inter-layer spacing between the surface and bulk is still d but the surface atoms are laterally shifted by β d where the proportionality factor β is in the range of 0 < β ≤ 1 . The third type of relaxation is the combination of normal and lateral relaxation with proportionality factors α and β . On the other hand, reconstruction refers to a change in the two-dimensional structure of the surface layers, in addition to changes in the position of the entire layer (relaxation). As a result, the two-dimensional periodicity of the surface layers will change and a new type of crystal symmetry will appear on the surface. One possible mechanism for a surface reconstruction is vacancy rows of atoms which is schematically indicated in Figure 2-1(c). Due to the missing rows of atoms the periodicity of this surface is changed from d to 2d so the surface has the 2× reconstruction. As a real example of this  reconstruction, Figure 2-1(d) shows the surface atomic model of a GaAs(001)- (2 × 4) unit cell with missing rows of gallium and arsenic. Due to the new periodicity along the [110] azimuth, the reconstruction in this direction is 4×. The details of most of the GaAs(001) surface reconstructions can be found in [13] and [14]. Determining when a surface will choose roughening, relaxation, or reconstruction simply by knowing the chemical species, crystal structure, and crystallographic orientation of the surface is nearly impossible due to the complex interdependency of these mechanisms [12]. In the case of adsorption of atoms onto the surface, the ultimate surface structure depends on [15]:  6  Chapter 2. Theory of Surface Structures  Figure 2-1: Schematic illustrations of surface atom rearrangements for (a) normal relaxation of topmost atomic layer with surface lattice spacing of α d ; (b) lateral relaxation of topmost atomic layer with lateral shift β d ; (c) surface reconstruction with missing row of atoms; (d) the atomic model of GaAs(001) α (2 × 4) surface reconstruction with missing rows of Ga and As.  •  The composition of substrate and adsorbate material (e.g. most adsorbate metals showed relaxation [16]).  •  The surface coverage of adsorbate layers on substrate.  •  The ambient condition (e.g. temperature, gas pressure).  2.2. Notation of Surface Reconstruction As a result of the new periodicity on the reconstructed surface, a new 2-D Bravais lattice G G called a superlattice with primitive basis vectors as and bs can be defined for the surface. Based on this assumption, two ways to describe the superlattice are used conventionally.  7  Chapter 2. Theory of Surface Structures G G The first one was proposed by Park and Madden [17] and it describes as and bs in terms G G of ideal (unreconstructed) basis vectors of substrate a and b in matrix notation. The  equations are:  G G G as = G11a + G12b G G G bs = G21a + G22b  (2.2)  G12 ⎞ ⎛G G = ⎜ 11 ⎟ ⎝ G21 G22 ⎠  (2.3)  where coefficients Gij form  G G G G The values of Gij determine whether the relation between the vectors as , bs and a , b is rational or not. If the relation between the unit vectors of the surface lattice and the substrate is not rational, then the superlattice is registered incoherently with the substrate plane. The second notation which describes the reconstruction more precisely was proposed by Wood [18]. In this method, the lattice periodicity ratio of the surface to the substrate as well as the rotation angle of superlattice basis vectors to the substrate basis vector is taken into account. Therefore when the adsorbate A is induced on the B(hkl) surface, the reconstruction is (m × n) with the following notation: B(hkl ) ( m × n ) Rϕ ° − A  (2.4)  where m and n are defined by  G as m= G a G bs n= G b  (2.5)  8  Chapter 2. Theory of Surface Structures  In this notation when the reconstruction of the superlattice is centered with the substrate mesh, the reconstruction is c(m × n) . A list of the relations between Wood notation and the matrix notation for the real cubic and hexagonal crystals can be found in [19].  2.3. The Electron Counting Model During the discovery of the reconstruction phases for the GaAs(001) surface, theoretical models for semiconductor surface reconstruction were also being formulated [12,13,20]. One of the fundamental models which is extensively used for predicting the possible reconstruction on semiconductor surfaces is the electron counting model (ECM). Based on this model, the lowest energy for the semiconductor surface is obtained (and hence the most stabilized structure) when the dangling bonds of the electronegative element (e.g. As) are filled and the dangling bonds on the electropositive element (e.g. Ga) are empty. In order to achieve this, the electron charges will transfer from the electropositive cations to the electronegative anions. This will necessarily result in no net charges on the surface and the surface will be semiconducting. On the other hand, if the dangling bonds are partially filled, the above condition is not satisfied and a metallic surface may appear. If a given reconstruction is allowed by the ECM, the total number of electrons in the superlattice unit cell must be counted for a given reconstruction and then should be equal to the number of electrons needed to fill all the bonds. To see how this is used to determine the possible surface reconstruction, let’s consider a GaAs(001) surface. This surface was studied a long time ago by scanning tunneling microscopy (STM), which showed that the well known GaAs- (2 × 4) reconstruction arises from dimerization of the As atoms on the surface, with every fourth dimer missing [20,21]. A model for this reconstruction is shown in Figure 2-2(a). This figure shows the atomic structure of the GaAs(001) unit cell with empty and filled dangling bonds of Ga and As, with the general (2 × N ) reconstruction where the 2× periodicity arises from arsenic dimer bonds and N × periodicity arises from missing arsenic dimers in (2 × N ) unit cell.  9  Chapter 2. Theory of Surface Structures  Figure 2-2: Atomic model for (a) the bonds and dangling bonds, both filled (shaded) and empty (open), of GaAs- (2 × N ) surface where N periodicity arises from missing dimers; (b) Bi/GaAs- (2 × 1) reconstruction with Bi dimers on top proposed in [21,22]. The Bi-dangling bonds on this structure are half filled.  If the total number of As dimers in one unit cell is denoted by D, then As dimer bonds are required to have the following number of electrons by the ECM: •  2D electrons in the As-As dimer bond.  •  8D electrons for bonding As dimers to the second layer Ga atoms.  •  4D electrons on dangling bonds in As dimers.  Moreover when VAs and VGa are the number of valence electrons in arsenic and gallium, the total number of electrons available from the top layer and the second layer are 2VAs D and 2 VGa N / 2 = VGa N respectively. The number of electrons available on  10  Chapter 2. Theory of Surface Structures  second layer is halved, since half of the Ga electrons are involved in bonding to the third layer. Altogether the electron balance equation is: 4 D + 2 D + 8 D = 2VAs D + VGa N  (2.6)  with VAs = 5 and VGa = 3 we have, 4 D = 3N  (2.7)  To satisfy this equation, the smallest unit cell with N=4 periodicity and D=3 dimer bonds will form on the surface and the most probable reconstruction is (2 × 4) . Therefore the removal of every fourth arsenic dimer is required in order to satisfy the ECM [19]. In addition to finding possible reconstructions, the ECM can easily determine whether the surfaces are metallic or semiconducting by counting the number of filled dangling bonds on the electronegative element (e.g. As). So in the case of GaAs- (2 × 4) , the number of dangling bonds N d is: N d = 2VAs D − 10 D  (2.8)  where:  2VAs D = Total number of available electrons on top layer 2D+8D= 10D = Total number of electron on As dimers Insert VAs = 5 and D=3 into equation (2.8) and the result is N d = 0 . Therefore all the dangling bonds are fully filled and there is no net charge on the GaAs- (2 × 4) surface and the surface is semiconducting. In general, the ECM predicts a semiconducting reconstruction with vacant dimer sites for III-V surfaces [22], but the Bismuth (Bi) adsorbate atoms on III-V surfaces have recently been found to behave differently from other group V stabilized III-V surfaces[23]. It has been shown that at high Bi coverage, the Bi/GaAs(100) surface has a  11  Chapter 2. Theory of Surface Structures  metallic or semiconducting unusual (2 × 1) reconstruction [22,23] which is in contrast with the ECM prediction. According to the ECM such small (2 × 1) unit cells should only have a metallic reconstruction with half filled dangling bonds but the observation is different. The reason for this behavior has remained unclear up to now. To see the ECM prediction for this structure, let’s consider Figure 2-2(b) where shows the recent STM finding of the Bi/GaAs- (2 × 1) atomic model [22,23]. The (2 × 1) unit cell is defined by the dashed lines. The top layer has two Bi-Bi dimer bonds with Bi-Ga bonds to the second layer. Therefore similar to the previous calculation, the number of dangling bonds on top layer is: N d = 2VBi D − 2 D − 4 D − 2 D  (2.9)  where  2VBiD = Total number of electrons available from the top layer.  2D = Total number of electrons available in Bi-Bi bonding. 4D = Total number of electrons available in the middle Bi-Ga bonding. 2D = Total number of electrons available from the topmost and the downmost  Bi-Ga bonding. Now when VBi = 5 and D=2, the number of empty dangling bonds becomes N d = 4 . Therefore four dangling bonds on top layer are unpaired and half filled. As a  result, the ECM predicts a metallic surface for Bi/GaAs- (2 × 1) .  12  Chapter 2. Theory of Surface Structures  2.4. Measurement of Surface Reconstruction The bulk crystal can be characterized by x-ray diffraction. Due to the extremely large penetration depth and the mean free path of x-rays and also due to the relatively tiny number of atoms on the surface, this method is not normally suitable for reconstructed surfaces. Consequently, much effort has been devoted to the invention of alternative surface sensitive techniques. In general these special techniques fall into two different categories: •  Electron diffraction based techniques such as reflection high-energy electron diffraction (RHEED), low energy electron diffraction (LEED) and grazing incidence x-ray diffraction (GIXD).  •  Atomic probe microscopy techniques such as scanning tunneling microscopy (STM) and the atomic force microscopy (AFM).  A highly surface sensitive techniques used in this study, is the reflection high-energy electron diffraction (RHEED). In this technique, a focused beam of high energy electrons ( 5 − 20 KeV) strikes a crystalline sample at a glancing angle ( ~ 1 − 5° ). This small incidence angle limits the beam penetration depth to a few monolayers of material and only the electrons in the top layer of sample are scattered elastically. Considering the G  G  elastic scattering, k f = ki , the diffraction condition is satisfied when the scattering vector matches a reciprocal lattice vector. In reciprocal space, a two-dimensional array of surface atoms can be visualized as infinitely long vertical lines named reciprocal lattice rods (or Bragg rods). Therefore wherever these rods cross the Ewald sphere, the condition for constructive interference of scattered electron beams is satisfied and a diffraction pattern is created. This diffraction pattern can be detected with a phosphor screen placed on the opposite side of the RHEED electron gun1. Figure 2-3 illustrates the basic principle of operation and the geometry of RHEED, and defines Laue zones.  1  See Appendix A for experimental details on making the phosphorescent screen.  13  Chapter 2. Theory of Surface Structures The appearance of the RHEED pattern can provide information about the surface crystal structure, surface orientation, and the surface morphology of materials. This information is obtained from the position, shape and the intensity of the RHEED pattern. In addition, the shape of the reciprocal lattice rods can significantly change the diffraction pattern of the surface. If the reciprocal lattice rods are infinitely narrow (corresponding to an atomically flat surface), the intersection of the rods with the Ewald sphere will approximate a point, and the RHEED image will appear spotty. But if the surface lattice spacing is different that the bulk crystal lattice spacing, the reciprocal lattice rods have some width and the intersection well broaden out into a streaky pattern [11]. Figure 2-4 shows the observed RHEED patterns of Bi-stabilized (2 × 1) and (1× 3) streaky reconstruction during the MBE growth of GaAs(1-x)Bix .  14  Chapter 2. Theory of Surface Structures  Reciprocal rods  Phosphor screen  (00)  Second order Laue zone  RHEED electron gun  e−  L2  Ewald sphere  L1 First order Laue zone  θ ~ 1 − 5°  L0 Zero order Laue zone  ki  Sample rotation  Reciprocal lattice origin  Specular reflection  Figure 2-3: Ewald sphere construction and diffraction geometry of RHEED. Intensity maxima of Laue zones (L0, L1, etc.) on the phosphor screen correspond to projected intersections of the Ewald sphere with the reciprocal rods. The specular reflection is located at the intersection of the zero order Laue zone with the (00) reciprocal lattice rod.  15  Chapter 2. Theory of Surface Structures  RHEED reconstruction along [01 1] azimuth  RHEED reconstruction along [011] azimuth  (a)  (b)  Figure 2-4: RHEED patterns of (a) (2 × 1) and (b) (1 × 3) Bi-stabilized reconstruction along [01 1 ] and [011] azimuths during the growth of GaAs(1-x)Bix at 300 ° C  16  Chapter 3 RHEED Surface Analysis of GaAs and GaAs(1-x)Bix  3.1. Molecular Beam Epitaxy Growth of GaAs Based Compounds Molecular beam epitaxy (MBE) is one of the best techniques for growing single crystals of GaAs with high purity and low defect density. In the MBE process, beams of atoms or molecules are thermally evaporated from solid source materials and incident on a crystalline substrate in an ultra-high vacuum (UHV) [24]. The base pressure inside the MBE chamber is typically on the order of 10-10 torr which means that the collision distance of gas molecules is several hundred kilometers so the evaporated atoms do not interact with each other and they form a directed beam toward the substrate. During growth, the background arsenic vapour pressure is typically 10-7 torr which still allows a long collision free beam path. By the use of shutters, each beam can be blocked or started in a fraction of second which is normally much shorter than the time needed to grow one monolayer (ML). Therefore the MBE process allows layer-by-layer growth and offers tremendous control over layer thickness, down to individual atomic layers. In particular, MBE is well prepared for the growth of GaAs and its ternary and quaternary alloys. MBE growth of high-quality GaAs crystals occurs under an As over pressure, at a temperature of about half the melting point of GaAs, around 550˚C to 600˚C, with a (2×4) surface reconstruction. Some of the main features of GaAs at this growth temperature can be summarized as follows: •  Low temperature, 500˚C - 600˚C, minimizes the number of thermodynamic defects in the GaAs crystal.  •  With the gallium effusion cell at a temperature near 900°C to obtain a 1 μm/h growth rate, every gallium atoms that impinges on the substrate at a temperature 17  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix of 600°C will remain and have enough thermal energy to find a lattice site [25]. In addition, at the 600°C growth temperature excess As, not bonded to Ga will readily evaporate. •  The growth of low temperature GaAs (LT-GaAs), at temperatures lower than 400°C, results in the formation of arsenic antisites in GaAs. These As antisites merge into As clusters with high temperature annealing.  On the other hand, the optimum growth conditions for GaAs(1-x)Bix crystals are not the same as for GaAs. Due to the large difference in the atomic size and the electronic structure of bismuth relative to arsenic and gallium, bismuth tends to surface segregate rather than incorporate. Therefore under standard growth conditions for GaAs, bismuth does not incorporate into the GaAs lattice but behaves as a surfactant. This results in a smoother surface for the grown GaAs films. In addition, bismuth surfactant growth of GaAs based compounds like GaNxAs(1-x) and InxGaNxAs(1-x) is also found to improve the surface smoothness and photoluminescence emission [5,26]. However S. Tixier et al. and E.C. Young et al. showed that bismuth can incorporate into GaAs under unconventional growth conditions where the V:III flux ratio is low (near stoichiometric) and the growth temperatures are less than 400 ºC [6,27]. By using these growth conditions, bismuth incorporation of up to 10% has been reported in the temperature range of 270°C-320°C [28]. It is found that these growth conditions are very close to the conditions where the metallic gallium and bismuth droplets form on the surface. These droplets can increase the surface roughness and create surface defects. In order to have better control over the formation of droplets, a low growth rate of about 0.1 μm/h is used for GaAs(1-x)Bix films. At this growth rate, the bismuth evaporation increases relative to incorporation so that excess bismuth will tend to evaporate rather than accumulate into droplets. Samples discussed in this study were grown in a VG-V80H molecular beam epitaxy reactor equipped with standard Knudson effusion cells for gallium and bismuth, and an As2 dual zone cracker. The group V:III flux ratio was always higher than one which means that there was an overpressure of arsenic during the growth. The flux of each molecular source was measured using a retractable ion gauge located inside the  18  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix deposition chamber. This system is also equipped with RHEED which is used for in-situ monitoring and measurement of the surface reconstruction during growth. The RHEED gun always operated at 15keV energy with the filament current of 1.5 to 1.6 A. In addition, to ensure a uniform film deposition, the samples were rotated at moderate speeds during growth. The rotation was stopped during the RHEED measurement at the  [011] and [0 11] azimuths. The temperature of the substrate was monitored using optical bandgap thermometry with an accuracy of 5°C [29].  3.2. RHEED Intensity Oscillation RHEED intensity oscillation is one of the most straightforward and useful methods to study the film growth dynamics during MBE deposition. This is used routinely to determine the growth rate and to see whether the growth mode is through island nucleation or step flow. The simplest explanation of these oscillations can be given by starting from an atomically flat surface where the RHEED diffracted peak intensity is maximum. When growth is initiated by opening the source material shutter, atomic scale islands nucleate on the surface. As a result, the roughness of the surface increases on the atomic scale and the RHEED diffracted beam broadens and decreases in intensity. As time passes and the surface coverage of the adatoms reaches 50% (Θ=0.5 ML), the surface roughness reaches its maximum value which corresponds to the minimum value in diffracted beam intensity. After this point, the surface becomes smoother by coalescing the islands and the peak intensity recovers until one monolayer is completed. This process corresponds to layer-by-layer growth. On the other hand, if during the growth process a new layer starts before the previous layer is completed then the interface roughness will gradually increase, producing a decay in the oscillation envelope [30]. Figure 3-1 shows a comparison of RHEED oscillations obtained during the layerby-layer growth of GaAs at 560°C with and without the presence of bismuth. Both growths had identical conditions and the oscillations began after opening the gallium source shutter starting from a growth interruption. The RHEED intensity was measured  19  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix  Figure 3-1: RHEED oscillations observed during growth of GaAs at 560°C with and without the Bi predeposition. These oscillations measured along the [0 11] azimuth when the GaAs surface reconstruction was (2×4). Both growths were carried out under identical conditions and the growths started by opening a gallium shutter. In the second oscillation, bismuth shutter was opened before opening a gallium shutter and remained open during the growth.  along the [0 11] azimuth where the GaAs surface had a (2×4) reconstruction. The first RHEED oscillation corresponds to the growth of GaAs without the bismuth surfactant where the oscillation damped rapidly 30 seconds after opening the gallium shutter. The next RHEED oscillation was obtained during a similar growth under a bismuth flux of 2.7×10-7 torr where the pre-deposition of bismuth caused the beam intensity to be lower prior to growth. In the presence of the bismuth flux, the RHEED oscillations are stronger in amplitude and damp more slowly. This suggests that the bismuth surfactant helps the GaAs to grow smoother and the diffusion length on the surface to be longer. Therefore more GaAs layer-by-layer mode can be obtained in the presence of bismuth. The growth rate obtained from the period of these oscillations is around 1 μm/h.  20  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix  Figure 3-2 : RHEED oscillation of GaAs(1-x)Bix films at substrate temperatures 290°C and 360°C. Each growth started by first opening the bismuth shutter and then the gallium shutter. The RHEED intensity is measured along the [0 11] azimuth. The bismide surface had a (1x3) reconstruction. The composition of each film was measured later with X-Ray Diffraction (XRD).  Figure 3-2 presents RHEED oscillations for the growth of GaAs(1-x)Bix along the [0 11] azimuth at two different substrate temperatures 290°C and 360°C. These growths were initiated first by opening the bismuth shutter causing bismuth atoms to build up on the GaAs surface. Therefore the RHEED intensity increased rapidly and the surface reconstruction changed to the bismuth stabilized reconstruction. Then by opening the gallium shutter, the growth was started. This caused a jump in the RHEED intensity and initiated growth oscillations. These bismide films were grown at As2:Ga beam equivalent pressure (BEP) ratio of three. Both of these oscillations lived long (near 2 minutes), which showed that the surface diffusion length is still high at low temperatures. For comparison, we tried to measure the RHEED oscillation of GaAs in the absence of bismuth at the mentioned low temperatures (at 300˚C), but no oscillations were observed. The composition of each film is also determined from the separation in epilayer and substrate diffraction peaks using high resolution x-ray diffraction (XRD). The bismuth  21  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix incorporation was 2.6% and 1.8% for the first and the second films. The growth rate acquired from the oscillation periods is about 0.13 μm/h which shows that the bismide film growth rate is low. The growth rates obtained from the RHEED oscillations are proportional to the gallium flux and can be calculated from,  FGa =  4rg d3  (3-1)  where we assume all the Ga atoms stick to the surface. The rd is the growth rate and d is the lattice constant for GaAs. The factor of 4 comes from the fact that two monolayers of Ga, and two monolayers of As are needed to complete the GaAs unit cell. By knowing the gallium flux, the flux of other materials can be determined from [31,32] 1/ 2  P η ⎛TM ⎞ Fi = FGa i Ga ⎜ i Ga ⎟ PGa ηi ⎝ TGa M i ⎠  (3-2)  where Fi denotes the flux of material i, Pi is the BEP, and Ti and Mi represent the absolute temperature and the molecular mass of material i. The ηi is the ion gauge sensitivity coefficient which for simple materials is given by [31]:  ηi =  0.6Zi + 0.4 14  (3-3)  Zi is the atomic number of element i. By using this equation the ion gauge sensitivity coefficients for gallium and bismuth are ηGa =1.74 and ηBi =3.96. In the case of complex molecules like As2 and As4, equation (3-3) may result in significant error. The direct quartz crystal monitoring (QCM) and ion gauge measurements for As2 and As4 were done by Preobrazhenskii et al. [31] which showed that ηAs2=4.0 and ηAs4 =6.8. In this study, the flux of different materials are calculated from equations (3-1) and (3-2). The atomic fluxes corresponding to Figure 3-1 are FGa = 6.20 nm-2s-1 and FAs2 =  22  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix 9.02 nm-2s-1. For Figure 3-2 we also found that FGa = 0.80 nm-2s-1, FAs2 = 1.19 nm-2s-1, and FBi = 0.02 nm-2s-1.  3.3. Surface Phase Diagram The surface reconstruction provides a useful indication of the state of the growth process in molecular beam epitaxy. In addition, since the surface reconstruction is sensitive to the substrate temperature and the flux of different materials, much work has been done to determine the form of the reconstruction as a function of the growth conditions. Such a function called a surface phase diagram is a useful tool to explore and optimize the growth condition of new materials like the bismides. Each phase diagram is divided into several different surface phases with a stable surface structure in a certain range of temperatures and BEPs. When the composition (BEPs) or the temperature varies beyond the range of stability of a region, a phase transition occurs and a new structure with a different reconstruction forms on the surface. These transitions are reversible as long as droplets do not form on the surface or the grown layer does not become rough or faceted. The first step in studying the surface phase diagram of GaAs(1-x)Bix is to observe the possible surface reconstruction in the absence of bismuth, i.e. phase diagram of GaAs. Such an experiment provides basic information to see later how much the phase diagram of GaAs is affected by the presence of bismuth. GaAs has a well established surface phase diagram. A number of complete and partial phase diagrams have been reported for GaAs(001). Most published phase diagrams are for growth temperatures of GaAs from 400°C to 700°C with the standard 1 μm/h growth rate [32,33]. Moreover, these phase maps differ substantially in presenting the positions of phase regions [32,33,34]. This is probably due to the great difficulties with precise measurement of the substrate temperature and the absolute fluxes of the molecular beams [32]. Since the GaAs(1-x)Bix films are grown at low temperatures, the phase map for GaAs that will be presented in this study is only for the low temperature GaAs growth conditions. In addition a low growth rate (0.1 μm/h) is used to have a better comparison to the phase diagram of GaAs(1-x)Bix. 23  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix All samples grown for the phase diagrams were deposited on 350 μm thick mechanical grade GaAs wafers. At the beginning of every growth, a 300-350 nm buffer layer was grown at standard GaAs growth condition where the V:III ratio was near 9:1 and the substrate temperature was at 560°C-580°C. Then by lowering the substrate temperature to the LT-GaAs region (≤ 400°C), 20-30 nm of GaAs epilayer was grown on the buffer layer, and the RHEED measurements were started along the [011] and [0 11] azimuths. All the observation of reconstructions were performed with the substrate temperature held fixed and the arsenic BEP varied by moving the arsenic valve. Figure 3-3 shows the low temperature surface phase diagram of GaAs(001) as a function of As2:Ga BEP ratios and the substrate temperature. This diagram can be divided into four main regions: I. As-rich surface structures with (2×4), (2×3), and (1×3) reconstructions. II. Ga-rich surface structures with (3×1) and (4×1) reconstructions. III. The (1×1) transition structure to divide the As-rich phases form Ga-rich phases. IV.  Faceting or roughening region where a chevron pattern appears in the RHEED. Due to the small group V:III flux ratio in this region, gallium droplets might also form on the surface. Faceting appears from the transmission diffraction through 3D clusters [30]. All of these surface phases except the (1×1) transition phase agree well with the  phase diagram proposed by L. Däweritz and R. Hey [33]. The arsenic terminated (2×4) reconstruction is the dominant reconstruction for GaAs(001) which is stable in the temperature range of 500°C to 650°C (standard GaAs growth condition). This phase is often called the “technologically important” reconstruction since it is utilized as the starting surface for growing high quality GaAs epilayers for commercial optoelectronic devices [12]. The (2×4) phase shown in this figure, is a small region starting from a substrate temperature near 360°C and continuing to higher temperatures. This is a small part of the large (2×4) reconstructed region which still exists at low temperatures. It is also observed that the main As-rich structure at substrate temperatures between 400°C and 325°C is (2×3) which is stable for As2:Ga BEP ratios from 2 to 10. When the  24  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix  Figure 3-3 Surface phase diagram of GaAs(001) at low substrate temperatures (LT-GaAs) and at low growth rate (0.1 μm/h). The surface reconstructions are plotted as a function of substrate temperature and the As2:Ga flux ratio expressed by the beam equivalent pressure (BEP) ratio. Data points and the different phases are shown by the filled colored circles and the shaded areas. Fits to the phase transition boundaries are shown by dashed lines.  25  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix substrate temperature goes below 325±10 °C, a phase transition occurs and the (2×3) reconstructed structures transform to (1×3). The (1×3) phase is observed to be a stable reconstruction in the BEP ratio range from 3 to 10. The phase transition boundaries between the reconstructed regions can be described by an Arrhenius temperature dependence law with the following form.  r = Ae  −  Ea RT  (3-4)  where A is the exponential prefactor, R is the gas constant, and r is the chemical reaction rate of the phase transition. Moreover, Ea is the activation energy for the phase transition which can be found from the slope of the transition boundaries in the phase diagram. By fitting the Arrhenius function to the observed transition boundaries, the activation energies presented in the following table (Table 3-1) were obtained. These fitted curves are shown by dashed lines in Figure 3-3. The results are close to the K. Regiński et al. calculation with an accuracy of ±0.5 eV [32].  Table 3-1 : Activation energy for surface reconstruction phase transitions on GaAs(001) surfaces  Surface  Phase transition  Activation energy (eV)  GaAs(001)  (2×3) ↔ (1×3)  2.86  GaAs(001)  (2×4) ↔ (2×3)  2.51  Figure 3-3 also presents a narrow, horizontal line of (1×1) region which exists over the entire substrate temperature range and in the BEP ratio range of 1.5 to 2. Due to the bulk structure of the (1×1) surface, this region is referred to as “bulk-terminated GaAs” and is the place where the As-rich regime meets the Ga-rich regime. Here, the phase transition boundaries between the As-rich and Ga-rich are horizontal at low temperatures, but L. Däweritz and R.Hey showed that these transition boundaries also obey an Arrhenius law when the substrate temperatures is high (≥ 600°C) [33]. This region is observed to be unstable in that the (1×1) reconstruction turns to a Ga-rich  26  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix reconstruction within the first few minutes of growth. Observation of the (1×1) reconstruction can be utilized to find the exact position of 1:1 fluxes in MBE. This becomes an important parameter for bismides since a very low As overpressure is needed for growing GaAs(1-x)Bix films. Below the (1×1) region in the phase diagram, two other (3×1) and (4×1) Ga-rich regions are observed. It is found that the GaAs growth with these reconstructions is problematic and results in irreversible degradation of the surface morphology. Most of the time, instead of RHEED streaky lines, a spotty pattern appears in the RHEED which turns into faceting in a few minutes. At this point, the surface of GaAs samples becomes rough which is visible under bright light illumination. To see the effect of bismuth on the GaAs phase map, the same measurements were done with the substrate exposed to gallium, arsenic, and bismuth beams. The flux of the gallium and arsenic used in this study was the same as before and the bismuth BEP flux was 3×10-9 torr. In addition, the samples were prepared in the same way as before except that after growing a 30 nm GaAs epilayer at low temperatures, the growth was interrupted for 10 minutes while lowering the arsenic flux and adjusting the substrate temperature. Then the growth of GaAs(1-x)Bix was started by opening the gallium and the bismuth shutters and the RHEED measurements were performed by varying the arsenic valve and the substrate temperatures. After the growth, each sample was examined by high resolution x-ray diffraction (XRD) to measure the bismuth incorporation in the film. The x-ray spectra will be discussed in the next chapter. Figure 3-4 shows the resulting surface phase diagram for GaAs(1-x)Bix at a growth rate of about 0.1 μm/h. This phase diagram is constructed from (2×4), (2×1), (2×3), (1×3), and faceting regions and is limited to the small range of As2:Ga BEP ratios, from 0 to 5.5. This smaller range of BEP ratios was used because no bismuth incorporation observed for As2:Ga BEP ratios higher than 5.5. In addition, the phase diagram of GaAs(1-x)Bix is also limited with respect to the substrate temperatures. It is observed that no bismuth incorporates into the film at temperatures above 400°C presumably because most of the bismuth atoms evaporate from the surface. Therefore at temperatures higher than 400°C, bismuth behaves as a surfactant and enhances the growth of GaAs but does not incorporate. As a result, the phase diagram of GaAs(1-x)Bix(001) will transform to the phase diagram of GaAs(001).  27  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix  Figure 3-4 : Surface phase diagram of GaAs(1-x)Bix at low substrate temperatures (LT-GaAs) and at low growth rate (0.1 μm/h). The arsenic BEP varies from 4×10-8 to 7×10-7 torr and the bismuth BEP is constant at 3×10-9 torr. This phase diagram transforms to the phase diagram of GaAs(001) above 400°C as no bismuth incorporates into the growing film. The starting point of the GaAs(001) phase diagram is shown by dashed lines. Data points and the different phases are shown by the colored circles and the shaded areas.  28  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix In Figure 3-4 this transformation is shown by the dashed lines. By comparing Figure 3-4 and Figure 3-3, we can find that the three As-rich surface structure of (1×3), (2×3), and (2×4) are common between GaAs(1-x)Bix(001) and GaAs(001). In addition, the (2×4)/(2×3) phase boundary looks similar between the two phase diagrams but the (2×3)/(1×3) boundary is very different. Other similarities and differences for each phase can be summarized as follows:  I. In the GaAs(1-x)Bix (1×3) phase, bismuth incorporation is obtained for BEP ratios from 3 to 5.5. Above 5.5, the GaAs(001) type (1×3) reconstruction is observed. In the same way from Figure 3-3, the (1×3) structure of GaAs(001) started from BEP ratios near 3 and extended to 10. In terms of the substrate temperature, the presence of the bismuth expands the (1×3) phase to the higher temperatures. II. The (2×3) GaAs(001) phase is one of the most stable As-rich structures which exists at temperatures above 325°C and for As2:Ga BEP ratios above 2. As bismuth starts to incorporate into the film, the shape of the (2×3) phase is radically changed and this region falls down below the (1×3) region. Therefore the (2×3) phase expands to the full temperature range (250°C to 400°C) but is limited to a narrow range of BEP ratios between 2.5 and 3.5. This phase may be a transition phase (mixed phase) between the (1×3) and (2×1) phases. III. The (2×4) phase also exists in the presence of bismuth. The location and the shape of this phase is similar between GaAs(001) and GaAs(1-x)Bix(001). In both of the phase diagrams, the (2×4) phase starts at a substrate temperature near 360°C and continues to higher temperatures. In terms of the As2:Ga BEP ratios, the GaAs (2×4) phase is between 2 and 4.2 but the GaAs(1-x)Bix (2×4) phase is limited to between 2 and 2.6, as the (2×3) phase pushes this region down. IV. In the case of GaAs(1-x)Bix, faceting is observed in the RHEED pattern (2×Chevron). Chevrons always appeared in the [011] direction which is the direction with low gallium adatom diffusion compared with the [0 11] direction. Similar faceting (4×Chevron) is observed for GaAs(001).  29  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix  The important new phase which appears due to the presence of bismuth is the (2×1) phase. This phase is not observed on the GaAs(001) surface and has a different behavior than the other phases. The (2×1) region with the curvy shape is located in the region with BEP ratio of less than 2.8 and over the entire substrate temperature range up to 400°C. As growing GaAs(1-x)Bix requires low As overpressure to reduce arsenic substitution for Bi, this area is of interest in defining the bismide growth condition. It appears that this phase is controlling the incorporation of Bi into GaAs(1-x)Bix since when the (2×1) phase ends at 400°C and a BEP ratio of 1.6, GaAs(1-x)Bix is ended as well. By decreasing the As2:Ga BEP ratio at a given temperature, less As2 molecules displace bismuth atoms on the surface, therefore the bismuth surface coverage increases and transforms the (1×3) reconstruction into the (2×1) reconstruction. As a result, the (2×1) phase has the maximum bismuth coverage on the surface which in turn results in higher incorporation of bismuth than the other reconstructions. Samples of such increase in Bi content are explained in section 4.2. from X-ray diffraction (XRD) measurement. To see the behavior of the (2×1) region better, we show in Figure 3-5 the observed phase diagram for the (2×1) phase at four different bismuth fluxes. The flux of gallium and arsenic used in these measurements was the same as before and the samples were prepared in the same way. In this figure, all of the (2×1) phases have the same shape. They follow a similar curve and they all fall down at high temperatures. It also shows that by increasing the flux by a factor of 13, the (2×1) region is expanded horizontally 70°C in substrate temperature and vertically by 0.9 in BEP ratios. Since the bismuth evaporates at a higher rate as the temperature increases, we can predict that by increasing the Bi flux, the (2×1) phase will eventually be limited as a function of temperature but will be expand more vertically in the BEP ratios. Figure 3-6 confirms this thought and shows the growth condition of the (2×1) phase which derives from the phase diagrams of Figure 3-5. It is observed that by increasing the bismuth flux, the BEP ratio increases linearly, but it has a weak dependence. On the other hand, the highest observed temperature for (2×1) phase (Tmax) has an Arrhenius BEP ratio dependence. This means that by increasing the bismuth flux, the Tmax increases slowly with in the  30  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix  Figure 3-5 : The phase diagram of the (2×1) phase for four different bismuth beam fluxes. The observed (2×1) phases shown by the shaded areas. The bismuth fluxes are labeled in each figure and they correspond to bismuth cell temperatures of 425˚C, 450˚C, 475˚C, and 500˚C. The growth rate in all of the phase diagrams is 0.1 μm/h.  31  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix  (a)  (b) 10  10  10  10  -7  FB i = 2.09 e  -8  − 1.23 ( eV ) kT m ax  -9  -10  1.4  1.45  1.5  1.55  Figure 3-6: (a) The As2:Ga BEP ratio versus the bismuth flux for the (2×1) surface phase. The observed growth condition is shown in shaded area with bar lines. The fitted line to the middle point in each growth condition is given by a dashed line. (b) The upper temperature limit of the (2×1) phase (Tmax) versus the bismuth flux. These fluxes correspond to bismuth cell temperatures of 425˚C, 450˚C, 475˚C, and 500˚C. The arsenic BEP flux varies from 4×10-8 to 7×10-7 torr and the growth rate is 0.1 μm/h.  32  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix logarithmic form. As a result, the (2×1) phase will be eventually limited in substrate temperature range. By fitting the Arrhenius function to the data points in Figure 3-6(b), the activation energy of 1.23±0.2 eV is obtained. Since at Tmax bismuth evaporates from the surface, this activation energy can be considered as the activation energy for bismuth desorption. This number is close to the E.C. Young et al. results for bismuth desorption activation energy of 1.8±0.4 eV [35]. Metallic droplets on the surface are undesirable because they create surface roughness and cause local variations in the amount of bismuth coverage and hence the local composition. Therefore a significant challenge in growing the bismide in the (2×1) phase is to find a way to suppress the formation of metallic Bi and Ga droplets on the surface. In an ideal growth condition the bismuth flux will exactly match the bismuth incorporation rate plus the evaporation rate from the surfactant layer. This requires careful control of both group V fluxes. Bismuth atoms are believed to be displaced by the flux of As2. One idea for controlling the droplets is to set the Bi flux and Ga fluxes to some desired Bi concentration, and then control the bismuth concentration by adjusting the As2 flux. Figure 3-7(a) shows the result of this idea for detecting the droplets in the (2×1) region. The RHEED specular intensity is measured as the arsenic BEP is decreased by closing the arsenic valve. Each point in this figure corresponds to bismide material grown for at least 15 minutes. After each 15 minutes of growth, the arsenic BEP was changed. It is observed that when the droplets start to form on the surface, the RHEED specular intensity decreases significantly. Figure 3-7(b) shows an optical microscope image of the droplets obtained after these RHEED measurements.  33  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix  (a) Surface reconstruction = (2×1) 9 Bi flux = 3.3×10- torr  Droplet nucleation on surface  (b)  Figure 3-7 (a) shows a measurement of RHEED specular intensity as the arsenic valve is closed. The RHEED intensity dropped fast and metallic droplets started to form on the surface when the As2 BEP reached 2×10-8 torr. The reconstruction during the growth was constant (2×1) and at each point on the diagram, bismide material was grown for at least 15 min. (b) An optical microscope image of the droplets after the growth. On average, the droplet size is in the one micron range.  34  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix  3.4. RHEED Observation of Metallic (2×1) Surface In this section the effect of different bismuth surface coverage on the temperature of the substrate is explored using in-situ RHEED measurements. In this experiment, the possible surface reconstructions and the substrate temperature of bismide are monitored as the As2:Ga BEP ratio changed from 10 to near 0 by closing the arsenic valve. This kind of measurement is similar to moving vertically on the bismide surface phase diagram from the As-rich surface to a Ga-rich surface. In addition, the power of the substrate heater is not changed during the experiment so we expect to have a stable substrate temperature during the measurements. Here the substrate temperature is monitored using optical bandgap thermometry which is sensitive to the optical absorption (emissivity). Figure 3-8 shows the result of this experiment at a substrate temperature near 400˚C and under a Bi flux of 7.0×10-9 torr. By closing the arsenic valve, the first two surface phases are (1×3) and (2×3). It is observed that under these phases the substrate temperature is quite stable. By decreasing the arsenic flux more, the bismuth surface coverage increases and the (2×4) phase will appear next on the RHEED. In this phase, the substrate temperature is observed to slightly shift up by an average amount of 3˚C, although this temperature increase is close to the resolution limit of the temperature measurements. This jump in substrate temperature may be due to the bismuth build up on the surface. Since bismuth is a metal, it has a higher IR reflectivity than GaAs therefore bismuth decreases the emissivity of the substrate and results in a higher substrate temperature. To confirm this thought, the jump in substrate temperature is estimated with a calculation presented in Appendix B. A more dramatic effect of bismuth surface coverage is observed at lower arsenic flux under the (2×1) phase. It is observed that when the reconstruction changes from (2×4) to (2×1), the substrate temperature shows a big jump of nearly 20˚C. Next, to check the reproducibility of this data and to confirm the effect of bismuth build up on the surface, the arsenic flux was rapidly increased in the (2×1) phase. As a result, the reverse transition in the surface reconstruction ( (2×1) → (2×4) → (2×3) → (1×3) ) is observed while the substrate temperature ramped down to lower temperature. It is observed that when the reconstruction changes to (1×3), the  35  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix substrate temperature returns to its initial value of 395˚C. This indicates that the built up bismuth atoms on the surface are gradually replaced by arsenic atoms. The surface reconstruction as well as the substrate temperature continuously changed under this transition. As a result, for the bismides the (1×3) phase can be identified as an arsenic dominant phase while the (2×1) is a bismuth dominant phase where the maximum bismuth coverage is obtained in this phase. This measurement suggests that the (2×1) surface phase is metallic while the other phases are semiconducting or semi-metals. This result is consistent with the metallic STM observation of P. Laukkanen et al. from Bi/GaAs-(2×1) surface [22]. The details of this measurement is presented at Ref. [22,23].  36  Chapter 3. RHEED Surface Analysis of GaAs and GaAs(1-x)Bix  440 As flux variation: 7.0e-7 to 2.5e-7 torr  As flux variation: 2.5e-7 to 2.35e-7 torr  As flux variation: 2.35e-7 to 1.8e-7 torr  (2×3)  (2×4)  substrate temperature (°C)  430  As flux rapidly varies from 9.5e-8 to 3.0e-7 torr  As flux variation: 1.8e-7 to 9.5e-8 torr  420  410  400  390  380  (1×3)  150  155  (2×1)  160  165  (2×3) & (2×4)  170  (1×3)  175  Time (minute) Figure 3-8: The effect of different bismuth surface reconstructions on the temperature of the substrate. The initial substrate temperature is around 400˚C and the power of the substrate heater is not changed during the experiment. The growth has been done with a bismuth flux of 7.0×10-9 torr. The occasional large scatter in data points is obvious and is caused by noise or pick up in the optical bandgap thermometry.  37  Chapter 4 Growth and Properties of the GaAs(1-x)Bix Alloys  4.1. Growth Procedure Analysis of surface phase diagrams plays an important role in understanding the MBE process. In each phase diagram, the crystal growth conditions can be specified by the distinct reconstruction surfaces, where each surface has particular electronic and optical properties. The surface reconstruction phase diagram of GaAs(1-x)Bix (explained in section 3.3.) shows two major (1×3) and (2×1) reconstructions for substrate temperatures between 250˚C to 420˚C. The (1×3) reconstruction is the bismide As-rich reconstruction and exists for As2 /Ga BEP ratios above 3, while the (2×1) reconstruction exists for BEP ratios, near the 1:1 flux ratio. In this chapter, we compare different properties of several GaAs(1-x)Bix samples which where grown with (1×3) and (2×1) reconstructions. All of these samples had an identical growth procedure with the following steps.  1. First a 450-500 nm GaAs buffer layer is grown at a substrate temperature between 570°C and 580°C with group V: III flux ratio near 10 (arsenic cell temperature 400°C; gallium cell temperature 950°C). 2. Then the arsenic and the gallium cell temperatures are ramped down to 350°C and 850°C in order to establish a low growth rate. 3. Next, the substrate temperature is turned down and the growth interrupted for 10-15 minutes in order to lower the arsenic flux and establish a constant substrate temperature.  38  Chapter 4. Growth and Properties of the GaAs(1-x)Bix Alloys 4. As the last step the bismide growth is started by opening the bismuth and gallium shutters and the growth stopped after 1 hour. No post annealing is applied after the growth. In addition to convenience in adjusting the arsenic flux and the substrate temperature before the bismide growth, a growth interruption (GI) improves the interface smoothness of the layers. This technique is widely used in the MBE growth of quantum wells where an abrupt heterostructure interface is needed [36, 37]. To explain this surface smoothness, Wada et al. [38] suggested that GI may prevent the formation of islands on the terraces. A growth interruption allows the adatoms on the surface to diffuse toward the atomic steps and leads to the consolidation of small islands on the terraces. This atomically smooth surface is limited by the width of extended terraces and the substrate misorientation. To see the effect of the GI, the RHEED specular intensity is recorded before and after the GI in Figure 4-1(a). It is observed that by stopping the growth, the RHEED intensity increased by about 35%. This significant change in the intensity can be interpreted as an evidence of surface smoothness. For more confirmation, Figure 4-1(b) shows the RHEED diffraction patterns of the same sample before and after the GI where a dramatic change appears in the RHEED. The first change comes from the intensity comparison of the streaky lines where the main and the reconstructed streaky lines become much brighter after the GI. The Kikuchi lines are also more visible after the GI. The second change is about the Laue zones where the GI results in the appearance of the second Laue zones on the RHEED screen. Table 4-1 and Table 4-2 summarizes the growth conditions of all the grown samples. These samples were grown with the (1×3) and (2×1) surface reconstructions at substrate temperatures near 300°C, 350°C, and 400°C. The thickness of all samples was near 100 nm. The gallium BEP in all the growths was 8.0×10-8 torr as read from an ion gauge. The fluxes of other chemical species are also listed in this table. For better comparison, samples at 300°C, r2138 and r2139, were grown successively in one day on the same GaAs mechanical wafer. The rest of the samples, r2167 r2168 and r2169, were grown from another wafer. After the growths, all samples were examined via optical microscope to see the possible droplets on the surface.  39  Chapter 4. Growth and Properties of the GaAs(1-x)Bix Alloys  (a) Specular RHEED intensity (arb. units)  160  140  120  100  Ga close  80 0  60  120  180  240  300  360  420  480  Time (sec)  (b)  Before Growth Interruption  After Growth Interruption  Figure 4-1: Effect of growth interruption of GaAs on (a) the specular RHEED intensity and on (b) RHEED patterns along [0 11] azimuth at substrate temperature near 380˚C. It is observed that by closing a gallium shutter, the intensity of specular RHEED streaky lines increased by 35%. In addition, the reconstruction lines become much brighter and both the first and second Laue zones (shown by white arrows) appeared on the RHEED screen.  40  Chapter 4. Growth and Properties of the GaAs(1-x)Bix Alloys Table 4-1: Summary of grown bismide samples.  Sample Log # r2138 r2139 r2167 r2168 r2169  Surface Reconstruction (1×3) (2×1) (1×3) (2×1) (2×1)  Bi [%]  Droplet  2.3 5.0 0 2.8 0.2  No droplet No droplet No droplet 1μm droplets No droplet  Table 4-2: Summary of growth conditions for bismide samples.  Sample Log # r2138 r2139 r2167 r2168 r2169  Substrate Temp. (°C) 295-300 300 350 350 395-400  BEP[As2] (torr) 2.5×10-7 2.2×10-7 3.0×10-7 1.7×10-7 1.7×10-7  BEP[Bi] (torr) 2.6×10-9 2.6×10-9 2.6×10-9 6.0×10-9 6.0×10-9  Growth Pressure (torr) 3.3×10-8 4.3×10-8 2.9×10-8 4.5×10-8 4.6×10-8  4.2. Ex-situ Characterization  4.2.1. High Resolution X-ray Diffraction High resolution x-ray diffraction (HR-XRD) is a well known method for characterization of the crystal structure of epitaxial films. By measuring the XRD rocking curves, information about the composition, layer thickness, strain and relaxation can be obtained. Figure 4-2 shows the [004] X-ray rocking curves of grown samples over several thousand arcseconds. In each rocking curve spectrum, the sharp peak is the [004] GaAs peak which comes from the substrate. The smaller satellite peak on the left side corresponds to the GaAs(1-x)Bix epilayers. The composition of each film is determined from the separation between the substrate and the epilayer peaks where every 300 arcseconds corresponds to one percent bismuth incorporation. Distinct pendellosung interference fringes are also observed, which indicates that the interfaces are smooth and that the Bi concentration is 41  Chapter 4. Growth and Properties of the GaAs(1-x)Bix Alloys uniform as function of thickness. In addition, these fringes allow a determination of the layer thicknesses. The first set of samples r2138 and r2139, where grown with (1×3) and (2×1) reconstructions, respectively. The (1×3) and (2×1) reconstructions were obtained by adjusting the As2 flux. The XRD results for these two samples shows two major differences. First, the peak separation in r2139 is nearly double the peak separation in r2138. Therefore r2139 has two times higher bismuth content than r2138. Second, the r2139 sample has much stronger pendellosung oscillations than r2138. Therefore the sample with (2×1) reconstruction shows better compositional uniformity. The next two samples, r2167 and r2168, were grown at 350°C, with the (1×3) and (2×1) reconstructions, respectively. Similar to r2139, r2168 showed strong fringes on either side of the satellite peak, while no fringes were observed in sample r2167. In addition, r2168 showed 2.8% bismuth incorporation while no bismuth was detected in r2167. Figure 4-2(c) shows the last sample, r2169, grown with a (2×1) reconstruction at 400°C. The bismuth composition obtained from this sample was very small (0.2%). For better observation of this small Bi concentration, a simulation fit to r2169 data is also presented in Figure 4-2(c). Most of the bismuth atoms must have evaporated off the substrate at this high temperature. This sample and samples r2167 and r2168 suggest that the bismuth would not incorporate into the film if the sample were grown with the (1×3) reconstruction at 400°C. In conclusion, samples with a (2×1) reconstruction showed better layer uniformity and higher bismuth incorporation than samples grown with the (1×3) reconstruction. Therefore during growth, a (2×1) reconstruction should be established in order to grow a high quality bismide films. In addition, it is observed that by increasing the substrate temperatures, the bismuth incorporation decreases. This bismuth concentration eventually goes to zero at high substrate temperatures as most of the Bi atoms evaporate from the surface rather than incorporate.  42  Chapter 4. Growth and Properties of the GaAs(1-x)Bix Alloys  (a)  (b)  (c)  Figure 4-2: [004] X-ray rocking curves of GaAs(1-x)Bix(001) epilayers at (a) 300˚C, (b) 350˚C, and (c) 400˚C substrate temperatures. Blue figures show samples grown with a (2×1) reconstruction while the red figures show samples grown with a (1×3) reconstruction. Fit to r2169 data set is shown with dash line.  43  Chapter 4. Growth and Properties of the GaAs(1-x)Bix Alloys 4.2.2. Photoluminescence Luminescence is the emission of optical radiation when a system decays from a high energy level (excited state) to a low energy level. Different types of luminescence are classified by the different method of initial excitation. In the case of photoluminescence (PL) in semiconductors, the excitation is with an optical source where the photons excite electrons from the valance band to the conduction band, creating electron-hole pairs. These pairs can either recombine radiatively by emitting photons or non-radiatively through defect, surface or Auger recombination. Therefore the PL intensity gives valuable information about the electronic properties of materials, such as the optical bandgap and the defect density. The high energy side of the PL emission spectrum is due to the thermal excitation of electrons and holes into higher levels in the conduction and valence bands. The shape of this tail for relatively high temperatures (T >100 K) can be modeled by a Boltzmann distribution,  f ( E ) = Ae  − E kBT  (4-1)  where f(E) is the energy distribution function, E is the photon energy and T is the absolute temperature. On the low energy side, due to structural inhomogeneities and thermal fluctuations in the semiconductor crystal lattice, emission below the bandgap is also possible and modeled with the product of an Urbach edge [39] and a Boltzmann function:  f (E) = α g  E − Eg − E E0 e e kBT  If  E < Eg  (4-2)  where αg is the absorption coefficient at 0 K. Eg is the bandgap and E0 is the Urbach parameter. For GaAs at room temperature, αg is 8000cm-1, Eg is 1.42 eV, and E0 is 7.5meV [40]. Figure 4-3 presents photoluminescence spectra of samples measured at room temperature (300K). The samples were excited with a 532 nm green diode pumped YLF laser and the PL was measured with a SpectraPro-300i spectrograph in which the InGaAs  44  Chapter 4. Growth and Properties of the GaAs(1-x)Bix Alloys detector array was cooled with liquid nitrogen. In addition, all the PL spectra were measured with the same integral time (10 sec) and the relative PL efficiency was calibrated using a p-GaAs reference sample were shown in Figure 4-4. The first set of samples was grown at 300°C and they show two different PL behaviors. Sample r2138 shows a small GaAs peak at 870 nm with no bismide peak. Sample r2139 has a weak GaAs peak at 870 nm and a strong GaAs(1-x)Bix peak at 1195 nm. This is a broad peak with a FWHM of 116 nm. Similar behavior is observed in samples r2167 and r2168 which were grown with (1×3) and (2×1) reconstructions respectively at 350°C. The GaAs peak for r2167 is again located at 870 nm and is nearly five times stronger than the GaAs peak in r2138. On the other hand, the GaAs(1-x)Bix peak of r2168 is shifted to 1030nm with FWHM of 92nm. In comparison with r2139, a possible reason why r2168 has a smaller bismide peak may be the metallic droplets which were observed on the surface of this sample. The droplets can absorb some of the emitted and pump radiation and therefore the detected PL is lower. However the surface coverage by Bi droplets might be very small and is unlikely to account for the large difference in PL intensity. The difference in Bi content may also explain the difference in PL intensity. Figure 4-3(c) illustrates the PL spectrum of the last sample (r2169) which was grown with a (2×1) reconstruction at 400°C. This sample shows a high GaAs PL intensity since the top Bi layer of this sample has only 0.2 % Bi and therefore the PL spectrum likely overlaps with GaAs PL emission. In comparison with sample r2167, the PL emission intensity from this sample is nearly twice the r2167 PL intensity. Moreover, the growth temperature of this sample was closer to the optimal GaAs growth temperature; therefore r2169 has a higher quality of GaAs layer. In summary, we observed that a strong, long wavelength GaAs(1-x)Bix emission spectrum can be obtained from samples that are grown with a (2×1) reconstruction. With decreasing Bi content, the GaAs(1-x)Bix spectra become weaker and narrower. In addition, all the GaAs(1-x)Bix spectra are observed to be much wider than the Boltzmann factor in equation (4-2) would suggest. This kind of behavior means that the PL emission is not controlled by thermal broadening. Instead, a wide bismide emission may be due to the distribution of localized levels close to the band edge or to fluctuations in bandgap where  45  Chapter 4. Growth and Properties of the GaAs(1-x)Bix Alloys  (a)  (b)  (c)  Figure 4-3: Room temperature photoluminescence of growm samples at (a) 300˚C, (b) 350˚C, and (c) 400˚C substrate temperatures. Samples are pumped with a 532 nm diode pumped frequency doubled YLF laser. Blue figures show samples grown with a (2×1) reconstruction while the red figures show samples grown with a (1×3) reconstruction. All PL measurements have the same integration times (10 sec) and the relative PL efficiency was calibrated using a p-GaAs reference sample.  46  Chapter 4. Growth and Properties of the GaAs(1-x)Bix Alloys  Figure 4-4: Room temperature photoluminescence from p-GaAs reference samples used for PL calibrations. In comparison with Figure 4-3, the emission peak of the first p-GaAs reference sample is 12% higher but the emission peak of the second p-GaAs reference sample is nearly halved.  the bandgap varies as the Bi concentration changes over the sample thickness. While the XRD results showed that bismuth can incorporate under the (1×3) reconstruction, no GaAs(1-x)Bix emission is observed in samples grown with a (1×3) reconstruction. Therefore the (2×1) should be recognized in order to obtain the broad infrared bismide emission. On the other hand, increasing the growth temperature results in a more intense GaAs PL spectrum. The most intense GaAs emission was obtained for a sample grown at 400°C with a (2×1) reconstruction. Therefore, it can be expected that by approaching the normal growth condition, 550˚C to 600˚C, the GaAs PL intensity increases which presumably produces the best GaAs. 47  Chapter 4. Growth and Properties of the GaAs(1-x)Bix Alloys 4.2.3. Atomic Force Microscopy The surface morphology of grown samples is probed with atomic force microscopy (AFM) with a vertical resolution of fractions of a nanometer. Figure 4-5 shows 1×1 μm and 5×5 μm AFM images of samples r2138 and r2139. The vertical scale for all images is 2 nm and the samples were scanned in the tapping mode with a Si3N4 tip with a 30 nm radius. It is observed that r2139 has periodic surface ripples parallel to the [1 10] azimuth. This suggests that the surface diffusion is stronger in the [1 10] azimuth. Similar ripples with larger periods are also observed on r2138. Both samples are very flat and the scale of the roughness does not seem to change with different bismuth incorporation. The rms roughness of r2138 is near 0.250 nm while the r2139 rms roughness is 0.192 nm. Therefore the sample grown with a (2×1) reconstruction looks a little smoother than the sample with a (1×3) reconstruction. In conclusion, our results show that bismide samples grown with a (2×1) reconstruction have the following properties: •  High crystal quality in XRD with strong pendellosung fringes  •  High bismuth incorporation  •  Intense, broad infrared photoluminescence peak  •  Smooth surface  •  Directional diffusion along the [1 10] azimuth  48  Chapter 4. Growth and Properties of the GaAs(1-x)Bix Alloys  r2138  r2139  (1×3)  (2×1) 2.00 nm  [110] [110]  200  0.00 nm  2.00 nm  [110]  [110]  0.00 nm Figure 4-5: 1×1 μm and 5×5 μm AFM images of r2138 and r2139 samples. These samples were grown at 300˚C substrate temperature with (1×3) and (2×1) reconstruction. The bismuth concentration in r2138 was 2.3% and in r2139, it was about 5.0%. The z scale is 2 nm in all the images.  49  Chapter 5 Conclusion  GaAs1-xBix is a new semiconductor alloy that shows promise for optical applications including light emitting diodes (LEDs), superluminescent diodes (SLDs), lasers, and solar cells. Due to the large band gap reduction and low material degradation associated with bismuth alloying, bismides are a potential replacement for the InGaAsN alloys and offer potential for longer wavelength devices. In this study, an attempt was made to explore the growth conditions required to grow this new material using RHEED. The insitu RHEED technique was used to provide information about the reconstruction of the growth surface. During the growths, the surface reconstruction and the RHEED intensity were recorded as the substrate temperature, arsenic flux, gallium flux, and bismuth flux were varied. After growth, the structures were characterized, using XRD, PL, and AFM. RHEED oscillations where observed during the growth of GaAs and GaAs1-xBix. In the case of GaAs, it was found that bismuth helps smooth the GaAs films likely through increasing the surface diffusion length. Thus, more layer-by-layer growth and more RHEED oscillation periods were observed when bismuth was pre-deposited before the growth. In the case of GaAs1-xBix, RHEED oscillations were observed at temperatures as low as 290˚C while no oscillations were observed in the absence of bismuth (LT-GaAs growth). To optimize the atypical growth condition of bismide alloys, the GaAs1-xBix surface phase map was explored in this study. For better comparison, the phase map of GaAs, at low temperatures (LT-GaAs) was also obtained. To the knowledge of the author, the GaAs1-xBix surface phase map is reported here for the first time. Our phase map investigation showed that (1×3), (2×3), (2×4) surface reconstructions are common between GaAs and GaAs1-xBix but due to the presence of bismuth flux, a new (2×1) reconstruction was observed in the phase map. This new reconstruction occurs for  50  Chapter 5. Conclusion substrate temperatures less than 400°C and for a As2:Ga BEP ratio less than 3. The (2×1) phase was acquired carefully for different bismuth fluxes, showing the evolution of this phase in substrate temperature and BEP. It is shown that by increasing the bismuth flux, the (2×1) phase expands slowly to higher BEP ratios and also to higher substrate temperatures. This is due to the fact that most of the bismuth atoms evaporate from the surface at temperatures above 400°C. In addition, the emissivity of the (2×1) surfaces was found to be lower than for the other As-rich reconstructed surfaces (e.g. (1×3) and (2×3) surfaces). This is interpreted as an indication that the (2×1) surface phase is metallic. In this work, several bismide films were grown with (1×3) and (2×1) reconstructions at three different substrate temperatures, 300°C, 350°C, and 400°C. Different properties of these samples were compared. High crystal quality, high bismuth incorporation, broad infrared PL spectra, and smooth surfaces and interfaces were observed for growth on the (2×1) reconstructed samples. Therefore during growth, the (2×1) reconstruction can be recognized as an indication of high quality bismide films. During the growth of bismide alloys, formation of metal droplet on the surface is very undesirable and needs further investigation. The composition of the droplets also needs more investigation to see if the droplets are bismuth or gallium or a mixture. In this regard, in-situ light scattering (LS) is an essential tool in detection of droplets during growth. Once this is achieved, it will be possible to determine the growth conditions for maximum bismuth incorporation.  51  Bibliography  [1] U. Tisch, E. Finkman, J. Salzman. The anomalous bandgap bowing in GaAsN. Appl. Phys. Lett., 81, 463, 2002.  [2] M. Fischer, D. Gollub, M. Reinhardt, M. Kamp, A. Forchel. GaInNAs for GaAs based lasers for the 1.3 to 1.5 micron range. J. Crystal Growth, 251, 353, 2003.  [3] E.C. Young. GaNAs and GaAsBi: Structural and electronic properties of two resonant state semiconductor alloys. PhD thesis, University of British Columbia, 2006.  [4] K. Oe, H. Okamoto. New semiconductor alloy GaAs1-xBix grown by metal organic vapor phase epitaxy. Japan. J. Appl. Phys., 37, 1283, 1998.  [5] S. Tixier, M. Adamcyk, E.C. Young, J.H. Schmid, T. Tiedje. Surfactant enhanced growth of GaNAs and InGaNAs using bismuth. J. Crystal Growth, 251, 449, 2003.  [6] S. Tixier, M. Adamcyk, T. Tiedje, S. Francoeur, A. Mascarenhas, P. Wei, F. Schiettekatte. Molecular beam epitaxy growth of GaAsBi. Appl. Phys. Lett., 82, 2245, 2003.  [7] J. Yoshida, T. Kita, O. Wada, K. Oe. Temperature dpendence of GaAs1-xBix band gap studied by photoreflectance spectroscopy. Japan. J. Appl. Phys., 42, 371, 2003.  [8] S. Francoeur, M.J. Seong, A. Mascarenhas, S. Tixier, M. Adamcyk, T. Tiedje. Bandgap of GaAs1-xBix, 0<x<3.6%. Appl. Phys. Lett., 82, 3874, 2003.  52  Bibliography [9] W. Shan, W. Walukiwiecz, J.W. Ager, E.E. Haller, J.F. Geisz, D.J. Fiedman, J.M. Olson, S.R. Kurtz. Band anticrossing in GaInNAs alloys. Phys. Rev. Lett., 82, 1221, 1999. [10] Y. Zhang, A. Mascarenhas, L.W. Wang. Similar and dissimilar aspects of III-V semiconductors containing Bi versus N. Phys. Rev. B, 71, 155201, 2005. [11] L. Landau, E.M. Lifshitz. Statistical physics. Vol. 5, Pergamon Press, Oxford 1959. [12] V.P. LaBella, M.R. Krause, Z. Ding, P.M. Thibado. Arsenic-rich GaAs(001) surface structure. Surface Science Reports, 60, 2005. [13] C.B. Duke. Semiconductor surface reconstruction: The structural chemistry of twodimensional surface compounds. Chem. Rev., 96, 1237, 1996. [14] D.A. Murdick, X.W. Zhou, H.N.G. Walley, D. Nguyen-Manh. Predicting surface free energies with interatomic potentials and electron counting. J. Phys. : Condens. Matter 17, 6123, 2005. [15] Surface reconstruction, http://en.wikipedia.org/wiki/Surface_reconstruction. [16] K. Oura,V.G. Lifshits,A.A. Saranin,A.V. Zotov,M. Katayama. Surface science: An introduction. Springer-Verlag, Berlin, 2003. [17] R.L. Park, H.H. Madden. Annealing changes on the (100) surface of palladium and their effect on CO adsorptionstar, Surf. Sci. 11, 188, 1968. [18] E.A. Wood. Vocabulary of surface crystallography. J. Appl. Phys., 35, 1306, 1964.  53  Bibliography [19] M.A. Van Hove, W.H. Weinberg, C.M. Chan. Low-energy electron diffraction: Experiment, theory and surface structure determination. Springer-Verlag, Berlin 1986. [20] M.D. Pashley. Electron counting model and its application to island structures on molecular-beam epitaxy grown GaAs(001) and ZnSe(001). Phys. Rev. B 40, 10481, 1989. [21] M.D. Pashley, K.W. Haberern, W. Friday, J.M. Woodall, P.D. Kirchner. Structure of GaAs(001) (2×4)-c(2×8) determined by scanning tunneling microscopy. Phys. Rev. Lett. 60, 2176, 1988. [22] P. Laukkanen, M.P.J. Punkinen, H.P. Komsa, M. Ahola-Tuomi, K. Kokko, M. Kuzmin, J. Adell, J. Sadowski, R.E. Perälä, M. Ropo, T.T. Rantala, I.J. Väyrynen, M. Pessa, L. Vitos, J. Kollár, S. Mirbt, B. Johansson. Anomalous bismuth-stabilized (2×1) reconstructions on GaAs(100) and InP(100) surfaces. Phys. Rev. Lett. 100, 086101, 2008. [23] M. P. J. Punkkinen, P. Laukkanen, H.P. Komsa, M. Ahola-Tuomi, N. Räsänen, K. Kokko, M. Kuzmin, J. Adell, J. Sadowski, R. E. Perälä, M. Ropo, T. T. Rantala, I. J. Väyrynen, M. Pessa, L. Vitos, J. Kollár, S. Mirbt, B. Johansson. Bismuth-stabilized (2×1) and (2×4) reconstructions on GaAs(100) surfaces: Combined first-principles, photoemission, and scanning tunneling microscopy study. Phys. Rev. B 78, 195304, 2008. [24] A.Y. Cho. The Technology and physics of molecular beam epitaxy, Plenum Press, 1985. [25] M. Melloch, J. Woodall, E. Harmon, N. Otsuka, F. Pollak, D. Nolte, R. Feenstra, M. Lutz. Low-temperature grown III-V materials. Annul Review of Materials Science 25, 547, 1995.  54  Bibliography  [26] E.C. Young, S. Tixier, T. Tiedje. Bismuth surfactant growth of the dilute nitride GaNxAs1-x. J. Crystal Growth, 279, 316, 2005. [27] E.C. Young, M.B. Whitwick, T. Tiedje, and D. Beaton. Bismuth incorporation in GaAs1-xBix grown by molecular beam epitaxy with in-situ light scattering. Phys. Stat. Sol. (C), 4, 1707, 2007. [28] X. Lu, D. Beaton, T. Tiedje, R. Lewis, M.B. Whitwick. Effect of MBE growth conditions on Bi content of GaAs1-xBix. Appl. Phys. Lett., 92, 2008. [29] S.R. Johnson. Optical bandgap thermometry in molecular beam epitaxy. PhD thesis, University of British Columbia, Canada, December 1991. [30] A. Ichimiya, P.L. Cohen. Reflection high energy electron diffraction. Cambridge University Press, 2004. [31] V.V.  Preobrazhenskii,  M.A.  Putyato,  O.P.  Pchelyakov,  B.R.  Semyagin.  Experimental determination of the incorporation factor of As4 during molecular beam epitaxy of GaAs. J. Crystal Growth, 201/202, 170, 1999. [32] K. Regiński, J. Muszalski, V.V. Preobrazhenskii, D.I. Lubyshev. Static phase diagrams of reconstructions for MBE-grown GaAs (001) and AlAs (001) surfaces. Thin Solid Films, 267, 54, 1995. [33] L. Däweritz, R. Hey. Reconstruction and defect structure of vicinal GaAs(001) and AlxGa1−xAs(001) surfaces during MBE growth. Surf. Sci., 236, 15, 1990. [34] V.P. LaBella, D.W. Bullock, C. Emery, Z. Ding, P. M. Thibado. Enabling electron diffraction as a tool for determining substrate temperature and surface morphology. Appl. Phys. Lett., 79, 3065, 2001.  55  Bibliography  [35] E.C. Young, S. Tixier, T. Tiedje. Bismuth surfactant growth of the dilute nitride GaNxAs1-x. J. Crystal Growth, 279, 316, 2005. [36] M.G. Cheong, H.S. Yoon, R.J. Choi, C.S. Kim, S.W. Yu, C.H. Hong, E.K. Suh, H.J. Lee. Effects of growth interruption on the optical and the structural properties of InGaN/GaN quantum wells grown by metalorganic chemical vapor deposition. J. Appl. Phys., 90, 5642, 2001. [37] J.R. Botha, A.W.R. Leitch. Influence of growth interruption on the heterointerface morphology of InGaAs/GaAs strained quantum wells. J. Crystal Growth, 169, 629, 1996. [38] K. Wada, A. Kozen, Y. Hasumi, J. Temmyo. Cathodoluminescence Study of substrate offset effects on interface step structures of quantum wells. Appl. Phys. Lett., 54, 436, 1989. [39] S.R. Johnson, T. Tiedje. Temperature dependence of the Urbach edge in GaAs. J. Appl. Phys., 78, 5609, 1995. [40] S.E. Webster. Semiconductor light source for optical coherence tomography. Master thesis, University of British Columbia, 2004. [41] J.R. Reitz, F.J. Milford, R.W. Christy. Foundations of electromagnetic theory. 3rd edition, Addison-Wesley, 1979. [42] E.D. Palik. Handbook of optical constants of solids. Academic Press Inc., London, 1985.  56  Bibliography [43] D.R. Liu, K.S. Wu, M.F. Shih, M.Y. Chern. Giant nonlinear optical properties of bismuth thin films grown by pulsed laser deposition. Optics Letters, Vol. 27, No. 17, 2002. [44] Table of total emissivity, http://www.monarchserver.com/TableofEmissivity.pdf.  57  Appendix A RHEED Screen Fabrication  RHEED patterns are commonly observed with fluorescent screens. These screens are widely used in MBE systems and usually made by depositing a fluorescent powder on a lead glass surface. Despite the extensive application of this kind of screen for monitoring the surface of GaAs, we experienced difficulties during the growth of GaAs(1-x)Bix by using these screens. Since the phosphor layer of the screen is uncapped and has a direct contact with the growth chamber and also since the bismuth is a heavy element, a gray Bi coating layer (or a compound of Bi and As2) formed on the screen. Therefore as a result of coating, the screen brightness decreased significantly and the diffraction spots become dim so the screen slowly died during use. To address this problem we attempted to make our own RHEED screens. In order to prevent charging of the loosely connected phosphor particles in the screen, it is advantageous to first coat the screen with a transparent conductor like indium-tin oxide (ITO). In addition, to enhance the brightness of the screen and further reduce charging, it is useful to put a thin aluminum coating on the back of the phosphor. The aluminum coating also blocks stray light from inside the chamber from interfering with the RHEED patterns. In this study, aluminum and ITO films were deposited by e-beam evaporation where the deposition chamber was evacuated to a pressure near 10-7 torr. Optimum results for ITO were obtained by thermal evaporation at a slow rate (~2 Å/sec) with a substrate temperature close to 300˚C. In addition, since the starting ITO material is reduced (loses oxygen) during evaporation, a high ambient O2 pressure, near 5x10-5 torr, is needed during the deposition. This pressure is provided by leaking O2 gas into the chamber. Therefore by using an e-beam, a mirror-like ITO film with a low resistivity will appear. To obtain a film with high transparency post-baking of ITO (≥ 300˚C) in air is 58  Appendix A. RHEED Screen Fabrication also essential. Figure A-1(a) shows the effect of post baking on the resistivity and the optical transmission of a 75 nm ITO film where the transmission of a green laser (λ= 532 nm) was measured by using neutral density filters. It is observed that by increasing the baking temperature, the resistivity of the film increases slowly but the transmission sharply improved after 300˚C. This improvement in optical transmission and increase in the resistivity can be attributed to the increase in stoichiometry of the films where the films may react and oxidize during baking. Figure A-1(b) illustrates the difference in the appearance of the ITO film before and after post-baking. By utilizing the above methods, two different types of RHEED fluorescent screen were made and examined in the MBE growth chamber, as summarized in Table 1-A. The first type of RHEED screen consisted of a P-22 phosphor (ZnS:Ag) layer and 65 nm aluminum cap layer. This screen worked well during the MBE bake near 200˚C but during the growth of GaAs(1-x)Bix, the screen was partially charged since RHEED spot distortion was observed. After closing the Bi shutter during the growth, the electrostatic charges on this screen gradually disappeared and the screen recovered.  Table A-1: Summary of two different kinds of RHEED screen made on the four inch lead glass plate and tested in the MBE chamber  I  II  Before / After MBE  Bismith  Film composition  bake test  growth test  Notes  Phosphor / Al (65 nm)  Worked /Worked  RHEED spot  The screen partially  distortion  charged  ITO (75 nm) / Phosphor /  Worked / The screen fell off  Al (50 nm)  during baking  The ITO and the phosphor N/A  didn’t attach strongly enough to each other  59  Appendix A. RHEED Screen Fabrication  (a)  (b)  Mirror-like screen before post-baking  Transparent screen after post-baking up to 400 ˚C  Figure A-1: (a) Variation of resistivity and the transmission of 75 nm ITO on glass as a function of post baking substrate temperature. Transmission measured by using the neutral density filters (ND) from a green laser at wavelength λ=532 nm; (b) Images of a conductive mirror-like ITO film just after the deposition via e-beam evaporation (before the post baking) and yellowish transparent ITO film after the baking in air up to 400 ˚C on the hot plate.  60  Appendix A. RHEED Screen Fabrication Therefore the performance of this screen is not adequate for use in the MBE. A second type of RHEED screen was made from three different layers of ITO, P-22 phosphor and an aluminum capping layer. Despite the fact that this screen worked before the MBE was baked, we observed that the screen collapsed during bake. This failure can be attributed to a weak bond between the ITO and the P-22 phosphor. Some possible solutions for this problem are: •  Replacing the phosphor layer from P-22 to other common phosphorescent materials that can make a better bond with ITO (e.g. most RHEED screen manufacturers use P43 phosphors).  •  Acid treatment of the ITO film to create a more adherent substrate for better bonding with the phosphor.  •  Make the aluminum capping layer thinner.  61  Appendix B Numerical Calculation of Bismide Infrared Absorption  In this appendix the change in optical emissivity and reflectivity of the substrate and the corresponding change in substrate temperature are estimated numerically when the thickness of a surface bismuth layer is varied by a few monolayers. This numerical simulation will be compared with the experimental results of section 3.4. Since the experimental results of section 3.4. are given at substrate temperature near 400ºC, based on Wien’s displacement law, all the calculations of this appendix are done at the following peak wavelength:  λmax  2.89 × 10−3 = ~ 4.3 μ m at Ts = 400D C Ts  (B.1)  Figure B-1 shows a schematic of the thermal radiation transfer between the heater and the substrate at two different thicknesses d and d+Δd. The change in the substrate thickness, Δd, is due to the change in the thickness of the bismuth coating layer. Now, by assuming that the thermal radiation obeys the Stefan-Boltzmann law, the thermal equilibrium between the input and output power on the first substrate can be written as, PHeater = PBack + PFront (1 − R) Aε Heaterσ TH 4 = Aε Backσ Ts 4 + Aε Frontσ Ts 4  (B.2)  62  Appendix B. Numerical Calculation of Bismide Infrared Absorption  d (a)  PBack Heater  Substrate  Vacuum  PFront Vacuum  PHeater  d+∆d  (b)  PBack Heater  Substrate  PFront Vacuum  Vacuum  PHeater Figure B-1: The schematic illustration of the thermal radiation between the heater and the substrate at two different thicknesses d and d+Δd.  where (1 − R) is the absorption factor of the back of the substrate, A is the radiating surface area, σ is the Stefan-Boltzmann constant, and TH and Ts are the heater and substrate temperatures. ε Back and ε Front are the emissivity from the back and front side of the substrate corresponding to the GaAs and the Bi layers and ε Heater is the emissivity of the heater. Now if the thickness of the bismuth coating increases by Δd, the temperature of the front side of the substrate would change to Ts+ΔTs. In addition, since ε = ε (λ , T ) is a function of temperature, the front side emissivity would also change to ε Front′ = ε Front − δ .  Therefore the new thermal equilibrium for the substrate can be written as,  63  Appendix B. Numerical Calculation of Bismide Infrared Absorption PHeater = PBack + P ' Front (1 − R) Aε Heaterσ TH 4 = Aε Backσ Ts 4 + A(ε Front − δ )σ (Ts + ΔTs ) 4  (B.3)  where by inserting equation (B.1) and then use of binomial expansion up to the first term, equation (B.2) becomes, 1 = (1 −  δ ε Front  )(1 +  4ΔTs ) Ts  (B.4)  Now by rearranging the above equation, the variation in substrate temperature due to the increase in bismuth amount is: ΔTs =  Ts δ 4 ε Front − δ  (B.5)  To calculate change in emissivity of the front side δ = ε Bi − ε Bi′ , let us look at the reflection from GaAs/Bi interface. Figure B-2 shows a schematic of the optical reflection and transmission from this interface when Δd=0 (two media) and when Δd≠0 (three media). It is assumed that the initial Bi coating thickness of the substrate is zero (i.e. dsubstrate = dGaAs). First for Δd=0, the Fresnel reflectivity amplitude r and the reflection R can be written as [41],  r=  1 − n1 1 + n1  R= r  (B.6)  2  where the refractive indexes of GaAs layer and vacuum are n1 and 1. Now when Δd≠0, the reflection R will change to:  64  Appendix B. Numerical Calculation of Bismide Infrared Absorption  t21r223r21t12e2iβ  n1  1 R  Vacuum  n2  n1  t23r221r223t12e5iβ/2 t23r21r23t12e3iβ/2  t21r23t12eiβ  T  I  1  t23t21eiβ/2  r12  GaAs Vacuum  Bismuth  I  (a)  GaAs  ∆d  (b)  Figure B-2: The schematic illustration the optical reflection and transmission from (a) GaAs/vacuum interface when Δd=0 (two media) (b) GaAs/Bi and Bi/vacuum interfaces when Δd≠0 (three media). The Fresnel amplitudes of reflection and transmission are labled by r and t.  r12 + r23eiβ r′ = 1 + r12 r23eiβ  (B.7)  R′ = r ′r ′* where r12 and r23 are the two medium reflectivity with the following definitions: 1 − nˆ2 1 + nˆ2 nˆ − n r23 = 2 1 nˆ2 + n1 r12 =  (B.8)  Since bismuth is a metal, the refractive index of bismuth is complex nˆ2 = n2 + ik2 . In addition, β is the phase difference between the waves reflected from the GaAs/Bi and the Bi/vacuum interfaces. β is defined as [41]:  β=  4Δd  λ  (n2 + ik2 )  (B.9)  65  Appendix B. Numerical Calculation of Bismide Infrared Absorption Now by changing the Bi coating thickness from zero to Δd, the reflection from the GaAs/Bi interface would change by:  ΔR = R − R′  (B.10)  In addition, since the back side of the GaAs substrate is saw cut, thermal radiation will be strongly scattered and trapped inside the wafer. Therefore, the optical transmission through substrate can be considered to be zero. As a result, the change in absorption radiation is:  ΔA = −ΔR  (B.11)  Now since at each wavelength the absorption radiation is equal to the emission radiation (definition of the black body), A= ε, then at each wavelength δ can be written as:  δ = R′ − R  (B.12)  For the optical properties of GaAs and Bi in Table B-1 and a monolayer of Bi on the surface (Δd=0.4 nm), the change in the emissivity δ is:  δ (λmax ) = 0.0235  (B.13)  Table B-1: Optical properties of GaAs and bismuth at λmax=4.3 μm from references [42,43]  Optical constants  GaAs  Bismuth  n  3.64  6.0  k  0  8.5  66  Appendix B. Numerical Calculation of Bismide Infrared Absorption At substrate temperature near Ts=400˚C=673˚K with ε Front = 0.34 [44], the jump in substrate temperature ΔTs from equation (B.5) is: ΔTs = 12.5°C  (B.14)  This estimated temperature is close to the observed experiment temperature jump in section 3.4., ΔTexperiment =20˚C. Therefore we conclude that a monolayer of metallic Bi on the surface can reduce the emissivity enough to explain the observed increase in substrate temperature. It is important to note that from the point of view of the emissivity, it is the conductivity of the surface that mattes not the composition. If for example, the (1×3) surface and the (2×1) surface have the same composition, but the (1×3) was semiconducting and the (2×1) was metallic, a temperature increase would be expected, going from (1×3) to (2×1).  67  

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