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Epitaxial growth of rare-earth trifluorides on III-V semiconductors Ritchie, Sayuri 1998

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E P I T A X I A L G R O W T H O F R A R E - E A R T H T R I F L U O R I D E S O N III-V S E M I C O N D U C T O R S By Sayuri Ritchie B. Sc. (Physics) University of Waterloo M. Sc. (Physics) University of Waterloo A THESIS S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S D E P T . OF PHYSICS We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F BRITISH C O L U M B I A September 1998 © Sayuri Ritchie, 1998 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Physics The University of British Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1Z1 Date: 1 6 Abstract Epitaxial growths of rare-earth trifluorides on III-V semiconductors have been investi-gated. Synchrotron photoemission spectroscopy showed a complete coverage of III-V substrates by LaF 3 and ErF 3 films and interfacial chemical reactions at the interface. In the LaF 3 films on GaAs(ll l) substrates, residual tensile strains were detected by high-resolution X-ray diffraction (HRXRD) contrary to the expected compressive strains in the case of a pseudomorphic growth. The tensile strains are interpreted as being due to the differential thermal contractions of the fluorides and the semiconductors during cooling. The correlations between the bulk structure and the surface structure of the LaF 3 films on GaAs and InP substrates have been studied by X-ray rocking curve measurements, grazing incidence X-ray scattering and atomic force microscopy. The lateral coherence lengths in the LaF 3 films from the X-ray rocking curves and the height-height surface correlation lengths from the X-ray scattering and the atomic force microscopy were com-parable to each other and were associated with the lattice mismatch of the system at the growth temperature. The results are interpreted in terms of strain relieving defects surrounding the columns of coherent crystals. The kinetics of LaF 3 film growths on III-V semiconductors were investigated using the self-affine surface structure analysis for the X-ray specular/diffuse scattering and the atomic force microscopy. The scaling exponents for the film growth obtained from the analysis were closest to the exponents predicted by the Villain-Lai-Das Sarma model in which the surface diffusion of deposited particles is the most important process in the film growth. ii InP single crystal islands have been grown on LaF 3 / InP(l l l ) heterostructures. The InP islands are observed to be faceted with three-fold symmetry as expected for (111) orientation. A small broadening of the InP substrate diffraction peak is interpreted as being due to inhomogeneous strains associated with the InP islands and differential thermal contraction of the LaF3 films during cooling. iii Table of Contents Abstract ii List of Tables vii List of Figures ix Acknowledgement xv 1 Introduction 1 1.1 Physical Properties of LaF 3 4 2 Sample Preparation 9 2.1 Substrate Cleaning 9 2.2 Fluoride Film Growth 10 2.3 Atomic Hydrogen Etching 12 2.3.1 GaAs wafers 13 2.3.2 InP wafers 17 2.3.3 Summary 22 3 Initial Stage of Fluoride F i l m Growth 23 3.1 Photoemission Spectroscopy 25 3.2 Surface Morphology 28 3.3 Formations of Chemical Bonds at the Film/Substrate Interface 34 3.4 Positions of Er 4f levels in ErF 3 /GaAs( l l l )B 42 iv 3.5 Band Alignments 49 3.6 Summary 49 4 Structural Properties 53 4.1 Crystal Orientations 56 4.2 Strains 61 4.3 Crystallinity 67 4.4 Summary 73 5 Surface Morphology 77 5.1 X-ray Scattering 81 5.2 Variation of the rms surface roughness a with film thickness and the growth exponent (3 84 5.3 Roughness exponent a and the correlation length £ 85 5.4 Atomic Force Microscopy 97 5.4.1 Method 97 5.4.2 Results 100 5.5 Discussion 109 5.5.1 Relationship between the bulk film structure and the surface morphology 109 5.5.2 Continuum equation describing film growth 110 5.5.3 Dynamical scaling 115 5.6 Summary 116 6 Semiconductor/Fluoride/Semiconductor Growth 118 6.1 Results 119 v 6.1.1 Formation of InP and GaAs islands on the fluoride/semiconductor structures 119 6.1.2 Chemical nature of islands 122 6.1.3 Crystallinity and strains in the InP islands on fluoride structures . 130 6.1.4 Self-affine surface structure analysis of the InP islands on LaF 3 . . 133 6.2 Summary 139 7 Conclusion 141 Appendices 144 A Calculation of hydrogen exposures 144 B Estimation of thickness of oxide and carbon layers 147 C X-ray specular and diffuse reflectivity calculation 151 C . l Specular Reflectivity 151 C.2 Diffuse Intensity 153 Bibliography 157 vi List o f Tables 1.1 Some physical properties of LaF 3, ErF 3 and CaF 2 4 1.2 Linear thermal expansion AL/L of LaF 3 where L is a length at 0°C, thermal expansion coefficients a of LaF 3, GaAs and InP as a function of temperature from Ref. [15] 7 3.3 Film/substrate photoemission peak intensity ratios for thick film and bare substrate obtained from measurements 32 3.4 Film thickness t and the range of the fractional coverage 7 obtained by angle dependent photoemission spectroscopy for the ErF 3 and LaF 3 films grown on GaAs(l l l )B and InP(l l l )B substrates at each annealing stage. 34 4.5 Gaussian FWHM and corresponding coherence lengths LX for the LaF 3 / InP( l l l ) samples obtained from the rocking curve measurements 70 5.6 Roughness exponent a obtained from the longitudinal diffuse scans for LaF 3 /GaAs( l l l )A and LaF 3 / InP(l l l )B samples 91 5.7 Correlation length £ obtained from the transverse diffuse scans for LaF 3 / GaAs(l l l )A and LaF 3 / InP(l l l )B samples 98 5.8 Characteristic q values and corresponding characteristic lengths LQ ob-served in the height-height correlation 5(g) for LaF 3 /GaAs( l l l )A and LaF 3 / InP( l l l )B 103 vii 5.9 Rms surface width a, the roughness exponent a and the correlation length f for the LaF 3 /GaAs(l l l )A, LaF 3 / InP(l l l )B samples and for the GaAs( l l l )A substrate obtained from the A F M images compared with the X-ray scat-tering results 108 5.10 Comparison of the bulk lateral coherence length L x measured by X-ray rocking curve and the surface correlation length £ determined from the A F M images for the LaF 3 /GaAs(l l l )A and LaF 3 / InP(l l l )B samples. . 109 5.11 Comparison of the scaling exponents obtained by X-ray scattering and the growth model I l l 6.12 Comparison of the roughness exponent a for the InP/LaF 3/GaAs, InP system with those of the LaF 3/GaAs, InP system 136 viii List of Figures 1.1 Projection along the c-axis of the trigonal structure of LaF 3 5 1.2 Projection along the c-axis and a view from the direction perpendicular to the c axis of the orthorhombic structure of ErF 3 6 1.3 Trigonal lattice constant (a-axis) of the rare earth trifluorides at room temperature 7 1.4 Refractive indices of films of CeF3, NdF 3 and LaF 3 as a function of wave-length 8 2.5 Schematic illustration of the fluoride evaporation setup for thin film sam-ples used in the photoemission experiments 11 2.6 Schematic illustration of the molecular beam epitaxy setup for thick film samples 12 2.7 Photoemission spectra of the Ga 3d and As 3d core levels from a ( l l l ) B GaAs wafer before atomic hydrogen etching 14 2.8 Photoemission spectra of the Ga 3d and As 3d core levels from a ( l l l ) B GaAs wafer after atomic hydrogen etching 15 2.9 Photoemission spectra from a ( l l l ) B InP wafer 18 2.10 Total electron yield spectra from a ( l l l ) B InP wafer 19 2.11 Carbon Is photoemission spectra for a ( l l l ) B InP wafer 21 3.12 Schematic illustration of growth process in thin film evaporation 24 3.13 Schematic illustration of a system of a film on a substrate 26 ix 3.14 Schematic illustration of occupied density of states and corresponding en-ergy distribution curve obtained by photoemission . • 27 3.15 Photoemission spectra of an ErF 3 /GaAs( l l l )B sample 29 3.16 Photoemission spectra of a LaF 3 /GaAs(l l l )B sample 30 3.17 Photoemission spectra of a LaF 3 / InP(l l l )B sample 31 3.18 Film/substrate intensity ratio vs. l /s in0 for the ErF 3 /GaAs( l l l )B , LaF 3 / GaAs(l l l )B and LaF 3 / InP(l l l )B samples obtained using angle dependent photoemission spectroscopy 33 3.19 Photoemission spectra for the Ga 3d and La 5p core levels from a LaF 3 / GaAs(l l l )B sample 36 3.20 Photoemission spectra for the As 3d core levels from a LaF 3 /GaAs( l l l )B sample 37 3.21 Photoemission spectra of La 4d core levels from a LaF 3 /GaAs( l l l )B sample. 38 3.22 The Ga 3d to As 3d photoemission intensity ratio as a function of annealing temperature for a LaF 3 /GaAs(l l l )B sample 39 3.23 Fit of the Gaussian-Lorentzian function to the La 4d core levels from the LaF 3 /GaAs(l l l ) sample after being heated to 600°C 40 3.24 Schematic illustration showing a configuration at the interface of the LaF 3 / GaAs(l l l ) samples: Model 1 43 3.25 Schematic illustration showing a configuration at the interface of the LaF 3 / GaAs(l l l ) samples: Model 2 44 3.26 Total electron yield spectra of Er 4d absorption edge (N edge) from a ErF 3 /GaAs( l l l )B sample 45 3.27 Resonant, non-resonant and the difference spectra of the Er 4f levels in the Er ions for the ErF 3 /GaAs( l l l )B sample with film thickness 2 nm. . 46 x 3.28 Difference spectra of the Er 4f levels in the E r 3 + ions for the ErF 3 /GaAs( l l l )B samples 47 3.29 Photoemission spectrum of a LaF 3 /GaAs(l l l )B sample of thickness 1.2 nm showing the GaAs valence band and the fluorine 2p valence band. . . 50 3.30 Interfacial band alignments in the LaF 3 / InP(l l l ) , LaF 3 /GaAs(l l l ) and ErF 3 /GaAs( l l l ) systems 51 4.31 Plan view of the (111) plane of GaAs (or InP) substrate showing the structural matching with LaF 3 and ErF 3 55 4.32 LEED pattern of a 1.5 nm thick LaF 3 film deposited on a GaAs ( l l l ) B substrate with the electron energy of 113.4 eV 57 4.33 Powder X-ray diffraction scans of the LaF 3 crystalline powder, LaF 3 / GaAs(l l l )A and LaF 3 / InP(l l l )B samples 58 4.34 Powder X-ray diffraction scans of a ErF 3 /GaAs( l l l )A sample 59 4.35 Powder X-ray diffraction scans of a LaF3/GaAs(100) sample 60 4.36 High resolution X-ray diffraction scans of the LaF 3 /GaAs(l l l )A, LaF 3 / InP(l l l )B, ErF 3 /GaAs( l l l )A samples 62 4.37 Plot of the in-plane tensile strain as a function of the LaF 3 film thickness for the LaF 3 films grown on GaAs(l l l )A and InP(l l l )B substrates. . . . 64 4.38 X-ray rocking curves of the LaF3(002) Bragg peak for the LaF 3 /GaAs( l l l )A and the LaF 3 / InP(l l l )B samples 69 4.39 Variation of FWHM of the rocking curves and the lateral coherence length L x with film thickness t for the LaF 3 /GaAs( l l l )A samples 70 4.40 Cross sectional SEM image of a LaF 3 /GaAs( l l l )A sample with film thick-ness t = 150 nm. A columnar structure commonly observed in thin film growths, is observed 72 xi 5.41 Schematic illustration of the scaling of a self-affine surface 78 5.42 Schematic illustration of a self-affine surface showing the parameters that describe it 80 5.43 Schematic illustration of X-ray experiment geometry 82 5.44 Schematic illustrations of (a) longitudinal and (b) transverse scans in re-ciprocal space 84 5.45 Schematic illustrations of the geometry of specular scans in the plane of incidence 85 5.46 Specular reflectivities of LaF 3 /GaAs( l l l )A samples 86 5.47 Specular reflectivities of LaF 3 / InP(l l l )B samples and the plot of the film/air interface width a vs. film thickness t 87 5.48 Film/air interface width a vs. film thickness t for the LaF 3 /GaAs( l l l )A and LaF 3 / InP(l l l )B samples 88 5.49 Schematic illustration of the geometry of longitudinal diffuse scans in the plane of incident '. 89 5.50 Longitudinal diffuse scans for the (a) LaF 3 /GaAs( l l l )A and (b) LaF 3 / InP(l l l )B samples 90 5.51 Schematic illustration of the geometry of a transverse diffuse scan in the plane of incidence 92 5.52 Transverse X-ray diffuse scans with 29 = 2° for the LaF 3 /GaAs( l l l )A and LaF 3 / InP( l l l )B samples 93 5.53 Transverse X-ray diffuse scans with 29 = 2° for the LaF 3 /GaAs( l l l )A samples with film thickness t = 48 nm 94 5.54 Transverse X-ray diffuse scans with 29 = 2° for the LaF 3 /GaAs( l l l )A samples 95 5.55 A F M images of a LaF 3 /GaAs( l l l )A sample 101 xii 5.56 A F M images of a LaF 3 / InP(l l l )B sample 102 5.57 Height-height correlation in reciprocal space S(q) of the LaF 3 /GaAs( l l l )A and the LaF 3 / InP(l l l )B sample 104 5.58 Mean square fluctuation g(r) and height-height correlation C(r) computed from the A F M image of the LaF 3 /GaAs( l l l )A and LaF 3 / InP( l l l )B sam-ples 106 5.59 A F M image of the atomic hydrogen etched polished GaAs( l l l )A sub-strate. The mean square fluctuation g(r) and height-height correlation C(r) computed from the A F M image 107 5.60 Schematic illustration of the surface relaxation mechanism described by the one dimensional discrete model 114 6.61 A F M image of the surface of InP/LaF 3 /InP(ll l )B sample 120 6.62 Cross-sectional SEM image of a InP/LaF 3 /InP(ll l )B sample 121 6.63 Cross sectional SEM image of a LaF 3 / InP/LaF 3 /GaAs(l l l )A sample. . . 122 6.64 A F M image of the surface of a InP/LaF 3 /GaAs(l l l )A sample (10pm x 10^m) 123 6.65 A F M image of the surface of the InP/LaF 3 /GaAs(l l l )A sample in Fig. 6.64 (2.4/xm x 2Apm) 124 6.66 A F M image of the surface of the InP/LaF 3 /GaAs(l l l )A sample in Fig. 6.64 (0.7pm x 0.7pm) 125 6.67 A F M image of a GaAs/ErF 3 /GaAs(l l l )A sample 126 6.68 X-ray photoelectron spectra of the InP/LaF 3 /InP(ll l )B sample taken at the take-off angle of 90° and 20° 127 6.69 Schematic illustration showing a substrate covered by islands of width L and thickness d and the photoelectron collected at take-off angle 6. . . . 128 xiii 6.70 Intensity ratio of In 4d to La 4d core levels as a function of 1/ tan# for the InP/LaF 3 /InP(ll l )B sample 129 6.71 X-ray specular reflectivity of the InP/LaF 3 /InP(ll l )B sample. . . . . . . 130 6.72 HRXRD 9-29 scan of the InP/LaF 3 /InP(ll l )B sample 131 6.73 6-29 scan of the InP/LaF 3 /GaAs(l l l )A sample using a powder X-ray diffractometer 133 6.74 The mean square fluctuation g(r) (a) and the height-height correlation C(r) (b) obtained from the A F M image of the InP/LaF 3 /InP(l l l )B sam-ple in Fig. 6.61 135 6.75 The mean square fluctuation g(r) (b) and the height-height correlation C(r) (a) obtained from the A F M image in Fig. 6.65 137 6.76 The PSD S(q) for the InP/LaF 3 / inP( l l l )B sample and the InP/LaF 3 /GaAs( l l l )A sample shown in the A F M images in Fig. 6.61 and Fig. 6.65. 138 B. 77 Schematic illustration of a GaAs wafer covered by a uniform layer of oxides of thickness and a carbon contaminant layer 148 C. 78 Schematic illustration of a system with two interfaces 152 C.79 Schematic illustration of an interfaces showing the incoming vectors and the out going vectors 153 C.80 Schematic illustration of a system with two interfaces 156 xiv Acknowledgement I would like to thank my mighty supervisor Tom Tiedje for his patient guidance and support. I would like to thank Jim McKenzie for countless help during my research. I thank Yuan Gao and Tony van Buuren for their help and assistance in the lab and at the Synchrotron Center in Wisconsin. I would like to thank Mario Beaudoin and Ahmad Kassai for their technical help in the lab and for their support during this difficult time. I thank Christian Lavoie and Shane Johnson for teaching me many things during my first years. I thank my Ph.D. committees, Birger Bergerson, Janis McKenna and Jeff Young for their suggestions and advise for my project. I thank Phil Wong for performing the XPS measurements for this project and Andrew Leung for taking the LEED photographs. I thank the people in the lab, past and present, Al , Anders, Christina, Duncan, Mari and Martin for various help and support. I thank Wen-Kai Zhong and Tom Pinnington for assisting me with atomic force microscope. I would like to thank my kendo teachers Dave Harding and Hiro Okusa for their support and encouragement during the last two years. I also thank the people in the UBC Kendo Club, especially Pierre and Bob for the friendship and for making the life enjoyable. I thank my Zen teacher Hosaka Sensei for teaching me the way of life. I would finally like to thank my husband Ken Ritchie for constant support and en-couragement during my study. xv Chapter 1 Introduction Epitaxial growth of fluorides on semiconductors has attracted considerable attention in the past decade due to its potential applications in the semiconductor industry. The epitaxial fluorides on III-V semiconductors such as GaAs and InP, in particular have applications in optical devices such as the integrated semiconductor pumped solid state lasers [1, 2] and the vertical cavity surface emitting lasers [3]. Other applications include gate insulators in three dimensional integrated devices. Use of epitaxial fluorides in these applications is especially important for compound semiconductors such as GaAs and InP since they lack a high quality native oxides analogous to Si0 2 for Si. Most of the previous work on the fluorides have been dedicated to the alkaline earth fluorides, CaF 2, SrF 2 and BaF 2 mainly due to their cubic-fluorite structure which is sim-ilar to diamond and zinc-blend structures of group IV and III-V semiconductors. Several studies have also been done on the growth of lanthanide trifluorides on semiconductors. Sinharoy et al. have reported the epitaxial growth of crack-free LaF 3 films of up to 200 nm thick on GaAs(ll l ) substrates [5]. They have characterized the surface of the films using low-energy electron diffraction (LEED) and reflection high-energy electron diffrac-tion (RHEED). Struumpler et al. have grown epitaxial LaF 3 films on Si(lll)[6]. They have studied the surface structure by LEED and scanning electron microscopy (SEM) and the crystal structure by X-ray diffraction (XRD) using the angle-dispersive scanning detection. They have observed the epitaxial islands on the film of thickness less than 15 nm. The surface of the films of thickness greater than 15 nm were found to be smooth. 1 Chapter 1. Introduction 2 They have also shown that the c-axis of LaF 3 films is oriented parallel to the [111] di-rection of Si substrates. The (111) surfaces of substrates were used instead of (100) surfaces because the structures and the lattice spacing of the trigonal face of the trifluo-rides are the closest to those of the (111) substrate surfaces of the semiconductors as we show in Sec. 1.1. A number of studies have been performed on interfacial reactions and band alignments of lanthanide trifluorides on Si ( l l l ) using photoemission spectroscopy [7, 8, 9, 10]. The surface structures of lanthanide trifluoride films on semiconductors has also been studied by LEED and RHEED [7, 10, 11]. They have shown that the trigonal structures of HoF 3 and GdF 3 which are normally only stable at high temperatures, are stable at room temperature for thin layers (1-20 nm) deposited on S i ( l l l ) , Ge( l l l ) and GaAs(l l l )B substrates. In this study, the epitaxial growth of rare-earth fluoride films on III-V semiconductors, particularly LaF 3 and ErF 3 films grown on GaAs and InP substrates are investigated. One aim of this study is to epitaxially grow high quality rare-earth fluoride films on III-V semiconductors. The term epitaxy means the oriented or single-crystalline growth of one material upon another such that there exist crystallographic relations between the film and the substrate. Certain crystallographic directions in the film and the substrate are parallel. Another aim of this study is to gain insights into the mechanisms whereby the insulator films grow on semiconductors. We will achieve this by studying the system from various aspects such as crystal structures using the high-resolution X-ray diffrac-tion (HRXRD), surface morphologies using the X-ray specular and diffuse scattering and chemical compositions of the film/substrate interface using the synchrotron photoemis-sion spectroscopy. The study of film crystal properties using the high-resolution X-ray diffraction have been performed on the epitaxial LaF 3 films for the first time. The surface morphology study using the X-ray specular and diffuse scattering of the fluoride films on semiconductors have never been performed previously. Chapter 1. Introduction 3 In the first part of this study, the growth process at the initial stages of the film growth are studied. For this purpose, very thin fluoride films of less than 10 nm are grown on III-V semiconductors. The growth process is determined by examining the surface mor-phologies and the chemical interactions at the film/substrate interfaces. The experiments are done by photoemission spectroscopy with synchrotron radiation. (Chapter 3) In Chapter 4, the growth mechanism at the later stage of the film growth is investi-gated. To achieve this, thick fluoride films of thickness 10-400 nm are grown on III-V semiconductors. The bulk structural properties of the films such as crystal orientations, strains and defects are studied by X-ray diffraction. Finally, the kinetic mechanisms of the film growth are described using the scaling laws for self-affine surfaces. For this purpose, the surface height is modelled with a self-affine correlation function and the evolution of surface morphology with time or the film thickness t and with the spatial frequency q is determined using X-ray scattering and atomic force microscopy. By comparing the results with theoretical continuum models, we can infer about the dominant mechanisms of the film growth such as surface diffusion, evaporation and recondensation of the deposited species. (Chapter 5) In Chapter 6, the growth of III-V semiconductors, InP and GaAs on rare-earth trifluoride/III-V semiconductor structures is investigated. The surface morphlogy of these structures is studied by A F M , SEM and X-ray scattering. The structure of the lay-ers is studied by X-ray diffraction and the chemical composition of the system is studied by X-ray photoelectron spectroscopy. The structural properties and surface morphology of the fluoride films are also techni-cally important. The crystalline properties of the films and the surface morphology affect the growth of the more complicated structures such as semiconductor/fluoride/semiconductor systems. The surface and interface roughness have a great influence on the power loss Chapter 1. Introduction Table 1.1: Some physical properties of LaF 3, ErF 3 and CaF 2 4 LaF 3 ErF 3 CaF 2 Crystal Structure Trigonal Orthorhombic Cubic-fluorite P3cl - Djd Pnma - D $ Lattice Parameters a = 7.185A a = 6.354 A a = 5.4640 A c = 7.351 A b = 6.846 A c = 4.380 A Mismatch with GaAs +3.8 % -8.6 % (a-axis), +9.0 % (c-axis) -3.3 % with InP -0.04% -12 % (a-axis), +5.4 % (c-axis) -6.9 % Melting Point 1493°C 1140°C 1423°C Density 5.938 g/cm3 7.772 g/cm3 3.179 g/cm3 6 molecules/cell 4 molecules/cell 4 molecules/cell Band Gap 9.92 eV - 12.1 eV in the optical waveguides through scattering and the carrier mobilities in electronic de-vices. The stability of the films upon annealing will also be important in the subsequent processing during device fabrication. 1.1 Physical Properties of L a F 3 The physical properties of LaF 3 are summarized in Table 1.1. The crystal structure of LaF 3 is trigonal (P3cl - D| d). A plan view of the ax a trigonal plane of LaF 3 is shown in Fig. 1.1. The ax a trigonal basal plane of LaF 3 is similar to the hexagonal (111) face of semiconductors with the diamond or zinc-blend structures. The crystal structure of ErF 3 is orthorhombic (Pnma). Projection along the c-axis and a view from the direction perpendicular to the c axis of the orthorhombic structure of ErF 3 is shown in Fig. 1.2. The rare-earth trifluorides SmF3 to LuF 3 are known to undergo high-temperature dimorphism, inverting from trigonal to orthorhombic crystals on cooling [14]. The triflu-orides LaF 3 to NdF 3 exist only in trigonal form. The trigonal lattice constant (a-axis) of Chapter 1. Introduction 5 Figure 1.1: Projection along the c-axis of the trigonal structure of LaF 3 showing the nine coordinations of the La atom at the (0.3401, 0.3401, 0.25) position. The numbers indicate the positions of the fluorine atoms along the c-axis. Double circles indicate that the atoms are overlapped at those positions. Chapter 1. Introduction 6 0 5A I I I I I I Figure 1.2: Projection along the c-axis (left) and a view from the direction perpendicular to the c-axis (right) of the orthorhombic structure of ErF 3 from Ref. [13]. The larger circles are the fluorine (F) atoms and the smaller circles are the erbium (Er) atoms. The numbers in the circles indicate the positions of atoms along the c-axis. the rare earth trifluorides at room temperature is plotted in Fig. 1.3. The lattice distances of hexagonal (111) faces of GaAs and InP are also plotted. Linear expansion coefficients of LaF 3 have been used to estimate the approximate constants at room temperature from the high temperature data in Ref [14]. The trigonal lattice constants of the trifluorides lies approximately between the hexagonal lattice spacing of GaAs and InP( l l l ) . The difference in thermal expansion coefficients between LaF 3 and GaAs or InP is smaller than the difference between CaF 2 and GaAs or InP. Linear thermal expansion and thermal expansion coefficients of LaF 3 are listed in Table 1.2. At room temperature, the thermal expansion coefficient of LaF 3 is 16 x l O - 6 K - 1 and that of CaF 2 is 19 x l O _ 6 K _ 1 whereas the thermal expansion coefficient of GaAs is 5.7 x 1 0 - 6 K - 1 and that of InP is 4.8 x 1 0 _ 6 K _ 1 . The LaF 3 crystal is also known to be mechanically hard and chemically stable [17, 14]. A summary of physical properties of LaF 3 can be found in Ref. [17]. The Chapter 1. Introduction 7 7 . 5 . < 7 . 4 -« ' 7 . 3 -* - 7 . 2 c CO - , .. 1 O 7 . 0 -o CD 6 . 9 -o -J CO O 6 . 6 -D ) u l 6 . 5 -GaAs(111) InP (111) La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Lanthanides Figure 1.3: Trigonal lattice constant (a-axis) of the rare earth trifluorides at room tem-perature. The dotted lines are the lattice distances of hexagonal (111) faces of GaAs and InP. Linear expansion coefficients of LaF 3 have been used to estimate the approximate constants at room temperature from the high temperature data in Ref [14]. Table 1.2: Linear thermal expansion AL/L of LaF 3 where L is a length at 0°C, ther-mal expansion coefficients a of LaF 3, GaAs and InP as a function of temperature from Ref. [15]. LaF 3 GaAs InP Temperature AL/L a a a ( °C) (%) (xlO- 6 K" 1 ) (xlO" 6 K" 1 ) (x lO" 6 K- 1 ) 29 0.014 15.8 5.7 4.3 180 0.291 18.0 6.5 4.7 380 0.669 20.6 6.9 -580 1.111 23.3 7.2 6.1 780 1.635 33.6 - -Chapter 1. Introduction 8 IBO 1501 I I I I I L I i ' "^02 0.4 06 OB 1.0 12 1.4 IB IB 20 VWWELENGTH IN MICRONS Figure 1.4: Refractive indices of films of CeF 3 , NdF 3 and LaF 3 as a function of wavelength from Ref. [16] refractive indices in the wavelength range from 0.2 to 2.0 /xm for LaF 3 , N d F 3 and CeF 3 are plotted in Fig. 1.4 from Ref. [16]. Chapter 2 Sample Preparation The preparation of the rare-earth fluoride/semiconductor samples involves two basic steps: substrate cleaning and fluoride thin film deposition. The surface of semiconduc-tors as received from manufacturers are generally contaminated with carbon compounds, silicon oxides and native oxides. For epitaxial growth of high quality films, these con-taminants must be removed. In this chapter, we describe the procedures for the sample preparation and discuss the effect of atomic hydrogen etching on the surface of GaAs and InP wafers. 2.1 Substrate Cleaning The thin film samples (< 10 nm) for surface analysis by photoemission were prepared at the Synchrotron Radiation Center in Wisconsin. The (111) and (100) oriented GaAs and InP wafers were etched in a concentrated H2SO4 solution to remove native oxides. They were rinsed with deionized water and blown dry with N 2 before being inserted in the U H V analysis chamber. The wafers were 400 to 500 pm thick and 1 to 2 cm 2 in area. The thick film samples (> 10 nm) used in the X-ray scattering and diffraction exper-iments were prepared in our lab at the University of British Columbia. The GaAs and InP wafers used for the samples were 2 in. diameter wafers, 400 to 500 /jm thick. The wafers were cleaved into 6 pie shaped pieces. The GaAs and InP wafers were first rinsed in concentrated H F solution for 1 min. to remove any residual S i 0 2 on the surface. S i 0 2 9 Chapter 2. Sample Preparation 10 on the surface is believed to be residual from the chemical polishing process at manufac-turer [18]. They were next rinsed in deionized water and oxidized in a UV ozone reactor. The ozone reactor consisted of a 60 W mercury UV lamp and a sample holder placed 1.5 in. away from the lamp [19]. Growth of oxide by UV ozone treatment helps remove carbon contaminants from the surface. The substrates were subsequently inserted in a UHV chamber with a typical background pressure of 5 to 10 x 10 - 1 0 mbar. The oxide on the GaAs and InP wafers was removed by atomic hydrogen etching in the vacuum chamber. The atomic hydrogen etching is one of the substrate cleaning methods for molecular beam epitaxy. A prepurified grade H 2 gas (99.99%) was used for the etching. The hydrogen pressure during the etching was 1 x 10 - 6 torr. The hydrogen molecules were dissociated thermally with a resistively heated tungsten filament placed at about 5 cm from the substrate surface. The temperature of the filament was between 1800 and 2000° C. The substrate was heated to 300° C by the substrate heater during etching. The temperature of the substrate was measured by a thermocouple situated between the heater and the substrate. The oxides were removed in approximately 10 min. at this condition as verified by reflection high energy electron diffraction (RHEED) [27], but the substrates were further cleaned by atomic hydrogen for approximately 20 min. in order to remove residual carbon. The secondary ion mass spectroscopy (SIMS) study of the hydrogen etched GaAs wafers showed that the amount of carbon contaminants on the wafers decreased with increasing hydrogen etching time [27]. 2.2 Fluoride F i l m Growth The rare-earth trifluoride films were grown by evaporation from a high purity (99.9 %) crystalline powder. For the thin film samples used in the photoemission experiments, the fluoride powder was evaporated from a 3 x 1 cm2 Ta boat, placed 10 cm from the Chapter 2. Sample Preparation 11 Substrate Holder i Substrate —- •" l Ci | |— Thickness Monitor Ta Boat (Source) Electrical Feedthru Figure 2.5: Schematic illustration of the fluoride evaporation setup for thin film samples used in the photoemission experiments carried out at the Synchrotron Radiation Center in Wisconsin. sample ( see Fig. 2.5 ). The Ta boat is attached to a feedthrough and heated resistively to the melting temperature of the fluoride (1493°C for LaF 3 and 1140°C for ErF 3). The pressure during evaporation was approximately 1 x 10 - 7 mbar. The sample was not independently heated during the evaporation, although the close proximity to the hot evaporator caused some unintentional heating. The film thickness ranged from 0.5 to 2 nm as measured by the thickness monitor located beside the sample. The thick film samples (10-400 nm) were prepared by molecular beam epitaxy in our lab at the University of British Columbia. The schematic illustration of the growth setup is shown in Fig. 2.6. The evaporation was done from a high temperature effusion cell (VG-6HT) with a tungsten crucible. The semiconductor substrates were placed on a heated stage in a UHV chamber with a typical background pressure of 1 x 10 - 9 mbar. The substrate temperature during growth was 600±20° C for GaAs and 400±20°C for InP as measured by a thermocouple situated between the heater and substrate. Typical Chapter 2. Sample Preparation 12 Substrate Holder Quartz Thickness Monitor Substrate HT Effusion Cell Figure 2.6: Schematic illustration of the molecular beam epitaxy setup for thick film samples. pressure during evaporation was 1 x 10~7 mbar. Although the Ta boat setup costs less and is easy to implement than the effusion cell setup, there are several advantages for using an effusion cell. One of the advantages for using an effusion cell over a Ta boat is that the effusion cell allows a deposition over a larger area than the Ta boat does. The deposition of a sample area up to 2 in. in diameter circle is possible with an effusion cell whereas the sample size is limited to about 1/2 in. in diameter circle. The effusion cell also allows us a better control of the source temperature than the Ta boat setup, hence a better control of the flux of the fluoride molecular beam. 2.3 Atomic Hydrogen Etching The effect of hydrogen etching on the surface of GaAs and InP wafers was studied by UV photoemission spectroscopy. We used photoemission to determine whether the atomic hydrogen etching removes oxides, carbon contaminants and other chemical species on Chapter 2. Sample Preparation 13 the surface. The basic principle of photoemission spectroscopy is described in Chapter 3. Photoemission experiments were performed at the Canadian Synchrotron Radiation Facility at Synchrotron Radiation Center at the University of Wisconsin-Madison, using a grazing-incidence grasshopper monochromator . The combined resolution of the analyser and the monochromator is 0.2 eV. The atomic hydrogen cleaning for the photoemission experiments was carried out in a similar manner to the MBE substrates. Typical base pressure in the analysis chamber was 1 x 10 - 9 mbar. High purity H 2 gas (99.99%) was used for the etching. The hydrogen pressure during the etching was 1 x 10~6 torr. The hydrogen molecules were dissociated thermally with a resistively heated tungsten filament placed at about 3 cm from the substrate surface. The temperature of the filament was between 1800 and 2000°C. The substrate was not intentionally heated, but has been heated by radiation from the hot filament. 2.3.1 G a A s wafers Photoemission spectra of the Ga 3d and As 3d core levels from a GaAs(l l l ) wafer (as-received) before the atomic hydrogen etching are shown in Fig. 2.7. The spectra taken before the atomic hydrogen etching show chemically shifted components separated by 1.2 eV in the Ga 3d core level and 2.9 eV in the As 3d core level. The components are commonly observed in oxidized GaAs [20, 21, 22]. The peaks at the lower binding energy are associated with the Ga-As bonds of the bulk GaAs and the peaks at the higher binding energy, with the surface oxides, Ga203 and As203 [20, 21, 22]. Photoemission spectra of the Ga 3d and As 3d core levels from a GaAs(l l l ) wafer after an exposure to 3 x 1016 c m - 2 of atomic hydrogen are shown in Fig. 2.8. The calculation of the hydrogen exposure is described in Appendix A. The intensities of oxide components Ga203 and As203 are no longer detected or they are below the noise level which is 1 % of the intensity before atomic-H etching. Chapter 2. Sample Preparation 14 Figure 2.7: Photoemission spectra of the (a) Ga 3d and (b) As 3d core levels from a ( l l l ) B GaAs wafer before atomic H-etching showing two components for each Ga 3d and As 3d core levels, separated by 1.2 and 2.9 eV, respectively. The component at the lower binding energy corresponds to the Ga-As bonds in the bulk GaAs. The component at the higher binding energy is associated with the chemical bonds in the surface oxides. The solid lines are fits of a Gaussian function to the data. Chapter 2. Sample Preparation 15 Figure 2.8: Photoemission spectra of the (a) Ga 3d and (b) As 3d core levels obtained from a ( l l l ) B GaAs wafer after atomic hydrogen etching. The solid lines are fits of a mixed Gaussian-Lorentzian function to the data. Chapter 2. Sample Preparation 16 To resolve the components present in the spectra, the Gaussian-Lorentzian mixed function of the form [23]: HT> * *) = i + ( L a ) 2 + (1 " V) e x p [ - ( ^ ? ) 2 ] (2.1) is fitted to the data as shown by solid lines in Fig. 2.8. In this expression, x is the binding energy, T is the width of the function, b = (l/2)\/ln2 = 0.60056 and n is the Lorentzian fraction. The basic shape of the photoemission peak is Lorentzian associated with the finite core hole life time. The Gaussian function represents other factors such as instrumental broadening and phonon broadening. In the spectrum of the Ga 3d core level (Fig. 2.8 (a)), two components separated by 0.4 eV are resolved. The chemical shifted components are also observed by Pianetta et al. [22]. The component at lower binding energy is GaAs bonds in the bulk GaAs and the component at higher binding energy corresponds to the Ga-0 bonds of the chemisorbed oxygen. In the As 3d core level spectrum shown in Fig. 2.8 (b), three components are resolved. The highest intensity peak reveals the Ga-As bonds in the bulk GaAs. The component shifted by 0.7 eV toward higher binding energy is associated with a single As-0 or As-OH bond of the As surface atoms [20]. Surface As-H bond produces a smaller chemical shift (0.3 eV) and may also be present [24]. The component shifted by 0.6 eV towards lower binding energy is the surface component of Ga-As bonds. The thicknesses of oxide and carbon contaminant layers etched by the atomic hydro-gen exposure of 3 • 1016 c m - 2 were determined from the ratio of photoemission intensities before and after etching. They were 0.9 nm and 0.6 nm respectively. Corresponding efficiencies of the atomic hydrogen etching are 0.3 nm/(1016 H atoms cm - 2) for the oxide layer and 0.2 nm/(1016 H atoms cm - 2) for the carbon layer respectively. A detailed de-scription of the calculation is included in Appendix B. It has been shown by laser light scattering [27] that the surfaces of atomic hydrogen etched GaAs wafers were smoother Chapter 2. Sample Preparation 17 than the surface of the thermally desorbed GaAs wafers. 2.3.2 InP wafers The effect of the atomic hydrogen etching as well as the HF etching on the surface of InP wafers was studied. Photoemission spectra from a ( l l l ) B InP wafer as received (a), after the HF etching (b) and after atomic hydrogen etching (c) are shown in Fig. 2.9. In the photoemission spectrum of the as-received InP wafer, silicon (Si) 2p core levels in addition to the phosphorus (P) 2p core levels are observed. Hence, the surface of the InP wafer is contaminated with Si, or more likely, Si0 2 . To further examine the presence of Si02, the total electron yield spectra of the InP wafer before and after the HF etching are obtained and shown in Fig. 2.10. An absorption peak at 105 eV corresponds to the Si L edge in Si0 2 and the smaller peak at 130 eV corresponds to the phosphorus (P) L edge. The photoemission spectrum of the InP wafer after being removed from the analysis chamber and being etched in concentrated HF for 1 min is shown in Fig. 2.9 (b). After this treatment the Si 2p core level is missing from the photoemission spectrum. The HF etching evidently removed the Si02 contamination. Similarly, the Si L edge absorption in the total electron yield spectrum of the InP wafer was not detected after the HF etching (Fig. 2.10 (b)). The intensity of the phosphorus (P) L edge in Fig. 2.10 (b) has increased by a factor of 2.5. Furthermore, the P 2p core levels after the HF etching (Fig. 2.9 (b)) has also increased. This suggests that the Si0 2 contamination covers the wafer rather uniformly. We believe that the Si0 2 contamination is a residue from the chem-mechanical process used to polish the wafers produced by an improper polishing procedure [18]. If the Si0 2 contamination were in the form of particles, the photoemission intensity of the substrate peak would not change so dramatically after HF etching, given that the escape depth of the 50eV photoelectrons is on the order of 1 nm. Chapter 2. Sample Preparation 18 -i 1 1 1 1 1 1 1 1 1 140 130 120 110 100 Binding Energy (eV) Figure 2.9: Photoemission spectra from a (1H)B InP wafer excited at a photon energy of 180 eV: (a) as-received, (b) after HF etching and (c) atomic hydrogen etching. Al l three curves show the P 2p core level; curves (a) and (b) show a chemically shifted P 2p core level (P-0 bonding); curve (a) also shows the Si 2p core level. Chapter 2. Sample Preparation 19 0.2-1 1 . 1 . , . 1 . , . 1 100 110 120 130 140 150 Photon Energy (eV) Figure 2.10: Total electron yield spectra from a ( l l l ) B InP wafer: (a) as-received and (b) after HF etch. Both the silicon L edge and phosphorous L edge are observed in spectrum (a), while only the phosphorous L edge is detected in spectrum (b). Chapter 2. Sample Preparation 20 The photoemission spectrum of the P 2p core levels for the as-received InP wafer in Fig. 2.9 (a) shows a component chemically shifted to a higher binding energy correspond-ing to the surface oxide. As can be seen in the spectrum in Fig. 2.9 (b), the surface oxide is reduced but not removed by the HF etch. The photoemission spectrum taken after HF etching followed by an exposure to 9 x 1016 c m - 2 of atomic hydrogen is shown in Fig. 2.9 (c). The oxide component of the P 2p core levels are not detected. This shows that the hydrogen etching removed the phosphorus oxide. The thicknesses of Si0 2 removed by HF etch and the oxide+carbon layer removed by atomic hydrogen are estimated as 0.9 and 0.4 nm respectively from the ratio of the pho-toemission signals. The corresponding efficiency of the atomic-H etching is 0.04 nm/(1016 H atoms cm - 2) for the oxide+carbon layer. The details of the calculations are described in Appendix B. The difference in efficiency between the InP wafer and the GaAs wafer (0.3 nm/(1016 H atoms cm - 2)) probably comes from the failure to estimate the atomic hydrogen exposure required to remove 0.4 nm of oxide+carbon layer in the InP wafer case. The actual atomic hydrogen exposure that removed 0.4 nm of oxide+carbon layer may have been less than total exposure 9 x 1016 cm - 2 . The lower efficiency for the InP substrate is not due to the presence of Si0 2 particles after HF etching, since the SIMS experiment showed that the atomic-H etching does not remove Si0 2 . The C Is core level spectra from a ( l l l ) B InP wafer before and after the atomic hydrogen etching are shown in Fig. 2.11. The spectrum in Fig. 2.11 (a) was taken after the HF etching and the spectrum in Fig.2.11 (b) was taken after the HF etching followed by the exposure to 3 x 1016 c m - 2 of atomic hydrogen. The intensity ratio of the C Is core levels in Fig. 2.11 before and after hydrogen etching is estimated to have an upper limit of Icnf/Icisi < 0.05. Therefore the carbon contamination was reduced by factor of at least twenty by atomic hydrogen etching. Other photoemission experiments not described here showed that atomic hydrogen etching did not remove the Si0 2 , consistent Chapter 2. Sample Preparation 21 Figure 2.11: Carbon Is photoemission spectra for a (1H)B InP wafer: (a) after an HF etch and (b) after an HF etch followed by an atomic-H etching which removed 75 % of the carbon. Chapter 2. Sample Preparation 22 with the SIMS measurements of the atomic hydrogen etched GaAs wafers in Ref. [27]. Although the photoemission measurements of C and Si02 contamination were carried out on InP substrates, we expect similar results for the GaAs substrates. 2.3.3 Summary Photoemission results showed that the atomic hydrogen etching effectively removed the surface oxides and carbon contaminants from the GaAs and InP wafers. The study also showed that layers of Si02 are present on the as-received wafers from the manufacturers. The Si0 2 layers can be removed by HF etching as shown by PES. The laser light scattering study of the atomic hydrogen etching [27] showed that the surface roughness of the wafer whose oxide was removed by thermal desorption was greater than the surface roughness of the wafer cleaned by atomic hydrogen etching. The thermal desorption roughens the surface whereas the hydrogen cleaning does not. Furthermore, the SIMS study of the atomic hydrogen etched GaAs wafers [27] showed that the oxide removal by thermal desorption does not remove the carbon contaminants. We conclude that the atomic hydrogen etching is the best method for the substrate preparation for the fluoride film growths. Chapter 3 Initial Stage of Fluoride F i l m Growth The quality of epitaxial thin films is often determined at the initial stages of the film growth. In this chapter, the growth process of the rare-earth fluoride films on III-V semiconductors at the initial stage of growth is studied. For this purpose, samples with film of thickness less than 10 nm are prepared. A series of anneals is performed on the samples. After each annealing, the electronic structures at the surfaces and interfaces are examined by photoemission spectroscopy. The first step of fluoride film growths involves the physisorption of fluoride molecules (e.g. CaF 2 and LaF 3 molecules) onto the substrate surface. At this stage, the fluoride molecules have not necessary formed chemical bonds at the film/substrate interface. The annealing provides the energy for the fluoride molecules to rearrange themselves and to form crystals. Depending on the film and substrate surface energies and also on the film/substrate interface energy, the film can form islands or wet the substrate surface as illustrated in Fig. 3.12. Further annealing can result in the reevaporation of the fluoride molecules. In this study, we explore the wetting between the rare-earth fluoride films grown on III-V semiconductors and the substrate surfaces by angle dependent photoemission spectroscopy. The re-evaporation caused by high temperature annealing is also studied by angle dependent spectroscopy. The wetting phenomena of a film on a substrate can be understood thermodynamically [31]. Consider a system of a film on a substrate in which the film/air interface makes a contact angle 9 with the substrate/air interface 23 Chapter 3. Initial Stage of Fluoride Film Growth 24 b Islanding a Physisorption Figure 3.12: Schematic illustration of growth process in thin film evaporation with sub-sequent high temperature annealing. The first step is the physisorption of the molecules onto the substrate (a). The annealing can cause the film to form islands (b) or to wet the substrates (c). The subsequent annealing can result in the reevaporation of the molecules (d). Chapter 3. Initial Stage of Fluoride Film Growth 25 as shown in Fig. 3.13. The interface free energies are defined as 7/ for film/air, js for substrate/air and jsf for film/substrate interfaces. The change in surface free energy A G accompanying a small displacement of the film such that the change in area of substrate covered AA, is: A G = AA(yBf - 7,) + AAVcos(e - A6) (3.2) At equilibrium: lim ^ = 0 (3.3) AA->0 AA and: 7s/ - Is + 7/ cos 9 = 0 (3.4) The condition for wetting is given by: Is > Isf + 7/ (3-5) The surface energy of fluorides are generally lower than that of covalent semiconductors because of the ionic bondings in fluorides. The surface energy of fluorides such as CaF 2 and BaF 2 ranges between 0.3 and 0.5 J/m 2 [32, 33], whereas that of semiconductors such as Si and GaAs ranges between 0.8 to 3.2 J/m 2 [34]. The surface energy of a material is different for each crystallographic surface. We expect the film/substrate interface free energy 7,7 to be lower than either film/air 7/ or substrate/air js interface energy. Since ^semiconductor > 7fluoride, if we neglect the film/substrate interface energy, the condition for wetting is satisfied. Therefore we expect a complete coverage of semiconductor substrates by fluoride films. 3.1 Photoemission Spectroscopy Photoemission spectroscopy reveals the electronic structures of materials or their occu-pied density of states. The synchrotron radiation is used as the photon source because of Chapter 3. Initial Stage of Fluoride Film Growth 26 substrate Figure 3.13: Schematic illustration of a system of a film on a substrate. The interface free energies are defined as 7/ for film/air, 7., for substrate/air and 7,,/ for film/substrate interfaces. its energy tunability and strong intensities. Photoemission experiments were performed at the Synchrotron Radiation Center at the University of Wisconsin-Madison, using a grazing incidence grasshopper monochromator. The photon energy ranged from 100 to 200 eV (soft X-rays), since the photoemission experiments performed at this energy range have maximum sensitivity for the material systems of interest here. The electron escape depths in this energy range lies between 0.5 to 3 nm. The combined resolution of the analyser and the monochromator is 0.2 eV. One often uses a three step model to represent the photoemission process. It consists of the optical transition (1), the transport to the surface (2) and the transmission through the surface (3). The kinetic energy Ek of the outgoing electron is given by: Ek = hu-Eb-<f> (3.6) where hv is the photon energy, Eb the electron binding energy and (j) the work function. The tunable photon energy allows data to be collected in several modes. Energy Chapter 3. Initial Stage of Fluoride Film Growth 27 E Mr»= ^ * EB-<I> Figure 3.14: Schematic illustration of occupied density of states and corresponding energy distribution curve revealing the bound valence band and a narrower core level, obtained by photoemission. distribution curves (EDC) are obtained to study the valence band and the core level structures of the fluoride/semiconductor samples. EDC is obtained by scanning the kinetic energy of the photoelectrons with photon energy fixed. It maps the occupied density of states as illustrated in Fig. 3.14. Absorption edges of the deep lying levels are studied by total electron yield measurements in which the photon energy is scanned while the intensity of the total emitted photoelectrons is measured. The film coverage at the initial stage of the film growth is determined by angle de-pendent photoemission spectroscopy. The fraction of the substrate area 7, covered by a film of thickness t is determined from the film/substrate photoemission intensity ratio given by [29]: If {9) If 7 [ l - e - « M ( g / ) i n t f ] 1,(6) If (1 - 7) + 7e-W*)sin0] 1 • ) where If,s(9) are the intensities of the film (f) and the substrate (s) signals at the escape angle 9, J~ s are the intensities from an infinite film (f) and an infinite substrate (s), Chapter 3. Initial Stage of Fluoride Film Growth 28 X(EftS) are the inelastic mean free path in the film at the kinetic energy of the film peak EjyS. The fractional coverage 7 and film thickness t are obtained by fitting Eqn. 3.7 to the plot of If(6)/Is(6) vs. l/sin0. The localized 4f levels of rare-earth ions in the rare-earth trifluorides are determined using resonant photoemission spectroscopy. They are otherwise difficult to locate because of their overlap with fluorine valence bands. An enhancement of photoemission occurs when there are two or more emission processes having the same final states. For example, in the 4d-4/ transitions in the Er ions in ErF 3 , one of the autoionization processes is: 4d 1 0 4/ u -»• 4d 94/ 1 2 4d 1 04/ 1 0 + e" (3.8) It has the same initial and final state as the direct emission process: 4d 1 0 4/ u -> 4d 1 04/ 1 0 + e" (3.9) When the photon energy has a same energy as the transition 4d 1 0 4/ n —» 4d 94/ 1 2, a resonance occurs and there will be an enhancement of the photoemission because of the extra autoionization process in addition to the direct process. A series of resonant scans are used to locate the positions of the localized 4f levels. It was also used to study the valencies of Er ions at the interface of ErF 3 /GaAs(l l l ) samples. For ErF 3 , the resonance is observed near the 4d absorption edge . The Er 4f levels in the Er ions are obtained by taking the difference between the valence band spectra taken at the resonant photon energy (resonance) and at the photon energy just below the resonant photon energy (non-resonance). 3.2 Surface Morphology Photoemission spectra of thin ErF 3 and LaF 3 films grown on the (111) surface of GaAs and InP substrates are shown in Fig. 3.15, 3.16 and 3.17. The photoelectron intensities Chapter 3. Initial Stage of Fluoride Film Growth 29 300 Binding Energy (eV) Figure 3.15: Photoemission spectra of an ErF 3 /GaAs( l l l )B sample taken after the in-dicated annealing temperatures showing the film and the substrate peaks. were normalized using the intensities of the incident photons. The film and the substrate peaks are observed as indicated in the figures. The intensities of the film peaks decreased while the substrate peak intensities increased with increasing annealing temperature for all the samples. Above about 500°C, sample temperatures were measured by infrared pyrometer with an estimated accuracy of ±20°C. Sample temperatures below 500°C were estimated by an extrapolation from high temperatures of a log-log plot of the temperature measured by pyrometer as a function of the heater current [30]. Chapter 3. Initial Stage of Fluoride Film Growth 30 50 40 30 20 10 0 Binding Energy (eV) Figure 3.16: Photoemission spectra of a LaF 3 /GaAs(l l l ) sample taken after the indi-cated annealing temperatures. Chapter 3. Initial Stage of Fluoride Film Growth 31 Figure 3.17: Photoemission spectra of the LaF 3 / InP(l l l )B sample taken after the indi-cated annealing temperatures. Chapter 3. Initial Stage of Fluoride Film Growth 32 Table 3.3: Film/substrate photoemission peak intensity ratios for thick film and bare substrate obtained from measurements. ErF 3 /GaAs( l l l )B I?2p/(I£a3d + LaF 3 /GaAs(l l l )B If2v/I%u 3.5 LaF 3 / InP(l l l )B IfJI^u 1-6 Angle dependent spectroscopy was performed to obtain the film thickness and the fractional coverage. The film/substrate photoemission intensity ratios If(9)/Is(9) as a function of l /s in0 for the ErF 3 /GaAs(l l l )B, LaF 3 /GaAs(l l l )B and LaF 3 / InP( l l l )B samples are shown in Fig. 3.18. The annealing temperature for each sample is indicated in the figure. The film thickness t and the fractional film coverage 7 are determined using the the film/substrate intensity ratio in Eqn. 3.7. The calculated intensity ratio are shown by solid lines in Fig. 3.18. The values of intensity ratios J£°/IJ° for the infinite materials used in the calculations were determined from the intensities of a thick film and a bare substrate. They are listed in Table 3.3. An inelastic mean free path of A = 1 nm at kinetic energy of 50 eV [25] was used for the fluoride films. The horizontal error bars in the figure correspond to the angular range subtended by the photoelectron detector. The film thickness and the fractional coverage obtained from the angle dependent scans for each sample are summarized in Table 3.4. The fractional coverage obtained from the angle dependent scans are consistent with the complete coverage of the substrates by the fluoride films upon deposition. As the samles are annealed, the film thickness decreases. Up to the monolayer coverage i.e. the thickness ~ 0.3 nm, the samples stay covered. The result for the LaF 3/InP sample shows that the further annealing Chapter 3. Initial Stage of Fluoride Film Growth 33 T = 580°C t = 0.29 n CO (/) _< + S 2 -CO O - ± 20 15 T3 •E 10" Q. CM .-• LL 5 ErF 3/GaAs(111)B Y=1 T = 600°C t = 1.5 nm LaF 3/GaAs(111)B = 430°C t = 0.96 nm Y= 0.94 LaF 3/lnP(111)B 3 1 / sin e Figure 3.18: Film/substrate intensity ratio vs. l /s in0 for the ErF 3 /GaAs( l l l )B , LaF 3 / GaAs(l l l )B and LaF 3 / InP(l l l )B samples obtained using angle dependent photoemis-sion spectroscopy. The annealing temperatures and the film thickness for each sample are indicated. The solid lines are the intensity ratio calculated using the expression for the film/substrate intensity ratio in Eqn. 3.7 using the values of the fractional coverage 7 indicated. The error bars correspond to the angle subtended by the photoelectron energy analyser. Chapter 3. Initial Stage of Fluoride Film Growth 34 Table 3.4: Film thickness t and the range of the fractional coverage 7 obtained by angle dependent photoemission spectroscopy for the ErF 3 and LaF 3 films grown on GaAs(l l l )B and InP(l l l )B substrates at each annealing stage. annealing temperature T thickness t coverage 7 (°C) (nm) 470 1.4 ±0 .2 0.9-1.0 ErF 3 /GaAs( l l l )B 540 0.3 ±0 .1 0.9-1.0 580 0.3 ±0 .1 0.9-1.0 LaF 3 /GaAs(l l l )B 600 1.5 ±0 .2 0.98- 1.0 370 1.0 ±0 .1 0.98-1.0 LaF 3 / InP( l l l )B 495 0.3 ±0 .1 0.98- 1.0 530 0.3 ±0 .1 0.5 - 0.6 results in a decrease in coverage. This suggests that the fluoride films re-evaporate rather uniformly without exposing the substrates up to the monolayer coverage without forming 3D islands. This is expected since the surface energy of the fluorides are lower than that of the semiconductor substrates. 3.3 Formations of Chemical Bonds at the Film/Substrate Interface The formation of chemical bonds at the rare-earth trifluoride/III-V semiconductor inter-face are studied by photoemission spectroscopy. Overview spectra of the LaF 3 /GaAs( l l l )B and LaF 3 / InP( l l l )B thin film samples in Fig. 3.16 and 3.17 showed some small com-ponents developing at the lower binding energy of the fluorine (F) 2p peaks which are usually the sign of chemical reactions at the interface between the film and the substrate. To further investigate the change in electronic structures of the samples, the core level spectra of a LaF 3 /GaAs(l l l )B sample are closely examined. Photoemission spectra showing the the substrate (Ga 3d, As 3d) and film (La 4d) Chapter 3. Initial Stage of Fluoride Film Growth 35 core levels for a LaF 3 /GaAs(l l l )B sample with LaF 3 film thickness of 2 nm are shown in Fig. 3.19 to 3.21. The relative thickness of the LaF 3 film is measured by quartz thickness monitor (see Fig. 2.5). The relative thickness was corrected by using the film thickness of LaF 3 films which were determined by angle dependent photoemission spectroscopy. The spectra are taken after the sample was annealed for 1 min. at the temperatures indicated in the figures. The temperatures of the samples were measured by an infrared pyrometer through a view port with an estimated accuracy of ±20°C. No chemically shifted components are detected in the spectra of As 3d and Ga 3d core levels. We interpret the overall shift of the Ga 3d peak towards a lower binding energy as the result of a Fermi level shift. Photoemission intensity of the Ga 3d core level as well as the La 5p core levels in Fig. 3.19 decreased with annealing. On the other hand, the intensity of the As 3d core level increased with annealing. The decrease of the La 5p level intensity and an increase in As 3d core level intensity is an indication that the fluoride thin film is evaporating as has been shown in Section 3.2 by angle dependent photoemission spectroscopy. The ratio of the Ga 3d to As 3d intensities as a function of annealing temperature is plotted in Fig. 3.22. The ratio of Ga 3d to As 3d photoemission intensities decreases with increasing annealing temperature. We have also observed a decrease in the intensity of F 2p peaks with increasing temperature. We interprete this loss of fluorine and the decrease in the Ga/As ratio as being due to the formation of volatile GaF x molecules with annealing. Some chemically shifted components develop in the La 4d core levels in Fig. 3.21 as the sample is heated to higher temperatures. To resolve the components present in the La 4d core levels, a mixed Gaussian-Lorentzian function in Eqn. 2.1 is fitted to the spectrum taken after the 600°C anneal and is shown in Fig. 3.23. The solid line in the figure is the fit of the function and the dashed lines are the two chemically shifted components separated by 1.5 eV. The component at the lower binding energy is labelled, La 1 and Chapter 3. Initial Stage of Fluoride Film Growth 36 Figure 3.19: Photoemission spectra for the Ga 3d and La 5p core levels from a LaF 3 /GaAs( l l l )B sample of film thickness 2 nm after being annealed for 1 min at the temperatures indicated. Chapter 3. Initial Stage of Fluoride Film Growth 37 Figure 3.20: Photoemission spectra for the As 3d core levels from a LaF 3 /GaAs( l l l )B sample with film thickness 2 nm after being annealed to the temperatures indicated. Chapter 3. Initial Stage of Fluoride Film Growth 38 160 140 H .-§120-c aTlOO "(/> a3 80 1 60 E I 40 204 La 4d LaF q / GaAs(111 )B / \\ R T f \ \ 540 °C ^ ^ ^ V V 600 °C \ 620 °C , f \640 °C 660 °C 118 116 114 112 110 108 106 104 Binding Energy (eV) Figure 3.21: Photoemission spectra of La 4d core levels from a LaF 3 /GaAs( l l l )B sample with film thickness 2 nm. The annealing temperatures are indicated. The two peaks correspond to La 4d 3/ 2 and La 4d5/2 core levels which are split by spin-orbit splitting. Chapter 3. Initial Stage of Fluoride Film Growth 39 7-6-5-• D • CO c/> _< 4-3d / 3-CO _ o • 2-1 -0-LaF 3/GaAs(111)B 600 610 620 630 640 650 Annealing Temperature (°C) 660 Figure 3.22: The Ga 3d to As 3d photoemission intensity ratio as a function of annealing temperature for a LaF 3 /GaAs(l l l )B sample with film thickness 2 nm. A decreace in the intensity ratio with annealing was observed. The decrease in the Ga/As intensity ratio as well as a loss of fluorine atoms with annealing suggest a formation of volatile GaF^ molecules with annealing. Chapter 3. Initial Stage of Fluoride Film Growth 40 Figure 3.23: Fit of the Gaussian-Lorentzian function to the La 4d core levels from the LaF 3 /GaAs( l l l ) sample after being heated to 600°C. The chemically shifted components, labelled La 1 and La 2 1.5 eV apart are present. The La 1 component is interpreted as being originated from the bulk La-F bonding and the La 2 component as from the interfacial La-As bonding. Chapter 3. Initial Stage of Fluoride Film Growth 41 the shifted component, La 2. Another component present in the La 4d spectrum taken after the 660°C anneal is labelled La 3. We interpret that the component at the lowest binding energy, La 1 originates from the La-F bond in the bulk LaF 3 film. The second component, La 2 is likely the interfacial component as a result of the formation of chemical bonds at the interface. The La atoms are probably bonded to the As atoms at the interface, since GaAs(l l l )B substrate is As terminated. In the overview spectra of this sample after the 640°C anneal, no fluorine peaks are detected indicating that the LaF 3 molecules are dissociated. The last component La 3 is attributed to the chemisorbed La atoms of the dissociated LaF 3 molecules on the substrate surface. Two configurations can be considered at the interface. The first configuration is when the fluorine atoms are situated right above the As atoms, the sites occupied by Ga atoms in the bulk GaAs. The fluorine atoms are bonded to the As atoms. The La atoms are situated above the Ga atoms. The schematic illustration of the configuration at the interface is shown in Fig. 3.24. In this configuration, the chemical shift in the La 4d core level can occur indirectly through the electron transfer from arsenic (As) to fluorine (F) atoms. In the second model, the La atoms are situated directly above the As atoms. The sites above the Ga atoms are then occupied by the fluorine atoms as illustrated in Fig. 3.25. In this model the chemical shifts in the La 4d core level occur as a results of formation of chemical bonds between arsenic (As) and lanthanum (La) atoms. We expect that the second model in Fig. 3.25 is more plausible of the two models because of the following reasons. Since the La atoms are more positively charged ones of the ionic LaF 3 molecules, they are most likely bonded to the As atoms which are more electronegative than the Ga atoms. We have observed a loss of fluorine atoms and a decrease in the intensity ratio of Ga 3d to As 3d levels with annealing suggesting a formation of volatile GaF x molecules. This is also consistent with the second model Chapter 3. Initial Stage of Fluoride Film Growth 42 where a loss of fluorine atoms are involved upon the formation of As-La bonds. The chemical shift of the La 4d levels is also in agreement with the second model, since the electron transfer in the second model directly involves the La ions. 3.4 Positions of E r 4f levels in E r F 3 / G a A s ( l l l ) B The positions of Er 4f levels in the Er ions in ErF 3 /GaAs( l l l )B samples are studied using resonant photoemission spectroscopy. The resonance is an enhancement of emission due to the interference between two or more emission processes having the same final states as described in Section 3.1. For ErF 3 , the resonance is observed near the Er 4d absorption edge due to the E r 3 + 4/ 1 1 ->• 4/ 1 0 transitions. The photon excitation energies where the resonance occurs are determined from a total electron yield spectrum of the Er 4d absorption edge. Typical total yield spectrum from the Er 4d absorption edge of an ErF 3 /GaAs( l l l )B sample is shown in Fig. 3.26. The peaks in the spectrum are due to the resonance involving the 4d-4/ transition in the E r 3 + ions. To locate the binding energy positions of E r 3 + 4/ 1 1 levels, the photoemission spectrum is taken with one of the resonant photon excitation energies. Next the photoemission spectrum with the non-resonant photoexcitation energy which is located just below the 4d absorption edge, is obtained. The intensities of the photoemission spectra are normalized by the incident flux of the Synchrotron beam. Since the enhancement of the photoemission intensity is due to the E r 3 + 4/ 1 1 —> 4/ 1 0 transition, the difference in intensity between the resonance and the non-resonant spectra must be from the E r 3 + 4/ 1 1 —>• 4/ 1 0 transition. Typical resonant, non-resonant and difference spectra of an ErF 3 /GaAs( l l l )B sample are shown in Fig. 3.27. The different spectra of the ErF 3 /GaAs( l l l )B samples of two film thicknesses are shown in Fig. 3.28. The resonant and non-resonant spectra were taken at 174 and 161 eV repectively for both samples. The thicknesses indicated in the Chapter 3. Initial Stage of Fluoride Film Growth 43 Figure 3.24: Schematic illustration showing a configuration at the interface of the LaF 3 /GaAs( l l l ) samples: Model 1. In this model, the fluorine atoms overlap with the As atoms. La atoms are situated above the Ga atoms. The figure shows the view along the c-axis of LaF 3 or the [111] direction of the GaAs substrate (a) and the view along the [110] direction of the GaAs substrate (b). Only the first layer of the one of the LaF 3 unit cell is shown in (a). The numbers indicated are the positions of the fluorine atoms along the c-axis in (a). Chapter 3. Initial Stage of Fluoride Film Growth 44 O O O O O O O O O As Figure 3.25: Schematic illustration showing a configuration at the interface of the L a F 3 / G a A s ( l l l ) samples: Model 2. In this model, the La atoms are situated directly above the As atoms. The sites above the Ga atoms are occupied by the fluorine atoms. The figure shows the view along the c-axis of LaF 3 or the [111] direction of the GaAs substrate (a) and the view along the [110] direction of the GaAs substrate (b). Only the first layer of the one of the LaF 3 unit cell is shown in (a). The numbers indicated are the positions of the fluorine atoms along the c-axis in (a). Chapter 3. Initial Stage of Fluoride Film Growth 45 ' T ' I 1 I 1 I ' I 1 I 1 1 160 165 170 175 180 185 190 Photon Energy (eV) Figure 3.26: Total electron yield spectra of Er 4d absorption edge (N edge) from a ErF 3 /GaAs( l l l )B sample. The peaks at hu = 163.0, 164.7, 166.9, 170.8 and 174.0 eV are due to the 4d-4f resonance of the E r 3 + ions. Chapter 3. Initial Stage of Fluoride Film Growth 46 100 1—1—I—1—I—1—I—1—I—1—I—1—I—1—I—1—I—1—I—1—I 6 8 10 12 14 16 18 20 22 24 26 Binding Energy (eV) Figure 3.27: Resonant (A), non-resonant (B) and the difference spectra of the Er 4f levels in the Er ions for the ErF 3 /GaAs( l l l )B sample with film thickness 2 nm. The excitation energies hu are indicated in the figure. Chapter 3. Initial Stage of Fluoride Film Growth 47 ^ 60-co •*—• E r F 3 / G a A s ( 1 1 1 ) B : Er 4f A a ' c _Q t = 1 nm / \ 03, 40-> ^ -»—» "co f~ 0 — 20-T3 CD N t = 0.5 nm / \ . b 05 o o-I 1 1 1 1 1 1 1 1 1 1 0 5 10 15 20 25 Binding Energy (eV) Figure 3.28: Difference spectra of the Er 4f levels in the E r 3 + ions for the ErF 3 /GaAs( l l l )B samples as in Fig. 3.27 for film thicknesses (a) 1 nm and (b) 0.5 nm. The resonant and non-resonant spectra were taken at 174 and 161 eV repectively for both samples. Chapter 3. Initial Stage of Fluoride Film Growth 48 figure are determined using angle dependent photoemission spectroscopy. In the 1 nm sample shown in Fig. 3.28 (a), two peaks separated by 4.8 eV are observed. The peaks are the results of the exchange splitting of E r 3 + 4f levels. The E r 3 + 4fn level has a ground state configuration of (4/ f) 7(4/ i) 4 with total spin S = 3/2. The final state configuration after the removal of an electron can be either (4/ t) 6(4/ i)A, S = 1 or (4/ t) 7(4/ I) 3 , 5 = 2. Since the 4/ t electron has a larger binding energy than the 4/ 1 electron, the peak at the higher binding energy in the difference spectrum of the 1 nm sample in Fig. 3.28 corresponds to the transition (4/ t) 7(4/ I) 4 -» (4/ t) 6(4/ I)4, whereas the smaller peak at the lower binding energy corresponds to the transition, (4/ f )7(4/ I) 4 ->• (4/ t) 7(4/ ! ) 3 . The ratio of the photoemission intensity of the transition (4/ t) 7(4/ i ) 4 -+ (4/ t) 6(4/ I) 4 to the transition (4/ f) 7(4/ | ) 4 -+ (4/ f) 7(4/ i ) 3 transition is expected to be approximately 7:4 since there are seven electrons to choose from in the former transition whereas there are only three electrons to choose from for the latter transition. The ratio between the two photoemission peaks were approximately 7 : 1 instead of 7 : 4. The discrepancy may be due to the change in experimental conditions between the acquisition of resonant and the non-resonant spectra, such as the chamber pressure and the angle or position of incident beam relative to the sample. There could also be more steps involved in the resonant photoemission mechanism than the simple transition process described above. In the 0.5 nm sample, the E r 3 + 4 / 1 1 resonant peak has been shifted to a lower binding energy as compared to the peak observed in the 1 nm sample. In the overview spectra of the same sample, the fluorine peaks were absent. Hence we interpret that the resonant photoemission intensity is originated from the Er ions of the dissociated ErF 3 molecules chemisorbed on the GaAs surface. Chapter 3. Initial Stage of Fluoride Film Growth 49 3.5 Band Alignments The relative positions of the electronic energy bands at the interface between the semi-conductor and the fluoride film were obtained by linear extrapolations of the sharp edges in the valence band photoemission spectra. Determining the band alignments is impor-tant in designing device structures. The band alignments were determined with films which were sufficiently thin that the substrate spectrum can be measured at the same time as the valence band of the films. An example of the linear extrapolation is shown in Fig. 3.29 for a LaF 3 /GaAs(l l l )B sample. An average of positions of the measurements for three samples for each system is taken. There were 6 to 8 photoemission spectra for each sample. The estimated accuracy of the relative positions is ±0.3 eV. The standard deviations of the measurements of three samples were less than or equal to 0.3 eV. The measured positions of the F 2p derived valence band in the fluoride films relative to the semiconductor valence band maxima are shown schematically in Fig. 3.30. Posi-tions of E r 3 + 4f levels determined by the resonant photoemission spectroscopy are also shown. Two peaks correspond to the exchange splitting of the E r 3 + 4f levels. The energy gaps between the conduction band and the valence band are 1.42 eV for GaAs, 1.35 for InP and 9.9 eV for LaF 3 [26]. 3.6 Summary The initial stage of rare-earth trifluoride film growths on III-V semiconductors was inves-tigated by photoemission spectroscopy. The angle dependent photoemission spectroscopy results were consistent with the complete coverage of semiconductor substrates by LaF 3 and ErF 3 films. We have also shown by angle dependent photoemission spectrosocpy that the LaF 3 and ErF 3 re-evaporate rather uniformly upon annealing without exposing the substrates. A decrease of Ga and fluorine atoms upon annealing suggests a formation Chapter 3. Initial Stage of Fluoride Film Growth 50 0 LaF~ / GaAs(111)B t=12A 3 2 1 0 i I 1 1 1 1 ' 1 1 1 • r ..GaAs VB edge 12 10 8 6 4 2 0 6.7 eV 16 14 12 10 8 6 4 Binding Energy (eV) Figure 3.29: Photoemission spectrum of a LaF 3 /GaAs(l l l )B sample of thickness 1.2 nm showing the GaAs valence band and the fluorine 2p valence band. The dashed lines are the linear extrapolation to determine the relative position of the valence band edges. The GaAs valence band edge is shown enlarged in the inset. Chapter 3. Initial Stage of Fluoride Film Growth 51 InP LaF 3 GaAs ErF 3 1.42 eV j CB t 1.52 eV | CB T 6.6 eV \ t VB t 6.2 eV 1 9.9 eV f 6.7 eV t VB iiil 1st! Figure 3.30: Interfacial band alignments in the LaF 3 / InP(l l l ) , LaF 3 /GaAs( l l l ) and ErF 3 /GaAs( l l l ) systems determined by linear extrapolations of the sharp edges in the valence band photoemission spectra with an estimated accuracy of ±0.3 eV. Positions of E r 3 + 4f levels are also shown. Two peaks correspond to the exchange splitting of the E r 3 + 4f levels. Chapter 3. Initial Stage of Fluoride Film Growth 52 of volatile GaF x molecules. The presence of La and Er atoms on the substrate surface upon annealing above 600°C, indicate that some fluoride molecules dissociate and form volatile GaF x molecules leaving the La and Er atoms behind on the substrate surface. From the core level photoemission spectroscopy, we have observed the formation of chemical bonds between the La and the substrate atoms. The loss of Ga and F atoms with annealing as well as the La 4d core level shifts are consistent with the interface bonding model in which the La atoms are chemically bonded to the As atoms at the interface. The band alignments or the relative positions of the film and the substrate valence band edges are determined by photoemission spectroscopy of the valence band regions. The positions of Er 4f levels in ErF 3 on GaAs were also determined by resonant pho-toemission spectroscopy. The relative positions of valence band edges at the insula-tor/semiconductor interface are useful in designing electronic or optoelectronic devices. Chapter 4 Structural Properties The bulk structures of fluoride films grown on semiconductors is one of the important factors which affect the subsequent growth of other materials on the fluoride films. The growths of semiconductors or other materials on fluorides are important in applications such as integrated devices and high reflectance mirrors. Our objective in this chapter is to characterize the structural properties of the fluoride films such as crystal orientations, strains and crystallinity. We have characterized the structural properties of rare-earth trifluoride films of thickness between 10 and 400 nm grown on GaAs and InP using X-ray diffraction. The crystal orientation of the fluoride films are first determined by X-ray diffraction using a powder X-ray diffractometer. The strains in the rare-earth fluoride films grown on GaAs and InP are measured by high resolution X-ray diffraction (HRXRD). The crystallinity of LaF 3 films are studied using the rocking curve measurements. From the rocking curve measurements, we determine the lateral coherence lengths in the LaF 3 films grown on GaAs and InP. The X-ray diffraction measurements of the LaF3/semiconductor samples were performed using a Cu Ka source with powder and four-crystal diffractome-ters (BEDE 200). The LaF 3 and ErF 3 films are grown on GaAs and InP substrates using a high temperature effusion cell as described in Chapter 2. The LaF 3 crystal has a trigonal structure with space group P3cl (D|d) and has lattice constants of a = 7.185 A and c = 7.351 A [12]. The trigonal a x a face of the LaF 3 crystal has the same symmetry as the hexagonal (111) face of GaAs or InP as shown in 53 Chapter 4. Structural Properties 54 Fig. 4.31 (a). In this configuration, the trigonal a x a unit cell of LaF 3 corresponds to \/3 x \/3 of the underlining hexagonal lattice of semiconductors or \/6a/2 x y/6a/2 of semiconductors where a is the lattice constant of the substrate. The lattice mismatch at room temperature in this configuration is +3.8 % for LaF 3 /GaAs(l l l ) and —0.04 % for LaF 3 / InP( l l l ) . It has been shown by Sinharoy et al. [5] using LEED and RHEED that the trigonal ax a face of the LaF 3 crystal is aligned parallel to the hexagonal (111) face of GaAs or the c-axis of LaF 3 is oriented parallel to the [111] axis of GaAs as in Fig. 4.31 (a). Due to the structural similarity, we expect the LaF 3 films on InP(l l l ) to be oriented in the same manner. The crystal structure of ErF 3 is orthorhombic at room temperature. A LEED study of GdF 3 deposited on Ge(l l l ) and GaAs(ll l)B substrates by Jenkins et al. [10] showed that the axe plane of orthorhombic GdF 3 crystals are aligned parallel to the (111) plane of the substrates or the 6-axis of the film is oriented parallel to the [111] axis of the substrate. The LEED pattern of a GdF 3 film 1.8 nm thick deposited on a GaAs( l l l )B substrate showed a symmetry which coincides with an orthorhombic mesh rotated by 120 and 240° along the [010] axis [10]. Therefore we expect the 6-axis of orthorhombic ErF 3 crystals to be oriented parallel to the [111] axis of the GaAs or InP substrates as well, as shown in Fig. 4.31 (b). In this configuration, the lattice mismatch of ErF 3 with GaAs at room temperature is —8.6 % along the a-axis and +9.0 % along the c-axis. The lattice mismatch of ErF 3 with InP is —12 % along the a-axis and +5.4 % along the c-axis. There is a large difference in thermal expansion coefficient between GaAs or InP and LaF 3 . At 300 K, the thermal expansion coefficients are 16 x 10~6 K _ 1 along the a axis for LaF 3 , 5.7 x 10~6 K " 1 for GaAs and 4.75 x lO" 6 K " 1 for InP. Chapter 4. Structural Properties 55 GaAs (111) o o o a o \ o Figure 4.31: Plan view of the (111) plane of GaAs (or InP) substrate showing the struc-tural matching with (a) LaF 3 and (b) ErF 3 assuming perfect lattice matching. The circles indicate the substrate atoms. The lines in (a) show the trigonal ax a plane of LaF 3 which matches \/6a/2 x y/Qa/2 of the substrate where a is the lattice constant of the substrate. The lines in (b) show the orthorhombic axe plane of ErF 3 which matches d x \/3d of the substrate. Six configurations are possible in (b): axe planes rotated by 120° and 240° to each other as shown in the figure and their mirror planes. Chapter 4. Structural Properties 56 4.1 Crystal Orientations A low energy electron diffraction (LEED) pattern of a LaF 3 film deposited on a GaAs( l l l )A substrate is shown in Fig. 4.32. The LaF 3 films for the LEED measurements were grown by the same method as the samples grown for photoemission experiments as described in Chapter 2. The thickness of the film was 1.5 nm as measured by a quartz thickness monitor. The LEED pattern in Fig. 4.32 shows two different structures. The first is the ( l x l ) pattern of the outer most dots which are related to the atomic spacings of the (111) hexagonal plane of the GaAs substrate. The second is the (\/3 x \/3) superstruc-ture of inner dots, which is associated with the lattice constant of the LaF 3 trigonal basal plane. The result shows that the (111) plane of the GaAs substrate is oriented parallel to the trigonal a x a plane of LaF 3 film as shown in Fig. 4.31. The orientations of the thicker films of LaF 3 and ErF 3 grown on GaAs and InP were also examined using a powder X-ray diffractometer. Fig. 4.33 shows 6-26 scans for the LaF 3 crystalline powder, LaF 3 films on GaAs(l l l )A and InP(l l l )B substrates. Strong (00/) type Bragg peaks in the scans of both LaF 3 films on GaAs and InP show that the films are single crystals and that the c-axis of the LaF 3 film is oriented parallel to the [111] axis of the substrates. The trigonal a x a plane of the LaF 3 crystal is thus aligned parallel to the (111) hexagonal face of the substrates as expected from the interfacial structural matching of this configuration. The result is consistent with the LEED and RHEED studies of the LaF 3 /GaAs( l l l )A system by Sinharoy et al. [5]. In the 6-26 scans of ErF 3 films grown on GaAs(l l l )A shown in Fig. 4.34, (0/0) type peaks as well as the (///) type peaks of the GaAs substrate were observed. This indicates that the 6-axis of the ErF 3 film is oriented parallel to the [111] axis of the GaAs substrate, i.e. the orthorhombic axe plane of ErF 3 is oriented parallel to the (111) plane of GaAs as shown in Fig. 4.31. This result agrees with the LEED study of GdF 3 deposited on Ge(l l l ) and Chapter 4. Structural Properties 57 1 X 1 Figure 4.32: L E E D pattern of a 1.5 nm thick LaF 3 film deposited on a GaAs ( l l l ) B sub-strate with the electron energy of 113.4 eV. It shows two different L E E D structures. The first is the ( l x l ) pattern of the outer most dots which are related to the atomic spacings of the ( l l l ) B hexagonal plane of the GaAs substrate. The second is the (\/3 x \/3) superstructure of inner dots, which is associated with the lattice constant of the LaF 3 trigonal basal plane. Chapter 4. Structural Properties 58 20-15-10-5-'c/T 0-"E 30-13 20-i i i •*—> 10-"to c CD -•—' 0-c 80-60-40-20-0-(002) (110) LU o n ) (300) (112) LaF 3 powder (113) (302) (221) (004f LaF 3 (002) GaAs (111) L a F 3 / G a A s ( 111 ) A LaF 0 (004) _ L _ GaAs (222) LaF 3 (002) InP (111) LaF q / lnP(111 )B LaF, InP 3 (222) (004) L _ 20 —r— 30 40 29 (°) —r— 50 60 Figure 4.33: Powder X-ray diffraction scans of (top) the LaF 3 crystalline powder, (center) LaF 3 /GaAs( l l l )A and (bottom) LaF 3 / InP(l l l )B samples. The strong (001) type LaF 3 peaks along with (III) type InP peaks indicate that the c-axis of the LaF 3 film is aligned parallel to the (III) direction of the substrate. Chapter 4. Structural Properties 59 6000 ErF 3/GaAs(111)A 5000 H GaAs «T 4000-^ (111) • | 2000 J ErF 3 GaAs (040) (222) L ioooH 0 4 0 20 40 60 80 28 (°) Figure 4.34: Powder X-ray diffraction scans of a ErF 3 /GaAs( l l l )A sample with the film thickness t = 41 nm. The (0/0) type ErF 3 peaks along with (///) type GaAs peaks are observed indicating that the 6-axis of the ErF 3 film is aligned parallel to the (///) direction of the substrate. GaAs(l l l )B substrates by Jenkins et al. [10]. We have also grown LaF 3 films on the (100) face of a GaAs substrate. A 6-26 scan of X-ray diffractions using a powder X-ray diffractometer is shown in Fig. 4.35. The top figure shows (002) and (004) peaks of the GaAs substrate. The bottom figure is an enlargement of the top figure. The scan only shows very small LaF 3 peaks when aligned to the (001) direction of the substrate. This indicates that the film is polycrystalline. We do not expect LaF 3 films to grow as single crystals on (100) surfaces of GaAs substrates, since the cubic (100) face of the semiconductor does not have a same symmetry as the trigonal structure of LaF 3. Chapter 4. Structural Properties 60 10 20 30 40 50 60 70 80 90 2 0 ( ° ) Figure 4.35: Powder X-ray diffraction scans of a LaF3/GaAs(100) sample. The top figure shows (002) and (004) peaks of the GaAs substrate. The marks "G" besides indices indicate that peaks are those of substrates'. The bottom is a blow up of the top figure. The scan only shows small LaF 3 peaks suggesting that the film is polycrystalline. Chapter 4. Structural Properties 61 4.2 Strains High resolution X-ray diffraction was performed on the LaF 3 and ErF 3 films grown on GaAs and InP to study the strains in the fluoride films. Typical 9-29 scans for the LaF 3 and ErF 3 films grown on GaAs and InP are shown in Fig. 4.36. The Bragg peaks of the films and the substrates are observed in the scans as indicated in the figure. To obtain the in-plane strains e\\ or the strains parallel to the film/substrate interface (a x a plane of LaF 3), the strain perpendicular to the interface e± or the strain along the c-axis of LaF 3 was first determined from the separation between the (111) GaAs and (002) LaF 3 peaks. The values of the lattice constant c = 7.351 A for LaF 3 [12] and a = 5.6534 A for GaAs substrate are used in the calculation. The measurements of the lattice constant are performed at two different azimuthal angles for each sample to ensure that the shift of the film peak is not due to the tilting of the c-axis of LaF 3 with respect to the [111] axis of the substrate. For an isotropic stress in the a x a plane, the relationship between the in-plane strain £|| and the perpendicular strain e± is given by [37]: £|1 = ~2%£L ( 4 ' 1 0 ) where C 3 3 and C i 3 are the elastic constants of theLaF 3 film, C i 3 = 5.9 • 1010 N m - 2 and C 3 3 = 22.2 • 1010 N m~ 2 [38]. Hexagonal symmetry is assumed as was suggested by Laiho et al [38]. The in-plane strains in the LaF 3 films grown on GaAs(l l l )A substrates were tensile for the films of thickness less than 200 nm. This is not as expected if the growth is simple pseudomorphic, as the lattice spacing of the trigonal face of LaF 3 is larger than that of the hexagonal (111) face of GaAs. The in-plane tensile strain e\\ is plotted as a function of film thickness in Fig. 4.37. The in-plane strain e\\ decreases with increasing film thickness. Chapter 4. Structural Properties 62 S 10U1 104-d 103-J ErF3/GaAs(111)B t = 41nm GaAs(111) ErF 3 (020) 14.0 Figure 4.36: High resolution X-ray diffraction scans of the (a) LaF 3 /GaAs( l l l )A, (b) LaF 3 / InP( l l l )B and ErF 3 /GaAs( l l l )A samples. Chapter 4. Structural Properties 63 Tensile strain has also been observed in the Rutherford back scattering (RBS) study of the CaF 2 /S i ( l l l ) system [39]. In the study, the tensile strain was attributed to the large difference in thermal expansion coefficients between CaF 2 (19 x 10 - 6 K _ 1 ) and Si (2.5 x 10 - 6 K _ 1 ) . The large difference in thermal expansion coefficients also exists between LaF 3 and GaAs. At the growth temperature of 600 °C, the lattice mismatch between LaF 3 and GaAs increases to +4.5 % from the RT value of +3.8 %. In Section 4.3, we will show that LaF 3 films on semiconductors have columnar struc-tures. The LaF 3 films have defects separating columns of coherent crystals. The sepa-rations between defects are found to be equal to the defect spacings required to accom-modate the lattice mismatch at the growth temperatures. This suggests that strains in the LaF 3 films caused by the lattice mismatch between the fluoride and the substrate are relaxed at the growth temperature by formation of columnar defects. Between the columnar defects, the fluoride crystals are coherent. We hence expect that the film lattice is registered with the substrate lattice at the film/substrate inter-face. As the system cools, the LaF 3 films have tendencies to contract more than the semiconductor substrate due to their larger thermal expansion coefficients. However, if the columnar defects are pinned at the interface, since the lattices are registered at the interface, the fluoride films are forced to contract according to the thermal contraction of the substrate. This differential thermal contraction can cause the tensile strains in the LaF 3 films on GaAs. As for the RBS study of CaF 2 on Si, we will analyse the residual strains in the LaF 3 film thickness using the energy balance model by Matthews et al. [40] under the assumption that the LaF 3 films are relaxed at the growth temperature through some relaxation processes. In the Matthews' model, the strains in the films are relaxed by formation of misfit dislocations by balancing the energy associated with elastic strains due to the lattice mismatch between the film and the substrate, and the energy associated Chapter 4. Structural Properties 64 0.005-0.004H 0.003H 0.002" 0.001 H 0.000H i — 50 LaF 3/GaAs(111)A LaF 3/lnP(111)B D/2B = 0.14; f = 0 . 7 % 100 150 200 Film Thickness (nm) 250 Figure 4.37: Plot of the in-plane tensile strain as a function of the film thickness for the LaF 3 film grown on GaAs(l l l )A and InP(l l l )B substrates. Chapter 4. Structural Properties 65 with the formation of dislocations accommodating the misfits. Although the type of defects in the LaF 3 films is unknown, we expect that the mech-anisms of strain relaxations in the LaF 3/GaAs system to be similar to the mechanisms described by the Matthews' model. In the LaF 3/GaAs system, the elastic strain en-ergy due to the differential thermal contraction increases with increasing film thickness. Therefore more strain relaxation processes occur in a thicker film than a thinner film. The strain relaxation processes in our system are not necessary a formation of misfit dislocations as in the Matthews' model, but can also be other defect formations or de-fect motions such as defect slips. Nonetheless, we expect the strain in the LaF 3 films to decrease with increasing film thickness as described by the Matthews' model. The in-plane residual strain £|| according to the Matthews' model is given by [40]: q i = [ - ^ ] l n 2 ( / - £ | | ) , (4.11) D ^ G0Gsb TT(GO + Gs)(1-O) In the above expression, Go, GS are the shear modulus for the film and the substrate respectively, b is the magnitude of the Burgers vector of the dislocations and o is the Poisson ratio of the film. The value of / is the lattice mismatch between the substrate and the film, if no strain relieving process occurs. The constant B for an isotropic film is given as: B = 2G0(l + o)/(l-o) (4.12) The analysis is for an isotropic film. However, since the elastic constants along the principal axes do not vary more than a order of magnitude, we expect the strains given by the analysis to be a good approximation for our LaF 3/GaAs system. The calculated in-plain strain e\\ using the Matthews' model in Eqn. 4.11 is plotted in Fig. 4.37 for the LaF 3 films on GaAs. The in-plain strain was calculated under the assumption that the LaF 3 films are relaxed at the growth temperature and they contract Chapter 4. Structural Properties 66 according to the thermal expansion coefficient of the substrate. We also assumed in the calculation that the Poisson ratio of the LaF 3 film is same as that of the substrate and that the magnitude of the Burger's vector b is b = a/2 where a is the lattice constant of LaF 3 . We used the elastic constants of GaAs and LaF 3 (D/2B = 0.14). We obtained a good agreement between the calculated in-plain strains and the measured strains. The estimated residual strain e\\ falls within 20 % of the measured residual strains. We estimated the value of / as follows. The lattice constant at the growth temperature of 600° C of the unstrained LaF 3 is a = 7.264 A according to the thermal expansion coefficient of LaF 3 . If the unstrained LaF 3 at 600°C is allowed to cool and it contracts according to the thermal contraction of the substrate then its room temperature lattice constant will be a' = 7.235 A. Thus the expected strain / in the case of no strain relaxation on cooling, is: / = (a' - a)/a = (7.235 - 7.185)/7.185 = +0.70 %, which is a tensile strain. The strains in the LaF 3 films.grown on InP(l l l )B substrates were also measured and are plotted in Fig. 4.37. No strains greater than the uncertainty in the measurements ~ 3 x 10~4, were detected. We expect that the strains in the LaF 3 films on InP to be less than those on GaAs. As we show later in Section 4.3, the columnar defects in the LaF 3 films on InP are less than that on GaAs because the lattice mismatch in LaF 3 on InP is less at the growth temperature. Therefore there are less defects pinned at the interface resulting in less strains in the films. We have calculated the strains using the Matthews' model in Eqn. 4.11 assuming that the films are unstrained at the growth temperature and contract according to the thermal contraction of the substrate. The calculated strains for LaF 3 on InP overlaps with those for the LaF 3/GaAs system, since the strains for LaF 3 on InP only differ from those on GaAs by less than 5 %. The calculated strains for LaF 3 films on InP are roughly in agreement with the measured strains. The measured residual strains fall within 20 % of the estimated strains taking the uncertainty of the Chapter 4. Structural Properties 67 measurements into account. The value of / in Eqn. 4.11 is estimated as follows. The lattice mismatch of the system at the growth temperature of 400°C is +0.41 % as compared to -0.04 % at RT. Using the same arguments for the LaF 3 /GaAs( l l l )A system, the value of expected strain / without any strain relaxation on cooling from a relaxed state at the growth temperature, for the LaF 3 / InP( l l l ) system is / = +0.46 % as compared to / = +0.7 % for the LaF 3 film on GaAs. The calculation was performed assuming the magnitude of the Burger's vector of b = a/2 where a is the lattice constant of LaF 3, and using the elastic constants of InP and LaF 3 (D/2B = 0.12) with / = 0.46. The strains in the ErF 3 films on GaAs(lll) shown in Fig. 4.36 were also calculated. The strains along the fr-axis of ErF 3 or along the direction perpendicular to the interface was calculated as e± — 0.0031 ± 0.0003 which is a tensile strain. This suggests that ErF 3 film is compressively strained along the interface. As we showed in Fig. 4.31, the lattice mismatch of ErF 3 on GaAs(ll l) along the a-axis is different from that along the c-axis. The mismatch along the a-axis is -8.6 % whereas that along the c-axis is +9.0 %. The estimation of in-plain strains corresponding to the measured perpendicular strains involves considerations of anisotropic strains along the interface. The calculation of in-plain strains for ErF 3 films on GaAs is out of scope of our study. 4.3 Crystallinity The crystallinity of the LaF 3 film was studied using X-ray rocking curve measurements. The width of the X-ray rocking curve is associated with the lateral dimension of the coherent region in the crystal [42]. A rocking curve is obtained by scanning the sample axis with detector-source angle fixed. The widths of rocking curves are associated with the lateral coherence lengths L through the relationship: L ~ 81n2/FWHM [43]. That is, Chapter 4. Structural Properties 68 narrower the widths of curves, longer the coherence lengths. Typical rocking curves of the LaF 3 (002) peaks for LaF 3 films on GaAs(l l l )A and InP(l l l )B are shown in Fig. 4.38. The rocking curves were modelled by Gaussian lineshapes. We note that the widths of the rocking curves for LaF 3 films on InP are significantly narrower than those for LaF 3 on GaAs. This indicates that the lateral coherence lengths or the sizes of coherent crystals in LaF 3 on InP are longer. This is expected, since the lattice mismatch in the LaF 3/InP system is an order of magnitude smaller than the mismatch in the LaF 3/GaAs system. The profiles of rocking curves for LaF 3 films on InP suggest that there exists more than one Gaussian peak in the curves. We were able to fit the curves with the sum of two Gaussian functions. This shows that there are regions in the films where the defects are concentrated. The fits with the two Gaussian functions are plotted Fig. 4.38. The Gaussian FWHM and the corresponding coherence lengths obtained from the rocking curves are listed in Table 4.5. The variation of the FWHM of the X-ray rocking curve and corresponding lateral coherence length with film thickness are plotted in Fig. 4.39. The lateral coherence length increases with increasing film thickness and saturates at 45-55 nm. We note that a part of data points is concentrated near the lateral coherence length 20-30 nm whereas other points are between 45 and 60 nm. This brings up the possibility that the increase in lateral coherence length can also be discontinuous. The discontinuous increase siginifies that there are two distinct regions with different defect concentrations which is consistent with the fit of two-Gaussian curves for the rocking curves of LaF 3 on InP shown in Fig. 4.38. In either case, i.e. whether continuous or discontinuous, the increase in the coherence length indicates that the concentration of defects is higher near the interface. The coherence lengths for the LaF 3 / InP(l l l )B samples are significantly longer, L x = 80-540 nm than those for the LaF 3 /GaAs(l l l )B samples, L x = 20-60 nm, consistent with the closer lattice match in the LaF 3 / InP(l l l ) system. Chapter 4. Structural Properties 69 Figure 4.38: X-ray rocking curves of the LaF3(002) Bragg peak for (a) the LaF 3 /GaAs( l l l )A and (b) the LaF 3 / InP(l l l )B samples with two different thicknesses. Solid lines in (a) are fits of Gaussian to the data. Solid lines in (b) are the fits of two Gaussian functions to the data. Dashed lines are the corresponding individual Gaussian curves for each two Gaussian curve. Chapter 4. Structural Properties 70 100 200 300 400 500 Film Thickness (nm) Figure 4.39: Variation of FWHM of the rocking curves and the lateral coherence length with film thickness for the LaF 3 /GaAs( l l l )A samples. Table 4.5: Gaussian FWHM and corresponding lateral coherence lengths L x for the LaF 3 / InP( l l l ) samples of different film thicknesses, obtained from the rocking curve measurements. FWHM are obtained using the two-Gaussian function. LaF 3 / InP(l l l )B thickness (nm) FWHM (sec) FWHM (nm"1) L (nm) 111 209 110 770 180 700 0.010 0.069 0.013 0.056 540 80 440 100 Chapter 4. Structural Properties 71 We have also performed a cross-sectional scanning electron microscopy (SEM) on a LaF 3/GaAs sample. The SEM image is shown in Fig. 4.40. The cleaved surface shows columnar structures aligned perpendicular to the interface. The columnar defect spac-ings (50-60 nm) are comparable to the corresponding lateral coherence length measured by rocking curves (47 nm) suggesting that the lateral coherence length represents the separations between the columnar defects. Columnar structures are commonly observed in polycrystalline thin film growth per-formed by physical vapor deposition (PVD) such as electron beam deposition and ion sputtering. The structure zone model popularized by Thornton [45] for sputtered films, is widely used in the PVD techniques for predicting the film morphology as a function of growth temperatures. In the structure zone model, the morphology of deposited films is determined by the ratio of the growth temperature T to the melting point of the deposited material, Tm. For growth temperature in the approximate range 0.3 <: T/Tm < 0.5, known as Zone 2, PVD films are found to have a columnar microstructure. The struc-ture results from a tradeoff between diffusive transport processes and shadowing in the presence of an incoming particle flux with a lateral component of the velocity. Due to the roughness on the surface, more particles arrives on the hills or the high surface sites than on the valleys or the low surface sites which are shadowed by the higher sites. For our LaF 3 growth, the temperature T/Tm was 873/1766 ~ 0.5 for the GaAs substrates and 673/1766 ~ 0.4 for the InP substrates. These temperature correspond to Zone 2, T/Tm >^ 0.3. Thus according to the structure zone model, one would expect a dense columnar structure in which the regions between the columns are filled with the defects. The columnar structure observed in the LaF 3 films (see Fig. 4.40) are consistent with the structure predicted by the structure zone model. In the deposition of the LaF 3 films, there is a lateral component in the velocity of arriving particles, since the incident beam of particles made an angle 30° with the surface normal. The structure zone model is Chapter 4. Structural Properties 72 Figure 4.40: Cross sectional S E M image of a L a F 3 / G a A s ( l l l ) A sample with film thick-ness t = 150 nm. A columnar structure commonly observed in thin film growths, is observed. not normally applied to the growth of epitaxial films. It is interesting that we observe a similar microstructure in our epitaxial LaF 3 films. In the present experiments, we find that the lateral size of the columns is related to the lattice mismatch. We observed that the LaF 3 films on InP which have a smaller lattice mismatch than the L a F 3 on GaAs have a longer coherent length or a larger columnar crystal size. The smaller lattice mismatch results in a lower strain in the film which allows larger coherent crystal islands to nucleate, thereby creating larger columns. From the point of view of epitaxial growth, the columnar defect structure in the LaF 3 films should be able to relieve the strain due to the lattice mismatch. In this picture, defects in the fluorides propagate perpendicular to the interface as opposed to along the interface as in the case of covalent semiconductors. The difference may be due to the fact that there are no directional covalent bonds in fluorides and consequently one would expect the strain relieving defects to be quite different. Chapter 4. Structural Properties 73 To see if the lateral coherence lengths are related to the strain relieving defects in the LaF 3 films, we estimate the spacing of structural defects required to accomodate the misfit at the growth temperature and compare this with the lateral coherence lengths for the LaF 3 films on GaAs and InP. For convenience in the analysis, we assume that the strain relieving defects are misfit dislocations. The spacings for misfit dislocations for the lattice mismatch S is given by: S = b/5 where b is the magnitude of the Burger's vector of dislocation. The defect spacings S were calculated using the lattice mismatch at the growth temperatures. For the LaF 3 /GaAs(l l l ) system, the defect spacing will be 8 - 16 nm assuming b = a/2 - a. The coherence lengths for the LaF 3 films on GaAs were 20-60 nm. Similarly, the defect spacing for the LaF 3 / InP(l l l ) system is 90 - 180 nm. The lateral coherence lengths for this system were 80-540 nm. The estimated defect spacing are comparable to the measured lateral coherence lengths for both systems. We can interpret that the columnar defects are formed at the growth temperature to accomodate the lattice mismatch between the film and the substrate. The defect spacings in the LaF 3 films on InP are longer than those on GaAs because the lattice mismatch in the LaF 3/InP system is an order of magnitude smaller. The relationship between the lateral coherence lengths and the lattice mismatch at the growth temperatures can be also observed by comparing the ratios of LaF 3/GaAs to LaF 3/InP for the two values. The ratios of the lateral coherence lengths for the LaF 3 films on GaAs and InP substrates are 4-9. The ratio of the coherence length is comparable to the ratio R of the lattice mismatch 5 at the growth temperatures of the two systems: R = SaaAs/Sinp = 4.5%/0.41% ~ 11. 4.4 Summary We have investigated the structural properties of LaF 3 and ErF 3 films grown on III-V semiconductors. We have shown by X-ray diffraction that the LaF 3 and ErF 3 films Chapter 4. Structural Properties 74 on GaAs and InP are single crystals. The epitaxial growth of L a F 3 films on InP is demonstrated for the first time. In the L a F 3 / G a A s ( l l l ) A and L a F 3 / I n P ( l l l ) B systems, we have shown that the trigonal ax a plane of the LaF 3 crystal is aligned parallel to the (111) hexagonal face of GaAs and InP substrates by X-ray diffraction and L E E D . This result is in agreement with L E E D and R H E E D study of the L a F 3 / G a A s ( l l l ) system by Sinharoy et al. [5]. In the E r F 3 / G a A s ( l l l ) B system, the orthogonal axe plane of the E r F 3 film is found to be oriented parallel to the (111) plane of the GaAs substrate by X R D . The result is consistent with the the L E E D study of G d F 3 deposited on G e ( l l l ) and G a A s ( l l l ) B substrates by Jenkins et al. [10]. We observed a columnar structure in the LaF 3 film grown on a G a A s ( l l l ) substrate. The L a F 3 film growth was done in the temperature range, Zone 2 in which the film is expected to have a dense columnar structure. The columnar structure results from the competition between the diffusive transport process and the shadowing in the presence of an incoming particle flux with a lateral component of velocity. The effect of the lattice mismatch on the column size may be associated with the initial size of the nuclei. The film/substrate interface energy is lower for a smaller lattice mismatch system where the strain is lower. It is hence thermodynamically favorable for a small lattice mismatch system to form larger size nuclei. From the epitaxial growth point of view, the columnar defects relieve the strain due to the lattice mismatch. The lateral coherence lengths of the LaF 3 films on GaAs and InP obtained by X-ray rocking curve measurements were comparable to the defect spac-ing required to accommodate the lattice mismatch at the growth temperature. The lateral coherence lengths for the LaF 3 films on InP were longer than on GaAs, since the lattice mismatch for the LaF 3 / InP system is lower. In this picture, the columns of coherent crystals are surrounded by regions of defects propagated perpendicular to Chapter 4. Structural Properties 75 the film/substrate interface and that the defects are formed to accommodate the lattice mismatch at the growth temperature. The propagation of defects in fluorides is different from that in semiconductors where the dislocations propagate along the film/substrate interface rather than perpendicular to the interface. This may be because in fluorides as opposed to for the semiconductors. The energy necessary for defects to propagate in the films is lower due to the ionic character of the bonds in fluorides than in the semiconductors. The columnar structure of LaF 3 films is consistent with tensile strains observed in LaF 3 films on GaAs by high-resolution X-ray diffraction (HRXRD). We interpret that the tensile strains in the LaF 3 films are due to the differential thermal contraction between the fluorides and the semiconductors during cooling. According to our interpretation, the LaF 3 films relieve strains due to the lattice mismatch at the growth temperature by formation of columnar regions of defects. LaF 3 films have tendencies to contract more than semiconductor substrates during cooling due to their greater thermal expansion coefficients. However, since the LaF 3 lattice is registered with the substrate lattice at the interface, if the defects are pinned at the interface, the films are unable to accommodate the differential thermal contractions. This results in tensile strains in the LaF 3 films. The tensile strains were not detected in the LaF 3 films on InP than on GaAs, since the lattice mismatch is smaller in the LaF 3/InP system. This is also consistent with our interpretation, since the number of defects that are pinned at the interface will be lower in LaF 3 films on InP than on GaAs, since the lattice mismatch in the LaF 3/InP system is smaller. Hence the LaF 3 films on InP are able to accommodate the differential thermal contraction during cooling through processes such as defect motions. Consequently there are less strains in the LaF 3 films on InP than on GaAs. We conclude that the lattice mismatch as well as the difference in thermal expansion coefficients between the film and the substrate are important factors in the structural Chapter 4. Structural Properties 76 perfection of deposited fluoride film in the rare-earth trifluoride/III-V semiconductor system. Chapter 5 Surface Morphology In this chapter, we will examine the surface morphology of the LaF 3 films grown on GaAs and InP. The surface and interface roughness in electronic and optoelectronic devices is one of the factors affecting the device performances such as carrier mobilities and optical losses. Therefore it is important to investigate the surface and interface roughness in the fluoride/semiconductor system. Our objective is to determine the surface and interface roughness of the LaF 3/GaAs, InP system. Another objective to apply a self-affine surface structural analysis to our fluoride/semiconductor system and to see if it can provide an insight into physical mechanisms by which fluorides grow on semiconductors. Self-affine surfaces are invariant under anisotropic transformations. That is if we enlarge a self-affine surface in a direction, for example in the ^-direction, differently than in the other direction, for example in the ^-direction, then the surface looks the same. The scaling of a self-affine surface is schematically illustrated in Fig. 5.41. Consider that the height of a self-affine surface is described by a function h(x) where x is the horizontal direction of the surface. If we enlarge the height function h(x) horizontally by a constant factor b (x —r bx), the h(x) is enlarged by a factor b a vertically (h —> b ah) where a is the roughness or scaling exponent. In other words, the h(x) has the following property: h(x) oc b~ ah(bx) (5.13) The self-affine description of surfaces can be used to study the growth phenomena of 77 Chapter 5. Surface Morphology 78 Figure 5.41: Schematic illustration of the scaling of a self-affine surface. If we enlarge a self-affine surface horizontally in a direction, for example in the x-direction, differently than in the other direction, for example in the z-direction, then the surface looks the same. the surfaces. The self-affine surfaces which have same or similar mechanisms of forma-tion, have same scaling exponents. The self-affine surfaces which scale in a similar way do not necessary have a same structure in microscopic detail, but have some essential factors that are common during their formations. The physical mechanisms by which self-affine surfaces are formed can be described by various theoretical models. These theoretical models also have scaling properties or have scaling exponents associated with them. Therefore by measuring the scaling exponents of the system of our interest from measurable quantities and by comparing the measured exponents with those predicted by theoretical models, we can learn about the mechanisms of formation of that system. The self-affine surface description is a convenient way to parameterise surface structures and to compare experiments with theoretical models. To determine the scaling exponents from experiments, we assume that the surface Chapter 5. Surface Morphology 79 height h(x) is Gaussian distributed about a mean height as shown in Fig. 5.42 for a case of one-dimensional surfaces. We describe the height-height correlation function of the surface by a function of the form [49, 46]: C(x) = (z(0)z(x)) = o 2 e ~ ^ 2 a (5.14) where z(x) = h(x)-(h(x)), o = ^(z(x)2), the rms width of the surface, a is the roughness exponent and £ is the correlation length of the surface roughness. The roughness exponent gives a quantitative measurement of the roughness of the function h(x). The lower the value of a, the more jagged the surface looks or there will be more high-frequency, low amplitude contributions to the surface profile. The higher the value of a, the more smooth the surface looks. The correlation length £ measures the length scale of the surface structure of the system studied. Two points separated by a distance longer than the correlation length £ are not correlated and hence, the structures of the length scale £ can be considered random. For a two-dimensional surface, the x in Eqn. 5.14 is replaced by: r = \fx2 + y2. The rms width or rms roughness a of a self-affine surface scales with the time t and the sample size L . At time t less than the saturation time tx, t <C tx, the o scales as o oc t& where /? is the growth exponent. At t tx, the rms roughness o is independent of time and scales as o oc La where L is the sample size and a is the roughness exponent. It is usually assumed that the growth rate is linear in time so that the film thickness is used as t in the above relationships. For t C f j , the correlation length £ of the surface roughness scales as £ oc txlz where z is the dynamic exponent given by z = a/8. For t ^> tx, the correlation length £ is proportional to the sample size i.e. £ oc L . In this study, the scaling exponents a, 8, the surface roughness o and the correlation length £ for the LaF 3 films grown on GaAs and InP substrates are obtained using the X-ray specular and diffuse scattering, and the atomic force microscopy (AFM). The scaling Chapter 5. Surface Morphology 80 h(x 0<ct<1 high a o low a Figure 5.42: Schematic illustration of a self-affine surface showing the parameters that describe it. The surface height is assumed to be Gaussian distributed around a mean height. The o is the rms width of the surface, the a is the roughness exponent and the £ is the correlation length of the surface roughness. The roughness exponent gives a quantitative measurement of the roughness of the function h(x). The lower the value of a, the more jagged the surface looks or there will be more high-frequency, low amplitude contributions to the surface profile. The higher the value of a, the more smooth the surface looks. The £ measures the length scale of the surface structure of the system studied. Two points separated by a distance which is more than the correlation length £ are not correlated and hence, the structures of the length scale £ can be considered random. Chapter 5. Surface Morphology 81 exponents for the system are compared with the ones predicted by known growth models. 5.1 X-ray Scattering In X-ray scattering experiments, samples are illuminated by a beam of X-rays and the intensity of scattered X-rays is measured. We have used a Cu Ka radiation as the X-ray source. The geometry for X-ray scattering experiments is schematically illustrated in Fig. 5.43. In the figure, the k x and k 2 are the wavevectors of incident and detected beams respectively. The 6\ and 92 are the angles of incidence and detection. The transfervector q is defined as q = k 2 — k i . The direction parallel to the interface in the plane of incidence is x and the direction perpendicular to the plane of the interface is z. The y direction is perpendicular to the plane of incidence (x-z plane). A narrow slit is used at the detector. The angle subtended by the detector slit is A92 = 0.0014 rad. The slit is wide in the y direction. The rms interface width o and the film thickness t are obtained from the specular intensity of X-rays (intensity when the angle of detection is equal to the angle of incidence) using the recursive method for stratified layers by Parratt [47]. The effect of the roughness is implemented using the expression for the specular reflectivity R by Nevot and Croce [48]: R = R f e - ^ 2 (5.15) In the expression, qz and q\ are the components of the transfervectors, perpendicular to the plane of the interface for the layer above and below the interface respectively. The o is the rms width of the interface and Rf is the fresnel reflectivity for an ideal interface. The method by which the specular reflectivity is calculated, is described in detail in Appendix C. Chapter 5. Surface Morphology 82 Z i i i i Figure 5.43: Schematic illustration of X-ray experiment geometry. The k i and k 2 are the wavevectors of incidence and detected beams respectively. The 9\ and 92 are the angles of incidence and detection. The transfervector q is defined as q = k 2 — k i . The direction parallel to the interface in the plane of incidence is x and the direction perpendicular to the plane of the interface is z. The y direction is perpendicular to the plane of incidence (x-y plane). A narrow slit is used at the detector. The angle subtended by the detector slit is A92 = 0.0014 rad. The slit is wide in the y direction. Chapter 5. Surface Morphology 83 The X-ray diffuse intensity for a single interface is given by Sinha et al. [49]: io /CoSmtfi \qvz\' 7 where 70 is the incident intensity, 9\ and 02 are the angles of incidence and detection, k\ and k2 are the wavevectors of the incident and detected beams, A0 2 is the angle subtended by the detector slit, k0 = 2ir/\ is the wavevector of the Cu K a radiation, Ap is the density difference at the interface, qz and qx are the transfer vectors perpendicular and parallel to the interface. Since a narrow slit (A02 = 0.0014 rad) is used at the detector, the intensity is integrated from +00 to -co in the ^/-direction (the direction perpendicular to the plane of incidence). The diffuse intensity is related to the correlation length £ and the roughness exponent a through the correlation function C(x) — (z(0)z(x)) = a2e~^x^^2a. The fluoride/semiconductor system in this study involves two interfaces: air/film and film/substrate interfaces. The diffuse intensities were thus calculated using the expression of the diffuse intensity for two interfaces similar to Eqn. 5.16, given by Sinha et al. [50]. The calculation of diffuse intensity for two interfaces is described in Appendix C. For each sample, the roughness exponent a is first determined from a longitudinal scan using the asymptotic limit for the diffuse intensity from Eqn. 5.16. The asymptotic limit for the diffuse intensity of Eqn. 5.16 when qz 3> 1/cr and qx <C 1/LX, where L x is the lateral size of the sample, is given by [49]: I{qz) oc g ; ( 3+ i / « ) a - i / « (5.17) The correlation length £ is next obtained from a transverse diffuse scan using the expression of the diffuse intensity for two interfaces in Appendix C with the values of o and a determined from the specular and longitudinal diffuse scan. The paths of the longitudinal and transverse diffuse scans in reciprocal space are illustrated in Fig. 5.44. The specular scans are along the qz axis. Chapter 5. Surface Morphology 84 Figure 5.44: Schematic illustrations of (a) longitudinal and (b) transverse scans in recip-rocal space. 5.2 Variation of the rms surface roughness o with film thickness and the growth exponent 8 The rms interface width o is determined from X-ray specular reflectivity. The geometry of a specular scan is illustrated in Fig. 5.45. The reflectivity R as a function of the momen-tum transfer perpendicular to the film/substrate interface qz for the LaF 3 /GaAs( l l l )B system is plotted in Fig. 5.46. The calculated specular reflectivities are shown by solid lines in the figure. The rms surface roughness o determined by the fit of the specular reflectivity ranged between 0.5 and 1.0 nm. The film/substrate interfacial roughness de-termined also from the recursive method for stratified layers [47], varied from 1.0 to 1.5 nm. No trend was observed in the variation of film/substrate interface roughness with thickness. The variation of the rms surface roughness o with film thickness t is plotted in Fig. 5.48. The growth exponent 8 determined from the linear fit of log o vs. logt plot using the scaling relationship o oc t13 is found to be 8 = 0.18 ± 0.16. If we exclude the data point for the sample with film thickness t = 150 nm, the value is 8 = 0.22 ± 0.06. The specular scans for the LaF 3 / InP(l l l )B samples are shown in Fig. 5.47. The rms surface roughness determined from the specular reflectivity fit ranged between 0.5 to Chapter 5. Surface Morphology 85 Figure 5.45: Schematic illustrations of the geometry of specular scans in the plane of incidence. 0.8 nm, but no significant trend was observed. The film/substrate interfacial roughness determined also from the fit specular reflectivity using the recursive method for stratified layers [47], ranged between 0.7 to 0.8 nm and no trend was detected with the thickness. The growth exponent 8 for this system is determined as/? = —0.1 ±0 .2 . 5.3 Roughness exponent a and the correlation length £ A longitudinal diffuse scan is a 6-26 scan at an off-specular condition obtained by tilting the detector by a small angle away from the specular angle. The geometry of a lon-gitudinal diffuse scan is illustrated in Fig. 5.49. Typical longitudinal diffuse scans for the LaF 3 /GaAs( l l l )A and LaF 3 / InP(l l l )B samples at off-set angles of A0 = 0.09° and 0.18° are shown in Fig. 5.50. The off-set angles are larger than the aperture size of the detector which is 0.08°. The solid lines in the figure are linear regressions for determining the roughness exponent a using the asymptotic limit for the diffuse intensity in Eqn. 5.17. Chapter 5. Surface Morphology 86 q z (nm - 1) Figure 5.46: Specular reflectivities of LaF 3 /GaAs( l l l )A samples. The film thickness is indicated for each sample. The solid lines are the fits of the stratified layer models to the data. Chapter 5. Surface Morphology 87 0 1 2 3 q z (nm - 1) Figure 5.47: Specular reflectivity scans of LaF 3 / InP(l l l )B samples. The film thickness t is indicated for each sample. The solid lines are the fits of the stratified layer models to the data. Chapter 5. Surface Morphology 88 E c 1 H 0 . 5 -LaF3/GaAs(111)A p = 0.18±0.16 i i 5 0 100 t (nm) I i i 5 0 0 E c LaF3/lnP(111)B P = -0.1 ±0.2 0 .5 1 ' I I I I I | 4 0 0 1 0 0 t (nm) 2 0 0 Figure 5.48: Film/air interface width o vs. film thickness t for the LaF 3 /GaAs( l l l )A (top) and LaF 3 / InP( l l l )B (bottom) systems. The growth exponents B determined from the linear fits of the data were f3 = 0.18 ± 0.16 for the LaF 3 /GaAs( l l l )A system and 8 = -0.1 ± 0.2 for the LaF 3 / InP(l l l )B system. Chapter 5. Surface Morphology 89 Detector Diffuse i Specular Interface Figure 5.49: Schematic illustration of the geometry of longitudinal diffuse scans in the plane of incidence. The detector is positioned at an angle AO away from the specular beam and then a 9-29 scan is performed. The linear fits are obtained near the region qz — 1-2 n m - 1 . Corresponding length scales for the two off-set angles are listed in Table 5.6. The roughness exponent a obtained from the scans are also listed in Table 5.6. The errors in the roughness exponents are from the linear regression and do not include the systematic errors which are expected to be larger. The values of roughness coefficients were different at the two off-set angles within the same system. However, the roughness exponents a at each off-set angle of the LaF 3 /GaAs( l l l )A and LaF 3 / InP(l l l )B systems are equal within the experimental accu-racy. The roughness exponent a determined by analysing the specular reflectivity in the same way for the LaF 3/GaAs and LaF 3/InP samples shown in Fig 5.50 were a = 0.3±0.1. The roughness exponent a determined at A6 = 0.09° lies between 0.3 and 0.4 and the exponents determined at A6 = 0.18° lies between 0.5 and 0.7 for the LaF 3 films on both GaAs(ll l ) and InP(l l l ) substrates. Chapter 5. Surface Morphology 90 1 q z (nm"1) Figure 5.50: Longitudinal diffuse scans taken at an offset angle Ad — 0.09° and 0.18° for (a) LaF 3 /GaAs( l l l )A, t = 150 nm and (b) LaF 3 / InP(l l l )B, t = 209 nm. Solid lines are the linear fits to the data. Chapter 5. Surface Morphology 91 Table 5.6: Roughness exponent a obtained from the longitudinal diffuse scans for LaF 3 /GaAs( l l l )A and LaF 3 / InP(l l l )B samples. The range in the x-component of the transfer vector, qx and corresponding length scale Lx where the longitudinal scans were performed, are also listed. Film thickness (nm) a A0 0.09° 0.18° qx range ( l f r 3 nm"1) 0.7-1.5 1.6 - 3.0 Lx range (nm) 4000-8000 2000-4000 LaF 3 /GaAs( l l l )A 37.5 48 150 180 0.36 ±0.05 0.66 ±0.04 0.38 ±0.05 0.54 ±0.05 0.36 ±0.05 0.58 ±0.05 0.36 ±0.06 0.6 ±0 .1 LaF 3 / InP( l l l )B 111 209 0.37 ±0.06 0.53 ±0.05 0.37 ±0.07 0.6 ±0 .1 Chapter 5. Surface Morphology 92 Detector k Diffuse hv Specular Interface Figure 5.51: Schematic illustration of the geometry of a transverse diffuse scan in the plane of incidence. A transverse scan is performed by rotating the sample around the specular reflection with source-detector angle 29 fixed. The correlation lengths £ are obtained from the transverse diffuse scans using the expression for the X-ray diffuse intensity for two interfaces (see Appendix C) [50]. A transverse diffuse scan is analogous to a rocking curve for a Bragg reflection and is obtained by rotating the sample around the specular reflection with source-detector angle 29 fixed. The geometry of a transverse diffuse scan is illustrated in Fig. 5.51. The transverse diffuse scans for LaF 3 /GaAs( l l l )A and LaF 3 / InP( l l l )B samples are shown in Fig. 5.52. The peak at qx = 0 in each scan is specular reflection. The two peaks at both sides of the specular beam are often referred to as the Yoneda wings. They arise when one of the incident or detected beam is at the total reflection condition. The transverse diffuse scans are the most sensitive to the correlation length £. The solid and dashed lines in the figure are the calculated diffuse intensities with minimum and maximum values of correlation lengths, using the values of o and a obtained from the specular and the longitudinal diffuse scans. The fits of the transverse diffuse scans Chapter 5. Surface Morphology 93 a LaF 3 /GaAs(111)A 1 0 0 4 1 0 4 CO Q . O CO c CD 1-d C 1 0 0 4 1 0 4 50 nm 100 nm . * / • . * • ' i • v» bLaF 3/lnP(111)B — i — i — i — i — i — i — i — i — i — i — i — 0 3 - 0 . 0 2 - 0 . 0 1 0 . 0 0 0 . 0 1 0 . 0 2 0 . 0 3 q x (nm-1) Figure 5.52: Transverse X-ray diffuse scans with 29 = 2° for (a) the LaF 3 /GaAs( l l l )A sample with t = 150 nm and (b) the LaF 3 / InP(l l l )B sample with t = 210 nm. The solid and dashed lines are the calculated diffuse intensity using the expression for diffuse intensities for two interfaces given by Sinha et al. in Ref. [50]. The coefficients used are (a) cr0 = 0.5 nm (film/air), o\ -- 1.5 nm (film/substrate) (b) OQ — 0.65 nm, o\ = 1.5 nm for the rms interface roughness and a = 0.6 for the roughness exponent for both samples with the cut-off lengths £ indicated. The dash-dot lines are the diffuse intensities assuming the two interfaces are uncorrelated, using the same parameters as the correlated interfaces with (a) £ = 75 nm and (b) £ = 85 nm. The dotted lines are the diffuse intensities calculated assuming there is only one interface (film/air) using (a) o = 0.5 nm, a — 0.6, £ = 75 nm and (b) o = 0.65 nm, a = 0.6 and £ = 85 nm. Chapter 5. Surface Morphology 94 1 1 1 1 1 LaF 3/GaAs(111)A -0.03 -0.02 -0.01 0.00 0.01 0.02 0.03 q x (nm-1) Figure 5.53: Transverse X-ray diffuse scans with 29 — 2° for the LaF 3 /GaAs( l l l )A samples with film thickness t — 48 nm. The solid and dashed lines for each sample are the calculated diffuse intensity using the expression for diffuse intensities for two interfaces given by Sinha et al. in Ref. [50] with two different roughness exponents a = 0.36 and a = 0.6 respectively. The coefficients used are OQ = 0.9 nm (film/air), o\ = 1.5 nm (film/substrate) for the rms interface roughness and £ = 700 nm for the correlation length with the roughness exponents indicated. Chapter 5. Surface Morphology 95 Figure 5.54: Transverse X-ray diffuse scans with 29 = 2° for the LaF 3 /GaAs( l l l )A samples. The thickness t and the range of correlation lengths £ obtained from the fit of diffuse intensities are indicated in the figure. The solid and dashed lines for each sample are the calculated diffuse intensity using the expression for diffuse intensities for two interfaces given by Sinha et al. in Ref. [50] with two different correlation lengths £. The roughness exponents a used in the calculation are a = 0.36 except for the t = 150 nm sample whose exponent was a = 0.6. The results of the fit are listed in Table 5.7. The coefficients used are cr0 = 0.9 nm (film/air), o\ = 1.5 nm (film/substrate) for the rms interface roughness and £ = 700 nm for the correlation length with the roughness exponents indicated. Chapter 5. Surface Morphology 96 were performed using the roughness exponent a obtained from the longitudinal diffuse scans performed at AO = 0.09° and 0.18°. An example of the fit for a LaF 3 /GaAs( l l l )A sample using roughness exponents obtained at two off-set angles are shown in Fig. 5.53. For the sample shown in Fig. 5.53, a better fit was obtained using the roughness exponent at AO = 0.09°, a — 0.36 than using the a at AO = 0.18°, a = 0.6. For some samples, we obtained better fits using the values of a determined at the off-set angle AO = 0.18°. The estimated correlation lengths £, the roughness exponents a are listed in Table 5.7. The rms interface roughness o used in the fits are also listed. For all calculations, the rms interface roughnesses obtained from the specular reflectivity fits were used. The importance of the diffuse intensities from the buried film/substrate interface can be seen from the diffuse intensities calculated using only the film/air interface shown in Fig. 5.52. In the calculation, the correlation length £ was assumed to be the same for the air/film and the film/substrate interfaces. The two interfaces are also assumed to be correlated i.e. the interference occurs between the diffuse beams from the two interfaces. The validity of this assumption can be seen from the diffuse intensities calculated for two uncorrelated interfaces shown in Fig. 5.52. The correlation lengths for the two LaF 3 / InP(l l l )B samples determined from the fit of the transverse diffuse scan were 30-60 nm and 70-120 nm. The estimated correlation length £ for the LaF 3 /GaAs( l l l )A samples were longer ranging between 500 and 1200 nm except for the sample with LaF 3 film thickness, t = 150 nm, whose estimated correlation length was 50 - 100 nm. The difference between the longer correlation lengths for the LaF 3/GaAs samples and the correlation lengths of the LaF 3/InP samples and of the t = 150 nm LaF 3/GaAs sample is almost an order of magnitude. The a associated with longer correlation lengths were 0.36-0.38 whereas the a associated with shorter correlation lengths were 0.5-0.6. The transverse scan was also performed on the atomic hydrogen etched bare GaAs (111) A Chapter 5. Surface Morphology 97 substrate. The correlation length £ determined from the fit of the transverse diffuse inten-sity was 300-500 nm using the value of roughness exponent a = 0.34 obtained from the longitudinal diffuse scan. This result suggests that the longer correlation length for the LaF3 film surface is associated with the surface structure of the GaAs substrates propa-gated through the LaF 3 film. The shorter correlation lengths for the LaF 3/InP samples and the 150 nm LaF 3/GaAs sample are likely associated with the surface structure of the film which is related to the characteristics of the films such as defects and the strain in the film. The comparison of the correlation lengths of the LaF 3 /GaAs( l l l ) samples and the GaAs substrate indicate that the correlation lengths determined in the present analysis represent the correlation lengths of the surface features which are dominant or which have greater rms roughness. We did not detect any trends in the correlation length as a function of film thickness. 5.4 Atomic Force Microscopy Atomic force microscopy was performed to further investigate the surface morphology of the LaF 3 films on III-V semiconductors. The scaling exponents for the surface morphol-ogy of the LaF 3 films are obtained from A F M images and are compared with the X-ray scattering results. 5.4.1 M e t h o d The correlation length £ and the roughness exponent a were obtained from the height-height correlation function C(x,y) calculated from the A F M images using Eqn. 5.14, C(r) = o2e~(Tl®2a. The two dimensional height-height correlation function C(x,y) is related to the height-height correlation in reciprocal space or power spectral density Chapter 5. Surface Morphology 98 Table 5.7: Correlation length £ obtained from the transverse diffuse scans for LaF 3 /GaAs( l l l )A and LaF 3 / InP(l l l )B samples. The values of rms interface rough-ness and roughness exponent a obtained from the specular and the longitudinal diffuse scans, used in the calculation are also listed. The correlation length £ was assumed to be the same for the air/film and the film/substrate interfaces and the two interfaces are assumed to be correlated. film thickness rms roughness a £ (nm) air/film film/substrate ( n m ) <7o (nm) o-! (nm) LaF 3 /GaAs( l l l )A 37.5 0.8 1.2 0.36 ± 0.05 800-1200 48 0.9 1.5 0.38 ±0.05 500-900 150 0.5 1.5 0.6 ±0 .1 50-100 180 1.1 1.2 0.36 ±0.06 700-1000 LaF 3 / InP( l l l )B 111 0.5 0.6 0.53 ±0.05 30-60 209 0.65 1.5 0.6 ±0 .1 70-120 Chapter 5. Surface Morphology 99 S{qx,Qy) through: C(x,y) S(qx,qy) C(x,y) = ±-J j^S(qx,qy)e-i^x+^dqxdqy (5.18) (5.19) The power spectral density S(qx,qy) is given by: S(qx,Qy) H(qx,qy)H(-qx,-qy) \H(qx,qy)\2 | f fL/2 h(x,y)ei^x+qyy^dxdy\2 (5.20) (5.21) where H(qx, qy) is the Fourier Transform of the surface height h(x, y) and L is the width of the A F M image. In the last step, the property of the Fourier transform, H(—qx, —qy) = H*(qx,qy) for real h(x,y) was used. We have used a two-dimensional FFT routine in Ref. [78] to perform the Fourier transforms of the A F M images. First the two dimensional arrays of surface height h n x j J l y from the A F M image was Fourier transformed to yield Hmx%rriy where nx>y and ffix^y Eire the indices for the arrays. In the program, the frequency / = q/2n rather than the wavevector q was used for simplicity in programming. The height in reciprocal space at f, H(fx, fy) is approximated through: where Ax>y = A is the pixel size or the width of each pixel in the image. Then, the power spectral density is given by: H(fx,fy) ~ A A H (5.22) = A2H, Tlx flly (5.23) S(fxJy) = j\H(fx,fy)\2 (5.24) 2 (5.25) (5.26) Chapter 5. Surface Morphology 100 where A = (NA)2 is the area of the A F M image and N is the number of pixels in one of the directions (N=512 in our case). Finally, the correlation function C(x, y) was obtained through: C(x,y) ~ A / X A / W [ S ( / X > / „ ) W (5-27) 1 A 2 2 (ATA) 2 lAT 2 1 = l^\Hnx,nY\2}FFT (5.29) where Afxjy = is the spacings in reciprocal space between Hnx<ny and [ ]FFT indicates the FFT of the expression in the bracket. The mean square fluctuation in surface height g(r) is given by [49]: g(r) = ({z(x',y')-z(x,y)}2) = 2o2-2C(r) (5.30) = 2a2[l - e-(f)2Q] (5.31) where r = \/x2 + y2. The radial average of C(x, y), C(r) was taken to obtain g(r) using Eqn. 5.31. The radial average is performed by integrating the two dimensional C(x,y) over an annulus of radius r. In this study, the height-height correlation in reciprocal space or the power spectral density (PSD), S(q), the correlation function C(r) and the mean square fluctuation g(r) are obtained from the A F M images. The roughness exponent a is first determined from g(r) using Eqn. 5.31 for small r: g(r) ~ 2a2(^)2Q (5.32) Next, the correlation length £ is determined from the height-height correlation C(r) using C(r) = o 2 e - ( r ^ 2 a in Eqn 5.14. Chapter 5. Surface Morphology 101 Figure 5.55: A F M images of a L a F 3 / G a A s ( l l l ) A sample with film thickness t = 150 nm. 5.4.2 Results A F M images of L a F 3 / G a A s ( l l l ) A and L a F 3 / I n P ( l l l ) B samples are shown in Fig. 5.55 and 5.56 . The radial averages of power spectral density, S(q) where q = ^Jq2, + g 2 for the L a F 3 / G a A s ( l l l ) A and L a F 3 / I n P ( l l l ) B samples are shown in Fig. 5.57. We observe a shoulder near L 0 = 0.03 n m " 1 in S(q) for the L a F 3 / G a A s ( l l l ) A sample and a shoul-der near L 0 = 0.02 n m - 1 in S(q) for the L a F 3 / I n P ( l l l ) B sample. Each characteristic Chapter 5. Surface Morphology 102 Figure 5.56: A F M images of a LaF 3 / InP(l l l )B sample with film thickness 209 nm. Chapter 5. Surface Morphology 103 10000-1000-£ 100-c o . H LaF3 AGaAs (111 )A t = 150 nm PSD from AFM -h = 0.65 \ = 50 nm a = 0.54 nm 0.01 q (nm"1) 0.1 100000 10000 1000 | 100 0.1 0.001 LaF3/lnP(111)B t = 209 nm •••• • PSD from AFM h = 0.68 $ = 90 nm a = 0.4 nm 0.01 q (nm"1) 0.1 Figure 5.57: Height-height correlation in reciprocal space S(q) obtained from the A F M images of (top) the LaF 3 /GaAs( l l l )A sample with film thickness t = 150 nm and (bot-tom) the LaF3/InP(l l l )B sample with film thickness t = 209 nm. The dashed lines are the function S(q) ~ q~z with z = 3. The solid lines are the height-height correla-tion S(q) obtained by Fourier transforming the the height-height correlation C(r) using C(r) = a 2 e- ( r / « 2 a in Eqn 5.14. Chapter 5. Surface Morphology 104 Table 5.8: Characteristic q values and corresponding characteristic lengths L 0 observed in the height-height correlation S{q) for LaF 3 /GaAs( l l l )A and LaF 3 / InP(l l l )B. The peak to peak distances D of the circular features observed in the A F M images are also listed. qo (nm - 1) L0 = 2n/q0 (nm) D (nm) LaF 3 /GaAs( l l l )A 0.03 210 100-200 LaF 3 / InP( l l l )B 0.018 350 250-450 wavevector q0 corresponds to a length in real space L 0 = 2ir/q0. The characteristic q0 and the corresponding lengths L for the LaF 3 /GaAs( l l l )A and LaF 3 / InP( l l l )B sam-ples are listed in Table 5.8. The characteristic length for the LaF 3 / InP( l l l )B sample, L0 = 350 nm is longer than the length for the LaF 3 /GaAs( l l l )A sample, L0 = 210 nm. We also list the peak to peak distances D of the circular features observed in the A F M images in Fig. 5.55 and 5.55 in Table 5.8 for comparison. The characteristic lengths L0 are comparable to the peak to peak distances D. In the PSDs of both LaF 3/InP and LaF 3/GaAs samples in Fig. 5.57, small features are observed in the region above q ~ 0.1 n m - 1 . If we assume that a surface structure needs at least three pixels corresponding to q = 27r/45 = 0.14 n m - 1 , to be identified, any features in the region above q ~ 0.1 n m - 1 do not reflect the surface structures of the samples. Hence we interpret that the features in the PSDs in the regions above q ~ 0.1 n m - 1 are due to noises at the resolution limit of the A F M and not due to the surface structures of the samples. The mean square fluctuation g(r) and height-height correlation C(r) obtained from the A F M images for the LaF 3 /GaAs( l l l )A and LaF 3 / InP( l l l )B samples are shown in Chapter 5. Surface Morphology 105 Table 5.9: Rms surface width cr, the roughness exponent a and the correlation length £ for the LaF 3 /GaAs(l l l )A, LaF 3 / InP(l l l )B samples and for the atomic-H etched GaAs( l l l )A substrate obtained from the A F M images. The film thicknesses t are also listed. The X-ray results for the same samples are listed for comparison. t (nm) cr (nm) a £(nm) LaF 3 /GaAs( l l l )A 150 A F M 0.58 ±0.05 0.65 ±0.05 50 ± 9 X-ray 0.5 ±0 .1 0.58 ±0.05 50 - 100 LaF 3 / InP( l l l )B 209 A F M 0.4 ±0 .1 0.68 ±0.06 90 ± 10 X-ray 0.4 ±0 .1 0.6 ±0 .1 70 - 120 GaAs(l l l )A - A F M 1.0 ±0 .1 0.37 ±0.05 -X-ray 0.9 ±0 .1 — 300 - 500 Fig. 5.58. The solid lines in the plot of g(r) are the linear regressions to determine the roughness exponents a using Eqn. 5.31. The solid lines in C(r) are the fits of height-height correlation in Eqn. 5.14 to determine the correlation length £. The value of the roughness exponent a was fixed to the values determined by linear regression of g(r) during the fits. The A F M microscopy was also performed on the atomic hydrogen etched bare GaAs( l l l )A substrate and is shown in Fig. 5.59. The mean square fluctuation g(r) and the height-height correlation C(r) obtained from the A F M images are also shown in Fig. 5.59. The values of a, o and £ determined from the A F M images are listed in Table 5.9. The results from the X-ray scattering are also listed for comparison. The values of rms surface roughness a and the correlation length £ measured by A F M and X-ray scattering Chapter 5. Surface Morphology 106 Figure 5.58: (a) Mean square fluctuation g(r) and (b) height-height correlation function C(r) computed from the A F M image of the LaF 3 /GaAs( l l l )A (top) and LaF 3 / InP( l l l )B (bottom) samples. The solid lines in (a) are the linear regression to obtain the roughness exponent a. The solid lines in (b) are the calculated correlation function C(r) = o2e~^\ " using the values of parameters indicated. Chapter 5. Surface Morphology 107 °S 100 100 80 cT 60 < 40 O 20 . GaAs(111)A substrate a a = 0.37 i i i i 11111 i . . . b • a = 0.9 nm • • • • — 1 1 1— | • • 1—r 10 100 1000 r (nm) Figure 5.59: A F M image of the atomic hydrogen etched GaAs(l l l )A substrate (top). The lower figure shows (a) the mean square fluctuation g(r) and (b) the height-height correlation C(r) computed from the A F M image. The lines in the A F M image are polishing marks from the manufacturer. The solid line in (a) is the linear regression to obtain the roughness exponent a. Chapter 5. Surface Morphology 108 are equal within the uncertainties of the measurements. The correlation length for the LaF 3 / InP( l l l )B sample is longer than that for the LaF 3 /GaAs(l l l )B sample by about a factor of two. The roughness exponents a measured by A F M agree with the values of a measured by X-ray scattering. Close inspection of the height-height correlation C(r) in Fig. 5.58 shows some fea-tures near r = 1000 nm in both samples. This implies that there are more than one characteristic length scale in the surface topography of the film. The A F M results sup-port our interpretation of the presence of the two ranges of correlation lengths obtained in the analysis of the X-ray transverse diffuse scans for the LaF 3 /GaAs( l l l )A system. The two ranges of correlation lengths £ correspond to the two surface features present on each LaF 3 film. The value of correlation length obtained by X-ray scattering is that of the surface feature which is dominant or in other words, the feature which has a larger surface roughness amplitude than others. 5.5 Discussion 5.5.1 Relationship between the bulk film structure and the surface morphology In this section we investigate the relationship between the crystal structures inside the film and the surface morphology of the films in the LaF3/semiconductor system. We compare in Table 5.10, the bulk lateral coherence lengths L x determined by X-ray rocking curve measurements in Chapter 4 with the surface correlation lengths £ determined from the A F M images. For the LaF 3 /GaAs(l l l )B sample, the coherence length (Lx — 47 nm) in the film obtained by XRD is equal to the correlation length (£ = 50 nm) measured by A F M within the experimental accuracy. For the LaF 3 / InP(l l l )B sample, the shorter bulk coherence length of the two lengths determined by rocking curve measurements Chapter 5. Surface Morphology 109 Table 5.10: Comparison of the bulk lateral coherence length L x measured by X-ray rocking curve, the surface correlation length £ and the characteristic length L determined from the A F M images for the LaF 3 /GaAs( l l l )A and LaF 3 / InP(l l l )B samples. Bulk Coherence Surface Correlation Length L x (nm) Length £ (nm) Rocking Curve A F M LaF 3 /GaAs( l l l )A 47 50 ± 9 LaF 3 / InP( l l l )B 100 90 ± 1 0 (Lx = 100 nm) is equal within the uncertainty of the measurements to the surface correlation length (£ = 90 ± 10 nm). The comparison is consistent with the columnar structures in the LaF 3 films on GaAs observed by scanning electron microscopy in Fig. 4.40. We interpreted in Chapter 4 that the bulk coherent lengths from X-ray rocking curves represent the spacings between the columnar regions of defects. The comparison between the bulk coherence lengths and the surface correlation length confirms that the bulk coherence lengths represent the columnar defect spacings. The comparison also shows that the columnar structure propagates through the LaF 3 films and is revealed on the film surface. In other words, the surface structures of the LaF 3 on GaAs and InP reflect the coherent domains underneath them. In Chapter 4, we also argued that the columnar defects are formed to accommodate the lattice mismatch between the fluoride and the semiconductor at the growth temperature. The observed relationship between the surface and the bulk coherence lengths suggests that the surface structures of the films are associated with the strain relieving defects formed during film growth. The lattice mismatch in the LaF 3/InP system (0.41%) is Chapter 5. Surface Morphology 110 smaller than that in the LaF 3/GaAs system (4.5 %). Therefore the surface coherence lengths are longer for LaF 3 films on InP than films on GaAs, since the defect spacings are longer in the LaF 3 films on InP. The study of the surface morphology of LaF 3 films on semiconductors as well as the bulk crystallinity of the fluoride films showed that the strain relieving defects are vertical regions around the periphery of coherent columns. 5.5.2 Continuum equation describing film growth The values of exponents obtained for the LaF 3 /GaAs( l l l )A and LaF 3 / InP( l l l )B sam-ples obtained by X-ray scattering and the exponents predicted by continuum models are summarized in Table 5.11. The similarity between the values of growth exponents and the roughness exponents for the two systems suggest that their growth processes are sim-ilar despite the difference in the growth temperature and lattice mismatch. The growth exponent and the roughness exponent measured X-ray scattering are closest to the value (P — 0.20, a = 0.67) predicted by the VLD model [53, 54]. In the following discussion of continuum models, the surface height h is assumed to be in the moving frame of reference i.e. h = hi — Ft where hi is the surface height in the inertia frame, F is the deposition flux and t is the time. The Edward-Wilkinson (EW) model is described by the equation of the form [56]: It has shown by Herring [57] that the term vV2h describes the mass transport through evaporation-recondensation. We expect that the desorption (evaporation) to be negligible in the MBE growth. The presence of a Schwoebel barrier [58] also lead to a vV2h term. A Schowebel barrier is a potential barrier at the edge of an island or a step which prevents the particles approaching to an edge of the island to jump off the edge. The term r](x, t) describes the noise due to the fluctuations in the deposition of atoms. d/i(x, t) dt = uV2h + rj(x,t) (5.33) Chapter 5. Surface Morphology 111 Table 5.11: Comparison of the scaling exponents obtained by X-ray scattering and the growth model. Growth Exponent Roughness Exponent 8 a LaF 3 /GaAs( l l l )A 0.2 ± 0.2 0.6 ±0 .1 LaF 3 / InP( l l l )B 0.0 ±0 .1 0.6 ±0 .1 Wolf and Villain [55] (WV) 0.25 1 Villain [53], Lai and Das Sarma [54] (VLD) 0.20 0.67 Kardar and Parizi and Zhang [52] (KPZ) . 0.24 0.38 Edward and Wilkinson [56] (EW) 0 0 Chapter 5. Surface Morphology 112 In the KPZ model, a nonlinear term §(V/i)2 is added to the EW equation [52]: ^ ) = ^ V 2 / i + ^ ( V / l ) 2 + ?7(x,t) (5.34) The KPZ equation is non-conservative and describes the lateral growth in the direction parallel to the interface. The lateral growth is present in the case where the deposited particles arrive isotropically. In the case of the MBE growth, the particles arrive as a beam of molecules. Hence we do not expect the process described by the KPZ model to play an important role. In the Wolf and Villain (WV) model [55], the evolution of the surface height /i(x) is described by the linear diffusion equation [55]: ® ^ = -^V*h + ri(x,t) (5.35) The WV equation is conservative i.e. it obeys the continuity equation: ^ | ^ + V. j (x , t ) = 0 (5.36) where j is the surface current driven by the difference in chemical potential \x: j cx-V/ / (x , i ) (5.37) In the W V equation, the chemical potential p is proportional to the surface curvature V 2 / i which increases with increasing number of neighbors or the chemical bonds that a particle may form at that site. Hence the —UiV4h term describes the surface diffusion whose current is controlled by the local chemical potential or the chemical bonds between the particles and the surface. We expect the process described by the term — uiV4h to be important in our MBE growth, since the chemical bonds between the particles on the surface and the surface of the film play an important role in the formation of the LaF 3 films. We also expect that the diffusion of the fluoride molecules to play an important Chapter 5. Surface Morphology 113 role in the surface relaxation at the growth temperature of the films for the reason below. The melting temperature of LaF 3 or the temperature required for the LaF 3 molecules to diffuse in the bulk LaF 3 is 1493°C. If we assume that the interaction energy between a LaF 3 molecule on the surface and the bulk LaF 3 is half of the energy for the molecules in the bulk LaF 3, we expect that the temperature required for the LaF 3 molecules to diffuse on the surface to be half of the melting point. The depositions of LaF 3 were performed at 600°C for GaAs and 400°C for InP, approximately half of the melting point of LaF 3 . The surface diffusion process described by the term — Ui V 4 / i is more important at a shorter length scale or a large q value as compared to the evaporation-condensation process described by the vV2h term in the KPZ and the EW models. In the VLD model, a nonlinear term is added to the WV equation which results in The renormalization group analysis of the equation [53, 54] results in the values of expo-nent B = 0.20 and a — 0.67. The values are closest to the experimental values obtained for the LaF 3 growth on GaAs and InP (B = 0.2 ± 0.2, a = 0.6 ± 0.1, see Table 5.11). A numerical simulation of the one-dimensional discrete model belonging to the same uni-versality class (the same scaling exponents) as the VLD model was introduced by Lai and Das-Sarma [54]. The Lai and Das-Sarma model is a discrete solid on solid model in which a particle arriving on a surface is allowed to move to a nearest kink site (a site with two neighbours) with high binding energy to lower its energy or to increase its number of neighbors. The model also allows the process where a atom in a kink site can break its two bonds and jump either up or down to a nearest kink site having a lower energy. The process described by the discrete model is shown schematically in Fig. 5.60. [53, 54]: dh(x, t) dt = -v{VAh + Ai V 2 (V/ i ) 2 + n(x, t) (5.38) Chapter 5. Surface Morphology 114 Figure 5.60: Schematic illustration of the surface relaxation mechanism described by the one dimensional discrete model by Lai and Das Sarma [54] which belong to the same universality class as the continuum model by Villain [53], Lai and Das Sarma [54] from Ref. [63]. In summary, the most appropriate theoretical model which describes the kinetic pro-cess of our LaF 3 growth is the VLD model. The evaporation-recondensation process described by the EW equation does not play a major role in the MBE growth. We expect the lateral growth process described by the KPZ model to be negligible in the MBE growth because of the directionality of arriving particles. In both the W V and VLD models, the surface diffusion controlled by the local chemical potential is the most important process in the surface relaxation. In our MBE growth condition, we expect the surface diffusion to play a major role in the surface relaxation. The scaling exponents for our LaF 3 growth were closer to those predicted by the VLD model than those predicted by the WV model. This is anticipated because the WV model is a special case of the more general VLD model. Other experimental results which showed similar values of roughness exponents a to Chapter 5. Surface Morphology 115 our values of a (a = 0.6) determined for LaF 3 on GaAs and InP include the deposition of Ag on Si (a = 0.70) [59] using X-ray scattering and STM, the growth of Cu on Cu(100) studied by He atom beam scattering [60] (a — 0.6 - 1) and Si on Si (a = 0.68) studied by STM [61]. 5.5.3 Dynamical scaling The scaling relation of the surface morphology can also be observed from the power spec-tral density (PSD) S(q). According to the Family-Vicsek dynamic scaling relationship, the PSD S(q) scales as [64]: where d is the dimension of the interface (d = 2 in our case), z is the dynamical exponent, t is the time and f(t/q~z) is the scaling function. For the growth model by Villain [53], Lai and Das Sarma [54] (VLD), the dynamical exponent z is related to the roughness exponent a through [54]: z = 2a+d. Also the function f(t/q~z) ~ constant for t/q~z » 1 or for a large q. In this case, the PSD S(q) obeys the power law of the form: S(q) oc q~z. For the VLD model the dynamical exponent is z = a/(5 = 0.67/0.20 ~ 3.4. We have plotted the power law S(q) oc q~z with z = 3.4 in Fig. 5.57. The scaling relation S(q) oc q~z is consistent for the regions above cut-offs (q > qo) for both the LaF 3 /GaAs( l l l )A and LaF 3 / InP( l l l )B samples. In order to estimate the cut-off wavevector q in S(q), the correlation function C(r) described by Eqn 5.14 are Fourier transformed through: where J 0 is the Bessel function of the zeroth order, o is the rms interface width, £ is the correlation length and a is the roughness exponent. The values of 5(g) for the S{q) = T d - 2 C 7 ( ^ ) (5.39) (5.40) (5.41) Chapter 5. Surface Morphology 116 LaF 3 /GaAs( l l l )A and LaF 3 / InP(l l l )B samples studied by A F M are evaluated numer-ically using the values of the roughness coefficient a, the cut-off length £ and the rms surface roughness o obtained from the A F M images. Calculated height-height correlation S(q) using the values of o, £ and a determined from the fit of the correlation function C{r) are shown in Fig. 5.57. The cut-off wavevector q0 for S(q) were q0 0.04 n m - 1 for the LaF 3 /GaAs( l l l )B sample and q0 ~ 0.02 n m - 1 for the LaF 3 / InP(l l l )B sample. Below the cut-off wavevector q0, the height-height correlation S(q) is nearly constant. Above the cut-off wavevector, the variation of the calculated S(q) agrees with that of the PSD S(q) obtained from the A F M images and also the dynamic scaling relationship S(q) oc q~z where z = 3.4. 5.6 Summary The surface morphology of LaF 3 films grown on III-V semiconductors were investigated by X-ray scattering and A F M . The surface correlation lengths of the LaF 3 films obtained by X-ray scattering and the bulk coherence lengths from X-ray rocking curve measurements were comparable to each other. The result is consistent with columnar defect structures of LaF 3 films observed in Chapter 4. We interpreted that the defects are formed to accommodate the lattice mismatch at the growth temperature. That is the lateral sizes of coherent regions in LaF 3 films are associated with the lattice mismatch of the system at the growth temperature. The comparison of the surface correlation lengths and the bulk coherence lengths for the LaF 3/GaAs, InP system suggest that the surface structures of LaF 3 films on semiconductors reflect the columnar structures underneath them. The surface coherence length for LaF 3 films on InP was longer than on GaAs since the lattice mismatch is smaller in the LaF 3/InP system at the growth temperature. The surface structures of the LaF 3 films are also associated with the strain relieving defects formed Chapter 5. Surface Morphology 117 to accomodate the lattice mismatch at the growth temperature. The surface coherence lengths from X-ray scattering and A F M , the bulk coherence lengths from X-ray rocking curves as well as cross sectional SEM showed that the strain relieving defects are vertical regions separating the columns of coherent crystals and the surface structures reflect the columnar structures underneath them. The surface morphology of the LaF 3 films on GaAs and InP was analysed using the self-affine surface model. The scaling exponents determined were closest to those predicted by the Villain-Lai-Das Sarma model [53, 54]. Chapter 6 Semiconductor/Fluoride/Semiconductor Growth Growth of semiconductor-fluoride multilayer structures has been investigated by a num-ber of researchers due to their applications in optical and electronic devices. Most of the research has been concentrated on semiconductor growth on difluorides such as CaF 2 and SrF2. Representative work on III-V semiconductor growth on difluoride/semiconductor structures include InP/(Ca, Sr)F2/InP(100) [67], GaAs/(Ca, Sr)F2/GaAs(100) [68], GaAs /(Ca, Sr)F2/Si(100) [69] and GaAs/CaF 2 /Si(l l l) [70]. In this chapter, the growth of InP and GaAs on the rare-earth trifluoride/III-V semiconductor structures: LaF 3 / InP( l l l )B , LaF 3 /GaAs( l l l ) and ErF 3 /GaAs( l l l ) , are studied. Previous studies of semiconductor/difluoride/semiconductor structures have shown that the semiconductors [41] have a tendency to form islands due to the lower surface energy of the difluoride (CaF2 and BaF2) which varies from 0.3 to 0.5 J/m 2 [32, 33] depending also on the orientation of the material as compared to the surface energy of semiconductors (Si and GaAs) which ranges from 0.8 to 3.2 J/m 2 [34]. As we discussed in Chapter 3, the condition for wetting for systems of a film on a substrate is [31]: 7. > 7/ + Isf (6.42) where js, 7/ and 7,,/ are the free energy for substrate/air, film/air and film/substrate in-terfaces respectively. In fluoride/semiconductor systems, we expect that the film/substrate interface free energy 7,,/ to be lower than either 7 S or 7/. Since the surface free energy of fluorides is generally lower than that of semiconductors or 7semiconductors > 7fluoride, 118 Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 119 neglecting the film/substrate interface energy, the condition for the wetting is satisfied for fluoride films on semiconductors. In Chapter 3, we showed by angle dependent pho-toemission spectroscopy that the fluoride films cover semiconductor substrates as we expected. For a semiconductor on fluoride system, we expect the semiconductors to form islands when deposited on fluorides, since the condition for wetting is not satisfied. The fluoride layers were grown by molecular beam epitaxy on GaAs( l l l )A and InP(l l l )B substrates as described in Chapter 2. After the fluoride film growth, the samples were transferred, without being exposed to air, to an adjacent chamber for the GaAs or InP growth. Typical substrate temperature was 500°C during the InP growth and 600°C during the GaAs growth as measured by the diffuse reflectance spectroscopy [71]. The V/III flux ratio was As 2 /Ga~ 4 for the GaAs growth and P 2 / I n ~ 12 for the InP growth. The X-ray diffraction experiments were done ex-situ using a Cu Kal (A = 1.5405 A) rotating anode X-ray source and a high resolution four crystal (double-axis) diffractometer (BEDE 200). 6.1 Results 6.1.1 Formation of InP and G a A s islands on the fluoride/semiconductor structures The growth of InP and GaAs were performed on the LaF3, ErF 3/III-V semiconductor structures. An A F M image of the surface of a InP/LaF 3 /InP(l l l )B sample is shown in Fig.6.61. Islands with a lateral size of 300 - 500 nm are observed in the image. The density of the islands is estimated to be 1 x 109 cm - 2 . Note that the most of the edges of the islands have angles of approximately 60 or 120°. The InP islands shape reflects the trigonal a x a face structure of the LaF 3 film consistent with the orientation of the LaF 3 film grown on GaAs(ll l) [5]. Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 120 Figure 6.61: A F M image of the surface of InP/LaF 3 /InP(ll l )B sample. InP islands whose edges have an angle of 60 or 120° are observed. The shape of the islands reflects the trigonal a x a face of the LaF 3 layer underneath the InP islands. Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 121 Air InP islands J LaF InP substrate Figure 6.62: Cross-sectional S E M image of the I n P / L a F 3 / I n P ( l l l ) B sample in Fig. 6.61. The InP islands are faceted suggesting that they are single crystals. The thickness of InP islands ranges between 30 and 40 nm. In order to further investigate the surface morphology of the I n P / L a F 3 / I n P ( l l l ) B sample, scanning electron microscopy was performed. A cross sectional S E M image of the I n P / L a F 3 / I n P ( l l l ) B sample near the edge of the sample is also shown in Fig. 6.62. The L a F 3 layer is 35 nm thick as measured from the interference fringes of the (002) LaF 3 X-ray diffraction peak. The InP islands have a faceted shape which suggests that they are single crystal, with thickness between 30 and 40 nm. Since the growth of InP lasted for 6 min., the growth rate is 5 to 7 nm/min. The formation of InP islands was also observed on the L a F 3 / G a A s ( l l l ) A structure. The cross sectional S E M image of a L a F 3 / InP/ L a F 3 / G a A s ( l l l ) A sample is shown in Fig. 6.63. The InP islands are 200-300 nm wide and 200-300 nm in height. The growth time of InP was 7 min. yielding an island growth rate of 30-40 nm/min. A F M images of a I n P / L a F 3 / G a A s ( l l l ) A sample at three different magnifications are shown in Fig. 6.64 to 6.66. InP islands 70-130 nm in diameter are observed in the A F M Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 122 Figure 6.63: Cross sectional S E M image of a LaF3 / InP/LaF 3 /GaAs( l l l )A sample show-ing InP island size is 200-300 nm across and 200-300 nm high. images. The density of the islands is approximately 4 x 109 c m - 2 . Growth of GaAs on a E r F 3 / G a A s ( l l l ) A structure was also studied. A n A F M image of the surface of the G a A s / E r F 3 / G a A s ( l l l ) A structure is shown in Fig. 6.67. The image shows rectangular shape islands, between 100 and 300 nm wide. Their shape is different than that of the InP islands on the LaF 3 film which had parallelogram or triangular shape with edge angles of 60 or 120°. The rectangular shape of the GaAs islands reflects the orthorhombic face of E r F 3 consistent with the L E E D study of the orthorhombic rare-earth fluoride deposited on a semiconductor substrate [10] where the orthorhombic axe face of the fluoride films was found to be aligned parallel to the (111) hexagonal face of the semiconductor substrates. 6.1.2 Chemical nature of islands In order to verify that the islands are in fact the semiconductors that we expect, we have performed the X-ray photoelectron spectroscopy on one of the I n P / L a F 3 / I n P ( l l l ) B Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 123 Figure 6.64: A F M image of the surface of a I n P / L a F 3 / G a A s ( l l l ) A sample (10/im x 10pm). Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 124 Figure 6.65: A F M image of the surface of the InP/LaF 3 /GaAs(l l l )A sample in Fig. 6.64 (2.4/xra x 2.4/im). Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 125 0 200 400 GOO Figure 6.66: A F M image of the surface of the InP/LaF 3 /GaAs(l l l )A sample in Fig. 6.64 (0.7pm x 0.7pm). Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 126 2 , 0 0 Figure 6.67: A F M image of a GaAs/ErF 3 /GaAs(ll l)A sample showing rectangular shape GaAs islands. Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 127 50 40 £. 30 o m O E2 0 >* w 10 c a> +-» c 0 -10 0 50 100 150 200 250 Binding Energy (eV) Figure 6.68: X-ray photoelectron spectra of the InP/LaF3/InP(lll)B sample taken at the take-off angle of 90° and 20°. The intensity of LaF 3 photoelectron peaks relative to the InP peaks decreases with decreasing take-off angle. samples (the sample shown in Fig. 6.61). The photoelectron spectra taken at two different take-off angles, 90° and 20°, are shown in Fig. 6.68. The photoelectron spectra show both InP and LaF 3 peaks as indicated in the figure. The intensity of the LaF 3 photoelectron peaks relative to the InP intensities decreases with decreasing take-off angle. In order to express the intensity ratio of the island peak (InP) to the peak from the layer underneath (LaF3) as a function of the take-off angle 9, assume the islands have width L and thickness d as shown in Fig. 6.69. Further assume that the separation between the islands is L . At the photoelectron take-off angle 9, an area of width x is shadowed by the islands. The inelastic mean free path in InP for the kinetic energy of Ek = 1500 eV is A = 2.5 nm [25]. For the InP/LaF 3 /InP(ll l )B sample studied, the thickness of the InP islands is estimated to be t = 40 - 70 nm from the SEM micrograph. Since t 3> X(Ek), the intensities from the InP islands and the LaF 3 layer are proportional to their respective exposed surface areas. Therefore the intensity of a photoelectron peak lnP/LaF3/lnP(111)B Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 128 Islands Substrate — L — d H x •*-Figure 6.69: Schematic illustration showing a substrate covered by islands of width L and thickness d and the photoelectron collected at take-off angle 9. from the InP islands is proportional to L + x and the intensity from the LaF 3 layer is proportional to L — x. Consequently the intensity ratio of an InP island peak to a LaF 3 peak is: Imp = ITnpL + d/ tan 9 haF3 I?aFzL-d/ tan 9 K ' ; where If^PtLaFi is intensity of the photoelectrons from the sample of thickness t X(Ek) where \(Ek) is the inelastic mean free path of the photoelectrons with kinetic energy E^. According to Eqn. 6.43, the intensity ratio of the InP to the LaF 3 peaks increases with increasing value of 1/ tan#. In Fig. 6.70, the intensity ratio of In 4d to La 4d core levels is plotted as a function of 1/ tan#. The intensity ratio increases with increasing value of 1/ tan0 (more grazing take-off angle), confirming that InP islands are above the LaF 3 layer. The fit of Eqn. 6.43 is also plotted in Fig. 6.70. The value of d/L was determined as d/L = 0.1 from the fit. Since the island thickness d was 30-40 nm as estimated from the SEM image, the island Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 129 0.50 lnP/LaF3/lnP(111)B 0.45 H 0.25 H 0.0 0.5 1.0 1.5 2.0 2.5 3.0 1 / tane Figure 6.70: Intensity ratio of In 4d to La 4d core levels as a function of 1/ tan# for the InP/LaF 3 / InP(l l l )B sample. The intensity ratio increases indicating that InP is on top of the LaF 3 layer. The solid line is a fit of Eqn. 6.43. The value of K was determined as K =  Ii?iul I'LaU = °- 2 6 - T n e r a t i o d l L w a s determined as d/L = 0.1. width and the island spacing L is estimated as L ~ 300-400 nm. The estimated value of L is in good agreement with the A F M value, L = 300-500 nm. X-ray specular reflectivity was also measured on the InP/LaF 3 /GaAs(l l l )A sample and is shown in Fig. 6.71. The specular reflectivity shows two peaks one at qz — 0.23 n m - 1 and other at qz = 0.42 n m - 1 . The critical angle of LaF 3, 8C = V25 = 0.00563 rad corresponds to the qz value of qzc = 2ksm8c = 0.459 n m - 1 where k = 2n/X = 40.8 n m - 1 and A = 0.15405 nm is the wavelength of the Cu K a radiation. Similarly, the qz value corresponding to the critical angle of InP is qz = 0.421 nm" 1 . The specular reflectivity measures the density variation along the z direction. Since the top InP layer in the InP/LaF 3/InP sample was comprised of islands, the average density in the x-y plane is lower than that of InP. If the InP island coverage was approximately 50 %, critical angle for total external reflection would be at 8 = J2SInP/2 = 0.00398 rad or at Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 130 0 1 2 3 qz(nm-1) Figure 6.71: X-ray specular reflectivity of the InP/LaF 3 /InP(ll l )B sample. The specular reflectivity shows two peaks one at the position corresponding to the critical angle of InP and another corresponding to the critical angle of LaF 3. This is particular to the island growths. qz = 2ksin9c = 0.33 nm" 1 roughly in agreement with the qz value of the peak at a lower qz. We interpret the peak at higher qz as the reflection from the InP/LaF 3 interface. X-ray specular reflectivity is consistent with the islands observed in the A F M and SEM images being InP and the coverage of the islands being approximately 50 %. 6.1.3 Crystallinity and strains in the InP islands on fluoride structures In order to see the crystallinity of the InP islands and the strains in the islands, we have performed the X-ray diffraction. A HRXRD 6-26 scan showing the InP(l l l ) peak and the LaF3(002) peak is shown in Fig. 6.72 for the InP/LaF 3 /InP(ll l )B sample in the A F M image in Fig. 6.61. A 6-26 scan from a LaF 3 / InP(l l l )B sample is also shown in Fig. 6.72 for comparison. The FWHM of the InP(l l l ) peak from the InP/LaF 3 /InP(l l l )B sample 85 arcsec, is more than double of F W H M ~ 25 arcsec. of the InP(l l l ) peak from the Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 131 10' Figure 6.72: HRXRD 9-29 scan of a InP/LaF 3 /InP(ll l )B sample (top). A 6-29 scan from a LaF 3 / InP( l l l )B sample is also shown (bottom). The inset shows the enlarged InP(l l l ) peaks revealing the broadening. LaF 3 / InP( l l l ) sample. Since the broadening was observed in the sample with InP islands on a fluoride film, but not in the samples with only fluorides on semiconductors, the presence of InP islands must be associated with the broadening. We were able to fit the broadened peak with two Gaussian functions. The separations of two components was A9 = —0.012 ± 0.003°, as shown in the inset in Fig. 6.72. The intensity of the smaller peak is too large to interpret it as arising from a layer of 40 nm thick islands. One interpretation is that the broadening is caused by an inhomogeneous strain in the InP substrate. As we have observed by X-ray diffraction in Chapter 4, the strains develop in the LaF 3 films on semiconductors during cooling due to the differential thermal contractions between the film and the substrate. The LaF 3 films have tendencies to contract more than the semiconductor substrates because of their larger thermal expansion coefficients. In the InP island system on fluorides, the InP islands act like clamps to prevent the LaF 3 films from contracting Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 132 according to the thermal contraction of the fluoride, but instead, help the LaF 3 films to contract according to the thermal contraction of the InP substrate. As a result, parts of the LaF 3 films where there are no InP islands on top, would have tendencies to contract more than the parts with InP islands on top in order to compensate the loss of contraction. This inhomogeneous contractions of the LaF 3 films can cause an inhomogeneous strain in the InP substrate. If we assume that the larger component of the InP peak is unstrained, then from the separation of the two component, we can estimate the strains in the component of the substrate. The separation of the peak corresponds to a strain perpendicular to the interface of e±_ = 0.0009 ± 0.0002. For a stress in the (112) direction, the relationship between the in-plane strain £|| and the perpendicular strain e± (along the (111) direction) is given by [37]: £ lCu + 2Ci2 + 4C744^ ( 6 4 4 ) 2 C\\ + 2Ci2 — 2C44 where C{j are the elastic constants of InP, Cn = 10.11 • 1010 N m - 2 , C12 = 5.61 • 1010 N m~ 2 and C 4 4 = 4.56 • 1010 N m - 2 [76]. The in-plane strain £|| is thus calculated as £|l = —0.0015 ± 0.0003, which is compressive. This is consistent with our interpretation in which parts of the InP substrate are compressively strained. Powder X-ray diffraction was performed on a InP/LaF 3 /GaAs(ll l) sample and is shown in Fig 6.73. The 8-26 scan shows the (004) reflection of the LaF 3 film, the (222) reflection of the GaAs substrate and a small peak which we interpret as the InP (222) peak. The GaAs(222) as well as the LaF3(004) peak show doublets corresponding to Cu K a l and Cu Ka2. The width of the X-ray diffraction peaks can be interpreted as being associated with the size of the coherent crystals. The Bragg peak of the InP islands on the LaF 3 / InP( l l l ) structure in the HRXRD in Fig. 6.72 as well as those observed in the powder XRD Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 133 100000 Q. O 1000-; w c CD 10000-J LaF 3 / InP / LaF 3 / GaAs(111 )A IW«X>4> ^ J \ lnP(222)' c 46 48 50 52 54 56 2 0 (°) Figure 6.73: 9-29 scan of the InP/LaF 3 /GaAs(l l l )A sample using a powder X-ray diffrac-tometer. It shows LaF3(004) reflection, GaAs(222) reflection from the substrate and a small peak which we interpret as the InP(222) reflection from the InP islands. of the same sample were significantly narrower than those of the InP islands on the LaF 3 /GaAs( l l l ) structure. The comparison suggests that the crystal size for the InP islands on LaF 3/InP is larger than the crystal size for the InP islands on LaF 3/GaAs. The result is consistent with the longer lateral coherence lengths of the LaF 3 films grown on InP substrates as compared to that of the LaF 3 films grown on GaAs substrates. 6.1.4 Self-affine surface structure analysis of the InP islands on L a F 3 In Chapter 5, the structure of laterally homogeneous surfaces (fluoride thin films, semi-conductor substrates) was analysed in terms of a scale invariant, self-affine, structure model. In this section we apply the same analysis to the laterally inhomogeneous semi-conductor island systems, and show that we obtain comparable quality fits to the height-height correlation function as in the homogeneous systems. The morphology of the InP islands on LaF 3 was investigated by A F M . The roughness Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 134 exponent a which appears in the scaling relationship: o oc L a , was determined from A F M images. The height-height correlation function C(r) and the mean square fluctuation g(r) were directly computed from the height information from A F M images as described in Chapter 5. The roughness exponent was determined from the mean square fluctuation g(r) for small r given in Eqn. 5.32: g(r) ~ 2o2C-)2a (6.45) The correlation length £ and the rms interface width o is determined by fitting Eqn. 5.14: C(r) — o-2e~(-r/&2a to the correlation function C(r) computed from the A F M image. The a was fixed to the value obtained from the fit to g(r). The mean square fluctuation g(r) and the correlation function C(r) computed from the A F M image in Fig. 6.61 for the InP/LaF 3 /InP(ll l )B sample, are shown in Fig. 6.74. The roughness exponent a for the InP/LaF 3 /InP(ll l )B sample was determined as: a = 0.73 ±0.03 from the fit of Eqn. 5.32 to g{r). The correlation length £ and the rms surface roughness o were found to be £ = 68.7 ± 0.6 nm and o = 17.5 ± 0.06 nm respectively. If we assume that the islands have a sinusoidal shape, the estimated thickness d of the InP islands is approximately d ~ 2^/2o = 50 nm which is similar to the value estimated from the SEM image in Fig. 6.62, t = 30 - 40 nm. The correlation length £ is approximately quarter of the islands size (300-500 nm). The roughness exponent a was also determined for the InP/LaF 3 /GaAs(l l l )A sample shown in Fig. 6.65. The height-height correlation C(r) and the mean square fluctuation g(r) computed from the A F M image in Fig. 6.65 are shown in Fig. 6.75. The linear fit of Eqn. 5.32 to g(r) to obtain the roughness exponent a and the fit of the correlation function in Eqn. 5.14, C(r) = o2e~^2h, to determine the correlation length £ and the rms surface roughness o, are also shown in the figure. The roughness exponent a was determined as a = 0.76 ± 0.03 from the fit. The correlation length £ and the rms surface Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 135 r (nm) Figure 6.74: The mean square fluctuation g(r) (a) and the height-height correlation C(r) (b) obtained from the A F M image of the InP/LaF 3 /InP(ll l )B sample in Fig. 6.61. The solid line in (b) is the linear fit of Eqn. 5.32 to g(r) to determine the roughness exponent a. The roughness exponent a was determined as a = 0.73 ± 0.03 from the fit. The solid line in (b) is the fit of a function C(r) = o2e~^ " to the height-height correlation C(r) obtained from the A F M image. Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 136 Table 6.12: Comparison of the roughness exponent a for the InP/LaF 3/GaAs, InP system with those of the LaF 3/GaAs, InP system. Roughness Exponent a InP/LaF 3 /InP(ll l )B 0.73 ± 0.03 InP/LaF 3 /GaAs(l l l )A 0.76 ± 0.03 LaF 3 /GaAs( l l l )A 0.6 ± 0.1 LaF 3 / InP(l l l )B 0.6 ±0 .1 roughness o were determined as £ = 32 nm and o = 3.2 nm. The correlation length £ is about half of the diameter of the islands observed in the A F M image as expected. We compare the roughness exponents a obtained for the InP/LaF 3/GaAs, InP system with those of the LaF 3/GaAs, InP system in Table 6.12. The roughness exponents a of the InP/LaF 3/InP system and the InP/LaF 3/GaAs system are close to each other, suggesting that the growth kinetics of the InP islands are similar in both systems. The roughness exponents for the InP/LaF 3/GaAs, InP system and those of the LaF 3/GaAs, InP system are also similar to each other. The power spectral density (PSD) S(q) of the InP/LaF 3/InP, GaAs(ll l ) systems were also computed from the A F M image and are shown in Fig. 6.76. The Fourier transforms of the correlation function: C(r) = o2e~(r/®2a using the parameters obtained from the fits of correlation functions from A F M are also plotted in Fig. 6.76. This is plotted to estimated the cut-off in q as we have discussed in Chapter 5. The PSDs for both LaF 3 on InP and GaAs showed power law behaviours: S(q) oc q~z with z ~ 4 above the cut-offs Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 137 O 0 InP / L a F q / lnP(111)B 10 a = 0.76 ± 0.3 i 1 — i — i — i — i — i — 1 1 1 — t a = 0.76 a = 3.2 ±0.1nm % = 32.1 ± 0.2 nm _i • • i i i i_ 100 r (nm) 1000 Figure 6.75: The mean square fluctuation g(r) (b) and the height-height correlation C(r) (a) obtained from the A F M image in Fig. 6.65. The solid line in (a) is the linear fit to g(r) to determine the roughness exponent a. The solid line in (b) is the fit of a function C(r) = o2e~^ to the correlation C(r) obtained from the A F M image. The parameters obtained from the fits are indicated in the figure. Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 138 InP/LaFg /lnP(111)B 0.1-I . . — — 0.01 0.1 q (nm"1) Figure 6.76: The PSD S(q) for the InP/LaF 3 /InP(ll l )B sample (top) and the InP/LaF 3 /GaAs(l l l )A sample (bottom) shown in the A F M images in Fig. 6.61 and Fig. 6.65. The solid lines show the Fourier transforms of the correlation function C(r) from the fits in Fig. 6.74 and 6.75. The dashed lines are the power law q~z where z — 4 Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 139 (q > 9o). 6.2 Summary In this chapter, the growth of semiconductor/rare-earth fluoride/semiconductor struc-ture has been investigated. The formation of the three-dimensional InP islands on the LaF 3/InP, GaAs(ll l) structures was observed. The island formation was expected be-cause of the lower surface energy of the fluoride as compared to that of the semiconduc-tors. The formation of GaAs islands was also observed on the ErF 3 /GaAs( l l l )A struc-ture. GaAs did not grow on LaF 3 /GaAs(l l l ) with the present growth condition (growth temperature of 600°C, III-V ratio of As2/Ga ~ 4) likely due to the large mismatch (+3.8 %) between GaAs and LaF 3. The result shows that the lattice mismatch is an important factor in the fabrication of semiconductor/rare-earth trifluoride/semiconductor structure. A strained InP component was observed by HRXRD in the InP/LaF 3 /InP(l l l )B system. We interpret the component as parts of the InP substrate strained due to the differential thermal contraction between the InP islands, the LaF 3 layer and the InP substrate. The self-affine surface structure analysis of the InP islands on LaF 3 was carried out by atomic force microscopy. We have obtained a comparable quality fits for the height-height correlation function of this system as in the homogeneous LaF 3 on semiconductor system in Chapter 5. The result shows that the self-affine surface structure analysis can also be applied to a laterally inhomogeneous semiconductor island system namely the InP/LaF 3/InP structure. In order for the epitaxial rare-earth trifluoride films to be used in the device appli-cation, the growth conditions must be improved. Mixing other rare-earth fluorides into the fluoride layer to lattice match the semiconductor film or growing lattice matched Chapter 6. Semiconductor/Fluoride/Semiconductor Growth 140 semiconductor layers on the fluoride layer may improve the quality of the semiconductor layers. The present study shows some promises towards a use of epitaxial rare-earth trifluoride films in the III-V semiconductor technologies. Chapter 7 Conclusion Epitaxial growth of the LaF 3 and ErF 3 films on GaAs(lll) and InP(l l l ) substrates by molecular beam epitaxy has been investigated. High-resolution X-ray diffraction showed a LaF3(002) peak 100 arcsec in width aligned with (111) direction of the InP substrate indicating a high quality epitaxial growth. The epitaxial growth of LaF 3 films on InP was demonstrated for the first time. We observed columnar structures in the LaF 3 films deposited on GaAs and InP by scanning electron microscopy. The columnar structure is consistent with the structure zone model by Thornton [45]. The growth of the LaF 3 films was done in the temperature range where the films are expected to have a dense columnar microstructure. From the epitaxial film growth point of view, the columnar structure is that the columnar defect structures are formed to relieve the strains due to the lattice mismatch at the growth temperature and that the strain relieving defects are regions surrounding columns of coherent crystals. The lateral bulk coherence lengths in the LaF 3 films ob-tained from X-ray rocking curve measurements were comparable to the defect spacings required to accommodate the lattice mismatch at the growth temperature. The lateral coherence lengths are longer in LaF 3 films on InP than on GaAs consistent with the smaller lattice mismatch at the growth temperature in LaF 3 on InP. We showed that the surface correlation lengths of LaF 3 films on GaAs and InP ob-tained by X-ray diffuse scattering were equal within the experimental accuracy to the lateral bulk coherence lengths from X-ray rocking curves. This result is consistent with 141 Chapter 7. Conclusion 142 the strain relieving columnar defect structures of the LaF 3 films on semiconductors. The coherent crystals in the LaF 3 films propagate perpendicular to the interface. Con-sequently the columnar structures are reflected in the surface structure. The surface correlation lengths were longer for LaF 3 films on InP than on GaAs because the lattice mismatch at the growth temperature is smaller for LaF 3 on InP. The residual tensile strains observed in LaF 3 films on GaAs were in agreement with the strain relieving defect interpretation of columnar structures of the films. According to our interpretation that the strains due to the lattice mismatch are relieved by formation of defects surrounding columns of coherent crystals. During cooling, the LaF 3 films have tendencies to contract more than the semiconductor substrates because of the larger thermal expansion coefficients of fluorides. However, if the defects are pinned at the interface, the columns of coherent crystals are unable to accommodate the differential thermal contraction between the film and the substrate. In such case, the columns of coherent crystals in LaF 3 films are forced to contract according to the thermal contraction of the semiconductor substrates resulting in the tensile strains in the films. The tensile strains observed by HRXRD were also consistent with the columnar strain relieving defect structure of LaF 3 films. We applied a self-affine surface structural analysis on the fluoride on semiconductor systems using the X-ray diffuse scattering and the atomic force microscopy (AFM). We were able to fit the X-ray diffuse intensities and the height-height correlation functions from atomic force microscopy using a self-affine surface structure model [49]. We ob-tained a good agreement between the two techniques on the scaling exponents, surface roughness and surface correlation lengths of LaF 3 films on semiconductors. The scal-ing exponents obtained by X-ray scattering and A F M were consistent with the scaling exponents predicted by the Villain-Lai and Das Sarma model [53, 54]. We demonstrated the growth of single crystal InP islands on the LaF 3 / InP( l l l ) Chapter 7. Conclusion 143 structure. We showed that the self-affine surface analysis can be applied to a laterally inhomogeneous semiconductor on insulator system, namely InP islands on LaF3. The superior crystal quality of InP islands grown on a LaF 3/InP structure as compared to InP islands on a LaF 3/GaAs showed that the lattice mismatch between the semiconductor and the fluoride is an important factor in this system. The strain analysis by XRD showed that differential thermal expansions between the semiconductor and the fluoride are also important in this heteroepitaxial semiconductor/fluoride system. In this study, we demonstrated the growth of epitaxial LaF 3 and ErF 3 films on (111) GaAs and InP substrates. Epitaxial growths of high quality epitaxial fluoride films on III-V semiconductors are important for applications such as integrated optoelectronic devices. We showed that the LaF 3 films on semiconductors possess columnar struc-tures and established the direct relationship between the lattice mismatch in the flu-oride/semiconductor system and the columnar defect structures. Characterizing film structures and understanding the origins of formations of the structures are necessary in controlling the film growths and improving the fluoride film qualities. In order for the epitaxial rare-earth trifluoride to be incorporated in the III-V technology, more re-search is needed. This includes making better semiconductor films on LaF 3 and finding a condition to grow the trifluoride films on (100) semiconductor substrates. Studying electronic and optical properties of trifluoride/semiconductor structures and developing the etching/microfabrication technology using epitaxial fluorides are also useful in the advancement of the epitaxial fluoride technology. Appendix A Calculation of hydrogen exposures The hydrogen exposure for a given H 2 pressure and a exposure time of atomic hydrogen etching is calculated as follows. Using an ideal gas approximation, the number density p of the H 2 molecules for a pressure P and a temperature T is given by: N P P=- = T^ (A-46) v kT where N is the number of molecules, v is the velocity of the molecules and k is the Boltzmann constant. For a room temperature T = 300 K, kT = 4 x 10 - 2 1 J . Using the H 2 pressure of P = 1.0 x 10~6 mbar, we have: , = £ (A.47) 1.0 x 10~6mbar Nm~2 4 x 10-21 J I0~2mbar 2.5 x 1017 H2molecules/m3 Using the equipartition theorem: 1 2 1,™ -mu 2 = -kT 2 2 where m is the mass of the H 2 molecules and v is the mean velocity of the H 2 molecules. Therefore the mean velocity of H 2 molecules is given by: (A.48) m 4 x IO" 2 1 \| 2 x 10-3/6 x 1023 = 1.1 x 103 m/s 144 Appendix A. Calculation of hydrogen exposures 145 The rate 7 of the H 2 molecules hitting an unit area is given by: 7 = y (A.49) = 1.1 x 103-2.5 x 1017/2 = 1.4 x 1019 H2molecules secern'2 The rate of H 2 molecules, hitting the W filament is: rH2 = lAfil (A.50) The rate of atomic hydrogens being produced is given by: r = rH2V (A.51) where n is the dissociation rate of the H2 molecules. The area of the filament with length L and diameter D is: AFIL = TTDL = n(2.5 x 10_4)(0.05) = 4 x 10 _ 5m 2 . The dissociation rate 77 of the H2 molecules at the temperature between 1800 and 2000°C is 77 = 0.3 [65]. Hence the rate of atomic hydrogens being produced is: T = TH2rj (A.52) = 1.4 x 1019 • 4 x 10 - 5 • 0.3 = 1.6 x 1014 Hatom/sec The rate per unit area of atomic hydrogen reaching the sample situated at the distance R = 3 cm away from the filament is: r 7r i? 2 1.6 x 1014 5.7 x 1012 Hatoms cm~2sec~x (A.53) Appendix A. Calculation of hydrogen exposures 146 Finally, the atomic hydrogen exposure during time t = 10 min. is: EH = It (A.54) = 5.7 x 1012 -10-60 = 3.4 x 1016 Hatoms cm"2 The atomic hydrogen exposure for the H2 molecules with the pressure P = 1.0 x 10 6 mbar and the exposure time 10 min. is estimated as 3 • 1016 cm - 2 . Appendix B Estimation of thickness of oxide and carbon layers The thicknesses of carbon contaminants and oxide layers on a GaAs wafer are calculated using the intensity ratio of photoemission peaks before and after the oxide and carbon contaminant removal by atomic hydrogen etching. We assume that the GaAs substrate is covered with a uniform layer of oxides of thickness d2 and a carbon contaminant layer of thickness d\ as shown in Fig. B.77. The intensity of a substrate peak covered by a uniform layer of thickness d is given by [29]: Is = I~e~WU* (B.55) where X(Ek) is the inelastic mean free path in the overlayers at the photoelectron energy Ek of the peak, is the intensity of the substrate peak from a substrate of thickness t 3> (Ek) and 9 is the escape angle or the angle between the interface normal and the detector. Therefore the intensity ratio of As 3d substrate peak before and after the oxide/carbon contaminant removal is: __d1+d2_ 1As3di _  IAs3de k T Too J-AsUf  1AsM d — g A(B f c)sin# where lAsZdi and iAsZdf are the intensities of the As 3d core levels before and after the atomic hydrogen etching. The intensity ratio of the bulk GaAs component before and after the hydrogen etching shown in Fig. 2.7 and 2.8 is iAsZdi/lAsUf — 1-2/16.4 = 0.075. 147 Appendix B. Estimation of thickness of oxide and carbon layers 148 d-i | Carbon Layer d 2 I Oxide Layer Substrate Figure B.77: Schematic illustration of a GaAs wafer covered by a uniform layer of oxides of thickness d 2 and the carbon contaminant layer of thickness d\. The total thickness d = d\ + d 2 of the oxide/carbon contaminant layers is calculated as: d = -inl^XsinO (B.56) = - In 0.075 x 0.83 sin 45° (B.57) ~ 1.52 nm (B.58) We have used the inelastic mean free path of A = 0.83 nm at the photoelectron kinetic energy of 50 eV [25] and the escape angle of 8 = 45° in the calculation. The oxide thickness is estimated using a relationship between the thickness d and the layer/substrate peak ratio R = Ii/Is given by [29]: where K = If°llf is the intensity ratio of the overlayer and the substrate, both of thickness t 3> \(Ek) • The intensity ratio R of a chemically shifted As oxide component (As 20 3) to a bulk GaAs component is R = IAszdoxidelIAsZdGaAs - 4.7/1.2 = 3.9. The Appendix B. Estimation of thickness of oxide and carbon layers 149 thickness of oxide layer d2 is thus: d2 = A esin0m[-^ + l] (B.60) = 0.83sin45°ln[3.9 + l] (B.61) ~ 0.9 nm (B.62) We assumed K ~ 1 and used the inelastic mean free path of Ae = 0.83 nm [25] and the escape angle of 9 = 45° in the calculation. The thickness of the carbon contaminant layer is estimated as di = d — d2 = 1.5 — 0.9 = 0.6 nm. The thicknesses of the oxide+carbon layer and the Si0 2 layer on the InP wafer are calculated from the photoemission intensity ratios. The surface of the InP substrate is assumed to be first covered with a uniform layer of oxide+carbon of thickness d2 followed by an uniform layer of Si0 2 of thickness d\. The thickness of the oxide+carbon layer removed by the atomic hydrogen etching is calculated from the intensity ratio of the oxide to the InP components of P 2p core levels using Eqn. B.59: d2 = A / n P sin01n[—— + 1] (B.63) IpinP = 0.48 sin 45° ln[— + 1] (B.64) 1.8 = 0.4 nm (B.65) The inelastic mean free path of A = 0.48 nm in InP at 50 eV[25], the escape angle of 9 = 45° and K = Ip°0/IpinP — 1 are used in the calculation. The thickness of Si0 2 layer removed by HF etching is estimated from the intensity ra-tio of the Si 2p and the P 2p photoemission peaks before the HF etching using Eqn. B.55. The intensity ratio K of the Si 2p core levels from a Si02 layer of thickness t >• Ek and the P 2p core levels from an InP wafer of thickness t 3> Ek is approximated as [66]: K = ^ ( ^ ) - o - 3 4 = 3^108^0.34 _ 0 g ( B 6 6 ) o~P2P Ep2p 4 132 Appendix B. Estimation of thickness of oxide and carbon layers 150 where oso.p,piv are the cross section of the Si 2p and P 2p core levels respectively from Ref. [77], Ef. is the kinetic energy of the photoelectrons. In Fig. 2.9, the intensities of the Si 2p and P 2p core levels are ISi2p — 16.9 and Ip2p = 1.76. The thickness of the SiC>2 layer is thus estimated as: di = A 5 i o 2 l n [ ^ T ^ £ e ~ ^ ^ r ? + 1] (B-6 7) = 0.88 nm (B.69) The inelastic mean free path, XInP = 0.48 nm in InP at 50 eV, A5J02 = 0.8 nm in Si02 [25] and the escape angle 6 = 45° are used in the calculation. Appendix C X-ray specular and diffuse reflectivity calculation C . l Specular Reflectivity The film thickness t and the rms surface roughness o are obtained using a recursive method for stratified layers [47]. Consider a system of N stratified layers. A system with two interfaces is illustrated in Fig. C.78 as an example. For a system of N stratified layers, the reflectivity Rj+i at the top of the layer j + 1 is given by a recursion formula: *>- = < C 7 0 ) Rj+i = a-jEj+i/Ej+i Si{e)-fi-M where Ej+i and Ej+1 are the amplitudes of the electric vectors for the incoming and reflected beams at the interface j + 1. The amplitude Oj is given by: a . = e ( - ^ ( 0 ; K / A ) ( a ? 1 ) where dj is the thickness of the layer j and fj(9) is the fresnel coefficient given by: /,-(0i) = ( 0 j - 2 ^ - 2 i & ) (C.72) The computation starts at the substrate level i.e. at j = N by noting that RN+I = 0. It ends at the film/air interface j = 0 where the reflectivity is R0 = EQ/E0, since a0 = 1. The coefficients 5 and 3 are related to refractive index of the medium n through: 71 = 1-6-0 (C.73) 151 Appendix C. X-ray specular and diffuse reflectivity calculation 152 Figure C.78: Schematic illustration of a system with two interfaces. Ei and E\ are the amplitudes of the electric vectors of the incoming and reflective beams at interface i. 6 + iB = (C.74) where r e is the electron radius, A is the wavelength of Cu Ka , is the Avogadro's number, pk is the mass density of k atom in a unit cell in g/cm3, Mk is the atomic mass of the k atom in g/mole. The quantity fk is given by: fok + Af'k + iAf'k- The values of fk for given ions can be found in the International X-ray Table. The value of reNA/2n is given by: re_ = 2-818 x l O - 1 3 6 Q 2 2 x i q 2 3 = x 1 0 i o ( c , G 5 ) ( c 7 5 ) 2?r 2?r v 1 v ' The effect of roughness is implemented using the expression of the reflectivity by Nevot 2 and Croce [48] Rj — RFje9zjgzj+iaj where qzj and qzj+i are the transfer vectors per-pendicular to the plane of the interface for the layer above and below the interface j respectively, Oj is the rms width of the interface j and Rp is the fresnel reflectivity for an ideal interface. The transfer vector qz is given by qzj = 2k0sin9 ~ 2kofj(6j). Appendix C. X-ray specular and diffuse reflectivity calculation 153 \ a 2 b 2 y Interface Figure C.79: Schematic illustration of an interfaces showing the incoming vectors with amplitudes ai, a2, and the out going vectors bi, b2. The incident and detected angles are 61 and 62 respectively. C.2 Diffuse Intensity The roughness coefficients a and the correlation length £ were obtained from X-ray diffuse scattering using the expression for the diffuse intensity given by Sinha et al. [50]. The expression uses the distorted wave Born approximation (DWBA). Since the systems studied involve two interfaces, the diffuse intensity for the multilayer interfaces are used. Consider a system of N stratified layers. At an interface, the amplitudes of incoming vectors are defined as a\, a2 and those of the outgoing vectors are defined as b\ and b2 as illustrated in Fig. C.79. The incident and detected angles are Q\ and 62 respectively. For each interface, we define the transfer vectors qz and qzp as: qz = klz - k2z = fc0(/i - /2) (C76) qzp = k\z + k2z = fc„(/i + /a) Appendix C. X-ray specular and diffuse reflectivity calculation 154 where k\z and k2z are the z component of the incident and scattered wavevectors re-spectively and k0 is the magnitude of the incident wavevector given by k0 = 2-K/X where A is the wavelength of the incident radiation. For Cu-Ko; radiation, the wavelength is A = 1.5401A. The function f(9j) is denned as: f(0j) = (0j - 2 5 - i2f3)1'2 .(C-77) where S and f5 is related to the refractive index of the medium above the interface, n through n = 1 — 5 — ifl. We also define four coefficients for each interface: A0 = a ^ i q ° Z (C.78) A i = A2 = A 3 = where the four transfervectors are defined as: % = ~{klz + k2z) = -qzp (C.79) 91 = -{hz ~ k2z) = -qz 92 = -{k2z ~ hz) = qz Q3 = - ( - h z - k2z) = qzp The diffuse intensity is then given by: W * i . h) = £ E A P i ( A P j ) M , ( i ) ^ 0 - ) ^ ^ , j) (C.80) F^ ( i , j) = 2e-^ [^<T'2+<<Ti ] f°°[e^jc(x) - l]cos(^X)dX •/ 0 where 6\ and 02 are the incident and the scattered angles respectively and A0 2 is the a\a2e iq0z Qo aib2e~ iqiz Qi a2bie~ iq2z Q2 bib2e~ •iq3z Q3 Appendix C. X-ray specular and diffuse reflectivity calculation 155 angle subtended by the detector. Api is the density difference at the interface i given by: A P i = M (n 2 -n 2 + 1 ) (C.81) where nf is the index of refraction of the medium above the interface given by: n2 = (1-Si- idi)2 ~ 1 - 25t - 2i8i (C.82) The density difference at the interface i, Api becomes: APi = ^(-2(5i + idi) + 2(6i+1 + i3i+l)) (C.83) The integral in Eqn. C.80 is evaluated numerically using the Fourier integral routine in Ref. [78]. To evaluate the amplitudes a; and we first calculate the reflectivity rj at each interface using the recursion method by Parratt [47]. We then set the amplitude a0 of incident ray to unity and work backswords to determine the rest of the amplitudes. The amplitudes of the incoming and the outgoing rays are defined as in Fig. C.80. The dj and bj are the amplitudes of the incoming and reflective rays at the interface j in the medium above the interface. The cxj+x and 3j+\ are the outgoing and the incoming rays at the interface j in the medium below the interface j. The outer most medium is defined as 0 with interface 0 below it. The layer thickness for the medium j is dj and the reflectivity at the interface j is rj. At the interface j — I, the relationship between the rays in the medium j — I, dj-i, and the rays in the medium j , OLJ and 3j is: dj + pj = dj-i + bj_i (C.84) Using otj = djeikiAi and pj = bjC~ ik^\ a.e-ikjdj + = a . _ x + h . _ x (C_85) {dj 4- bje-2ik^)eik^ = o,-_i + fej-i (C.86) Appendix C. X-ray specular and diffuse reflectivity calculation 156 Medium 0 2 Figure C.80: Schematic illustration of a system with two interfaces. The dj and bj are the amplitudes of the incoming and the reflected rays at interface j in the medium above the interface. The ctj+\ and fij+\ are the outgoing and incoming rays at the interface j in the medium below the interface j. We also know that bj = djTj and Rj = rje~2lkjdj: + Rj)eik^ = dj-i + (C.87) Finaly we obtain the amplitude dj as: Bibliography [1] H. D. Miiller and J. Schneider Appl. Phys. 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