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Light scattering measurements of surface morphology during molecular beam epitaxy growth of GaAs-based… Lavoie, Christian 1994

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LIGHT SCATTERING MEASUREMENTS OF SURFACE MORPHOLOGY DURINGMOLECULAR BEAM EPITAXY GROWTh OF GaAs-BASED SEMICONDUCTORSbyCHRISTIAN LAVOIEB. Ing., École Polytechnique de Montréal, 1988M. Sc. A., École Polytechnique de Montréal, 1990A THESIS SUBMITfED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIES(Department of Physics)We accept this thesis as conformingto the required standarçlTHE UNIVERSITY OF BRiTISH COLUMBIADecember 1994© Christian Lavoie, 1994In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.Department ofThe University of British ColumbiaVancouver, CanadaDate(Signature)DE-6 (2/88)IIABSTRACTRecent theoretical and experimental work has shown that the surface of epitaxialfilms is in general not atomically flat during growth due to the interplay between therandom nature of the deposition process and the effects of surface diffusion. Thisdeveloping roughness can be measured in-situ using elastic light scattering. The verticalsensitivity of the technique approaches the atomic scale while laterally the length scaleprobed depends on the wavelength of the light and the scattering geometry.We have performed in-situ elastic light scattering measurements simultaneously atvarious collection angles during molecular beam epitaxy using the 488 nm line of an argon-ion laser. At selected points in time during the growth, ex-situ angle-resolved lightscattering measurements give the surface power spectral density function over the range0.1< q < 20 tm-1. Using the time evolution of the in-situ measurements, together with theex-situ angle-resolved scattering measurements on quenched epilayers, we investigated thechanges in surface morphology during growth of lattice matched systems (GaAs on GaAs)and lattice mismatched systems (InGaAs on GaAs). Effects of crystallographic orientationand spatial frequency were studied. The light scattering results were compared withreflection high energy electron diffraction (RHEED), atomic force microscopy (AFM),scanning tunneling microscopy (STM), field emission scanning electron microscopy (FESEM) and Nomarski microscopy.Growth of GaAs on the rough thermally-cleaned surface shows smoothing at spatialfrequencies greater than 5 Im1 and roughening for smaller spatial frequencies. Bothroughening and smoothing behaviors are found to be anisotropic: the growing surfaceexhibits larger roughness along the [1101 direction than along the [110] direction. Thedependence on crystal orientation results from the fact that group III atoms diffuse fasteralong the [110] direction of a (2X4) reconstructed surface than along the [110]. In eachifidirection, we determined that the time and spatial frequency dependence of the observed1—exp(—2aqt)roughening behavior follow g(q,t) 2 where g(q,t) is the powerqspectral density of the surface morphology which depends on the spatial frequency q andthe time t. As predicted for unstable growth on singular surfaces, we show that this timedependence is consistent with mounds forming on the surface that exhibit constant slope ifthe height of the mound is linearly dependent on the growth rate.In-situ and ex-situ elastic light scattering were also used to measure the evolution ofthe surface morphology of InGai..As films during molecular beam epitaxy growth onGaAs epilayers. The light scattering measurements are compared with atomic forcemicroscopy (AFM) images of the surface morphology and x-ray measurements. The AFMresults are in good agreement with the rms roughness obtained from light scattering andboth techniques show the familiar cross-hatched pattern in the surface structure of therelaxed films. The effect of indium concentration and substrate temperature on the onset ofrelaxation were studied. In particular, we find that the growth of an InGaAs film with lowindium content (—1.5%) at high substrate temperature (—600°C) provoke a drasticsmoothing of the rougher surface morphology obtained from growing GaAs epilayers onGaAs substrates.ivTABLE OF CONTENTSAbstract.Table of contents .ivList of tables viList of figures viiAcknowledgments xiiiCHAPTER 1 INTRODUCTION 1CHAPTER 2 REFLECTIVITY AND LIGHT SCATTERING SET-UP 52.1 Specular reflectivity 52.1.1 Single surface 52.1.2 Growing film 72.2 Light scattering, diffuse reflectivity 102.2.1 Singlesurface 102.2.2 Growing film 192.3 Experimental set-up 26CHAPTER 3 SUBSTRATE PREPARATION AND OXIDE REMOVAL 343.1 Substrate Preparation 343.2 Thermal Desorption of the Oxide 383.3 Atomic Hydrogen Etch of the Oxide 573.4 Arsenic cap desorption 59VCHAPTER 4 EPITAXIAL GROWTH OF GaAs ON GaAs .624.1 Kinetic roughening 624.2 Effects of contaminants on light scattering during growth 704.3 Growth on clean oxide desorbed surfaces 814.3.1 Evolution of the power spectral density (PSD) 814.3.2 Reproducibility, effects of polarization 854.3.3 High spatial frequency smoothing 884.3.4 Low spatial frequency roughening 934.4 Growth on hydrogen etched surfaces 1044.5 Discussion 1084.5.1 Source of scattering and time evolution 1084.5.2 Stable vs unstable growth 1124.5.3 Smoothing after growth 1144.5.4 Anisotropic surface roughness 1174.6 Summary 119CHAPTER 5 InGaAs STRAINED LAYER RELAXATION 1215.1 Dislocations and misfit 1225.2 Dependence of the scattered intensity on crystal orientation and spatialfrequency 1275.3 Surface morphology versus epilayer thickness 1315.4 Influence of indium concentration 1435.5 Influence of substrate temperature 1555.6 Summary 162CHAPTER 6 CONCLUSIONS 164BIBLIOGRAPHY 167viLIST OF TABLESTable 2.1 Spatial frequencies and length scales detected at different positions foran incident angle of 25° (port B) and a wavelength of 488 nm 28Table 2.2 Solid angle of detection at various position for detectors using aspherical lens 31Table 4.1 Characteristic decay times ‘r and coefficients V deduced from thesmoothing at the three spatial frequencies shown in Fig. 4.17 and Fig. 4.18 91Table 4.2 Characteristic times ‘r and coefficient V deduced from the rougheningat the four spatial frequencies shown in Fig. 4.21 and Fig. 4.23 98Table 4.3 Characteristic times T and coefficient V deduced from the scatteredintensity increase along [1101 and [1101 at the given spatial frequencies 105Table 5.1 Percentage relaxation obtained from x-ray measurements 137Table 5.2 Rms roughness along the given crystal orientations evaluated from thepower spectral density and rms roughness evaluated from AFM images 141Table 5.3 Light scattering measurements of rms surface roughness of 0.5 tmthick InGaAs films with increasing indium concentration as deduced from thePSD along each direction 151viiLIST OF FIGURESFigure 2.1 Reflection geometry for oblique incidence showing the coordinatesystem and the notation used 6Figure 2.2 Schematic showing the multiple beam interference when growing anepilayer with optical properties different from the underlying substrate 8Figure 2.3 Scattering geometry defining the angles 00, O and c 11Figure 2.4 Relation between the scattering vector K and the spatial frequency(q) of the detected Fourier component 13Figure 2.5 Spatial frequency probed as a function of angle I — for anglesof incidence of 25° and 65°. Detection is in the plane of incidence(4=0) 15Figure 2.6 Variation of the angle dependent parts of the optical factor as afunction of spatial frequency for an angle of incidence of 25° ( = 0) 16Figure 2.7 Variation of the optical factor as a function of spatial frequency forthree different angles of incidence (00, 15°, 25° and 65°) with 2 =488 nm 16Figure 2.8 Comparison of the optical factors for s and p-polarized light whenthe laser is incident at 25° ( = 0) 17Figure 2.9 Schematics showing (a) the multiple sources of scattering and (b)the multiple beam interference for each scattering source 20Figure 2.10 Calculated interference oscillations in the specular and diffusereflectivities for an A1GaAs film growing on a GaAs substrate 24Figure 2.11 Measured interference oscillations in the specular and diffusereflectivities for an A1GaAs film growing on a GaAs substrate 25Figure 2.12 Plan view of the growth flange of the VG V8OH molecular beamepitaxy system. 27Figure 2.13 Cross section of the growth chamber in the plane of incidence forthe most used geometry 27Figure 2.14 Detector arrangement for small spatial frequency detection 30Figure 2.15 Measured solid angle for each element of the diode array 32Figure 3.1 Schematic of the Teflon disk used for back surface etching showntogether with the obtained rough surface 35Figure 3.2 Schematic of the UV ozone reactor used for sample oxidation 36Figure 3.3 Nomarski microscopy and FE-SEM pictures of a GaAs surface fromwhich a 4 mm UV-ozone oxide has been thermally desorbed 40vifiFigure 3.4 STM images of a GaAs surface from which (a) a 4 mm UV-ozoneand (b) a 2 mm UV-ozone oxide has been thermally desorbed 41Figure 3.5 AFM pictures of (a) a polished substrate (25 tm x 25 urn x 30 A)(3.2 A rms) and of (b) a GaAs surface from which a 4 mm UV-ozone oxidehas been thermally desorbed (25. urn x 25 pm x 500 A) (63 A rms) 42Figure 3.6 Ex-situ light scattering measurement of the power spectral density ofa polished wafer and a 4 mm UV-ozone oxide-desorbed sample 44Figure 3.7 Evolution of RHEED pattern in parallel with the variation inscattered intensity during oxide desorption 45Figure 3.8 Scattered intensity at 3 spatial frequencies given by 3 differentscattering angles during the oxide desorption 47Figure 3.9 Time dependence of scattered intensity durinE oxide evaporation forvarious spatial frequencies ranging from 0.27 to 16 trn’ 48Figure 3.10 Time evolution of the scattered (q=5.9 11rn) and specular intensityduring oxide desorption 49Figure 3.11 Evolution of scattered intensity during oxide desorption as measuredby two different lasers with two different spot sizes on the sample 51Figure 3.12 Time dependence of scattered intensity at q=5.7 tm1 during oxidedesorption for 4 samples oxidized for different lengths of time 54Figure 3.13 Desorption temperature versus oxidation time for UV-ozone andplasma-ozone oxidized wafers 55Figure 3.14 Desorption temperature versus rate of the temperature ramp duringoxide desorption of 15 mm plasma-ozone oxides 56Figure 3.15 Schematic of the hydrogen etching technique 58Figure 3.16 Typical behavior of the specular and diffuse reflectivities(q=5.7 11m’) associated with the desorption of a clean arsenic cap 59Figure 3.17 Typical behavior of the specular and diffuse reflectivities(q=5.7 pm1)associated with the desorption of an oxidized arsenic cap 60Figure 4.1 Expected evolution ofw2(L,t) for different system sizes 64Figure 4.2 Time evolution of the power spectral density. as predicted by thedynamical scaling theory of kinetic roughening 66Figure 4.3 Time evolution of the specular and diffuse reflectivity during oxideevaporation and growth of GaAs 70Figure 4.4 SEM picture of a sample for which growth as been stopped at themaximum in the oscillation 74Figure 4.5 SEM picture of a typical scattering center after 50 nm of growth 74ixFigure 4.6 SEM picture of a typical scattering center after 180 nm of growth 75Figure 4.7 SEM picture of a typical scattering center after 500 nm of growth 75Figure 4.8 Time evolution of the scattered intensity during growth of GaAs forthree different substrate preparations 76Figure 4.9 Evolution of RHEED pattern in parallel with the variation inscattered intensity during growth of GaAs after oxide evaporation 78Figure 4.10 Evolution of the scattering intensity on a log scale for spatialfrequencies of 0.12, 5.4 and 16 jim-1 for growth on a surface from which anative oxide has been removed thermally 79Figure 4.11 Evolution of the scattering intensity for spatial frequencies of 0.12,5.4 and 16 jima for growth on a surface from which a native oxide has beenremoved thermally. All curve maximum have been normalized to 1 80Figure 4.12 Ex-situ light scattering measurements showing the evolution of thesurface power spectral density during MBE processing 82Figure 4.13 Ex-situ light scattering measurements of the surface power spectraldensity for a sample with a 2 p.m GaAs epilayer 83Figure 4.14 In-situ scattered intensity detected using the 32 element diode arrayafter growth of a 4 p.m GaAs epilayer 85Figure 4.15 Reproducibility of in-situ light scattering measurements.Comparison between two runs that were nominally identical 86Figure 4.16 Evolution of the light scattering intensity during desorption andgrowth for the two different states of polarization 87Figure 4.17 Scattering intensity for spatial frequencies of 5.4, 11 and 17 p.m1during growth of GaAs for scattering vector along the [1101 direction 90Figure 4.18 Scattering intensity for spatial frequencies of 5.4, 11 and 17 j1mduring growth of GaAs for scattering vector along the [iTO] direction 90Figure 4.19 Scattered intensity at a spatial frequency of 17 p.m during theoxide desorption and the subsequent growth for scattering along the two notedcrystallographic directions 92Figure 4.20 Evolution of scattered intensity at 0.9 p.m4 during growth of GaAsfor scattering along the indicated crystallographic directions 93Figure 4.21 Scattered intensity for four low spatial frequencies during growthwhen the spatial frequencies detected are along the [110] direction 94Figure 4.22 Time evolution of the scattered intensity at 0.9 and 16 p.m duringgrowth for scattering along the [1101 and the [1101 directions 96Figure 4.23 Plot of Iq2 versus q2t for the four set of data shown in Fig. 4.21 97xFigure 4.24 Plot of Iq2 versus qt for the four set of data shown in Fig. 4.21 99Figure 4.25 Scattered intensity for four low spatial frequencies during growthwhen the spatial frequencies detected are along the [110] direction. Atypicalbehavior 100Figure 4.26 Evolution of the surface morphology after growth of GaAs for (a)3 mm and (b) 30 mm 102Figure 4.27 AFM image showing the surface morphology after growth of GaAsfor 30 mm 102Figure 4.28 Evolution of the scattered intensity at q=5.4 jim-1 during growth ofGaAs on a surface from which the oxide has been removed using atomichydrogen 106Figure 4.29 Evolution of the scattered intensity at q=0.8 im during growth ofGaAs on a surface from which the oxide has been removed using atomichydrogen 106Figure 4.30 Evolution of the scattered intensity along the [1101 direction at fourdifferent spatial frequencies during growth of GaAs on a surface from whichthe oxide has been removed using atomic hydrogen 107Figure 4.31 Calculated characteristic times for the scattered intensity variationsplotted as a function of detected spatial frequency. The letters A and B in thecaption refer to two different samples 110Figure 4.32 AFM image of the surface morphology after 4, hours of GaAsgrowth on a hydrogen-etched surface. (32 jim x 40 jim x 100A) 110Figure 4.33 Schematics of (a) a miscut surface and (b) a singular surfacetogether with the expected variation in potential energy at the step edges 112Figure 4.34 Time evolution of the scattered intensity at q=0.4 im duringgrowth and after growth is terminated by switching off the gallium flux. Thesurface is then left at 600°C under an As2 flux 115Figure 4.35 Typical RHEED patterns obtained during growth when the 12 KeVelectron beam is incident along the [110] or the [110] direction 118Figure 4.36 Arsenic stabilized (2x4) reconstructed surface 118Figure 5.1 Pure edge dislocation (left) and a pure screw dislocation (right) lyingat the interface, shown for a simple cubic lattice 123Figure 5.2 Nomarski picture of the standard cross-hatched pattern obtainedwhen a fully strained layer relaxes through the formation of dislocations 126Figure 5.3 Photograph of the reflected intensity (457 nm) on a large screenplaced about 2 m from the sample. The scattering is distributed mainly alongsharp lines perpendicular to the running dislocations 126xiFigure 5.4 Time evolution of the scattered intensity along the [1101 orientationfor q=5.4 jim-1 and 11 jim1 during relaxation of anIn2Ga8As alloy grown at490°C on a GaAs epilayer 129Figure 5.5 Time evolution of the scattered intensity along the [110] orientationfor q=5.4 j1m and 11 jima during relaxation of anIn2Ga8As alloy grown at490°C on a GaAs epilayer. Growth rate 129Figure 5.6 Early stages of the time evolution of the scattered intensity along the[1101 orientation for q=5.4 pm1 during relaxation of an In2Ga8As alloygrown at 490°C on a GaAs epilayer. Growth rate 131Figure 5.7 Evolution of the scattered intensity along the [1101 direction for aspatial frequency of 5.4 jim1 during growth of In 18Ga82As at 490°C 133Figure 5.8 Power spectral densities of the surface morphology along the [1101orientation for four different epilayer thicknesses ofIn18Ga82As 134Figure 5.9 Power spectral densities of the surface morphology along the [110]orientation for four different epilayer thicknesses ofIn18Ga82As 135Figure 5.10 Power spectral densities of the surface morphology along the [100]orientation for four different epilayer thicknesses of In 18Ga82As 136Figure 5.11 Atomic force microscope image of a 33 nm thick In18Ga82Asepilayer grown on a 0.8 jim thick GaAs buf1er layer. Correspond to point (a)in Fig. 5.7. (10 jim x 10 jim x 150 A) 138Figure 5.12 Atomic force microscope image of a 58 nm thick In18Ga82Asepilayer grown on a 0.8 jim thick GaAs buff0er layer. Correspond to point (b)in Fig. 5.7. (10 jim x 10 jim x 120 A) 138Figure 5.13 Atomic force microscope image of a 83 nm thick In18Ga82Asepilayer grown on a 0.8 jim thick GaAs buffer layer. Correspond to point (c)in Fig. 5.7. (5 jim x 5 jim x 120 A) 139Figure 5.14 Atomic force microscope image of a 250 nm thickIn18Ga82Asepilayer grown on a 0.8 jim thick GaAs buffer layer. Correspond to point (d)in Fig. 5.7. (10 jim x 10 jim x 120 A) 139Figure 5.15 Power spectral densities along the [100], [1101 and [110] directionsfor the thicker In.l8Ga.2As sample 141Figure 5.16 Evolution of the scattered intensity at 5.4 jim1 for InGaAs films ofdifferent % indium concentrations when q is parallel to the [110] direction 144Figure 5.17 Evolution of the scattered intensity at 5.4 jim1 for InGaAs films ofdifferent % indium concentrations when q is parallel to the [110] direction 143Figure 5.19 Critical layer thickness as determined by optical scattering showntogether with the models of Matthews-Blaskelee and People-Bean 146Figure 5.20 Evolution of the PSD of 0.5 jim thick InGaAs films with increasingindium content for scattering along the [1101 direction 149xiiFigure 5.21 Evolution of the PSD of 0.5 tm thick InGaAs films with increasingindium content for scattering along the [1101 direction 149Figure 5.22 Evolution of the PSD of 0.5 Jim thick InGaAs films with increasingindium content for scattering along the [1001 direction 150Figure 5.23 AFM image In28Ga.7As film (10 im x 10 JIm) 0.5 im thick 152Figure 5.24 Nomarski photograph of a 1.5 im thick InGaAs film grown at540°C. The width of the image is 225 jim 154Figure 5.25 AFM image of a 1.5 urn thick InGaAs film grown at 540°C 154Figure 5.26 Time evolution of the scattered intensity at q=5.4 jim1 along the[1101 direction for substrate temperatures ranging from 408°C to 515°C 156Figure 5.27 Time evolution of the scattered intensity at q=5.4 tm1 along the[1101 direction for substrate temperatures ranging from 515°C to 589°C 157Figure 5.28 Time evolution of the scattering intensity at q=5.4 im1 along the[110] direction during desorption, growth of GaAs and InGaAs at 589•C 158Figure 5.29 AFM images of (a) the surface after 30 mm of GaAs growth(19 A rms) and (b) after the high temperature InGaAs is grown for 30 mmover a 60 mm GaAs buffer layer (2.3 A rms) 159Figure 5.30 PSD of the surface morphology along the [1101 direction on the twosamples shown in Fig. 5.29 160Figure 5.31 RHEED pattern evolution when changing the growth from GaAs toInGaAs at a substrate temperature of 589°C 161XIIIACKNOWLEDGMENTSI would first like to thank my supervisor and friend Dr. Tom Tiedje for hisguidance and unfailing support throughout the four years duration of this work. It was apleasure to work in such a privileged environment.I also wish to thank Jim MacKenzie, Shane Johnson, Dr. Mark Nissen, TomPinnington and Stefan Eisebitt not only for their help during the experiment, analysis andredaction but also for all the energy they put in making me learn all those English wordsand expressions I didnt know about...I want to give credit to Eric Nodwell and Bernard Haveman for carrying out crucialparts of the in-situ and ex-situ light scattering experiments. I am grateful to RachelGoldmann and Karen Kavanagh from University of California in San Diego for providingresults from x-ray and TEM measurements on InGaAs samples. I am thankful to KarenKavanagh, Tom Pinnington and Jeff Hutter for providing AFM images that completed thisthesis and allowed for quantitative comparison with light scattering measurements.Many thanks to Dave, Duncan, Jim, Mark, Robin, Sayuri, Stefan, Steve, LittleTom, Big Tom and Tony. A team it was a pleasure to work in.Writing a thesis requires lots of time and quite a few sacrifices. To Moyra, I owemany kind thanks for practical and moral support and apologies for not being around asmuch as I would have liked.1CHAPTER 1 INTRODUCTION.The scattering of waves from randomly rough surfaces has been studied fordecades both theoretically and experimentally. The complexity of the theoreticaldevelopment has led to numerous approximations and consequently to a copious literaturefor acoustic waves as well as for electromagnetic waves from the radio-wave range up tothe visible. The scattering of light, in particular, has been used extensively to characterizeoptical coatings. An introductory book by Bennett and Mattsson1on the characterization ofroughness covers the relationship between various roughness measurements performedwith light, and other more direct characterization techniques such as stylus measurements,scanning tunnelling microscopy and atomic force microscopy. Extensive reviews of wavescattering theories and experiments can also be found in the literature, including forexample Beckmann and Spizzichino2,Beckmann3,Ishimaru4,Valenzuela5,Bass andFuks6 and the recent book by Ogilvy7.Our goal is to use light scattering to study the evolution of the surface morphologyof compound semiconductor films during growth by molecular beam epitaxy (MBE)8’9.Ingeneral one would expect the surface of a growing film to roughen as it grows even if thestarting substrate is a perfectly smooth single crystal. The reason for this is that the atomsfrom the vapor are deposited in a random manner which causes fluctuations in the height ofthe surface of the growing film. This roughening, which is caused by the randomdeposition of atoms, is known as kinetic roughening and competes with the smoothing dueto surface diffusion. Although kinetic roughening has been studied extensively incomputer simulations there are very few experimental observations of this process in thegrowth of real films. In addition the equations that describe the time evolution of thesurface morphology during growth are not known, even for some of the best understoodsystems such as epitaxial GaAs films on GaAs. The development of theoretical models for2the growth is hampered by the complexity of the atomic scale surface diffusion processeswhich control the time evolution of the macroscopic surface morphology.As an illustrative example we consider the effect of atomic steps. The potentialbarriers at steps are believed to play an important role in the diffusion of atoms 10,11,12For example it may be easier for mobile surface atoms to attach to a step edge from belowthan it is for them to drop over the top of a step from above. In this case there will be atendency for deposited atoms to diffuse towards the higher step and hence to pile up andform mounds. This type of diffusion bias is believed to lead to unstable growth on singlecrystal substrates that are “singular”, or in other words oriented parallel to a principalcrystallographic plane. This growth mode should lead to surface roughening.Another physical situation where surface roughening can occur is in the growth of alattice-mismatched film, such as InGaAs on GaAs. For very thin films the overlayer isstrained to match the lattice constant of the substrate. Eventually as the strained filmbecomes thicker than a critical thickness, it becomes unstable against the formation of misfitdislocations at the interface which relax the strain in the film 13,14 The relaxed film is theninhomogeneously strained which affects the surface morphology of the growing films.The resulting morphology change can be detected with light scattering.The continuous acquisition of information about surface morphology during growthis important not only for developing an understanding of growth mechanisms but also forprocess contro11526. In this regard optical techniques have several important advantagesover more conventional in-situ monitoring using electron diffraction1548 or massspectrometry1921.Unlike electron beam techniques, light scattering is equally effective ingas ambients or in vacuum. In addition it is highly sensitive to changes in the surface andis even capable of resolving single atomic layers22’3. Light scattering is also relativelyinexpensive and easy to do. On the negative side, elastic light scattering is notorious forbeing difficult to interpret quantitatively. One of the goals of this thesis is to explore the3extent to which we can obtain quantitative information about surface morphology from lightscattering.The roughness of semiconductor surfaces and interfaces is becoming increasinglyimportant in the performance of electronic and optoelectronic devices. For exampleinterface roughness scattering is an important factor in determining the electron mobility inheterojunction transistors. In quantum well and quantum wire structures used in state ofthe art semiconductor lasers, the uniformity of the quantum confinement structures iscritical to the definition of the electronic energy levels and the optical properties.Fluctuations in the width of quantum wells will broaden sharp electronic transitions.Surface morphology is important in other applications as well, such as in x-ray multilayermirrors and optical waveguides.Light scattering has been used by a number of groups over the last eight years tostudy surface morphology during epitaxial semiconductor film growth. Light scatteringhas been used to study the desorption of an arsenic cap from a GaAs substrate32’6,theoxide removal283t’33 8,the growth of GaAs2832’36 840,silicon27,InGaAs strainedlayers30-2’9and ZnSe3335 on GaAs substrates. The results presented in this thesis aremore comprehensive than any of the previous studies and a number of new results arereported. In the growth of GaAs the scattered light was measured simultaneously at up toseven different angles, each detecting a different spatial frequency in the surfacemorphology. The power spectral density of the GaAs surface has been measured as afunction of spatial frequency by light scattering. The effect of crystal orientation has beenexplored for both GaAs on GaAs and for strained InGaAs films on GaAs. The timedependence of the surface roughening (or smoothing) has been explored from a smooth (orrough) surface initial condition. In-situ results from light scattering are compared withreflection high energy electron diffraction (RHEED), ex-situ light scattering measurements,and microscopy measurements including Nomarski microscopy, scanning electron4microscopy, scanning tunnelling microscopy and atomic force microscopy. The ex-situlight scattering measurements lead to a quantitative measure of the roughness that can becompared to values obtained from scanning probe microscopy.This thesis is divided as follows: Chapter 2 describes the experimentalmeasurement techniques and the theory behind them; Chapter 3 describes the substratecleaning and preparation procedure; Chapter 4 describes the growth of GaAs on itself; andChapter 5 describes the growth of InGaiAs strained layers on GaAs epilayers.5CHAPTER 2 REFLECTIVITY AND LIGHT SCATTERING SET-UP.In the first parts of this chapter, we present the equations for the reflectivity of asingle surface and for the reflectivity of a thin film during deposition. This is done first forthe coherent field (specular reflectivity) and then for the incoherent field (diffusereflectivity) obtained from first order perturbation theory. In the following part, the in-situand ex-situ light scattering experiments will be described in detail.Section 2.1 and sub-section 2.2.1 summarize the literature on reflectivity. Thetreatment of the interference oscillations observed in the diffuse reflectivity (sub-section2.2.2) is original.2.1 Specular reflectivity.2.1.1 Single surface.The reflectivity and transmissivity for the coherent field can be found easily byapplying boundary conditions to the solutions of Maxwell’s equations. From the fact thatthe tangential components of the electric and magnetic field must be continuous across theinterface, the reflection and transmission coefficients for the fields at a perfectly smoothinterface can be evaluated41’2:0cos(0)—n6 n0cos(01)—n8 )rs=ncos(8)+n16 r = cos(0)+ns(O)(2.1)— 2n0cos(0) — 2n0cos(0)—ncos(0)+n18 p —ncos(01)+n8Fig. 2.1 shows the selected coordinate system together with the different vectors ofthe electric field. Subscript 0 or 1 refers to the two different media and subscript s or p6refers to the orientation of the polarization. The s-polarized electhc field is perpendicular tothe plane of incidence while the p-polarized field is contained in it. The index of refractionis n and the angle of incidence or refraction is represented by 0.Figure 2.1 Reflection geometry for oblique incidence showing the coordinatesystem and the notation used.Since the index of refraction of semiconducting material is in general complex, thereflection coefficients for the fields are complex as well. The reflectances (R, R) andtransmittances (Ta, T) are defined as the ratio of the reflected or transmitted energy andthe incident energy. They are the measurable quantities and using the reflection andtransmission coefficient, they can be written as:*R = rsrsR = rr,T =T =(2.2)The complex nature of the field reflection coefficient means that upon reflection oflight there will be a significant phase shift at the interface if the imaginary part of the indexof refraction is not small compared to the real part. In addition, the magnitude ofreflectivity can vary. To quantify these effects, we develop the reflection coefficient of thenoni7s-polarized wave. Using n0 — ik0 and n1—i/c1 for the index of refraction of the two mediaand substituting into Equation 2.1, rs can be rewritten in a more general way as:rs=e° (2.3)where:+ kg)— B2(n? + k?))2+ 4A2B(k1n0— konj)212[ ((n0A+n1B) +(k0A+1B) ) J— _1E 2AB(kn—k)co—tan i[A2(n+k)—B2(n? ÷k?)The coefficients A and B are given by A = cos(00) and B = cos(81). The angleq represents the phase shift at the interface and r is the magnitude of r. Typical valuesfor n and k for GaAs at room temperature vary from 3 to 4.8 for n and 0 to 0.5 for kdepending on the wavelength. For the in-situ measurements at 488 nm, we find for thes-polarized electric field incident on a GaAs surface at room temperature in vacuum that thephase shift is 2.3° and that the reflection coefficient is 0.9 % higher than it would be if theimaginary part of the index of refraction were neglected. The phase shift will not influencethe reflectance measurement on a single surface, however the change in Irsi leads to a1.8 % change in R. Since these changes are small, in most cases of homoepitaxy theywill not be significant as only one reflection occurs. In this case the index of refraction canbe considered to be real when calculating the reflectances.2.1.1 Growing film.The theory of reflectivity from a growing film with a different refractive index thanthe substrate has been developed42.Because of interference between light rays which haveexperienced multiple reflections in the thin film, the total reflected intensity will oscillate asthe thickness of the film increases. Moreover, since any light transmitted within the film8will be partly absorbed in the material, the interference oscillations will be damped at a ratethat depends on the value of the extinction coefficient k1. Fig. 2.2 schematically showsthe light paths in the growing film. Every light ray that comes out of the sample is labeledby the interactions with all interfaces that it has encountered. The coefficients r1, r2 andt1 represent reflection or transmission of a wave with a component in the +z direction. Forr1 and t1, the wave is traveling in the -z direction. In Fig. 2.2, the fact that r1 = —r1 hasbeen used.Ano___________________________IFigure 2.2 Schematic showing the multiple beam interference when growing anepilayer with optical properties differentfrom the underlying substrate.In addition to the intensity contributions at the interfaces, the correct phase changefor each ray must be considered. The phase change associated with crossing a film ofthickness d1 can be written:zl=n1dcos(O)I(2.4)9Making the summation of all the outgoing rays, the reflection coefficient for theamplitudes becomes:r = r1 + titr2e_2—t1rre’ + tjtr?re’(2.5)•, —214 , —2i4r7—--r,er=r+ =1+r12e4 1+rjr2e_14The imaginary part of the parameter 4 is the source of the damping. The index ofrefraction being complex, n1 can be replaced by it1— ik1 and 4 can be rewritten as:4 =nid1cos(O)—ikd1cos(0)=6—lad1 (2.6)Substitution in Equation 2.5 leads to:r1 +2e’e6r= (2.7)1+rr2e ‘e 1The measured reflectance will therefore have the form:R — * — r +re4a1 +2r1°”lcos(26)2 8)— rr— 1 + r?re’ +2rrecos(2ö)In Equation 2.8, r1 and r2 are either for s or p-polarization, r1 is given directly byEquation 2.1 and r2 can be calculated from Equation 2.1 by replacing the indices 0 and 1by 1 and 2 respectively. The coefficients a and 6 are given by Equation 2.6.The phase shifts described by Equation 2.3 can be large at an interfacecharacterized by n1 n2,n1,2 >> k1, and k1 <<k2. These shifts will be observed in theexperiments as a starting phase of up to r/2 at the start of the interference oscillations.102.2 Light scattering, diffuse reflectivity.The evaluation of the specular reflectivity of a smooth surface only leads to thecomplex index of refraction of the material (n,k). In fact, for very small roughness,information on the morphology of the interface cannot be extracted because the reflectedspecular intensity is not significantly affected by the presence of a small diffuse field. Onthe other hand, non-specular light scattering at the surface is dependent on the surfacemorphology. The larger the surface roughness, the more intense will be the scattered light.2.2.1 Single surface.For many years various authors have established relations between the angulardependence of the scattering intensity and the surface structure. Although the first theoriesfor light scattering were developed in the last century43’4,much of the more recent workwas done in relation to the radar waves and their interactions with the surface of theearth2’45. This work is directly applicable to the scattering of light by rough surfaces.There are many approaches to light scattering calculations. The appropriate theoreticaltreatment depends on the type and size of the scatterers. In general, geometrical optics isused to model structures that are large compared to the wavelength of the light. Theoriessimilar to the one developed by Mie46’7 are used for modeling diffraction patterns fromparticles of sizes comparable to the wavelength. In the case where the magnitude of theresidual roughness is much smaller than the wavelength, a relation between surfacestructure and light intensity can be obtained using first order perturbation theory orKirchhoff theory for scalar or vector wave scattering7.When probed with visible light, theroughness of molecular beam epitaxy films is expected to be small enough that effects suchas shadowing or second order scattering are not significant (Born approximation). In thiscase perturbation theory yields essentially the same results as Kirchhoff theory7.11Following the notation used by J. Bennett and L. Mattsson1,in the far field, theexpression for the power scattered elastically in the solid angle 2 can be derived48’9if thefilm is free of defects or particles:1 dP 16,r2 2 2- =cos(00)cos (0) IQab(8o,8s,øs, g(’j,)Optical Surfacefactor factor (2.9)where P0 and P are the incident and diffuse power, A is the wavelength of thelight, and 00 and O are the incident and scattering angles. Fig. 2.3 shows the scatteringgeometry defming the angles O, O and 4. The right hand side of Equation 2.9 can bedivided into two distinct factors, the optical factor and the surface factor, which describedifferent aspects of the physics involved in the scattering. The optical factor contains theinverse fourth power of the wavelength, the cosine functions and the Q0b coefficient. Thesurface factor is the power spectral density function g(q) which depends only on themorphology of the surface by the spatial frequency q.----y,Figure 2.3 Scattering geometry defining the angles O, Os and .12The optical factor depends only on the detection geometry, the optical properties ofthe material studied and on the wavelength of the light. The dependence is the samefactor as in Rayleigh scattering which is typical of dipole radiation. The coefficientQab(0o’ Ø e) depends on the geometry of the experiment, on the selectedpolarization of the incident and detected scattered light and on the permittivity of themedium. The two subscripts a and b refer to the incident and detected polarizations(s or p). In the general case of scattering from a medium of complex dielectric constant,using first order perturbation theory (in surface height), the possible Qab coefficients canbe written4’8—(e—1)cos(5)__________Qss_(g2)(g2)—(e—1)sin(ç5)-,Jc_sin2(O0)SP ( cos(eo)+ge_sin2(ea))(cos(8)+gE_s 2(es))(e—1) (esin(Oo) sin(es)cos(s)ge_sin2(oo)gE_sin2(os))— (ecos(e0)÷gE_sin2(oQ))(ecos(o5+-Je_sin2eQ——(E_1)sin(bs)ge_sin2(os)PS (cos(60)+ge_ 1n2o ecos(8s)÷ge_sin2(85(2.10)For scattered intensity detected in the plane of incidence (Ø=O), we have= Q = 0. Thus in this particular geometry, no cross polarization effects areexpected from first order perturbation theory. Since for most of the experiments perfonnedin this work the incident light was s-polarized and the scattered light was detected in the13plane of incidence, the coefficient to consider is Q. In some cases, the other coefficientswill also be of interest.The power spectral density function (the surface factor in Equation 2.9) is thesquare of the Fourier transform of the surface morphology. It can be written:g(q)= JJ h(x,2(2.11)The function h(x, y) describes the surface topography and the components q andqy represent the spatial frequency of the Fourier component probed by the geometry andwavelength used. Fig. 2.4 shows schematically how the spatial frequency (q , qy) isrelated to the incident and scattering angles. For simplicity, the case of scattering in theplane of incidence has been considered.zxIf we write k and k as the incident and scattered wave vectors, the vector Krepresents the necessary momentum transfer (from the surface) to generate scattering in thegiven direction. When detecting the specular reflection, the vector K is normal to thesubstrate but for any other geometry, it will have a component in the plane of the surface.This in-plane component of K corresponds to the spatial frequency (q) of the FourierqFigure 2.4 Relation between the scattering vector K and the spatialfrequency (q) ofthe detected Fourier component.14component that is probed in this geometry. In general, taking the projection of k1 in thepositive x direction, the spatial frequency probed for a given set of angles O, 0 and Øbecomes:q (sin(80)—sin(05)cos Ø)(2.12)q=—(sin(05)sin) {=O forThe smallest spatial frequency that can be detected will depend on access toscattering angles close to the specular beam (8 O and çt 0). This small spatialfrequency gives the largest detectable lateral length scale. On the other hand, the highestspatial frequency is limited by the wavelength. The limit is q = 4 ir/A and it represents agrazing incidence photon that is backscattered in the incoming direction. The smallestlength scale probed with a wavelength A can therefore not be smaller than A /2. Therelation between q and I O0 0I is graphed in Fig. 2.5 for light scattering in the plane ofincidence (=O) and A =488 nm. The function was plotted for 2 different angles ofincidence: 25° and 65°. Considering that our detector can get as close as 0.5° to specularreflection, the smallest detectable spatial frequency varies from 0.05 to 0.1 J1m’depending on the angle of incidence. The highest spatial frequency almost reaches20 tm-1 for an angle difference of 100°. This range of spatial frequency translates in realspace into a range of lateral length scales of 0.3 tm to 60 tm.15:-‘10Q—.Cl)0.010.1 1 10 100ie—o0 (deg)Figure 2.5 Spatial frequency probed as afunction ofangle 10—for angles ofincidence of2S°an4 65°. Detection is in the plane of incidence (=0).Fig. 2.6 shows how the angle dependent part of the optical factor varies as afunction of spatial frequency (q) for a GaAs substrate for 2 =488 nm, at room temperature(e = 18.1- i 4.2) and at an angle of incidence of 25°. The three curves shown representcos(00)cos2(05, 1Q552 and their product (cos(00) os0 The angledependent part of the optical factor is slowly varying for q< 1.tm It goes through amaximum as the scattered angle O goes through zero (detection normal to the surface) andfalls to zero for higher spatial frequency when O reaches 900. Most of the angulardependence of the optical factor comes from cos2(0), as the variation of the cos2(0)function is large compared to the changes in 1Q55 2 in the accessible range of spatialfrequencies.The variation of the complete optical factor, (16ir2/A4) cos(0 )cos2(0) Q55, at488 nm is shown in Fig. 2.7 for four different angles of incidence (0°,15°,25° and 65°).From Fig. 2.7 we can first conclude that for low spatial frequencies (long wavelengths),the larger the angle of incidence is, the smaller the optical factor will be. Second, the16maximum in the curve is displaced toward higher spatial frequencies as the angle ofincidence is increased. Third, for higher angles of incidence the accessible range of spatialfrequencies is larger because the difference I — that can reach up to 1800 for grazingincidence compared to 90° for normal incidence (see Fig. 2.5).I.0.80.60.40.20—2Log (q (tm’))Figure 2.6 Variation of the angle dependent parts of the optical factor as afunction ofspatialfrequencyfor an angle of incidence of25° (ckc = 0).1200-‘ 10008006004002000Log(q (tim’))Figure 2.7 Variation of the optical factor as afunction ofspatialfrequency for threedifferent angles of incidence (0 15°, 25° and 65°) with 2. —488 nm (ç = 0).‘<sscos0cos2 0 Q2—1 0 1—2 —1 0 117Fig. 2.8 shows a comparison of the optical factor for the two different incidentpolarizations when the laser is incident at 250 and the scattered intensity is detected in theplane of incidence. The differences are exclusively due to the angular behavior of Q andQ,. (In the plane of incidence, Q, = = 0.). Although the shape of the two curvesis similar, the amplitude of the optical factor for the p-polarized wave is much higher.40003500EJ 3000‘ 250020001500010005000Log (q (jim’))Figure 2.8 Comparison of the optical factors for s and p-polarized light when thelaser is incident at 250 and the scattered intensity is detected in the plane ofincidenceIn summary, from an experimental point of view, the pertinent parameters are thepolarization and angle of the incident light, the angle of detection and finally the measuredintensity of the scattered light. The scattering angle, together with the incident one, leads tothe lateral length scale of the roughness probed and the angle-dependent intensitymeasurements give the surface power spectral density function (PSD).The PSD function g(q) contains most of the information about the surface. Theonly information not contained is the relative phase of each Fourier component. The PSDfunction being the square of a Fourier transform, it carries the magnitude of each Fouriercomponent but not the relative phase between them. The real surface can therefore not bereconstructed from g(q). However, many surface parameters can be evaluated. The rms—2 —1 0 118surface roughness (o), the nns slope (m) and the nns curvature (c) are calculated49usingintegrals from —00 to +00:2=l fJ g(q) dqdqrn2=12 if q2 g(q) dqdqc2=(l) if q’1 g(q) dqdq (2.13)An average surface wavelength can also be defined as 2 7cc/rn. Since the PSD ismeasured only in a given range of spatial frequencies the values of s, rn and c obtainedare bandwidth limited. The experimentally obtainable range of spatial frequencies isusually the one shown in Fig. 2.5.Experimentally, the power spectral density is measured along one crystal orientationgiving the dependence along only one component of q. Reasonable approximations ong(q) can facilitate the evaluation of the rms roughness. If the roughness is isotropic thenthe rms roughness depends on q only through its magnitude and becomes:1 j g(q) qdq (2.14)(2 ic)In another limit, the surface h(x,y) could be rough only in one dimension so thath(x,y) h(x). In this case, the right hand side of Equation 2.9 is different by a factor2ic/A and d2 has to be replaced by d8 on the left hand side49. The equation then leadsto the one-dimensional PSD. The rms roughness along one given direction can still bewritten in terms of the two-dimensional PSD and the detection angle dO 2 r/d (r is theradius of the detector and d is the distance detector-sample):192d Jgw dq (2.15)In the following chapters, the isotropic and one-dimensional rms roughnesses willbe used to compare different surfaces.2.2.2 Growing film.The treatment of interference oscillations observed in the diffuse reflectivity whengrowing an epilayer of material with a different index of refraction than the substrate hasnot been found in the literature, It is however a simple extension of the specular casedeveloped earlier. We used Equation 2.9 to define a diffuse reflection coefficient for agiven solid angle on a rough surface. This coefficient is dependent on the energy of thereflected light. The quantity of interest for the interference oscillations is the reflectioncoefficient, which is phase sensitive, rather than the reflectance. Equation 2.9 can berewritten in terms of the reflection coefficient. Instead of the power spectral density g(q)the direct Fourier transform of the surface morphology F(q) is used together with thecoefficients Qab given by Equation 2.10 that are already phase sensitive. Considering thatthe phase change is only related to the surface and the generalized Fresnel coefficient Qab’the relation for an incident field E0 scattered into a solid angle 2 becomes:E JQcos(O0)cos2( ) Qab F(q) E0 (2.16)The diffuse reflection coefficient for the field at the n interface can be normalizedto the specular values. It is defined as the product of the reflection coefficient for thespecular field r and a diffuse coefficient D. This is done in order to approximate thescattering when the field is transmitted at the interface by using the same coefficient D.The notation will be useful for determining the oscillations in the reflectivities. For thereflection at interface n and the transmission at the surface from the film to the vacuum weget:20(2.17)As seen in Fig. 2.2, the specular beam is reflected many times in the film until itdies out because of absorption. Each of those reflections at the surface or at the interfacebecomes a source of scattered light. This is schematically shown in Fig. 2.9 a. The dottedlines represent the light scattered at a given angle from each of the scattering centers. Thetransmitted light from one center (each dotted line) is once again made up of a series ofspecular reflections in the film (Fig. 2.9 b).4 44 44 44 44I I I I I I I II I I I I I I I I‘4. I I I I I I I I II I I I I I I I I‘4. I I I I I I I I I‘4. I I I I I I I I I‘4. I I I I I I I I IXI I I I I I I I IXI I I I I I I I Ino i I I I I I I I I(a)44444\ 11111‘4. ihillX II I IX lullX l ll11111IllI IX I 1111no I I I I IJILL,1 3q 5i a a a a‘ Il II II I I’I I I II II II II‘ I I IhIhlilln IllilillI Illhllil111111*1II II II IIII II II IIII II II II2 4(b) n2Figure 2.9 Schematics showing (a) the multiple sources of scattering and (b) themultiple beam interference for each scattering source.21To develop an expression for the field reflection coefficients, the summation of allrays from one scattering center is first considered. A second summation over all scatteringcenters leads to the full expression. It is assumed that the probability of scattering from anyinterface is small enough that the scattering of a scattered ray can be neglected (Bornapproximation): the rays considered undergo only a single scattering event. One light raycan specularly reflect many times before and after it scatters on an interface.We label the scattering centers starting with 1 and following the specular path asshown in Fig. 2.9 a. Each odd number represents a scattering center at the surface of thefilm while each even number represents a scattering center at the interface with thesubstrate. A similar development as for the specular reflectivity leads to a field reflectivityR1 for each scattering center:R1 = D1r+ Pg(D1tr2e’ — rjre2 ) Dr1 + D1tr2e’1+r12e”’—2i4 D2t1re’R2 = P9 ( D2t1re —r1e ) =1+r12e’—2i41?3 = Pg (D1tr2e, — rre4d) = D1tr2e1+rr2e2 —3iLl—lAd —2i4_______________________Pg( —D2t1rre S —r12e d ) = D2t1re1+rlr2et2 —4izl—2izla -D1tr2e SR5 = Pg ( —D1tre4’ —r1e )= 1+r12e2 3 t5As14dRJ = P9(D2t1rre —i4 , —r12e) =D2t1re1+r12ePg (D1trre6” 2tAd (2.18)—r1r2e )=1+r12e22The function Pg (a, b) = a + ab + ab2 + ab3+... is a geometrical progression andthe phase differences zI and Lid for the specular and diffuse light rays are calculated bysubstituting 8 and 8d respectively into Equation 2.4. The angles O and 6d between thenormal to the surface and the specular and diffuse light rays are measured inside the film.In the derivation, we have considered the coefficients r1, r2 and t1 to be the same for thereflections before and after the scattering event.From Equation 2.18, two new geometric progressions can be isolated. Thescattering centers at the surface and the ones at the interface split naturally into:R.1 = R1 + R3 + R5 + R7+... = R1 + Pg(D1tr2e, —r12e’)1+rr2e—i24— R D1tr2eS— 1 + (1 +r12e)( 1 +rjr2e)R2.= R2 + R4 + R6 +R8+... = Pg(D2tre , —r12e’)• (2.19)—________________________________(1 +r12e’)(1 +rir2e_t)Adding the results of these two summations leads to an expression for the reflectioncoefficient of the fields:R = D1r+ (1— r12)r2D12ed) + Dj(e2t+ )+ Dre”(1+r]r2e_tLict )(1 +r12e”’)(2.20)In the case where the path differences in the material are similar before and after thescattering event (4 Lid LI), the equation can be simplified to:23—4i4 i--., -. ,-.. —2tzDfl .,, 2 L.’1r2e +L)1’2)e— -r (1 — r1 1r2—2i4 2(1+rr2e ) (2.21)— D1r+ Dirire4tL+r2(2D1+D(1_r))e_4— (1 +rlr2e_4 )2This approximation is realistic since the index of refraction of the grown film islarge (-.4) leading to only small refracted angles in the film independently of the incident orscattered angles. Moreover in certain cases it is possible to have exactly= 8d when thedetector is placed on the cone normal to the surface that is defined by the incident andreflected specular beam. ( 0 in Fig. 2.3.)As in the specular case, since the index of refraction is complex, the phase changeis also complex and is the source of the damping. As discussed earlier, the coefficientsr1 and r2 are also complex but will only change the phase of the interference oscillationsand not their period. The evolution of the reflectivity during deposition depends not onlyon A but also on the coefficient D1. At the start of the growth, we have D1=D2 becausethere is only one surface. As the material is deposited the surface is roughening orsmoothing and D1 will increase or decrease. The light is probing the same Fouriercomponent in each interface but there can be a phase shift between the components.Therefore, the phase between the two coefficients D1 and can vary as the film isgrowing.To get the measurable reflectivities the reflection coefficient for the fields has to bemultiplied by its complex conjugate. Fig. 2.10 shows calculated oscillations in the specularreflectances together with the oscillations expected in the diffuse signal during growth forthree different case: (a) D1= 132 (same roughness interfaces), (b) D1 becomes much larger132 (roughening) and (c) D1 becomes much smaller than D2 (smoothing). For the threegraphs, the indices of refraction are 4.1-0.311 and 3.5-0.031 for the substrate and theepilayer respectively. The phases of D and are taken equal. The specular signal isnormalized so that both signal can by compared on the same scale.240.0060.00550.0050. 00450.004(a)0.0060.00550.0050.00450.004(b)0.0060.0050.0040.0030.0020.00100 0.2 0.4 0.6Film Thickness (arb. units)(c)Figure 2.10 Calculated interference oscillations in the specular and diffuse refiectivitiesfor an A1GaAs film growing on a GaAs substrate. (a) D1=2 (same roughnessinterfaces), (b) D1 becomes larger D2 (roughening) and (c) D1 becomes muchsmaller than 2 (smoothing).0.40 0.2 0.6 0.8 10 0.2 0.4 0.6 0.8 10.8 125For comparison purpose we present the interference oscillations we measured in thespecular and diffuse intensity at q = 5.9 11m (632.8 nm) for an AIGaAs film growingon a GaAs epilayer (Fig. 2.11). The diffuse signal has been scaled for comparison. Whilethe oscillations in the specular intensity seem very regular, the oscillations in the diffusesignal are peculiar. Their general increase is a sign that the growing surface is roughening.Also, the diffuse oscillations start in phase with the specular ones but quickly go out ofphase within the first five oscillations and stay out of phase for the rest of the growth. Thisbehavior in which the phase of the oscillations is changing has not been observed ingeneral. We believe that this is a consequence of a phase variation between the Fouriercomponents of the surface and the interface as the film is growing. By introducing avariable phase shift between D1 and D2 similar behaviors have been simulated.0.70.50 10 20 30 40 50 60 70Growth Time (mm)Figure 2.11 Measured interference oscillations in the specular and diffusereflectivities for an AlGaAsfilm growing on a GaAs substrate.In the first two sections of this chapter, the equations for the reflectivity of a singlesurface and for the reflectivity of a thin film during deposition have been presented for thecoherent field (specular reflectivity) and for the incoherent field (diffuse reflectivity). In thefollowing one, the in-situ and ex-situ light scattering experiments are described in detail.262.3 Experimental set-up.The problem of coupling light into an evaporation chamber can be solved in severalways. Coating of windows due to deposition can be avoided by either using shutters tolimit the exposure of windows to the beam, by placing windows in positions where theycan see the substrate only through mirrors or by heating the windows to reduce the stickingcoefficient of the incoming metal atoms. We have used mirror-coupled optical ports for thelight scattering and temperature measurements. The gallium atoms and arsenic moleculescoming from the deposition region will strike the mirrors and cover them. The windowswill not get coated since they are not in line of sight with the hot substrate. Once coated,the reflectivity of the mirrors will not vary significantly for visible light. A crossarrangement provides double optical access at a single port (see Fig. 2.14). Placing opticalports at a variety of angles on the growth chamber, permits a discrete range of spatialfrequencies to be sampled.Fig. 2.12 shows a plan view of the growth flange of the VG V8OH molecularbeam epitaxy system. The eight ports outside the diameter together with the circular onesinside it represent the shutter ports and the effusion cell ports respectively. Ports that arenot shaded and identified by a letter have been transformed into mirror coupled opticalports. The center port, originally designed for optical pyrometry, has been used for acarbon dopant source and is now also used for light scattering. Double access ports arelocated on ports D and F.Depending on which port is used for the input of the laser light, different spatialfrequencies are accessible. In the most often used geometry, the laser is incident throughport B and goes through a small aperture before it is reflected off the sample surface outthrough port D. A cross section of the chamber in the plane of incidence is shown inFig. 2.13. Using Equation 2.12, the spatial frequencies detected at different detector27E101A01Figure 2.12 Plan view of the growth flange of the VG V8OH molecular beamepitaxy system. The letters represent the optical ports. Arrows indicate a typicalorientation of the GaAs substrate in the system.AlxFigure 2.13 Cross section of the growth chamber in the plane of incidence for themost used geometry.GD C BE28positions for an incident wavelength of 488 nm in port B are calculated and presented inTable 2.1 together with the length scales probed.Detector q (pm-1) qy (p.m-1) Iqi (jim1) 0 q (deg) 1 (tm)PositionA -16.0 0 16.0 0 0.39C -5.4 0 5.4 0 1.16D -0.1 to -1.5 0 0.1 to 1.5 0 4.2 to 60E 5.1 0 5.1 0 1.23F -5.4 -5.4 7.6 -45.0 0.83G -5.4 -10.5 11.8 -62.8 0.53Table 2.1 Spatialfrequencies and length scales detected at differentpositions for anincident angle of25° (port B) and a wavelength of488 nm.For the given conditions, the accessible spatial frequency range covers more thantwo orders of magnitude, from 0.1 to 16 tm1. The equivalent lateral length scales varyfrom 0.39 to 60 $Im. The angles Øq between the q vectors and the plane of incidence arealso tabulated. They give the direction of the detected Fourier component of the surfaceroughness. Since we expect different scattering behavior for different crystal orientations,the alignment of the GaAs crystal with respect to the plane of incidence is critical. In theexperiments performed, one of the two principal crystal orientations of a (001) surface (i.e.[1101 or [110]) is aligned in the plane of incidence. This permits the angles q to be easilyrelated to crystal orientations.Though most of the latest experiments were performed using the 488 nm line of anair-cooled Ar ion laser, many other wavelengths have been used. The 457 nm line of thesame laser allowed us to reach up to 17 J1m’ in-situ. A HeNe laser (633 nm) and a diode29pumped YLF laser (523 and 1047 nm) were also used. The infrared laser can only beused to probe the front surface of the GaAs sample at high temperature since at lowtemperature the substrate is transparent to 1047 nm radiation (A > Agap) and a scatteredintensity orders of magnitude higher than the signal from the front surface is generatedfrom the back surface of the wafer. This effect is the same as the one exploited for thetemperature measurement52.In another geometry, the laser is incident normal to the sample (port C) and thesample is rotated until the crystal orientations match the two arrows shown in Fig. 2.12.The advantage of this geometry is that the two crystal orientations can be probedsimultaneously. The disadvantage is that only spatial frequencies of 5.4 and 10.5 jimt canbe detected through port A, F, B and G. The low frequency range is not accessible in thisset-up.For large spatial frequencies (q>5 jimt), a spherical lens is used to image thesample on a silicon photodetector with a built-in preamplifier. The EG&G HUV-1 100 BGphotodiode is mounted with a 10 M2 feedback resistor to have sufficient gain. An apertureplaced on the detector selects only the region of the sample probed by the laser ensuringthat the background light from the area around the sample is removed. The infraredradiation from a hot substrate and other visible wavelengths are absorbed by a 10 nm-widelaser line filter. A lock-in detector discriminates against constant background light that hasthe same wavelength as the laser but does not have the frequency of the chopped laserbeam. All this filtering is needed because the scattered light intensity is much smaller thanthe background light intensity in the MBE system. The scattered light intensity is 8 to 11orders of magnitude smaller than the specular intensity. Typical voltages measured rangefrom 1 iV to 1000 tV using the 10 M2 resistor. The noise levels originating from thelaser, the background light and the electronics are about 0.2 tV for the lowest intensitysignals when one second time constants are used in lock-in detection.30When the laser is incident at 25°, a continuous range of spatial frequencies (0.1 to1.5 11m’) close to the specular reflection in port D is detected using a 32-element diodearray located in the plane of incidence. As shown in Fig. 2.14, the specular beam isaligned such that it is on one side of the cross port close to the center. The divider thenensures that scattering produced by the specular beam hitting the mirror or the windowdoes not affect the measurement of the scattered light intensity on the other side of thecross.DiodeArrayWindowMBE portFigure 2.14 Detector arrangementfor small spatialfrequency detection.An aperture is used to limit the contributions to the signal at the diode array due toscattering from the input mirror in port B. Scattered rays from the first mirror wouldnormally be reflected specularly on the substrate and detected by the diode array.Positioning an aperture after this mirror, blocks this scattering, ensuring that the detectedintensity is mainly due to the small angle scattered light from the sample. The aperture isplaced 20 cm after the mirror using a UHV compatible mechanical feedthrough that allowfor linear and angular motion. The light is focused on the diode array by a cylindrical lensLensCylindricalWindow31as shown in Fig. 2.14. As for the other detectors, a laser line filter is placed on thedetector and lock-in detection is used. A feedback resistor ten times smaller (1M2) wasused because of the much higher scattering intensity close to the specular beam. The diodearray is then read by the computer through a lock-in amplifier, one channel at a time using amultiplexer. In general, during growth we repeatedly read four diodes that are equallyspaced on a log scale of spatial frequency. At any time during the process, a full scan ofthe 32 diodes can be performed and saved.The intensity at each detector depends on the solid angle over which the lens isintegrating. Table 2.2 gives the area of the limiting surface (smallest aperture) and itsdistance to the substrate for a large spatial frequency detector using a spherical lens. Thesolid angle is obtained by dividing the area by the square of the distance. The experimentalset-up is such that the solid angle of detection is similar for detectors placed at 25° or morefrom the specular beam.Detector A dposition (cm2) (cm) (sr)B, D, F 14 60 4.OxlO-3A,E,G 7 37.5 5.OxlO3C 10 71.5 2.0x103Table 2.2 Solid angle ofdetection at various position for detectors using a sphericallens.32The solid angle is about an order of magnitude smaller for each element of the diodearray. This is due to the fact that the cylindrical lens, integrates only over one dimension(qy). Moreover, because of the circular shape of the mirror, the detected solid angle variesalong the diode array. Fig. 2.15 gives the solid angle for each diode as evaluated from themeasured limiting aperture. Diode #31 is the closest to the beam. The solid angle is aboutan order of magnitude smaller than for the large-angle detectors.1.J I I I I I I I I I I I I I I I I I I I I I I I I I I I I I210-a1.51051001005 10 15 20 25 30Diode #Figure 2.15 Measured solid angle for each element of the diode array.The spatial frequency of each diode depends on the position of the specular beamwith respect to the diode array. Depending on the alignment, the spatial frequency of theclosest diode (#3 1) vary from 0.12 11m’ to 0.97 tm1 while the spatial frequency of thefurthest one (#1) vary from 0.64 pm1 to 1.5 p.m1 under the same conditions. Though itallows for detection of small spatial frequencies, the use of a cylindrical lens is moresusceptible to background light. Since one of the dimensions is not integrated over, theintensity in this direction cannot be apertured at the detector as is done in the spherical lenscase.33In order to measure the power spectral density continuously over the accessiblerange of spatial frequencies, an ex-situ scatterometer was built. The scatterometerconsisted of an air-cooled Ar ion laser (or an HeNe laser), sample holder and silicon diodedetector all mounted on an optical breadboard in such a way that the angle of incidence, andthe scattering angle defined by the detector position, could be controlled independently inthe plane of incidence. The sample could be rotated around its surface normal in order totest for crystal orientation effects in the surface roughness. The laser was focused onto thedetector in the specular direction to a spot about 0.5 mm in diameter with a long focallength lens. The laser was mounted on the MBE system in such a way that the incidentelectric wave was s-polarized and the laser spot was 1-2 mm in diameter on the sample. Insome cases, the laser was focused onto the sample to test for spot size dependence. Carewas taken to locate the laser spot at a position on the sample that is free of visible defects.The laser was chopped at 100-400 Hz and the scattered light signal was detected in theplane of incidence with the same 2.5 mm diameter silicon detector as the one use for in-situdetection. A possible choice of two feedback resistors (1K2 or 1OM)) allow forcontinuous detection from the specular scattering to the furthest backscattering. The solidangle for light collection was around 1 O sr and changed slightly from one series ofexperiment to another as the set-up was slightly modified. For most measurements, theangle of incidence was fixed at 65° relative to the sample normal.The evolution of the surface morphology can therefore be measured in-situ duringMBE growth at various discrete spatial frequencies. At any point during the process, asample can be quenched to room temperature, taken out of the MBE system andcharacterized using ex-situ light scattering. Since in this set-up, the scattering angle can bechanged progressively, a continuous power spectral density can be measured.34CHAPTER 3 SUBSTRATE PREPARATION AND OXIDE REMOVAL.The final cleaning step before molecular beam epitaxy growth is the removal of theprotective oxide layer in ultra high vacuum, leaving a bare crystalline substrate. Thesurface is then cleaner not only because the oxide is removed, but also because the residualcontaminants that were at the surface of the oxide tend to be reduced as well. As soon asthe desorption of the oxide is detected, the substrate temperature is stabilized to the requiredvalue and growth is started. In this chapter, we study the removal of the oxide by thermaldesorption and atomic hydrogen etch using diffuse elastic light scattering, RHEED andmicroscopy. The effects of the oxide thickness, the rate of the temperature ramp during thedesorption, the spatial frequency detected, the laser wavelength and different oxidationtechniques are investigated.3.1 Substrate Preparation.The substrates used for the desorption studies were semi-insulating (100) 2 inchdiameter GaAs wafers either on-axis (±0.5°) or 2° off the (100) orientation. Varioussubstrate preparations were tested. First, a nitric acid etch of the back surface95,leaving atextured surface, was performed in order to enhance the diffuse signal for the temperaturemeasurement and to improve the thermal radiation coupling of the wafer to theheater50’1,52 This is achieved using a machined Teflon disk shown in Fig. 3.1. Thecenter hole is slightly overfilled with HNO3 forming a convex liquid surface because ofsurface tension. The back surface of the GaAs wafer is then centered on the disk andetched for about 30 seconds. The groove on the outside prevents the acid from reachingthe front surface. After the etch is done, the wafer is rinsed in running de-ionized waterand blown dry using prepurified nitrogen. The obtained texture is a dark matte finish.3520 mni-j w- fr- 10 cm- 15 mn T2 5 ff11117.0cmInitially, great care was taken to remove hydrocarbons from the surface using astandard sequence of solvents: trichioroethane (TCE), acetone, methanol and de-ionizedwater. In some cases, up to 3 baths of each of these solvents were used, the first 2 being at40 °C for TCE and acetone. The etching of a few microns of material was also testedusing 2 types of solutions: H2S04 H202: H20 and NH4O : H202:H20. In bothsolutions, the sulfuric acid or the ammonium hydroxide etches the surface oxide generatedby the hydrogen peroxide. When the front surface is considered clean, the oxide layer isetched using either HC1, H2S04or NH4O then the wafer is rinsed in de-ionized water,blown dry with prepurified nitrogen and oxidized for specific times using an ozonegeneration process. The reactivity of ozone helps the formation of a thicker oxide layerwhich when removed will leave a cleaner surface53.Two different techniques were used for sample oxidation. Initially, the substrateswere oxidized in a low-pressure oxygen plasma discharge. At the operating pressure ofI. 5.1cm IFigure 3.1 Schematic of the Teflon disk used for back surface etching showntogether with the obtained rough surface.36200 mTorr the mean free path (MFP) between collisions for oxygen molecules is about250 JIm54. The high energy ions in the plasma will therefore react to produce ozone eitherin the plasma volume or a few millimeters around it. The sample is located 45 cm away(—2000 MFP) from the plasma discharge ensuring that the surface is protected from thedamaging ions. This reactor has been replaced by a more compact arrangement shown inFig. 3.2 in which the ozone is generated in a home-built reactor using a 60 W mercurylamp. The sample is inserted face-down directly over the UV light bulb at a distance of 1.5inches. Typical oxidation times for both techniques ranged from 2 to 20 mm, producingoxide thickness of 7.5 to 15 A for the plasma reactor as determined by x-ray photoelectronspectroscopy (XPS) and slightly smaller thicknesses for the UV ozone reactor as deducedfrom the desorption temperature dependence (see Fig. 3.13)._______________________7.0 inches_______________________After the samples were oxidized, they were cleaved in four pie-shaped pieces. Eachof the 4 sectors were then mounted on indium free molybdenum wafer holders and loadedinto UHV.Figure 3.2 Schematic of the UV ozone reactor usedfor sample oxidation.37All wafer handling was carried out in a I{EPA filtered laminar flow hood located ina normal laboratory environment, not in a clean room. It was found that the more thesubstrates were handled, the more contamination was finally detected. As we will showlater, even if the optical signature during the oxide removal is independent of thepreparation conditions, the roughness developed during the growth is highly sensitive tocontaminants. Since light scattering is sensitive to particulates on the surface and tocontamination we found it useful to keep wafer handling to a minimum. Only the stepwhere the back surface is darkened using HNO3 was necessary. Before oxidation, thewafer front surface was therefore only in contact once with de.-ionized water and blown drywith prepurified nitrogen.The recent addition of a pyrolytic boron nitride diffuser plate on the back of thewafer holder allowed us to eliminate the back surface etching step as well. Hence, the mostrecent samples were only cleaved, mounted on holders then oxidized and loaded into theMBE chamber. Cleaving the sample generates some particulates, but these will mainly belocated within 3 mm of a cleaved edge55. In the optical scattering measurements, the laserspot probes the center of the quarter wafer segment, about 1 cm away from these edges.Once the samples are loaded into UHV, two different techniques are used to removethe surface oxide. In the first one, the oxide is thermally desorbed by radiatively heatingthe sample through the oxide desorption point. In the second, the oxide is removed atlower temperature by etching the surface with atomic hydrogen.383.2 Thermal Desorption of the Oxide.To remove an oxide thermally, the sample is placed into the growth position underan arsenic flux similar to the one used in subsequent film growth. The substratetemperature was ramped through the oxide desorption point at about 5 °C/min for most ofthe experiments. The GaAs oxide desorbs in 2 definite steps. The arsenic oxides (As20,As202, As205)evaporate at 400 to 500 °C while the gallium oxide (Ga203) has beenreported to evaporate between 500 and 640 °C depending on the preparation conditions andon the temperature measurement technique56. We found the desorption temperatures torange from 550 °C to more than 630 °C as measured with diffuse reflectance spectroscopy(DRS)50-2,depending on the oxide thickness and on the rate of the temperature ramp.The thermal desorption of an oxide generates roughness on the surface28’931,33,34, 36, 37, 57• We have imaged the surface before and after desorption using field emissionscanning electron microscopy (FE-SEM), optical Nomarski microscopy, in-air scanningtunnelling microscopy (STM) and atomic force microscopy (AFM). Fig. 3.3 shows aNomarski picture (a) together with a FE-SEM picture (b) of a 4 mm UV-ozone oxidedesorbed surface. On the optical picture only a light texture can be seen. From the 90 pmwidth of the picture, the spacing between the small dots is estimated to be of the order of amicron. When the image of a similar desorbed wafer is taken using the FE-SEM, thetexture can be magnified. Imaging was done at a tilt angle of 45° between the samplenormal and the incident electron beam in order to enhance the secondary electron emissionfrom small surface structure. The vertical axis is therefore scaled down by a factor of 1.4.It is seen that the surface seems to be covered with pits of varying size, the biggest onesbeing about 1.5 iim apart which is consistent with the optical microscopy. It is interestingto note that at high magnification, slight texture is observed down to the 100 A scale.39To image GaAs in air using STM, passivation of the surface is necessary sinceinsulating and unstable oxides prevent reproducible imaging. The surface was treated witha (NH4)2S:0(1:9) solution at 40 °C for 20 mm and after this passivation step, thesubstrate was imaged reproducibly for many hours58. The results for a bias voltage of+6 volts on the tunnelling probe and for a tunnelling current of 0.16 nA are presented inFig. 3.4 for two different oxide thicknesses, the thinner oxide clearly leaving a smoothersurface. The gray scale of both images represent 200 A from black to white. The constantcurrent image of the oxide-desorbed surfaces indicates that the surface is covered withsmall indentations. Topographic scan lines taken across the images show the largest pits tobe at least 100A deep. This is in agreement with other published results28’29, 31Fig. 3.5 shows an image of the same oxide-desorbed wafer together with an imageof a polished wafer, as obtained with atomic force microscopy (AFM). The conclusions onthe morphology of the oxide-desorbed surface are basically the same as those drawn fromthe STM data. The rms roughness calculated from the AFM images is 3.6 A and 63 A forthe polished and oxide-desorbed wafer respectively. As seen on the image, polishingmarks axe the main contributions to the roughness of the as-received polished wafer.40-.-.--— — -.— 4% —fl4 Ar_ a—” —.4- %.-——.4—.4-w -_ wçç2*t%,--- .-, t,,:.1r—’ -- -- -r’j - .F -.S - - -4— # -!‘— .- , —- : --—-.INi-‘44—0’- _‘N_.4— ..0 —at —-, A’, — k.Ø4 -_.-s-.— ——- -J•1 E—’ :.— —1- %.Ø’ _- 4— ‘41-r ‘• 4—00231.8 25.0kV x3o.eKf:o’0Figure 3.3 Nomarski microscopy and FE-SEM pictures of a GaAs suiface fromwhich a 4 mm UV-ozone oxide has been thermally desorbed.41(b)Figure 3.4 STM images of a GaAs surface from which (a) a 4 mm UV-ozone and (b)a 2 mm UV-ozone oxide has been thermally desorbed (3 Wn x 3 1um x 200 A).42Figure 3.5 AFM pictures of(a) a polished substrate (25 um x 25 4um x 30 A) (3.2A mis) and of (b) a GaAs surface from which a 4 mm UV-ozone oxide has beenthermally desorbed (25. #m x 25 #m x 500 A) (63 A rms)43-4:i. 10I10:i ::::10.1• Polished wafero Oxide desorbed1 10Spatial frequency (j.im1)Figure 3.6 Ex-situ light scattering measurement of the power spectral density of apolished wafer and a 4 mm UV-ozone oxide-desorbed sample.The power spectral density (PSD) as measured with ex-situ light scattering ispresented for a polished substrate and an oxide-desorbed surface in Fig. 3.6. It isremarkable that the PSD can be continuously measured over six orders of magnitude, adefinite advantage of light scattering. The scattering set-up as well as the way to deduce thePSD from the scattering intensity has been described in section 2.3. For spatial frequenciesranging from 0.2 to 20 urn-’, there is a clear increase in roughness of up to 3 orders ofmagnitude. The integration of the PSD from 0.3 to 17 tm1 using equation 2.14, leads toa rms roughness of 5.0 A and 79 A for the polished and the oxide-desorbed surfacerespectively. These values are consistent with the roughness seen on the STM and AFMimages (3.2 and 63 A) considering that the two techniques do not quite measure the samespatial frequency range. Moreover, a bump in the PSD of the oxide-desorbed sample at q= 4 im1 represents a correlation in the position of surface features of about 1.6 tm. Thisdistance corresponds well to the average spacing observed between the largest pits onFig. 3.3 and Fig. 3.4.-3____________________________________________10 I 1111111 I I 11111110..000••..I I I..a’•.44RHEED is the most commonly used technique for detecting the oxide desorption.At low temperature, the reflection of 12 keV electrons off the non-crystalline oxidegenerates a uniform green glowing background on the phosphorous screen as the electronsare incoherently scattered. When the temperature is ramped through the desorption point,sharp diffraction spots appear on the screen as expected from a bare GaAs crystallinesurface. In-situ light scattering experiments also provide insight into the development ofthe surface morphology by tracing the evolution of the structure factor (PSD) for givenspatial frequencies. Fig. 3.7 compares the time evolution of the RHEED pattern withvariations in scattered intensity at q= 7.4 I.tm’ during the oxide evaporation. The timeevolution on the x-axis corresponds to a temperature ramp of 5 °C/min. The step inscattered intensity during the desorption has been shown on a logarithmic scale in order toenhance the small feature that is typically seen 20 to 40 °C before the sharper increase. Theevolution of the RHEED pattern is presented using 8 pictures labeled (a) to (h) eachcorresponding to a time on the x-axis of Fig. 3.7. The uniform illumination of theRHEED screen at room temperature is shown in picture (a). It appears that the RHEEDintensity distribution is already slightly changing on (b) which is more than 50 °C beforethe main increase in scattered light. As the light scattering increases to form the “prebumparound 6 mm, the surface starts to show some order as lines appear on the RHEED screen.The lines become sharper from (c) to (e), finally developing into diffraction spots when thelight scattering increases dramatically. The RHEED pattern evolution seems to stop whenthe light intensity saturates (f) showing good agreement between the two detectiontechniques. Picture (h) corresponds to the RHEED pattern when the substrate is rotated toalign the electron beam along the [1101 crystal orientation and clearly shows a 3-dimensional pattern typical of rough surfaces. This correlates well with high resolutionFE-SEM imaging that shows a rough surface morphology.45C,)1(e(g)I I I 3- 7.411m”(b) (c)(f)I I I I •.? I I I r I I I I(d)0 2 4 6 8 10 12Time (mm)(a)(b)(c)(d)Figure 3.7 Evolution ofRIJEED pattern in parallel with the variation in scatteredintensity during oxide desorption.46The increase in scattered intensity was also shown to coincide with the appearanceof the Ga20 species in the mass spectrometer57.The correlation between the signatures oflight scattering, mass spectrometry and RHEED confirms that the roughness detectedoptically is generated during the desorption and is due to the evaporation process. Themeasurement of scattered light intensity can therefore be used to measure the end point ofthe thermal desorption.Fig. 3.8 shows the evolution of the intensity of the scattered light as the oxidedesorbs for three different detection angles at least 25° away from the specular reflection.Once again, the time scale on the x-axis corresponds to a temperature ramp of 5 °C/min andthe increase in scattered intensity during the desorption has been adjusted to go from 1 to10 on a logarithmic scale for comparison. The spatial frequencies of 5.1, 5.4 and 16 tnr1correspond to scattered angles of 55°, 00 and -55° and to detection positions A, C and E onFig. 2.12 respectively. As shown in this schematic, the laser (488 nm) was incident at 250and all detectors were in the plane of incidence. Note that the two spatial frequencies of 5.1and 5.4 tm1, though similar numerically are detected at two very different scatteredangles. As expected, we find in this case that the detected signal depends on the detectiongeometry only through the spatial frequency probed. Moreover, the fact that similar spatialfrequencies have the same optical signatures when detected at different angles also indicatesthat the initial assumption for the model is valid, i.e. the roughness is small enough not togenerate significant shadowing or second order scattering.4710110Figure 3.8 Scattered intensity at 3 spatialfrequencies given by 3 different scatteringangles during the oxide desorption.Lower spatial frequencies can be reached in-situ using the diode array as describedin Chapter 2. Fig. 3.9 shows the scattered intensity as a function of temperature forvarious spatial frequencies ranging from 0.27 to 16 J1m’. The curves shown correspondto three similar oxide desorptions that are denoted by a, b, and c. The intensities have beendivided by the solid angle of detection to allow comparison between different spatialfrequencies and the background has been subtracted in order to illustrate the oxidedesorption features more clearly. It is striking that the scattering signal for small spatialfrequencies goes through a maximum while at higher q the increase is monotonic duringoxide evaporation. The height of the maximum is roughly the same for different spatialfrequencies. Interpretation of this result should be done cautiously since in the desorptionof some samples, a variation of up to a factor of 2 in the height of the maximum has beenobserved. Another surprising feature is that the spatial frequency dependence of the overallstep intensity increases with q up to 5.4 pm1 and decreases for higher spatial frequenciesas shown by the dotted line representing q=16 tm1. The final intensity values are2 4 6 8Time (mm)48-lIS• —cd,IFigure 3.9 Time dependence of scattered intensity for 3 similar samples a,b and cduring oxide evaporation for various spatial frequencies ranging from 0.27 to16 j1m.To complete the spatial frequency dependence study, the behavior of the specularreflectivity (q = 0p5m1) during the evaporation is compared with that of the scatteredintensity in Fig. 3.10. There is a small “dip” in the specular intensity associated with thegain in diffusely scattered light intensity during the oxide evaporation.consistent with the intensities that led to Fig. 3.6 showing the PSD after the desorption ofa similar oxide.0.350.30.25 (a) - q=5.4 tm’0.2(b) - q=1.5 I.tm-10.15(b) - q=1.2 j.im’0.1 (a)-q= 16.tm(a) - q=.64 jim-’0.05 (a) - q=.40 jim-10 (c) - q=.27 jim’-10 -5 0 5 10Temperature (TTcies) (°C)490.7 0.96 c.’)0.6 0.950.5 0.940.93. V.’.,.0.92 •tl) 1’-)4_ J30.2 090.1 0.890 0.88.’0 1 2 3 4Time (mm)Figure 3.10 Time evolution of the scattered (q=5.9 um1)and specular intensityduring oxide desorption.As proposed by van Buuren et al, we believe the roughening occurs because thegallium oxide does not desorb homogeneously over the whole surface57.The desorption ofthe arsenic oxides at lower temperature leave a gallium oxide layer which is non uniform.The presence of the bump before the main intensity increase in Figs 3.7 and 3.8 suggestthat the oxide is reacting with the underlying substrate before the desorption. When thedesorption temperature is reached, the gallium oxide desorbs first around the weakestpoints in the layer (cracks or defects) causing a non-uniform desorption of Ga20 that leavespits on the surface. While the roughness is developing, scattering at any spatial frequencyincreases monotonically until all the oxide is desorbed. The difference between thescattering observed at higher and lower spatial frequencies at the end of the desorptioncould be the result of a final faceting of each pit. Such faceting would result in a reductionin roughness on length scales greater than the distance between the largest pits (1.5 rim)corresponding to a decrease in scattering at lower spatial frequencies (q < 4 tm1).5 6 750Roughness on smaller length scales would continue to increase but at a slower rate as thesurface reaches equilibrium.To check if the roughening associated with the oxide evaporation is dependent onthe substrate conditions, we desorbed a 4 mm UV-ozone oxide from a GaAs substrate,grew a 1 tm buffer layer and then removed the sample from the UHV chamber and didanother 4 mm UV-ozone oxidation of the epitaxial layer. Light scattering measurementswere performed while this oxide was evaporated in UHV. The optical signature duringdesorption was similar for both the oxidized substrate and the oxidized epilayer. Also, nodifferences in roughness were observed in FE-SEM images of the two desorbed surfaces.This suggests that the non-uniform desorption is not linked to defects or impurities at thesurface of a GaAs wafer but to the desorption mechanism itself.The temperature interval over which the substrate roughening takes place issufficiently narrow that its width can be attributed entirely to the temperature gradientacross the sample. To demonstrate this, the diffuse reflectivity was measuredsimultaneously with two different lasers during the desorption of a 15 mm plasma-ozoneoxide. A diode-pumped frequency doubled YLF laser (523 nm) and a HeNe laser(633 nm) were coupled into the vacuum through ports B and D respectively as shown inFig. 2.11 and Fig. 2.12. Using a cross port arrangement such as the one shown inFig. 2.13, both scattering signals were detected in the same port (F). The spatialfrequencies of detection were 5.7 and 7.4 Jim’ for the red (633 nm) and green (523 nm)laser respectively. The result, illustrated in Fig. 3.11, shows a wider transition in thereflectivity for the green (523 nm) laser for which the spot diameter is about 3±0.2 mmthan for the red (633 nm) laser for which the spot size is smaller (1.9±0.2 mm). The stepheights are normalized to 10 to facilitate the comparison and the step widths are measuredfrom 5% to 95% of the full step. We believe that the differences between the two signalscannot be attributed to the different spatial frequencies since they only differ by 25%.51Moreover, if the spatial frequency difference was responsible for the effect seen, the firstsignal to rise would be the green one sine it correspond to the higher spatial frequency.The opposite behavior is observed.The ratio of the widths in the two diffuse reflectivity steps (1.8) is equal to the ratioof the laser spot sizes (1.6±0.3) within the experimental error, as one would expect if thewidth was entirely due to a temperature gradient. From the data in Fig. 3.11 and the5 °C/min ramp rate, we evaluate the temperature gradient on the surface of the sample to be17±8 °C/cm. Note that the offset between the two reflectivity steps in Fig. 3.11 is 20 swhich corresponds to 1.7 °C. The calculated temperature gradient across the surface isused to convert this temperature offset into a predicted distance of 1 mm between the centerof the two beams. This is consistent with the experiment since the two laser spots weretouching on the substrate but not completely overlapping.l26s 163s•S 128.::;‘t: 95%: - 632.8nm +523nm4 ..- 89s •. ÷÷98s-._++I I , , I • I • I60 80 100 120 140 160 180 200Time (s)Figure 3.11 Evolution of scattered intensity during oxide desorption as measuredby two different lasers with two different spot sizes on the sample.Using the above beam size ratio, the light scattering step widths and the temperatureramp rate (5 °C/min), the maximum temperature width for the intrinsic surface roughening52step was estimated to be less than 1 °C. Such an abrupt transition suggests that the oxidedesorption and the related surface roughening is associated with a phase transition orinstability in the surface oxide.To explore the desorption of the surface oxide further, we performed an oxideevaporation in the FE-SEM. A 0.5x0.5 cm GaAs sample covered with a 120 mm UVozone oxide was wrapped in a tantalum sheet leaving only a small area of the surfaceexposed for observation with the electron beam. The tantalum jacket is used as a radiationshield and also to improve temperature uniformity. The system is heated by flowing a largecurrent through two 0.0 10 inch diameter tantalum wires spot welded to the 0.005 inch thicktantalum sheet. The temperature was measured with a thermocouple also welded to thetantalum. No significant degradation of the vacuum was noticed during sample heating andno modification of the surface was observed due to exposure from the imaging electronbeam. When the heating current is ramped so that the sample temperature slowlyapproaches the oxide desorption temperature, the roughness appears gradually over about30 seconds which corresponds to a temperature range of only 3 °C. This temperaturerange is slightly wider than the evaluated scattered intensity step widths during thedesorption in the MBE chamber. This discrepancy could be due to the much higheroxidation time for the sample desorbed in the SEM. Also, unlike in the MBE chamber, thedesorption in the SEM is done without an As2 flux while in the SEM chamber, thedesorption is performed while imaging with a 30 KeV electron beam.It is interesting to note that no significant roughening was observed when the thickoxide was chemically removed with HC1, NH4O or H2S04 before being loaded intoUHV. The oxide formed within 2 mill in DI water and in air is sufficiently thin that, withno further surface treatment, a faint structure can be observed on the RHEED screencorresponding to the crystallinity of the underlying substrate. When this oxide is desorbed,there is no increase in scattered light intensity suggesting that the surface stays smooth53during the desorption. However, this procedure should not be considered as an alternativefor producing smooth surfaces because, as will be shown in the next chapter, growth onthese types of surfaces generates large scattering signals, due to residual contaminants.The fact that the evaporation of a native oxide does not generate roughness suggests that theoxide thickness is the principal factor in the development of the surface morphology.To quantify the dependence of the light scattering signature on the oxide thickness,four oxides of different thickness were desorbed. The thicknesses correspond toexposures of 5, 10, 15 and 20 mm in the low pressure oxygen plasma reactor. Fromearlier work57’9,it is known that this range of oxidation times corresponds to only a smallvariation in oxide thickness from about 11 to 15 A. To ensure that the light scatteringintensities could be compared from sample to sample, great care was taken not to changethe laser alignment. Since the oxide desorption step is isotropic, the alignment of thecrystal orientation with respect to the beam is not important. Each sample was oriented toface the effusion cells and rotated until the HeNe laser reflection followed exactly the sameoptical path for all the samples. This was not done in general since in other experiments,the sample and the laser were repositioned slightly during alignment of the crystalorientation with the plane of incidence. To avoid variations due to sample preparation, thefour samples were taken from the same wafer which was cleaved after preparation andbefore oxidation. The diffuse reflectivity at q=5.7 11m’ measured at 90° to the plane ofincidence is shown in Fig. 3.12 as a function of temperature during the desorption of thefour oxides. Thin oxides formed by short exposure to the oxygen plasma, evaporate atlower temperature than the thicker oxides. This effect has also been observed byothers28’56.The desorption temperatures of samples oxidized using both oxidation techniquesmentioned earlier (Fig 3.2), are shown in Fig. 3.13 for different oxidation times. Thedesorption temperatures observed vary from 549 °C to 612 °C depending on the oxidation54time and on the technique used. The fact that the 120 mm UV-ozone oxide desorbs at alower temperature than a 20 mm plasma-ozone oxide could be attributed to the betterefficiency of the plasma oxidation for producing an oxide. It should be considered as wellthat the two oxidation method could produce oxides with different stoichiometry. Theroughness generated by the desorption could also vary with the oxidation technique, evenwhen the desorption temperature is the same. These effects have not been studied.Figure 3.12 Time dependence of scattered intensity at q=5. 7 im1desorptionfor 4 samples oxidizedfor different lengths of time.during oxideI1.61.20.80.40580 590 600 610Temperature (°C)62055, 620c-)0600590580570560550540Oxidation Time (mm)Figure 3.13 Desorption temperature versus oxidation time for UV-ozone andplasma-ozone oxidized wafers.As expected from the STM images of Fig. 3.4, the height of the step in Fig. 3.12,depends also on the oxidation time. Thinner oxides leave a smoother surface. It is alsointeresting to note that the width of the desorption steps in Fig. 3.12 for the 5, 15 and20 mm oxides are the same: if each step is normalized vertically and shifted for comparisonthe three steps fall on top of each other. This is consistent with the earlier interpretation thatthe width of the step is due to the temperature gradient across the surface of the substrate.The 10 mm oxide has a slightly narrower transition and a higher background signal at thestart. We believe that this results from the presence of impurities or particulates on thesurface which increase the scattering and also contribute to a local change in emissivity,modifying the surface temperature at that point. The fact that the thinner oxide iscompletely removed before the desorption of the thicker one begins, was already observedusing mass spectrometry57’9and suggests that the oxide desorption is not a layer by layerevaporation process.1 10 10056Since the desorption is a non-equilibrium process, the final roughness should alsodepend on the rate at which the temperature is ramped. This effect has been studied forfour identical substrates oxidized for 15 mm in the low pressure plasma reactor. A rangeof temperature ramp rates has been tested, from 2.2 °Clmin to more than 10 °C/min. Themaximum temperature ramp rate was limited to 10 °C/min in order to avoid surfacedamage. We observe surface degradation after evaporation if the ramp rate is too fast,since the desorption occurs too close to the congruent evaporation temperature. Fig. 3.14shows the variation in desorption temperature for identical oxides as a function of thetemperature ramp rate. As expected, the desorption temperature increases for fastertemperature ramps.II 1111111111 I 111111111L)640I-’620 I IIII6001580 +560I I I I I I I0 2 4 6 8 10 12Temperature Ramp Rate (°C/min)Figure 3.14 Desorption temperature versus rate of the temperature ramp duringoxide desorption of 15 mm plasma-ozone oxides.The roughening associated with the standard thermal cleaning of the GaAs in UHVenabled us to study various aspects of the desorption process using light scattering. Thenext section shows how the oxide can be etched at lower temperature using atomichydrogen, without surface roughening.573.3 Atomic Hydrogen Etch of the Oxide.For most MBE applications planar interfaces are needed. These are usuallyachieved by growing a “buffer layer” of GaAs over the rough oxide-desorbed substrateuntil the surface is planarized as detected by a change in RHEED pattern from3-dimensional to 2-dimensional growth. However, in some cases such as regrowth onpatterned substrates, the growth of a buffer layer is not an acceptable option. Therefore theproduction of smooth and clean substrate surfaces is of great importance for MBEtechnology.Etching of the oxide using atomic hydrogen was investigated in order to find out ifany changes in surface morphology occur during the process. This technique is known toremove the oxide at lower temperature6063. In the hydrogen cleaning technique, aretractable tungsten filament and a tube are brought close to the wafer as shown inFig. 3.15. When the substrate is at about 300 °C, a flow of hydrogen gas (H2) isintroduced into the chamber through the small tube. The leak valve is gradually openeduntil the pressure in the chamber reaches 1x106Torr, after which power is applied to thefilament. As measured with a disappearing filament optical pyrometer, the temperature ofthe filament is typically 1800 °C during the etch which causes an increase of about 70 °Cin the substrate temperature. Part of the constant flow of hydrogen molecules coming outof the tube reaches the hot filament and is decomposed into hydrogen atoms. Some of theatoms will react with the oxide layer. The reaction has been studied by different groups6062 and, as for the thermal desorption, is believed to occur in two stages. The arsenicoxides are the first ones to be removed and the products of the reaction are believed to bewater and molecular arsenic (As4) with very little arsine (AsH3) formation. The morestable gallium oxide (Ga203) is then transformed into the volatile Ga20 and water whichevaporate. It has also been proven that the hydrogen etch will remove carbon contaminants58for substrate temperature as low as 200 0C62. The surface is therefore expected to be freeof oxide and carbon contaminants.W Filament,,, ftSubstrateFigure 3.15 Schematic of the hydrogen etching technique.Under the conditions given, the RHEED pattern appears after etching a 5 mm UVozone oxide for about 15 mm. Contrary to the thermal desorption shown in Fig. 3.8, theRHEED pattern observed is made of diffraction lines which is typical of two-dimensionalsurface suggesting that no roughness appeared during the oxide removal. Light scatteringwas also used to monitor the evolution of the surface roughness during the etch. On alllength scales probed by the light (400 nm to 50 .im) no intensity increase was observedshowing that no significant roughness is generated on these length scales. FE-SEMimaging of those surfaces could not resolve any structure. The surface is believed to beclean and as smooth as the initial polished wafer./— /‘,//,‘_,,_// / // 7 / /— / ,/ //— / /,/ // ///Tube593.4 Arsenic cap desorption.An arsenic layer is sometimes used to protect the sample surface from oxidationwhen it is transferred through air from one vacuum chamber to another. The arsenic can beevaporated at a relatively low temperature without damaging the surface. The diffusereflectivity can be used to detect the evaporation of this arsenic cap from the substrate.Fig. 3.16 shows the typical behavior of the specular and diffuse reflectivity (q=5 .7 tm1)associated with the desorption of a clean (non-oxidized) arsenic cap. As the temperature isramped through the desorption point, the scattered signal decreases by a factor of 2. Thiscan result from both a decrease in surface roughness and a change in reflectivity (becausethe materials have very different indices of refraction). From 290 to 315 °C, the specularreflectivity oscillates. We interpret these oscillations as interference fringes associated withlayer by layer evaporation.8+* ,,÷ *;_ ., •* 4, * + +* + •+44 **4*+S.—.,..4>. 4 - Diffuse3-2- **1-0 • I i I I • I280 290 300 310 320 330Temperature (°C)Figure 3.16 Typical behavior of the specular and diffuse reflectivity (q=5.7 f.ttw1)associated with the desorption ofa clean arsenic cap.60A similar measurement on an oxidized arsenic cap is presented in Fig. 3.17. Thearsenic cap was oxidized as a result of exposure to an uncontrolled air leak in thepreparation chamber. The measurement showed a higher desorption temperature (330-340 °C), a shorter period in the specular reflection oscillations and an increase in thediffuse signal before a sharp drop. As for the desorption of the oxide-free arsenic layer,there is a small overall decrease in reflectivity. The differences observed are due to thepresence of the oxide layer in the second case, which creates a barrier that blocks thearsenic evaporation. Presumably, the roughness is generated because the arsenic oxidedesorption is very non-uniform. The arsenic oxide evaporates first in small areas andallows the arsenic underneath to evaporate locally, causing the surface to roughen. Whenall the oxide is gone, the roughening stops and the interference oscillations restart with asmaller period because of the higher temperature. They persist until the arsenic cap isremoved completely.1IE________________I I I I I I I I I I I I I320 330 335 340 345Temperature (°C)Figure 3.17 Typical behavior of the specular and diffuse reflectivity (q=5.7pm1)associated with the desorption of an oxidized arsenic cap.SpecularDiffuse32561In this chapter, we presented first the substrate preparation before loading thesample into UHV. Then, the evolution of the surface morphology during the removal ofthe oxide by thermal desorption or atomic hydrogen etch and during the evaporation of anarsenic cap was studied using the light scattered at different angles. In Chapter 4, theevolution of the surface morphology is measured with light scattering during growth ofGaAs on the various surfaces discussed in this chapter.62CHAPTER 4 EPITAXIAL GROWTH OF GaAs ON GaAs.The evolution of the surface morphology when growing a GaAs epilayer on a GaAssubstrate is investigated. In-situ and ex-situ light scattering corroborated with atomic forceand scanning tunnelling microscopy provide information on the evolution of the surfaceroughness and on the surface power spectral density.The expected light scattering signature is first derived from kinetic rougheningtheory which supposes that the only source of roughness is the noise in the depositionfluxes. The study of the surface morphology during homoepitaxy of GaAs will bepresented for growth on the rough oxide-desorbed surface and the smooth hydrogen etchedsurface after a discussion of the influence of contaminants and particles on the scatteredlight intensity.4.1 Kinetic roughening.Recent theoretical work and computer simulations have shown that the surface ofepitaxial films is in general not atomically flat during growth due to the interplay betweenthe random nature of the deposition process and the effects of surface diffusion6473.Although MBE produces fairly smooth interfaces using relatively slow growth rates, thinfilm growth is a non-equilibrium process. The noise in the deposition flux contributes tosurface roughening while surface diffusion mechanisms act to reduce this roughness. Thisnoise contains all spatial frequencies. Surface diffusion will be able to smooth out the highspatial frequency roughness. However, the long length scale noise in the lateral dimensionof the beam generates some low spatial frequency roughness that surface diffusion does nothave time to heal during deposition. This roughness will build up until a steady state isreached in which there is a balance between the roughening due to the noise in thedeposition flux and the smoothing due to surface diffusion.63The gain in roughness is called kinetic roughening since it appears only in thepresence of deposition fluxes. The roughening can be described using the width of theinterface or the rms roughness:1LL(h1.—h) (4.1)L 1=1 j=1The discrete function (h —Ii) represents the deviation of the actual surface from.the mean flat surface at point (i, j). The function is locally discrete because of the discretenature of the deposition. For long length scales the surface is approximated by a smoothfunction h(x,y) and the summations can be approximated by integrals.Under the kinetic roughening theory, the shape fluctuations of the surface followstatistical scale invariance. In the steady state, over a range of spatial frequencies, thesurface becomes a seif-affine fractal which is scale invariant. A seif-affine surface, unlike aself-similar fractal, scales with different exponents along the directions normal and parallelto the surface. The scaling property of such a surface over the range of interest can bewritten:j((h(r+d)_h(r))2) (4.2)The brackets represent an average over r. The scaling exponent cx represents howthe dimension perpendicular to the surface scales with the dimensions parallel to thesurface.During growth, the roughness will not only scale with the spatial dimensions butalso with time t. This is called dynamical scaling. For a portion of the surface of size L2,the dynamical scaling hypothesis can be written using the variance w2 of the growingsurfaceM,70:64w2(L,t) = L2a fQ.Lwith f(x) = x2Z for x << 1 (small times) (4.3)f(x)= const for x>>1 (long times)Fig. 4.1 shows the expected time evolution of w2 (Equation 4.3) for differentsystem sizes. For short time intervals, the increase in w2 follows a power law withexponent 2 a/z and saturates when the lateral correlations reach the size of the system aftert —Lx. Therefore, the saturation happens later for larger systems. This behavior is thoughtto be universal in the sense that it is believed that it can describe any type of roughening.Different physical mechanisms that control the roughening will only lead to different valuesfor the exponents a and z. One set of exponents (a, z) defines all the processes in thesame universality class.rdDz-Log [t] (arb. units)Figure 4.1 Expected evolution ofw2(L,t) for different system sizes.65We want to measure the evolution of the surface as well as the final roughness aftera long growth time in order to verify that the assumptions which lead to Equation 4.3 arereasonable for molecular beam epitaxy. As discussed in Chapter 2, light scattering issensitive to g(q), the power spectral density (PSD) of the surface morphology. We aretherefore interested in the scaling form of the PSD function to be able to verify it in-situ.The equivalent of Equation 4.3 in Fourier space is69:g(q,t) = q_Z s(qzt)with S(x) = x for x <<1 (small times) (4.4)S(x) = const for x >> 1 (long times)Fig. 4.2 shows the predicted time evolution of the power spectral density (PSD) asdescribed by Equation 4.4. The first graph gives the change in the PSD at given spatialfrequencies. At the start of growth, each spatial frequency evolves linearly with time untilsaturation. The smaller the spatial frequency, the longer it will take to reach saturation.After a really long time, the power spectral density is constant and follows a q_Zdependence as shown in the second graph of Fig. 4.2.66C-U)4-ICC)0-JLog [q] (arb. units)Figure 4.2 Tune evolution of the power spectral density. as predicted by the dynamicalscaling theory ofkinetic roughening.Alternatively the kinetic roughening can be described using a continuum differentialequation valid at length scales that are long compared to the spacing between atomic scalefeatures on the surface. The general stochastic equation describes the rate of increase of thelocal film thickness during growth and has the form6572:={vv2h+ (Vh)2— KV4h+ aV2(Vh)2+...}+ F+ (4.5)Log [t] (arb. units)t>> Ltislope = -z67This equation shows how the atoms will move around in reaction to heightdifferences across the surface. In other words, it describes how the surface roughness willreact with time. The right hand side depends on surface slope, curvature and higher orderderivatives. The coefficient F is the net deposition flux (deposition minus desorption) andTJ(r, t) is the local noise in the flux and is taken to be uncorrelated in space and time. InEquation 4.5, if there is no noise in the beam and the surface is flat, all the terms in bracesare zero (all derivatives are zero) and, as expected, the rate at which the surface is movingcorresponds to the net flux F. The noise in the beam generates surface roughness and thesurface will heal in a way that depends on the magnitude of the coefficientsv, A, K and a in Equation 4.5.We are interested in the case where desorption is not significant. In that case, ifthere are no voids or overhangs in the film, the flux of atoms diffusing on the surface mustbe conserved:(4.6)Where j is considered a two-dimensional current that flows on the surface, In thecase of growth or surface diffusion without desorption, the first non-linear term inEquation 4.5 is not present because it is not consistent with the volume conservation law (agradient term cannot be isolated from it). It is interesting to note that Equation 4.5 withoutthe non-linear terms is solvable analytically:={vv2h_Kv4h}+F÷n (4.7)dtA complete solution of this equation is developed by J. Villain65 Changing thereference frame to the moving averaged flat surface and solving in Fourier space for thecase of uncorrelated white noise leads to:68g(q,t)— ]—exp(—2(vq2±Kq4)t) (4.8)vq +KqThis result can then be compared with the predictions of the dynamical scalingtheory (Equation 4.4 and Fig. 4.2(a)). For small times, the exponential can be expandedin a series and the power spectral density increases linearly with time. For very long times,the exponential term is negligible and g(q) can be written:1for t—>°o, g(q)— 2 4 (4.9)vq +KqDepending on the range of spatial frequencies and on the relative weight of thecoefficients v and K, the power spectral density could have a slope -2 or -4 if non-linearterms in Equation 4.5 are not important. The slope gives some of the possible values of thedynamical exponent z.These results represent the light scattering signature of the roughening behaviorexpected for growth starting on a smooth surface provided the roughening is caused by thenoise in the deposition fluxes and that non-linear terms are neglected. From Chapter 3, weknow that the starting surface can exhibit large surface roughness caused by thermaldesorption. The magnitude of the kinetic roughening expected is much less than the depthof the pits formed during oxide desorption. Therefore, when growth begins on this roughsurface, a different behavior is expected.For a surface, rough on the length scale probed, the noise term in Equation 4.7 canbe neglected. In the moving frame, the Fourier transform of Equation 4.7 without noisecan be written:ah—9--+(vq2+K4)hq=O (4.10)69Where hq is the Fourier transform of the surface topography. The solutions of(4.10) describe the smoothing of the rough surface at a given spatial frequency (q). Thepower spectral density and thus the light scattering signature should decay exponentiallywith characteristic time ‘r = [2( vq2 + Kq4)f1. Once again, the behavior depends on therelative weight of the coefficients v and K.In general, smoothing from a rough surface is in competition with kineticroughening. After a long growth time the kinetic roughening should become the dominantfactor. When the optical signal becomes stable, the expected behavior of the power spectraldensity should be described by Equation 4.4 or Fig. 4.2 (b) if non-linear terms are notimportant in the range of spatial frequency studied.704.2 Effects of contaminants on light scattering during growth.Light scattering is a standard tool for measuring particle density, either in air or on asurface. As mentioned earlier, since we want to measure the morphology of the film itself,it is necessary to make sure that the scattered signal is not a result of scattering from manylocal centers but from an intrinsic surface texture. Microscopy (SEM, AFM, STM andNomarski) revealed that the scattering signal from an oxide-desorbed wafer is related to thegeneral topography and not to particulate scattering. When growth is started on an initiallyrough surface, smoothing is expected. Fig. 4.3 shows the time evolution of the specularreflectivity together with the diffuse reflectivity, measured simultaneously on the samesample both while the oxide evaporates and during the growth of GaAs. The HeNe laser(633 nm) was incident through port B and the diffuse light was collected at port F onFig. 2.13. No special care was taken to align the incident laser beam with acrystallographic orientation.2015100500Figure 4.3 Time evolution of the specular and diffuse reflectivity during oxideevaporation and growth of GaAs. The 1.5 hour break in the time axis represents thetime required to complete preparationfor growth.0.5 1 1.5Time (hrs)71This sample was cleaned with solvents (TCE, acetone, methanol), etched inhydrochloric acid to remove the oxide of unknown thickness left by the preparationconditions of the supplier and ozoned for 15 minutes in the plasma reactor. The oxide wasdesorbed using a 5°C/mm temperature ramp. The usual signature for the high spatialfrequency scattering and for the specular reflection during desorption is seen before the 1.5hour break on the time axis. This break represents the time required to completepreparation for the growth and to bring the substrate to the growth temperature of 565°C inthis case. The growth rate for the GaAs is about 1.2 jim/hr.When growth begins, the specular signal increases while the diffuse one decreases.This is consistent with the expected smoothing of the rough oxide-desorbed surface.However, instead of being monotonic, both signals undergo a large oscillation before theintensity becomes stable. The fact that the material grown has the same index of refractionas the substrate rules out the possibility that this variation in signal is due to interferenceeffects in the epilayer. As mentioned earlier, for the specular intensity, any degradation ofthe smooth surface signal can be related to the rms roughness of the surface. It is clear thatthe surface smoothes at first since the specular signal is increasing, gets rougher and thensmoothes again at a slower rate.The same smoothing-roughening-smoothing behavior is seen on the diffusereflectivity signal. There, the temporary roughening is related to one Fourier component ofthe surface topography. The signal at this 1.1 jim length scale is even higher at the peakthan it is immediately after the oxide desorption, suggesting larger roughness on that lengthscale. It is clear from Fig. 4.3 that, in this case, it is necessary to grow about 0.2 jim ofmaterial before the specular intensity becomes stable. On the other hand, 0.5 jim ofmaterial is needed before the scattering signal drops back close to the initial value beforeoxide desorption. This shows the high sensitivity of the diffuse reflectivity toimperfections in the surface.72A similar feature has been reported in the diffuse reflectivity from silicon substratesduring the initial stages of epitaxial silicon deposition by chemical vapor deposition and byMBE27. In the silicon case, the effect was attributed to the increase in surface roughnessassociated with carbon contamination. The effect disappeared when the wafers werecleaned by exposure to ozone before being loaded in the growth chamber. It has beenknown since the early 70’s that contamination leads to faceting and to defects in theepilayer9. In particular, GaAs does not wet carbon contaminants. As the film is growing,the material accumulates first around the contaminants forming a “crater”. Eventually, thecrater is filled because the slope becomes too large and the contaminants gets covered.We believe that a similar impurity effect is responsible for the oscillation in thereflectivity in Fig. 4.3. We believe that the background texture of the film is in factsmoothing monotonically and a large roughness is developing locally around a particle or acontaminant. To check this hypothesis, we grew a series of samples in which weinterrupted the growth at various points in the diffuse signal. Since the roughnessgenerated by the desorption was easily imaged with the scanning electron microscope, thesame instrument can be used to image the sample at the peak in the diffuse reflectivity.Since at this peak the diffuse signal is even higher than after the oxide desorption, sometopography or features should be observable.Fig. 4.4 shows an SEM picture of a sample for which growth as been stopped atthe maximum in the oscillation. Compared to the oxide-desorbed pictures in Fig. 3.3 and3.4 there is no general texture in the film. The film was found uniform and smooth downto the 100 A scale. Since the picture has the large field of view, small defects can be seendistributed randomly in the film. Using ten images of the same size covering about a1 mm2 area, we evaluate the surface density of those scattering centers to (5.8 ±0.5) x105cm2. On average, there is one defect in an area of 13 x 13 urn. Within a laser spot ofabout 1 mm2 as many as 6000 scattering centers are present and we believe they are73responsible for the peak in the scattering. Figs 4.5, 4.6 and 4.7 show the general evolutionof those centers as more and more material is deposited. The three pictures represent thetypical shape of the scattering centers for epilayer thicknesses of 50, 180 and 500 nmrespectively. Each thickness corresponds to a different point in a scattering curve similar toFig. 4.3. For the first, second and third sample respectively, growth was stopped at theminimum in scattering before the oscillation, at the maximum in scattering and after theoscillation where the signal becomes low and stable. As already observed 20 years ago9, itis clear that the growth is not uniform over some point defects, contaminants or smallparticulates. The first two SEM pictures indicates that the scattering intensity will beamplified as material accumulates around each point defect forming a larger scatteringcenter shaped like an elongated empty cup. This account for the peak in intensity.Eventually with enough deposition the point defects are covered up, the cup will start fillingwith GaAs and the scattering will be reduced to a level that is closer to the expectedscattering of the background film texture.74Figure 4.4 SEM picture of a sample for which growth as been stopped at themaxiimim in the oscillation.Figure 4.5 SEM picture ofa typical small scattering center after 50 nm ofgrowth75/0188 25.0kv ><30.ék i’hFigure 4.6 SEM picture ofa typical small scattering center after 180 nm ofgrowthFigure 4.7 SEM picture ofa typical small scattering center after 500 nm ofgrowth76This interpretation is further supported by the results shown in Fig. 4.8. Webelieve that the cleaning procedure is responsible for the presence of the point defects orparticulates on the sample. As mentioned in Chapter 3, the samples were not prepared in aclean room environment but under a filtered air laminar flow hood. The three curvespresented in Fig. 4.8 are obtained from three differently prepared samples. All thesamples were first etched on the back surface using HNO3 then rinsed with deionized waterand blown dry with prepurified nitrogen. Sample (a) had an additional preparation step inthat it was etched with HC1 to remove the residual oxide and rerinsed with DI water. Then,all the samples were oxidized for 2 minutes using the UV ozone treatment. Samples (a)and (b) only differ by the HC1 etch step and yet the effect of the scattering centers is alreadymuch smaller for sample (b). Samples (b) and (c) had the same preparation steps butgreater care was taken to avoid particulate contamination for the latter. We find that thecleanest sample with the fewest preparation steps has the fastest decrease in scatteredintensity.C,)1IS.-II.)C.)C,,-5 0 5 10 15 20Growth Time (mm)Figure 4.8 Time evolution of the scattered intensity during growth of GaAs for threedifferent substrate preparations. The expected order of cleanliness is c, b and a where cis the cleanest UHV loaded sample.25 3077We believe that both the number and size of the defects is reduced for cleanersamples, decreasing the amplitude of the oscillation and reducing the smoothing time as theroughness (elongated cup) surrounding each defect is more quickly built up and thenburied. A small shoulder in the decay of the scattering intensity for sample (c) is stillpresent. Interpretation of the fast falling intensity must be done carefully because it can beeither controlled by the smoothing of the rough oxide-desorbed surface or dominated by theburying of point defects.The decay in intensity can be compared with the evolution of the RHEED pattern.In Chapter 3, a comparison between RHEED and light scattering was presented for theoxide desorption in Fig. 3.6. Fig. 4.9 compares the two techniques during growth ofGaAs when the 12 KeV electron beam is incident parallel to the [1101 direction. Each ofthe RHEED patterns is presented using a picture labeled from (a) to (g) corresponding to atime on the x-axis of the scattered intensity graph (7.4 tm1). The 3-dimensional RHEEDpattern obtained after the oxide desorption is shown in picture (a). Within the first 2 mmof growth, from (a) to (d), the scattered intensity goes through the oscillation describedearlier and the diffraction spots on the screen develop into sharp lines typical of2-dimensional growth. From (d) to (g), the scattered intensity shows a definite smoothingat 7.4 pm1, but the RHEED pattern hardly evolves, demonstrating that after 2 mm ofgrowth, the rough oxide-desorbed surface has essentially recovered on the length scalesprobed by the high energy electrons even though for longer length scales, the surface is stillsmoothing after 15 mm of growth. The presence of the oscillation suggests that the lightscattering signal at 7.4 im1 would decrease faster if the substrate was cleaner, in whichcase, the difference in the surface smoothing between scattered light and scattered electronsshould become smaller.78C’)41Cl)C.)100 5 10 15 20 25Growth Time (mm)(a) (e)(b) (f)(c) (g)(d)Figure 4.9 Evolution ofRHEED pattern in parallel with the variation in scatteredintensity during growth of GaAs after oxide evaporation.79As mentioned in Chapter 3, when the oxide was first chemically removed withHC1, NH4O or H2S04 before being loaded into UHV, no significant roughening wasobserved during the desorption of the resulting thin oxide. Fig. 4.10 shows the evolutionof the scattering intensity on a log scale for spatial frequencies of 0.12, 5.4 and 16 tm1when growth starts on such a surface. The scattering intensities for negative timesrepresent the background intensity level for the smooth surface in the MBE system. Asexpected, the background intensity is much larger for scattering closer to the reflectedspecular beam (small q). The increase of up to more than three orders of magnitude at alldetected spatial frequencies clearly shows the same oscillation as the one observed on awafer that is believed to have been insufficiently cleaned. Removing the oxide by wetetching before it is transferred into UHV should therefore not be considered as a mean ofproducing smooth surfaces for regrowth because the grown overlayer becomes rough.However, the cleaning not being performed in a clean room could lead to higher defectdensities. Because of its high sensitivity to defects, light scattering can be used to optimizethe cleaning technique.CM. 10210110010_ii0io0 20 40 60 80 100Growth Time (mm)Figure 4.10 Evolution of the scattering intensity on a log scale for spatialfrequenciesof 0.12, 5.4 and 16 pin1for growth on a surface from which a native oxide has beenrenwved thermally.80If the three signals in Fig. 4.10 are divided by their maximum and the result isplotted on a linear scale, Fig. 4.11 is obtained. This clearly shows the shift in the positionof the maximum with spatial frequency detected. The larger the spatial frequency, theearlier the signal goes through the peak. This is consistent with the faster smoothing of thesmall length scale features.-.‘.—CC1-4C-)C,,Figure 4.11 Evolution of the scattering intensity for spatial frequencies of 0.12, 5.4and 16 /im1for growth on a surface from which a native oxide has been removedthermally. All curve maximum have been normalized to 1.It is clear that the local defects can play a very important role in the scatteringintensity measured. For a given experiment, if the source of the scattering cannot be clearlyestablished, definite conclusions will not be attainable.1.21.00.80.60.40.20.00 20 40 60Growth Time (mm)80 100814.3 Growth on clean oxide desorbed surfaces.Using samples for which the number of preparation steps had been reduced to aminimum, we studied the evolution of the scattering intensity during growth of a GaAsepilayer on a GaAs substrate. The substrates were only etched on the back surface, rinsedand blown dry with nitrogen. They were then cleaved and carefully mounted on waferholders and subsequently oxidized in the UV ozone reactor before being loaded into UHV.As described in Chapter 3, the samples are placed in the growth position and the oxide wasthermally removed by ramping the substrate temperature at 5°C/mm under an arsenic flux.Following the desorption, the sample is first stabilized at 590 °C then the gallium flux isswitched on and the atoms start impinging on the substrate.4.3.1 Evolution of the power spectral density (PSD).In Chapter 3 we showed the change in the surface power spectral density due to theoxide evaporation. These power density spectra are reproduced in Fig. 4.12 together withthe power spectral density obtained when 0.5 pm of material (30 mm growth) is depositedon the oxide-desorbed surface. The PSD decreases at high spatial frequencies as expectedfrom smoothing of the oxide desorption pits. At low spatial frequencies however, thescattered intensity increases. This could be a sign of the long length scale rougheningexpected from kinetic roughening theory described in section 4.1.1 02182• 111111 I I I 111111 I -• Polished wafer0 Oxide desorbed• 30 mm growth0Iio5 r106io’ r1080.1...•.1%•IbI• 00• 04I1 10Spatial frequency (l.1m 1)Figure 4.12 Ex-situ light scattering measurements showing the evolution of the surfacepower spectral density during MBE processing.If the dynamic scaling description of surface roughening is valid, the power spectraldensity should follow a q-Z dependence according to Equation 4.4 or Fig. 4.2(b). Tocheck this hypothesis, an epilayer of GaAs was grown for two hours then quenched toroom temperature for ex-situ scattering measurements. The PSD obtained for this 2 jimlayer is shown in Fig. 4.13. Very similar behavior is obtained for both crystallographicorientations. Linear fits to the data give an exponent of -2.41 for the scattering vector in the[0111 direction and -2.05 for scattering in the [110] direction. It is not clear whether thisdifference between the two crystal orientations reflects an anisotropy in the surfacemorphology or whether it is attributable to systematic errors in the scatterometry resultingfrom inhomogeneities across the surface of the wafer. The measured differences inscattering in the two crystallographic directions are complicated by the fact that the oval83shape of the laser spot on the sample does not illuminate exactly the same area when thesample is rotated to change the orientation of the scattering vector relative to the crystalaxes. At some spatial frequencies, the power spectral density differs by as much as a factorof three between the two crystal orientations. However, this variation has a relatively smalleffect on the slope of the power spectral density over the full range of the data which spansmore than four orders of magnitude.1 10Spatial frequency (pm 1)Figure 4.13 Ex-situ light scattering measurements of the surface power spectral densityfor a sample with a 2 jim GaAs epilayer.The thick line in Fig. 4.13 represents the best fit to all the data points of a line withslope -2. The close fit suggests that if the increase in scattered intensity is due to the noisein the deposition fluxes, it could be described using the continuum Equations 4.7 to 4.10neglecting the fourth order term (taking K—0) for the range of spatial frequencies studied.1 02111106io71 080.184When growth starts on a smooth surface, the expected roughening would then be describedby:g(q,t) 1—exp(—2vq2t) (4.11)The smoothing behavior observed when growth starts on the rough oxide-desorbedsurface would be described by:g(q,t) - exp(—2vq2t) (4.12)It should be noted here that this predicted evolution supposes that the differentlength scale roughnesses do not interact with each other. If various non-linear terms inEquation 4.5 were taken into account, the behavior would be much more complicated thanEquations 4.11 and 4.12.The -2 slope has also been observed in-situ using the diode array set-up describedin Chapter 2. After four hours of growth, the sample was quenched to room temperature.Before removing the sample from the growth chamber, a full scan of the 32 diodes wascollected. The intensity results are presented in Fig. 4.14. The black circles represent theraw intensity data and the crosses correspond to normalization to constant solid anglesusing Fig. 2.16. The variation in the optical factor is not significant for such small spatialfrequencies as can be seen in Fig. 2.6. Once again, the solid line represents the best -2slope that fits all the data points. The fact that the slope of the power spectral density is thesame for the in-situ or the ex-situ measurement is an indication that the ex-situ signature isnot affected by the particulates that end up on the wafer in the process of removing it fromthe UHV chamber.855.—rJ)10.80.60.40.3 0.4 0.5 0.6 0.7Spatial Frequency (.tm 1)Figure 4.14 Scattered intensity detected using the 32 element diode array aftergrowth ofa 4 pm GaAs epilayer. The black circles represent the raw intensity dataand the crosses correspond to the data when normalized using the solid angles ofeach diode. The solid line is the best -2 slope thatfits the data.4.3.2 Reproducibility, effects of polarization.Fig. 4.15 shows the light scattering signal as a function of time during the oxidedesorption and subsequent film growth for two different spatial frequencies (0.9 Im1 and5.4 jim-1). As expected from the light scattering measurement of the PSD, when growthbegins, the low spatial frequency signal increases while the high spatial frequency onedecreases. We show two independent runs (solid and dotted lines) that were nominallyidentical, in order to illustrate the reproducibility of the measurements from run to run.Although there are differences in overall intensity, the shapes of the two sets of data as afunction of time are very similar. Since for every sample the laser is moved to correct thealignment, we believe that the intensity variations could be due to differences in opticalalignment between successive runs. It is also possible that uncontrolled variations in the+• •••••.0.286Irate of substrate temperature ramp during the desorption lead to different surfacemorphologies. It was shown in Chapter 3 that the temperature ramp rate has a large effecton the desorption temperature and therefore on the final surface morphology.0.010.000.050.00Growth Time (mm)Figure 4.15 Reproducibility of in-situ light scattering measurements. Comparisonbetween two runs that were nominally identical.0 15 3087To verify that the polarization of the light affects the scattering only by a constantfactor (see Fig. 2.8) two runs were carried out in which only the state of polarization of theincident light was changed between the runs. Fig. 4.16 shows the evolution of thescattered light intensity (q=16 jim-i) during thermal oxide desorption and growth of GaAsfor s and p-polarized incident light. For light detected in port A of Fig. 2.14, the ratio ofthe intensities measured for s and p-polarization throughout the process is about 10From Fig. 2.8, the expected ratio is about 0.3. This factor of more than 30 is explained bythe presence of the mirror port. The light coming from the sample hits the GaAs coatedmirror at an angle of incidence of about 72° (see Fig. 2.14, port A). This is very close tothe Brewster angle at which the reflection coefficient for p-polarization is zero. As a result,the true ratio of reflected s and p polarized light cannot be determined accurately.-4-‘ 10.-5•-II)II. in-6I’.,C.)C,)-15 -10 -5 0Growth time (mm)Figure 4.16 Evolution of the light scattering intensity during desorption and growth forthe two different states ofpolarization.5 10884.3.3 High spatial frequency smoothing.The high spatial frequency smoothing was studied by carrying out three identicalgrowths in order to access in-situ a wider range of spatial frequencies by modifying thegeometry of the experiment. For the first sample, the laser was incident normal to thesample surface through port C in Fig. 2.13 and 2.14. The sample was oriented such thatthe crystallographic orientations match the arrows in Fig. 2.13. As mentioned inChapter 2, detectors were placed on ports A, B, F and G to probe simultaneously thesmoothing along both crystal directions at spatial frequencies of 5.4 and 11 urn-1. Toensure an equivalent detection geometry for the two crystal axes, the incident polarizedwave was oriented along the [010] orientation, at 45° to the two principal axes (seeFig. 2.13). This removes variation associated with polarization because at each spatialfrequency an equivalent polarization is detected for each of the crystallographicorientations. If the plane of incidence is taken perpendicular to the polarization (choosingthe polarization as s), the coefficients Q and Qç, (Equation 2.10) can be calculated andhave the same magnitude for both orientations. The scattered waves in the two directionswill therefore have the same optical factor (Equation 2.9).For the two other samples, the geometry described by Fig. 2.14 was used. Sincein this geometry only one crystallographic direction can be probed, two similar growthswere needed to probe both orientations. These growths were done in order to access thehighest possible spatial frequency that can be probed in-situ with our system. By selectingthe 457 nm line of the Ar+ ion laser, a spatial frequency of 17 um’ can be detected in portA of Fig. 2.14. This corresponds to a lateral length scale of 0.37 urn.The preparation steps for all three runs were reduced to a minimum as describedearlier. After the desorption, the substrate power heater was fixed to give a growthtemperature of 590°C as measured with DRS5052. The growth rate was 1 urn/hr and the89ratio of As2 to Ga was 3.5 as measured with a retractable ion gauge, with no correctionmade for the differential ionization probability. Figs 4.17 and 4.18 show the smoothingbehavior after the thermal desorption of the oxide for the three spatial frequencies detected.The oxide desorption step has been normalized to go from 0 to 1 in order to better comparethe subsequent behavior of the different spatial frequencies. The intensity decay for thefirst 15 minutes of growth (2500 A) is presented in Fig. 4.17 and 4.18 for the scatteringvector along the [1101 and the [110] direction respectively.The differences observed here are certainly significant for the 5.4 and 11 im1signals since all four curves were detected simultaneously from the same sample. We relyalso on the normalized signals detected at 17 tm1 from two different samples since theyfollow well the trend established at 5.4 and 11 jam1The higher the spatial frequency, the faster is the intensity decay. Also, theintensity level reached after the decrease is lower for higher spatial frequencies. These twoobservations are consistent with the behavior expected from a combination of both thesmoothing and the roughening described in section 4.1. The faster smoothing of smalllength scale structures is qualitatively consistent with Equation 4.12 since the characteristictime of the decay depends on the spatial frequency q. However, this dependence does notfollow the square of the spatial frequency. Fitting equation 4.12 to the exponential part ofeach curve, the characteristic time ‘r for the decay of the intensity can be evaluated. Thesecharacteristic times are presented in Table 4.1 together with the deduced value for thecoefficient V for the three spatial frequencies shown and the two different crystaldirections.Cr,2‘1)Ct0‘IDGrowth time (mm)Figure 4.17 Scattering intensity for spatial frequencies of 5.4, 11 and ]7unr1 duringgrowth ofGaAs when the scattering vector is along the [110] direction.90Cr,I110.80.60.40.200 2 4 6 8 10 12 141-d10.80.200 2 4 6 8 10 12 14Growth time (mm)Figure 4.18 Scattering intensity for spatial frequencies of 5.4, 11 and l7jtn’r1 duringgrowth ofGaAs when the scattering vector is along the [170] direction.91[110] [110]Spatial‘r v vFrequency(jim1) (mm) (1O’ cm2/s) (mm) (1O’3 cm2ls)5.4 2.63 10.9 3.24 8.8211 1.14 6.0 2.12 3.2517 0.85 3.4 1.48 1.95Table 4.1 Characteristic decay times r and coefficients V deduced from thesmoothing at the three spatial frequencies shown in Fig. 4.17 and Fig. 4.18.If the characteristic time of the decays followed the square of the spatial frequency,as predicted by Equation 4.12, the coefficient V would be constant. However, it can beseen from the table that the characteristic times almost follow a q-1 dependence. Thisdependence will be discussed later.Comparison of the characteristic decay times in Table 4.1 reveals some anisotropybetween the two crystallographic orientations. Along the [110] direction, the intensitydecay is slightly faster. This suggests that the surface smoothes more rapidly along the[110] than along the [1101 direction.After 15 minutes of growth, the scattered intensity stabilizes at higher values forlower spatial frequencies. This spatial frequency dependence is expected from kineticroughening theory after long times and is related to the slope of the power spectral density.Comparison of the final intensities after the growth of 250 nm of material, in Fig. 4.17and Fig. 4.18, suggests that the surface is rougher along the [110] direction.A similar anisotropy effect is observed during the period between the oxidedesorption and the start of growth. Fig. 4.19 shows the scattered intensity at a spatialfrequency of 17 tm1 during the oxide desorption and the subsequent growth forscattering in the two crystallographic orientation. The two curves correspond to the same92experiments as the ones shown in Fig. 4.17 and 4.18. The different time delays betweenthe oxide desorption and the start of growth are not of interest, as they only represent thetime necessary to equilibrate the substrate to the selected growth temperature. During theperiod between the oxide desorption and the start of growth, the scattered intensity alongthe [110] direction decreases with the substrate exposure time to the As2 flux while thescattering along the [1101 direction stays constant. This suggests again that the surfacemorphology becomes anisotropic with height variations along [110] decreasing inamplitude while height variations along [1101 remain unchanged. The anisotropy effectwill be discussed later in this chapter.1.0.80.60.41 o.:-15 -10 -5 0Growth Time (mm)Figure 4.19 Scattered intensity at a spatial frequency of 17 um1 during the oxidedesorption and the subsequent growth for scattering along the two notedcrystallographic directions.5 10934.3.4 Low spatial frequency roughening.The evolution of the PSD during growth (Fig. 4.12) shows an intensity decreasefor high spatial frequencies and an intensity increase for low spatial frequencies. At longerlength scales, the increase in intensity is also anisotropic. Fig. 4.20 shows the evolution ofthe scattered intensity at low spatial frequency (q=0.9 jtm-’) during growth of GaAs whenthe scattering vector is either along the [110] or the [1101 direction. Once again, there is asignificant difference in the optical signatures between the crystallographic orientations.The faster increase along the [1101 direction suggests that the surface becomes rougher inthis direction. This is consistent with the earlier observation that after the oxide desorption,the surface is smoothing faster along the [1101 direction. This behavior has been alsoreported by others28 and was related to the anisotropic surface morphology measured byAFM.-.—Cl)-.‘I:rj 00 5 10 15 20 25 30Growth Time (mm)Figure 4.20 Evolution of scattered intensity at 0.9 un1 during growth of GaAs forscattering along the indicated ciystallographic directions.94The increase in scattered intensity at low spatial frequencies during growth ispresented in Fig. 4.21 when the spatial frequencies detected are along the [1 101 direction.The signals for four different low spatial frequencies acquired on four channels of the diodearray have been divided by the solid angle of detection, and to facilitate the comparison thebackground has been subtracted so that the four signals have the same starting value.Roughening is observed at each spatial frequency. As expected from kinetic roughening,the overall increase in scattered intensity is larger at smaller spatial frequencies. Also, afteran initial increase, each scattering signal tends to saturate at long times and the characteristictime for saturation is larger for small spatial frequencies. This behavior is similar to what ispresented in Fig. 4.2 with the exceptions (1) that there is a delay of about 20 mm beforethe scattered signals begin to increase along the [110] direction, (2) that the scatteringgrows more rapidly for smaller spatial frequencies and (3) that after an obvious saturation,the four signals seem to increase linearly instead of logarithmically.- 2101.61O1.2108 10-6410-640 60 80 100 120Growth time (mm)Figure 4.21 Scattered intensity for four low spatial frequencies during growth whenthe spatialfrequencies detected are along the [110] direction.2095We believe that the roughening delay at the start of growth is caused by the roughstarting surface. This is supported by the results presented in Fig. 4.22 in which theevolution of the scattered intensities at 0.9 and 16 I.tm1 are shown during growth forscattering along the [110] and the [110] directions. Each graph represents a different run.From both graphs, it is clear that the scattered intensity at 0.9 tm1 does not increasebefore the 16 I..tm’ signal decreases to an almost stable value. Moreover, the delay beforeroughening is longer when the spatial frequency probed is along the [1101 direction. Thisis consistent with the fact that along the [1101 direction the surface tends to be rougher andtakes a longer time to smooth after desorption.96I I I I I I I I I I I2 [110] O.9pm1 -.—I-,,) 1--ci)-1- l6pm -0 I I I I I I IO 2 4 6 8 10 12I I I I I I I I I I I I I I I I II - [110] -1O.9prn1- l6pm -0 I I I I I0 2 4 6 8 10 12Growth Time (mm)Figure 4.22 Time evolution of the scattered intensity at 0.9 and 16 wn4 duringgrowthfor scattering along the [110] and the [110] directions.97Because the power spectral density predicted by Equation 4.11 has a q2dependence after a long growth time, it should be possible to describe the roughening seenin Fig. 4.22 with Equation 4.11. Neglecting the slight variation in the optical factor forsmall angles, the power spectral density is proportional to the measured intensity I. Inthis case:1— exp(—2 vqt)2 (4.13)vqIf the roughening follows the behavior predicted by Equation 4.13, a plot of Iq2versus q2t should make the four curves coincide. Fig. 4.23 shows such a dependence forthe four sets of data shown in Fig. 4.21. A background was subtracted from each data setbefore multiplication by the square of the corresponding spatial frequency. Thebackground was taken as the extrapolation of the roughening curve to the beginning of thegrowth. The data sets for all four spatial frequencies follow a similar curve, except for thepart of the data before the onset of the roughening. Interpreted as being dependent on thesmoothing of the initially rough surface, it is consistent that this initial delay does not scalewith the rest of the data.io-5*6q2 * tFigure 4.23 Plot ofIq2 versus q2tfor the four set of data shown in Fig. 4.21.0 5 10 15 20 25 30 35 4098The scaling of the four sets of data is not perfect but a priori seems to confirm the q2 dependence for the increase in scattered intensity when the starting surface is rough.From the four sets of data, values for the characteristic times and for the coefficient V canbe extracted. The fit of Equation 4.13 through each data set was found to be very sensitiveto the slow linear increase in intensity at long times. When this linear increase is subtractedfrom the data, the accuracy of the fit is reasonable (±7%) except for the higher spatialfrequency curve (±40%). The characteristic time and the coefficient V calculated for eachof the four spatial frequencies detected are presented in Table 4.2. We find thatV = (1.3±0.2)x101cm2/s. This value is more than one order of magnitude larger thanthe average of the values presented in Table 4.1.SpatialT VFrequency(jiml) (mm) (10- cm2/s).40 29.6 1.77.49 24.5 1.42.64 16.6 1.23.94 11 0.85Table 4.2 Characteristic times r and coefficient V deducedfrom the roughening atthe four spatial frequencies shown in Fig. 4.21 and Fig. 4.23.As for the high spatial frequency smoothing studied earlier, the values calculated forv supposing the characteristic time depends on q2 are not constant. Once again, thecharacteristic times seem to depends more closely on q1. This suggest that the argumentof the exponential function in Equation 4.13 should be proportional to qt instead of q2tUsing the same data as in Fig. 4.21 and Fig. 4.23, we plotted 15q2 versus qt inFig. 4.24. The collapse of the data is much more convincing showing that the time99evolution depends on q1. Therefore, by analogy with Equation 4.13, the evolution of thedata for the roughening at low spatial frequencies is best described by:1—exp(—2aqt) (4.14)qThe functional dependence of the light scattering data described by Equation 4.14shows a time evolution that depends on the inverse of q. Also, consistently with the -2slope observed in the PSD in Fig. 4.13, the scaling of the in-situ data predicts adependence at long times. This behavior was not predicted by a simple linear model ofkinetic roughening. If kinetic roughening is to be used to described the data, non-linearterms will have to be included in the development.iO-5*Cl)10-6q*tFigure 4.24 Plot ofIq2 versus qtfor the four set of data shown in Fig. 4.21.From Fig. 4.22, we concluded that, consistent with a longer time interval forsmoothing along the [110] direction, the delay before roughening was longer when themeasured spatial frequency was along the [1101 direction than when it was along the [1101direction. From Fig. 4.20, we also know that the increase in scattering is larger along the[1101 direction. This behavior is typical of intensity variations for roughening along the0 10 20 30 40 50 60 70100[1101 direction observed during growth in other runs. Fig. 4.25 is an example of anatypical result. The two runs that led to Fig. 4.21 and Fig. 4.25 were nominally identicalexcept for the orientation of the scattering vector. Although the scattering signal is alwaysslightly noisier along the [1101 direction, in this case we noted some rather largeoscillations. The scattered intensity behavior differs also by the fact that though the growthstarts on the rough oxide-desorbed surface, the roughening starts as soon as the growthbegins: there is no observable delay in the roughening as detected at these four spatialfrequencies.810-s6 i0410210-sCl) 01000 50 100 150 200 250 300 350 400Growth time (mm)Figure 4.25 Scattered intensity for four low spatial frequencies during growthwhen the spatial frequencies detected are along the [110] direction. The observedbehavior is not typical.The evolution of the surface in which the topography at low spatial frequenciesgrows and the topography at high spatial frequencies decreases during growth has beenstudied using in-air scanning tunnelling microscopy and atomic force microscopy. InChapter 3, the same microscopy techniques were used to study the surface of the asreceived polished GaAs substrate and surfaces from which the oxide had been desorbed.Growth begins on the rough surface morphology generated by the desorption of a 4 mm101UV-ozone oxide (Fig. 3.4). The two STM images presented in Fig. 4.26 show theevolution of the surface morphology of a GaAs wafer after growth of GaAs for (a) 3 mmand (b) 30 mm at a growth rate of 1 p.m/hr.(a)(b)102Figure 4.26 Evolution of the surface morphology after growth of GaAs for (a) 3 mmand (b) 30 mi Scale: 3 1um x 3 pm x 150 A. Growth rate = 1 pm/hr.From the evolution revealed in the three STM images (Fig. 3.4 and Fig. 4.26), itis clear that the high spatial frequency roughness decreases with buffer layer thickness. Anincrease in the correlation length of the roughness can also be observed. The anisotropy inthe surface roughness after the growth of 0.5 jim of GaAs is better shown in Fig. 4.27using a slightly larger scale AFM image. The [1101 direction is oriented along the blackline on the image.Figure 4.27 AFM image showing the surface morphology after growth of GaAs for30 mm. Scale: 5 pmn x 5 pm x 120 A. Growth rate = 1 pm/hr.In Fig. 4.27, the gray scale of 120 A (from black to white) clearly shows a peak topeak roughness of about 100 A with a lateral separation of about 0.5 jim between themaximum and the minimum. This roughness which is larger than the roughness expectedfrom kinetic roughening, is similar to the one observed by others7476 on GaAs (100)singular surfaces and was attributed to unstable growth due to barriers at step edges. Thiswill be discussed in the last section of this chapter.103The presence of many particles which appear as white spots in the AFM images, isdue to the fact that these measurements were performed more than a year after the sampleswere grown. Since earlier measurements (light scattering, STM, Nomarski) wereperformed in air, gradual contamination is expected.1044.4 Growth on hydrogen etched surfaces.As presented in Chapter 3, the removal of the oxide layer using atomic hydrogenleaves a surface that is believed to be cleaner and as smooth as the initial polished wafer.Starting growth on such a surface should lead to roughening on all of the length scalesaccessible by light scattering. The expected behavior is the one predicted byEquation 4.11.For this recent experiment, the back surface etch of the substrate was not requiredbecause of the addition of a pyrolytic boron nitride diffuser plate on the back of each waferholder. Therefore, the samples were only cleaved, mounted on holders, then oxidized andloaded into the MBE chamber. The substrates used for the experiment were n-doped (001)on-axis (±0.2°) 2-inch GaAs wafers. The oxide was removed using atomic hydrogen asdescribed in section 3.3. The sample was then ramped to 600 °C and growth was started.The incident laser beam was coupled into the chamber using port B and the lightscattering intensity was detected through ports C and D of Fig. 2.14. For each growth,the scattering along only one crystal orientation was monitored. To compare the twodifferent crystal orientations, two different samples had to be processed identically.Fig. 4.28 shows the evolution of the scattered intensity at q=5.4 im1 for the growth ofGaAs on a surface from which the oxide had been removed using atomic hydrogen.Contrary to the smoothing behavior observed at this spatial frequency for growth on asurface from which the oxide was evaporated, both signals increase as the epilayer getsthicker. The two curves represent the signal variation along the two crystal directions. Asexpected, the intensity detected along the [1101 is higher than the intensity along the [1101direction. The solid lines represent the best fits of Equation 4.11 to each set of data points.Fig. 4.29 shows the roughening during growth of the same samples as in Fig. 4.28 but ata lower spatial frequency, as detected by one channel of the diode array (0.80 and1050.83 jim-1 for [110] and [110] respectively). The results still show the anisotropybetween the crystal directions.Fitting the data in Fig. 4.28 and Fig. 4.29 with Equation 4.11 leads to thecharacteristic time and the coefficient V for each crystal orientation. The results arepresented in Table 4.3 together with the values obtained from the increase in scatteredintensity for the smallest spatial frequency measured (0.27 and 0.30 jima) in eachdirection.[110] [110]Spatial SpatialT V ,r VFrequency Frequency(jim-1) (mm) (10-13 cm2/s) (jim-1) (mm) (10-’ cm2/s)0.27 —6000 1.9 0.30 —4400 2.10.80 930 1.4 0.83 610 2.05.4 46 .62 5.4 50 .57Table 4.3 Characteristic times t and coefficient V deducedfrom the scattered intensityincrease along [110] and [110] at the given spatialfrequencies.Unlike the coefficients obtained in Table 4.1 and 4.2, the decrease in V here ismuch smaller considering the large range of spatial frequency probed. It suggests that thetime evolution of the intensity in this case depends more closely on q2 than on q1.The values obtained for the v coefficient at low spatial frequency are in the samerange as the values calculated for the high spatial frequency smoothing shown inFig. 4.17, Fig. 4.18 and Table 4.1. However, the estimates for these low spatialfrequencies are not precise since the curves are nearly linear and the fits are not verysensitive to V.106C-,ICMIFigure 4.29 Evolution of the scattered intensity at q=0.8 pm1 during growth ofGaAs on a surface from which the oxide has been removed using atomic hydrogen.The two curves represent the signal variations along [110] and [170].0 50 100 150 200__0.0120.010.0080.0060.0040.0020Growth time (mm)Figure 4.28 Evolution of the scattered intensity at q=5.4 pnr1 during growth ofGaAs on a surface from which the oxide has been removed using atomic hydrogen.The two curves represent the signal variations along [110] and [170].__1.41.210.80.60.40.200 50 100Growth time150 200(mm)107Figure 4.30 Evolution of the scattered intensity along the [170] direction at fourdifferent spatial frequencies during growth of GaAs on a surface from which the oxidehas been removed using atomic hydrogen.Fig. 4.30 shows the increase in scattered intensity along the [110] direction for fourspatial frequencies detected by four channels of the diode array. Though all curves show aroughening that is larger at smaller spatial frequencies, the slope at the start of growth islarger for smaller spatial frequencies. The different slopes which have been observed ingeneral can neither be attributed to different background intensities nor to the varying solidangle of detection along the diode array (Fig. 2.15). This behavior is not expected fromthe development made in section 4.1. However, we note that the slopes vary like q1which is what is expected from the empirical Equation 4.14.810-4610-4I• 4 10-4210-401000 50 100 150Growth time (mm)200 2501084.5 Discussion.4.5.1 Source of scattering and time evolution.The interpretation of a variation in scattered intensity must be done carefully. Asmentioned in Section 4.2, there is a possibility that the intensity measurements aredominated by surface defects and particles instead of intrinsic surface morphology.Supported by the comparisons of roughnesses measured optically or by AFM, we believethat in some cases the intrinsic surface morphology is measured while in others thebehavior observed is associated with defects in the epilayer.Both smoothing from the rough oxide-desorbed surface and roughening from thesmooth hydrogen-etched surface have been observed during growth at 5.4 p.m’. Thecharacteristic times for the evolution of the surface morphology calculated from theroughening (46 and 50 mm for the [110] and [1101 respectively) are more than one orderof magnitude larger than values obtained from the smoothing of the rough oxide-desorbedsurface (2.6 and 3.2 mm in Table 4.1).To compare the smoothing and roughening behaviors observed in precedingsections, we plot in Fig. 4.31 the characteristic times taken from Tables 1, 2 and 3 as afunction of detected spatial frequency. The full and open symbols represent thecharacteristic times observed for the evolution in scattering along the [ilo] and [1101directions respectively. The largest characteristic times are measured for the rougheningduring growth on hydrogen-etched surfaces (diamonds). For growth on oxide-desorbedsurfaces, the circles and the squares represent the characteristic times calculated for the lowspatial frequency roughening and the high spatial frequency smoothing respectively. Thedotted line has the slope -1 proposed earlier for the smoothing and roughening behaviorobserved for growth on the rough oxide-desorbed surface.109The characteristic times for low spatial frequency roughening during growth onhydrogen-etched surfaces (diamonds) are two orders of magnitude larger than the onesobtained for low spatial frequency roughening during growth on the oxide-desorbedsurface (circles). We note as well that after two hours of growth, the scattered intensitiesalong the [110] measured in Fig. 4.21 for the growth on an oxide-desorbed sample(denoted as sample A in the following text) are about 30 times smaller than the intensitiesmeasured in Fig. 4.30 for the growth on the hydrogen-etched surface (sample B). Thearbitrary units of the y-axis are the same for the two figures. This suggests that if thescattering signal is due to the intrinsic surface topography in both cases, the roughness ofsample A is smaller than the roughness of sample B by a factor Jd=5.5 (if the ratio of 30is constant over the accessible range of spatial frequencies). Direct measurements ofsurface roughness on sample A were not performed because the sample was maintained atthe growth temperature for an extended period of time after growth modifying the surfacetopography. The samples could therefore not be directly compared using ex-situtechniques. However, a comparison between the roughnesses obtained from the opticalPSD and an AFM image for sample B can determine if the intensity measured originatesfrom the intrinsic surface morphology or from scattering by defects.The isotropic integration of the PSD from .2 to 10 tm1 leads to rms roughnessvalues of 43 A and 32 A for the [1101 and [110] directions with an average of 38 A. Thisroughness can be compared with the rms roughness obtained directly from the 32 jim x40 jim AFM image of sample B displayed in Fig. 4.32. Even though the film isembedded with features possibly related to the cleaning technique, the overall roughness ofthe surface is only 9 A rms. This is more than four times smaller than the roughnesscalculated from the PSD. Therefore, the scattering intensity is too high to be representingthe intrinsic surface roughness and must arise mainly from particles and defects in the film.110Spatial frequency (jima)Figure 4.31 Calculated characteristic times for the scattered intensity variationsplotted as a function of detected spatial frequency. The letters A and B in thecaption refer to two different samples. A slope -1 is shown by the dotted line.Figure 4.32 AFM image of the surface morphology after 4 hours of GaAs growthon a hydrogen-etched surface. (32 jim x 40 jun x bOA).A • [110] roughening - DESB • [110] roughening - H[110] roughening - Hc [110] smoothing - DES• [110] smoothing - DES1IElvC.)clj) 1‘CL)C.)c-)0.1•0I- - . -i-.CC0.1 1 10 100111Although we attribute it to defects in the layer, the observed increase in scatteredintensity during growth on the hydrogen-etched surface (Fig. 4.28 and Fig. 4.29,sample B) still follows Equation 4.11. Together with the rough agreement to a slope of -2exhibited by the data in Fig. 4.31, this result suggests that scattering from defects in agrowing epilayer follows a dependence similar to the one expected from kinetic rougheningtheory: a slope of -2 in the PSD of a thick GaAs buffer layer could either be the signatureof scattering by the intrinsic surface morphology or the signature of scattering from defects.It is interesting to note that the rms roughness of the 10 I.tm x 10 tm smoothsection designated by the square in Fig. 4.32 is only 6 A. Analysis of the PSD for thissample led to a rrns roughness of 38 A. As mentioned earlier, the roughness determinedoptically for sample A is about 5.5 times smaller than for sample B as predicted by the ratioof the in-situ intensities during growth. The expected value for the rms roughness of thefilm grown on the oxide-desorbed surface (sample A) should therefore be around 7 A.This is very close to the background texture displayed in the AFM image of sample B (6A), which suggests that the measured scattered intensity for sample A is mainly due to theintrinsic surface roughness.The fast smoothing at large spatial frequencies and the roughening at low spatialfrequencies during growth on the rough oxide-desorbed surface reveal that thecharacteristic times follow a q1 dependence rather than a q2 dependence. It isinteresting that the line (of slope -1) fitted through the high spatial frequency smoothingdata, in Fig. 4.31 coincides with the one fitted through the points representing the lowspatial frequency roughening of a similar oxide-desorbed sample. This suggests that thecharacteristic time can be written ‘C = l/(2aq) where a has units of velocity. From theslope in Fig. 4.31, we find a=2.4±0.1 pm/min or 6.7±0.3 A/s.1124.5.2 Stable vs unstable growth.The fact that the necessary time to reach saturation is inversely proportional to thespatial frequency probed seem consistent with a surface roughness that exhibits constantslope. The formation of mounds or ridges of constant slope have been observedexperimentally74-6for growth on surfaces with very few steps ((100) on-axis). Thesestructures have been related to the presence of potential barriers at step edges10’1,12 thatare the result of the smaller number of neighbors for an atom that is falling over a stepedge. Atoms that freshly landed on a terrace therefore tend to incorporate in the crystal atthe upper step more than at the lower one. This effect leads to stable growth on miscutsurfaces and to unstable growth on singular surfaces (low index crystal plane). Fig. 4.33shows the two possible surfaces together with the variation in potential energy due to stepedges. In the case of a miscut surface (a), the crystal grows with the steps flowing acrossthe surface. Because the atoms tend to attach to the upper step, the wider terraces (AB,CD)collect more atoms which reduce their widths. The narrow terraces (BC) therefore grow atthe expense of the wide ones until the terrace width is uniform. Growth on a miscutsurface is stable in the sense that no roughening is generated by surface diffusion barriers.In this case, the only intrinsic surface roughness should be due to kinetic roughening.(a) (b)Figure 4.33 Schematics of(a) a miscut surface and (b) a singular surface togetherwith the expected variation in potential energy at the step edges113The case of a singular surface is different. As the first layer of atoms is depositedon a surface without steps, islands are nucleated such as the one shown schematically inFig. 4.33 (b). From then on, an atom that falls on the island prefers to stay on it than tofall to the lower level. The formation of islands on the island is favored as it is easier toform another layer than to finish the one started. As a result, mounds develop on thesurface. The slope of these mounds increases until it reaches a steady state when theprobability that atoms go down the top terrace becomes similar to the probability ofnucleating a new terrace.The height d of a mound of lateral dimension 2m will therefore increase until thesteady state slope is reached. From then on, d and A, will increase in the same ratio so thatthe slope of the mound stays constant. In this view, the time taken for the slope to reachthe steady state value should be directly dependent on the size Am since to firstapproximation we expect d to increase linearly with time. A time limit tmjfl on how fast agiven steady state slope is reached can be defined using the growth rate g: t,1n=dJg. Sincethe barriers at step edges are not infinite, we expect the real time for saturation to be longerbecause atoms will also slowly fill the valleys between the mounds reducing the real heightof each mound and hence reducing the increase in the slope.The characteristic time measured optically was found to be proportional to thelength scale probed. This is consistent with a roughness that exhibits constant slope.Equating the characteristic time 1/(2aq) and the minimal time d/g to reach a given slope,we find that the steady state slope mobserved on sample A has to be smaller than:m =dq/1r= m11=gI2ira114Substituting the calculated value of a and the growth rate of 1 tm/hr, we find thatthe observed slope should be smaller than 0.066 or that the angle on the surface has to besmaller than 3.8°. It should be noted that this development rely on the hypothesis that theheight of the mound is increasing linearly. However, it is not clear how the height of themounds will evolve if they grow by competing with other neighboring mounds after thesteady state slope is reached.It is unfortunate that the surface morphology of sample A after saturation cannot bestudied ex-situ for comparison. However, the highest slope we have observed is about1.2° (Fig. 4.27) suggesting that for the growth conditions mentioned, the build up of themounds is three times slower than the growth rate. Others have reported slopes varyingfrom 1° to 3° depending on substrate temperature and growth rate7576.It is surprising that the high spatial frequency smoothing displays not only the samedependence for the characteristic time (1/(2aq)) but also the same magnitude for thecoefficient a. This might be a consequence of the surface morphology of the oxidedesorbed surface. The biggest pits being also the deepest ones suggest that the startingslope might also be a constant. This slope being much larger (— 6 times) than the steadystate slope, the atoms will flow downward over the step edges. Since the same potentialbarriers control the diffusion, a similar value for the coefficient a describing the smoothingdoes not seem unreasonable.4.5.3 Smoothing after growth.We associate the increase in scattered intensity in Figs 4.21 and 4.23, observedduring growth of sample A, with an evolution of the intrinsic surface roughness. In thekinetic roughening theory or in the case of unstable growth, the intrinsic surface roughnesscorresponds to a steady state between the noise in the deposition flux and the surface115diffusion. Therefore, if the deposition is stopped, the surface should smooth since thedriving force for the roughening is absent. On the other hand, if the roughening is causedby particles, contaminants or oval defects in the film, ending the growth should notengender a large decrease in scattering intensity. The local scattering centers, though theycould facet, would not likely disappear.Fig. 4.34 shows how the scattered signal at q=O.4 11m’ increases during growth(same as Fig. 4.21) and decreases after growth is terminated by switching off the gallium510.1 4.310-so 50 100 150 200 250 300 350 400Time (mm)Figure 4.34 Time evolution of the scattered intensity at q=0.4 pm4 during growth andafter growth is terminated by switching off the galliumflux. The surface is then left at600°C under an As2flux.flux. It is clear from the graph that in 140 minutes, the decrease observed corresponds toabout 55% of the total increase during 240 minutes of growth. At the end of theacquisition, the signal is still decreasing. Fitting an exponential decay to the data, we find116that the characteristic time of the decay is 93±3 mill so that the scattering intensity shouldreach a plateau at 0.37. This means that 70% of the scattered intensity gained duringgrowth is lost due to smoothing as the surface approaches equilibrium. The balance of theintensity (30%) could be due to either the background surface morphology at equilibrium orthe scattering from defects. As mentioned earlier, it is interesting to note that theroughening during growth can be described as the superposition of two behaviors. Thefirst one is linear at the start of the roughening and saturates after 60 minutes of growth andit follows the predictions of kinetic roughening. The second one, most clearly seen fromabout 90 to 240 minutes is a linear increase and corresponds to about 30% of the totalintensity gain. Because this gain in intensity and the residual intensity level at the endcorrespond well, we find it plausible that this part of the scattering is due to oval defects inthe epilayer. These defects have been attributed to the “spitting” of gallium from thegallium cell. If the defects do not get quickly and completely buried, the defect densityshould increase linearly with growth time. If these scattering centers are far enough fromeach other that they do not interact, the optical signal should also increase linearly, which iswhat is observed.There is another indication that the measured roughness that we believe intrinsic forsample A, is due to the flux of incoming atoms. When InGaAs is grown at high substratetemperatures over a “rough” GaAs buffer layer the surface smoothes extremely rapidly, aconsequence of a fundamental change in surface reconstruction. Besides the fact that thiscan have some very important consequences for the growth of planar interfaces, the effectsuggests that since the large scattering signal vanishes so quickly, it could not be due todefects in the epilayer but to the growth mechanism itself. This effect is discussed furtherin section 5.5.1174.5.4 Anisotropic surface roughness.The anisotropy in the surface morphology was revealed by differences in theevolution of the scattered intensity along [110] and [110] at high spatial frequencies afteroxide desorption (Fig. 4.19) and during growth (Fig. 4.17 and Fig. 4.18), and at towspatial frequencies during growth (Fig. 4.20). It was also observed in AFM imagesobtained after the growth of thick buffer layers. Several other groups have also observedthis anisotropic surface morphology74-80.This anisotropy was even found to beresponsible for different mobilities of a two-dimensional electron gas (2-DEG) along the[1101 and [ilO] directions81. In all cases exhibiting anisotropy, the [1 101 crystallographicdirection displays smaller roughness than the [1101 as inferred either from the lowerscattered intensity along [110] or directly observed from microscopy of the surface. Webelieve that this is a consequence of the anisotropy in the surface reconstruction observedwhen GaAs is grown under arsenic rich conditions. Typical RHEED patterns obtainedwhen the 12 KeV electron beam is incident (a) along the [110] or (b) along the [1101direction are shown in Fig. 4.35. The distance d between the bright lines represents theperiodicity of the GaAs lattice. Typical of the (2x4) reconstruction, the dimmer lines dividethe distance between the bright ones into two sections for pattern (a) and into four sectionsfor pattern (b). This gives a periodicity in real space that is twice as large as the GaAscrystal periodicity in the [110] direction and four times as large in the [110] direction. Notethat when the electron beam is parallel to the [1101, the periodicity detected is along [1101and vice versa since the direction measured is normal to the beam.Different surface reconstructions that exhibit the (2x4) periodicity have beenproposed8284. The experimental observations of the (2x4) reconstruction have beenclassified into three different phases (x, f3 and ‘082. The relative intensities of the fourRHEED lines when the electron beam is parallel to the [110] direction discriminates amongthe phases. A recent comprehensive study of the GaAs (001) surface involving STM,118RHEED observations and RHEED calculations85has confirmed that the unit cell of all thephases of the (2x4) reconstructed surface contains two arsenic dimers oriented along the[1101 crystallographic direction. The phases differ in the second and third layer, and by thesizes of domains and open areas. Fig. 4.36 is a representation of the f3 phase of the (2x4)reconstructed surface first suggested by Farrel and Palmstrom82.[1101 IffolFigure 4.35 Typical RHEED patterns obtained during growth when the 12 KeVelectron beam is incident along the [110] or the [110] direction.GaAs (100) (2x4) —o — 1st Layer As2Layer GaFigure 4.36 Arsenic stabilized (2x4) reconstructed surface.119From STM measurements77-9,it was found that the steps along the [1 10] directionare much smoother than steps along the [1101 direction. This implies that it is much easierfor a freshly landed gallium atom to diffuse along the [110] direction than along the [1101direction. As a result of this anisotropy in the diffusion, macroscopic structures that areelongated in the [110] direction develop on the surface during growth74-5.The surfaceroughness along the [1101 direction should always be larger than along the [110] asdeduced from the light scattering measurements.4.6 Summary.We began this chapter with a description of the signature of the light scatteringexpected during growth according to kinetic roughening theory. It was shown that if thescattering is caused solely by the noise in the deposition fluxes and not by particles ordefects in the epilayer, the slope of the power spectral density describes the scaling of thesurface topography and can be used to define a possible continuum equation thatcharacterizes the evolution of the topography during growth.The source of the scattering has to be clearly established in order to relate theevolution of the scattered intensity to the evolution of the surface morphology. Since theAFM measurements were insensitive to defects and particles in the film, we considered thatwhen the rms roughness calculated from the optical measurements was similar to theroughness obtained from AFM images of the same samples, the scattering was due to theintrinsic surface morphology not to defects. Defects would cause the rms roughnessdetected optically to be larger than the intrinsic one.Both smoothing at high spatial frequencies and roughening at low spatialfrequencies were observed during growth of GaAs on a surface from which the oxide had120been thermally desorbed. When the time evolution of the scattering is fitted usingexponential decays, the characteristic times are found to vary inversely with the spatialfrequency probed. The behavior of the scattering signal as a function of time and spatialfrequency was found to be different from the predictions of kinetic roughening theorywhen non-linear terms are not included. The detected intensity, which is closely related tothe PSD, was found to follow:1— exp(—2aqt) ( Rougheningq Low spatial frequencies( Smoothing1exp(—2aqt) IHigh spatial frequencieswith a =6.7±0.3 A/s or 2.4±0.1 Jim/mm. We showed that (if the height of themounds increases linearly) the linear dependence of the characteristic time on the inverse ofthe spatial frequency is consistent with the formation of mounds or ridges seen in the caseof unstable growth on singular surfaces.The increase in scattered intensity observed at all spatial frequencies during growthof GaAs on a surface from which the oxide had been etched with atomic hydrogen, wascontrolled by defects or contaminants that could either originate from the cleaning methodof from the gallium cell. In this case, as well as in the case where large oscillations wereobserved in the scattered intensity, we believe that the optical signature cannot be directlyrelated to the intrinsic surface morphology of the growing film. We find that thecorresponding in-situ optical signature and power spectral density after growth, althoughgenerated by defects in the epilayer, nevertheless display a behavior similar to that predictedby kinetic roughening theory for the intrinsic surface morphology. Hence, it is crucial toidentify the source of the scattering correctly if the interpretation of the data is to bemeaningful.121CHAPTER 5 InGaAs STRAINED LAYER RELAXATION.In the previous chapter, the case of homoepitaxy was considered. The interfacebetween the growing GaAs epilayer and the GaAs substrate is crystallographically perfectsince the substrate and the epilayer are in perfect registry with each other. The case ofgrowing InGaAs on a GaAs substrate is distinct in that the bulk lattice constant of eachalloy is slightly different resulting in different degrees of lattice mismatch at thesubstrate/epilayer interface. If the misfit between the substrate and the epilayer issufficiently small, the first atomic layers deposited are strained so that the overlayer adoptsthe in-plane lattice constant of the underlying substrate. As in the case of homoepitaxy, acrystallographically perfect interface will then be formed. The strain energy per unit areafor such an epilayer increases linearly with thickness. After a certain thickness, the strainenergy becomes so large that it becomes favorable for the epilayer to relax either through amorphological instability (surface roughening)86’7 or through formation of misfitdislocations13’4which have an energy that is only slightly dependent on the epilayerthickness. Relaxation through surface roughening has been observed for SiGe/Si87 andInGaAs/GaAs88systems for growth under specific conditions. Large surface undulationsat the surface of strained layer can be formed if the film partially relaxes through elasticdeformation. The amplitude of this almost sinusoidal surface topography can be of thesame order as the film thickness. Reported results show oscillation of up to -50% of thefilm thickness87. In the elastically deformed epilayer, the lattice constant is larger in areasof the films that are thicker and smaller in the thinner areas. The average strain is reducedsince the volume of the strain-reduced thick region is larger than the volume of the strainincreased thin region87. While the strain energy after deformation is on average lower afterdeformation, the surface energy is higher. The two competing mechanisms explain whylarge surface undulations would be observed under certain growth conditions and122dislocations observed under others. In the case where the misfit is too large, the growth ofa coherent layer will be impossible and the grown layer will consist of InGaAs clusters.In this chapter, the evolution of the surface morphology during the relaxation ofInGaAs strained layers grown on GaAs substrates is studied using in-Situ elastic lightscattering. The in-situ measurements are compared with post growth measurementsincluding ex-situ elastic light scattering, Nomarski microscopy and atomic forcemicroscopy. After a brief introduction describing dislocations, we present the typicaloptical signature of the relaxation at various spatial frequencies and along different crystalorientations. Following this, we study the evolution of the surface morphology during therelaxation of a coherent epilayer of compositionIn18Ga82As using four samples withdifferent thickness epilayers. Two other studies, the influence of the indium concentrationand the effect of substrate temperature on the optical signature during the relaxation, willthen be presented.5.1 Dislocations and misfit.A dislocation in a crystal can be described by the dislocation line and the Burgersvector89. The dislocation line simply follows the dislocation through the crystal and theBurgers vector represents the necessary displacement of the bulk crystal for theintroduction of the dislocation. In Fig. 5.1, a pure edge dislocation and a pure screwdislocation are shown for a simple cubic lattice. They are both lying at the interfacebetween the substrate and the epilayer. The Burgers vector is perpendicular to thedislocation line for an edge dislocation and parallel to the dislocation line for a screwdislocation. As can be deduced from the figure, only the edge dislocation helps in reducingthe coherency strain. Pure screw dislocations do not affect the misfit-related strain at theinterface. In reality, most dislocations will have an edge and a screw component. Forthose dislocations, the angle between the Burgers vector and the dislocation line (p6) will123be between 0 and 900. Only the edge component that is in the plane of the interface willreduce coherency strain.EpilayerSubstrateFigure 5.] Pure edge dislocation (left) and a pure screw dislocation (right) lying atthe inteiface, shown for a simple cubic lattice (from Tsao89).The strain in the vicinity of a dislocation is proportional to the displacement of thecrystal around it and therefore to the Burgers vector. Since the energy associated with adislocation depends on the square of the strain, it will be dependent on the square of theBurgers vector. Therefore, the dislocations with the shortest Burgers vector will be morecommon because of their lower energy. In fcc GaAs-based crystals the most commonBurgers vectors are along the six [1101 directions since the smallest lattice vectors (a /-J)are along these directions.It is easiest for a dislocation line to move in the crystal plane which has the highestatomic density. In GaAs crystals, these so-called slip planes are the (111) planes. Theycontain both the Burgers vector and the dislocation line. As the strain reaches a criticalthreshold, the dislocations (existing or nucleated) will move on the slip plane to reach theinterface and relieve the excess strain as they create a step on the surface of the InGaAsepilayer. The dislocation lines at the interface between an InGaAs epilayer and a GaAssubstrate are oriented along [1101 and the [1101 orientations since these directions represent124the intersection of the (001) interface and the slip planes. The Burgers vector is in the slipplane making an angle of 60° with the dislocation line. The dislocation has therefore bothan edge and a screw component. The screw component ensures that the dislocation canmove in a direction non-parallel to the interface allowing for the dislocation to reach theinterface where the edge component can relieve the coherency strain.The density of dislocations in an epilayer of arbitrary thickness is highly dependenton the difference in the bulk lattice constant of the two materials. The lattice constant ofInGaAs varies linearly with indium concentration from 5.65 A for GaAs to 6.05 A forInAs90. The misfit, defined as the ratio of the difference in lattice constants betweenInGaAs and GaAs to the GaAs lattice constant, varies linearly as a function of indiumconcentration in the epilayer. The maximum misfit for InGaAs/GaAs structures reaches7.1% for pure InAs grown on GaAs.A Nomarski picture of the cross-hatched pattern seen when a strained layer relaxesthrough the formation of dislocations, is presented in Fig. 5.2. The lateral size of theimage is 900 jim. The sample shown is a 0.5 jim thick InGaAs layer grown at a substratetemperature of 490°C. The observed cross grid pattern follows the expected direction ofthe dislocations and it can also be noticed that the density of vertical lines running along the[110] direction is higher than the density of horizontal lines. The dislocations aregenerating corrugated surfaces with morphologies that are different along the two crystalorientations.The azimuthal variation of light scattering from such a surface is of interest. Thescattering will be distributed mainly along sharp lines perpendicular to the dislocations.Fig. 5.3 is a photograph of the reflected intensity on a white piece of paper. The specularbeam (Ar+ laser, 457 nm) goes through a small hole in the wall and is reflected back ontothe wall. The sample is placed about two meters from the wall and the photograph is about125one meter across. The scattering lines seen on the photograph clearly show that thescattering is not isotropic. Because these lines are extremely sharp, the alignment of thesample with respect to the detection ports is critical when measuring the onset of relaxationusing in-situ light scattering.126Figure 5.2 Nomarski picture of the stan4ard cross-hatchedpattern obtained when afully strained layer relaxes through the formation ofdislocations.Figure 5.3 Photograph of the reflected intensity (457 nm) on a large screen placedabout 2 mfrom the sample. The scattering is distributed mainly along sharp linesperpendicular to the running dislocations.1275.2 Dependence of the scattered intensity on crystal orientation and spatialfrequency.In the first detection geometry used, the laser was incident normal to the substratethrough port C and the onset of relaxation was measured simultaneously along the twocrystal orientations at 5.4 tm1 and 11 11m’ with detectors on ports A, B, F and G ofFig. 2.13. Unfortunately, when the wafer is rotated during the alignment, it wobbles: thenormal to the wafer is precesses around the average normal at an angle of about 2°. Thealignment is further complicated by the fact that in this geometry, the exact position of thewafer when it is moved at the beginning of the run to face the effusion cells is not very welldefined. The solid angle of detection can compensate for an azimuthal misalignment ofabout ± 1.5°. This means that, in Fig. 2.13, if the crystal is rotated more than 1.5° fromthe ideal position represented by the arrows, the scattering line will fall out of the solidangle of detection and will not be detected. We found only in a few cases that thealignment was good enough to detect the scattering lines along both crystallographicorientations.The time evolution of the scattered intensity along the [1101 and [110] orientationsfor q=5.4 pm1 and 11 .im1 for the first 15 mm of growth (0.25 rim) is presented inFig. 5.4 and Fig. 5.5 during relaxation of an In2Ga8As alloy grown at 490°C on a GaAsepilayer. Prior to growth, the (001) GaAs on-axis (±0.5°) substrates were oxidized for5 mm using UV-ozone, and the oxide was removed thermally in UHV. A GaAs bufferlayer was grown for one hour with the substrate temperature held at 590°C during the first55 mm and then ramped to 490°C in the last 5 mm. Then, the indium shutter was openedand a 0.5 tm thick InGaAs layer was deposited on top of the GaAs buffer. Beforegrowth, a flux ratio of As2 to Ga of 3.5 was measured with a retractable ion gauge. Thebackground intensities at the start of the InGaAs have been scaled so that each curve starts128at the same intensity (one). The light scattering signal at the beginning of the InGaAsgrowth is characteristic of the surface roughness of a thick GaAs epitaxial layer from whichthe scattering intensity is larger along the [110] direction as discussed in Chapter 4. Asverified after growth, the scattering lines were observable through the detection solid angleof each detector.129I I I I I I I I I I • I I I I I I I I I I I I I I I I J. •1’ 1. 7 - 11imJ F ---- / •.‘5.4 jim’4- .-... 3- [110]2 —1--- -.- -----I0C,, () 1111111111111.11.1111111.111111-2 0 2 4 6 8 10 12 14Growth Time (InGaAs) (mm)Figure 5.4 Time evolution of the scattered intensity along the [110] orientation forq=5.4 pm1 and]] pm1 during relaxation of an In2Ga8As alloy grown at 490°C ona GaAs epilayer. Growth rate: 1pm/hr.111111 I 11111111111 11111111111 I ICf)16.________II_________ii__ — —5 - .- 5.4urn’0 iiiii I 1111.111111 iiiiii I. iii. I I-2 0 2 4 6 8 10 12 14Growth Time (lnGaAs) (mm)Figure 5.5 Time evolution of the scattered intensity along the [110] orientation forq=5.4 pm and 11 pm1 during relaxation of an In.2Ga.SAs alloy grown at 490°C ona GaAs epilayer. Growth rate: 1pm/hr.130The roughening observed in both figures is dependent on the spatial frequencydetected. Along both orientations, higher spatial frequency signals rise sooner, suggestingthat the relaxation occurs first on smaller length scales. Even though the increase inscattered intensity at 5.4 tm-1 is smaller at the beginning, it persists for a longer time sothat the intensity becomes larger than at 11 tm-1. This is clearly seen for scattering along[1101 and was also observed in this case for scattering along [1101 after 15 mm of growthwhich is out of the window shown in Fig. 5.4.The scattering intensity associated with roughening along the [1101 direction risesslightly earlier than that along the [1101 direction which indicates that the relaxation lines(Fig. 5.2) develop first along the [1101 direction, relaxing the strain along the [110]direction. This tendency is reverted as the film continues to grow (Fig. 5.5). As before,an anisotropic surface morphology results that is rougher along the [1101 direction.Initially, the extra roughness is mainly at higher spatial frequencies but it shifts towardslower frequencies as the film grows.Fig. 5.6 shows a magnification of the 5.4 im1 scattering signal presented inFig. 5.4. It shows the initial behavior of the scattered intensity along the [1101 orientation.We have separated the time evolution into the three distinct regions A, B, and C shown onthe graph.1311.81.6IF“0.8-1 0 1 2 3 4 5Growth Time (InGaAs) (mm)Figure 5.6 Early stages of the time evolution of the scattered intensity along the[110] orientation for q=5.4 pm4 during relaxation ofanIn•2Ga8Asalloy grown at490°C on a GaAs epilayer. Growth rate: 1pm/hr.At the start of the InGaAs growth (region A), due to the index of refraction changeat the interface, the signal undergoes a small oscillation similar to the oscillations describedin Chapter 2. This interference oscillation is rapidly damped because of the higherabsorption coefficient of InGaAs. In region B, the scattered intensity increases gradually.The corrugated surface roughness is revealed in region C by the detection of the intensenarrow scattering line.We are interested in relating the intensity increase to the surface morphology, inorder to know if the onset of the roughening (t<4 mm in Fig. 5.6) is a consequence ofrelaxation controlled by morphological instability or by dislocation formation.61325.3 Surface morphology versus epilayer thickness.Since the alignment was not reproducible from sample to sample, the detectiongeometry of section 5.2 was changed to the one shown in Fig. 2.14. The laser (488 nm)is incident through port B at 25° and the scattered signals are detected at ports A, C and D.In this geometry, the plane of incidence is easy to adjust by controlling the position of thereflected specular beam. This ensures that the plane of incidence and the plane containingdetectors A, C and D are coincident. The problem of aligning the crystal axis with theplane of detection was solved by using the laser beam to orient the wafer. The laser spot isswept across the wafer using an alignment mirror that can be rocked on one axis, and thewafer is rotated until a cleaved edge is aligned along the sweeping direction. Since thisdirection is the same from run to run, the wafer orientation will also be the same. Thealignment mirror was mounted on a rotating stage so that the sweeping direction could bealigned with the detection plane (also the plane of incidence). To do this, an alreadyrelaxed InGaAs sample was rotated until one of the scattering lines was in the center of alldetection ports. The alignment mirror was then rotated until the sweeping directionfollowed the cleaved edge of the well-aligned wafer. Using this technique, every wafer canbe aligned reproducibly. We evaluated that after the alignment, the position of the wafer iswithin 0.5° of the desired orientation which is sufficient to always have the scattering line inthe solid angle of detection.The disadvantage of this geometry is that in order to probe both crystal orientations,two different samples have to be processed. However, unlike the set-up of section 5.2,detection of small spatial frequency scattering is possible.To study the evolution of the surface morphology, different thicknessIn18Ga82Assamples were grown on thick GaAs buffer layers at a substrate temperature of 490°C.After growth, the samples were quenched to room temperature to enable post growth133characterization by atomic force microscopy, ex-situ light scattering and x-ray diffraction.Fig. 5.7 shows the evolution of the scattered intensity along the [1101 direction for aspatial frequency of 5.4 tm-1. The letters a, b, c and d represent the time at which thegrowth was stopped for four similar samples. The four growth times of 2, 3.5, 5, and15 minutes correspond to InGaAs epilayer thicknesses of 33, 58, 83 and 250 nm. We areinterested in correlating the surface morphology at these four points with the measuredintensity of the light scattering. The first 8 mm of growth, magnified in the inset of Fig.5.7, show that at point b, the scattering signal has just started to increase.4.0i.3.5Q0.500Figure 5.7 Evolution of the scattered intensity along the [110] directionfor a spatialfrequency of 5.4 #m’ during growth ofIn.l8Ga.g2As at 490°C.We first present the results of ex-situ scattering measurements on the four samples.The power spectral densities obtained along the [110] direction are shown in Fig. 5.8. Forthe 33 nm thick film, the scattering intensity on all the length scales measured in-situ hasnot increased significantly. Therefore we consider this power spectrum as representingalso the starting GaAs surface morphology. Two main conclusions can be drawn from a4 8 12 16In18Ga82As growth time (mm)zL—01)0134comparison of the four curves. The increase in intensity starts first at higher spatialfrequencies and is monotonic for up to 15 mm of growth for this crystal orientation. Also,it is clear that there is no increase for spatial frequencies lower than 1 Jimt. We believethat the variations in the PSD for these low frequencies are related to a run-to-run variationor a position variation across the sample and are not significant as far as the relaxation isconcerned.10-s I I 11111111010-s10-610-vI I 111111 I• 33ftmo 58nm• 83nm -o 250nm000••.•108 i ....nI0.1 1 10Spatial Frequency (J..Lm1)Figure 5.8 Power spectral densities of the surface morphology along the [110]orientationforfour different epilayer thicknesses ofIn. l8Ga.2As.The PSDs obtained along the [110] orientation for the same samples are presentedin Fig. 5.9. The result is very similar except that the roughening observed for the highestspatial frequencies is not monotonic. After the roughening expected from the relaxation, itis clear that the surface smoothes on small length scales while it is stifi roughening on largerones. The roughening along [1101 observed in the preceding graph is slightly larger thanthe one seen here along [1101. The anisotropy in the surface morphology follows the same135I.CDI.)Ibehavior as the one observed for the GaAs growth in Chapter 4. Because the RHEED wasnot operational at the time of this experiment the surface reconstruction is unknown.However, from the scattering variations, it is clear that the diffusion on the surface is fasteralong the [110] direction, a result obtained for GaAs growth when the reconstruction is(2x4).cP010-s1 0-1 0-10-610-v108• 33nmo 58nm• 83iim250nm004.0.1 1 10Spatial Frequency (.tm 1)Figure 5.9 Power spectral densities of the surface morphology along the [110]orientation forfour different epilayer thicknesses ofIn• l8Ga.82As.The ex-situ scattering measurement of the PSD along the [100] direction for thesame four samples is presented in Fig. 5.10. The variation from sample to sample is smallcompared to variations along the two other directions measured. At the start of the InGaAsgrowth, the scattering intensity increases slightly as the film thickens but decreases for thethickest film (250 nm). From the PSD measurements only, it is not clear if the variations inscattering observed along the [1001 direction as the film relaxes from a coherent epilayer to136a semi-coherent film represent a real change in surface morphology or if they are due tosample-to-sample variations or lateral non-uniformity across the sample surface.1 I I 1111111 I I 1111111 I• 33nm0 53nm10• 83nm250nm10-10-6-J)in-7--C•____1 0_8 11111.1 I 111111 I0.1 1 10Spatial Frequency (pm-1)Figure 5.10 Power spectral densities of the surface morphology along the [100]orientation forfour different epilayer thicknesses ofIn.18Ga82As.The three figures showing the evolution of the PSD along three crystal orientations(Fig. 5.8, 5.9 and 5.10) confirm the anisotropy in elastic light scattering seen earlier inFig. 5.4. They also show that there is no significant roughening at low spatialfrequencies. For the growth conditions studied (18% indium, T=490°C) and filmthicknesses of up to 250 nm, the relaxation was only observed ex-situ at spatialfrequencies larger than 2 tm1. This is consistent with the in-situ scatteringmeasurements, in which no significant variation in scattering was detected close to thereflected specular beam (corresponding to low spatial frequency scattering) duringrelaxation of the strained layer.137The indium concentration of 18%, first evaluated before growth by measuring theflux ratio of indium and gallium, has since been calibrated by optical transmission andx-ray diffraction measurements91. In addition to the indium concentration, the x-raymeasurements yield the percentage relaxation along each crystallographic orientation. Theyare presented in Table 5.1 for the three thinner samples.Sample % Relaxation % Relaxationthickness [1101 [110](nm)33 <0.5 <0.558 11 783 31 22Table 5.1 Percentage relaxation obtainedfrom x-ray measurements91.Figs 5.11 to 5.14 show, in order of increasing film thickness the atomic forcemicroscopy (AFM) images of the four In.l8Ga.2As samples92 The [110] and [110]directions are indicated on the axis beside each image. After 33 nm of growth ofIn.18Ga.8As (Fig. 5.11), the surface morphology observed is anisotropic. Since there isno increase in the in-situ scattering for such a film, as mentioned earlier, and also since thecalculated rms roughness is in the range of the values obtained for growth of GaAs onGaAs (see Table 5.2), we believe that the higher roughness along the [1101 direction is dueto the anisotropy of the starting surface, not the result of the InGaAs growth. Theanisotropy is in fact slightly stronger than for the surface shown in Fig. 4.27. This couldbe due to the fact that in Figs 5.11 to 5.14, the buffer layers were grown for half an hourlonger and we have shown that the anisotropy increases with film thickness.138Figure 5.12 Atomic force microscope image of a 58 nm thick In.J8Ga.2Asepilayer grown on a 0.8 Wn thick GaAs buffer layer. Correspond to point (b) inFig. 5.7. (10um x 10um x 120A)Figure 5.11 Atomic force microscope image of a 33 nm thick Inj8Ga•2Asepilayer grown on a 0.8 jim thick GaAs buffer layer. Correspond to point (a) inFig. 5.7. (10pm x 10pm x ISOA)139Figure 5.14 Atomic force microscope image of a 250 nm thick In.l8Ga.82Asepilayer grown on a 0.8 urn thick GaAs buffer layer. Correspond to point (d) inFig. 5.7. (10 um x 10 ,im x 120 A)Figure 5.13 Atomic force microscope image of a 83 nm thickIn18Ga82Asepilayer grown on a 0.8 urn thick GaAs buffer layer. Correspond to point (c) inFig. 5.7. (5 urn x Sum x 120 A)140For the thinnest sample, the AFM does not reveal the presence of a cross-hatchedpattern. This is consistent with the x-ray diffraction measurements on that sample whichalso do not detect any relaxation in the film. A maximum of 0.5% of the epilayer could stillbe relaxed because of the limit in the sensitivity of the X-ray technique. After 58 nm ofgrowth (Fig. 5.12), at which point the in-situ scattering signal just started to increase, theAFM images show clear relaxation lines running along the [1101 direction. As the film isgrowing (Figs 5.13 and 5.14), lines appear in the other direction and the cross-hatchedpattern becomes more evident: the corrugated roughness and by implication the number ofdislocations is increasing.The rms roughness evaluated from the optical PSD measurements can be comparedto that obtained directly from the AFM images. The rms calculation from the PSD isperformed using Equations 2.14 and 2.15. As mentioned earlier, the isotropic integrationusing Equation 2.14 leads to the rms roughness that would be present if the PSD measuredalong one direction represented all the surface roughness. On the other hand,Equation 2.15 gives the one dimensional rms roughness along the measured direction. Tocalculate the overall surface rms roughness we proceed as follows. The PSD along the[100] direction is assumed to be isotropic in 2D and integrated (Equation 2.14) from0.5 tm1 to 16 im1 to estimate the background random roughness of the surface. Theintegration range approximately matches the spatial resolution of the AFM images. Wenext calculate the one-dimensional roughness (Equation 2.15) along both the [110] and[110] directions. The one dimensional integration of the PSD along these two directions isdone only over the spatial frequencies where the PSD exceeds the PSD along the [1001direction. An example of the selected limits of integration is given in Fig. 5.15 whichrepresents the PSD along the three given directions for the 58 nm thick InGaAs sample.Spatial Frequency (u-1)Figure 5.15 Power spectral densities along the [100], [110] and [110] directionsfor the thickIn•18Ga82Assample. The three double-sided arrows represent therange of integrationfor each direction.Finally, the three calculated roughnesses are considered independent and addedtogether in quadrature. These results are compared in Table 5.2 with the values of rmsroughness obtained from the 10 tm x 10 p.m AFM images.SCATI’ERING MEASUREMENTS_______ AFMSample Roughness Roughness Roughness Total Roughnessthickness [110] (1D) [110] (1D) [100] (2D) roughness(nm) (A) (A) (A) aT(A) (A)(a)33 0 0 11 11 11(b)58 1.1 0.8 15 15 12(c)83 2.1 1.5 14 14 11(d)250 5.0 3.6 9 11 13Table 5.2 Rms roughness along the given ciystal orientations evaluatedfrom thepower spectral density and rms roughness evaluatedfrom AFM images.1410. 1<I IIII1J —- I• [110]o [1001• [110] -‘ItI.C.)‘1)10io-1 0-10-s10-61010-8[100]• -•cr0[fo0.1 1 10142As shown in the table, the surface anisotropy observed in the AFM images isreflected in the directional roughness estimates extracted from the scattering measurements.While the roughness along the [1001 direction is rather stable, the roughness along [1101and [110] dramatically increases as the film thickens, corresponding to the formation of thecross-hatched pattern. The increase in scattering is larger along the [1101 direction, whichis the signature of an anisotropic surface morphology. This is consistent with the AFMimages, in which the cross-hatched pattern observed is not symmetric. The number oflines per unit length observed in Fig. 5.13 and Fig. 5.14 is larger along the [1101 directionthan along the [110] direction. This is further corroborated by the fact that the X-raycharacterization measures a larger relaxation along the [1101 direction. However, for the58 nm thick sample in Fig. 5.12, for which the x-ray measures a larger relaxation alongthe [1101 direction, the AFM detects lines parallel to the [110] direction only. The AFMimage is consistent with the earlier rise of the [110] signal in Figs 5.4 and 5.5. The largerrelaxation along the [1101 direction for this sample is not reflected in the measured surfacemorphology.The relatively stable roughness observed in the AFM images along the [1001direction as the thickness of the sample increases agrees qualitatively with the smallvariations in the optical measurements for this orientation. Moreover, both techniquesseem to suggest that the formation of the cross-hatched surface morphology along the [1101and [110] directions slightly reduces the roughness in other directions. However, it is notclear if the observed changes represent a significant effect or if they are a consequence ofsample-to-sample variations.1435.4 Influence of indium concentration.The thickness at which the InGaAs epilayer starts to relax depends on theaccumulated strain in the overlayer. Since the strain depends in turn on the indiumconcentration in the film, we have first used in-situ light scattering to measure the onset ofrelaxation as a function of indium concentration. After the samples were etched on the backsurface, they were oxidized using UV ozone for 5 mm and then loaded into UHV. Theoxide was removed thermally and a GaAs buffer layer was grown for 1 hour. In the last5 mm, the substrate temperature was ramped down from 590°C to 490°C. On the resultingsurface, 0.5 p.m thick InGaAs films with different indium concentrations weresubsequently grown at a substrate temperature of 490°C. Fig. 5.16 and Fig. 5.17 showthe time evolution of the scattered intensity at q=5.4 p.m1 during the growth of the InGaAsfilms, when the scattering vector is oriented along the [110] or the [110] directionsrespectively. After the background had been normalized to one, successive curves wereshifted vertically by 0.05 so that each signal is artificially separated for easier comparison.The small variation in signal in the first 30 nm of deposited material interpretedearlier as an interference oscillation is larger for samples with larger indium concentrations.This is expected since with more indium in the film, the difference in index of refraction islarger at the interface. From both figures, it can also be seen that the thickness at which theroughening occurs is smaller for increasing indium concentrations, up to 23% indium. For28% or 34% indium the increase in roughness is more gradual indicating a transition ingrowth mechanism between indium concentrations of 23% and 28%.144liii 1111111111 111111 IIIlIIIII IlIllIlli1.8- 23%I 18% / 28% -— I1.6 Is —.-41.4 - /c.ø• ‘‘— 9.8% 6.3%1.2C-)C-I)I ii.IiiiiIiiii 1111111. iii iii 111111111110 50 100 150 200 250 300 350 400InGai.As Thickness (nm)Figure 5.16 Evolution of the scattered intensity at 5.4 uin4for InGaAs films ofdifferent % indium concentrations when q is parallel to the [110] direction.111111 III 111111111111111111111111111111.8 23%D1.698q143qC-.)ta)C-)C-I)I,II1II111I1 111IIII1I1II lIlt 111111111110 50 100 150 200 250 300 350 400InGaiAs Thickness (nm)Figure 5.17 Evolution of the scattered intensity at 5.44um1for InGaAs films ofdifferent % indium concentrations when q is parallel to the [110] direction.145Comparison of the two graphs reveals that the onset of relaxation along the [1101direction occurs slightly earlier than along the [110] direction. This is different from whathas been observed earlier and could partly be due to the normalization before comparison:the different normalization factors for the two crystal orientations resulting from the twodifferent background signals, slightly affect the rate of increase at the relaxation. However,the increase in scattered intensity is generally higher along the [1101 direction. This isconsistent with the fact that the measured percentage of relaxation along the [1101 is largerthan along the [110] as shown in Table 5.1.The evolution of the scattered intensity at a higher spatial frequency (16 11m’ ) forthe same samples is shown in Fig. 5.18 when q is parallel to the [110] direction. Onceagain, the interference effect and the roughening due to the relaxation can be seen. At thishigher spatial frequency, the observed smoothing is not present for the highest indiumconcentration film.Cl).2.51.5C.)ru 10 50 100 150 200 250 300 350 400In Ga1.As Thickness (nm)Fig. 5.18 Evolution of the scattered intensity at 16 urn1 for InGaAs films ofdifferent indium concentrations when q is parallel to the [110] direction.146101 010010Figure 5.19 Critical layer thickness as determined by opticaltogether with the models ofMatthews-Blaskelee and People-Bean.0.25scattering shown(5.1)The onset of the roughening detected with light scattering can be related to thecritical thickness for the formation of the dislocations. In Fig. 5.19 we plot the criticalthickness inferred from light scattering as a function of indium concentration together withthat predicted by theoretical models of Matthews-Blakeslee13and People-Bean14(solidcurves).I1000I0 0.05 0.1 0.15 0.2Indium concentrationIn the Matthews-Blakeslee model the critical thickness is determined frommechanical equilibrium theory. The misfit stress generates a force on an existing threadingdislocation. When this force, which increases linearly with film thickness, exceeds thetension in the dislocation line, the dislocation bends to release the strain at the interface. Inthis case, the relation between the critical thickness h and the misfit f is given by:h b ((1_vcos2f3)) [1+1n()]C 8irf i\(1+v)cos(A)) bThe coefficient f3 represents the angle between the Burgers vector ( b) and thedislocation line and A represents the angle between b and the normal to the dislocation147line that is in the plane of the interface. The Poisson’s ratio v, defined as the negative ofthe ratio between lateral and longitudinal strains under uniaxial longitudinal stress, is 1/3 inthis case89. For fcc-lattice-based zincblende crystals A =13 = 600. The lower solid curveof Fig. 5.19 is plotted using Equation 5.1 with b = a The misfit f as a function ofindium concentration is known from Fig. 5.2.The other solid line (People-Bean) is obtained from energy balance. In this model,the film is assumed to be initially free of dislocations. When the thickness of the strainedepilayer is sufficiently large, the strain energy reaches the energy necessary to nucleatedislocations. Since the dislocations have to be generated, it is expected that for smallmisfits, the critical thickness will be larger than in the Matthews-Blakeslee case. Therelation between the critical thickness h and the misfit f becomes:h b (1— v) ln() (5.2)C 32ir f2 (1+v) bFor each sample grown, the critical thickness was measured using in-situ lightscattering at two different spatial frequencies and along two crystal orientations. This leadsto four values of the critical thickness. The experimental points in Fig. 5.19 represent thesmallest critical thickness measured for each sample. It should be noted however that thefour measured values are very similar and the difference between the average h andthe minimum h measured is smaller than the size of the point on a log scale. The arrowshown for an indium concentration of 2.7% indicates that this value is a lower limit for therelaxation as the epilayer was not thick enough to measure a definite sharp relaxation.All the experimental values fall within the limits of the two models. For highermisfits, the measured h is well described by the model proposed by People and Bean.The values measured by F. Celii et a130 for scattering at 9 tm1 along the [1101 directionare smaller than the values reported here. We attribute this difference to the slightly higher148temperature at which the InGaAs layers were grown in their case (515°C). As will beshown in the next section, the strained layers relax earlier when the substrate temperatureduring growth is 20°C to 30°C higher.Ex-situ light scattering measurements of the surface power spectral density wereperformed on five of the resulting 0.5 tim-thick InGaAs films corresponding to indiumconcentrations of 2.7%, 6.3%, 9.8%, 23% and 34%. Fig. 5.20, Fig. 5.21 andFig. 5.22 compare the PSD obtained for all the samples mentioned along the [1101, the[1 101, and the [1001 directions respectively.As usual, the tendencies observed for the [110] and [110] in Fig. 5.20 and 5.21are similar. As the indium concentration increases up to 23%, the roughness increases forspatial frequencies as low as 0.5 tm1. At the highest spatial frequencies (q > 10tm),this trend is reversed and there is a decrease in scattered intensity when the indiumconcentration reaches 23%. As expected, the roughness of each film is larger along the[1101 direction and the smoothing effect at large spatial frequency when the indiumconcentration is large is more pronounced along the [110] direction. For the samplecontaining 34% indium, the roughening behavior is different as one would expect from thein-situ measurements (Fig. 5.16, 5.17 and 5.18). The roughening of this sample is onlyobserved for spatial frequencies larger than 3 J1m. It is found to be larger for largerspatial frequencies as well as larger along the [1101 direction.1491 IIIII1 I I 1111111 I• 2.7%0 0 6.3%io • 9.8%23%÷ 34%I..+_.0+••.•0 +÷ %%• +++0.•3 1O .•CI) CI.)io’1 0_8 I • I0.1 1 10Spatial frequency (rim 1)Figure 5.20 Evolution of the PSD of 0.5 jim thick InGaAs films with increasingindium contentfor scattering along the [110] direction.1 I I 1111111 I I 1111111 II• 2.7%LI 0 6.3%I.-• 9.8%LI 23%L• II + 34%I:I I..— •c/i io-°0+ 00 +—1 06 - + +%o0cbc±++:..,•w,*Ia•• 0io 0c• •i...iI •1081 10Spatial frequency (.tm 1)Figure 5.21 Evolution of the PSD of 0.5 ,iin thick InGaAs films with increasingindium contentfor scattering along the [110] direction.150The evolution of the PSD of 0.5 im thick InGaAs films with increasing indiumcontent is also shown along the [100] in Fig. 5.22. Although the film with 23% indiumcontent seems to generate a slightly higher PSD, the only very different behavior isobserved for the film with 34% of indium. This high indium content film exhibits a similarPSD along all three orientations. For high indium concentrations we conclude that themorphology is more isotropic, with increased roughening on small scales, than for filmswith lower indium content.-3_____________________________________________1 : ‘ I 111111 I••OD1 0_80.1 1 10Spatial frequency (.tm 1)Figure 5.22 Evolution of the PSD of 0.5 JIm thick InGaAs films with increasingindium contentfor scattering along the [1001 direction.To extract the magnitude of the roughness from the PSD measurements, weproceed the same way as earlier. The uniform intrinsic roughness is estimated byintegrating the PSD along the [100] direction isotropically from 0.5 pm1 to 16 .im1using Equation 2.14. The one-dimensional integration of the PSD (Equation 2.15) along•.III,.• 2.7%o 6.3%• 9.8%o 23%÷ 34%151[110] and [110], for the range of spatial frequencies at which the PSD differs from the PSDalong the [1001 direction, yields rms values for the corrugated roughness in each direction.Since for the sample containing 34% indium the cross-hatched pattern was not observed,the PSD was integrated isotropically for the three directions. For 0.5 im thick InGaAsfilms of increasing indium concentration, the results of the integrations appear in Table 5.3.Indium Roughness - Roughness Roughness Totalconcentration [1101 (l-d) [110] (1-d) [100] (2-d) roughness(A) (A) (A) (A)2.7 .6 < .2 9.0 9.06.3 0.9 < .2 12 12.09.8 4.7 2.2 11 12.223 5.9 3.0 16 17.3(2-d) (2-d) average (A)34 106 60 74 80Table 5.3 Light scattering measurements of rms surface roughness of 0.5 umthick InGaAs films with increasing indium concentration as deducedfrom the PSDalong each direction.For the first four samples in the table, as the indium concentration increases, theroughness increases more along the [110] than along the [110] direction while theroughness is not varying monotonically along the [100] direction. This is again a result ofthe anisotropy of the cross-hatched pattern developed during relaxation throughdislocations.For the highest concentration film, the roughness is dramatically larger than for theother samples along the [100] direction. As deduced directly from the PSD and from thein-situ measurements, the roughening mechanism is different for the samples containing28% and 34% indium. At these concentrations, the misfit is so large that no coherent layercan be grown on the substrate: the growth is three-dimensional from the start. The152resulting surface morphology is more isotropic and the roughness is much larger on smalllength scales. A the comparison of the three rms values for the last sample reveals that thesurface morphology is still anisotropic with a maximum in the roughness along the [1101direction and a minimum along the [110] direction, as in the case of GaAs growth.Fig. 5.23 is an atomic force microscope image of a 0.5 im thick InGaAs filmcontaining 28% indium. As expected from light scattering measurements on this sample,the anisotropic cross-hatched pattern observed in previous images (Fig. 5.12 to 5.14) is notpresent for this high concentration film, and the surface is much rougher on smaller lengthscales. The rms roughness calculated from the 10 im x 10 pm image is 200 A. Forcomparison, the rms roughness calculated from a AFM image of the sample containing23% indium was only 32 A for an image 6 times larger.Figure 5.23 AFM image of a 0.5 pm thickIn.2SGa.72As film (10 pm x 10 pm).153It is interesting to note that at the transition between two-dimensional and three-dimensional growth, it is possible to have both types of growth occuring simultaneously onthe same substrate. Fig. 5.24 is a Nomarski photograph of an earlier sample grown athigher substrate temperature (540°C). The width of the photograph is 900 tm. Theconcentration of indium has not been measured. Both the cross-hatched pattern typical of2D growth and the rough surface morphology associated with 3D growth are presentsimultaneously on the surface. The AFM image presented in Fig. 5.25 reveals the heightdifference between the large rough islands and the lower cross-hatched pattern to be morethan 1500A representing over 10% of the film thickness (1.5 jim). This reflects a similarpercentage by volume of voids in the film for the 3D growth mode.154Figure 5.24 Nomarski photograph of a 1.5 wn thick InGaAs fun grown at540 °C. The width of the image is 225 ,um.Figure 5.25 AFM image o(a 1.5 wn thick InGaAsfih,n grown at 540°C.(35#m x 35wn x 2000A)1555.5 Influence of substrate temperature.As mentioned earlier, the thickness at which the InGaAs epilayer starts to relaxdepends on the accumulated strain in the overlayer. Beside the obvious dependence of thestrain on the indium concentration in the film the strain should also depend to a lower extenton the substrate temperature at which the film is grown. If the substrate temperature ishigher it should be easier for a dislocation to move to the interface and relax the strain. Thehigher substrate temperature also means that the diffusion of adatoms is faster on thesurface possibly allowing for more relaxation through surface roughening.We have used the in-situ light scattering technique to measure the onset ofrelaxation as a function of substrate temperature. The samples were prepared in the waydescribed in Sections 5.3 and 5.4. The GaAs buffer layer was grown for 55 mill at asubstrate temperature of -590°C. In the following 5 mm of GaAs growth, the substratetemperature was ramped to the desired temperature for the growth of the InGaAs layer. Aseries of ten InGaAs films were grown in which the substrate temperature was varied fromsample to sample from 408°C up to 589°C. The ratio of In and Ga atoms striking thesurface was such that an InGaAs alloy with 18% indium would grown if there were nodesorption of either Ga or In during the growth. The evolution of the scattered intensityduring deposition, measured at q=5.4 tm1 along the [110] direction, is presented inFig. 5.26 for substrate temperatures ranging from 408°C to 515°C. The background signalat the start of the InGaAs growth represents the scattering level characteristic of a 0.8 urnthick GaAs buffer layer and has been described in Chapter 4. To facilitate the comparison,the seven curves shown have been normalized to one at the start of the InGaAs growth.The optical signature of the relaxation is very similar for substrate temperatures rangingfrom 408°C to 474°C. No trend is observed in the increases in signal for these five samplesgrown at the lowest temperatures. The random differences could be dependent onvariations of the starting surface morphology or on slight variations in deposition fluxes or156alignment. However, the critical thickness at which the signal starts to increase is around70 nm for all these samples. When the substrate temperature is increased to 484°C, therelaxation starts at smaller thickness and the increase in scattering is more than three timesfaster. If the temperature is further increased to 515°C, this trend is even morepronounced. This is most likely a consequence of the fact that the generation and themovement of dislocations is easier at higher temperature.In addition to the roughening effect, the interference oscillation seen at thebeginning of the InGaAs growth is different at a substrate temperature of 515°C. Themeasured intensity is slightly lower than expected. This could be a consequence of thedesorption of some of the indium from the growing surface.1.5rID1.4-e1.340 80 120InGaAs Thickness (nm)Figure 5.26 Time evolution of the scattered intensity at q=5.4 jiin1 along the[1101 directionfor substrate temperatures rangingfrom 408°C to 515°CThe evolution of the scattered intensity during deposition, measured the same wayas in Fig. 5.26 is shown in Fig. 5.27 for substrate temperatures ranging from 5 15°C to589°C. The curve obtained at 515°C is reproduced from Fig. 5.26. The tendency to160157smooth at the start of growth first demonstrated for the sample grown at 5 15°C, is evolvinginto a clear trend as the substrate temperature is increased further. At the maximumtemperature of 589°C, only a smoothing is observed: no roughening due to the relaxationtakes place. At this temperature, most of the indium desorbs from the sample.1.51C0.50rID0Figure 5.27 Time evolution of the scattered intensity at q=5.4 um1 along the[110] directionfor substrate temperatures rangingfrom 515°C to 589 °C.We are interested in the time evolution of the surface morphology for the InGaAssample grown at high temperature (589°C). Fig. 5.28 shows the complete evolution of thescattering intensity at q=5.4 Jim’ along the [1101 direction during the processing of thissample. The typical step for the desorption of a 5 mm UV-ozone oxide is seen at about-15 mm on the time axis. The zero on the time axis corresponds to the start of the GaAsgrowth. The rate of smoothing and the intensity level observed after 60 mm of growth arerepresentative of the growth parameters and detection conditions. At t=60 mm, the indiumshutter is opened and indium and gallium atoms in a ratio of 1 to 4.6 start to accumulate onthe substrate. In the case where there is no desorption, the growth rate is 1 pm/hr and the0 40 80 120 160InGaAs Thickness (nm)158In/Ga ratio corresponds to a composition of in.18 Ga.82 As. The rapid decrease inscattered intensity when the indium flux is started clearly shows that the surface is gettingsmoother. The rate at which the intensity decays is one order of magnitude faster thanduring the GaAs growth that smoothes the oxide-desorbed surface.12I1:: 4I.)0-40 -20 0 20 40 60 80 100Growth Time (mm)Figure 5.28 Time evolution of the scattering intensity at q=5.4 ,um along the[110] direction during desorption, growth of GaAs and InGaAs at 589.C.Fig. 5.29 compares AFM images of the surface after 30 mm of GaAs growth andafter the InGaAs is grown for 30 mm over a one hour GaAs buffer layer. The lateralscales are 5x5 im for the GaAs sample and lOxlO pm for the InGaAs sample. Thevalues of rms roughness obtained from the images are 19.1A and 2.5A respectively. Therms roughness for the InGaAs sample is even lower than the one measured for the polishedwafer. It should be noted however that the roughness of the polished wafer is not due tobackground texture but to numerous polishing marks (see Fig. 3.5; sigma rms=3.2 A).The roughness of the InGaAs sample was deduced from a larger image. Note that if thesame size images were used, the difference would be even larger.159(a)(b)Figure 5.29 4FM images of (a) the surface after 30 mm of GaAs growth (5 jim x5 um x 120 A) (19 A rms) and (b) after the high temperature JnGaAs is grown for30 miii over a 60 mm GaAs buffer layer (10 pmxl0 jim x 25 A) (2.3 A rms)160Power spectral densities extracted from the ex-situ light scattering measurements onthe two samples are shown in Fig. 5.30. Clearly, the intensity measured from the InGaAsfilm is lower for all angles except the ones very close to the beam (q < 0.5 jimt).Therefore, for length scales smaller than —10 jim, the surface of the InGaAs sample issignificantly smoother. The integration of the PSD from 1 to 16 jim’1 yields an rmsroughness of 10 A and 40 A for the JnGaAs and GaAs samples respectively. The fact thatthese results are higher than the rms roughness calculated from AFM images (3.2 A, 15 A)could again be due to a defect or particulate effect. The InGaAs smoothing is howeverunequivocal.1 021O•g 10I108 -0.1liii I I I II liii• GaAs0 InGaAs.•••00•c:aIb.oo •.o.cP0o •OocPcb •.I I III.... I III....1 10Spatial frequency (j.im 1)Figure 5.30 PSD of the surface morphology along the [110] direction on the twosamples shown in Fig. 5.29.We believe that the smoothing behavior is a consequence of a change in thedynamics of the diffusion on the surface due to the indium evaporation. The concentrationof the indium in the InGaAs layer was only 1.5% as measured by secondary ion mass161spectroscopy (SIMS)93. This means that 11 out of 12 incoming indium atoms desorb fromthe surface. Fig. 5.31 shows the drastic change in RHEED pattern when changing thegrowth from GaAs to InGaAs. The surface reconstruction clearly switches from the (2x4)seen under arsenic-rich conditions to the (4x2) reconstruction typical of gallium or indium(group III) terminated surfaces. In order to verify that the group III terminated surface isnot a consequence of a lack of arsenic, the same experiment was performed again with afive-fold increase in the As2 flux. The (4x2) reconstruction is still present during theInGaAs growth and a similar smoothing is observed.GaAs589 °CInGaAs589 °C1101 f1101Indium segregation during growth has been studied directly during growth usingmass spectrometry94.It is known that indium atoms tend to “float” over the arsenic duringFigure. 5.31 RHEED pattern evolution when changing the growth from GaAs toInGaAs at a substrate temperature of589 °C.162growth. This can also be deduced from the fact that the resulting interface when InGaAs isgrown on GaAs is sharper than the interface when GaAs is grown over InGaAs. In thelatter, the indium is incorporated into the GaAs close to the interface because of its tendencyto segregate and stay over the arsenic-stabilized surface. We explain the observedsmoothing behavior in the following way. The important desorption of indium togetherwith the fact that indium naturally prefers to be located over the arsenic ensures that thesurface during growth under an indium flux at high substrate temperature is indiumterminated and has a (4x2) reconstruction. The presence of the (2x4) reconstructed surfacein the preceding GaAs growth, generates an initial anisotropic roughening in which thesurface is rougher along the [1101 direction. During the transition to a (4x2) reconstructionafter the indium shutter is opened, we believe that the direction of easiest diffusion changesas well and becomes the [1101 direction. The anisotropy in the surface roughness that wasdeveloped during the growth of GaAs is rapidly eliminated as the scattering signal along the[1101 direction rapidly decays. The fact that the roughness at the surface of the GaAssample decreases so quickly when the dynamics of the surface adatoms is modified is agood indication that the scattered intensity is not mainly due to defects but to an intrinsicsurface texture of the epilayer. Though roughness can be eliminated quickly if it does notrepresent a steady state situation with the noisy flux, the defects will not likely disappear.5.6 Summary.In Chapter 5, we have demonstrated that the light scattering signature duringrelaxation of InGaAs strained layers is not only dependent on the crystal orientation butalso on the magnitude of the spatial frequency measured. The relaxation is detected earlierat higher spatial frequencies and along the [1101 direction.The increase in scattered intensity along the [1101 and [110] directions together witha stable intensity along the [1001 direction is the signature of the typical cross-hatched163surface morphology generated by the relaxation of coherency strain through dislocations.Unlike the [1101 direction, after an initial increase the scattered intensity along the [1101decreases, indicating that the surface is smoothing along this direction. The higherscattered intensity measured along the [1101 direction is related to the variation in thepercentage of relaxation along the two crystal directions.The critical thickness measured as a function of indium concentration in the filmwas shown to be within the limits set by the mechanical equilibrium theory of Matthewsand Blakeslee and by the energy balance model of People and Bean. The values obtainedfor the critical thickness are larger than reported ones measured with the same technique.This is consistent with the measured temperature dependence of the critical thickness. Thecritical thickness is found to be the same for films grown at temperatures ranging from408°C to 474°C. Then, the critical thickness is seen to decrease as the temperature rangesfrom 484°C to 515°C. For higher temperatures the behavior is very different as the indiumstarts desorbing significantly, provoking a drastic smoothing of the surface. For very highindium concentrations (28%), the relaxation mechanism was different. The resultingsurface morphologies were more isotropic and rougher on small length scales than for lowindium content films. This is due to the fact that for those concentrations the misfit is toolarge and the growth is not coherent at start. The transition at which the growth changesfrom two dimensional to three dimensional is certainly dependent on indium concentrationbut will most likely be dependent also on substrate temperature during growth. Thetransition was determined to occur between indium concentrations of 23% and 28% forgrowth at 490°C.164CHAPTER 6 CONCLUSIONS.In this work, we presented the evolution of the surface morphology during MBEgrowth of GaAs-based semiconductor compounds as measured in-situ with elastic lightscattering. The theoretical development of the reflectivities presented in Chapter 2 led to aquantitative interpretation of the light scattering. When the density of defects in the layerwas small, we found in general that the rms roughness calculated from light scatteringmeasurements is in reasonable agreement (—±20%) with the roughness obtained from AFMor STM images.The light scattering intensity was measured simultaneously at up to seven differentangular positions each detecting a different length scale in the surface topography. Thisallowed us to study the time and spatial frequency dependencies of the light scatteringduring the removal of the oxide from GaAs substrates, the growth of GaAs the cleansubstrates and the growth of InGaAs films on the GaAs epilayers.The in-situ evolution of the light scattering during oxide removal clearly showed aroughening when the oxide was thermally removed and no roughening when the oxide wasetched with atomic hydrogen. As expected from theory, the optical signature during thedesorption was found to be dependent on the detection angle only through the magnitude ofthe spatial frequency probed. The roughening associated with the thermal desorptionproduces a sharp step in the light scattering at high spatial frequencies and a peak at thelowest spatial frequencies. A small feature in the optical signature 20 to 40°C below thedesorption temperature was attributed to a reaction between the oxide layer and theunderlying substrate. Using the high spatial frequency signature, we found that thickeroxides desorb at higher temperature and leave a rougher surface. The desorptiontemperature was also found to be dependent on the rate of the temperature ramp during thedesorption.165During growth of GaAs, the time evolution of the scattered intensity was found tobe anisotropic. The growing surface exhibits larger roughness along the [1101 direction.This was explained by the different diffusion coefficients along the [1101 and the [110]directions for an arsenic-stabilized (2x4) reconstructed surface.When the scattering is a result of the intrinsic surface morphology, we determinedthat the time evolution of the scattered intensity I during growth of GaAs depends on q1 atfirst and then saturates giving a q2 dependence at long times. On an oxide-desorbedsurface, the smoothing observed at high spatial frequencies is described by:exp(—2aqt)while the roughening at low spatial frequencies follows:1—exp(—2aqt)q2This last equation was shown to be consistent with the formation of mounds orridges seen in the case of unstable growth on singular surfaces75’6if the height of themound increase linearly with time.We also found that when the scattering is dominated by defects in the layer, theevolution of the scattering intensity and the power spectral density after growth display abehavior similar to that predicted by kinetic roughening theory. Hence, the source of thescattering has to be correctly identified to develop a meaningful interpretation.The evolution of the surface morphology during growth of InGaAs films on GaAsepilayers was also studied in-situ with light scattering and ex-situ with light scattering,AFM and x-ray diffraction. The optical signature of the relaxation is strongly anisotropic.When the cross-hatched pattern typical of relaxation through dislocation formation appearson the surface, there is a large intensity increase along the [110] and [1101 directions while166the intensity remains fairly stable along the [100] direction. The onset of rougheningduring the relaxation was detected slightly earlier at larger spatial frequencies. From x-raymeasurements91,we also found that dislocations appear before the surface roughens. Forthe growth conditions presented, the roughening is therefore a consequence of theformation of dislocations not of a morphological instability.Using light scattering, the dependence of the onset of roughening on the indiumconcentration in the film was investigated. Though higher than values previously reported,the onset of roughening was within the limits set for critical thicknesses by the mechanicalequilibrium theory of Matthews and Blakeslee13and by the energy balance model of Peopleand Bean14. For high indium concentration (23%), the observed growth was 3D as thestrain was too large to permit growth of a coherent epilayer.The thickness to reach the onset of roughening was found to be independent ofsubstrate temperature in the range 408-474°C and decreased slightly as the substratetemperature reached 515°C. For higher temperatures, as the indium desorbs from thesurface, the reconstruction switches from (2x4) to (4x2) provoking a drastic smoothing ofthe starting surface. This effect could have important consequences for the fabrication ofdevices where planar interfaces are needed.We have shown that elastic light scattering can be used for monitoring variousaspects of epitaxy and can be useful in process control. 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