Contains an introduction and reports on three research projects.Joint Services Electronics Program Contract DAAL03-92-C-000

Birgeneau, Robert J.

Blum, Kenneth I.

Mak, Alan

Noh, Do-Young

Nuttall, William J.

Ramstad, Monte J.

Salvucci, Elizabeth M.

McCaffery, Elizabeth M.

DSpace@MIT

Chapter 2. Synchrotron X-ray Studies of Surface DisorderingChapter 2. Synchrotron X-ray Studies of Surface DisorderingAcademic and Research StaffProfessor Robert J. Birgeneau, Dr. Kenneth I. Blum, Dr. Do-Young NohGraduate StudentsWilliam J. Nuttall, Monte J. RamstadTechnical and Support StaffElizabeth M. McCaffery2.1 IntroductionSponsorJoint Services Electronics ProgramContract DAAL03-92-C-0001In this research program we use modern x-ray scat-tering techniques to study structures and phasetransitions in thin films and on surfaces. We havetwo principal experimental facilities, one at MIT andthe other at the National Synchrotron Light Sourceat Brookhaven National Laboratory. At MIT, wehave four high-resolution computer-controlled x-rayspectrometers. The angular resolution can bemade as fine as 1.8 seconds of arc, which enablesus to probe the development of order from dis-tances of the order of the x-ray wavelength -1 A,up to 30,000 A. The sample temperature can bevaried between 2 K and 500 K with a relative accu-racy of 2 x 10- 3 K. At the National SynchrotronLight Source, in collaboration with IBM, we havethree fully instrumented beam lines. Two of thesebeam lines allow us to make studies with photonsvarying in energy between 3 and 12 keV; the thirdhas a fixed energy of 17 keV. These facilities makepossible high-resolution scattering experiments witha flux of more than three orders of magnitude largerthan that of a rotating anode x-ray generator.Several years ago, as part of this JSEP program,we built an x-ray-compatible, high-vacuum singlecrystal apparatus. This enabled us to usesynchrotron radiation to study the structures andtransitions occurring at a single surface, and suchexperiments are now becoming routine. In collab-oration with Professor Simon G.J. Mochrie, we havenow designed, built and commissioned a second-generation x-ray surface facility which is extremelyversatile allowing a wide range of surface scatteringexperiments.Our basic scientific objective is to understand themorphologies and microscopic structures of simplesemiconductor and metal surfaces at high temper-ature. Possible phase changes include surfaceroughening, surface reconstruction, melting,amorphization and dilution. These phenomena areparticularly interesting on stepped surfaces, wherethere may be an interplay between step structures,faceting, reconstruction, and roughening.2.2 Metal Surface StudiesStep interactions play a central role in determiningthe equilibrium morphology of a crystalline surface.Different interactions are known to result in suchdiverse phenomena as step pairing, surfacefaceting, and surface roughening. A small densityof steps may be incorporated onto a metal surfaceby deliberately cutting the crystal at an angleslightly off from a high symmetry direction. If thehigh symmetry surface does not reconstruct, thetheory of equilibrium crystal shapes (ECS) predictsthat at low temperatures the steps should eithercluster together or spread uniformly across thesurface. In the former case, a "hill and valley"structure of densely stepped rough regions coex-isting with flat, high symmetry facets will result.The fraction of the surface comprised of flat facetsshould decrease with increasing temperature, fallingto zero at some temperature below the rougheningtransition temperature of the facet. In the lattercase, the surface is predicted to be rough at alltemperatures. That is, entropically wandering stepsshould result in a logarithmic divergence of themean square height fluctuations as a function oflateral distance across the surface. X-ray scat-tering, low energy electron diffraction and atomscattering studies have reported surface rougheningof numerous metal crystalline facets, includingCu(110), Ag(110), Cu(113) and Ni(113). In addi-tion, studies of vicinally miscut Cu(110) andAg(110) have reported low temperature surfacephase separation into a hill and valley structure.The situation for Ag(110) is, however, controversial.In 1987 we carried out a high resolution x-ray scat-123Chapter 2. Synchrotron X-ray Studies of Surface Disorderingtering study of a vicinal Ag(110) surface using acrystal which had been inadvertently miscut by- 0.50; we interpreted the data on the basis of aroughening transition of the flat (110) facets at -725 K. More recently, Robinson and coworkershave re-addressed this problem using a Ag(110)crystal miscut by - 0.20. They assert that, in equi-librium, their 0.20 vicinal Ag(110) surface phaseseparates into flat (110) facets together withstepped regions for temperatures below 790 K andthat a uniform step structure is only stable abovethat temperature. In order to resolve this contro-versy and to understand generally the behavior ofstepped Ag(110) surfaces, we have carried outx-ray scattering and scanning tunneling microscopy(STM) studies of a Ag(1 10) sample miscut 10 fromthe (110) axis along the (110) direction. The STMmeasurements have been performed at IBM byR.M. Feenstra and G.A. Held.For a clean and well annealed surface, we find thatat all temperatures above 300 K, the surface iscomprised of a uniform density of single atomicheight meandering steps. That is, we find no evi-dence for vicinal phase separation. However, asthe surface is annealed to sufficiently high temper-atures, we find that impurities are driven to thesurface and that this, in turn, results in the forma-tion of large, flat (110) terraces. The latter is thebehavior reported by Robinson and coworkersalthough they interpreted their data assuming aclean surface. For the clean surface we observediffraction characteristic of uniform, albeitmeandering, steps at all temperatures between 300K and 875 K. With increasing temperature, thestep peaks lose intensity and undergo an evolutionin lineshape consistent with a decrease in step-stepcorrelations, most noticeably in the (001) direction.While our data above 670 K are consistent with arough surface, the peak evolution is not consistentin detail with the simplest model of entropicallyrepulsive steps.2.3 Semiconductor Surface StudiesAs discussed above, vicinal surfaces, that is, sur-faces of crystals cut close to a high symmetry direc-tion, exhibit remarkably rich and diverse physicalbehavior. At equilibrium, such surfaces may exhibitroughening, faceting, and/or reconstruction transi-tions. Novel non-equilibrium phenomena also mayoccur. One of the most interesting and well-studiedsystems is vicinal Si(111). At temperatures imme-diately above the 1 x 1 to 7 x 7 reconstruction tran-sition at 1100 K, this surface can be described byflat (111) terraces separated by uniformly spacedsingle Si(111) bilayer steps. In recent synchrotronx-ray experiments we demonstrated that the "uni-formly" stepped surface is in fact rough with loga-rithmically divergent height fluctuations. Below1100 K the 1 x 1 -- 7 x 7 transition drives a facetingtransition in which the steps phase-separateyielding flat, reconstructed (111) terraces and well-ordered but higher-angle stepped regions.We have determined the temperature dependenceof the surface roughness above 1100 K, a regimewhere significant numbers of atoms sublimate.Remarkably, the surface height fluctuations exhibita logarithmic divergence up to 1275 K even undersignificant sublimation. This is best represented bya power-law line shape diffraction profile of the steplattice characterized by the exponent Tr. Represen-tative power law diffraction profiles are shown infigure 1. At - 1275 K, the surface undergoes asharp morphological transition to one characterizedby large uniform (111) terraces plus highly disor-dered stepped regions. This faceting was appar-ently observed previously, although on a Si(111)surface with a very small miscut (8') compared witha 30 miscut on our Si( 111) sample.Our x-ray experiment reveals that the faceting isaccompanied by a step disordering transition inwhich the step correlations change drastically.Above the disordering transition the height fluctu-ations of the surface diverge much faster than thethermal logarithmic divergence. Data on thestepped region diffraction peak position and widthare shown in figure 2. We speculate that the "tran-sition" is a non-equilibrium phenomenon driven by acombination of sublimation and electromigration.Our results are consistent with theoretical predic-tions for growing stepped surfaces. The discoveryof this new transition on thoroughly studied andstructurally perfect silicon surfaces should cast lighton the general problems of surface morphology athigh temperatures.2.4 Model Surface OverlayersMuch of the basic physics of surface systems,including both clean surfaces and surfaces withphysisorbed or chemisorbed overlayers, is deter-mined by general structural and symmetry consider-ations. For this reason, experiments on modelsystems such as rare gas overlayers on graphitecan provide important insights with implications forall surface systems. An important illlustration of thisis the chiral 3-states Potts model description of themelting of the 1 x 3 reconstruction of Si(113) asdescribed by Simon G.J. Mochrie in this report.The theory for this semiconductor surface transitionwas ofnginall developed to describe the melting ofthe 3 x3 structure of monolayer krypton ongraphite.124 RLE Progress Report Number 135Chapter 2. Synchrotron X-ray Studies of Surface DisorderingFigure 1. Longitudinal scans of the primary stepsuperlattice peak for a 30 miscut Si(111) crystal below1270 K with background subtracted. The scans areplotted relative to the integer order peak position of the(111) facets. The solid curves are the results of fits to apower law singularity form for the step correlations.There is no change in the lineshape in this temperaturerange other than sharpening due to annealing.Recently, we have carried out a series of exper-iments on xenon overlayers physisorbed onto singlecrystal graphite. These experiments have focusedon two issues: (1) the evolution of the structure asa function of temperature for one, two, three and sixlayers; and (2) the nature of the melting transitionfor coverages in the monolayer region. Results ofboth sets of experiments are still being analyzed.The essential features of the multilayer studies maybe summarized as follows. Monolayer xenon exhi-bits a commensurate-incommensurate transition atabout 65 K. Bilayer xenon exhibits more elaboratebehavior. For temperatures above 60 K, the twolayers have the same lattice constant with a valueincommensurate with respect to the substrate. At -60 K the layer of xenon closest to the graphitelocks into registry with the substrate while thesecond layer remains incommensurate. On theFigure 2. Longitudinal and transverse scans of the stepsuperlattice peak across the disordering transition near1275 K. The solid curves are the results of fits of thestep peak to an anisotropic displaced Lorentzian. Notethe drastic change in the width of the longitudinal scans.other hand, the three- and six-layer xenon systemsremain uniform and incommensurate at all temper-atures.Monolayer xenon on graphite has been viewed as amodel system for studying melting in two dimen-sions. There is, however, disagreement in theinterpretation of thermodynamic and scattering dataon the order of the melting transition at various cov-erages. Specifically, scattering studies suggest acontinuous melting process whereas themodynamicdata have been interpreted on the basis of firstorder melting transition for coverages near butbelow one monolayer. We have studied the meltingas a function of pressure and hence chemicalpotential at fixed temperatures of 121 K, 140 K, and146 K. At the two higher temperatures, we find thatthe solid diffraction peak decreases progressively inintensity with decreasing pressure evolving contin-uously into the diffraction pattern characteristic of astrongly correlated fluid with well-developedorientational order. This necessitates that themelting transition is at least nearly continuous. Weare currently carrying out a detailed line-shapeanalysis of the diffraction profiles to obtain quantita-tive information on the melting transition.125Professor Sylvia T. Ceyer126 RLE Progress Report Number 135

Synchrotron X-Ray Studies of Surface Disordering

Contains an introduction, reports on three research projects and a list of publications.Joint Services Electronics Program DAAL03-89-C-000

Chapter 2. Synchrotron X-Ray Studies of Surface DisorderingChapter 2. Synchrotron X-Ray Studies of SurfaceDisorderingAcademic and Research StaffProfessor Robert J. Birgeneau, Dr. Kenneth I. BlumGraduate StudentsAlan Mak, Do-Young Noh, William J. Nuttall, Monte RamstadTechnical and Support StaffElizabeth M. Salvucci2.1 IntroductionSponsorJoint Services Electronics ProgramDAAL03-89-C-0001In this research program we use modern x-rayscattering techniques to study structures andphase transitions in thin films and on surfaces. Wehave two principal experimental facilities, one atMIT and the other at the National SynchrotronLight Source at Brookhaven National Laboratory.At MIT, we have four high-resolution computer-controlled x-ray spectrometers using high-intensity, rotating anode x-ray generators. Theangular resolution can be made as fine as 1.8seconds of arc, which enables us to probe thedevelopment of order from distances of the orderof the x-ray wavelength, - 1iA, up to 30,000A.The sample temperature can be varied between 2K and 500 K with a relative accuracy of2 x 10- 3 K. At the National Synchrotron LightSource at Brookhaven National Laboratory, in col-laboration with IBM, we have three fully instru-mented beam lines. Two of these beam linesallow studies with photons varying in energybetween 3 and 12 keV; the third has a fixed energyof 17 keV. These facilities make possible high-resolution scattering experiments with a flux ofmore than three orders of magnitude larger thanthat of a rotating anode x-ray generator, openingup a new generation of experiments.Several years ago, as part of this JSEP program,we built an x-ray-compatible, high vacuum singlecrystal apparatus. This enabled us to usesynchrotron radiation to study the structures andtransitions occurring at a single surface, and suchexperiments are now becoming routine. As aresult of our recent research, we have determinedthat a new chamber allowing access to a widerrange of reciprocal space is required. In collab-oration with Professor Simon G.J. Mochrie, wehave designed, and are currently constructing, thissecond-generation x-ray surface facility.Our basic scientific objective is to understand themorphologies and microscopic structures of simplesemiconductor and metal surfaces at high temper-ature. Possible phase changes include surfaceroughening, surface reconstruction, melting,amorphization and dilution. These phenomena areparticularly interesting on stepped surfaces, wherethere may be an interplay between step structures,faceting, reconstruction, and roughening.2.2 Metal Surface StudiesPreviously, we carried out a detailed synchrotronx-ray study of the surface phases and phase transi-tions of a Au(110) surface. This specific Au(110)crystal had as its stable structure a 1 x 3missing-row reconstruction. This corresponds to aperiodic array of 4-atom wide (111) microfacets.The transition from this 1 x 3 structure to a 1 x 1structure at 760 K involved a simultaneous decon-struction and roughening.After further treatment of this same Au crystal wewere able to obtain a stable 1 x 2 phase on the(110) surface. This latter phase is the one mostcommonly observed in previous experiments. The1 x 2 structure corresponds to a periodic array of3-atom wide (111) microfacets. There are subtledistortions at these faces of the atoms away fromtheir bulk positions. We have performed asynchrotron x-ray scattering study of the thermaldisordering of this Au(110) 1 x 2 reconstructedsurface. Observing the temperature dependence ofthe in-plane superlattice and integral order surfacepeaks, as well as the (t e 0) specular reflectivity,115Chapter 2. Synchrotron X-Ray Studies of Surface Disorderingwe find that at Tc = 735 K the 1 x 2 surfaceundergoes a reversible deconstruction transitioncharacterized by a proliferation of compact anti-phase defects with no measurable change in thedensity of surface steps. This transition isdescribed by critical exponents close to thosecharacterizing a two-dimensional Ising transition.We also find that by 784 K there has been a signif-icant increase in the density of surface steps of thetype associated with surface roughening. Thissuggests that the Au(110) surface disorders in atwo step process, deconstruction followed byroughening, with a difference in the two transitiontemperatures of less than 50 K. This contrastswith the behavior we previously found forAu(110) 1 x 3 and which has been found recentlyby Robinson and coworkers1 in Pt(110).2.3 Semiconductor SurfaceStudies2.3.1 Ge(111)Currently, experimental information on the mor-phology of semiconductor surfaces near the bulkmelting point is very limited, in spite of its evidentimportance in many growth processes. TheGe(111) surface has been reported to undergo aphase transition at a crystal temperature of about1050 K, which is 160 K below the bulk meltingtemperature Tm (1210 K). The nature of the tran-sition remains controversial.At room temperature, a c(2 x 8) structure on theGe( 11) surface is stable. Near 573 K, thec(2 x 8) reconstruction converts to a (1 x 1) phase.The (1 x 1) structure may not have an ideally ter-minated bulk structure; adatoms are believed to bepresent. At higher temperatures a second struc-tural transition of the Ge(111) surface was firstsuggested by Lever in 1968.2 He found that thesticking coefficient of oxygen on Ge( 111) droppedprecipitously with increasing crystal temperaturenear 1050 K. McRae and Malic recently studiedthis reported transition in a Low-Energy ElectronDiffraction (LEED) experiment.3 The intensity ofthe surface diffraction peaks decreased rapidly near1050 K saturating at a low but non-zero value.The results were interpreted on the basis of aheuristic model in which the outermost doublelayer of the Ge(111) consists of incommensuratecrystalline islands surrounded by a disordered sea.Electron Energy Loss Spectroscopy done on aGe(111) single crystal surface, as well as on liquidand amorphous Ge overlayers, suggested that thehigh temperature disordered Ge( 11) surfaceresembles an amorphous layer more than a liquidlayer. Ion scattering indicated that above- 1050 K there are local departures of surfaceatoms from their equilibrium lattice positions.We have studied the Ge( 11) surface usingsynchrotron x-ray scattering techniques with aglancing angle scattering geometry. Represen-tative scans through the (10) peak at a series oftemperatures bracketing 1070 K are shown infigure 1. It is evident that well-defined sharppeaks are observed up to temperatures near bulkmelting; significantly, there is no important changein lineshape throughout this temperature range.Similar data are obtained for the (20) peak. The(10) and (20) peak intensities decrease graduallywith increasing temperature above - 900 K, gothrough pronounced minima at about 1070 K andthen partially recover.From these data one may exclude all existingmodels for the surface disordering of Ge(111).We have, however, been able to show that amodel involving surface vacancies gives a uniquedescription of our data and is consistent with pre-vious results. Specifically, we hypothesize thatnear 1000 K, thermally-generated random vacan-cies in the surface bilayer begin to proliferate.From a quantitative analysis we find that thesurface vacancy concentration rises rapidlybetween - 950 K and 1080 K and then saturates;the limiting vacancy concentration is near 50percent. We are also able to demonstrate that thevacancy concentration decays rapidly to the inte-rior layers.One important consequence of the high surfacevacancy concentration is a dramatic growth in therate of sublimation. So far there is little quantita-tive information on sublimation from defected sur-faces. We plan to study this problem in moredetail in the future.1 I.K. Robinson, E. Vlieg, and K. Kern. Phys. Rev. Lett. 63: 2578 (1989).2 R.F. Lever, Surf. Sci. 9: 370 (1968).3 E.R. McRae and R.A. Malic, Phys. Rev. Lett. 58: 1437 (1987); Phys. Rev. B 38: 13163 (1988).116 RLE Progress Report Number 133Transverse1.85 0qY (g-1)LongitudinalFigure 1. Longitudinal and transverse scans throughthe (10) peak are shown for four different temperatures:929 K, 995 K, 1095 K, and 1156 K. The central portionof each of the longitudinal scans is fit to a Gaussiancurve. All widths fall within + 10% of the instrumentalwidth of 0.0022A- 1 HWHM.2.4 Stepped Si(111) SurfacesThe behavior of vicinal surfaces (surfaces cut afew degrees away from low index facets) involvesessential aspects of surface structures includingequilibrium crystal shapes, roughening, faceting,and surface reconstruction. The stability of vicinalsurfaces is determined by the shape of the equilib-rium crystal surface. By studying a series of vicinalsurfaces with various surface normals, one canBoth future experiments and future theoreticalanalysis are planned on this important problem.2.5 PublicationsKeane, D.T., P.A. Bancel, G.L. Jordan-Sweet, G.A.Held, A. Mak, and R.J. Birgeneau. "Evidencefor Two-Step Disordering of the Au(110) 1 x 2Reconstructed Surface." Surface Sci. Forth-coming.Mak, A., K. Evans-Lutterodt, K. Blum, D.Y. Noh,J.D. Brock, G.A. Held, and R.J. Birgeneau."Synchrotron X-ray Diffraction Study of theDisordering of the Ge(111) Surface at HighTemperatures." Submitted to Phys. Rev. Lett.117Chapter 2. Synchrotron X-Ray Studies of Surface Disorderingmap out the equilibrium crystal shape. A vicinalsurface, when it is stable, forms a structure con-sistent with low-index terraces separated by stepswhose spacing is usually incommensurate with the102 bulk substrate lattice. As in the case of incom-mensurate domain wall problems, there can not betrue long range order in the structure of the incom-100 mensurate steps. This is due to the overwhelmingamplitude of the long wavelength thermal fluctu-o ations in two-dimensional systems with contin-:- uous symmetry. As a result, an incommensurate10 stepped surface is rough in an exact sense. Avicinal surface becomes unstable when the freeenergy of a nearby low index facet is lowered100 drastically by some mechanism such as recon-struction. One might expect that the lowering ofthe free energy of a low-index facet would break avicinal surface into a low-index facet and rough02 faces with a higher misorientation angle.K102We have carried out a preliminary synchrotronx-ray scattering study of a vicinal Si(111) surface10o  misoriented by 3.50 toward the (112) direction. Attemperatures higher than the 7 x 7- to -1 x 1 tran-,o sition, we find that the surface is composed ofsteps with a mean separation of - 60A which are102 correlated beyond 3000A. Below the transition,the surface is split into large ( > 3000A) perfectlyflat (111) facets together with stepped regions100 whose misorientation angle increases as temper-ature is decreased. The transition is first order,indicating that it is induced by the 7 x 7 recon-10-2 struction of the (111) facets. We are currently0.05 analyzing these data in terms of the equilibriumcrystal shape of Silicon. We also have discoveredother faceting configurations with higher indiceswhich are presumably stabilized by impurities.Eoo0-o00C,0LUt-I-z10-2 11.75 1.80qx (A-,)Theoretical studies conducted by Professor John D. Joannopoulos have provided many of the first ab-initio calculations for the electronic and geometric structure of solids.118 RLE Progress Report Number 133

Contains introduction, reports on two research projects and a list of publications.Joint Services Electronics Program Contract DAAL03-89-C-0001Joint Services Electronics Program Contract DAAL03-92-C-000

Chapter 2. Synchrotron X-Ray Studies of Surface DisorderingChapter 2. Synchrotron X-Ray Studies of SurfaceDisorderingAcademic and Research StaffProfessor Robert J. Birgeneau, Dr. Kenneth I. Blum, Dr. Do-Young NohGraduate StudentsWilliam J. Nuttall, Monte J. RamstadTechnical and Support StaffElizabeth M. Salvucci2.1 IntroductionSponsorJoint Services Electronics ProgramContract DAAL03-89-C-0001Contract DAAL03-92-C-0001In this research program we use modern x-rayscattering techniques to study structures andphase transitions in thin films and on surfaces. Wehave two principal experimental facilities, one atMIT and the other at the National SynchrotronLight Source at Brookhaven National Laboratory.At MIT, we have four high-resolution computer-controlled x-ray spectrometers using high-intensity, rotating anode x-ray generators. Theangular resolution can be made as fine as 1.8seconds of arc, which enables us to probe thedevelopment of order from distances of the orderof the x-ray wavelength -1BA up to 30,000A. Thesample temperature can be varied between 2 Kand 500 K with a relative accuracy of 2x10 - 3 K. Atthe National Synchrotron Light Source, in collab-oration with IBM, we have three fully instrumentedbeam lines. Two of these beam lines allow us tomake studies with photons varying in energybetween 3 and 12 keV; the third has a fixed energyof 17 keV. These facilities make possible high-resolution scattering experiments with a flux ofmore than three orders of magnitude larger thanthat of a rotating anode x-ray generator, openingup a new generation of experiments.Several years ago, as part of this JSEP program,we built an x-ray-compatible, high vacuum singlecrystal apparatus. This enabled us to usesynchrotron radiation to study the structures andtransitions occurring at a single surface, and suchexperiments are now becoming routine. As aresult of our recent research, we determined that anew chamber allowing access to a wider range ofreciprocal space was required. In collaborationwith Professor Simon G.J. Mochrie, we havedesigned, built and are now commissioning thissecond-generation x-ray surface facility.Our basic scientific objective is to understand themorphologies and microscopic structures of simplesemiconductor and metal surfaces at high temper-atures. Possible phase changes include surfaceroughening, surface reconstruction, melting,amorphization and dilution. These phenomena areparticularly interesting on stepped surfaces, wherethere may be an interplay between step structures,faceting, reconstruction, and roughening.2.2 Metal Surface StudiesIn 1987 we reported a detailed study of a possibleroughening transition of the Ag(110) surface.Specifically, we discussed the detailed line shapeof the Ag(110) surface peak for temperaturesbetween 100'C and 5250C. At -450'C weobserved a crossover to a pure power lawlineshape, indicative of a rough surface, for thenear-surface diffraction. Above 4500C the profilescould be described by the power law singularityform (Q - Q110) - 2+q with r changing rapidly withtemperature. Accordingly, we identified 4500C asthe roughening temperature.Our more recent experiments and those by otherson crystals with very small miscuts ( 0.50)suggest that the story may be more complicated.Specifically, the experiments suggest that below-450 0 C to 5000C, the Ag(110) surface may befacetted. In order to explore this further, we havebegun a systematic set of experiments on vicinalAg(110) crystals with miscuts in the (110) direc-tion of up to 4'. Our initial experiments on acrystal miscut by ~ 2.30 indeed show facettedbehavior below ~5000C. Further experimentsshould elucidate the full nature of the roughening-facetting transition on this prototypical noble metalsurface.129Chapter 2. Synchrotron X-Ray Studies of Surface Disordering2.3 Semiconductor SurfaceStudies2.3.1 Stepped Si(111) SurfacesThe behavior of vicinal surfaces (surfaces cut afew degrees away from low index facets) involvesessential aspects of surface structures includingequilibrium crystal shapes, roughening, faceting,and surface reconstruction. The stability of vicinalsurfaces is determined by the shape of the equilib-rium crystal surface. By studying a series of vicinalsurfaces with various surface normals, one canmap out the equilibrium crystal shape. A vicinalsurface, when it is stable, forms a structure con-sistent with low-index terraces separated by stepswhose spacing is usually incommensurate with thebulk substrate lattice. As in the case of incom-mensurate domain wall problems, there can not betrue long range order in the structure of the incom-mensurate steps. This is due to the overwhelmingamplitude of the long wavelength thermal fluctu-ations in two-dimensional systems with contin-uous symmetry. As a result, an incommensuratestepped surface is rough in an exact sense. Avicinal surface becomes unstable when the freeenergy of a nearby low index facet is lowereddrastically by some mechanisms such as recon-struction. One might expect that the lowering offree energy of a low-index facet would break avicinal surface into a low-index facet and roughfaces with a higher misorientation angle.We have carried out a detailed synchrotron x-rayscattering study of a vicinal Si(111 ) surface miso-riented by 3.5' toward the (112) direction. Attemperatures higher than the "7 x 7-to-1 x 1"transition, we find that the surface is composed ofsteps with a mean separation of - 60A which arecorrelated beyond 3000A. Below the transition,the surface is split into the large ( > 3000A) per-fectly flat (111) facets together with steppedregions whose misorientation angle increases astemperature is decreased. The transition is firstorder, indicating that it is induced by the 7 x 7reconstruction of the (111) facets. In the facettedphase, the f ac% angle a follows the law tana I T - TI with A = 2.3+8:. This disagreessomewhat with the theoretical predication 2 = 3/2for models in which the interaction between stepsis entropic in character.At temperatures above 1110 K, we observed twostep superlattice peaks bracketing the (10) posi-tion of the (111) surface. Figure 1 shows highresolution longitudinal and transverse scansthrough the first-order step peak at 1120 K. Thesimplest model leads us to believe that this peakresults from the ordering of steps by the entropicrepulsion. To test this idea quantitatively, we fitthe high temperature peak profile to a 2D powerlaw singularity of the formS(q) = (qH + Bq2)(-2+ il)/2convolved with the instrumental resolution func-tion. Figure 1 shows the optimal simultaneous fitsto the longitudinal and transverse scans withh = 0.6 + 0.1 and B = 15 + 7. It is evident thatthe power law form fits the data very well. Thelarge value of ll is fully consistent with scatteringfrom a rough surface whose height variancediverges logarithmically with distance. We notethat as in the stripe domain commensurate-incommensurate problem the Pokrovsky-Talapovmodel leads to the prediction r1 = 2/9, indepen-dent of temperature. This is in clear disagreementwith our results. More elaborate models of theinteraction between the steps are needed toexplain the large value of r/l.More recently, we have been studying thebehavior of vicinal Si(111) at very high temper-atures. Remarkably, we find that at -1300 K thereis a second phase transition in the step structurewhich mimics a surface melting transition. We arecurrently exploring this new-found phenomenon.2.4 PublicationsBlum, K.I., D.Y. Noh, A. Mak, K.W. Evans-Lutterodt, J.D. Broch, G.A. Held, and R.J.Birgeneau. "Structure and Phase Transitions ofGe(111) and Si(111) Surfaces at High Tem-peratures." In Surface X-Ray and Neutron Scat-tering. Vol. 61, pp. 27-31. SpringerProceedings in Physics. Ed. H. Zabel and I.K.Robinson. Berlin/Heidelberg: Springer-Verlag,1992.Keane, D.T., P.A. Bancel, G.L. Jordan-Sweet, G.A.Held, A. Mak, and R.J. Birgeneau. "Evidencefor Two-Step Disordering of the Au(110) 1 x 2Reconstructed Surface." Surf. Sci. 250: 8(1991).Mak, A., K. Evans-Lutterodt, K.I. Blum, D.Y. Noh,J.D. Brock, G.A. Held, and R.J. Birgeneau."Synchrotron X-ray Diffraction Study of theDisordering of the Ge(111) Surface at HighTemperatures." Phys. Rev. Lett. 66: 2002(1991).Noh, D.Y., K. Blum,Birgeneau. "Longon Vicinal Si(111)(1991).M.J. Ramstad, and R.J.Range Separation of Steps" Phys. Rev. B 44: 10969130 RLE Progress Report Number 134Chapter 2. Synchrotron X-Ray Studies of Surface Disordering4101021010-0.02-0.01A0 0.01 0.02 -0.01 0 CH (A-') AK (A-1)IFigure 1. Longitudinal and transverse scans through the first order Si(111) step surface peak. The dotted curvesare the resolution. The solid curves are the result of fits to the power-law lineshape with r = 0.6 and B = 15.131=:vC(./Z)).01 0.02Professor Sylvia T. Ceyer132 RLE Progress Report Number 134

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Synchrotron X-Ray Studies of Surface Disordering

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