Contains research summary and reports on three research projects.Joint Services Electronics Program (Contract DAAG29-83-K-0003

Joannopoulos, John D.

Contains summary of research and reports on two research projects.Joint Services Electronics Program (Contract DAAG29-83-K-0003

DSpace@MIT

Semiconductor Surface Studies9. Semiconductor Surface StudiesAcademic and Research StaffProf. J.D. Joannopoulos, Dr. D.H. Lee, Dr. Y. Bar-YamGraduate StudentsK. Rabe, E. KaxirasJoint Services Electronics Program (Contract DAAG29-83-K-0003)John D. JoannopoulosUnderstanding the properties of surfaces of solids and the interactions of atoms and moleculeswith surfaces has been of extreme importance, both from technological and academic points ofview. The recent advent of ultrahigh vacuum technology has made microscopic studies ofwell-characterized surface systems possible. The way the atoms move to reduce the energy ofthe surface, the number of layers of atoms involved in this reduction, the electronic andvibrational states that result from this movement, and the final symmetry of the surface layer areall of utmost importance in arriving at a fundamental and microscopic understanding of the natureof clean surfaces, chemisorption processes, and the initial stages of interface formation. Actually,one of the most difficult and fundamental problems in surface studies, both from the experimentaland theoretical points of view, is simply the determination of the precise positions of the atoms ona surface. Currently, there are many surface geometries, even for elemental surfaces, that remainextremely controversial.The theoretical problems associated with these systems are quite complex. We are, however,currently in the forefront of being able to solve for the properties of real surface systems (ratherthan simple mathematical models). In particular, we have recently developed a method ofcalculating the total ground-state energy of a surface system from "first principles" so that wemay be able to provide accurate theoretical predictions of surface geometries. Our efforts in thisprogram are concentrated in two areas: i) chemisorption and ii) structural phase transitions andsurface reconstruction geometries.9.1 ChemisorptionUsing "first principles" total energy calculations, it is possible to determine on a microscopicscale how atoms and molecules behave when they are placed on the surface of a solid. This is afundamental problem that has plagued both theorists and experimentalists for decades. Thedifficulty lies with the very strong interactions that may exist between the deposited atoms (ormolecules) and the host atoms constituting the surface of the solid. These interactions canRLE P.R. No. 127Semiconductor Surface Studiesstrongly disturb the original atomic arrangement at the surface, can allow foreign atoms to stickonly at particular positions on the surface, or can induce these atoms to move only along specificpaths on the surface. The very exciting possibility then arises of actually calculating theoreticallytopographical atom-surface interaction energy maps, illustrating the various migration pathsatoms might follow, as well as the places at which these atoms might like to bond. The result ofthe first "map" of this type is shown in Fig. 9-1.Al-GaAs (110) INTERACTIONENERGY MAPGa OAs *Figure 9-1: Interaction energy of Al with GaAs(110). The energybetween the lowest dip and highest peak is -1.5 eV.This represents the total interaction energy of an atom (AI) with a semiconductor surface(GaAs(110)) as a function of the position of the atom along the surface. The substrate atoms areallowed to relax in response to the presence of the Al atom. Several interesting features emerge.There is considerable structure across the surface, several metastable bonding sites can beidentified, information about vibrational excitations is available, and two "easy" diffusionchannels can be noted. The barriers along these channels are a couple of tenths of an eV. It isclear that diffusion is highly anisotropic occurring almost entirely along the (110) direction. Asimple calculation also shows that at room temperature the Al atoms could easily move alongthese channels. It is then quite likely that adsorption of Al atoms at room temperature results inthe formation of clusters or puddles on the GaAs surface. Calculations of this type can be apowerful theoretical tool in surface studies. They can help provide us with a realistic picture anda fundamental understanding of how atoms interact with surfaces.RLE P.R. No. 127Semiconductor Surface Studies9.2 Structural Phase TransitionsAlong a different direction, it is now possible to study the statistical mechanics and phasetransitions of real surfaces of solids. This is a completely new and unexplored area. As anexample, the myriad of surface reconstructions that may exist on clean semiconductor surfaces atdifferent temperatures is an extremely interesting and fundamental problem that needs to beinvestigated. Modern studies of phase transitions utilize a powerful theoretical tool which is therenormalization group scheme. The scheme is based on scaling ideas, and has as input simplespin Harniltonians which model the degrees of freedom of the system. Until now, there has beenno way of calculating what these Hamiltonian parameters should be for real surfaces of solids.The total energy calculations described above, however, should provide precisely the kind ofinformation needed. The exciting possibility then arises of coupling the results of microscopicstudies of surface systems (at zero temperature) with simple spin Hamiltonians and therenormalization group approach to study phase transitions at finite temperatures from "firstprinciples".P: PARAMAGNETICF: FERROMAGNETICAF: ANTIFERROMAGNETICLAF: LAYERED ANTIFERROMAGNETICFigure 9-2: Phase diagrams in reduced parameter space for (a) "(2X1)"and (b) "c(2X2)" families. The "X"'s correspond tointersections of a particular set of interaction parameters ofthe Si(100) system at varying temperatures. In (a) F is 2X1,LAF is p(2X2) and AF is c(4X2). In (b) F is c(2X2) and LAF isp(2X4). In each case, P denotes a disordered phase.We have recently succeeded in developing such a scheme and have applied it to the Si(100)surface, resolving important questions regarding the structure of the Si(100) surface. Forexample, we show that the (2X1) reconstruction geometry is not the ground state of the Si(100)surface and that higher order reconstructions can exist on the surface. In fact, it is found that twoRLE P.R. No. 127Semiconductor Surface Studiesdistinct families of reconstructed geometries (the "2X1" family and the "c(2X2)" family) can existon the surface, with independent phase transitions occurring within each. Two critical transitiontemperatures are predicted representing order-disodrder transitions. A phase diagram for theSi(100) surface which can be used simultaneously for systems belonging to the same universalityclass such as Ge(100) and diamond (100) is shown in Fig. 9-2.RLE P.R. No. 127

Semiconductor Surface Studies

Semiconductor Surface Studies10.0 Semiconductor Surface StudiesAcademic and Research StaffProf. J.D. Joannopoulos, Dr. Y. Bar-Yam, Dr. G. Gomez-SantosGraduate StudentsK. Rabe, E. Kaxiras, M. NeedlesJoint Services Electronics Program (Contract DAAG29-83-K-0003)John D. JoannopoulosUnderstanding the properties of surfaces of solids and the interactions of atoms andmolecules with surfaces has been of extreme importance both from technological andacademic points of view. The recent advent of ultrahigh vacuum technology has mademicroscopic studies of well-characterized surface systems possible. The way atomsmove to reduce the energy of the surface, the number of layers of atoms involved in thisreduction, the electronic and vibrational states that result from this movement, and thefinal symmetry of the surface layer are all of utmost importance in arriving at a funda-mental and microscopic understanding of the nature of clean surfaces, chemisorptionprocesses, and the initial stages of interface formation. Actually, one of the most diffi-cult and fundamental problems in surface studies, both from the experimental and the-oretical points of view is simply the determination of the precise positions of the atomson a surface. Currently, there are many surface geometries, even for elemental surfaces,that remain extremely controversial.The theoretical problems associated with these systems are quite complex. We are,however, currently in the forefront of being able to solve for the properties of real sur-face systems (rather than simple mathematical models). In particular, we are continuingour goal of calculating the total ground-state energy of a surface system form the "firstprinciples" so that we may be able to provide accurate theoretical predictions of surfacegeometries. Our efforts in this program have concentrated in the areas of surface growthreaction pathways, surface reconstruction geometries, structural phase transitions, andhyrdogenation.10.1 Surface Reconstruction GeometriesUsing "first principles" total energy calculations, it is possible to determine on a mi-croscopic scale how atoms behave when they are on the surface of a solid. This is afundamental problem that has plagued both theorists and experimtalists for decades.The difficulty lies with the very strong interactions that may exist between the surfaceatoms and the host atoms constituting the rest of the solid. These interactions canstrongly disturb the original idealized atomic arrangement at the surface changing thenature of the bonding and even the original stoichiometry.Semiconductor Surface StudiesIn recent years there has been considerable activity focused on determining the exactequilibrium geometry of the [111] surfaces of the III-V compounds. One of the mostpopular and intriguing models is the Ga/vacancy geometry where the removal of oneout of four Ga atoms on the surface was believed to proceed exothermically and resultin the lowest energy structure. For binary compound surface systems, however, it be-comes meaningless to simply ask "What is the lowest energy surface geometry?" It iscrucial to know the preparation conditions and the nature of the Ga and As reservoirsduring the growth process. The relevant atomic reservoirs for the GaAs (111) surfaceare Ga-gas, As2 -gas, Ga-metal droplets and the GaAs-bulk. In Fig. 10.1 we illustratethe energies of several possible (2x2) recontruction geometries we have studied, alongwith the corresponding reservoirs, relative to the ideal surface. We note that underAs-rich conditions the lowest energy (2x2) reconstruction is a new model, the As-triangle geometry. This is shown in Fig. 10.2 and consists of three As adatoms bondedthrough As-As bonds which effectively compensate for the energy required todissociate As2 molecules which are the source of excess As atoms. Moreover, the tri-angle results in a nearly perfect geometric coordination of the remaining surface As andGa atoms.-0.8 eV-3.1 eVAs-Trlangle-5.1 eVFigure 10.1. : As triangle model. Total energy in electronvolts per 2x2 unit cell for various reconstructionsof the (111) surface of GaAs under As-rich conditions.Finally, under Ga-rich conditions, we find that the Ga-vacancy geometry is indeedmost favorable. Our results predict, then, that by varying the relative chemical potentialof As and Ga, a phase transition should occur between the As-triangle and Ga-vacancygeometries. There are indirect experimental observations that appear to be consistentwith this prediction.10.2 Structural Phase TransitionsAll the calculations described in the previous section were at zero temperature. It isnow becoming possible, however, to begin studying the statistical mechanics andtemperature phase transitions of surfaces of solids. This is a completely new and unex-64 R.L.E. P.R. No. 129Semiconductor Surface StudiesFigure 10.2.: As triangle model. Upper panel: side view [(100)plane] of the GaAs(111)2x2 surface As tri-angle model. Larger size atoms are in the plane of the paper. Smaller size atoms are in a parallelplane. Lower panel: top view of the As-Triangle model. Dashed lines indicate a 2x2 cell unit.plored area. As an example, the myriad of surface reconstructions that may exist onclean semiconductor surfaces at different temperatures is an extremely interesting andfundamental problem that needs to be investigated. Modern studies of phase transitionsutilize a powerful theoretical tool which is the renormalization group scheme. Thescheme is based on scaling ideas, and has as input simple spin Hamiltonians whichmodel the degrees of freedom of the system. Until now there has been no way of cal-culating what these Hamiltonian parameters should be for real surfaces of solids. Thetotal energy calculations described above, however, should provide precisely the kindof information needed. The exciting possiblity then arises of coupling the results ofmicroscopic studies of surface systems (at zero temperature) with simple spinHamiltonians and the renormalization group approach to study phase transitions at fi-nite temperatures from "first principles."Using a simple semi-empirical total energy approach we succeeded in developingsuch a scheme and have applied it to the Si(100) surface, resolving important questionsregarding the structure of the Si(100) surface. For example, we show that the (2x1)reconstruction geometry is not the ground state of the Si(100) surface and that higherorder reconstructions can exist on the surface. In fact, it is found that two distinctfamilies of reconstructed geometries (the "2x1" family and the "c(2x2)" family) canexist on the surface, with independent phase transitions occuring within each. Twocritical transition temperatures are predicted representing order-disorder transitions.We are presently investigating the possible phase transitions that may occur on theGe(100) surface. This system, however, cannot be described accurately by a semi-empirical approach so that we are forced to use the more powerful and much morecomplex ab-initio total energy method discussed in section 10.1.To perform these studies we have been developing a new scheme for relaxing asystem with many degrees of freedom to its lowest energy configuration. The schemeSemiconductor Surface Studiesis based on a molecular dynamics approach to calculating quantum mechanical totalenergies and resembles a simulated quench. Our calculations of the Ge(100) surfaceare currently underway.10.3 HydrogenationThe interaction of atomic hydrogen with cleaned semiconductor surfaces has beenextensively studied for over a decade. Hydrogen atoms appear to saturate surfacedangling bonds resulting in a nearly ideal, bulk-terminated plane of exposed surfaceatoms. It is interesting that in cases where the surface does not have the geometry andperiodicity of the bulk-terminated plane, the interaction of hydrogen with surface atomsis strong enough to unreconstruct the complicated reconstruction patterns. This proc-ess takes place for example on the (2x1) Si(111) surface, which exhibits a low-energy7r-bonded-chain reconstruction. Upon hydrogenation this chain of Si atoms with (2x1)periodicity reverts to the (1xl) pattern of the bulk-terminated plane. Similarphenomema have been observed on the Ge(l 111) surface. Theoretically, this processis not very well understood and a realistic, first-principles study with adequated accu-racy to define precise low energy positions of atoms, corresponding total energies, andvibrational excitations above the ground state is completely lacking. Such a study iscurrently underway. Preliminary results, using ab-initio quantum mechanical total en-ergy calculations, indicate that the atomic positions of the hydrogenated Si andGe( 111) surfaces differ significantly from those of an ideal bulk-terminated plane.66 R.L.E. P.R. No. 129

Semiconductor Surface Studies10. Semiconductor Surface StudiesAcademic and Research StaffProf. J.D. Joannopoulos, Dr. Y. Bar-Yam, Dr. M. PayneGraduate StudentsK. Rabe, E. Kaxiras, M. NeedlesJoint Services Electronics Program (Contract DAAG29-83-K-0003)John D. JoannopoulosUnderstanding the properties of surfaces of solids and the interactions of atoms and moleculeswith surfaces has been of extreme importance, both from technological and academic points ofview. The recent advent of ultrahigh vacuum technology has made microscopic studies ofwell-characterized surface systems possible. The way the atoms move to reduce the energy ofthe surface, the number of layers of atoms involved in this reduction, the electronic andvibrational states that result from this movement, and the final symmetry of the surface layer areall of utmost importance in arriving at a fundamental and microscopic understanding of the natureof clean surfaces, chemisorption processes, and the initial stages of interface formation. Actually,one of the most difficult and fundamental problems in surface studies, both from the experimentaland theoretical points of view, is simply the determination of the precise positions of the atoms ona surface. Currently, there are many surface geometries, even for elemental surfaces, that remainextremely controversial.The theoretical problems associated with these systems are quite complex. We are, however,currently in the forefront of being able to solve for the properties of real surface systems (ratherthan simple mathematical models). In particular, we are continuing our goal of calculating thetotal ground-state energy of a surface system from "first principles" so that we may be able toprovide accurate theoretical predictions of surface geometries. Our efforts in this program areconcentrated in three areas: (i) surface energy barriers, (ii) surface growth reaction pathways,and (iii) structural phase transitions and surface reconstruction geometries.10.1 Surface Energy BarriersUsing "first principles" total energy calculations, it is possible to determine on a microscopicscale how atoms behave when they are on the surface of a solid. This is a fundamental problemthat has plagued both theorists and experimentalists for decades. The difficulty lies with the verystrong interactions that may exist between the surface atoms and the host atoms constituting therest of the solid. These interactions can strongly disturb the original idealized atomicRLE P.R. No. 128Semiconductor Surface Studiesarrangement at the surface changing the nature of the bonding and even the originalstoichiometry.In recent years there has been considerable activity focused on determining the exactequilibrium geometry of the [111] surfaces of the Ill-V compounds. One of the most popular andintriguing models is the Ga/vacanc geometry where the removal of one out of four Ga atoms onthe surface is believed to proceed exothermicallyl Unfortunately, no realistic theoreticalevaluation of such a model has been possible until now. The exciting possibility then arises ofusing our ab-initio total energy scheme to actually calculate the precise barrier for removingatoms from the surface. This would allow us to follow microscopically how an atom might escapefrom a surface. The results of our calculations are shown in Fig. 10-1.>,"oC,0C40a,ea)2.ZCuLU00~-5.0 -4.0 -3.0 -2.0 -1 0 0.0 1.0 2,0Position on z-axis in A3.0 4.0 5.0Figure 10-1: Relaxed surface total energy per 2x2 unit cell as a functionof the position on the z-axis of the symmetry breakingatom.Here we study the energetics of vacancy formation by gradually displacing Ga and As atoms onthe (111) and (111) surfaces of GaAs, respectively. Let us consider the (111) surface first.Vacancy formation can proceed by either removing one Ga atom per 2x2 unit cell into the vacuumor into the bulk. We note that as the Ga atoms are displaced toward the bulk, the energyessentially grows monotonically apart from a small glitch at Z F -1.5 A . The vacancy geometrywould certainly not be energetically favorable along this channel. If we displace the Ga atomsaway from the surface, toward vacuum, the energy initially decreases significantly. However, itsoon begins to rise rapidly resulting in an endothermic vacancy formation energy of 2.5eV. This isRLE P.R. No. 228Semiconductor Surface Studiesin sharp contrast to the exothermic energies predicted from simple model estimates. We note thatthe lowest energy geometry would appear to be a buckled growing with Z= 0.7 A . This isdeceiving, however, as discussed in detail in the next section.We conclude this section by noting that for the (TiT) surface the energetics of As removal arecompletely different. It is quite clear that vacancy formation would be highly untenable.10.2 Surface Reaction ChannelsFor binary compound surface systems it becomes meaningless to simply ask "what is the lowestenergy surface geometry?" It is crucial to know the preparation conditions and the nature of theGa and As reservoirs during the growth process. The relevant atomic reservoirs for the GaAs(111) surface are Ga-gas, As2-gas, Ga-metal droplets and GaAs-bulk. In Fig. 10-2 we illustratethe energies of a variety of possible 2x2 reconstruction geometries we have studied, along withthe corresponding reservoirs relative to the ideal surface.1.7 OV0.6 eVAs gas0.0 eV As-Subatitutlonal-0.8 eV -0. e-1.1 eV-3.1 eVFigure 10-2: Total energy per 2x2 unit cell of various reconstructionmodels for the (111) surface of GaAs.For the vacancy model, removing the Ga atom to a Ga-gas reservoir is energetically unfavorableby 1.7eV. As described earlier, this corresponds to an endothermic removal energy of 2.5eV withrespect to the buckled geometry. However, if the Ga-atom is placed in a Ga-metal droplet,vacancy formation can proceed exothermicallyl In fact, if excess As2-gas is available, formationRLE P.R. No. 128Semiconductor Surface Studiesof GaAs bulk pairs can lead to an even lower energy configuration. We note that theAs-substitutional and As-adatom geometries do not compare favorably with the vacancygeometry. In fact, an interesting aspect of Fig. 10-2 is that it suggests that irrespective ofexperimental conditions (which lead to the presence of excess As or Ga atoms) the vacancygeometry has the lowest energy of all of the models proposed so far. A combination of thevacancy and adatom geometries is not favored because the respective relaxations oppose eachother. We are currently investigating various reaction mechanisms appropriate for the (111)surface.10.3 Structural Phase TransitionsAlong a different direction, it is now possible to study the statistical mechanics and phasetransitions of real surfaces of solids. This is a completely new and unexplored area. As anexample, the myriad of surface reconstructions that may exist on clean semiconductor surfaces atdifferent temperatures is an extremely interesting and fundamental problem that needs to beinvestigated. Modern studies of phase transitions utilize a powerful theoretical tool which is therenormalization group scheme. The scheme is based on scaling ideas, and has as input simplespin Hamiltonians which model the degrees of freedom of the system. Until now, there has beenno way of calculating what these Hamiltonian parameters should be for real surfaces of solids.The total energy calculations described above, however, should provide precisely the kind ofinformation needed. The exciting possibility then arises of coupling the results of microscopicstudies of surface systems (at zero temperature) with simple spin Hamiltonians and therenormalization group approach to study phase transitions at finite temperatures from "firstprinciples."Using a simple semi-empirical total energy approach we succeeded in developing such ascheme and have applied it to the Si(100) surface, resolving important questions regarding thestructure of the Si(100) surface. For example, we show that the (2x1) reconstruction geometry isnot the ground state of the Si(100) surface and that higher order reconstructions can exist on thesurface. In fact, it is found that two distinct families of reconstructed geometries (the "2x1" familyand the "c(2x2)" family) can exist on the surface, with independent phase transitions occurringwithin each. Two critical transition temperatures are predicted representing order-disordertransitions. We are presently investigating the possible phase transitions that may occur on theGe(100) surface. This system, however, cannot be described accurately by a semi-empiricalapproach so that we are forced to use the more powerful and much more complex ab-initio totalenergy method discussed in section 10.1. These calculations are currently underway.RLE P.R. No. 228

Contains research summary and reports on three research projects.Joint Services Electronics Program (Contract DAALO3-86-K-0002

Semiconductor Surface Studies10.0 Semiconductor Surface StudiesAcademic and Research StaffProf. J.D. Joannopoulos, Dr. G. Gomez-Santos, Dr. E. Kaxiras, Dr. O. AlerhandGraduate StudentsT. Arias, M. Needles, A. Rappe, E. Tarnow, J. WangJoint Services Electronics Program (Contract DAALO3-86-K-0002)John D. JoannopoulosUnderstanding the properties of surfaces of solids and the interactions of atoms andmolecules with surfaces has been of extreme importance both from technological andacademic points of view. The recent advent of ultrahigh vacuum technology has mademicroscopic studies of well-characterized surface systems possible. The way atomsmove to reduce the energy of the surface, the number of layers of atoms involved in thisreduction, the electronic and vibrational states that result from this movement, and thefinal symmetry of the surface layer are all of utmost importance in arriving at a funda-mental and microscopic understanding of the nature of clean surfaces, chemisorptionprocesses, and the initial stages of interface formation. Actually, one of the most diffi-cult and fundamental problems in surface studies, both from the experimental and the-oretical points of view is simply the determination of the precise positions of the atomson a surface. Currently, there are many surface geometries, even for elemental surfaces,that remain extremely controversial.The theoretical problems associated with these systems are quite complex. We are,however, currently in the forefront of being able to solve for the properties of real sur-face systems (rather than simple mathematical models). In particular, we are continuingour goal of calculating the total ground-state energy of a surface system from "firstprinciples" so that we may be able to provide accurate theoretical predictions of surfacegeometries. Our efforts in this program have concentrated in the areas of surface growthreaction pathways, surface reconstruction geometries, structural phase transitions, andhyrdogenation.10.1 Surface Reconstruction GeometriesUsing "first principles" total energy calculations, it is possible to determine on a mi-croscopic scale how atoms behave when they are on the surface of a solid. This is afundamental problem that has plagued both theorists and experimentalists for decades.The difficulty lies with the very strong interactions that may exist between the surfaceatoms and the host atoms constituting the rest of the solid. These interactions canstrongly disturb the original idealized atomic arrangement at the surface changing thenature of the bonding and even the original stoichiometry.In recent years there has been considerable activity focused on determining the exactequilibrium geometry of the [111] surfaces of the III-V compounds. In particular, theSemiconductor Surface Studies(111) As-terminated surface of GaAs stands out as a system that is very poorly under-stood. Even the relative abundance of Ga and As atoms in the surface region is notestablished with sufficient accurac . The multitude of diffraction patterns observed onthis surface (e.g., (2x2), (3x3), ( 19 x 19 )) and their sensitivity to preparation con-ditions make the problem very intriguing. The layer of exposed As atoms that consti-tutes the unreconstructed (111) bulk plane is apparently unstable leading to a richvariety of surface reactions and atomic arrangements. No model has yet to emerge asa satisfactory candidate for any of these reconstructions.In this work we have focused on the most stable observed pattern, namely the (2x2)reconstruction. The variety of structural models, for the reconstructions of this surface,that we have considered are shown in figure 10.1. The total energies for these struc-tures, calculated as a function of the relative chemical potential of Ga and As atoms aresummarized in figure 10.2.Figure 10.1. Structural models for the (111) surface (2x2) reconstructions. The first four atomic layers areshown in perspective. The atoms in each layer outline the (2x2) unit cell, in the ideal configuration. The sameatoms and their nearest neighbors are shown in the other reconstructions. Solid circles represent As atoms andempty circles represent Ga atoms. (a) Ideal surface. (b)Buckled geometry; a variation of this is thesubstitutional geometry. (c) Vacancy geometry; variations of this are Ga-vacancy plus Ga-substitutional ge-ometry and the Ga-vacancy plus As p -bonded geometry. (d) Adatom geometry. (e) Triangle geometry.From these results we can predict that phase transitions will occur, as the relativechemical potential scans its range, whenever two lowest energy lines cross and differentreconstructions become the lowest energy configuration. Note that two such crossingsoccur in figure 10.2. The results presented here are for perfectly equilibrated surfacesand care must be taken to include kinetic effects which can be crucial in certain cases.Thus the very low sticking coefficient of As indicates it is unlikely that As-adatommodels (either the single As adatom of the As-triangle) will be observable on the As-80 RLE Progress Report Number 130Semiconductor Surface Studies1StaggeredFAsV7 . aStg'g.. ,d \ . ,-,.,o,,-, IfianalSli l 0.0 1.0 (eV)Figure 10.2. Energy versus relative chemical potential by of the different reconstruciton models of the (111)surface. The range of by scans the values consistent with the Ga bulk and As2 gas reservoirs. The closed dotsare the calculated energies per (2x2) unit cell with respect to the ideal surface. The dashed line indicates theupper limit of Cby constistent with an As4 gas reservoir.terminated surface. It may, in fact, be rather difficult to simulate the surface As-richenvironment at all. It is more reasonable to suggest that an experimentally observedAs-rich reconstruction should be one of the two lowest energy geometries in the-0.3 < by < -0.1 eV range. That is, either the staggered As vacancy or the Ga-adatomconfigurations. We are inclined to favor the staggered As vacancy. On the other hand,the Ga-rich reconstruction is most certainly the Ga-triangle, both from energetic andstructural considerations. It is the lowest-energy geometry among all the negativestochiometry models and presents the most favorable coordination once all the surfaceAs and part of the surface Ga has been removed.10.2 Structural Phase TransitionsAll the calculations described in the previous section were at zero temperature. It isnow becoming possible, however, to begin studying the statistical mechanics andtemperature related phase transitions of surfaces of solids. This is a completely new andunexplored area. As an example, the myriad of surface reconstructions that may existon clean semiconductor surfaces at different temperatures is an extremely interestingand fundamental problem that needs to be investigated. Modern studies of phasetransitions utilize a powerful theoretical tool which is the renormalization group scheme.The scheme is based on scaling ideas, and has as input simple spin Hamiltonians whichmodel the degrees of freedom of the system. Until now there has been no way of cal-culating what these Hamiltonian parameters should be for real surfaces of solids. Thetotal energy calculations described above, however, should provide precisely the kindof information needed. The exciting possiblity then arises of coupling the results ofmicroscopic studies of surface systems (at zero temperature) with simple spinHamiltonians and the renormalization group approach to study phase transitions at fi-nite temperatures from "first principles."In the past, using a simple semi-empirical total energy approach we succeeded indeveloping such a scheme and have applied it to the Si(100) surface, resolving impor-Semiconductor Surface Studiestant questions regarding the structure of the Si(100) surface. We are investigating thepossible phase transitions that may occur on the Ge(100) surface. This system, how-ever, cannot be described accurately by a semi-empirical approach so that we are forcedto use the more powerful and much more complex ab-initio total energy method dis-cussed in section 10.1.To perform these studies we have been developing a new scheme for relaxing asystem with many degrees of freedom to its lowest energy configuration. The schemeis based on a molecular dynamics approach to calculating quantum mechanical totalenergies and resembles a simulated quench.Using this approach we have calculated the total energy of various dimer modelswith either (2x1) or C(4x2) symmetry. The lowest energy dimer configuration for eachrconstruction is shown in figure 10.3. We find, in particular, that the C(2x4) recon-struction is lower in energy that the (2x1) by 0.05 eV/dimer. The reason for this lies inthe relaxation of the atoms in the second layer with respect to the dimers. Moreover,we find for the C(2x4) case that the energy surface is surprisingly flat for lateral dis-placements of the dimers along the surface. This should result in a distinct softsurface-phonon mode for the system.At present we are performing total energy calculations on P(2x2) and C(2x2) re-constructions in order to have a large enough data-base to calculate a structural phasetransistion termperature for Ge(100).Figure 10.3. Perspective view of dimer models of the Ge(100) surface. The solid atoms are the surface layer.(a) Buckled (2x1) symmetry configuration. (b) Lowest- energy c (4x2)-symmetry dimer configuration ob-tained from our calculations.82 RLE Progress Report Number 130Semiconductor Surface Studies10.3 HydrogenationThe interaction of atomic hydrogen with cleaned semiconductor surfaces has beenextensively studied for over a decade. Hydrogen atoms appear to saturate surfacedangling bonds resulting in a nearly ideal, bulk-terminated plane of exposed surfaceatoms. It is interesting that in cases where the surface does not have the geometry andperiodicity of the bulk-terminated plane, the interaction of hydrogen with surface atomsis strong enough to unreconstruct the complicated reconstruction patterns. This proc-ess takes place for example on the (2x1) Si(l 111) surface, which exhibits a low-energy2-bonded-chain reconstruction. Upon hydrogenation this chain of Si atoms with (2x1)periodicity reverts to the (1xl) pattern of the bulk-terminated plane. Similarphenomema have been observed on the Ge(l 111) surface. Theoretically, this processis not very well understood and a realistic, first-principles study with adequated accu-racy to define precise low energy positions of atoms, corresponding total energies, andvibrational excitations above the ground state has been completely lacking.Recently we have undertaken precisely such a study. Using ab-initio quantum me-chanical total energy calculations, we find that the atomic positions of thehydrogenated Si and Ge( 11) surfaces differ significantly from those of an ideal bulkterminated plane. In particular, the Si-H and Ge-H bonds are found to be considerablylarger than the sum of covalent radii. The substrate relaxations are small and theirphysical origin can be explained in terms of electronic charge transfer which eliminatesthe surface dipole moment, by shifting charge from the hydrogen bond to the back-bonds. This is very clearly illustrated for both Si( 11):H and Ge(ll11):H by examiningthe total valence electron charge densities as shown in figure 10.4. As indicated in thethird panel for each system, charge transfer drives the relaxations in order to cancel thedipole moment induced by the difference in electronegativity between H and Si(Ge).Semiconductor Surface StudiesFigure 10.4. Valence charge density of Si(111):H and Ge(111):H plane. Open dots correspond to Si or Geatoms and solid dots to H atoms. The difference between the ideal and fully relaxed configurations is givenin the third panel for each case. Positive contours are shown in continuous lines, negative ones in dotted lines.84 RLE Progress Report Number 130difference x 8difference x 4.. .. ..

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