- Email: [email protected]
Theoretical modelling of semiconductor surfaces and interfaces
Vacuum 57 (2000) 121}129
Theoretical modelling of semiconductor surfaces and interfaces G.P. Srivastava* Department of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK
Abstract Progress in ab initio theoretical modelling of semiconductor surfaces and interfaces is reviewed. Results for equilibrium atomic geometry, electronic structure and bonding, using the plane wave pseudopotential method, are presented for clean Si(0 0 1) and III}<(1 1 0) surfaces, dissociative adsorption of NH on Si(0 0 1), dissociative adsorption of H S on III}<(1 1 0), and adsorption of elemental S on Si(0 0 1) and InP(0 0 1). The passivating nature of S, H S and NH adsorbates is discussed. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Density functional calculations; Pseudopotential; Surface relaxation; Surface states; Adsorption; Dissociation PACS: 71.15.M; 71.15.H; 68.35.B
1. Introduction Accurate determination of atomic geometry at a surface or interface and the corresponding electronic structure is vital in accessing technological applicability of a semiconductor device. A large number of experimental techniques are required to study di!erent aspects of atomic and electronic structure of such systems. In this respect, theoretical modelling of semiconductor surfaces and interfaces plays a very important role in surface science. In general, there are two principal requirements for such a modelling: structural representation of surface/interface and dealing with relevant interactions involving electrons and nuclei present in the system. The "rst issue is traditionally dealt with by modelling the system in the form of a "nite size cluster, a semi-in"nite slab, or a repeated slab (i.e. a supercell geometry). The second issue can
* Tel.: #44-1392-264-080; fax: #44-1392-264-111 . E-mail address: [email protected] (G.P. Srivastava). 0042-207X/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 0 ) 0 0 1 1 5 - 9
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be dealt with by using empirical forms of inter-atomic potential, or by employing ab initio methods to determine electron}ion and electron}electron interactions. This paper will provide a brief review of the progress made in theoretical modelling of semiconductor surfaces/interfaces using the supercell technique, based on ab initio pseudopotentials and the density functional theory. We will discuss general principles for surface reconstruction. Results of theoretical investigations of atomic geometry and electronic states will be presented for adsorption of elemental sulphur, and NH and H S molecules on semiconductor surfaces. These results will be compared with recent experimental investigations, and will be used to discuss mechanisms of surface passivation.
2. Supercell+pseudopotential+density functional method This is the most widely used method for surface studies. In this method, one considers an arti"cially repeated slab geometry along the normal to the surface under investigation. Each slab contains a "nite number, say M, of atomic layers with appropriate two-dimensional surface reconstruction, say (n;m). Neighbouring slabs are separated by a vacuum region which can "t a "nite number, say N, of atomic layers. The surface of interest can be represented as one or both sides of a slab. This construction leads to an arti"cially generated three-dimensional periodic system which, on the basis of Bloch's periodic conditions, can be described by a supercell containing p;n;m;M atoms, where p is the number of atoms in the primitive (1;1) surface unit cell. The slab and vacuum regions are chosen such that there is minimum interaction between the electronic wave functions from the two sides of a slab, and from two neighbouring slabs. This can be satis"ed for a supercell containing slab thicknesses with M*7 and vacuum regions corresponding to N*4. The quantum mechanical problem is set up by invoking several approximations. As chemical e!ects mainly arise from electrons in valence shells, core electrons can be frozen with their corresponding nuclei. This allows an atom to be considered as an ion core surrounded by (valence) electrons. The adiabatic approximation is used to decouple the motion of much heavier ions from that of the electrons. The ion}ion interaction is treated classically, with long range Coulomb e!ects usually handled by Ewald's summation method. The electronic part of the problem is solved fully quantum mechanically. The SchroK dinger equation is turned into the so-called Kohn}Sham equation which is goverened by the Hamiltonian in the form H"¹ #< #< . Here ¹ represents the kinetic energy operator corresponding to a set of non-interacting electron gas, < is a pseudopotential representing the interaction between electrons and ion cores, and < is a screening potential which includes the inter-electronic Coulomb repulsion and quantum mechanical exchange}correlation interactions. Norm-conserving, non-local, ionic pseudopotentials are generated from "rst-principles [1,2]. The screening potential has three contributions: < "< #< #< , viz. Hartree (Coulomb), exchange and correlation, respectively. The ex & change and correlation potentials are considered as a universal functional of electronic charge density. This is the so-called density functional theory [3,4]. In practice, either a local density approximation (LDA) or a generalised gradient approximation (GGA) is adopted for the evaluation of < . Within the LDA the central quantity of interest is the exchange}correlation energy per electron of a uniform gas. A number of prescriptions have been made available, with the
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Ceperley}Alder form [5] being the most widely used for semiconductors. The electronic charge density o, the central quantity of the density functional theory, is expressed as o(r)" " (r)", H where is the wave function of a "ctitious single-particle which satis"es the Kohn}Sham equation with the Hamiltonian given above, and the sum over j considers all occupied electronic states. The wave function can be expressed using a basis set of atomic orbitals, or plane waves, or a combination of plane waves and atomic orbitals. The resulting Kohn}Sham equation is solved self-consistently. From the solutions of the Kohn}Sham equation, the total energy per unit cell and the forces on all the atoms can be evaluated. Total energy and force results can be used to relax atoms towards their equilibrium con"guration. Details of such techniques can be found in [6}8].
3. Principles of surface relaxation, reconstruction and passivation Ideal termination of bulk semiconductors into surfaces leads to dangling chemical bonds which contain less than two spin-paired electrons. This is an undesirable situation and surface atoms re-adjust themselves to acquire a minimum in the system's free energy. One or more of four guiding principles can be involved in such a re-adjustment. In some cases surface atoms may simply relax their coordinates from the ideal bulk positions. On surfaces containing both cations and anions, atomic relaxation may be accompanied by more electronegative anions having their dangling bonds fully paired at the cost of less electronegative cations whose dangling bond become fully empty, following the so-called electron counting rule. In addition to relaxation, surface reconstruction may take place. Dangling bonds from neighbouring surface atoms may be coupled to create new bonds, leading to fully occupied or fully empty energy states. This process may involve formation of surface dimers or trimers. Finally, the requirement for the system's charge neutrality may result in a change in the surface chemical composition compared to the bulk. Detailed discusssions, with many examples, exist in the literature [9,10]. The relaxation and reconstruction phenomena may lead to semiconducting nature of a surface, but the bulk fundamental band gap may still contain occupied and/or unoccupied surface electronic states. Developing a process to remove or neutralise unwanted surface states from the band gap is central to the concept of passivation. This can be achieved by chemisorption of selected atoms or molecules with submonolayer, monolayer or thicker coverages on the surface in question. The chemisorbed species passivate surface dangling bonds and may, in addition, give rise to new electronic states. Chemisorption in general leads to substantial changes in the relaxation and reconstruction observed on the clean surface. As mentioned, chemisorption of only selected species can passivate a given surface. In experimental studies or technological applications, surface passivation is usually achieved by trialand-error methods, making the whole process quite an expensive exercise. Thus, understanding surface passivation mechanism and "nding the best passivating species for a chosen surface are important issues both fundamentally as well as from the technological point of view. In this paper, we will present a few examples of theoretical investigations of atomic and electronic structure of surfaces and interfaces, and discuss atomic-scale processes involved in passivation of surfaces.
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4. Clean and chemisorbed surfaces 4.1. Clean Si(0 0 1)-(2;1) surface The MBE grown Si(0 0 1) surface exhibits a c(4;2) reconstruction at low temperatures, which changes to a (2;1) reconstruction at room temperature. The building block of these reconstructions is surface dimer formation. For the bulk terminated geometry, i.e., for the ideal (1;1) structure, each atom of the (0 0 1) surface contains two partially occupied dangling bonds. Surface relaxation and reconstruction mechanisms combine together to lower the surface energy and make the system semiconducting. A ppr bond is formed by sharing of electrons in one dangling bond from each of two neighbouring silicon atoms along the [1 1 0] direction, leading to a (2;1) reconstruction with dimer formation. Atomic relaxation helps complete charge transfer from the remaining dangling bond at one dimer component to the other. The dimer component with the fully occupied dangling bond is pushed away from the bulk, while the other component relaxes towards the bulk. The vertical buckling between the dimer components is approximately 0.62 As and the dimer length is about 2.25 As [11]. The resulting surface is semiconducting, with a small band gap of around 0.12 eV within the LDA. (This value change to about 0.4 eV when a quasiparticle calculation is made.) Fig. 1 shows the geometry and band structure of the surface. 4.2. Chemisorption of elemental sulphur on Si(0 0 1)-(2;1) Recent experimental investigations [12] suggest that adsorption of elemental sulphur on Si(0 0 1) leads to a (2;1) structure for half-monolayer coverage (hemisulphide structure) and the unreconstructed (1;1) structure for full monolayer coverage (monosulphide structure). Of the two
Fig. 1. (a) Relaxed atomic geometry and (b) electronic states on the Si(0 0 1)(2;1) surface. The surface states D and D are localised at the up and down components of the dimer, respectively. The localised states n and nH result from the symmetrically constrained dimer geometry.
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coverages, the half-monolayer coverage with the hemisulphide structure totally passivates the Si(0 0 1) surface [13]. For this coverage S atoms are adsorbed on the bridge sites of the Si dimers. The calculated equilibrium geometry is shown in Fig. 2(a). The Si dimer becomes symmetric and is slightly elongated to a length of 2.30 As . The S}Si bond length is 2.17 As , and the Si}S}Si bond angle is 643. The perpendicular distance between the Si dimer and the S atom is 1.84 As , in excellent agreement with the experimentally obtained value of 1.87 As in [12]. For the hemisulphide structure the surface Si atoms become four-fold co-ordinated (but not in the typical tetrahedral form) and the S atoms are two-fold co-ordinated. Thus, the surface dangling bond states are saturated and the corresponding electronic states are pushed outside the fundamental band gap of silicon bulk. However, one fully occupied interface state is found just above the bulk valence continuum around the KM point on the surface Brillouin zone (see Fig. 2(b)). As shown in Fig. 2(c), this state has a novel character composed of the p orbital from S and the ungerade X n orbital at the symmetric dimer on the Si(0 0 1)(2;1) surface. 4.3. Chemisorption of ammonia on Si(0 0 1)-(2;1) The adsorption of the excellent nitration agent ammonia (NH ) is dissociative, with co-existence of the NH group and H at di!erent Si dimer components on the Si(0 0 1)(2;1) surface. First principles theoretical investigations of this structure have been made [14]. The chemisorption energy of (NH #H) : Si(0 0 1) relative to free NH and clean Si(0 0 1) surface is nearly 100 kcal/mol, clearly indicating that the process is exothermic. Fig. 3 shows the optimized
Fig. 2. Bridge geometry for half-monolayer coverage of S on Si(0 0 1)(2;1): (a) atomic geometry, (b) band structure, (c) orbital character of the highest occupied surface state. Distances are in As .
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Fig. 3. Atomic geometry for the dissociative adsorption of ammonia on Si(0 0 1)(2;1).
geometry. Upon the adsorption of NH , the Si dimer becomes almost symmetric (tilt angle smaller than 23) and gets elongated by approximately 5% to 2.36 As . The N}Si bond length is 1.75 As , and the Si}Si}N angle is approximately 1023. The inclination of the N}Si bond is 103 with respect to the surface normal. The Si}NH group retains the pyramidal geometry of the NH molecule. The theoretically obtained local atomic geometry of the NH species agrees reasonably well with the results determined from the photoelectron di!raction technique [15]. The dissociative adsorption of NH passivates the Si(0 0 1)(2;1) surface, with an occupied s-like nitrogen state lying just above the bulk continuum near the KM point. The Si}N bond is highly ionic in character. 4.4. Clean III}V(1 1 0) surfaces The clean cleaved III}<(1 1 0) surfaces of zincblende materials are perhaps the most studies and best understood. These surfaces retain their primitive (1;1) periodicity, but exhibit a well established relaxation pattern. Surface anions move away from the bulk, seeking a pyramidal-like geometry. Surface cations move into the bulk, seeking a planar-like geometry. The surface is thus characterized by a tilt of the cation}anion chain. This is indicated by the tilt angle u in Fig. 4(a). The angle u lies in the range 283}323 for III}Sb, III}As and III}P, but it takes a much smaller value for III}N [10,16]. As seen in Fig. 4(b), that there is a linear correlation between the surface buckling and the surface bond length [16]. The bulk band gap is usually free of surface states. The highest
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Fig. 4. The III}<(1 1 0) surface: (a) key structural parameters, (b) trend in vertical buckling of the surface chain.
surface state lies at least a few tenth of an eV below the bulk valence band maximum and is localized on surface anions. 4.5. Chemisorption of hydrogen disulphide on III}V(1 1 0) The atomic and electronic structure of adsorption of H S on III}<(1 1 0) surfaces has been studied in detail [17,18]. Similar to ammonia, the adsorption of H S also takes place dissociatively. The dissociated species H> and (SH)\ are attached to the surface anion and cation dangling bonds, respectively. Fig. 5(a) presents schematic relaxed geometry, obtained from theoretical investigations [19]. Upon the adsorption of the molecule, the tilt of the (1 1 0) surface layer for InP, GaAs and GaP lies in the range (!73)}(!53), i.e. it is reversed and now assumes a small magnitude. The vertical buckling of the top surface layer is reduced accordingly. The calculated perpendicular average distance between the sulphur atom and the topmost InP layer is 1.87 As , in reasonably good agreement with the X-ray standing wave measurement by Dudzik et al. [17]. Similar to NH , the adsorption of H S passivates III}<(1 1 0) surfaces. Fig. 5(b) shows the calculated electronic states for H S/InP(1 1 0) together with a comparison with data from angle resolved photoelectron spectroscopic measurements in [18]. While more work is needed to make a detailed comparison between experiment and theory, it is clear that there are no states in the bulk fundamental band gap. 4.6. Chemisorption of sulphur on InP(0 0 1) Successful sulphur passivation of III}<(0 0 1) surfaces have been reported (see, e.g. [20]). Tao et al. [21] concluded that the InP(0 0 1) surface is passivated by a full monolayer coverage of
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Fig. 5. Dissociative adsorption of H S on III}<(1 1 0): (a) schematic side view, (b) electronic states for the H S/InP(1 1 0) surface. In (b) open circles denote experimental angle-resolved photoemission data from [18] and solid curves represent the theoretical results.
S atoms, bonding exclusively to In and occupying the bridge sites corresponding to P vacancies, and leading to a (1;1) structure. However, Szuber [22] has shown that for S/GaAs(0 0 1) at room temperature both Ga}S and As}S bonds exist. Similarly, recent experiments [23] have provided evidence for thermodynamically favoured P}S exchange, with sub-surface sulphur on S/InP(0 0 1), leading to a (2;1) pattern. Theoretical investigations [24] indicate that the S/InP(0 0 1)(1;1) system, with S atoms in bridge positions, is metallic, in sharp contrast to the claim of the passivating nature observed in experiments. Further calculations for a stable (2;1) structure [25], with a full monolayer of S on the In-terminated surface and additional S replacing alternate P atoms in the second layer, suggest that the system is semiconducting but with a much smaller gap than the bulk band gap. Given the thermodynamic ability of S to strongly react with such surfaces, it is not surprising that more theoretical and experimental works are needed to understand sulphur passivation of III}<(0 0 1) surfaces.
5. Summary A brief review was presented for ab-initio theoretical investigations into atomic and electronic structure of clean and adsorbate covered semiconductor surfaces. Results of pseudopotential calculations, within the local density approximation, were presented for Si(0 0 1)(2;1), III}<(1 1 0), S/Si(0 0 1)(2;1), S/InP(0 0 1), NH /Si(0 0 1)(2;1), and H S/III}<(1 1 0) systems. Where possible, a comparison between theory and experiment was made. The theoretical results were interpreted in terms of the passivating nature of the adsorbates.
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References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25]
Bachelet GB, Hamann DR, SchluK ter M. Phys Rev B 1982;26:4199. Trullier N, Martins JL. Phys Rev B 1991;43:1993. Hohenberg P, Kohn W. Phys Rev 1964;136:B864. Kohn W, Sham LJ. Phys Rev 1965;140:A1133. Ceperley DM, Alder BJ. Phys Rev Lett 1980;45:566. Srivastava GP, Weaire D. Adv Phys 1986;36:463. Payne MC, Teter MP, Allan DC, Arias TA, Joannopoulos JD. Rev Mod Phys 1992;64:1045. Umerski A, Srivastava GP. Phys Rev B 1995;51:2334. Duke CB. Chem Rev 1996;96:1237. Srivastava GP. Rep Prog Phys 1997;60:561. Jenkins SJ, Srivastava GP. J Phys Condens Matter 1996;8:6641. Papageorgopoulos A, Corner A, Kamaratos M, Papageorgopoulos CA. Phys Rev B 1997;55:4435. C7 akmak M, Srivastava GP. J Appl Phys 1998;84:6070. Miotto R, Srivastava GP, Ferraz AC. Phys Rev B 1998;58:7944. Franco N, Avila J, Davila ME, Asensio MC, Woodru! DP, Scha! O, Fernandez V, Schindler KM, Fritzsche V, Bradshaw AM. Phys Rev Lett 1997;79:673. Miotto R, Srivastava GP, Ferraz AC. Surf Sci 1999;426:75. Dudzik E, Leslie A, O'Toole E, McGovern IT, Patchett A, Zahn DRT, Ludecke J, Woodru! DP, Cowie BCC. J Phys Condens Matter 1996;8:15. Dudzik E, Leslie A, O'Toole E, McGovern IT, Patchett A, Zahn DRT. Apply Surf Sci 1996;104/105:101. C7 akmak M, Srivastava GP. Phys Rev B 1998;57:4486. Szuber J, Hollinger G, Bergignat E. Electron Technol 1998;31:328. Tao Y, Yelon A, Sacher E, Lu ZH, Graham MJ. Appl Phys Lett 1992;60:2669. Szuber J. Res Placement Rep, Ecole Centrale de Lyon, 1995. Chasse T, Chasse A, Peisert H, Streubel P. Appl Phys A 1997;65:543. Ferraz AC, Srivastava GP. Surf Sci 1997;377}379:121. Ferraz AC, Srivastava GP. Appl Surf Sci 1999;142:23.
Theoretical modelling of semiconductor surfaces and interfaces G.P. Srivastava* Department of Physics, University of Exeter, Stocker Road, Exeter EX4 4QL, UK
Abstract Progress in ab initio theoretical modelling of semiconductor surfaces and interfaces is reviewed. Results for equilibrium atomic geometry, electronic structure and bonding, using the plane wave pseudopotential method, are presented for clean Si(0 0 1) and III}<(1 1 0) surfaces, dissociative adsorption of NH on Si(0 0 1), dissociative adsorption of H S on III}<(1 1 0), and adsorption of elemental S on Si(0 0 1) and InP(0 0 1). The passivating nature of S, H S and NH adsorbates is discussed. 2000 Elsevier Science Ltd. All rights reserved. Keywords: Density functional calculations; Pseudopotential; Surface relaxation; Surface states; Adsorption; Dissociation PACS: 71.15.M; 71.15.H; 68.35.B
1. Introduction Accurate determination of atomic geometry at a surface or interface and the corresponding electronic structure is vital in accessing technological applicability of a semiconductor device. A large number of experimental techniques are required to study di!erent aspects of atomic and electronic structure of such systems. In this respect, theoretical modelling of semiconductor surfaces and interfaces plays a very important role in surface science. In general, there are two principal requirements for such a modelling: structural representation of surface/interface and dealing with relevant interactions involving electrons and nuclei present in the system. The "rst issue is traditionally dealt with by modelling the system in the form of a "nite size cluster, a semi-in"nite slab, or a repeated slab (i.e. a supercell geometry). The second issue can
* Tel.: #44-1392-264-080; fax: #44-1392-264-111 . E-mail address: [email protected] (G.P. Srivastava). 0042-207X/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 0 ) 0 0 1 1 5 - 9
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be dealt with by using empirical forms of inter-atomic potential, or by employing ab initio methods to determine electron}ion and electron}electron interactions. This paper will provide a brief review of the progress made in theoretical modelling of semiconductor surfaces/interfaces using the supercell technique, based on ab initio pseudopotentials and the density functional theory. We will discuss general principles for surface reconstruction. Results of theoretical investigations of atomic geometry and electronic states will be presented for adsorption of elemental sulphur, and NH and H S molecules on semiconductor surfaces. These results will be compared with recent experimental investigations, and will be used to discuss mechanisms of surface passivation.
2. Supercell+pseudopotential+density functional method This is the most widely used method for surface studies. In this method, one considers an arti"cially repeated slab geometry along the normal to the surface under investigation. Each slab contains a "nite number, say M, of atomic layers with appropriate two-dimensional surface reconstruction, say (n;m). Neighbouring slabs are separated by a vacuum region which can "t a "nite number, say N, of atomic layers. The surface of interest can be represented as one or both sides of a slab. This construction leads to an arti"cially generated three-dimensional periodic system which, on the basis of Bloch's periodic conditions, can be described by a supercell containing p;n;m;M atoms, where p is the number of atoms in the primitive (1;1) surface unit cell. The slab and vacuum regions are chosen such that there is minimum interaction between the electronic wave functions from the two sides of a slab, and from two neighbouring slabs. This can be satis"ed for a supercell containing slab thicknesses with M*7 and vacuum regions corresponding to N*4. The quantum mechanical problem is set up by invoking several approximations. As chemical e!ects mainly arise from electrons in valence shells, core electrons can be frozen with their corresponding nuclei. This allows an atom to be considered as an ion core surrounded by (valence) electrons. The adiabatic approximation is used to decouple the motion of much heavier ions from that of the electrons. The ion}ion interaction is treated classically, with long range Coulomb e!ects usually handled by Ewald's summation method. The electronic part of the problem is solved fully quantum mechanically. The SchroK dinger equation is turned into the so-called Kohn}Sham equation which is goverened by the Hamiltonian in the form H"¹ #< #< . Here ¹ represents the kinetic energy operator corresponding to a set of non-interacting electron gas, < is a pseudopotential representing the interaction between electrons and ion cores, and < is a screening potential which includes the inter-electronic Coulomb repulsion and quantum mechanical exchange}correlation interactions. Norm-conserving, non-local, ionic pseudopotentials are generated from "rst-principles [1,2]. The screening potential has three contributions: < "< #< #< , viz. Hartree (Coulomb), exchange and correlation, respectively. The ex & change and correlation potentials are considered as a universal functional of electronic charge density. This is the so-called density functional theory [3,4]. In practice, either a local density approximation (LDA) or a generalised gradient approximation (GGA) is adopted for the evaluation of < . Within the LDA the central quantity of interest is the exchange}correlation energy per electron of a uniform gas. A number of prescriptions have been made available, with the
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Ceperley}Alder form [5] being the most widely used for semiconductors. The electronic charge density o, the central quantity of the density functional theory, is expressed as o(r)" " (r)", H where is the wave function of a "ctitious single-particle which satis"es the Kohn}Sham equation with the Hamiltonian given above, and the sum over j considers all occupied electronic states. The wave function can be expressed using a basis set of atomic orbitals, or plane waves, or a combination of plane waves and atomic orbitals. The resulting Kohn}Sham equation is solved self-consistently. From the solutions of the Kohn}Sham equation, the total energy per unit cell and the forces on all the atoms can be evaluated. Total energy and force results can be used to relax atoms towards their equilibrium con"guration. Details of such techniques can be found in [6}8].
3. Principles of surface relaxation, reconstruction and passivation Ideal termination of bulk semiconductors into surfaces leads to dangling chemical bonds which contain less than two spin-paired electrons. This is an undesirable situation and surface atoms re-adjust themselves to acquire a minimum in the system's free energy. One or more of four guiding principles can be involved in such a re-adjustment. In some cases surface atoms may simply relax their coordinates from the ideal bulk positions. On surfaces containing both cations and anions, atomic relaxation may be accompanied by more electronegative anions having their dangling bonds fully paired at the cost of less electronegative cations whose dangling bond become fully empty, following the so-called electron counting rule. In addition to relaxation, surface reconstruction may take place. Dangling bonds from neighbouring surface atoms may be coupled to create new bonds, leading to fully occupied or fully empty energy states. This process may involve formation of surface dimers or trimers. Finally, the requirement for the system's charge neutrality may result in a change in the surface chemical composition compared to the bulk. Detailed discusssions, with many examples, exist in the literature [9,10]. The relaxation and reconstruction phenomena may lead to semiconducting nature of a surface, but the bulk fundamental band gap may still contain occupied and/or unoccupied surface electronic states. Developing a process to remove or neutralise unwanted surface states from the band gap is central to the concept of passivation. This can be achieved by chemisorption of selected atoms or molecules with submonolayer, monolayer or thicker coverages on the surface in question. The chemisorbed species passivate surface dangling bonds and may, in addition, give rise to new electronic states. Chemisorption in general leads to substantial changes in the relaxation and reconstruction observed on the clean surface. As mentioned, chemisorption of only selected species can passivate a given surface. In experimental studies or technological applications, surface passivation is usually achieved by trialand-error methods, making the whole process quite an expensive exercise. Thus, understanding surface passivation mechanism and "nding the best passivating species for a chosen surface are important issues both fundamentally as well as from the technological point of view. In this paper, we will present a few examples of theoretical investigations of atomic and electronic structure of surfaces and interfaces, and discuss atomic-scale processes involved in passivation of surfaces.
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4. Clean and chemisorbed surfaces 4.1. Clean Si(0 0 1)-(2;1) surface The MBE grown Si(0 0 1) surface exhibits a c(4;2) reconstruction at low temperatures, which changes to a (2;1) reconstruction at room temperature. The building block of these reconstructions is surface dimer formation. For the bulk terminated geometry, i.e., for the ideal (1;1) structure, each atom of the (0 0 1) surface contains two partially occupied dangling bonds. Surface relaxation and reconstruction mechanisms combine together to lower the surface energy and make the system semiconducting. A ppr bond is formed by sharing of electrons in one dangling bond from each of two neighbouring silicon atoms along the [1 1 0] direction, leading to a (2;1) reconstruction with dimer formation. Atomic relaxation helps complete charge transfer from the remaining dangling bond at one dimer component to the other. The dimer component with the fully occupied dangling bond is pushed away from the bulk, while the other component relaxes towards the bulk. The vertical buckling between the dimer components is approximately 0.62 As and the dimer length is about 2.25 As [11]. The resulting surface is semiconducting, with a small band gap of around 0.12 eV within the LDA. (This value change to about 0.4 eV when a quasiparticle calculation is made.) Fig. 1 shows the geometry and band structure of the surface. 4.2. Chemisorption of elemental sulphur on Si(0 0 1)-(2;1) Recent experimental investigations [12] suggest that adsorption of elemental sulphur on Si(0 0 1) leads to a (2;1) structure for half-monolayer coverage (hemisulphide structure) and the unreconstructed (1;1) structure for full monolayer coverage (monosulphide structure). Of the two
Fig. 1. (a) Relaxed atomic geometry and (b) electronic states on the Si(0 0 1)(2;1) surface. The surface states D and D are localised at the up and down components of the dimer, respectively. The localised states n and nH result from the symmetrically constrained dimer geometry.
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coverages, the half-monolayer coverage with the hemisulphide structure totally passivates the Si(0 0 1) surface [13]. For this coverage S atoms are adsorbed on the bridge sites of the Si dimers. The calculated equilibrium geometry is shown in Fig. 2(a). The Si dimer becomes symmetric and is slightly elongated to a length of 2.30 As . The S}Si bond length is 2.17 As , and the Si}S}Si bond angle is 643. The perpendicular distance between the Si dimer and the S atom is 1.84 As , in excellent agreement with the experimentally obtained value of 1.87 As in [12]. For the hemisulphide structure the surface Si atoms become four-fold co-ordinated (but not in the typical tetrahedral form) and the S atoms are two-fold co-ordinated. Thus, the surface dangling bond states are saturated and the corresponding electronic states are pushed outside the fundamental band gap of silicon bulk. However, one fully occupied interface state is found just above the bulk valence continuum around the KM point on the surface Brillouin zone (see Fig. 2(b)). As shown in Fig. 2(c), this state has a novel character composed of the p orbital from S and the ungerade X n orbital at the symmetric dimer on the Si(0 0 1)(2;1) surface. 4.3. Chemisorption of ammonia on Si(0 0 1)-(2;1) The adsorption of the excellent nitration agent ammonia (NH ) is dissociative, with co-existence of the NH group and H at di!erent Si dimer components on the Si(0 0 1)(2;1) surface. First principles theoretical investigations of this structure have been made [14]. The chemisorption energy of (NH #H) : Si(0 0 1) relative to free NH and clean Si(0 0 1) surface is nearly 100 kcal/mol, clearly indicating that the process is exothermic. Fig. 3 shows the optimized
Fig. 2. Bridge geometry for half-monolayer coverage of S on Si(0 0 1)(2;1): (a) atomic geometry, (b) band structure, (c) orbital character of the highest occupied surface state. Distances are in As .
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Fig. 3. Atomic geometry for the dissociative adsorption of ammonia on Si(0 0 1)(2;1).
geometry. Upon the adsorption of NH , the Si dimer becomes almost symmetric (tilt angle smaller than 23) and gets elongated by approximately 5% to 2.36 As . The N}Si bond length is 1.75 As , and the Si}Si}N angle is approximately 1023. The inclination of the N}Si bond is 103 with respect to the surface normal. The Si}NH group retains the pyramidal geometry of the NH molecule. The theoretically obtained local atomic geometry of the NH species agrees reasonably well with the results determined from the photoelectron di!raction technique [15]. The dissociative adsorption of NH passivates the Si(0 0 1)(2;1) surface, with an occupied s-like nitrogen state lying just above the bulk continuum near the KM point. The Si}N bond is highly ionic in character. 4.4. Clean III}V(1 1 0) surfaces The clean cleaved III}<(1 1 0) surfaces of zincblende materials are perhaps the most studies and best understood. These surfaces retain their primitive (1;1) periodicity, but exhibit a well established relaxation pattern. Surface anions move away from the bulk, seeking a pyramidal-like geometry. Surface cations move into the bulk, seeking a planar-like geometry. The surface is thus characterized by a tilt of the cation}anion chain. This is indicated by the tilt angle u in Fig. 4(a). The angle u lies in the range 283}323 for III}Sb, III}As and III}P, but it takes a much smaller value for III}N [10,16]. As seen in Fig. 4(b), that there is a linear correlation between the surface buckling and the surface bond length [16]. The bulk band gap is usually free of surface states. The highest
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Fig. 4. The III}<(1 1 0) surface: (a) key structural parameters, (b) trend in vertical buckling of the surface chain.
surface state lies at least a few tenth of an eV below the bulk valence band maximum and is localized on surface anions. 4.5. Chemisorption of hydrogen disulphide on III}V(1 1 0) The atomic and electronic structure of adsorption of H S on III}<(1 1 0) surfaces has been studied in detail [17,18]. Similar to ammonia, the adsorption of H S also takes place dissociatively. The dissociated species H> and (SH)\ are attached to the surface anion and cation dangling bonds, respectively. Fig. 5(a) presents schematic relaxed geometry, obtained from theoretical investigations [19]. Upon the adsorption of the molecule, the tilt of the (1 1 0) surface layer for InP, GaAs and GaP lies in the range (!73)}(!53), i.e. it is reversed and now assumes a small magnitude. The vertical buckling of the top surface layer is reduced accordingly. The calculated perpendicular average distance between the sulphur atom and the topmost InP layer is 1.87 As , in reasonably good agreement with the X-ray standing wave measurement by Dudzik et al. [17]. Similar to NH , the adsorption of H S passivates III}<(1 1 0) surfaces. Fig. 5(b) shows the calculated electronic states for H S/InP(1 1 0) together with a comparison with data from angle resolved photoelectron spectroscopic measurements in [18]. While more work is needed to make a detailed comparison between experiment and theory, it is clear that there are no states in the bulk fundamental band gap. 4.6. Chemisorption of sulphur on InP(0 0 1) Successful sulphur passivation of III}<(0 0 1) surfaces have been reported (see, e.g. [20]). Tao et al. [21] concluded that the InP(0 0 1) surface is passivated by a full monolayer coverage of
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Fig. 5. Dissociative adsorption of H S on III}<(1 1 0): (a) schematic side view, (b) electronic states for the H S/InP(1 1 0) surface. In (b) open circles denote experimental angle-resolved photoemission data from [18] and solid curves represent the theoretical results.
S atoms, bonding exclusively to In and occupying the bridge sites corresponding to P vacancies, and leading to a (1;1) structure. However, Szuber [22] has shown that for S/GaAs(0 0 1) at room temperature both Ga}S and As}S bonds exist. Similarly, recent experiments [23] have provided evidence for thermodynamically favoured P}S exchange, with sub-surface sulphur on S/InP(0 0 1), leading to a (2;1) pattern. Theoretical investigations [24] indicate that the S/InP(0 0 1)(1;1) system, with S atoms in bridge positions, is metallic, in sharp contrast to the claim of the passivating nature observed in experiments. Further calculations for a stable (2;1) structure [25], with a full monolayer of S on the In-terminated surface and additional S replacing alternate P atoms in the second layer, suggest that the system is semiconducting but with a much smaller gap than the bulk band gap. Given the thermodynamic ability of S to strongly react with such surfaces, it is not surprising that more theoretical and experimental works are needed to understand sulphur passivation of III}<(0 0 1) surfaces.
5. Summary A brief review was presented for ab-initio theoretical investigations into atomic and electronic structure of clean and adsorbate covered semiconductor surfaces. Results of pseudopotential calculations, within the local density approximation, were presented for Si(0 0 1)(2;1), III}<(1 1 0), S/Si(0 0 1)(2;1), S/InP(0 0 1), NH /Si(0 0 1)(2;1), and H S/III}<(1 1 0) systems. Where possible, a comparison between theory and experiment was made. The theoretical results were interpreted in terms of the passivating nature of the adsorbates.
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