Diffusion of Atomic Oxygen on the Si(100) Surface Pooja Arora Iowa State University

Chemistry Publications Chemistry

7-2010 Diffusion of Atomic Oxygen on the Si(100) Surface Pooja Arora Iowa State University

Wei Li Michigan State University

Piotr Piecuch Michigan State University

James W. Evans Iowa State University, [email protected]

Marvin Argulla Albao Iowa State University

SeFoe nelloxtw pa thige fors aaddndition addal aitutionhorsal works at: http://lib.dr.iastate.edu/chem_pubs Part of the Applied Mathematics Commons, Astrophysics and Astronomy Commons, and the Chemistry Commons The ompc lete bibliographic information for this item can be found at http://lib.dr.iastate.edu/ chem_pubs/534. For information on how to cite this item, please visit http://lib.dr.iastate.edu/ howtocite.html.

This Article is brought to you for free and open access by the Chemistry at Iowa State University Digital Repository. It has been accepted for inclusion in Chemistry Publications by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. Diffusion of Atomic Oxygen on the Si(100) Surface

Abstract The processes of etching and diffusion of atomic oxygen on the reconstructed Si(100)-2 × 1 surface are investigated using an embedded cluster QM/MM (Quantum Mechanics/Molecular Mechanics) method, called SIMOMM (Surface Integrated Molecular Orbital Molecular Mechanics). Hopping of an oxygen atom along the silicon dimer rows on a Si15H16 cluster embedded in an Si136H92 MM cluster model is studied using the SIMOMM/UB3LYP (unrestricted density functional theory (UDFT) with the Becke three- parameter Lee−Yang−Parr (B3LYP) hybrid functional) approach, the Hay−Wadt effective core potential, and its associated double-ζ plus polarization basis set. The er lative energies at stationary points on the diffusion potential energy surface were also obtained with three coupled-cluster (CC) methods, including the canonical CC approach with singles, doubles, and noniterative quasi-perturbative triples (CCSD(T)), the canonical left-eigenstate completely renormalized (CR) analogue of CCSD(T), termed CR-CC(2,3), and the linear scaling variant of CR-CC(2,3) employing the cluster-in-molecule (CIM) local correlation ansatz, abbreviated as CIM-CR-CC(2,3). The ap thway and energetics for the diffusion of oxygen from one dimer to another are presented, with the activation energy estimated to be 71.9 and 74.4 kcal/mol at the canonical CR- CC(2,3)/6-31G(d) and extrapolated, CIM-based, canonical CR-CC(2,3)/6-311G(d) levels of theory, respectively. The canonical and CIM CR-CC(2,3)/6-31G(d) barrier heights (excluding zero point vibrational energy contributions) for the etching process are both 87.3 kcal/mol.

Disciplines Applied Mathematics | Astrophysics and Astronomy | Chemistry

Authors Pooja Arora, Wei Li, Piotr Piecuch, James W. Evans, Marvin Argulla Albao, and Mark S. Gordon

This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/chem_pubs/534 J. Phys. Chem. C 2010, 114, 12649–12658 12649

Diffusion of Atomic Oxygen on the Si(100) Surface

Pooja Arora,† Wei Li,‡ Piotr Piecuch,‡ James W. Evans,§ Marvin Albao,§,| and Mark S. Gordon*,† Department of Chemistry and Ames Laboratory, Iowa State UniVersity, Ames, Iowa 50011, Department of Chemistry, Michigan State UniVersity, East Lansing, Michigan 48824, Ames Laboratory and Departments of Physics & Astronomy and Mathematics, Iowa State UniVersity, Ames, Iowa 50011, and Insitute of Mathematical Science and Physics, UniVersity of the Philippines Los Banos, Laguna 4031, Philippines ReceiVed: April 2, 2010; ReVised Manuscript ReceiVed: June 5, 2010

The processes of etching and diffusion of atomic oxygen on the reconstructed Si(100)-2 × 1 surface are investigated using an embedded cluster QM/MM (Quantum Mechanics/Molecular Mechanics) method, called SIMOMM (Surface Integrated Molecular Orbital Molecular Mechanics). Hopping of an oxygen atom along the silicon dimer rows on a Si15H16 cluster embedded in an Si136H92 MM cluster model is studied using the SIMOMM/UB3LYP (unrestricted density functional theory (UDFT) with the Becke three-parameter Lee-Yang-Parr (B3LYP) hybrid functional) approach, the Hay-Wadt effective core potential, and its associated double- plus polarization basis set. The relative energies at stationary points on the diffusion potential energy surface were also obtained with three coupled-cluster (CC) methods, including the canonical CC approach with singles, doubles, and noniterative quasi-perturbative triples (CCSD(T)), the canonical left- eigenstate completely renormalized (CR) analogue of CCSD(T), termed CR-CC(2,3), and the linear scaling variant of CR-CC(2,3) employing the cluster-in-molecule (CIM) local correlation ansatz, abbreviated as CIM- CR-CC(2,3). The pathway and energetics for the diffusion of oxygen from one dimer to another are presented, with the activation energy estimated to be 71.9 and 74.4 kcal/mol at the canonical CR-CC(2,3)/6-31G(d) and extrapolated, CIM-based, canonical CR-CC(2,3)/6-311G(d) levels of theory, respectively. The canonical and CIM CR-CC(2,3)/6-31G(d) barrier heights (excluding zero point vibrational energy contributions) for the etching process are both 87.3 kcal/mol.

1. Introduction is very important to attain uniformity and precision in the size and shape of microelectronic devices, including transistors and The silicon atoms of the topmost layer of the Si(100) surface capacitors that are made of semiconductor material such as can form covalent bonds with adjacent surface atoms to form silicon.7,15,16 Therefore, understanding the mechanisms of ad- pairs called silicon dimers. The surface reconstructs by forming sorption, diffusion, and desorption of oxygen on the silicon silicon dimer rows as shown in Figure 1. Even after the surface at the atomic level is crucial. reconstruction, the dimer Si atoms are bonded to only three other The main goal of this paper is to study the detailed mechanism atoms. Since Si does not readily form π bonds, these surface × Si atoms are highly reactive. A common terminology is to say of the diffusion of atomic oxygen on the Si(100)-2 1 surface that the surface Si atoms have “dangling bonds”.1 from one Si dimer to an adjacent dimer. Repeated hopping between adjacent dimers leads to long-range diffusion of oxygen The Si(100)-2 × 1 surface oxidizes to form silicon dioxide along dimer rows, a key process for oxide island formation. To (SiO ) by thermal oxidation. Silicon dioxide is known to be an 2 study this mechanism, a quantum mechanics/molecular mechan- insulator,2,3 which has technological importance in the fabrica- ics (QM/MM) hybrid approach, referred to as the surface tion/doping of microelectronic devices.4-7 The silicon dioxide integrated molecular orbital MM (SIMOMM)17 model, has been film formed on the silicon surface due to thermal oxidation acts used. SIMOMM is a computationally less expensive method to block a dopant from reaching the silicon surface. than full quantum mechanical calculations on a given size Several studies have been reported on the oxidation of the system and can account for the chemistry of the surface atoms 8-12 silicon surface. Depending upon the surface temperature and as well as (to some degree) the bulk effects in large clusters oxygen pressure, active oxidation/etching by oxygen or passive with reasonable accuracy. The SIMOMM method has been used 13,14 oxidation/oxide formation can occur. At low-T or high-P, in several studies on Si(100)18-20 and SiC(100)21 surfaces. passive oxidation is observed, resulting in the formation of an An additional goal is to explore the SiO desorption/etching oxide film on the surface. At high-T or low-P, removal of Si mechanism at higher levels of theory than those that were used by desorption of volatile SiO (etching) is observed. Controlling earlier, to assess the accuracy of previously reported barrier the process of oxidation and etching by varying the conditions heights.22 This involves calculations at three different levels of * To whom correspondence should be addressed. coupled-cluster (CC) theory, namely, the canonical CC approach † Department of Chemistry and Ames Laboratory, Iowa State University. with singles (S), doubles (D), and noniterative quasiperturbative ‡ Department of Chemistry, Michigan State University. triples (T), i.e., CCSD(T),23 the left-eigenstate completely § Ames Laboratory and Departments of Physics & Astronomy and renormalized (CR) analogue of canonical CCSD(T), termed Mathematics, Iowa State University. 24-26 | Insitute of Mathematical Science and Physics, University of the CR-CC(2,3), and the linear scaling extension of CR-CC(2,3) Philippines Los Banos. employing a suitably modified variant of the local correlation 10.1021/jp102998y  2010 American Chemical Society Published on Web 07/06/2010 12650 J. Phys. Chem. C, Vol. 114, No. 29, 2010 Arora et al.

Figure 1. Si(100) surface reconstruction.

calculations are augmented by the canonical and CIM CR- CC(2,3) calculations, since some of the stationary points on the pathway describing the diffusion process have a significant diradical character.20,33 As illustrated below, the CR-CC(2,3) approach is capable of removing failures of CCSD(T) in regions of the potential energy surface (PES) that exhibit significant diradical character.24-26,34-41 Some of the earlier studies of the reaction mechanisms for the oxidation and etching processes have been described22,42-44 using QM/MM and kinetic Monte Carlo (KMC)45 simulation methods. The QM/MM method is described above. KMC45 is a method to analyze the evolution of lattice-gas models describing the configuration of oxygen adatoms and oxide islands on the Si(100) surface, given that rates for all relevant processes are specified. Choi et al.22 studied the mechanism for the SiO desorption process using the SIMOMM model. The geometries were obtained using the complete active space self- consistent field (CASSCF) method and the effective core potential (ECP) HW(d) basis set.46 This was augmented by multireference second-order perturbation (MRMP2) theory47 with a mixed basis set: HW(d) for the silicon atoms and the 6-311G(d) basis set48 for the oxygen atom. These authors calculated the overall barrier for the SiO desorption process to be 89.8 kcal/mol. This is a little higher than the 83.0-87.6 kcal/ mol barrier predicted by Uchiyama et al.49 using plane wave density functional theory (DFT) within the generalized gradient Figure 2. Previously suggested stationary points for the etching approximation (GGA).50 Another KMC simulation predicted the mechanism obtained by Choi et al. at CASSCF(8,7)/HW(d) geometries: SiO desorption barrier to be in the range 73.8-80.7 kcal/mol,43 (a) on top structure; (b) TS between a and c; (c) back-bond structure; but the modeling incorporated assumptions regarding O diffusion (d) TS connecting c and e; (e) minimum with trivalent O atom; (f) TS and oxide formation. An experimental value (79.3 kcal/mol) connecting e and g; (g) minimum with triangle configuration. See ref 22. was determined by employing X-ray photoelectron spectroscopy (XPS) and supersonic molecular beam techniques.13 In another cluster-in-molecule (CIM) ansatz of refs 27 and 28, developed experiment, the etching barrier, as measured by TPD (temper- in refs 29-32, abbreviated as CIM-CR-CC(2,3). The canonical ature programmed desorption) studies,8,14 is in the range of CCSD(T), canonical CR-CC(2,3), and CIM-CR-CC(2,3) ap- 80-90 kcal/mol. So, the experiments have reported an approaches are also applied to the diffusion of the oxygen atom proximately 10 kcal/mol range for this barrier height. The on the Si(100)-2 × 1 surface. The two processes of interest experimental uncertainties increase this range. here, diffusion and etching, are not entirely disconnected, since Figure 2 (adapted form ref 22) shows the SiO desorption one key structure (referred to below as the back-bond species) stationary points (minima and transition states (TSs)) for the plays a central role in both processes. The traditional CCSD(T) etching mechanism proposed by Choi et al.22 Structure a Diffusion of Atomic Oxygen on the Si(100) Surface J. Phys. Chem. C, Vol. 114, No. 29, 2010 12651

Figure 3. The SIMOMM model of Si15H16 QM region (in blue) embedded in a Si136H92 MM cluster (in black). Side and top views are shown. represents the on-top structure, in which the oxygen atom is on top of one of the silicon dimer atoms; structure c is the back- bond structure, a minimum on the PES, in which the oxygen atom is bonded to a Si atom of the surface and to a silicon atom in the next layer; b is the TS between the on-top and back- bond species. Structure g is formed just before the final etched product of the SiO desorption mechanism is formed. The final etched product is also referred to as SOLA21 (Si surface with One Less silicon Atom) and is formed after one silicon atom has been removed by an oxygen atom. Long-range diffusion of the oxygen atom between surface dimers was previously studied using the KMC simulation method by Pelz and co-workers.51 They employed a 55.3-57.7 kcal/mol diffusion activation energy. Another KMC study by Esteve et al. assumed the activation energy to be 57.6 kcal/ mol.52 A plane wave DFT/GGA study by Hemeryck et al. most recently predicted the activation energy for the diffusion process Figure 4. Top and side views of the Si15H16 cluster. to be 42.8 kcal/mol.10 These authors used a pseudopotential,53,54 and modeled the Si(100) surface as a periodic slab to simulate The present paper examines the role of the back-bond species the bulk. So, there is a 15 kcal/mol range in the theoretical and other stationary points on the PES for the diffusion of × predictions. Experimental scanning tunneling microscopy (STM) oxygen on the Si(100)-2 1 surface using the SIMOMM QM/ measurements were used by Pelz and co-workers55,56 to study MM approach, augmented with CC calculations. the oxidation of Si(100). They predicted the activation energy 2. Computational Methods for the diffusion process to be 56.3 kcal/mol. Several secondary ion mass spectrometry (SIMS) experiments have also been The SIMOMM model employed here is composed of a QM performed to study the diffusion of oxygen atoms at the Si/ Si15H16 (two-dimer) quantum region embedded in a larger 57-59 SiO2 interface. The values predicted by SIMS experiments Si136H92 MM cluster, as shown in Figure 3. The Si15H16 cluster are in the range of 41.5 to 76.1 kcal/mol. So, the experiments is shown in Figure 4. The QM/MM system is a much bigger on the diffusion process do not appear to be definitive, nor are cluster containing 9 Si-Si dimers and is 9 layers deep, as shown the previous DFT and KMC calculations. The central result that in Figure 3. arises from most of the previous studies is that an important To study the diffusion process, the QM/MM (OSi136H92) structure in the diffusion mechanism is the back-bond species. clusters were optimized using unrestricted DFT (UDFT)/ 12652 J. Phys. Chem. C, Vol. 114, No. 29, 2010 Arora et al.

Figure 5. The active space orbitals used in the calculation of SiO desorption barrier.

SIMOMM with the Becke three-parameter Lee-Yang-Parr subsystem design are the assignment of “central occupied (B3LYP) hybrid functional.60-63 The HW ECP basis set46 LMOs”, which are used to generate each CIM subsystem, to augmented with one set of d polarization functions was used atoms in a molecule of interest, and the use of a single parameter for the O and Si atoms, and the 3-21G basis set64 was employed to identify additional “environment LMOs” that are associated for the H atoms in the QM cluster. The 6-31G(d) basis set65,66 with the central LMOs of each CIM subsystem. A given was also employed to assess basis set effects. The most accurate occupied LMO j is recognized as an orbital belonging to the relative energies characterizing the diffusion pathway were then environment of a specific central LMO i if the absolute value obtained with the CC methods. As mentioned in the Introduc- of the off-diagonal element of the Fock matrix, |〈i| f |j〉|, is tion, the two canonical CC methods used in this study were greater than .32 Throughout this paper, a CIM-CC calculation CCSD(T) and CR-CC(2,3), both with the 6-31G(d) basis set. with a given value is abbreviated CIM()-CC. For example, The CR-CC(2,3) approach was used because it can account for CIM(0.005)-CR-CC(2,3) refers to the CIM-CR-CC(2,3) ap- the significant diradical character that has been observed in proach with ) 0.005. The basis sets used in the CIM-CR- previous work on this surface.20,33 The CC relative energies were CC(2,3) calculations for the stationary points along the diffusion calculated at the SIMOMM:UB3LYP/6-31G(d) optimized ge- pathway were 6-31G(d) and 6-311G(d). Much of the CIM-CC ometries, using the SIMOMM:UB3LYP/6-31G(d) zero point effort in this work focuses on the so-called mixed CIM-CR- vibrational energy corrections as well. Note that the CC CC(2,3) calculations,29-31 in which one adds the local triples calculations were performed only on the QM clusters, since the correction of CR-CC(2,3) to the canonical CCSD energy. main effect of the bulk contained in the embedded cluster model To study the SiO desorption/etching process, the QM/MM 67 will be on the predicted structure. (OSi136H92) structures were optimized using the SIMOMM: Recently, the Piecuch group developed local correlation CASSCF(12,11) method, where the notation (12,11) means that extensions of CCSD, CCSD(T), and CR-CC(2,3), based on 12 electrons are distributed in all possible ways among the 11 refined versions of the CIM ansatz, abbreviated CIM-CCSD, orbitals in the CASSCF active space. The CASSCF active CIM-CCSD(T), and CIM-CR-CC(2,3).29-32 The CIM-CC meth- orbitals for the SiO desorption process are shown in Figure 5. ods are characterized by the use of orthonormal localized The active space includes the π and π* SiO orbitals and molecular orbitals (LMOs), natural coarse grain parallelism, electrons (a (4,4) space), the bonding and antibonding orbitals noniterative character of local triples corrections of CCSD(T) of the newly formed Si-Si σ bond (a (2,2) space), the two and CR-CC(2,3), and low-order scaling of CPU time with the dangling bonds on silicon (a (2,2) space), and the σ and σ* system size, replacing the N6 and N7 steps of the canonical SiO orbitals and electrons and the 3s orbital on the Si in SiO (a CCSD and CCSD(T)/CR-CC(2,3) approaches by steps that scale (4,3) space). As noted above, the HW ECP basis set was used linearly with the size of the system once the system becomes for the O and Si atoms, and the 3-21G basis set was used for large enough. Thus, they can be applied to larger molecular the H atoms in the QM cluster. In addition to the HW(d) basis problems of the type studied in this work. Much of the success set, the 6-31G(d) basis set was also used to optimize the of the CIM-CC methods depends on the appropriate design of geometry of the QM/MM cluster. To incorporate dynamic the local orbital domains called CIM subsystems. This work correlation, single point energy calculations were subsequently adopts a CIM subsystem design that defines the so-called single- performed with the SIMOMM:MRMP2(12,11)/6-31G(d) method environment CIM approach.32 The main characteristics of this at the SIMOMM:CASSCF(12,11)/6-31G(d) geometries. The Diffusion of Atomic Oxygen on the Si(100) Surface J. Phys. Chem. C, Vol. 114, No. 29, 2010 12653

Figure 6. Stationary points a to e on the O atom diffusion path along adjacent Si-Si dimers obtained with SIMOMM:UB3LYP/6-31G(d): (a) on-top structure; (b) TS connecting a and c; (c) back-bond (Si1-Si6) structure; (d) TS with a trivalent oxygen connecting c and e; (e) back-bond (Si3-Si6) structure. Stationary points c and f are also on the etching PES, with f representing the SOLA+SiO etched products. The CASSCF values from ref 22 are given in parentheses. etching barrier was also calculated using the canonical CCSD 73-75 were used for the MM part of the calculations. The QM/ and CR-CC(2,3) approaches, and the pure and mixed CIM-CR- MM (SIMOMM) calculations were carried out using the CC(2,3) methods, all using the 6-31G(d) basis set at the GAMESS/Tinker interface.76,77 SIMOMM:CASSCF(12,11)/6-31G(d) geometries. As noted above, the CC calculations were performed only on the QM 3. Results and Discussion cluster. A. Comparison of the UB3LYP and CASSCF Geometries. All geometries were fully optimized in both the QM and MM SIMOMM:CASSCF(12,11)/HW(d) geometry optimizations were regions. All of the stationary points, including minima and TS carried out for the structures including TS (b) and on-top (a) structures, were characterized by computing and diagonalizing on the diffusion PES (see Figure 6) to compare the predicted the Hessian. A positive deﬁnite Hessian indicates that a local geometries with those obtained using the SIMOMM:UB3LYP/ minimum has been found, while one negative eigenvalue HW(d) level of theory. Figure 6 shows the structures and bond suggests that a saddle point (TS) has been located. The zero lengths of the diffusion stationary points a-e. Structure c in point energy corrections for the diffusion stationary points were Figure 6 is also a stationary point on the etching PES, as is calculated using the UB3LYP method. For the etching part of structure f (etched products). The UB3LYP Si-Si dimer bond the calculations, zero point vibrational energies were calculated lengths are similar to the available CASSCF bond lengths,22 using the CASSCF level of theory. Intrinsic reaction coordinate with deviations on the order of ∼0.1 Å. Most of the bond (IRC)68 calculations were used to connect the TS structures with distances shown in Figure 6 are in even better agreement. the reactants and products. The IRC calculations were performed In addition, the two most important structures on the etching using the second-order method developed by Gonzalez and PES (back-bond c and the etched surface/SOLA f) have been Schlegel (GS2)69,70 using a step size of 0.3 (amu)1/2 bohr. All optimized using the SIMOMM:CASSCF(12,11)/HW(d) method of the calculations were performed without imposing any to compare the geometrical differences with the SIMOMM: symmetry constraints on the structures. UB3LYP level of theory (see Figure 6 and Table 1). Again, The GAMESS (General Atomic and Molecular Electronic the UB3LYP bond lengths are in very good agreement with Structure System) program71 was used in all of the computations the CASSCF geometries. Table 1 shows all of the bond lengths (including canonical CC calculations that rely on the routines that were obtained at both the CASSCF and the UB3LYP levels described in refs 72 and 24), except for the local CIM-CC of theory, as well as the angles on the diffusion PES. As in the calculations. The CIM-CC calculations were performed using case of the diffusion pathway, the UB3LYP method does a the suite of computer programs described in refs 29-32 which reasonable job of reproducing the CASSCF bond lengths and are interfaced with the GAMESS Hartree-Fock, orbital local- angles. Since the UB3LYP method is computationally less ization, and integral transformation routines. The CIM orbital expensive than CASSCF and has fewer convergence problems, subsystems were determined using the single-environment CIM UB3LYP has been used for the generation of all other structures algorithm described in ref 32. The MM3 parameters of refs on the etching PES. 12654 J. Phys. Chem. C, Vol. 114, No. 29, 2010 Arora et al.

TABLE 1: Comparison of SIMOMM:CASSCF(12,11)/HW(d) and SIMOMM:UB3LYP/HW(d) Bond Lengths and Bond Angles for the Structures and Atom Numbering Shown in Figure 6 Bond Lengths (Å) diffusion stationary points etching stationary points on-top (a)TS(b) back-bond (c) etched product (f) UB3LYP CASSCF UB3LYP CASSCF UB3LYP CASSCF UB3LYP CASSCF Si1-O 1.61 1.56 1.62 1.62 1.65 1.65 1.53 1.54 Si6-O 2.64 2.54 1.71 1.71 Si3-Si4 2.26 2.25 2.26 2.25 Si1-Si2 2.40 2.54 2.36 2.35 2.26 2.25 Si3-Si6 2.57 2.58 Bond Angles (deg) diffusion stationary points on-top (a)TS(b) UB3LYP CASSCF UB3LYP CASSCF Si6-Si1-O 80 76 Si2-Si1-O 124 118 127 126 TABLE 2: The Canonical and CIM CCSD, and Canonical, CIM, and Mixed CIM CR-CC(2,3) Relative Energies, Obtained with the 6-31G(d) Basis Set, for the Etching Stationary Points Shown in Figure 6 CCSD CR-CC(2,3) structure canonicala CIM(0.003)a canonicala CIM(0.003)a mixed CIM(0.003)a back-bond (c)0000 0 etched products (f) 86.8 87.3 87.3 87.7 87.3 a The relative energies are reported in kcal/mol.

TABLE 3: CPU Times and RAM Requirements B. Evaluation of the CIM-CC Methods. The CR-CC(2,3) Characterizing the Calculations of the Canonical and CIM method is a single-reference CC approach that can provide high- CCSD Energies and the Canonical and CIM CR-CC(2,3) Triples Corrections for the Etching Stationary Points Shown quality relative energies in diradical regions of a PES that result, c for example, from single bond breaking24-26,38-41 or reaction in Figure 6 mechanisms involving species with significant diradical char- triples correction of acter.24,25,35-37 This suggests that CR-CC(2,3) is a viable method CCSD CR-CC(2,3) to describe the dangling bonds on the Si(100) surface (see Figure CIM CIM 1), which can improve the accuracy of the CCSD(T) calculations structure canonicala (0.003)a,b canonicala (0.003)a,b when the degree of diradical character becomes significant. The back-bond (c) 34 (6.4) 9 (2.6) 166 (14.4) 129 (8.6) 7 canonical CR-CC(2,3) approach, with its intrinsic N scaling etched products (f) 42 (6.4) 8 (2.1) 165 (14.4) 81 (6.7) of the CPU time, is generally limited to molecules of small to a moderate size. To reduce the computer costs associated with CPU times are reported in hours. The numbers in parentheses correspond to RAM requirements in GB. b CPU times and RAM the canonical CR-CC(2,3) calculations, the local correlation requirements characterizing each CIM-CC calculation correspond to CIM-CR-CC(2,3) approach in the pure as well as mixed forms the largest CIM orbital subsystem. c All of the calculations were mentioned in Section 2, which replaces the N7 CPU steps performed using the 6-31G(d) basis set on an SGI Altix 3700 B×2 associated with the triples correction of CR-CC(2,3) by steps system, equipped with 1.6 GHz Itanium2 processors. that scale linearly with the system size, is employed in this study. Table 2 compares the relative energies predicted by the vs canonical CR-CC(2,3) is defined almost entirely by the canonical and CIM CCSD and CR-CC(2,3) methods using the accuracy of the preceding CCSD calculation. The CPU times 6-31G(d) basis set for two stationary points on the etching PES, and memory requirements characterizing the CIM-CC ap- the back-bond structure c and the etched products f. The proaches, when the 6-31G(d) basis set is employed, compared threshold used in the CIM-CC calculations summarized in with the corresponding canonical CC calculations for the etching Table 2 was set at 0.003. The error in the relative energy stationary points, are shown in Table 3. Despite the use of a resulting from the pure CIM-CR-CC(2,3) calculations, relative rather tight threshold ( ) 0.003), the CIM-CC methodology to the canonical CR-CC(2,3) method, is ∼0.4 kcal/mol. Much offers noticeable savings in the computer effort, by a factor of of this difference between the canonical and CIM-CR-CC(2,3) ∼2 in the triples correction part. These savings become more relative energies originates from the error in the CIM-CCSD significant when larger basis sets and less strict threshold calculations, which produce a relative energy that differs from values are employed, as illustrated below for the diffusion the corresponding canonical CCSD energy by 0.5 kcal/mol (see pathway. Table 2). When the mixed CIM-CR-CC(2,3) approach, in which Table 4 compares the relative energies of the stationary points one adds the local triples correction of CIM-CR-CC(2,3) to the along the diffusion pathway obtained using various CC methods canonical CCSD energy, is used, the accuracy improves and and basis sets. The mixed CIM-CR-CC(2,3) calculations for the the error relative to canonical CR-CC(2,3) decreases to 0.04 6-31G(d) basis set were performed at two different values, kcal/mol. This is because the bulk of the correlation energy is 0.005 and 0.01. The mixed CIM-CR-CC(2,3) calculations for in the CCSD part, so the relative accuracy of CIM-CR-CC(2,3) the larger 6-311G(d) basis set were performed using ) 0.01 Diffusion of Atomic Oxygen on the Si(100) Surface J. Phys. Chem. C, Vol. 114, No. 29, 2010 12655

TABLE 4: Relative Energies of the Stationary Points along the Diffusion Pathway Shown in Figure 6 Obtained in the Canonical and Mixed CIM CR-CC(2,3) Calculations Using the 6-31G(d) Basis Set and the Mixed CIM-CR-CC(2,3) Calculations Using the 6-311G(d) Basis Setc 6-31G(d) 6-311G(d) mixed mixed mixed mixed canonical CIM(0.005)- CIM(0.01)- canonical CIM(0.01)- CIM(0.005)- canonical structure CR-CC(2,3)a CR-CC(2,3)a CR-CC(2,3)a CCSD(T)a CR-CC(2,3)a CR-CC(2,3)a,b CR-CC(2,3)a,b back-bond (Si1-Si6) (c) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 TS (d) 71.9 73.9 77.0 66.2 79.5 76.4 74.4 back-bond (Si3-Si6) (e) 3.7 3.4 2.8 3.8 2.6 3.2 3.5 TS (b) 49.5 48.7 49.8 44.3 51.0 49.9 50.7 on-top (a) 50.1 51.0 52.3 28.0 52.2 50.9 50.0 a The relative energies are reported in kcal/mol. b The values are estimated assuming the additivity of basis set and level of theory. c All of the reported energy values include zero point energy corrections calculated using the UB3LYP method.

TABLE 5: The CPU Timings and RAM Requirements Characterizing the Calculations of the Triples Corrections of the Canonical and Mixed CIM CR-CC(2,3) Approaches Using the 6-31G(d) and 6-311G(d) Basis Sets for the Stationary Points along the Diffusion Pathway Shown in Figure 6d 6-31G(d) 6-311G(d) structure canonicala CIM(0.005)a,b CIM(0.01)a,b canonicala,b,c CIM(0.01)a,b back-bond (Si1-Si6) (c) 119 (12.6) 51 (5.9) 15 (2.5) 881 (50.5) 134 (14.7) TS (d) 141 (12.6) 88 (8.0) 28 (4.2) 1051 (50.5) 219 (19.5) back-bond (Si3-Si6) (e) 145 (12.6) 50 (5.9) 17 (3.2) 1081 (50.5) 145 (15.8) TS (b) 146 (12.6) 85 (8.3) 29 (4.9) 1082 (50.5) 231 (22.6) on-top (a) 141 (12.6) 103 (8.0) 13 (2.8) 1046 (50.5) 139 (13.4) a The CPU times are reported in hours. The numbers in parentheses correspond to RAM requirements in GB. b The CPU timings and RAM requirements characterizing each CIM-CR-CC(2,3) calculation correspond to the largest CIM orbital subsystem. c The CPU timings characterizing the triples parts of the canonical CR-CC(2,3)/6-311G(d) calculations were obtained by extrapolating the analogous CPU timings 3 4 of the canonical CR-CC(2,3)/6-31G(d) calculations using the theoretical 2no nu scaling of the CPU time with the numbers of occupied (no) and unoccupied (nu) orbitals employed in the post-Hartree-Fock calculations. The RAM requirements of the canonical CR-CC(2,3) calculations 2 2 2 2 3 3 2 2 3 were determined using the equation no + nu + 2no + 2nu + 6nonu + 2no nu + 2nonu + 3nu + 3no nu + 5no nu + 3nonu which defines the memory requirements of the computer implementation of CR-CC(2,3) described in ref 24 and used in this study. d All of the calculations were performed using the Altix 3700 B×2 system from SGI, equipped with 1.6 GHz Itanium2 processors. to conserve computer time. As shown in Table 4, the use of closer to the canonical ) 0 limit. The extrapolated canonical the less tight threshold in the mixed CIM-CR-CC(2,3) CR-CC(2,3)/6-311G(d) relative energies are within 1 kcal/mol calculations changes the relative energies of the stationary points or less of the results of the canonical CR-C(2,3)/6-31G(d) along the diffusion pathway by ∼3 kcal/mol or less compared calculations except for the high-energy TS d located at ∼70 to the tighter ) 0.005 value when the smaller, 6-31G(d) basis kcal/mol above the c structure, for which the difference is 2.5 set is used. The general agreement between the mixed CIM(0.01)- kcal/mol. CR-CC(2,3) and canonical CR-CC(2,3) relative energies for the As implied by the analysis of the CASSCF and CCSD wave 6-31G(d) basis set is excellent, with errors on the order of 1 functions, structure a has a particularly significant diradical kcal/mol or less. An exception is the high-energy TS d for which character. This lowers the CCSD(T) energy so much that the the error is ∼5 kcal/mol. As shown in Table 5, the use of the activation barrier corresponding to the a f c transformation, less strict threshold ) 0.01 results in significant savings in defined by the difference of the b and a energies, is overesti- the CPU time and memory relative to ) 0.005, not to mention mated by CCSD(T) by ∼15 kcal/mol compared to the extrapo- the canonical calculations, making the mixed CIM-CR-CC(2,3)/ lated canonical CR-CC(2,3)/6-311G(d) result. As discussed in 6-311G(d) calculations affordable in a situation where the Section 3D, the CR-CC(2,3) results are consistent with the corresponding canonical CR-CC(2,3)/6-311G(d) calculations are SIMOMM:UB3LYP data in this regard (see Figure 7). virtually impossible to perform on computers of modest C. Etching of the Silicon Surface (Si(100)) by an Oxygen capability. Atom. The etching/desorption process corresponds to the Also shown in Table 4 are the mixed CIM(0.005)-CR-CC(2,3)/ removal of a silicon atom from the Si(100) surface by an oxygen 6-311G(d) and canonical CR-CC(2,3)/6-311G(d) relative energies atom. The stationary points (minima and TS structures) for the that were extrapolated assuming that the corrections for the level etching mechanism proposed by Choi et al.22 are summarized of theory and basis set are additive. Specifically, the extrapolated in Figure 2. It was found in the previous work that the back- mixed CIM(0.005)-CR-CC(2,3)/6-311G(d) results were obtained bond structure (c) is a key minimum on the PES. The product by adding the [CIM(0.005)-CR-CC(2,3) - CIM(0.01)-CR- structure corresponding to SiO + the etched surface (SOLA) is CC(2,3)] energy differences obtained with the 6-31G(d) basis the highest energy structure on the PES. Choi et al. calculated set to the corresponding CIM(0.01)-CR-CC(2,3)/6-311G(d) the corresponding overall MRMP2 activation barrier by taking energies. Similarly, the extrapolated canonical CR-CC(2,3)/6- the energy difference between the back-bond structure and that 311G(d) results were obtained by adding the [canonical CR- of SOLA+ SiO, obtaining ∼90 kcal/mol. CC(2,3) - CIM(0.01)-CR-CC(2,3)] energy differences obtained In this work the etching barrier is defined in the same manner: with the 6-31G(d) basis set to the CIM(0.01)-CR-CC(2,3)/6- that is, by calculating the energy difference between the back- 311G(d) energies. As one can see in Table 4, by reducing the bond/lowest-energy structure (c) and the SOLA/etched structure value of , the CIM-CR-CC(2,3)/6-311G(d) energies become + SiO (f) shown in Figure 6. The SIMOMM:MRMP2(12,11)/ 12656 J. Phys. Chem. C, Vol. 114, No. 29, 2010 Arora et al.

Figure 7. Relative energy diagram for structures a to e in Figure 6. Energies are obtained using SIMOMM:UB3LYP/6-31G(d) geometries. All values are in kcal/mol. Values in parentheses include SIMOMM:UB3LYP/6-31G(d) zero point vibrational energy corrections. The values shown in italics correspond to the extrapolated values based on the assumption of the additivity of basis set and level of theory.

TABLE 6: Energies (kcal/mol) Relative to the Back-Bond Structure (see Figure 6)a 6-31G(d) canonical mixed CIM(0.003)- canonical MRMP2(12,11)/ MRMP2(12,11) CCSD(T) CR-CC(2,3) CR-CC(2,3) MIXEDb,22 GGA33 KMC30 experiment8,11,14 81.4 (78.7) 88.6 (85.9) 87.3 (84.6) 87.3 (84.6) 89.8 83.0-87.6 73.8-80.7 80.0-90.0

a The calculations were done with the SIMOMM OSi15H16;OSi136H92 model shown in Figure 4 and the geometries were obtained with CASSCF(12,11)/6-31G(d). All relative energies include both QM and MM contributions. The values in parentheses include zero point vibrational energy corrections calculated using the CASSCF method. b CASSCF(8,7)/HW(d) geometry.

6-31G(d) etching barrier is 81.4 kcal/mol, approximately 8 kcal/ broken and a new Si6-O bond is formed (see Figure 6). The mol lower than the value predicted by Choi et al. using the SIMOMM:UB3LYP/6-31G(d) energy difference (barrier height) mixed basis set (see Table 6). As shown in Table 6, the etching between TS b and on-top a is ∼1 kcal/mol (see Figure 7). This barrier calculated using the canonical CR-CC(2,3) and mixed barrier essentially disappears in the CR-CC(2,3) calculations, CIM-CR-CC(2,3) methods employing the 6-31G(d) basis set, including all CIM methods, and is only 0.7 kcal/mol when the of 87.3 kcal/mol, is approximately 2 kcal/mol lower than that CIM-CR-CC(2,3)/6-311G(d) energies are extrapolated to the calculated by Choi et al. All of these barriers, predicted by high canonical CR-CC(2,3)/6-311G(d) limit. This indicates that the 8,11,14 - levels of theory, are within the experimental range of 80 90 on-top structure is near a TS and that the diffusion of the oxygen 43 kcal/mol, suggesting that the previous KMC predictions are atom toward the formation of the back-bond structure c is either slightly low. barrierless or proceeds through a tiny activation barrier on the D. Diffusion of Oxygen on the Silicon Surface. Five order of 1 kcal/mol or less. The SIMOMM:MRMP2(12,11) stationary points were found on the PES for the diffusion of an calculations22 predict that TS b is 4.2 kcal/mol higher in energy oxygen atom from one dimer to an adjacent dimer on the Si(100) than the on-top structure. This small difference may reﬂect, in surface. The structures of these stationary points along with a part, the use of B3LYP geometries in the present calculations. comparison of the corresponding bond lengths are shown in In any case, it appears that the on-top structure can easily be Figure 6. The predicted singlet PES for the diffusion of an O converted to the back-bond structure c. atom between two adjacent dimers on the Si(100)-2 × 1 surface d at several levels of theory using the SIMOMM:UB3LYP/6- TS (see Figures 6 and 7) connects the back-bond structure 31G(d) geometries is shown in Figure 7 (cf., also, Table 4 for c with another back-bond structure e. As shown in Figure 6, the information pertaining to the CC calculations). TS d has the oxygen atom bonded to three silicon atoms (Si1 - As shown in Figures 6 and 7, the starting point for the and Si3 from the two Si Si dimers and Si6 from the next layer diffusion pathway is the on-top position a.TSb connects the in the cluster). TS d is formed when the oxygen atom connects global minimum (back-bond structure c) on the PES with the two adjacent silicon dimers via a siloxane bridge structure 10 structure a, shown in Figure 6. The O atom moves toward the (sBO). Stationary point e is also a back-bond structure, formed second dimer in a perpendicular direction to the dimer rows when the oxygen atom moves toward the adjacent silicon dimer (cf. Figure 3). The Si6-O bond length decreases from 3.0 Å to (Si3-Si4) from the back-bond structure c. The two structures 2.6 Å as the oxygen moves from the on-top position a to the c and e are similar and nearly isoenergetic. The difference in TS b. In the back-bond structure c, the oxygen atom has inserted the bond lengths of these two back-bond structures is ∼0.02 into a bond (Si1-Si6) that connects a surface silicon atom (Si1) Å, and the energy differences between the e and c structures to a silicon atom (Si6) in the next layer. A Si6-Si1 bond is obtained with the CIM and extrapolated canonical CR-CC(2,3)/ Diffusion of Atomic Oxygen on the Si(100) Surface J. Phys. Chem. C, Vol. 114, No. 29, 2010 12657

TABLE 7: Comparison of the Barrier Heights [back-bond (Si1-Si6) c to back-bond (Si3-Si6) e] for the Long-Range Diffusion Process (see Figure 6) with Previous Calculations and Experimentsa UB3LYP 6-31G(d) 6-311G(d) mixed mixed KMC/water canonical CIM(0.005)- canonical CIM(0.01)- canonical covered HW(d) 6-31G(d) CCSD(T) CR-CC(2,3) CR-CC(2,3) CR-CC(2,3) CR-CC(2,3)b GGA10 Si(100)38 Pelz37 experiment41,42 68.0 66.7 66.2 73.9 71.9 79.5 74.4 42.8 57.6 55.3-57.7 41.5-76.1 a All values are zero point vibrational energy corrected at UB3LYP level of theory. All the values are in kcal/mol. b Estimated assuming the additivity of basis set and level of theory.

6-311G(d) methods are only ∼3 kcal/mol, with the canonical back-bond e structure with previous calculations and with CR-CC(2,3)/6-31G(d) result being almost identical. experiments is given in Table 7. The c f e activation energy Although structures c and e have similar energies, the calculated in the present study using SIMOMM:UB3LYP and conversion of the back-bond structure c to the back-bond CC methods is about 66-74 kcal/mol, with (extrapolated) structure e via the siloxane bridge (TS d) has a rather large canonical CR-CC(2,3) giving ∼72-74 kcal/mol. The range of activation energy of more than 70 kcal/mol. As shown in Figure barrier heights in Table 7 is a bit higher than that predicted by 7, the activation barriers for the conversion of c f e calculated the previous KMC simulations that included water on the at the SIMOMM:UB3LYP, CCSD(T), and CR-CC(2,3)/6- surface.52 As noted in the Introduction, the range of experimental 31G(d) or extrapolated CR-CC(2,3)/6-311G(d) levels of theory values for this barrier height55-59 is quite large and encompasses agree reasonably well with each other. The c f e barrier heights all of the theoretical values.10,51,52 calculated at these levels of theory lie in a range of 66-74 kcal/ mol. This suggests that using SIMOMM to predict geometries 4. Conclusions (thereby incorporating bulk effects) and then using the QM cluster model for high-level [i.e., CR-CC(2,3)] calculations to The mechanism of the long-range diffusion of atomic oxygen obtain accurate energies is a reasonable strategy. This also on the Si(100)-2 × 1 surface has been studied using accurate suggests that the major contribution to the activation barrier energies resulting from a variety of CC calculations that were comes from the QM part of the system at correlated levels of obtained at the geometries determined using UB3LYP, in theory and the small QM clusters consisting of 15 silicon atoms concert with the SIMOMM embedded cluster approach. The reasonably mimic the silicon surface for the diffusion of O on diffusion PES reveals that the structure with the back-bond the silicon surface. The overestimated activation barrier at the insertion of the oxygen atom into a subsurface Si-Si bond is mixed CIM(0.01)-CR-CC(2,3)/6-311G(d) level of theory (79.5 the lowest-energy structure, in agreement with previous DFT/ kcal/mol) relative to the extrapolated canonical CR-CC(2,3)/6- GGA studies by Hemeryck et al.10 Another back-bond structure 311G(d) result (74.4 kcal/mol) or its true CR-CC(2,3)/6-31G(d) that is formed on the second Si-Si dimer is also a minimum analogue (71.9 kcal/mol) can almost certainly be attributed to on the diffusion PES. These two back-bond minima are the use of a loose threshold parameter in the CIM calculations. connected via a TS involving a siloxane bridge structure, again As shown in Table 4 and Figure 7, the extrapolated canonical in agreement with the DFT calculations of Hemeryck et al.10 CR-CC(2,3)/6-311G(d) and calculated CR-CC(2,3)/6-31G(d) Another stable intermediate on the PES, the on-top structure, activation barriers for the c f e transformation, 74.4 and 71.9 is connected to the back-bond structure via a TS that is similar kcal/mol, respectively, agree to within ∼2 kcal/mol. to the initial oxidation pathway of the etching mechanism Yamasaki et al.78 predicted that the activation energy corre- observed in previous theoretical studies by Choi et al.22 The sponding to the c f e conversion decreases when the coverage CC activation energy for the diffusion process is within the is more than 3 oxygen atoms and the sBO d configuration rather large experimental range of 41-76 kcal/mol. In particular, becomes energetically favorable. Hemeryck et al. studied the the CR-CC(2,3) approach, after extrapolating the local CIM- diffusion process using plane wave GGA density functional CR-CC(2,3) results to the canonical limit, gives the activation theory.10 They found two additional metastable structures that energy of ∼72-74 kcal/mol when the 6-31G(d) and 6-311G(d) connect the sBO structure that in turn connects the two back- basis sets are employed. The theoretical values of the diffusion bond structures. This is in contrast to the results in the present barrier found previously lie in the range of 42.8 (DFT)-57.7 work where the sBO structure directly connects the two back- (KMC simulations) kcal/mol. There have, to our knowledge, bond structures (c and e) and the activation energy is ap- been no previous ab initio calculations on this process. The proximately 30 kcal/mol higher than that predicted by Hemeryck studies presented here employ the most accurate electronic et al. (see Table 7). In the present work, the pathway along the structure theory methods that have been employed to date on diffusion process was confirmed using intrinsic reaction coor- this process. While cluster calculations can be limited by “edge dinate (IRC) calculations that connect the TS d with the back- effects”, the use of large QM/MM clusters as in the present bond structures c and e. No intermediate structure was detected. work very likely minimizes such effects. The present work does The low activation energy calculated by Hemeryck et al. has not include an exhaustive examination of the entire potential been attributed to the omission of Hartree-Fock exchange in energy surface for the Si cluster + O atom. So, it is possible the GGA calculations.79,80 The results in the present study are that there are other stationary points that are relevant to the likely to be more reliable than the predictions made by previous present estimate of the height of the diffusion barrier. However, DFT studies because in the present study the relative energies due to weak bonding in the troughs between dimer rows,67 are calculated using more robust high-level ab initio methods, diffusion along the troughs and perpendicular to the dimer rows such as CR-CC(2,3). Previous KMC studies employed barrier is inhibited due to high energy barriers. heights to optimize the agreement with experimental observa- The SiO desorption barrier for the etching process has also tions. A comparison of the diffusion activation energies corre- been calculated by taking the energy difference between the sponding to the conversion of the back-bond c structure to the final etched product and the back-bond structure, which is the 12658 J. Phys. Chem. C, Vol. 114, No. 29, 2010 Arora et al. lowest-energy structure on the etching PES. The canonical and Piecuch, P., Maruaniv, J., Delgado-Barrio, G., Wilson, S., Eds.; Springer: - CIM CR-CC(2,3) methods have been used to calculate the Dordrecht, The Netherlands, 2009; pp 131 195. (32) Li, W.; Piecuch, P. J. Phys. Chem. A. DOI: 10.1021/jp100782u. barrier and assess the accuracy of previous calculations. It has Published Online: April 7, 2010. been found that the etching barrier height is 87.3 kcal/mol at (33) Redondo, A.; Goddard, W. A. J. Vac. Sci. Technol. 1982, 21, 344. the canonical CR-CC(2,3)/6-31G(d) and mixed CIM-CR- (34) Kinal, A.; Piecuch, P. J. Phys. Chem. A 2007, 111, 734. (35) Cramer, C. J.; Włoch, M.; Piecuch, P.; Puzzarini, C.; Gagliardi, L. CC(2,3)/6-31G(d) levels of theory. This result lies in the higher J. Phys. Chem. A 2006, 110, 1991; 2007, 111, 4871 [Addition/Correction]. end of the range of the previous theoretical (73.8-89.8 kcal/ (36) Cramer, C. J.; Kinal, A.; Włoch, M.; Piecuch, P.; Gagliardi, L. J. mol) and experimental (80-90 kcal/mol) values. Phys. Chem. A 2006, 110, 11557; 2007, 111, 4871 [Addition/Correction]. (37) Cramer, C. J.; Gour, J. R.; Kinal, A.; Włoch, M.; Piecuch, P.; Shahi, A. R. M.; Gagliardi, L. J. Phys. Chem. A 2008, 112, 3754. Acknowledgment. This work has been supported by a grant (38) Piecuch, P.; Włoch, M.; Varandas, A. J. C. Theor. Chem. Acc. 2008, from the Chemical Sciences Division, Basic Energy Sciences, 120, 59. U.S. Department of Energy (Chemical Physics and PCTC (39) Song, Y. Z.; Kinal, A.; Caridade, P. J. S. B.; Varandas, A. J. C.; Piecuch, P. J. Mol. 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