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 threeparameter Lee−Yang−Parr (B3LYP) hybrid functional) approach, the Hay−Wadt effective core potential, and its associated double-ζ 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. 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 Si 15 H 16 cluster embedded in an Si 136 H 92 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 lefteigenstate 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 C...

Accurate and systematically improvable density functional theory embedding for correlated wavefunctions

“…The matrix elements of Finally, the correlation energy from the triple excitations within subsystem A is given by (13) where the first summation spans the occupied orbitals of subsystem A, the indices i, j, k represent occupied orbitals, and the indices r, s, t represent unoccupied orbitals. S rr is an element of the overlap matrix of the projected atomic orbitals, (ir | js) are two-electron integrals, and t …”

CASSCF and MRMP2 investigation of the interaction of arsenic adatoms with carbon dimers on the diamond (100)-2 × 1 surface

“…1(a)). A double-dimer cluster model as C 15 H 16 has been largely employed in computational chemistry studies involving surfaces like the diamond C(100) [22][23][24][25]. The carbon dimers are the reactive part of the surface, and how they interact with the As adatom is discussed in Section 3.…”

“…1(b). The model cluster C 292 H 120 was constructed based on the C 15 H 16 model and grown up in size because it was able to properly reproduce the C\ \C bond length found in the bulk crystaldiamond, 1.545 Å [5]; besides, it is consistent with other size clusters adopted in similar studies [23][24][25]. All geometries were optimized using the CASSCF approach [26], as will be described in the next section.…”

“…The methodology adopted in the present investigation is consistent with other works described in the literature [23][24][25]. The QM/MM approach was chosen in order to make feasible the application of the CASSCF and MRMP2 methods to the study of surface science problems.…”

Accurate basis set truncation for wavefunction embedding

“…Among these are the QM/MM, [1][2][3][4][5][6] ONIOM, 7,8 fragment molecular orbital (FMO), [9][10][11][12][13][14][15] and wavefunction theory (WFT)-in-density functional theory (DFT) embedding [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] approaches, which allow for the treatment of systems that would not be practical using conventional WFT approaches. In particular, WFT-in-DFT embedding utilizes the theoretical framework of DFT embedding to enable the WFT description of a given subsystem in the effective potential that is created by the remaining electronic density of the system.…”