A super-cell approach for the study of localized defects in solids: carbon substitution in bulk silicon

Abstract

Carbon substitution in bulk silicon has been investigated using the super-cell approach, in conjunction with the periodic ab initio Hartree-Fock method. The convergence of the defect formation energy and of the relaxed defect geometry as a function of the super-cell size is discussed with reference to super-cells containing 8, 16, 32 and 64 atoms. It turns out that the convergence of the unrelaxed defect formation energy is rapid, in spite of the large local charge redistribution around the defect (the net charge on carbon is 1.2 mod e mod ); the relaxation effects are very large (about 2.0 eV) and involve mainly the first and second neighbours; however, the relaxation of the fifth neighbours of the defect (which is possible only with the biggest super-cell considered) lowers the energy by a further 0.06 eV. The defect formation energy and the atomic displacements obtained with the 32 and 64 atoms super-cells are similar, whereas the energy difference between the 16 and 32 atoms cells is as large as 0.4 eV.

Softening the ultra-stiff: Controlled variation of Young’s modulus in single-crystal diamond by ion implantation

“…An atomistic approach was employed to simulate the damage-induced modification of from first principles. To this purpose, the quantum-mechanical ab initio code CRYSTAL14 [38,39] was employed, which allows the prediction of the structural and elastic properties of a defected material [40] through a [41]. In this context, a supercell is defined as a multiple of the unit cell that contains a vacancy at its body center.…”

Cluster and supercell calculations for carbon-doped silicon

“…The cluster model proves to be adequate to describe the local charge distribution surrounding the defect. As was found in periodic supercell calculations [23], the purely electrostatic perturbation due to the carbon impurity is very short ranged and screened virtually completely by the nearest Si neighbours, to the extent that it is described well even in the smallest cluster. In the absence of relaxation, we find a difference of only 0.03 eV in substitution energy compared to supercell calculation with the same basis set and computational conditions.…”

“…The medium and large clusters were constructed subject to the constraint that silicon atoms at the cluster surface were connected to a maximum of two hydrogens. The Gaussian basis sets adopted for silicon and carbon were the same as in previous bulk [27] and supercell [23] studies. Two sp shells and one d shell (13 atomic orbitals) per atom were used, with core electron states represented by Durand-Barthelat pseudopotentials [28].…”

“…This latter method involves a periodic array of unit cells of the host crystal containing the carbon impurity at the centre. If the cell is sufficiently large, interaction between the defects belonging to different cells is negligible; it was shown in a previous paper [23] that a 64-atom supercell containing the carbon impurity is large enough to describe an isolated defect consistently. Both supercell and cluster calculations were performed using the same computer code, namely CRYSTAL92 [24,25,26].…”

Comparison between cluster and supercell approaches: the case of defects in diamond

“…This latter method involves a periodic array of unit cells of the host crystal containing the defect at the centre. If the cell is sufficiently large, interactions between the defects belonging to different cells is negligible; it was shown in a previous paper [42] that a 128 atom supercell is large enough to accurately describe the defects we are going to discuss here. Both supercell and cluster calculations were performed using the same computer code, namely CRYSTAL [43], basis set and DFT functional.…”