Formation energies and structural features of 2-dimensional extended defects (twin boundaries and stacking faults) in silicon were investigated using an order-N density-matrix tight-binding technique. A slow numerical convergence of the formation energies with respect to calculational parameters was observed and analyzed. Structural features were found to converge faster than formation energies. These observations were shown to be associated with the small energies involved in the formation of these defects, which make the reference to a bulk crystal calculation (needed for the evaluation of the formation energies) to be adequate only at relatively high values of the real-space truncation cut-off associated with the density-matrix approximation. The results were obtained assuming separation-based spherical cut-offs, and suggested that calculations of stacking-fault energies could be used to compare the various truncation schemes for the density matrix that had been proposed in the literature. Converged tight-binding values for the formation energies agreed well with those from available experimental studies.

Order-N Study of the Structure and Energetics of Stacking Faults in Silicon. M.M.de Araújo, R.W.Nunes: Computational Materials Science, 2008, 41[4], 602-6