Order-N study of the structure and energetics of stacking faults in silicon

Formation energies and structural features of two-dimensional extended defects (twin boundaries and stacking faults) in silicon are investigated using an order-N density-matrix tight-binding technique. A slow numerical convergence of the formation energies with respect to calculational parameters is observed and analyzed. Structural features are found to converge faster than formation energies. These observations are 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 cutoff associated with the density-matrix approximation. Our results are obtained assuming separation-based spherical cutoffs, and suggest that calculations of stacking-fault energies may be used to compare the different truncation schemes for the density matrix that have been proposed in the literature. Converged tight-binding values for the formation energies agree well with those from available experimental studies.