Defect migration in crystalline silicon

A number of vacancy and interstitial defect migration mechanisms are characterized for crystalline silicon using supercells containing 64 and 216 atoms and a tight-binding approach. We investigate various defect configurations corresponding to minima and the pathways that connect them. A modified eigenvector-following approach is used to locate true transition states. We exploit the fact that only one Hessian eigenvector is needed to define the uphill search direction and use conjugate gradient minimization in the tangent space to produce a hybrid algorithm. Two implementations of this approach are considered, the first where second derivatives are available but full diagonalization of the Hessian would be the most time-consuming step, and the second where only first derivatives of the energy are known.