First-principles molecular dynamics approach to amorphous silicon and silicon clusters

Abstract

We present the results of tight binding molecular dynamics calculations for studying the equilibrium structures and the bonding properties of Sin clusters up to n = 18. With a limited number of parameters in the tight binding scheme, the structures of minimum energy are well reproduced, compared to previous ab initio quantum mechanical calculations. We find the abundant cluster sizes of n = 4, 7, and 10, which are in good agreement with other theoretical and experimental results. For n ≥ 7, the surface-like compact structures with a pentagon or a hexagon base are found to be energetically favorable, resulting in the metallic nature of cluster bonding, while a core-based structure firstly appears for $Si_{15}$. We also present an efficient scheme of minimizing the energy functional related to the large-scale system in a self-consistent manner. In the framework of the preconditioned conjugate gradient minimization of the energy functional, we replaces the modified Jacobi relaxation for preconditioning and use for band by band minimization the restricted block Davidson algorithm, in which only the previous wave functions and the relaxation vectors are included additionally for subspace diagonalization. The present scheme is found to be comparable with the preconditioned conjugate gradient method for both large ordered and disordered Si systems, while it is more rapidly converged for systems with transition metal elements. We also present the explicit symmetric formulas for the nonlocal pseudopotential contribution to the stress tensor. The symmetric stress tensor can be derived by applying the scaling procedure of wavevectors $\vec{K}$, which satisfies the symmetric properties of $∂K_γ/∂ε_{αβ}=∂K_γ /∂ε_{βα}}$ for the symmetric strain $ε_{αβ}$. We note that this scaling procedure gives rise to the same expression for the stress tensor as that derived using a semilocal or a separable nonlocal pseudopotential. Using these highly efficient method of total energy calcu...