A density functional tight-binding approach for modelling Ge and GeH structures

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Abstract
We present here details of a density-functional-based non-orthogonal tight-binding approach for germanium. This is carried out within the framework of the LCAO ansatz, using a two-centre approximation for the evaluation of the Hamiltonian matrix elements. The Hamiltonian and overlap matrix elements for Ge - Ge, Ge - H are derived using a localized atomic basis set and existing parameters for H - H are utilized. These are tested against results from existing experimental and theoretical data for bulk germanium and germanium surface reconstructions, both with and without hydrogen. In addition we generate the first fully self-consistent ab initio LDA results for small Ge clusters and Ge - H molecules using the AIMPRO program and compare DF-TB results against these. Finally we describe our study of H point defects in bulk germanium. These are the first calculations of this type done on Ge using large fully optimized supercells and confirm self-consistent ab initio calculations done on small clusters. We consequently demonstrate that, despite the extreme simplicity of the approach, it is accurate and highly transferable across a broad range of structural systems ranging from clusters to the bulk phase.