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Onsite matrix elements of the tight-binding Hamiltonian of a strained crystal: Application to silicon, germanium, and their alloys

2009; American Physical Society; Volume: 79; Issue: 24 Linguagem: Inglês

10.1103/physrevb.79.245201

1550-235X

Yann-Michel Niquet, D. Rideau, C. Tavernier, H. Jaouen, Xavier Blase,

Force Microscopy Techniques and Applications

We discuss a model for the onsite matrix elements of the $s{p}^{3}{d}^{5}{s}^{\ensuremath{\ast}}$ tight-binding Hamiltonian of a strained diamond or zinc-blende crystal or nanostructure. This model features onsite, off-diagonal couplings among the $s$, $p$, and $d$ orbitals and is able to reproduce the effects of arbitrary strains on the band energies and effective masses in the full Brillouin zone. It introduces only a few additional parameters and is free from any ambiguities that might arise from the definition of the macroscopic strains as a function of the atomic positions. We apply this model to silicon, germanium, and their alloys as an illustration. In particular, we make a detailed comparison of tight-binding and ab initio data on strained Si, Ge, and SiGe.