GeSi alloys: A study of short-range order

A cluster Bethe lattice method has been employed for a study of the effects of short-range order on the electronic and optical properties of binary SiGe alloys. A realistic six-parameter tight-binding parameter Hamiltonian has been used for the study of chemically ordered and random sequences. In random alloys, one observes properties which are simply averages over the properties of the constituent atoms weighted with their concentrations. In chemically ordered alloys, the ionicity manifests itself as a dip in the valence-band electron density of states. The amount of ionicity is proportional to the strength of the dip which increases with the concentration of one constituent in minority to a maximum for a ${\mathrm{Si}}_{0.5}$ ${\mathrm{Ge}}_{0.5}$ alloy. One observes an "ionic gap" of width ∼ 1.2 eV in the ${\mathrm{Si}}_{0.5}$ ${\mathrm{Ge}}_{0.5}$ alloy. This degree of short-range order may be measurable by photoemission experiments. The variation of the band gap with concentration is seen to be in good agreement with the experimental data available for the optical gap in crystalline SiGe alloys. We also observe a small impurity band in the band gap in both sequences except in the ${\mathrm{Si}}_{0.5}$ ${\mathrm{Ge}}_{0.5}$ alloy which simulates a zinc-blende-type alloy.