Band structure calculations of Si-Ge-Sn alloys: achieving direct band gap materials

摘要

Alloys of silicon (Si), germanium (Ge) and tin (Sn) are continuously attracting research attention as possible direct band gap semiconductors with prospective applications in optoelectronics. The direct gap property may be brought about by the alloy composition alone or combined with the influence of strain, when an alloy layer is grown on a virtual substrate of different compositions. In search for direct gap materials, the electronic structure of relaxed or strained Ge_(1-x)Sn_x and Si_(1-x)Sn_x alloys, and of strained Ge grown on relaxed Ge_(1-x-y)Si_xSn_y, was calculated by the self-consistent pseudo-potential plane wave method, within the mixed-atom supercell model of alloys, which was found to offer a much better accuracy than the virtual crystal approximation. Expressions are given for the direct and indirect band gaps in relaxed Ge_(1-x)Sn_x, strained Ge grown on relaxed Si_xGe_(1-x-y)Sn_y and strained Ge_(1-x)Sn_x grown on a relaxed Ge_(1-y)Sn_y substrate, and these constitute the criteria for achieving a (finite) direct band gap semiconductor. Roughly speaking, good-size (up to ～0.5 eV) direct gap materials are achievable by subjecting Ge or Ge_(1-x)Sn_x alloy layers to an intermediately large tensile strain, but not excessive5 because this would result in a small or zero direct gap (detailed criteria are given in the text). Unstrained Ge_(1-x)Sn_x bulk becomes a direct gap material for Sn content of > 17%, but offers only smaller values of the direct gap, typically ≤ 0.2 eV. On the other hand, relaxed Sn_xSi_(1-x) alloys do not show a finite direct band gap.