The two gap transitions in Ge 1 - X Sn x: Effect of non-substitutional complex defects

Abstract

The existence of non-substitutional β-Sn defects in Ge1-xSnx alloys was confirmed by emission channeling experiments [Decoster et al., Phys. Rev. B 81, 155204 (2010)], which established that, although most Sn enters substitutionally (α-Sn) in the Ge lattice, a second significant fraction corresponds to the Sn-vacancy defect complex in the split-vacancy configuration (β-Sn), in agreement with our previous theoretical study [Ventura et al., Phys. Rev. B 79, 155202 (2009)]. Here, we present the electronic structure calculations for Ge1-xSnx, including the substitutional α-Sn as well as the non-substitutional β-Sn defects. To include the presence of the non-substitutional complex defects in the electronic structure calculation for this multi-orbital alloy problem, we extended the approach for the purely substitutional alloy by Jenkins and Dow [Phys. Rev. B 36, 7994 (1987)]. We employed an effective substitutional two-site cluster equivalent to the real non-substitutional β-Sn defect, which was determined by a Green's functions calculation. We then calculated the electronic structure of the effective alloy purely in terms of substitutional defects, embedding the effective substitutional clusters in the lattice. Our results describe the two transitions of the fundamental gap of Ge1-xSnx as a function of the total Sn-concentration: namely, from an indirect to a direct gap, first, and the metallization transition at a higher x. They also highlight the role of β-Sn in the reduction of the concentration range, which corresponds to the direct-gap phase of this alloy of interest for the optoelectronics applications.