Atomistic analysis of localisation and band mixing effects in Gel-ϰC,Sn)ϰ group-IV alloys

We present a theoretical analysis of the electronic structure of the group-IV alloys Ge
_1-x
(C,Sn)
_x
. Our analysis is based on a semi-empirical tight-binding model, parametrised via hybrid density functional theory calculations. Using atomistic alloy supercell calculations we identify and quantify the respective roles played by C-related localised impurity states and Sn-induced band mixing in determining the nature of the indirect- to direct-gap transition in Ge
_1-x
C
_x
and Ge
_1-x
Sn
_x
. For exemplar calculations on 64-atom Ge
₆₃
(C,Sn) (x=1.56%) supercells we derive and parametrise model Hamiltonians which provide quantitative and physically transparent descriptions of these localisation and band mixing mechanisms, and comment on the implications of the Ge
_1-x
(C
₂
Sn)
_x
alloy band structure for technologically relevant material properties.