Comparative analysis of electronic structure evolution in Ge1-xSnx and Ge1−xPbx alloys

We present a comparative analysis of electronic structure evolution and the indirect- to direct-gap transition in Ge
_1-x
(Sn,Pb)
_x
group-IV semiconductor alloys. We present first principles disordered alloy electronic structure calculations for Ge
_1-x
(Sn,Pb)
_x
special quasi-random structures, and find a significantly larger band gap reduction in Ge
_1-x
Pb
_x
than in Ge
_1-x
Sn
_x
at fixed x. We calculate that Ge
_1-x
Pb
_x
becomes a direct gap semiconductor close to the composition (x ≈ 7%) at which it also becomes a zero-gap semiconductor. The indirect-to direct-gap transition in Ge
_1-x
Sn
_x
occurs over an extended composition range, also centered around 7%, and is driven by Sn-induced mixing of Ge Γ and L conduction states. The pronounced band mixing effects present in Ge
_1-x
Sn
_x
alloys will have significant implications for optical and transport properties.