Electronic structure evolution in dilute carbide Ge_{1- x}C_x alloys and implications for device applications

We present a theoretical analysis of electronic structure evolution in the highly-mismatched dilute carbide group-IV alloy Ge 1 - xC x. For ordered alloy supercells, we demonstrate that C incorporation strongly perturbs the conduction band (CB) structure by driving the hybridization of A 1-symmetric linear combinations of Ge states lying close in energy to the CB edge. This leads, in the ultradilute limit, to the alloy CB edge being formed primarily of an A 1-symmetric linear combination of the L-point CB edge states of the Ge host matrix semiconductor. Our calculations describe the emergence of a "quasidirect" alloy bandgap, which retains a significant admixture of indirect Ge L-point CB edge character. We then analyze the evolution of the electronic structure of realistic (large, disordered) Ge 1 - xC x alloy supercells for C compositions up to x = 2%. We show that short-range alloy disorder introduces a distribution of localized states at energies below the Ge CB edge, with these states acquiring minimal direct (Γ) character. Our calculations demonstrate strong intrinsic inhomogeneous energy broadening of the CB edge Bloch character, driven by hybridization between Ge host matrix and C-related localized states. The trends identified by our calculations are markedly different to those expected based on a recently proposed interpretation of the CB structure based on the band anticrossing model. The implications of our findings for device applications are discussed.