Electronic structure evolution in dilute carbide Ge_1−xC_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$1−x$C$x$⁠. For ordered alloy supercells, we demonstrate that C incorporation strongly perturbs the conduction band (CB) structure by driving the hybridization of $A1$-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 $A1$-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$1−x$C$x$ 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.