Electronic structure evolution in dilute carbide Ge$_{1-x}$C$_{x}$ alloys and implications for device applications

TL;DR

This study provides a theoretical analysis of how dilute C incorporation affects the electronic structure of Ge alloys, revealing a quasi-direct band gap and disorder effects relevant for device engineering.

Contribution

It offers new insights into the electronic structure evolution of Ge$_{1-x}$C$_{x}$ alloys, challenging previous band anti-crossing interpretations and highlighting disorder-induced inhomogeneity.

Findings

Formation of a quasi-direct band gap with mixed character.

Presence of localized states below the conduction band edge.

Strong energy broadening of the conduction band edge due to disorder.

Abstract

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 hybridisation of $A_{1}$-symmetric linear combinations of Ge states lying close in energy to the CB edge. This leads, in the ultra-dilute 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 "quasi-direct" alloy band gap, which retains a significant admixture of indirect Ge L-point CB edge character. We then analyse 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 localised states at energies below the Ge CB edge, with these states acquiring minimal direct ($\Gamma$) character. Our calculations demonstrate strong intrinsic inhomogeneous energy broadening of the CB edge Bloch character, driven by hybridisation between Ge host matrix and C-related localised 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 anti-crossing model. The implications of our findings for device applications are discussed.