The carbon state in dilute germanium carbides

Abstract

Conduction and valence band states for the highly mismatched alloy (HMA) Ge:C are projected onto Ge crystal states, Ge vacancy states, and Ge/C atomic orbitals, revealing that substitutional carbon not only creates a direct bandgap but also the new conduction band is optically active. Overlap integrals of the new Ge:C conduction band state with states from unperturbed Ge show that the new band cannot be attributed to any single Ge band but is a mixture of multiple Ge states. The Ge Γ conduction band valley state plays the largest single role, but L and X valley states collectively contribute a larger share than Γ due to the multiplicity of degenerate states. C sites structurally resemble uncharged vacancies in the Ge lattice, similar to Hjalmarson's model for other HMAs. C also perturbs the entire Ge band structure even at the deepest crystal core energy levels, particularly if staggered supercells are used to mimic a disordered alloy. Projection onto atomic sites shows a relatively weak localization compared with other HMAs, but it does show a strong anisotropy in probability distribution. L-valley conduction band states in Ge contribute to the conduction band minimum in Ge:C, but the optical transition strength in Ge:C remains within a factor of 2 of the direct gap transition in Ge.