Atomistic analysis of band-to-band tunnelling in direct-gap $\mathrm{Ge}_{1-X}\mathrm{Sn}_{x}$ group-IV alloys

The emergence of a direct band gap in $\mathrm{Ge}_{1-x}\mathrm{Sn}_{x}$ alloys has stimulated interest in developing $\mathrm{Ge}_{1-x}\mathrm{Sn}_{x}$ alloys and nanostructures for applications in Si-compatible electronic and photonic devices. The direct band gap of $\mathrm{Ge}_{1-x}\mathrm{Sn}_{x}$, combined with the strong band gap reduction associated with Sn incorporation, makes $\mathrm{Ge}_{1-x}\mathrm{Sn}_{x}$ a promising material system for the development of Si-compatible tunnel field-effect transistors (TFETs) due to an expected strong increase in band-to-band tunnelling (BTBT). Based on a semi-empirical tight-binding model, we establish quantum kinetic BTBT current calculations for atomistic $\mathrm{Ge}_{1-x}\mathrm{Sn}_{x}$ alloy supercells. Recent analysis suggests that $\mathrm{Ge}_{1-x}\mathrm{Sn}_{x}$ possesses hybridised conduction band edge states for $x \lesssim 10{\%}$. We demonstrate that Sn-induced band mixing opens up a pathway for direct BTBT in ordered alloy supercells, strongly enhancing BTBT current compared to Ge. The framework we establish allows for quantitative prediction of the properties and performance of $\mathrm{Ge}_{1-x}\mathrm{Sn}_{x}$-based TFETs.