Tuning Band Tails in Mono- and Multilayered Transition-Metal Dichalcogenides: A Detailed Assessment and a Quick-Reference Guide

Abstract

Transition-metal dichalcogenides (TMDs) are promising candidates for a wide variety of ultrascaled electronic, optoelectronic, and quantum-computing applications. The electronic density of states exponentially decaying into the band gap (also known as the band tail) has a strong impact on the performance of TMD applications. In this work, the band tails of various TMD monolayer and multilayer systems is predicted with density-functional-theory-based nonequilibrium Green's functions when placed on several dielectric substrates such as ${\mathrm{Hf}\mathrm{O}}_{2}$, ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$, ${\mathrm{Si}\mathrm{O}}_{2}$, and $h$-BN. Nonlocal scattering of electrons on polar optical phonons, charged impurities, and remote scattering on phonons in the dielectric materials is included in the self-consistent Born approximation. The band tails are found to critically depend on the layer thickness, temperature, doping concentration, and particularly on the chosen dielectric substrate. The underlying physical mechanisms are studied in high detail and an analytical interpolation formula is given to provide a quick reference for Urbach parameters and to guide the design work in ${\mathrm{Mo}\mathrm{S}}_{2}$, ${\mathrm{WS}}_{2}$, and ${\mathrm{WSe}}_{2}$.