Electron transmission and mean free path in molybdenum disulfide at electron-volt energies

Abstract

In van der Waals (vdW) materials, the electron mean free path (MFP) is largely influenced by the discrete states in the unoccupied band structure. So far, the influence of these states has only been measured in graphene, while all measurements on other vdW materials lack energy resolution. Here, we present reflection and transmission spectra of freestanding, few-layered molybdenum disulfide $(\mathrm{Mo}{\mathrm{S}}_{2})$ samples in the $0--55$ eV electron range. Our measurements reveal states of enhanced electron transmissivity above the vacuum level, that correspond to the (unoccupied) density of states. We also show a full quantum-mechanical calculation that confirms a good understanding of the elastic scattering in $\mathrm{Mo}{\mathrm{S}}_{2}$. A model is developed to extract the inelastic MFP spectrum, which is a measure of the inelastic scattering cross section. As $\mathrm{Mo}{\mathrm{S}}_{2}$ is a complicated system of different atomic planes, we expect that our methods generalize well to other van der Waals materials and heterostacks thereof.