Unoccupied bands in the molybdenum dichalcogenides MoS$_2$, MoSe$_2$, and MoTe$_2$

We present angle-resolved reflected electron spectroscopy (ARRES) data for the three molybdenum-based transition metal dichalcogenides (TMDs) \mos, \mose, and \mote. To follow the changes as the series moves from S to Se to Te in more detail, we determine accurate IV-spectra for monolayers and bulk TMDs. These experimental data sets are then compared with theoretical predictions for both the unoccupied band structure and the scattering density of states. We find good agreement, especially for lower energies where inelastic effects are relatively unimportant. Furthermore, we identify a series of interlayer resonances for which the dependence of the hybridization effects on the layer count is observed. Although these resonances bear similarity to interlayer resonances in hBN and graphene, they differ in their character, being dominated by unoccupied $d$-states of the chalcogen-atoms. The unoccupied states studied and analyzed here play a key role in all processes that require an electron to temporarily reside in a state above the vacuum level, such as in photoemission and secondary electron emission experiments.