Efficient evaluation of epitaxial MoS$_{\mathrm{2}}$ on sapphire by direct band structure imaging*

The electronic band structure evaluation of two-dimensional metal dichalcogenides is critical as the band structure can be greatly influenced by the film thickness, strain, and substrate. Here, we performed a direct measurement of the band structure of as-grown monolayer MoS$_{\mathrm{2}}$ on single crystalline sapphire by reciprocal-space photoelectron emission microscopy with a conventional laboratory ultra-violet He I light source. Arrays of gold electrodes were deposited onto the sample in order to avoid charging effects due to the insulating substrate. This allowed the high resolution mapping ($\Delta E = $0.2 eV$; \Delta k = $0.05 {\AA}$^{\mathrm{-1}})$ of the valence states in momentum space down to 7 eV below the Fermi level. The high degree of the epitaxial alignment of the single crystalline MoS$_{\mathrm{2}}$ nuclei was verified by the direct momentum space imaging over a large area containing multiple nuclei. The derived values of the hole effective mass were 2.41 \textpm 0.05 m$_{\mathrm{0}}$ and 0.81 \textpm 0.05 m$_{\mathrm{0}}$, respectively at $\Gamma $ and K points, consistent with the theoretical values of the freestanding monolayer MoS$_{\mathrm{2}}$ reported in the literature.