The emergence of transition metal dichalcogenides (TMDs) as 2D electronic materials has stimulated proposals of novel electronic and photonic devices based on TMD heterostructures. Here we report the determination of band offsets in TMD heterostructures by using microbeam X-ray photoelectron spectroscopy ({mu}-XPS) and scanning tunneling microscopy/spectroscopy (STM/S). We determine a type-II alignment between $textrm{MoS}_2$ and $textrm{WSe}_2$ with a valence band offset (VBO) value of 0.83 eV and a conduction band offset (CBO) of 0.76 eV. First-principles calculations show that in this heterostructure with dissimilar chalcogen atoms, the electronic structures of $textrm{WSe}_2$ and $textrm{MoS}_2$ are well retained in their respective layers due to a weak interlayer coupling. Moreover, a VBO of 0.94 eV is obtained from density functional theory (DFT), consistent with the experimental determination.
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