We report epitaxial growth of vanadium diselenide (VSe$_2$) thin films in the octahedrally-coordinated (1T) structure on GaAs(111)B substrates by molecular beam epitaxy. Film thickness from a single monolayer (ML) up to 30 ML is demonstrated. Structural and chemical studies using by x-ray diffraction, transmission electron microscopy, scanning tunneling microscopy and x-ray photoelectron spectroscopy indicate high quality thin films. Further studies show that monolayer VSe$_2$ films on GaAs are not air-stable and are susceptible to oxidation within a matter of hours, which indicates that a protective capping layer should be employed for device applications. This work demonstrates that VSe$_2$, a candidate van der Waals material for possible spintronic and electronic applications, can be integrated with III-V semiconductors via epitaxial growth for 2D/3D hybrid devices.
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