Transition metal dichalcogenides (TMDCs), together with other two-dimensional (2D) materials have attracted great interest due to the unique optical and electrical properties of atomically thin layers. In order to fulfill their potential, developing large-area growth and understanding the properties of TMDCs have become crucial. Here, we used molecular beam epitaxy (MBE) to grow atomically thin MoSe$_2$ on GaAs(111)B. No intermediate compounds were detected at the interface of as-grown films. Careful optimization of the growth temperature can result in the growth of highly aligned films with only two possible crystalline orientations due to broken inversion symmetry. As-grown films can be transferred onto insulating substrates allowing their optical and electrical properties to be probed. By using polymer electrolyte gating, we have achieved ambipolar transport in MBE-grown MoSe$_2$. The temperature-dependent transport characteristics can be explained by the 2D variable-range hopping (2D-VRH) model, indicating that the transport is strongly limited by the disorder in the film.
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