Barium stannate (BaSnO₃) has a high single crystal mobility ~ 300cm²/V/s, compared to other perovskite oxides, due to the fact that the conduction band is made up of the tin 5s states. However, mobility in thin films of BaSnO₃ have not matched that of single crystals. In this study, we grow thin films of BaSnO₃ using the low-energy deposition technique called molecular beam epitaxy (MBE). In MBE, tin metal is normally used to supply the tin. However, tin has a low oxidation potential and excess oxygen could damage the filaments in the MBE chamber. Therefore, we use tin dioxide powder to supply the tin, as it is pre-oxidised. The primary reason for low mobility in thin films is defects such as misfit dislocations due to lattice mismatch between the film and the substrate. Dislocations cause electron scattering, which reduces mobility, and decreased defect concentration in the film could result in higher mobility. We optimize growth parameters to improve the material quality and reduce the number of defects, leading to thin films with superior mobility. We perform X-ray diffraction and atomic-force microscopy to characterize the thin films grown using MBE. High mobility BaSnO₃ thin films would allow integration with other perovskite oxides and fabrication of high speed oxide devices.