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We report the use of suboxide molecular-beam epitaxy (S-MBE) to grow β-Ga2O3 at a growth rate of ∼1 µm/h with control of the silicon doping concentration from 5 × 1016 to 1019 cm−3. In S-MBE, pre-oxidized gallium in the form of a molecular beam that is 99.98% Ga2O, i.e., gallium suboxide, is supplied. Directly supplying Ga2O to the growth surface bypasses the rate-limiting first step of the two-step reaction mechanism involved in the growth of β-Ga2O3 by conventional MBE. As a result, a growth rate of ∼1 µm/h is readily achieved at a relatively low growth temperature (Tsub ≈ 525 °C), resulting in films with high structural perfection and smooth surfaces (rms roughness of <2 nm on ∼1 µm thick films). Silicon-containing oxide sources (SiO and SiO2) producing an SiO suboxide molecular beam are used to dope the β-Ga2O3 layers. Temperature-dependent Hall effect measurements on a 1 µm thick film with a mobile carrier concentration of 2.7 × 1017 cm−3 reveal a room-temperature mobility of 124 cm2 V−1 s−1 that increases to 627 cm2 V−1 s−1 at 76 K; the silicon dopants are found to exhibit an activation energy of 27 meV. We also demonstrate working metal–semiconductor field-effect transistors made from these silicon-doped β-Ga2O3 films grown by S-MBE at growth rates of ∼1 µm/h.