  This paper introduces a growth method---suboxide molecular-beam epitaxy
(S-MBE)---which enables the growth of Ga2O3 and related materials at growth
rates exceeding 1 micrometer per hours with excellent crystallinity in an
adsorptioncontrolled regime. Using a Ga + Ga2O3 mixture with an oxygen mole
fraction of x(O) = 0.4 as an MBE source, we overcome kinetic limits that had
previously hampered the adsorption-controlled growth of Ga2O3 by MBE. We
present growth rates up to 1.6 micrometer per hour for Ga2O3--Al2O3
heterostructures with unprecedented crystalline quality and also at
unparalleled low growth temperature for this level of perfection. We combine
thermodynamic knowledge of how to create molecular-beams of targeted suboxides
with a kinetic model developed for the S-MBE of III-VI compounds to identify
appropriate growth conditions. Using S-MBE we demonstrate the growth of
phase-pure, smooth, and high-purity homoepitaxial Ga2O3 films that are thicker
than 4 micrometer. With the high growth rate of S-MBE we anticipate a
significant improvement to vertical Ga2O3-based devices. We describe and
demonstrate how this growth method can be applied to a wide-range of oxides.
S-MBE rivals leading synthesis methods currently used for the production of
Ga2O3-based devices.
