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In this study, we explore the growth of ultrathin and highly-mismatched InAs directly on SOI islands. SOI islands allow the termination of misfit dislocations at the island edges to relieve the strain. For MOSFETs, the ability to tailor the ratio of InAs to Si in an ultrathin (~3 nm) channel allows optimization of both the channel density-of-states effective mass and the bandgap, for achieving high channel current at low voltage. We show that flat, planar, growth of InAs can be achieved, despite the 11.6% lattice mismatch, on submicron SOI islands by molecular beam epitaxy (MBE) toward realization of MOSFETs. Furthermore, metalorganic chemical vapor deposition is shown to nucleate InAs selectively on SOI islands and first back-gated transistor results are presented.