We report Al2O3/In0.53Ga0.47 As MOSFETs having both self-aligned in situ Mo source/drain ohmic contacts and self-aligned InAs source/drain n(+) regions formed by MBE regrowth. The device epitaxial dimensions are small, as is required for 22-nm gate length MOSFETs; a 5-nm In0.53Ga0.47 As channel with an In0.48Al0.52 As back confinement layer and the n(++) source/drain junctions do not extend below the 5-nm channel. A device with 200-nm gate length showed I-D = 0.95 mA/mu m current density at V-GS = 4.0 V and g(m) = 0.45 mS/mu m peak transconductance at V-DS = 2.0 V.