InAs and high indium concentration InGaAs have very high electron mobilities and saturation velocities. Using them as the metal oxide semiconductor field effect transistor (MOSFET) channel materials is a very promising way to keep improving the integrated circuit chip performance beyond Moore's law. One major obstacle is the growth of these high mobility channel materials on lattice-mismatched substratcs. In this work, we studied the molecular beam epitaxy growth of InAs, In0.8Al0.2As, and In0.8Ga0.2As on lattice-mismatched GaAs substrate using a thin indium-rich InAs wetting layer. Reflection high energy electron diffraction and atomic force microscopy were used to optimize the growth conditions. A surface roughness of similar to 0.5 nm rms was obtained for InAs layers. A new MOSFET structure with In0.8Ga0.2As channel and In0.8Al0.2As buffer layer was also demonstrated. High mobility depletion mode MOSFET characteristics were demonstrated. (C) 2008 American Vacuum Society.