We show by Monte Carlo simulation that electron mobility is greater when strained-silicon inversion layers are grown on SiGe-on-insulator substrates than when unstrained-silicon-on-insulator devices are employed (as experimentally observed). However, the electron mobility in strained-Si/SiGe-on-insulator inversion layers is strongly dependent on the strained-silicon layer thickness, T-Si, due to an increase of the phonon scattering, which partially counteracts the increase in the mobility achieved by the strain. This effect is less important as the germanium mole fraction, x, is reduced, and as the value of T-Si increases. (C) 2002 American Institute of Physics.