High-quality epitaxial films of 0.5-3.9-mu-m GaAs/Si [001], InP/GaAs [001] and InP/GaAs/Si [001] were grown at T(t) = 560-700-degrees-C using a 30 nm buffer layer produced at T(b) = 277-460-degrees-C. The 4% lattice mismatch between InP and GaAs or GaAs and Si and the different thermal expansion coefficients alpha(InP)/alpha(GaAs) = 0.8 and alpha(GaAs)/alpha(Si) = 1.8 causes a 0.1-1.8 parts per thousand reduction of lattice constants and a tetragonal distortion below a critical temperature T(c). This temperature approaches T(t) for InP/GaAs, T(b) for GaAs/Si - after thermal treatment - and about 150-degrees-C lower temperatures for InP/GaAs/Si.