A method to obtain thin (less than 300 nm) strain-relaxed Si1-xGex buffer layers on Si or silicon-on-insulator (SOI) substrates. These buffer layers have a homogeneous distribution of misfit dislocations that relieve the strain, remarkably smooth surfaces, and a low threading dislocation (TD) density, i.e. less than 106 cm2. The approach begins with the growth of a pseudomorphic or nearly pseudomorphic Si1-xGex layer, i.e., a layer that is free of misfit dislocations, which is then implanted with He or other light elements and subsequently annealed to achieve the substantial strain relaxation. The very effective strain relaxation mechanism operating with this method is dislocation nucleation at He-induced platelets (not bubbles) that lie below the Si/Si1-xGex interface, parallel to the Si(001) surface.