Structural investigations of high quality Si/Ge strained-layer superlattices (SLSs) on [001] oriented Ge substrates prepared by molecular beam epitaxy are presented. Cross-sectional transmission electron microscopy reveals that a defect-free superlattice is achieved for a structure composed of a 20-period sequence of 3 monolayers (ML) Si and 9 ML Ge. High-resolution lattice images and electron diffraction patterns show that the whole structure is matched to the Ge substrate. Experimental values for the tetragonal deformation of the Si layers within the SLS are in good agreement with theory. An equivalent sample containing 120 periods exceeds the critical thickness for pseudomorphic growth of the SLS and shows the formation of twin lamellae. Applied Physics Letters is copyrighted by The American Institute of Physics.