Transmission electron microscopy has been used to characterize the microstructure of heteroepitaxial CdTe (111) layers grown by molecular beam epitaxy directly on nominal and misoriented Si(001) substrates. High‐resolution electron micrographs showing atomic‐scale details of the CdTe (111)/Si(001) interface have been recorded. Layer quality depended on the substrate tilt parameters, including the offcut orientation angle &thgr;, and the azimuthal angle &fgr; relative to [110]. Small &fgr; values (4° and 10°) gave high densities of stacking fault twins throughout the epilayer whereas larger misorientation angles led to a rapid falloff away from the substrate. Under optimized growth conditions, the occurrence of twins effectively dropped to zero within a distance of less than 2.5 &mgr;m from the substrate surface. ©1995 American Institute of Physics.