The thermal conductivity of Si–Ge superlattices with superlattice periods30<L<300Å, and aSi0.85Ge0.15thin film alloy is measured using the 3&ohgr;method. The alloy film shows a conductivity comparable to bulk SiGe alloys while the superlattice samples have a thermal conductivity that is smaller than the alloy. For30<L<70Å, the thermal conductivity decreases with decreasingL; these data provide a lower limit to the interface thermal conductanceGof epitaxial Si–Ge interfaces:G> 2 × 109 W m−2 K−1at 200 K. Superlattices with relatively longer periods,L>130Å, have smaller thermal conductivities than the short-period samples. This unexpected result is attributed to a strong disruption of the lattice vibrations by extended defects produced during lattice-mismatched growth. ©1997 American Institute of Physics.