A method is provided for achieving device-quality active layers in lattice-mismatched-heteroepitaxial systems. The method eliminates strain and dislocations resulting from lattice mismatch with respect to the substrate (12) of a heteroepitaxial active layer (14). The optimized heterostructure comprises a substrate (12), a compositionally step-graded region terminated with a buffer layer (14), an intermediate region (16), an active layer (18), and a capping layer (20). Concepts of the invention are demonstrated in douple heterostructures containing the semiconductor alloys Ga.sub.xIn.sub.1-xAs and InAs.sub.yP.sub.1-y.
CONTRACTURAL ORIGIN OF THE INVENTION
 The United States Government has rights in this invention under Contract No. DE-AC36-99GO10337 between the U.S. Department of Energy and the National Renewable Energy Laboratory, a division of Midwest Research Institute.