DETERMINATION OF THE LATTICE STRAIN AND CHEMICAL-COMPOSITION OF SEMICONDUCTOR HETEROSTRUCTURES BY HIGH-RESOLUTION X-RAY-DIFFRACTION

In order to determine the strain field of highly mismatched semiconduc tor heterostructures by high-resolution x-ray diffraction with high ac curacy,we derived a new second-order approximation of the incidence pa rameter considering an arbitrary lattice deformation. Our calculations show that, almost independently from the substrate orientation and th e considered material system, for low Miller-index reflections a latti ce mismatch greater than 0.004 is the value for which quadratic correc tions must be considered. The quadratic approximation increases the ra nge of validity by one order of magnitude, i.e., to a lattice mismatch up to 4%. In addition, the analytical expression which relates the st rain components measured by x-ray diffraction to the lattice mismatch is derived for semiconductor epitaxial layers grown on arbitrarily ori ented substrate crystals. Using Vegard's rule, our formula allows us t o determine the chemical composition of ternary compounds even for low -symmetry substrate orientations. We show that in this case shear stra in components have a non-negligible weight in the determination of the chemical composition of ternary compounds. Several examples consideri ng III-V, II-VI, and IV-IV semiconductor material systems are reported and discussed. (C) 1996 American Institute of Physics.