Improved model for the determination of strain fields and chemical composition of semiconductor heterostructures by high-resolution x-ray diffractometry

In this work we present an improved approach for the analysis of high-resolution X-ray diffraction measurements of lattice-mismatched semiconductor heterostructures. Our model considers all the second-order components of the dynamical X-ray incidence parameter for an arbitrary lattice deformation. We demonstrate that higher-order approximations are necessary in order to determine the correct lattice mismatch value and the strain status of epitaxial structures. In addition, we derive an analytical expression which relates the strain components to the lattice mismatch and which allows us to determine the chemical composition (mole fraction) of coherent, partially or fully relaxed ternary compound heterostructures grown on high as well as on low-symmetry substrate surfaces with very high accuracy.