Lattice Parameters and Strains in Epitaxial Layers and Multilayers

Abstract

In this chapter we describe the method of strain analysis in expitaxial layer systems. Epitaxial growth onto a crystalline substrate always is associated with the appearance of strain. Since the free lattice parameters of the layer system differs from that of the substrate, the lattice matching at the interface will result in lattice deformation perpendicular to it to minimize the strain energy of the layer. Often the strain energy of the substrate is neglected, as long as the substrate can be assumed as infinitely thick. For cubic material and epitaxy onto (001) the applied strain in the layer is bi-axial and an initially cubic material becomes tetragonally deformed. For epitaxy onto higher indexed planes the strain relaxation will result in a lattice of much lower symmetry. X-ray high-resolution diffraction is a nondestructive tool to analyze the strain state of epitaxial layers. Here the accuracy is high as long as one measures the lattice mismatch between the (non-deformed) substrate and the deformed layer lattice on the relative scale. In a completely lattice-matched system it is often sufficient to measure the out-of-plane lattice mismatch, partially relaxed systems require two independent measurements, one parallel and another perpendicular to the surface normal. This can be performed by measuring one Bragg diffraction with symmetric and the other with asymmetric scattering geometry. Since the layer is very thin one has to use strong-asymmetric diffraction in order to enhance the scattering signal of the layer. In this case the in-plane lattice mismatch can be measured uniquely by x-ray grazing-incidence diffraction.