A refined model for epitaxial tilt of elastically strained epilayers grown on miscut substrates

Abstract

A refined model of the origin of epitaxial tilt on miscut (or vicinal) substrates due to elastic lattice deformation is presented. The Nagai tilt model [Nagai, J. Appl. Phys. 45, 3789 (1974)] is often cited to explain the tilt of low index lattice planes in a pseudomorphic layer deposited on a miscut substrate that is observed in, for example, high resolution x-ray diffraction measurements. Here, however, we show that the Nagai model applies biaxial stress incorrectly to the epitaxial layer. Most importantly, the stress applied to an epitaxial layer on a miscut substrate is not along a low index plane but is rather along the surface plane. For example, the surface plane of a nominally (001) cubic substrate with a miscut of 10° toward [110] is the (118) plane and the stress applied is parallel to the (118) plane and not (001). Furthermore, under the framework of reciprocal space, the {00l} reflections would be symmetric reflections for on-axis substrates but asymmetric reflections for miscut substrates. The tilt that is experimentally observed between the low index substrate planes and the epitaxial layer planes [(001) for example with a miscut substrate] matches that which is predicted by treating the low index reflections as asymmetric reflections. An epitaxial tilt equation is provided which describes the tilt between epitaxial and substrate layers based on the lattice parameter mismatch as well as Poisson’s ratio of the layer that is applicable to any crystal system. This approach negates the need for the uneven distortions at the interface that are presented in the Nagai illustration. The approach presented here shows that a physically accurate biaxial deformation accounts for all of the observed experimental phenomena and provides a direct approach to determining the unit cell distortions.