  A refined model of the origin of epitaxial tilt on miscut (or vicinal)
substrates is explained by employing crystal modeling and reciprocal space
analysis. The Nagai tilt model (H. Nagai, J. Appl. Phys., 45, 3789 (1974)) is
often cited to explain the tilt of lattice planes in a pseudomorphic layer
deposited on a miscut substrate that is observed in high resolution x-ray
diffraction measurements. Here, however, we demonstrate how that model
incorrectly describes how the substrate applies biaxial stress onto the
epitaxial layer. Most importantly, the stress applied to an epitaxial layer on
a miscut substrate is not along a low index plane. For example, the surface
plane of a nominally (001) cubic substrate with a miscut of 10{\deg} towards
the [110] is the (118) plane and the stress applied is parallel along 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 the Poisson ratio of
the layer that is applicable to any crystal system.
