Abstract

We have extended the matrix representation of the dynamical theory of x-ray diffraction to include Bragg planes that are oblique with respect to the surface of a flat crystal wafer. In place of the two independent 2×2 matrices of the Abelés method for planes parallel to the surface, we use a single 8 × 8 matrix. With such a matrix, rays may be skew with respect to the oblique Bragg planes and the wafer surface. The new approach brings out the close analogy between the diffraction of visible light by blazed gratings and the diffraction of x rays by edges of oblique Bragg planes near the crystal surface. Matrix methods present no special problem in cases where the layers near the surface do not have the same spacing normal to the surface as those deeper down, resulting in curved oblique planes. Thus epitaxial layers of varying composition, and crystals strained by ion implantation, can be treated as easily as uniform wafers so long as distorted 3-D order remains. An additional set of diffracting Bragg planes parallel to the surfaces can be included with little complication, thus allowing investigation of double-diffraction effects at the intersection of two diffraction cones.

© 1987 Optical Society of America