A Novel Method of Analyzing Peak Broadening Due to Mosaicity for Cubic Crystals on (001) Substrate using Double-Crystal X-ray Diffraction Measurements

Abstract

A novel method of analyzing X-ray peak broadening due to mosaicity for double-crystal X-ray diffraction measurements is proposed, which is an improved version of a conventional method using azimuthal angle dependence. The method is applicable to cubic crystals grown on a (001) substrate. The novelty of the method lies in the fact that the dependence of the full width at half-maximum (FWHM) on various reflection indices hkl is analytically derived in detail. The geometric relation between a tilted epilayer and the hkl measurement configuration is clarified, and a theoretical formula is derived. The resultant value of the FWHM divided by cos θC, where θC is the angle between (001) and (hkl) planes, is independent of the reflection index when the broadening is due to local tilt distribution caused by crystal mosaicity. The analytical method can be used as a criterion to judge whether or not X-ray peak broadening is due to the mosaicity. It is demonstrated that this formula holds for InAsP/InGaAsP SLS (strained layer superlattice) samples. The presented method is especially useful for samples with very weak peak intensity due to a high degree of mosaicity, to which reciprocal lattice-mapping measurement cannot be applied.