On the role of secondary extinction in the measurement of the integrated intensity of X-ray diffraction peaks and in the determination of the thickness of damaged epitaxial layers

Abstract

The integrated intensity of X-ray diffraction reflections has been measured for a series of epitaxial layers of AIII nitrides (GaN, AlN, AlGaN) grown on different substrates (sapphire, SiC) and characterized by different degrees of structural perfection. It has been shown that, despite a high density of dislocations and a significant broadening of the diffraction peaks, the obtained values are not described by the kinematic theory of X-ray diffraction and suggest the existence of extinction. The results have been analyzed on the basis of the Darwin and Zachariasen extinction models. The secondary extinction coefficients and the thicknesses of epitaxial layers have been determined using two orders of reflection both in the Bragg geometry (0002 and 0004) and in the Laue geometry ($10\bar 10$) and $10\bar 20$). It has been demonstrated that the secondary extinction coefficient is the greater, the smaller is the broadening of the diffraction peaks and, consequently, the dislocation density. It has been found that, for epitaxial layers with a regular system of threading dislocations, the secondary extinction coefficient for the Laue reflections is substantially greater than that for the Bragg reflections.