Grazing incidence diffraction of X-rays in semiconductor heterostructures: Application of the integral mode

Abstract

The grazing incidence diffraction (GID) of X-rays enables to characterize thin subsurface layers in semiconductor heterostructures having a thickness smaller than 100 nm. The dynamical theory of X-ray diffraction is extended for the case of identical in plane lattice parameters at the heterointerface. Especially the variation in the specular diffracted (220) Bragg intensity measured with open detector (integral mode) is evaluated in dependence on the grazing angle Φ0 of the primary beam with respect to the (001) surface. Using a parallel beam an oscillation behaviour occurs at the high angle side Θc < Φ0≦0.50(Θc is the angle of total external reflection) of the diffraction curveI(Φ0) which can be related to the thickness of the perfect crystalline part of the epilayertK. Having an incident beam divergence and a small difference in the effective refractive indices of the layer and the substrate the oscillations are almost leveled. They are further visible in case of a minute inclination of the (220) lattice plane with respect to the surface normal. In the interval 0 < Φ0<Θc the slope of the integral curve depends on the thickness of the subsurface layertAwhich does not contribute to the Bragg diffraction. The integral mode is sensitive for layers of about 0<tA<15 nm and 15<tK<80 nm. The proposed theory working principally for multilayer structures is presently suplicated to interpret GID curves ofAIIIBvheterostructures.