X-ray rocking-curve analysis of crystals with buried amorphous layers. Case of ion-implanted silicon

X-ray rocking-curve analysis of implanted silicon is commonly used to investigate damage accumulation with increasing ion dose. The damage build-up is observed by the trends of either the maximum of the lattice strain normal to the surface (epsilon(perpendicular to)) or the depth integral of the epsilon(perpendicular to) profile. However, for doses high enough to produce a buried amorphous layer, the determination of the peak value of the al depth profile, and hence of its integral, is not possible. This is demonstrated by means of a simple diffraction model which describes the amorphous layer as a material for which the structure factor is reduced to zero by sufficiently high values of the static Debye-Waller factor and for which the expansion mu normal to the surface is given by the product of the fractional change of the interplanar spacing of the perfect crystal (epsilon(perpendicular to alpha)) and the thickness of the amorphous layer (t(alpha)). Since this expansion can be written as mu = epsilon(perpendicular to alpha)t(alpha) = (n + x)d, where n is an integer (n = 0, 1,2,...), 0 less than or equal to x < 1 and d is the spacing of the diffraction planes of the perfect crystal, the diffraction model shows that, for given thickness t(alpha) and fraction x of n, there exists a discrete, in principle infinite, set of mu values able to give identical rocking curves. This prevents the rigid outward displacement of the damaged surface crystalline region with respect to the substrate from being determined.