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]._⊥) or the depth integral of the [epsilon]._⊥ profile. However, for doses high enough to produce a buried amorphous layer, the determination of the peak value of the [epsilon]._⊥ 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 u normal to the surface is given by the product of the fractional change of the interplanar spacing of the perfect crystal ([epsilon]._⊥α) and the thickness of the amorphous layer (t_α). Since this expansion can be written as u = [epsilon]._⊥αt_α = (n + x)d, where n is an integer (n = 0, 1, 2, ...), 0 ≤ x < 1 and d is the spacing of the diffraction planes of the perfect crystal, the diffraction model shows that, for given thickness t_α and fraction x of d, there exists a discrete, in principle infinite, set of u 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.