Rocking curve peak shift in thin semiconductor layers

A simple x-ray diffraction method for determining layer composition and mismatch is by measurement of the separation of peaks in a rocking curve. This method can only be used for layers with a thickness above a certain value. This minimum thickness can be significantly large for layers with a small lattice mismatch as in AlGaAs/GaAs or isoelectronic-doped III-V semiconductor layers. We give such an example and show that the interference between the diffraction amplitudes of the thin layer and that of the substrate is responsible for the peak shifting of the layer Bragg peak. When this peak shifting is significant, the kinematical diffraction theory and the peak separation method should not be used for the mismatch measurement, and only the dynamical diffraction theory simulation should be used. We present a criterion on the layer thickness, below which the dynamical theory simulation must be used. This thickness is inversely proportional to the lattice mismatch and does not depend on the diffraction geometry, wavelength, and substrate material.