Simulation of X-ray double-crystal rocking curves at multiple and inhomogeneous heteroepitaxial layers

Synchrotron radiation has been used to obtain double-crystal X-ray rocking curves from inhomogeneous layers of GaInAs on InP at a range of wavelengths. The consistency of the lattice-parameter profiles deduced by simulating the rocking curves using the Takagi-Taupin equations is shown to be good. The computational method has been extended to calculate the rocking curves from relatively thick multilayer structures of GaAlAs on GaAs grown by molecular beam epitaxy. This dynamical-theory approach permits the prediction of positions, heights and widths of major and satellite peaks. Results are in excellent agreement with experimental measurements, and by comparing experimental and calculated profiles the structural parameters of the layer can be deduced. The dynamical theory is particularly suitable for calculating the complete rocking curve especially where thick confining layers are present and the computational model is directly applicable to multi-layers with varying layer thicknesses.