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

Abstract

Synchrotron radiation has been used to obtain double-crystal X-ray rocking curves from inhomogeneous layers of GalnAs 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 GaA1As 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 multilayers with varying layer thicknesses.

Fourier-coefficient method of X-ray rocking-curve interpretation

“…For the graded layers with linear strain, our method allows us to compute parameters N, eo and A e, in contrast to the method of Fresnel's layers (Kolpakov & Punegov, 1988), if the rocking curve does not have clearly visible oscillations (Hill, Tanner, Halliwell & Lyons, 1985;Kolpakov & Punegov, 1985;Macrander, 1988;Macrander, Minami & Berreman, 1986) but only some broadening of the peak caused by diffraction from the epitaxic layer. This fact is illustrated in Fig.…”

“…For such distortions, the rocking curves have complicated fringe structures (Hill, Tanner, Halliwell & Lyons, 1985;Kolpakov & Punegov, 1985;Macrander, 1988;Macrander, Minami & Berreman, 1986) and the solution of the inverse double-crystal X-ray diffractometry problem by the least-squares method is a nontrivial one. The use of (4) allows us to find the parameters eo and Ae without any problems; really, the modulus of Uk depends only on the gradient Ae and has the form lukl = Ipl21~l 2k…”

X-ray diffraction evidence for transient composition effects in MOVPE multilayer growth for Ga1−x Al x As alloys

“…Interference effects become predominant in the building of the intensity output, and computer simulation following well established procedures (Halliwell, Lyons & Hill, 1984;Hill, Tanner, Halliwell & Lyons, 1985;Bensoussan et al, 1987) has to be used. Since in the present case the introduction of the design parameters in the calculation did not lead to a satisfactory match between experimental and simulated curves, a more general procedure has been thought of and some guidelines are proposed which use the reflectivity ratios and possible periodicities apparent in the reflexion profile.…”

A Statistical Method for the Fitting of Double-Crystal X-ray Rocking Curves

“…Owing to the scientific and technological importance of this type of characterization, numerous methods have been developed for simulating double-crystal rocking curves via computer analysis. Both kinematic (Speriosu & Vreeland, 1984;Kyutt, Petrashen & Sorokin, 1980) and dynamic © 1997 International Union of Crystallography Printed in Great Britain -all rights reserved (Halliwell, Lyons & Hill, 1984;Hill, Tanner, Halliwell & Lyons, 1985) models have been described in the literature, and several vendors now offer such rocking-curve simulation packages as software products. Methods involving the Fourier transform of the double-crystal reflectivity profile have also been reported (Stepanov, 1994).…”