RECIPROCAL SPACE MAPPING OF SEMICONDUCTOR STRUCTURES -- EXPERIMENT AND SIMULATION

Z. Sourek and J. Kub

Institute of Physics, Academy of Sciences of the Czech Republic Na Slovance 2, 180 40 Praha 8, Czech Republic

Keywords: Epitaxial thin layers, superlattice, X-ray diffraction

We have investigated series of semiconductor heteroepitaxial multilayers and superlattices grown by MO CVD. The experiments were performed using double-crystal and triple-crystal diffractometer and CuKa radiation. A double reflection Ge 400 channel-cut single crystal was used as a beam conditioner. The diffraction curves of the samples examined were recorded in the nearly parallel setting Bragg geometry in the vicinity of the symmetric 400 reflection. Triple-crystal analyses were performed by inserting a four reflection Si (111) channel-cut crystal between the sample and detector to serve as an analyser crystal. The measurements of the intensity around a reciprocal lattice vector q from the vicinity of the reciprocal lattice vector q_hkl give reciprocal space map. This map is given by the distribution of diffracted intensity I(q - q_hkl) modified by the experimental distortion.

Large variety of demands for characterization of the quality and structure properties of different materials calls for a rather uniform experimental arrangement of monochromators and analysers. In such a case a good understanding of given experimental conditions and the influence of instrumental distortion is necessary. The results are represented by reciprocal space maps and the attention is turned to simulation program, which takes into account the experimental conditions as much as possible.

The effect of the off-cut of the surface from the exactly (001) plane is shown. The respective maps were measured in three different crystal positions, the azimuth differs always by 90^o. The slope of the main line for both asymmetrical cases is the same, changing just the sign, in the symmetrical case the main line follows the line q_|| = 0. Moreover the additional lateral lines at both sides of the main line are to be seen. This effect is the same for both asymmetrical cases and disappeared completely in the symmetrical one. It is given by periodicity in the only lateral direction given by giant steps on the interfaces created during the growth process of the superlattice due to the off-cut.

To understand better the features of the maps and distinguished between experimental distortions and real crystal properties a simulation program was written. The intensity of X-rays around q_hkl in the (q vs. q/2q) representation (i.e. as measured, including experimental distortion) can be expressed by a complex integral R. The functions describing the properties of focus, slits, crystal functions of respective crystals are taken into account as well as spectral distribution, horizontal and vertical divergence of the beam and also the influence of the frequent curvature of the sample. The comparison of the experimental space map of superlattice GaInSb/GaSb and its theoretical simulation in the case of perfectly plane surface and in the case when an appropriate curvature is applied are presented.

By means of the simulations of experimental distortion it is possible not only to judge the influence of single elements of the experimental setting and to optimise the experiment in advance, but also to give much better structural characterization of the investigated samples.

This work is partially supported by the projects from the Grant Agency of the Czech republic No. 202/96/0458 and 202/97/0003.