Theory of X-ray diffraction on a superlattice with quantum wires

Within the statistical kinematical theory of X-ray diffraction the problem of X-ray scattering from superlattice with lateral composition modulation (LCM) is solved. The general solution for scattered intensity in reciprocal space are derived. The theory takes into account fluctuations of lateral modulation amplitude. In our model, superlattice was considered as an (A nB m) multilayer heterostructure. Upper and lower heterointerfaces of A-type layers oscillate sinusoidally along the surface and shifted from each other by half of an undulating wavelength. Such quasiperiodical nanostructure forms quantum nanowires. Those quantum nanowires had been previously observed in superlattices with small-misfit strains. Using this LCM model, numeric simulations of reciprocal space maps (RSMs) for (InAs) n/(GaSb) m sluperlattice were obtained. RSMs were performed about the (004) Bragg peak in the plane perpendicular and parallel to the lateral modulation. Influence of LCM parameters (such as undulation wavelength, undulation amplitude etc.) on RSMs was determined. It was established that the presence of lateral composition modulation leads to appearance of specific additional peaks on RSMs. Size, form and location of additional peaks strongly depend on LSM parameters. If diffraction plane is parallel to quantum wires, then all additional peaks are located on q z axis; if diffraction plane is perpendicular to quantum wires, then all additional peaks are shifted along q x axis.