Lattice Mismatch and Interfacial Disorder in Superlattices

We have developed a general X-ray diffraction model which enables to investigate interfacial disorder in crystalline/amorphous and crystalline/ crystalline multilayers. Using classical structure factor calculations, we simulate the evolution of the diffracted X-ray intensities as a function of the fluctuation amplitude, the superlattice wavelength and the interatomic distances. From experimental X-ray diffraction patterns, the interfacial disorder is extracted as a function of superlattice wavelength for various crystalline/ crystalline systems. An enhanced lattice mismatch between the two components gives rise to an increase of interfacial disorder. The production and investigation of new materials that do not occur naturally is an issue of much current interest. Thin film deposition techniques, such as molecular beam epitaxy and sputtering, are being extensively used to prepare artificially layered structures. Most work to date has been performed on semiconductor and metallic superlattices which are lattice matched [l]. It has been shown that it is possible to achieve superlattice growth of materials with a large lattice mismatch and different crystal symmetry [2], which enables the investigation of the problem of coherence across an interface. Moreover, these superlattices are found to exhibit a series of interesting physical properties [3]. In this work we relate the structural properties of several metallic superlattices to crystal symmetry and lattice mismatch, using a recently developed model for superlattices [4]. Structural properties of superlattices are most easily studied by standard 6 26 X-ray diffraction techniques [3]. In order to interpret the measured X-ray intensity profiles, structural models have to be developed and the calculated intensities compared to the data. To date, a variety of models for compositionally modulated structures have been calculated. In the sample step model [3] the lattice spacings of the two constituent materials retain their bulk value within each layer, whereas the uniform strain model [5] assumes that one single lattice spacing is maintained throughout all layers. These two models can explain the positions and relative intensities of X-ray peaks of crystalline/crystalline multilayers [5, 121, but cannot account for the observed large peak widths. An even larger discrepancy is found in crystalline/ amorphous multilayers [ 131, where at high 26 angles only one broad peak is observed, caused by a reduction of the structural coherence length 5. In realistic models, structural disorder has to be built in as a mechanism to reduce long range coherence. Most models assume gaussian fluctuations of the modulation wavelength A [7, 151 or of the individual layer thicknesses Physica Scripta 39 [l 1, 131. A distinction is to be made between continuous gaussian fluctuations, which originate from an amorphous interface, and discrete gaussian fluctuations resulting from crystalline interfaces. A discrete fluctuation distribution with one interatomic distance width has little effect on the highangle X-ray spectra from crystalline/crystalline multilayers, except for a disappearance of secondary superlattice maxima and a slight reduction in intensity [16]. In contrast, a continuous gaussian distribution with the same width leads to the disappearance of all high-angle superlattice peaks. For instance a continuous fluctuations of about 2 A on the amorphous layer thickness in crystalline/amorphous multilayers explains the observed loss of all superstructure at high angles Here we present a model for crystalline/crystalline multilayers taking into account continuous gaussian fluctuations only on the interface distance (the distance between two planes of different material). We consider a superlattice consisting of M bilayers of N, planes of material A at distance d, and with atomic scattering factor fa, and Nb planes of material B at distance db and with atomic scattering factorf,. We assume each interface distance to be continuous gaussian distributed around an average 6, conventionally taken to be (d, + db)/2, and with distribution width c-' . Using kinematical structure factor calculations [4], the average diffracted intensity (with scattering vector q perpendicular to the layers), is given as: Z(q) = M(A2 + l? + 2AB exp (-q2/4c2) cos (qA/2)) 1131.