Small-angle X-ray scattering of two-phase atomistic models for amorphous silicon–germanium alloys

Abstract The present work deals with a detailed analysis of the small-angle X-ray scattering in amorphous silicon–germanium alloy using the simulation technique. We envisage the two-phase alloy model consisting in a mixture of Ge-rich and Ge-poor domains at the nanoscale. By substituting Ge atoms for Si atoms in a continuous random network, compositionally nanoheterogeneous alloys are generated with various composition-contrasts between the two phases. After relaxing the as-generated structure, we compute its radial distribution function, and then we deduce by the Fourier transform technique its X-ray scattering pattern. Using a smoothing procedure, the computed small-angle X-ray scattering patterns are corrected for the termination errors due to the finite size of the model, allowing so, for the first time at our best knowledge, a rigorous quantitative analysis of this scattering. Our simulation shows that the relative alloy composition of the two phases is a determinant parameter for the occurrence of small-angle X-ray scattering. A composition-contrast threshold, independent of the overall composition of the alloy as well as the relative volume fraction of the phases, has been demonstrated. Thus, two-phase silicon–germanium alloy with composition-contrast smaller than 0.3 behaves as compositionally homogeneous alloy in the context of small-angle X-ray scattering experiment. Our simulation also shows that the experimentally derived characteristics of the compositional heterogeneity in the alloy, such as radius of gyration and correlation volume, are composition-contrast dependent; they are generally smaller or equal to the actual values.