Abstract
The present work deals with a detailed analysis of the small-angle X-ray scattering of nanoporous atomistic models for amorphous germanium. Structures with spherical nanovoids, others with arbitrarily oriented ellipsoidal ones, with monodisperse and polydisperse size distributions, were first generated. 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. The Guinier’s law is found to be valid irrespective of size and shape of the nanovoids over a scattering vector-range extending beyond the expected limit. A weighted combination of the Guinier’s forms accounts for well the nanovoid size distribution in the amorphous structure. The invariance of the Q-factor and its relationship to the void volume fraction are also confirmed. Our findings support then the quantitative analyses of available small-angle X-ray scattering data for amorphous germanium.
Highlights
Amorphous semiconductors have been the subject of extensive experimental and theoretical investigations
The obtained models are relaxed starting with initial configuration in which all the atoms in the supercell are randomly displaced from their positions in the continuous random network (CRN)
We have presented a detailed analysis of the small-angle X-ray scattering of nanoporous atomistic models for amorphous germanium (a-Ge)
Summary
Amorphous semiconductors have been the subject of extensive experimental and theoretical investigations. By correlating small-angle scattering results with those derived from other experiments [14,15,16,17,18,19,20], the mass-density measurements principally [19], many authors have postulated the existence of nanovoids in a-Si and a-Ge films. Such structural inhomogeneities are commonly believed to result in the mass-density of a-Si and a-Ge being lower than their corresponding crystalline phases; they generate significant fluctuations in the density at the nanoscale which can be at the origin of the intense small-angle scattering in these materials. Many attempts have been made to analyze quantitatively the small-angle scattering data in a-Si and AMPC
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