Abstract
Amorphous silicon ( a-Si) is a widely studied noncrystalline material, and yet the subtle details of its atomistic structure are still unclear. Here, we show that accurate structural models of a-Si can be obtained using a machine-learning-based interatomic potential. Our best a-Si network is obtained by simulated cooling from the melt at a rate of 1011 K/s (that is, on the 10 ns time scale), contains less than 2% defects, and agrees with experiments regarding excess energies, diffraction data, and 29Si NMR chemical shifts. We show that this level of quality is impossible to achieve with faster quench simulations. We then generate a 4096-atom system that correctly reproduces the magnitude of the first sharp diffraction peak (FSDP) in the structure factor, achieving the closest agreement with experiments to date. Our study demonstrates the broader impact of machine-learning potentials for elucidating structures and properties of technologically important amorphous materials.
Highlights
Amorphous silicon (a-Si) is a fundamental and widely studied noncrystalline material, with applications ranging from photovoltaics and thin-film transistors to electrodes in batteries.[1−5] Its atomic-scale structure is traditionally approximated in a Zachariasen-like picture[6] with all atoms in locally “crystal-like”, tetrahedral environments, but without long-range order.[7−9] the real material contains a nonzero amount of coordination defects, colloquially referred to as “dangling bonds” and “floating bonds”
We note at the outset that, defect sites in a-Si may be passivated by hydrogenation in some synthetic conditions, we here focus on the archetypical, hydrogen-free material as made in ion-implantation or sputter-deposition experiments.[10−14]
We recently introduced a ML potential for amorphous carbon,[34] based on the Gaussian approximation potential (GAP) framework[27] and the Smooth Overlap of Atomic Positions (SOAP) atomic similarity kernel,[35] which captures the intricate structural, mechanical, and surface properties of the material[34] and, more recently, has enabled accurate large-scale simulations of the growth mechanism.[36]
Summary
(c) Angle distribution functions for a-Si GAP structures. Points show original data, sampled from short (5 ps) MD simulations; lines show Gaussian fits; data for different quench rates are vertically offset for clarity. (d) Medium-range order in these a-Si networks, assessed by shortest-path ring statistics.[42] that is largely comparable to DFT, but with a computational cost that is orders of magnitude lower, and with linear We survey results of RMC modeling, which is an established means of extracting structural information from diffraction data.[17] Recent work by some of us showed that reasonable restraints can improve the RMC modeling of a-Si.[18] In particular, the SOAP similarity measure, initially developed to encode atomic structure in ML potentials,[35] proved useful for this purpose.[48] SOAP-RMC output, subsequently relaxed using DFT, has been shown to provide a high-quality structural model of a-Si.[48] We take the same structures but anneal them further using GAP: heating to 1100 K, holding, and cooling back to 300 K, for a total simulation time of 50 ps This relatively short annealing is thought to be appropriate, as a recent DFT-MD study showed that annealing a quenched structure at 10 ps versus 20 ps had no appreciable effect on the outcome.[24] We performed the same annealing procedure.
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