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Machine learning reveals the complexity of dense amorphous silicon

Transitions between amorphous forms of solids and liquids are difficult to study. Machine learning has now provided fresh insight into pressure-induced transformations of amorphous silicon, opening the way to studies of other systems.
Paul F. McMillan is in the Department of Chemistry, University College London, London WC1H 0AJ, UK.
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Machine-learning approaches are being developed to produce accurate simulations of the structure and chemical bonding of disordered solids and liquids, modelling a sufficient number of atoms to enable direct comparison with experimental data. Writing in Nature, Deringer et al.1 report their use of this approach to probe the structure of amorphous silicon under compression, as the element transforms from semiconducting to metallic states. Their work demonstrates that the structural transformations of amorphous forms of materials can take place much more gradually than those between crystalline phases, and can involve the formation of nanostructured domains and localized atomic arrangements that are not found in any of the crystalline states.

Silicon is one of a small class of elements whose density increases on melting2. This unusual behaviour is shared with crystalline ice, which floats on top of liquid water. Such unexpected reversal of solid and liquid densities has been linked to a phenomenon called polyamorphism — the ability of a substance to exist as different amorphous phases that have distinct structures and properties.

Liquid silicon is a metallic electrical conductor, whereas solid silicon is a semiconductor in ambient conditions, a fact that underpins its use in technologies ranging from computer chips to solar panels. The solid can adopt either a crystalline or a structurally disordered amorphous form at room temperature and pressure; in both cases, each atom bonds to four others in a tetrahedral arrangement. However, both the crystalline and amorphous solids transform into denser structures under compression, a process that is accompanied by a transition to metallic conducting behaviour.

In the 1970s, calorimetric experiments were carried out to study the energy changes that accompany the transformations between amorphous and crystalline forms of silicon during heating and cooling3. Analysis of the results suggested that two amorphous forms of silicon exist, with a phase transition between them. Simulations have since suggested that silicon transforms from a low-density amorphous (LDA) phase, in which the coordination number — the number of neighbouring atoms around each silicon atom — is four, to a high-density amorphous (HDA) phase whose structure is similar to that of metallic liquid silicon3,4. The LDA–HDA transition has been observed both during rapid heating of the amorphous solid and on compression of amorphous silicon at ambient temperature57.

Structural transformations between crystalline phases of silicon are readily observed using diffraction methods8, but those involving the amorphous state are more difficult to study because they occur less abruptly as density increases. This is where computational simulations come into play: they can visualize the arrangements of atoms in different phases, and predict and explain the resulting properties. The main challenge is always to model enough atoms to enable the comparison of simulation results with macroscopic data for real samples, while maintaining sufficient accuracy to describe the arrangements and bonding of the atoms.

Computational simulations are also limited by their characteristic timescales when studying phase transitions. Currently available computational resources often restrict simulations based on accurate quantum-mechanical calculations to systems that incorporate a few tens to hundreds of atoms, which are typically examined over timescales of up to several femto-seconds (1 femtosecond is 10−15 s). Simulations that use less computationally demanding modelling strategies can be extended to several hundreds or a few thousands of atoms. However, the accuracy of the predictions of the structural and physical properties of the material being investigated is sacrificed as the system size increases, or as the simulation time is extended.

Deringer et al. now describe a machine-learning approach that gives unprecedented levels of information about the structure and bonding energetics for a system of 100,000 silicon atoms as it is cooled from the liquid state and compressed to pressures up to 200,000 atmospheres (20 gigapascals). This represents a great increase in the number of atoms that can be modelled (see Extended Data Fig. 1 of the paper1). The accuracy of the method approaches those of the best simulations carried out from first principles using quantum-mechanical calculations.

Crucially, the modelled system was large enough to reveal the metastable aggregation of amorphous clusters of atoms. The simulations also uncovered crystallization phenomena that could not be observed using simulations with smaller numbers of atoms, or by using less-accurate models to describe the atomic interactions. The findings closely reproduce the temperatures and pressures observed experimentally for the macroscopic melting of silicon, for the other phase transitions, and for the onset of metallic behaviour.

The simulations show that the structural changes that occur on compression are more complex than was previously realized (Fig. 1). The atoms do not transform simultaneously between an arrangement with a coordination number of four to a phase that has a higher coordination number, as occurs in transitions between crystalline phases of silicon8. Instead, the amorphous structure evolves more gradually to produce high-density nanoscale domains of high coordination number, which develop within the original tetrahedral LDA structure. Linkages form between the HDA domains as the density increases, producing a material that exhibits bulk metallic conduction. It might be possible to modify this metallic conductivity in the real world by applying directionally oriented stresses to compressed silicon.

Figure 1 | Large-scale simulations of amorphous silicon. Deringer et al.1 used machine learning to simulate a system of 100,000 silicon atoms at increasing pressures and at 500 kelvin, to predict the resulting changes in structure and properties of the element. The colour of each atom indicates the number of other atoms bonded to it (the coordination number, N). The coordination number is four at ambient pressure. a, At 13.5 gigapascals, most atoms still have a coordination number of four, corresponding to a low-density semiconducting phase of silicon, but high-density regions of atoms with higher coordination numbers and metal-like conductivity have appeared. b, At 15 GPa, these regions predominate, and have coalesced to form a high-density metallic phase. c, At 17 GPa, domains of a new, very-high-density amorphous phase have started to form within the material. d, At 20 GPa, the amorphous structure has rapidly equilibrated to produce a crystalline metallic phase that has a simple hexagonal structure. (Images from Extended Data Fig. 4 of ref. 1.)

The authors’ simulations also show that, as the system is compressed further, it quickly collapses by about 25% of its volume, thus producing a very-high-density metallic state. This crystallizes rapidly on the nanosecond time-scale of the simulations, to form nanodomains of a metallic phase of silicon.

The results have implications for our understanding of how polyamorphic transitions might emerge between different liquid phases and glassy structures more generally9. Deringer and colleagues’ machine-learning approach has allowed them to accurately simulate amorphous silicon structures on a picosecond timescale (1 picosecond is 10−12 s), and over temperature and pressure ranges that are relevant to transitions between liquids and crystal phases, between liquids and glasses, and between two amorphous phases. Their findings therefore offer the chance to study transitions of a wide array of amorphous materials that have previously been difficult to probe.

The authors’ approach could also now be used to explore the possibilities of transforming amorphous silicon, or ‘doped’ materials in which silicon contains small amounts of other elements, to produce nanostructures that contain metallic and semiconducting domains. Such nanostructures could open up many opportunities for developing new technology, such as in electronic communication, data processing and energy harvesting.

Nature 589, 22-23 (2021)

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