Searching for materials on Piz Daint supercomputer

In order to find the optimum silicon structures, the materials researchers carried out elaborate calculations. For a system containing N silicon atoms, there are theoretically 3^N possible metastable states, explains Goedecker. Each structure has a specific energy, and the structure of naturally occurring materials is usually very low in energy. Metastable structures, are in somewhat higher-energy states, in which the crystal or a molecule lies in an energy minimum (local minimum) for a specific period of time. Without outside intervention, metastable structures can take a very long time to revert to the lowest energy ground state – the carbon allotrope diamond would not be sought-after gemstone if it could suddenly turn into graphite.

An astronomical number of possibilities

In investigating metastable crystal forms of silicon, the task is to identify those whose stability is sufficient and which meet the requirements for use in efficient solar cells, namely a high light absorption coefficient. Solar cells made out of such materials could be thinner and therefore more cost-effective to produce. “With the astronomical number of possibilities, however, searching for the ‘correct’ structure is like looking for a needle in a haystack,” says the physicist.

Theoretically, an optimum crystal structure that corresponds to these requirements can be found by computing all of the possibilities, but this is too time-consuming and expensive, even for a powerful supercomputer. In 2004, however, Goedecker developed a method that can be used to directly identify only those metastable structures that have low energies. This makes the search process significantly faster.

Hopping into local minima

Using this so-called minima hopping method (see box), Goedecker and his team have discovered 44 promising metastable clathrate-like silicon structures from a large number of possibilities with the help of the Piz Daint supercomputer. Given that these kinds of structures with cavities have already been successfully synthesised in the laboratory, they are considered promising candidates for efficient solar cells, says Goedecker. For the simulation, the researchers modified their chosen algorithm accordingly, so that the simulation mimics the clathrates’ experimental preparation in the laboratory.

When computing possible structures, there is an energy barrier that must be overcome in order to move from one structure to the next, explains Goedecker. This can be compared to a mountain pass. The Bell-Evans-Polanyi principle, which is frequently used in chemistry, states that the height of the pass will be lower if the process releases a lot of energy so that the final structure represents a low-energy state. The researchers have now turned this principle around: to put it simply, the minima hopping method assumes that a crystal’s metastable configuration, which is reached by overcoming a small energy barrier (the mountain pass), is typically also a low-energy state. This transition is computed using molecular dynamics, and the structure’s energy state is determined using density functional theory (DFT).