Between 1966 and 1989, when density functional theory (DFT) was still in its infancy, Keating, Stillinger (together with Weber) and Tersoff independently proposed empirical interatomic potentials for covalently bonded semiconductors as a means of calculating the force fields of interacting atoms in crystal structures. This in time allowed the realization of molecular dynamics of semiconductor materials as a computationally cheap alternative to full quantum mechanical calculations.

Over the last two decades the major drawbacks and inconsistencies of what had become commonly known as the valence force field (Keating), Stillinger-Weber and Tersoff potentials had become clear. In particular the impossibility of finding a single parameterization that would result in accurate elastic and vibrational properties suggested that the total absence of long ranged forces was a crucial omission. Solving this inconsistency by inclusion of second and third nearest neighbour interactions in the functional form was generally considered either very difficult or too computationally expensive.

Our new paper presents a new empirical potential that incorporates the interactions between distant neighbours either as polynomial functions of the interatomic distances or as Fourier series expansions of the crystal structure’s angles. In this way only the terms that have an impact on the elastic and vibrational properties are selected. Furthermore such distant neighbour’s interaction are included within a computationally “cheap” loop, therefore only marginally affecting the total running time of molecular dynamics simulations. Using this new potential, which we like to call MMP from the initials of the surnames of the original developers (Monteverde, Powell and Migliorato), the elastic properties and phonon spectrum of both silicon and germanium are reproduced for all branches with unprecedented accuracy not just at the high symmetry points but also in between. This is crucial if one hopes to use the potential to model thermodynamic properties.

Furthermore we have tested the potential in molecular dynamics simulations, showing that the predicted bond lengths are within 1% of those predicted by ab initio DFT (in the local density approximation). We can also report that using our proposed potential to evaluate a preconditioned input for DFT calculations, the computation cost of the geometry optimization routine is significantly reduced and the total running time is cut by 50%.

                             
The in house developed potential is currently limited to Si, Ge and C but we intend to expand it to all III-Vs in the near future.