Ab initio simulations of liquid semiconductors using the pseudopotential-density functional method

One of the most difficult problems in condensed matter physics is describing the microscopic nature of the liquid state. Owing to the dynamical nature of the liquid state, it is not possible to discuss a particular microscopic structure; only ensemble averages can be specified. Such averages can be performed via well crafted molecular dynamics simulations: the length of the simulation, the size of the ensemble and the nature of the interatomic forces must all be carefully analysed. Historically, a problematic issue in doing such simulations is that of how to describe the interatomic forces in the liquid state. This matter is especially challenging for the melt of semiconductors, such as silicon or gallium arsenide, where the chemical bond contains a strong covalent component. It is difficult to use pairwise interatomic potentials in such cases. Although many-body potentials can be utilized for simulations of these materials, one must map quantum phenomena such as hybridization onto classical interatomic potentials. This mapping is complex and difficult. In this review, we illustrate how one can avoid this problem by utilizing quantum forces to simulate liquids. Our focus is on the pseudopotential-density functional method. Within the pseudopotential method, only the valence electrons are explicitly treated and within the density functional theory, exchange and correlation terms are mapped onto an effective one-electron potential. These two approximations allow one to extract quantum forces at every time step of the simulation. The pseudopotential-density functional method is highly accurate and well tested for semiconductors in the solid state, but has only recently been applied to liquids. In this review, we illustrate this approach for a number of semiconducting liquids such as liquid Si, Ge, GaAs, CdTe and GeTe. For these liquids, we will present results for the microstructure, the dynamical properties such as the diffusion constants and the electronic properties such as the conductivity.