The accuracy of filtered basis functions for the first principles modelling of defects in semiconductors

Abstract

This work presents the results of calculations using filtered basis functions performed with the ab initio modelling program (AIMPRO). The filtration method works by projecting out (filtering) components of a reference basis function that are not required for a description of the occupied states, thereby producing functions that are localised in energy. This leads to a significant reduction in the number of functions that are needed. It is demonstrated that when studying diamond, silicon and defects in these materials, the use of filtered basis sets using just four basis functions per atom can achieve a comparable accuracy to conventional calculations that use 30–40 basis functions. This enables a massive increase in computational efficiency that could have far reaching consequences for first principles modelling calculations. The accuracy of the filtration method is first examined for the bulk materials diamond and silicon, in which the energy, lattice constant, bulk modulus and band structure are studied. It is shown that the filtration approximation applied with an efficient spatial cut-off is able to reproduce current calculated values for these to a very high degree of accuracy. A study of the energies of various reconstructed surfaces in diamond and silicon is then presented. It is first demonstrated that the AIMPRO modelling software without filtration reproduces previous published values of surface energies to within about 100 meV per 1x1 surface cell, with this difference being related to different choices for the pseudo-potential and other details of the calculation. It is also demonstrated that iv changes of this degree also occur when changing the exchange-correlation functional used to model the surface. In contrast, the use of filtered basis sets changes these energies by only 1–2 meV, one hundred times smaller, indicating the excellence of this approach and showing that filtered basis calculation with efficient cut-off radii are of essentially equal quality to those of conventional localised basis functions. Finally a series of defect structures in diamond is considered, including both native defects and nitrogen containing defects. Properties studied include formation energies, binding energies, localised vibrational modes, and hyperfine coupling matrices. In all these cases it is shown that the filtration method produces results which closely match those with conventional basis sets and demonstrate that this method has excellent potential for modelling defecting semiconductor structures in the future. The asymptotic speed up of two to three orders of magnitude will then enable a new range of systems with significantly increased size and complexity to be modelled.