A systematic approach to choosing parameters for modelling fine structure in electron energy-loss spectroscopy

A potential methodology is presented for the systematic prediction of EELS edges using DFT, suitable for codes that calculate ELNES for a specific atom in a unit cell. The method begins with the selection of a unit cell, chosen as the smallest cell that still provides a physically valid representation of the bulk material. Within this small cell, a single electron core-hole is included in the atom for which the EELS ionisation edge is to be calculated. The basis-set size and k-point mesh of the DFT calculation are converged specifically against the predicted EELS result. Subsequently, the cell size is increased until the theoretical core-holes no longer interfere. At this point one can then modify the exact core-hole approximation. This methodology was applied to the new EELS module of the CASTEP pseudopotential DFT code, as well as the all-electron code Wien2k. Aluminium K edges were investigated for various aluminium metal systems. It was observed that as the cell size was increased the predicted EELS result became less sensitive to the exact core-hole approximation used. It was noted however that due to high screening in metals a ground state single cell calculation is often acceptable. The semiconductor aluminium nitride (wurtzite form) was also investigated. It was observed that for both Wien2k and CASTEP, with careful convergence of the key DFT code parameters, single cell ground state calculations gave a reasonable agreement with experiment, contrary to what might be expected for a semiconductor with a large band gap. This was particularly true of the Wien2k result. Given the greater computational effort required for supercell calculations, these results are likely to form the beginnings of a detailed investigation into accepted methods of ELNES predictions.