A Determination Method of the Work function using the Slab Model with a First-Principles Electronic Structure Calculation

We have reinvestigated the method to determine the work function of metals by the first-principles electronic structure calculation using the plane-wave expansion method with pseudo-potentials. Changing width of a vacuum layer of a slab model, we obtained the Fermi level measured from the effective Kohn-Sham potential at the center of the vacuum layer. By extrapolating the values of the Fermi level to the infinite vacuum-layer limit, the Fermi energy is determined. We propose a fitting function for the extrapolation. This function works well for determination of the highest occupied level and the lowest unoccupied level of materials with a surface relative to the vacuum level in the Kohn-Sham scheme. The obtained work functions for [100], [110] and [111] surfaces of three noble metals, Rh, Pd and Pt are comparable to the known theoretical estimation as well as the experimental values.