A general phenomenological model for work function

A general phenomenological model is presented for obtaining the zero Kelvin work function of any crystal facet of metals and semiconductors, both clean and covered with a monolayer of electropositive atoms. It utilizes the known physical structure of the crystal and the Fermi energy of the two-dimensional electron gas assumed to form on the surface. A key parameter is the number of electrons donated to the surface electron gas per surface lattice site or adsorbed atom, which is taken to be an integer. Initially this is found by trial and later justified by examining the state of the valence electrons of the relevant atoms. In the case of adsorbed monolayers of electropositive atoms a satisfactory justification could not always be found, particularly for cesium, but a trial value always predicted work functions close to the experimental values. The model can also predict the variation of work function with temperature for clean crystal facets. The model is applied to various crystal faces of tungsten, aluminium, silver, and select metal oxides, and most demonstrate good fits compared to available experimental values.