Uncertainty, topography, and work function

A simple procedure has been found that enables the zero-temperature, zero-field work function for elemental crystal surfaces to be estimated within a few tenths of an eV. It uses the local-density-approximation value for the Fermi energy to obtain the Heisenberg uncertainty distance, equates this distance to the distance from the surface at which the image force begins to act, and further assumes that the image force acts as if it were done to an isolated conducting sphere of the same radius as that of the atoms of which the surface is composed. The importance of this result is that it gives a clear physical picture of the emission process that takes into account the microscopic surface structure, and lends credence to the concept of continuous decoherence from quantum to classical states. Variation of work function between crystal faces is plausibly shown to be mainly due to variation with direction of the effective mass of an electron with the Fermi energy inside the crystal. Work functions of optimum electropositive monolayer adsorbates on refractory metal substrates calculated by this method also agree closely with experiment, indicating that the electrons are emitted from exposed substrate atoms. A model for the topological structure of a crystal surface on an atomic scale is proposed for which classical methods indicate that the field at the tips of the atoms is typically 2.5 times that estimated on the basis that the surface is a smooth plane. The consequential effect on thermionic and field emission is discussed. Order-of-magnitude estimates of the variation of the work function with temperature and stress are also made.