Jellium Surfaces Electron Spillout, Surface Dipole, and Work Function

Jellium Surfaces Electron Spillout, Surface Dipole, and Work Function 

Take the jellium model that we introduced earlier for the infinite crystal and terminate the positive background (n+) abruptly along a plane at 2 = 0, with the 

This integral across the surface boundary is obviously an electric dipole, the surface dipole, which is related to the work function, 4 , through 

A similar reasoning, although with the necessary introduction of a crystal lattice, explains the well-established fact that for real crystals, d can differ from one facet to the other, a concept known as work function anisotropy. For example, the measured values of O for the (111), (100), and (110) surfaces of Cu are 4.74,4.64, and 4.52 eV, respectively [60]. Since /c or f in Eq. (2.39) is a bulk quantity, the anisotropy in 4 comes directly from the different dipoles established at the different surfaces. Generally, it is known that the more open a surface is, the smaller is the D and consequently, the smaller is 4 , as we see for Cu above. Obviously, for jellium, D is the same for all surface orientations. However, for a real crystal, say fee, the electron density is quite smooth at the (111) surface, getting more corrugated at 

20) An alternative and common definition of the work function is that it is the energy difference between a lattice with an equal number of ions and electrons, and the 

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