Surface states and resonances in field emission from low-index facets of clean tungsten

The energies, widths, and shapes of features observed in the total energy distributions in field emission from W(1 0 0) and W(1 1 1) are compared with the results of a full-potential LAPW calculation of the surface density of states based on a supercell model of the crystal structure at the metal–vacuum interface. The Swanson hump on W(1 0 0) is attributed to two bands of surface states and surface resonances of d_z² symmetry that are highly localised at , and a second peak observed at lower energy is attributed to a band of surface resonances, also of d_z² symmetry, centred at from along . The energy scale of the calculated total energy distribution is compressed by about 20% relative to the experimental data. The present calculation yields strong evidence that the broad asymmetric peak observed on W(1 1 1) is due to emission from a band of surface resonances. Further calculations for W(1 1 1) are proposed both to test the accuracy of the band model and to take into account the velocity factor that enters in a calculation of the emission current.