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(100) and W(111) 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(100) is attributed to two bands of surface states and surface resonances of dz^2 symmetry that are highly localised at the center of the surface Brillouin zone (Gamma_bar), and a second peak observed at lower energy is attributed to a band of surface resonances, also of dz^2 symmetry, centred at 0.11 A^(-1) along Gamma_bar to X_bar. 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(111) is due to emission from a band of surface resonances. Further calculations for W(111) 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.