Field emission as a probe of the surface density of states

Field-emission measurements of the total-energy distribution from a clean metal surface are shown to provide information about the density of states near the surface. Specifically, we find the field-emitted current per unit energy at energy ω to be given approximately by $j({ω}){}({2{}}{m})S{{λ}}^{{-}2}({ω}){Σ}{m}^{}{D}₀²({E}_{{⊥}}ᵐ)×{}{|{{ψ}}ₘ({x}ₘ)|}²{δ}({ω}{-}{{ε}}ₘ)$, where ${D}₀²$ is the usual barrier-penetration probability with image potential corrections, ${E}_{{⊥}}ᵐ={ω}{-}{{{}}²{k}_{{∥}}²}{2m}$, where ${k}_{{∥}}$ is the electron momentum parallel to the surface, $|{{ψ}}ₘ({x}ₘ)|$ is the amplitude of the metal electron at the classical turning point (${x}ₘ{~}1{-}2A),{λ}({ω})$ is a slowly varying function of ${ω}$, and $S$ is the metal surface area. The ${D}₀²$ factor in $j({ω})$ strongly weights electron states with small ${k}_{{∥}}$ and consequently $j({ω})$ measures the density of states at ${x}ₘ$ arising from the component of the bulk band structure normal to the surface. Measurements of $j({ω})$ for several single-crystal planes of tungsten will be presented and compared to the relevant photoemission data.