Energy Distribution in Field Emission from Adsorbate-Covered Surfaces

A calculation of the total energy distribution of field-emitted electrons in the presence of chemisorbed atoms shows that [j(ω)-j₀(ω)]j₀(ω)=u(ω)² ImGₐₐ(ω) if the adsorbate resonance level lies within the conduction band of the metal. j(ω) and j₀(ω) are the current densities per unit energy in the presence and absence of the adsorbate, respectively; the energy ω is measured from the vacuum level; xₐ is the surface-adsorbate distance; and (1π ImGₐₐ is the local density of states at the adsorbate. $u{({ω})}²{∝}exp{2{({-}{2m{ω}}{{{}}²})}1/2{x}ₐ+[4/3{({2m}{{{}}²})}1/2{({-}{ω})}3/2{(eF)}^{{-}1}×{}(v(y){-}1)]}$, where $F$ is the electric field and $v(y)$ is the image-potential correction factor. The expression given above for the tunneling current is general and independent of the explicit form of ${G}ₐₐ$. if the adsorbate resonance lies below the bottom of the conduction band, then ${[j({ω}){-}{j}₀({ω})]}{{j}₀({ω})}<0$, in agreement with the results of Duke and Alferieff.