Energy Distribution in Field Emission from Adsorbate-Covered Surfaces

Abstract

A calculation of the total energy distribution of field-emitted electrons in the presence of chemisorbed atoms shows that $\frac{[j(\ensuremath{\omega})\ensuremath{-}{j}_{0}(\ensuremath{\omega})]}{{j}_{0}(\ensuremath{\omega})}=u{(\ensuremath{\omega})}^{2}$ $\mathrm{Im}{G}_{\mathrm{aa}}(\ensuremath{\omega})$ if the adsorbate resonance level lies within the conduction band of the metal. $j(\ensuremath{\omega})$ and ${j}_{0}(\ensuremath{\omega})$ are the current densities per unit energy in the presence and absence of the adsorbate, respectively; the energy $\ensuremath{\omega}$ is measured from the vacuum level; ${x}_{a}$ is the surface-adsorbate distance; and ($\frac{1}{\ensuremath{\pi}} \mathrm{Im}{G}_{\mathrm{aa}}$ is the local density of states at the adsorbate. $u{(\ensuremath{\omega})}^{2}\ensuremath{\propto}\mathrm{exp}{2{(\ensuremath{-}\frac{2m\ensuremath{\omega}}{{\ensuremath{\hbar}}^{2}})}^{\frac{1}{2}}{x}_{a}+[\frac{4}{3}{(\frac{2m}{{\ensuremath{\hbar}}^{2}})}^{\frac{1}{2}}{(\ensuremath{-}\ensuremath{\omega})}^{\frac{3}{2}}{(\mathrm{eF})}^{\ensuremath{-}1}\ifmmode\times\else\texttimes\fi{}(v(y)\ensuremath{-}1)]}$, 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 ${G}_{\mathrm{aa}}$. if the adsorbate resonance lies below the bottom of the conduction band, then $\frac{[j(\ensuremath{\omega})\ensuremath{-}{j}_{0}(\ensuremath{\omega})]}{{j}_{0}(\ensuremath{\omega})}<0$, in agreement with the results of Duke and Alferieff.