Field emission from adsorbate covered surfaces. II

A previous calculation of the total energy distribution of field-emitted electrons in the presence of chemisorbed atoms by Penn, Gomer, and Cohen (PGC) is reexamined with respect to the following point. PGC assumed that the metal-adsorbate system could be represented by the Anderson model; however, the Anderson model is phenomenological. Anderson and McMillan have shown how the model can be reformulated in a way which makes it more quantitative. Use of the reformulated model leads to a significant change in the PGC result for the field-emission current. We find $\frac{\Delta j\left(\omega \right)}{j_0\left(\omega \right)}=R^{-1\mathrm{}}{u}^{\prime 2}{\rho }_a$, where $\Delta j\left(\omega \right)$ is the change in the current at energy $\omega$ due to the presence of the adsorbate and $j_0\left(\omega \right)$ is the current in the absence of the adsorbate. ${\rho }_a$ is the density of states at the absorbate and $u^{\prime 2}$ and $R^{-1\mathrm{}}$ are given in the text. This result differs from that of PGC by the factor $R={[1+{\xi }^{\frac{3}{2}}{\left(\pi \alpha \right)}^{-\frac{1}{2}}]}^2$, where $\xi ={(-\frac{2m{E}_F}{{\hslash }^2})}^{\frac{1}{2}}$ and $\alpha =\frac{2meF}{{\hslash }^2}$. Energies are measured from the vacuum level, $E_F$ is the metal Fermi energy, and $F$ is the strength of the external electric field. For typical experimental conditions $R^{-1\mathrm{}}\approx \frac{1}{16}$.