Surface Barrier Analysis for the Highly Refractory Metals by Means of Schottky Deviations

Abstract

The theory for the deviation from the Schottky effect is redeveloped for the thermionic case, using the Herring and Nichols coefficients $\ensuremath{\mu}$ and $\ensuremath{\lambda}$, which are typical of the two reflection regions of the metallic surface barrier. The assumptions of Guth and Mullin are used, but correction of their calculations leads to new results; a method of data analysis based on these results is described. In this method the Guth-Mullin assumptions regarding the form of the barrier are taken as a first approximation to the real case. The method is applied to available experimental data on tungsten, tantalum, and molybdenum. One may draw the following conclusions: The outer ($\ensuremath{\lambda}$) reflection region behaves in accordance with the mirror-image law, while the innermost ($\ensuremath{\mu}$) is field-independent. The phase change suffered by an electron wave crossing the $\ensuremath{\mu}$-region is less than that computed for the theoretical box model. All three metals studied are mutually similar as regards the potential form in the $\ensuremath{\mu}$-region. Apparently, it is not yet possible to evaluate the zero-field reflection coefficient from deviation amplitudes; this is probably due to the parabolic approximation used for the $\ensuremath{\lambda}$-region in the theory.