Electron Emission of Metals in Electric Fields. I. Explanation of the Periodic Deviations from the Schottky Line

Abstract

The periodic deviations from the Schottky line observed by Phipps and his collaborators and by Nottingham in measuring the thermionic emission of electrons from tungsten and tantalum can be interpreted as being due to the partial reflections of the electron waves on the potential hill at the surface of the metal. These partial reflections give rise to interference and thus to a periodic term in the transmission coefficient for the escaping electrons. The transmission coefficient is obtained by using the functions of the parabolic cylinder to establish the connection between the asymptotic expansions of the wave functions to the left and right of the top of the potential hill. The calculated positions of the maxima and minima of the deviations agree very well with the observed positions. In agreement with experiment, it is found that the positions of the maxima and minima are sensibly independent of temperature; and the amplitude decreases as the temperature is increased. The calculated amplitude of the deviations increases with the field, as does the observed amplitude. A dependence upon the work function of the emitting metal is obtained; however, since the heights of the surface potential barriers of tungsten and tantalum are very nearly equal no experimental data on this dependence are available.