The theory of the surface photoelectric effect in metals—I

Abstract

1. In the electron theory of metals it is usually assumed that the electrons can be regarded as moving independently in a periodic potential field, and for certain properties it is sufficient to use the simpler Sommerfeld model, in which the potential inside the metal is constant. The photoelectric effect is not, however, one of these, as the electrons are effectively free, and, as is well known, the photoelectric effect cannot take place with free electrons on account of the impossibility of satisfying simultaneously the laws of conservation of energy and momentum. Because of this, Tamm and Schubin have proposed that the photoelectric emission from a metal should be regarded as arising from the superposition of two effects, the surface effect, due to the rapid changes of potential energy at the surface of the metal, and the volume effect, due to the internal variations of potential; and have further given a theory of the surface effect for an idealized case. Theories apparently of the surface effect, in that they neglect potential variations inside the metal, have also been given by Fröhlich and Wentzel, and the results of all three theories are at variance. The question is examined anew in the present paper, and the conclusion is reached that none of the earlier theories can be accepted as representing the surface effect even for the very idealized case considered. The theory which is believed to be correct is given, and and certain results briefly discussed, leaving to a later paper a more detailed comparison with the empirical facts.