The photoelectric effect in thin metallic films

In spite of the many attempts to obtain a mathematical treatment of the photoelectric effect it cannot be said that a satisfactory account has yet been given. The problem is not made any easier by the discordance which exists between the results of various observers. Although there is no doubt that Einstein’s law of photoelectric emission holds with extreme accuracy, many other features seem to defy certainty, among which may be mentioned the dependence of the current from a thin film on the thickness and on the direction of polarisa­tion of the incident light. Perhaps the most puzzling feature of the whole effect, however, is the extreme inefficiency of the light in producing photo­electrons, the very best result ever obtained in practice being about 100 quanta for each photoelectron emitted, while usually it takes very many more. This means that any electron stimulated by the light has a very poor chance of ever escaping from the metal and it is only by estimating this chance that agree­ment with experiment can be obtained. It seems certain that any theory which does not take into account such things as the damping of the light wave or the absorption of the electrons in trying to escape from the metal (although the relative importance of these two is by no means clear), cannot hope to represent adequately the experimental material. Fröhlich has given a treatment of the photoelectric effect from a thin metallic film, considering it as a potential trough, the electrons being perfectly free. On the basis of this model he calculates the dependence of the current on the frequency and finds that the emerging electrons have a velocity dis­tribution. No account was taken either of the absorption of the light, or of the inelastic collisions of the electrons with the other particles of the lattice. The surprising feature emerged that the current was independent of the thick­ness of the film. This was because free electrons in a field of constant potential have no absorption frequencies (other than zero), and he assumed that the light wave was undamped. An independent treatment of the same problem has been given by Tamm and Schubin, who first consider the electrons as free to get the surface effect, and then as bound to get a volume effect, the photoelectric yield being the sum of the two. The following investigation was undertaken in the hope of improving on these models by taking into account the absorption of the light and to represent, in some measure, the fact that the electrons are not free, but must be considered as partially bound. With this improvement of the model, there is a considerable gain in agreement with experiment, although in some points the model still fails. This may be because we have taken no account of the electrons being absorbed in the film itself, or of the surface layer of impurities which always seems to be present and whose influence is considerable.