Notes on some electronic properties of conductors and insulators

Abstract

1. Introduction. Tamm’s Surface Levels .—This paper contains a number of minor results to which I have been led in attempting to co-ordinate various phenomena exhibited by semi-conductors and insulators, and their contacts with metals. It is essentially a critical survey. Much of it has obviously been inspired by the beautiful theory of the “surface levels” proposed by Tamm, which I have strenuously tried to incorporate significantly into the general theory. It is natural at first sight to experiment with the view that the existence of these surface levels in crystalline insulators is one fundamental reason for their insulating properties. This view, however, one is forced to abandon, as will be shown here. The insulating property is not after all so subtle. But I believe the discussion I shall present will help to clear up ideas on these subjects and on a number of allied ones, which have been until recently more obscure, at least to me, than they need have been. After considering, therefore, the nature of insulation by a crystal (as opposed to an amorphous glass) we discuss it in terms of Tamm’s surface levels and show what properties are required of these levels if they are to be responsible for the insulation. These properties are possible but peculiar. We then examine the origin of the surface levels more exactly and show how they have to fit into the scheme of lattice levels. It is not possible to conclude that they cannot be concerned in the insulation, but it does seem possible to conclude that it is unlikely that they are concerned in any fundamental way. We then take up the question of the surface conditions on an insulator on a wider basis and show that the necessary surface charge of extra or missing electrons can always be accommodated on the conductors in contact with the insulator which separates them. The paper concludes with certain applications of these ideas of surface conditions to the phenomena of photoconductivity. The main subject matter of the paper has close affinities with von Hippel’s work on electrical breakdown in crystalline insulators but the same questions are not handled. None the less, it is important to record that everything we have to say is in conformity with his theory.