Characteristics of Electrons in Solids

The origin of the familiar valence band-forbidden gap-conduction band features of the electronic energy level scheme of a crystalline solid is developed according to 1) the extension of the atomic energy level scheme for individual atoms, 2) examination of the quantized momentum spectrum of a valence electron gas in a periodic potential enclosure, and 3) analogy with the pass-band and stop-band features in the frequency characteristic of a periodically-loaded mechanical transmission line. Since the first two approaches are amply treated in the conventional literature, this paper dwells particularly on the third approach, which may be preferred over the other two by readers having more extensive backgrounds in mechanical or electrical engineering than in theoretical physics. A simple mechanical wave transmission apparatus is described, with which the frequency characteristic can be observed and plotted. This characteristic is then related to the energy band picture of a solid by recognizing that a crystal can be regarded as a "loaded" transmission line for electron waves.