Negative Differential Resistance: A Brief History and Review

The simplest considerations concerning power consumption in an electrical circuit soon leads to the idea that if the circuit contained an element with a negative differential resistance (NDR) it would be possible to create a.c. power rather than consume it. Such an element would have highly non-linear electrical properties, but it was well known from the study of dielectric breakdown that large non-linearities were common in insulators at high fields. The cause of breakdown was seen to have its origin in either a thermal runaway through excessive Joule heading or in purely electrical effects. The latter were infinitely more interesting since thermal breakdown was often synonymous with melting. The first theory by Zener in 19341 described breakdown in terms of quantum-mechanical tunnelling between valence and conduction bands, but the critical fields predicted proved to be significantly larger than those observed in the alkali halides. It took the invention of the Zener diode for this theory to come into its own, though, ironically in its role as a switch, the breakdown, in practice, is frequently a consequence of avalanche rather than tunnelling. To compound the irony, pure Zener tunnelling has been exploited in the “tunnel diode” which is famous for its NDR. Other mechanisms of breakdown emphasized impact ionization and subsequent avalanche effects, phenomena familiar from the studies of breakdown in gases. Theories of how electrons in a polar solid could pick up more energy from the field than they could dissipate in a single collision were developed by von Hippel2 and Fröhlich3,4 and subsequently elaborated by Callen5 and Fröhlich and Paranjape.6 This was really the beginning of the study of hot electrons, and a parallel study by Davydov7,8 and others in the USSR on the effect of a field on the distributed function of an electron and its mobility in a semiconductor helped to lay the theoretical foundations of the topic.