THEORY OF SOLITARY WAVES AND SPONTANEOUS CURRENT INSTABILITIES IN DC VOLTAGE BIASED EXTRINSIC SEMICONDUCTORS

An analysis of the spontaneous current instability in dc voltage biased extrinsic semiconductors is given. I use a standard rate equation model of electrical conduction in long one-dimensional extrinsic semiconductors which includes effects of field-dependent impurity impact ionization. It is shown that a solution consisting of a solitary wave moving on top of the steady state exists for a certain interval of the dc voltage bias, during the time needed for the wave to reach the receiving contact. I discuss the uniqueness and stability of this situation. A new result is that the solitary wave may be a high or a lower field domain, according to the resistivity of the injecting contact. The theory is used to interpret recent observations on p-type ultrapure germanium.