Development of Drift-Diffusion Models

Abstract

The basic principle underlying the function of a transistor element is that current flows between oppositely directed p/n junctions (or does not flow), depending upon controlling currents or voltages elsewhere in the element. A junction occurs when regions with contrasting doping characteristics abut in a semiconductor. Thus, a p-region is one with an excess of free hole carriers and an n-region, on the other hand, contains an excess of free electrons. Such charge imbalances are induced by the process of doping, whereby impurity concentrations are injected into pure crystalline semiconductor materials. From the standpoint of valence chemistry, the impurity atoms have numbers of electrons in their outer shells different from the semiconductor atoms. Preponderance of donor impurities creates n-regions as well as net concentrations of positive ions, and acceptor impurities create p-regions and negative ions. The net charge at any point in the device is obtained by combining the ions with the free electron and hole carriers. Thus, an electric field is created via the first Maxwell equation, often called the Poisson equation in the theory of electrostatics. There are also quantum mechanical interpretations related to the impurity injection process; these include energy band bending and wave packet identifications as classical particles (see [87, 122]).