One-dimensional modeling of TRIM

This paper describes the operation of a p-π-p structure with injecting contact in a mode similar to that of an equivalent p-n-p bipolar transistor. Minority carrier injection takes place from an adjacent n-type layer. Such structures occur in Tri-mask (TRIM) integrated circuits, for example. Because of the low doping in the π region, high injection level effects occur virtually at the onset of conduction (current densities > 10 mA/cm²). The π region is then divided into two regions, a low-field region and a high-field region. Overall behavior is similar to that of a normal bipolar transistor, the plasma behaving as an injected base layer, the high-field region behaving as the usual base-collector depletion region (output space). An appropriate closed-form solution is derived that gives physical insight into the operation of the structure. It gives gain (and base transit time) results identical in form to those for transistors at high-level injection. A more complete computer analysis of specific structures gave results consistent with the approximate model. The physical picture of TRIM transistors that results from this model indicates that for both gain and frequency response of these transistors, the collector voltage is an important parameter for a given collector current and width of π region. This study, motivated by TRIM structures, is more generally applicable as a one-dimensional analysis of any high-injection bipolar transistor operating in the active mode.