Physical modeling of lateral scaling in bipolar transistors

The dependence of important transistor characteristics, such as transit frequency, on emitter width and length is modeled on a physical basis. Closed-form explicit analytical equations are derived for modeling the emitter size dependence of the low-current minority charge and transit time, the critical current indicating the onset of high injection in the collector, and the stored minority charge in the collector at high injection. These equations are suited for application in various compact transistor models such as the SPICE Gummel-Poon model (SGPM) as well as the advanced models HICUM and MEXTRAM. As demonstrated by two- and three-dimensional device simulation and measurements, combination of the derived equations with HICUM results in accurate prediction of the characteristics of transistors with variable emitter length and width. As a consequence, the new model makes the conventional transistor library unnecessary and offers bipolar circuit designers the flexibility to use the transistor size that fits the application best.