A new solution for minority-carrier injection into the emitter of a bipolar transistor

A new analytic solution for minority-carrier injection into the emitter of a bipolar transistor has been derived. Effects such as Shockley-Read-Hall (SRH) recombination, Auger recombination, bandgap narrowing, graded impurity profile, and position-dependent mobility have been included. A quantitative definition of "transparency" in an emitter is presented. Numerical results show the appearance of a minimum in injected minority-carrier current with respect to the impurity concentration at the surface. This minimum is due to the interaction of Auger recombination and the built-in electric field as impurity concentration is increased. The relative ease and speed necessary to obtain numerical results makes this method very useful for the design and optimization of transistors.