Analytical modelling of base transit time considering recombination in the non-uniformly doped base under base pushout condition

The main objective of this paper is to show that recombination in the base needs to be taken into account in determining base transit time under base pushout condition. In previous analytical works for this transit time with base pushout, recombination in the base was neglected, since inclusion of this mechanism leads to an analytically intractable governing differential equation. In this work, the intractability problem is resolved by applying the concept of perturbation theory and by using an elegant exponential approximation technique. The developed model considers both SRH and Auger recombination with doping dependent lifetime and also, considered the energy-bandgap-narrowing effects as well as doping and field dependent mobility due to heavy doping. The model shows that recombination has significant effects on the base transit time of a heavily doped base under base pushout condition.