Effect of recombination on the base transit time model considering base pushout

Base pushout due to current-induced perturbation is one of the dominant factor for the degraded speed performance of the modern bipolar junction transistors (BJT). With the scaling down of the feature size of the modern BJT´s, the degrading effects due to base pushout becomes increasingly prominent. Therefore, an accurate modeling of base transit time, which is the most significant component in determining the speed performance of BJT´s under base pushout condition, is required. However, the present day BJT´s use heavy base doping in order to improve its performance which leads to various non-ideal effects such as bandgap narrowing effects, doping and field dependency of carrier mobility and carrier lifetime, recombination in the base, modulation of electric field due to high-injection level etc. Moreover, at such high base doping Auger recombination becomes significant along with the trap-assisted SRH recombination. Inclusion of all these effects in the base transit time modeling leads the governing equation to a second order, variable-coefficient, non-homogeneous, nonlinear differential equation which is analytically intractable. The model becomes even more complicated under base pushout condition. Conventionally all analytical models considering base pushout condition neglects recombination mechanisms to obtain an analytically solvable governing equation. However, as the modern BJT´s are continuing to scale down, the justification for neglecting recombination mechanisms is questionable. Therefore, 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 τ_B under base pushout condition. In this work both SRH and Auger recombination with doping dependent lifetime is considered. The energy-bandgap-narrowing effects as well as doping dependent mobility due to heavy doping are also considered in the proposed model. An exponential approximation technique is used to - - overcome the analytical intractability problem of the governing differential equation. The developed model shows that the recombination has significant effects on the base transit time of a heavily doped base under base pushout condition.