Optimum base-doping profile for minimum base transit time considering velocity saturation at base-collector junction and dependence of mobility and bandgap narrowing on doping concentration

We used variational calculus, the trial function, and the iterative procedure method to evaluate the optimum base doping concentration profile that will yield the minimum base transit time τ_B. All methods were extended to include the velocity saturation at the base collector junction, and the dependence of mobility and bandgap narrowing on the base doping concentration. We showed that all methods produce almost the same τ_B, although the profiles differ. Among them, the iterative method always produces the minimum τ_B and variational calculus clearly shows the dependence of τ_B on physical parameters