Analytical base transit time of bipolar junction transistor (BJT) considering Kirk effect

Abstract

In this thesis analytical expressions of effective base width and base transit time for exponentially doped base of a BJT considering Kirk effect are developed. The present treatment also includes bandgap narrowing and finite velocity saturation effect in the calculation of base transit time. In modern bipolar junction transistors, the collector is more lightly doped than the base. Therefore, high values of current and collector-emitter voltage saturate the carrier velocity. With carrier-velocity saturation the positions of the space-charge region boundaries become function of collector current. We have studied the influence of velocity saturation in the base-collector depletion layer, and compared the base transit time with velocity saturation to that without velocity saturation. From the comparison we have observed that the base transit time is increased by velocity saturation. Considering bandgap narrowing we found that the base transit time will be underestimated if we do not consider it. The aiding electric field weakens if bandgap narrowing takes place, thereby reducing the drift-aided movement of minority carriers in the base which increases the base transit time. In our work we have incorporated Kirk effect for calculating effective base width and base transit time and found that incorporating Kirk effect the effective base width is increased significantly. Since carriers injected from the emitter have to spend more time in the effective base region, the base transit time becomes higher than that without considering base width widening condition or Kirk effect. So for proper modeling of bipolar junction transistors finite velocity saturation, bandgap narrowing and Kirk effect must be considered.