Higher Order Base Dynamics of a Bipolar Transistor with Nonuniform Doping

摘要

The modeling of bipolar transistors is studied in the case when the quasi-static assumption does not hold, i.e., the base and collector currents follow the controlling voltages not instantaneously but with certain time delays. In the case of nonuniform base doping, the magnitudes of these delays are calculated by first solving numerically the minority carrier distribution in the base region. A simple but realistic model for the doping density is presented. A higher order carrier distribution is then found, enabling one to obtain the time delays. They are found to be slightly larger but in the same order of magnitude compared to the base transit time as in the case of constant base doping, although the transit time is greatly diminished due to the base doping gradient.