Analytical relations pertaining to collector current density and base transit time in bipolar transistors

Modern high speed bipolar transistors request optimum base doping profiles and high collector current densities (Jn) to reduce base transit times (τb). An analytical Jn and model of uniform doping base for high injection levels was proposed and developed for arbitrary doping base before the onset of the Kirk effect. However, the equations forms for Jn and τb are not concise to express Jn and τb as the functions defined by existing models. Hence, this paper derives analytical equations for collector current density and base transit time that can be respectively expressed as two concise relations with some existing models. These equations are valid for all injection levels and can give a clear physical insight into device operation.