Threshold Current for the Onset of Kirk Effect in Bipolar Transistors With a Fully Depleted Nonuniformly Doped Collector

We derive a generalized expression for the threshold current of the Kirk effect (base widening) in bipolar transistors that have a fully depleted collector and a nonuniform dopant distribution in the collector. This generalized expression can be helpful to the analysis of the electrical characteristics, such as the cutoff frequency as a function of bias conditions, and hence to the optimization of such devices