Integral relations for bipolar transistor modelling-rigorous results

It is shown how current-spreading, current-driven generalization/recombination phenomena, transient effects, and series-resistance effects can rigorously be considered within integral relations characterizing bipolar transistor behavior such as H.K. Grummel´s (1970) integral charge control relation. The proposed approach applies concepts that reestablish a vanishing divergence of the transfer current and allows the derivation of consistent, closed-form expressors for the base and collector current of a three-dimensional BJT (bipolar junction transistor) of arbitrary geometry. The approach provides in particular a rigorous definition of electron current transit time in terms of AC quantities that reduces to the quasistatic definition in the limit as omega approaches 0.<>