A lumped minority carrier storage model for transistors and diodes

Minority carrier storage in transistors has been treated by Ebers and Moll. In particular their results are convenient for estimation of storage delay in saturated transistors. The basic assumptions in their approach amount to use of the linear diffusion model of the transistor and to a rational approximation for the transcendental transport factor (approximately ). The present paper shows that the same results can be arrived at from a lumping approximation of the diffusion process in the base region of the transistor. This approach makes possible some simple extensions applying to more complicated cases in addition to giving a novel view of the Ebers-Moll results. Here the key characteristic of behavior of the transistor used is linearity of the minority carrier density-current relationship. A five-element lumped model is used to duplicate the Ebers-Moll treatment. The element values are determined uniquely by the values for , and Ico. After the equilibrium conditions are solved in terms of the variables minority carrier density and current, voltage is brought in as a variable through the relationship p = pn, ε qV/KT.