The general transient charge control relation: a new charge control relation for semiconductor devices

A new charge control relation, the general transient charge control (GTCC) relation, is developed and shown to be a natural extension to conventional charge control theory by correctly accounting for the partitioning of stored charge within semiconductor devices. Although the transient integral charge control (TICC) relation was originally thought to represent such an extension, it is shown that the TICC relation neglects the influence of recombination on the displacement components of the non-quasi-static (NQS) currents, and is therefore only a special case of the GTCC relation. From the GTCC relation, a physically based weighting function emerges which is shown to be the optimum weighting function with which to weight the continuity equation in the generalized partitioned-charge-based (PCB) modeling methodology. An extended TICC relation that is valid for transparent emitters with widely varying emitter surface recombination velocities is developed. Also, a new charge control relation for the emitter is developed which yields a semianalytic expression, involving the static minority-carrier charge distribution, for calculating the optimum charge partitioning in arbitrarily doped emitters. The TICC, the extended TICC, and the GTCC relations are compared with accurate AC numerical calculations of charge partitioning in a wide variety of Gaussian emitter profiles