Integral relations for determining non-quasi-static charge partitioning in bipolar devices from static charge distributions

Integral relations are rigorously derived for the non-quasi-static charge partitioning in bipolar devices in terms of static carrier distributions in low-level injection. The resulting expressions are simpler than previous charge partitioning expressions for arbitrary impurity profiles and, in contrast to previous expressions, take into account minority-carrier recombination, which is required in the emitter region of bipolar transistors. The simplicity of the derived integral relations permits the development of a semianalytic expression for the charge partitioning in the base region which does not require a static minority carrier solution, and which is similar in computational complexity to the base transit line