Comparison and extension of recent one-dimensional bipolar transistor models

Various nonquasistatic (NQS) improvements of the Gummel-Pooh integral charge-control model are considered for both small-signal and large-signal excitations. The comparison includes the partitioned-charge-based (PCB) model by J.G. Fossum and S.V. Veeraraghaven (1986), the transient integral charge-control model (TICC) by H. Klose and A.W. Wieder (1987), and negative-capacitance (NC) and inductive (L) NQS equivalent circuits derived by truncation in the complex-frequency domain. For forward-active operation and an exponential doping profile in the base layer, the NC model is equivalent to the TICC model. For a uniform doping profile, the NC, TICC, and PCB models are equivalent. These three models, however, predict that the magnitude of the transconductances rises with frequency for high frequencies, a trend that, in principle, is incorrect. Truncation in the s-domain gives insight concerning this trend and provides a better model, i.e., the L model. The method of truncation used is well suited to bipolar transistors; is not suited to MOS and other devices in which space-charge-limited flow prevails