An accurate charge control approach for modeling excess phase shift in the base region of bipolar transistors

The conventional charge control approach is extended to enable the accurate determination of excess phase shift in the ac common-emitter current gain of bipolar transistors arising from distributed stored minority carrier charge in the neutral base. Generalized expressions, valid for transistors with arbitrary impurity profiles and position-dependent transport parameters, are presented from which the excess phase shift can be determined solely from device structure and process data. The ac model parameters which result from the extended charge control approach are used in an existing high-frequency compact nonquasi-static bipolar model which is suitable for SPICE simulation