Computation of bipolar transistor base parameters for general distribution of impurities in base

A procedure is suggested by which dc and ac base gain parameters can be computed for general impurity distributions in the base. The procedure consists of solving the current equation as series in the recombination time (1/τ). The series expansion coefficients are computed for a Gaussian distribution up to first order, along with the resulting base alpha transport factor and the transit time. Mobility variation with impurity concentration is also taken into account. Explicit expressions for cutoff frequencies and excess phase shift (
\omega_{T}, \omega_{\alpha}, \omega_{beta}, m
) are developed using the coefficients of the series expansion up to the second order. Computation of these parameters for the case of an exponential distribution, with and without assumption of diffusion coefficient variation, results in new expressions and values.