Modeling of small-signal minority-carrier transport in bipolar devices at arbitrary injection levels

A detailed analytical treatment of small-signal minority-carrier transport in quasi-neutral regions with position-dependent material parameters at arbitrary injection levels is presented. First, the small-signal minority-carrier transport equations are derived in a simple form which is amenable to analytical integration, thereby facilitating physical insight. Secondly, analytical solutions of the transport equations are derived by means of the integral series solution method. Next, it is shown that these solutions provide a mathematically sound basis for a systematic derivation of all nonquasi-static models hitherto presented in the literature for both the base and emitter regions of bipolar transistors. An important consequence of the above analysis is that the exact expression of all model parameters is obtained. These parameters include the conductance, transit time, charge partitioning factor and phase-shift factor. The dependence of these parameter on the most significant technological parameters and on the operating point is analyzed in detail.