Bjt Modeling for Circuit Simulation

Physical models for transport mechanisms important in bipolar transistors are developed, implemented in SPICE3 for DC, AC, and transient analyses, and assessed with numerical device simulations. The analytical model of quasi-saturation, or base -push-out, is derived for all current levels. Deficiencies in previous quasi-saturation models are revealed and overcome. The quasi-saturation model is based on a derivation of the current-induced-base charge and the electric field in the collector for all bias conditions. Physical models for base-width modulation (BWM) at the collector-base (cb) junction and impact ionization in the collector are formulated as functions of the electric field; inclusion of these two effects greatly improves the accuracy in the output resistance. The impact ionization model gives a first -order description of avalanche breakdown, or snapback. The dynamic charge storage effects are investigated in detail with AC and transient analyses. The proper partitioning of the dynamic charging currents is made possible by the addition of an internal collector node and increases accuracy especially under quasi-saturation conditions. The cb junction capacitance and the cb junction transit time tau _{cv} are expressed as functions of the field E_1 at the cb junction. As E_1 decreases with increasing current due to the Kirk effect, the variable tau _{cv} and the BWM effect on the base-diffusion charge each can cause f_ {T} to fall-off at a current several times below that for the onset of quasi-saturation, which causes a more rapid f_{T} fall -off. The current-induced-base charge significantly reduces the effective base resistance as the dynamic base current flows laterally through the current-induced-base. Simulation results suggest that an AC emitter crowding model previously derived for low injection conditions is a good approximation even under base-push-out conditions. The delay time approach and the quasi-static charge-partition approach are compared; the former is found to be better in simulating the high frequency effects due to non-quasi-static conditions in the quasi-neutral base and current-induced-base regions. A non-quasi-static model for the charge in the quasi-neutral base region is developed and implemented in SPICE3 for transient analysis. The methodology to solve for the instantaneous carrier distribution by a series solution including all injection levels and the effect of the built-in field is presented. The solution applies for forward and reverse modes of operation. Analytic equations for the instantaneous base charge partitions are derived for the calculation of the instantaneous node currents. For switching times comparable to the base transit time, the non-quasi-static model is significantly more accurate than the Gummel-Poon model and previous quasi-static charge -partition models, as verified with numerical device simulations.