We show the bipolar transistor models in low injection region, where the injected minority carrier concentration is much smaller than doping concentration. We describe the emitter, base, and collector current models, and related circuit parameters. The transit times in emitter, base, and collector regions are also important for circuit performance, and corresponding models are described. We first treat models for uniformly doped device, and extend them to the ones for non-uniform doped devices. Polycrystalline Si (poly-Si) is used for diffusion source to form emitter region in bulk Si. This poly-Si also plays a role as an emitter, and the related models are described. Further, we analyze the optimum base doping profile to minimize base transit time. We also cover the models for base width modulation and base resistance related to the lateral current flow beneath emitter region. Finally, we describe small signal, and large signal circuit model.
Keywords: Bandgap narrowing, Base resistance, Base transit time, Base transport coefficient, Bipolar transistor, Collector transit time, Current gain, Cut-off frequency, Diffusion capacitance, Early effect, ECL propagation delay time, Emitter injection efficiency, Emitter transit time, Partitioned charge, Velocity saturation.