Modifications of equivalent circuits for narrow-base transistors

Conventional equivalent circuits for the large-signal and small-signal behavior of bipolar transistors are all based on the assumption that carriers flow in the base region by drift and diffusion. For a very narrow base, this assumption becomes questionable, and the equivalent circuits based on it need modification. We find that the interconnections of circuit elements conventionally used still apply, independent of base width; but that the functional dependence of certain parameters of the equivalent circuits change as the base becomes narrower. For the limiting case of very narrow bases, we show that the Early effect vanishes; and we give expressions for the functional dependencies of Beta, saturation current, forward charge-control time constant, transconductance, and gain-bandwidth product. All of these parameters derive less benefit from decreasing base width than conventional theory predicts.