Modifications of drift-diffusion transport in the analysis of thin-base transistors

An examination was made of the base region of a bipolar transistor, an internal region critical to device performance. A semi-automatic argument is first presented to indicate that, of the set of equations describing the bipolar transistor, the equations for transport by drift and diffusion becomes questionable first with shrinking base width. For the limiting case of small base widths, a simple physical model was proposed that yields the behavior of the various equivalent circuit parameters of the transistor. Comparison then shows that many of these parameters derive less benefit from decreasing base width than conventional theory predicts. To describe behavior intermediate between the two limiting cases of small and large base widths, two approaches are considered. First, the applicability of the Boltzmann transport equation is examined, and certain difficulties are exposed. Second, a physical model is proposed to include the effects of ionic scattering. The model involves various approximations. Each of these is examined in detail.