Fundamentals of Modern VLSI Devices by Taur Yuan & Ning Tak H

Author:Taur, Yuan & Ning, Tak H.
Language: eng
Format: epub
Publisher: Cambridge University Press
Published: 2009-08-05T16:00:00+00:00

Current-Density Equation for Electrons in a p-Type Base

Let us consider the electrons injected from the emitter into the p-type base region of an n–p–n transistor. Instead of starting with Eq. (6.10), it is often convenient to reformulate the electron current density in terms of carrier concentrations (Moll and Ross, 1956). To this end, we start with the electron current density given by Eq. (2.63), namely

(6.21)

where n is the electron quasi-Fermi potential. As we shall show later, the hole current density in the p-type base is small, being smaller than the electron current density by a factor of about 100 (see Section 6.2.3). Also, as indicated in Fig. 6.2, the base region has a reasonably high doping concentration, typically greater than 1018 cm− 3 for a modern bipolar transistor. Therefore, the IR drop along the electron-current flow path (which is perpendicular to the intrinsic-base layer) in the p-type base is negligible, which, as discussed in Appendix 4, implies that the hole quasi-Fermi potential ϕfp is approximately constant. That is, we have

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