Hot Carrier Effects in the Integral Charge-Control Model for Bipolar Transistors

The integral charge-control model (ICM) provides an elegant and compact description of the one-dimensional transport physics of transistors by relating collector current to the junction voltages and total base majority carrier charge. 1,2 The original derivation of the model indicates a possible need for supplementing the base charge in the I C M relation with a term inversely proportional to the minority carrier saturation velocity when base widths are very small ( ~ 1 0 0 0 A). 1 It is shown herein that this term is an artifact arising from inappropriate treatment of the diffusion current contribution to the transport equation. There are, however, additional hot carrier modifications of the charge-control relation that have not been included in previous treatments. These originate in the heating of a reverse current by the built-in field in a junction not supporting a large reverse bias, and should be manifest only in saturated or near-saturated transistor operation. With this exception, the standard I C M relation [equation (15) of Ref. 1] remains valid to the same extent as the macroscopic current transport equation, even for very narrow base widths. 455