Overview

To derive the continuity equation for holes, let us consider a unidimensional current flow and the box shown in Fig. D.1, where J _p is the hole current density, and G _p and R _p refer to the generation and recombination rates for holes, per unit time per unit volume. The continuity equations result from the charge conservation principle.

Fig. D.1: Illustration of the continuity equation for a one-dimensional flow of holes.

Conservation of holes implies that the net number of holes entering the volume of cross section A and length ? y per unit time, namely,

plus the number of holes generated within the volume per unit time

equals the increase in the number of holes in the volume per unit time

Thus, equating the above terms, and dividing by the volume ? y.A, gives

In the limit case as ? y ? 0, we have

A similar relation holds for electrons

Bibliography

[1] Richard B. Adler, Arthur C. Smith, and Richard L. Longini, Introduction to Semiconductor Physics , SEEC Series, vol. 1, John Wiley&Sons, New York, 1964.