B.2. Base-Width Dependence on Junction Voltage
In real transistors, the base width depends on the voltage applied across a pn junction. The effect is known as base-width modulation. A diagrammatic representation of the effect is illustrated in Fig. B.6. Not shown in the diagrams in Unit B.1 of the pnp structure are the depletion regions, which are shown shaded in Fig. B.6. These are the transition regions that are depleted of free carriers, and in which the barrier is formed that impedes electron and hole flow to the p regions and n region, respectively. The base width (n region) is actually the width between the depletion regions. In the diagram of Fig. B.6, we define wBo for VBC = 0 and wB for VBC > 0.
Figure B.6. Diagrammatic pnp structure showing the effect of base – collector voltage on base width.
The magnitude of saturation current, IS, in (B.3) is specifically defined for VBC = 0 or wBo. In a circuit application, though, VBC will in general be nonzero and the base width can vary as shown; in the example of Fig. B.6, the base width is wB for a given applied VBC. To a reasonable approximation, the relationship between the effective saturation current with a nonzero VBC can be accounted for with the form.
Equation B.4
where 
is the effective saturation current for a reverse-applied base – collector voltage. The approximate form assumes that VBC << VAF. The expression in the denominator, 1 – VBC/VAF, comes from the fact that 
is approximately inversely proportional to the base width, and the base width is roughly
Equation B.5
The parameter VAF is called the Early voltage for forward-active operation. It has a counterpart for reverse-active operation, VAR. The base-width dependence on junction voltage is included in the nonideal factors taken up in Unit B.3.