SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

7.5. HIGH-FREQUENCY BEHAVIOR OF A BJT 327

(a)

0 wB

Δnp(0) |ΔQF|

(b)

0 wB

Δnp(0) |ΔQF|

Δnp(wB)

Figure 7.10: Charge profile in the base when device is modulated. (a) Approximate base charge
profile with Shockley boundary conditions. (b) Base charge profile when velocity saturation in
the collector is included.

whereΔQFfor this case is shown in figure 7.10a. However, as we saw in the case of the Kirk
effect, the carrier density cannot drop to zero at the collector side of the neutral base. Instead,
np(wB)is given by

np(wB)=

IC/AE

evsat

(7.5.8)

wherevsatis the electron saturation velocity in the material andAEis the emitter area. If we
increase the current in the device by an amountΔIC, the electron density at the collector side
of the base also rises, as indicated in figure 7.10b. This results in additional charge that must
be supplied to the base region. In figure 7.10b, the charge above the dotted line is equal to
the total charge supplied when Shockley boundary conditions are assumed (figure 7.10a). The
charge below the dotted line is the additional charge due to velocity saturation in the collector.
Including velocity saturation effects,τBcan be written as

τB=

w^2 B

2 DnB

+

wB

vsat

(7.5.9)

In the base-collector depletion region, the change in stored chargeΔQBCresults from two
separate effects.

1. The base-collector depletion width changes due to the variation in the base-collector volt-
   age, as was illustrated in figure 7.1b. We will refer to the associated change in space charge
   asΔQBC 1.


2. As discussed in the derivation ofτB, because of velocity saturation, themobile charge
   density in the base-collector depletion region must also increase whenICincreases (this
   is the origin ofΔnp(wB)in figure 7.10b). Because this increased mobile charge cannot
   result in a change in voltage across the depletion region (the voltage is fixed by the bias
   conditions), the base-collector depletion widths are adjusted by anadditional amount to