SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

320 CHAPTER 7. TEMPORAL RESPONSE OF DIODES AND BIPOLAR TRANSISTORS

It is useful to examine the charge in the device in the forward active mode. In figure 6.8b
we showed the minority charge injected in the emitter, base, and collector. The excess minority
charge injected into the base region is given by

QF=

eAWbnnb 0

2

(

exp

eVBE

kBT

− 1

)

(7.4.6)

We can define the collector current in terms of the excess charge by defining a time constantτF
which is the forward transit time of minority carriers through the base. We have

QF=τFIC (7.4.7)

In other words, for a collector currentICto be maintained, the excess minority charge in the
baseQFmust be replaced everyτFseconds. As discussed in chapter 3 , the forward transit time
is

τF=

Wbn^2

2 Db

(7.4.8)

ThebasecurrentIBis due to recombination in the neutral base with the minority charge and
hole injection into the emitter. These two effects can be summarized by a time constantτBFand
we can write

IB=

QF

τBF

(7.4.9)

The current gain is then

βF=

IC

IB

=

τBF

τF

(7.4.10)

Now let us examine what happens when the junction voltages are modulated. Consider the
transistor connected in a common emitter configuration shown in figure 7.7. When the emitter-
base voltage is increased byΔVBE, the currentand the stored charge in the device both change.
The collector current increases by some amountΔIC, causing the collector voltagevoutto drop
by an amountΔvout=ΔIC·RCC.Thisdecreases the reverse bias across the base-collector
junction, causing the base-collector depletion region to become narrower, as illustrated in fig-
ure 7.7b. Additionally, becauseVBEhas increased, the emitter-base depletion region becomes
narrower, and the injected minority charge in the baseQFincreases in magnitude. The variation
in emitter-base and base-collector depletion widths implies a change in the amount of stored
charge in each of the depletion regions, as indicated in figure 7.7b.
Figure 7.7c shows a schematic diagram of the current at each of the three terminals. Additional
stored charge in the emitter, base, and collector regions must be supplied by the emitter, base,
and collector currents. Including the current required to supply the additional stored charge,iC,
iB,andiEcan be written as

iC =

QF

τF

−

dQBC

dt

iB =

QF

τBF

+

dQF

dt

+

dQBC

dt

+

dQBE

dt

iE = iC+iB=QF

(

1

τF

+

1

τBF

)

+

dQF

dt

+

dQBE

dt

(7.4.11)