274 CHAPTER 6. BIPOLAR JUNCTION TRANSISTORS
6.6 SECONDARY EFFECTS IN REAL DEVICES .................
In the derivations of the bipolar device characteristics, we have made a number of simplifying
assumptions. There are important secondary effects that make the device characteristics deviate
from those derived so far. These deviations have important effects on circuit design as well as
on the limits of device performance.
6.6.1 HighInjection:TheKirkEffect ......................
As will be shown in our high frequency analysis of the bipolar transistor in chapter 7, in order
to achieve high frequency device operation, it is essential to operate the device at high current
density. The reason for this in essence is that many important delays in the transistor have their
origin in charging capacitances of the form
C=Aj
wd(6.6.1)
whereAjis the area of the capacitor (typically the area of thep-njunction) andwdis the junction
depletion depth. Delays in the device are of the form
τ=rj·C (6.6.2)where
rj=∂V
∂I
=
kBT
eI(6.6.3)
is the ac resistance of the junction. The delay timeτcan therefore be written as
τ=kBT
eI·
Aj
wd=
kBT
ewd·
1
J
(6.6.4)
whereJ=I/Ajis the current density. Thus it is imperative to increaseJif one needs to reduce
τand hence increase the maximum device operating frequency.
There is, however, a maximum current density that the device can be operated at, above which
theβof the transistor and the device frequency response drop catastrophically. Essentially, once
the current density reaches this maximum value, the effective base length (i.e. the length between
the emitter and the collector which electrons must diffuse across) becomes wider as a result of
space-charge injection into the collector. This phenomenon is known as the Kirk Effect, and the
associated current density at which it occurs is called the Kirk Threshold ,JKirk. We will now
explain why this occurs.
The basic analysis of bipolar transistors carried out in this chapter involved applying Shock-
ley boundary conditions at the reverse biased base-collector junction. Under this assumption,
the minority carrier density drops to zero at the collector edge of the base region and is zero
everywhere within the base-collector depletion region. This of course is physically not possible,
because having zero minority carriers within the junction requires carriers to travel at extremely
high velocities as dictated by current continuity.
JC=enp,Cve (6.6.5)