6.6. SECONDARY EFFECTS IN REAL DEVICES 277
JC < Jcrit
JC = Jcrit
JC = JKirk
xpC wC xnC
|E|
Figure 6.18: Electric field profile in the collector whenJC <Jcrit,JC = Jcrit,and
JC=JKirk. The depletion extension into the base and subcollector are labeledxpCandxnC,
respectively.xpCandxnCshown in this figure correspond to the profile withJC=Jcrit.
zero and the area underneath the electric field isVCB+Vbi. From that we get the following set
of equations.
1
2
EmaxwC=VCB+Vbi (6.6.10)Emax
wC=
dE
dx=
e
(nKirk−Nd,C) (6.6.11)nKirk=JKirk
evs(6.6.12)
Combining these equations and solving forJKirkgives us
JKirk=[
2
ew^2 C(VCB+Vbi)+Nd,C]
evs (6.6.13)Let us examine the consequence of reaching the Kirk threshold. If one assumed that the
process of electric field modification with increasing current density described in this section
were to continue, then a situation occurs where thedirection of the electric field reverses in a
regionwrevnear the base-collector edge, as shown in figure 6.19a. This corresponds to the band
diagram shown in figure 6.19b. However, this is an unphysical situation for homojunctions, as
there is no blocking barrier for holes. Hence the holes from the base would flood the collector to
achieve the physical situation of the holes being contained within a regionΔwBin the collector.
Here, they neutralize the injected negative charge, resulting in zero electric field within this
region. This is shown in figure 6.20.