264 CHAPTER 6. BIPOLAR JUNCTION TRANSISTORS
unity. We have from equation 6.3.16 and equation 6.3.17 (in the forward active mode, the
collector current is essentially due to electron injection from the emitter)
B=IC
IEn∼=^1
cosh(
Wbn
Lb) (6.4.8)
For small base width we have
B∼= 1 −Wbn^2
2 L^2 b(6.4.9)
Note that the base transport factor depends upon the neutral base width, not the chemical base
width. Thus it depends upon the bias conditions. This causes the Early effect discussed later.
Collector Efficiencyγc
The collector efficiency is the ratio of the electron current that reaches the collector to the
base-collector current. Due to the high reverse bias at the base-collector junction, essentially all
the electrons are swept into the collector so that the collector efficiency can be taken to be unity.
Current Gain
Since we know how the expression for the emitter efficiency and base transport factor we can
now examine the current gain. We are primarily interested in the ratio of the collector current
and the base current. The parameterαdefined as the ratio of the collector current to the emitter
current is given by
α =IC
IE
=
BIEn
IEn+IEp=γeB=
[
1 −
peoDeWbn
nboDbLe][
1 −
Wbn^2
2 L^2 b]
(6.4.10)
The ratio of the collector current to the base current is extremely important since it is the base
current that is used to control the device state. This is given by
β=α
1 −α(6.4.11)
We can see that heavy emitter doping and narrow base width are critical for highβ.An
important parameter characterizing the device performance is the transconductance, which de-
scribes the control of the output current (IC) with the input bias (VBE). The transconductance is
(IC ∝ exp(eVBE/kBT))
gm=∂IC
∂VBE
=
eIC
kBT=
eβIB
kBT(6.4.12)
The transconductance of bipolar devices is extremely high compared to that of field-effect tran-
sistors of similar dimensions. This is because of the exponential dependence ofIConVBEin
contrast to a weaker dependence of current on “gate bias” for field effect transistors.