322 CHAPTER 7. TEMPORAL RESPONSE OF DIODES AND BIPOLAR TRANSISTORS
This is valid at current densities much below the Kirk threshold density (section 6.6.1) where
ΔQBC≈ΔQ
′
BC(see figure 7.7).
Reverse Active Mode
In the reverse active mode the EBJ is reverse biased while the BCJ is forward biased. Note that
bipolar devices are asymmetrically doped, i.e.,NdeNdc, and the reverse active mode has a
poor current gain. The current and excess minority charge can be written, in analogy with the
forward active mode case (note that the collector is now acting as the emitter):
QR =
eAWbnnb 0
2[
exp(
eVBC
kBT)
− 1
]
iE =−QR
τR+
dQVE
dtiB =QR
τBR+
dQR
dt+
dQVC
dt+
dQVE
dtiC = −QR(
1
τR+
1
τBR)
−
dQR
dt−
dQVC
dt(7.4.12)
Cutoff Mode
In the cutoff mode, both junctions are reverse biased and we may write
IE = −IES+αRICS
IC = −αFIES+ICS (7.4.13)In the cutoff mode the terminal currents are extremely small and there is an effective open circuit
at the terminals.
Saturation Mode
In the saturation mode the EBJ and the BCJ are both forward biased. In this case a good approx-
imation to the current-voltage equations is
IE = IESexp(
eVBE
kBT)
−αRICSexp(
eVBC
kBT)
IC = αFIFSexp(
eVBE
kBT)
−ICSexp(
eVBC
kBT)
(7.4.14)
In saturation there is charge injected into the base from the emitter(QF)and the collector(QR).
The charge in the depletion region charge is negligible, since the junction voltages do not change
much once the device is in saturation. The current-charge relations can be written as
iC =QF
τF−QR
(
1
τR+
1
τBR)
−
dQR
dtiB =QF
τBF+
QR
τBR+
d
dt