21.4 Bipolar Diodes
569
R p
R s
I ph
I d
I r
nr
Fig. 21.53 Equivalent circuit of a pn diode. Serial (R s ) and parallel (R p ) resistance and diode currents: I d (due to
diffusion, n ≈ 1), I nr
r (nonradiative recombination due to band-impurity recombination, n ≈ 2) and an ideal current
source due to photogeneration (as discussed in Sect. 22.3)
Often, a clear distinction between the n = 1 and n = 2 regimes cannot be made. In this case,
an intermediate ideality factor 1 ≤ n ≤ 2 is fitted to the I –V characteristic as in (21.158). If the
current can be separated into a n = 1 (diffusion) and a n = 2 (recombination-generation) process, the
characteristic is given by (see Fig. 21.51)
I = I
n=1
s
exp
e (V − R s I )
kT
− 1
+
I
n=2
s
exp
e (V − R s I )
2 kT
− 1
+
V − R s I
R p
.
(21.159)
In summary, the pn diode has the equivalent circuit given in Fig. 21.53; the photocurrent source I ph
is discussed below in Sect. 22.3.
21.4.5 Breakdown
If a large voltage is applied in the reverse direction, the pn junction breaks down. At breakdown, a
small voltage increase leads to a dramatic increase of the current. There are three mechanisms that
lead to breakdown: thermal instability, tunneling, and avalanche multiplication [1768–1770]. Defects
cause localized pre-breakdown sites [1770, 1771].
Thermal Instability
The reverse current at large applied voltage leads to a power dissipation and heating of the junction.
This temperature increase leads to a further increase of the saturation current (21.133). If the heat sink,
e.g. the mounting of the chip, is not able to transport the heat away from the device, the current increases
indefinitely. If not limited by a resistor, such a current can destroy the device. The thermal instability
is particularly important for diodes with high saturation current, e.g. Ge at room temperature.
Tunneling
At large reverse bias, charge carriers can tunnel between conduction and valence band through the
junction. A more detailed discussion will be given below in Sect. 21.5.9 about the tunneling diode.
Since for the tunneling effect a thin barrier is necessary, breakdown due to tunneling is important for
diodes where both sides are highly doped. For Si and Ge diodes, tunneling dominates the breakdown
if the breakdown voltage V br is V br < 4E g /e. For V br > 6E g /e avalanche multiplication dominates.
The intermediate regime is a mixed case.
With increasing temperature, the tunneling current can be achieved already with a smaller field
(since the band gap decreases with increasing temperature), thus the breakdown voltage decreases
(negative temperature coefficient).
569
R p
R s
I ph
I d
I r
nr
Fig. 21.53 Equivalent circuit of a pn diode. Serial (R s ) and parallel (R p ) resistance and diode currents: I d (due to
diffusion, n ≈ 1), I nr
r (nonradiative recombination due to band-impurity recombination, n ≈ 2) and an ideal current
source due to photogeneration (as discussed in Sect. 22.3)
Often, a clear distinction between the n = 1 and n = 2 regimes cannot be made. In this case,
an intermediate ideality factor 1 ≤ n ≤ 2 is fitted to the I –V characteristic as in (21.158). If the
current can be separated into a n = 1 (diffusion) and a n = 2 (recombination-generation) process, the
characteristic is given by (see Fig. 21.51)
I = I
n=1
s
exp
e (V − R s I )
kT
− 1
+
I
n=2
s
exp
e (V − R s I )
2 kT
− 1
+
V − R s I
R p
.
(21.159)
In summary, the pn diode has the equivalent circuit given in Fig. 21.53; the photocurrent source I ph
is discussed below in Sect. 22.3.
21.4.5 Breakdown
If a large voltage is applied in the reverse direction, the pn junction breaks down. At breakdown, a
small voltage increase leads to a dramatic increase of the current. There are three mechanisms that
lead to breakdown: thermal instability, tunneling, and avalanche multiplication [1768–1770]. Defects
cause localized pre-breakdown sites [1770, 1771].
Thermal Instability
The reverse current at large applied voltage leads to a power dissipation and heating of the junction.
This temperature increase leads to a further increase of the saturation current (21.133). If the heat sink,
e.g. the mounting of the chip, is not able to transport the heat away from the device, the current increases
indefinitely. If not limited by a resistor, such a current can destroy the device. The thermal instability
is particularly important for diodes with high saturation current, e.g. Ge at room temperature.
Tunneling
At large reverse bias, charge carriers can tunnel between conduction and valence band through the
junction. A more detailed discussion will be given below in Sect. 21.5.9 about the tunneling diode.
Since for the tunneling effect a thin barrier is necessary, breakdown due to tunneling is important for
diodes where both sides are highly doped. For Si and Ge diodes, tunneling dominates the breakdown
if the breakdown voltage V br is V br < 4E g /e. For V br > 6E g /e avalanche multiplication dominates.
The intermediate regime is a mixed case.
With increasing temperature, the tunneling current can be achieved already with a smaller field
(since the band gap decreases with increasing temperature), thus the breakdown voltage decreases
(negative temperature coefficient).