21.4 Bipolar Diodes
571
(a)
10
3
10
10
10
2
1
0
10
14
10
15
10
16
10
17
10
18
N (cm )
B
-3
Si
Ge
GaAs
GaP
(b)
10
2
10
10
1
0
10
-1
10
14
10
15
10
16
10
17
10
18
N (cm )
B
-3
10
6
10
5
m
Si
Ge
GaAs
GaP
Ge
GaP
Si
GaAs
Fig. 21.54 a Avalanche breakdown voltage for one-sided abrupt junctions in Ge, Si, (100)-GaAs and GaP at T = 300 K.
The dashed line indicates the limit of avalanche breakdown at high doping due to tunneling breakdown. b Depletion-layer
width w at breakdown and maximum electric field E m for the same junctions. Adapted from [1772]
Fig. 21.55 Temperature
dependence of a n + p
Si-diode with
N B = 2.5 × 10 16 cm −3 and
a guard-ring structure (see
Fig. 21.56d). The
temperature coefficient
∂ V br /∂ T is 0.024 V/K.
Adapted from [1776]
α = A E
7
.
(21.166)
for silicon with A = 1.8 × 10
−35 (cm/V)
7 cm
−1 . For the breakdown condition (21.165), using (21.9)
and (21.166) the depletion layer width at breakdown w B (w B in cm, N D in cm
3 ) is found to be
w B = 2.67 × 10
10 N
−7/8
D
.
(21.167)
From this the breakdown voltage can be calculated with (21.15) (V B in V, N D in cm
3 ) [1774]
V B = 6.40 × 10
13 N
−3/4
D
.
(21.168)
In GaAs, the impact-ionization coefficients and therefore the breakdown voltage are direction dependent. At a doping of N B = 10
16 cm
−3 , the breakdown voltage is the same for (001) and (111) orientation;
for smaller doping the breakdown voltage of (001)-oriented GaAs is smaller, for larger doping that of
GaAs (111) [1775].
At higher temperatures, the charge carriers release their excess energy faster to the lattice.
24 Thus,
less energy is available for impact ionization and the required electric field is higher. Therefore, the
24 The scattering rate becomes higher with increasing temperature and, e.g., the mobility decreases, see Sect. 8.3.11, and
the drift saturation velocity decreases, see Sect. 8.4.1.
571
(a)
10
3
10
10
10
2
1
0
10
14
10
15
10
16
10
17
10
18
N (cm )
B
-3
Si
Ge
GaAs
GaP
(b)
10
2
10
10
1
0
10
-1
10
14
10
15
10
16
10
17
10
18
N (cm )
B
-3
10
6
10
5
m
Si
Ge
GaAs
GaP
Ge
GaP
Si
GaAs
Fig. 21.54 a Avalanche breakdown voltage for one-sided abrupt junctions in Ge, Si, (100)-GaAs and GaP at T = 300 K.
The dashed line indicates the limit of avalanche breakdown at high doping due to tunneling breakdown. b Depletion-layer
width w at breakdown and maximum electric field E m for the same junctions. Adapted from [1772]
Fig. 21.55 Temperature
dependence of a n + p
Si-diode with
N B = 2.5 × 10 16 cm −3 and
a guard-ring structure (see
Fig. 21.56d). The
temperature coefficient
∂ V br /∂ T is 0.024 V/K.
Adapted from [1776]
α = A E
7
.
(21.166)
for silicon with A = 1.8 × 10
−35 (cm/V)
7 cm
−1 . For the breakdown condition (21.165), using (21.9)
and (21.166) the depletion layer width at breakdown w B (w B in cm, N D in cm
3 ) is found to be
w B = 2.67 × 10
10 N
−7/8
D
.
(21.167)
From this the breakdown voltage can be calculated with (21.15) (V B in V, N D in cm
3 ) [1774]
V B = 6.40 × 10
13 N
−3/4
D
.
(21.168)
In GaAs, the impact-ionization coefficients and therefore the breakdown voltage are direction dependent. At a doping of N B = 10
16 cm
−3 , the breakdown voltage is the same for (001) and (111) orientation;
for smaller doping the breakdown voltage of (001)-oriented GaAs is smaller, for larger doping that of
GaAs (111) [1775].
At higher temperatures, the charge carriers release their excess energy faster to the lattice.
24 Thus,
less energy is available for impact ionization and the required electric field is higher. Therefore, the
24 The scattering rate becomes higher with increasing temperature and, e.g., the mobility decreases, see Sect. 8.3.11, and
the drift saturation velocity decreases, see Sect. 8.4.1.