21.4 Bipolar Diodes
559
Fig. 21.43 Debye length
in Si at room temperature
as a function of the doping
level N B according to
(21.114)
Fig. 21.44 Width of the
depletion layer and
capacitance per area for
one-sided, abrupt Si
junctions for various values
of V bi − V − 2kT /e as
labeled. The dash-dotted
line is for zero bias, the
dashed line is the limit due
to avalanche breakdown.
Adapted from [574]
10
2
10
10
10
10
1
0
-1
-2
10
10
10
10
10
2
3
4
5
6
2
N (cm )
B
-3
10
13
10
14
10
15
10
16
10
17
10
18
0.1V
1V
10V
100V
Si
21.4.3 Capacitance
The capacitance of the depletion layer is the charge change upon a change of the external bias. It is
given as
C =
dQ
dV
=
d(eN B w)
d(w 2 eN B /2 s )
=
s
w
=
s
√
2 L D
1
√ βV bi − βV − 2
.
(21.116)
Therefore, the capacitance of the depletion layer is inversely proportional to the depletion-layer width
(see the two scales in Fig. 21.44). A detailed treatment has been given in [1762]. 1/C
2 is proportional
to the external bias
1
C 2 =
2 L
2
D
2
s
(βV bi − βV − 2) .
(21.117)
From C–V spectroscopy the doping level can be obtained from the slope
d(1/C
2
)
dV
=
2 β L
2
D
2
s
=
2
e s N B
.
(21.118)
From the extrapolation to the voltage for which 1/C
2
= 0 the built-in voltage can be obtained.