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Review of Basic Device Physics
2.3.7 pn-Junction Dynamic Behavior
Besides electrostatic behavior, pn-junctions are often subject to varying
voltages. In such dynamic operations, charges in the pn-junction vary, resulting in an additional current not predicted by the DC current (Equation 2.119).
There are two types of stored charge in a pn-junction: (1) the charge Q dep due
to the depletion or space-charge region on each side of the junction and (2)
the charge Q dif due to minority carrier injection. Remember that it is these
injected (excess) mobile carriers that generate current I d and also represent a
stored charge Q dif in a pn-junction. The latter is given by the area between the
curve representing p n (or n p ) and the steady state level p no (or n po ) as shown in
Figure 2.23. These two types of stored charges result in two types of capacitances: the junction capacitance C j due to Q dep and the diffusion capacitance
due to Q dif , as discussed in Sections 2.3.7.1 and 2.3.7.2, respectively.
2.3.7.1 Junction Capacitance
In a pn-junction, a small change in the applied voltage causes an incremental
change in the depletion region charge Q dep due to the corresponding change
in the depletion width. If the applied voltage is returned to its original value,
carriers flow in such a direction that the previous increment of charge is
neutralized. The response of the pn-junction to the incremental voltage thus
results in a generation of an effective capacitance C j referred to as the transition capacitance, junction capacitance, or depletion layer capacitance. Recalling
the definition of capacitance per unit area in terms of an incremental charge
dQ dep per unit area induced by an applied voltage dV d , we have
C
dQ
dV
j
dep
d
=
(2.132)
Considering, Q dep = qN a x p = qN d x n from Equation 2.92, we can show
C qN
dx
dV
qN
dx
dV
j
a
p
d
d
n
d
= =
(2.133)
Then using Equation 2.95 or 2.96, the pn-junction capacitance per unit area
can be shown as
C
qK
V
N N
N N
j
si
bi
d
a d
a
d
=
−
(
)
+
ε
φ
0
2
(2.134)
Equation 2.134 is the expression for the diode capacitance for a step profile
in terms of the physical parameters of the device. Remember that Equation
2.134 is valid for V d < f bi , that is, for reverse bias only. Comparing Equations
2.134 and 2.101, it is easy to see that
Review of Basic Device Physics
2.3.7 pn-Junction Dynamic Behavior
Besides electrostatic behavior, pn-junctions are often subject to varying
voltages. In such dynamic operations, charges in the pn-junction vary, resulting in an additional current not predicted by the DC current (Equation 2.119).
There are two types of stored charge in a pn-junction: (1) the charge Q dep due
to the depletion or space-charge region on each side of the junction and (2)
the charge Q dif due to minority carrier injection. Remember that it is these
injected (excess) mobile carriers that generate current I d and also represent a
stored charge Q dif in a pn-junction. The latter is given by the area between the
curve representing p n (or n p ) and the steady state level p no (or n po ) as shown in
Figure 2.23. These two types of stored charges result in two types of capacitances: the junction capacitance C j due to Q dep and the diffusion capacitance
due to Q dif , as discussed in Sections 2.3.7.1 and 2.3.7.2, respectively.
2.3.7.1 Junction Capacitance
In a pn-junction, a small change in the applied voltage causes an incremental
change in the depletion region charge Q dep due to the corresponding change
in the depletion width. If the applied voltage is returned to its original value,
carriers flow in such a direction that the previous increment of charge is
neutralized. The response of the pn-junction to the incremental voltage thus
results in a generation of an effective capacitance C j referred to as the transition capacitance, junction capacitance, or depletion layer capacitance. Recalling
the definition of capacitance per unit area in terms of an incremental charge
dQ dep per unit area induced by an applied voltage dV d , we have
C
dQ
dV
j
dep
d
=
(2.132)
Considering, Q dep = qN a x p = qN d x n from Equation 2.92, we can show
C qN
dx
dV
qN
dx
dV
j
a
p
d
d
n
d
= =
(2.133)
Then using Equation 2.95 or 2.96, the pn-junction capacitance per unit area
can be shown as
C
qK
V
N N
N N
j
si
bi
d
a d
a
d
=
−
(
)
+
ε
φ
0
2
(2.134)
Equation 2.134 is the expression for the diode capacitance for a step profile
in terms of the physical parameters of the device. Remember that Equation
2.134 is valid for V d < f bi , that is, for reverse bias only. Comparing Equations
2.134 and 2.101, it is easy to see that