21.5 Applications and Special Diode Devices
581
Fig. 21.67 Equivalent
circuit of a varactor diode
with parasitic capacitance
C p and inductance L p and
variable capacitance C j and
resistance R s
R s
C j
C p
L p
21.5.5 Varactors
A diode exhibits a voltage-dependent capacitance. This effect can be used to tune an oscillator using
the diode bias (voltage-controlled oscillator, VCO). The equivalent circuit is shown in Fig. 21.67. The
capacitance consists of a parasitic capacitance C p due to mounting and bonding. This effect also causes
a parasitic inductance. The series resistance due to mounting can typically be neglected. The variable
junction capacitance C j and the ohmic resistance R s are bias dependent.
The C(V ) dependence has generally a power law with an exponent γ (which itself may depend on
the bias voltage)
C =
C 0
(1 + V /V bi ) γ ,
(21.174)
where C 0 is the-zero bias capacitance. Since the frequency f of an LC oscillator circuit depends on
C
−1/2 the frequency, f depends on the voltage as f ∝ V
γ /2 . Therefore, a γ = 2 dependence is most
desirable.
For uniformly doped profiles, the capacitance depends with an inverse square root law on the applied
voltage (21.117), i.e. γ = 0.5. Hyperabrupt junctions are typically made by ion implantation or epitaxy
with graded impurity incorporation to create a special nonuniform doping profile (Fig. 21.68a). For a
doping profile
N B (z) = ˆ
N B
z
z 0
m
(21.175)
the capacitance is given as
C =
e ˆ
N B
m+1
s
(m + 2) z
m
0 (V bi − V )
1
m+2
=
C 0
(1 + V /V bi )
1/(m+2)
.
(21.176)
Ideally, m = −3/2 results is a linear frequency versus voltage relation. The C–V characteristic of
an implanted, hyperabrupt diode exhibits a part that has an exponent γ = 2 (Fig. 21.68b). A γ = 2
C(V ) dependence and therefore a linear f (V ) curve can be achieved over more than one octave using
computer-controlled variable epitaxial-layer doping (Fig. 21.68c).
581
Fig. 21.67 Equivalent
circuit of a varactor diode
with parasitic capacitance
C p and inductance L p and
variable capacitance C j and
resistance R s
R s
C j
C p
L p
21.5.5 Varactors
A diode exhibits a voltage-dependent capacitance. This effect can be used to tune an oscillator using
the diode bias (voltage-controlled oscillator, VCO). The equivalent circuit is shown in Fig. 21.67. The
capacitance consists of a parasitic capacitance C p due to mounting and bonding. This effect also causes
a parasitic inductance. The series resistance due to mounting can typically be neglected. The variable
junction capacitance C j and the ohmic resistance R s are bias dependent.
The C(V ) dependence has generally a power law with an exponent γ (which itself may depend on
the bias voltage)
C =
C 0
(1 + V /V bi ) γ ,
(21.174)
where C 0 is the-zero bias capacitance. Since the frequency f of an LC oscillator circuit depends on
C
−1/2 the frequency, f depends on the voltage as f ∝ V
γ /2 . Therefore, a γ = 2 dependence is most
desirable.
For uniformly doped profiles, the capacitance depends with an inverse square root law on the applied
voltage (21.117), i.e. γ = 0.5. Hyperabrupt junctions are typically made by ion implantation or epitaxy
with graded impurity incorporation to create a special nonuniform doping profile (Fig. 21.68a). For a
doping profile
N B (z) = ˆ
N B
z
z 0
m
(21.175)
the capacitance is given as
C =
e ˆ
N B
m+1
s
(m + 2) z
m
0 (V bi − V )
1
m+2
=
C 0
(1 + V /V bi )
1/(m+2)
.
(21.176)
Ideally, m = −3/2 results is a linear frequency versus voltage relation. The C–V characteristic of
an implanted, hyperabrupt diode exhibits a part that has an exponent γ = 2 (Fig. 21.68b). A γ = 2
C(V ) dependence and therefore a linear f (V ) curve can be achieved over more than one octave using
computer-controlled variable epitaxial-layer doping (Fig. 21.68c).