1) The document discusses the electrical characteristics of a varactor diode, which is a diode with a variable capacitance that depends on the applied reverse bias voltage. 2) It explains the doping profile and Poisson's equation that governs the electric field and potential distribution in the diode. 3) Equations are derived for the junction capacitance as a function of the applied reverse bias voltage based on the doping profile and boundary conditions of the p-n junction.

1. Course: Electronic Devices
paper code: EC301
Course Coordinator: Arpan Deyasi
Department of Electronics and Communication Engineering
RCC Institute of Information Technology
Kolkata, India
9/3/2020 1Arpan Deyasi, RCCIIT, India
Topic: Varactor Diode

2. Varactor = Variable Reactor
9/3/2020 2Arpan Deyasi, RCCIIT, India
Doping profile: p+n or pn+
p
p+n+
n
z z
n
n

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Electrical Characteristics of Varactor Diode
Doping profile of pn+ device
( ) m
DN z Bz=
B: background concentration
m: doping index
z: actual depth of the region

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Electrical Characteristics of Varactor Diode
Poisson’s equation:
2
2
d
dz
φ ρ
ε
= −
2
2
( )D
d q
N z
dz
φ
ε
= −

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Electrical Characteristics of Varactor Diode
2
2
md q
Bz
dz
φ
ε
= −
( 1)
1
( 1)
m
d qB z
C
dz m
φ
ε
+
=− +
+

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Electrical Characteristics of Varactor Diode
( 2)
1 2
( 1)( 2)
m
qB z
C z C
m m
φ
ε
+
=− + +
+ +
Boundary conditions
at z = 0, φ = 0
at z = W, dφ/dz = 0
at z = W, φ = VA+Vbi

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Electrical Characteristics of Varactor Diode
at z = 0, φ = 0 2 0C =
at z = W, dφ/dz = 0
( 1)
1
( 1)
m
qB W
C
mε
+
=
+

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( 2) ( 1)
( 1)( 2) ( 1)
m m
qB z qB W
z
m m m
φ
ε ε
+ +
=− +
+ + +
Electrical Characteristics of Varactor Diode
at z = W, φ = VA+Vbi
( 2)
( 2)
m
A bi
qB W
V V
mε
+
+ =
+

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( )1
2
( 2)( )
m
A biW m V V
qB
ε +
 
= + + 
 
Electrical Characteristics of Varactor Diode

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Electrical Characteristics of Varactor Diode
Total charge stored in depletion region
0
( )
W
D DQ qA N z dz= ∫
0
W
m
DQ qAB z dz= ∫

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Electrical Characteristics of Varactor Diode
( 1)
( 1)
m
D
qAB
Q W
m
+
=
+
( )1
2
( 2)( )
( 1)
m
m
D A bi
qAB
Q m V V
m qB
ε
+
+
 
= + + 
+  

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( )
D
j
A bi
dQ
C
d V V
=
+
Electrical Characteristics of Varactor Diode
Junction capacitance
( )1
( 2)
( 1)
( 2)( )
m
j
A bi
m qB
C A
m V V
ε +
 +
=  
+ + 

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Electrical Characteristics of Varactor Diode
at m = 0, ND(z) = B
at m = 1, ND(z) = Bz
at m = -1, ND(z) = B/z
at m = -3/2, ND(z) = Bz-1.5
( ) m
DN z Bz=

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