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p-n junction: built-in potential and constant Fermi level
1. Course: Electronic Devices
paper code: EC301
Course Coordinator: Arpan Deyasi
Department of Electronics and Communication Engineering
RCC Institute of Information Technology
Kolkata, India
8/19/2020 1Arpan Deyasi, RCCIIT, India
Topic: Junction
2. Calculation of built-in potential
EF
EV
EC
EFI
qΦFp
qΦFn
Vbi
8/19/2020 2Arpan Deyasi, RCCIIT, India
3. Calculation of built-in potential
Equilibrium electron concentration
0 exp F FI
i
E E
n n
kT
−
=
0 exp Fn
i
q
n n
kT
φ
=
8/19/2020 3Arpan Deyasi, RCCIIT, India
4. 0
lnFn
i
nkT
q n
φ
=
Calculation of built-in potential
ln D
Fn
i
kT N
q n
φ
=
8/19/2020 4Arpan Deyasi, RCCIIT, India
5. Calculation of built-in potential
Equilibrium hole concentration
0 exp FI F
i
E E
p n
kT
−
=
0 exp
Fp
i
q
p n
kT
φ
=
8/19/2020 5Arpan Deyasi, RCCIIT, India
6. Calculation of built-in potential
0
lnFp
i
pkT
q n
φ
=
ln A
Fp
i
kT N
q n
φ
=
8/19/2020 6Arpan Deyasi, RCCIIT, India
7. Calculation of built-in potential
bi Fn FpV φ φ= +
ln lnD A
bi
i i
kT N kT N
V
q n q n
+
8/19/2020 7Arpan Deyasi, RCCIIT, India
8. ln lnD A
bi
i i
kT N N
V
q n n
+
Calculation of built-in potential
2
ln D A
bi
i
kT N N
V
q n
=
8/19/2020 8Arpan Deyasi, RCCIIT, India
9. Extrinsic Fermi Level is constant
8/19/2020 9Arpan Deyasi, RCCIIT, India
We consider p-n junction under external bias
0pJ =
Under equilibrium
0
0 0p z p
dp
qp E qD
dz
µ − =
10. 8/19/2020 10Arpan Deyasi, RCCIIT, India
0
0 p z p
dp
p E D
dz
µ =
Extrinsic Fermi Level is constant
0
0
p
z
p
D dp
p E
dzµ
=
11. 8/19/2020 Arpan Deyasi, RCCIIT, India 11
Extrinsic Fermi Level is constant
0
0 z
dpkT
p E
q dz
=
0 exp FI F
i
E E
p n
kT
−
=
12. 8/19/2020 Arpan Deyasi, RCCIIT, India 12
0
expi FI F
FI F
dp n E E
dz kT kT
dE dE
dz dz
−
=
× −
Extrinsic Fermi Level is constant
0
0 z
dpkT
p E
q dz
=
13. 8/19/2020 Arpan Deyasi, RCCIIT, India 13
Extrinsic Fermi Level is constant
z
dV
E
dz
= −
FI
z
d E
E
dz q
=− −
1 FI
z
dE
E
q dz
=
0
0 z
dpkT
p E
q dz
=
14. 8/19/2020 Arpan Deyasi, RCCIIT, India 14
Extrinsic Fermi Level is constant
1
exp
exp
FI F FI
i
i FI F FI F
E E dE
n
kT q dz
nkT E E dE dE
q kT kT dz dz
−
× =
−
× × −
15. 8/19/2020 Arpan Deyasi, RCCIIT, India 15
FI FI FdE dE dE
dz dz dz
= −
Extrinsic Fermi Level is constant
0FdE
dz
=