Physics and electrical properties of M-s contact

1. Course: Electronic Devices
paper code: EC301
Course Coordinator: Arpan Deyasi
Department of Electronics and Communication Engineering
RCC Institute of Information Technology
Kolkata, India
9/7/2020 1Arpan Deyasi, RCCIIT, India
Topic: Metal-Semiconductor Contact

2. Metal-Semiconductor Contact
Heterostructure --- different materials in terms of bandgap
Classified based on the work function difference
ΦM > ΦS(n)
ΦM < ΦS(n)
ΦM > ΦS(p)
ΦM < ΦS(p)
9/7/2020 2Arpan Deyasi, RCCIIT, India
For unidirectional current --- Schottky contact
For bidirectional current ---- Ohmic contact

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M S(n)
Ec
EV
EFn
EFi
ΦM > ΦS(n)
M S(n)
qΦM
qΦS
Ec
EV
EFn
EFi
qχS bending

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M S(n)
Ec
EV
EFn
EFi
ΦM > ΦS(n)
I
Schottky
Contact

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M S(p)
Ec
EV
EFp
EFi
ΦM > ΦS(p)
M S(p)
qΦM
qΦS
Ec
EV
EFp
EFi
qχS
bending

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M S(p)
Ec
EV
EFp
EFi
ΦM > ΦS(p)
I
Ohmic
Contact

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ΦM < ΦS(n)
M S(n)
qΦM qΦS
Ec
EV
EFn
EFi
qχS
bending
EV
EFi
EFn
Ec
M S(n)

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ΦM < ΦS(n)
EV
EFi
EFn
Ec
M S(n)
I
Ohmic
Contact

9. 9/7/2020 9Arpan Deyasi, RCCIIT, India
ΦM < ΦS(p)
M S(p)
qΦM
qΦS
Ec
EV
EFp
EFi
qχS
M S(p)
Ec
EFi
EFp
EV
bending

10. 9/7/2020 10Arpan Deyasi, RCCIIT, India
ΦM < ΦS(p)
M S(p)
Ec
EFi
EFp
EV
I
Schottky
Contact

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Criteria Nature of Contact
ΦM > ΦS(n) Schottky contact
ΦM > ΦS(p) Ohmic Contact
ΦM < ΦS(n) Ohmic Contact
ΦM < ΦS(p) Schottky contact

12. Electrical Characteristics of Schottky Diode
Poisson’s equation: 2
2
d
dz
φ ρ
ε
= −
2
2
( )D
d q
N z
dz
φ
ε
= −
We consider metal/n-type junction
9/7/2020 12Arpan Deyasi, RCCIIT, India

13. Electrical Characteristics of Schottky Diode
( )D
dE q
N z
dz ε
=
1( ) D
q
E z N z C
ε
= +
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14. Electrical Characteristics of Schottky Diode
at z = W, E = 0
1 D
q
C N W
ε
= −
( ) ( )D
q
E z N W z
ε
=− −
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15. Electrical Characteristics of Schottky Diode
Maximum electric field
max ( 0)E E z= =
max
DqN
E W
ε
=
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16. Electrical Characteristics of Schottky Diode
( )D
d q
N W z
dz
φ
ε
= −
2
2
1
( ) ( )
2
D
q
z N Wz z Cφ
ε
= − +
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17. at z = 0, φ = φMS
Electrical Characteristics of Schottky Diode
2 MSC φ=
21
( ) ( )
2
D MS
q
z N Wz zφ φ
ε
= − +
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18. Electrical Characteristics of Schottky Diode
Built-in potential
( )bi MSV z Wφ φ= = −
2
2
D
bi
qN
V W
ε
=
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19. Electrical Characteristics of Schottky Diode
Space-charge width
2
bi
D
W V
qN
ε
=
Maximum electric field
max
2 D biqN V
E
ε
=
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20. Electrical Characteristics of Schottky Diode
For reverse-bias voltage VR
2
( )bi R
D
W V V
qN
ε
= +
max
2 ( )D bi RqN V V
E
ε
+
=
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21. Electrical Characteristics of Schottky Diode
Junction capacitance
( )
D
j
A bi
dQ
C
d V V
=
+
DQ qN WA=
where
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22. Electrical Characteristics of Schottky Diode
j
A
C
W
ε
=
2( )
D
j
bi R
q N
C A
V V
ε
=
+
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23. Schottky Diode: Lowering of barrier potential
q +q
Force on electron
2
2
4 (2 )
q
F
zπε
= −
z z F qE= −
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24. Schottky Diode: Lowering of barrier potential
Potential
( )z Edzφ = −∫
( )
16
q
z
z
φ
πε
=
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25. Schottky Diode: Lowering of barrier potential
Modified potential
mod ( )
16
q
z Ez
z
φ
πε
= +
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26. Schottky Diode: Lowering of barrier potential
For maximum barrier lowering
mod ( ) 0
d
z
dz
φ =
0
16
d q
Ez
dz zπε
 
+ = 
 
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27. Schottky Diode: Lowering of barrier potential
max
16
q
z
Eπε
=
zmin: position of minimum barrier
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28. Maximum barrier lowering
Schottky Diode: Lowering of barrier potential
min
min16
q
Ez
z
φ
πε
∆= +
16 16
qE qE
φ
πε πε
∆= +
4
qE
φ
πε
∆ =
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