Metal-Semiconductor Junctions/uploads/18...Metal-Semiconductor Junctions Professor Peter Bermel...
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ECE-305: Fall 2016 Metal-Semiconductor Junctions Professor Peter Bermel Electrical and Computer Engineering Purdue University, West Lafayette, IN USA [email protected] Pierret, Semiconductor Device Fundamentals (SDF) Chapter 14 (pp. 477-487) 10/17/2016 1
Transcript of Metal-Semiconductor Junctions/uploads/18...Metal-Semiconductor Junctions Professor Peter Bermel...
Bermel ECE 305 F16
ECE-305: Fall 2016
Metal-SemiconductorJunctions
Professor Peter BermelElectrical and Computer Engineering
Purdue University, West Lafayette, IN [email protected]
Pierret, Semiconductor Device Fundamentals (SDF)Chapter 14 (pp. 477-487)
10/17/2016 1
Outline
1) Importance of metal-semiconductor junctions
2) Equilibrium band-diagrams and Vbi
3) Band diagram under bias
4) Conclusions
Ref. SDF, Chapter 14 (pp. 477-487)
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NP junctions
3
FnFP
q Vbi VA
What happens here?
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Metal-semiconductor Diode
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M N
Symbols
DN
Metal Wire
N
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Applications of M-S diode ….
www.fz-juelich.de/ibn/index.php?index=674
Originally, Galena (PbS), Si as semiconductor and Phosphor Bronze for metal (cat’s whisker)
detectors STM on semiconductor
Original Bipolar CNT Transistors
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Outline
1) Importance of metal-semiconductor junctions
2) Equilibrium band-diagrams and Vbi
3) Band diagram under bias
4) Conclusions
Ref. SDF, Chapter 14 (pp. 477-487)
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Topic Map
Equilibrium DC Small signal
Large Signal
Circuits
Diode
Schottky
BJT/HBT
MOSFET
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Drawing Band diagram in Equilibrium…
1P P P
pr g
t q
= +
J
+ = + D AE q p n N N
P P Pqp E qD p= J
1N N N
nr g
t q
= +
J
J = + N N Nqn E qD n
equilibrium
DC dn/dt=0Small signal dn/dt ~ jwtn
Transient --- full sol.
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metal energy bands semiconductor energy bands
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E
V
filled states
E
C
empty states
EG= 1.1eV
E
F
E
F
top most band is half-filled
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metal: p-type junction
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EC
EV
EFP
Ei
metal
EFM
E0
FM FS
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now the band diagram
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EC
EV
EFS
Ei
metal
EFM
E0
FM = 4.5
FBP
FS
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band diagram
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EC
EV
EF
Ei
metal
EF
FBPqVbi
“Schottky barrier”for holes.
from the band diagram….potential, e-field, p(x), rho(x)
depleted
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metal: p-type junction
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qVbi = EFM EFS
EC
EV
EFP
Ei
metal
EFM
E0
FM FSqVbi = E0 FM E0 FS
qVbi = FS FM
ΦM is a known material parameter
What is the built-in voltage of a MS junction?
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Semiconductor workfunction
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EC
EV
EFS
Ei
E0
FS
cElectron affinity, χ, and bandgap are known material parameters.
FS = c + EG EFS EV bulk
p0 = NA = NVe EV EFS kBT
EFS EV = kBT lnNA
NV
æ
èçö
ø÷
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“Schottky barrier height”
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EC
EV
EFP
Ei
metal
EFM
E0
FMFS
c
FBP
FBP = c + EG FM
a known material parameter
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Vbi example for silicon
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EC
EV
EFS
Ei
metal
EFM
E0
FM = 4.5 FS
Vbi =FBP EFS EV
FB
q
c = 4.05
FBP
FBP = 4.05 +1.12 4.5 = 0.67
NA = 1016 cm-3
FBP = c + EG FM
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Vbi example for silicon
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EC
EV
EFS
Ei
E0
FS
c = 4.05NA = 1016 cm-3
p0 = NV e EV EFS /kBT cm-3
EFS EV = kBT lnNV
NA
æ
èçö
ø÷
NV = 1.83´1019 cm-3
EFS EV
q= 0.026 ln
1.83´1019
1016
æ
èçö
ø÷= 0.2
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Vbi
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EC
EV
EFS
Ei
metal
EFM
E0
FM FS
qVbi = FBP EFS EV bulk
FBP
qVbi = FS FM
FS = c + EG EFS EV bulk
Φ� = � + �� − Φ��
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Vbi example
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EC
EV
EFS
Ei
metal
EFM
E0
FM = 4.5 FS
Vbi = FBP EFS EV FB= 0.67 0.20 = 0.47
c = 4.05
FBP
FBP
q= 0.67
EFS EV
q= 0.2
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Band-diagram
DN
Vacuum level
EC
EV
EF
c
A p D nN x N x=
FM
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Recall:
Complete Analytical Solution
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Full Depletion Approximation
Actual
ρ
qND
Xd
QM = -QD
QD =NDXn
x Xn
E
x
dE(x)/dx = ρ/ksε0
0s
QdA
K =�E
0 0
max
D D n
ss s
Q qN x
K K = = E
xXn
AV
2max n
a
E xV =
d ( x ) ( x )dx
= E
( x ) ( x )dx = E
xXd
E
aV B
q
CE
FE
VE
iE
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Analytical Solution
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Charge
E-field
Potential
xp
xn+
-Position
Position
Position
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0 0
0 0
2 2
2 2
+
= +
= +
n p
bi
M pD n
s s
x xqV
qN xqN x
k k
E E
0
0
0
0 ?
+
=
=
=
D n
s
M p
s
D n M p
qN x
k
qN x
k
N x N x
E
E
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Depletion Regions
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0 02 2
M pD nbi
s s
qN xqN xqV
k k= +
D n M pN x N x=
0 02 2 1s M sn bi bi
D M D D
k N kx V V
q N N N q N=
+
02
0s Dp bi
M M D
k Nx V
q N N N=
+
xnxp
DN
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Outline
1) Importance of metal-semiconductor junctions
2) Equilibrium band-diagrams and Vbi
3) Band diagram under bias
4) Conclusions
Ref. SDF, Chapter 14 (pp. 477-487)
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Band-diagram with Bias
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EC-Fn
qVbi
VA
EC-Fnq(Vbi-V)
Forward Bias
VA
EC-Fn
Reverse Bias
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Depletion Regions with Bias
0 02 2 1s M s
n bi bi A
D M D D
k N kx V V V
q N N N q N=
+
02
0s Dp bi
M M D
k Nx V
q N N N=
+
xnxp
DN
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Conclusion
1) Schottky diode is a metal-semiconductor majority carrier
device with many applications. We can compare/contrast
them with semiconductor p-n junctions.
2) The depletion structure of Schottky diode is similar to a
one-sided p-n junction transistor, since the electron
concentration in metals is very high.
3) The depletion region under bias can also be understood
by comparison with p-n junctions.
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