barcelona, 31 may- 2 june 20101 contacts to high-resistivity semiconductors arie ruzin school of ee,...
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Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 11
Contacts to High-Resistivity Semiconductors
Arie Ruzin
School of EE, Faculty of Engineering, Tel Aviv University, Israel
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 22
Outline
• Motivation
• Schottky and Ohmic contacts to Low- semiconductors
• Simulated results for Low- and High- semiconductors
• Injecting contacts to High- semiconductors
• Space Charge Limited Current
• Summary
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“Classic” Presentation for High- Energy Bands (??)
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Taking Into Account Majority Carriers Only (??)
Majority Carriers only?
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Thermionic Emission (??)
Thermionic emission ?
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Thermionic emission ?
Thermionic Emission (??), 1.5eV barriers (?)
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Textbook Contacts (Low-Textbook Contacts (Low- Semiconductor) Semiconductor)
Ei
Schottky Ohmic Ohmic injecting?
EF
qB EC
EV
Metal Semiconductor
qF
qs
EF
Ei
EC
EV
qF
Metal Semiconductor
EF
Ei
EC
EV
qF
qB
Metal Semiconductor
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Low- CdTe Diode (ND=1015,B=1eV)(The diode is 1 mm long)
Zoom on the front 10 m
Zero Bias
Low Bias
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 2 4 6 8 10
Depth [m]
En
erg
y [
eV
]
ConductionBandEnergy
ValenceBandEnergy
eQuasiFermiPotential
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 2 4 6 8 10
Depth [m]
En
erg
y [
eV
]
C-Band V-Band
C_Band-0.5V V_Band-0.5V
C-Band+0.5V V-Band+0.5V
Energy band structure
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Forward Bias
-2.E+03
0.E+00
2.E+03
4.E+03
6.E+03
8.E+03
1.E+04
1.E+04
1.E+04
2.E+04
2.E+04
0 2 4 6 8 10Depth [um]
E-F
ield
[V
/cm
]
VB=0V
VB=0.5V
VB=2V
VB=5V
VB=8V
VB=10V
Reverse Bias
-1.E+04
0.E+00
1.E+04
2.E+04
3.E+04
4.E+04
5.E+04
6.E+04
7.E+04
0 2 4 6 8 10Depth [um]
E-F
ield
[V
/cm
]
VB=0V
VB=-0.5V
VB=-2V
VB=-5V
VB=-8V
VB=-10V
Low- CdTe Diode (ND=1015,B=1eV)(The diode is 1 mm long)
Zoom on the front 10 mE-field profiles under bias
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 1010
Reverse Bias
1.E-01
1.E+01
1.E+03
1.E+05
1.E+07
1.E+09
1.E+11
1.E+13
1.E+15
0 2 4 6 8 10Depth [m]
e-
De
ns
ity
[c
m-3
]
VB=0V
VB=-0.5V
VB=-2V
VB=-5V
VB=-8V
VB=-10V
Reverse Bias
1.E-111.E-09
1.E-071.E-051.E-031.E-01
1.E+011.E+031.E+05
1.E+071.E+09
0 10 20 30 40 50Depth [m]
h-
De
ns
ity
[c
m-3
]
VB=0V
VB=-0.5V
VB=-2V
VB=-5V
VB=-8V
VB=-10V
Forward Bias
0.E+001.E+142.E+143.E+144.E+145.E+146.E+147.E+148.E+149.E+141.E+15
0 2 4 6 8 10
Depth [um]
e-D
ensi
ty [
cm-3
]
VB=0V
VB=0.5V
VB=2V
VB=5V
VB=8V
VB=10V
Forward Bias
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+10
0 200 400 600 800 1000
Depth [um]
h-D
en
sit
y [
cm
-3]
VB=0V VB=0.5V
VB=2V VB=5V
VB=8V VB=10V
Low- CdTe Diode (ND=1015,B=1eV)Free carrier densities
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 1111
Low- CdTe Diode (ND=1015,B=1eV)(The diode is 1 mm long)
Current density
1.E-07
1.E-05
1.E-03
1.E-01
1.E+01
1.E+03
1.E+05
1.E+07
1.E+09
-1 0 1 2Bias [V]
J [
nA
/cm
2 ]
JT0.8eV [nA/cm2]
JT1.0eV [nA/cm2]
JT1.5eV [nA/cm2]
JT1.3eV [nA/cm2]
Thermionic emission limited
Bulk limited
2
0.16
1.50.16 2.4
0.1
nq n
V AJ
cm cm
E
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EF
Ei
qB EC
EV
Metal Semiconductor
qF
qs
EF
Ei
EC
EV
qF
qB
Metal Semiconductor
EF
Ei
EC
EV
qF
Metal Semiconductor
High- Schottky Diode (?)
Schottky Ohmic Ohmic injecting?
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 1313
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
Depth [m]
En
erg
y [
eV
]
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
Depth [m]
En
erg
y [
eV
]
C-Band V-BandC-Band-0.5V V-Band-0.5VC-Band-2V V-Band-2V
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0 200 400 600 800 1000
Depth [m]
En
erg
y [
eV
]
C-Band V-Band
C-Band+0.5V V-Band+0.5V
C-Band+2V V-Band+2V
High- CdTe Diode (ND=106,B=1eV)
Zero Bias
Low Bias
Energy band structure
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 1414
Reverse Bias
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
1.E+09
0 200 400 600 800 1000
Depth [m]
h-
De
ns
ity
[cm
-3]
VB=0V
VB=-0.5V
VB=-2V
VB=-5V
VB=-8V
VB=-10V
Reverse Bias
1.E+01
1.E+02
1.E+03
1.E+04
1.E+05
1.E+06
0 200 400 600 800 1000Depth [m]
e-
De
ns
ity
[c
m-3
]
VB=0V
VB=-0.5V
VB=-2V
VB=-5V
VB=-8V
VB=-10V
Forward Bias
1.E+03
1.E+04
1.E+05
1.E+06
1.E+07
1.E+08
1.E+09
1.E+10
0 200 400 600 800 1000
Depth [m]
h-D
en
sit
y [
cm
-3]
VB=0V
VB=0.5V
VB=2V
VB=5V
VB=8V
VB=10V
Forward Bias
1.0E+00
1.0E+01
1.0E+02
1.0E+03
1.0E+04
1.0E+05
1.0E+06
1.0E+07
0 200 400 600 800 1000Depth [m]
e-D
en
sit
y [
cm
-3]
VB=0V
VB=0.5V
VB=2V
VB=5V
VB=8V
VB=10V
High- CdTe Diode (ND=106,B=1eV)
Free carrier densities
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 1515
-5.0E-13
0.0E+00
5.0E-13
1.0E-12
1.5E-12
2.0E-12
2.5E-12
-10 -5 0 5 10
Bias [V]
Cu
rren
t [A
]
-4.0E-17
-3.5E-17
-3.0E-17
-2.5E-17
-2.0E-17
-1.5E-17
-1.0E-17
-5.0E-18
0.0E+00
-10 -8 -6 -4 -2 0
Bias [V]
Cu
rren
t [A
]
High- CdTe Diode (ND=106,B=1eV)
Forward and Reverse Currents
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 1616
-1.5
-1
-0.5
0
0.5
1
1.5
0 200 400 600 800 1000
Depth [ m ]
En
erg
y [e
V]
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0 200 400 600 800 1000
Depth [m]
En
erg
y [e
V]
C-Band V-Band
C-Band+0.5V V-Band+0.5V
C-Band+2V V-Band+2V
-3.5-3
-2.5-2
-1.5-1
-0.50
0.51
1.52
0 200 400 600 800 1000Depth [m]
En
erg
y [e
V]
C-Band V-Band
C-Band-0.5V V-Band-0.5V
C-Band-2V V-Band-2V
High- CdTe Diode (ND=106,B=1.3eV)
Zero Bias
Low Bias
Energy band structure
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 1717
High- CdTe Diode (ND=106,B=1.3eV)Free Carrier Concentration
Reverse Bias
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
0 200 400 600 800 1000
Depth [m]
e- D
ensi
ty [
cm-3
]
VB=0V VB=-0.5V
VB=-2V VB=-5V
VB=-8V VB=-10V
Reverse Bias
1.E+03
1.E+05
1.E+07
1.E+09
1.E+11
1.E+13
1.E+15
0 200 400 600 800 1000
Depth [m]
h-
Den
sity
[cm
-3]
VB=0V
VB=-0.5V
VB=-2V
VB=-5V
VB=-8V
VB=-10V
Forward Bias
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+10
0 200 400 600 800 1000
Depth [m]
e-D
ensi
ty [
cm-3
]
VB=0V VB=0.5V
VB=2V VB=5V
VB=8V VB=10V
Forward Bias
1.E+03
1.E+05
1.E+07
1.E+09
1.E+11
1.E+13
1.E+15
0 200 400 600 800 1000Depth [m]
h-D
ensi
ty [
cm-3
]
VB=0V VB=0.5V
VB=2V VB=5V
VB=8V VB=10V
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 1818
High- CdTe Diode (ND=106,B=1.3eV)
E-Field and Potential profilesReverse Bias
-12
-10
-8
-6
-4
-2
0
2
0 200 400 600 800 1000Depth [m]
Po
ten
tial
[eV
]
VB=0V
VB=-0.5V
VB=-2V
VB=-5V
VB=-8V
VB=-10V
Reverse Bias
1
10
100
1000
0 200 400 600 800 1000
Depth [um]
E-F
ield
[V
/cm
]
VB=0V VB=-0.5V VB=-2V
VB=-5V VB=-8V VB=-10V
Forward Bias
-2
0
2
4
6
8
10
12
0 200 400 600 800 1000
Depth [m]
Po
ten
tia
l [e
V]
VB=0V
VB=0.5VVB=2V
VB=5V
VB=8VVB=10V
Forward Bias
0.01
0.1
1
10
100
1000
0 200 400 600 800 1000Depth [m]
E-F
ield
[V
/cm
]
VB=0V VB=0.5VVB=2V VB=5V
VB=8V VB=10V
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 1919
Forward Bias =10V
-1
-0.5
0
0.5
1
1.5
2
0 50 100 150 200 250 300
Depth [m]E
ne
rgy
Ba
nd
s [
eV
]
High- CdTe Diode (ND=106,B=1.3eV)
Band Structure under forward bias
EC
EV
Forward Bias
-1
-0.5
0
0.5
1
1.5
2
0 200 400 600 800 1000Depth [m]
Va
len
ce
Ba
nd
En
erg
y [
eV
]
VB=0V
VB=0.5V
VB=2V
VB=5V
VB=8V
VB=10V
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 2020
High- CdTe Diode (ND=106,B=1.3eV)
Forward and Reverse Currents
-4.E-17
-4.E-17
-3.E-17
-3.E-17
-2.E-17
-2.E-17
-1.E-17
-5.E-18
0.E+00
-10 -8 -6 -4 -2 0Bias [V]
Cur
rent
[A
]
-5.E-12
0.E+00
5.E-12
1.E-11
2.E-11
2.E-11
3.E-11
3.E-11
-10 -5 0 5 10Bias [V]
Cu
rren
t [A
]0.E+00
5.E-12
1.E-11
2.E-11
2.E-11
3.E-11
3.E-11
0 2 4 6 8 10Bias [V]
I [A
]
Itotal,1.3eV
J*A (Mott's)
2
0 3
9
8Mott CdTe
VJ
L
Mott’s Law fit:
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 2121
Reverse Bias
1.E-041.E-031.E-021.E-011.E+001.E+011.E+021.E+031.E+041.E+051.E+061.E+07
0 200 400 600 800 1000
Depth [m]
e-
De
ns
ity
[cm
-3]
VB=0V VB=-0.5V
VB=-2V VB=-5V
VB=-8V VB=-10V
Reverse Bias
1.E+031.E+041.E+051.E+061.E+071.E+081.E+091.E+101.E+111.E+121.E+131.E+14
0 200 400 600 800 1000
Depth [m]
h-
De
ns
ity
[c
m-3
]
VB=0V
VB=-0.5V
VB=-2V
VB=-5V
VB=-8V
VB=-10V
High- CdTe Diode (ND=106,B=1.3eV,SRH)
With SRH RecombinationReverse Bias
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
0 200 400 600 800 1000
Depth [m]
e- D
ensi
ty [
cm-3
]
VB=0V VB=-0.5V
VB=-2V VB=-5V
VB=-8V VB=-10V
Reverse Bias
1.E+03
1.E+05
1.E+07
1.E+09
1.E+11
1.E+13
1.E+15
0 200 400 600 800 1000
Depth [m]
h-
Den
sity
[cm
-3]
VB=0V
VB=-0.5V
VB=-2V
VB=-5V
VB=-8V
VB=-10V
Without SRH Recombination
Free Carrier Concentration with and without SRH
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 2222
Forward Bias
1.E+03
1.E+05
1.E+07
1.E+09
1.E+11
1.E+13
1.E+15
0 200 400 600 800 1000
Depth [m]
h-D
en
sit
y [
cm
-3]
VB=0V VB=0.5VVB=2V VB=5V
VB=8V VB=10V
Forward Bias
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
0 200 400 600 800 1000Depth [m]
e-D
en
sit
y [
cm
-3]
VB=0V VB=0.5V
VB=2V VB=5V
VB=8V VB=10V
High- CdTe Diode (ND=106,B=1.3eV,SRH)Free Carrier Concentration with and without SRH
With SRH Recombination Without SRH RecombinationForward Bias
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+10
0 200 400 600 800 1000
Depth [m]
e-D
ensi
ty [
cm-3
]
VB=0V VB=0.5V
VB=2V VB=5V
VB=8V VB=10V
Forward Bias
1.E+03
1.E+05
1.E+07
1.E+09
1.E+11
1.E+13
1.E+15
0 200 400 600 800 1000Depth [m]
h-D
ensi
ty [
cm-3
]
VB=0V VB=0.5V
VB=2V VB=5V
VB=8V VB=10V
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 2323
High- CdTe Diode (ND=106,B=1.3eV,SRH)Currents with and without SRH
-5.E-12
0.E+00
5.E-12
1.E-11
2.E-11
2.E-11
3.E-11
3.E-11
-10 -5 0 5 10
Bias [V]
Cu
rre
nt
[A]
Itotal, 1.3eV, +SRH
Itotal,1.3eV, -SRH
1.E-19
1.E-18
1.E-17
1.E-16
1.E-15
1.E-14
-10 -8 -6 -4 -2 0
Bias [V]
AB
S(C
urr
en
t) [
A]
Itotal, 1.3eV, +SRH
Itotal,1.3eV, -SRH
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 2424
High- CdTe Diode (ND=106,B=0.2eV)Energy band structure
-2
-1.5
-1
-0.5
0
0.5
1
0 200 400 600 800 1000
Depth [m]
En
erg
y [e
V]
EC
EV
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
0 200 400 600 800 1000
Depth [m]
En
erg
y [
eV
]
C-Band V-BandC-Band-0.5V V-Band-0.5VC-Band-2V V-Band-2V
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
3
0 200 400 600 800 1000Depth [m]
En
erg
y [
eV
]
C-Band V-BandC-Band+0.5V V-Band+0.5VC-Band+2V V-Band+2V
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 2525
High- CdTe Diode (ND=106,B=0.2eV)Free Carrier Concentration
Reverse Bias
1.E-05
1.E-03
1.E-01
1.E+01
1.E+03
1.E+05
1.E+07
0 200 400 600 800 1000
Depth [m]
h-
De
ns
ity
[c
m-3
]
VB=0V VB=-0.5V VB=-2V
VB=-5V VB=-8V VB=-10V
Reverse Bias
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
1.E+10
1.E+12
1.E+14
1.E+16
0 200 400 600 800 1000
Depth [m]
e- D
ensi
ty [
cm-3
]
VB=0V VB=-0.5V
VB=-2V VB=-5V
VB=-8V VB=-10V
Forward Bias
1.E-05
1.E-03
1.E-01
1.E+01
1.E+03
1.E+05
0 200 400 600 800 1000
Depth [m]
h-D
ensi
ty [
cm-3
]
VB=0V VB=0.5VVB=2V VB=5VVB=8V VB=10V
Forward Bias
1.E+04
1.E+06
1.E+08
1.E+10
1.E+12
1.E+14
1.E+16
0 200 400 600 800 1000Depth [m]
e-D
ensi
ty [
cm-3
]
VB=0V VB=0.5V
VB=2V VB=5V
VB=8V VB=10V
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 2626
High- CdTe Diode (ND=106,B=0.2eV)
Reverse Bias
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
0 200 400 600 800 1000
Depth [m]
E-F
ield
[V
/cm
]
VB=0V VB=-0.5VVB=-2V VB=-5VVB=-8V VB=-10V
Forward Bias
1.E+01
1.E+02
1.E+03
1.E+04
0 200 400 600 800 1000
Depth [m]
E-F
ield
[V
/cm
]
VB=0V VB=0.5VVB=2V VB=5V
VB=8V VB=10V
Forward Bias
0
2
4
6
8
10
12
0 200 400 600 800 1000
Depth [m]
Po
ten
tia
l [e
V]
VB=0V
VB=0.5V
VB=2V
VB=5V
VB=8V
VB=10V
Reverse Bias
-12
-10
-8
-6
-4
-2
0
2
0 200 400 600 800 1000
Depth [m]
Po
ten
tia
l [e
V]
VB=0V VB=-0.5V
VB=-2V VB=-5V
VB=-8V VB=-10V
E-Field and Potential profiles
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 2727
High- CdTe Diode (ND=106,B=0.2eV)
Reverse Bias
-3
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
0 200 400 600 800 1000Depth [m]
Co
nd
uct
ion
Ban
d E
ner
gy
[eV
]
VB=0V VB=-0.5V
VB=-2V VB=-5VVB=-8V VB=-10V
Reverse Bias=-10V
-2
-1.5
-1
-0.5
0
0.5
1
0 100 200 300 400
Depth [um]
Co
nd
uc
tio
n B
an
d E
ne
rgy
[e
V]
Band Structure
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 2828
High- CdTe Diode (ND=106,B=0.2eV)Currents
Itotal,1.3eV
-4.0E-10
-3.5E-10
-3.0E-10
-2.5E-10
-2.0E-10
-1.5E-10
-1.0E-10
-5.0E-11
0.0E+00
5.0E-11
-10 -8 -6 -4 -2 0
Bias [V]
Cu
rre
nt
[A]
Itotal,0.2eV
J*A (Mott's)
-4.E-10
-4.E-10
-3.E-10
-3.E-10
-2.E-10
-2.E-10
-1.E-10
-5.E-11
0.E+00
5.E-11
-10 -5 0 5 10
Bias [V]
Cu
rre
nt
[A]
0.E+00
1.E-14
2.E-14
3.E-14
4.E-14
5.E-14
6.E-14
0 2 4 6 8 10Bias [V]
Cu
rren
t [A
]
2
0 3
9
8Mott CdTe
VJ
L
Mott’s Law fit:
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 2929
Conclusions
• Band bending in high- semiconductors is mainly attributed to free carrier charge – NOT dopant ions
• In high- semiconductors Schottky devices thermionic emission is not the dominant forward current mechanism
• In case on any band bending (positive or “negative” barrier) the “bulk” resistivity is strongly affected by free carrier injection
• In case of significant Schottky barrier the current transport is dominated by minority carriers
• Space Charge Limited Current may occur both, in Schottky and “Ohmic” contacts (except flat-band conditions)
Barcelona, 31 May- 2 June 2010Barcelona, 31 May- 2 June 2010 3030
Thank you