![Page 1: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/1.jpg)
EE130 Lecture 10, Slide 1Spring 2007
Lecture #10
OUTLINE
• Poisson’s Equation
• Work function
• Metal-Semiconductor Contacts– equilibrium energy-band diagram– depletion-layer width
Read: Chapter 5.1.2,14.1, 14.2
![Page 2: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/2.jpg)
EE130 Lecture 10, Slide 2Spring 2007
Gauss’s Law:
s : permittivity (F/cm) : charge density (C/cm3)
Poisson’s Equation
E(x) E(x+x)
x
area A
![Page 3: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/3.jpg)
EE130 Lecture 10, Slide 3Spring 2007
Charge Density in a Semiconductor
• Assuming the dopants are completely ionized:
= q (p – n + ND – NA)
![Page 4: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/4.jpg)
EE130 Lecture 10, Slide 4Spring 2007
Work Function
M: metal work function S: semiconductor work function
0: vacuum energy level
![Page 5: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/5.jpg)
EE130 Lecture 10, Slide 5Spring 2007
There are 2 kinds of metal-semiconductor contacts: • rectifying
“Schottky diode”
• non-rectifying“ohmic contact”
Metal-Semiconductor Contacts
![Page 6: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/6.jpg)
EE130 Lecture 10, Slide 6Spring 2007
![Page 7: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/7.jpg)
EE130 Lecture 10, Slide 7Spring 2007
Ideal MS Contact: M > S, n-type
MBn
Band diagram instantly after contact formation:
Equilibrium band diagram:
Schottky Barrier :
![Page 8: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/8.jpg)
EE130 Lecture 10, Slide 8Spring 2007
Ideal MS Contact: M < S, n-type
Band diagram instantly after contact formation:
Equilibrium band diagram:
![Page 9: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/9.jpg)
EE130 Lecture 10, Slide 9Spring 2007
![Page 10: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/10.jpg)
EE130 Lecture 10, Slide 10Spring 2007
Ideal MS Contact: M < S, p-type
M
Si
Bp
W
qVbi = Bp– (EF – Ev)FB
p-type Simetal
Ev
EF
Ec
Eo
Bp =+ EG -M
![Page 11: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/11.jpg)
EE130 Lecture 10, Slide 11Spring 2007
Effect of Interface States on Bn
Eo
MSi
Bn
W
qVbi = B – (Ec – EF)FB
n-type Simetal
Ev
EF
Ec
M >S
• Ideal MS contact:Bn =M –
• Real MS contacts: A high density of
allowed energy states in the band gap at the MS interface pins EF to the range 0.4 eV to 0.9 eV below Ec
![Page 12: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/12.jpg)
EE130 Lecture 10, Slide 12Spring 2007
Bn tends to increase with increasing metal work function
Metal Er Ti Ni W Mo Pt
M (eV) 3.12 4.3 4.7 4.6 4.6 5.6
Bn (eV) 0.44 0.5 0.61 0.67 0.68 0.73
Bp (eV) 0.68 0.61 0.51 0.45 0.42 0.39
Schottky Barrier Heights: Metal on Si
![Page 13: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/13.jpg)
EE130 Lecture 10, Slide 13Spring 2007
Silicide-Si interfaces are more stable than metal-silicon interfaces. After metal is deposited on Si, a thermal annealing step is applied to form a silicide-Si contact. The term metal-silicon contact includes silicide-Si contacts.
Silicide ErSi1.7 TiSi2 CoSi2 NiSi WSi2 PtSi
M (eV) 3.78 4.18 4.6 4.65 4.7 5
Bn (eV) 0.3 0.6 0.64 0.65 0.65 0.84
Bn (eV) 0.8 0.52 0.48 0.47 0.47 0.28
Schottky Barrier Heights: Silicide on Si
![Page 14: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/14.jpg)
EE130 Lecture 10, Slide 14Spring 2007
The Depletion Approximation
The semiconductor is depleted of mobile carriers to a depth W
In the depleted region (0 x W ):
= q (ND – NA)
Beyond the depleted region (x > W ):
= 0
![Page 15: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/15.jpg)
EE130 Lecture 10, Slide 15Spring 2007
Electrostatics
• Poisson’s equation:
• The solution is:
ss
DqN
x
xWqN
x D s
xdxxV )(
E
E
E
![Page 16: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/16.jpg)
EE130 Lecture 10, Slide 16Spring 2007
Depleted Layer Width, W
2
D
bis
qN
VW
2
02xW
K
qNxV
S
D
At x = 0, V = -Vbi
• W decreases with increasing ND
![Page 17: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/17.jpg)
EE130 Lecture 10, Slide 17Spring 2007
Summary: Schottky Diode (n-type Si)
Equilibrium (VA = 0)-> EF continuous,
constant
Bn =M –
Eo
MSi
Bn
W
qVbi = Bn – (Ec – EF)FB
n-type Simetal
Ev
EF
Ec
M >S
2
D
bis
qN
VW
Depletion width:
![Page 18: Spring 2007EE130 Lecture 10, Slide 1 Lecture #10 OUTLINE Poisson’s Equation Work function Metal-Semiconductor Contacts – equilibrium energy-band diagram](https://reader035.vdocument.in/reader035/viewer/2022062221/56649d595503460f94a38c7a/html5/thumbnails/18.jpg)
EE130 Lecture 10, Slide 18Spring 2007
Summary: Schottky Diode (p-type Si)
M
Si
Bp
W
qVbi = Bp– (EF – Ev)FB
p-type Simetal
Ev
EF
Ec
Eo
M <S
Equilibrium (VA = 0)-> EF continuous,
constant
Bp =+ EG -M
2
A
bis
qN
VW
Depletion width: