Transcript 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 Spring 2007 EE130 Lecture 10, Slide.

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
Spring 2007
EE130 Lecture 10, Slide 1
Poisson’s Equation
Gauss’s Law:
area A
s : permittivity (F/cm)
 : charge density (C/cm3)
E(x)
E(x+Dx)
Dx
Spring 2007
EE130 Lecture 10, Slide 2
Charge Density in a Semiconductor
• Assuming the dopants are completely ionized:
 = q (p – n + ND – NA)
Spring 2007
EE130 Lecture 10, Slide 3
Work Function
E0: vacuum energy level
FM: metal work function
Spring 2007
FS: semiconductor work function
EE130 Lecture 10, Slide 4
Metal-Semiconductor Contacts
There are 2 kinds of metal-semiconductor contacts:
• rectifying
“Schottky diode”
• non-rectifying
“ohmic contact”
Spring 2007
EE130 Lecture 10, Slide 5
Ideal MS Contact: FM > FS, n-type
Band diagram instantly
after contact formation:
Schottky
Barrier :
Equilibrium
band diagram:
Spring 2007
FBn  FM  
EE130 Lecture 10, Slide 6
Ideal MS Contact: FM < FS, n-type
Band diagram instantly
after contact formation:
Equilibrium
band diagram:
Spring 2007
EE130 Lecture 10, Slide 7
Ideal MS Contact: FM < FS, p-type
metal
p-type Si
Eo
Si
Ec
FM
EF
Ev
FBp
qVbi = FBp– (EF – Ev)FB
W
Spring 2007
EE130 Lecture 10, Slide 8
FBp =  + EG - FM
Effect of Interface States on FBn
metal
FM > FS
n-type Si
•
Ideal MS contact:
FBn = FM – 
•
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
Eo
Si
FM
qVbi = FB – (Ec – EF)FB
FBn
Ec
EF
Ev
W
Spring 2007
EE130 Lecture 10, Slide 9
Schottky Barrier Heights: Metal on Si
Metal
FM (eV)
FBn (eV)
Er
3.12
0.44
Ti
4.3
0.5
Ni
4.7
0.61
W
4.6
0.67
Mo
4.6
0.68
Pt
5.6
0.73
FBp (eV)
0.68
0.61
0.51
0.45
0.42
0.39
 FBn tends to increase with increasing metal work function
Spring 2007
EE130 Lecture 10, Slide 10
Schottky Barrier Heights: Silicide on Si
Silicide ErSi1.7 TiSi2 CoSi2 NiSi
WSi2
PtSi
FM (eV) 3.78 4.18
FBn (eV) 0.3
FBp (eV) 0.8
4.6 4.65 4.7
5
0.6 0.64 0.65 0.65 0.84
0.52 0.48 0.47 0.47 0.28
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.
Spring 2007
EE130 Lecture 10, Slide 11
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
Spring 2007
EE130 Lecture 10, Slide 12
Electrostatics
E  qND
 
• Poisson’s equation:
x
s
s
• The solution is: E x   
qND
s
W  x 
V x     E( x)dx
Spring 2007
EE130 Lecture 10, Slide 13
Depleted Layer Width, W
 qND
W  x 2
V x  
2K S 0
At x = 0, V = -Vbi
2 sVbi
 W
qND
• W decreases with increasing ND
Spring 2007
EE130 Lecture 10, Slide 14
Summary: Schottky Diode (n-type Si)
metal
FM > FS
n-type Si
Depletion width:
Eo
Si
FM
qVbi = FBn – (Ec – EF)FB
FBn
Ec
EF
Ev
W
Spring 2007
EE130 Lecture 10, Slide 15
2 sVbi
W
qND
Equilibrium (VA = 0)
-> EF continuous,
constant
 FBn = FM – 
Summary: Schottky Diode (p-type Si)
metal
FM < FS
p-type Si
Eo
Depletion width:
Si
Ec
FM
EF
Ev
FBp
qVbi = FBp– (EF – Ev)FB
W
Spring 2007
EE130 Lecture 10, Slide 16
2 sVbi
W
qN A
Equilibrium (VA = 0)
-> EF continuous,
constant
FBp =  + EG - FM