Lecture 7
OUTLINE
• Work Function
• Metal-Semiconductor Contacts
– Energy band diagrams
– Depletion-layer width
– Small-signal capacitance
Reading: Pierret 14.1-14.2; Hu 4.16
Metal-Semiconductor Contacts
There are 2 kinds of metal-semiconductor contacts:
• rectifying
“Schottky diode”
• non-rectifying
“ohmic contact”
EE130/230A Fall 2013
Lecture 7, Slide 2
Work Function
E0: vacuum energy level
R.F. Pierret, Semiconductor Fundamentals, Figure 14.1
FM: metal work function
EE130/230A Fall 2013
FS: semiconductor work function
Lecture 7, Slide 3
Ideal M-S Contact: FM < FS, n-type
Band diagram instantly
after contact formation:
Equilibrium band diagram:
EE130/230A Fall 2013
Lecture 7, Slide 4
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.2
Ideal M-S Contact: FM > FS, n-type
Band diagram instantly
after contact formation:
Equilibrium band diagram:
Schottky Barrier Height:
qVbi = FBn– (Ec – EF)FB
n
FBn  FM  
W
EE130/230A Fall 2013
Lecture 7, Slide 5
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.2
Effect of Interface States on FBn
• Ideal M-S contact:
FBn = FM – 
• Real M-S contacts:
A high density of allowed
energy states in the
band gap at the M-S
interface “pins” EF to be
within the range 0.4 eV
to 0.9 eV below Ec
FM
FBn
C. C. Hu, Modern Semiconductor Devices for ICs, Figure 4-35
EE130/230A Fall 2013
Lecture 7, Slide 6
Schottky Barrier Heights: Metal on Si
•
Metal
FM (eV)
Er
3.12
Ti
4.3
Ni
4.7
W
4.6
Mo
4.6
Pt
5.6
FBn (eV)
0.44
0.5
0.61
0.67
0.68
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
EE130/230A Fall 2013
Lecture 7, Slide 7
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 and hence are much more prevalent in ICs.
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.
EE130/230A Fall 2013
Lecture 7, Slide 8
The Depletion Approximation
The semiconductor is depleted of mobile carriers to a depth W
 In the depleted region (0  x  W ):
r = q (ND – NA)
Beyond the depleted region (x > W ):
r=0
EE130/230A Fall 2013
Lecture 7, Slide 9
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.4
Electrostatics
• Poisson’s equation:
• The solution is:

r qN D
 
x
s
s
 x   
qN D
s
W  x 
V x      ( x)dx
EE130/230A Fall 2013
Lecture 7, Slide 10
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.4
Depletion Width, W
 qN D
W  x 2
V x  
2K S 0
At x = 0, V = -Vbi
2 sVbi
 W
qN D
• W decreases with increasing ND
EE130/230A Fall 2013
Lecture 7, Slide 11
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.4
Voltage Drop across the M-S Contact
• Under equilibrium conditions
(VA = 0), the voltage drop across
the semiconductor depletion
region is the built-in voltage Vbi.
• If VA  0, the voltage drop across
the semiconductor depletion
region is Vbi - VA.
EE130/230A Fall 2013
Lecture 7, Slide 12
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.3
Depletion Width, W, for VA  0
Last time, we found that
V x  
 qN D
W  x 2
2K S 0
At x = 0, V = - (Vbi - VA)
2 s (Vbi  VA )
 W
qN D
• W increases with increasing –VA
• W decreases with increasing ND
EE130/230A Fall 2013
Lecture 7, Slide 13
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.4
Charge Storage in a Schottky Diode
• Charge is “stored” on both sides of the M-S contact.
– The applied bias VA modulates this charge.
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.4
EE130/230A Fall 2013
Lecture 7, Slide 14
Small-Signal Capacitance
• If an a.c. voltage va is applied in series with the d.c. bias VA,
the charge stored in the Schottky contact will be modulated at
the frequency of the a.c. voltage
 displacement current will flow:
CA
EE130/230A Fall 2013
s
W
Lecture 7, Slide 15
dva
iC
dt
Using C-V Data to Determine FB
CA
s
W
A
s
2 s
Vbi  VA 
qN D
qN D s
A
2Vbi  VA 
1
2(Vbi  VA )

2
C
qN D s A2
Once Vbi and ND are known, FBn can be determined:
qVbi  F Bn  ( Ec  EF ) FB  F Bn
EE130/230A Fall 2013
Lecture 7, Slide 16
Nc
 kT ln
ND
Ideal M-S Contact: FM > FS, p-type
p-type
semiconductor
Band diagram instantly
after contact formation:
Equilibrium band diagram:
EE130/230A Fall 2013
Lecture 7, Slide 17
R.F. Pierret, Semiconductor Fundamentals, p. 482
Ideal M-S Contact: FM < FS, p-type
p-type
semiconductor
Band diagram instantly
after contact formation:
Equilibrium band diagram:
Schottky Barrier Height:
F Bp    EG  F M
FBp
qVbi = FBp– (EF – Ev)FB
W
EE130/230A Fall 2013
Lecture 7, Slide 18
R.F. Pierret, Semiconductor Fundamentals, p. 482
W for p-type Semiconductor
V x  
qN A
W  x 2
2 K S 0
p-type
semiconductor
At x = 0, V = Vbi + VA
2 s (VA  Vbi )
 W
qN A
• W increases with increasing VA
• W decreases with increasing NA
EE130/230A Fall 2013
Lecture 7, Slide 19
Summary
EF
Ec
Ec
EF
Ev
Ev
Ec
EF
EF
Ev
Ev
R.F. Pierret, Semiconductor Fundamentals, p. 481
2 s (Vbi  VA )
For rectifying contacts: W 
qN D
W
2 s (VA  Vbi )
qN A
small-signal capacitance C  A s / W
EE130/230A Fall 2013
Lecture 7, Slide 20
Summary: Rectifying Contacts
• Schottky barrier height, FB:
– Energy barrier that must be surmounted in order for a
carrier in the metal to enter the semiconductor
• Built-in potential, qVbi:
FBn-(EC-EF)FB for n-type Si, FBp-(EF-Ev)FB for p-type Si
– Ideally qVbi is equal to the work function difference
between the metal and semiconductor.
In practice, for Si:
FBn  (2/3)EG and FBp  (1/3)EG
EE130/230A Fall 2013
Lecture 7, Slide 21