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1. Lecture 8
OUTLINE
• Metal-Semiconductor Contacts (cont’d)
– Current flow in a Schottky diode
– Schottky diode applications
– Small-signal capacitance
– Practical ohmic contacts
Reading: Pierret 14.2-14.3; Hu 4.17-4.21

2. 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.
EE130/230M Spring 2013 Lecture 8, Slide 2

3. Depletion Width, W, for VA  0
)(2
D
Abis
qN
VV
W



   2
02
xW
K
qN
xV
S
D




At x = 0, V = - (Vbi - VA)
• W increases with increasing –VA
• W decreases with increasing ND
Last time, we found that
EE130/230M Spring 2013 Lecture 8, Slide 3

4. W for p-type Semiconductor
)(2
A
biAs
qN
VV
W



   2
02
xW
K
qN
xV
S
A


At x = 0, V = Vbi + VA
• W increases with increasing VA
• W decreases with increasing NA
EE130/230M Spring 2013 Lecture 8, Slide 4
p-type
semiconductor

5. • Current is determined by
majority-carrier flow across
the M-S junction:
o Under forward bias, majority-
carrier diffusion from the
semiconductor into the metal
dominates
o Under reverse bias, majority-
carrier diffusion from the
metal into the semiconductor
dominates
REVERSE BIAS
FORWARD BIAS
EE130/230M Spring 2013 Lecture 8, Slide 5
Current Flow

6. Thermionic Emission Theory
• Electrons can cross the junction into the metal if
• Thus the current for electrons at a given velocity is:
• So, the total current over the barrier is:
 Abixx VVqmv 
2
2
1
K.E.
 Abi
n
x VV
m
q
vv  *min
2
)(, xxvMs vnqAvI x




 
min
)(
v
xxxMs dvvnvqAI
EE130/230M Spring 2013 Lecture 8, Slide 6

7. Schottky Diode I - V
For a nondegenerate semiconductor, it can be shown that
We can then obtain
In the reverse direction, the electrons always see the same
barrier FB, so
Therefore
2/2
0
*
/
//2
3
2*
A/cm120where,
4
kTn
S
kTqV
S
kTqVkTn
MS
BA
AB
eT
m
m
JeAJ
eeAT
h
kqm
I
F
F




      2*
2//
3
2*
4 xncF vkTmkTEEn
x ee
h
kTm
vn 










 0  AMSSM VII
SS
kTqV
S AJIeII A
 where)1( /
EE130/230M Spring 2013 Lecture 8, Slide 7

8. Applications of Schottky Diodes
• IS of a Schottky diode is 103 to 108 times larger than that of a
pn junction diode, depending on FB .
 Schottky diodes are preferred rectifiers for low-voltage,
high-current applications.
EE130/230M Spring 2013 Lecture 8, Slide 8
Block Diagram of a Switching Power Supply

9. Charge Storage in a Schottky Diode
• Charge is “stored” on both sides of the M-S contact.
– The applied bias VA modulates this charge.
EE130/230M Spring 2013 Lecture 8, Slide 9

10. W
AC s

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:
dt
dv
Ci a

EE130/230M Spring 2013 Lecture 8, Slide 10

11. Once Vbi and ND are known, FBn can be determined:
22
)(21
AqN
VV
C sD
Abi



D
c
BnFBFcBnbi ln)(
N
N
kTEEqV FF
Using C-V Data to Determine FB
 
 Abi
sD
Abi
D
s
ss
VV
qN
A
VV
qN
A
W
AC




22



EE130/230M Spring 2013 Lecture 8, Slide 11

12. Practical Ohmic Contact
• In practice, most M-S contacts are rectifying
• To achieve a contact which conducts easily in both
directions, we dope the semiconductor very heavily
 W is so narrow that carriers can “tunnel” directly through
the barrier
EE130/230M Spring 2013 Lecture 8, Slide 12

13. DABn NVH
nDthxDMS
onns
emkTqNvqPNJ
mmhmH
/)(*
13/2*9*
2/
Vcm/104.5/4where
F






D
Bns
qN
W
F

2
DABn NVH
eP
)(
yprobabilittunneling
F

Tunneling Current Density
Ec, EFS
Ev
EFM
Equilibrium Band Diagram Band Diagram for VA0
Ec, EFS
Ev
EFM
qVbiFBn
q(Vbi-VA)
EE130/230M Spring 2013 Lecture 8, Slide 13

14. EE130/230M Spring 2013 Lecture 8, Slide 14
Example: Ohmic Contacts in CMOS

15. Specific Contact Resistivity, rc
• Unit: W-cm2
– rc is the resistance of a 1 cm2 contact
• For a practical ohmic contact,
 want small FB, large ND for small contact resistance
DB NH
c e
/F
r
contact
c
contact
A
R
r

EE130/230M Spring 2013 Lecture 8, Slide 15

16. Approaches to Lowering FB
• Image-force barrier lowering
 4
aNq
s
F
N = dopant concentration in surface region
a = width of heavily doped surface region
FBo
EF
F
Ec
metal n+ Si
A. Kinoshita et al. (Toshiba), 2004 Symp. VLSI Technology Digest, p. 168
• FM engineering
– Impurity segregation via silicidation
– Dual ( low-FM / high-FM ) silicide technology
A. Yagishita et al. (UC-Berkeley), 2003 SSDM Extended Abstracts, p. 708
M. C. Ozturk et al. (NCSU),
2002 IEDM Technical Digest, p. 375
• Band-gap reduction
– strain
– germanium incorporation
 Very high active dopant concentration desired
EE130/230M Spring 2013 Lecture 8, Slide 16

17. Voltage Drop across an Ohmic Contact
• Ideally, Rcontact is very small, so little voltage is
dropped across the ohmic contact, i.e. VA  0 Volts
 equilibrium conditions prevail
EE130/230M Spring 2013 Lecture 8, Slide 17

18. Summary
• Charge is “stored” in a Schottky diode.
– The applied bias VA modulates this charge
and thus the voltage drop across the
semiconductor depletion region
 The flow of majority carriers into the
metal depends exponentially on VA
2/2
0
*
/
A/cm120where
)1(
kTn
S
kTqV
S
B
A
eT
m
m
J
eAJI
F


EE130/230M Spring 2013 Lecture 8, Slide 18
W
AC s
small-signal capacitance
)(2
D
Abis
qN
VV
W




19. EF
Ec
Ev
EF
Ec
Ev
EF
Ec
Ev
EF
Since it is difficult to achieve small FB in practice, ohmic
contacts are achieved with heavy doping, in practice:
EF Ec
Ev
EF
Ec
Ev
Ec
Ev
EE130/230M Spring 2013 Lecture 8, Slide 19
Summary (cont’d)