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
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
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
EE130/230M Spring 2013
Lecture 8, Slide 3
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
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Lecture 8, Slide 4
Current Flow
FORWARD BIAS
REVERSE BIAS
EE130/230M Spring 2013
• Current is determined by
majority-carrier flow across
the M-S junction:
o Under forward bias, majoritycarrier diffusion from the
semiconductor into the metal
dominates
o Under reverse bias, majoritycarrier diffusion from the
metal into the semiconductor
dominates
Lecture 8, Slide 5
Thermionic Emission Theory
• Electrons can cross the junction into the metal if
1
2
K.E. x  mvx  qVbi  VA 
2
2q
Vbi  VA 
vx  vmin 
*
mn
• Thus the current for electrons at a given velocity is:
I s   M , v x  qAvx n(vx )
• So, the total current over the barrier is:
 v min
I s  M  qA
 v n(v )dv
x

EE130/230M Spring 2013
Lecture 8, Slide 6
x
x
Schottky Diode I - V
For a nondegenerate semiconductor, it can be shown that
 4kTmn*2   E  E  / kT m* / 2 kT v 2
F
c
n
x
n v x   
e
e

3
h


We can then obtain
4qmn* k 2
2  F / kT qV / kT
I S  M 
AT
e
e
3
h
mn* 2 F / kT
qV / kT
 AJ S e
, where J S  120
T e
A/cm 2
m0
In the reverse direction, the electrons always see the same
barrier FB, so I M  S   I S  M VA  0
B
A
A
Therefore
B
I  I S (e qVA / kT  1) where I S  AJ S
EE130/230M Spring 2013
Lecture 8, Slide 7
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.
Block Diagram of a Switching Power Supply
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Lecture 8, Slide 8
Charge Storage in a Schottky Diode
• Charge is “stored” on both sides of the M-S contact.
– The applied bias VA modulates this charge.
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Lecture 8, Slide 9
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
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s
W
Lecture 8, Slide 10
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
EE130/230M Spring 2013
Lecture 8, Slide 11
Nc
 kT ln
ND
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
Tunneling Current Density
Band Diagram for VA0
Equilibrium Band Diagram
W
2 sF Bn
qN D
qVbiFBn
Ec, EFS
EFM
q(Vbi-VA)
EFM
Ec, EFS
Ev
tunneling probabilit y P  e
Ev
 H ( F Bn VA )
where H  4  s m / h  5.4 10
*
n
9
J S  M  qPN D vthx  qN D kT / 2m e
*
n
EE130/230M Spring 2013
Lecture 8, Slide 13
ND
*
n
m / mo cm
3/2
 H ( F Bn V A ) / N D
V
1
Example: Ohmic Contacts in CMOS
EE130/230M Spring 2013
Lecture 8, Slide 14
Specific Contact Resistivity, rc
• Unit: W-cm2
– rc is the resistance of a 1 cm2 contact
• For a practical ohmic contact,
rc  e
HF B / N D
 want small FB, large ND for small contact resistance
Rcontact 
EE130/230M Spring 2013
rc
Acontact
Lecture 8, Slide 15
Approaches to Lowering FB
• Image-force barrier lowering
F
q N a N = dopant concentration in surface region
FBo
F 
 s 4 a = width of heavily doped surface region
EF
Ec
metal
n+ Si
 Very high active dopant concentration desired
• FM engineering
– Impurity segregation via silicidation
A. Kinoshita et al. (Toshiba), 2004 Symp. VLSI Technology Digest, p. 168
– Dual ( low-FM / high-FM ) silicide technology
• Band-gap reduction
– strain A. Yagishita et al. (UC-Berkeley), 2003 SSDM Extended Abstracts, p. 708
C. Ozturk et al. (NCSU),
– germanium incorporation M.
2002 IEDM Technical Digest, p. 375
EE130/230M Spring 2013
Lecture 8, Slide 16
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
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
I  AJ S (e qVA / kT  1)
mn* 2 F B / kT
where J S  120 T e
A/cm 2
m0
small-signal capacitance C  A
EE130/230M Spring 2013
s
W
Lecture 8, Slide 18
W
2 s (Vbi  VA )
qN D
Summary (cont’d)
EF
Ec
Ec
Ev
EF
EF
Ev
Ec
EF
Ev
Ec
Ev
Since it is difficult to achieve small FB in practice, ohmic
contacts are achieved with heavy doping, in practice:
EF
EE130/230M Spring 2013
Ec
Ec
Ev
EF
Lecture 8, Slide 19
Ev
Summary of Key Points
• Schottky barrier height:
– Energy barrier that must be surmounted in order for a carrier in
the metal to enter the semiconductor
• Built-in potential: FBn-(EC-EF)FB for n-type S, FBp-(EF-Ev)FB for p-type S
– Ideally is equal to the work function difference between M and S
• But in practice (for Si) FBn  (2/3)EG and FBp  (1/3)EG
• In equilibrium the flow of carriers from M to S (IMS) equals the flow
of carriers from S to M (ISM)
• Under forward bias ISM increases exponentially and dominates
• Under reverse bias ISM decreases exponentially so that IMS (which
is independent of VA) dominates
*
qV
m


I  I S  e kT  1 where I S  120
AT 2 e F / kT
m0


A
B