Lecture 8
OUTLINE
• Metal-Semiconductor Contacts (cont’d)
– Current flow in a Schottky diode
– Schottky diode applications
– Practical ohmic contacts
Reading: Pierret 14.2-14.3; Hu 4.17-4.21
Current Flow
FORWARD BIAS
REVERSE BIAS
• 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
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.3
EE130/230A Fall 2013
Lecture 8, Slide 2
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
R.F. Pierret, Semiconductor Fundamentals, Fig. 14.3
• 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

EE130/230A Fall 2013
Lecture 8, Slide 3
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
EE130/230A Fall 2013
B
I  I S (e qVA / kT  1) where I S  AJ S
Lecture 8, Slide 4
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
EE130/230A Fall 2013
Lecture 8, Slide 5
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
EE130/230A Fall 2013
Lecture 8, Slide 6
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
EE130/230A Fall 2013
Lecture 8, Slide 7
ND
*
n
m / mo cm
3/2
 H ( F Bn V A ) / N D
V
1
Example: Ohmic Contacts in CMOS
EE130/230A Fall 2013
Lecture 8, Slide 8
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 
EE130/230A Fall 2013
rc
Acontact
Lecture 8, Slide 9
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
EE130/230A Fall 2013
Lecture 8, Slide 10
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
EE130/230A Fall 2013
Lecture 8, Slide 11
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
EE130/230A Fall 2013
Lecture 8, Slide 12
W
2 s (Vbi  VA )
qN D
Summary (cont’d)
• 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
Since it is difficult to achieve small FB in practice, ohmic
contacts are achieved with heavy doping, in practice.
EF
Ec
Ec
EF
Ev
EE130/230A Fall 2013
Lecture 8, Slide 13
Ev