Lecture #13
ANNOUNCEMENTS
• Quiz #2 next Friday (2/23) will cover the following:
– carrier action (drift, diffusion, R-G)
– continuity & minority-carrier diffusion eq’ns
– MS contacts (electrostatics, I-V characteristics)
• Review session will be held Friday 2/16 at 12:30PM
• No office hour or coffee hour today 
OUTLINE
• Metal-semiconductor contacts (cont.)
– practical ohmic contacts
– small-signal capacitance
• Introduction to pn junction diodes
Reading: Finish Ch. 14, Start Ch. 5
Spring 2007
EE130 Lecture 13, Slide 1
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
Spring 2007
EE130 Lecture 13, Slide 2
Band Diagram for VA0
Equilibrium Band Diagram
W
2 s Bn
qN D
qVbiBn
EFM
q(Vbi-VA)
Ec, EFS
EFM
Ec, EFS
Ev
tunneling probabilit y P  e
Ev
 H (  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
Spring 2007
EE130 Lecture 13, Slide 3
ND
*
n
m / mo cm
3/2
 H (  Bn V A ) / N D
V
1
Specific Contact Resistivity, rc
• Unit: W-cm2
– rc is the resistance of a 1 cm2 contact
• For a practical ohmic contact,
rc  e
H B / N D
 want small B, large ND for small contact resistance
Rcontact 
Spring 2007
rc
Acontact
EE130 Lecture 13, Slide 4
Approaches to Lowering fB
qfBo
• Image-force barrier lowering
f
q N a N = dopant concentration in surface layer
f 
 s 4 a = width of heavily doped surface layer
EC
EF
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
– germanium incorporation M. C. Ozturk et al. (NCSU),
2002 IEDM Technical Digest, p. 375
Spring 2007
EE130 Lecture 13, Slide 5
Voltage Drop across an Ohmic Contact
• Ideally, Rcontact is very small, so little voltage is
dropped across the ohmic contact, i.e. VA 0V
 equilibrium conditions prevail
Spring 2007
EE130 Lecture 13, Slide 6
Review: MS-Contact Charge Distribution
• In a Schottky contact, charge is stored on either side
of the MS junction
– The applied bias VA modulates this charge
Spring 2007
EE130 Lecture 13, Slide 7
Schottky Diode: 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
dva
 displacement current will flow: i  C
dt
CA
Spring 2007
s
W
EE130 Lecture 13, Slide 8
Using C-V Data to Determine B
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, Bn can be determined:
qVbi  q Bn  ( Ec  EF ) FB  q Bn
Spring 2007
EE130 Lecture 13, Slide 9
Nc
 kT ln
ND
Summary
EF
Ec
Ev
EF
Ec
EF
Ev
Ec
EF
Ev
Ec
Ev
Since it is difficult to achieve small B, practical ohmic
contacts are achieved with heavy doping:
EF
Ec
Ev
Ec
EF
Ev
Charge storage in an MS junction  small-signal capacitance:
Spring 2007
EE130 Lecture 13, Slide 10
CA
s
W
pn Junctions
Donors
N-type
P-type
– V +
I
I
N
P
V
Reverse bias
Spring 2007
Forward bias
EE130 Lecture 13, Slide 11
diode
symbol
Terminology
Doping Profile:
Spring 2007
EE130 Lecture 13, Slide 12
Idealized Junctions
Spring 2007
EE130 Lecture 13, Slide 13