Lecture 8 OUTLINE Metal-Semiconductor Contacts (cont’d) – Current flow in a Schottky diode –...
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Transcript of Lecture 8 OUTLINE Metal-Semiconductor Contacts (cont’d) – Current flow in a Schottky diode –...
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
)(2
D
Abis
qN
VVW
2
02xW
K
qNxV
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
W for p-type Semiconductor
)(2
A
biAs
qN
VVW
2
02xW
K
qNxV
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-typesemiconductor
• 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
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
1K.E.
Abin
x VVm
qvv
*min
2
)(, xxvMs vnqAvIx
min
)(v
xxxMs dvvnvqAI
EE130/230M Spring 2013 Lecture 8, Slide 6
Schottky Diode I - VFor a nondegenerate semiconductor, it can be shown that
We can then obtain
In the reverse direction, the electrons always see the same barrier B, so
Therefore
2/2
0
*/
//23
2*
A/cm 120 where,
4
kTnS
kTqVS
kTqVkTnMS
BA
AB
eTm
mJeAJ
eeATh
kqmI
2* 2//3
2*4xncF vkTmkTEEn
x eeh
kTmvn
0 AMSSM VII
SSkTqV
S AJIeII A where)1( /
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 B .
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
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
WAC 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
dvCi a
EE130/230M Spring 2013 Lecture 8, Slide 10
Once Vbi and ND are known, Bn can be determined:
22
)(21
AqN
VV
C sD
Abi
D
cBnFBFcBnbi ln)(
N
NkTEEqV
Using C-V Data to Determine B
Abi
sD
AbiD
s
ss
VV
qNA
VVqN
AW
AC
22
EE130/230M Spring 2013 Lecture 8, Slide 11
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
DABn NVHnDthxDMS
onns
emkTqNvqPNJ
mmhmH
/)(*
13/2*9*
2/
Vcm /104.5/4 where
D
Bns
qNW
2
DABn NVHeP )(y probabilit tunneling
Tunneling Current Density
Ec, EFS
Ev
EFM
Equilibrium Band Diagram Band Diagram for VA0
Ec, EFS
Ev
EFM
qVbiBnq(Vbi-VA)
EE130/230M Spring 2013 Lecture 8, Slide 13
EE130/230M Spring 2013 Lecture 8, Slide 14
Example: Ohmic Contacts in CMOS
Specific Contact Resistivity, c
• Unit: -cm2
– c is the resistance of a 1 cm2 contact
• For a practical ohmic contact, want small B, large ND for small contact resistance
DB NHc e /
contact
ccontact A
R
EE130/230M Spring 2013 Lecture 8, Slide 15
Approaches to Lowering B
• Image-force barrier lowering
4
aNq
s
N = dopant concentration in surface region
a = width of heavily doped surface region
Bo
EF
Ec
metal n+ Si
A. Kinoshita et al. (Toshiba), 2004 Symp. VLSI Technology Digest, p. 168
• M engineering– Impurity segregation via silicidation
– Dual ( low-M / high-M ) 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
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
2/2
0
*
/
A/cm 120 where
)1(
kTnS
kTqVS
B
A
eTm
mJ
eAJI
EE130/230M Spring 2013 Lecture 8, Slide 18
WAC s
small-signal capacitance
)(2
D
Abis
qN
VVW
EF
Ec
Ev
EF
Ec
Ev
EFEc
Ev
EF
Since it is difficult to achieve small B 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)