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8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
1/25
ECE 4813 Dr. Alan Doolittle
ECE 4813Semiconductor Device and Material
Characterization
Dr. Alan Doolitt le
School of Electrical and Computer Engineering
Georgia Institute of Technology
As with all of these lecture slides, I am indebted to Dr. Dieter Schroder from Arizona State
University for his generous contributions and freely given resources. Most of (>80%) the
figures/slides in this lecture came from Dieter. Some of these figures are copyrighted and can befound within the class text, Semiconductor Device and Materials Characterization. Every serious
microelectronics student should have a copy of this book!
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
2/25
ECE 4813 Dr. Alan Doolittle
Contact Resistance
Metal-semiconductor Contacts
Specific Contact ResistanceTransfer Length
Contact String
Transfer Length MethodFour-terminal Method
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
3/25
ECE 4813 Dr. Alan Doolittle
Metal Semiconductor Contacts
MB
Every semiconductor device has contacts Contact resistance is a parasit ic resistance
Contacts are almost always metal-semiconductor contacts
qM q
Sq
qB
EC
qVbi
EF
EV
W
Accumulat ion Neutral Depletion
FBFCs )( EE +=
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
4/25
ECE 4813 Dr. Alan Doolittle
Metal Semiconductor Contacts
Energetic barriers are most often described by the Electron Affin ity Model (EAM).
EAM is a purely theoretical model and REAL CONTACTS
RARELY FOLLW THIS MODEL.
Nevertheless, EAM explains several aspects (depletion
widths, capacitance, general IV shape, etc) of ohmic andSchottky barrier diodes suff iciently that it is widely used.
Reasons for the barrier height not agreeing with theory:
Image force lowering (lower than expected barrier)
Fermi-level pinning
Interface state filling (i.e. partially pinned or voltage
dependent interface state occupation).
Lack of complete model understanding. Can you
improve on the existing model?
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
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ECE 4813 Dr. Alan Doolittle
Carrier Motion In an ohmic contact, electrons must flow from metal to
semiconductor or f rom semiconductor to metal
Current is controlled by barrier widthrather than barrier
height
Low ND Intermediate ND High ND
Field
Emission
Thermionic/Field
Emission
Thermionic
Emission
I
V
FE
TFE
TE
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
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ECE 4813 Dr. Alan Doolittle
Energy band diagrams for ideal MS
contacts
M >
S
M S
After the contact formation, electrons will begin to flow fromthe semiconductor to the metal.
The removal of electrons from the n-type material leavesbehind uncompensated Nd
+donors, creating a surfacedepletion layer, and hence a built-in electr ic f ield (similar top+-n junction).
Under equilibrium, the Fermi-level will be constant and noenergy transfer (current) flows
A barrierB forms blocking electron flow from M to S.
Based on the Electron Affini ty Model (EAM), the simplest ofmodels used to describe MS junctions,
B = M ...
ideal MS (n-type) contact.
B is called the barrier height . Electrons in a semiconductor wil l encounter an energy
barrier equal toM Swhile flowing from S to M.
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
8/25ECE 4813 Dr. Alan Doolittle
Since MS Schottky diode is a majority carrier device (i.e only majority carriers are
injected from semiconductor to the metal) and thus has no minority carrier storage, the
frequency response of the device is much higher than that of equivalent p+n diode.
The turn on voltage of a Schottky diode is typically smaller than a comparable p-njunction since the barrier to forward current flow (m-s) is typically small. This turn
on voltage can be as small as 0.3 Volts in some Si Schottky diodes.
This makes a Schottky diode the best choice for power switch protection in inductive
load applications (motors, solenoids, coils, etc) and in high frequency rectification but
not a good choice when low leakage or high breakdown voltage is required.
I-V Characteristics
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
9/25ECE 4813 Dr. Alan Doolittle
I-V Characteristics
Leakage in a Schottky diode is dominated by:
1) Thermionic Emission (metal electrons emitted over the barrier not likely)
2) Thermionic Field Emission (metal electrons of higher energy tunneling through
the barrier more likely)
3) Direct tunneling (metal electrons tunneling through the barrier most likely inhigher doped semiconductors or very high electric fields).
Since generation does not require the entire bandgap energy to be surmounted, the
reverse leakage current for a Schottky diode is generally much larger than that for a
p+n diode. Likewise, breakdown (for the same reason) is generally at smaller
voltages.
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
10/25ECE 4813 Dr. Alan Doolittle
MS (n-type) contact with
M > S
A forward bias will reduce the barrier
height unbalancing the electron current
flow, resulting in a huge forward current
that increases exponentially with applied
voltage
A reverse bias will increase the barrier
height resulting in a small reverse
current flow that will be dominated bytunneling currents for high doped
semiconductors and/or thermally assisted
field emission for moderate/low doped
semiconductors.
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
11/25
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
12/25ECE 4813 Dr. Alan Doolittle
Generalization of Metal Semiconductor
Contact Energy Relationships
n-type p-type
M> S rectifying ohmic
M< S ohmic rectifying
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
13/25ECE 4813 Dr. Alan Doolittle
Carrier Motion
n-type and p-type substrates are analogs of oneanother
n - Substrate p - Substrate
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
14/25ECE 4813 Dr. Alan Doolittle
Specific Contact Resistivity
The specific contact resistivity, c, is an area-independentparameter
Thermionic emission
For B= 0.6 V,A* = 110 A/cm2
K2
, T= 300 K
1
0
=
=
V
cdV
dJ
1* //2
kTqVkTq eeTAJ B
kTqkTq
cBB ee
TqA
k /1
/
*
=
c= 1600 -cm2 Rc= 1.6x10
11
(A= 1
mx1
m)
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
15/25ECE 4813 Dr. Alan Doolittle
Specific Contact Resistivity
Thermionic emission
Thermionic-field emission
Field emission
oB Eq
c eC/
11
=
ooB Eq
c eC
/
21
=
10-3
10-2
10-1
100
1016 1017 1018 1019 1020 1021
E00,
kT(eV)
Doping Density (cm-3)
TE TFE FE
E00
kT
kTq
cBe /1
=
kTEEE ooooo /coth
*4 tunnos
Doo
mK
NqhE
=
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
16/25ECE 4813 Dr. Alan Doolittle
Specific Contact Resistivity
cis very sensitive to doping density
10-8
10-7
10-6
10-5
10-4
10-3
1016 1017 1018 1019 1020 1021
c(ohm-cm
2)
ND(cm-3)
n-Si10-8
10-7
10-6
10-5
10-4
10-3
1016 1017 1018 1019 1020 1021
c(ohm-cm
2)
NA(cm-3)
p-Si
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
17/25ECE 4813 Dr. Alan Doolittle
Contact Resistance
Contacts are characterized by:Contact resistance, Rc()
Specific contact resistivi ty,c(-cm
2)
LWA
R c
c
cc
p
n-Type
Current Flow
Direction
WLA
RT
c
eff
cc
Ac =actual contact area Aeff =effective contact area
Aeffcan be lessthanAc
p
n-Type
shcT RL /
tor.semiconductheof)(outintometalthe
(from)toansferscurrent trthe(1/e)most""over whichdistancetheisLengthTransferT
L
Not derived in
notes. See text
page 141-142for discussion
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
18/25ECE 4813 Dr. Alan Doolittle
Contact - Current Crowding
Current flowing into/out of a contact can crowd into aportion of the contact
Current has the choice to flow throughcor Rsh
sh
cT
T
Tcsh
RL
LLZ
LxLRIxV
==
;/sinh
cosh)(
n-type
p-type
I
Rsh
c
I
0 L x
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
19/25ECE 4813 Dr. Alan Doolittle
Contact - Current Crowding
LT: transfer length
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10
V(x)
x (m)
c=10-5 cm210-6
10-7
10-8
L=10 m, Z=50 mRsh=10 /square
10-6
10-5
10-4
10-3
10-2
10-8 10-7 10-6 10-5 10-4 10-3 10-2
LT(c
m)
Rsh=10 /square
c( cm2)
30 100300
1000
sh
cT
T
Tcsh
RL
LLZ
LxLRIxV
=
=
/sinh
cosh)(
n-type
p-type
I
Rsh
c
I
0 L x
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
20/25ECE 4813 Dr. Alan Doolittle
Contact String (Chain)
2Nseries-connectedcontacts aremeasured(N100-1000 ormore)
Does not allowseparation of Rm,Rs, and Rc
Suitable forprocess control,but not for
detailed contactcharacterization
Must know Rsfromindependentmeasure of sheetresistance in order
to extract RC
)2()2( cscsm RRNRRRNR
Rc
pn
n pI
I
V
V
Rm
Rc
RS
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
21/25ECE 4813 Dr. Alan Doolittle
Contact String (Chain) Contact string consists of pnjunctions
The junctions are reversebiased
When the junction voltage exceeds VBD, it breaks down
Can have the case where poor contacts, i.e., high Rc, cannot be
detected because junctions break down
Measurement depends on substrate grounded or not
Rm
Rs
Rc
Grounded?
I VV1 V2
n pI
V
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
22/25ECE 4813 Dr. Alan Doolittle
Transfer Length Method (TLM)
Consists of identical contacts with varying spacings d
W
dR
WLRRR
sh
T
c
scT ++= 2
2
W
L d1 L d2 L d3 L d4 L
n-typep-substrate
2RcSlope =Rsh/W
0 d2LT
c
RT
( ) ( )W
LdR
W
dR
WL
LRR
Tshsh
T
Tsh
T
222
+=+
shcTRL /
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
23/25
ECE 4813 Dr. Alan Doolittle
Four Terminal (Kelvin) Method
Determines the contact resistanceindependent of the sheet
resistance
WLRI
VR ccC ;
12
I I1
p 2
n
p
II
n2
1 V1
V2
V1I
Rc R
s
Rc
Rc
Rs
V2
I
Heed warnings on accuracy (too complex to discuss in class) summarized in our text on pages 150-156.
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
24/25
ECE 4813 Dr. Alan Doolittle
Via Contact Resistance
Level
1
Level 2
Current
Voltage
Rc
Current
Current Current
Level 1
Level 2
Rc
8/9/2019 Lecture4ContactResistance slides tlm importante.pdf
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Review Questions
What is the most important parameter to givelow contact resistance?
What are the three metal-semiconductor
conduction mechanisms?
What is Fermi level pinning? Does the contact chain give detailed contact
characterization? Why or why not?
What is the transfer length method?
Why is the Kelvin contact test structure best for
contact resistance measurements?