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Tuning Carbon Nanotube
Band Gaps with Strain
Presented by:
J.R. Edwards
Zhuang Wu
Pierre Emelie
Michael Logue
Carbon Nanotubes
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Long, thin cylinder
of carbon---graphite
sheet rolled into a
tube
Unique because
different nanotubes
can exhibit either
metallic or
semiconductor
properties
Metallic or Semiconductor
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If n1-n2=3q then
metallic else
semiconductor
Orientation of the lattice along the tube is
determined by both the diameter and chirality as
indicated by the wrapping indices.
Band Diagrams
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
Cone like dispersion at k
point
Energy gap observed at
slices away from k point
Effect of Strain on Band Gap
Experimental Device
Fabrication
AFM
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Atomic Force Microscope
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Contact Mode
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Non-Contact Mode
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Scan sample with tip in close contact with the sample
Measure deflection of cantilever
Feedback loop moves sample to maintain constant deflection
Scan sample with tip just above the sample
Apply small oscillations to tip
Measure change in amplitude, phase, or frequency of cantilever in response
to Van der Waals forces
Feedback loop
Tapping Mode
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Scan sample with oscillating tip intermittently contacting the sample
Measure change in amplitude due to energy loss from contact with surface
features
Feedback loop
Experimental Setup
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Tapping Mode
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Scan to create image of
the nanotube structure
Contact (+) Mode
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Scan to apply strain
Tip operates as gate
The
 L0
length of the tube is Ltube
is the distance between the two gold contacts
People
first measure the force on the tip in a open circuit
Force on the tip
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Strain force pointing
upwards
The range is long
Adhesion force
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Pointing downwards
Short range
Adhesion force is
Van der Waals force
Force vs. z
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A:NT with d=5.3±0.5nm,
L0=1.0±0.1μm
B:NT with d=2.3±0.5nm,
L0=1.5±0.1μm
Slack: for A, slack=11nm,
YA=2 μm; for B,
slack=22nm YA=2.9 μm
Slack
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Slack =Ltube-L0 where the Ltube is the original
length of the tube
From the distance between pushing and
pulling onsets, ±zonset, the ‘‘slack’’ of a
suspended NT can be determined.
Nearly all NTs measured were slack, with
typically 5–10 nm of slack for a 1 μm tube.
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We see a 0-force
range, which
represents the slack
state.
Positive force (strain)
keeps going up as -z
becomes larger and
larger.
Adhesion force gets
larger in certain
range, but when z
goes out of the range,
adhesion force
suddenly disappears.
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σ(z) represents how much the length of the tube has
changed.
In constant YA, Y is the effective Young’s modulus,
and A is an effective cross-section area.
Here, the bending modulus of the NT has been
ignored.
Difference due to different d’s
•The magnitude of YA values goes linearly with d
•This results in the difference in force magnitude.
• The magnitude of YA values and linearity with diameter d suggest
that a single shell is carrying the mechanical load
MWNT
Electromechanical Response of Nanotubes
1st experiment: Constant-tip-voltage experiment
• Conductance G is measured with Gold contacts
• Strain is applied by moving the tip on the z-axis
• Vtip is held at 0V
 The change in conductance will only be due to strain
Electromechanical Response of Nanotubes
1st experiment: Constant-tip-voltage experiment
2nd
• d=6.5nm and L0=1.9μm
1st
• G is related to strain in
agreement with previous results
• Other NTs showed different
behavior
 Another experiment is
needed to understand the origin
of this behavior
Pushing
Slack
Pulling
G is lowered
G=0
G is lowered
G=0
Electromechanical Response of Nanotubes
2nd experiment: G-Vtip
• The tip is used as a gate
• Vtip is swept ~3 times a second over a range of a few volts
• Strain is slowly increased
• G vs. Vtip is observed for different strains for two p-type NTs
Electromechanical Response of Nanotubes
2nd experiment: G-Vtip
Semiconducting NT
Evac
Evac
5.1 eV
EC
EV
~4.5 eV
EC
5.1 eV
EV
~0.7 eV/d (nm)
EF
EF
Au
Vtip=0
Au
Au
 G increases
 G>0
As Vtip becomes negative, there is an
accumulation of holes and G increases
Valence band is partially filled and electrons are thermally
activated from the valence band to the conduction band
Evac
Evac
5.1 eV
Au
Vtip<0
EC
EV
p
5.1 eV
EF
n
p
EC
EV
EF
Au
Vtip=V1>0
Au
 G is minimum
As Vtip is increased, G decreases because the holes
are depleted until reaching its minimum value
Au
Tunneling
Au
Vtip>V1
 G increases
As Vtip is increased above V1, a p-n-p junction forms
in the middle of the tube and G increases due to
tunneling current
Electromechanical Response of Nanotubes
2nd experiment: G-Vtip
Metallic NT
Evac
~4.5 eV
5.1 eV
EF
Au
Au
G is constant and is not affected by Vtip
G
Semiconducting NT
G
Metallic NT
G0
0
V1
Vtip
Vtip
Electromechanical Response of Nanotubes
2nd experiment: G-Vtip
Metallic behavior at zero strain
d=3 ±0.5nm and L0=1.4 ±0.1μm
• An asymmetric dip centered at V1
develops as the NT is strained
• V1≈1 V
Semiconducting d=4 ±0.5nm and L =1.1 ±0.1μm
0
behavior at zero strain
• Increase of G with strain
• Reduction of the asymmetry of the dip
Electromechanical Response of Nanotubes
Interpretation
dE gap
 sign (2 p  1)3t0 (1  ) cos 3
d
t0  2.7eV
  0.2
 is the NT chiral angle
p  1,0,1 with n1  n2  3q  p
Metallic and half of semiconduc ting NTs : p  0,1 
Half of semiconduc ting NTs : p  1 
dE gap
d
0
dE gap
d
0
Electromechanical Response of Nanotubes
Interpretation
Constant-tip-voltage experiment
• Strain causes G to decrease
 dEgap/dσ>0 because there are less
thermally activated carriers
• Strain causes G to increase
 dEgap/dσ<0 because there are more
thermally activated carriers
 NTs show different electromechanical response
Metallic
Semiconducting
p=+1
Semiconducting p=1
dEgap/dσ>0
dEgap/dσ>0
dEgap/dσ>0
Strain causes G to
decrease
Strain causes G to
decrease
Strain causes G to
increase
Electromechanical Response of Nanotubes
Interpretation
G-Vtip
• Increasing the strain causes to go from a
metallic to a semiconducting behavior
 A bandgap is created in this initially
metallic NT
• The different curves show that the
bandgap is increased since G decreases
• Increasing the strain causes to increase G
in this semiconducting NT
 The bandgap is decreased
• Size of the conductance dip depends on
the bandgap which changes with strain
Electromechanical Response of Nanotubes
Conclusion
• The 1st experiment shows how the strain has an influence on G and
therefore on the bandgap
• This influence depends on the NT
• The 2nd experiment shows we can create a bandgap in a metallic NT
• It also shows how we can change the bandgap in a semiconducting NT
 Strain can be used to continuously tune the bandgap of a NT
• In the next part, we will see how we can use this phenomenon to
characterize NTs and other possible applications
Conductance relation to
bandgap
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For both the semiconducting and metallic nanotube
(NT), there is a dip in the conductance at a tip
voltage of about 1V.
The dip is much greater and sharper for metallic
NT’s. This dip is due to a charge carrier depletion in
the NT’s middle section as the NT transitions from ptype to n-type.
The resistance of the NT’s are modeled by the
equation Rtot=RS + h/(|t|28e2)[1 + exp(Egap/kT)],
where Egap=E0gap + (dEgap/dσ)σ
This resistance equation is neglecting tunneling and
is for low bias voltage.
Conductance relation to
bandgap
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As you can see, as Vtip
increases EC dips toward
EF at the middle. EC = EF
at about 1V and at Vtip >
1V, EF is above EC in the
middle.
A p-n-p junction in the
middle of the tube. The
transport due to tunneling
increases as ζ decreases
Analysis of data
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The equations for Rtot and Egap give physical meaning to
the fitting parameters, R0, R1, and β, used in the
equation for the maximum resistance as a function of
strain.
The most important parameter is β, where dEgap/dσ
=βkT. From the measured β values, values for dEgap/dσ
where found for the tubes in figure 4a and 4b.
The chiral angle was then estimated for the tubes using
this data and the equation:
dEgap/dσ= sign(2p
+1)3t0(1 + ν)cosφ
Analysis of data
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Additional device insight can be gained from the fitting parameter R1,
where R1= h/(|t|28e2)exp(E0gap/kT).
For the metallic tube (E0gap=0), the transmission probability |t|2=.25.
Thus the transport of thermally activated electrons across the
junction is not ballistic, but still highly transmissive. This is expected
long mean free paths in NT’s.
For the semiconducting tube, using |t|2=.25 as an estimate, E0gap is
inferred to be 160meV. This value corresponds to a diameter of
4.7nm (using Egap=2t0r0/d).
The diameter of 4.7nm is in reasonable agreement with the value of
4 +/- .5 nm measured by AFM. This agreement supports the validity
of the resistance equation.
Future Research
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Accurate quantatative comparison with theory requires an
independent determination of the chiral angles of each
NT.
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Variable temperature studies are needed to definitively
separate out the tunneling and thermal activation
contributions, which is not possible with current AFM
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A possible way to do this would be through advances in high
resolution TEM
A WKB model was used to estimate the effect of tunneling
current. It was found that the tunnel current was smaller than
the thermal current for ε<10meV/nm, where ε is the steepness
of the barrier
Looking at effect of higher strains: requires new methods
of device fabrication and different AFM techniques
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At higher strains problems such as the NT slipping up the side
of the AFM tip or sliding across the oxide surface occur
Potential Applications
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NT heterojunctions for things such as 1-D
super-lattice of quantum wells using a
periodically strained NT
New nano-electromechanical devices:
pressure gauges, strain gauges (expected to
be much more sensitive than doped Si strain
gauges)
Transducers, amplifiers, and logic devices
Summary
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It has been shown that metallic NTs can be
made semiconducting with applied
mechanical strain, and that the bandgap of
semiconducting NTs can be modified by
strain.
The change in bandgap causes a
measurable change in the conductance of the
NT’s.
This research is consistent with previous
research linking change in bangap with strain
and with chirality.