Tuning%20Carbon%20Nanotube%20Band%20Gaps%20with%20Strain

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Tuning Carbon Nanotube Band Gaps with Strain

• Presented by
• J.R. Edwards
• Zhuang Wu
• Pierre Emelie
• Michael Logue

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Carbon Nanotubes

• Long, thin cylinder of carbon---graphite sheet
  rolled into a tube
• Unique because different nanotubes can exhibit
  either metallic or semiconductor properties

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Metallic or Semiconductor

• If n1-n23q 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.

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Band Diagrams

• Cone like dispersion at k point
• Energy gap observed at slices away from k point

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Effect of Strain on Band Gap
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Experimental Device Fabrication
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AFM

• Atomic Force Microscope
• Contact Mode
• Scan sample with tip in close contact with the
  sample
• Measure deflection of cantilever
• Feedback loop moves sample to maintain constant
  deflection
• Non-Contact Mode
• 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
• Scan sample with oscillating tip intermittently
  contacting the sample
• Measure change in amplitude due to energy loss
  from contact with surface features
• Feedback loop

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Experimental Setup

• Tapping Mode
• Scan to create image of the nanotube structure
• Contact () Mode
• Scan to apply strain
• Tip operates as gate

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• The length of the tube is Ltube
• L0 is the distance between the two gold contacts
• People first measure the force on the tip in a
  open circuit

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Force on the tip

• Strain force pointing upwards
• The range is long

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Adhesion force

• Pointing downwards
• Short range
• Adhesion force is
• Van der Waals force

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Force vs. z

• ANT with d5.30.5nm, L01.00.1µm
• BNT with d2.30.5nm, L01.50.1µm
• Slack for A, slack11nm, YA2 µm for B,
  slack22nm YA2.9 µm

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Slack

• 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 510 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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• s(z) represents how much the length of the tube
  has changed.
• In constant YA, Y is the effective Youngs
  modulus, and A is an effective cross-section
  area.
• Here, the bending modulus of the NT has been
  ignored.

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Difference due to different ds

• 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

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MWNT
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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

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Electromechanical Response of Nanotubes
1st experiment Constant-tip-voltage experiment
2nd

• d6.5nm and L01.9µm
• 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

1st
Pushing G is lowered
Slack G0
Pulling G is lowered
G0
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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

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Electromechanical Response of Nanotubes
2nd experiment G-Vtip
Semiconducting NT
Evac
Evac
EC
EC
4.5 eV
5.1 eV
5.1 eV
EV
EV
0.7 eV/d (nm)
EF
EF
Au
Au
Au
Au

• Vtiplt0
• G increases

• Vtip0
• Ggt0

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
p
p
n
EC
EC
5.1 eV
5.1 eV
EV
EV
EF
EF
Tunneling
Au
Au
Au
Au

• VtipV1gt0
• G is minimum

• VtipgtV1
• G increases

As Vtip is increased, G decreases because the
holes are depleted until reaching its minimum
value
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
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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
Metallic NT
Semiconducting NT
G
G
G0
0
V1
Vtip
Vtip
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Electromechanical Response of Nanotubes
2nd experiment G-Vtip
Metallic behavior at zero strain
Semiconducting behavior at zero strain
d3 0.5nm and L01.4 0.1µm
d4 0.5nm and L01.1 0.1µm

• An asymmetric dip centered at V1 develops as the
  NT is strained
• V11 V

• Increase of G with strain
• Reduction of the asymmetry of the dip

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Electromechanical Response of Nanotubes
Interpretation
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Electromechanical Response of Nanotubes
Interpretation
Constant-tip-voltage experiment

• Strain causes G to decrease
• dEgap/dsgt0 because there are less thermally
  activated carriers
• Strain causes G to increase
• dEgap/dslt0 because there are more thermally
  activated carriers

• NTs show different electromechanical response

Metallic Semiconducting p1 Semiconducting p-1
dEgap/dsgt0 dEgap/dsgt0 dEgap/dsgt0
Strain causes G to decrease Strain causes G to decrease Strain causes G to increase
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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

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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

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Conductance relation to bandgap

• 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
  NTs. This dip is due to a charge carrier
  depletion in the NTs middle section as the NT
  transitions from p-type to n-type.
• The resistance of the NTs are modeled by the
  equation RtotRS h/(t28e2)1 exp(Egap/kT),
  where EgapE0gap (dEgap/ds)s
• This resistance equation is neglecting tunneling
  and is for low bias voltage.

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Conductance relation to bandgap

• As you can see, as Vtip increases EC dips toward
  EF at the middle. EC EF at about 1V and at Vtip
  gt 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 ?
  decreases

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Analysis of data

• The equations for Rtot and Egap give physical
  meaning to the fitting parameters, R0, R1, and ß,
  used in the equation for the maximum resistance
  as a function of strain.
• The most important parameter is ß, where dEgap/ds
  ßkT. From the measured ß values, values for
  dEgap/ds 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/ds sign(2p 1)3t0(1 ?)cosf

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Analysis of data

• Additional device insight can be gained from the
  fitting parameter R1, where R1
  h/(t28e2)exp(E0gap/kT).
• For the metallic tube (E0gap0), the transmission
  probability t2.25. 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 NTs.
• For the semiconducting tube, using t2.25 as an
  estimate, E0gap is inferred to be 160meV. This
  value corresponds to a diameter of 4.7nm (using
  Egap2t0r0/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.

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Future Research

• Accurate quantatative comparison with theory
  requires an independent determination of the
  chiral angles of each NT.
• A possible way to do this would be through
  advances in high resolution TEM
• Variable temperature studies are needed to
  definitively separate out the tunneling and
  thermal activation contributions, which is not
  possible with current AFM
• 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
  elt10meV/nm, where e is the steepness of the
  barrier
• Looking at effect of higher strains requires new
  methods of device fabrication and different AFM
  techniques
• At higher strains problems such as the NT
  slipping up the side of the AFM tip or sliding
  across the oxide surface occur

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Potential Applications

• 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

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Summary

• 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 NTs.
• This research is consistent with previous
  research linking change in bangap with strain and
  with chirality.