Tuning Carbon Nanotube Band Tuning Carbon Nanotube Band Gaps with Strain Gaps with Strain Jo Sung Ph.D. Student, Dept. of Electrical Engineering & Computer Science Ken Loh Ph.D. Student, Dept. of Civil & Environmental Engineering EECS 598 Nanoelectronics Week 8 Presentation Ann Arbor, MI November 1, 2005
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Tuning Carbon Nanotube Band Gaps Tuning Carbon Nanotube Band Gaps with Strainwith Strain
Jo SungPh.D. Student, Dept. of Electrical Engineering & Computer Science
Ken LohPh.D. Student, Dept. of Civil & Environmental Engineering
EECS 598 Nanoelectronics Week 8 PresentationAnn Arbor, MI
November 1, 2005
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Presentation OutlinePresentation Outline Review of Carbon Nanotubes Research Purpose and Motivation Experimental Setup
Nanotube fabrication with CVD Suspending the nanotube AFM setup Measurements
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Carbon NanotubesCarbon Nanotubes Left: Energy diagram of metallic carbon nanotubes Right: Energy diagram of semiconducting carbon nanotubes
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
To demonstrate that strain modifies the band structure of nanotubes Employ AFM tip to simultaneously vary the nanotube strain and to
electrostatically gate the tube Find, under strain, conductance of the nanotube can increase or decrease
Experimental setup
Measuring conductance with gold contacts L0 is the distance between anchoring points z is the distance the center of the nanotube is displaced
Research Purpose and MethodologyResearch Purpose and Methodology
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Tombler, Tombler, et al.et al. (2000) (2000) Pioneering experiment showed the conductance of a metallic
nanotube could decrease orders of magnitude when strained by an AFM tip Tombler, et al. (2000) ~ Hongjie Dai group
SWNT formed using CVD method Large diameter tube (or small bundle), d = 3.1 ± 0.2 nm
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Tombler, Tombler, et al.et al. (2000) (2000) Using t ~ 3.4 Å (van der Waals wall thickness), yields Y (Young’s Modulus) ~
1.2 TPa Corresponds with results from literature, where Y ~ 0.6 – 1.3 TPa F(δ) α δ3 relation indicates SWNT deflection can be modeled as elastic string under
initial loading at its center Assume deflected SWNT forms triangle with its original configuration, we
can define Global strain parameter
Angle between deflected nanotube and its original configuration
l
ll
224
l
2tan 1
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Tombler, Tombler, et al.et al. (2000) (2000) Cantilever deflection during cycle
of pushing and releasing nanotube
Inset, F(δ) versus nanotube deflection curve Fitted solid line
Arrow highlights deviation point from F(δ) α δ3
3
8
l
YAF
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Tombler, Tombler, et al.et al. (2000) (2000)
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Tombler, Tombler, et al.et al. (2000) (2000) To understand results, authors performed order-N non-orthogonal
tight-binding molecular-dynamics simulation of an AFM tip deflecting a (5, 5) SWNT Electrical measurements indicated nanotube is metallic in nature, hence, MD
simulation performed on a (5, 5) SWNT Simulations carried out at 300 K
Calculated conductance evolution as nanotube is deflected Found conductance decreased two-fold at θ = 7.0° Conductance decreased more significantly at larger bending angles
Analysis indicated that local bonding deformation induced by AFM tip responsible for large conductance decrease When pushed, region proximal to tip exhibits significant change in atomic
bonding configuration Nanotube responds elastically, but exhibits large bond distortion
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Tombler, Tombler, et al.et al. (2000) (2000)
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Maiti, Maiti, et al.et al. (2002) (2002) Argue that drop in conductance due to a band gap induced in the
nanotube as it is axially stretched Explore conductance change under tube bending and tip-induced deflection
Tip deflection accomplished with 15-atom Li tip Main difference is there is an overall stretching in a tip-deformed tube
In bending, extra compressive strain on the bottom side is relieved through formation of a kink beyond a critical angle
Find that under bending and tip-deformation, carbon nanotubes essentially remain all hexagonal Conductance drop distributed over the entire tube, rather than focused at the
tip region
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Maiti, Maiti, et al.et al. (2002) (2002)
Conductance of uniformly stretched tube compared to that of a tip-deformed one. Inset shows transmission for a uniform strain of 10% and a deformation angle of 25° as
compared to an undeformed one.
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Experimental SetupExperimental Setup Samples consist of nanotubes suspended over a trench and
clamped at both ends by electrical contacts
Walters, et al. (1999) Nygard, et al. (2001)
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
FabricationFabrication Fabrication steps
Pattern catalytic islands on Si substrate Electron-beam lithography Deposition of Fe(NO3)3·9H2O, MoO2(acac)2 and alumina nanoparticles in the
liquid phase Lift-off
Chemical vapor deposition (CVD) growth is utilized to grow nanotubes with diameters between 1 and 10 nm Growth initiated at lithographically defined catalyst sites on Si substrate with a
500-nm oxide Based on Kong, et al. (1998)
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Kong, Kong, et al. et al. (1998)(1998) A: E-beam used to fabricate square holes
on PMMA layer
B: 0.05-mmol Fe(NO3)3·9H2O, 0.015-mmol of MoO2, and 15-mg of alumina nanoparticles added to 15 mL methanol; drop of suspension deposited on substrate
C: Lift-off of PMMA in 1,2-dichloroethane leads to the final substrate containing catalyst islands
D: CVD of methane at 1,000 C produces SWNTs off islands
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Kong, Kong, et al. et al. (1998)(1998) A: SEM images show line-like
substances (nanotubes) extend off island after CVD
B: High-magnification SEM image of same sample
C: Typical large-scale phase image recorded by tapping mode AFM
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Establish Electrical ContactsEstablish Electrical Contacts Once nanotubes are grown using CVD, metal contacts are patterned
using photolithography Rosenblatt, et al. (2002) 5 nm Cr 50 – 80-nm Au Spaced 1 – 3 μm between source and drain
Annealed at 600 C for 45 minutes in an argon environment to improve the contact resistance Typically by an order of magnitude
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Fabrication ProcessFabrication Process Ashing step removes photoresist residue and improves contact
resistances 400 C for 10-min in Ar atmosphere
Suspend carbon nanotube HF etch
6:1 BHF, etch rate 80-nm/min Critical point drying Device conductance not significantly changed by etching process
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
MeasurementsMeasurements Dimension 3100, Digital Instruments AFM system used for
simultaneous electrical measurements and AFM imaging/manipulation
Park, et al. (2002) Sample stage modified to allow mechanical probes to make contact to the
sample pads during imaging Metallized AFM tips (Pt-Ir coated) is employed Voltage can be applied using the AFM controller electronics After identifying nanotube, tip brought down until it is very near or in contact
with the nanotube
Left: Perspective-view of a carbon nanotube on an oxide layer imaged in tapping-mode AFM
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Making MeasurementsMaking Measurements Following the process of Kong, et al. (2002), measurements can be
made using AFM In addition, Nanosensor EFM tips are utilized
Nominal radius of 20-nm Coated with a Pt-Ir metal layer
To prove mechanical and electromechanical properties, the AFM tip is centered above a suspended nanotube using a tapping mode image for guidance
Tube moved in the z-direction while monitoring the static deflection of the cantilever and the conductance of the tube
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Force-Distance MeasurementsForce-Distance Measurements Plot upward force on the cantilever Fz as a function of tip height z
while raising AFM tip Force the tube exerts on the tip
can be both positive (upward) and negative (downward)
Separated by region of near-zero force when tip is near the plane of the contacts Curve A: d = 5.3 ± 0.5 nm, L0 =
1.0 ± 0.1 μm Curve B: d = 2.3 ± 0.5 nm, L0 =
1.5 ± 0.1 μm Curves show strong adhesion
between AFM tip and nanotube
Inset shows a number of fitted YA values
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
SlackSlack From distance between pushing and pulling onsets, ±zonset, the
“slack” of a suspended nanotube can be determined Slack defined as Ltube – L0
Ltube = tube length and is greater than L0, the separation between anchoring points
Nearly all nanotubes were slack, with typically 5 – 10-nm of slack for a 1-μm tube Slack consistent with curved path nanotubes followed across oxide surface
before etching
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Theoretical AnalysesTheoretical Analyses Find force-distance curves ca nbe accurately fit by ignoring bending
modulus of the tube Assume linear proportionality between nanotube tension T and axial strain σ Write proportionality constant as YA
Y = effective Young’s modulus A = effective cross-sectional area
For |z| ≥ zonset and Fz(z) = 0 for |z| ≤ zonset
For |z| ≥ zonset
Magnitude of YA values and linearity with diameter d suggests that a single shell is carrying the mechanical load, even for large diameter tubes likely having multiple walls
220 4
22sin2
zL
zzYATzFz
tube
tubez L
LzL
220 4
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Derivation of Force-Deflection EquationDerivation of Force-Deflection Equation
L
L
sin2TFz
L/2T
θ
T sinθ
Since the structure is symmetric, the total resultant vertical component is
From Hooke’s Law, we know that:where, σ = stress, ε = strain, and E = Young’s ModulusAnd,
E
z
L/2
x
By Pythagorean’s Theorem, we can calculate x:
22
02
2z
Lx
2
2
0
2z
Lx
220 42 zLx
tube
tube
tube
tubenew
L
LzL
L
LL
220 4
Again, due to symmetry:
Thus, strain =
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Salvetat, Salvetat, et al. et al. (1999)(1999) Magnitude of YA values are similar to what Salvetat, et al. (1999) have
determined To measure Young’s modulus, they first determine the location of a nanotube using an
AFM tip Determine its diameter, suspended length, and deflection midway along the
suspended length From a series of images taken at different loads
d, deflection, can be calculated as such (from small-deformation theory)
F is the applied force, I is the second moment-of-area, a = 192 for a clamped beam For a hollow cylinder, I can be computed as such
Ro = outer radius, Ri = inner radius
aEI
FLd
3
4
44io RR
I
Ro
Ri
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Mechanics of MaterialsMechanics of Materials Calculating deflection of idealized-beam elements
Simply-supported beam
Fixed-fixed beam
EI
FL
48
3
F
L/2 L/2
F
L/2 L/2 EI
FL
192
3
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Salvetat, Salvetat, et al. et al. (1999)(1999) Reversibility of the tube deflection and the linearity of the d-F curve
shows that the nanotube response is linearly elastic
Slope of the curve gives directly the Young’s modulus of the CNT Found to be 810 ± 410 GPa (taken as a minimum value)
Tuning Carbon Nanotube Band Gaps Tuning Carbon Nanotube Band Gaps with Strain (Part II)with Strain (Part II)
Ken LohPh.D. Student, Dept. of Civil & Environmental Engineering
EECS 598 Nanoelectronics Week 8 PresentationAnn Arbor, MI
November 1, 2005
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Deflection Force & ConductanceDeflection Force & Conductance When cantilever is deflected, G is lowered
When Strained Two s.c. tubes: increasing G, One s.c. tube & two metallic tubes: decreasing G Two metallic tubes: nearly same G
Why?
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
The gate voltage versus the conductance The tube can be turned on by applying negative voltage, and turned off with a
positive voltage. The device turns on at a negative voltages because holes are added to the tube.
Because the contact resistance is quite high, the conductance eventually stops increasing and becomes constant.
Conductance of the S.C. CNTsConductance of the S.C. CNTs
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Conductance of the S.C. CNTsConductance of the S.C. CNTs No surface state problem
Tubes are inherently two dimensional materials and the cylinder as no edges The conductance is limited by any barriers that holes see as they
traverse the tube The resistance of the tube will be dominated by the highest barriers in the tube
Barriers – due to structural defects, atoms adsorbed on the tube or localized charges
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
The map of barriers to conduction to be produced The tip of a scanning probe microscope can be used to map the barriers. The
conductance of tubes is measured as the positively biased tip is scanned over the sample. The bright spots are where the tip decreased the conductance, with greater intensity corresponding to greater change in the conductance.
Conductance of the S.C. CNTsConductance of the S.C. CNTs
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Conductance of the Metallic CNTsConductance of the Metallic CNTs The conductance of the metallic carbon nano tubes is not noticeably
affected by the addition of a carriers. Many groups have made tubes with conductances that are between
25% and 50% of the value of 4e2/h that has been predicted for perfectly conducting ballistic nanotubes. Very long mean free path (~um)
At low temperature, the tube acts like a long box (quantum dot).
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Nanotube quantum dots reveal a great deal about the behaviour of carriers in nanotubes Periodic oscillation: the electronic states are extended along the entire length
of the tube – if there were many scattering , the oscillation would be less regular
Electrons can travel for long distance without being back scattered – fundamental difference between conventional metal (e.g. Cu) and nanotube
Conductance of the Metallic CNTsConductance of the Metallic CNTs
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
To understand the characteristic of strain versus conductance, we need to investigate the band structure of the NT
Tip is used as a gate
Metallic CNT
Semiconducting CNT
max 0 1( ) exp( )R R R
Carrier depletion
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Deformed Carbon NanotubeDeformed Carbon Nanotube When deformed, we need to consider the change in kF relative to k lines
| kF – k |
0
0
(1 ) cos3 sin 3
(1 ) sin 3 cos3
t and c denote components along the tube axis and circumference
and are strains along t (uniaxial) and c (torsional)
: poisson's ratio
: the chiral
cF
tF
k r
k r
angle
F V Fk k k
t
L. Yang et al., Phys. Rev. Lett. 85 154 (2000)
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
The Effect of Strain on the EThe Effect of Strain on the Egg
The rate of change of band gap with respect to strain
0sign(2 1)3 (1 )cos3gapdEp t
d
0
1 2
2.7
0.2 : Poisson ratio
: NT chiral angle
1, 0 1, ( 3 )
t eV
p or n n p q
0
max
3 (1 ) 100meV/%gapdEt
d
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Semiconducting NTs
p = 1 Strain causes G to decrease
p = -1 Strain causes G to increase
If G does not change
1 21 1, ( 3 )p or n n p q
/ 0gapdE d
/ 0gapdE d
/ 0gapdE d
L. Yang et al., Phys. Rev. Lett. 85 154 (2000)
(%)
P = 1
P = -1
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
The Effect of Strain on BandgapThe Effect of Strain on Bandgap Density of States
(a) (17 0) p= -1 (b) (18 0) p= 0
(c) (19 0) p= 1
Strain (%)
4
3
1
0
E (eV)-1.5 0 1.5
DOS
/ 0gapdE d / 0gapdE d
/ 0gapdE d
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Initially P-type contact
S. J. Tans et al., Nature 393 49 (1998)
Work function: Pt(5.7 eV), CNT(~4.5eV)
Fermi level pinning
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Field effect doping e.g.
J. Park et al., APL. 79 1363 (2001)
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Tip gate affects the center part of the tube & the sections near the contacts are held p-type
P P
P P
P
N
Tunneling occurs
Few electrons & large barrier
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Potassium doping of individual SWNTs: n-type tubes
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Possible Reasons for Initially P-typePossible Reasons for Initially P-type P-type
Oxygen increases the conductivity of the CNT It is believed that the metal electrodes as well as chemical species absorbed
on the tube “dope” the tube to p-type Fermi-level pinning
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Two terminal conductance (Metallic CNTs) Landauer’s equation
If no scattering inside the tube & contacts
As for semiconducting CNTs or when there are strains the band gap term must be included in the conductance modeling
2
2
2
2: quantum of conductance
: the transmission of a contributing channel(subband)
N
ii
i
eG T
h
e
hT
1 1/ 6.5
( #of contributing channels is 2 at ambient temperature)iT R G k
P. Avouris. MRS Bulletin/June (2004)
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Modeling of the R( )Modeling of the R( ) The low-bias resistance of the device
From the fitting model
From the
0 gapgap gap
dEE E
d
/gapdE d kT
2 2
11 exp
| | 8gap
tot S
EhR R
t e kT
= Junction resistance
0/ sin(2 1)3 (1 )cos3gapdE d p t
max 0 1( ) exp( )R R R
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
ResultsResults From the measured value
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Selective Bandgap EngineeringSelective Bandgap Engineering Fullerenes or endohedral metallofullerenes such as Gd
encapsulated inside C82 (GdMF) can be inserted into SWNTs e.g. keeping GdMFs with SWNTs in a sealed glass ampoule at 500C for 3
days
J. Lee. Nature. 415 1005 (2002)
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Unified ModelUnified Model The band gap change under small strain
L. Yang et al., Phys. Rev. Lett. 85 154 (2000)
0(2 1)3 [(1 ) cos3 sin3 ]
: uniaxial strain
: tosional strain
gapE sign p t
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
ConclusionConclusion The 1D character of CNTs greatly reduces the phase space for
scattering
The effective way for bandgap engineering of NTs: the strain
Applying selective strain on different sections: NT heterostructures
Estimating the chiral angle by measurement of the - useful for small-diameter tubes
/gapdE d
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Appendix A: Poisson’s RatioAppendix A: Poisson’s Ratio Poisson's ratio is the ratio of transverse contraction strain to longitudinal
extension strain in the direction of stretching force. Tensile deformation is considered positive and compressive deformation is considered negative. The definition of Poisson's ratio contains a minus sign so that normal materials have a positive ratio.
/ /trans longitudinal L L
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Appendix B: Quantum of ConductanceAppendix B: Quantum of Conductance The conductivity
For a 1-D conductor with one channel
2
*: mean free time (mean scattering time)
*: effecive mass
m
m
ne
m
m
( 2 / )Fn k
2
*F
m
kT
Lm
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005
Appendix C: Tight Binding ModelAppendix C: Tight Binding Model
Tuning Carbon Nanotube Band Gap With StrainTuning Carbon Nanotube Band Gap With StrainEECS 598 Nanoelectronics Week 8 Presentation – November 1, 2005