Tuning Carbon Nanotube Band Gaps with Strain Jo Sung Ph.D. Student, Dept. of Electrical Engineering...

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

Experimental Results Force-deflection relationship Force/Conductance-deflection relationships Conductance-voltage relationships Evolution of energy-band diagram

Conclusion


Carbon NanotubesCarbon Nanotubes Carbon nanotubes can be thought

of as the rolling of a single graphene sheet Depending on how the graphene

sheet is rolled, nanotubes can be either metallic or semiconducting

n1 – n2 = 3q ~ metallic n1 – n2 ≠ 3q ~ semiconducting


Carbon NanotubesCarbon Nanotubes Left: Energy diagram of metallic carbon nanotubes Right: Energy diagram of semiconducting carbon nanotubes


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


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


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


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


Tombler, Tombler, et al.et al. (2000) (2000)


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


Tombler, Tombler, et al.et al. (2000) (2000)


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


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.


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)


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)


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


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


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


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


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


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


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


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


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


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 =


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


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


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

Sung Hyun JoPh.D. Student, Dept. of Electrical Engineering & Computer Science

EECS 598 Nanoelectronics Week 8 PresentationAnn Arbor, MI

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?


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


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


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


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).


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


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


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)


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


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


(%)

P = 1

P = -1


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


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


Field effect doping e.g.

J. Park et al., APL. 79 1363 (2001)


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


Potassium doping of individual SWNTs: n-type tubes

C.Zhou et al., Science 290 1552 (2000)

http://www.sciencemag.org/content/vol290/issue5496/images/large/se4509009001.jpeg


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


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)


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


ResultsResults From the measured value


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)


Unified ModelUnified Model The band gap change under small strain


0(2 1)3 [(1 ) cos3 sin3 ]

: uniaxial strain

: tosional strain

gapE sign p t


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


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


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


Appendix C: Tight Binding ModelAppendix C: Tight Binding Model

Tuning Carbon Nanotube Band Gaps with Strain Jo Sung Ph.D. Student, Dept. of Electrical Engineering...

Documents

Transcript of Tuning Carbon Nanotube Band Gaps with Strain Jo Sung Ph.D. Student, Dept. of Electrical Engineering...