Oxidation of CNTs and graphite

1. Unzipping of carbon lattice (crack formation in graphite)

(GO: graphite oxide)

OHO

epoxy hydroxyl

1.42Å

Fault line

This value is significant but it considerably reduced in an oxidative solution

Cutting of nanotube

Crack formation

Epoxy alignment

Nanotechnology, 16, S539, 2005

PRL, 81, 1869, 1998

D = 10 nm ~ d002 = 0.34 nm

strain

1/d002

Gas adsorption sites in a tube bundle

Thermoelectric effect

Thermoelectric effect is the direct conversion of temperature differences to electric voltage and, vice versa.

Seebeck effect is the conversion of temperature differences directly into electricity.

SA and SB are the Seebeck coefficients (also called thermoelectric power orthermopower of the metals A and B as a function of temperature, and T1 and T2 are the temperatures of the two junctions.

thermoelectric voltage: ΔV

temperature difference: ΔT

electric field E, the temperature gradient     

(TEP, Seeback coefficient)

PRL, 80, 1042, 1998

TEP

T

Metals

TEP

(1/T)

Semiconductor

Metals however have a constant ratio of electrical to thermal conductivity (Widemann-Franz-Lorenz law) so it is not possible to increase one withoutincreasing the other.

TEP

T

Metals

J

P

180K

MetallicSemiconductor

Pristine: M-S transition

Semiconductor

Why pristine single-walled CNT ropes show a M-S transition at low temp ?and sintered rope is semiconductor at all temperature regime?

: metallic (: resistivity)

: semiconductor

This is why sintered nanotube rope was measured in comparison with un-sintered CNT rope; the former has minimized intertube contact.

Interesting ! but why ?

Two possibilities

a. Charge carrier drift and phonon drag

b. Breaking of electron-hole symmetry due to intertube interaction (charge transfer between tubes)

hot colde-

charge drifting

phe-

Phonon drag

Let’s have a look at (a)

So, contribution to TEP by charge drift is ruled out!

What about phonon drag

So, phonon drag is also excluded!

A side view of tube bundle, red: semiconductor tube, blue: metallic tubes (majority)

Charge transfer

The Aharonov-Bohm effect in carbon nanotubes

In classical mechanics, the motion of a charged particle is not affected bythe presence of magnetic fields (B) in regions from which the particle is excluded.This is because the particles can not enter the region of space where the magneticfield is present.

e-

N

S

B

Charged particle deflected by magnetic field (B) e-

Charged particle remains moving pathat a distance from B

N

S

B

N

S

B 0

B 0

B 0

B 0

B ~ 0

In classical mechanics

e-

Extended magnet

large deflection

e-

small deflection

e-No deflection

For a quantum charged particle, there can be an observable phase shift in the interference pattern recorded at the detector D. This phase shift results from the factthat although the magnetic field is zero in the space accessible to the particle, the associated vector potential is not. The phase shift depends on the flux enclosed by the two alternative sets of paths a and b. But the overall envelope of the diffraction pattern is not displaced indicating that no classical magnetic force acts on the particles.

What is a vector potential = magnetic potential (similar to electric potential)

N

S

B 0 B = 0vector potential 0

B = 0vector potential 0

Phase shift in interference pattern

Double-slit

Let’s have a look at double-slit diffraction at B = 0

Electromagnetic coil for B creation

I (current)

B

A: magnetic vector potential

e-

B

phase shift

Vector potential 0

Double-slit

B

V

I

Boron doping effect

1. Effect on structure

B

a. C: 3 sp2 (3 ) and 1 2pz (1 ) bonds B: 3 sp2 (3 )

b. Bond length: C-C = 1.42 Å, B-C = 1.55 Å

c. Electrical ring current (resonance) disappears when B substitutes C

2. Effect on electronic band profiles

CNT

metallic

EF

CB

VB

Semiconductor

EF

CB

VB

Eg

BC3 tubeFree electronic-like (metallic)

EF

CB

VB

*

2. Effect on electronic band profiles

Random doping of B in CNT

metallic

EF

CB

VB

Semiconductor

EF

CB

VB

EF depression to VB edge

more than 2 sub-bands crossing at EF

i.e. conductance increases

BC3 state (acceptor)

Eg

New Eg

Eg reduction by EF depression

B-doping

a. EF depression Eg reduction (semiconductor tube) and number of conduction channel increase (conductance > 4e2/h, metallic tube).

b. Creation of acceptor state near to VB edge and increase in hole carrier density (11016 spins/g for CNTs, 61016 spins/g for BCNTs).

c. Electron scattering density increase by B-doping centers (i.e. shorter mean free path and relaxation time compared with CNTs, = 0.4 ps and 4-10 ps for BCNTs and CNTs)

B+

e-

electron trapped by B-center (scattering)

d. The actual conductivity depends on competition between scattering density and increase in hole carrier (in practice, the latter > the former, so conductance )

e. Electron hopping magnitude in -band increase

B dopant

-band (VB)

-band (CB)e-

hopping

-band (CB)

Overlap of -electron wave function

BC3 state

f. Less influence on conductivity upon strain application

For CNT

R

Deflection angle

Temporary formation of sp3 character upon bending

Resistance reduction is due to (i) temporary formation of sp3 at bend regionand (ii) increasing hopping magnitude upon bending

bending

Planar sp2

Tetrahedral sp3

e- hopping

bending

planar-band

-band

-band

For BCNTs

-band

BC3-state is less affected by bending, so channel remains openedfor conduction.

-band is blocked by bending

(note that tube bending induced distortion only occurs in -wave function and valence band essentially remains intact, if, only if, distortionalso takes place in valence band the tube fractureoccurs)

Work function (W)

Definition: difference in potential energy of an electron between the vacuum level and the Fermi level.

EF

Vacuum level

W

a. The vacuum level means the energy of electron at rest at a point sufficiently far outside the surface so that the electrostatic image force on the electron may be neglected (more than 100Å from the surface)

Metal surface

100 Å

b. Fermi level means electrochemical potential of electron in metal.

Fowler-Nordheim equation and field emission

The image force is the interaction due to the polarization of the conducting electrodes by the charged atoms of the sample.

+

Two neutral substrates sufficiently close to each other

When one atom is positively charged-

Counter charge is automatically generated on the other side

Coulomb interaction occurs between two substrates

q1 and q2: charge on the two substrates (coul), 1 and 2: surface charge densities (coul/m2), o = 8.85 x 10-12 farad/m (permittivity constant), ke dielectric constant of the medium, and dsep : distance between charge centers.

Cu : 100 4.59 eV 110 4.48 eV 111 4.98 eV

Crystal planes Work function

100 110

111 Best field emission site(electrons easily escape from 110)

Why different crystal planes give different work function?

metal

Surface atoms encounter asymmetrical environment

vacuum

Surface atom

Attraction from underlying metal substrate

+

Electric double layer

Vacuum (no attraction)

-+

-

+ + + ++ + + +

+ + + ++ + + +

+ + + ++ + + +

+ + + ++ + + +

++++

+ + + + ++ + + ++ + + +

+ + + ++ + + +

++++

++++

+ + + + + +

111 110 100

positive ion density 111 > 100 >110

The less positive ion density the easier electrons to escape

++ + ++ + Polarized surface

+

-

V

Field emission device

vacuum

insufficient potential

e-

e-

hole+

Coulomb attraction

electrons return

Space charge

Electron bouncing on surface: space charge

Metal

surface

Work function

effective surface dipole

Fermi energy (negative sign means electrons bounded in solid)

+

-

Occurrence of field emission must > W

electrons do not return to surface

How do we make field emission, not space charge

1. Reduction of work function

2. Increases the applied voltage

V

The second method is not good

How to reduce work function

1. Selection of low work function materials (metals)2. Use of sharp point geometry

A B C

+ + +

- - -

Why use sharp point as field emitter Field emission (Fowler-Nordheim tunneling) is a form of quantum tunneling in which electrons pass through a barrier in the presence of a high electric field. This phenomenon is highly dependent on both the (a) properties of the material (low work function) and (b) the shape of the particular emitter.

higher aspect ratios produce higher field emission currents

length

Diameter (width)

Aspect ratio = Length/diameter

Electron tunneling through barrier without EElectron tunneling through barrier with E

voltage applied here

Electric field evenly created on surface

E E E E E

E E E E E

+

-E1

E2

E3E4

Energy required for electron field emission at E1 = E2 = E3 = E4

E E E E E

+

voltage applied here

-

EE

E

EE

E

E Field enhancement appeared at the tip

EE

EE

Field enhancement means that electrons obtain larger “pushing” energyto escape from surfaces

Pushing energy > W (work function)

The current density produced by a given electric field is governed by the Fowler-Nordheim equation.

V = voltage (volts) t = thickness of oxide (meters)

E = V/t electric field (volts per meter) I = current (amperes)

A = area of oxide, square meters J = I/A

J = current density in amperes per square meter K1 is a constant K2 is a constant

1. Current increases with the voltage squared multiplied by an exponential increase with inverse voltage.

2. E2 increases rapidly with voltage

3. Assume that K2 is normalized to 1

a. The factor exp(-1/E) increases with E

b. If E is near zero, the exponent is large, and exp(-large) is near zero

c. If E is large, 1/E is small, and almost zero: exp(0) = 1

d.Therefore, exp(-1/E) gets larger as E gets larger

Exp(-1/E) maintain a value between zero and one.

We do not know precisely the K1 and K2 stand for?

A much clear formula

I/A = A(E)2/W. exp(-BW3/2/E)

A, B: constant: enhancement factor to microscope field ~h/rW: work function (or effective barrier height)

h:heightr: radius

Reference websitehttp://ipn2.epfl.ch/CHBU/NTfieldemission1.htm#Field%20emission%20basics

CNT field emission

Field emission involves the extraction of electrons from a solid by tunneling through the surface potential barrier. The emitted current depends directly on the local electric field at the emitting surface, E, and on its work-function, f, as shown below. In fact, a simple model (the Fowler-Nordheim model) shows that the dependence of the emitted current on the local electric field and the workfunction is exponential-like. As a consequence, a small variation of the shape or surrounding of the emitter (geometric field enhancement) and/or the chemical state of the surface has a strong impact on the emitted current.

The numerous studies published since 1995 show that field emission is excellent for nearly all types of nanotubes. The threshold fields are as low as 1 V/µm and turn-on fields around 5 V/µm are typical. Nanotube films are capable of emitting current densities up to a few A/cm2 at fields below 10 V/µm.