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 ~ d 002 = 0.34 nm

 strain 1/d 002

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. S A and S B are the Seebeck coefficients (also called thermoelectric power or thermopower of the metals A and B as a function of temperature, and T 1 and T 2 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 without increasing 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 cold e-e- charge drifting ph e-e- 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 by the 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 magnetic field is present. e-e- N S B Charged particle deflected by magnetic field (B) e-e- Charged particle remains moving path at a distance from B

N S B N S B  0 B ~ 0 In classical mechanics e-e- Extended magnet large deflection e-e- small deflection e-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 fact that 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 = 0 vector potential  0 B = 0 vector 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-e- B phase shift Vector potential  0 Double-slit

B V I

Boron doping effect 1. Effect on structure B a.C: 3 sp 2 (3  ) and 1 2p z (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 EFEF CB VB Semiconductor EFEF CB VB EgEg

BC 3 tube Free electronic-like (metallic) EFEF CB VB  **

2. Effect on electronic band profiles Random doping of B in CNT metallic EFEF CB VB Semiconductor EFEF CB VB E F depression to VB edge more than 2 sub-bands crossing at E F i.e. conductance increases BC 3 state (acceptor) EgEg New E g E g reduction by E F depression

B-doping a.E F depression  E g reduction (semiconductor tube) and number of conduction channel increase (conductance > 4e 2 /h, metallic tube). b. Creation of acceptor state near to VB edge and increase in hole carrier density (1  spins/g for CNTs, 6  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+B+ e-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-e- hopping  -band (CB) Overlap of  -electron wave function BC 3 state

f. Less influence on conductivity upon strain application For CNT R Deflection angle

Temporary formation of sp 3 character upon bending Resistance reduction is due to (i) temporary formation of sp 3 at bend region and (ii) increasing hopping magnitude upon bending bending Planar sp 2 Tetrahedral sp 3

e - hopping bending planar  -band  -band

For BCNTs  -band BC 3 -state is less affected by bending, so channel remains opened for 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, distortion also takes place in valence band the tube fracture occurs)

Work function (W) Definition: difference in potential energy of an electron between the vacuum level and the Fermi level. EFEF 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 q 1 and q 2: charge on the two substrates (coul),  1 and  2 : surface charge densities (coul/m 2 ),  o = 8.85 x farad/m (permittivity constant), k e dielectric constant of the medium, and d sep : distance between charge centers.

Cu : eV eV eV Crystal planes Work function 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) - + -

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- 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 tunnelingquantum tunneling in which electrons pass through a barrier in the presence of a high electric field.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 E Electron tunneling through barrier with E

voltage applied here Electric field evenly created on surface EEEEE EEEEE + - E1E1 E2E2 E3E3 E4E4 Energy required for electron field emission at E 1 = E 2 = E 3 = E 4

EEEEE + voltage applied here - E E E E E E E Field enhancement appeared at the tip E E E E

Field enhancement means that electrons obtain larger “pushing” energy to escape from surfaces Pushing energy > W (work function)

The current density produced by a given electric field is governed by the Fowler-Nordheim equation.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 K 1 is a constant K 2 is a constant

1.Current increases with the voltage squared multiplied by an exponential increase with inverse voltage. 2. E 2 increases rapidly with voltage 3. Assume that K 2 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 K 1 and K 2 stand for? A much clear formula I/A = A(  E) 2 /W. exp(-BW 3/2 /  E) A, B: constant  : enhancement factor to microscope field ~h/r W: work function (or effective barrier height) h:height r: radius

Reference website 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.