Transcript 投影片 1 - National Tsing Hua University

Oxidation of CNTs and graphite
1. Unzipping of carbon lattice (crack formation in graphite)
O
epoxy
OH
hydroxyl
(GO: graphite oxide)
1.42Å
Fault line
This value is significant but it considerably reduced in an oxidative solution
Cutting of nanotube
Epoxy alignment
Crack formation
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 or
thermopower 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
Metals
Semiconductor
TEP
TEP
T
(1/T)
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.
Metals
TEP
T
J
P
Semiconductor
180K
Semiconductor
Pristine: M-S transition
Metallic
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)
Phonon drag
hot
e--
ph
e
charge drifting
cold
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!
Charge transfer
A side view of tube bundle, red: semiconductor tube, blue: metallic tubes (majority)
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.
Charged particle
remains moving path
at a distance from B
N
e-
B
S
Charged particle deflected by magnetic field (B)
e-
In classical mechanics
Extended magnet
B0
B0
N
N
B~0
B
S
S
B0
large deflection
B0
small deflection
ee-
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)
Phase shift in interference pattern
Double-slit
N
B=0
vector potential  0
B0
S
B=0
vector potential  0
Let’s have a look at double-slit diffraction at B = 0
B
I (current)
A: magnetic vector potential
Electromagnetic coil for B creation
phase shift
B
Double-slit
e-
Vector potential  0
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
CB
metallic
EF
VB
CB
CNT
EF
Eg
VB
Semiconductor
CB *

EF
VB
BC3 tube
Free electronic-like (metallic)
2. Effect on electronic band profiles
CB
metallic
EF
VB
EF depression to VB edge
more than 2 sub-bands crossing at EF
i.e. conductance increases
CB
EF
Random doping of B in CNT
New Eg
Eg
BC3 state (acceptor)
VB
Semiconductor
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
(11016 spins/g for CNTs, 61016 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)
d. The actual conductivity depends on
competition between scattering density
and increase in hole carrier (in practice,
the latter > the former, so conductance )
B+
eelectron trapped by B-center (scattering)
e. Electron hopping magnitude in -band increase
Overlap of -electron wave function
hopping
e-
-band (CB)
-band (VB)
-band (CB)
B dopant
BC3 state
f. Less influence on conductivity upon strain application
For CNT
R
Deflection angle
Resistance reduction is due to (i) temporary formation of sp3 at bend region
and (ii) increasing hopping magnitude upon bending
Temporary formation of sp3 character upon bending
bending
Planar sp2
Tetrahedral sp3
-band
-band
planar
-band
e- hopping
bending
For BCNTs
-band is blocked by bending
-band
BC3-state is less affected by
bending, so channel remains opened
for conduction.
(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)
Fowler-Nordheim equation and field emission
Work function (W)
Definition: difference in potential energy of an electron between
the vacuum level and the Fermi level.
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)
EF
100 Å
Metal surface
b. Fermi level means electrochemical potential of electron
in metal.
The image force is the interaction due to the polarization of the
conducting electrodes by the charged atoms of the sample.
Counter charge is automatically generated on the other side
-
+
When one atom is positively charged
Two neutral substrates sufficiently close to each other
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.
Crystal planes
Cu :
Work function
100
110
111
4.59 eV
4.48 eV
4.98 eV
Best field emission site
(electrons easily escape from 110)
111
100
110
Why different crystal planes give different work function?
vacuum
Electric double layer
Surface atoms encounter
asymmetrical environment
metal
Vacuum (no attraction)
+
-
+
Surface atom
-
Attraction from underlying metal substrate
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110
Polarized surface
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100
positive ion density 111 > 100 >110
The less positive ion density the easier electrons to escape
e-
Space charge
Coulomb attraction
hole+
+
electrons return
insufficient potential
vacuum
V
e-
Electron bouncing on surface: space charge
Field emission device
Work function
Fermi energy (negative sign means electrons bounded in solid)
+
effective surface dipole
-
surface
electrons do not return
to surface
Metal
Occurrence of field emission must > W
How do we make field emission, not space charge
1. Reduction of work function
2. Increases the applied voltage
The second method is not good
V
How to reduce work function
1. Selection of low work function materials (metals)
2. Use of sharp point geometry
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A
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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
Diameter (width)
length
Aspect ratio = Length/diameter
Electron tunneling through barrier without E
Electron tunneling through barrier with E
+
E E E E E
Electric field evenly created on surface
E E E E E
-
E1
E2
E3
E4
voltage applied here
Energy required for electron field emission at E1 = E2 = E3 = E4
+
E E E E E
E
Field enhancement appeared at the tip
E E
E E
E
E
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E
E
E
E
voltage applied here
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.
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/r
W: work function (or effective barrier height)
h:height
r: radius
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.
Reference website
http://ipn2.epfl.ch/CHBU/NTfieldemission1.htm#Field%20emission%20basics
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.