* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download 投影片 1 - National Tsing Hua University
Survey
Document related concepts
Quantum vacuum thruster wikipedia , lookup
Electromagnetism wikipedia , lookup
Electromagnet wikipedia , lookup
Electric charge wikipedia , lookup
Condensed matter physics wikipedia , lookup
Lorentz force wikipedia , lookup
Mathematical formulation of the Standard Model wikipedia , lookup
Electron mobility wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Field (physics) wikipedia , lookup
Superconductivity wikipedia , lookup
Electrical resistivity and conductivity wikipedia , lookup
Transcript
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 B0 B0 N N B~0 B S S B0 large deflection B0 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 B0 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 (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) 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 + + + + + + + + + + + + + + + + + + + + + 111 + + + + + ++ ++ ++ ++ ++ + + + + + + + + + + + + 110 Polarized surface + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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 + + - - 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 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 - 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.