Slide 1

Conductance in One Dimension: Nanotubes and Molecules Michael S. Fuhrer Department of Physics and Center for Superconductivity Research University of Maryland Slide 2 Outline I.Electronic properties of semiconducting carbon nanotubes a. Charge-carrier mobility b. Saturation velocity II. Electronic transport through single organometallic molecules collaborators: Larry Sita (UM Chemistry), Harold Baranger (Duke), Weitao Yang (Duke) Slide 3 Graphite Band Structure 2 identical atoms 2 electrons per unit cell 2 half-full bands - no anti-crossing Near Fermi surface: Fermi surface is six points E(k) is linear near Fermi energy bands are cones Slide 4 Rolling up Graphite to Make a Nanotube Pick a lattice vector in graphite Cut out a strip perpendicular to that vector Roll up the strip to form a tube! Graphics courtesy Rick Smalley Slide 5 Nanotube Band Structure k r R = n (integer) krkr Metal Semiconductor E k 3 0 -3 E k 2 0 - -2 ~ 350 meV/[d(nm)] v F ~ 9.3 x 10 7 cm/s Slide 6 Chemical Vapor Deposition Chemical Vapor Deposition after Dai (Stanford), Lieber (Harvard) Si SiO 2 Fe(NO 3 ) 3 C 2 H 4 CH 4 H 2 Dip chip in ferric nitrate H 2 900C Reduce to iron nanoparticles Flow methane => nanotubes C 2 H 4, CH 4, H 2 900C Slide 7 How to wire a nanotube, or: Find em and Wire em Alignment marks (Au/Cr) Nanotubes on oxidized Si substrate: Deposit nanotubes from solution or Grow nanotubes using CVD Pattern alignment markers Find nanotubes with AFM or SEM Pattern leads using e-beam lithography voltage-contrast SEM Slide 8 Crossed Nanotube Devices Crossed Nanotube Devices Fuhrer, McEuen, Zettl, et al. (2000) - UCBerkeley Optical micrograph showing five sets of leads to crossed nanotube devices AFM image of one pair of crossed nanotubes (green) with leads (yellow) Slide 9 200 m Very Long Nanotube Devices Very Long Nanotube Devices Drkop, et al., (2004) L > 300 mm Very difficult to image/locate with AFM! Optical micrograph FESEM micrograph Slide 10 Conductance of Nanotube Devices Metallic SWNTSemiconducting SWNT EFEF EFEF Conductance independent of gate voltage Acts like field-effect transistor Slide 11 Conductance Quantization in 1D lead1D Channellead E k Left-moving states Right-moving states lead1D Channellead E k Left-moving states Right-moving states E=eV Apply voltage V, Calculate current I: 2e 2 h = G o (quantum of conductance) Slide 12 How Well do Nanotubes Conduct? Generalized 1D conductance: Nanotube has 4 modes (2 bands x 2 spins) Maximum conductance (T i =1) is: or This appears as a contact resistance to 1D channel. V I (T i = transmission probability of ith mode) Slide 13 Metallic Nanotubes Metallic Nanotubes McEuen, Fuhrer, Park (2002) Conductance can approach G max = 4e 2 /h at low temperature Conductivity ~10 -6 -cm! At higher V sd : conductance drops... zone-boundary phonon emission at eV sd ~ hv Yao, Kane, Dekker (2000) But most nanotubes have G AC-EFM on Metallic SWNT Measured R = 40k R tube < 3k R contact = 40k Ballistic transport: T > for l > 1 m Bachtold, Fuhrer, et al. (2000) UC Berkeley Slide 16 What about Semiconducting Nanotubes? EFEF EFEF Slide 17 Schottky Barrier Transistor see IBM group Avouris, et al. subthreshold swing S G(V g ) fn. of Schottky barriers; not intrinsic to nanotube S is large, T-independent ambipolar behavior metalnanotubemetal c v Ti NT vacuum level e.g. titanium electrodes Ti < NT c v c v metalnanotubemetal c v Slide 18 3D Schottky Barrier metal 3D semiconductor c v metal-induced gap states metal 1D semiconductor c v metal-induced gap states 3D: Dipole causes band offset 1D: Dipole decays rapidly Ohmic contact is possible 1D Schottky Barrier Slide 19 subthreshold swing S Ohmically-Contacted Transistor Javey et al., (2003), Yaish, et al. (2003), Durkop, et al. (2004) c v c v c v metalnanotubemetal c v Au NT vacuum level e.g. gold electrodes Au > NT G(V g ) controlled by nanotube Subthreshold swing due to thermal activation over barrier S ~ T Unipolar behavior metalnanotubemetal Slide 20 Semiconducting Nanotube Conductivity L = 325 m 1D resistivity: mean-free-path (assuming 2 channels): Assume ALL resistance is in nanotube (no contact resistance): Note: comparable to good metals! Long, Ohmically contacted nanotube Slide 21 Mobility of Semiconducting NTs L = nanotube length C g = nanotube capacitance (from Coulomb blockade) V th = threshold voltage of nanotube Mobility is conductivity normalized by carrier density*: = ne In 1D: Mobility: *(alternately: ) Slide 22 Mobility of Semiconducting NTs at Room Temp. Mobility at RT Si (p): 450 cm 2 /Vs PbTe (p): 4,000 cm 2 /Vs Si (n): 1,500 cm 2 /Vs InSb (n): 77,000 cm 2 /Vs NT (p): >100,000 cm 2 /Vs! Previous room temp. record: 77,000 cm 2 /Vs (n-InSb) Drkop, et al., Nano Letters (2004) Slide 23 Pennington and Goldsman (UMCP) calculated the mobility assuming only electron-phonon scattering: = 120,000 cm 2 /Vs at RT Pennington, Goldsman, PRB 68, 045426 (2003) Is this mobility reasonable? Note: graphite has 20,000 cm 2 /Vs at RT Nanotube is a way to engineer a bandgap in graphite! Slide 24 Scanned-Gate Microscopy Voltage V g applied to tip. Image is sample conductance as a function of tip position. I(x,y) Electrostatic Force Microscopy: Apply an AC voltage to sample at tip freq. : tip will oscillate when near sample. V ac sin( o t) oo Slide 25 Semiconducting SWNT Scanned Gate Microscopy AC-EFM Bright spots = large R change Local high points in potential Resistance is 9.3k / m l = 700nm Fuhrer, et al. (2001) UMD + UCB Slide 26 Cleaner Nanotubes? suspended nanotubes (no substrate) length tens of microns Slide 27 High-bias Behavior: What Limits the Current? k=0 phonon emission at ~ 160 meV limits current to I = (4e/h) ~ 25 A But this vertical transition doesnt exist in semiconducting nanotubes... Subband spacing also much narrower intersubband scattering important? E k 3 0 -3 E k 2 0 - -2 metallicsemiconducting Yao, Kane, Dekker (2000) Slide 28 High-bias Behavior: What Limits the Current? L = 25 m Nearly perfect electron- hole symmetry: Schottky contacts Electron and hole currents can exceed 25 A (!) Nanotube w/Schottky contacts: Slide 29 Transconductance holeselectrons holeselectrons Slide 30 lead1D Channellead E k E=eV VgVg Quantization of Transconductance Conductance quantization (2 bands): Transconductance quantization (2 bands): where: c g,e is the electrostatic capacitance c q = e 2 D(E) is the quantum capacitance quantum efficiency of gate Slide 31 Charge-Controlled vs. Potential-Controlled Transistor for c g,e >> c q : gate voltage controls potential of nanotube quantum capacitance limit achievable with thin, high-k dielectrics our devices: c g,e 0.2 pF/cm 2 pF/cm gate voltage controls charge in nanotube I = qv F v F = 9.3 x 10 7 cm/s relatively independent of E (ballistic) Slide 32 Charge-Controlled Transistor contd: Ambipolar Transistor I e,d = -q v F = c g v F (V g ' - V d ), V g ' - V d 0 I h,d = q v F = c g v F (V d - V g '), V d - V g ' 0 I e,s = -q v F = c g v F (V g ' - V s ), V g ' - V s 0 I h,s = q v F = c g v F (V s - V g '), V s - V g ' 0 4 equations: electron, hole currents at source, drain V g = V g V th ; V th is threshold for electrons or holes V g -V d I e, I h slope 16.8 S EgEg increasing V d V g -V s I e, I h increasing V d I = qv F Slide 33 Charge-Controlled Model: Experiment 3.8 S holes electrons Charge-controlled model agrees qualitatively, but: Experimental slope is 3.8 S < 16.8 S Gap between onset of electron, hole currents is much greater than E g (not surprising nanotube not ballistic, has Schottky barriers) Note: electron, hole currents dont add (I = I e + I h ); rather, I = max (I e, I h ) recombination! Slide 34 EFEF c v Charge-Controlled Transistor Model w/Schottky Barriers EFEF c v VcVc negatively charged region EFEF c v V > V c EFEF c v VcVc Charge density here is that which raises potential by V - V c V Assume Schottky barrier is opaque for V < V c transparent for V > V c I e,d = -q v s = c g v s (V g ' - V d - V c ), V g ' - V d V c I h,d = q v s = c g v s (V d - V g ' - V c ), V d - V g ' V c I e,s = -q v s = c g v s (V g ' - V s - V c ), V g ' - V s V c I h,s = q v s = c g v s (V s - V g ' - V c ), V s - V g ' V c Slide 35 Velocity Saturation I = qv F Ballistic transistor: Conventional semiconductors at high bias: Velocity independent of electric field at high fields I = qv s Current reduced by factor v s /v F from ballistic case v s /v F = (3.8 S/16.8 S) 0.23 v s 2 x 10 7 cm/s V g -V d I e, I h slope 16.8 S EgEg increasing V d 3.8 S holes electrons Slide 36 V/2 -V/2 Recombination: I I e + I h ! I = max(I e, I h ) = I e = I h Differential Conductance at V g = 0 Apply V s = V/2; V d = -V/2 Electron, hole currents equal 1.9 S Slide 37 Scanned-Gate Microscopy Voltage V g applied to tip. Image is sample conductance as a function of tip position. I(x,y) Electrostatic Force Microscopy: Apply an AC voltage to sample at tip freq. : tip will oscillate when near sample. V ac sin( o t) oo Slide 38 Scanned-Gate Microscopy of Schottky Barriers 0V -8V topography -8V 0V IhIh IeIe Slide 39 Scanned-Gate Microscopy of Schottky Barriers V g = -4.5VV g = -4.3VV g = -4.1VV g = -3.9VV g = -3.7VV g = -3.5VV g = -3.3V I (A) topography -8V 0V IhIh IeIe -8V Tip = -4V (always enhances conductance) Slide 40 Conclusions: Nanotubes Hole mobility in carbon nanotubes exceeds 10 5 cm/s at room temperature, higher than any known semiconductor Mean free paths of several microns possible at room temperature Saturation velocity for electrons and holes is 2 x 10 7 cm/s, more than twice as high as in Si FETs Slide 41 Outline I.Electronic properties of semiconducting carbon nanotubes II. Electronic transport through single organometallic molecules collaborators: Larry Sita (UM Chemistry), Harold Baranger (Duke), Weitao Yang (Duke) Slide 42 Molecular Electronics Use delocalized orbital network as conducting pathway between metal elctrodes Insert functional groups to make switches which respond to electric field, light, chemical environment... Slide 43 Electromigration of Au wires nm-scale gaps after Hongkun Park (Harvard) Electromigration to failure Si Al (gate) SiO 2 Al 2 O 3 (~2-3 nm) Au side view devices fabricated at Cornell Nanoscale Facility Slide 44 Breaking Voltage for Wires fabricated at UMfabricated at CNF Slide 45 Controlling Gap Size Electromigration performed at low (substrate) temperature: quenches wire configuration after break. Substrate temperature affects residual current in bare gap junctions: hotter substrate wider gap Lower current (wider gaps) observed on SiO 2 than Al 2 O 3 ; possibly due to differences in adhesion. Slide 46 Bare nanogaps no molecules Simple tunnel junction: low conductance monotonic positive curv. of dI/dV vs. V Au particle: Coulomb blockade small charging energy many accessible charge states Slide 47 ~3nm Ferrocene-based phenylethynyl dithiol Sita group (UM Chemistry) Engtrakul, C., Sita, L. R. "Ferrocene-Based Nanoelectronics: 2,5- Diethynylpyridine as a Reversible Switching Element," NanoLetters 2001, 1, 541-549 Metal redox center + conjugated backbone Long l 3 nm Well-understood chemistry Family of chemically engineered devices Slide 48 Simple Theory: Mesoscopic Regime leadmoleculelead E=eV VgVg 2-spin, single channel transport: Perfect transmission limit G 0 = 2e 2 /h = 77.5 S Molecular levels broaden to Lorentzian resonances G(V) and G(V g ) have Lorentzian peaks 1, 2 coupling to electrodes 1,2 Slide 49 Transport in Ferrocene Species Theory Rui Liu, San-Huang Ke, Harold Baranger, Weitao Yang (Duke) DFT calculations of electronic structure Green function technique T(E) constant-density surface at resonance: conjugation extends across Fc T(E) shows resonance just above E F Slide 50 Transport in Ferrocene species Generic features: Resonance peaks Transport in Control Molecule T = 1.3 K large gap > 200 mV small conductance (< 0.01 G 0 ) G = 0 at zero bias Coulomb-blockade-like features: Slide 54 Dilemma of Molecular Electronics: Dilemma of Molecular Electronics: Conjugated organic molecules should conduct well Y. Xue, S. Datta, and M. A. Ratner, J. Chem. Phys. 115, 4292 (2001). M. DiVentra, S. T. Pantelides, and N. D. Lang, Phys. Rev. Lett. 84, 979 (2000). Y. Xue and M. A. Ratner, Phys. Rev. B 68, 115407 (2003). S.-H. Ke, H. U. Baranger, and W. Yang, http://xxx.lanl.gov/abs/cond-mat/0405047. J. Taylor, M. Brandbyge, and K. Stokbro, Phys. Rev. B 68, 121101 (2003). But experimentally, they dont M. A. Reed et al., Science 278, 252 (1997). J. Reichert et al., Appl. Phys. Lett. 82, 4137 (2003). S. Kubatkin et al., Nature 425, 698 (2003). A. M. Rawlett et al., Appl. Phys. Lett. 81, 3043 (2002). C. Zhou et al., Appl. Phys. Lett. 71, 611 (1997). J. G. Kushmerick et al., Nano Lett. 3, 897 (2003). Why? (Or why does ferrocene molecule follow the rules?) Benzene rings rotate out-of-plane in OPE Ferrocene allows flexing of molecule binding to electrodes Other disruption of -conjugation? Slide 55 Future Au Fe Au Fe Au Fe Au Family of ferrocene-based molecular electronics? Au Fe Au Fe Au Fe N Next step: diferrocene w/various linkers Alkyl chain (insulator): Conjugated linker (conductor): Linker w/dipole: Slide 56 Many Thanks! Tobias Durkop Todd Brintlinger Enrique Cobas Stephanie Getty FESEM; long NT Yung-Fu Chen velocity saturation in NT 200 m http://www.physics.umd.edu/condmat/mfuhrer Stephanie Getty Lixin Wang (UM Chem) electrical measurements on molecules Rui Liu (Duke) San-Huang Ke (Duke) Harold Baranger (Duke) Weitao Yang (Duke) molecules - theory Chai Engtrakul (UM Chem) Lixin Wang (UM Chem) Laura Picraux (UM Chem) Larry Sita (UM Chem) molecules synthesis, characterization