Conductance%20in%20One%20Dimension:%20Nanotubes%20and%20Molecules

1
Conductance in One Dimension Nanotubes and
Molecules
Michael S. Fuhrer Department of Physics
and Center for Superconductivity
Research University of Maryland
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)

3
Graphite Band Structure
2 identical atoms 2 p electrons per unit cell
2 half-full p bands - no anti-crossing
Near Fermi surface
Fermi surface is six points E(k) is linear
near Fermi energy bands are cones
4
Rolling up Graphite to Make a Nanotube
Graphics courtesy Rick Smalley

• Pick a lattice vector in graphite
• Cut out a strip perpendicular
• to that vector

• Roll up the strip
• to form a tube!

5
Nanotube Band Structure
Metal
Semiconductor
kr
krR n (integer)
6
Chemical Vapor Depositionafter Dai (Stanford),
Lieber (Harvard)
Fe(NO3)3
Dip chip in ferric nitrate
SiO2
Si
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How to wire a nanotube, orFind em and Wire em

• 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
8
Crossed Nanotube Devices Fuhrer, McEuen, Zettl,
et al. (2000) - UCBerkeley
AFM image of one pair of crossed nanotubes
(green) with leads (yellow)
Optical micrograph showing five sets of leads to
crossed nanotube devices
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Very Long Nanotube Devices Dürkop, et al., (2004)
FESEM micrograph
Optical micrograph
200 ?m
200 ?m
L gt 300 mm Very difficult to image/locate with
AFM!
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Conductance of Nanotube Devices
Metallic SWNT
Semiconducting SWNT
EF
Conductance independent of gate voltage
Acts like field-effect transistor
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Conductance Quantization in 1D
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How Well do Nanotubes Conduct?
Generalized 1D conductance Nanotube has 4
modes (2 bands x 2 spins) Maximum conductance
(Ti1) is or This appears as a contact
resistance to 1D channel.
(Ti transmission probability of ith mode)
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Metallic NanotubesMcEuen, Fuhrer, Park (2002)
Conductance can approach Gmax 4e2/h at low
temperature
At higher Vsd conductance drops...
zone-boundary phonon emission at eVsd hv Yao,
Kane, Dekker (2000)
Conductivity 10-6 W-cm!
But most nanotubes have G ltlt 4e2/h Where is
extra resistance?
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Scanned-Gate Microscopy
Electrostatic Force Microscopy
Apply an AC voltage to sample at tip freq. wo
tip will oscillate when near sample.
I(x,y)
Voltage Vg applied to tip. Image is sample
conductance as a function of tip position.
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AC-EFM on Metallic SWNT
Bachtold, Fuhrer, et al. (2000) UC Berkeley
Measured R 40kW
Rtube lt 3kW Rcontact 40kW
Ballistic transport T gt ½ for l gt 1mm
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What about Semiconducting Nanotubes?
EF
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Schottky Barrier Transistorsee IBM group
Avouris, et al.
metal
nanotube
metal
v
c
?Ti
?NT
vacuum level

• G(Vg) fn. of Schottky barriers
• not intrinsic to nanotube
• S is large, T-independent
• ambipolar behavior

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3D Schottky Barrier
1D Schottky Barrier
metal-induced gap states
v
c
3D semiconductor
metal
1D Dipole decays rapidly Ohmic contact is
possible
3D Dipole causes band offset
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Ohmically-Contacted TransistorJavey et al.,
(2003), Yaish, et al. (2003), Durkop, et al.
(2004)

• G(Vg) controlled by nanotube
• Subthreshold swing due to
• thermal activation over barrier
• S T
• Unipolar behavior

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Semiconducting Nanotube Conductivity
Assume ALL resistance is in nanotube (no contact
resistance)
1D resistivity
Long, Ohmically contacted nanotube
mean-free-path (assuming 2 channels)
L 325 mm
comparable to good metals!
Note
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Mobility of Semiconducting NTs
Mobility is conductivity normalized by carrier
density s nem
In 1D
Mobility
L nanotube length Cg nanotube
capacitance (from Coulomb blockade) Vth
threshold voltage of nanotube
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Mobility of Semiconducting NTs at Room Temp.
Mobility at RT Si (p) 450
cm2/Vs PbTe (p) 4,000 cm2/Vs Si (n)
1,500 cm2/Vs InSb (n) 77,000 cm2/Vs
NT (p) gt100,000 cm2/Vs!
Dürkop, et al., Nano Letters (2004)
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Is this mobility reasonable?
Pennington and Goldsman (UMCP) calculated the
mobility assuming only electron-phonon
scattering µ 120,000 cm2/Vs at RT
Note graphite has µ ? 20,000 cm2/Vs at
RT Nanotube is a way to engineer a bandgap in
graphite!
Pennington, Goldsman, PRB 68, 045426 (2003)
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Scanned-Gate Microscopy
Electrostatic Force Microscopy
Apply an AC voltage to sample at tip freq. wo
tip will oscillate when near sample.
I(x,y)
Voltage Vg applied to tip. Image is sample
conductance as a function of tip position.
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Semiconducting SWNT
Fuhrer, et al. (2001) UMD UCB
Scanned Gate Microscopy
Bright spots large R change Local high points
in potential
AC-EFM
Resistance is 9.3kW/mm l 700nm
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Cleaner Nanotubes?
suspended nanotubes (no substrate) length tens of
microns
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High-bias Behavior What Limits the Current?
metallic
semiconducting
k0 phonon emission at hO 160 meV limits
current to I (4e/h) hO 25 µA
But this vertical transition doesnt exist in
semiconducting nanotubes... Subband spacing also
much narrower ? intersubband scattering
important?
Yao, Kane, Dekker (2000)
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High-bias Behavior What Limits the Current?
Nanotube w/Schottky contacts
L 25 µm
Nearly perfect electron-hole symmetry Schottky
contacts
Electron and hole currents can exceed 25 µA (!)
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Transconductance
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Quantization of Transconductance
lead
1D Channel
lead
Conductance quantization (2 bands)
Transconductance quantization (2 bands)
quantum efficiency of gate
where cg,e is the electrostatic capacitance cq
e2D(E) is the quantum capacitance
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Charge-Controlled vs. Potential-Controlled
Transistor
for cg,e gtgt cq
gate voltage controls potential of
nanotube quantum capacitance limit achievable
with thin, high-k dielectrics
our devices
cg,e 0.2 pF/cm
2 pF/cm
gate voltage controls charge in nanotube
vF 9.3 x 107 cm/s relatively independent of E
I qvF
(ballistic)
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Charge-Controlled Transistor contdAmbipolar
Transistor
I qvF
4 equations electron, hole currents at source,
drain
Ie,d -q vF cg vF (Vg' - Vd), Vg' - Vd ?
0 Ih,d q vF cg vF (Vd - Vg'), Vd - Vg' ?
0 Ie,s -q vF cg vF (Vg' - Vs), Vg' - Vs ?
0 Ih,s q vF cg vF (Vs - Vg'), Vs - Vg' ? 0
Vg Vg Vth Vth is threshold for electrons or
holes
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Charge-Controlled Model Experiment

• Charge-controlled model
• agrees qualitatively, but
• Experimental slope is
• 3.8 µS lt 16.8 µS
• Gap between onset of
• electron, hole currents
• is much greater than Eg
• (not surprising nanotube not ballistic, has
  Schottky barriers)

Note electron, hole currents dont add (I Ie
Ih) rather, I max (Ie, Ih) ? recombination!
34
Charge-Controlled Transistor Modelw/Schottky
Barriers
Assume Schottky barrier is opaque for V lt
Vc transparent for V gt Vc
Ie,d -q vs cg vs (Vg' - Vd - Vc), Vg' - Vd
? Vc Ih,d q vs cg vs (Vd - Vg' - Vc), Vd -
Vg' ? Vc Ie,s -q vs cg vs (Vg' - Vs - Vc),
Vg' - Vs ? Vc Ih,s q vs cg vs (Vs - Vg' -
Vc), Vs - Vg' ? Vc
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Velocity Saturation
I qvF
Ballistic transistor
Conventional semiconductors at high
bias Velocity independent of electric field at
high fields
I qvs
Current reduced by factor vs/vF from ballistic
case vs/vF (3.8 µS/16.8 µS) 0.23 vs 2 x 107
cm/s
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Differential Conductance at Vg 0
Apply Vs V/2 Vd -V/2
Electron, hole currents equal
Recombination I ? Ie Ih! I max(Ie, Ih)
Ie Ih
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Scanned-Gate Microscopy
Electrostatic Force Microscopy
Apply an AC voltage to sample at tip freq. wo
tip will oscillate when near sample.
I(x,y)
Voltage Vg applied to tip. Image is sample
conductance as a function of tip position.
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Scanned-Gate Microscopy of Schottky Barriers
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Scanned-Gate Microscopy of Schottky Barriers
Tip -4V (always enhances conductance)
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Conclusions Nanotubes

• Hole mobility in carbon nanotubes exceeds 105
  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 107 cm/s, more than twice as high as in Si FETs

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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)

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Molecular Electronics
Use delocalized p orbital network as conducting
pathway between metal elctrodes Insert
functional groups to make switches which respond
to electric field, light, chemical environment...
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Electromigration of Au wires ? nm-scale
gapsafter Hongkun Park (Harvard)
Electromigration to failure
Al2O3 (2-3 nm)
Au
Al (gate)
SiO2
Si
side view
devices fabricated at Cornell Nanoscale Facility
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Breaking Voltage for Wires
fabricated at UM
fabricated at CNF
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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 SiO2 than Al2O3 possibly due to differences
in adhesion.
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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

47
Ferrocene-based phenylethynyl dithiolSita group
(UM Chemistry)

• Metal redox center conjugated backbone
• Long l 3 nm
• Well-understood chemistry
• Family of chemically engineered devices

3nm

• Engtrakul, C., Sita, L. R. "Ferrocene-Based
  Nanoelectronics 2,5-Diethynylpyridine as a
  Reversible Switching Element," NanoLetters 2001,
  1, 541-549

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Simple Theory Mesoscopic Regime
lead
molecule
lead
DEeV
Vg
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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 conjugatio
n extends across Fc
T(E) shows resonance just above EF
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Transport in Ferrocene species

• Generic features
• Resonance peaks lt100 mV
• Conductance 0.1-1 G0

• Finite G at V 0
• Low-energy structure

Strong coupling Gate Ineffective
Moderate coupling Working Gate Electrode
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Control Molecule

• oligo-Phenylethynyl dithiol (OPE)
• Replace ferrocene with phenyl ring
• Keep 3-nm length
• Similar molecules studied extensively
  experimentally and theoretically

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Control Molecule Theory Rui Liu, San-Huang
Ke, Harold Baranger, Weitao Yang (Duke)
constant-density surface at resonance first
particle-in-box state
T(E) shows resonance just above EF
Should also conduct well...
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Transport in Control Molecule
T 1.3 K
Coulomb-blockade-like features

• large gap ? gt 200 mV
• small conductance (lt 0.01 G0)
• G 0 at zero bias

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Dilemma of Molecular ElectronicsConjugated
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 p-conjugation?
55
Future
Family of ferrocene-based molecular electronics?
Next step diferrocene w/various linkers
Au
Au
Fe
Fe
Alkyl chain (insulator)
Au
Au
Fe
Fe
Conjugated linker (conductor)
Au
Au
Fe
Fe
Linker w/dipole
N
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Many Thanks!
Tobias Durkop Todd Brintlinger Enrique
Cobas Stephanie Getty FESEM long NT
Yung-Fu Chen velocity saturation in NT
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
Stephanie Getty Lixin Wang (UM Chem) electrical
measurements on molecules
http//www.physics.umd.edu/condmat/mfuhrer