Topics on Molecular Electronics

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Topics on Molecular Electronics M. F.
Goffman Laboratoire dÉlectronique Moléculaire
CEA Saclay
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Introduction

• Feynmans Talk in 1959
• There is Plenty of Room at the Bottom
• http//www.zyvex.com/nanotech/feynman.html
• "I don't know how to do this on a small scale in
  practical way, but I do know that computing
  machines are very large they fill rooms. Why
  can't we make them very small, make them of litle
  wires, little elements- and by little, I mean
  little. For instance, the wires should be 10 or
  100 atoms in diameter, and the circuits should be
  a few thousand of angstroms acrossthere is
  plenty of room at the bottom to make them
  smaller. There is nothing that I can see in the
  physical laws that says the computer elements
  cannot be made enormously smaller than they are
  now. In fact, there may be certain advantages."

Can we control the position of individual
Molecules to make them do useful tasks?
Can we use electronic properties of Molecules to
build up devices?
? MOLECULAR ELECTRONICS
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Molecular Electronics possible building blocks
Synthetic Molecules
Nanoparticules

• electronic properties Û chemical structure
• easy to fabricate IDENTICAL in huge quantities
  (1023)
• Self-assembly

quantification of energy levels
ADN/ARN
Nanotubes de carbone Nano-leads

• Self-assembly Þ templates for other nano-objects

• Metallic or semiconducting
• Link between µm and nm scale

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Why Synthetic Molecules?

• Electronic functions can be adjusted by design
  of the chemical structure

Diodes
Switches
Storage
In principle a whole set of functions can be
embedded in a circuit by appropriate choice of
the molecule
Electronic Function is a property of the
Metal-Molecule-Metal structure
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Basic device Metal-Molecule-Metal junction
Electronic Function is a property of the
Metal-Molecule-Metal structure
Current-Voltage (IV) Characteristic (Electronic
Function)
I
V
Source
Drain
Metal-Molecule Coupling (G) plays a key role
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Scanning Tunneling Microscope as a two electrode
probe
Topographic measurement (I fixed)
C. Joachim et al Phys. Rev. Lett. 74
(1995)2102 S. Datta et al Phys. Rev. Lett.
79(1997) 2530 L. A. Bumm et al Science 271
(1996) 1705 A. Dhirani et al J. Chem. Phys. 106
(1997) 5249 V. Langlais et al, Phys. Rev. Lett.
83 (1999) 2809 L. Patrone et al Chem Phys. 281
(2002) 325
Drawbacks
Advantages
Asymmetric contacts Reduced in plane position
stability no gating I(V) spectroscopy only in
rare cases
Imaging and electrical measurements Tip
Manipulation
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STM experiments on C60 (I)
IV measurement (z fixed)
D. Porath et al. J. Appl. Phys. 81, 2241
(1997) Phys. Rev. B 56, 9829 (1997)
C60 molecule
C60 Monolayer

• Current "blocked" up to Vth
• IV highly non-linear

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STM experiments on C60 (II)
C. Joachim et al. Phys. Rev. Lett. 74, 2102
(1995) Europhys. Lett. 30, 409 (1995)
C60 molecules on Au 110

• Linear IV characteristic at low V

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Metal- Molecule Coupling G plays a key role
V
V
I
I
Weak coupling regime
Strong coupling regime
single electron effects ? Coulomb addition energy
Eadd
Strong hybridization ? Coherent transport
(Landauer-Buttiker formalism)
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Outline I
Molecular conduction in the weak limit regime

• Energy diagram of the metal-molecule-metal
  structure
• Description of metallic electrodes
• Characteristic energies of the molecule Eadd
  and Molecular Levels (ML)
• Coupling to metallic electrodes G

• Weak Coupling limit G?Eadd ? Single electron
  effects

Analogy with Quantum Dots
Revisiting Quantum Dot physics Addition
spectrum from conductance measurements
Stability Diagram in the (V,Vg) plane

• Experiments on single molecules in the weak
  coupling limit

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1. To Build Up the Energy Level Diagram
Weak Coupling G ? Transfer of e- by sequential
tunneling
In the transport process the molecule will be
oxydized or reduced
Metal Reservoir
Metal Reservoir
Molecule
M0 ?M
?M0
M0?M -
?M0

• Description of metallic electrodes ? Energy cost
  for extracting a conduction electron

• Description of the molecule ?? Energies involved
  in reactions M0 ? M
• M0 ? M -

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Metallic Electrodes
In the independent electron approximation
Ground state of N (1023 ) electrons system ?
energy levels of a single electron
W
empty states
Fermi level µ
occupied states
For Au(111) W 5.3 eV
Good aproximation continuous distribution of
states
W Energy required to remove an electron (Work
function)
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Energy Level Diagram
Molecule
Metal Reservoir
Metal Reservoir
Characteristic Energies of a Molecule
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Isolated Molecule
The density functional theory (DFT) can provide
the ground state energy of the molecule M0 and
its ions M?k.
E(N) Total energy of the N-electron Molecule (M
0)
Energy Levels and Total Energy E(N)
E(N)
LUMO
HOMO
??
??
of electrons
N1
N -1
N
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Characteristic energies of a molecule
E(N) Total energy of the N-electron Molecule (M
0)
E(N)
N1
N -1
of electrons
N
Ionization Potential
Electron affinity
How this characteristic energies determine the
Coulomb addition energy Eadd ?
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Coulomb Addition Energy Eadd of an Isolated
Molecule
The Coulomb Addition Energy is defined as
The capacitance of a charged system can be
defined as
Amount of work per unit charge, DV, required to
bring a fixed charged, DQ, from the vacuum level
to the system
From an atomistic viewpoint
Since
Electron affinity
Ionization Potential
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Energy Diagram of an isolated molecule
Eadd
Example
Isolated C60 in vacuum I07.58 eV and A02.65 eV
? Eadd 4.93 eV
Can we estimate Eadd using the geometry of the
molecule ?
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Geometrical Calculation of Eadd
The geometrical capacitance
D
D7.110.2 Å
Does this estimation generally work?
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Experiments vs Geometrical Estimation
For Molecules DFT reveals
If HOMO level is fully populated
The Larger N
Better the agreement
Important remark
Ionization and Affinity of the molecule depends
on the environment where the molecule is
embedded.
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Modification by Metallic Electrodes (Image
Potential Effect)
Ex. adsorbed molecule
M-1
M1
e-
e
-

x
d
The image force acting on the outgoing electron
at position x is
The resulting force is repulsive for x gt d and I0
is decreased by an amount
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Modification by Metallic Electrodes (Image
Potential Effect)
Similarly, when an additional electron approaches
and thus
For C60 weakly coupled to a metal electrode
For d 6.2 Å (van der Waals)
D ? 7.1 Å
d
Addition energy of the embedded molecule Eadd is
modified by metallic electrodes as
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Coupling to Metallic Electrodes (G)
G can be related to the time t it takes for un
electron to escape into the metallic contact
G
M0
Metal Reservoir
can be interpreted as the rate at which electrons
are injected into the molecule from the contact
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Characteristic Energies of the Metal-Molecule-Meta
l structure
determined by the extent of the electronic wave
function in the presence of metal electrodes.
determined by the overlap of the electronic wave
function and the delocalized wave function of
metal electrodes.
Weak Coupling ?
Transfer of e- by sequential tunneling
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Energy Diagram of Metal-Molecule-Metal structure
In equilibrium, V0 ? Statistical Mechanics
The probability of having N electrons in the
Molecule is
?
if (I-W) and (W-A) are greater than kBT ? The
molecule will remain neutral (N0)
? Current will be blocked (Coulomb blockade)
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Energy Diagram of Metal-Molecule-Metal structure
µL
µR µLµ
Eadd
When current will flow?
More generally electrons can flow when
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Analogy with quantum dot
For a Molecule
For a Quantum Dot (JanMartineks lectures)
µL
µL
µR
µR
Transport experiment in weak coupling limit
spectroscopy of a molecule embedded in a circuit
Does the Constant Interaction Model used for QD
apply to Single molecules?
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Revisiting Quantum Dot Theory (few electron QD)
Constant Interaction Model

• Electron-electron interactions are parameterized
  by a constant capacitance C
• Single electron energy spectrum calculated for
  non-interacting e- is unaffected by interactions

The total ground state energy of an N electron
dot can be approximated by
CL
CR
I
QD
L
R
Cg
-V/2
V/2
Where
Vg
Chemical potential of the dot is
Chemical Potential of the Electrodes are
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Measuring the Addition Spectrum
L
R
Electrons can flow when
At V?0
N0
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Measurering the Addition Spectrum
L
R
Electrons can flow when
At V?0
N0
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Measurering the Addition Spectrum
L
R
Electrons can flow when
At V?0
N0
N01
N02
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Measuring the Addition Spectrum
L
R
Electrons can flow when
µL
µR
At V?0
N0
N01
N02
N0-1
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1
N01
N0-1
N0
2
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Stability Diagram
3
1
V
N01
N0
N0-1
VC(N0) is obtained by equating
Then
Stability diagram ? Experimental determination of
the addition spectrum Eadd(N)
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Experiments on Single Molecules
To address single molecules individually
1. Fabricate two metallic electrodes separated
by the size of the molecule ? Small
molecules 1-3nm ? Long Molecules (like
CNT or DNA) 100 nm
2. Connect the molecule to the electrodes
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Fabrication of Single-Molecule Transistors I
S. Kubatkin,et al, Nature 425, 698 (2003).
Shadow evaporation technique _at_ 4.2K
3. Annealing _at_ 70 K for activating thermal
motion of molecules
4. Monitoring of I for trapping detection
1. Electrode separation controlled by a in situ
conductance measurements (2nm GW )
2. Deposition of OPV5 molecules by quench
condensation _at_ low temperatures
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Experimental Results on OPV5
Addition Energy Spectrum
S. Kubatkin,et al, Nature 425, 698 (2003).
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Experimental Results on OPV5
Image charge effect ? localization of charges
near electrodes
Hubbard Model
pz orbitals
t adjusted to give the optical H-L gap (2.5 eV)
where d 4.7 Å
in reasonable agreement with van der Waals
distances
Eadd strongly depends on the embedding
environement of the molecule
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Fabrication of Single-Molecule Transistors II
Electromigration-induced break-junctions
H. Park et al., APL 1999 M. Lambert et al
Nanotech. 2003.
Adsorption of molecules
Breakdown Trapping
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C60 based Single Electron Transistor
Al2O3
without C60
I
with C60
V is swept up to 2.5 V to ensure I though the
junction in the tunneling regime.
I
Vg
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C60 based Single Electron Transistor
IV characteristics _at_ different gate bias Vg

• strongly suppressed conductance near zero bias
• step-like current jumps at higher voltages

• The voltage width of the zero-conductance region
  modulated by Vg

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Experiments C60 based Single Electron Transistor
Two-dimensional Differential Conductance
(G?I/?V) plot (4 different samples)
G (nS)
0
N
N1
N
N1
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N
N
N1
N1
What are the meaning of the lines (white arrows)
parallel to the boundary of the Coulomb
diamonds?
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Excitation Spectrum
Excited States (ES) of N-charged Molecule
Vg
N-1
N
Excited States (ES) of (N-1)-charged Molecule
Tunneling into GS or ES of N-charged Molecule
Tunneling out from GS or ES of (N-1)-charged
Molecule
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C60 transistor Excitation Spectrum
Park et al Nature 407 57-60(2000)
Experimental Facts
5meV excitation energy independent of the number
N of electrons in the C60 molecule
Excited electronic states?
No
Vibrational excitation ?
Possible
Coupling between vibronic modes and electrons are
important
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Experiments on OPV5
Van der Zant group (DELFT)
Molecular vibration assisted tunneling
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Conclusions
In the weak coupling limit
Transport experiment spectroscopy of a
molecule embedded in a circuit
Addition Spectrum Eadd(N)
Excited states
Experiments show that spectra are not
well-described by simple models of
non-interacting electrons (Constant Interaction
Model)
Why study the spectra of discrete states ?
Good way to learn about the consequences of
electron interactions at a very fundamental level
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Single molecule transistor
McEuen Ralph groups Nature 2002 Park group
Nature 2002
Charge state of Co ion well defined
Co2? Co3
3d7
3d6
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Kondo Resonance