Transcript part 1

Topics on Molecular Electronics
M. F. Goffman
Laboratoire d’Électronique Moléculaire
CEA Saclay
M. F. Goffman
Introduction
• Feynman’s 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 across…there 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
M. F. Goffman
Molecular Electronics: possible building blocks
Synthetic Molecules
O
S
S
S
S
S
Nanoparticules
O
• electronic properties  chemical structure
• easy to fabricate IDENTICAL in huge quantities (1023)
• Self-assembly
ADN/ARN
• Self-assembly  templates for other nano-objects
quantification of energy levels
Nanotubes de carbone
Nano-leads
• Metallic or semiconducting
• Link between µm and nm scale
M. F. Goffman
Why Synthetic Molecules?
• Electronic functions can be adjusted by design of the chemical structure
Molecular Wires
Switches
Diodes
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
M. F. Goffman
Basic device: Metal-Molecule-Metal junction
Electronic Function is a property of the Metal-Molecule-Metal structure
Current-Voltage (IV) Characteristic (Electronic Function)
V
Source
Drain
I
Metal-Molecule Coupling (G) plays a key role
M. F. Goffman
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
piezo scanning
unit
I=cte
Metallic
Tip
z
V
Electrically conducting surface
Advantages
Imaging and electrical measurements
Tip Manipulation
Drawbacks
Asymmetric contacts
Reduced in plane position stability
no gating
I(V) spectroscopy only in rare cases
M. F. Goffman
STM experiments on C60 (I)
Topographic measurement (I fixed)
z
GT
V
Insulating
layer
IV measurement (z fixed)
V
GS
I
I=cte
D. Porath et al.
J. Appl. Phys. 81, 2241 (1997)
Phys. Rev. B 56, 9829 (1997)
C60 Monolayer
C60 molecule
• Current "blocked" up to Vth
• IV highly non-linear
M. F. Goffman
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
V
I
• Linear IV characteristic at low V
M. F. Goffman
Metal- Molecule Coupling G plays a key role
V
V
I
Weak coupling regime
single electron effects

Coulomb addition energy Eadd
I
Strong coupling regime
Strong hybridization  Coherent transport
(Landauer-Buttiker formalism)
M. F. Goffman
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
M. F. Goffman
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
e
e
Molecule
Metal
Reservoir
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 
M0 
M+
M-
M. F. Goffman
Metallic Electrodes
In the independent electron approximation
Ground state of N (~1023 ) electrons system  energy levels of a single electron
-
2
2m
2  r   U  r    E  r 
Vacuum Level
empty
states
W
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)
M. F. Goffman
Energy Level Diagram
Molecule
Metal
Reservoir
Metal
Reservoir
Characteristic Energies of a Molecule
M. F. Goffman
Isolated Molecule
1023 )
Isolated Molecule (M0) : Strong correlated N-electron system with (N
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)
M+
MM0
LUMO
HOMO
??
??
# of electrons
N -1
N
N+1
M. F. Goffman
Characteristic energies of a molecule
E(N) : Total energy of the N-electron Molecule (M 0)
E(N)
M+
MM0
N -1
I0  E N - 1 - E N  -µMOL N
Ionization Potential
N
N+1
# of electrons
A0  E N - E N  1  -µMOL N  1
Electron affinity
How this characteristic energies determine the Coulomb addition energy Eadd ?
M. F. Goffman
Coulomb Addition Energy Eadd of an Isolated Molecule
The Coulomb Addition Energy is defined as
Eadd
e2

CMOL
CMOL : Capacitance of the molecule
The capacitance of a charged system can be defined as
1
CMOL

V
Q
Amount of work per unit charge, V, required to bring a
fixed charged, Q, from the vacuum level to the system
From an atomistic viewpoint
eV   N  N -  N
Q  eN
e2
 MOL N  1 - MOL N
CMOL
with N  1 
MOL N : Chemical Potential of the molecule
Since
MOL N  1  E N  1 - E N  -A0 N
MOL N  E N - E N - 1  -I0 N
Electron affinity
Ionization Potential
Eadd  I0 - A 0
M. F. Goffman
Energy Diagram of an isolated molecule
Vacuum Level
-A0  µ N  1
Eadd
-I0  µ N
Example
Isolated C60 in vacuum I0=7.58 eV and A0=2.65 eV
 Eadd = 4.93 eV
k B T @ RT ( 0.025 eV )
Can we estimate Eadd using the geometry of the molecule ?
M. F. Goffman
Geometrical Calculation of Eadd
I0 - A 0  4.93 eV
The geometrical capacitance
D
D=7.1~10.2 Å
e2
e2

  2.8
C G 20D
Why is underestimated ?
4.1 eV
M0
Anwser:C60 has a completely filled HOMO
LUMO (N0 ) - HOMO (N0 )  1.5 1.7 eV
Eadd
e2

 LUMO (N0 ) - HOMO (N0 )   3.3
CG
5.8  eV
Does this estimation generally work?
M. F. Goffman
Experiments vs Geometrical Estimation
For Molecules DFT reveals
I - A (eV)
10
I N - A N  
LUMO
0
(N) - 
e2
(N) 
CG
If HOMO level is fully populated
C60
5
HOMO
C70
0
5
e2/CG
The Larger N
10

Better the agreement
Important remark:
Ionization and Affinity of the molecule depends on
the environment where the molecule is embedded.
M. F. Goffman
Modification by Metallic Electrodes (Image Potential Effect)
Ex. adsorbed molecule
e+
M-1
M+1
+
-
ex
d
The image force acting on the outgoing electron at position x is

e2  1
1
Fx 


4 0   2 x 2  x  d2 


The resulting force is repulsive for x > d and I0 is decreased by an amount

e2
Wim   Fx .dx 
160 d
d
 I  I0 - Wim
M. F. Goffman
Modification by Metallic Electrodes (Image Potential Effect)
Similarly, when an additional electron approaches
and thus
e2 
1 
Fx 

4 0   2 x 2 


d
A  A 0 -  Fx .dx  A 0  Wim

For C60 weakly coupled to a metal electrode
For d = 6.2 Å
D  7.1 Å
d
(van der Waals)
Eadd  I0 - A 0 - 2Wim  3.8 eV
CG  20  f  d,D

e2
CG
  LUMO - HOMO 
3.9 eV
Addition energy of the embedded molecule Eadd is modified by metallic electrodes as
Eadd  I - A
M. F. Goffman
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
t
M0
G
M0
Metal
Reservoir
Isolated Molecule
tG 0
G
t finite  G finite
can be interpreted as the rate at which electrons
are injected into the molecule from the contact
M. F. Goffman
Characteristic Energies of the Metal-Molecule-Metal structure
Eadd
determined by the extent of the electronic wave function
in the presence of metal electrodes.
Eadd  I - A
G
determined by the overlap of the electronic wave function and
the delocalized wave function of metal electrodes.
Weak Coupling  Eadd
G
Transfer of e- by sequential tunneling
M. F. Goffman
Energy Diagram of Metal-Molecule-Metal structure
Vacuum Level
-A  µMOL N0  1
GL
µL
W
GR
µR= µL=µ
Eadd
-I  µMOL N0 
In equilibrium, V=0  Statistical Mechanics
The probability of having N electrons in the Molecule is
pN 

1 - E N -µN / kB T
e
Z
PN0 1  PN0 .e
- µMOL (N0 1) -µ / kB T
- E N -µN / k B T
where Z= e 
N
and PN0 -1  PN0 .e
- µ-µMOL (N0 )  / kB T
if (I-W) and (W-A) are greater than kBT  The molecule will remain neutral (N0)
 Current will be blocked (Coulomb blockade)
M. F. Goffman
Energy Diagram of Metal-Molecule-Metal structure
Vacuum Level
-A  µMOL N0  1
GL
µL
GR
µR= µL=µ
Eadd
-I  µMOL N0 
PN0 1  PN0 .e
- µMOL (N0 1) -µ / kB T
and PN0 -1  PN0 .e
- µ-µMOL (N0 )  / kB T
When current will flow?
Answer : when PN0  PN0 1 or PN0  PN0 -1
a V  0 will induce a current through intermediate states:
N0  N0  1  N0  N0  1 

µ  µMOL N0  1
N0  N0 - 1  N0  N0 - 1 

µ  µMOL N0 
More generally electrons can flow when µL  MOL N  µR
M. F. Goffman
Analogy with quantum dot
For a Molecule
For a Quantum Dot (JanMartinek’s lectures)
Vacuum Level
Vacuum Level
DOT N  1
-A  MOL N  1
µL
eV
-I
MOL N
µR
eV
µL
DOT N
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?
M. F. Goffman
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
2
e
2
E N 
N - q0 / e   i

2C
i 1
N
Where C  CL  CR  C g
L
CL
CR
R
QD
Cg
-V/2
Vg
I
V/2
Chemical potential of the dot is
e2
DOT N  E N - E N - 1 
N - q0 / e - 1 / 2  N
C
Chemical Potential of the Electrodes are
L   e V  e Vg
R  - e 1 -   V  e Vg
where =
2CR  C g
2C
and =
Cg
M. F. Goffman
C
Measuring the Addition Spectrum
L
e2
DOT N 
N - q0 / e - 1 / 2  N
C
R
DOT N0  2
µL
L   e V  e Vg
DOT N0  1
µR
DOT N0 
R  - e 1 -  V  e Vg
Electrons can flow when
DOT N0 - 1
µL  DOT N  µR
At V0
G  I / V
N0
 Vg
M. F. Goffman
Measurering the Addition Spectrum
L
e2
DOT N 
N - q0 / e - 1 / 2  N
C
R
DOT N0  2
µL
µ
L
µL
µR
µ
R
µR
DOT N0  1
DOT N0 
L   e V  e Vg
R  - e 1 -  V  e Vg
Electrons can flow when
DOT N0 - 1
µL  DOT N  µR
At V0
G  I / V
N0
VgN0 1
 Vg
M. F. Goffman
Measurering the Addition Spectrum
L
µ
µLL
µ
L
e2
DOT N 
N - q0 / e - 1 / 2  N
C
R
µ
µRR
µ
R
DOT N0  2
L   e V  e Vg
DOT N0  1
R  - e 1 -  V  e Vg
DOT N0 
Electrons can flow when
DOT N0 - 1
µL  DOT N  µR
At V0
G  I / V
N0
N0+1
VgN0 1
N0+2
VgN0  2
 Vg
M. F. Goffman
Measuring the Addition Spectrum
L
e2
DOT N 
N - q0 / e - 1 / 2  N
C
R
DOT N0  2
L   e V  e Vg
DOT N0  1
R  - e 1 -  V  e Vg
DOT N0 
µL
Electrons can flow when
µR
DOT N0 - 1
At V0
µL  DOT N  µR
G  I / V
N0-1
VgN0 -1
N0
VgN0
N0+1
VgN0 1
N0+2
VgN0  2
 Vg
M. F. Goffman
At a given Vg


VgN0  Vg  VgN0 1 current will flow if
DOT N0  1
µL
µL
µL
µL
µR
µR
DOT N0 
DOT N0  1
DOT N0 
DOT N0 - 1
DOT N0 - 1
1
N0
g
R  e  V

VVgN0 - Vg
1-

N0  N0 - 1  N0
1
DOT N0 - 1
2
 N0 1
Vg - Vg



3
3
N0+1
N0
µR
µR
DOT N0 
VgN0 1
 Vg
N0  N0  1  N0
4
4
µL
µL
DOT N0  1
µR
µR
DOT N0 
DOT N0 - 1
2
L  e  VgN0  V 

VgN0
L  e VgN0 1  V 
V
N0-1
DOT N0  1
µL
µL
µR
µR
 N0
Vg - Vg




N0 1
R  e VgN0 1  V  V
- Vg
g
M.1F.-Goffman



Stability Diagram
1
V-

VgN0 - Vg
1-


VC N0 
N0-1
V
V
N0+1
N0
VgN0
 N0 1
Vg - Vg



3
 Vg
VgN0 1
-VC N0 
VC(N0) is obtained by equating
VC N0   -

 N0 1
VgN0 - VgC 
Vg - VgC
1-





 VgC  VgN0  1 -  VgN0 1
Then
VC N0   Eadd N0 
Stability diagram  Experimental determination of the addition spectrum Eadd(N)
M. F. Goffman
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
M. F. Goffman
Fabrication of Single-Molecule Transistors I
Shadow evaporation technique @ 4.2K

S. Kubatkin,et al, Nature 425, 698 (2003).
3. Annealing @ 70 K for activating
thermal motion of molecules
PMMA
Al2O3
4. Monitoring of I for trapping detection
Al Gate
Oxidized Si wafer
1. Electrode separation controlled by 
in situ conductance measurements
(2nm ~ GW
2. Deposition of OPV5 molecules by quench
condensation @ low temperatures
I
V/2
Vg
-V/2
M. F. Goffman
Experimental Results on OPV5
Addition Energy Spectrum
S. Kubatkin,et al, Nature 425, 698 (2003).
400
#1
#2
#3
Eadd (meV)
350
300
250
200
150
100
50
-3
-2
-1
0
1
2
3
N
Interpretation within the CI model
M-2
M-
M++
LUMO
HOMO
M+
LUMO
HOMO
Eadd  -2  E
Eadd  -1  E
M0
LUMO
HOMO
LUMO
HOMO
LUMO
HOMO
Eadd 1  E
Eadd  0   E  LUMO - HOMO  H - L gap
0.2 eV
H -L gap
M. F. Goffman
10 times lower than isolated
OPV5 !
Experimental Results on OPV5
Image charge effect  localization of charges near electrodes
Hubbard Model
pz orbitals
*
U, i  i - image
t
400
#1
#2
#3
Hubbard Model
Eadd (meV)
350
t adjusted to give the optical H-L gap (2.5 eV)
image   /  r  d
300
where d = 4.7 Å
250
in reasonable agreement with van der Waals distances
200
150
100
50
-3
-2
-1
0
1
2
3
N
Eadd strongly depends on the embedding environement of the molecule
M. F. Goffman
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
V
Breakdown
& Trapping
M. F. Goffman
C60 based Single Electron Transistor
Al2O3
without C60
with C60
I
V
V is swept up to ~2.5 V to ensure I though the junction in the tunneling regime.
I
V
Vg
M. F. Goffman
C60 based Single Electron Transistor
G(V)
Current I
IV characteristics @ 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
M. F. Goffman
Experiments: C60 based Single Electron Transistor
Two-dimensional Differential Conductance (G=I/V) plot (4 different samples)
G (nS)
N
N+1
N
N+1
N
N+1
0
30
N
N+1
What are the meaning of the lines (white arrows) parallel
to the boundary of the Coulomb diamonds?

N
Information on the quantized excitations spectrum of C 60 (white arrows)
M. F. Goffman
Excitation Spectrum
Excited States (ES) of
N-charged Molecule
N-1
N
Vg
Excited States (ES) of
(N-1)-charged Molecule
µL
MOL N
MOL N - 1
µL
µR
MOL N
MOL N - 1
N -1  N  N -1
Tunneling into GS or ES of
N-charged Molecule
N  N -1  N
Tunneling out from GS or ES of
(N-1)-charged Molecule
M. F. Goffman
µR
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?
Vibrational excitation ?
No
Possible
Internal vibrations of C60 33meV (lowest energy mode)
Eexp = 35 meV
k
e-
f  1 / 2 k/M  f
1.2THz  2 f
M
k =70 Nm-1
5 meV
Coupling between vibronic modes and electrons are important
M. F. Goffman
Experiments on OPV5
Van der Zant group (DELFT)
Molecular vibration assisted tunneling
M. F. Goffman
Conclusions
In the weak coupling limit Eadd
G
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
M. F. Goffman
Single molecule transistor
McEuen & Ralph groups Nature 2002
Park group Nature 2002
Charge state of Co ion well defined
Co2+ Co3+
S0
3d6
S
1
2
3d7
M. F. Goffman
Kondo Resonance
TK  1 2 GU exp  0  0  U / GU
M. F. Goffman