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e. Strong coupling regime. e. Molecule. First Lecture. Chemical structure. Functions: macroscopic electronic properties . Molecular Wires. Diodes. Negative Differential Resistance (NDR) elements. Switches and storage elements.

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first lecture

e

Strong coupling regime

e

Molecule

First Lecture

Chemical structure

  • Functions: macroscopic electronic properties 

Molecular Wires

Diodes

Negative Differential Resistance (NDR) elements

Switches and storage elements

  • Transport mechanisms are determined by Metal-molecule coupling G

Weak coupling regime

Molecule

second lecture

e

Strong coupling regime

e

Molecule

2

1

3

Second Lecture

Chemical structure

  • Functions: macroscopic electronic properties 

Molecular Wires

Diodes

Negative Differential Resistance (NDR) elements

Switches and storage elements

  • Transport mechanisms are determined by Metal-molecule coupling G

Weak coupling regime

Molecule

Qualitative Picture

Final Remarks

molecular conduction qualitative picture
Molecular Conduction: Qualitative Picture

Two Basic Ingredients:

Energy Diagram showing the molecular levels relative to the electrochemical potential of electrodes

Potential Profile across the molecule due to the applied bias.

strong coupling to metallic electrodes g

Chemically bonded

G

Mdn

E

G

Fermi level µF

Local Density of States

Broadening of the energy levels (G)

Discrete Energy Levels

M0Mdn Fractional charge transfer

Strong Coupling to Metallic Electrodes (G)

Isolated Molecule

M0

E

LUMO

HOMO

Which is the location µF with respect to HOMO-LUMO levels?

location of the fermi energy

E

Local Density of States

Location of the Fermi Energy

UPS Experiments (UV Photo Electron Spectroscopy )

Vacuum Level

UPS spectrum

e-

µF

# e per second

e-

µF

E

Vacuum Level

e-

G

HOMO

# e per second

Mdn

µF

E

EHOMO

e-

energy diagram
Energy Diagram

At equilibrium (V=0)

-V/2

R

V/2

L

R

L

µ L

µ L=µR

eV

µR

But how are µL and µR disposed with respect to the molecular levels?

 Potential profile inside the molecule

potential profile

-V/2

R

V/2

L

Potential Profile

V/2

Potential Profile

-V/2

r

To the lowest approximation Molecular Levels shift "rigidly" by

Let us denote this average potential as:

Taking the molecular levels as our reference, the electrochemical potential of electrodes are shifted by

This voltage division factor has a profound effect on Current-Voltage Characteristics

energy level diagram 0
Energy Level Diagram (=0)

=0  Molecular levels remain fixed to µ L

µR

LUMO

LUMO

µ L

µ L

eV

eV

µR

HOMO

HOMO

V<0  LUMO Conduction

V>0  HOMO Conduction

I-V Characteristics can look asymetric

Positive branch (V>0) and Negative branch (V<0) involve different Molecular levels

energy level diagram 1 2

LUMO

LUMO

µ L

µR

µ L

eV/2

eV/2

µR

HOMO

HOMO

Energy Level Diagram (=1/2)

=1/2  Molecular levels shift with respect to µ L by half the applied bias

Conductiontakesplacethroughthenearestmolecular level

(HOMO in this case) for either bias polarity.

toy model

R

L

G

e

Toy Model

Toy Moldel: single level e (HOMO or LUMO) that incorporates relevant ingredients:

(1) Location of e with respect to µF

(2) Broadening GL,GR due to contacts (G=GL+GR)

(3) Potential Profile

µ L

µR

discrete one level model

-V/2

R

V/2

L

µR

Current as a "balancing act"

Discrete One-Level Model

GR

GL

µ L

e

discrete one level model1

-V/2

R

V/2

L

Discrete One-Level Model

GR

GL

µ L

e

The net flux across left junction will be

discrete one level model2

-V/2

R

V/2

L

µR

Discrete One-Level Model

GR

GL

The net flux across right junction will be

e

discrete one level model3
Discrete One-Level Model

At the steady state IL+IR=0 (no charge accumulation in the molecule)

The current through the metal-molecule-metal structure will be

one level model current i vs voltage v

µ L

µ L

µ L

µR

µR

µR

One-level Model: Current (I) vs. Voltage (V)

e

Let us take into account Broadening G of the level

broadening g
Broadening G

We replace the discrete level by a Lorentzian density of states:

µ L

µR

G

e

Expression of the current will be modified

We could write in the Landauer-Büttiker form

I let for you the demostration that the maximum value of

one level model current i vs voltage v1

G

One-level Model: Current (I) vs. Voltage (V)

Conductance Quantum

Next: Potential Profile

potential profile1

-V/2

R

V/2

L

CL

CR

-V/2

V/2

Potential Profile

The potential profile VMOL(r) will be obtained by solving

A solution can be visualized in terms of a capacitance circuit model:

The potential U that raises the position of the level is

Charging Energy Eadd

self consistent solution
Self Consistent Solution

Iterative Procedure for calculating N and U self-consistently

one level model current i vs voltage v2

µ L

µ L

µR

µR

V<0

V>0

Positively charges the molecule

 shift e down

One-level Model: Current (I) vs. Voltage (V)

IV asymetric

Coupling asymetry + charging

e

summary

G

Summary

Asymetric IVs  asymetric coupling + charging effect (Eadd)

even if transport is associated with a single level (symetric molecule)

HOMO conduction  I is lower for positive bias on the stronger contact

LUMO conduction  I is higher for positive bias on the stronger contact

  • I increases when e is crossed at V~2(µF-e)
  • I increases over a voltage width G+kBT
  • I dragged out by charging Eadd
realistic models
Realistic Models

Non-Equilibrium Green's Function (NEGF) Formalism

Let us rewritte the previous eq. in terms of a Green Function G(E)

Then the density of states will be proportional to the so called Spectral function defined as

The mean number of excess electrons N and the current can be written as

negf formalism
NEGF Formalism

For a multilevel Molecule (n levels) all quantities are replaced by a corresponding matrix (n x n )

H : Molecule + surface atoms

S : Coupling to bulk contacts

U : appropriate functional

A pedagogical tutorial: S. Datta, Nanotechnology 15, S433 (2004).

slide25

Experiments on Molecular Wires

Well coupled to electrodes (at least one of them)

molecular wires

L~nm

A) How conductance depends on the length L

of the wire?

B) How conductance depends on the binding

group of the wire?

C) How conductance depends on the

structure of the wire?

Molecular Wires

Large delocalized p systems

Conductance is a property of the Metal-Molecule-Metal structure

slide27

How one can measure transport properties

of molecular wires?

1) STM: Scanning Tunneling Microscope

2) Break-junctions

Mechanically controlled

Electronmigration-induced

3) Shadow evaporation on

Self-assembled Monolayers (SAMs)

mbe molecular beaker epitaxy

Tip

s

s

s

s

s

s

s

s

s

Adsorption

MBE: Molecular "Beaker" Epitaxy

Au (111)

Solution

Thiol-ended

Molecules

Au (111)

STM Image

Organization

conductive afm on self assembled monolayers
Conductive AFM on Self-Assembled Monolayers

Sakaguchi et al., APL 2001

Measured

g=0.41Å-1 for oligothiophene

g=1.08 Å-1 for alkanethiol

Theory

g=0.33Å-1 for oligothiophene

g=1.0 Å-1 for alkanethiol

stm on specially designed molecular wire
STM on specially designed molecular wire

Langlais et al., PRL 1999

Conductance depends exponentially onL

explanation

M. P. Samanta et al., PRB 53, R7626 (1996).

µ L

eV

µR

Explanation

V/2

-V/2

L

R

At low voltages µF is far from HOMO and/or LUMO  Tunneling Transmission

slide33

B) How conductance depends on

the bindinggroup of the molecular wire?

slide34

S

S

CH3COX

X

S

Influence of thebindinggroupof electroactive molecules

X = S or Se

Theoretical studies

Conductance of molecular wires: Influence of molecule-electrode binding. S.N. Yaliraki, M. Kemp, and M.A. Ratner,

J. Am. Chem. Soc. 121(14), 3428 (1999)

Se > S

Molecular alligator clips for single molecule electronics. Studies of group 16 and isonitriles interfaced with Au contacts. J.M. Seminario, A.G. Zacarias, and J.M. Tour

J. Am. Chem. Soc. 121(2), 411 (1999)

S > Se

Experiments are needed

X=S T3

X=Se Se3

influence of the binding group se vs s

Investigation of T3 and Se3

S

S

T3

CH3COS

SCOCH3

S

Se3

quite similar IPs

“Identical” HOMOs

S

S

CH3COSe

SeCOCH3

S

6.50 eV

6.52 eV

Se3

T3

Influence of the binding group: Se vs S
sample preparation

Adsorption

Sample Preparation

Au (111)

Insertion

Solution

Thiol-ended

Insulating Molecules

Solution

Conducting

Molecules

Organization

molecular structure transport properties relationship

T3

S

S

CH3COS

SCOCH3

S

Se3

S

S

CH3COSe

SeCOCH3

S

h

x

Molecular structure - transport properties relationship

STM tip

L. Patrone et al, Chem. Phys.281(2002)325

PRL 91(03) 096802

28 nm T3,Vt = +0.78V, It = 10.7pA

molecular structure transport properties relationship1

T3

S

S

CH3COS

SCOCH3

S

Se3

S

S

CH3COSe

SeCOCH3

S

h

x

Molecular structure - transport properties relationship

STM tip

L. Patrone et al, Chem. Phys.281(2002)325

PRL 91(03) 096802

28 nm T3,Vt = +0.78V, It = 10.7pA

molecular structure transport properties relationship2

T3

S

S

CH3COS

SCOCH3

S

Se3

S

S

CH3COSe

SeCOCH3

S

h

x

Molecular structure - transport properties relationship

STM tip

L. Patrone et al, Chem. Phys.281(2002)325

PRL 91(03) 096802

The apparent height is a (relative) measure of

the conductance of the molecular junction

28 nm T3,Vt = +0.78V, It = 10.7pA

s vs se experimental comparison

Topography: 1.0 nm

T3

Topography: 1.0 nm

Se3

S vs Se: Experimental comparison

STM on T3 and Se3 Molecules inserted in a dodecanethiol Matrix

L. Patrone et al,

Chem. Phys. 281(2002)325

STM tip

It

It

28 nm T3,Vt = +0.78V, It = 10.7pA

s vs se experimental comparison1

Se3 (Se)

T3 (S)

Se3 > T3

S vs Se: Experimental comparison

Se give rise to a more efficient transport than S

current voltage characteristic

T3

V

eV

2(EF-EHOMO)

Position of the HOMO level/ Fermi level

(EF-EHOMO) : T3 > (EF-EHOMO) : Se3

Current-Voltage characteristic

I

I

Se3

LUMO

HOMO

EF

EF-EHOMO

eV

position of the homo fermi level
Position of the HOMO / Fermi level

UPS (UV Photoelectron Spectroscopy)

1 monolayer adsorbed onto gold

T3 :EF-EHOMO> Se3:EF-EHOMO

c comparaison of backbone conductance
C) Comparaison of backbone conductance

Kushmeric, Ratner et al JACS 2003

OPV > OPE OPV vs Othiophene?

c influence of the conjugated body t3 vs opvn

(15.6 Å)

S

S

T3

CH3COS

SCOCH3

S

CH3COS

OPV2 (12.67 Å)

SCOCH3

CH3COS

OPV2 :HOMO - EF 0.7 eV

OPV3:HOMO - EF 0.35-0.7 eV

SCOCH3

C) Influence of the conjugated body: T3 vs OPVn

2.0 Å

4.2 Å

OPV3 (19.04 Å)

7.3 Å

 OPVs are more conducting than Othiophene

slide47

Which is the IV characteristic

of a Metal-single molecule-Metal device?

single molecule measurement

Tip

Metallic substrate

Single Molecule Measurement

Conducting AFM on Alkanedithiol on a alkanethiol matrix

X.D. Cui et al., Science 2001.

single molecule measurement1
Single Molecule Measurement

Conductance histograms with STM

N. J. Tao, Science 2003.

contacting single molecules
Contacting Single Molecules

Mechanically Controlled break-junctions

J. M. van Ruitenbeek et al Rev. Sci. Instrum. 67 (1995) 108

Advantages

High stability

accuracy dl/Dz~10-5

Freshly exposed metal surfaces

dl

Drawbacks

No image of contacted molecules

No gating

Dz

mcbjs results on different molecules @300k

S

S

S

S

S

MCBJs Results on Different Molecules (@300K)

Kergueris et al PRB 59(1999)12505

M. A. Reed et al, Science 278 (1997) 252

Reichert et al PRL 88(2002)176804

Single Molecule IV characteristics ?

probably yes
Probably Yes!
  • "Lock-in" behavior
  • Similar molecules (length, binding groups) with different spatial
  • symmetry gives corresponding behaviour on IVs
  • modeling consistent with a single molecule

NEGF Formalism calculation

J. Heurich et al., PRL 88, 256803 (2002).

conclusions for molecular wires
Conclusions for Molecular Wires

At low Voltage Bias

A) Exponential dependence on L is confirmed.

B) The role of the bindinggroup has been decoupled from that of the rest of the molecule:

Se yields a better molecule-metal coupling efficiency than S since the Fermi level is nearer to the HOMO level.

C)

Phenylene-Vinylene (OPV) is more efficient than thiophene as backbone.

IVs

Single Molecule IV characteristics can be measured.

Qualitative agreement between experiments and theory

2 diodes

V/2

-V/2

L

R

V>0

V<0

2. Diodes

Aviram & Ratner Theoretical Proposal (1974)

Rectifying behavior: expected from asymmetry of the D-A structure

the langmuir blodgett technique

a

Solution

molécules

eau

b

The Langmuir-Blodgett technique

Special design of the molecule

Hydrophobic part

Transfer to a solid substrate

Single Molecular Film formation

2 diodes1

Al

Al

2. Diodes

Metzger et al.,JACS 119, 10455 (1997).

Experimental Realization

Some differences

Metzeger et al

Aviram & Ratner

Spacer: s-saturated

Spacer: p-conjugated

aliphatic chain (donor side)

Is Rectification due to the Aviram & Ratner mechanism ?

Answer: No!

which is the rectification mechanism

HOMO

Which is the Rectification Mechanism

Aviram & Ratner

Metzeger et al

Spacer: s-saturated

Spacer: p-conjugated

Donor and Acceptor molecular orbitals remain localized

LUMO

DFT calcultion: HOMO and LUMO delocalized

rectification mechanism asymmetric coupling

r

V/2

Al

GD

GA

Al

-V/2

V/2

Potential Profile

Rectification Mechanism: Asymmetric Coupling

Metzger et al.,JACS 119, 10455 (1997).

aliphatic chain (donor side) 

-V/2

As a first approximation

Asymetric Coupling can be used for fabricating Diodes.

using asymmetric coupling for diode function
Using asymmetric coupling for Diode function

Two step fabrication:

N. Lenfant et al., Nanoletters 3, 741 (2003).

Self-assembly of alkyl chains

p-conjugated groups

Control measurement on Alkyl chains

Al

Al

n-doped Silicon

n-doped Silicon

2 diodes and ndr
2. Diodes and NDR

N. P. Guisinger et al, Nanoletters 4, 55 (2004)

NDR behavior: due to resonance conditions

The NDR bias varies by as much as 1 V from experiment to experiment

3 switches

D+

A-

D

A

R'

R'

R

R

3. Switches

At least two different stable states  different conductance (high /low)

Reduction-Oxidation

(Redox) process

Collier at al., Science 285, 391 (1999)

Collier at al., Science 289, 11721 (2000)

D. R. Stewart at al., NanoLett. 4, 133 (2004)

Conformation Change

light-triggered

R

R

R

R

UV

Open form

Closed form

Recent review: Masahiro Irie, Chem. Rev.100, 1685 (2000).

light triggered switches
Light-triggered Switches

Courtesy of D. Dulić and S.J. van der Molen

Typically

Switches in Toluene

Closed

Absorption

Open

l (nm)

Does it work in a solid state device ?

breakjunction experiment

No switching back !?

One way Photochromism

Breakjunction experiment

D. Dulić et al, PRL 91,207402 (2003).

l=546 nm

l=313 nm

Why closing is quenched?

OPEN QUESTION

final remarks
Final Remarks
  • Conductance properties of single molecules can be probed. However reproducibility and stability remains a challenge.
  • More experiments are needed in order to refine theory and more theoretical calculation are needed to design interesting experiments (feedback!).
  • Molecular Diodes can be obtained using asymetric coupling.
  • Molecular Electronics on silicon can be a way of fabricating hybrid devices taking profit of the powerful infrastructure of the silicon-based IC industry  Resonant tunneling devices.
  • Light Triggered switches are promising molecules. Tuning of the coupling between the active part and the electrodes are needed to get reversible operation.
mcbjs results on different molecules @4k

CH3COS

SCOCH3

MCBJs Results on Different Molecules (@4K)

Improved Stability

High stability (>10 hs) at 4K

d2I/dV2 spectrum  Fingerprint of the molecule ?

A. Isambert, D. Dulić, JP Bourgoin, M. F. Goffman, unpublished