M. F. Goffman

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

Nanoparticules

Nanotubes de carboneNano-leads

Synthetic Molecules

SS

SS S OO

ADN/ARN

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

• Self-assembly templates for other nano-objects • Metallic or semiconducting• Link between µm and nm scale

quantification of energy levels

M. F. Goffman

Why Synthetic Molecules?

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

Molecular WiresDiodes

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

M. F. Goffman

IV Source Drain

Basic device: Metal-Molecule-Metal junction

Current-Voltage (IV) Characteristic (Electronic Function)

Metal-Molecule Coupling () plays a key role

Electronic Function is a property of the Metal-Molecule-Metal structure

M. F. Goffman

Scanning Tunneling Microscope as a two electrode probe

Topographic measurement (I fixed)

V

I=cte

z

piezo scanning

unitMetallic

Tip

Electrically conducting surface

Advantages

Imaging and electrical measurementsTip Manipulation

Drawbacks

Asymmetric contactsReduced in plane position stabilityno gatingI(V) spectroscopy only in rare cases

C. Joachim et al Phys. Rev. Lett. 74 (1995)2102S. Datta et al Phys. Rev. Lett. 79(1997) 2530

L. A. Bumm et al Science 271 (1996) 1705A. Dhirani et al J. Chem. Phys. 106 (1997) 5249

V. Langlais et al, Phys. Rev. Lett. 83 (1999) 2809L. Patrone et al Chem Phys. 281 (2002) 325

M. F. Goffman

STM experiments on C60 (I)

D. Porath et al.J. Appl. Phys. 81, 2241 (1997)Phys. Rev. B 56, 9829 (1997)

• Current "blocked" up to Vth

• IV highly non-linear

S

T V

I

IV measurement (z fixed)

Insulating layer

Topographic measurement (I fixed)

V

I=cte

z

C60 moleculeC60 Monolayer

M. F. Goffman

STM experiments on C60 (II)

C. Joachim et al. Phys. Rev. Lett. 74, 2102 (1995)Europhys. Lett. 30, 409 (1995)

• Linear IV characteristic at low V

V

I

C60 molecules on Au 110

M. F. Goffman

V

I

Metal- Molecule Coupling plays a key role

V

I

Weak coupling regime Strong coupling regime

single electron effects

Coulomb addition energy Eadd

Strong hybridization Coherent transport (Landauer-Buttiker formalism)

M. F. Goffman

Outline I

• 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

Molecular conduction in the weak limit regime

Analogy with Quantum Dots

• Weak Coupling limit Eadd Single electron effects

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

Metal Reservoir

Metal Reservoir

Molecule

e

M0 M+

e

M0

e e

In the transport process the molecule will be oxydized or reduced

Weak Coupling Transfer of e- by sequential tunneling

M0M M0

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

• Description of the molecule Energies involved in reactions : M0 M+

M0 M

M. F. Goffman

Metallic Electrodes

2

2 r U r E r2m

occupied states

empty states

In the independent electron approximation

Ground state of N (~1023 ) electrons system energy levels of a single electron

Fermi level µ

Vacuum Level

W

W: Energy required to remove an electron (Work function)

Good aproximation: continuous distribution of states

For Au(111) W ~ 5.3 eV

M. F. Goffman

Energy Level Diagram

Metal Reservoir

Metal Reservoir

Molecule

Characteristic Energies of a Molecule

M. F. Goffman

M

M0

Isolated Molecule

Energy Levels and Total Energy E(N)

The density functional theory (DFT) can provide the ground state energy of the molecule M0 and its ions Mk.

Isolated Molecule (M0) : Strong correlated N-electron system with 23(N 10 )

M+

E(N) : Total energy of the N-electron Molecule (M 0)

E(N)

LUMO

HOMO

N N+1N -1

# of electrons??

??

M. F. Goffman

Characteristic energies of a molecule

Electron affinity

M0 OLE N 1 E N µI N M0 OLE N E N 1A µ N 1

How this characteristic energies determine the Coulomb addition energy Eadd ?

E(N) : Total energy of the N-electron Molecule (M 0)

M

M0

M+E(N)

N N+1N -1 # of electrons

Ionization Potential

M. F. Goffman

Coulomb Addition Energy Eadd of an Isolated Molecule

addMOL

2eE

C

The Coulomb Addition Energy is defined as

MOL : Capacitance of the mC olecule

The capacitance of a charged system can be defined as

From an atomistic viewpoint

e V N N N

Q e N

MOL QC1 V

MOL

2

MOL MOL

ewith N 1

CN 1 N

Amount of work per unit charge, V, required to bring a fixed charged, Q, from the vacuum level to the system

Since 0MOL N 1 E N 1 AE N N Electron affinity

0MOL N E N E NN 1 I Ionization Potential

0add 0IE A

MOL N : Chemical Potential of the molecule

M. F. Goffman

Energy Diagram of an isolated molecule

Vacuum Level

Eadd

0 NA µ 1

0 µI N

ExampleIsolated C60 in vacuum I0=7.58 eV and A0=2.65 eV

Eadd = 4.93 eV Bk T @ RT ( 0.025 eV )

Can we estimate Eadd using the geometry of the molecule ?

M. F. Goffman

Geometrical Calculation of Eadd

2 2

0G

e e2.8 4.1 eV

2 DC

00 4. eVI A 93

D The geometrical capacitance

D=7.1~10.2 Å

LUMO HOMO0 0(N ) (N ) 1.5 1.7 eV

Why is underestimated ?M0

Anwser:C60 has a completely filled HOMO

2

LUMO HOMO0add

G0

e(N ) (N ) 3.3 5.8

CeE V

Does this estimation generally work?

M. F. Goffman

Experiments vs Geometrical Estimation

0

5

10

0 5 10

C70

C60

I -

A (

eV

)

e2/CG

The Larger N Better the agreementImportant remark:

Ionization and Affinity of the molecule depends on the environment where the molecule is embedded.

For Molecules DFT reveals

2

LUMO HOMO

G

e(A N N)

C)I N (N

If HOMO level is fully populated

M. F. Goffman

Modification by Metallic Electrodes (Image Potential Effect)

The image force acting on the outgoing electron at position x is

Ex. adsorbed molecule

2

x 2 20

e 1 1F

4 2x x d

M+1 e-e+

x

d

The resulting force is repulsive for x > d and I0 is decreased by an amount

0 imI I W

M-1

+

2

im x0d

eW F .dx

16 d

M. F. Goffman

Modification by Metallic Electrodes (Image Potential Effect)

Similarly, when an additional electron approaches

2

x 20

e 1F

4 2x

d

im0 0xF .A A Adx W

and thus

For C60 weakly coupled to a metal electrode

d

For d = 6.2 Å (van der Waals)

D 7.1 Å

addE AI

Addition energy of the embedded molecule Eadd is modified by metallic electrodes as

0add im0E I 2W .8A 3 eV

2

0 LUMOG HOMOG

C Ce2 f d,D 3.9eV

M. F. Goffman

Coupling to Metallic Electrodes ()

can be related to the time it takes for un electron to escape into the metallic contact

can be interpreted as the rate at which electrons are injected into the molecule from the contact

Isolated Molecule

0

M0

Metal Reservoir

finite finit e

M0

M. F. Goffman

Characteristic Energies of the Metal-Molecule-Metal structure

Weak Coupling addE

addE determined by the extent of the electronic wave functionin the presence of metal electrodes.

determined by the overlap of the electronic wave function and the delocalized wave function of metal electrodes.

addE AI

Transfer of e- by sequential tunneling

M. F. Goffman

Energy Diagram of Metal-Molecule-Metal structure

In equilibrium, V=0 Statistical Mechanics

B BE N µ N / k T E N µ N / k TN

N

1p e where Z= e

Z

if (I-W) and (W-A) are greater than kBT The molecule will remain neutral (N0)

Current will be blocked (Coulomb blockade)

The probability of having N electrons in the Molecule is

MOL 0 B MOL 0 B

0 0 0 0

µ (N 1) µ / k T µ µ (N ) / k TN 1 N N 1 NP P .e and P P .e

Vacuum Level

µL µR= µL=µ

MOL 0µA N 1

MOL 0I µ N

Eadd

L R

W

M. F. Goffman

Energy Diagram of Metal-Molecule-Metal structure

Vacuum Level

µL

MOL 0µA N 1

MOL 0I µ N

Eadd

L R

When current will flow?

MOL 0 B MOL 0 B

0 0 0 0

µ (N 1) µ / k T µ µ (N ) / k TN 1 N N 1 NP P .e and P P .e

µR= µL=µ

0 0 0 0N N 1 N N 1Answer : when P P or P P

a 0 will induce a current through intermediate stV ates:

0 0 0 0N N 1 N N 1

MOL 0µ µ N 1

0 0 0 0N N 1 N N 1

MOL 0µ µ N

More generally electrons can flow when L MOL Rµ N µ

M. F. Goffman

Analogy with quantum dot

Vacuum Level

-I

eV

MOL NA 1

MOL N

For a Molecule For a Quantum Dot (JanMartinek’s lectures)

Vacuum Level

eV

DOT N

DOT N 1

µL µL

µRµR

Transport experiment in weak coupling limit : spectroscopy of a molecule embedded in a circuit

Does the Constant Interaction Model used for QD apply toSingle molecules?

M. F. Goffman

Revisiting Quantum Dot Theory (few electron QD)

2

DOT 0 N

eN E N E N 1 N q / e 1/

C2

2 N

2

0 ii 1

eE N N q /

Ce

2

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

QD

V/2Vg

L RCL CR

Cg

I

-V/2Where L gRC C C C

Chemical potential of the dot is

Chemical Potential of the Electrodes are

gLg gR

Rg

2Ce e e 1 e where = and

C C

C CVV VV =

2

M. F. Goffman

Measuring the Addition Spectrum

DOT 0N

DOT 0N 1

DOT 0N 1

DOT 0N 2

L R 2

DOT 0 N

eN N q / e 1/ 2

C

At V0 G / VI

Electrons can flow when

L DOT Rµ N µ

gV

N0

µL µR

gL V Ve e

gR e 1 V Ve

M. F. Goffman

gR e 1 V Ve

Measurering the Addition Spectrum

DOT 0N

DOT 0N 1

DOT 0N 1

DOT 0N 2

L R 2

DOT 0 N

eN N q / e 1/ 2

C

At V0 G / VI

Electrons can flow when

L DOT Rµ N µ

gV0 1

gNV

N0

µL µR

µL µRµL µR

gL V Ve e

M. F. Goffman

DOT 0N

DOT 0N 1

DOT 0N 1

DOT 0N 2 µL µRµL µRµL µR

Measurering the Addition Spectrum

L R 2

DOT 0 N

eN N q / e 1/ 2

C

gL V Ve e

At V0 G / VI

Electrons can flow when

L DOT Rµ N µ

gV0 1

gNV

N0 N0+1 N0+2

0 2gNV

gR e 1 V Ve

M. F. Goffman

Measuring the Addition Spectrum

DOT 0N

DOT 0N 1

DOT 0N 1

DOT 0N 2

L R 2

DOT 0 N

eN N q / e 1/ 2

C

gL V Ve e

At V0 G / VI

Electrons can flow when

L DOT Rµ N µ

gV0 2

gNV 0 1

gNV 0N

gV0 1gNV

N0 N0+1 N0+2N0-1

µL µR

gR e 1 V Ve

M. F. Goffman

DOT 0N

DOT 0N 1

DOT 0N 1

4

µL µR

µR

µL

µRµL

DOT 0N

DOT 0N 1

DOT 0N 1

3

µL

µR

µL µR

DOT 0N 1

DOT 0N 1

DOT 0NµL

µR

µRµL

DOT 0N 1

DOT 0N 1

DOT 0N

µL

µR

0 0L g

Ng gN VVe V V

2

0 0N Ng

1g g gAt a given current will flow iV V fV V

0 0 0N N 1 N 0 0 0N N 1 N

0 1gNV 0N

gV

gV

V1

N0-1 N0N0+1

0 0NR g g g

N Ve1

V V V

1

2

3

0 0N 1 N 1g gL gVV Ve V

4

0 0g g gN 1 N 1

R VV V Ve1

M. F. Goffman

Stability Diagram

gV

0 1gNV 0N

gV

N0N0+1N0-1

V 0g gNV

1VV

0N 1

g gV VV

0 0N NC Cg g g gC

10 V VN

1V VV

0 0NCg g

1g

NV V1V

VC(N0) is obtained by equating

1 3

Then aC 0 0ddEV N N

Stability diagram Experimental determination of the addition spectrum Eadd(N)

0CV N

0CV 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

1. Electrode separation controlled by in situ conductance measurements

(2nm ~ G

Al2O3

Al Gate

Oxidized Si wafer

PMMA

-V/2

V/2

I

Vg

2. Deposition of OPV5 molecules by quench condensation @ low temperatures

3. Annealing @ 70 K for activating thermal motion of molecules

4. Monitoring of I for trapping detection

S. Kubatkin,et al, Nature 425, 698 (2003).

M. F. Goffman

Experimental Results on OPV5

S. Kubatkin,et al, Nature 425, 698 (2003).Addition Energy Spectrum

-3 -2 -1 0 1 2 3

50

100

150

200

250

300

350

400 #1 #2 #3

Ead

d (m

eV)

N

LUMO HOMO

H L gap

add E 0H L gapE .2 eV0

addE 1 E

M0

HOMOLUMO

M-

HOMOLUMO

M-2

HOMOLUMO

M+

HOMOLUMO

addE E1

Interpretation within the CI model

10 times lower than isolated OPV5 !

M++

HOMOLUMO

addE E2

M. F. Goffman

Experimental Results on OPV5

Image charge effect localization of charges near electrodes

-3 -2 -1 0 1 2 3

50

100

150

200

250

300

350

400 #1 #2 #3 Hubbard Model

Ead

d (m

eV)

N

Hubbard Model pz orbitals

t adjusted to give the optical H-L gap (2.5 eV)

image r/ d where d = 4.7 Å

in reasonable agreement with van der Waals distances

t

U, *i i image

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 1999M. Lambert et al Nanotech. 2003.

Breakdown& Trapping

Adsorption of molecules

V

M. F. Goffman

C60 based Single Electron Transistor

VI

without C60

with C60

V is swept up to ~2.5 V to ensure I though the junction in the tunneling regime.

Al2O3

VI

Vg

M. F. Goffman

C60 based Single Electron Transistor

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

G(V

)

Curr

ent

I

M. F. Goffman

Experiments: C60 based Single Electron Transistor

Two-dimensional Differential Conductance (G=I/V) plot (4 different samples)

G (nS)

030

N N+1 N N+1

N

N+1N N+1

What are the meaning of the lines (white arrows) parallel to the boundary of the Coulomb diamonds?

Information on the quantized excitations spectrum of (white arrows)N60C

M. F. Goffman

Excitation Spectrum

µR

µL

MOL N

MOL N 1 µR

µL

MOL N

MOL N 1

NN-1

Excited States (ES) of N-charged Molecule

Excited States (ES) of (N-1)-charged Molecule

N 1 N N 1 N N 1 N

Tunneling into GS or ES of N-charged Molecule

Vg

Tunneling out from GS or ES of (N-1)-charged Molecule

M. F. Goffman

C60 transistor: Excitation Spectrum

Park et al Nature 407 57-60(2000)

5meV excitation energy independent of the number N of electrons in the C60 molecule

Experimental Facts

Excited electronic states? No

Vibrational excitation ? Possible

Internal vibrations of C60 33meV (lowest energy mode)

Eexp = 35 meV

f 1/ 2 f 1.2THz 2 f 5meV k/M

k

k =70 Nm-1

M

e-

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 addE

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

McEuen & Ralph groups Nature 2002Park group Nature 2002

Single molecule transistor

Charge state of Co ion well defined

Co2+ Co3+

12SS 0

3d73d6

M. F. Goffman

Kondo Resonance

12K 0 0T Uexp U / U