MENU

Molecular ElectronicsMolecular Coherent Transport - Devices/MechanismCoherent Gating Inductance and Magnetic LayersCoherence and its Loss – transport

- stereochemical gating

Utility of simple models

1987

Why molecular electronics?

Size

TunabilityRecognitionAssemblyDynamical stereochemistry

Space Organizing Structures

Molecule atom

Characteristic Molecular Organization of Solid Matter

• Closed shell, stable, knobby structure• Interact weakly by exchange, tunneling

terms• Interact strongly by steric, van der Waals

terms• Structurally soft, insulating diamagnetic

Can a molecule act as an interconnect in

A conducting nanojunction??

First Transport Measurements through Single Molecules

Molecule between two electrodes

Adsorbed molecule addressed by STM tip

Molecule lying on a surface

Single-wall carbonnanotube on Pt

Break junction:dithiols between gold

Au(111)

Pt/Ir Tip

SAM1 nm

~1-2 nm

Self-assembled monolayers

Dekker et al. Nature 386 (97) @ Delft

Dorogi et al. PRB 52 (95) @ Purdue

Nanopore

Reed et al. APL 71 (97) @ Yale

Reed et al. Science 278 (97) @ Yale

Nanotube on AuC60 on gold

STMtip

Au

Lieber et al. Nature 391 (98) @ HarvardJoachim et al. PRL 74 (95) @ ToulouseGimzewski @ IBM-Zürich

Intramolecular Electron transfer

Hush, Paddon-Row,Verhoeven

V

Molecular wires and Electron transfer?

Wire junction ET

L R D-B-A

electron tunneling electron tunnelingElectrode sink vibronic sinkElectrode interface Donor,acceptor,bridgeLandauer approach Marcus formulaConductance Rate constant

a bLocal orbitals Molecular orbitals

energy

Metals mix with molecular states

I. Landauer Coherent Conductance

Tii= transition probability in the ith transverse channel∑=

iiiT

heg

2

T=1

T=0

I. Landauer Conductance / Molecular Wires

Atomic metal wires — Tii = 1 for all open channelsI.a 1

Reed, 1997

Main Result for SINGLE Molecular Wire

injecting energy Green’s function spectral density

moleculeleft

electroderight

electrode

self-energy

)()(),(~),(~2)( '''', ''

2

EEEGEGeEg rrllrlrl rl

lr ∆∆ΣΣ= ∗∑∑ηπ

conductance

Typical Spectrummolecular levels

poles of LUMO HOMO

Levels broadened ( ∆)

gap

all levels contribute at the gap

&Note that g depends dramaticallyon the injecting energy

G~

Transport depends both on the Molecule and on the electrodes, as well as the interfaces

Quantized conductance at poles

II. Nonresonant Coherent Tunneling

)}()()({)( 2 EEGETrET RLRL ∆∆=

L R

∑ Σ−−=

S SSLR EE

RSSLG

So T will drop below unity ifa) E ≠ Es (non-resonant)b) Overlap of state |s > is small at either L or R electrodes

What really happens at the interface?

Electronic Band Formation at Organic-Metal Interfaces: Role of Adsorbate-Surface Interaction

Gregory Dutton and X.-Y. Zhu*

Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455

J. Phys. Chem. B 2001, 105, 10912-10917

Measurement of benzene-1,4-dithiolMeasurement of benzene-1,4-dithiol•• reflective: T ~ 5 x 10reflective: T ~ 5 x 10--44

•• single? observe integer units (1,2,…)single? observe integer units (1,2,…)•• power dissipation?power dissipation?

•• J ~ 10J ~ 1088 A/cmA/cm2 2

•• P ~ 1P ~ 1mmW (1 molecule ?!)W (1 molecule ?!)•• nonnon--equilibrium transportequilibrium transport

S

SH

S

SH

S

SX

S SX

SSX

SSH

S

HS

SHS

SXS

SXS

8.46 Å

SHS

Gold Electrode

Current Gold ElectrodeS S

SHS

experiment:experiment:M.A. Reed M.A. Reed et. alet. al, Science , Science 278278, 252 (1997), 252 (1997)

(plus self energy)

Calculation level:

DFT , PW91 functionalSoft pseudopotentialsExtended basis on molecular sectionNon-equilibrium Green function self-energy

Default geometryminimal basis set, truncated, on AuFully coherent scattering analysis

Charge Transfer Induced Potential ChangeCharge Transfer Induced Potential Change

• Charge transfer into the molecule increases the electrostatic potential leading to a potential barrier at the interface.

• The potential barrier may cause reduced transmission.

• Reduced transmission even without potential barrier, if no states at the Fermi-level.

Contact Resistance in Metal-Molecule-Metal Junctions Based on Aliphatic SAMs: Effects of Surface Linker and Metal Work Function

Jeremy M. Beebe,† Vincent B. Engelkes,‡ Larry L. Miller,† and C. Daniel Frisbie*,‡

Departments of Chemistry, Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, Minnesota 55455

-2 0 2

Expt.Transmission Property

Dynamically unstableInterface

H. Weber et.al.,PRL 2002

Thiol/Gold Interfaces??•Schottky barriers from charge flow•Fluid geometry from Lewis binding•Sigma/pi problems•Relatively poor spectral density

•Facile and general structure formation

ALTERNATIVES?

• BETTER LEWIS BINDING (ISOCYANIDE/Pt)• COVALENT BINDING AT SEMICONDUCTORS

MENU

Molecular ElectronicsMolecular Coherent Transport - Devices/MechanismCoherent Gating Inductance and Magnetic LayersCoherence and its Loss – transport

- stereochemical gating

Utility of simple models

Coherent switching

Change state densities as a function of voltage

TEMPO on Si

20 nm × 20 nm, -2 V, 0.1 nA

M. C. Hersam and J. Michl, unpublished

NDR on Si (100) - M. C. Hersam, NU

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0

V (Volts)I

(nA

)

I-V Curve of Individual TEMPOMolecule on Clean Si(100)

NDC-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0

V (Volts)

I (n

A)

I-V Curve of Clean Si(100)

•Poor DC conductance in sigma system

•NDC from gaps in Si spectral density

A

B

Ralph, McEuen, Abruna, Coates et al, 2002

Electromigration Break Junctions (Park, McEuen, 1999)

• After breaking, the gap width can be estimated from the tunneling resistance.•Typically 1-3 nm.

Flexible way to make gated nanojunctions.Can stick many things in the gap, after breaking in situ.Molecular geometry is uncertain.

100 nm

AFM image

Co Co

SH

SH

HS

HS

N NN

NNN

N NN

NNN 13 Å24 Å

A BGATED

Single wire junctions

Coulomb blockade (long wire) Kondo resonance (short wire)

MENU

Molecular ElectronicsMolecular Coherent Transport - Devices/MechanismCoherent Gating Inductance and Magnetic LayersCoherence and its Loss – transport

- stereochemical gating

Utility of simple models

Ferromagnetic Chiral Junction

i_

+

U

- -

-

_-B

anode

cathode

Indirect Exchange Interaction of Localized Spins

[ ]( ) ( ) aan ,nnnnUaaaa)(

.c.c)a)/ikrexp(a(cVtcc)(H

rr00rr00mol

,kr0k

,kkkk

+−+−+

σσ

+σσ

+σ

σσσ

+σ

σσ

+σ

=+++µ−ε+

+++−µ−ε=

∑

∑∑ η

occupation double prevents )U( molecule at therepulsion Coulomb - U

LUMO) (occupied levelmolecular - )(

energy) (Fermi potential chemical -

)2mk electrons free of model -

m2k(electron ofenergy kinetics

0

0

2F

2

kk

µ>+ε

µ<ε

µ

µ==ε−ε

Indirect Exchange Interaction of Localized Spins – Perturbation theory (RKKY)

-

-

_-

anode

cathode ninteractio RKKY - J(r)-

)/cos(2t),(

1t2 - E

)/exp(1t - E

0

0kk 0

2

0

kk 0

2

0

kk 0

22

0

F

F

F

r

rk

r

kr

kr

Ukr

VU

UV

Uikr

V

σσ

σσεε

σσ

εεδσσ

εεδσσ

ρρ

ρρη

η

=

=−+

−=

−+=→−=

−++

=→=

∑

∑

∑

<

<

<

0 r

RKKY Interaction – Analytical Behaviors (free electrons)

Inte

ract

ion

-J

(eV

)

0

0.1

-0.1Distance, r

η/(2kF) η/kF

3F

0 r)/rk2cos(J)r(J η

−=

RKKY Interaction – Interaction Strength for Neighboring Molecules r ~ 6 Å

-

-

_-

anode

a 1

METAL

A17.0~

),aexp()r(J)r(J:Expect

−−β

β−−=

0 r

Ferromagnetic Transition in RKKY Interacting Planar Layer

σ=

σ−+σσ−−σ

>=σ=<σ

σσ−=

σ>=σ<

σσ−= ∑><

TkJ4tanh

))Tk/(J4exp())Tk/(J4exp())Tk/(J4exp())Tk/(J4exp(

,J4H

eApproach Field Mean

JH

BBB

BBz

zMF

zi

ijji

ρρ

ρρ

4J > kBT (Phase Transition σ≠0)1

4J < kBT (σ=0)

0kBTC = 4J1

Estimate of TC for closely packed layer

re) temperatu(room eV026.0eV054.0~)2exp(eV4.0Tk

es)polyalaninin (O2A ~aAu)in (Fe eV1.0)A6(J

A17.0~

),aexp()A6(J4)A6(J4~Tk:Expect

CB

-

1

METALCB

>−>

≈

−β

β−=

−

expect collective magnetism!

Suggestion of Ferromagnetic Chiral Junctions

i_

+

U

- -

-

_-B

anode

cathode

(1) Large voltage charges anisotropic molecules: makes unpaired electrons

(2) Exchange interaction through the metal can ensure magnetic ordering at room temperature(3) Magnetization direction is controlled by the magnetic field of current: direction of voltage

Gold

Polyalanine self-assembled layer

Problems to Address

Both Au and polyalanine are entirely nonmagnetic

See above

Time reversal symmetry yields the same energy for two degenerate ground states M and -M

Estimates

Preparation in the magnetic field B of the non-equilibrium injection current jmol

3B

12mol

B

mol2

2

B

BB

10~/ s10/electron 1~j

Tkj

dmce10~

TkB~/ Yields

−− µµ→

µµµ

η

For N spins ∆N > N1/2 (standard fluctuation) creates sufficient driving force to predetermine the final magnetization

Needs N > 106 - satisfied in the experiment

Direction of jmol is defined by the initial polarization (C or N terminal) and thesign of proportionality factor between j and B is defined by the chirality –explains magnetization control

Nature of Local Spins?

(1) Chemisorption to compensate the Coulomb repulsion of dipoles, should fight against 4eV difference of Au work functionand polyalanine LUMO

(2) Itinerant Magnetism: fractional charging of polyalanine

All requires quantum chemistry and experimental tests

Some Conclusions

(1) Exchange interaction of induced local spins within self-assembled layers can lead to the collective magnetism at room temperature

(2) Magnetization direction can be controlled by the current in molecular junction or even by their static properties: chirality and polarization

(3) Local spins can be formed without application of strong DC field: chemisorption, singlet-triplet transition or itinerant spins can all be due to the large polarization of molecules

(4) CAN ACT AS INDUCTANCE STRUCTURE, CUTTING OFF CURRENT DUE TO MAGNETIC (PAULI) BLOCKAGE

MENU

Molecular ElectronicsMolecular Coherent Transport - Devices/MechanismCoherent Gating Inductance and Magnetic LayersCoherence and its Loss – transport

- stereochemical gating

Utility of simple models

Distance Dependence - Purely Electronic

Barrier tunneling

Superexchange

L

energy

)1/()/(ln2)exp(

0

0

⟨⟨=

−=

VVR

Lkk

ωωβ

β

21

0

)}(2{

)exp(

EVm

Lkk

−=

−=

β

β

V

ω

Time Dependence - Purely Electronic

V12V23

B1 B2

VD1 VnA

Bn...

E B3

ADH β=

ddt

}{ nijnnin jnji i ρββρρ −= ∑

∑

],[)( jiji

jiji

ij ij

aaHiaadtd

aa ρ

=⟩⟨

=⟩⟨

++

+

ji aa +

Multiple Oscillations

Density Matrix formalismUsed for systems with partial information

diss /dt)d]i[H,/ ρρρ

ρρ

+=

==

dtd

coherencesspopulation

ij

ii

Time Dependence - Addd VibronicCouplings, Dephasings

12 //)1():

)],[

TTdt

dBloch

dtd

Hidt

d

ijijijijdissij

dissijij

ρδδρρ

ρρ

ρ

+−=

+=

-

rate processesDamped oscillations

So – apply to donor/bridge/acceptor junctions

Steady-State Density Matrix Theory of Bridge Assisted ET

Mathematica Results:

2

N2

2N2

ETVV4k

ωγ+

κω=

+

γ=

NV2k

2

ET

ω > V, κ > γ

γ > ω, κ, V

2/1 T=γEquations:

[ ] DS L,H +−= ρρη

& i

CA +⋅= ρρ&

CA 1SS ⋅= −ρ

SSDD

SS,ETCRATE

ρ=

≈VDB

D

B1 BN

A

VB

VBAωDB

γ

NN C8H17

O

O

O

O

WIRE

WIRE = 1.

2.

3.OR

RO

4.

5.

OR

RO

OR

RO

R = 2-ethylhexyl

Tetracene (TET) Pyromelletimide (PI)

hν

e-485 nm

1010

1011

k CS (

s-1)

β = 0.72 Å-1

No β

See both diffusive coherent

mechanisms

PAY SOME EXPONENTIAL COST TO MOVE*

exp(-∆/RT)B1

activated

V

D A

B2 B3

exp(- βr) coherent

V V

ktot = kcoherent + kactivated

ln kln k

T N

*in molecular systems

A. J. STORM, C. DEKKER et.al., APP. PHYS. LETT., 2002

TWO MECHANISMS SEEN

EXPERIMENTMODEL

MENU

Molecular ElectronicsMolecular Coherent Transport - Devices/MechanismCoherent Gating Inductance and Magnetic LayersCoherence and its Loss – transport

- stereochemical gating

Utility of simple models

Molecules can be more than interconnects –

Use stereochemical dynamics to switch(slowly)

Molecular Rectification Through Electric Field Induced Conformational Changes, J. Am. Chem. Soc., 50, 2002

A SYSTEM WITH ONLY ONE THROUGH-SPACE COUPLING AND VERY HIGH ON/OFF CONDUCTANCE RATIO

CN

CN

SH SH

SH

Pote

ntia

l ene

rgy

/ a.u

.

Cur

rent

/ ar

bitr

ary

units

Voltage

V 12

Cou

plin

g / c

m-1

-1V

0V

+1V

kB×300K300K

100K

V12

DNA-Driven Assembly of Biomaterials

B

B

A

A

T T> m

T T< m

target oligo(anthrax ??)

B B

A A

A A

BB

BB

AA

Mirkin group, 2000

“Prediction is very difficult,

Especially of the future ”

attributed to Niels Bohr

Nanotube NOR gate (Dekker,2001)

A quote to remember:

“The Federal Patent Office should be closed,because everything that can be inventedhas been invented.”

Charles DuellCommissionerFederal Office of Patents1929

Citations to nanostructures

900800700600500400300200100

87 89 91 93 95 97 99 01 year

http://www.hedweb.com/April, 2002

The Hedonistic Imperative outlines how genetic engineering and nanotechnology will abolish suffering in all sentient life.

The abolitionist project is hugely ambitious but technically feasible. It is also instrumentally rational and ethically mandatory. The metabolic pathways of pain and malaise evolved because they served the fitness of our genes in the ancestral environment. They will be replaced by a different sort of neural architecture. States of sublime well-being are destined to become the genetically pre-programmed norm of mental health. The world's last unpleasant experience will be a precisely dateable event.

There is more day to dawnThe sun is but a morning star.

H. D. Thoreau

Optical Properties of Semiconductor Nanoparticles

CdSe/ZnS Core-Shell nanoparticles havesize-dependent optical properties.

CdSe

ZnS

2.3 nm 4.2 nm 4.8 nm 5.5 nm

Larger Band Gap

Smaller Band Gap

Courtesy of Bawendi and Coworkers.

Size Compression Effects in Nanoscale Organic Heterostructures (Almost None!)

ElectroluminescenceNanodiode Array

Technologies: Ultra-High Resolution Displays, Photodetectors, Sensors, Ultra-High Capacity Data Storage, Real-Time Holography, Interferometric Position Sensors

0

100

200

300

400

500

600

450 500 550 600 650Wavelength (nm)

EL. I

nten

sity

(arb

. uni

ts) macro

43 nm90 nm

Weakly coupled alq lumiphores showNO quantum size effect

NO

NO N

OAl

alq

T. J. MARKS ET AL, 2002

Control size scaling

If subunits couple strongly, see size variation

If subunits couple weakly, size independent

interconnect

Experimental results: (30C-30G,air)

-4 0 4

-1

0

1

Cur

rent

[nA]

Voltage [V]

- 4 0 4

- 1

0

1

Cur

rent

[nA]

V o l t a g e [ V ]

Observations:• No conductance at low bias• Finite conductance beyond threshold voltage

Expt: Barton, Zewail et.al,2001 Model: Burin, Berlin, MR 2002

The DFT Calculation: Au-thiol interaction

VWN functional

Double-zeta, polarization, diffuse basis

Geometry Optimization

Nonequilibrium Green’s function for metal

Full many-body self-consistent self-energy

Selective Molecular Adsorption of Selective Molecular Adsorption of NorbornadieneNorbornadiene on Siliconon Silicon

Norbornadiene (NBE) is conformationally predisposed to react with adjacent Si(100)dimers to form organosilicon “cage” structures ([2+2] cycloaddition reaction).

150 Å X 150 Å200 Å X 200 Å

After 2nd NBE Dose

Abeln, Hersam, Thompson, Hwang, Choi, Moore, Lyding, 2001

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

Si

2NBE

Landman et. Al.2001

QUANTUM SIZE EFFECTYEA OR NAY?A simple model

.).( 2122

11 chsstsEsEH zz +++= −+

E2E1 t

absorption

ENERGY

UncoupledWeak coupling (no qse)

Strong mixing (qse)2tE2E1

Carbon substrate

mercury

1.5 nm

V

i

+

-

NN

N O 2

NN

N O 2

NN

N O 2

McCreery and Collaborators. Note :

•Covalent binding•Semiconductor electrode

At (gated) resonance

)(/

/,)(

∆+−><><=

∆−≈∆∆≈

∑ iEjssi

iGresonanceatGGTrT

ssijG ε

(G is Green function∆ is spectral density)

So at resonance, T is unity, and expect Quantized conductance,(even with bad contacts)

Significance?

Wires can talk togetherThiolized gold is not bare gold

work function differscoupling is affected by neighbors on surface

,TUNNELING AND HOPPING,

CLEARLY SEEN

SIMPLE THEORY MODEL(TIGHT-BINDING)

energy tt tt t

t

Tunneling interactionGC pairAT pair

I-V traces at different gate voltages - Coulomb blockade

Vg = -1.00VVg = -0.86VVg = -0.74VVg = -0.56VVg = -0.41V

-50 0 50 100-1.0

-0.5

0.5

I(nA

)

V (mV)

0

-100

So - thiol/Au is bad.

Perhaps use semiconductor interfaces??(McCreery, Hamers, Marks)

What of

Distance dependence??

Nanotube logic Structure(Dekker,2001)

Chiral Molecule (polypeptide helix) as a Solenoid

Does not work for single molecule because of a very weak magnetic interaction

i _

+

U

-B

anode

cathode 0001.0~222

<

ce

cv

η

Comment: 2-D Peculiarity

MFCMFC

ij ij

jijidip

ij

zj

zi

ijji

TdAJ

Tyields

rnSnSSS

V

SSAAny

fMean

JH

,32,

C

32

SO

C

))/,max(/ln(T

))((3

Von transitiphase restoresn interactio icrelativist canisotropi

nsfluctuatio todue 0T ails,Approach Field

dimensions 2 ,

≅=

−=

−=

=

−=

∑

∑

∑

><

><

µ

µ

σσ

ρρρρρρ

ρρ

Main Facts

(1) Ferromagnetism for self-assembled poly-alanine layer at the gold surface for left and right (not mixed) molecules; holds both for C and N terminal connections

(2) Magnetization is controlled both by chirality and polarization

+-Right

-+Left

N-terminalC-terminal

Magnetic Junctions

HAVE: Molecular Resistances, Capacitors

Molecular Rectifiers

WANT: Molecular Inductors!

Molecular Switches

Lewis, Letsinger, Wasielewski groups

DNA – A Tentative Picture

1. For short distances, big gapssuperexchange

2. For longer distances, smaller gapsincoherent motion

3. For multiple stopping placesmultisite hopping