Electron Transport through Molecular Electronic Devices

Electron Transport through

Molecular Electronic Devices

D.John Thiruvadigal

SRM University,INDIA

ICTP-IOP,Hanoi 24/12/2009

SRM University,INDIA


SUMMARY OF THIS PRESENTATION

• Limit of silicon technology

• Moletronics-An alternative?

• Extended Huckel theory(EHT)

• Non equilibrium Greens’s function


• Non equilibrium Greens’s function

formalism(NEGF)

• Landauer Formula

• Some results on I-V characteristics

Modern CMOS

Beginning ofSubmicron CMOS

Deep UV Litho

90 nm in 2004

Moore's Law Trend

10 µm

1 µm

39 Years of Scaling History

Summary: density↑↑↑↑speed ↑↑↑↑

functionality↑↑↑↑cost/bit


Presumed Limitto Scaling

100 nm

10 nm

1 nm

1970 1980 1990 2000 2010 2020

Scaling History

� Every generation– Feature size shrinks by 70%– Transistor density doubles– Chip cost comes down by 40%

� Generations occur regularly– On average every 2.9 years over

the past 39 years– Recently every 2 years

Source: Dennis Buss, 2005 Gordon E Moore

CMOS-Current Status

• Heat dissipation.

– 500 MHz microprocessor with 10 million transistors emits almost 100 watts--more heat than a stove-top cooking surface.

• Leakage from one device to another.


• Leakage from one device to another.

– Some electrons can gain sufficient energy to hop from one device to another, especially when they are closely packed.

• Fabrication methods (Photolithography).

– Device size is limited by diffraction to about one half the wavelength of the light used in the lithographic process.

• ‘Silicon Wall.’


• ‘Silicon Wall.’

– At 50 nm and smaller it is not possible to dope silicon uniformly. (This is the end of the line for bulk behavior.)

CMOS

CMOSAlternative devices

Fe

atu

reF

ea

ture

Siz

e (

Siz

e (

µµ µµ µµ µµm

)m

)

0.1µµµµm in 2002

CMOS IC evolutionCMOS IC evolution100

10

1

CMOS: past and futureCMOS: past and future


Alternative

devices

After J.D. Plummer, Proceedings of IEEE, 2001.

Fe

atu

reF

ea

ture

0.1µµµµm in 2002

Transition Region

Quantum devices

Atomic dimensions

YearYear

0.1

0.01

0.001

1960 1980 2000 2020 2040

Which of Current Nanoelectronic

Concepts Will Become the NEW

SWITCH?

Molecular

Spintronics

???


Single

Electronics

Molecular

Electronics

1D-devices

NEW

SWITCH

The 2001 Feynman Prize

Mark Ratner

MOTIVATION


Mark Ratner

Northwestern University

Father of Molecular Electronics

Molecular Electronics-An

Alternative Technology?• Sometimes called moletronics

• Molecular electronics is a branch of applied physics which aims at using


applied physics which aims at using molecules as passive or active electronic components.

• These molecules will perform the functions currently performed by semiconductors.

Why Molecules?

• Size

• Power

• Speed

• Low Manufacturing Cost


• Low Manufacturing Cost

• Easier to Manufacture

Size

• Molecular Electronics is a way to extend

Moore’s Law past the limits of standard

semiconductor Circuits.


semiconductor Circuits.

• 100X smaller than their counterparts

Power / Speed

• Currently Transistors cannot be stacked,

which makes them quite inefficient!

• Molecular technology will be able to add a


• Molecular technology will be able to add a

3rd dimension.

• Femtoseconds switching times.

Manufacturing

• Most designs use Self-Assemblyprocess.

• Individual Molecules can be made exactly


• Individual Molecules can be made exactly the same by the Billions.

• Molecular assembly tends to occur at Room Temperature.

Molecular energy levelsThe orbitals have discrete energy levels

– Highest Occupied Molecular Orbital (HOMO)-like valence band

– Lowest Unoccupied Molecular Orbital (LUMO)-like conduction band


(LUMO)-like conduction band

HOMO

LUMOESeparated by a HLG

(HOMO-LUMO Gap)

A Two Terminal Molecular Device

Here a Benzene dithiol (BDT) molecule is attached to the surfaces of predefined electrodes through appropriate thiolate groups.


L

ELECTRODE R

ELECTRODEMOLECULE


eV

VI

Molecular

Orbitals

Our Scope-Trying to address…

• What controls current flow and hence conductance in molecules ?

• How best to deal


• How best to deal with geometry, contact, quantum interference, charging effects …?

Our Approach

• Extended Huckel Theory (EHT), a semi empirical method


coupled with

• Non equilibrium Green’s Function (NEGF)formalism.

• EHT accounts for the electronic structures

of the molecule and the contacts

• The nonequilibrium Green’s function

NEGF formalism accounts for quantum


NEGF formalism accounts for quantum

transport in molecular conductors out of

equilibrium.

Why Semi-empirical method?• Quantum mechanical description of electrons based on same principles as ab Initio, but with many (more) approximations built into the equations to make calculations go faster.

– Also commonly contain some parameterization (design of computational equations or input parameters) based on


equations or input parameters) based on experimental (empirical) data.

• Calculations are faster than ab Initio

• Semi-empirical calculations have been most successful in the description of molecules are of moderate size.

Extended Huckel Theory(EHT)• In the quantum chemistry

community, Hückel is best known for introducing in 1930 a simple theory for the treatment of conjugated molecules and aromatic molecules.

• This theory came to be known

Eric Hückel


• This theory came to be known as"Hückel molecular orbital theory" or simply"Hückel Theory".

• This was later extended by Roald Hoffmann (1963)and has been widely used in organic and inorganic chemistry as Extended Huckel Theory(EHT).

Roald

Hoffmann

• EHT is based on the Hückel method but,

while the original Hückel method only

considers pi orbitals, the extended method

also includes the sigma orbitals.


• It involves calculations of the electronic

interactions in a rather simple way where the

electron-electron repulsions are not explicitly

included and the total energy is just a sum of

terms for each electron in the molecule

• The off-diagonal Hamiltonian matrix

elements are given by an approximation

due to Wolfsberg and Helmholz that

relates them to the diagonal elements and


relates them to the diagonal elements and

the overlap matrix element.

Hij = K Sij (Hii + Hjj)/2

K is the Wolfsberg-Helmholtz constant.

In the extended Hückel method, only

valence electrons are considered; the

core electron energies and functions are

supposed to be more or less constant


supposed to be more or less constant

between atoms of the same type.

• The method uses a series of parametrized energies calculated from atomic ionization potentials or theoretical methods to fill the diagonal of the Fock matrix.


• After filling the non-diagonal elements and diagonalizing the resulting Fock matrix, the energies (eigenvalues) and wavefunctions (eigenvectors) of the valence orbitals are found.

Non Equilibrium Green’s function

formalism(NEGF)

H + USCF µ1 µ2


Σ1 Σ2

2

S. Datta, Quantum Transport: Atom to Transistor, Cambridge, 2005

Supriyo Datta,

Purdue University

• The molecular Green’s function G is given by

S is the overlap matrix

( ) 1

21)( −Σ−Σ−+−= SCFUHESEG


S is the overlap matrix

H is the Hamiltonian of the molecule.

• The self consistent potential USCF is calculated by employing a simple self consistent field method

)( eqSCF NNUU −=

• Neq is the equilibrium number of electrons in

the molecule as given by

( )foeq EfN −= ε2


• The number of electrons on the molecule is

calculated using the following equation.

( )foeq

[ ]∫∞

∞−

++ Γ−+Γ−= )()()()(2

12211 GGTrEfGGTrEfdEN µµ

π

Landauer Formula

• The current flowing through the device is

calculated with the help of the standard

Landauer- formula.


Landauer- formula.

Where, ( )VETI ,α

)(),( 21

+ΓΓ= GGtraceVET

The current flowing through the device is

[ ]dEEfEfGGTrh

eI )()()((

22121 µµ −−−ΓΓ= ∫

∞

∞−

+


f(E- µµµµ1,2) denotes the Fermi distributions with

electrochemical potential defined as

22,1

eVE f ±=µ

Some Results…on I-V characteristics

• Effect of rotation

• Effect of anchoring groups

• Effect of Isomery


• Effect of Isomery

• Effect of substitute groups

Effect of rotation

0o

The switching between

the configuration before

and after rotation will

result in significantly

4,4’- BPD


30oresult in significantly

changed transport

properties of the

molecule. Therefore 4,4’-

bipyridine molecular

Junction can be used as

a switch.

P.A.Priya,C.P.Kala,D.J.Thiruvadigal ,Int.J. of Nanoscience Vol. 8,

Nos. 1 & 2 (2009)

Effect of anchoring groups

BDA

BDT

•By changing from thiol

to amino anchoring

groups,the spread of

molecular conductance

gap is reduced.


gap is reduced.

•The increased

conductance in BDT is

due to the chemical

versatility of the gold-

sulphur bondP.A.Priya,C.P.Kala,D.J.Thiruvadigal ,IEICE TRANS. ELECTRON.Vol.E92-

C,No.12(2009)

Effect of Isomery

4,4’

2,6’

2,4’

2,2’

We observe that 2, 2’

bipyridine junction has

the highest conduction,

followed by 4, 4’

bipyridine junction and 2 ,


2,4’

bipyridine junction and 2 ,

4’ bipyridine junction has

the poorest conductance

owing to its

nonsymmetrical

arrangement

P.A.Priya,C.P.Kala,D.J.Thiruvadigal ,J. of Computational and Theoretical

Nanoscience Vol.6 (2009)

Effect of substitute groups


Electron-donating groups increases the σ-orbital electron density in

the benzene ring, leading to an increase in the energy of the σ -

system and thereby shifting the HOMO closer to EF.

Effect of single and double substitute

groups


The results demonstrate that side groups attached to molecular devices

offer the possibility of modifying their transport behaviors in a controlled

way and can improve/add some particular functionality for the design of

molecular electronic devices. By applying multiple functional groups to the

same parent molecule it may be possible to obtain stronger influence.

To Conclude..

Electron Transport through Molecular Electronic Devices

EHT NEGF

SIMULATOR I-V characteristics

Effect of rotation

Effect of anch.


EHT NEGF LFEffect of anch.

groups

Effect of Isomery

Effect of

substitute groups

My THANKS to my collaborators

SRM UNIVERSITY,INDIA

1.P.Aruna Priya

2.C.Preferencial Kala


2.C.Preferencial Kala

3.R.Hariharan

Theoretical Physics Division,IGCAR,INDIA

4.R.Valsakumar

5.S.Mathijaya

MERRY MERRY MERRY MERRY CHRISTMAS CHRISTMAS CHRISTMAS CHRISTMAS

& & & &


& & & &

HAPPY HAPPY HAPPY HAPPY

NEW YEAR NEW YEAR NEW YEAR NEW YEAR 2010201020102010

Electron Transport through Molecular Electronic Devices

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