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
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• 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
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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.
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• 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.’
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• ‘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
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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
???
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Single
Electronics
Molecular
Electronics
1D-devices
NEW
SWITCH
The 2001 Feynman Prize
Mark Ratner
MOTIVATION
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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
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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
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• Low Manufacturing Cost
• Easier to Manufacture
Size
• Molecular Electronics is a way to extend
Moore’s Law past the limits of standard
semiconductor Circuits.
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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
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• 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
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• 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
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(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.
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Our Scope-Trying to address…
• What controls current flow and hence conductance in molecules ?
• How best to deal
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• How best to deal with geometry, contact, quantum interference, charging effects …?
Our Approach
• Extended Huckel Theory (EHT), a semi empirical method
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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
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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
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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
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• 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.
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• 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
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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
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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.
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• 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
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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
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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
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• 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.
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Landauer- formula.
Where, ( )VETI ,α
)(),( 21
+ΓΓ= GGtraceVET
The current flowing through the device is
[ ]dEEfEfGGTrh
eI )()()((
22121 µµ −−−ΓΓ= ∫
∞
∞−
+
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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
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• 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
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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.
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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 ,
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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
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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
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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.
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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
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2.C.Preferencial Kala
3.R.Hariharan
Theoretical Physics Division,IGCAR,INDIA
4.R.Valsakumar
5.S.Mathijaya