Electron Transport through Molecules
and Wires in Nano-Scale Contacts
by Egill Skúlason
DTU Course: Modern Physics, 7th of March 2006
1 µm
K. S. Thygesen, K. W. Jacobsen, PRL, 91 (2003)
E. Scheer et al., Nature, 394 (1998), SEM
Outline
•
•
•
•
Motivation
Molecular Electronics
Theoretical Scheme
Electron Transport Calculations
– Wires: Al, Na and Pt
– Molecules: H2 and CO
• Summary
1
From microelectronics
to nanoelectronics … ?
Moore’s law:
The number of
transistors on a
square inch of
integrated circuits
is doubled every
18 months
Can molecular
electronics solve
the problems ?
2
Figure taken from presentation by Cees Decker: mb.tn.tudelft.nl/user/dekker/files/carbonnanotubes.pdf
The Idea of Molecular Electronics
E. Scheer et al., Nature, 394 (1998)
Change the on/off electron
transport using external field,
e.g. STM tip (animated figure)
Molecular Biophysics homepage at
the Delft University of Technology: mb.tn.tudelft.nl/
Change the on/off electron
transport mechanically,
Mechanically Controllable
Break Junction (scanning
electron microscope figure)
Build up electronic devise
with organic molecules 3
The Interests in Molecular Electronics
4
Molecular Biophysics homepage at the Delft University of Technology: mb.tn.tudelft.nl/
Theoretical Scheme for Electron Transport
• Numerical Green’s function method: Calculating the linear
response conductance of molecules and nano-contact.
• The system is divided into a central scattering region and
attached leads
e.g. of S region:
G = I/V
• The electronic structure of both the scattering region and the
leads is described using Density Functional Theory (DFT).
• A set of localized basis functions consisting of partly occupied
Wannier functions (WFs) is used to represent the electronic
states. (Can be constructed from e.g. plane-waves based DFT ).
5
K. S. Thygesen, K. W. Jacobsen, Chem. Phys., 319 (2005)
Wannier Functions
By adding unoccupied states in
the DFT calculations, one can
get partly occupied WFs
K. S. Thygesen et al., PRL, 94 (2005)
The transmission function can be calculated when selected orbitals
are missing in the basis set, to understand which states are playing
the main part of the conductance.
6
K. S. Thygesen, K. W. Jacobsen, Chem. Phys., 319 (2005)
Outline
•
•
•
•
Motivation
Molecular Electronics
Theoretical Scheme
Electron Transport Calculations
– Wires: Al, Na and Pt
– Molecules: H2 and CO
• Summary
7
Single Atom Contacts
Molecular Dynamic Simulations
Transmission Electron Microscopy
Au
Cu
Out of Cu, Ag, Au, Ni, Pd and Pt
only Au and Pt form chains.
Snapshot showing the timeevolution of the elongation
of a Au nanowire
Taken from presentation by K.S. Thygesen, Ph.D. course at DTU, Modern Physics,
dcwww.fys.dtu.dk/~mrs/Moderne_Fysik/E02/Conductance.ps (2002)
8
Conductance Oscillation in Monatomic Wires
Al
Conductance oscillation
Al : 4 atom period (50% osc. ampl.)
Na : 2 atom period (5% osc. ampl.)
Oscillation amplitude
increases ca. 10% with
the 3 atom basis
9
K. S. Thygesen, Ph.D. Thesis, CAMP, DTU (2005)
K. S. Thygesen, K. W. Jacobsen, PRL, 91 (2003)
Origin of Oscillation?
Local charge neutrality:
Conductance oscillations for
monovalent metals (Na) are even/odd
but for Al wires it is four-atom period.
However, it can not account for the
phase, max in N = 2, 6, … but not at
N = 3, 7, …
When you add an atom into the
chain between the leads, you get
resonance in the transmission
10
K. S. Thygesen, Ph.D. Thesis, CAMP, DTU (2005)
Simple Model for Conductance Oscillations
Illustration in k space the evolution of the
discrete spectrum of the free wire as a
function of the wire length
For each eigenvalue, the width of the
corresponding resonance is indicated (∝ 1/N)
The Fermi level is fixed by the macroscopic
electrodes which fixes the Fermi level for
wires of any length.
- Fermi level for Al wire is at k = π/4.
- As N increases the resonances move down
through the Fermi level in a systematic
fashion.
- The Fermi level coincide with the center of a
resonance in periodic event of period four
starting at N = 3.
This Model:
Period of the conductance osc.
In addition it provides the
actual position of the
resonances.
First max: N = 3
First min: N = 5
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The Fermi level for metals with a half-filled
K. S. Thygesen, K. W. Jacobsen, PRL, 91 (2003)
valance band (e.g. Na) is at k = π/2
Simple Model vs. First Principles Calculations
Testing the simple model
quantitatively to reproduce the
first-principles results, using:
Except for the shortest wires (N = 1, 2)
the model gives a good description of
the conductance with an average
deviation of less than 15%.
12
K. S. Thygesen, K. W. Jacobsen, PRL, 91 (2003)
point contact
values 2.0-2.3
G (2e /h)
PtPt point
contact andTheoretical
Pt
short
chain
are in a good agreement with the
0
2
experimental value 2.1 G0
Pt point contact
Pt short chain
Pt short chain
Theoretical values 1.3-2.0 G0 are
in a good agreement with the
experimental value 1.5 G0
When the contacts breaks the
conductance decays exponentially
The increase in the conductance
just before the contact breaks
could be related to the linearization
of the chains which activates more
conductance channels
13
M. Strange et al., Accepted in PRB, (2006)
Pt-H2-Pt Contact
Full transmission: Wide plateau with T ≈
1 crossing the EF referred to 1G0 plateau
From where comes the 1G0 plateau?
Wannier functions describing the H2
consist of two s-like orbitals, and form
bonding and anti-bonding combinations
The narrow peak around -7 eV is
completely gone when the bonding state is
removed but is not affected by the absence
of the anti-bonding state.
For energies above -3 eV we have the
opposite situation where the removal of
the bonding state has no significant effect
on the transmission.
Conclusion: The peak at -2 eV &
the 1G0 plateau determines the
conductance due to transmission
through the anti-bonding state
14
K. S. Thygesen, K. W. Jacobsen, PRL 94, (2005)
Experimentally, when CO gas is in the Pt
contact, the conductance peaks are at 0.5 and
1.1 G0 instead of 1.5 and 2.1 G0 without CO gas
Pt-CO-Pt Contact
Theory: Pt-CO-Pt Contact
T function for A & B show G
around 1.5 and 0.5 G0 at EF
G decreases linearly from 2.1 to 1.5 G0
(upright bridge). When one of the C-Pt
bonds breaks (tilted bridge), G jumps
to ~ 0.5 G0
Group Orbitals
LUMO
(mainly d-like centered on Pt)
The peak at 1.1 G0 from experimental
The current is15carried
histograms is not explained by these
out by the LUMO’s
calculations
M. Strange et al., Accepted in PRB, (2006)
Summary
• The main idea of molecular electronics has
been explained.
• The theoretical scheme for electron transport
calculations was briefly illustrated.
• The main features of electron transport
calculations through wires and small
molecules was presented.
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