Electron Transport Modeling for Conduction Optimization of NanoEngineered Molecular Interconnects

1
Electron Transport Modeling for Conduction
Optimization of Nano-Engineered Molecular
Interconnects

• G. Sirinakis, R. E. Geer, E. Eisenbraun, J. Welch
  and A. E. Kaloyeros
• School of Nanosciences and Materials
• University at Albany, SUNY 12203

2
Introduction

• Molecular conductors have received significant
  attention as potential nanoscale interconnects
  for giga-scale integration
• Bridge dimensional regime between lithographic
  structures and atomic sizes
• Exploit spontaneous or directed self-assembly
• Understanding and controlling the electron
  transport mechanisms of such molecular conductors
  is of primary importance
• How is conductance affected by the internal
  structure of the molecule?
• How is conductance affected by the coupling of
  the molecule to the contacts?
• Landauers theory A simple and powerful approach
  to predicting the conductance and current-voltage
  characteristics of a system

contacts
molecular interconnect
leadsconductor
3
Landauers Theory of Conductance Zero
Temperature
Conduction is taking place through a single
energy channel near the Fermi energy
LEAD1
LEAD 2
Total current is given by
CONTACT
CONTACT
CONTUCTOR
Energy channel in the conductor
Conductance is given by
The conductance, G, is quantized and proportional
to the number of transverse modes M

• M number of transverse modes in LEAD1
• T Transmission probability of the conductor

S. Datta, 1997
4
Landauers Theory of Conductance Non-Zero
Temperature
S. Datta, 1997
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Landauers Theory for Molecular
InterconnectsConduction Regimes

• Coherent electron tunneling resonant (ballistic)
  transport
• The Fermi level of the contact becomes resonant
  or near resonant with the energy levels of the
  molecular wire
• Coherent electron tunneling Non-resonant
• The Fermi level of the contact occurs in the
  middle of the HOMO/LUMO gap of the molecular wire
• Incoherent transfer
• The electronic levels in the molecular wire
  couple with phonons
• The electronic states in the wire will develop an
  effective intra-molecular lifetime
• Ohmic conduction

M. Magoga C. Joachim, 1998 A. Aviram M.
Ratner, 1998 S. Datta, 1996
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Coherent Electron Tunneling Resonant (Ballistic)
Transport
Resonances with molecular energy levels

• Conductance per energy channel

T
1
This resistance (G-1) arises from the interface
between the molecular interconnect and the
contacts Quantum contact resistance
HOMO
LUMO
V
0
Transport under these conditions will result in
no length dependence
M. Magoga C. Joachim, 1998 A. Aviram M.
Ratner, 1998 S. Datta, 1996
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Coherent Electron Tunneling Non-Resonant
Transport
Energy range where the conduction is taking place
T

• Damping factor ?
• HOMO-LUMO gap
• Electronic structure of the molecule
• Coefficient G0
• Interactions between the molecule and the leads

1
LUMO
HOMO
V
0
For a given molecular structure it is possible to
modify G0 without any changes in ?. Therefore, it
is possible to independently construct the wire
and the electrode contact moieties to
simultaneously optimize G0 and ?
A. Aviram M. Ratner, 1998 M. Magoga C.
Joachim, 1998
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Incoherent Transfer Ohmic Conductance
t
?10000cm-1
E

1
2
N
?1.0cm-1
?
k electron transfer rate ? dephasing rate
Donor
Acceptor
?0.001cm-1

• Small ? limit
• kk0(t/?)N?t2/ ?2

• Large ? limit
• kk0 ?2/N ?

In the weak dephasing limit there are two
independent channels for electron transfer
tunneling and inelastic scattering
Evolution of the electron transfer rates as N,
the number of bridge sites (?1500cm-1, t300cm-1)
For long interconnects in the strong dephasing
limit, inelastic scattering channel will begin to
dominate. Under these conditions the conductivity
will dependent on inverse length, as suggested by
Ohms law
W.B. Davis et al 1997 A. Aviram M. Ratner,
1998
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Requirements for Molecular Interconnects

• In general, to support effective charge transfer,
  molecular interconnects require (a) set of
  overlapping electronic states which connects (b)
  two or more distant functional groups at the
  contacts (alligator clips)

• Delocalization of the electronic structure along
  one axis
• A typical candidate for building block of a
  molecular interconnect would have a delocalized
  ?-orbital
• Structural stability of the molecular chain
• Maximization of the overlap between the
  delocalized electronic states of the molecule
  leads to lowest resistance
• High degree of molecular order along interconnect
  required for resonant tunneling
• Alligator clips that can form direct chemical
  attachments to the electrode surfaces
• Interconnection of the electrode energy bands and
  the molecular states

A. Aviram M. Ratner, 1998 M. Magoga C.
Joachim, 1998
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Proof-of-Concept Candidate for Nano-Engineered
Molecular Interconnects

• Construct building block for self-assembling,
  1D ordered molecular array
• Anti-parallel strands of the ala-gly sequence
  enhance the stability of the structure to provide
  a single strand b-sheet
• ?-turns Attachment and Conduction Groups
• Cysteine Thiol or silyl moiety for promotion of
  directed self assembly on Au or SiO2
• Phenyalanine ?-? unit comprised of 6-member
  carbon ring for proof-of-concept demonstration

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Proof-of-Concept Candidate for Nano-Engineered
Molecular Interconnects
On-axis spacing

• Physical dimension targets
• On-axis lattice spacing lt 2.0
• Line width 2nm
• Line height 6nm
• Electrical property targets
• Electrical breakdown field 106 V/m
• Electrical conductivity (as c-axis graphite)
  200??-cm

Substrate
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Performance Targets Nano-Engineered Molecular
Interconnects
Best case scenario Conjugated pendant groups
form 1D semi-metal comparable to c-axis graphite

• Assume conjugated ?-? electrons associated with
  1D molecular crystal can achieve resistivity
  comparable to c-axis graphite ? 200 ??-cm
• Conservative estimates for Cu resistivity in a
  line with cross-sectional area of 2 nm x 6 nm
  12 nm2 gt 500 ??-cm if perfect crystallinity is
  not maintained (Extrapolated from data on CVD Cu
  with indium surfactant on TaN substrate,
  Belyansky, Eisenbraun, Kaloyeros)
• Assume breakdown electric field for 1D molecular
  crystal can exceed 106 V/m
• Maximum current density Jmax V/(?I) E/ ? 5
  x 107 A/cm2
• This exceeds the estimated current density
  required by the ITRS roadmap for the 2014
  generation (4.6 x 106 A/cm2)

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Current Status

• Self-assembly demonstration on patterned
  substrates underway
• Evaluate surface attachment
• Au substrate (Thiol moiety)
• SiO2 substrate (Trichlorosilane,
  Trimethoxyalkysilane moiety)
• BioMolecular Synthesis
• DNA Synthesis underway

Next Steps

• Self-assembly demonstration on patterned
  substrates
• Evaluate molecular interconnect conformation on
  template
• Lamellae formation Single strand attachment
• Test Structure evaluation (See Adjacent Poster)
• Evaluate current-voltage characteristics
• Electrical nanoprobe, Electrical test structure
• Optimize charge transport
• Variation of conducting moiety/contact moiety