Transcript 4471 Session 4: Numerical Simulations

Summary of 4471 Session 5:
Simulations and Surfaces
More on numerical simulation techniques:
•
•
•
Extracting information from Monte Carlo calculations (e.g. energy, heat
capacity, free energy)
Comparison of molecular dynamics and Monte Carlo methods
Interatomic interactions beyond the pair potential
Structure of (crystalline, clean) surfaces:
•Two-dimensional crystallography
•Low Energy Electron Diffraction (LEED)
• The silicon (001) surface as an example of a surface reconstruction driven by local
bonding changes
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4471 Session 7: Nanotechnology
• A survey of possibilities for nanotechnology
• Ways of making and characterising nanoscale structures
– Lithography (conventional, electron-beam, ‘soft’)
– Scanning probe microscopy
– Self-assembly and directed assembly
• Some electronic properties of nanoscale systems
– Coulomb blockade
– Conductance quantization
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Richard Feynman’s 1959 Lecture
• Richard Feynman at the 1959
annual meeting of the
American Physical Society:
But I am not afraid to consider the final
question as to whether, ultimately---in the
great future---we can arrange the atoms
the way we want; the very atoms, all the
way down! What would happen if we
could arrange the atoms one by one the
way we want them…?
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What is Nanotechnology?
• A set of tools and ideas for the manipulation and control of
matter in the size range between 0.1nmand 1m
• Corresponds to the range of sizes between current
electronics and atomic/molecular dimensions
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Possible applications in
electronics
• Current CMOS electronic technology may be approaching
fundamental limits in hardware performance and cost
• New types of electronic components (e.g. wires,
transistors) operating at smaller length scales
• Completely new ways of manipulating information (e.g.
using reorientable magnetisation of small magnetic
particles)
• New ways of coupling light to electronic processes (e.g.
using patterns on the scale of the optical wavelength)
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Possible applications in
biomedicine
• Understanding of the function of biomolecules particularly the cooperation between them, and their
function in cell membranes (difficult to study by
conventional crystallography)
• Controlling interaction of cells with their environment (e.g.
tissue culture, biocompatibility of implants)
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Richard Feynman’s 1959 Lecture
• Richard Feynman at the 1959 annual
meeting of the American Physical
Society:
Another thing we will notice is that, if we go down
far enough, all of our devices can be mass produced
so that they are absolutely perfect copies of one
another. We cannot build two large machines so that
the dimensions are exactly the same. But if your
machine is only 100 atoms high, you only have to get
it correct to one-half of one percent to make sure the
other machine is exactly the same size---namely, 100
atoms high!
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Methods for producing structure
on the nanoscale
• How do we pattern matter on the nanometer lengthscale?
–
–
–
–
–
Using layer-by-layer growth
By interaction with a ‘beam’ of light or particles
By interaction with a scanning probe tip
By using contact with a ‘stamp’ or ‘mask’
By exploiting molecules’ natural tendency to order as a result of
their mutual interactions
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Optical or UV lithography
• Standard method for current generation semiconductor
device processing (CMOS)
• Use a ‘resist’ whose susceptibility to etching is affected by
light
Activated resist
Chemical etch
(e.g. HF)
• Resolution depends on wavelength of light used: current
(2001) standards for fabrication 0.15m
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Electron beam lithography
• Just as have higher spatial resolution in imaging with
shorter-wavelength electron microscopes, have higher
resolution in patterning too
• Sensitive to electrons because can induce free radical
formation (promoting resist removal) or crosslinking
(preventing resist removal)
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Electron beam lithography
• Possible to produce
feature sizes down to
about 5nm using this
technique
• Figure shows 5nm
metallic line on silicon
surface (Welland et al.,
Cambridge)
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Soft lithography - nanoimprint
lithography
• Can print a structure directly on to a ‘soft’ surface (e.g. a
polymer) from a ‘hard’ mould (e.g. a metal surface
prepared by e-beam lithography)
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Soft lithography - nanoimprint
lithography
• Get a variety of structures e.g. holes and pillars
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•
Soft lithography lithographically induced selfassembly
(LISA)
Apply a large electric field between a mask and a polymer
film
• Polymer film spontaneously grows up towards mask:
Mask
Polymer film
• Pillars form when mask-polymer separation between
200nm and 800nm
• Works because polymer attracted to high-field region
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The scanning probe idea
• Get very high spatial resolution by
– Scattering very short-wavelength waves
Sample
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The scanning probe idea
• Get very high spatial resolution by
– Scattering very short-wavelength waves and
detecting them a long way away (e.g. electron
microscopy, neutron or X-ray diffraction)
Sample
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The scanning probe idea
• Get very high spatial resolution by
– Scattering very short-wavelength waves and
detcecting them a long way away (e.g. electron
microscopy, neutron or X-ray diffraction)
– Bringing a small detector up to the sample
Sample
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The scanning probe idea
• Get very high spatial resolution by
– Scattering very short-wavelength waves and
detcecting them a long way away (e.g. electron
microscopy, neutron or X-ray diffraction)
– Bringing a small detector up to the sample and
arranging for a very localised interaction
between them
Sample
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The scanning probe idea
• Get very high spatial resolution by
– Scattering very short-wavelength waves and
detcecting them a long way away (e.g. electron
microscopy, neutron or X-ray diffraction)
– Bringing a small detector up to the sample and
arranging for a very localised interaction
between them
Scan detector
Sample
across sample
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The STM
(Scanning Tunnelling Microscope)
• Electrons tunnel across small
(few Å) vacuum gap between
tip and sample.
• Relies on sensitivity of
tunnelling to tip-surface
distance (hence localised
interaction).
• Normal mode of operation is
‘constant-current’: feedback
loop keeps current constant as
tip is scanned across surface.
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Tersoff-Hamann Theory
• Assume
– Tip-sample tunnelling probability small (so
‘perturbation theory’ can be applied);
– Spherically symmetric tip;
– Initial state for tunnelling is an s state on tip
• Fermi’s golden rule for rates in quantum physics then gives
conductance:
dI e 2

dV h
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2
|
M
|
 12  ( E1  E2 )
12
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Tersoff-Hamann Theory (2)
• Write the matrix element in terms of the current operator as
2
2
*
*
M

d
r
[





1 ] and that
1 constant
2
2potential,

• Assuming S 12
lies in
a
region
of
2me S
we tip wavefunction is an exponentially decaying s-wave,
we can do all the integrals to get
dI

dV
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2
|

(
r
)
|
 sample tip  ( E1  E2 )
sample
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What does this mean?
• Conductance proportional
to probability of finding
highest-energy electrons
outside the sample near
the tip
• The STM measures the
‘local density of states’
(under certain conditions)
dI

dV
2
|

(
r
)
|
 sample tip  ( E1  E2 )
sample
Surface

Tip
rtip
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Atomic manipulation with the
STM: the ground state
• Can use presence of tip to
affect the potential energy
of atoms on or near the
surface
• Allows movement of
individual atoms along the
surface (‘parallel
process’)...
Atom on surface
Potential energy
Distance along
surface
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Atomic manipulation with the
STM: the ground state
• Can use presence of tip to
affect the potential energy
of atoms on or near the
surface
• Allows movement of
individual atoms along the
surface (‘parallel
process’)...
STM tip
Potential energy
Distance along
surface
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Atomic manipulation with the
STM: the ground state
• Can use presence of tip to
affect the potential energy
of atoms on or near the
surface
• Allows movement of
individual atoms along the
surface (‘parallel
process’)...
Potential energy
Distance along
surface
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Atomic manipulation with the
STM: the ground state
• Can use presence of tip to
affect the potential energy
of atoms on or near the
surface
• Allows movement of
individual atoms along the
surface (‘parallel
process’)...
Potential energy
Distance along
surface
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Atomic manipulation with the
STM: the ground state
• Can use presence of tip to
affect the potential energy
of atoms on or near the
surface
• Allows movement of
individual atoms along the
surface (‘parallel
process’)...
Potential energy
Distance along
surface
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Atomic manipulation example:
Xe atoms on Ni at T=4K
• Individual Xe atoms
manipulated by the
parallel process at T=4K
• STM tip moves `up’ over
atoms, showing that
electrons tunnel more
easily through them than
through vacuum
Don Eigler et al (IBM Almaden)
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Atomic manipulation example:
Xe atoms on Ni at T=4K
• Individual Xe atoms
manipulated by the
parallel process at T=4K
• STM tip moves `up’ over
atoms, showing that
electrons tunnel more
easily through them than
through vacuum
Don Eigler et al (IBM Almaden)
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STM manipulation example:
‘molecular abacus’
• Produced from C60
molecules (about 5Å
across)
• Can be ‘pushed along’
with the STM tip
Jim Gimzewski et al (IBM Zurich)
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STM manipulation: use of
electronic forces
• Can use the electronic
state to manipulate atomic
positions in various ways
• The ‘electron wind effect’
(electrons transfer
momentum to atoms)
• This is believed to be the
physics behind the ‘atomic
switch’ (on and off states
correspond to atom on tip
and on surface)
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e-
e-
Atom on
surface
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Surface
Force
32
STM manipulation: use of
electronic forces
• Can also exploit transient
change of chemical
environment as a
tunnelling electron passes
through the system
• Temporary occupation of
antibonding electronic
states can lead to
desorption of atoms
(‘DIET’- desorption
induced by electronic
transitions)
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Potential energy
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Antibonding state
occupied by tunnelling
electron
Distance from
surface
Electronic ground state
33
STM manipulation: use of
electronic forces
• Example: removal of
H atoms from a
passivated Si(001)
surface
• Conducting `line’ of
reactive bonds, one
atom wide
• Behaves like an
atomic wire
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H atoms removed here
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Hitosugi et al, Tokyo
University and Hitachi
34
Single-molecule vibrations
• Study vibrations of
individual molecules and
individual bonds by
looking at phonon
emission by tunnelling
electrons
Wilson Ho et al., UC Irvine
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Single-molecule vibrations
• Study vibrations of
individual molecules and
individual bonds by
looking at phonon
emission by tunnelling
electrons
• New possibilities for
inducing reactions by
selectively exciting
individual bonds….
Wilson Ho et al., UC Irvine
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Scanning Force Microscopy
(SFM)
• We would like to
– be able to image insulating (as well as conducting) surfaces
– measure forces, as well as currents, on the atomic scale, in order to
• learn more about them
• control the manipulation process
• The solution: scanning force microscopy (SFM)
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Scanning force microscopy
• Measure deflection of small ‘cantilever’ on which tip is
mounted, by deflection of a laser beam
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Scanning force microscopy
• It used to be thought that contact mode would give
the best resolution, but the interpretation is
complicated by strong mechanical interactions
between the tip and the sample
Alex Shluger et al, CMMP,
UCL
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Scanning force microscopy
• Most recent development is ‘non-contact’
force microscopy: tip vibrates above sample
and only approaches briefly
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Scanning force microscopy
• Allows truly atomic-resolution force
microscopy images to be obtained for the
first time.
Defects on
surface
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Defects
‘migrate’
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Ernst Meyer et al, Basel
41
Scanning force microscopy
• Allows truly atomic-resolution force
microscopy images to be obtained for the
first time.
Atomic ‘step’
on surface
Ernst Meyer et al, Basel
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Scanning force microscopy
• Understanding the physics behind the
formation of these images is complicated...
Image of NaCl
‘island’
Simulated
tip scan
Ernst Meyer et al, Basel
Adam Foster and Alex Shluger, CMMP, UCL
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Other ways of producing
structure with SPM
• Find a local chemical
reaction promoted by
the presence of a tip for example
oxidation…
• …or exposure of a
resist (as in e-beam
lithography)
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Other ways of producing
structure with SPM
• Find a local chemical
reaction promoted by
the presence of a tip for example
oxidation…
• …or exposure of a
resist by the local
electron current (as in
e-beam lithography)
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Self-assembly
• Exploit chemical forces to produce organization into
desired patterns
• Inspired by biology (and soap!): e.g. spontaneous
formation of bilayer membranes (living cells and soap
films)
Hydrophilic
headgroups (polar)
Hydrophobic tails (nonpolar)
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Self-assembly
• Generate films on metal surfaces by a similar method: end
‘tail’ part of molecule with an S-H group that reacts with
gold
• Head group can now be arbitrary (e.g. a biological
antibody or antigen)
Headgroup
C-S-Au bonds
Gold substrate
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Quantum dots and huts
• Also get spontaneous self-organization in other ways, for
example during ‘strained’ growth of one material on
another when their lattice parameters differ
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Examples of atomic-scale lines
• Lines of Si ad-dimers
formed by annealing
(heating) the Si-rich
SiC(001) surface
• Self-assembly, probably
mediated by long-range
elastic interactions
between the lines
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Directed growth
• Try to combine the idea of control (as in lithography) and
spontaneous formation of an ordered structure (as in selfassembly) by ‘directed growth’ that is spontaneous
following some initiation event
• For example, use an SPM initiation (slow, expensive, can
only be done at a limited number of sites) followed by a
self-propagating chemical reaction
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Molecular device:
Self-directed ‘wire’ growth
• Lines of molecules can
be grown on silicon by
a self-directed process
• Follows use of STM
tip to produce a single
unpaired electron in a
dangling bond
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Lopinski et al, Nature 406 48
(2000)
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Molecular device:
Self-directed ‘wire’ growth
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Molecular device:
Self-directed ‘wire’ growth
•Do the resulting ‘wires’
conduct? Watch this space...
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Richard Feynman’s 1959 Lecture
• Richard Feynman at the 1959 annual
meeting of the American Physical
Society:
When we get to the very, very small world---say circuits of
seven atoms---we have a lot of new things that would
happen that represent completely new opportunities for
design. Atoms on a small scale behave like nothing on a
large scale, for they satisfy the laws of quantum
mechanics. So, as we go down and fiddle around with the
atoms down there, we are working with different laws, and
we can expect to do different things. We can manufacture
in different ways. We can use, not just circuits, but some
system involving the quantized energy levels, or the
interactions of quantized spins, etc.
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Electronic and magnetic
properties of nanosystems
• Electronic and magnetic properties of nanoscale structures
differ from bulk (because electrons and other excitations
experience the nanoscale structure, on the same scale as
their own de Broglie wavelength, and are confined)
• They also differ from conventional molecules, because the
structures are in intimate contact with their environment
and so the systems are `open’
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Atomic manipulation example:
‘quantum corals’
• ‘Coral’ (circle of iron
atoms on copper
surface) gradually
assembled by moving
atoms across surface
Don Eigler et al (IBM Almaden)
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Atomic manipulation example:
‘quantum corals’
• ‘Coral’ (circle of iron
atoms on copper
surface) gradually
assembled by moving
atoms across surface
• When circle complete,
‘ripples’ observed
within it
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Don Eigler et al (IBM Almaden)
57
Atomic manipulation example:
‘quantum corals’
• ‘Coral’ (circle of iron
atoms on copper
surface) gradually
assembled by moving
atoms across surface
• When circle complete,
‘ripples’ observed
within it
Don Eigler et al (IBM Almaden)
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Atomic manipulation example:
‘quantum corals’
• Ripples do not arise
from shape of surface
• Come from presence
of electron ‘standing
wave’ quantum states
• This affects the local
density of states and
produces the apparent
`ripples’
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Don Eigler et al (IBM Almaden)
59
Atomic manipulation example:
`quantum corals’
• Shape of ripple pattern
depends on shape of
coral - it’s quite
different for a
rectangle
Don Eigler et al (IBM Almaden)
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Coulomb blockade
• When a metallic
nanoparticle is almost
isolated from its
surroundings, there is a
non-negligible charging
energy to add an electron
• This charging energy can
‘block’ current flow in a
certain voltage range
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Coherent transport
• Another difference compared with current flow on the
macroscopic scale: transport in small structures is coherent
(occurs as the result of a single quantum process)
• As a result conventional formulae, such as the series and
parallel addition of resistances, no longer hold
• Must be replaced by a way of thinking involving two new
quantities: the transmission coefficient and the Green’s
function
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Coherent transport: STM of
benzene on the graphite surface
• Molecule appears
triangular in the STM,
even although its true
shape is hexagonal
• Arises from quantum
mechanical
interference (like
double slit
experiment)
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Origin of the interference
• There are no benzene
states at the Fermi energy
• Tunnelling takes place
through highest occupied
and lowest unoccupied
molecular states, some
distance away in energy
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•These two routes for charge
transport (corresponding to
positive and negative transient
charging) can interfere
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How the interference works
• Bonding orbital: same
sign on adjacent carbon pz
orbitals
+
+
-
-
Bonding
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How the interference works
• Bonding orbital: same
sign on adjacent carbon pz
orbitals
• Antibonding orbital:
opposite signs on adjacent
pz orbitals
+
+
+
-
-
-
-
+
Bonding
E   / 2
Antibonding
E   / 2
( is molecular energy
gap)
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How the interference works
• Bonding orbital: same
sign on adjacent carbon pz
orbitals
• Antibonding orbital:
opposite signs on adjacent
pz orbitals
• Transport is controlled by
the Green function
+
+
+
-
-
-
-
+
Bonding
G( E )  
n
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Antibonding
top  n  n bottom
E  En
67
How the interference works
• Direct transmission
through an atom into the
substrate: the two
contributions cancel out
because the energy
denominators have
opposite signs
+
+
+
-
-
-
-
+
Bonding
G( E )  
n
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Antibonding
top  n  n bottom
E  En
68
How the interference works
• Transmission involving a
hop along the molecular
bond: electron picks up an
extra sign change in the
antibonding state and
produces constructive
interference
+
+
+
-
-
-
-
+
Bonding
G( E )  
n
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Antibonding
top  n  n bottom
E  En
69
Conductance quantization
• When transmission
probability in a particular
‘channel’ is close to unity,
get ‘quantization’ of
conductance in units of
e2/h
• Happens in specially
grown semiconductor
wires grown by e-beam
lithography, or in metallic
nanowires
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Conductance
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Extension
Jacobsen et al.
(Lyngby)
70
Conductance quantization
• Such nanowires can be
produced by pulling an
STM tip off a surface, or
simply by a ‘break
junction’ in a macroscopic
wire
Jacobsen et al.
(Lyngby)
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Conductance quantization
• Such nanowires can be
produced by pulling an
STM tip off a surface, or
simply by a ‘break
junction’ in a macroscopic
wire
• Understood on the basis of
simultaneous changes in
atomic and electronic
structure
Jacobsen et al.
(Lyngby)
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Extreme nanotechnology:
single-molecule electronics
• Experiments now
possible on the
conductance properties
of individual
molecules
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Langlais et
al. 1999
73
Extreme nanotechnology:
single-molecule electronics
• Experiments now
possible on the
conductance properties
of individual
molecules
• Those chosen for
conducting
applications are
invariably conjugated
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Langlais et
al. 1999
74
Extreme nanotechnology:
single-molecule electronics
• Experiments now
possible on the
conductance properties
of individual
molecules
• Those chosen for
conducting
applications are
invariably conjugated
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Langlais et
al. 1999
75
Molecular device: Example
Molecular Transducer
• ‘Transducer’ made
from single C60
molecule
• Conductance of
molecule changes as it
is ‘pressed’ by the tip
Jim Gimzewski et al (IBM Zurich)
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Summary and Conclusions
• A variety of methods now available to manipulate and
control matter on the atomic and molecular scale
• Focus is now on novel properties of the resulting
structures, potential for applications, and on combining
lithography and directed growth for ‘mass production’
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