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Summary of 4471 Session 5: Simulations and Surfaces

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4471 Solid-State Physics. 1. Summary of 4471 Session 5: Simulations and Surfaces ... 4471 Solid-State Physics. 3. Richard Feynman's 1959 Lecture ... – PowerPoint PPT presentation

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Title: Summary of 4471 Session 5: Simulations and Surfaces


1
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

2
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

3
Richard Feynmans 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…?
4
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

5
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)

6
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)

7
Richard Feynmans 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!
8
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

9
Optical or UV lithography
  • Standard method for current generation
    semiconductor device processing (CMOS)
  • Use a resist whose susceptibility to etching is
    affected by light
  • Resolution depends on wavelength of light used
    current (2001) standards for fabrication 0.15?m

Activated resist
Chemical etch (e.g. HF)
10
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)

11
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)

12
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)

13
Soft lithography - nanoimprint lithography
  • Get a variety of structures e.g. holes and pillars

14
Soft lithography - lithographically induced
self-assembly (LISA)
  • Apply a large electric field between a mask and a
    polymer film
  • Polymer film spontaneously grows up towards mask
  • Pillars form when mask-polymer separation between
    200nm and 800nm
  • Works because polymer attracted to high-field
    region

Mask
Polymer film
15
The scanning probe idea
  • Get very high spatial resolution by
  • Scattering very short-wavelength waves

Sample
16
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
17
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
18
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
19
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 across sample
Sample
20
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.

21
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
  • Fermis golden rule for rates in quantum physics
    then gives conductance

22
Tersoff-Hamann Theory (2)
  • Write the matrix element in terms of the current
    operator as
  • Assuming S lies in a region of constant
    potential, and that we tip wavefunction is an
    exponentially decaying s-wave, we can do all the
    integrals to get

23
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)

Surface
Tip
?
rtip
24
Atomic manipulation with the STM the ground state
Atom on surface
  • 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
25
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
26
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
27
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
28
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
29
Atomic manipulation example Xe atoms on Ni at
T4K
  • Individual Xe atoms manipulated by the parallel
    process at T4K
  • STM tip moves up over atoms, showing that
    electrons tunnel more easily through them than
    through vacuum

Don Eigler et al (IBM Almaden)
30
Atomic manipulation example Xe atoms on Ni at
T4K
  • Individual Xe atoms manipulated by the parallel
    process at T4K
  • STM tip moves up over atoms, showing that
    electrons tunnel more easily through them than
    through vacuum

Don Eigler et al (IBM Almaden)
31
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)
32
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)

e-
e-
Atom on surface
Surface
Force
33
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)

Potential energy
Antibonding state occupied by tunnelling electron
Distance from surface
Electronic ground state
34
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

H atoms removed here
Hitosugi et al, Tokyo University and Hitachi
35
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
36
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
37
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)

38
Scanning force microscopy
  • Measure deflection of small cantilever on which
    tip is mounted, by deflection of a laser beam

39
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
40
Scanning force microscopy
  • Most recent development is non-contact force
    microscopy tip vibrates above sample and only
    approaches briefly

41
Scanning force microscopy
  • Allows truly atomic-resolution force microscopy
    images to be obtained for the first time.

Defects on surface
Defects migrate
Ernst Meyer et al, Basel
42
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
43
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
44
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)

45
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)

46
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 (non-polar)
47
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
48
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

49
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

50
Directed growth
  • Try to combine the idea of control (as in
    lithography) and spontaneous formation of an
    ordered structure (as in self-assembly) 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

51
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

Lopinski et al, Nature 406 48 (2000)
52
Molecular device Self-directed wire growth
53
Molecular device Self-directed wire growth
  • Do the resulting wires conduct? Watch this
    space...

54
Richard Feynmans 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.
55
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

56
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)
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)
58
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)
59
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

Don Eigler et al (IBM Almaden)
60
Atomic manipulation example quantum corals
  • Shape of ripple pattern depends on shape of coral
    - its quite different for a rectangle

Don Eigler et al (IBM Almaden)
61
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

62
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 Greens function

63
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)

64
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
  • These two routes for charge transport
    (corresponding to positive and negative transient
    charging) can interfere

65
How the interference works
  • Bonding orbital same sign on adjacent carbon pz
    orbitals


-
-
Bonding
66
How the interference works

-
  • Bonding orbital same sign on adjacent carbon pz
    orbitals
  • Antibonding orbital opposite signs on adjacent
    pz orbitals


-
-

-

Bonding
Antibonding
(? is molecular energy gap)
67
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
Antibonding
68
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
Antibonding
69
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
Antibonding
70
Conductance quantization
Conductance
  • 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

Extension
Jacobsen et al. (Lyngby)
71
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)
72
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)
73
Extreme nanotechnology single-molecule
electronics
  • Experiments now possible on the conductance
    properties of individual molecules

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

Langlais et al. 1999
75
Extreme nanotechnology single-molecule
electronics
  • Experiments now possible on the conductance
    properties of individual molecules
  • Those chosen for conducting applications are
    invariably conjugated

Langlais et al. 1999
76
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)
77
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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