20 February 20014471 Solid-State Physics1 Summary of 4471 Session 5: Simulations and Surfaces More on numerical simulation techniques: Extracting information

20 February 2001 4471 Solid-State Physics 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


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


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…?


What is Nanotechnology?

• A set of tools and ideas for the manipulation and control of matter in the size range between 0.1nmand 1m

• Corresponds to the range of sizes between current electronics and atomic/molecular dimensions


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)


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)




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!


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


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 0.15m

Activated resist

Chemical etch (e.g. HF)


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)


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)


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)


Soft lithography - nanoimprint lithography

• Get a variety of structures e.g. holes and pillars


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


The scanning probe idea

• Get very high spatial resolution by– Scattering very short-wavelength waves

Sample



• 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



• 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



• 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



• 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

SampleScan detector across sample


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.


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:

)(|| 2112

212

2

EEMh

e

dV

dI


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

Se

rdm

M ][2 1

*22

*1

22

12

sample

212

tipsample )(|)(| EErdV

dI


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)

sample

212

tipsample )(|)(| EErdV

dI

rtip

Tip

Surface


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

Atom on surface

Distance along surface





STM tip

Potential energy






Potential energy






Potential energy






Potential energy



Atomic manipulation example: Xe atoms on Ni at T=4K

• Individual Xe atoms manipulated by the parallel process at T=4K

• STM tip moves ùp’ over atoms, showing that electrons tunnel more easily through them than through vacuum

Don Eigler et al (IBM Almaden)


Atomic manipulation example: Xe atoms on Ni at T=4K

• Individual Xe atoms manipulated by the parallel process at T=4K

• STM tip moves ùp’ over atoms, showing that electrons tunnel more easily through them than through vacuum



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)


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)

Force

e-e-

Surface

Atom on surface



• 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)

Distance from surface

Electronic ground state

Antibonding state occupied by tunnelling electron

Potential energy



• 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


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


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


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)


Scanning force microscopy

• Measure deflection of small ‘cantilever’ on which tip is mounted, by deflection of a laser beam



• 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



• Most recent development is ‘non-contact’ force microscopy: tip vibrates above sample and only approaches briefly



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

Defects on surface

Defects ‘migrate’

Ernst Meyer et al, Basel



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

Atomic ‘step’ on surface




• Understanding the physics behind the formation of these images is complicated...

Image of NaCl ‘island’

Simulated tip scan


Adam Foster and Alex Shluger, CMMP, UCL


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)


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)


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)


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

Gold substrate

C-S-Au bonds


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


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


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


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)





•Do the resulting ‘wires’ conduct? Watch this space...




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.


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 òpen’


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





• When circle complete, ‘ripples’ observed within it




• 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)


Atomic manipulation example: `quantum corals’

• Shape of ripple pattern depends on shape of coral - it’s quite different for a rectangle



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


• 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

Coherent transport


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)


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


How the interference works

• Bonding orbital: same sign on adjacent carbon pz orbitals

+

- -

+

Bonding




• Antibonding orbital: opposite signs on adjacent pz orbitals

+

- -

+ -+

- +

Bonding Antibonding

2/ E 2/ E

( is molecular energy gap)




• Antibonding orbital: opposite signs on adjacent pz orbitals

• Transport is controlled by the Green function

+

- -

+ -+

- +

Bonding Antibonding

n n

nn

EEEG

bottomtop)(



• Direct transmission through an atom into the substrate: the two contributions cancel out because the energy denominators have opposite signs

+

- -

+ -+

- +

Bonding Antibonding

n n

nn

EEEG

bottomtop)(



• 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

n n

nn

EEEG

bottomtop)(


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

Conductance

Extension

Jacobsen et al. (Lyngby)



• Such nanowires can be produced by pulling an STM tip off a surface, or simply by a ‘break junction’ in a macroscopic wire




• 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



Extreme nanotechnology: single-molecule electronics

• Experiments now possible on the conductance properties of individual molecules

Langlais et al. 1999




• Those chosen for conducting applications are invariably conjugated Langlais et

al. 1999




• Those chosen for conducting applications are invariably conjugated Langlais et

al. 1999


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)


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’

Documents

20 February 20014471 Solid-State Physics1 Summary of 4471 Session 5: Simulations and Surfaces More on numerical simulation techniques: Extracting information