WO2007008088A1

WO2007008088A1 - Nanoscale and microscale lithography methods and resultant devices

Info

Publication number: WO2007008088A1
Application number: PCT/NZ2006/000173
Authority: WO
Inventors: Simon Anthony Brown; Rene Reichel; James Gordon Partridge; Aruna Awasthi; Shaun Cameron Hendy; Peter Anthony Zoontjens
Original assignee: Nano Cluster Devices Ltd
Priority date: 2005-07-08
Filing date: 2006-07-04
Publication date: 2007-01-18

Abstract

The invention relates to a method of preparing a pattern of micron sized, and smaller particles on a substrate surface. The pattern can take the form of a conducting pathway of atomic clusters between contacts. The method of the invention can be an alternative to conventional lithographic patterning techniques which does not require a lift-off step.

Description

NANOSCALE AND MICROSCALE LITHOGRAPHY METHODS AND

RESULTANT DEVICES FIELD OF THE INVENTION

The present invention relates to a method of preparing patterns or arrangements of particles (particularly atomic clusters) on a substrate surface. More particularly but not exclusively it relates to a method of preparing patterns or arrangements useful in lithography ^"and the preparation of electronic devices both on the nanoscale and optionally up to the micronscale.

BACKGROUND TO THE INVENTION

Lithography is a generic term which, in the microelectronic industry, incorporates a variety of well established techniques based on the patterning of a polymeric material. For example, optical and electron beam lithographies rely on polymeric resists whose chemical nature is changed by exposure to light or electrons respectively. After exposure, a typical lithography process includes subsequent removal of either the exposed or the unexposed polymer, and then either etching of the substrate through, or evaporation of metal into, the resulting apertures in the resist. In the case of the metallization procedure a further "lift-off stage is usually required to remove both the resist which remains on the substrate and more importantly the unwanted metal evaporated onto it.

Over the last few years, significant attention has been devoted to the properties of clusters on surfaces, and possible applications of clusters, including nano-electronic devices based on clusters. Key pre-requisites for the achievement of such devices are systems which allow deposition of clusters on substrates, but more importantly the positioning of clusters at selected surface sites, ideally between electrical contacts.

The prior art includes several examples of attempts to achieve patterning of cluster films. Using Si(I I l) with its natural (7x7) surface reconstruction, Yamaguchi et al. [1] deposited Ni nanoclusters and found that they self-align by soft-landing along the patterned surface of the silicon at room temperature. This is a rather simple method to self-align clusters on a surface where no sample preparation is necessary. Similarly, Francis et al. [2] deposited Ag clusters on Highly Oriented Pyrolytic Graphite (HOPG). They have noted that the clusters self-organize along the step edges into one- dimensional wire-like structures due to diffusion on the graphite at elevated temperatures. The drawback for both methods is however, that the position of the surface sites can not be controlled, making it impossible to align the cluster assembled structures with electrical contacts.

Therefore, a method of selectively pre-patterning the surface is desirable. Parker et al. [3] used standard optical lithographic methods to achieve resist patterns/lines with a line width of 2 μm. Gold clusters then were deposited onto the samples followed by a lift-off step. The clusters preferentially accumulated along the edges of the resist structures. Changing the surface from hydrophobic to hydrophobic resulted in the formation of a cluster film within the exposed patterns, but preferential accumulation at the resist edges was still observed. Another example of surface patterning using photo resist is given by Liu et al [4]. Here, atomic copper was sputtered onto 2 to 5 μm wide resist patterns. Cu clusters formed on the surface via aggregation of the deposited atomic material. Preferential nucleation sites were reported at the boundaries between the bare SiO_x substrate and the resist lines.

Both the methods of Refs. [3] and [4] allow preferential cluster accumulation by pre- patterning the substrate. However, in both cases a lift-off step is required i.e. that the photo resist must be removed after the cluster deposition/formation due to the presence of a distribution of clusters over the entire sample, and in order to reveal a pattern of clusters. Also, Refs. [3] and [4] use photo resist as a patternable material which limits the minimum possible feature size.

Using electron sensitive resist like high molecular weight (HMW) polymethyl methacrylate (PMMA) feature sizes down to 20 nm can be achieved using standard electron beam lithography procedures. Aligning of arbitrary shaped patterns on top of electrical contacts on otherwise insulating substrates is also straightforward. The developing process exposes the substrate and electrical contacts within the region of the e-beam exposed pattern, while an undeveloped film of HMW PMMA surrounds it. In standard electron beam lithography procedures, a metallization step (evaporation of atomic metal vapour onto the substrate) coats the entire substrate surface (i.e. both the apertures and the surrounding PMMA are coated). This is normally followed by a liftoff process where the remaining film of HMW PMMA and the atomic layer are removed, leaving only the metallic material deposited within the opened patterns. Liftoff can be a difficult procedure to execute properly, since large unexposed areas can be difficult to lift-off, and the edges of the remaining metal (which necessarily run up the sides of the apertures onto the unexposed PMMA prior to lift off) can contain vertical spikes or otherwise be relatively rough.

OBJECT OF THE INVENTION

It is an object of the invention to provide a technique useful in lithography which overcomes one or more of the abovementioned disadvantages, and/or which obviates or reduces the need for a lift-off step and/or which at least provides the public with a useful alternative.

SUMMARY OF THE INVENTION According to a first aspect of the invention there is provided a method of depositing particles on a patterned region of a substrate comprising the steps of providing a patterned substrate, the pattern having one or more first regions (the first region) and one or more second regions (the second region) and directing a plurality of particles with an average diameter less than 1 micron towards the pattern to form an arrangement of particles on the patterned region, with a greater percentage of the particles retained by one of the first or second regions than is retained by the other of the first or second regions .

Preferably the particles are atomic clusters. Preferably the method includes controlling the behaviour of the clusters on impact with the first and second regions to be one or both of plastic and/or elastic thereby influencing the probability that the clusters adhere to one or both of the first and second regions.

Preferably the method includes controlling the directing of clusters towards the pattern and/or the nature of the first and second regions such that upon impact of the clusters with the patterned substrate one or more of the following occurs: elastic deformation of the clusters resulting in sticking of one or more clusters to a region, and/or elastic deformation of the clusters resulting in reflecting or bouncing or sliding of one or more clusters from a region, and/or - plastic deformation of the clusters resulting in sticking of one or more clusters to a region, and/or - plastic deformation of the clusters resulting in reflecting or bouncing of one or more clusters from a region.

Preferably wherein one or both of the regions comprises a plurality of substantially independent sections. Alternatively wherein the region which retains the greater percentage of clusters is continuous.

Preferably the method includes depositing the clusters to form a pathway (as defined herein).

Preferably the method includes depositing the clusters to form a pathway capable of electrical conduction.

Preferably the method includes a further step of forming at least two contacts on the substrate with the pathway existing generally between the two contacts. Preferably the contacts are separated by a distance smaller than 10 microns, more preferably smaller than 1 micron, more preferably smaller than lOOnm.

In one embodiment the method includes first forming the contacts and then depositing the clusters on the substrate between the contacts.

Preferably the method includes monitoring the steps of depositing and forming the arrangement of clusters by monitoring conduction between the two contacts where deposition is ceased at or near the onset of conduction.

In an alternative embodiment the method includes forming the contacts after forming the arrangement of clusters.

Preferably the method includes including providing a patterned substrate with least one dimension of one of the regions of the pattern less than 1 micron, more preferably less than lOOnm.

Preferably the method includes directing a plurality of clusters with an average diameter between 0.3nm and l,000nm, more preferably between 0.5nm and lOOnm, even more preferably between 0.5nm and 40nm towards the pattern

Preferably the first or second regions of the substrate comprise different materials. Alternatively one of the first and/or second regions comprise the same material as the substrate but modified.

Preferably the first and second regions have different surface hardness or softness characteristics.

Preferably the first and second regions have different surface roughness.

Preferably the first and second regions have different surface wettability.

Preferably the first and second regions have different reflectivity to the clusters. Preferably the first and second regions have different surface elasticity characteristics.

Preferably the first and second regions are at different temperatures.

Preferably the method includes patterning the insulating or semiconductor substrate by one or more of lithography, etching or metalisation.

Preferably the method includes patterning the insulating or semiconductor substrate with a second material, which is preferably non-conducting.

Preferably the method includes patterning an insulating or semiconductor substrate with a developed or undeveloped polymeric material or a self-assembled monolayer (SAM).

A Preferably the method includes providing an insulating or semiconductor substrate, coating it with a polymeric material or having a SAM form thereon, and patterning the polymeric material or SAM to result in one or more first and second regions.

Preferably the method includes patterning the polymeric material or SAM by forming one or more apertures through the polymeric material or the SAM so that the insulating or semiconductor substrate is at least partially, if not completely accessible to the clusters through the one or more apertures.

Preferably the method includes patterning the polymeric material or SAM by forming at least one slot in the polymeric material or SAM running between and/or partially overlapping with the two contacts (when present).

Preferably the pattern is formed in a polymeric material selected from the group consisting of PMMA, photoresist, electron-beam resist and SU8. More preferably the pattern is formed in a polymeric material comprising a bi-layer of high molecular weight (HMW) and low molecular weight (LMW) PMMA.

Alternatively the pattern is formed in a SAM selected from the group consisting of C12-SiCl₃, C12-Si(OEt)₃, and CF-Si(OEt)₃.

Preferably the method includes forming the pattern in the polymeric material or SAM by lithography and/or by etching.

Preferably the method includes controlling one or more of: the incident momentum of the clusters during deposition of the clusters; and/or the kinetic energy of the incident clusters during deposition of the clusters; and/or the velocity of the incident clusters during deposition of the clusters; and/or ■ the identity of the clusters during deposition of the clusters; and/or the size of the clusters during deposition of the clusters; and/or the temperature of the clusters during deposition of the clusters; and/or the angle of incidence of the clusters during deposition of the clusters; and/or other factors affecting the degree of chemical bonding and/or strength of interaction between the clusters and a surface during deposition of the clusters; and/or the thermodynamic phase of the clusters; and/or the crystallinity of the clusters; and/or the shape of the clusters.

Preferably the method includes directing the clusters towards the pattern with a selected or controlled velocity.

More preferably the method includes directing the clusters towards the pattern with kinetic energy of the clusters selected so as to be sufficient to cause at least part or the majority or substantially all of the clusters incident upon the surface of one of the first or second regions to bounce from that region whilst at the same time low enough to cause at least part or substantially all of the clusters incident upon the surface of the other of the first or second regions to remain on the surface (whether substantially immediately upon contacting the surface or some time after first contacting the surface).

Preferably the method includes calculating the velocity thresholds between the regimes of plastic and elastic behaviour of the clusters and then controlling the velocity of the clusters to be within a selected regime upon impact with one or both or the first and second regions.

Preferably the method includes calculating the velocity thresholds between the regimes of elastic deformation with sticking behaviour, elastic deformation with bouncing behaviour, plastic deformation with sticking behaviour, and plastic deformation with bouncing behaviour for the given cluster and/or substrate and/or environment, and then controlling the velocity of the clusters to result in the behaviour of the atomic cluster upon impact with the first and/or second regions falling within a particular regime.

Preferably the step of calculating the thresholds between the regimes includes calculation of the required velocity for the given cluster and/or substrate and/or environment in accordance with measurements of the proportion of clusters that bounce from (or stick to) the first and the second regions.

Alternatively the step of calculating the velocity for the given cluster and/or substrate and/or environment in accordance with molecular dynamics simulations of the proportion of clusters that bounce from (or stick to) each of first and second regions.

Preferably the clusters directed towards the pattern are selected from one or more of the group consisting of platinum, palladium, bismuth, antimony, aluminium, silicon, germanium, silver, gold, copper, iron, nickel, and cobalt. Preferably the substrate is selected from the group consisting of silicon, silicon nitride, silicon oxide, aluminium oxide, indium tin oxide, germanium, gallium arsenide, quartz, and glass.

Preferably the method includes preparing the clusters by a method which involves gas aggregation. Preferably the method includes preparing the clusters by evaporating a cluster source material from a crucible or by sputtering a cluster source material from a target to produce a vapour and condensing the vapour by cooling through an inert gas to form clusters.

Preferably the method includes controlling the velocity and/or kinetic energy of the clusters produced at least partially by controlling the flow rate of an inert gas flow into a chamber of the cluster source material in which the clusters are prepared.

Preferably the method includes including imparting a kinetic energy to the clusters corresponding to a velocity in the range lm/s to 2000 m/s; more preferably in the range lOm/s to 300 m/s.

Alternatively or additionally the method includes imparting a kinetic energy to the clusters corresponding to a kinetic energy per cluster atom in the range 5xlO^"26 J to 2x10^"19 J, more preferably in the range 5x10^"24 J to 5x10^"21 J.

Preferably the method includes directing copper or palladium clusters towards the substrate with diameters in the range 5-20nm and with velocities is in the range 100- 400m/s.

Alternatively the method includes directing bismuth or antimony clusters towards the substrate with diameters in the range 10-lOOnm and with velocities in the range 10-lOOm/s. In one embodiment the method includes including depositing the clusters to form one pathway or wire. hi an alternative embodiment the method includes depositing the clusters to form a plurality of wires. In one embodiment the method includes depositing the clusters to form a percolating film.

In one embodiment the method includes a pre-step of forming (by any means whatsoever) a wire or configuration structure on the substrate followed by forming the pathway of clusters over or in addition to the pre-existing wire or configuration. Preferably the pathway of clusters is formed at a pre-selected angle to the preexisting wire or configuration, preferably at right angles to the pre-existing wire or configuration.

In one embodiment one of the first or second regions is comprised of one material which is conducting and a second material which is insulating and encapsulates the first. Preferably the method includes forming the conducting material so as to be useful as a gate. Preferably the method includes encapsulating at least a portion of the deposited clusters in an insulating or dielectric material.

Preferably the method includes forming a further contact or other structure on the surface of the insulating or dielectric material which is isolated from the pattern of clusters and can act as a gate.

Preferably the method includes forming the pathway of clusters on a multi-layer substrate, one layer of which is electrically conducting and can act as a gate.

In one embodiment one of the first or second regions is angled with respect to the other of the first or second regions and the method includes directing the clusters substantially orthogonally to one of the first or second regions. Preferably the first and second regions of the pattern define a V-groove or inverted pyramid and the method includes directing the clusters so that they eventually accumulate or aggregate at the apex of the V-groove or inverted pyramid.

Preferably the method includes imparting a cluster with a velocity component perpendicular to the angled surface at such a level that the cluster deformation on impact with the angled surface is weak, leading to sticking or sliding, while elasto- plastic or plastic deformation takes place on impact on the surfaces orthogonal to the cluster beam, resulting in that clusters are at least partially reflected from those surfaces.

Preferably the method includes including imparting a cluster with a velocity component perpendicular to the angled surface at such a level that elasto-plastic bouncing takes place, leading to accumulation of clusters at the apex of the V-groove or inverted pyramid while the clusters impacting on the orthogonal planar surfaces are fully plastically deformed and at least partially reflected from those surfaces.

In one embodiment the method includes directing clusters with a range of particle sizes and with a temperature such that at least some of the smaller clusters of the range are liquid while at least some of the larger clusters are solid and the smaller, liquid clusters preferentially accumulate in one region of the first or second regions while the larger solid, clusters bounce away from that region.

Preferably the method includes including patterning the substrate so that the smaller clusters of the range are retained by one of the first or second regions whilst bouncing from the other of the first and second regions and larger clusters of the range are not retained in either region.

According to a second aspect of the invention there is provided an arrangement of particles on a patterned region of a substrate prepared substantially according to the abovementioned method. Preferably the clusters form a conducting pathway between two contacts on the substrate surface.

Preferably the average diameter of the clusters is between 0.3nm and l,000nm. Preferably the contacts are separated by a distance smaller than 10 microns.

According to a further aspect of the invention there is provided method of preparing a pathway of atomic clusters between two contacts on a substrate comprising the steps of providing a substrate with two contacts on its surface, modifying a region on the substrate substantially between and/or overlapping the two contacts, directing a plurality of atomic clusters with average diameter less than

1 micron towards the substrate generally in the area between the two contacts so that the modified region retains some of the clusters on its surface to form a pathway of atomic clusters between the contacts and the non-modified region of the substrate resists at least a large part of the clusters incident upon it.

Preferably the method includes monitoring the formation of a conducting pathway between the contacts by monitoring the conduction between the two contacts.

Preferably the method includes providing contacts separated by a distance smaller than 10 microns, more preferably smaller than lOOnm.

Preferably the method includes providing a substrate of an insulating or semiconductor material coated with a polymeric or self-assembled monolayer (SAM) layer, modifying the region in the area between the two contacts by forming one or more slots in the polymeric or SAM layer positioned substantially between the contacts, so that the insulating or semiconductor material is accessible through the slot.

Alternatively the method includes modifying a region between the two contacts by providing a (or taking advantage of a pre-existing) ridge, depression, step-edge or defect, or array or pattern of ridges, depressions, step-edges or defects, and forming a pathway between the two contacts, the clusters impacting on the modification experiencing a "soft-landing" site so that the clusters stick while bouncing away from the non-modified regions.

Preferably the modification comprises naturally occurring step edges.

Preferably the substrate is silicon and the modification occurs on an exposed Si(5 5 12) or Si(I 1 3) facet.

Alternatively the method includes engineering the ridges, depressions, step-edges or defects.

Preferably the method includes directing the clusters towards the substrate with a velocity high enough so at least part of, if not the majority of, the clusters bounce away from the unmodified region and low enough so that at least part of, if not the majority of the clusters incident upon the surface of the modification remain on the surface of the modification (whether substantially immediately upon contacting the surface or some time after first contacting the surface).

Preferably the method includes calculating the velocity thresholds between the regimes of plastic and elastic behaviour of the clusters upon impact with the first and second regions and then controlling the velocity of the clusters to be within a selected regime upon impact with one or both or the first and second regions.

Preferably the substrate is selected from the group comprising silicon, silicon nitride, silicon oxide, aluminium oxide, indium tin oxide, germanium, gallium arsenide, quartz, or glass. According to a further aspect of the invention there is provided a pathway of atomic clusters between two contacts on a substrate prepared according to the abovementioned method.

According to a further aspect of the invention there is provided a method for performing lithography including the steps of providing a substrate, coating the surface of the substrate with an electron- or photo-sensitive polymer layer, exposing some regions of the polymer layer to electron (for an electron sensitive polymer) or photons (for a photon-sensitive polymer), developing the polymer to remove one but not both of the exposed or unexposed regions, and depositing clusters on to the substrate to substantially coat one but not both of the exposed or unexposed regions and wherein the method does not include a lift-off step.

Preferably the method includes depositing clusters onto the substrate according to the abovementioned method.

Other aspects of the invention may become apparent from the following description which is given by way of example only and with reference to the accompanying figures.

As used herein the term "and/or" means "and" or "or", or both.

As used herein "(s)" following a noun means the plural and/or singular forms of the noun.

The term "comprising" as used in this specification and claims means "consisting at least in part of. When interpreting statements in this specification and claims which include that term, the features, prefaced by that term in each statement, all need to be present but other features can also be present. Related terms such as "comprise" and "comprised" are to be interpreted in the same manner. It is intended that reference to a range of numbers disclosed herein (for example, 1 to 10) also incorporates reference to all rational numbers within that range (for example, 1, 1.1, 2, 3, 3.9, 4, 5, 6, 6.5, 7, 8, 9 and 10) and also any range of rational numbers within that range (for example, 2 to 8, 1.5 to 5.5 and 3.1 to 4.7).

The entire disclosures of all applications, patents and publications, cited above and below, if any, are hereby incorporated by reference.

To those skilled in the art to which the invention relates, many changes in construction and widely differing embodiments and applications of the invention will suggest themselves without departing from the scope of the invention as defined in the appended claims. The disclosures and the descriptions herein are purely illustrative and are not intended to be in any sense limiting.

DEFINITIONS

"Particle" as used herein has the following meaning - a particle with dimensions in the range 0.5nm to lOOmicrons, which includes atomic clusters formed by inert gas aggregation or otherwise. "Nanoparticle" as used herein has the following meaning - a particle with dimensions in the range 0.5 to 1000 nanometres, which includes atomic clusters formed by inert gas aggregation or otherwise.

"Development" or "developed" as used herein has the following meaning — in relation to a polymeric material, having been treated by chemical means such as exposure to a solvent, in order to remove part or substantially all of the polymeric material.

Development after exposure of an electron sensitive or photo sensitive polymer to electrons or light is usually carried out in order to reveal a pattern of exposure.

"Nanoscale" as used herein has the following meaning - having one or more dimensions in the range 0.5 to 1000 nanometres. "Micronscale" as used herein has the following meaning - having one or more dimensions in the range 1 to 1000 micrometers. "Cluster" as used herein has the following meaning - a particle with dimensions in the range 0.5 to 1000 nanometres, which includes atomic clusters formed by inert gas aggregation or otherwise. It is typically composed of between 2 and 10⁷ atoms. "Wire" as used herein has the following meaning - any nanowire, microwire, or wire of larger dimensions. It includes chains, cluster-assembled wires and lithographically defined wires. A wire formed by the assembly of nanoparticles may be electrically conducting partially, substantially or entirely via ohmic conduction or substantially or entirely by tunnelling conduction. Such a wire is not restricted to a single linear form but may be direct, or indirect. It may also have side branches or other structures associated with it. The nanoparticles may or may not be partially or fully coalesced. The definition of wire may even include a film of particles which is homogeneous in parts but which has a limited number of critical pathways.

"Conducting" as used herein has the following meaning - conducting electrical current (i.e. a flow of electrons) partially, substantially or entirely via ohmic conduction or substantially or entirely by tunnelling conduction.

"Contact" as used herein has the following meaning - an area on a substrate, usually but not exclusively comprising an evaporated metal layer, whose purpose is to provide an electrical connection between the cluster-deposited pattern and an external circuit or another electronic device. "Substrate" as used herein has the following meaning — an insulating or semiconducting material comprising one or more layers which is used as the structural foundation for the fabrication of the device. The substrate may be modified by the deposition of electrical contacts, by doping or by lithographic processes intended to cause the formation of surface texturing. "Pathway" as used herein has the following meaning — a structure which lies between at least two regions of or on a substrate that is made up of individual units which may or may not be wholly interconnected (i.e. while it may be a connected network, there may also be some spaces between the units). Like a wire it is not restricted to a single linear form but may be direct, or indirect. It may also have side branches or other structures associated with it. The particles may or may not be partially or fully coalesced. The definition of pathway may even include a film of particles which is not homogeneous. The pathway may or may not conduct. "Wires" as formed according to the method of the invention is a subset of "pathway".

"Aperture" as used herein has the following meaning - a gap, space or opening in a layer of polymeric material (such as PMMA, photo resist, or SU8) on a substrate. It is not restricted to shape or dimension. It is usually (but not only) used in relation to fully enclosed openings.

Where, in this specification, we use the term "deformation" we mean a change in shape due to the impact between a particle and a surface or other particle, which may be reversible or irreversible, and / or due to the conversion of kinetic energy into elastic (stored) energy or due to the dissipation of kinetic energy by plastic work.

Where, in this specification, we use the term "plastic deformation" we mean a change in shape due to the impact between a particle and a surface or other particle, which is irreversible due to the dissipation of kinetic energy by plastic work. Where, in this specification, we use the term "elasto-plastic deformation" we mean a change in shape due to the impact between a particle and a surface or other particle which is at least partially, but not entirely, irreversible due to the dissipation of kinetic energy by plastic work, and wherein there is a region of the particle which is at least partially, but not entirely, reversibly deformed. Where, in this specification, we use the term "elastic deformation" we mean a change in shape due to the impact between a particle and a surface or other particle, due to the conversion of kinetic energy into elastic (stored) energy, which is substantially reversible.

"Elastic" as used herein has the following meaning — deforming in such a way that substantially the original shape of the object is recovered after the deformation or interaction with another object is completed. For example, in an elastic collision with a surface the deformation of a particle is expected to be limited to a region neighbouring the particle surface or facet in contact with the surface.

"Fully Plastic" and "Plastic" as used herein has the following meaning - deforming in such a way that the original shape of the object is altered after the deformation or interaction with another object is completed. For example, in a plastic collision with a surface the deformation of a particle is expected to extend through a substantial volume of the particle and may include substantially the entire volume of the particle.

"Elasto-plastic" as used herein has the following meaning - a deformation of a particle which is partially elastic and partially plastic. In a typical elasto-plastic collision with a surface a particle may exhibit a region neighbouring the particle surface or facet in contact with the surface which is plastically deformed and a second region more distance from the particle surface or facet in contact with the surface which is elastically deformed.

The following abbreviations are also used in the specification: "PMMA" - polymethyl methacrylate.

"HMW" - high molecular weight.

"LMW" - low molecular weight.

"MIBK" - methyl isobutyl ketone.

"IPA" - iso propyl alcohol. "FE-SEM" - field emission scanning electron microscope

BRIEF DESCRIPTION OF THE FIGURES

The invention is further described with reference to the accompanying figures: Figure 1. FE-SEM images of antimony clusters within 3x3 μm² partially-exposed patterns in PMMA produced with increasing electron-beam doses for an overall cluster-layer thickness (as read from the rate deposition monitor) of54±6 nm.

Figure 2. FE-SEM images of antimony clusters within 3x3 μm² partially-exposed patterns in PMMA produced with increasing electron-beam doses for an overall cluster-layer thickness (as read from the rate deposition monitor) of 34±1 nm.

Figure 3. FE-SEM images of bismuth clusters within 3x3 μm² partially exposed patterns in PMMA produced with increasing electron-beam doses for an overall cluster-layer thickness (as read from the rate deposition monitor) of 21±3 nm. Figure 4. a) Variation in antimony cluster coverage within 3x3 μm² partially exposed patterns in PMMA with varying electron-beam dose for two different overall cluster-layer thicknesses as measured from the deposition rate monitor (diamonds: 54±6 nm; triangles 34±1 nm). b) Variation in bismuth cluster coverage within 3x3 μm² partially exposed patterns in PMMA produced with varying electron-beam dose for an overall cluster-layer thickness (as read from the rate deposition monitor) of 21 ±3 nm. c) Variation of RMS roughness within the 3x3 μm² partially exposed PMMA pattern for varying electron-beam dose.

Figure 5. Atomic force microscope images of partially exposed and developed patterns in PMMA which have been used to provide the RMS roughness data shown in Figure 4c).

Figure 6. FE-SEM image of a cluster-assembled film suitable for four-point electrical conductivity measurements and formed in patterned HMW-

PMMA.

Figure 7. FE-SEM image of Sb clusters assembled within an aperture-slot in the HMW-PMMA film and aligned to planar Au contacts separated by a lμm gap- Figure 8. FE-SEM image of Bi clusters assembled within an aperture-slot in the HMW-PMMA film and aligned to planar Au contacts separated by a lμm gap. Figure 9. FE-SEM image of a contacted Bi cluster-assembled wire (contacts not shown). Figure 10. FE-SEM image of a Sb cluster-assembled film within a 'New Zealand silhouette' aperture in HMW PMMA. Figure 11. . FE-SEM image of a Bi cluster-assembled film within a 'New Zealand silhouette' aperture in HMW PMMA.

Figure 12. Current- Voltage characteristic at 95K (dotted line) and 300K (solid line) for the cluster-assembled film shown in Figure 8. Figure 13. Current- Voltage measurement for the cluster-assembled wire formed between the middle contacts of the four-point device shown in Figure 6. Figure 14. Schematic of the patterning of HMW PMMA on SiN substrates, a)

PMMA spun on wafer, b) patterned PMMA, c) clusters in slots Figure 15. FE-SEM image of a bismuth clusters accumulated in a 200 nm wide slot- aperture sample. Figure 16. FE-SEM image of an alignment mark surrounded by a ring of bismuth clusters.

Figure 17. FE-SEM image of antimony clusters on an aperture-slot sample which was exposed to an electron-beam prior to the cluster deposition experiment.

Figure 18. The bi-layer PMMA process.

Figure 19. FE-SEM image of a SiO_x passivated V-grooved substrate with planar Au contacts and an aperture formed in conventional optical photo resist.

Figure 20. Bi cluster coverage on substrates with differing coatings measured from

FE-SEM images.

Figure 21. Cu cluster coverage on substrates with differing coatings measured from

FE-SEM images.

Figure 22. Bi cluster coverage on substrates with differing coatings (including SU8) measured from FE-SEM images.

Figure 23. FE-SEM images of Bi clusters supported on (a) PMMA (b) Photo resist

(c) Si_xNy and (d) SiO_x substrate layers.

Figure 24. FE-SEM images of Cu clusters supported on (a) PMMA (b) Photo resist

(c) Si_xN_y and (d) SiO_x substrate layers.

Figure 25. FE-SEM images of Bi clusters supported on (a) SU8 (b) SiO_x (c) Au and

(d) Si_xN_y substrate layers.

Figure 26. Multiple parallel cluster-assembled wires formed around an SU8 template and planar electrical contacts and supported on a SiO_x passivated Si substrate. Figure 27. I(V) characteristics of a cluster-assembled wire of width 600nm and length 1 OOμm at temperatures ranging from 300K, 330K, 370K, 400K,

430K and 460K.

Figure 28. FE-SEM images of (a) a cluster-assembled wire deposited and characterised on a surface held at room temperature and (b) a cluster- assembled wire deposited at room temperature and subsequently heated to 460K.

Figure 29. FE-SEM image of NiCr/Au four point contacts with cluster wire. Figure 30. FE-SEM images of Voltage annealed wire. Figure 31. FE-SEM image of Current annealed wire.

Figure 32 Examples of results of measurement of cluster velocity as a function of cluster diameter for a variety of source conditions. Figure 33 Examples of results of measurement of cluster velocity as a function of cluster diameter for a variety of source conditions. Figure 34 Examples of results of measurement of ion current as a function of a retarding potential applied to a Faraday cup, yielding cluster velocity data. Figure 35 Bi cluster film formed within an aperture in AZl 500 photo resist and overlaying multiple NiCr/Au contacts on a SiO_x passivated Si substrate. Figure 36 Simulated snapshots showing a selection of 147-atom liquid (bottom) and solid (top) clusters after equilibration on surfaces with various C values. Figure 37 Simulated configuration for the collisions studied at V₀ = 0.4v_c, 1.6v_c and

2.6v_c.

Figure 38 Plot of the center of mass z_cm of a 147 atom icosahedron colliding with the target surface, plotted versus time for three impact velocities, 0.4v_c,

1.6v_c and 2.6v_c. Figure 39 Plot of translational velocity of center of mass along z-direction, v_z, of

147 atom icosahedra from Figure 38, plotted versus time.

Figure 40 Plot of radius gyration along z-direction, R₂, of 147 atom clusters from Figure 38 as a function of time. Figure 41 Simulated snap shots of the impacts of 147 atom clusters from Figure 38 att = 9.

Figure 42 Plots of the evolution of (a) total potential energy per atom, (b) cluster internal energy per atom and (c) cluster-surface potential energy per atom for 147-atom icosahedra with C=0.35 corresponding to the data in

Figures 38-40.

Figure 43 Plot of time evolution of the thermal kinetic energy of 147 atom clusters equilibrated initially at T=O.13 during collisions with the surface as per Figs 38-41. Figure 44 Plot of probability of sticking (P(stick)) versus normal incidence velocity (V₀ in units of v₀ = ε/m), averaged over 50 trials with C=0.35 for (a) three different cluster sizes incident on the flat surface and (b) liquid 147-atom icosahedron incident on the flat surface and the equivalent solid cluster collision with the surface having defects. Figure 45 Plot of coefficient of restitution, e, as a function of impact velocity at C=0.35, averaged over 100 trials, for normal incidence of three different cluster sizes on the flat surface. Figure 46 Plot of E^a _fN° ⁵ as a function of impact velocity for the three different cluster sizes. Figure 47 Plot of the ratio of the reflected kinetic energy E^κ _f to E^a _f (the Weber number, We) at the point of peak reflected velocity for the different size clusters with C=0.35.

Figure 48 Plot of probability of sticking (P(stick)) versus incidence velocity averaged over 50 trials for a 147-atom icosahedron on a surface with an adatom and a surface with a step edge. Also shown is the probability of sticking for a liquid 147-atom droplet incident on the flat (111) surface. Figure 49 Plot of probability of sticking (P(stick)) versus incidence velocity (of 147-atom icosahedron for different C-values i.e. corresponding to different cluster-surface interactions. Figure 50 Plot of probability of sticking (P(stick)) versus normal incidence velocity averaged for non-normal incidence of 147-atom icosahedron on the substrate.

Figure 51 Plot of the coefficient of restitution, e, versus normal impact velocity at C=0.35 for the oblique impacts of 147-atom icosahedron.

Figure 52 Plot of final velocity of the cluster as a function of initial horizontal velocity. Figure 53 Plot of maximum deformation of the cluster at the moment of peak reflection velocity versus impact velocity for different size solid clusters and a liquid droplet.

Figure 54 Onset of conduction for a Bi cluster-assembled wire produced using an aperture in a PMMA template layer with length lOOμm and minimum width 200nm.

DETAILED DESCRIPTION OF THE INVENTION

The preferred form of the present invention relates to our method of fabricating patterns (preferably conducting) of clusters, (particularly nanoclusters) and particularly wire-like structures, including pathways (on the nanoscale or micronscale), by deposition of clusters capable of conduction into or around apertures or patterns present or formed on a substrate. The advantages of our technology (compared with many competing technologies) include that:

- Apertures/patterns can be formed within the non-conducting material on the surface of the substrate. These can be formed using standard lithographical techniques, i.e. electron-beam or projection lithography and dry-etching. - No lift-off step is required after metallization because the clusters do not stick to the unexposed surfaces (usually a non-conducting layer) thus there is no need to remove excess metal deposited on the polymer.

- When desired the resulting wires (nano- and micronscale) are automatically connected to electrical contacts as part of the formation process. This enables electrical characterisation before, during and after the formation of the cluster- assembled films or wires or pathways. When desired electrical current can be passed along the wires as soon as they are formed. - No manipulation of the clusters is required to form the cluster-assembled films or wires or pathways.

In particular in a preferred embodiment using atomic cluster deposition instead of atomic deposition and a pattern of polymeric material on the substrate surface, we show that a high selectivity between the unexposed polymer (such as HMW PMMA) and the patterns can be achieved. This can be realized either by carefully selecting the cluster and/or substrate material and/or electron sensitive resist. The clusters can also be fine- tuned to select the optimum momentum to attain maximum reflection from the PMMA but almost unity sticking to the substrate. After successful cluster deposition, there is no need for a lift-off. This means, that potential nano-scale devices are not exposed to further chemical processes and possible subsequent damage. METHOD OF THE INVENTION

The invention relies upon a number of steps and/or techniques:

1. Preparation/provision of a substrate,

2. patterning the substrate,

3. the formation of atomic clusters, 4. deposition of the clusters onto the patterned substrate,

5. optionally: monitoring the formation of the nanowire pathway or wire. which are described in this section below. In addition, this section describes the basic processes of molecular dynamics simulations which are employed to reveal the importance of elasticity and plasticity when a cluster impacts a surface.

1. Preparation/Provision of a Substrate

Preparation of a substrate may be as simple as selecting the substrate material or it may include formation of electrical contacts on the surface. The invention covers scenarios when contacts are not required. However in most embodiments electrical contacts will be employed to allow establishment of an electrical circuit. In most cases formation of the contacts will precede the step of depositing the clusters. However it is possible that the clusters are deposited first and the contacts formed at some point afterwards. The invention covers the different combinations.

Substrates can be any surface which is capable of supporting a cluster-assembled film and evaporated contact materials and which can be installed into a vacuum deposition chamber. We often use Si wafers with SiO_x or Si_xNy insulating top layers. Alternatives may be GaAs, GaN, AlGaAs or SiGe substrates (amongst many others) with passivation provided by SiO_x, Si_xNy, AlO, spin-on glasses and polymers (amongst many others), so long as they have the properties which allow preferably a cluster-assembled pathway to be formed on the substrate surface.

The preferred method of contact formation relies on evaporation or sputtering of a metal or alloy. Possible metals or alloys include Ti, NiCr, Al, Au, Ag, Cu, W, Mo, Pd, Pt, Bi, and Sb. We prefer NiCr and/or NiCr/Au films deposited through a shadow-mask with large scale features so as to define contact pads as well as the electrical contacts to the device. The shadow-mask is positioned between the substrate material and the chosen evaporation source so that the evaporated film replicates the features of the mask. The preferred deposition for the contacts is of atomic vapour generated via thermal or electron beam evaporation. However, other deposition procedures as known in the art may be used. The planar electrical contacts allow in-situ monitoring of the current through cluster-assembled wires/pathways/films.

Electron beam lithography and photolithography are well-established techniques in the semiconductor and integrated circuit industries and offer an alternative means of contact formation. These techniques are routinely used to form many electronic devices ranging from transistors to solid-state lasers.

As will be appreciated by one skilled in the art, other techniques of the art which allow for nanoscale and micronscale contact formation will be included in the scope of the invention in addition to electron beam lithography and photolithography, for example nanoimprint lithography.

2. Patterning the Surface The preferred pattern is formed using a layer of non-conducting material. The preferred non-conducting materials used in this step are photo-patternable materials such as standard photo resists used in optical lithography, or electron-beam patternable materials used in electron beam lithography. We normally use HMW PMMA which can be easily patterned using standard e-beam lithography but other suitable materials are within the scope of the invention as mentioned below. A typical scenario is as follows:

HMW PMMA is spun onto the clean substrate at 3000 rpm for 1 minute followed by baking at 185 ⁰C for 30 minutes to evaporate off the solvents. Exposure is done using a Raithl50 Electron Beam Lithography system. The exposed patterns are then developed in 1:3 IPA:MIBK for 30 seconds.

Further resists which may be used include, but are not limited to AZ1500, S1813, UV-3, UV-5, PMGI₃ SU8, ZEP, NEB-31, EBR-9 and many others as would be appreciated by one skilled in the art.

In the applications and devices where an electrical circuit is necessary it is important that the layer of material is non-conducting because it ensures that there is no additional conduction path between the contacts parallel to or parasitic to the final pattern of conducting clusters/the resulting cluster assembled wires. We note that in addition to the many polymeric photo- and electron beam- patternable materials discussed above, many other non-conducting materials can be coated onto a substrate and subsequently patterned using standard lithography procedures. For example, SiO_x, Si_xN_y and many semiconductor materials or layers of insulating or semiconducting materials would serve this purpose. We further note that in some circumstances the patterned layer may be of a conducting material. For example, a layer of Si or Al or other material which has been oxidised on its surface (either by natural or thermal oxidation) would provide sufficient electrical isolation. In this case the conducting material, which is isolated from the conducting cluster structure by the oxide, can be employed as a gate, providing very small gate — channel distances which may be advantageous for the construction of high performance transistors.

Furthermore the provision of a metallic material to which the clusters stick, may be used as an alternative method of achieving a cluster pattern on the substrate, if, for example, the clusters do not adhere well to the original substrate but adhere preferentially to the metallic layer. In this case the cluster structure may grow (by sequential sticking of clusters to those that have previously stuck to the surface) from one part of the metallic pattern to another part, forming a bridge or wire. In this case the metallic materials may be subsequently used as electrical contacts to the bridge or wire structure.

Standard electron-beam lithography or optical lithography is used to produce the electrical contacts and the template features on our samples. The contacts may be entirely produced using optical lithography or a combination of optical and electron- beam lithography can be used where nanoscale contacts are required. Typically an optical photo resist layer such as AZl 500 is spun onto the substrate, baked and UV- exposed and developed in order to remove selected areas of the resist and expose an underlying (Si_xNy or SiO_x) passivated Si substrate in those areas. Metallisation is added by thermal evaporation and subsequent dissolution of the photo resist translates the pattern of the photo resist layer into the metallic layer on the substrate surface.

AZl 500 is a positive photo resist meaning that the UV-exposed regions of an AZl 500 layer are soluble in AZ-developer. Negative resists (e.g. SU8) are designed such that the unexposed regions are dissolved by the developer and the exposed regions remain after development). PMMA has been chosen as a suitable electron-beam resist to form the nanoscale contact structures on our samples. This resist is positive and can be dissolved in acetone thereby providing lift-off capability i.e. the unwanted metallic layer can be removed in acetone whilst the desired pattern remains on the substrate.

Optical and electron-beam resists can be used as the patterned template layer which is formed over the substrate surface and planar contacts. As in the case of contact formation, the resists are exposed and developed in order to remove selected areas and expose the underlying surface/contacts. Positive or negative resist layers may be used for this purpose and arbitrary 2-D patterns can be produced in either. The limiting factors are the resolution of the exposure tool and the sensitivity and thickness of the resist layer. Patterns with minimum feature sizes of <25nm may be produced in 50nm thick PMMA electron-beam resist and similar results have been achieved with SU8 layers. As the template-layer and contacts are formed with optical/electron-beam lithography the inherent accuracy in alignment of these methods may be used to accurately position the template pattern with respect to the contacts.

3. Formation of atomic clusters

Our preferred method is a process whereby metal vapour is evaporated into a flowing inert gas stream which causes the condensation of the metal vapour into small particles. The particles are carried through a nozzle by the inert gas stream so that a molecular beam is formed. Particles from the beam can be deposited onto a suitable substrate. This process is known as inert gas aggregation (IGA), but clusters could equally well be formed using cluster sources of any other design (see e.g. the sources described in the review [5], but most particularly by sputtering of the cluster material from a target). Clusters can be of Si, Pd, Pt, Cu, Bi, Pb, Sb, Ag and Au or of many other materials. We prefer Si, Bi, Sb, Pd and Cu. Sizes of cluster can range from less than 0.5nm to lOOOnm in diameter. We prefer clusters with diameters in the l-50nm range and an apparatus as described in [6].

4. Deposition of the clusters onto the patterned substrate The basic design of a cluster deposition system is described in Refs [5] and [6], the contents of which are hereby incorporated by way of reference. Following the cluster source are a series of differentially pumped chambers that allow ionisation, size selection, acceleration and focussing of clusters before they are finally deposited on a substrate. In fact, while such an elaborate system is desirable, it is not essential, and our devices have frequently been formed in relatively poor vacuums without ionisation, size selection, acceleration or focussing.

It is a feature of the deposition systems described in Refs. [5,6] that the flowing inert gas stream, and the clusters contained within it, is accelerated by the flow of gas through the nozzles between differential pumping stages. There may be a supersonic expansion at one or more nozzles. This results in clusters with some degree of translational kinetic energy, which is directed towards the substrate, and which is in fact crucial to the invention.

A feature of our technique is that the clusters deposited within apertures in nonconducting material on the substrate and between the electrical contacts (if they are in existence) may form a conducting chain or wire whilst those clusters which are deposited on top of, and happen to stick to the non-conducting material (generally <1% in our best embodiments, see below), are isolated from the electrical contacts. Deposition of atomic vapour from a standard evaporator would result in similar metallic layers blanketing the substrate; in a standard lithography process the metal on top of the insulating material would need to be "lifted-off ', in order to yield an observable metallic pattern (i.e. to reveal the metal that was deposited into the lithographically patterned apertures).

Despite the scenarios mentioned above, the key to the present invention is that the deposited clusters do NOT stick to the patterned insulating material, thereby eliminating the need for a lift-off process i.e. preferentially the non-conducting material and cluster materials are such that the clusters bounce from the non-conducting material, while sticking to the substrate (or within the apertures created in the non-conducting material). In general, the selectivity of the clusters for the surface (and vice versa) is due to or contributed to by one or more of:

- the identity and/or nature of the materials of regions of the pattern - the identity and/or nature of the surface of the regions of the pattern

- the identity and/or other characteristics of the clusters

More specifically, there are several possible material properties that can be selected in order to achieve selective sticking of clusters to one part of the substrate and not to another. These properties can be selected from

• Hardness / softness - a soft layer may provide a 'feather bed' in which the clusters are able to nestle, while they are unable to settle on a hard surface

• Roughness / smoothness - the texture of the substrate surface may affect the ability of a cluster to wet the surface, or, a large degree of roughness may provide effective soft landing sites for clusters.

• Wettability — the wettability of a surface determines the area of the interface between the substrate surface and a cluster adhered to it, and hence the energy of attachment to the surface.

• Reflectivity to clusters - a greater degree of reflectivity to clusters will ensure that the clusters are less able to stick to the surface.

• Elasticity - a highly elastic surface of the substrate on which the cluster lands may cause an increased likelihood of reflection of incident clusters.

• Implantation depth — clusters with sufficient incident momentum may embed themselves in the surface on which they land. • Chemical bonding — chemical interaction may occur between the surface of the substrate on and the cluster causing a greater degree of binding to the surface.

A further embodiment of the invention relies on surface texturing of the substrate surface. Focused Ion Beam, Reactive Ion Etching or Sputter-Etching can be used to locally roughen areas of Si_xN_y or SiO_x surfaces in accurately defined locations and with nano-scale dimensions. Similarly, the underlying silicon substrates can be roughened prior to formation of the passivation layer. In both^' cases, the low reflectivity of the roughened surface causes selective adhesion of clusters deposited onto it, whilst the untreated areas of the substrate, having higher reflectivity, remain free of clusters. The textured areas of the Si_xN_y/SiO_x may or may not be aligned to electrical contacts formed on the insulating surface prior to the deposition process in order to cause localised pathways of cluster between the contacts.

The projection of the particles towards the surface is a distinguishing feature of the invention. The differences in the abovementioned properties provide qualities which may cause particles to be unable to overcome their tendency to bind to the surface in one area of the substrate (so they stick), while causing the particles to have greater energy than that which might bind the particles to the surface in another area, causing the particles to be reflected, or at least not to stick efficiently in those areas. There is, then, a clear distinction between the present invention and those methods of the prior art wherein there is provided a chemically patterned surface to which chemically functionalised nanoparticles choose to adhere, due to the formation of chemical bonds, when said nanoparticles diffuse into contact while in a solution containing both nanoparticles and the substrate.

The interaction between the clusters and the surface that they impact on is obviously of significant importance in determining whether the cluster adheres or bounces, and one way of parameterising the interaction is by the wetting angle of a cluster resting on the surface. Indeed, we have demonstrated that the wetting of a surface by a cluster can dramatically influence the likelihood of the cluster bouncing: clusters which wet the surface generally adhere more strongly than those clusters which do not wet the surface significantly. In previous reports, the bouncing or sliding of clusters resulted in their accumulation at the apex of a V-groove etched into the surface of the substrate, and reflection from planar regions of the substrate. On a relatively simple level, an understanding of the bouncing of clusters from a surface can be understood by considering the interaction of liquid droplets with a surface. In this case the bouncing phenomenon and its explanation is similar to that of the bouncing of water droplets from a surface [7, 8]. Put simply, a sufficiently energetic cluster can overcome the energy of attraction to the surface which results from the cluster wetting the surface. The energy of attraction is calculated from the change in surface energy of the cluster when it wets the surface, and if the kinetic energy of the rebounding droplet is greater than this binding energy the cluster will leave the surface. This interpretation ignores the state of the cluster (solid clusters may have different interactions with a surface than liquid clusters) and treats dissipation of energy in the collision by applying a phenomenological factor which identifies the rebounding kinetic energy as a fixed fraction of the kinetic energy of the incoming drop [8]. It is clear that a more sophisticated explanation should include all dissipation of energy in the collision due, for example, to plastic or viscous flow during deformation of the cluster and / or the surface. A solid cluster at small incident velocities will experience only elastic deformation (i.e. a rebounding cluster recovers its initial shape, there is no permanent deformation), while at higher incident velocities the cluster may be permanently deformed when the pressure experienced exceeds the yield stress of the cluster material.

In the invention the velocity of the clusters can be controlled so that at low velocity the clusters experience elastic collisions with the surface, and are then held in contact with the surface by the attraction of the cluster to the surface. Then as the velocity of the clusters increases the clusters are elastically deformed sufficiently that they rebound from the surface. As the velocity of the clusters increases further they are at least partially plastically deformed so that they contact the surface over a larger area, increasing their tendency to stick to the surface. As the velocity of the clusters increases still further the clusters are further deformed and the energy of recoil is sufficient for the clusters to bounce from the surface.

We have found that at low velocities (v<0.3v_c where v_c is the characteristic velocity where the v_c=ε/m, and ε is the depth of the atomic interaction potential between cluster atoms and m is the mass of an atom comprising the cluster) clusters stick because they are unable to overcome the attraction of the cluster to the surface. At slightly higher velocity (v~0.3v_c) this energy can be overcome, and the cluster bounces. At velocities in the regime 0.7v_c <v<2.5v_c clusters are plastically deformed on impact, increasing the area of contact with the surface, and hence the binding energy to the surface and the probability of sticking. At sufficiently high velocity (v>2.5v_c) the kinetic energy is sufficient to overcome the additional binding energy caused by the plastic deformation and the clusters bounce. In other words as the velocity increases from low velocities the clusters go through a region of sticking behaviour, a region of bouncing, a region of sticking and again region of bouncing. These regions are identified and labeled regions I, II, III and IV in Figure 44. Thus I = elastic sticking; II = elastic bouncing; III = plastic sticking and IV = plastic bouncing.

In general terms the invention includes the possibilities 1) we can use preferential sticking at step edges or other defects such as ridges or depressions, to create wires/structures

2) we can use the fact that small clusters could be liquid while large clusters are solid to get preferential accumulation of the small clusters and hence narrower wires or smaller structures. 3) we can take advantage of the two distinctly different regimes where higher velocity can lead to bouncing instead of sticking within each regime (the elastic one at low velocities, the plastic one at higher velocities). 4) in some situations we can get clusters to stick better by increasing the velocity (i.e when we shift from the elastic to plastic regimes). 5) we can use different surfaces (with different binding energies for the clusters) to ensure sticking or bouncing in one or other of the regime due to either the plastic or elastic bouncing.

6) we can employ a change (increase) of wetting angle with size (or equivalently a decrease in effective interaction energy with the surface) which allows us to engineer additional bouncing of the larger clusters. 5. Monitoring the Formation of the Wire

This is an optional step of the invention which involves the monitoring of the conduction between a pair of electrical contacts (when present) and ceasing deposition of atomic clusters upon the formation of a conducting connection between the contacts. Alternative or further embodiments may involve monitoring the formation of more than one wire structure where more than one wire may be useful.

We monitor the formation by checking for the onset of conduction between two contacts. This requires incorporating into our deposition system electrical feedthroughs into the deposition chamber, to allow electrical measurements to be performed on devices during deposition.

It should be emphasised that monitoring of conduction is an optional step which may be omitted from the process. This step provides greater control over the deposition process, but is not essential in many applications.

6. Simulation Model and Methodology

Here we use standard molecular dynamics (MD) techniques to model the interactions between the atoms comprising the clusters and the surface that the cluster impacts on. The interaction between atoms separated by a distance r is modeled using modified form of the Lennard-Jones (LJ) potential [9], which is a standard schematic potential employed in preference to more realistic potentials to simplify and speed up simulations,

V(r) = 4ε [ (σ/r)¹²- C (σ/r)⁶] (1)

for r < r_c where r_c is a cut-off chosen here to be 6σ. σ is the LJ radius and ε is the depth of potential well. For our system the parameters ε and σ are the same for all atoms, although the constant C, which is applied as a scaling factor to the attractive part of the potential, is varied to control the attraction between surface and cluster atoms. The atoms within the cluster and within the surface interact via standard LJ potential with C=I. Here we will consider collisions for values of C between 0.2 and 0.7. Simulations using similar parameters have shown that varying C between 0.5 to 1.0 leads to transitions from non-wetting to wetting behavior for a liquid drop on a solid substrate [9]. We discuss below the effect of C on contact angle in our system.

We have simulated the collisions of various sizes of Mackay icosahedra with a (H l)- terminated fee surface, although we expect that similar qualitative behaviour will be observed for any cluster structure (e.g. decahedral, fee, cuboctahedral). The Mackay icosahedra are made up of 20 tetrahedrally shaped fee units which share a common vertex. The surface slab consists of fixed bottom layer and 15 layers of dynamic atoms with about 8000 atoms arranged in fee crystalline structure and exposing a (111) surface facet. The surface has the dimensions of 11.7 σ x 11.3 σ x 10.3 σ to allow for substantial deformation and broadening of the cluster on impact. Newtonian dynamics is applied to the central part of atoms while outer region follows Langevin dynamics [10] at a temperature T. The friction parameter is varied linearly from 0 at the Langevin- Newtonian interface to 2 at the Langevin exterior in Langevin region. This block of 5846 Langevin atoms regulates the temperature of the 1344 Newtonian atoms and absorbs energy from the cluster impact. The surface computational cell is repeated periodically in the two dimensions parallel to the (111) surface plane, with no periodic boundary conditions applied in the z-direction. This arrangement of atoms was selected after a checking the convergence of the energetics of the collisions.

Both the Newton and Langevin equations of motion are integrated with a velocity Verlet scheme, with a time step Δt = 0.01 τ where τ is the corresponding atomic time scale (mc^/ε)^{0 5}. The solid clusters, liquid clusters and surface were equilibrated at temperatures of 0.13 ε/kβ, 0.33 ε/kβ and 0.2 ε/kβ, respectively for 10,000 time steps to allow them to adopt relaxed configurations. At each size and velocity investigated we typically performed 50-100 impact simulations by varying the cluster orientation randomly. The impact velocity was then assigned to the cluster atoms in the normal direction of incidence onto the surface and the collision then followed. In the rest of this paper, all quantities are expressed in LJ reduced units using σ, ε and τ as characteristic length, energy and time scales, respectively.

EXAMPLES PART I: ILLUSTRATING THE EXPERIMENTAL METHOD In this section we give examples illustrating the basic lithography and cluster deposition processes which underly the method of the invention, including experimental examples of

• fabrication of contacts on substrates

• fabrication of aperture-slots in PMMA and photo resist • use of single and bi-layer PMMA

• preparation of clusters by the gas aggregation method

• deposition of the clusters, focussing on the effect and importance of cluster velocity

• controlling the deposition of clusters by monitoring the onset of conductivity of a device

In a subsequent section (Examples Part II) we give examples illustrating the usage of these techniques in preparing patterns of clusters and cluster devices.

A.l. Fabrication of contacted substrates

Passivated substrates featuring lithographically defined contacts were prepared using standard lithography procedures similar to those described elsewhere [17, 18]. The substrates were commercially available Si_xNy passivated Si wafers. Large-area metallic contact pads were fabricated using optical lithography whilst contact features with sub- micron dimensions were defined using electron-beam lithography. The metallic contacts were then coated in a PMMA layer which was patterned using electron-beam lithography. This lithography step is required in order to define apertures in which the clusters are able to land and connect to the contacts while the PMMA layer prevents deposition of clusters on the majority of the substrate surface. These steps are described in more detail in the following sections. A.1.1. Substrate preparation

Prior to the lithography processes, the wafers were coated with photo resist and cleaved into 10 x 10 mm² substrates. Cleaning was then performed by immersing the substrates into ultrasonically agitated acetone, methanol and isopropyl alcohol. After the three- solvent cleaning process, the substrates were dried using N₂ gas and oven-baked at 95 ⁰C.

Alternatively, the planar NiCr/ Au contacts are formed on a wafer prior to the dicing stage using standard photolithography. An array of 25 chip layouts is exposed and developed in a l-2μm thick AZ1500 photo resist layer and the metal layers are thermally evaporated onto the whole wafer surface. Acetone is used to dissolve the AZl 500 layer and remove the unwanted metallisation in a lift-off process. The metallised wafer is then transferred to a dicing saw and twenty-five 10 x 10mm² chips with large-scale planar electrical contacts are produced.

A.1.2. Optical Lithography

Before discussing the fabrication of planar contacts to the devices, we note that contacts to the substrate have also been formed using similar processes. Vertical interconnects (Vias) through the SiN layer on the substrate were formed using Reactive Ion Etching (RIE) with a CHF₃/Ar etch-chemistry. These vias were eventually coated with metal and provide electrical contact to the Si substrate which provides a means to create a variable electric-field in close proximity to the deposited clusters i.e. a "back gate" contact which can be used to control the electron concentration in a device.

As discussed above the preferred way of forming the large scale contacts is using a shadow mask technique, however we have also formed contacts routinely by photolithography. A UV-sensitive photo resist ^"(Clariant AZl 500) was spun onto the clean Si_xN₃, coated substrates at 3000 rpm. A Karl Suss MA6 mask-aligner with a UV light-source was then used to expose the photo resist through a chrome/glass mask featuring the appropriate large-area contact patterns. After developing, the large-area contact patterns were translated into voids in the photo resist layer. Ti (or NiCr) and Au layers (with respective thicknesses 5nm and 50nm) were evaporated over the entire substrate using an Edwards Auto 306 thermal evaporator. The large-area contact pattern was finally revealed using an acetone lift-off process to remove both the photo resist and the Ti (or NiCr) /Au adhered to the photo resist. At this stage in the process, large area contacts have been produced with a contact separation of 100 μm.

A.I .3. Electron Beam Lithography

After the large-area contacts were completed, all the subsequent substrate patterning processes were carried out using electron-beam lithography and electron-beam sensitive resist was spun onto the substrates rather than conventional photo resist. (Since electrons have a smaller wavelength than UV light, smaller patterns can be achieved). A Raithl50 Electron Beam Lithography System was used to perform the electron-beam exposure.

High Molecular Weight PolyMethyl MethAcrylate (HMW PMMA) was the chosen E- beam resist. HMW PMMA offers highly selective development characteristics and can be spun to very thin layers (~50nm) using moderate spin-speeds. When exposed to an electron-beam, HMW PMMA transforms into Low Molecular Weight PMMA (LMW PMMA) which can then be dissolved in a solvent, leaving only the HMW PMMA in unexposed areas. This characteristic of PMMA is exploited in the bi-layer lift-off process used to produce the nano-scale metallised contacts used for the invention.

A.1.3.1. Bilayer process for metallisation of small scale contacts The following bilayer process is used to form small scale metal contacts with separations between 200nm and lOOOnm. All examples of small scale contacts shown in the figures were created using the bi-layer process and subsequent metallisation.

In the bilayer process, LMW PMMA is spun onto the clean substrate and then baked at 185 ⁰C for 30 min. Next, HMW PMMA is spun on top of the LMW PMMA and baked again at 185 ⁰C for 30 min. The differing solvent bases for the HMW- and LMW- PMMA ensure that the layers do not merge during spinning/baking. After exposing and developing the bilayer PMMA, an undercut forms due to the higher dissolution rate of the underlying LMW PMMA (Figure 18). In lift-off processes (particularly those required to produce submicron features) resist-undercut is advantageous for clean removal of the excess metal and clean edge-profiles. This technique was used for defining the nanoscale contacts and could be used for the openings in the final passivation layer but in the examples presented here a single HMW PMMA layer is preferred for the passivation layer (with the exception of Fig. 9).

A.1.3.2. Single layer PMMA process for passivation of substrate and formation of aperture-slots

Following the fabrication of the small scale contacts (as in the previous section), it is necessary to fabricate an aperture-slot which extends between the contacts and allows the clusters to impact (and stick to) the bare substrate (while the remainder of the substrate is covered in a material which the clusters do not stick to).

In order to form a nanoscale aperture-slot, a single HMW PMMA layer is spun onto the contacted sample at 3000 rpm and then baked at 185 °C for 30 min. This also forms a passivation layer over the substrate/contacts which eliminates the possibility of parasitic conduction across the substrate through clusters deposited far from the contact-gap. Electron-beam lithography is then used to create an aperture (aligned over the contacts) in the HMW PMMA layer. Figure 14 shows the process of forming a passivation layer, developing a pattern in that layer, and subsequent cluster deposition into the aperture- slots. An example of contact-fingers, a lμm x 3μm PMMA aperture and a Bi cluster film assembled within the PMMA aperture, are shown in Figure 8. Other contact separations, aperture dimensions and aperture geometries are readily achieved using EBL; examples are shown in Figures 6-8 and 10-11.

Of course, the passivation layer can also be formed using the bi-layer process described above. In Figure 9, a bi-layer passivation was used and the aperture-slot was formed in the bilayer material. The underlying LMW PMMA is more easily developed that the HMW PMMA top-layer. The LMW PMMA therefore has a larger opening in it and the LMW PMMA can be seen as a lighter grey region in Fig. 9 with an edge approximately lOOnm from the edge of the cluster wire. The size of the cluster wire is governed by the size of the narrow slot/opening in the top HMW PMMA layer. Note that the dark regions surrounding the wire is the region where the HMW PMMA remains in place, but the LMW PMMA has been removed from underneath it.

Once the electron-beam lithography processes were complete, the contacted, passivated samples were mounted on the sample-arm of a cluster-deposition system. Electrical contact to the samples was established using push-pin contacts and electrical feed- throughs in the deposition chamber enabled the necessary connections to a voltage source and current- and volt-meters required for electrical measurements.

A.I.3.3. SU8 process for passivation of substrate and formation of aperture-slots SU8 can be used in a very similar manner to PMMA to provide passivation and patterned template features for selective cluster-assembly. SU8 2000.5 was spun on selected Si_xN_y passivated Si samples at 4000rpm to produce a layer thickness of 500nm. The SU8 layer was baked on a hot-plate at 100°C for 60-seconds. The SU8 layer could then be patterned optically or using an electron-beam. Optical exposures were performed on a Karl Suss MJB-3 UV mask aligner equipped with a 200W UV-bulb and the exposure periods were typically 10-12s. SU8 is extremely sensitive to electron- beam exposure and the electron-beam dose used for nanoscale patterning of the SU8 layers was approximately 1/50^th the dose required to expose PMMA (approximately lμC/cm²). After exposure the SU8 was baked at 100°C for 60-seconds in order to enhance the cross-linking of the exposed resist. The samples were then immersed in standard SU8 developer for 90-seconds in order to develop away the non-exposed regions.

B. Formation of clusters Our preferred apparatus is described in Ref. [6]. Clusters are produced in an inert-gas condensation source. The apparatus may be operated with a thermal source or a magnetron source. When operated with the thermal source, metal contained in a crucible is heated and evaporated. The sputter source produces metallic or semiconducting vapour from a magnetron sputter head and can therefore produce clusters from materials with very high-melting points. In both the thermal and magnetron source the metallic/semiconducting vapour is mixed with inert gas which causes clusters to nucleate and grow. The cluster/gas mixture passes two stages of differential pumping (from ~1 Torr in the source chamber down to ~1(T⁶ Torr in the main chamber) such that most of the gas is extracted. Typically, the beam enters the main chamber through a nozzle having a diameter of about 1 mm and an opening angle of about 0.5 degrees, although different nozzles are sometime used. In order to determine the intensity of the cluster beam, a quartz crystal deposition rate monitor is used. The samples are mounted on a movable rod and are positioned in front of the quartz deposition rate monitor during deposition.

Note that the specific range of source parameters appears not to be critical: clusters can be produced over a wide range of pressures (0.01 Torr to 100 Torr) and evaporation temperatures and deposited at almost any pressure from 1 Torr to 10^"12 Torr. Any inert gas, or mixture of inert gases, can be used to cause aggregation, and any material that can be evaporated or sputtered may be used to form clusters. The cluster size is determined by the interplay of gas pressure, gas type, metal evaporation temperature, and nozzle sizes used to connect the different chambers constituting the deposition apparatus.

C. Deposition of the Clusters onto the surface

Apart from the nature of the material on which the clusters impinge, the key parameter which controls the probability of adhesion of a cluster to a surface is the velocity of the cluster. We discuss the control and measurement of cluster velocity in this section.

Cl. Cluster velocities Our favoured method of controlling the cluster velocity is to control the flow rate of gas into the cluster source chamber (the deposition system design is described in [6]). Note that, as discussed in [12], whilst the velocity of the inert gas leaving the source can be calculated (given the nozzle diameter and inlet flow rate), the unknown size of the velocity slip effect (clusters are accelerated by the gas flowing through the source chamber exit nozzle but are unlikely to reach the speed of the gas flow) means that precise calculation of the cluster velocity is not possible. We therefore prefer to quote the experimental source inlet gas flow rates when describing this work, but estimate that the average velocity of the clusters incident on the V-grooved substrates is approximately equal to the source exit gas velocity. Source exit gas velocities of 36, 41, 47 and 55 m/s were calculated for the source configuration used in Ref. [12], for Ar inlet flow-rates of 30, 60, 90 and 150 seem, respectively.

Using the standard inert gas aggregation source, and associated nozzles and pumping configuration [6], the estimated Bi cluster velocity with the current source configuration and using a source-inlet Ar gas flow-rate of lOOsccm is 50m/s (corresponding to an estimated kinetic energy per (25nm-diameter) cluster of 1.0 x 10^"16 Joules). Using the gas aggregation source based on magnetron sputtering, and associated nozzles and pumping configuration [6], the measured Cu cluster velocity with source-inlet Ar and He gas flow-rates of 700sccm and lOOsccm respectively is 260m/s (corresponding to an estimated kinetic energy per (IOnm-diameter) cluster of 1.5 x 10^'16 Joules). In this case, the nozzle was a 10mm long Laval nozzle with inlet/outlet diameters of 5.5mm and 4.9mm and a throat diameter of 3.3mm, and measurement of the Cu cluster velocity was performed using a deflector plate and a Faraday cup arrangement housed in the deposition system. Ionised Cu clusters were deflected using a voltage pulse applied to the deflector plate. A current pulse associated with the clusters was then detected on the Faraday cup and the time difference between the deflection-pulse and the detected cluster pulse (the time of flight) was converted into a cluster velocity. We have characterised the cluster velocities for clusters of a wide range of masses produced using a range of magnetron sputtering source conditions, including aggregation length L, gas flow rate F (for He and Ar and mixtures thereof) and sputter power P. Some examples of these characterisation studies are shown in Figures 32 and 33.

Further extensive measurements of cluster velocity have been performed for a variety of source conditions using a combination of a mass filter [11] to select individual cluster sizes and a retarding potential applied to a Faraday cup on which the clusters are incident [6]. An example of the data from this method is shown in Figure 34, resulting in the velocity and mass data in Table 2 below. In Figure 34 the ion current on the Faraday cup is measured as function of the retarding potential (U), which has been converted into an equivalent cluster velocity (v) using eU^/_∑mv², and the mean cluster velocity is inferred from the point of inflexion in each curve. The ion current changes sign due to an uncorrected offset current. Note that in Table 2 the calculated gas velocity is an estimate based on the gas flow rate into the source chamber [12], and the actual velocity is less than this due to the "velocity slip effect" referred to above.

Table 2. Summary of gas velocity calculation and the measured cluster velocity for a long nozzle with 4mm diameter opening.

D. Monitoring of the Deposition

The measurement of the current flowing in the device during deposition is important to the realisation of several of the device designs, since the onset of conduction marks the formation of a percolating film or a continuous wire. The surface coverage of the deposited nanoparticle film can therefore be controlled and the cluster-assembled film can be electrically characterised immediately after formation and in-vacuum. Clearly monitoring the deposition in this way requires that contacts are first prepared on the surface.

Figure 54 shows the measured onset of conduction for a Bi cluster-assembled wire which was formed between dual planar NiCr/ Au contacts on a Si_xN_y passivated Si substrate supporting a PMMA template layer. The conductance is seen to rise sharply through two orders of magnitude approximately 310s after the deposition process started. This rapid and significant increase in the conductance between the contacts indicates the formation of a conducting wire. The Bi cluster-assembled wire which produced the onset characteristic shown in Fig. 54 was lOOμm in length and had a minimum width of 200nm. The constituent clusters were deposited using a source inlet Ar gas flow-rate of lOOsccm and the cluster-coverage on the PMMA layer was less than l% ofone-monolayer.

EXAMPLES PART II: EXPERIMENTAL RESULTS, PATTERN FORMATION AND DEVICE FABRICATION

In this section we give examples illustrating results of the method of the invention, including the effects on cluster adhesion of

• Controlling the electron dose to a layer of PMMA

• Surface roughness

• Differing surface materials before then giving some specific examples of devices fabricated using patterned aperture slots in each of PMMA, photo resist and SU8.

We however begin by showing some preliminary illustrative examples of the results of fabricating cluster devices and patterns of clusters. A. Preliminary examples of cluster-assembly on HMW-PMMA aperture on Si_xNy substrates

In the following examples, the selective cluster accumulation is achieved using a patternable, non-conducting polymer (HMW PMMA) as a passivation/reflection layer. When deposited with sufficient incident momentum, clusters are reflected from the areas patterned with HMW PMMA whilst adhering to exposed Si_xNy, SiO_x and metallic surfaces.

Unless otherwise stated, the examples in this section result from deposition of Bi clusters with mean diameter ~25nm, produced in an inert gas aggregation source with source inlet flow rate lOOsccm of Argon, crucible temperature 750°C to 820⁰C, source pressure 23 Torr.

A.I. Example: pattern formation using EBL on PMMA coated Si_xN_y substrates Figure 14 illustrates schematically the use of electron-beam lithography to generate patterns in HMW PMMA layers that were spun onto a Si_xNy (or Au coated Si_xNy - metal coated substrates are included within the description of substrate) substrate. After exposure of the PMMA to electrons development of the pattern in the PMMA thereby exposes the underlying films of Si_xN_y or Au. Clusters are then deposited onto the HMW PMMA layers and into the patterned areas and the resulting films can be inspected using a Field-Emission Scanning Electron Microscope. Typically the clusters stick to the substrate but not to the PMMA, resulting in the desired cluster patterns.

Figures 6-11 are SEM images showing examples of patterns formed by the deposition of Bi clusters into apertures in PMMA on Si_xN_y substrates. The examples in Figures 10 and 11 show that arbitrarily shaped cluster patterns may be achieved by this method; in this case the patterns of clusters are maps of New Zealand. The clusters in Figure 10 are

Sb clusters (see details below). In the examples in Figures 6 to 9 the cluster patterns are wires connected to NiCr/Au contacts (Figures 7-9) or contacts which comprise clusters themselves (Figure 6). In each of these cases the momentum of the Bi clusters was such that the clusters adhere to the Si_xN₅, surface but are almost entirely reflected from the PMMA. For contrast, Figure 15 shows the results if the momentum of the clusters is not sufficient to achieve reflection from the PMMA i.e. a relatively uniform film of clusters adheres to the PMMA In Figure 15 the low selectivity resulted from a low source-inlet argon flow corresponding to a low velocity of clusters and therefore small average cluster-momentum (note that a high density of clusters in the aperture slot can just be identified in the centre of the image in Figure 15 but that this is difficult due to the high density of clusters on the surface of the PMMA). In other examples (not shown) low selectivity results from reducing the cluster size as this also reduces the cluster momentum.

B. Detailed examples illustrating the principles of the invention In this section we discuss examples which illustrate the underlying principles of the invention. We begin by discussing the effects of controlled exposure of PMMA to an electron beam, which result in formation of cluster patterns on partially exposed (roughened) PMMA surfaces, or on the underlying substrate which is revealed when the PMMA is fully removed from an area of the substrate. We then move on to a discussion of the differing adhesion of clusters to different surfaces, and in particular the tendency for clusters to adhere to a substrate surface such as SiO_x or Si_xN_y while bouncing from the surface of a polymer such as photoresist or PMMA.

B.I. Control of the electron dose applied to a PMMA layer

The exposure dose provided by the electron-beam is of particular importance when patterning the HMW-PMMA and affects the quality of the surface on which the incident clusters land. Dose tests have therefore been performed with the aim of finding the optimum dose required to completely remove the HMW PMMA from within the patterned areas whilst achieving nanoscale resolution. The roughness of the patterned areas after development has been measured using Atomic-Force Microscopy (AFM) and the results of this analysis have been used to explain both the cluster reflection from the HMW PMMA layer and cluster accumulation in the apertures. Figure 3 shows bismuth clusters (with a mean diameter of 30 to 40 nm; inert gas aggregation source with source inlet flow rates 1 OOsccm of Argon, crucible temperature 785°C, source pressure 22.4 Torr) deposited within partially exposed and developed patterns in HMW PMMA (i.e. the PMMA was exposed to electron beam doses smaller than required to fully remove the exposed PMMA). The total deposited thickness (as measured at the rate deposition monitor) of clusters was fixed to be ~21±3 nm in each case but the cluster coverage on the surface clearly increases with increasing electron dose (from 40μC/cm² in a) in steps of 10μC/cm² to 80 μC/cm² in e)). Hence it is clear that the electron dose is effective in controlling the adhesion of the clusters to the exposed region.

A similar experiment with antimony clusters (with a mean diameter ~30nm and produced in the inert gas aggregation source with source inlet flow rates 40sccm of Helium and 40sccm of Argon, crucible temperature 650°C, source pressure 6.8 Torr) leads to very similar results, as shown in Figure 1 for a deposited thickness of clusters of 54±6nm (Doses: a) 40 μC/cm², b) 50 μC/cm², c) 60 μC/cm², d) 70 μC/cm² and e) 80 μC/cm²) and Figure 2 for a deposited thickness of clusters of 34±lnm (Doses: (a) 45 μC/cm², b) 55 μC/cm², c) 65 μC/cm² and d) 75 μC/cm²). The thicknesses are as measured at the rate deposition monitor.

In order to derive a relationship between cluster coverage and the electron-beam dose, the surface coverages in the FE-SEM images shown in Figure 1, Figure 2 and Figure 3 were quantified using image processing software. The images were binarised (i.e. converted into black and white) using a threshold grey value which preserved the shape of the cluster patterns in the original images. The number of black and white pixels in the resultant image was then digitally counted and converted to a surface coverage.

Figure 4a shows the Sb cluster surface coverage measured by analysing binarised versions of the images in Figures 1 and 2, while Figure 4b shows similar results for the Bi clusters in Figure 3. Increased electron-beam dose results in increased cluster coverage. As discussed in more detail below, this effect arises from a combination of increased surface roughness in the partially exposed patterns (dose 40-80μC/cm²) and the greater propensity for clusters to stick to the Si_xNy surface which is exposed at higher doses (>80μC/cm²).

5 Increasing the total deposited thickness of Sb clusters also results in higher total coverage within the partially exposed patterns, as is also shown in Figure 4a (compare the diamonds: 54±6 nm and triangles: 34±1 nm). This effect arises because Sb clusters which are incident on clusters which have already landed tend to stick more readily and therefore aggregate at these 'soft-landing' sites. Further evidence to support this 10 assertion is shown in Figure 10. Here Sb clusters have adhered to the patterned region of a HMW PMMA layer and have formed "clumps" due to preferential accumulation of clusters around previously landed clusters.

B.1.1. Correlation of surface roughness with cluster adhesion

15 Surface roughness on the nanoscale is commonly measured using an atomic force microscope (AFM). Figure 5 shows atomic force microscope images used to determine the RMS roughness within HMW PMMA patterns which have undergone electron-beam exposures ranging from 0-140μC/cm² (Electron dosage was a) 0 i.e. unexposed HMW PMMA, b) 40 μC/cm², c) 50 μC/cm², d) 60 μC/cm², e) 70 μC/cm², f) 80 μC/cm² and g)

20 140 μC/cm² i.e. fully developed.). RMS roughness is plotted against electron-beam exposure dose in Figure 4c. The roughness increases for increasing dose until it reaches a maximum when the dose is approximately 65 μC/cm². The increase of cluster- coverage for a dose of 40 — 65 μC/cm² in Figures 4a and 4b can therefore be explained by the increase in surface roughness within the void. Increased surface roughness

25 provides a greater number of soft landing sites and a greater opportunity for the clusters to interact with the surface and therefore to stick to it. In contrast, a smooth PMMA surface (0 dose) is hard and flat and clusters are therefore unable to find soft-landing sites or otherwise adhere when they land.

30 Electron-beam doses higher than 65 μC/cm², are sufficient to remove enough PMMA to cause parts of the underlying substrate (see Figure 5e and 5f) to be exposed after development. The further increase in coverage in Figures 4(a) and 4(b) is then explained by the increased surface-wetting / surface adhesion behaviour for both the Bi and Sb clusters on the Si_xNy compared to the HMW PMMA surfaces. Put simply, both Bi and Sb clusters bounce from unexposed PMMA layers, but stick to bare Si_xN_y surfaces.

We note that in the molecular dynamics models of the cluster interaction with a surface described below, the strength of the interaction can be controlled using a single parameter, C. A strong interaction (e.g. between a cluster and a rough surface, or for Bi rather than Sb) is modelled using a large C value, while C~0 represents a very weak interaction.

B.1.2. Comparison of Sb and Bi: influence of wetting angle / attraction energy and demonstration of the effect of the cluster material

The Sb clusters were deposited with lower average incident velocity than the Bi clusters due to the choice of lower gas inlet flow rates and the addition of He to the gas mix

(flow rates were 40/40sccm Ar/He for Sb and lOOsccm Ar for Bi). When adhered to either Si_xN_y or SiO_x surfaces, Sb clusters have a higher contact angle than Bi clusters (ie.

Sb clusters typically wet the Si_xN₅, or SiO_x surface appreciably less than Bi clusters[12]).

As a result, Sb clusters are reflected from Si_xNy or SiO_x surfaces when their incident momentum is far lower than would be required to cause reflection of Bi clusters from the same Si_xNy or SiO_x surfaces.

The differences in wetting /adhesion of the different cluster materials to a single surface illustrates the need to optimise the source inlet gas-flow and therefore the average cluster momentum, in order to produce the desired cluster reflection and assembly characteristics. The precise flow rate values chosen depend on the material from which the clusters are grown.

B.2. Adhesion of clusters to different surfaces In order to demonstrate the effects on cluster assembly of a polymer layer on the surface of the substrate, experiments were devised and performed in order to demonstrate the selective adhesion and reflection of Bi and Cu clusters from substrate surface layers of AZl 500 photo resist, PMMA electron-beam resist, MBE grown Si_xN_y, thermally grown SiO_x and SU8 (an epoxy based resist which can be patterned optically or with an electron-beam).

B.2.1 Illustration of differences in adhesion for various surfaces

Figure 20 shows measured Bi cluster coverages achieved after three deposition experiments onto the aforementioned surface layers. The source-inlet Ar flow-rate was lOOsccm and the average cluster diameter was approximately 25nm. The deposition periods were selected in order to deposit cluster films of thickness 15 A, 41 A and 140 A on a quartz crystal film-thickness-monitor, which are then the nominal thicknesses of material deposited on the substrate, corresponding to surface coverages of 35%, 95%, and 330 % respectively. It is clear from Figure 20 that a far higher proportion of the incident Bi clusters adhere to the Si_xN_y and SiO_x surfaces than adhere to the PMMA and AZl 500 surfaces. Under these deposition conditions, Bi clusters were reflected from all surfaces (the total coverage on the Si_xN_y and SiO_x layers amounts to a significantly lower volume of material than that recorded by the FTM crystal). Percolating Bi cluster films (with a coverage of ~70% of one monolayer) were however formed on Si_xNy or SiO_x surface layers whilst the cluster-coverage measured on the PMMA surface layer after the same deposition process was less than 3% of one monolayer.

Figure 21 shows Cu cluster-coverage data collected after Cu clusters were deposited onto similar samples. The Cu clusters were deposited with combined Ar and He flow- rates of 700sccm and lOOsccm and the average diameter of these clusters was approximately IOnm. The deposition periods were selected in order to deposit cluster films of thickness 65 A, 118A and 140 A on a quartz crystal film-thickness-monitor, which are then the nominal thicknesses of material deposited on the substrate, corresponding to surface coverages of 40%, 70% and 85% respectively. Similar results to those obtained for the Bi clusters were obtained for the Cu clusters. The central result is that Bi and Cu clusters can be assembled into conducting films on a Si_xN_y surface layer whilst there is minimal accumulation of clusters on a PMMA surface layer (or photo resist layer in the case of Bi clusters). The source inlet Ar and/or He flow-rates are chosen to produce clusters which have sufficient kinetic energy to be reflected from a PMMA layer (see discussion of resultant velocities below).

Figure 22 shows measured Bi cluster coverages achieved after three deposition experiments onto SU8, PMMA, Si_xNy, SiO_x and Au. The source-inlet Ar flow-rate was lOOsccm and the average cluster diameter was approximately 25nm. The deposition periods were selected in order to deposit cluster films of thickness 17 A, 34 A and 51 A on a quartz crystal film-thickness-monitor. Again a far higher proportion of the incident Bi clusters adhere to the Si_xN_y, Au and SiO_x surfaces than adhere to the PMMA and SU8 surfaces. The cluster-coverage measured on the PMMA and SU8 surface layers was less than 3% of one monolayer after a deposition which causes a percolating layer to be formed on Si_xNy or SiO_x surface layers.

Figures 23 and 24 show Field-Emission SEM images of AZl 500 photo resist, PMMA Electron-beam resist, MBE grown Si_xNy and thermally grown SiO_x surface layers supporting Bi clusters (Fig. 23) and Cu clusters (Fig. 24). (Measurements of surface coverage from these images were shown in the cluster-coverage data in Fig. 20 and Fig. 21). Fig. 23 shows the Bi cluster-coverage obtained on each surface after a deposition process with an estimated total deposited Bi cluster layer thickness of 4lA. Fig. 24 shows the Cu cluster-coverage obtained on each surface after a deposition process with an estimated total deposited Cu cluster layer thickness of 65 A. Figure 25 shows Field- Emission SEM images of SU8 photo resist, PMMA Electron-beam resist, MBE grown Si_xN_y and thermally grown SiO_x surface layers supporting Bi clusters. The estimated total deposited Bi cluster layer thickness was 51 A. (Measurements of surface coverage from these images were shown in the cluster-coverage data in Fig. 22).

The source conditions for the Bi cluster depositions (Fig. 23) using the standard inert gas aggregation source based on thermal evaporation were as follows: source-inlet Ar gas flow-rate lOOsccm, source pressure approximately 25mbar, crucible temperature 800-

820⁰C and deposition rate 0.6-0.7 A/s. The source conditions for the Cu cluster depositions (Fig. 24) using the gas aggregation source based on magnetron sputtering were as follows: source-inlet Ar and He gas flow-rates 700sccm and lOOsccm respectively, source pressure approximately 3.0 Torr, sputter-head power IOOW and deposition rate 0.2 A/s.

The data in figures 20-25 show clearly that coating with a polymeric material such as PMMA or photo resist may significantly increase the reflectivity of the clusters from regions of the surface of the substrate.

C. Fabrication of Cluster-assembled devices

In this section we show, in turn, examples of devices fabricated in patterned PMMA, photo resist and SU8. Simple electrical characteristics of the devices are also illustrated.

Cl. Fabrication of Cluster-assembled devices and films using PMMA Figures 6-11 illustrate selective assembly of Bi and Sb clusters within apertures formed in HMW PMMA films. In Figures 6-9, the cluster-assembled films have been formed on electrical contacts thus enabling electrical characterisation of the films as soon as they become electrically conducting. Figure 6 shows a Bi cluster-assembled film suitable for four-point electrical conductivity measurements and formed in patterned HMW PMMA. The Bi clusters are distributed evenly within the aperture and the cluster-assembled film is of uniform thickness.

An image of Sb clusters assembled within an aperture-slot is shown in Figure 7. The Sb clusters have adhered to the Au contacts whilst clusters have been reflected from both the HMW PMMA film and the substrate area within the aperture, leading to low cluster coverage over these areas. In this deposition experiment, the source inlet gas flow (and therefore the average incident momentum of the clusters) was sufficiently high to prevent selective assembly within the aperture. The cluster-assembled film has grown into the aperture as clusters aggregate on the Au contacts and with other clusters. Figure 8 shows a similar aperture and contact arrangement with an electrically conducting Bi cluster-assembled film bridging the gap between the contacts. In this deposition experiment, the source inlet flow was optimised to produce selective assembly within the aperture and minimal cluster-coverage on the surrounding PMMA.

Patterns and/or contacts within the HMW PMMA are not limited to geometrical forms; Figure 10 and Figure 11 show silhouette-maps of New Zealand patterned in HMW

PMMA and filled with clusters. In Figure 10, 'bunching' or 'clumping' of the Sb clusters is clearly visible. This effect is attributed to the soft landing of the Sb clusters on top of pre-existing clusters or surface defects; Sb clusters incident on pre-landed clusters are more likely to remain on the substrate than those incident on unoccupied areas, and therefore aggregates or 'bunches' of clusters form on the substrate during the deposition and their size is dependant on the total number of clusters deposited onto the substrate.

C.1.1. Adhesion of clusters to Au contacts The intrinsic differences in the wetting / adhesion of clusters to different surfaces is further evidenced in Figure 7, which shows Sb clusters deposited on two planar gold contacts which are exposed to the cluster beam within a window opened in a surrounding PMMA layer (as marked with vertical white lines). Here, the Sb clusters have adhered to the gold contacts whilst neither the Si_xNy substrate nor the surrounding PMMA support a comparable amount of clusters.

Figure 9 shows an FE-SEM image of a contacted Bi cluster-assembled wire (contacts not shown). As can be seen in Figure 9 devices with minimum dimensions as small as one cluster width can be produced and contacted.

C.1.2. Electrical characterisation

Following formation of the device, the contacts may be used to characterise the electrical characteristics of the device.

Figures 12 and 13 show post-formation Current- Voltage (1(V)) characteristics taken from contacted cluster-assembled films formed within apertures in PMMA. Figure 12 shows a nonlinear 1(V) characteristic for the sample shown in Figure 8. The I(V) measurements were performed at room temperature and at 95 K. The solid line in Figure 13 is a two-point 1(V) measurement of the innermost contacts in Figure 6, and therefore the measurement includes the resistance associated with the contacts to the cluster- assembled wire. A four-point measurement (dotted line in Figure 13) de-embeds the contact resistance and therefore provides an I(V) characteristic for the cluster-assembled wire alone. The difference in the two- and four- point resistance measurements is attributed to bismuth-oxide tunnelling barriers at the contact/cluster interface and/or potential barriers at the Bi/Au interface, caused by the differing work functions of these materials.

The 4 point sample shown in Figure 6, as well as the contacts to the nanoscale device of interest, were formed by cluster deposition. Connections to the Bi cluster wire in Figure 8 were provided by planar NiCr/Au contacts and only the wire itself was formed by cluster deposition. The difference in the Current- Voltage characteristics between the two otherwise similar samples (similar device dimensions) is therefore related to the device/contact interfaces. For the 4 point sample in Figure 6, the device and the contacts are formed by the same method and same material; no contact potential or significant tunnelling barriers are expected.

C.1.3 Effect on adhesion to PMMA after exposure to high electron doses

HMW PMMA is a positive resist and so exposed patterns are developed away.

However, it is commonly known that when PMMA is exposed with a very high dose, it will crosslink such that it becomes a negative resist. This effect can be seen in Figure 16. Here an alignment mark was imaged with an electron microscope for a sufficient time to turn the resist negative. The ring of clusters around the alignment mark is due to exposure by secondary reflection and was high enough to turn the HMW PMMA into LMW PMMA and to be at least partially developed. The clusters stick in this region for the reasons described above (discussion of Figures 1-5). Figure 17 shows a sample that has been exposed to an Sb cluster beam for a much longer time than is usual in our work. The majority of the surface of the PMMA surface is covered with Sb clusters — this is simply because even with a small probability of sticking to the surface, deposition of a large enough number of clusters results in appreciable surface coverage. The feature of interest is the darker region in the centre of the image (surrounding a pair of contacts which lie under the PMMA and are only just visible) which was imaged in an SEM prior to cluster deposition, thus partially exposing the PMMA. There has clearly been a greater degree of reflection from the previously imaged area. This is because exposing the PMMA to an electron beam (in this case, even without development) can harden and/or smoothen the surface and therefore change the reflective properties for clusters. [Note that the original process of writing an aperture between the contacts was unsuccessful in this sample, and has no bearing on the main features of Figure 17.]

C .2. Fabrication of Cluster-assembled devices and films using Photo Resist

Figure 19 shows an aperture which has been patterned in conventional optical photo resist (Clariant AZl 500) over a SiO₂ passivated V-grooved silicon sample. Sb clusters were deposited onto the sample and assembled in the dual V-grooves (running vertically in the centre of the image) between planar Au contacts (lighter shade at top and bottom, with diagonal edges). The cluster deposition process was stopped immediately after conduction between the contacts was observed (indicating that a continuous cluster- assembled wire had formed in one of the V-grooves). The image shows that a greater number of clusters have adhered to the SiO_x covered areas (between the Au contacts), than have adhered to the optical photo resist layer (at each side of the image). Similarly, a greater number of clusters are found on the exposed Au contacts than on the optical photo resist layer. The difference in cluster coverage on the SiO₂, photo resist and Au contacts is attributed to the difference in wettability of the photo resist and the SiO_x whilst the Au contacts are known to have greater RMS surface roughness than either the SiO_x or the photo resist. Figure 35 shows a further example of a slot-aperture device fabricated using optical lithography and photo resist. In this case the image shows one end of a "Hall bar" device i.e. a device which has a contact at each end of an elongate slot-aperture and several contacts along each of the sides. In Figure 35 three contacts are visible underneath a layer of clusters which has covered the surface at the bottom of the aperture. Relatively few clusters adhere to the surface of the photo resist. In this case the photo resist (AZ1500) was 1.5 microns thick, the aperture was of dimension 30 x 10 microns² and the contacts were 5nm NiCr / 30nm Au. The clusters were 35nm Bi clusters deposited from an inert gas aggregation source with flow rate 100 seem of Ar resulting in a source pressure of 23.4 Torr. The thickness was 27nm as read from the rate deposition monitor. We have extensively studied Hall bar samples of this sort over a range of temperatures and magnetic fields in order to measure the carrier concentration and mobility of cluster- assembled films.

C.3. Fabrication of Cluster-assembled devices and films using SU8

Figure 26 shows an array of cluster-assembled wires which have been formed between planar Au electrical contacts (at top and bottom of the image) on a SiO_x passivated Si substrate. An SU8 template layer with aperture-slots (width approximately 5μm) enabled the selective assembly of incident Bi clusters into conducting cluster-assembled wires on the SiO_x and Au surfaces whilst the measured coverage on the SU8 amounted to less than 5% of one-monolayer.

C.3.1. Electrical Characterisation

In Figure 27 the I(V) characteristics of a single cluster-assembled wire (with minimum width l.Oμm and length lOOμm) are shown. A FE-SEM image of this wire is shown in Figure 28(b). The Bi clusters were deposited with an Ar-mlet flow-rate of lOOsccm onto a SU8 templated substrate held at room temperature (293K). Upon completion of the deposition process a linear 1(V) characteristic was recorded and the two-point wire resistance was lOkΩ. A heater and temperature controller were then used to raise the temperature of the sample-arm and sample to 300K, 330K, 370K₅ 400K, 430K and finally 460K. As shown in Figure 27, the conductance of the wire increased as the temperature of the sample was increased and the conductance at 460K was 70% higher than that measured immediately after deposition at 293K. The wire was then cooled to room temperature, and a final two-point resistance of 6.5KΩ was measured, suggesting a permanent change in the morphology of the wire. In fact Figure 28 shows that a larger average grain size had resulted from the heating process: Figure 28(a) shows a cluster- assembled wire which was subjected to temperatures no higher than 300K (Fig. 28(a)) next to the cluster-assembled wire which was heated to 460K (Fig. 28(b)).

Cluster wires can be accurately positioned over an arbitrary number of metal contacts and these can be arranged and shaped with equal arbitrariness. The contacts on the sample shown in Figure 29 have been formed using electron-beam lithography, followed by a standard metal deposition and lift-off. The separations between the contacts are 750nm, 500nm, and 750nm respectively. The two inner contacts are both lμm wide. Bismuth clusters with a mean diameter ~30nm (inert gas aggregation source with source inlet flow rates lOOsccm of Argon, crucible temperature 805°C, source pressure 22.5 Torr) have been used to form the cluster wire in Figure 29. The wire is 230nm wide and approximately 6μm long. The wire itself forms in the pre-formed slot-aperture which may be accurately aligned to the contacts (in the present example the contacts are substantially wider than the slot, but the contacts could be much smaller in a commercial device. Ultimately, the size of the wire is limited by the resolution of the electron- beam/resist used (which may be smaller than IOnm), by the combination of substrate and electron-beam resist materials, and by the cluster size.

C.3.2. Annealing of cluster wires using the electrical contacts After deposition the cluster wire can be annealed to reduce the resistance of the wire. This has been done by joule heating i.e. a voltage was applied to the contacts and the resultant current flow anneals cluster-cluster junctions and cluster-contact junctions. However, in this case once the wire anneals the resistance of it drops and the current flowing increases further, meaning further heating/annealing of the wire. If nothing is done to prevent it, this process continues and eventually we reach the point where the current is sufficiently high to melt the wire completely, resulting in a 'blob' of bismuth, as can be seen in Figure 30. In Figure 31, a controlled anneal was performed by putting an external resistor (with similar or higher resistance to the wire) in series with the wire. Now, even when the wire anneals the current is limited by the external resistor. The voltage was only applied to the pair of contacts on the right^" in Figure 31, and it is clear that the wire is only annealed in the region of those contacts.

SEMULATIONAL RESULTS

In this section we present the results from a large number of molecular dynamics (MD) simulations using the methodology outlined in section 6 of the method of the invention section above. Collisions were simulated for a range of parameters including the incident cluster velocity v₀, the angle of incidence, the cluster-surface interaction C, and the cluster size. The following threshold values of V₀ are likely to be specific to the LJ potential used. The LJ potential is an approximation of interatomic potential and this may not be appropriate for each actual experimental scenario. Thus other threshold values for V₀ will exist for a particular system. This is within the scope of the invention.

For values of C < 0.5, we find a transition between adhesion and reflection that takes place at low velocities (in the region 0.2v_c < V₀ < 0.5v_C; where v_c=ε/m). For values of C between 0.3 and 0.4 we observe a reentrant transition from reflection to adhesion at intermediate velocities (the onset of adhesion occurs in the region 0.5v_c < V₀ < 1.5v_c) followed once more by a transition to reflection. This reentrant transition occurs at the onset of a large deformation regime which increases the cluster contact area with the surface and thereby increases the adhesion energy. We find that collisions at non-normal incidence follow a very similar behaviour if one analyzes the results in terms of the normal velocity component. We begin by looking at the effect of C on the wetting of the surface by the cluster. We then discuss several collisions in detail, followed by the results for C=0.35 where we focus on the origin of the reentrant adhesion transition. Next we examine the effect of varying C between 0.2 and 0.7. Finally, we look at the effect of surface defects, collisions of a liquid droplet and collisions with non-normal incidence. A. Relationship between C and cluster contact angle

Figure 36 shows a selection of snapshots of the solid and liquid 147-atom cluster after equilibration on the (111) surface for 5xlO⁵ time steps. The solid clusters (top row) were equilibrated at T=0.27 ε/kβ and the liquid clusters (bottom row) were equilibrated at T=0.4 ε/kβ. To estimate each contact angle we fitted a spherical cap to the positions of the cluster atoms. The contact angles θ_w found are given in as shown in Table 3 for a variety of cluster sizes and C-values. Note that the solid clusters also show wetting behavior. In Ref. [9] the contact angle for a liquid drop as a function of C was approximated as cos θ_w = -1 + 2C. This approximation is also shown in the table; note that the contact angles for the liquid 309-atom droplet agree better with this approximation than the values for the 147-atom droplet. Indeed the contact angle for the 147-atom liquid droplet shows a much stronger dependence on C than for the larger droplets (or for the solid cluster) which is presumably reflects the curvature dependence of surface energies at this scale.

Table 3

We note that for C < 0.5, the solid clusters effectively do not wet the surface at all over the relaxation times examined here. Interestingly, although they remain bound, we observe significant diffusion of the cluster on the surface for C < 0.5 for both the liquid and solid clusters. In their experiments Partridge et al [12] estimated contact angles of θ~120° for Sb and θ~30° for Bi on SiO_x using AFM imaging. Using the approximation

C-0.5 (1+cos θ) gives C-0.25 and C~0.9. These estimates must be treated with some caution however. Firstly, as can be seen in Table 1, the behaviour of the solid clusters is poorly described by this approximation. Secondly, it is possible that some of the clusters were molten prior to deposition, or even melted during the collision, but later solidified as they cooled on the substrate. Also it is likely that the impact of the clusters lead to spreading of the cluster on the surface. These factors make it difficult to estimate appropriate values of C that resemble those for Sb and Bi on SiO_x. We will consider the relationship between the simulated and experimental collisions in more detail below.

B. A sample of individual collisions

We now examine three collisions in detail for a solid 147-atom icosahedral cluster oriented as shown in Figure 37 (the lighter surface atoms follow Newtonian dynamics and the darker surface atoms follow Langevin dynamics), before summarizing results over all trials over a range of velocities, orientations and C-values in the next section.

Figure 38 shows plot of center of mass position Zc_m (where z is the coordinate component in the direction normal to the surface) versus time for clusters with initial velocities V₀ = 0.4v_c, 1.6v_c and 2.6v_c. At the beginning of the simulation, Z_0n, decreases linearly with time during the free flight period before beginning to interact with the surface. The initial distance of the cluster from the surface was chosen so that impact occurred at approximately t = 8τ as is evident in Fig. 38. Note that for t > 8τ, Zc_m increases linearly with time for vo=O.4v_c and v_o=2.6v_c which corresponds to the free flight after the collision. However for V₀=I.6v_c, we see that Zc_m peaks and then declines indicating that the cluster has adhered to the surface. We will see in subsequent sections that this propensity for clusters to stick at intermediate velocities is typical for C=O.35.

Figure 39 shows the center of mass velocities corresponding to the data in Fig. 38. Note the slight acceleration and deceleration of the cluster in each case just before and after the collision are due to the attraction between the cluster and the surface. For this reason we define the coefficient of restitution, e, for the collision as the ratio of the peak velocity after collision to that before the collision as shown in Figure 39 i.e. e = -v/Vi.

The velocity of the bound cluster, which had initial velocity V₀ =1.6v_c, oscillates about zero whereas the other two clusters that escape attain a constant velocity directed away from the surface. Figure 40 shows the evolution of the z-component, R_z, of the radius of gyration which is a measure of the distribution of mass within the cluster about the z-axis. This is a useful quantity for tracking the deformation of the cluster during the impact. In all three cases R_z increases sharply at the collision. At v_o=O.4v_c the deformation is small and reversible suggesting that the deformation is largely elastic. At V₀=I.6v₀ some of the initial deformation relaxes but there is substantial permanent (or plastic) deformation. For vo=2.6v₀ the cluster bounces and the radius of gyration increases by about 30% but eventually settles down to a value below that of the cluster that adhered to the surface. Both of . the higher velocity collisions show evidence of irreversible (plastic) deformation. Fig. 41 shows snapshots of the collisions taken at t = 9τ, which is close to the moment of maximum deformation. This clearly illustrates the increase in deformation with impact velocity.

The total cluster potential energy per atom, E_pot, is the sum of cluster internal energy per atom, E_c and cluster-surface interaction energy per atom, E_cs. As seen in Fig. 42 (a) and (c), Eo_s at first decreases as the cluster approaches the surface due to the attraction between the cluster and surface. During the collision E₀ increases as the cluster is deformed by the impact. At V₀=O.4v_c, E_c is restored to its precollision value indicated that the collision is elastic (as was indicated by the deformation in Fig. 40). For the two faster collisions the change in E_c is permanent, indicating that the collision is largely plastic. In the case of the collision at v_o=1.6v_c, we see that there is a subsequent relaxation of E_cs as the cluster begins to equilibrate with the surface.

We note that the plastic deformation of the clusters during impact leads to an increase in cluster temperature as shown in Fig. 43. Further at both vo=1.6v_c and V(p2.6v_c the cluster appears to liquefy as it reaches a temperature above its melting point (T₀ = 0.33 ε/kβ). This is evident from the spike in thermal kinetic energy at impact; the drop in thermal kinetic energy after the rapid increase is due to the latent heat of melting of the cluster. We associate the three examples vo=O.4v_c, 1.6v_c, 2.6v_c with the elastic, elasto-plastic and plastic regimes.

C. Probability of adhesion averaged over cluster orientation for C=0.35 In this section the collision of the 147, 309 and 561 atom icosahedral clusters on the flat (11 l)-terminated surface was examined with a cluster-surface interaction parameter of C=0.35. For each cluster size 50-100 trials were performed at a range of impact velocities ranging from v_o=O.2 to 3.2v_c. Between each trial the cluster was randomly reorientated prior to the collision to average out the effect of cluster orientation on the collision probability. Beginning with solid clusters, Fig. 44 shows that the probability of sticking as a function of incident velocity is bimodal for each cluster size. Clusters stick to the surface at very low velocities (v_o<O.3v_c) but start bouncing at intermediate velocities 0.3v_c > V₀ > 0.5v_c. At higher velocities, v_o>O.5v_c, the sticking probability increases but once more starts to decrease for v_o>1.5v_c. As we will show in more detail below, this is because there are essentially two deformation regimes. For v_o<O.3-O.4v_c, little deformation occurs, so that the area of contact (and hence the adhesion energy) depends only weakly on the incident velocity. At higher velocities i.e. for vo > 0.5v_c, the deformation starts to grow substantially, leading to an increase in contact area (and adhesion energy) which depends strongly on velocity. In this strong deformation regime (vo > 0.5v_c), the adhesion energy initially increases faster than the reflected kinetic energy as the deformation produces a larger contact area. This is reflected in the increase in adhesion probability between 0.5v_c < V₀ < 1.5 v_c. Eventually, the reflected kinetic energy begins to dominate adhesion (v₀ > 1.5v_c) and the probability of adhesion decreases. All three cluster sizes display this bimodality, although the large clusters are less likely to stick in general.

Figure 45 shows the variation of coefficient of restitution, e, with the impact velocity. Each data point shown in the figure represents an average of 100 trials for each cluster size. The data shows a rough trend for e to decrease as the cluster size increases, e is approximately constant for low velocities but shows a strong dependence on velocity at Vo>O.5v_c. The dependence of e on velocity varies as e~v₀ ^"0593, e~vo^"°'⁵⁸⁸ and e~v₀ ^"0567, for 147, 309 and 561 icosahedra, respectively. This dependence on velocity is much stronger than that predicted by small deformation contact mechanics [13].

The dependence of the adhesion energy per atom of the cluster at the moment of peak reflected velocity, EY=-E^CS _f, is shown in Fig. 46 in the form E^a _f N⁰⁵ versus velocity. At low velocities (v₀ < 0.5v_c), in the elastic regime, E^af ~ N^'0'5 as is shown by the coincidence of the values of E^a _fN⁰⁵ for all cluster sizes. This is in fact consistent with

Hertz's contact law [13] for an elastic sphere undergoing weak deformation on a plane.

For V₀ » 0.5v_c, in the strong plastic deformation regime, the dependence on N is weaker and scales more like N^"033. This is consistent with a 'pancaking' of the cluster on the surface (see the snapshots in Figure 41).

In Figure 47 we have plotted the Weber number, We i.e. the ratio of kinetic energy, Eκ^f, to the adhesion energy, E^a _f, at the moment of peak reflection velocity to understand the transition from adhesion to reflection. We note that We correlates well with the probability of reflection. As the average value of We approaches and then exceeds 1, the number of cluster being reflected dramatically increases. From this plot, we can identify several collision regimes for the solid clusters. At low velocities (v₀ < 0.5v_c) the clusters undergo little deformation, and both the adhesion energy and coefficient of restitution are approximately constant. In this low deformation regime the reflected kinetic energy grows to dominate the adhesion, and consequently the probability of adhesion decreases with impact velocity. However for v₀ > 0.5v_c we begin to see substantial plastic deformation of the cluster. In this strong deformation regime both the coefficient of restitution and the adhesion energy depend on the velocity. Initially, the adhesion energy grows more rapidly, leading to an increase in adhesion probability. However, at high velocities the reflected kinetic energy begins to dominate again and the probability of adhesion decreases once more.

D. Collisions of a 147-atom liquid droplet We have also considered the collision of a liquid 147-atom droplet with the surface. The probability of sticking (from 50 trials) for the liquid droplet with C=0.35 is shown in Figure 48. The liquid droplets stick much more frequently than their solid counterparts at all velocities. The deformation of a liquid droplet at a given velocity is always more than the equivalent solid cluster. As the liquid droplet spreads more easily on the surface they are more likely to stick than the equivalent solid cluster. While both e (see Fig. 45) and the dependence of E^a _f on the deformation are quite similar for the liquid droplet and the corresponding solid cluster, the larger deformation of the liquid droplet at a given velocity produces a larger adhesion energy E^a _f during impact. This leads to a smaller Weber number for the liquid droplet which is then reflected in the much higher probability of adhesion for the droplet.

The state of the cluster (liquid / solid) can be controlled by the source conditions or by a thermalisation stage subsequent to the source. Thus the amount of bouncing or sticking to the surface can be controlled.

Also, in a further aspect of the invention, the plurality of particles deposited on the substrate have a size distribution but are all at substantially the same temperature (this is typical of inert gas aggregation sources such as the one we use [6]). In this case one can take advantage of the well known size dependence of the melting temperature of nanoparticles (rapid decrease with decreasing size) to achieve a situation where the small particles are above their melting temperature while the large particles are below their melting temperature. Since liquid particles are stickier than solid particles, the liquid particles may stick while the solid particles bounce. Hence one can effectively select small particles from a size distribution and assemble devices from them in preference to the larger particles (preferentially the molten particles will cool and solidify once in contact with the substrate).

E. Effect of surface defects

In this section, we briefly examine the influence of surface defects on the adhesion probability for the 147-atom icosahedron. In contrast to the collisions with perfect (111) surface, the adhesion behavior shown in Fig. 48 is markedly increased when the cluster lands at the edge of a stepped surface, i.e. a surface with a step of one atomic layer beginning at the point at which the cluster lands. This increase in adhesion seems to be due to the step-edge providing a large surface area and hence greater adhesion energy. For the collision of the cluster onto an adatom placed on the surface the probability of adhesion is increased only slightly which leads us to conclude that small amount of surface roughness will not strongly influence adhesion.

Therefore, in a further aspect of the invention, the substrate has on it a series of steps, grooves, or other structures which can be considered to be "defects" on a perfectly planar surface. These defects may be naturally occurring, such as the step edges on graphite [2], or engineered, such as V-grooves etched into the surface of a Si wafer with a standard KOH etch [17]. Clusters impacting on the defect will experience a "soft- landing site" and thereby stick to the substrate at the location of the defect, whereas clusters hitting a defect-free planar surface are substantially more likely to bounce away from the substrate. Typically the defects will be arrayed between a pair of contacts so that a conducting pathway, wire, or set of tunnelling junctions is achieved between the contacts and thereby comprising an electronic device.

F. Effect of varying C

Figure 49 illustrates the effects of varying the strength of cluster-surface attraction, C, showing the adhesion probability of 147-atom icosahedron as a function of the impact velocity. It is seen that the adhesion probability strongly depends on C and the transition from adhesion to reflection of the cluster is observed as the value of C is decreased from

C=0.7 to C-0.2. The bimodal behavior of adhesion probability is evident at C=0.3-0.4 but disappears outside this range as either the reflected kinetic energy dominates at small C or the adhesion energy dominates at large C.

G. The effect of angle of incidence

Finally we have considered the adhesion of the 147-atom cluster with off-normal incident velocities. In Figure 50 we have plotted the probability of adhesion versus the normal velocity component Vj₂ at angles from 30-90 degrees (again the cluster was randomly re-orientated before incidence and 50 trials were performed for C=0.35 - the lines are to guide the eye). Note that the probability of adhesion as a function of the normal velocity component for the non-normal collisions is very similar to that of the normal collisions. Figure 52 shows the velocity component parallel to the surface at the end of the same simulations, averaged over the clusters that adhere to the surface. It can be seen that this velocity component is approximately conserved during the collision. Thus clusters landing and adhering with velocity components parallel to the surface may be characterized as sliding rather than sticking (these clusters are still counted as adhering in Fig. 50).

For the oblique collisions, the normal coefficient of restitution is defined as the ratio of the maximum normal velocity components after and before impact (see Figure 51). In the small deformation regime v_Oz < 0.5v_c, a constant restitution coefficient close to 0.8 is observed. For V₀₂ > 0.5v_C5 e varies as Vo_z ^"°^'68. This is a somewhat stronger dependence on velocity than in the normal case.

H. Comparison with experimental data

It is of interest to compare our results with the collisions of Sb and Bi clusters with SiO_x surfaces in Ref [12]. We have investigated a collision regime with typical velocities Vo~v_c=ε/m. For Ar, ε = 1.65xlO^'21 J/atom, this characteristic velocity is v_c~150m/s. Similarly for Sb and Bi, we find characteristic velocities of 520m/s and 350m/s respectively (estimating the bond energy as ε~ 5.5xlO^"20 J/atom for Sb and 4.4xlO^"20 J/atom for Bi). In [12] it was estimated that their clusters had impact velocities of 100- 200 m/s.

In our simulations, we saw the onset of strong plastic deformation at v^t:=0.5v_c. Indeed, we observe a quadratic dependence of deformation on velocity (Fig. 53) which is consistent with plastic deformation, where the kinetic energy is dissipated largely at the cluster yield stress, Y i.e. the plastic work YΔ(R ) ~ Y R ΔR is proportional to the translational kinetic energy pv²R³ so that ΔR/R~ (p/Y)v². For Ar, this corresponds to a velocity of 75m/s although we note that we have only considered pairwise interactions here which will tend to delay the onset of plastic deformation in our simulations [14].

However, we might expect Sb and Bi to be considerably more ductile relative to their binding energies. Dimensional analysis suggests the onset velocity for plastic deformation should satisfy v^Y/p)⁰'⁵. Finite element simulations [15,16] found that this onset velocity was approximately v^=0.1(Y/p)^0'5 for an ideal substrate. For Sb and

Bi, by assuming that the yield stress is roughly 10^"2-10^'3 of the bulk shear modulus, we estimate that v^~5-20m/s. Thus it seems likely that the collisions in Ref. [12] occurred in a plastic regime.

Clearly an important dimensionless number to be considered here is the Weber number We = E^k _f/E^a _f. However, we have shown that the dependence of We on velocity is different in the small deformation and strongly plastic collision regimes. In the small deformation regime We~Vj² whereas in the plastic regime the velocity dependence is weaker. For instance, for the 147-atom cluster we found that We-V;⁰⁵ in the plastic collision regime. However the Sb and Bi clusters studied in Ref [12] were 15-40 nm in diameter, so to compare our results with experiment we need to consider how We scales with size.

Hertz's contact law [13] suggests that the contact area should scale as R^3/2 in the small deformation regime so that E^a ~ R^"3/2 (since E^a is the adhesion energy per cluster atom). Good agreement with this scaling was found for velocities V₀ < 0.5v_c (see Fig. 44 in the small deformation regime. Thus, if we take the coefficient of restitution e to be independent of cluster size, We ~ v₀ ²R^3/2 in this regime. However, at impact velocities above 0.5 in the strongly plastic regime we find that E^a scales as R^"1 so We~v₀ ^α5R. Thus for a 30 nm Sb cluster, which is 10 times the radius of the 561 -atom cluster, and for a given impact velocity, we would expect We to be 30 times larger in these clusters in the small deformation regime, and 10 times larger in the strongly plastic regime. As noted above, the Sb and Bi collisions are probably in the strongly plastic regime. The reflection-adhesion transition in our simulations takes place over velocities between 2- 3v₀ at C=0.3-0.4. The scaling argument above suggests that a 30 nm Sb cluster should achieve similar Weber numbers to those that occur at this transition at velocities of 10- 15 m/s. As the V-grooves were at an angle of 35° to the plane, clusters with velocities of ~100 m/s, would have effective incident velocities of v_Oz~6Om/s. Based on these estimates the experimental velocities seem to be too high to exploit the reflection- adhesion transition. However as E^a~C, we expect our estimate of the transition velocity to depend quadratically on the value of C that best describes the experimental system. If the substrates were more adhesive than suggested by the estimates of contact angle from the FE-SEM images (possibly because the cluster were far from their equilibrium geometries), our estimated transition velocity would likely be higher. It is also possible that multiple collisions play an important role. In the V-groove clusters are incident at 35° to the substrate plane, and if reflected, will almost certainly impact on the opposite side of the V-groove. This secondary impact will occur at substantially reduced impact velocity almost certainly leading to adhesion.

It is also of interest to compare our results with larger scale simulations of elastic-plastic impacts. We note that in the elastic regime the coefficient of restitution was constant whereas in the plastic regime the coefficient exhibits a strong dependence on velocity: e ~ Vo^"0'⁵⁸. This is a much stronger dependence on velocity than that given by Hertzian contact mechanics [13] but is close to the V₀ ^"0'⁵ dependence found by finite-element simulations of strongly plastic collisions [15]. Indeed, the quadratic dependence of deformation on velocity (Fig. 53) is consistent with strong plastic deformation, where the kinetic energy is dissipated largely at the cluster yield stress, Y i.e. the plastic work ~ YΔ(R³) ~ Y R² ΔR is proportional to the translational kinetic energy Vj²R³ so that ΔR/R~Vj². We have found that this relationship is relatively insensitive to both the values of C and the cluster sizes examined here.

I. Simulational Summary We have observed two collision regimes on weakly attractive substrates in which cluster reflection can occur. At low velocities we find an elastic collision regime, where the cluster progresses from adhesion to reflection as the reflected kinetic energy of the cluster overcomes the adhesion energy. This low deformation process seems to be reasonably well described by Hertzian contact mechanics. At higher velocities the cluster begins to deform plastically. Initially in this plastic regime the adhesion energy grows faster than the reflected kinetic energy leading to an increase in adhesion probability. However, eventually the reflected kinetic energy grows to dominate the adhesion energy and the adhesion probability decreases once more. This strong deformation regime is well described by strongly plastic contact mechanics.

RESULTANT TECHNOLOGIES - INDUSTRIAL APPLICABILITY

In one preferred embodiment, the invention involves deposition of nanoscale clusters onto patterned regions of a substrate. The preferred patterning takes the form of micro- and/or nanoscale apertures formed in non-conducting layer on a substrate. The substrate may include electrical contacts which are monitored throughout the cluster deposition process thereby indicating the exact time at which the cluster-assembled wire is completed. In-situ monitoring of the conduction between the contacts also provides precise control over the duration of the deposition process (and therefore the thickness of cluster-assembled wire). The apertures in the non-conducting polymer are formed using standard lithographic and/or etching techniques.

The invention is applicable to the fabrication of self-contacting cluster-assembled wires and films on planar and non-planar substrates.

The invention is applicable to a variety of cluster/substrate systems and the size of the incident clusters is unimportant, although preferably the average cluster momentum is sufficient to prevent adhesion on the surface of the non-conducting polymer. The source inlet gas flow can be adjusted so that the momentum of the incident clusters is sufficient for the clusters to reflect from the surface of the non-conducting polymer. The bouncing of clusters from surfaces was studied extensively in [17]. The apparatus and the method according to the invention make it possible to fabricate self-contacting single or multiple, parallel or non-parallel cluster-assembled wires with widths from ~20nm to >100μm. The technique is not limited to wire-like patterns; also possible are arbitrarily shaped 2D cluster-assembled films (and arrays of arbitrarily shaped 2D cluster-assembled films). Provided the aforementioned structures are deposited between suitably arranged planar electrical contacts, monitoring of the conduction of the cluster-assembled structures is possible throughout the deposition process. The onset of conduction indicates the production of a conducting cluster- assembled pathway.

Creation of metallised regions on insulating or semiconducting substrates using standard optical or electron beam lithography and atomic deposition methods is only possible if the deposition process is followed by a 'lift-off or 'etch-back' process. (This is because atoms deposited during a standard deposition process adhere where they land and therefore uniformly coat target substrates). In a 'lift-off process, the resist layer (normally sensitive to UV-light or electron-beam) used to define the desired pattern on the substrate is dissolved to remove both the resist and the unwanted areas of the deposited layer, but 'lift-off processes have attributes which are undesirable for some applications. The lift-off process requires the substrate to be immersed in a resist stripping wet chemical which may attack the substrate material(s). Additionally, the resist layer thickness must be significantly greater than the deposited layer thickness in order to produce a well defined break in the film around the perimeter of the desired feature and hence produce a clean lift-off. Furthermore, it is often of advantage to form a undercut in the resist layer, assisting a clean lift-off. The latter requirements significantly limits the ability to produce high-aspect ratio structures with nanoscale dimensions, and the method of the invention may be used to avoid these limitations.

By contrast, the apparatus and the method according to the invention make it possible to selectively form metallised, insulating or semiconducting regions (with lithographically defined dimensions and location) on an insulating, semiconducting or conducting substrate with no requirement to dissolve or otherwise remove the surface template layer which causes the clusters to assemble. In many cases the deposited material and / or the substrate may be susceptible to damage from resist stripping chemicals or wet/dry etchants and so the method and invention can be applied in order to eliminate any possibility of damage during the lift-off process.

An example of this is in the production of Al side-gates for a cluster-assembled wire. The Al side-gate layer is covered (or encapsulated) with a patternable polymer layer (eg. SU8) in order to prevent complete oxidation of the Al and the polymer layer is then patterned to leave a selected area of the Al open through an aperture. The Al oxidizes in this region and forms an AlO layer on which the clusters are deposited. The non- exposed and non-oxidised Al layer then lies in close proximity to the cluster wire/film and can serve as a side-gate electrode

The apparatus and the method according to the present invention allow the fabrication of cluster-assembled structures with feature sizes of less than 20 ran. This may include cluster-assembled wires with uniform widths below 20nm or cluster-assembled wires which feature sections with minimum dimensions of less than 20nm. Quantum effects have been observed in wires and films with similar dimensions, and the present invention enables efficient electrical characterisation of such effects.

An important application of the technique is in the provision of a device where the electrical contacts are formed by deposition of cluster material through apertures within the non-conducting polymer i.e. the step of formation of electrical contacts is omitted, and a large area of deposited clusters provides the contact to the wire or other structure that is formed.

An important characteristic of the wires formed by the method of the invention is that in general they will be sensitive to many different external factors (such as light, temperature, chemicals, magnetic fields or electric fields) which in turn give rise to a number of applications. Devices of the invention may be employed in any one of a number of applications. Applications of the devices include, but are not limited to:

- Transistors or other switching devices,

- Magnetic field sensors, - Chemical sensors,

- Light emitting or detecting devices,

- Temperature sensors.

Such devices are described in more detail in [18], and this description is herein incorporated by reference.

A particular application of interest is the formation of a hydrogen sensor using the methods described herein. Pd nanoparticles are known to expand on absorption of hydrogen such that a Pd nanoparticle film with coverage initially slightly below the percolation threshold will become conducting on absorption of hydrogen. By depositing Pd particles through apertures in a non-conducting polymer it is straightforward to define patterns of any shape of Pd nanoparticles located between 2 or more electrical contacts. The expansion of the particles on absorption of hydrogen then provides a mechanism by which the conductivity of the device changes, providing a sensor. It is important to emphasize here that a pathway of clusters (which is not yet conducting but will conduct upon the absorption of hydrogen) is required. This is within the scope of the invention, as described and claimed.

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15 C. Y. Wu, L. Y. Li and C. Thornton, Int. J. Impact Eng. 28, 929-946 (2003).

16 C Y. Wu, L. Y. Li and C. Thornton, Int. J. Impact Eng. 32, 593-604 (2005).

17 S. A. Brown and J. G. Partridge, Templated cluster assembled wires'. New Zealand Patent Application No. 524059. International Patent Application number PCT/NZ2004/00012.

18 S. A. Brown and J. Schmelzer, jr, International Patent Application number PCT/NZ02/00160; NZ Patent Application number 513637, "Nanoscale Electronic Devices and Fabrication Methods".

Claims

WHAT WE CLAIM IS:-

1. A method of depositing particles on a patterned region of a substrate comprising the steps of providing a patterned substrate, the pattern having one or more first regions (the first region) and one or more second regions (the second region) and directing a plurality of particles with an average diameter less than 1 micron towards the pattern to form an arrangement of particles on the patterned region, with a greater percentage of the particles retained by one of the first or second regions than is retained by the other of the first or second regions .

2. A method as claimed in claim 1 wherein the particles are atomic clusters.

3. A method as claimed in claim 2 including controlling the behaviour of the clusters on impact with the first and second regions to be one or both of plastic and/or elastic thereby influencing the probability that the clusters adhere to one or both of the first and second regions.

4. A method as claimed in claim 3 including controlling the directing of clusters towards the pattern and/or the nature of the first and second regions such that upon impact of the clusters with the patterned substrate one or more of the following occurs:

- elastic deformation of the clusters resulting in sticking of one or more clusters to a region, and/or elastic deformation of the clusters resulting in reflecting or bouncing or sliding of one or more clusters from a region, and/or - plastic deformation of the clusters resulting in sticking of one or more clusters to a region, and/or

- plastic deformation of the clusters resulting in reflecting or bouncing of one or more clusters from a region.

5. A method as claimed in any one of the preceding claims wherein one or both of the regions comprises a plurality of substantially independent sections.

6. A method as claimed in any one of the preceding claims wherein the region which retains the greater percentage of clusters is continuous.

7. A method as claimed in any one of the preceding claims including depositing the clusters to form a pathway (as defined herein).

8. A method as claimed in claim 7 including depositing the clusters to form a pathway capable of electrical conduction.

9. A method as claimed in either one of claims 7 or 8 including a further step of forming at least two contacts on the substrate with the pathway existing generally between the two contacts.

10. A method as claimed in claim 9 including forming the contacts to provide contacts separated by a distance smaller than 10 microns.

11. A method as claimed in claim 10 including forming the contacts to provide contacts separated by a distance smaller than 1 micron.

12. A method as claimed in claim 11 including forming the contacts to provide contacts separated by a distance smaller than lOOnm.

13. A method as claimed in any one of claims 9 to 12 including first forming the contacts and then depositing the clusters on the substrate between the contacts.

^■ 14. A method as claimed in claim 13 including monitoring the steps of depositing and forming the arrangement of clusters by monitoring conduction between the two contacts where deposition is ceased at or near the onset of conduction.

15. A method as claimed in any one of claims 9 to 12 including forming the contacts after forming the arrangement of clusters.

16. A method as claimed in any one of the preceding claims including providing a patterned substrate with least one dimension of one of the regions of the pattern less than 1 micron.

17. A method as claimed in claim 16 including providing a patterned substrate with at least one dimension of the of the regions of the pattern less than lOOnm

18. A method as claimed in any one of the preceding claims including directing a plurality of clusters with an average diameter between 0.3nm and l,000nm towards the pattern.

19. A method as claimed in claim 18 including directing a plurality of clusters with an average diameter between 0.5nm and lOOnm towards the pattern.

20. A method as claimed in claim 19 including directing a plurality of clusters with an average diameter between 0.5nm and 40nm towards the pattern.

21. A method as claimed in any one of the preceding claims wherein the first or second regions of the substrate comprise different materials.

22. A method as claimed in claim any one of claims 1 to 20 wherein one of the first and/or second regions comprise the same material as the substrate but modified.

23. A method as claimed in claim 21 or 22 wherein the first and second regions have different surface hardness or softness characteristics.

24. A method as claimed in claim 21 or 22 wherein the first and second regions have different surface roughness.

25. A method as claimed in claim 21 or 22 wherein the first and second regions have different surface wettability.

26. A method as claimed in claim 21 or 22 wherein the first and second regions have different reflectivity to the clusters.

27. A method as claimed in claim 21 or 22 wherein the first and second regions have different surface elasticity characteristics.

28. A method as claimed in claim 21 or 22 wherein the first and second regions are at different temperatures.

29. A method as claimed in any one of the preceding claims including patterning the insulating or semiconductor substrate by one or more of lithography, etching or metalisation.

30. A method as claimed in any one of the preceding claims including patterning the insulating or semiconductor substrate with a second material.

31. A method as claimed in claim 30 including patterning an insulating or semiconductor substrate with a non-conducting second material.

32. A method as claimed in claim 31 including patterning an insulating or semiconductor substrate with a developed or undeveloped polymeric material or a self-assembled monolayer (SAM).

33. A method as claimed in claim 32 including providing an insulating or semiconductor substrate, coating it with a polymeric material or having a SAM form thereon, and patterning the polymeric material or SAM to result in one or more first and second regions.

34. A method as claimed in claim 33 including patterning the polymeric material or SAM by forming one or more apertures through the polymeric material or the SAM so that the insulating or semiconductor substrate is at least partially, if not completely accessible to the clusters through the one or more apertures.

35. A method as claimed in claim 34 including patterning the polymeric material or SAM by forming at least one slot in the polymeric material or SAM running between and/or partially overlapping with the two contacts (when present).

36. A method as claimed in claim 34 or 35 wherein the pattern is formed in a polymeric material selected from the group consisting of PMMA, photoresist, electron-beam resist and SU8.

37. A method as claimed in claim 36 wherein the pattern is formed in a polymeric material comprising a bi-layer of high molecular weight (HMW) and low molecular weight (LMW) PMMA.

38. A method as claimed in any one of claims 32 to 35 wherein the pattern is formed in a SAM selected from the group consisting of C 12-SiCl₃, C 12-Si(OEt)₃, and

CF-Si(OEt)₃.^"

39. A claim as claimed in any one of claims 34 to 38 including forming the pattern in the polymeric material or SAM by lithography and/or by etching.

40. A method as claimed in any one of the preceding claims including controlling one or more of:

- the incident momentum of the clusters during deposition of the clusters; and/or - the kinetic energy of the incident clusters during deposition of the clusters; and/or the velocity of the incident clusters during deposition of the clusters; and/or the identity of the clusters during deposition of the clusters; and/or

- the size of the clusters during deposition of the clusters; and/or - the temperature of the clusters during deposition of the clusters; and/or

- the angle of incidence of the clusters during deposition of the clusters; and/or other factors affecting the degree of chemical bonding and/or strength of interaction between the clusters and a surface during deposition of the clusters; and/or

- the thermodynamic phase of the clusters; and/or

- the crystallinity of the clusters; and/or

- the shape of the clusters.

41. A method as claimed in claim 40 including directing the clusters towards the pattern with a selected or controlled velocity.

42. A method as claimed in claim 41 including directing the clusters towards the pattern with kinetic energy of the clusters selected so as to be sufficient to cause at least part or the majority or substantially all of the clusters incident upon the surface of one of the first or second regions to bounce from that region whilst at the same time low enough to cause at least part or substantially all of the clusters incident upon the surface of the other of the first or second regions to remain on the surface (whether substantially immediately upon contacting the surface or some time after first contacting the surface).

43. A method as claimed in claim 42 including calculating the velocity thresholds between the regimes of plastic and elastic behaviour of the clusters and then controlling the velocity of the clusters to be within a selected regime upon impact with one or both or the first and second regions.

44. A method as claimed in claim 43 including calculating the velocity thresholds between the regimes of elastic deformation with sticking behaviour, elastic deformation with bouncing behaviour, plastic deformation with sticking behaviour, and plastic deformation with bouncing behaviour for the given cluster and/or substrate and/or environment, and then controlling the velocity of the clusters to result in the behaviour of the atomic cluster upon impact with the first and/or second regions falling within a particular regime.

45. A method as claimed in claim 44 wherein the step of calculating the thresholds between the regimes includes calculation of the required velocity for the given cluster and/or substrate and/or environment in accordance with measurements of the proportion of clusters that bounce from (or stick to) the first and the second regions.

46. A method as claimed any one of claims 1 to 44 including calculating the velocity for the given cluster and/or substrate and/or environment in accordance with molecular dynamics simulations of the proportion of clusters that bounce from (or stick to) each of first and second regions.

47. A method as claimed in any one of the preceding claims wherein the clusters directed towards the pattern are selected from one or more of the group consisting of platinum, palladium, bismuth, antimony, aluminium, silicon, germanium, silver, gold, copper, iron, nickel, and cobalt.

48. A method as claimed in any one of the preceding claims wherein the substrate is selected from the group consisting of silicon, silicon nitride, silicon oxide, aluminium oxide, indium tin oxide, germanium, gallium arsenide, quartz, and glass.

49. A method as claimed in any one of the preceding claims including preparing the clusters by a method which involves gas aggregation.

50. A method as claimed in claim 49 including preparing the clusters by evaporating a cluster source material from a crucible or by sputtering a cluster source material from a target to produce a vapour and condensing the vapour by cooling through an inert gas to form clusters.

51. A method as claimed in claim 50 including controlling the velocity and/or kinetic energy of the clusters produced at least partially by controlling the flow rate of an inert gas flow into a chamber of the cluster source material in which the clusters are prepared.

52. A method as claimed in claim 51 including imparting a kinetic energy to the clusters corresponding to a velocity in the range lm/s to 2000 m/s.

53. A method as claimed in claim 52 including imparting a kinetic energy to the clusters corresponding to a velocity in the range 10m/s to 300 m/s.

54. A method as claimed in claim 45 including imparting a kinetic energy to the clusters corresponding to a kinetic energy per cluster atom in the range 5x10^"26 J to 2x10^'19 J.

55. A method as claimed in claim 54 including imparting a kinetic energy to the clusters corresponding to a kinetic energy per cluster atom in the range 5xlO^"24 J to 5x10^"21 J.

56. A method as claimed in any one of the preceding claims including directing copper or palladium clusters towards the substrate with diameters in the range 5- 20nm and with velocities is in the range 100-400m/s.

57. A method as claimed in any one of claims 1 to 55 including directing bismuth or antimony clusters towards the substrate with diameters in the range 10-lOOnm and with velocities in the range 10-lOOm/s.

58. A method as claimed in any one of the preceding claims including depositing the clusters to form one pathway or wire.

59. A method as claimed in any one of claims 1 to 57 including depositing the clusters to form a plurality of wires.

60. A method as claimed in any one of claims 1 to 57 including depositing the clusters to form a percolating film.

61. A method as claimed in any one of claims 7 to 60 including a pre-step of forming (by any means whatsoever) a wire or configuration structure on the substrate followed by forming the pathway of clusters over or in addition to the pre-existing wire or configuration.

62. A method a claimed in claim 61 including forming the pathway of clusters at a pre-selected angle to the pre-existing wire or configuration.

63. A method as claimed in claim 62 including forming the pathway of clusters at right angles to the pre-existing wire or configuration.

64. A method as claimed in any one of the preceding claims wherein one of the first or second regions is comprised of one material which is conducting and a second material which is insulating and encapsulates the first

65. A method as claimed in claim 64 including forming the conducting material so as to be useful as a gate.

66. A method as claimed in any one of the preceding claims including encapsulating at least a portion of the deposited clusters in an insulating or dielectric material.

67. A method as claimed in claim 66 including forming a further contact or other structure on the surface of the insulating or dielectric material which is isolated from the pattern of clusters and can act as a gate.

68. A method as claimed in any one of claims 7 to 65 including forming the pathway of clusters on a multi-layer substrate, one layer of which is electrically conducting and can act as a gate.

69. A method as claimed in any one of the preceding claims wherein one of the first or second regions is angled with respect to the other of the first or second regions and the method includes directing the clusters substantially orthogonally to one of the first or second regions.

70. A method as claimed in claim 69 wherein the first and second regions of the pattern define a V-groove or inverted pyramid and the method includes directing the clusters so that they eventually accumulate or aggregate at the apex of the V- groove or inverted pyramid

71. A method as claimed in claim 70 including imparting a cluster with a velocity component perpendicular to the angled surface at such a level that the cluster deformation on impact with the angled surface is weak, leading to sticking or sliding, while elasto-plastic or plastic deformation takes place on impact on the surfaces orthogonal to the cluster beam, resulting in that clusters are at least partially reflected from those surfaces.

72. A method as claimed in claim 71 including imparting a cluster with a velocity component perpendicular to the angled surface at such a level that elasto-plastic bouncing takes place, leading to accumulation of clusters at the apex of the V- groove or inverted pyramid while the clusters impacting on the orthogonal planar surfaces are folly plastically deformed and at least partially reflected from those surfaces.

73. A method as claimed in any one of the preceding claims including directing clusters with a range of particle sizes and with a temperature such that at least some of the smaller clusters of the range are liquid while at least some of the larger clusters are solid and the smaller, liquid clusters preferentially accumulate in one region of the first or second regions while the larger solid, clusters bounce away from that region.

74. A method as claimed in claim 73 including patterning the substrate so that the smaller clusters of the range are retained by one of the first or second regions whilst bouncing from the other of the first and second regions and larger clusters of the range are not retained in either region.

75. An arrangement of particles on a patterned region of a substrate prepared substantially according to the method claimed in any one of claims 1 to 74.

76. An arrangement as claimed in claim 75 wherein the clusters form a conducting pathway between two contacts on the substrate surface.

77. An arrangement as claimed in claim 76 wherein the average diameter of the clusters is between 0.3nm and l,000nm.

78. An arrangement as claimed in claim 77 wherein the contacts are separated by a distance smaller than 10 microns.

79. A method of preparing a pathway of atomic clusters between two contacts on a substrate comprising the steps of providing a substrate with two contacts on its surface, modifying a region on the substrate substantially between and/or overlapping the two contacts, directing a plurality of atomic clusters with average diameter less than 1 micron towards the substrate generally in the area between the two contacts so that the modified region retains some of the clusters on its surface to form a pathway of atomic clusters between the contacts and the non-modified region of the substrate resists at least a large part of the clusters incident upon it.

80. A method as claimed in claim 79 including monitoring the formation of a conducting pathway between the contacts by monitoring the conduction between the two contacts.

81. A method as claimed in claim 80 including providing contacts separated by a distance smaller than 10 microns.

82. A method as claimed in claim 81 including providing contacts separated by a distance smaller than lOOnm.

83. A method as claimed in any one of claims 79 to 82 including providing a substrate of an insulating or semiconductor material coated with a polymeric or self-assembled monolayer (SAM) layer, modifying the region in the area between the two contacts by forming one or more slots in the polymeric or SAM layer positioned substantially between the contacts, so that the insulating or semiconductor material is accessible through the slot.

84. A method as claimed in any one or claims 79 to 83 including modifying a region between the two contacts by providing a (or taking advantage of a pre-existing) ridge, depression, step-edge or defect, or array or pattern of ridges, depressions, step-edges or defects, and forming a pathway between the two contacts, the clusters impacting on the modification experiencing a "soft-landing" site so that the clusters stick while bouncing away from the non-modified regions.

85. A method as claimed in claim 84 wherein the modification comprises naturally occurring step edges.

86. A method as claimed in claim 85 wherein the substrate is silicon and the modification occurs on an exposed Si(5 5 12) or Si(I 1 3) facet.

87. A method as claimed in claim 84 including engineering the ridges, depressions, step-edges or defects.

88. A method as claimed in any one of claims 79 to 87 including directing the clusters towards the substrate with a velocity high enough so at least part of, if not the majority of, the clusters bounce away from the unmodified region and low enough so that at least part of, if not the majority of the clusters incident upon the surface of the modification remain on the surface of the modification (whether substantially immediately upon contacting the surface or some time after first contacting the surface).

89. A method as claimed in claim 88 including calculating the velocity thresholds between the regimes of plastic and elastic behaviour of the clusters upon impact with the first and second regions and then controlling the velocity of the clusters to be within a selected regime upon impact with one or both or the first and second regions.

90. A method as claimed in claim 88 or 89 wherein the substrate is selected from the group comprising silicon, silicon nitride, silicon oxide, aluminium oxide, indium tin oxide, germanium, gallium arsenide, quartz, or glass.

91. A pathway of atomic clusters between two contacts on a substrate prepared according to the method claimed in any one of claims 79 to 90.

92. A method for performing lithography including the steps of providing a substrate, coating the surface of the substrate with an electron- or photo-sensitive polymer layer, exposing some regions of the polymer layer to electron (for an electron sensitive polymer) or photons (for a photon-sensitive polymer), developing the polymer to remove one but not both of the exposed or unexposed regions, and depositing clusters on to the substrate to substantially coat one but not both of the exposed or unexposed regions and wherein the method does not include a lift-off step.

93. A method as claimed in claim 92 including depositing clusters onto the substrate according to one of claims 1 to 78 or 79 to 90.

94. A method of depositing particles on a patterned region of a substrate substantially as herein described with reference to one or more of the Figures and/or Examples.

95. An arrangement of particles on a patterned region of a substrate substantially as herein described with reference to one or more of the Figures and/or Examples.

96. A method of preparing a pathway of atomic clusters between two contacts on a substrate substantially as herein described with reference to one or more of the Figures and/or Examples.

97. A pathway of atomic clusters between two contacts on a substrate substantially as herein described with reference to one or more of the Figures and/or Examples.

98. A method for performing lithography substantially as herein described with reference to one or more of the Figures and/or Examples.