METHODS OF FORMING MICROWIRES OR NANOWIRES

Abstract

Methods of forming microwires or nanowires, microwires or nanowires formed using the method, and electronic devices and semiconductor components including the wires. A method of forming a microwire or nanowire includes disposing a plurality of metal particles in a portion of a channel that is a nanochannel or a microchannel. The method includes etching the metal particles with an activation agent to form a flux that penetrates an additional portion of the channel. The flux includes an etching product of the activation agent and the metal particles. The method includes allowing the activation agent to at least partially evaporate to form a wire that is a microwire or a nanowire.

Description

BACKGROUND

Moore's law has inspired disparate advances but facing a duo challenge of fabrication in <5 nm space and associated need for complex metrology of fabrication tools. Demand for multi-material, multi-dimensional, and multi-scale electronic components calls for new fabrication methods. Lithography, the most widely used fabrication platform in electronic manufacturing, relies on selective deposition or abstraction of materials to create organized structures for a myriad of applications. Lithographic methods fall into two main categories, viz; i) top-down, and ii) bottom-up methods. Top-down method deploy physical (e.g., e-beam lithography and photolithography) or chemical (wet or dry) abstraction to create patterns on generally hard materials (e.g., semiconductor, glass, metal). Top-down methods are widely used in fabrications of electronics, microfluidic chips, optical devices, among others. In contrast, the bottom-up approach is based on cross-linking (primary bonds) or organization/self-assembly (secondary bonds) of individual building blocks across nano- and meso-scales. Depending on size and property of the building block, bottom-up methods generally give higher resolution. Both top-down or bottom-up lithographic methods often require complex instrumentation, strict operating conditions, sophisticated design, are energy intensive, and often require skilled manpower limiting their widespread adoption. In the few autonomous lithographic processes, e.g., diffusion-limited precipitated reactions, dimensional control and post-assembly processing is challenging.

SUMMARY OF THE INVENTION

The present invention provides a method of forming a microwire or nanowire. The method includes disposing a plurality of metal particles in a portion of a channel that is a nanochannel or a microchannel. The method includes etching the metal particles with an activation agent to form a flux that penetrates an additional portion of the channel. The flux including an etching product of the activation agent and the metal particles. The method also includes allowing the activation agent to at least partially evaporate to form a wire that is a microwire or a nanowire.

The present invention provides a method of forming a microwire or nanowire including disposing a plurality of liquid metallic core-shell particles in a portion of a channel that is a nanochannel or a microchannel. Each liquid metallic core-shell particle includes a liquid metallic core including a metal or alloy, and a solid outer shell on the liquid metallic core. The method includes etching the liquid metallic core-shell particles with an activation agent to form a flux that penetrates an additional portion of the channel. The flux includes an etching product of the activation agent and the liquid metallic core-shell particles. The method also include allowing the activation agent to at least partially evaporate to form a wire that is a microwire or a nanowire.

The present invention provide a wire formed by the method of forming a microwire or nanowire of the present invention described herein.

The present invention provides an article or device that includes one or more wires formed by the method of forming a microwire or nanowire described herein.

The present invention provides a semiconductor device including one or more wires formed by the method of forming a microwire or nanowire described herein. For example, the semiconductor device can be a transistor, a diode, or a combination thereof.

The present invention provides an optical article including one or more wires formed by the method of forming a microwire or nanowire described herein.

The present invention provides a guided-mode resonance device (GMR) including one or more wires formed by the method of forming a microwire or nanowire described herein.

In various aspects, the metal particle organizes metal adducts on its surface, then with treatment by the activation agent causing either a) sequential etching or b) depletion of the top most layer (where the core is liquid), metal species and formed in solution. Fluid flow and/or capillary action directs the metal species to the growth zone of the channel, established from the initial etch and flow (Taylor dispersion) of the metal species. Sequential etching, such as with liquid metallic core-shell particles including a liquid metallic core and a metal oxide shell, can cause a compositional gradient along the longitudinal direction of the wire. In various aspects, pyrolysis of such wires can form graphene-, graphene oxide-, and/or graphitic carbon-coated wires. The coated wires can include a compositional gradient along the longitudinal direction of the wire which can cause a corresponding gradient in the bandgap along the longitudinal direction of the wire.

In various embodiments, the method of forming the microwire or nanowire can be used to fabricate patterned mixed metal or single metal electrical (diodes/rectifiers), optical (gratings), plasmonic, or opto-electronic (resonance sensors) components. The method of forming the microwire or nanowire can provide multi-component wire arrays. The microwires or nanowires formed by the method can possess ultrahigh aspect ratio even after calcination. Calcination of the wires can also achieve concomitant wire composition transformation from organometallic to mixed-oxide material.

BRIEF DESCRIPTION OF THE FIGURES

The drawings illustrate generally, by way of example, but not by way of limitation, various embodiments of the present invention.

FIG. 1a is a schematic illustration of performing metal-ligand reaction on mold leads to autonomous lithography of nanowires, in accordance with various embodiments.

FIG. 1b is a scanning electron microscope (SEM) image showing arbitrary beam formation from a metal-ligand reaction in a growth zone, in accordance with various embodiments.

FIG. 1c is a SEM image showing formation of discontinuous wires in a growth zone, in accordance with various embodiments.

FIG. 1d is an SEM image showing alignment of continuous wires in a collection zone, in accordance with various embodiments.

FIGS. 1e-g are SEM images showing wires of various widths formed via D-Met, in accordance with various embodiments.

FIG. 1h illustrates an Energy Dispersive X-ray Spectroscopy (EDS) line scan spectrum of pristine wires from D-Meting undercooled Field's metal particles (FM) or undercooled Indium Tin particles (InSn), in accordance with various embodiments.

FIGS. 1i-j illustrates EDS spectra of calcined wires from D-Meting undercooled Field's metal particles (FM) or undercooled Indium Tin particles (InSn), in accordance with various embodiments.

FIG. 2a illustrates a SEM image of a PDMS mold, in accordance with various embodiments.

FIG. 2b illustrates a SEM image of a PDMS mold, in accordance with various embodiments.

FIG. 2c illustrates a SEM image of a PDMS mold, in accordance with various embodiments.

FIG. 2d illustrates a width summary of the PDMS molds shown in FIGS. 2a-c and wires formed with the corresponding mold using D-Met, in accordance with various embodiments.

FIG. 2e illustrates a SEM image and EDS characterizations of FM particles, in accordance with various embodiments

FIG. 2f illustrates a SEM image and EDS characterizations of InSn particles, in accordance with various embodiments.

FIG. 2g illustrates a SEM image of 3-time activated D-Met wires, in accordance with various embodiments.

FIG. 2h illustrates a SEM image of 5-time activated D-Met wires, in accordance with various embodiments.

FIG. 2i illustrates a SEM image of 8-time activated D-Met wires, in accordance with various embodiments.

FIG. 3a is a diagram illustrating open channel growth showing perpendicular agent evaporating and monomer coordinating directions, in accordance with various embodiments.

FIG. 3b is a SEM image of wires formed by the open channel growth shown in FIG. 3a, in accordance with various embodiments.

FIG. 3c is a diagram illustrating closed channel growth with evaporating and coordinating directions were forced to be parallel, in accordance with various embodiments.

FIG. 3d is a SEM image of wires formed by the closed channel growth shown in FIG. 3c, in accordance with various embodiments.

FIG. 3e illustrates penetrativity and vapor pressure of AcOH with various solvents, in accordance with various embodiments.

FIGS. 3f-h illustrate SEM images of wires formed in the growth zone using the solvents shown in FIG. 3e, in accordance with various embodiments.

FIGS. 3i-k illustrate SEM images of wires generated in the collection zone using the solvents shown in FIG. 3e, in accordance with various embodiments.

FIG. 4a illustrates EDS maps illustrating a homogenous elemental distribution of FM wires calcined at 600° C. for one hour, in accordance with various embodiments.

FIG. 4b illustrates elemental content of FM particle, pristine FM wire, and calcined FM wires, in accordance with various embodiments.

FIG. 4c illustrates an X-ray powder diffraction (XRD) spectrum of calcined FM wires, in accordance with various embodiments.

FIG. 4d illustrates EDS maps of InSn wires calcined at 800° C. for one hour, in accordance with various embodiments.

FIG. 4e illustrates elemental content of InSn particle, pristine InSn wire, and calcined InSn wire, in accordance with various embodiments.

FIG. 4f illustrates an XRD spectrum of calcined InSn wires, in accordance with various embodiments.

FIG. 5a illustrates a EDS maps of FM pristine wire, in accordance with various embodiments.

FIG. 5b illustrates EDS maps of InSn pristine wire, in accordance with various embodiments.

FIG. 5c illustrates an X-ray spectrum of FM pristine wire, in accordance with various embodiments.

FIG. 6a illustrates a SEM image of high-aspect ratio pristine FM wires from mold-1, in accordance with various embodiments.

FIG. 6b illustrates a SEM image of calcined FM wires showing continuity preservation, in accordance with various embodiments.

FIG. 6c illustrates atomic force spectroscopy (AFM) line profiles of pristine and calcined FM wires from mold-1, in accordance with various embodiments.

FIG. 6d illustrates a width and height summary of parent mold-1, pristine FM wires from the mold, and the resulting calcined FM wires, in accordance with various embodiments.

FIG. 6e illustrates a SEM image of defect-free pristine FM wires from mold-2, in accordance with various embodiments.

FIG. 6f illustrates a SEM image of calcined FM wires from mold-2, in accordance with various embodiments.

FIG. 6g illustrates AFM line profiles of pristine and calcined FM wires from mold-2, in accordance with various embodiments.

FIG. 6h illustrates a width and height summary of parent mold-2, pristine FM wires from the mold, and the resulting calcined FM wires, in accordance with various embodiments.

FIG. 6i illustrates a SEM image of defect-free pristine InSn wires from mold-2, in accordance with various embodiments.

FIG. 6j illustrates a SEM image of calcined InSn wires from mold-2, in accordance with various embodiments.

FIG. 6k illustrates AFM line profiles of pristine and calcined InSn wires from mold-2, in accordance with various embodiments.

FIG. 61 illustrates a width and height summary of parent mold-2, pristine InSn wires from the mold, and the resulting calcined InSn wires, in accordance with various embodiments.

FIG. 7a illustrates a AFM image of, and a plot illustrating the line profile of, pristine FM wires, in accordance with various embodiments.

FIG. 7b illustrates SEM images of pristine and calcined FM wires formed using mold-2, in accordance with various embodiments.

FIG. 7c illustrates SEM images of pristine and calcined InSn wires formed using mold-2, in accordance with various embodiments.

FIG. 8a illustrates current density curves of pristine and calcined FM wires, in accordance with various embodiments.

FIG. 8b illustrates current density curves for pristine and calcined InSn wires, in accordance with various embodiments.

FIG. 8c illustrates gating behavior of three-terminal devices based on FM wires, in accordance with various embodiments.

FIG. 8d illustrates gating behavior of three-terminal devices based on InSn wires, in accordance with various embodiments.

FIG. 8e is a scheme illustrating application of pristine InSn nanowires as guided mode resonance (In GMR) device, in accordance with various embodiments.

FIG. 8f illustrates transverse electric (TE) transmission measurement and simulation of InSn GMR, with near-field distributions inserted, in accordance with various embodiments.

FIG. 8g illustrates transverse magnetic (TM) transmission measurement and simulation of InSn GMR, with near-field distributions inserted, in accordance with various embodiments.

FIG. 8h is a scheme illustrating fabrication of chessboard patterns with 2-time D-Met, in accordance with various embodiments.

FIG. 8i is a SEM image of a product from the fabrication method shown in FIG. 8h, in accordance with various embodiments.

FIG. 8j is a SEM image illustrating a varying-period pattern obtained by D-Met when the mold is truncated to create mixed spacing, in accordance with various embodiments.

FIG. 9a is a photograph of a parent mold under sunlight, in accordance with various embodiments.

FIG. 9b is a photograph of D-Meted wires under sunlight, in accordance with various embodiments.

FIG. 9c is a green laser diffraction pattern of the parent mold shown in FIG. 9a, in accordance with various embodiments.

FIG. 9d is a green laser diffraction pattern of the D-Meted wires shown in FIG. 9b, in accordance with various embodiments.

FIG. 9e illustrates refractive index n and extinction coefficient k of InSn pristine nanowires, in accordance with various embodiments.

FIG. 9f is a scheme illustrating conductivity measurement, in accordance with various embodiments.

FIG. 10 illustrates a NOR gate, in accordance with various embodiments

FIG. 11 illustrates a computation architecture for SVM classification, in accordance with various embodiments.

FIG. 12 illustrates a soft error mitigation cell, in accordance with various embodiments.

FIG. 13 illustrates coding based soft error mitigation techniques, in accordance with various embodiments.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to certain embodiments of the disclosed subject matter, examples of which are illustrated in part in the accompanying drawings. While the disclosed subject matter will be described in conjunction with the enumerated claims, it will be understood that the exemplified subject matter is not intended to limit the claims to the disclosed subject matter.

Throughout this document, values expressed in a range format should be interpreted in a flexible manner to include not only the numerical values explicitly recited as the limits of the range, but also to include all the individual numerical values or sub-ranges encompassed within that range as if each numerical value and sub-range is explicitly recited. For example, a range of “about 0.1% to about 5%” or “about 0.1% to 5%” should be interpreted to include not just about 0.1% to about 5%, but also the individual values (e.g., 1%, 2%, 3%, and 4%) and the sub-ranges (e.g., 0.1% to 0.5%, 1.1% to 2.2%, 3.3% to 4.4%) within the indicated range. The statement “about X to Y” has the same meaning as “about X to about Y,” unless indicated otherwise. Likewise, the statement “about X, Y, or about Z” has the same meaning as “about X, about Y, or about Z,” unless indicated otherwise.

In this document, the terms “a,” “an,” or “the” are used to include one or more than one unless the context clearly dictates otherwise. The term “or” is used to refer to a nonexclusive “or” unless otherwise indicated. The statement “at least one of A and B” or “at least one of A or B” has the same meaning as “A, B, or A and B.” In addition, it is to be understood that the phraseology or terminology employed herein, and not otherwise defined, is for the purpose of description only and not of limitation. Any use of section headings is intended to aid reading of the document and is not to be interpreted as limiting, information that is relevant to a section heading may occur within or outside of that particular section.

In the methods described herein, the acts can be carried out in any order without departing from the principles of the invention, except when a temporal or operational sequence is explicitly recited. Furthermore, specified acts can be carried out concurrently unless explicit claim language recites that they be carried out separately. For example, a claimed act of doing X and a claimed act of doing Y can be conducted simultaneously within a single operation, and the resulting process will fall within the literal scope of the claimed process.

The term “about” as used herein can allow for a degree of variability in a value or range, for example, within 10%, within 5%, or within 1% of a stated value or of a stated limit of a range, and includes the exact stated value or range.

The term “substantially” as used herein refers to a majority of, or mostly, as in at least about 50%, 60%, 70%, 80%, 90%, 95%, 96%, 97%, 98%, 99%, 99.5%, 99.9%, 99.99%, or at least about 99.999% or more, or 100% The term “substantially free of” as used herein can mean having none or having a trivial amount of, such that the amount of material present does not affect the material properties of the composition including the material, such that about 0 wt % to about 5 wt % of the composition is the material, or about 0 wt % to about 1 wt %, or about 5 wt % or less, or less than, equal to, or greater than about 4.5 wt %, 4, 3.5, 3, 2.5, 2, 1.5, 1, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.01, or about 0.001 wt % or less, or about 0 wt %.

As used herein, the term “polymer” refers to a molecule having at least one repeating unit and can include copolymers

Method of Forming a Microwire or Nanowire.

Various embodiments of the present invention provide a method of forming a wire that is a microwire or a nanowire. The method can include disposing a plurality of metal particles in a portion of a channel. The channel is a nanochannel or a microchannel. The method can include etching the metal particles with an activation agent to form a flux. The flux that is formed penetrates an additional portion of the channel. The flux includes an etching product of the activation agent and the metal particles. The method can also include allowing the activation agent to at least partially evaporate to form a wire that is a microwire or a nanowires.

The metal particle can be any suitable type of metal particles. The metal particles can be liquid metal particles, solid metal particles, or the metal particles can include a liquid metal core with a solid metal or metal oxide shell. The metal particles can include unary metals or can include combinations of two, three, or more metals. The metal particles can include a mixture of metals that is a eutectic composition or a non-eutectic composition. The metal particle can include any suitable one or more metals. The metal particle can include Field's metal, InSn alloy, eutectic InSn alloy, Galinstan, GaIn alloy, eutectic GaIn alloy, InBi alloy, eutectic InBi alloy, SnBi alloy, eutectic SnBi alloy, SnZn alloy, eutectic SnZn, Fe, Sn, Bi, In, Cu, Ag, Ge, Te, Sb, SnCu, SnAg, or a combination thereof. The metal particle can include an undercooled liquid metal that has a temperature that is lower than a melting point of the liquid metal. The metal particle can include a liquid metal that has a temperature equal to or greater than a melting point of the liquid metal. The metal particles can have any suitable diameter, such as a diameter (e.g., a number-average diameter) of 1 nm to 10 cm, or 1 nm to 990 nm, or less than or equal to 10 cm and greater than or equal to 1 nm, 2 nm, 3, 4, 5, 6, 8, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 125, 150, 175, 200, 250, 300, 350, 400, 450, 500, 600, 700, 800, 900 nm, 1 micron, 2, 4, 6, 8, 10, 50, 100, 150, 200, 500, 750 microns, 1 mm, 2, 4, 6, 8 mm, 1 cm, 2, 4, 6, 8, or 9 cm.

The metal particle can include Bi and Sn. The metal particle can include Bi and Sn, and one or more additives as described in Table 1.

TABLE 1
Metal particle compositions including
Bi, Sn, and one or more additives.
					Δ(Yield)
Additives	E0 (V)	ΔTf (K)	ΔTm (K)	Δ(ΔT) (K)	(%)
None (BiSn)	−0.14 (Sn)	263.9	411.3	147.4	89.13
In (eut.)	−0.34	−39.9	−74.4	−34.5	+10.87
Pb (eut.)	−0.13	−8.4	−44.7	−36.3	+10.87
Pb, Cd (eut.)	−0.4 (Cd)	+6.7	−68	−74.7	+5.79
Pb, Cd, In	(see	+14.6	−90.3	−104.9	+10.87
(eut.)	above)
Ga (trace)	−0.56	+13.3	−17.7	−31.1	−15.7
Ge (trace)	0.1	+0.3	0	−0.3	−1.73
Ge (trace or	0.1	+28.2	−1.2	−39.4	−1.70
15%)
Sb (trace)	−0.51	+21.9	+3.3	−18.6	−25.88
Te (trace)	−0.9	+1.4	−0.1	−1.5	−8.57
Ho (trace)	−2.33	+39.1	−0.2	−39.2	−6.83
Au (trace)	1.83	+13.7	+0.3	−13.5	−24.02

The metal particles can include liquid metal particles including a liquid metal or alloy. The liquid metal particles can include a solid shell, or the liquid metal particles can be free of a solid shell.

The metal particles can include solid metal particles including a solid metal or alloy. The solid metal particles can include a solid or liquid core.

The metal particles can include liquid metallic core-shell particles. Each liquid metallic core-shell particle can include a liquid metallic core that includes a metal or metal alloy. Each liquid metallic core-shell particle can also include a solid outer shell on the liquid metallic core. The wire can include a concentration and/or compositional gradient along a longitudinal direction along the wire. The composition of the flux can change as the metal oxide shell is etched and removed and replenished by the core, causing the compositional and/or concentration gradient. The liquid metallic core-shell particle can be an undercooled liquid metallic core-shell particle having a temperature that is below a melting point of the liquid metallic core. The liquid metallic core-shell particle can be a liquid metallic core-shell particle having a temperature that is equal to or above a melting point of the liquid metallic core. The liquid metal core can include Field's metal, InSn alloy, eutectic InSn alloy, Galinstan, GaIn alloy, eutectic GaIn alloy, InBi alloy, eutectic InBi alloy, SnBi alloy, eutectic SnBi alloy, SnZn alloy, eutectic SnZn, Fe, Sn, Bi, In, Cu, Ag, Ge, Te, Sb, SnCu, SnAg, or a combination thereof. The liquid metal core can include Field's metal, eutectic InSn alloy, or a combination thereof.

The solid shell of the liquid metal particle can include one or more oxides of the liquid metal core. The solid shell of the liquid metal particle can include one or more stabilizing ligands. The one or more stabilizing ligands can form an adlayer on the outside of the solid shell of the undercooled liquid metal particle. The stabilizing ligand can include a conjugate base of a C₁-C₂₀ mono- or di-carboxylic acid. The stabilizing ligand can include acetate.

The metal particle can include a eutectic metal alloy. The wire formed from the eutectic metal alloy can include a mixed composition that is based on kinetics of the etching of spinodal lines of the metal particle surface. The composition of the flux can change due to changes in the concentration of the accessible metal ions which are presented on the surface based on spinodal decomposition.

The metal particle can include a combination of metals in a non-eutectic composition.

The metal particle can include a unary metal. The wire formed from the unary metal can include a uniform composition. The rate of formation of the wire can depend on whether the particle is a liquid or a solid, and whether the particle has a liquid or solid core.

The metal particle can include a ternary metal alloy. The wire formed from the ternary metal alloy can include a concentration and/or composition gradient of a third metal ion that is not initially produced in the flux as the ternary alloy surface is depleted by the etching.

The flux formed from the reaction of the activation agent and the metal particles can penetrate the additional portion of the channel without external assistance. For example, the flux can penetrate the additional portion of the channel via capillary action and/or fluidic flow.

The channel can be open along its length. The method can be a method of evaporative lithography.

The channel can be closed along its length. The channel can be closed along at least one portion of its length and open along at least one other portion of its length. The channel can be closed along its entire length. The method can be a method of directed and/or guided precipitation lithography. Disposing the metal particles in the portion of the channel can include disposing the metal particles between the portion of the channel and a substrate. The method can further include disposing the metal particles in the channel or on a mold including the channel and then placing the channel against the substrate. The method can further include disposing the metal particles on the substrate and then placing the channel against the substrate. The method can further include removing the channel from the wire, to provide the wire disposed on the substrate. The substrate can include includes silicon, glass, mica, graphene, graphene oxide, MoS₂, one or more metals, a metal foil, aluminum, aluminum foil, copper, copper foil, one or more coinage metals, one or more metal oxides, one or more minerals, one or more polymers (e.g., polyethylene, polypropylene, polyvinylidene chloride, or a combination thereof. The substrate can include silicon, glass, or a combination thereof.

The channel can include a uniform width, or a nonuniform width. The channel can have or include a width of 1 nm to 10 microns, or 1 nm to 990 nm, or 30 nm to 1.5 microns, or less than or equal to 10 microns and greater than or equal to 1 nm, 2 nm, 3, 4, 5, 6, 8, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 125, 150, 175, 200, 250, 300, 350, 400, 450, 500, 600, 700, 800, 900 nm, 1 micron, 2, 3, 4, 5, 6, 7, 8, or 9 microns. The channel can have a length of 1 mm to 100 cm, or 1 mm to 25 cm, or less than or equal to 100 cm and greater than or equal to 1 mm, 2, 3, 4, 5, 6, 7, 8, 9 mm, 1 cm, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 40, 50, 60, 70, 80, or 90 cm.

The channel can have any suitable cross-sectional profile. The channel can have a cross-sectional profile that is curved, round, square, rectangular, polygonal or a combination thereof. The channel can have a cross-sectional profile that is square or rectangular.

In various aspects, the channel is part of a mold. The mold that includes the channel can be formed of any suitable material, such as an elastomer (e.g., PDMS, ecoflex, epoxy), a thermoset polymer, a thermoplastic polymer, an inorganic material (e.g., glass, silica, anodized aluminum oxide), a coinage metal (e.g., Au, Ag, Cu), or a combination thereof. Examples of thermoset polymers and/or thermoplastic polymers includes ABS, polystyrene, polyethylene, plexiglass, or a combination thereof. The mold can include PDMS (polydimethysiloxane).

The method can include using more than one channel, such as more than one channel in a mold. The method can include forming the wire in more than one of the channels to form a plurality of the wires. The channels can have any suitable spacing, such as a spacing of 1 nm to 10 microns, 30 nm to 2 microns, or less than or equal to 10 microns and greater than or equal to 1 nm, 2 nm, 3, 4, 5, 6, 8, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 125, 150, 175, 200, 250, 300, 350, 400, 450, 500, 600, 700, 800, 900 nm, 1 micron, 2, 3, 4, 5, 6, 7, 8, or 9 microns. Together the channels can form a grating. A mold can include the channels that form the grating. A mold including PDMS can include the channels that form a grating.

The portion of the channel where the metal particles are initially deposited can be a growth zone of the channel. The portion of the channel where the metal particles are initially deposited can be an entrance to the channel. The additional portion of the channel where the flux penetrates the channel can be a collection zone.

Disposing the plurality of metal particles in the portion of the channel can include disposing a solution including metal particles in the portion of the channel, wherein the solution has a concentration of the metal particles of 0.001 wt % to 100 wt %, such as greater than or equal to 0.001 wt % and less than or equal to 0.01 wt %, 0.1, 0.5, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 82, 84, 86, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 99.9, 99.99, or 99.999 wt %. The solution can have a concentration of the metal particles of about 100%. The solution can include a solvent. The solvent can include any suitable aqueous or organic solvent, such as water, an organic solvent, an alcohol, a ketone, an ester, an amine, an aromatic compound, or a combination thereof. The solution can include a solvent including a C₂-C₂₀ mono- or di-carboxylic acid, such as acetic acid.

The activation agent can be a solution that includes a solvent and an acid (e.g., organic acid and/or mineral acid such as HCl or H₂SO₄), and/or comprising etchant, alkaline conditions (e.g., highly basic), an applied bias (e.g., to release/etch the metal ions from the surface, e.g., as dictated by the corresponding Pourbaix diagrams), an amide, a thioester, a urea, a highly reactive metal (e.g., europium), or a combination thereof. Amides can be especially useful because they introduce nitrogen in the pyrolyzed structure and hence “dope” the semiconductor materials through heterogeneity in composition. The solvent can be any suitable aqueous or organic solvent, such as acetone, ethanol, water, ethyl acetate, toluene, benzene, methylene chloride, THF, methanol, petroleum ether, or a combination thereof. The solvent of the activation agent can include acetone, ethanol, water, or a combination thereof. The acid of the activation can be any suitable acid that etches the metal particle to form the flux, such as a carboxylic acid, acetic acid, stearic acid, benzoic acid, butyric acid, butanoic acid, adipic acid, malonic acid, muconic acid, an amino acid (e.g., one or more of proline, arginine, histidine, alanine, tryptophan, glutamic acid, cysteine, and structural analogs thereof), or a combination thereof. The acid can include acetic acid. The solution can have any suitable volumetric ratio of the acid to the solvent, such as 1:100 to 100:1, or 1:5 to 5:1, or, greater than or equal to 1:100 and less than or equal to 1:90, 1:80, 1:70, 1:60, 1:50, 1:40, 1:30, 1:20, 1:10, 1:9, 1:8, 1:7, 1:6, 1:5, 1:4, 1:3, 1:2, 1:1, 2:1, 3:1, 4:1, 5:1, 6:1, 7:1, 8:1, 9:1, 10:1, 20:1, 30:1, 40:1, 50:1, 60:1, 70:1, 80:1, or 90:1. Allowing the activation agent to at least partially evaporate can include allowing the solvent of the activation agent to at least partially evaporate. The acid in the activation agent can combine with metal atoms on the surface of the metal particles that are etched to form free metal ions chelated with a conjugate base of the acid in the activation agent. The free metal ions chelated with the conjugate base can solubilize into the activation agent. The free metal ions chelated with the conjugate base can polymerize to form the wire.

The method can include controlling the rate of evaporation from one or more portions of the flux. Controlling the rate of evaporation from the one or more portions of the flux can control morphology of corresponding portions of the formed wire.

The wire formed by the method can have any suitable profile. The wire can have a straight profile. The wire can have a curved profile. The wire can have any suitable cross-sectional profile. The wire can have a curved or round cross-sectional profile. The wire can have a square, rectangular, or polygonal cross-sectional profile. The wire can have a flat profile.

The wire can have any suitable height, such as a height of 1 nm to 10 microns, or less than or equal to 10 microns and greater than or equal to 1 nm, 2 nm, 3, 4, 5, 6, 8, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 125, 150, 175, 200, 250, 300, 350, 400, 450, 500, 600, 700, 800, 900 nm, 1 micron, 2, 3, 4, 5, 6, 7, 8, or 9 microns.

The wire can have any suitable width, such as a width of 1 nm to 10 microns, or less than or equal to 10 microns and greater than or equal to 1 nm, 2 nm, 3, 4, 5, 6, 8, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 125, 150, 175, 200, 250, 300, 350, 400, 450, 500, 600, 700, 800, 900 nm, 1 micron, 2, 3, 4, 5, 6, 7, 8, or 9 microns.

The wire can have any suitable aspect ratio (width to height), such as an aspect ratio of 1:1000 to 5:1, or less than or equal to 5:1 and greater than or equal to 1:1000, 1:900, 1:800, 1:700, 1:600, 1:500, 1:400, 1:300, 1:200, 1:100, 1:50, 1:20, 1:10, 1:9, 1:8, 1:7, 1:6, 1:5, 1:4, 1:3, 1:2, 1:1, 2:1, 3:1, or 4:1.

The wire can have a homogeneous elemental distribution. The wire can have a distribution of one or more elements that varies in concentration along a longitudinal direction of the wire. The wire can have a substantially uniform diameter and/or cross-sectional area from end to end. The wire can include an organometallic compound.

The method can further include calcining the wire to form a calcined wire. The calcining can include heating the wire to a temperature of 300° C. to 2000° C., or 500° C. to 1000° C., or 600° C. to 800° C., or less than or equal to 2000° C. and greater than or equal to 300° C., 350, 400, 450, 500, 550, 560, 580, 600, 620, 640, 660, 680, 700, 720, 740, 760, 780, 800, 820, 840, 850, 900, 950, 1000, 1100, 1200, 1500, 1750, or 1900° C. In various aspects, the metal particle includes a liquid metal core that includes Field's metal and the calcining includes heating the wire to a temperature of 550° C. to 650° C. In various aspects, the metal particle includes a liquid metal core that includes InSn eutectic and the calcining includes heating the wire to a temperature to 750° C. to 850° C. The calcining can include maintaining the temperature for any suitable time period, such as 1 min to 24 h, 30 min to 2 h, or less than or equal to 24 h and greater than or equal to 1 min, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 min, 1 h, 1.5, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, or 22 h. The calcining can include heating the wire in an environment including air, nitrogen, argon, or a combination thereof.

The method can further including pyrolyzing the wire to form a pyrolyzed wire. Pyrolysis of the wire can form a graphene, graphene oxide, and/or graphitic coating on the wire. For wires including a compositional gradient along the longitudinal direction of the wire, the compositional gradient can cause a corresponding gradient in the backgap along the longitudinal direction of the wire. The pyrolysis conditions can be the same as those used in ACS Matt. Letts 2020 2, 1211-1217 and in U.S. Patent Publication No. 2018/0311655, both of which are hereby incorporated by reference. The pyrolysis can include heating the wire to a temperature of 300° C. to 2000° C., or 500° C. to 1000° C., or 600° C. to 800° C., or less than or equal to 2000° C. and greater than or equal to 300° C., 350, 400, 450, 500, 550, 560, 580, 600, 620, 640, 660, 680, 700, 720, 740, 760, 780, 800, 820, 840, 850, 900, 950, 1000, 1100, 1200, 1500, 1750, or 1900° C. The pyrolysis can include maintaining the temperature for any suitable time period, such as 1 min to 24 h, 30 min to 2 h, or less than or equal to 24 h and greater than or equal to 1 min, 2, 3, 4, 5, 6, 7, 8, 9, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55 min, 1 h, 1.5, 2, 3, 4, 5, 6, 8, 10, 12, 14, 16, 18, 20, or 22 h. The pyrolysis can include heating the wire in an environment including air, nitrogen, argon, or a combination thereof. In various embodiments, pyrolysis at lower temperatures such as around 300° C. can provide carbon (1) or carbon (2) mixtures, while pyrolysis at higher temperatures such as about 600° C. can provide mostly carbon (0) graphene/graphitic carbon/graphene oxide mixtures. Pyrolysis at even higher temperatures such as exceeding 800° C. can cause the formation of substantially all graphitic carbon. Performing the pyrolysis on rare earth metals instead of post-transition metals can provide high carbon (0) content with pyrolysis at lower temperatures, such 80 wt % or more carbon (0) at 550° C.

The wire can include an organic metallic compound, and the calcination can transform the wire into a calcined wire that is substantially free of the organometallic compounds. The calcination can shrink the wire; for example, the calcination can shrink one or more dimensions of the wire by 1% to 50%, such as less than or equal to 50% and greater than or equal to 1%, 2, 4, 6, 8, 10, 15, 20, 25, 30, 35, 40, or 45%. The calcination can shrink the wire more in height than in length and width. The calcined wire can be substantially free of organometallic compounds. The calcined wire can be predominantly inorganic compounds. The calcined wire can be predominantly inorganic mixed oxides. The calcined wire can have a homogeneous elemental distribution, or an elemental distribution that varies in concentration along a longitudinal direction of the wire.

In various aspects of the method, the channel can be closed, and the method further includes performing one or more additional cycles of the disposing, etching, and formation of the wire on top of previously-formed wire. The one or more additional cycles can include orienting the channel in a different direction than used to form the previously-formed wire, such as a direction that varies from the channel used to form the previously-formed wire by less than 180° but equal to or greater than 1°, 2, 4, 6, 8, 10, 15, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, or 170°. The different direction can be about 90° different than the direction of the channel used to form the previously-formed wire.

The method can include adjusting porosity of the wire including tuning the volume of a ligand (e.g., stabilizing ligand) that is included on the solid shell of a liquid metal particle used to form the wire.

The method can include adjusting a proportion of residual carbon in a pyrolyzed wire including tuning the type of ligand (e.g., stabilizing ligand) that is included on the solid shell of a liquid metal particle used to form the wire; for example, benzoic acid does not thermally decompose as well as propionic acid, and so leaves more carbon.

The method can further include at least partially dissolving some of the formed wire.

The method can be a method of forming an article or device including the wire. The article or device can be any suitable article or device, such as a semiconductor device, an optical article, a plasmonic component, an opto-electronic component, a resonant sensor, a radiofrequency sensor, or a combination thereof. The article or device can include a diode, a transistor (e.g., a field-effect transistor (FET)), a computation device, a rectifier, or a combination thereof.

The method can be a method of forming a guided-mode resonance device (GMR), wherein the method includes disposing a plurality of the wires on a substrate. The substrate can include a glass substrate.

Wire.

In various aspects, the present invention provides a wire formed by the method described herein, such as the wire after evaporation, after calcination, after pyrolysis, or after calcination and pyrolysis. The wire is a microwire or nanowire formed by a method including disposing a plurality of metal particles in a portion of a channel that is a nanochannel or a microchannel. The method includes etching the metal particles with an activation agent to form a flux that penetrates an additional portion of the channel. The flux includes an etching product of the activation agent and the metal particles. The method also includes allowing the activation agent to at least partially evaporate to form the wire. The wire can be a wire formed from any suitable one or more types of metal particles described herein.

The wire can be formed from liquid metallic core-shell particles and the wire can include a concentration and/or compositional gradient along a longitudinal direction along the wire.

The wire can be formed from a metal particle that includes a eutectic metal alloy. The wire formed from the eutectic metal alloy can include a mixed composition that is based on kinetics of the etching of spinodal lines of the metal particle surface. The composition of the flux can change due to changes in the concentration of the accessible metal ions which are presented on the surface based on spinodal decomposition.

The wire can be formed from a metal particle that includes a unary metal. The wire formed from the unary metal can include a uniform composition.

The wire can be formed from a metal particle that includes a ternary metal alloy. The wire formed from the ternary metal alloy can include a concentration and/or composition gradient of a third metal ion that is not initially produced in the flux as the ternary alloy surface is depleted by the etching.

In various aspects, the wires can be sequentially deposited, such as in different sizes or composition. Such sequentially deposited wires can create function points of contact that can, for example, serve as computational nodes, memory, and/or gates (e.g., transistors); for example, see FIGS. 8h-j. In various aspects, the wires can be deposited and/or assembled in more than 1 dimension, such as 2 dimensions or 3 dimensions, and/or in various architectures.

Article or Device.

In various aspects, the present invention provides an article or device including one or more wires formed by the method described herein, such as the wire after evaporation, after calcination, after pyrolysis, or after calcination and pyrolysis. The wires are microwires or nanowires formed by a method including disposing a plurality of metal particles in a portion of a channel that is a nanochannel or a microchannel. The method includes etching the metal particles with an activation agent to form a flux that penetrates an additional portion of the channel. The flux includes an etching product of the activation agent and the metal particles. The method also includes allowing the activation agent to at least partially evaporate to form the wire.

The article or device can be any suitable article or device that includes one or more of the wires formed by the method described herein. The article or device can be a semiconductor device, an optical article, a transistor (e.g., a field-effect transistor (FET)), a diode, a computation device, a guided-mode resonance device (GMR), or a combination thereof.

EXAMPLES

Various embodiments of the present invention can be better understood by reference to the following Examples which are offered by way of illustration. The present invention is not limited to the Examples given herein.

Materials: Field's metal (eutectic indium (51%, wt %)-bismuth (32.5%, wt %)-tin (16.5%, wt %)) and tin metal was purchased from Rotometals. Indium metal (99.999%) was from Alfa Aesar). Glacial acetic acid (99.7%), trichloroacetic acid (99.8%), ethyl acetate (reagent grade, 99.9%), and acetone (HPLC grade, 99.7%) were from Fisher Scientific. Diethylene glycol (99.9%) was purchased from VWR. Ethanol (anhydrous) was from Decon laboratories Inc. The above chemicals were used as received. Deionized water was prepared using a Thermo Scientific Smart2Pure® 6 UV water purifier system. Si substrates (University wafers) and glass slides (J. Melvin Freed brand) were used after cleaning with ethanol. Polydimethylsiloxane (PDMS) gratings were prepared by soft lithographic replication from a glass grating and cut with scissor along orthogonal to the length of the channel to expose inlets or outlets.

Particle synthesis: Undercooled liquid metal particles were synthesized using the SLICE (Shearing Liquids Into Complex particlEs) method, described in I. D. Tevis, L. B. Newcomb, M. Thuo, Langmuir 2014, 30, 14308, hereby incorporated by reference in its entirety. For Field's metal particles, the metal (10 g) and diethylene glycol (200 mL) were placed in Cuisinart® (SBC-1000FR) soup maker and heat to ca. 118° C. using the built-in base heater and heating tape wrapped around the soup maker jug. Then 2 mL glacial acetic acid was added to the blender and the mixture was sheared at ˜9000 rpm (setting 2) for 10 minutes. The resulting suspension was quenched in ethanol and allowed to equilibrate to ambient conditions. The slurry was then filtered using a Buchner funnel with Whatman GF/F filter. The filtered particles were washed with copious amounts of ethanol, followed by an ethyl acetate rinse. The remaining particles were then harvested and stored in ethyl acetate. For indium-tin particles, eutectic InSn alloy was made by first mixing 10.20 g indium metal into 12.05 g molten tin, then the alloy was cooled down to room temperature. For particle synthesis, mixture of 4.32 g InSn alloy, 200 mL Diethylene and 1.04 g Trichloroacetic acid was preheated to 140° C. on a hot plate. After immediate transferring to a 10°-tilted Cuisinart® (SBC-1000FR) soup maker, the mixture was sheared at a speed of ˜17000 rpm (setting 4) for 4 minutes. Obtained particles were filtered following same procedure with field's metal particles.

Activation agent preparation: AcOH/Ace was prepared by mixing 5 mL glacial acetic acid with 5 mL acetone. AcOH/EtOH and AcOH/H₂ O were prepared following same procedure by replacing acetone with ethanol and deionized water, respectively.

Particle deposition and activation: For open channel process, undercooled metal particle solution (ca. 1 μL) was deposited on y-axis end of PDMS grating with Eppendorf® micropipette. One droplet of fluxing agent was dropped onto deposited particles with a Pasteur pipette. The entire PDMS grating surface was fluxed with liquid automatically. Around 30 minutes were allowed to elapse until the agent dried out then the fluxing procedure was repeated two times. For wires prepared with close channel process, undercooled metal particle solution (ca. 1 μL) was deposited on substrates (Si, glass, and the like). Then, PDMS grating with grating grooves facing down was put onto deposited particles with a tweezer. One droplet of fluxing agent was dropped onto deposited particle with Pasteur pipette. PDMS grating channels were fluxed with liquid automatically. About 30 minutes passed while the agent dried out then the fluxing procedure was repeated two times.

Calcination: Wires deposited on Si or glass substrates were placed in a muffle furnace at 600° C. (Field's metal, “FM”) or 800° C. (InSn) at 20° C./min in air. Temperature was hold for 1 hour before cooling down to ambient temperature.

Imaging. For imaging purpose, wires made with open channel process were lifted off with Cu tape then adhered to a flat SEM stub (Ted Pella, Inc.). Wires on Si substrate was imaged directly after adhering to a SEM stub. Morphology characterizations were done using scanning electron microscopy (FEI-SEM Quanta 250) with 3.0 a.u. spot size and 10 mm working distance. For calcined wires, the working voltage was 10.0 kV while pristine wires were imaged with lower voltage (7.0 kV). Back Scattered electron (BSE) detector was used to differentiate beam and substrate. Composition analysis was carried out using Energy Dispersive X-ray Spectrometer (EDS). Accelerating voltage of 10 kV and a working distance of 10 mm were applied as standards. For element mapping, spot size of 5.0 was applied to improve signaling while 4.0 spot size was chosen for element analysis with better resolution.

X-Ray Powder Diffraction (XRD): XRD was done on calcined wires detached from Si substrate. Ground beam powder was spread onto zero diffraction substrate with a thin Vaseline® layer. Sample were characterized by Siemens® D500 x-ray with a copper X-ray tube. Phase identification and pattern fitting were done using the Jade® software.

Conductivity measurement: Wires on Si substrate were used as samples. Two Eutectic Gallium Indium (EGaIn) liquid metal droplets (c.a. 0.04 μL) were deposited 1 mm apart along y axis onto wires and served as electrodes. For samples with limited areas, two EGaIn dropletts were attached, as electrode connection points, to a continuous area under 10× magnification using a ME520TA reflective microscope. A Keithley 6430 Sub-Femtoamp Remote Sourcemeter was connected to electrodes and applied cyclic voltage (V) from −5 V to 5 V with a 0.5 V step while current (I) was recorded. A hundred I-V cycles were recorded for reaching a steady state.

Atomic Force Microscopy (AFM): AFM images were collected using a Digital Instruments (now Bruker®) Multi-Mode AFM in contact mode with SNL probes. Captured images were processed with plaintiffs and flatten routines. The feature height, feature width and cross section spectrum were analyzed automatically using the integrated Nanoscope Analysis v2.0 Software.

Optical transmission measurement: The transmission measurements were carried out using a home-built setup. The setup used a fiber-coupled broadband light source as the excitation. The excitation light was collimated using a fiber tip collimator. The sample under test was mounted on a stage. The transmitted light was coupled into a collection fiber and analyzed using a spectrometer. The reference spectrum was taken by measuring the transmission of a glass. The reference spectrum was used to calculate the transmission coefficients.

Electromagnetic simulation: The RCWA simulations were performed using a commercial modeling tool (DiffractMOD, Synopsys). The simulation domain included only one period of the 1D structures with the periodic boundary conditions to truncate the 1D grating at the x-axis. The refractive index (n(λ)) and extinction coefficient (k(λ)) of film were interpolated using the results obtained from the ellipsometry measurement. The incidence of plane-wave was linearly polarized along the x-axis and y-axis. The transmission spectra were calculated in the wavelength range of 400 nm to 800 nm. At the resonance wavelength, the electric field (|E/Einc|2) distributions in the simulation domain were calculated.

Calculation of fluxing agent physical properties: For a binary liquid mixture, if only laminar interaction of flux and capillary channel was considered, surface tension of solution was estimated by assuming additivity: γ=X₁γ₁+X₂γ₂.¹ If fluxing agent was treated ideally, viscosity could be calculated using the Arrhenius equation: In η=X₁ln η₁+X₂ln η₂.²Mixture vapor pressures were calculated from Raoult's law: P=X₁P₁+X₂P₂. X_i, γ_i, η_i and P_i are the mole fraction, surface tension, viscosity, and vapor pressure for pure components (Dortmund Data Bank, wwww.ddbst.com). Obtained results are summarized in Table 2.

TABLE 2
Physical properties of fluxing agent at 293.15 K.
	Surface	Contact
Fluxing	tension γ	angle θ on	Viscosity η	Penetrativity p
agent	(mN/m)	PDMS (°)	(mPa · s)	(m/s)
AcOH/Ace	25.55	40.32 ± 1.78	0.68	14.27
AcOH/EtOH	24.83	45.76 ± 1.04	1.20	7.23
AcOH/H2O	61.89	76.08 ± 1.50	1.05	7.08

Calculation of Conductivity: Resistance reciprocal was calculated using 1^st derivative of linear part in last-cycle I-V curve. Then resistivity and conductivity of wires was calculated by using obtained resistance and wire dimension parameters from AFM and SEM data.

Example 1. Autonomous Organometallic Wire Lithography Using D-Met

Recently reported ad infinitum polymerization of semiconductor material synthons via so-called HetMet reactions present potential for autonomous bottom-up fabrication, and patterning, of semiconductor features. In brief, HetMet reactions utilize liquid metals as metal ion reservoirs, a conjugate acid-base pair as both an etchant and ligand, and partial miscibility to in situ generate organometallic adducts that then oligomerize, precipitate through directed self-assembly, to form mesoscale assemblies of pre-designed shapes. In solution, the products are stochastically oriented. We inferred that introduction of geometric confinement with concomitant oriented evaporation would lead to; i) directed formation of a nuclei near the point of rapid evaporation due to Taylor dispersion and at the highest concentration or largest assemblies of the organometallic adducts, ii) ad infinitum polymerization along the channel dimension based on solvent (vapor pressure) characteristics, iii) related to (ii) and reaction kinetics, size-tunable growth of HetMet semiconductor synthons, iv) post-synthesis thermal reconstruction to form requisite semiconductor oxide already pre-organized in a desired pattern. Exploiting underlying fluid dynamics (Taylor dispersion, Jurin's law, and Marangoni flow), reaction kinetics, in situ self-assembly, and evaporation dynamics (Raoult's and Dalton's laws), we infer that a tunable Directed metal-ligand reaction (for brevity abbreviated as D-Met) can be realized by confining the etched adducts in a channel. Continuously replenishing for evaporative loss implies that this process can continue until the channels are filled with requisite semiconductor synthon(s).

Consider a rectangular channel of length L (x direction) and height H (y direction) where H/L<<1. The liquid (solvent) and metal adduct (particle) mixture that initially fills the channel may be considered a thin film in this limit. The mixture fills the channel with solvent mass-fraction (mass/mass) denoted #, and metal adduct particle mass fraction denoted ϕ_m=1−ϕ_s. Since the adducts agglomerates, and are denser than the liquid, they settle in the channel forming a stratified layer of the solvent on top of mostly metal adduct-beside liquid that may be trapped in the particle's interlayer regions. The vapor-liquid interface profile for a liquid that fills a rectangular channel has a shape akin to that of the channel, thus the z profile (3^rd direction), is nearly uniform except at the 3-phase contact line. We, therefore hypothesize that the liquid in the channel can be treated as a 2 dimensional thin-film, and assume that the constituent local-mass fractions vary with time and space as ϕ_s=ϕ_s(x, t) and ϕ_m=#m(x, t). The solvent-layer profile maintains a shape similar to a composite Heaviside function H(x)−H(x−L) for 0≤x≤during evaporation, but with a magnitude that decreases with time as mass is transported from the liquid to vapor. Here we assume the rate of change for the interface varies with time according to β(t)=β₀−β₁(t), where constant β₀ is the liquid initial height at time t=0. We now write the interface profile as h(x, t)=β(t)[H(x)−H(x−L)] for 0≤x≤L and t≥0. Under limited Marangoni flow the interface shear stress is zero i.e. ∂u/∂y=−∂v/∂x [2] where these derivatives are evaluated at the vapor-liquid interface y=h(t); and the interface profile evolves according to v=∂h/∂t+J/ρ [2]. Here J=Dn·∇c is the flux of solvent into the vapor phase where n·∇c is computed at the gas-liquid interface y=h(t) with outward point normal n=∇(y−h(x, t))/|∇(y−h(x, t))| and D denotes the solvent-vapor diffusivity, where c is the concentration (mass/volume) of solvent in the vapor-phase. Furthermore, the concentration gradient computed at the interface y=h(t) is a function of x and t only; and we therefore let n·∇c=f(x, t) denote this gradient. Noting that the derivative of a Heaviside function is a delta function, it follows that ∂[H(x)−H(x−L)]/∂x=δ(x)−δ(x−L), where δ is the Dirac delta function, then we can express the streamwise velocity using an integral derived from shear stress u=−∫₀^h(t)∂v/∂x after inserting expressions for h(t) and J into the interface evolution equation. This yields a streamwise velocity u=[−β₁[δ(x)−δ(x−L)]−D(df/dx)/ρ]y. In the H/L<<1 limit the end channel regions that corresponds to x=0 and x=L are negligible. If we only consider the domain, 0<x<L, the equation reduces to u=−D[df/dx]y/ρ.

Thus, the velocity u primarily drives flow to minimize gradients in f(x, t)=n·∇c i.e. larger df/dx results in larger u. We would normally need only to find solutions for the concentration profile by solving a Laplacian equation ∇²c=0 to estimate the velocity magnitude, but this is not necessary if we consider the combination of Raoult's law for the solvent-vapor concentration above the liquid as a function of liquid phase solvent concentration, and Dalton's law for the solvent-vapor pressure as a function of the total pressure. Combining these law's results in an expression for solvent concentration c=ρP_vapx_s/P where x_s is the solvent liquid phase mol fraction that is related to the liquid phase mass fraction via x_s=ϕ_s/[[1−ϕ_s](MW_s/MW_m)+ϕ_s] where ϕ_s is the liquid phase solvent mass fraction, and ρP_vap is the solvent equilibrium vapor pressure. MW_s and MW_m denote the solvent and metal adduct molecular weights respectively. This relation directly implies precipitation with increase in molecular weight of the adducts. These expressions were derived assuming only two component liquid-solvent and metal adduct; the assumption is still valid for other mixtures as long as the solute/particle possess lower vapor pressure relative to the solvent. Using the chain rule we can write df/dx=(dx_s/dx) df/dx_s. The second derivative may be computed using the expression written here for x_s. One more application of the chain rule yields dx_s/dx=(dϕ_s/dx) dx_s/dϕ_s. Therefore, the velocity u appears to minimize gradients in solvent, and likewise in metal-adduct concentration. Use of nm to μm wide channels and low viscosity fluids implies rapid channel filling as dictated by Jurin's law

$\left(h=\frac{2\gamma \cos \theta }{\mathrm{\rho ℊ}{r}_0}\right).$

Initial profile, h(x, t=0), may therefore affect precipitation based on Taylor dispersion where a particle layer may form due to initial filling of the channel by capillary forces. But these would only enhance this flow through the transient profile gradient and normal, i.e., an increase in magnitude for |∂[∂h/∂t]/∂x]. The scalar concentration gradient computed at the interface is n·∇c<0 for all time with zero initial solvent concentration in the vapor. Directed evaporation, however, becomes a paramount condition for controlled uniform growth of these polymerizing adducts.

Recently, undercooled liquid metal particles emerged as a promising precursor for expedient functional material fabrications. Stabilized by its passivating oxide shell (0.7-5 nm), the metastable liquid metal core possesses room-temperature reactivity (ΔG≈kT). To utilize this inherent activity, the passivating oxide shell needs to either be physically (mechanical force) or chemically (etching) activated. Previous results have shown continual chemical activation can achieve in-situ synthesis of organometallic nanobeams through Heterogenous Metal/ligand reaction (HetMet). However, non-restricted synthesis conditions in this process generated nonuniform beams growing in arbitrary directions in the solution.

FIGS. 1a-j show a schematic summary of Directed Metal-ligand reaction (D-Met). FIG. 1a is a schematic illustration of performing metal-ligand reaction on mold leads to autonomous lithography of nanowires. FIG. 1b is a SEM image showing arbitrary beam formation from a metal-ligand reaction in a growth zone. FIG. 1c is a SEM image showing formation of discontinuous wires in a growth zone. FIG. 1d is an SEM image showing alignment of continuous wires in a collection zone. FIGS. 1e-g are SEM images showing wires of various widths formed via D-Met. FIG. 1h illustrates an Energy Dispersive X-ray Spectroscopy (EDS) line scan spectrum of pristine wires from D-Meting undercooled Field's metal particles (FM) or undercooled Indium Tin particles (InSn). FIGS. 1i-j illustrate EDS spectra of calcined wires from D-Meting undercooled Field's metal particles (FM) or undercooled Indium Tin particles (InSn).

Regarding to the versatility of HetMet reaction, we infer that autonomous alignment of nano features could be achieved by directing HetMet reaction with molds (Directed Heterogeneous Metal-ligand reaction, D-Met, FIG. 1a). Analogous to HetMet reaction, activation agent (composed of acid and solvent, denoted as acid/solvent) was utilized to trigger metal/ligand reaction. After dropping acetic acid/ethanol solution on liquid metal particles pre-deposited on Polydimethylsiloxane (PDMS) grating, oxide shell is etched with metal ions releasing. Free metal ions chelated with conjugate base into octahedron metal/ligand monomers. These metal complex solubilize in the activation agent, forming a monomer containing flux (dissolve zone, FIG. 1b). Rapidly, mold channels were penetrated with low-viscosity flux, driven by capillary action following Jurin's law (Equation 1):

$\begin{array}{cc}h=\frac{2\gamma \cos \theta }{\mathrm{\rho ℊ}{r}_0}& \left(1\right)\end{array}$

Where h (m) is the equilibrium liquid height, γ (mN/m), θ (°) are flux surface tension and its contact angle on tube wall, p is mass density (mg/m³), g is gravitational acceleration (m/s²) and r₀ (m) is the tube radius. During the penetration of flux, polymerization was triggered whenever monomer concentration reached its critical value. Thus, intermittent wires were formed in the middle of mold channels (growth zone, FIG. 1c). The flux proceeded until the end of the channel, where activation agent evaporation starts. By forming liquid quarter dome at the grating end, surface curvature caused difference in agent evaporation rate. Faster evaporation at high curvature spots resulted in monomer concentration variation with concomitant creation of surface tension gradient ∇σ across the liquid-air interface. Thus, Marangoni flow was produced in the flux following Navier-Strokes equation (Equation 2):

n·T·t=−t·∇σ  (2)

Where n and t are the unit vector normal and tangent to surface, respectively and T is the stress tensor. Evaporation-induced Marangoni flow drives monomers to grating end, triggering ad-infinitum polymerization with formation of continuous wires pinned to the grating end (collection zone, FIG. 1d). Thus, D-Met achieved autonomous organometallic wire lithography by combining metal/ligand reaction with self-driven fluid dynamics from molds. Apart from being autonomous, we infer that D-Met could achieve high-level morphological and compositional control. Indicated by Equation 1, decreasing r₀ benefits formation of capillary flux inside channel. We infer wire width could be controlled by applying different parent molds with D-Met. Scanning Electron Microscope (SEM) images proved the generation of wires with various widths (down to 44 nm, FIGS. 1e-g) corresponding to its parent mold feature sizes (FIGS. 2a-d). FIG. 2a illustrates a SEM image of a PDMS mold. FIG. 2b illustrates a SEM image of a PDMS mold. FIG. 2c illustrates a SEM image of a PDMS mold. FIG. 2d illustrates a width summary of the PDMS molds shown in FIGS. 2a-c and wires formed with the corresponding mold using D-Met. FIG. 2e illustrates a SEM image and EDS characterizations of FM particles. FIG. 2f illustrates a SEM image and EDS characterizations of InSn particles. FIG. 2g illustrates a SEM image of 3-time activated D-Met wires. FIG. 2h illustrates a SEM image of 5-time activated D-Met wires. FIG. 2i illustrates a SEM image of 8-time activated D-Met wires. Non-selectivity of HetMet made it applicable to a variety of undercooled particles. Thus, we anticipated a similar non-selectivity with D-Met. The line-scan profiles of Energy Dispersive X-Ray Spectroscopy (EDS) showed that pristine wires from D-Met of Field's metal (FM for simplicity) were multi-component organo-metallic wires (FIG. 1h) and carbon was removed by calcination (FIG. 1i). As-expected, D-Meting of InSn undercooled particles (InSn) produced wires with different composition (FIG. 1j).

To test our hypothesis, we compared evaporative lithography (open channels) to directed/guided precipitation lithography (closed channels), specifically paying attention to deposit morphologies, dimensions, and reproducibility. Undercooled liquid metal particles were synthesized through the Shearing Liquids Into Complex particlEs (SLICE) process. Obtained Field's metal (FM, 51 wt % In, 36.5 wt % Bi and 12.5 wt % Sn) and eutectic indium tin (InSn, 52 wt % In, 48 wt % Sn) particles were spheres with average diameter of 1.93±1.13 μm 1.54±0.91 μm, respectively. Homogeneous elemental distribution from Energy Dispersive X-Ray Spectroscopy (EDS) characterization verifies that the particles were amorphous at room temperature (FIGS. 2e-f).

Morphology Control Base on Evaporation.

Direction and speed of Marangoni flow were determined by activation agent evaporation. We infer that controlling evaporation, thus the flow vector would tune wire morphology for D-Met. Firstly, evaporation direction was studied. FIG. 3a is a diagram illustrating open channel growth showing perpendicular agent evaporating and monomer coordinating directions. FIG. 3b is a SEM image of wires formed by the open channel growth shown in FIG. 3a. FIG. 3c is a diagram illustrating closed channel growth with evaporating and coordinating directions were forced to be parallel. FIG. 3d is a SEM image of wires formed by the closed channel growth shown in FIG. 3c. FIG. 3e illustrates penetrativity and vapor pressure of AcOH with various solvents. FIGS. 3f-h illustrate SEM images of wires formed in the growth zone using the solvents shown in FIG. 3e. FIGS. 3i-k illustrate SEM images of wires generated in the collection zone using the solvents shown in FIG. 3e. When D-Met was directly performed within the mold (open channel, FIG. 3a), wires were generated inside the channels and lifted-off before imaging. Obtained SEM images showed curled wires arranged upon the Cu tape (FIG. 3b). When PDMS mold was flipped onto Si substrate before performing D-Met (close channel, FIG. 3c), sharp-edge wires were directly aligned on the substrate (FIG. 3d). For the open channel growth, agent evaporated in z direction and created vertical Marangoni flows. This vertical Marangoni flow induced a monomer moving tendency perpendicular to polymerization direction along y-axis. This mismatch resulted in less ordered monomer coordination, manifested as deteriorated wires created inside the mold. The wires were further curved by necessity of adhesion during wire transportation. However, when D-Met was performed with mold flipped onto substrate, evaporation was forced to happen at the grating end, creating Marangoni flow parallel to monomer self-coordination direction inside channels. This consistency between tangential stress and monomer coordination generated sharp-edge wires directly pinned on the substrate. We infer that wire morphology could be improved by reconciling agent evaporating and monomer coordination directions. Closed channel method was applied for following the studies unless stated.

Carrying monomers inside channels, activation agent moving speed was crucial to wire formation thus carefully investigated with close channel growth. In this study, the acetate-based fluxing agents were prepared by equivoluminally mixing acetic acid (AcOH) with 3 types of solvent, namely acetone (AcOH/Ace), ethanol (AcOH/EtOH) and water (AcOH/H2O). After agent droppage, grating grooves were filled by the liquid with the speed conceivably be represented by penetrativity (p, m/s) (Equation 3):

$\begin{array}{cc}p=\frac{\gamma \cos \theta }{2\eta }& \left(3\right)\end{array}$

where η (mPa*s) is viscosity of penetrating flux, γ (mN/m) and θ (°) are surface liquid tension and its contact angle on the grating material.

FIGS. 4a-f illustrate composition transformation of FM and InSn wires after calcination. FIG. 4a illustrates EDS maps illustrating a homogenous elemental distribution of FM wires calcined at 600° C. for one hour. FIG. 4b illustrates elemental content of FM particle, pristine FM wire, and calcined FM wires. FIG. 4c illustrates an X-ray powder diffraction (XRD) spectrum of calcined FM wires. FIG. 4d illustrates EDS maps of InSn wires calcined at 800° C. for one hour. FIG. 4e illustrates elemental content of InSn particle, pristine InSn wire, and calcined InSn wire. FIG. 4f illustrates an XRD spectrum of calcined InSn wires. Obtained p value possessed unit of m/s, reflecting monomer moving speed in growth zone (FIG. 4e). When AcOH/Ace was applied as activation agent (p=14.27 m/s), long but less wires were generated in the growth zone (FIG. 4f). Wires formed with AcOH/EtOH (p=7.23 m/s) and AcOH/H2O (p=7.08 m/s) were denser albeit shorter (FIGS. 4g-h). In the collection zone, monomer accumulation rate was assumed to be proportional to the activation agent vapor pressure (P) at room temperature (FIG. 4e). Wires generated with AcOH/Ace (P=11.66 kPa) possessed the largest continuity. However, this continuity was demolished by the appearance defects and bundles (FIG. 4i). In contrast, wires generated by AcOH/EtOH (P=3.68 kPa) were moderate in length and had less defect (FIG. 3j), while wires formed by AcOH/H₂O (P=2.15 kPa) were the shortest but nearly defect-free (FIG. 3k). In either the growth or the collection zone, higher penetrating or evaporating speed of activation agent resulted more monomers accumulating in unit time. Thus, application of activation agent possessing larger penetrativity and vapor pressure results in the generation of longer wires. However, better continuity was compensated with defects from uncontrolled nucleation triggered by overwhelming monomers. Since activation agent was treated as ideal binary liquid, the solvent determines the overall physical property of the agent (Table 2). We infer that choice of solvent with different surface tensions or viscosities determines the wire continuity and morphology. For best results, ethanol was applied as standard solvent of activation agent for the following studies.

Apart from choice of solvent, number of activation agent droppage and dry-out cycle determined the overall accumulated monomer quantity, thus affecting the product structure of D-Met. For open channel growth, 3-time activation generated discrete wires (FIG. 2g). 2 more cycles started the formation of bulk structures besides single cord (FIG. 2h) and increasing activation cycles to 8 generated concreted plate composed of individual wires (FIG. 2i). We infer that monomers from extra activation cycles interconnected individual wires into bulk. For keeping wires aligned separately, activation circle of 3 was chosen as standard.

Composition Analysis Pre- and Post-Calcination.

Synthesized from metal alloys (e.g. FM: 60.13 at. % In, 18.82 at. % Sn, 21.05 at. % Bi), we infer that the pristine wires made by D-Met was an organometallic compound, which could be transformed into inorganic material after heat-treatment. FIG. 5a illustrates a EDS maps of FM pristine wire. FIG. 5b illustrates EDS maps of InSn pristine wire. FIG. 5c illustrates an X-ray spectrum of FM pristine wire. From Energy Dispersive X-ray Spectroscopy (EDS) mapping, pristine FM wires were composed of homogeneously distributed In, Sn, Bi, C and O (FIG. 5a). After one-hour calcination at 600° C., C signal became weaker while other elements remained the same (FIG. 4a). Elemental analysis revealed a C drop from 34.21 at. % to 8.47 at. % post heat treatment, creating a nearly carbon free material when carbon residue on Si substrate was taken as adventitious carbon (FIG. 4b). Regardless of C removal, relative atomic contents of metal elements were pertained before and after heat-treatment (pristine: In: 36.45±0.61, Sn: 48.60±0.57, Bi: 14.95±1.10; calcined: In: 37.37±1.03, Sn: 47.82±0.41, Bi: 14.82±0.67, FIG. 4b). X-Ray Powder Diffraction (XRD) was utilized to further understand wire composition. Compared to the organic nature of pristine wire XRD spectrum (FIG. 5c), calcined FM wires were a complex mixture of In₂O₃, SnO₂, Bi₂O_2.5, as well as Sn₂Bi₂O₇. We infer one-hour aerobic heat-treatment transferred organometallic pristine wires into mixed-oxide materials with C removal and oxidation.

Powder Diffraction (XRD) Spectrum of Pristine FM Wires.

Similar to FM particles, wires from InSn undercooled metal showed homogeneous elemental distribution for pristine (FIG. 5b) and calcined wires (800° C., one hour, FIG. 4d) as well as a complete C removal with heat (FIG. 4e). Due to the lack of Bi in the precursor, however, the calcined InSn wires were composed of only In₂O₃ and SnO₂ (FIG. 4f). Significant In drop with concomitant Sn rise due to elective etching was observed in the pristine FM wires compared to FM particles (FIG. 4b). While this preferential behavior was inconspicuous for InSn wires (FIG. 4e), we infer the presence of Bi affected the monomer formation thus resulted in wires with different internal structures.

Morphology Analysis Pre- and Post-Calcination.

While calcination achieved organic to inorganic composition transformation, potential volume shrinkage due to heat creates concomitant risk of wire breakage. Thus, we studied wire morphology change before and after heat-treatment. FIGS. 6a-l illustrate morphology transformation of FM and InSn wires after calcination. FIG. 6a illustrates a SEM image of high-aspect ratio pristine FM wires from mold-1. FIG. 6b illustrates a SEM image of calcined FM wires showing continuity preservation. FIG. 6c illustrates atomic force spectroscopy (AFM) height (top) and line (bottom) profiles of pristine and calcined FM wires from mold-1. FIG. 6d illustrates a width and height summary of parent mold-1, pristine FM wires from the mold, and the resulting calcined FM wires. FIG. 6e illustrates a SEM image of defect-free pristine FM wires from mold-2. FIG. 6f illustrates a SEM image of calcined FM wires from mold-2. FIG. 6g illustrates AFM line profiles of pristine and calcined FM wires from mold-2. FIG. 6h illustrates a width and height summary of parent mold-2, pristine FM wires from the mold, and the resulting calcined FM wires. FIG. 6i illustrates a SEM image of defect-free pristine InSn wires from mold-2. FIG. 6j illustrates a SEM image of calcined InSn wires from mold-2. FIG. 6k illustrates AFM line profiles of pristine and calcined InSn wires from mold-2. FIG. 61 illustrates a width and height summary of parent mold-2, pristine InSn wires from the mold, and the resulting calcined InSn wires. FIG. 7a illustrates an AFM image of, and a plot illustrating the height line profile of, pristine FM wires. FIG. 7b illustrates SEM images of pristine and calcined FM wires formed using mold-2. FIG. 7c illustrates SEM images of pristine and calcined InSn wires formed using mold-2. SEM images of pristine FM wires from mold-1 showed hundreds micrometer scale wire continuity with enlarged well-defined shape (FIG. 6a). This sharp-edged shape was confirmed by line profiles obtained with Atomic Force Microscope (AFM). Line profile of pristine wires was in rectangular shape resembling line profile of its parent mold (FIGS. 6c and 7a). However, minor dip existed in the middle of each wire, counting for the height inconsistence between parent mold and the pristine wires (pristine wire height: 531.63±17.94 nm, calcined wire height: 334.43±46.88 nm, FIG. 6d). After heating pristine wires at 600° C. in air for one-hour, minor breakages and defects were observed in the calcined wires (FIG. 6b). Despite the extensive wire height shrinkage caused by heat (37.09%), the wire continuity was preserved (FIG. 6d). We infer that this preservation comes from the self-coordinated internal structure of formed wires. From FIG. 1a, self-regulating assembly of monomers created wires with ordered internal elemental distribution. Instead of being amorphous, pristine wires were presumably crystalline and composed of carbon-carbon sheet (C-C) inserted in-between carbon-metal chess boards (C-M) (FIG. 5c). During calcination, C-C sheets were more accessible to oxygen thus heavily removed by heat, while C-Ms were largely preserved. This asymmetric elemental removal by heat resulted in a severe shrinkage in z direction compared to xy direction, resulting in severer shrinkage of wire height (37.09%) compared to length and width (15.41%).

Continuity was preserved for FM wires made with narrower parent mold (FIGS. 6e-f). Length sustention was more prominent with nanoscale molds, creating nanowires possessing aspect-ratio up to 1000 (with aspect ratio defined as wire length divided by wire width, FIG. 7b). The line profiles of pristine and calcined FM nanowires were in rectangular shapes (FIG. 6g), and evident elimination of dipping top present in FIG. 6c was observed. We infer that decreasing mold channel width resulted in decrease in Reynold's number (Re), where smaller Re in narrower channels prevents turbulent flows. Turbulent flows were possible cause of uneven deposition of monomers near channel wall. InSn nanowires synthesized with mold-2 possessed continuity-preserving and high-aspect-ratio features (FIGS. 6i-j and 7c). However, AFM line profile showed a lager height contraction from InSn nanowires compared to FM nanowires after calcination (FIGS. 6h, 6k-l). This observation agreed with our former hypothesis that internal coordinating structure was different for FM and InSn wires. We infer that felicitous choice of starting materials would achieve compositional and morphological control of D-Met products.

Potential Applications.

Based on above study, we demonstrated various applications for aligned nanowires obtained from D-Met lithography. FIGS. 8a-j illustrate potential applications of D-Met lithography. FIG. 8a illustrates current density curves of pristine and calcined FM wires. FIG. 8b illustrates current density curves for pristine and calcined InSn wires. FIG. 8c illustrates gating behavior of three-terminal devices based on FM wires. FIG. 8d illustrates gating behavior of three-terminal devices based on InSn wires. FIG. 8e is a scheme illustrating application of pristine InSn nanowires as guided mode resonance (In GMR) device (Λ_1D=415 nm, w=150 nm, t≈100 nm). FIG. 8f illustrates transverse electric (TE) transmission measurement and simulation of InSn GMR, with near-field distributions inserted. FIG. 8g illustrates transverse magnetic (TM) transmission measurement and simulation of InSn GMR, with near-field distributions inserted. FIG. 8h is a scheme illustrating fabrication of chessboard patterns with 2-time D-Met. FIG. 8i is a SEM image of a product from the fabrication method shown in FIG. 8h. FIG. 8j is a SEM image illustrating a varying-period pattern obtained by D-Met when the mold is truncated to create mixed spacing. FIG. 9a is a photograph of a parent mold under sunlight. FIG. 9b is a photograph of D-Meted wires under sunlight. FIG. 9c is a green laser diffraction pattern of the parent mold shown in FIG. 9a. FIG. 9d is a green laser diffraction pattern of the D-Meted wires shown in FIG. 9b. FIG. 9e illustrates refractive index n and extinction coefficient k of InSn pristine nanowires. FIG. 9f is a scheme illustrating conductivity measurement, showing two gold needle electrodes attached on D-Met wires located on a silicon wafer under a microscope, and acquisition of a current-voltage diagram to determine the conductivity of the material. FIGS. 9a-b illustrate the similar appearance of the parent mold and the D-Meted wires under sunlight.

Towards conductivity, I/A-V curve of pristine FM wires was a horizontal line with calculated conductivity equaled to 1.7 Ω·m for V>0 (demoted as +R) and 2.49 Ω·m for V<0 (denoted as −R). After calcination, the +R remained similar value of 1.02 Ω·m. However, −R was reduced by an order of magnitude to 4.56×10⁻² Ω·m (FIG. 8a). Similar conductivity enhancement was observed from pristine to calcined InSn wires (pristine: −R=4.48×10⁻² Ω·m, calcined: −R=2.22×10⁻² Ω·m) (FIG. 8b). Rectified I-V curses indicated asymmetric elemental arrangement inside the wires, with potential to be applied as diodes. Optically, same ordering endowed the parent mold and structured wires similar appearance and diffraction patterns (FIGS. 9a-d). Apart from apparent optical phenomenon, refractive index of pristine InSn wires from mold-2 was larger than glass and air in 400-500 nm range (FIG. 9e). We infer nanowires form D-Met could be applied as Guided-Mode Resonance devices (GMR) when deposited on glass substrate (FIG. 8c). Under the illumination of Incident plane waves with their electric field polarized parallel (TE) or perpendicular (TM) to the grating bars, the resonance of transmittance was found to follow the guide-mode resonance line-shape at λ_TE=580 nm and λ_TM=500 nm, respectively (FIGS. 8d-e). The TM mode resonance phenomenon can result in nearly five order magnitude higher electric field compared to the incidence (FIG. 8e, inserted). D-Met process also showed versatility in fabricating complex patterns. By applying D-Met process two times in perpendicular directions (FIG. 8f), a chessboard structure was composed with crossing FM nanowires (FIG. 8g). Patterns with doubled aligning period was also fabricated by dissolving FM nanoarray partially (FIG. 8h).

Conclusions.

In conclusion, we demonstrated an autonomous lithography method by Directing Metal/ligand reaction with mold (D-Met). Sharp-edged wires were aligned directly on substrate by controlling evaporation direction and physical properties of activation agents. By calcination, the multi-component organometallic pristine wires were transformed into mixed-oxide product, with continuity preserved despite severe volume shrinkage caused by heat. Obtained wire alignment showed unique conductivity and could be directly applied as optical devices. We infer that by coupling fluidic dynamics of capillary structures with metastability of undercooled liquid metal particles, D-Met can be a powerful autonomous lithography method for the fabrication of next generation electronic and optical devices.

Example 2. Hypothetical. Proposal for Computing Structures and Related Devices that Include Wires Formed by the Method of the Present Invention

The overall goal of this proposal is to design computing structures and related devices based on new materials, structures, physics, and deposition methods for microelectronics. Specifically, we aim to; i) Enable continued growth in microelectronics, by deploying autonomous self-assembly processes, ii) introduce atom-by-atom assembly with concomitant organization/patterning as a one-step synthesis, deposition, and fabrication method, iii) Advance predicted progress in computation devices into the atomic and functional interfaces regime via energy efficient processes, iv) introduce new paradigms based on few atom components for edge-computing and data classification or scaling, v) develop sensors and computing structures for edge-computing based on self-assembly, and, vi) by shortening the distance over which a ‘function/process’ is executed, reduce computation time and energy need per processing event. To achieve this, we seek to design and direct synthesis and self-assembly of novel graphene-covered hetero-structures into new devices and sensors. By design, these hetero-structures incorporate compositional gradients, hence are inherently asymmetric charge carriers. Our one-step fabrication method is based on the untapped ad infinitum self-assembly of metal oxides synthons, where single metal atoms are captured by a ligand, ferried to a capillary-defined nucleation zone, then grown to desired dimensions. These organometallic adducts are then partially reduced to create a semiconductor crystal (metal center) enveloped by graphitic carbon (from the ligand). By coupling composition and interface asymmetry, new functional components will be realized. Asymmetry in electron density across the graphene-semiconductor interfaces, a Schottky-type interface, can be perturbed by an applied field. The structures are therefore ideal for fabrication of gates, capacitors or memory, all essential components in computing.

Exploiting autonomous self-assembly processes (ligand assisted atom-by-atom assembly) lowers the energy cost in the fabrication, while increasing the resolution of the deposited components. Based on envisioned computation architecture/structures, requisite devices will be designed in silico followed by their translation to synthesis, self-assembly and patterning. The ability to pre-organize synthons via a Templated Reactive Media Assisted Deposition (TRe-MAD), followed by transformation to desired graphene-covered hetero-structures necessitate an integrated team of material scientist, chemists, physicists, fluid dynamics and self-assembly experts, device/circuit experts, and computation structure experts. By coupling materials chemistry, physics, device fabrication, materials characterization, and systems architecture, we will accelerate development of ‘beyond CMOS’ devices.

Background Metal-oxide semiconductor field-effect transistors (MOSFET) have long been the basis of computational component architecture. As complementary metal-oxide-semiconductors (CMOS), transistors get hyper scaled-for example IBM recently reporting a 2 nm device, Moore's law transitions to ‘more's law’ in that the fabrication of these hyper-scaled devices requires more energy, more tools/metrology, more resources, more cycle-time, and are more costly. Unfortunately, computational power is also on a steady rise, with a projected limit likely to occur in 2035, when advances in computing will be limited by power supply. Interestingly, scaling (Moore's law) beyond 90 nm does not provide continued gains in energy efficiency. It is therefore critical that new ultra-energy efficient devices be realized from energy efficient processes. Given the proliferation of CMOS, the new types of devices should be readily integrated with existing technologies for them to have near-term use and/or adoption.

Moore's law has for the last five decades, seen number of transistors per chip double every two years (a total of 24 times). Under the current limit, scaling will only enable up to three more doubling events hence new approaches to device fabrication and/or new types of devices are needed for continued growth. With hyper-scaled devices, computation is consuming significant amount of globally generated power, hence new ultra-energy efficient devices/platforms are needed. With these new devices, new computation paradigms must be simultaneously developed.

A Jakob's ladder view of the challenge(s) in microelectronics has been proposed, revealing opportunities of non-scaling-based approaches to microelectronic advances beyond Moore's (and more's) law. Adopting chemical or biological time scales as computation tools, either as systems-on-chip, system-in-package, or a hybrid, almost doubles chip densification relative to Moore's law. Alternatively, functional interfaces and atomic level component differentiation can lead to >3× the current chip density. Atomic level precision and differentiation in device fabrication is, therefore, likely to transform microelectronics with concomitant change in energy demands given the short distance charge is carried per computing event. Combining functional interfaces and atomic level component fabrication, however, can lead to enhanced device density in a previously unconceived way. A major caveat in this approach is lack of manufacturing capabilities with atomic precision while concomitantly installing functional interfaces at this scale. Atomically precise manufacturing, however, has the potential to increase energy efficiency in semiconductor materials. Precision, however, is considered alongside cost, process intensity and throughput for such a method to be adopted. Computational devices call for minimization of physical size and increased precision for energy efficiency and lower computation time. The Institute of Electrical and Electronic Engineers (IEEE) International Roadmap of Devices and Systems (IRDS) highlights emerging devices and technologies beyond the CMOS era. Among these 1D carbon-based/nanowire-based FET, 2D materials-based devices, and tunneling field-effect transistors (TFET) stand out. The tunneling, rather than thermionic, based TFET had been postulated for >60 years before band-to-band tunneling had been demonstrated, but scale-up has been hampered by need for atomic level precision in defining the tunneling barrier. Carbon nanotubes and graphene on the other hand can have varying properties ranging from metallic to semiconductor. Graphene was the first described 2D channel FET, but its lack of a bandgap limits its use in digital components. The lack of a bandgap, however, makes graphene suitable for analog applications, hence edge-computing. Despite the lack of a bandgap, bilayer graphene forms the basis of the proposed ‘beyond CMOS’ energy efficient Bilayer pseudoSpin Field-Effect Transistor (BiSFET). Despite these shortcomings, BiSFETs capture the potential of graphene in the future of microelectronics. Graphene has, however, not found widespread use in sensors, microelectronics, or computing devices largely due to the above challenges coupled with; (a) inability to reproducibly synthesize high quality (defect free) materials; (b) poor incorporation into functional device; and (c) ability to tune properties.

Graphene is uniquely appealing since hydrocarbons can be pre-organized on a semiconductor synthon, then reduced with concomitant transformation of the synthon to requisite semiconductor. Recently, we demonstrated that graphene-semiconductor hetero-structures enable bandgap tuning in semiconductors. Graphene heterostructures may, therefore, provide a framework to address challenges above. We, therefore, infer that graphene heterostructures could lead to the next generation of ultra-energy-efficient electronic devices.

Given the potential of atomic level precision, 1D/2D materials and functional interfaces, we hypothesize that placing graphene on oxide surfaces would induce a large surface dipole leading to induced gap states and band bending. These induced gap states render the interface functional, and when coupled with atomic level control of the metal centers on the oxide, a cascading bandgap structure can be established leading to integration of active and inactive components that are chemically bonded. Tuning the assembly process allows for functional components to be concomitantly realized.

One goal is to demonstrate new methods to fabricate ‘beyond CMOS’ components, using self-assembly and chemical synthesis to achieve atomic level precision in organization, followed by intercalation of a 2D material on the semiconductor. The compositional combinatorial space is large and unexplored. Thus, our intent is to use an exemplar (diode and gate) that has the desired properties based on metal oxide compositional gradient, hence a cascading bandgap across three dissimilar oxides, and the surface graphene.

The three main objectives of this Example: i) To develop a method of synthesizing and organizing graphene heterostructures and associated ohmic interconnects, ii) translation of the synthesized and organized materials into functional sensors and onboard computation devices, iii) translation of these devices into a functional computation architecture and structure amenable to edge-computing, data classifiers, or data filtering platform. The objectives will be accomplished via three broad tasks as detailed below.

Specific Aim I: Synthesis and Organization of Graphene/Oxide Heterostructures.

The overall goal of this specific aim is to; i) develop a method to assemble, atom-by-atom, chelated metal centers into 1D wires with a built in compositional gradient presaged by autonomous composition speciation and organization of precursor passivation oxide, ii) direct self-assembly of these 1D wires through coordination center geometry, fluid dynamics, and geometric confinement in nanochannels in a manner that can enable device and sensor fabrication (aim II) and edge-computing (aim III), iii) conversion of the assembled organometallic synthons into metal oxides with concomitant reduction of ligands into oxide-crystal templated graphene to generate GMO heterostructure. This aim will be achieved via four specific tasks. First is atom-by-atom synthesis of 1D wires by felicitous choice of metal-ligand pairs. We propose a method to pre-organize metallic elements as speciated passivating oxides, followed by their in situ assembly into a compositional gradient on a 1D adduct. Directed growth into 3D components is attained via coordination geometry and kinetics. Ligand ablation into graphene coats the semiconductors with bandgap tuning, hence carrier mobility. This property forms the basis for their translation into functional microelectronic devices (specific aims II and III).

Task 1.1: Atom-by-Atom synthesis: Borrowing from block polymer synthesis methodology, we hypothesize that analogous inorganic coordination adducts can be realized if, i) an infinite metal ion reservoir is present, and ii) where the metal ions are pre-organized on the reservoir, then a layer-by-layer release (etch) of the metal ions would lead to a similar organization in the resulting organometallic adducts. To establish steady state kinetics, and therefore ad infinitum growth while promoting self-assembly and precipitation, a solvent in which adducts are partially miscible is employed. This allows us to maintain a saturated, albeit low concentration, solution where continuous growth occurs akin to hydrocarbon polymerization. This method will be validated with ternary alloys, Galinstan (GaInSn) and Field's metal (BiInSn). Given the role surface compositional plasticity may play in regeneration of the passivating oxide, the latter will be evaluated both in liquid and solid states. Galinstan′ surface is dominated by Ga and when etched with a carboxylic acid will give synthons for the high band gap (4.7 ev) Ga₂O₃. Surface reconstruction of the thin passivating oxide (ca. 5 nm—Cabrera-Mott oxidation regime) on the metal ion reservoir (particle) ensures that only Ga ions are available in solution unless in case of significant depletion where Sn and In begin to etch and incorporate into the precipitated material. Lack of surface plasticity in solid BiInSn, however, implies that the dominant In etches followed by Sn and finally Bi. Asymmetry in etch rates, however, implies that transition zones, akin to statistical co-polymer, will herald the one-component zones enabling smooth structural transition and creating a Guggenheim-type interface between dissimilar oxide blocks. Upon conversion of these synthons to graphene coated metal oxides, this compositional gradation will lead to asymmetry in charge transport, hence diode like behavior. Give the perturbation of oxide band structure by graphene, we hypothesize that this asymmetry can be gated leading to a transistor. By maintaining a thin passivating oxide shell, we control the size of each oxide block and therefore attain kinetics defined atom-by-atom assembly. We will optimize this layer-by-layer mild etch for optimized assembly of the 1D components and their concomitant translation to diodes and transistors. Given the success in our preliminary work with acetic acid, we will first optimize synthesis with acetic (2 carbons) and formic (1 carbon) acids. Inter-digitation of the acetate carbons implies that one to three layers of graphene can form on the surface of the oxides while in formic acid only a single layer is expected. The quality and thickness of the graphene layer will be investigated as described below.

Task 1.2: Material Characterization: To ensure quality of the deposited materials, continuous multi-pronged material characterization will be adopted at each stage of the synthesis. The characterization will range from structural, atomic arrangement, optical, chemical, and coupled with in silico tools or predictions.

Task 1.2.1 Chemical Characterization: Besides use of standard analytical techniques such as FT-IR, UV-vis, and x-ray methods, we will develop solid-state NMR spectroscopy methods to; (i) determine the crystal structures of powdered coordination polymer precursors, and (ii) show that pyrolysis results in formation of semiconducting metal oxides that are in molecular contact with graphitic carbon. Rossini is an expert in studying the structure of solid materials with exotic and unconventional NMR active nuclei. Thuo and Rossini have previously used ⁷¹Ga and ¹³C SSNMR spectroscopy to determine the three dimensional molecular structures of gallium-based coordination polymers produced by etching eutectic GaIn in acidic solutions. SSNMR is invaluable for characterization of these precursor materials because, in the macroscale (see preliminary work), they are often obtained as fine powders that may have some structural disorder/defects (e.g., incorporation of solvent) and are hence challenging to characterize by single-crystal or powder X-ray diffraction. Dynamic nuclear polarization (DNP) enhanced ¹³C and room temperature ⁷¹Ga SSNMR was used to study pyrolyzed Ga coordination polymers. Crucially, these SSNMR experiments demonstrated that pyrolysis leads to the formation of semiconducting gallium oxide that is inter-mixed with graphitic carbon. Our preliminary data clearly demonstrates the value of SSNMR spectroscopy to elucidate the organization of inorganic and organic components.

With regards to (i) we propose to develop “NMR crystallography” protocols that can be used for crystal structure determination of the powdered coordination polymer precursors by combining solid-state NMR spectroscopy, powder X-ray diffraction and planewave DFT calculation. First, SSNMR spectra of ¹H, ¹³C and the metal center (e.g., ²⁷Al, ⁷¹Ga, ¹¹⁹Sn, ¹⁹Sn, ²⁰⁹Bi, etc.) are used to determine number of each type of atom within the asymmetric unit and to gain insight into the symmetry at the metal nucleus. Second, analysis of PXRD data can then be used to determine the unit cell, and the Free Objects for Crystallography (FOX) program can be used to optimize the position of heavy metal atoms and ligand atoms (O, C) within the unit cell. Finally, the structures derived from FOX can be subjected to plane-wave DFT calculations to ensure that they are energetically stable. DFT is also used to calculate NMR parameters for the structures, and comparison to the experimental NMR parameters provides a final validation of the determined structures.

With regards to (ii), SSNMR of the metal nucleus will be used to confirm the conversion of the coordination polymer to an oxide upon pyrolysis. ¹H and ¹³C chemical shifts can be used to confirm the conversion of organic ligands to graphitic carbon. By using DNP, we can enhance SSNMR sensitivity and allow more advanced 2D ¹³C[X] dipolar dephasing experiments, with X=²⁷Al, ⁷¹Ga, etc. These experiments will be used to directly prove that the graphitic carbon is molecularly mixed with the metal oxides. Alternatively, if DNP enhancements are insufficient, ¹³C ligand precursors are readily available and affordable thus could be used to obtain ¹³C labelled materials amenable to conventional, room temperature SSNMR analysis. Overall, the SSNMR experiments will allow us to obtain a complete molecular picture of the coordination polymer precursors and monitor their conversion to semiconducting oxides with graphitic carbon intrusions.

Task 1.2.2Microscopy: Electron beam techniques, including scanning electron microscopy (SEM) and transmission electron beam microscopy (TEM), play a critical role in understanding materials due to their unique capabilities to directly probe structure information down to the atomic level. In this project we will apply multiscale multi-model electron beam microscopy techniques to investigate the correlation between synthesis condition, material structure, and device performance. For example, we will use SEM to explore the overall assembly, chemical distribution, crystallinity/faceting and void defects after calcination and sintering.

A key factor that controls the device performance is the graphene heterostructure's interface structure and charge transfer. High-resolution high-angle-annular-dark-field (HAADF) scanning transmission electron microscopy (STEM) imaging and Geometric Phase Analysis (GPA) can directly map atom arrangement and strain distribution in the vicinity of the interface, while off-axis electron holography is a unique advanced TEM method to measure interfacial charge distribution from the phase shift of the electron beam. In our previous work, we have successfully studied the structure and strain distribution across Li_0.33La_0.56TiO₃/Li₂TiO₃ interface, where periodic misfit dislocations are clearly revealed. We also identified a two-dimensional electron gas (2DEG) at the AlInN/AlN/GaN interface using off-axis electron holography. Moreover, we will perform spatially resolved bandgap mapping of the oxides using STEM electron energy loss spectroscopy (EELS). The result will be correlated to local structural and chemical information. Our comprehensive structural study will provide critical information for the material synthesis optimization and theoretical prediction of properties/performance.

Task 1.2.3 Local Electronic Structure and Charge Transport: Macroscale charge transport characteristics will be studied using a conducting probe atomic force microscope (AFM) and a four-point probe station. To bridge the gap between these global properties and theoretically predicted behavior for defined, model structures and their correlation with STEM experiments, we will employ local characterization based on advanced scanning tunneling microscopy/spectroscopy (STM/S). For single probe STM/S work we will grow the graphene heterostructures on well-defined metallic substrates (Au, Cu) and use ultra-high vacuum (UHV) low-temperature (LT) STM. Well-defined conditions and cryogenic temperatures ensure high stability required for atomic-scale (sub-Angstrom) lateral resolution in imaging and spectroscopy. That will allow us to determine electronic and structural properties related to single building blocks within locally ordered (quasi-crystalline) 1D wires or 2D sheets of metal oxides. The expected outcome of this work will be to systematically determine influence of nanocrystal-graphene interface type (none, single, bilayer or tri-layer graphene, etc) as well as metal atom type on the local electronic structure (i.e., overall band-gap, relative conduction and valance band locations).

Further understanding of charge transport across 1D wires or 2D sheets of the assembled materials, or their surfaces, will be investigated using UHV multi-probe STM (MP-STM). In this case the graphene heterostructures will be grown on technologically relevant insulating substrates, i.e., SiO₂, Al₂O₃, to closely reproduce conditions present in prototypic devices studied under Aim II. Due to lack of interconnects fabrication step, techniques based on MP-STM allow non-invasive, in-situ determination of charge transport from mesoscale down to atomic-level. In classical 2- and 4-probe methods, STM tips are navigated by scanning electron microscope or high-resolution optical microscope typically in micrometer scales down to hundreds of nanometers. These mesoscopic MP-STM protocols have been downscaled by developing methodology for 2-probe STM/S with the atomic level of precision. In this case current source and drain probes are positioned in atomically defined locations with respect to the characterized nanosystems. These MP-STM experiments rely on fully STM-based tip positioning with probe-to-probe separation distances reaching tens of nm. Such probe-to-probe lateral positioning precision is combined with pm vertical sensitivity in establishing probe-to-system contacts. These two factors enable realization of two-probe scanning tunneling spectroscopy (2P-STS) experiments, where transport properties can be characterized by macroscopic probes kept in well-defined conditions ranging from purely tunneling to defined Ohmic contact regimes. In this case, energy-dependent two-probe STS conductance measurements can be realized. Here, we plan to apply both mesoscale 4-probe technique as well as local 2P-STS to determine electronic transport properties of heterostructure beams and single crystallite nanowires, respectively. In both length scale regimes, we aim to determine the relation between structure/composition to the local conductivity of graphene-metal-oxide heterostructures. Moreover, multi-probe STM setup could be further used to test hypothetical device geometries before incorporation of externally fabricated interconnects, thus bridging our fundamental STM-based characterization with the exact device architectures proposed under Aim II.

Characterization of the transport properties with MP-STM will be studied with unique LT-MP-STM.

Task 1.2.4 Electronic and Electromagnetic Property from Theoretical Predictions: In parallel, numerical prediction of electronic properties will be investigated to inform the design of these graphene heterostructures. The proposed technique will enable the fabrication of nanoscale (quasi-)two-dimension (sheets, ribbons) and (quasi-)one-dimensional (nanowire, nanorods) graphene heterostructures in contact with dielectric oxide cores and also dielectric substrates. In order to predict the electromagnetic behavior of these structures and of nanoscale, spatially pattered device building block thereof, we need to understand their optical properties (at about THz frequencies). The electromagnetic properties of graphene are practically completely determined in terms of its surface plasmon-polaritons, which are essentially charge-density waves, i.e., hybrid dressed states between delocalized electronic states and photons of the surrounding electromagnetic field, brought about by the coulomb interaction between the electrons and the resulting electrostatic screening. Nanoscale graphene structures can have operating frequencies easily reaching THz frequencies while still being small enough to have essentially quasi-static (deeply subwavelength) electromagnetic interactions similar to a conventional electronic circuit. To be able to understand and predict possible device functionalities we need to obtain and understand the complex optical sheet conductivity of our graphene structures.

Normally, for large scale, flat graphene sheets, this optical conductivity can be derived from a Kubo formalism knowing the electronic band structure and coulomb screening in RPA approximation, like the one below (Equation 4).

$\begin{array}{cc}\sigma \left(\omega \right)=\frac{e^2{E}_F}{{\mathrm{\pi \hslash }}^2}\frac{i}{\omega +i{\tau }^{-1}}+\frac{e^2}{4\hslash }\left(\theta \left(\mathrm{\hslash \omega }-2E_F\right)+\frac{i}{\pi }\log ❘\frac{\mathrm{\hslash \omega }-2E_F}{\mathrm{\hslash \omega }+2E_F}❘\right)& 4\end{array}$

The strong dependence of the conductivity on the Fermi energy, E_F, both in its reactive and dissipative part is responsible for the unique tunability of the electromagnetic/plasmonic properties of graphene. Note that the optical conductivity is normally Drude-like from the intra-band electron population with significant Lorentz-like inter-band contributions at higher frequencies, the latter allowing the occurrence of either (regular) TM plasmons or unconventional TE plasmons, between which we can transition by changing biasing E_F, hence enabling switching for the plasmonic states in the graphene heterostructures. The picture becomes much less clear for realistic experimental graphene with defects and on substrates. Electronic interaction with the substrates strongly influences E_F and controls the charge carrier concentration in the conduction band. Charge-neutral graphene in vacuum would have E_F right at the Dirac point of its electronic band structure and almost no conductivity; to be useful for electric devices we need substantial shift of the E_F by several hundred meV due to substrate interactions and doping from defects. This is hard to obtain with any precision from theory and usually must be determined experimentally by optical scattering experiments from either graphene sheets or surfaces with pattered graphene heterostructures via electromagnetic models. Similar problems need to be overcome with respect to the scattering lifetime of the plasmons. This depends on many factors, including scattering of defects and substrate phonons hence must be determined experimentally.

We intend to use modulation of the graphene properties due to the controlled chemical gradient in the grown nanostructures for functionality, e.g., spatially changing band structure and E_F gradient in the nanowires to create diodes, i.e., nonreciprocal current flow devices that can be used for switching or field-effect transistor like graphene channels where the conduction can be controlled by the plasmonic near field of a second, control nanowire. The proper action of these devices will require detailed knowledge and control of the electronic and plasmonic properties over a wide range of parameters. For instance, for the switching element of a FET we locally need a low optical conductance with low reactance (for switching speed) that can be strongly modulated by the near filed of the plasmon in a control wire (gate), while for the coupling between active sites we need a highly metallic graphene nanowire with low dissipation and high tolerance of its plasmonic band structure against fringe fields.

While the proposed technique will open the door to the fabrication of nanostructured graphene patterns for potential electronic devices, the very reduction to (quasi-) one-dimensional structures raises additional problems for understanding the electromagnetic properties of the graphene structure. Finite size effect will occur, both in the electronic band structure of graphene but also in the dispersion of the plasmons and hence the optical conductivity due to the dominant electromagnetic fringe fields.

We will develop theory and numerical simulations based on actual device geometry to understand and quantify these effects. This should enable us to give predictive guidance for the device design and operational parameters. To understand the optical properties of the fundamental building blocks of our approach, we will develop numerical models for the optical/THz scattering from large scale arrays of graphene/core nanowires, which will allow direct experimental determination of the graphene optical conductivity independent of substrate, oxide core, and chemical gradient in the nanostructures. For simulations of the electromagnetic response of arbitrary graphene heterostructures we have FEM simulations tools like COMSOL, but also quasi-analytic scattering and transfer matrix codes in frequency domain. To characterize dynamic response, inclusive of ultrashort optical pumping/control, we also have specific FDTD codes.

Finally, most graphene-based structures have direct bandages of Dirac cones which make them amenable for ultrafast, optically induced charge carriers (and hence modulation of the optical conductivity) by external or potentially endogenous photons. This constitutes another potential control mechanism which we will explore.

Task 1.3: Evaporation driven Assembly: Considering each chelated metal ion as a ‘nanoparticle carrier’ of atomic precursor to the synthon; we infer that the fluidic media can be engineered to drive, and tune, the organization of such adducts. When fluid characteristics are coupled with on-going chemistry in a confined geometry, structure of the deposited material can be engineered into a shape of uniform profile (2D wire) of width determined by evaporation geometry. This will be optimized in silico and results used to inform choice of the reaction media and vessel/channel as discussed here.

Consider a rectangular channel of length L in the x direction and height H in the y direction where H/L<<1. The liquid-solvent metal-particle mixture that initially fills the channel may be considered a thin film with total height h in this limit. The solvent-metal mixture fills the channel with local solvent mass-fraction (mass/mass) denoted #, and local metal-particle mass fraction denoted ϕ_m=1−ϕ_s. The particles are denser than the liquid, and under non-colloidal conditions they can settle in the channel forming a stratified layer of liquid solvent on top of mostly metal beside the liquid that fills the metal particle's porous regions. Taylor dispersion can also contribute to spatial variations in metal-particle mass fraction in the initial profile where the initial particle layer forms due to channel filling caused by capillary forces.

The vapor-liquid interface profile for a liquid that fills a rectangular channel has a shape similar to that of the channel. Thus the profile along z, the 3^rd direction, is nearly uniform besides wetting of the liquid at the 3 phase contact line; therefore, we hypothesize that the liquid in the channel can be treated as a 2 dimensional thin-film, and assume that the constituent local-mass fractions vary with time and space according to ϕ_s=ϕ_s(x, t) and ϕ_m=ϕ_m(x, t). The liquid solvent-layer profile maintains a shape similar to a composite Heaviside function H(x)−H(x−L) for 0≤x≤L during evaporation, but with a magnitude that decreases with time as mass is transported from the liquid to vapor. Here we assume the rate of change for the interface varies with time according to β(t)=β₀−β₁(t), where constant β₀ is the liquid initial height at time t=0. We now write the interface profile as h(x, t)=β(t)[H(x)−H(x−L)] for 0≤x≤L and t≥0. In the absence of Marangoni flow the interface shear stress is zero i.e. ∂u/∂y=−∂v/∂x where these derivatives are evaluated at the vapor-liquid interface y=h(t); and the interface profile evolves according to v=∂h/∂t+J/ρ. Here J=Dn·∇c is the flux of solvent into the vapor phase where n·∇c is computed at the gas-liquid interface y=h(t) with outward point normal n=∇(y−h(x, t))/|∇(y−h(x, t))| and D denotes the solvent-vapor diffusivity, where c(x, y) is the concentration (mass/volume) of solvent in the vapor-phase. We would normally need to only find solutions for the concentration profile by solving a Laplacian equation ∇²c=0 to estimate this velocity magnitude. But we can estimate the concentration at y=h(t) if we consider the combination of Raoult's law for the solvent-vapor concentration above the liquid as a function of liquid phase solvent concentration, and Dalton's law for the solvent-vapor pressure as a function of the total pressure. Combining these laws results in an expression for solvent concentration at the interface c(x, y=h(t))=ρP_vapx_s(ϕ_s)/P where x_s(ϕ_s) is the solvent liquid phase mol fraction that is related to the liquid phase mass fraction via x_s=ϕ_s/[[1−ϕ_s](MW_s/MW_m)+ϕ_s] where ϕ_s is the liquid phase solvent mass fraction, and P_vap is the solvent equilibrium vapor pressure. MW_s and MW_m denote the solvent and metal adduct molecular weights.

Preliminary data using micro- to nano-channels demonstrate the arguments made above. Extension of this approach to single digit nanometer channels will be explored as well as translation beyond the two-layered systems demonstrated here. Comparison of quality of assembly in open channels under different environments will be explored as well as effect of mass of the single metal center adducts on assembly kinetics at the nanometer scale. The self-assembly process will be optimized to minimize volumetric changes upon conversion of the synthons to GMO heterostructures. Preliminary data indicates minimal changes in the shape, hence our inference that enhancing interdigitation of the ligands (tighter assembly) may mitigate volumetric changes, especially in nanostructures.

Task 1.4: Diversifying the metal centers and ligand structures: Given the performance of the products from task 1.1, and associated in silico predictions from task 1.2.3, other metal combinations will be investigated based on their potential to stage a graded/cascading band gap structure. Combinations of p-block metals and metalloids (e.g., Sb, Ge and Te) in combination with transition metals of similar valences will be explored. Similarly, ligand structure will be varied from the C₂ demonstrated in the preliminary work to span the C₀-C₈ range. Special attention will be given to odd-even chain parity (symmetry) as it may influence packing, hence quality of the interfacial graphene layer(s). Introduction of amides, in lieu of carboxylic acids will be explored to synthesize metal oxide/metal nitride hybrid structures.

Specific Aim II: Design. Fabrication. And Integration of GMO Nanowire-Based Devices for Sensing and Logic Computing.

Based on our preliminary data, essential components based on this new material will be designed, fabricated, and characterized to realize high-performance, low-power, and lightweight sensors and edge computing systems. The essential components include GMO nanowire-based transistors, diodes, capacitors, and resistors, which can be fabricated using the bottom-up approach. A variety of sensors, such as chemical and biological sensors, thermal sensors, optical sensors, and vibration sensors, will be developed using these components. Moreover, the on-chip data processing capacity will be built next to the sensors using the monolithic integration. The advanced machine-learning algorithms can be implemented using the proposed edge-computing architecture to analyze the sensor outputs locally. The integration of sensors and data-processing units on the same chip would significantly reduce energy consumption by eliminating power loss and energy consumed by data transmission.

Here, we propose developing and implementing high-integrity devices, fabrication processes, and architecture that allow sensors and integrated circuits to operate reliably and efficiently. A major challenge to realizing this goal is the ability to organize components developed in task 1.1, as informed by task 3 and task 1.2.3, using self-assembly and methods developed in task 1.3. The design goals therefore include: (1) Design, fabricate and characterize high-performance transistors, diode, capacitors, and resistors using the bottom-up approach on rigid and flexible substrates. The objective is to lay the device foundations for the fully integrated IoT and edge computing system. (2) Design, fabricate, and characterize multiple sensor components based on the GMO nanowire transistors. The objective is to build high-performance sensors that can generate multi-dimensional data to be processed using the edge-computing engine. (3) Design, fabricate, and verify logic gates for machine-learning processing engines to analyze sensor data. The objective is to design and test the basic building blocks that would run machine-learning algorithms of use in demanding IoT tasks.

Task 2.1 Connection of Material to Devices:

Heterojunction transistors: The bottom-up synthesized nanowire materials offer well-controlled size and bandgap that is beyond silicon and current lithography approach. Since the bandgap can be controlled, we will adopt the nanowire heterostructures to avoid doping, reduce scattering, and achieve a higher carrier mobility. Here, the GMO nanowires will be deposited on an insulator substrate such as a flexible plastic substrate or a SiO₂ surface. The top gate oxide layer will be applied by in-situ synthesis of high-x dielectrics (HfO₂ or ZrO₂) thin film. Out of the gate region, the organic moieties will be reduced to locally deposit graphene for the source and drain regions. Metal electrode will be fabricated through DUV/EUV lithography to complete the field effect transistor structure. Detailed carrier transport studies will be carried out to characterize the fabricated heterojunction transistors. The I-V_ds curves and transconductance g_m=dI/dV_g will be studied for transistors with different bandgaps, gate lengths, and nanowire diameters. The successful demonstration of the GMO nanowire transistors will serve as the building block for the following tasks.

Capacitors: In addition to transistors, capacitors are also indispensable elements for integrated circuits and power management circuitry. We aim to develop high-performance metal-oxide-GMO nanowires capacitors. The nanowires and gate metals will serve as the electrodes, which are separated by the high-x dielectric material. IBM developed MOS capacitors with silicon trench structures with a capacitance density of 120 nF/mm² for their 90 nm and 65 nm technology nodes. Here, we will use the array of GMO nanowires to fabricate high density and low loss MOS capacitors without using expensive dry etching processes. The array of nanowires with different periods, duty cycles, and wire diameters will be tested by measuring the C-V characteristics.

Task 2.2 GMO nanowire sensors: biosensor, optical sensor, IR sensor, strain gauge: Based on the heterojunction transistors developed in the previous task, we will explore the application of these transistors for sensing applications. Later on, the sensors can be incorporated with the logic circuits on the same substrate. A universal process will be adopted to design and fabricate the GMO nanowire FET sensors. We will focus on the development of three types of sensors: biosensors, infrared sensors, and vibration sensors. The signal transducer will be incorporated into the gate region. The change of gate potential will be measured by the change of source-drain current (I_ds).

To date, nanowire FET sensors have been demonstrated for high sensitivity and label-free detection of biomaterials, such as DNAs, proteins, and small compounds. The nanowire FET-based biosensors offer several significant advantages, including low sensor cost, reduced footprint, low sample volume, and multiplexed detection. Here, we will take advantage of flexibility and improved performance of the GMO heterojunction transistors to develop lab-on-a-chip biosensors. To detect analyte(s), the surface of the gate dielectric layer will be functionalized using a bio-recognition coating. Depending on the type of analyte, the bio-recognition materials, such as antibodies, single-strand DNA probe, molecular imprinted polymers, will be utilized. To demonstrate the sensing performance, the fabricated sensor will be used to for COVID tests. We will apply the GMO nanowire sensor to quantify IgG and IgM concentrations in bloods samples, SARS-COVID-2 virus in nasal swaps or saliva samples, and the specific RNA sequences carried by the virus. The results will be compared to existing lateral flow and quantitative PCR tests.

In addition to the biosensor, the heterojunction transistors will also be explored as a thermal sensor and vibration sensor. To detect infrared radiation, the gate oxide/metal coating will be replaced by a pyroelectric material, such as LiTaO₃, AlN, and polyvinyl fluorides, and an IR absorber. Illuminated by IR light, the pyroelectric material will be polarized to change the gate potential and result in a change to the source-drain current. In contrast to the existing pyroelectric sensors, the integration of pyroelectric material to the gate of GMO nanowire can improve the sensor sensitive and reduce device footprint. Since the nanowires are highly sensitive to the strain induced by the surrounding environment, we will test the array of nanowire devices for their piezoresistive signature. We will compliment this work with advanced TEM techniques proposed in task 1.1.2 to map out strain distribution inside the nanowires. The gage factor to the change of nanowire resistance due to axial and lateral strained will be measured.

Task 2.3 GMO nanowire circuits for edge computing. The objective of this task is to design and fabricate GMO nanowire-based logic gates. These logic gates will be the building blocks of the edge computing engines to run machine-learning algorithms, such as the support vector machines classifier. Based on the transistor, we will further develop the logic gate to build the support vector machines classifier. To date, silicon nanowire NOT gate has been demonstrated with the operating speed of 1 MHz. The heterojunction GMO nanowires would offer a high operation speed. Based on the GMO nanowire transistor developed in task 2.1, we will construct high performance logic gates, including NOT, NOR, and NAND gates. These gates can be fabricated on flexible and rigid substrate along with the sensors. To construct these logic gates, metal contacts will be patterned along the nanowires. The dynamic operations of the logic gates will be characterized using a digital oscilloscope.

Specific Aim III: Computing Structures.

The proposed self-assembled, unidirectional current flow devices are a good candidate building block for edge computing devices that integrate sensors, machine learning engine for sensor data streams, and nonvolatile storage to keep the edge node state and computing parameters. Given the natural lower energy needs of the proposed devices, such an edge node is likely to be highly energy efficient. The sensor data streams need not travel from the edge to the backbone or the server farms. Inclusion of nonvolatile memory also makes intermittent harvested energy source, battery-less computing feasible. Challenges related to the development of such an energy-efficient, self-contained, edge node are: (1) Logic synthesis for logic gates built with unidirectional control flow devices, (2) Machine learning engine design, (3) Sensor design, (4) Non-volatile memory design, (5) fault tolerant architectures to tolerate native statistical faults induced by self-assembly, (6) Hybrid system level simulation. Topics (3) and (4) are being addressed via design in specific aims I and II. We address Topics (1), (2), (5) and (6) in the following.

Task 3.1 Logic Gates with Unidirectional Current Flow Devices: A device with gradual bandgap gradient that supports unidirectional current flow has already been synthesized, and hence will serve as a building block for computing systems in the initial phases. A unidirectional current flow device as opposed to a bi-directional p-channel or n-channel CMOS transistor is not a hindrance in realizing typical digital logic blocks.

FIG. 10 illustrates a NOR gate. Z=XNOR Y is 1 iff both X and Y equal 0. The diode like symbol with a control input is meant to represent our unidirectional current flow device. We have assumed that these devices may exist in complementary configurations as in CMOS p-channel and n-channel transistors. The upper network is the charging (pull-up) network to turn the output Z to 1. The lower network is the discharging (pull-down) one to switch the output Z to 0. Only when both inputs X and Y equal 0 turning on the two devices in series, the charging network turns on. Similarly, if either X or Y equals 1, the corresponding device path for discharging turns on. Similar logic level implementations for any logic gate are feasible and can be incorporated into a logic synthesis tool like the ones from Cadence and Synopsys. Specific subtasks are Task 3.1.1—Build SPICE like models of the devices emerging from Task 2.3, Task 3.1.2—Build logic level models of basis gates that may include characterized area, delay, and energy parameters derived either from Subtask 3.1.1 simulations or for actual device measurements, Task 3.1.3—Integrate this library of gates into a logic synthesis tool—preferably Cadence.

Task 3.2 Support Vector Machines (SVM) Classifier: To create an integrated sensing/computing element for the edge, multiple data streams—some with high throughput and some with low energy demands, need to be classified at the source. High throughput sensor data streams are reduced to much lower throughput classification streams reducing the edge and backbone network congestion and communication energy. Low energy needs such as in the harvested energy, battery-less scenarios, where the sensors are integrated into an infrastructure like a bridge, machine learning classification needs to be performed with very low energy.

Application specific implementations of machine learning (ML) classifiers have a significant edge in the classification energy needs. Deep learning based on CNN architecture is not well suited for such low energy applications. Support vector machines (SVM) offer a good balance of low resource needs with good performance and accuracy for a broad set of applications. We focus on SVM in the following task.

Support Vector Machines (SVM) is a generalization of linear classifiers that forms an optimal separating hyperplane between two perfectly separated classes. Note that these classes may not be separable with a linear boundary. The separating hyperplane is computed to maximize the margin to the nearest training points. The training points that define this margin are the support vector. In the worst case, if N training points were used, there can be up to N support vectors. The complexity of the separating hyperplane, or the model, is determined by this N, the number of support vectors. Classification/prediction/decision can be stated as sign({circumflex over (f)}(x)=K({right arrow over (w)}, x)^T {circumflex over (β)}+β₀). Here, {circumflex over (β)}=Σ_i=1^N{circumflex over (α)}_ix_iy_i where x_i is training data with class label y_i and {right arrow over (w)}, is the separating model. The number of input training points N used in the model determines the complexity of the model. It often equals N_SV, the number of support vectors. An alternate formulation of the classification function is given by sign({circumflex over (f)}(x)=Σ_i=1^NSVy_iα_iK(x_i, x)+b). Note that since the model {right arrow over (w)}, is dominated by the support vectors, this formulation has just assumed the kernel K to be a function of support vectors x_i.

FIG. 11 illustrates a computation architecture for SVM classification. Note that the classification performs kernel transformation of the input data first, followed by model fitting. Often kernel transformation is assumed to be fixed point arithmetic. Although the model typically is a floating-point computation, we will use approximate fixed point arithmetic to implement for simplicity. FIG. 11 shows a generic model hyperplane computation without the preceding kernel transformation of the input data. The primary computational blocks in SVM perform dot product (multiply-accumulate) and comparisons. The primary decision in these SVM architectures is the degree of parallelism. Parallelism almost always costs extra energy. The number of MACs and comparators will give various trade-offs in this design space that will be explored. Note that since all the basis logic gates are realizable with unidirectional current flow devices, multiplier and ALU designs will follow their traditional design spaces. Specific subtasks include: Task 3.2.1—Based on the characterization of Task 2.2 sensor data throughputs, develop the requirements for SVM engines in terms of throughput and energy, Task 3.2.2—Develop various designs for multiple sensor throughput & energy requirements, Task 3.2.3—Characterize area, delay, and energy needs of various SVM engine designs.

Task 3.3 Reliability and Fault Tolerance: Self-assembled systems are inherently prone to errors in the assembly process. Potential sources of error in atom level assembly include (1) the variability in the number of targeted atom layers—getting multiple layers where one was targeted. This variability could occur only at certain points in the atom level growth described in task 1.1. (2) the mechanisms to bond or grow atoms are statistical in nature, and hence can lead to some atoms in a layer/region that are not targeted. This is like a contaminant in a channel. (3) Aperture or direction of growth shows some variation. (1) and (2) can lead to significant variation in the device characteristics such as on-current or delay. This is analogous to design for manufacturability (DFM) in the current silicon processes. If the drive currents of two transistors are significantly out of balance, a simple 6-transistor static RAM cell will cease to function. There can be similar additional arrayed or non-regular computation structures that may require redundancy in the design to tolerate these non-functioning sub-blocks. (3) could even lead to the traditional stuck at faults. For instance, if a specific self-assembled branch takes off at an unintended seed point and grows into an unintended part of another self-assembled structure, there could be an open circuit that may be reflected in a stuck-at-0 fault. Given that a coordination shell around the metal center establishes apriori spatially resolved atom-by-atom arrangement in the synthon wires, this type of fault is less likely in a homogeneous wire but could occur when the metal center changes. Using SSNMR (task 1.2.1) and TEM (task 1.2.2) proliferation of types of defects responsible for this fault will be mapped and mitigated through task 1.1 and task 1.3. Where such defects cannot be fully eliminated, fault tolerance as described herein will be deployed.

Technology scaling has also radically increased susceptibility to soft errors. In the past, the issue of soft errors in the form of single event upsets (SEUs) and single event transients (SETs) were only a major concern in space applications that were exposed to high radiation levels. The cascading effect of single point of failure induced by soft errors leads to hardware modules that are increasingly brittle and error prone. It is expected that the soft error rates will continue to increase. We propose to develop and deploy lightweight high-integrity mechanisms that allow circuits to aggressively, yet reliably, operate. In addition, we will further develop our conceptual high-integrity building blocks to increase system level power efficiency. Specific subtasks include: Task 3.3.1—design and deploy novel lightweight high-integrity building blocks that will be used to effectively realize the computing potential of self-assembled devices. Task 3.3.2—explore and demonstrate how we can use these building blocks to balance a system's reliability, performance, and power efficiency while extending the design space. Task 3.3.3—develop simulation and hardware infrastructure to evaluate the architectural schemes.

Task 3.4 Framework for High-integrity System Design: We describe a framework that we have developed to tolerate soft errors and timing errors using two novel high-integrity building blocks: 1) a Soft Error Mitigation cell, and 2) a Soft and Timing Error Mitigation cell. The clock frequency of a pipelined system is determined by the pipeline stage with the longest critical path, under worst-case conditions. The circuit delay has a strong association with the data being processed and hence, not all inputs of a task cause its worst-case delay. The infrequent occurrence of critical timing delays opens a new domain of study for increasing system performance by using timing speculation at the circuit level. Operating a system faster than worst-case allows us to exploit data dependent circuit delay variance and execute more efficiently.

The main concern with shorter time is that timing errors may occur. To reliably take advantage of performance improvements, the system must be made tolerant to these potential timing errors. Our adaptive and reliable overclocking approach uses circuitry placed between pipeline stages to locally detect and recover from timing errors. Such a circuit will include two or more registers that are clocked using different clocks CLK-1, CLK-2, and CLK-3, which are always of the same frequency, but are phase shifted, as shown in FIG. 12, which illustrates a soft error mitigation cell. The amount of phase shift is such that the time delay from the rising edge of CLK-1 to the rising edge of CLK-3 (FIG. 12) is not less than the maximum propagation delay of the circuit. Two points to be noted are—1) Computation that begins at the first rising edge of CLK-1 will produce a correct result by the rising edge of CLK-3; and 2) If the input of the combinational circuit changes at the first rising edge of CLK-1, then the output of the combinational circuit will not change until the rising edge of CLK-3. FIG. 12 shows such a soft error mitigation cell.

Soft errors can be mitigated using the following methods. (1) Use of redundant logic where multiple homogeneous/heterogeneous modules are used that with an appropriate voting providing correct output. (2) Use of dual rail signal (signal and its complement) and self-checking circuitry to produce the expected output. An example of a self-checking circuit of a one-bit adder is shown from literature as shown below (FIG. 13) that takes a dual rail values of three inputs and produces two-bit dual rail signals out. (3) Use of error detecting and error correcting codes such as parity, Hamming codes, or RS codes to detect single and multiple contiguous bit errors in memory-type applications. Specific subtasks include: Task 3.4.1—demonstration of design of a logical building block deploying redundancy to overcome impact of an identified fault type. Task 3.4.2—use of complementary logic design using dual rail signals. Tasks 3.4.3—use of information redundancy in register and memory logic design.

Task 3.5 Hybrid System Level Simulation: It is difficult to predict what level of integration would be feasible towards the end of the proposal period. It is likely that we are only able to assemble test chips with thousands of devices. An edge computing node needs significantly more devices. An alternative to perform a system level evaluation is to use these components in hardware (such as a sensor or two), and the remaining ones (such as memory and SVM engine) as simulated behaviors at multiple abstractions. Simple and computationally tractable abstraction is function level. We can also characterize the devices, and potentially integrate them into a SPICE like simulator, which can be further abstracted into function unit level parameters (such as delay and energy for a multiplier and an adder). The hybrid simulation environment will serve as an evaluation platform. Specific subtasks include Task 3.5.1—Selection of an application domain for the developed edge computing node with sensors, SVM engine, and nonvolatile memory, Task 3.5.2—Build a system level architecture for this application domain edge node, Task 3.5.3—Evaluate this edge node with mixed abstraction level simulation.

The terms and expressions that have been employed are used as terms of description and not of limitation, and there is no intention in the use of such terms and expressions of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the embodiments of the present invention. Thus, it should be understood that although the present invention has been specifically disclosed by specific embodiments and optional features, modification and variation of the concepts herein disclosed may be resorted to by those of ordinary skill in the art, and that such modifications and variations are considered to be within the scope of embodiments of the present invention.

Exemplary Aspects.

The following exemplary aspects are provided, the numbering of which is not to be construed as designating levels of importance:

Aspect 1 provides a method of forming a wire that is a microwire or nanowire, the method comprising:

disposing a plurality of metal particles in a portion of a channel that is a nanochannel or a microchannel;

etching the metal particles with an activation agent to form a flux that penetrates an additional portion of the channel, the flux comprising an etching product of the activation agent and the metal particles; and

allowing the activation agent to at least partially evaporate to form the wire.

Aspect 2 provides the method of Aspect 1, wherein the metal particles comprise liquid metal particles comprising a liquid metal or alloy.

Aspect 3 provides the method of Aspect 2, wherein the liquid metal particle comprises a solid shell or wherein the liquid metal particles are free of a solid shell.

Aspect 4 provides the method of Aspect 1, wherein the metal particles comprise solid metal particles comprising a solid metal or alloy.

Aspect 5 provides the method of Aspect 4, wherein the solid metal particles comprise a solid or liquid core.

Aspect 6 provides the method of Aspect 1, wherein the metal particles comprise liquid metallic core-shell particles, each liquid metallic core-shell particle comprising

a liquid metallic core comprising a metal or alloy, and

a solid outer shell on the liquid metallic core.

Aspect 7 provides the method of Aspect 6, wherein the wire comprises a concentration and/or compositional gradient along a longitudinal direction along the wire.

Aspect 8 provides the method of any one of Aspects 6-7, wherein the liquid metallic core-shell particle is an undercooled liquid metallic core-shell particle having a temperature that is below a melting point of the liquid metallic core, or wherein the liquid metallic core-shell particle is a liquid metallic core-shell particle having a temperature that is equal to or above a melting point of the liquid metallic core.

Aspect 9 provides the method of Aspect 1, wherein the metal particle comprises a eutectic metal alloy.

Aspect 10 provides the method of Aspect 9, wherein the wire comprises a mixed composition based on kinetics of the etching of spinodal lines of the metal particle surface.

Aspect 11 provides the method of Aspect 1, wherein the metal particle comprises a combination of metals in a non-eutectic composition.

Aspect 12 provides the method of Aspect 1, wherein the metal particle comprises a unary metal.

Aspect 13 provides the method of Aspect 12, wherein the wire comprises a uniform composition.

Aspect 14 provides the method of Aspect 1, wherein the metal particle comprises a ternary metal alloy.

Aspect 15 provides the method of Aspect 14, wherein the wire comprises a concentration and/or composition gradient of a third metal ion as the ternary alloy surface is depleted by the etching.

Aspect 16 provides the method of any one of Aspects 1-15, wherein the metal particle comprises an undercooled liquid metal that has a temperature that is lower than a melting point of the liquid metal.

Aspect 17 provides the method of any one of Aspects 1-16, wherein the metal particle comprises a liquid metal that has a temperature equal to or greater than a melting point of the liquid metal.

Aspect 18 provides the method of any one of Aspects 1-17, wherein the metal particle comprises Field's metal, eutectic InSn alloy, Galinstan, eutectic GaIn alloy, eutectic InBi alloy, eutectic SnBi alloy, eutectic SnZn, Fe, Sn, Bi, In, or a combination thereof.

Aspect 19 provides the method of any one of Aspects 1-19, wherein the flux penetrates the additional portion of the channel via capillary action and/or fluidic flow.

Aspect 20 provides the method of any one of Aspects 1-20, wherein the channel is open along its length.

Aspect 21 provides the method of Aspect 20, wherein the method is a method of evaporative lithography.

Aspect 22 provides the method of any one of Aspects 1-21, wherein the channel is closed along its length.

Aspect 23 provides the method of Aspect 22, wherein the channel is closed along at least one portion of its length and open along at least one other portion of its length.

Aspect 24 provides the method of any one of Aspects 22-23, wherein the method is a method of directed and/or guided precipitation lithography.

Aspect 25 provides the method of any one of Aspects 22-24, wherein disposing the metal particles in the portion of the channel comprises disposing the metal particles between the portion of the channel and a substrate.

Aspect 26 provides the method of Aspect 25, further comprising disposing the metal particles in the channel or on a mold comprising the channel and then placing the channel against the substrate.

Aspect 27 provides the method of any one of Aspects 25-26, further comprising disposing the metal particles on the substrate and then placing the channel against the substrate.

Aspect 28 provides the method of any one of Aspects 25-27, further comprising removing the channel from the wire, to provide the wire disposed on the substrate.

Aspect 29 provides the method of any one of Aspects 25-28, wherein the substrate comprises silicon, glass, mica, graphene, graphene oxide, MoS₂, one or more metals, a metal foil, aluminum, aluminum foil, copper, copper foil, one or more coinage metals, one or more metal oxides, one or more minerals, one or more polymers, or a combination thereof.

Aspect 30 provides the method of any one of Aspects 25-29, wherein the substrate comprises silicon, glass, or a combination thereof.

Aspect 31 provides the method of any one of Aspects 1-30, wherein the channel comprises a uniform width and/or height.

Aspect 32 provides the method of any one of Aspects 1-31, wherein the channel has a width of 1 nm to 10 microns.

Aspect 33 provides the method of any one of Aspects 1-32, wherein the channel has a width of 1 nm to 990 nm.

Aspect 34 provides the method of any one of Aspects 1-33, wherein the channel has a length of 1 mm to 100 cm.

Aspect 35 provides the method of any one of Aspects 1-34, wherein the channel has a length of 1 mm to 25 cm.

Aspect 36 provides the method of any one of Aspects 1-35, wherein the channel has a cross-sectional profile that is curved, round, square, rectangular, polygonal or a combination thereof.

Aspect 37 provides the method of any one of Aspects 1-36, wherein the channel has a cross-sectional profile that is square or rectangular.

Aspect 38 provides the method of any one of Aspects 1-37, wherein a mold comprises the channel.

Aspect 39 provides the method of Aspect 38, wherein the mold comprises an elastomer, a thermoset polymer, a thermoplastic polymer, an inorganic material, a coinage metal, or a combination thereof.

Aspect 40 provides the method of any one of Aspects 38-39, wherein the mold comprises PDMS.

Aspect 41 provides the method of any one of Aspects 1-40, wherein the method comprises forming the wire in more than one of the channels to form a plurality of the wires.

Aspect 42 provides the method of Aspect 41, wherein the channels have a spacing of 1 nm to 10 microns.

Aspect 43 provides the method of any one of Aspects 41-42, wherein the channels have a spacing of 30 nm to 2 microns.

Aspect 44 provides the method of any one of Aspects 41-43, wherein together the channels form a grating.

Aspect 45 provides the method of any one of Aspects 41-44, wherein a mold comprises the channels which form a grating.

Aspect 46 provides the method of Aspect 45, wherein a mold comprising PDMS comprises the channels which form a grating.

Aspect 47 provides the method of any one of Aspects 1-46, wherein the portion of the channel wherein the metal particles are deposited is a growth zone.

Aspect 48 provides the method of any one of Aspects 1-47, wherein the portion of the channel wherein the metal particles are deposited is an entrance to the channel.

Aspect 49 provides the method of any one of Aspects 1-48, wherein the additional portion of the channel wherein the flux penetrates the channel is a collection zone.

Aspect 50 provides the method of any one of Aspects 6 or 17-49, wherein the liquid metal core in the particle is a liquid below a melting point of the liquid metal core.

Aspect 51 provides the method of any one of Aspects 6 or 17-49, wherein the liquid metal particle has a temperature that is below a melting point of the liquid metal core.

Aspect 52 provides the method of any one of Aspects 6 or 17-51, wherein the solid shell of the liquid metal particle comprises one or more oxides of the liquid metal core.

Aspect 53 provides the method of any one of Aspects 6 or 17-52, wherein the solid shell of the liquid metal particle comprises one or more stabilizing ligands.

Aspect 54 provides the method of Aspect 53, wherein the one or more stabilizing ligands form an adlayer on the outside of the solid shell of the undercooled liquid metal particle.

Aspect 55 provides the method of any one of Aspects 53-54, wherein the stabilizing ligand comprises a conjugate base of a C₁-C₂₀ mono- or di-carboxylic acid.

Aspect 56 provides the method of any one of Aspects 53-55, wherein the stabilizing ligand comprises acetate.

Aspect 57 provides the method of any one of Aspects 1-56, wherein the metal particles have a diameter of 1 nm to 10 cm.

Aspect 58 provides the method of any one of Aspects 1-57, wherein the metal particles have a diameter of 1 nm to 990 nm.

Aspect 59 provides the method of any one of Aspects 6 or 17-58, wherein the liquid metal core comprises Field's metal, eutectic InSn alloy, Galinstan, eutectic GaIn alloy, eutectic InBi alloy, eutectic SnBi alloy, eutectic SnZn, Fe, Sn, Bi, In, or a combination thereof.

Aspect 60 provides the method of any one of Aspects 6 or 17-59, wherein the liquid metal core comprises Field's metal, eutectic InSn alloy, or a combination thereof.

Aspect 61 provides the method of any one of Aspects 1-60, wherein disposing the plurality of metal particles in the portion of the channel comprises disposing a solution comprising metal particles in the portion of the channel, wherein the solution has a concentration of the metal particles of 0.001 wt % to 100 wt %.

Aspect 62 provides the method of Aspect 61, wherein solution has a concentration of the metal particles of about 100%.

Aspect 63 provides the method of any one of Aspects 61-62, wherein the solution comprises a solvent comprising water, an organic solvent, an alcohol, a ketone, an ester, an amine, an aromatic compound, or a combination thereof.

Aspect 64 provides the method of any one of Aspects 61-63, wherein the solution comprises a solvent comprising acetic acid.

Aspect 65 provides the method of any one of Aspects 1-64, wherein the activation agent comprises a solution comprising a solvent and an acid (e.g., organic acid and/or mineral acid), and/or comprising etchant, alkaline conditions, an applied bias, an amide, a thioester, a urea, a highly reactive metal, or a combination thereof.

Aspect 66 provides the method of Aspect 65, wherein the solvent of the activation agent comprises acetone, ethanol, water, ethyl acetate, toluene, benzene, methylene chloride, THF, methanol, petroleum ether, or a combination thereof.

Aspect 67 provides the method of any one of Aspects 65-66, wherein the solvent of the activation agent comprises acetone, ethanol, water, or a combination thereof.

Aspect 68 provides the method of any one of Aspects 65-67, wherein the acid comprises a carboxylic acid, acetic acid, stearic acid, benzoic acid, butyric acid, butanoic acid, adipic acid, malonic acid, muconic acid, an amino acid, or a combination thereof.

Aspect 69 provides the method of any one of Aspects 65-68, wherein the acid comprises acetic acid.

Aspect 70 provides the method of any one of Aspects 65-69, wherein a volumetric ratio of the acid to the solvent in the activation agent is 1:100 to 100:1.

Aspect 71 provides the method of any one of Aspects 65-70, wherein a volumetric ratio of the acid to the solvent in the activation agent is 1:5 to 5:1.

Aspect 72 provides the method of any one of Aspects 65-71, wherein allowing the activation agent to at least partially evaporate comprises allowing the solvent of the activation agent to at least partially evaporate.

Aspect 73 provides the method of any one of Aspects 65-72, wherein the acid in the activation agent combines with metal atoms on the surface of the etched metal particles to form free metal ions chelated with a conjugate base of the acid in the activation agent.

Aspect 74 provides the method of Aspect 73, wherein the free metal ions chelated with the conjugate base solubilize into the activation agent.

Aspect 75 provides the method of any one of Aspects 73-74, wherein the free metal ions chelated with the conjugate base polymerize to form the wire.

Aspect 76 provides the method of any one of Aspects 1-75, further comprising controlling the rate of evaporation from one or more portions of the flux.

Aspect 77 provides the method of Aspect 76, wherein controlling the rate of evaporation from the one or more portions of the flux controls morphology of corresponding portions of the formed wire.

Aspect 78 provides the method of any one of Aspects 1-77, wherein the wire has a straight profile.

Aspect 79 provides the method of any one of Aspects 1-77, wherein the wire has a curved profile.

Aspect 80 provides the method of any one of Aspects 1-79, wherein the wire has a curved or round cross-sectional profile.

Aspect 81 provides the method of any one of Aspects 1-79, wherein the wire has a square, rectangular, or polygonal cross-sectional profile.

Aspect 82 provides the method of any one of Aspects 1-81, wherein the wire has a flat profile.

Aspect 83 provides the method of any one of Aspects 1-82, wherein the wire has a height of 1 nm to 10 microns.

Aspect 84 provides the method of any one of Aspects 1-83, wherein the wire has a width of 1 nm to 10 microns.

Aspect 85 provides the method of any one of Aspects 1-84, wherein the wire has an aspect ratio (width to height) of 5:1 to 1:1000.

Aspect 86 provides the method of any one of Aspects 1-85, wherein the wire has a homogeneous elemental distribution.

Aspect 87 provides the method of any one of Aspects 1-86, wherein the wire has a substantially uniform diameter and/or cross-sectional area from end to end.

Aspect 88 provides the method of any one of Aspects 1-87, wherein the wire comprises an organometallic compound.

Aspect 89 provides the method of any one of Aspects 1-88, further comprising calcining the wire to form a calcined wire.

Aspect 90 provides the method of Aspect 89, wherein the calcining comprises heating the wire to a temperature of 300° C. to 2000° C.

Aspect 91 provides the method of any one of Aspects 89-90, wherein the calcining comprises heating the wire to a temperature of 500° C. to 1000° C.

Aspect 92 provides the method of any one of Aspects 89-91, wherein the liquid metal core comprises Field's metal and the calcining comprises heating the wire to a temperature of 550° C. to 650° C.

Aspect 93 provides the method of any one of Aspects 89-92, wherein the liquid metal core comprises InSn eutectic and the calcining comprises heating the wire to a temperature to 750° C. to 850° C.

Aspect 94 provides the method of any one of Aspects 89-93, wherein the calcining comprises heating the wire for a time of 1 min to 24 h.

Aspect 95 provides the method of any one of Aspects 89-94, wherein the calcining comprises heating the wire for a time of 30 min to 2 h.

Aspect 96 provides the method of any one of Aspects 89-95, wherein the calcining comprises heating the wire in an environment comprising air, nitrogen, argon, or a combination thereof.

Aspect 97 provides the method of any one of Aspects 89-96, wherein the calcination transforms the wire comprising an organometallic compound into the calcined wire that is substantially free of organometallic compounds.

Aspect 98 provides the method of any one of Aspects 89-97, wherein the calcination shrinks the wire.

Aspect 99 provides the method of any one of Aspects 89-98, wherein the calcination shrinks one or more dimensions of the wire by 1% to 50%.

Aspect 100 provides the method of any one of Aspects 89-99, wherein the calcination shrinks the wire more in height than in length and width.

Aspect 101 provides the method of any one of Aspects 89-100, wherein the calcined wire is substantially free of organometallic compounds.

Aspect 102 provides the method of any one of Aspects 89-101, wherein the calcined wire is predominantly inorganic compounds.

Aspect 103 provides the method of any one of Aspects 89-102, wherein the calcined wire is predominantly inorganic mixed oxides.

Aspect 104 provides the method of any one of Aspects 89-103, wherein the calcined wire has a homogeneous elemental distribution.

Aspect 105 provides the method of any one of Aspects 1-104, wherein channel is closed, wherein the method further comprises performing one or more additional cycles of the disposing, etching, and formation of the wire on top of previously-formed wire.

Aspect 106 provides the method of Aspect 105, wherein the one or more additional cycles comprise orienting the channel in a different direction than used to form the previously-formed wire.

Aspect 107 provides the method of any one of Aspects 105-106, wherein the different direction is about 90° different than the direction of the channel used to form the previously-formed wire.

Aspect 108 provides the method of any one of Aspects 1-107, further comprising at least partially dissolving some of the formed wire.

Aspect 109 provides the method of any one of Aspects 1-108, wherein the method is a method of forming an article or device including the wire.

Aspect 110 provides the method of Aspect 109, wherein the article or device comprises a semiconductor device, an optical article, a plasmonic component, an opto-electronic component, a resonant sensor, a radiofrequency sensor, or a combination thereof.

Aspect 111 provides the method of any one of Aspects 109-110, wherein the article or device comprises a diode, a transistor, a rectifier, a computation device, or a combination thereof.

Aspect 112 provides the method of any one of Aspects 1-111, wherein the method is a method of forming a guided-mode resonance device (GMR), wherein the method comprises disposing a plurality of the wires on a substrate.

Aspect 113 provides the method of Aspect 112, wherein the substrate comprises a glass substrate.

Aspect 114 provides a method of forming a wire that is a microwire or nanowire, the method comprising:

disposing a plurality of liquid metallic core-shell particles in a portion of a channel that is a nanochannel or a microchannel, each liquid metallic core-shell particle comprising

• • a liquid metallic core comprising a metal or alloy, and
  • a solid outer shell on the liquid metallic core;

etching the liquid metallic core-shell particles with an activation agent to form a flux that penetrates an additional portion of the channel, the flux comprising an etching product of the activation agent and the liquid metallic core-shell particles; and

allowing the activation agent to at least partially evaporate to form the wire.

Aspect 115 provides a wire formed by the method of any one of Aspects 1-114.

Aspect 116 provides an article or device comprising a wire formed by the method of any one of Aspects 1-114.

Aspect 117 provides a semiconductor device comprising a wire formed by the method of any one of Aspects 1-114.

Aspect 118 provides an optical article comprising a wire formed by the method of any one of Aspects 1-114.

Aspect 119 provides a transistor comprising a wire formed by the method of any one of Aspects 1-114.

Aspect 120 provides a diode comprising a wire formed by the method of any one of Aspects 1-114.

Aspect 121 provides a guided-mode resonance device (GMR) comprising a wire formed by the method of any one of Aspects 1-114.

Aspect 122 provides the method, wire, article, device, transistor, diode, or GMR of any one or any combination of Aspect 1-121 optionally configured such that all elements or options recited are available to use or select from.

Claims

1. A method of forming a wire that is a microwire or nanowire, the method comprising: disposing a plurality of metal particles in a portion of a channel that is a nanochannel or a microchannel;etching the metal particles with an activation agent to form a flux that penetrates an additional portion of the channel, the flux comprising an etching product of the activation agent and the metal particles; andallowing the activation agent to at least partially evaporate to form the wire.

2. The method of claim 1, wherein the metal particle comprises Field's metal, InSn alloy, eutectic InSn alloy, Galinstan, GaIn alloy, eutectic GaIn alloy, InBi alloy, eutectic InBi alloy, SnBi alloy, eutectic SnBi alloy, SnZn alloy, eutectic SnZn, Fe, Sn, Bi, In, Cu, Ag, Ge, Te, Sb, SnCu, SnAg, or a combination thereof.

3. The method of claim 1, wherein the metal particles comprise liquid metal particles comprising a liquid metal or alloy.

4. The method of claim 1, wherein the metal particles comprise solid metal particles comprising a solid metal or alloy.

5. The method of claim 1, wherein the metal particles comprise liquid metallic core-shell particles, each liquid metallic core-shell particle comprising a liquid metallic core comprising a metal or alloy, anda solid outer shell on the liquid metallic core;wherein the wire comprises a concentration and/or compositional gradient along a longitudinal direction along the wire.

6. The method of claim 5, wherein the liquid metallic core-shell particle is an undercooled liquid metallic core-shell particle having a temperature that is below a melting point of the liquid metallic core.

7. The method of claim 1, wherein the channel is open along its length.

8. The method of claim 1, wherein the channel is closed along at least part of its length.

9. The method of claim 8, wherein disposing the metal particles in the portion of the channel comprises disposing the metal particles between the portion of the channel and a substrate, wherein the substrate comprises silicon, glass, mica, graphene, graphene oxide, MoS2, one or more metals, a metal foil, aluminum, aluminum foil, copper, copper foil, one or more coinage metals, one or more metal oxides, one or more minerals, one or more polymers, or a combination thereof.

10. The method of claim 1, wherein a mold comprises the channel, wherein the mold comprises an elastomer, a thermoset polymer, a thermoplastic polymer, an inorganic material, a coinage metal, or a combination thereof.

11. The method of claim 1, wherein the method comprises forming the wire in a plurality of the channels to form a plurality of the wires.

12. The method of claim 1, wherein the portion of the channel wherein the metal particles are deposited is an entrance to the channel.

13. The method of claim 1, wherein the activation agent comprises a solvent and an acid, wherein the acid comprises a carboxylic acid, acetic acid, stearic acid, benzoic acid, butyric acid, butanoic acid, adipic acid, malonic acid, muconic acid, an amino acid, or a combination thereof.

14. The method of claim 1, further comprising calcining the wire to form a calcined wire, wherein the calcining comprises heating the wire to a temperature of 300° C. to 2000° C.

15. The method of claim 1, further comprising pyrolyzing the wire to form a coating on the wire comprising graphene, graphene oxide, and/or graphite.

16. A method of forming a wire that is a microwire or nanowire, the method comprising: disposing a plurality of liquid metallic core-shell particles in a portion of a channel that is a nanochannel or a microchannel, each liquid metallic core-shell particle comprising a liquid metallic core comprising a metal or alloy, anda solid outer shell on the liquid metallic core;etching the liquid metallic core-shell particles with an activation agent to form a flux that penetrates an additional portion of the channel, the flux comprising an etching product of the activation agent and the liquid metallic core-shell particles; andallowing the activation agent to at least partially evaporate to form the wire.

17. A wire formed by the method of claim 1.

18. The wire of claim 17, wherein the wire comprises a concentration and/or compositional gradient along a longitudinal direction along the wire.

19. An article or device comprising a wire formed by the method of claim 1.

20. The article or device of claim 19, wherein the article or device comprises a semiconductor device, an optical article, a plasmonic component, an opto-electronic component, a resonant sensor, a radiofrequency sensor, a diode, a transistor, a rectifier, a computation device, or a combination thereof.