PURIFICATION OF CARBON NANOTUBES VIA SELECTIVE HEATING

[0001] This application claims the benefit of priority to U.S. provisional Patent Application 61/808,572 filed Apr. 4, 2013, which is hereby incorporated by reference in its entirety.

[0002] This invention was made with government support awarded by the following agency: U.S. Department of Energy Grant DEFG02-91 ER45439. The United States government has certain rights in the invention.

[0003] Since their discovery in the early 1990s, a great deal has been learned about the composition and properties of carbon nanotube materials. This research has demonstrated that carbon nanotubes exhibit extraordinary mechanical, electronic and chemical properties, which has stimulated substantial interest in developing applied technologies exploiting these properties. Accordingly, substantial research is directed at developing techniques for organizing, arranging and incorporating carbon nanotube materials into useful functional devices.

[0004] Carbon nanotubes are allotropes of carbon comprising one or more cylindrically configured graphene sheets and are classified on the basis of structure as either single walled carbon nanotubes (SWNTs) or multiwalled carbon nanotubes (MWNTs). Typically having small diameters (≈1-30 nanometers) and large lengths (up to several microns), SWNTs and MWNTs commonly exhibit length to diameter ratios of ≈10² to about 10⁷. Carbon nanotubes exhibit either metallic or semiconductor electrical behavior, and the energy band structure of nanotube materials varies considerably depending on their precise molecular structure and diameter.

[0005] Single walled carbon nanotubes (SWNTs), in particular, are identified as candidates for functional materials in a new generation of high performance passive and active nanotube based electronic devices. SWNTs are made up of a single, contiguous graphene sheet joined with itself to form a hollow, seamless tube, in some cases with capped ends similar in structure to smaller fullerenes. SWNTs typically have very small diameters (≈1 nanometer) and are often present in curled, looped and bundled configurations. SWNTs are chemically versatile materials capable of functionalization of their exterior surfaces and encapsulation of materials within their hollow cores, such as gases or molten materials.

[0006] A number of unique properties of SWNTs make these materials particularly attractive for a variety of emerging applied technologies, including sensors, light emissive systems, flexible electronics and novel composite materials. First, SWNTs are believed to have remarkable mechanical properties, such as tensile strengths at least 50 times that of steel. Second, the electron transport behavior in SWNTs is predicted to be essentially that of a quantum wire, and the electrical properties of SWNTs have been observed to vary upon charge transfer doping and intercalation, opening up an avenue for potentially tuning the electrical properties of nanotube materials. Finally, SWNTs have also been demonstrated to have very high intrinsic field affect mobilities (e.g., about 10,000 cm²V⁻¹s⁻¹) making them interesting for possible applications in nanoelectronics.

[0007] Despite substantial progress in developing a SWNT-based electronic device platform, several factors impede commercialization of these systems. First, the device mobilities that have been achieved with these networks are far below the intrinsic tube mobilities inferred from measurements of transistors that incorporate an individual tube (or small number of tubes) spanning the gap between the source and drain electrodes. Second, films comprising SWNT networks are typically a mixture of metallic tubes and semiconducting tubes. The presence of metallic tubes in the network often results in a significant extent of purely metallic conductive pathways between the source/drain (S/D) electrodes of SWNT-based thin-film transistor (TFT) devices. Such metallic conductive pathways decrease the device on/off ratio attainable and generally increase the static power consumption, thereby preventing their applications for important classes of electronics systems.

[0008] It will be appreciated from the foregoing that there is currently a need in the art for improved device geometries, components, and fabrication methods to enable carbon nanotube electronic devices.

[0009] The present invention provides device component geometries and fabrication strategies for enhancing the electronic performance of electronic devices based on thin films of semiconducting carbon nanotubes. The invention provides, for example, processes utilizing selective heating of a subset of carbon nanotubes having one or more selected physical and/or chemical properties so as to selectively separate nanotubes of the subset from a precursor layer containing nanotubes, such as a layer containing substantially aligned carbon nanotubes. In some embodiments, for example, a flow of a thermocapillary resists is generated via selective heating of carbon nanotubes so as to expose nanotubes having one or more selected physical and/or chemical properties, thereby allowing subsequent separation from the precursor layer, for example via removal or transfer processes. Examples of processes useful in the present invention for achieving selective heating and separation of carbon nanotubes based on one or more selected physical and/or chemical properties include absorption of electromagnetic radiation (e.g., via laser or microwave source), application of an electromagnetic field, electric field, magnetic field and/or application or a voltage. In some embodiments, for example, one or more of the following are applied simultaneously, electromagnetic radiation, electromagnetic field, electric field, magnetic field and/or application or a voltage.

[0010] In certain aspects, devices and methods of the present invention provide for the purification of mixtures of metallic and semiconducting carbon nanotubes. For example, mixtures of substantially aligned single-walled carbon nanotubes may be purified by methods involving selective heating of one class of nanotubes, which may be separated from the mixture. In an embodiment, metallic nanotubes are selectively heated to induce flow of a thermocapillary resist away from the metallic nanotubes to expose the metallic nanotubes while semiconducting nanotubes remain covered by the resist. Separation of the exposed and unexposed nanotubes may be carried out, for example, by etching, ablation, transfer printing, and other known methods. In an embodiment, additional processing may be carried out to protect the exposed nanotubes followed by removal of the thermocapillary resist, and optionally the nanotubes underlying the thermocapillary resist.

[0011] The present purification methods are versatile, thereby providing a platform enabling improved nanotube-based electronic devices and systems well suited for a range of device applications, including thin film electronics, large area electronics (e.g., macroelectronics), flexible electronics, and sensing. Methods and devices of the present invention are compatible with low temperature processing and assembly on a wide range of device substrates, including mechanically flexible substrates such as polymer substrates. Processing methods and design strategies of the present invention are complementary to conventional microfabrication and nanofabrication platforms, and can be effectively integrated into existing photolithographic, etching and thin film deposition patterning strategies, systems and infrastructure. In specific embodiments, methods of the present invention enable low cost fabrication of high performance nanotube based semiconductor devices, such as thin film transistors, transistor arrays, and integrated electronic circuits.

[0012] In an aspect, a method for purifying a layer of carbon nanotubes comprises: providing a precursor layer of substantially aligned carbon nanotubes supported by a substrate, wherein the precursor layer comprises a mixture of first carbon nanotubes and second carbon nanotubes; covering the precursor layer of carbon nanotubes with a thermocapillary resist, wherein the thermocapillary resist is in thermal contact with at least a portion of the carbon nanotubes; selectively heating the first carbon nanotubes, thereby causing thermocapillary flow of the thermocapillary resist away from the first carbon nanotubes to expose the first carbon nanotubes; and separating the first carbon nanotubes from the second carbon nanotubes, thereby generating a purified layer of carbon nanotubes.

[0013] In an aspect, a method for making an electronic device comprises: providing a precursor layer of substantially aligned carbon nanotubes supported by a substrate, wherein the precursor layer comprises a mixture of first carbon nanotubes and second carbon nanotubes; covering the precursor layer of carbon nanotubes with a thermocapillary resist, wherein the thermocapillary resist is in thermal contact with at least a portion of the carbon nanotubes; selectively heating the first carbon nanotubes, thereby causing thermocapillary flow of the thermocapillary resist away from the first carbon nanotubes to expose the first carbon nanotubes; separating the first carbon nanotubes from the second carbon nanotubes, thereby generating a purified layer of carbon nanotubes; and providing one or more device component structures in electrical or physical contact with the purified layer of carbon nanotubes, thereby making the electronic device.

[0014] In an embodiment, first carbon nanotubes can be a first set of nanotubes, a first class of nanotubes, or a first distribution of nanotubes. Second carbon nanotubes can be a second set of nanotubes, a second class of nanotubes, or a second distribution of nanotubes. Each type, set, class or distribution of nanotubes may be characterized by an electronic, optical, physical, chemical or other property in common. In an embodiment, the precursor layer comprises an array of substantially longitudinally aligned carbon nanotubes, such as an array generated using a guide growth substrate or guided deposition substrate.

[0015] In an embodiment, the selective heating results from absorption of electromagnetic radiation, electronic resistance, mobility, direct thermal contact or electromagnetic induction.

[0016] Carbon nanotubes of the present invention may be single walled carbon nanotubes, multiwalled carbon nanotubes or a mixture of both. Use of single walled nanotubes (SWNTs) is preferred for some applications given their particularly useful semiconducting properties. In an embodiment, the precursor layer is a monolayer or sub-monolayer of carbon nanotubes. As used herein, the terms “nanotube surface concentration” and “nanotube density” are used interchangeably and refer to the number of nanotubes per area of substrate having the nanotubes. In an embodiment, carbon nanotubes of the precursor layer are a mixture of semiconducting nanotubes and metallic nanotubes, wherein there are more semiconducting nanotubes than metallic nanotubes. For example, the first carbon nanotubes may be metallic carbon nanotubes and the second carbon nanotubes may be semiconducting carbon nanotubes. Conventional sources of carbon nanotubes, such as SWNTs, typically generate mixtures having more semiconducting nanotubes than metallic nanotubes, for example mixtures having between 60-80% semiconducting nanotubes and 40-20% metallic nanotubes or mixtures having between 65-75% semiconducting nanotubes and 35-25% metallic nanotubes. In an embodiment, carbon nanotubes of the precursor layer are a mixture of semiconducting nanotubes and metallic nanotubes, wherein there are more semiconducting nanotubes than metallic nanotubes, for example a mixture wherein there are at least 1.5 times more semiconducting nanotubes than metallic nanotubes, and in some embodiments wherein there are 1.5-4 times more semiconducting nanotubes than metallic nanotubes. Carbon nanotubes of the precursor layer can be generated by a range of synthetic methods including, chemical vapor deposition, pyrolysis, arc discharge, catalytic methods and laser ablation methods. Precursor layers of carbon nanotubes of the present invention may further comprise additional components, such as dopants or components enhancing the mechanical properties of the nanotube layer.

[0017] A precursor layer of the present invention comprises one or more carbon nanotubes in a selected geometry. In an embodiment, the precursor layer may be provided by growing substantially aligned carbon nanotubes on a substrate comprising a guided growth substrate or by printing substantially aligned carbon nanotubes onto a substrate. Suitable methods for printing the substantially aligned carbon nanotubes may for example be selected from ink jet printing, thermal transfer printing, contact printing, dry transfer printing or screen printing.

[0018] The carbon nanotubes of the precursor layer generally have an average length selected from a range of 20 nanometers to 100 microns, or 50 nanometers to 10 microns, or 75 nanometers to 1 micron, or 100 nanometers to 500 nanometers. Further, an average spacing between adjacent carbon nanotubes of the precursor layer is typically selected from a range of 2 nm to 100 μm, or 5 nm to 10 μm, or 10 nm to 1 μm, or 20 nm to 500 nm, or 30 nm to 250 nm. In an embodiment, an average spacing between adjacent carbon nanotubes of the precursor layer is at least 2 nm, or at least 5 nm or at least 10 nm, or at least 20 nm, or at least 30 nm.

[0019] A surface concentration of carbon nanotubes of the precursor layer is typically selected from a range of 0.2 carbon nanotubes micron⁻² to 100 carbon nanotubes micron⁻², or 0.5 carbon nanotubes micron⁻² to 50 carbon nanotubes micron⁻², or 1 carbon nanotube micron⁻² to 25 carbon nanotubes micron⁻², or 2 carbon nanotubes micron⁻² to 15 carbon nanotubes micron⁻². In an embodiment, the precursor layer of substantially aligned carbon nanotubes includes less than 100 carbon nanotube crossings per square micron, or less than 50 carbon nanotube crossings per square micron, or less than 25 carbon nanotube crossings per square micron, or less than 10 carbon nanotube crossings per square micron.

[0020] The layer of substantially aligned carbon nanotubes typically has a thickness less than or equal to 10 nanometers, or less than or equal to 5 nanometers, or less than or equal to 2 nanometers. In an embodiment, the layer of substantially aligned carbon nanotubes is a monolayer film or a substantially monolayer film.

[0021] Carbon nanotubes of the present invention may be covered by a thermocapillary resist. Useful thermocapillary resists for covering the nanotubes, and optionally a portion of a substrate, include but are not limited to thermocapillary resists having a room temperature viscosity selected from a range of 0.5 Pa·s to 50 Pa·s, or 1 Pa·s to 30 Pa·s, or 3 Pa·s to 15 Pa·s.

[0022] Generally, the thermocapillary resist comprises a conformal layer on and between the carbon nanotubes, where the thermocapillary resist is in physical contact with the carbon nanotubes. In an embodiment, the thermocapillary resist comprises a substantially uniform layer. The substantially uniform layer may, for example, have a thickness selected from a range of 1 nm to 10 μm, or 5 nm to 1 μm, or 10 nm to 500 nm, or 10 nm to 50 nm, or a thickness less than or equal to 500 nm, or less than or equal to 250 nm, or less than or equal to 100 nm, or less than or equal to 50 nm. In an embodiment, the substantially uniform layer is a continuous layer.

[0023] In an embodiment, the thermocapillary resist comprises a molecular organic species. For example, the thermocapillary resist may be selected from the group consisting of α,α,α′-Tris(4-hydroxyphenyl)-1-ethyl-4-isopropylbenzene polymethylmethacrylate (PMMA), polystyrene (PS), and low molecular weight silicon containing polymers such as poly(styrene-dimethylsiloxane) (PS-PDMS); oligosaccharide-trimethylsilylstyrene, and polyhedral oligomeric silsesquioxane (FOSS). In an embodiment, the thermocapillary resist comprises a molecular weight selected from a range of 50 g/mol to 1000 kg/mol, or 500 g/mol to 500 kg/mol, or 1 kg/mol to 100 kg/mol.

[0024] In an embodiment, at least 1%, 5%, 10%, 20%, 50% or 75% of a lateral cross section of each of the first carbon nanotubes is exposed by the step of selectively heating the first carbon nanotubes.

[0025] In an embodiment, the step of separating the first carbon nanotubes from the second carbon nanotubes may include: etching exposed carbon nanotubes, transfer printing the exposed carbon nanotubes, transfer printing the carbon nanotubes covered by the thermocapillary resist, removing the exposed carbon nanotubes from the precursor layer, or removing the covered carbon nanotubes from the precursor layer (e.g., by performing steps of applying a protective layer to the exposed nanotubes, removing the thermocapillary resist and separating the previously covered carbon nanotubes from the precursor layer).

[0026] As a further processing step, any of the methods described herein may include a step of removing the thermocapillary resist after the step of separating.

[0027] Carbon nanotubes and devices or device components of the present invention may be supported by a substrate. Useful substrates for supporting the nanotubes, devices and device components of the present invention include but are not limited to mechanically flexible substrates such as polymer substrates, rigid substrates, dielectric substrates, metal substrates, ceramic substrates, glass substrates, semiconductor substrates and functional substrates prepatterned with one or more device components. The present invention also includes devices and device components provided on (i.e. supported by) contoured substrates, including curved substrates, curved rigid substrates, concave substrates, and convex substrates.

[0028] The step of selectively heating a type, set, class or distribution of nanotubes may be carried out by application of electromagnetic energy, current, an electric field, a magnetic field, microwave energy or laser radiation to the nanotubes of the precursor layer. In an embodiment, selective heating comprises absorption of energy by metallic carbon nanotubes, wherein the energy is insufficient to overcome the Schottky barrier of semiconducting carbon nanotubes.

[0029] In an embodiment, a ratio of a temperature increase of the first carbon nanotubes to a temperature increase of the second carbon nanotubes during the step of selective heating is 1.25 or greater, or 1.7 or greater, or 2 or greater, or 2.5 or greater.

[0030] In an embodiment, an average temperature gradient within the thermocapillary resist proximate to the first carbon nanotubes is at least 1 K/μm, or at least 1.5 K/μm, or at least 2 K/μm

[0031] In an embodiment, the selective heating is provided by one or more of an optical source, a microwave source, a laser source, a DC source, an AC source, or an acoustic source. The source may be pulsed or continuous.

[0032] In an embodiment, selective heating of the nanotubes occurs in a transistor configuration, where the carbon nanotubes of the precursor layer are in electrical contact with a source electrode, a drain electrode and a gate electrode. The selective heating is provided by one or more of a DC source and an AC source delivering a power per carbon nanotube selected from a range of 5 μW/μm/tube to 50 μW/μm/tube, or 10 μW/μm/tube to 30 μW/μm/tube, to the source electrode. In an embodiment, the source is pulsed at a frequency selected from a range of CW (i.e., 0 Hz) to 100 MHz, or CW (i.e., 0 Hz) to 10 MHz, or CW (i.e., 0 Hz) to 1 MHz, or CW (i.e., 0 Hz) to 500 Hz, and the source is activated for a duration selected from a range of 1 ns to 100 minutes, or 10 ns to 10 minutes, or 100 ns to 1 minute.

[0033] In an embodiment, selective heating of the nanotubes occurs via laser irradiation using a laser source producing radiation having an energy selected from a range of 100 nJ to 100 mJ, or 1 μJ to 10 mJ and a power less than 1 kJ/m², or less than 0.5 kJ/m². In an embodiment, the laser source produces radiation having a wavelength selected from a range of 1 μm to 10 μm, or 1.5 μm to 8 μm, or 2 μm to 5 μm. The laser source may be pulsed at a frequency selected from a range of 1 Hz to 100 MHz, or 1 Hz to 1000 KHz or 1 Hz to 100 KHz, or 1 Hz to 10 KHz. In an embodiment, the laser source is activated for a duration selected from a range of 1 nm to 300 minutes, or 10 ns to 200 minutes, or 100 ns to 100 minutes, or 1 μs to 10 minutes, or 1 ms to 1 minute.

[0034] In an embodiment, selective heating of the nanotubes occurs in a microwave configuration, where the carbon nanotubes of the precursor layer are in electromagnetic communication with at least one microwave antennae. The electromagnetic communication may involve physical contact, electrical contact or both physical and electrical contact. In an embodiment, the electromagnetic communication does not comprise physical contact.

[0035] In an embodiment, the microwave source produces radiation having an energy selected from a range of 50 J/sec to 10 kJ/sec, or 100 J/sec to 1 kJ/sec. In an embodiment, the microwave source is pulsed at a frequency selected from a range of CW (i.e., 0 Hz) to 100 MHz, or CW (i.e., 0 Hz) to 10 MHz, or CW (i.e., 0 Hz) to 1 MHz, or CW (i.e., 0 Hz) to 500 Hz. In an embodiment, the microwave source is activated for a duration selected from a range of 0.1 μs to 300 minutes, or 1 μs to 300 minutes, or of 0.1 μs to 100 minutes or 1 μs to 100 minutes, or 1 ms to 10 minutes.

[0036] In some embodiments, the selective heating comprises differential absorption of a preselected wavelength of radiation between the first carbon nanotubes and the second carbon nanotubes, wherein the first carbon nanotubes absorb more than 1.25 times, or more than 1.5 times as much energy as the second carbon nanotubes. The preselected wavelength may, for example, be selected from a range of 100 nm to 20 μm, or 300 nm to 20 μm, or 0.5 μm to 10 μm, or 1 μm to 5 μm.

[0037] In an embodiment, selective heating of the nanotubes occurs in a two-terminal configuration, where the first and second carbon nanotubes of the precursor layer are in electrical contact with a first electrode and a second electrode. An electrode bias voltage between the first electrode and the second electrode may, for example, be selected from a range of 0.01 V to 500 V, or 0.1 V to 500 V, or 0.01 V to 100 V, or 1 V to 50 V, or 5 V to 25 V. In an embodiment, the first and second electrodes are interdigitated. The selective heating may be provided, for example, by one or more of a DC source and an AC source delivering a current selected from a range of 0.01 mA to 100 A, or 0.1 mA to 10 A, or 1 mA to 1 A, or 10 mA to 1 A. In an embodiment, the DC or AC source is pulsed at a frequency selected from a range of 1 Hz to 500 MHz, or 1 Hz to 100 MHz, or 10 Hz to 500 MHz, or 100 Hz to 50 MHz, or 1 MHz to 5 MHz. In an embodiment, the DC or AC source is activated for a duration selected from a range of 0.1 μs to 100 minutes, or 1 μs to 10 minutes, or 1 ms to 1 minute.

[0038] In an aspect, a method for purifying a layer of carbon nanotubes comprises: providing a precursor layer of substantially aligned carbon nanotubes supported by a substrate, wherein the precursor layer comprises a mixture of first carbon nanotubes and second carbon nanotubes; and selectively heating the first carbon nanotubes to separate the first carbon nanotubes from the second carbon nanotubes, thereby providing a purified layer of carbon nanotubes comprising at least 50%, 60%, 70%, 80%, or 90% of the first or the second carbon nanotubes.

[0039] In an embodiment, the present invention provides a transistor wherein the nanotube layer provides a semiconductor channel between first and second electrodes comprising source and drain electrodes. Transistors of the present invention may further comprise a gate electrode and dielectric layer; wherein the dielectric layer is provided between the gate electrode and the precursor layer. In some embodiments, the gate electrode is electrically isolated from, and positioned close enough to, the semiconductor channel such that electron transport through the channel is modulated by application of an electric potential to the gate electrode. In some embodiments, the layer has a strip geometry and comprises a plurality of strips of interconnected carbon nanotube networks, wherein strips of interconnected carbon nanotubes extend lengths from source to drain electrodes and are aligned in the electron transport direction of the transistor, optionally in a parallel strip orientation. In an embodiment, a transistor of this aspect is a thin film transistor. In an embodiment, a transistor of this aspect has an on/off ratio greater than or equal to 100, and preferably for some applications greater than or equal to 1000. In an embodiment, a transistor of this aspect has a field effect mobility greater than or equal to 0.1 cm² V⁻¹ s⁻¹, and preferably for some applications a field effect mobility greater than or equal to 10 cm² V⁻¹ s⁻¹. The invention provides nanotube-based transistor arrays and integrated circuits comprising a plurality of nanotube-based transistors.

[0040] In another aspect, the invention provides an electronic device comprising: a first electrode; a second electrode; and a layer of substantially aligned carbon nanotubes positioned between and in electrical contact with the first electrode and the second electrode, wherein the layer of substantially aligned carbon nanotubes comprises at least 90% semiconducting carbon nanotubes. In an embodiment, fabrication of the electronic device does not include a fluidic assembly step.

[0041] Electronic devices of the present invention include a range of nanotube-based devices. Electronic devices of the present invention include for example, transistors, diodes, light emitting diodes, integrated circuits and photodetectors comprising one or more layers of carbon nanotubes. For example, when the electronic device is a transistor, the first electrode may be a source electrode, the second electrode may be a drain electrode and the layer of substanstially aligned semiconducting carbon nanotubes may be a semiconductor channel of the transistor. In an embodiment, the layer of substantially aligned semiconducting carbon nanotubes provides a semiconductor channel between first and second electrodes, wherein the semiconductor channel has a length selected from a range of 50 nanometers and 1000 microns.

[0042] In an embodiment, contact printing of carbon nanotubes is achieved using soft lithography methods, such as dry transfer printing techniques using a conformable transfer device such as an elastomeric stamp.

[0043] Without wishing to be bound by any particular theory, there can be discussion herein of beliefs or understandings of underlying principles or mechanisms relating to the invention. It is recognized that regardless of the ultimate correctness of any explanation or hypothesis, an embodiment of the invention can nonetheless be operative and useful.

[0129] In general, the terms and phrases used herein have their art-recognized meaning, which can be found by reference to standard texts, journal references and contexts known to those skilled in the art. The following definitions are provided to clarify their specific use in the context of the invention.

[0130] “Carbon nanotube” and “nanotube” are used synonymously and refer to allotropes of carbon comprising one or more cylindrically configured graphene sheets. Carbon nanotubes include single walled carbon nanotubes (SWNTs) and multiwalled carbon nanotubes (MWNTs). Carbon nanotubes typically have small diameters (≈1-10 nanometers) and large lengths (up to several microns), and therefore may exhibit length to diameter ratios≈10² to about 10⁷. The longitudinal dimension of a nanotube is its length and the cross sectional dimension of a nanotube is its diameter (or radius). Carbon nanotubes include semiconducting carbon nanotubes, metallic carbon nanotubes, semi-metallic carbon nanotubes and mixtures of these. In some embodiments, the compositions and methods of the present invention include a mixture of semiconducting and metallic carbon nanotubes, for example, wherein the ratio of semiconducting nanotubes to metallic nanotubes is selected from a range of 9-0.5. In some embodiments, the compositions and methods of the present invention include a mixture of semiconducting and metallic carbon nanotubes, for example, wherein the ratio of semiconducting nanotubes to metallic nanotubes is greater than or equal to 1, preferably for some application greater than or equal to 2. In some embodiments, the compositions and methods of the present invention include a mixture of semiconducting and metallic carbon nanotubes, for example, wherein the extent of semiconducting nanotubes is enriched, for example using fractionation or other purification techniques.

[0131] “Supported by a substrate” refers to a structure that is present at least partially on a substrate surface or present at least partially on one or more intermediate structures positioned between the structure and the substrate surface. The term “supported by a substrate” may also refer to structures partially or fully embedded in a substrate, structures partially or fully immobilized on a substrate surface via an encapsulating layer (e.g., polymer layer) and structures partially or fully laminated on a substrate surface.

[0132] “Substantially aligned nanotubes” have lengths extending in longitudinal directions that are aligned with respect to each other but not provided in an absolutely parallel configuration. In some embodiments, for example, substantially aligned nanotubes have a partially linear geometry wherein their lengths assume a configuration with deviations from absolute linearity greater than about 10%, and in some embodiments with deviations from absolute linearity greater than about 20%. As used in this context, the term “parallel” refers to a geometry in which the lengths of carbon nanotubes are equidistant from each other for at least a portion of the points along their respective lengths and have the same direction or curvature. In one embodiment, for example substantially aligned nanotubes are aligned relative to each other with deviations from absolute parallelism that are greater than or equal to 20 degrees, and in some embodiments deviations from absolute parallelism that are greater than or equal to 10 degrees. In some embodiments, compositions and methods of the invention include carbon nanotube networks comprising substantially aligned nanotubes having at least one nanotube crossing. Alternatively, compositions and methods of the invention include carbon nanotube networks comprising randomly oriented nanotubes having at least one nanotube crossing.

[0133] “Monolayer of nanotubes” refers to a layer of nanotubes on a substrate surface wherein the coverage of the area of the surface of the substrate having nanotubes is less than 100%, preferably for some embodiments substantially less than 100%. In some embodiments, for example, a monolayer refers to a layer of nanotubes wherein the coverage of the area of the surface of the substrate having nanotubes is less than 10%, preferably for some applications less than 2%, and preferably for some applications less than 1%. In some embodiments, for example, a monolayer refers to a layer of nanotubes wherein the coverage of the area of the surface of the substrate having nanotubes is selected over the range of 0.1-10%, or preferably for some embodiments selected over the range of 0.5-2%. In some embodiments a monolayer of carbon nanotubes has a thickness less than or equal to 20 nanometers, preferably for some applications less than or equal to 10 nanometers and preferably for some applications less than or equal to 5 nanometers. Use of monolayers of carbon nanotubes in some embodiments of the invention are useful for achieving effective gate modulation in a nanotube-based electronic devices.

[0134] “Flexible” refers to a property of an object, such as a substrate, which is deformable in a reversible manner such that the object or material does not undergo damage when deformed, such as damage characteristic of fracturing, breaking, or inelastically deforming. Flexible polymers are useful with the methods described herein. Specific flexible polymers include, but are not limited to: rubber (including natural rubber, styrene-butadiene, polybutadiene, neoprene, ethylene-propylene, butyl, nitrile, silicones), acrylic, nylon, polycarbonate, polyester, polyethylene, polypropylene, polystyrene, polyvinyl chloride, polyolefin, elastomers and other flexible polymers known to those of skill in the art. In certain embodiments, flexible objects or materials can undergo strain levels selected over the range of 1% to 1300%, 10% to 1300%, or 100% to 1300% without resulting in mechanical failure (e.g., breaking, fracturing or inelastically deforming). In some embodiments, flexible objects or materials can be deformed to a radius of curvature selected over the range of 100 μm to 3 m without resulting in mechanical failure (e.g., breaking, fracturing or inelastically deforming).

[0135] A “Schottky barrier” is a potential energy barrier for electrons formed at a metal-semiconductor junction. In some cases, thermally excited electrons may absorb sufficient energy to overcome the barrier.

[0136] A “thermocapillary resist” is an material capable of responding to a localized temperature increase by migrating away from a heat source. This occurs when the material has a higher affinity for itself than for the surface material of the heated object. A “thermocapillary resist” also protects objects against at least one chemical and/or physical challenge applied to the resist. A thermocapillary resist may comprise an encapsulating material, a coating material and/or a conformal material.

[0137] “Substantially uniform” refers to a continuous, pinhole free layer of material.

[0138] “Nanotube crossings” in this context refers to a configuration wherein two or more nanotubes are in electrical contact, physical contact and/or in an overlapping configuration. For example, nanotube crossings in some embodiments refers to a configuration with two, three or four different nanotubes are provided on top of or underneath each other.

[0139] “Electronic device” generally refers to a device incorporating a plurality of components, and includes large area electronics, printed wire boards, integrated circuits, component arrays, biological and/or chemical sensors, physical sensors (e.g., temperature, strain, etc.), nanoelectromechanical systems, microelectromechanical systems, photovoltaic devices, communication systems, medical devices, optical devices and electro-optic devices.

[0140] “Semiconductor” refers to any material that is an insulator at a very low temperature, but which has an appreciable electrical conductivity at a temperature of about 300 Kelvin. In the present description, use of the term semiconductor is intended to be consistent with use of this term in the art of microelectronics and electronic devices.

[0141] A “component” is used broadly to refer to an individual part of a device. Components include, but are not limited to, thin film transistors (TFTs), transistors, diodes, electrodes, integrated circuits, circuit elements, control elements, photovoltaic elements, photovoltaic elements (e.g. solar cell), sensors, light emitting elements, actuators, piezoelectric elements, receivers, transmitters, microprocessors, transducers, islands, bridges and combinations thereof. Components may be connected to other components such as one or more contact pads as known in the art, such as by metal evaporation, wire bonding, and application of solids or conductive pastes, for example. Electronic devices of the invention may comprise one or more components, optionally provided in an interconnected configuration.

[0142] The terms “directly and indirectly” describe the actions or physical positions of one component relative to another component. For example, a component that “directly” acts upon or touches another component does so without intervention from an intermediary. Contrarily, a component that “indirectly” acts upon or touches another component does so through an intermediary (e.g., a third component).

[0143] “Encapsulate” refers to the orientation of one structure such that it is at least partially, and in some cases completely, surrounded by one or more other structures, such as a substrate, adhesive layer or encapsulating layer. “Partially encapsulated” refers to the orientation of one structure such that it is partially surrounded by one or more other structures, for example, wherein 30%, or optionally 50% or optionally 90%, of the external surfaces of the structure are surrounded by one or more structures. “Completely encapsulated” refers to the orientation of one structure such that it is completely surrounded by one or more other structures.

[0144] “Contiguous” refers to materials or layers that are touching or connected throughout in an unbroken sequence. In one embodiment, a contiguous layer of an implantable biomedical device has not been etched to remove a substantial portion (e.g., 10% or more) of the originally provided material or layer.

[0145] “Substrate” refers to a material, layer or other structure having a surface, such as a receiving surface, that is capable of supporting one or more components or devices. A component that is “bonded” to the substrate refers to a component that is in physical contact with the substrate and unable to substantially move relative to the substrate surface to which it is bonded. Unbonded components or portions of a component, in contrast, are capable of substantial movement relative to the substrate and may be referred to herein as in physical contact with the substrate.

[0146] “Processing” is used broadly to refer to treatment of a device or surface to obtain one or more desired functional attributes, including a functional attribute such as electrical interconnection. Examples of processing include providing a material such as by deposition of one or more components, including active electronic components, structural, barrier, or encapsulating layer(s), removal or partial removal of materials, or transformation or partial transformation of materials to obtain a desired physical parameter.

[0147] “Dielectric” refers to a non-conducting or insulating material. In an embodiment, an inorganic dielectric comprises a dielectric material substantially free of carbon. Specific examples of inorganic dielectric materials include, but are not limited to, silicon nitride, silicon dioxide, silk, silk composite, elastomers and polymers.

[0148] “Polymer” refers to a macromolecule composed of repeating structural units connected by covalent chemical bonds or the polymerization product of one or more monomers, often characterized by a high molecular weight. The term polymer includes homopolymers, or polymers consisting essentially of a single repeating monomer subunit. The term polymer also includes copolymers, or polymers consisting essentially of two or more monomer subunits, such as random, block, alternating, segmented, grafted, tapered and other copolymers. Useful polymers include organic polymers or inorganic polymers that may be in amorphous, semi-amorphous, crystalline or partially crystalline states. Crosslinked polymers having linked monomer chains are particularly useful for some applications. Polymers useable in the methods, devices and components include, but are not limited to, plastics, elastomers, thermoplastic elastomers, elastoplastics, thermoplastics and acrylates. Exemplary polymers include, but are not limited to, acetal polymers, biodegradable polymers, cellulosic polymers, fluoropolymers, nylons, polyacrylonitrile polymers, polyamide-imide polymers, polyimides, polyarylates, polybenzimidazole, polybutylene, polycarbonate, polyesters, polyetherimide, polyethylene, polyethylene copolymers and modified polyethylenes, polyketones, poly(methyl methacrylate), polymethylpentene, polyphenylene oxides and polyphenylene sulfides, polyphthalamide, polypropylene, polyurethanes, styrenic resins, sulfone-based resins, vinyl-based resins, rubber (including natural rubber, styrene-butadiene, polybutadiene, neoprene, ethylene-propylene, butyl, nitrile, silicones), acrylic, nylon, polycarbonate, polyester, polyethylene, polypropylene, polystyrene, polyvinyl chloride, polyolefin or any combinations of these.

[0149] “Elastomeric stamp” and “elastomeric transfer device” are used interchangeably and refer to an elastomeric material having a surface that can receive as well as transfer a material. Exemplary conformal transfer devices useful in some methods of the invention include elastomeric transfer devices such as elastomeric stamps, molds and masks. The transfer device affects and/or facilitates material transfer from a donor material to a receiver material. In an embodiment, a method of the invention uses a conformal transfer device, such as an elastomeric transfer device (e.g. elastomeric stamp) in a microtransfer printing process, for example, to transfer one or more single crystalline inorganic semiconductor structures, one or more dielectric structures and/or one or more metallic conductor structures from a fabrication substrate to a device substrate. Stamp is used broadly herein to refer to a substrate that can pick up components from one surface and transfer them to another surface. Accordingly, in an aspect the stamp may be a material having an adhesive surface that facilitates pick-up by adhesive forces, wherein the adhesive forces are less than subsequent contact forces when the stamp is brought into contact with a receiving surface. In an embodiment, the transfer printing may be direct surface-to-surface contact, from donor to a receiving surface.

[0150] “Elastomer” refers to a polymeric material which can be stretched or deformed and returned to its original shape without substantial permanent deformation. Elastomers commonly undergo substantially elastic deformations. Useful elastomers include those comprising polymers, copolymers, composite materials or mixtures of polymers and copolymers. Elastomeric layer refers to a layer comprising at least one elastomer. Elastomeric layers may also include dopants and other non-elastomeric materials. Useful elastomers include, but are not limited to, thermoplastic elastomers, styrenic materials, olefinic materials, polyolefin, polyurethane thermoplastic elastomers, polyamides, synthetic rubbers, PDMS, polybutadiene, polyisobutylene, poly(styrene-butadiene-styrene), polyurethanes, polychloroprene and silicones. In some embodiments, an elastomeric stamp comprises an elastomer. Exemplary elastomers include, but are not limited to silicon containing polymers such as polysiloxanes including poly(dimethyl siloxane) (i.e. PDMS and h-PDMS), poly(methyl siloxane), partially alkylated poly(methyl siloxane), poly(alkyl methyl siloxane) and poly(phenyl methyl siloxane), silicon modified elastomers, thermoplastic elastomers, styrenic materials, olefinic materials, polyolefin, polyurethane thermoplastic elastomers, polyamides, synthetic rubbers, polyisobutylene, poly(styrene-butadiene-styrene), polyurethanes, polychloroprene and silicones. In an embodiment, a polymer is an elastomer.

[0151] “Conformable” refers to a device, material or substrate which has a bending stiffness that is sufficiently low to allow the device, material or substrate to adopt any desired contour profile, for example a contour profile allowing for conformal contact with a surface having a pattern of relief features. In certain embodiments, a desired contour profile is that of a tissue in a biological environment.

[0152] “Conformal contact” refers to contact established between a device and a receiving surface. In one aspect, conformal contact involves a macroscopic adaptation of one or more surfaces (e.g., contact surfaces) of a device to the overall shape of a surface. In another aspect, conformal contact involves a microscopic adaptation of one or more surfaces (e.g., contact surfaces) of a device to a surface resulting in an intimate contact substantially free of voids. In an embodiment, conformal contact involves adaptation of a contact surface(s) of the device to a receiving surface(s) such that intimate contact is achieved, for example, wherein less than 20% of the surface area of a contact surface of the device does not physically contact the receiving surface, or optionally less than 10% of a contact surface of the device does not physically contact the receiving surface, or optionally less than 5% of a contact surface of the device does not physically contact the receiving surface. In an embodiment, a method of the invention comprises establishing conformal contact between a conformal transfer device and one or more single crystalline inorganic semiconductor structures, one or more dielectric structures and/or one or more metallic conductor structures, for example, in a microtransfer printing process, such as dry transfer contact printing. The receiving surface may functionally correspond to a release layer that is later used to release the components from a substrate that supports the release layer.

[0153] “Young's modulus” is a mechanical property of a material, device or layer which refers to the ratio of stress to strain for a given substance. Young's modulus may be provided by the expression:

$\begin{array}{cc}E=\frac{\left(\mathrm{stress}\right)}{\left(\mathrm{strain}\right)}=\left(\frac{L_0}{\Delta L}\right)\left(\frac{F}{A}\right),& \left(1\right)\end{array}$

[0154] where E is Young's modulus, L₀ is the equilibrium length, ΔL is the length change under the applied stress, F is the force applied, and A is the area over which the force is applied. Young's modulus may also be expressed in terms of Lame constants via the equation:

$\begin{array}{cc}E=\frac{\mu \left(3\lambda +2\mu \right)}{\lambda +\mu },& \left(2\right)\end{array}$

[0155] where λ and μ are Lame constants. High Young's modulus (or “high modulus”) and low Young's modulus (or “low modulus”) are relative descriptors of the magnitude of Young's modulus in a given material, layer or device. In some embodiments, a high Young's modulus is larger than a low Young's modulus, preferably about 10 times larger for some applications, more preferably about 100 times larger for other applications, and even more preferably about 1000 times larger for yet other applications. In an embodiment, a low modulus layer has a Young's modulus less than 100 MPa, optionally less than 10 MPa, and optionally a Young's modulus selected from the range of 0.1 MPa to 50 MPa. In an embodiment, a high modulus layer has a Young's modulus greater than 100 MPa, optionally greater than 10 GPa, and optionally a Young's modulus selected from the range of 1 GPa to 100 GPa. In an embodiment, a device of the invention has one or more components, such as substrate, encapsulating layer, inorganic semiconductor structures, dielectric structures and/or metallic conductor structures, having a low Young's modulus. In an embodiment, a device of the invention has an overall low Young's modulus.

[0156] “Low modulus” refers to materials having a Young's modulus less than or equal to 10 MPa, less than or equal to 5 MPa or less than or equal to 1 MPa.

[0157] “Guided growth” refers to growth of carbon nanotubes on a substrate wherein growth of individual nanotubes occurs along nanotube growth axes having selected spatial orientations, such as an orientation that is parallel to at least a portion of the growth axes of other nanotubes in the array and/or an orientation that is parallel to a principle guided growth axis of the guided growth substrate. Guided growth in the present invention arises from electrostatic, energetic and/or steric interactions between the nanotubes and or catalyst with the guided growth substrate. For example, guided growth of nanotubes may occur via a mechanism involving energetically favorable van der Waals interactions between growing nanotubes and/or catalyst particles with the lattice arrangement of the guided growth substrate. Guided growth of nanotubes may also occur via interaction of the nanotubes and/or catalyst particles with step edges, microfacets, nanofacets or other surface features of the receiving surface of the guided growth substrate.

[0158] “Guided deposition” refers to assembling and/or positioning materials, such as carbon nanotubes, on a substrate via a concerted process providing for spatial orientation, position and/or organization selected with good accuracy and precision. In some embodiments, guided deposition methods of the present invention provide a means of assembling and/or positioning carbon nanotubes in spatial orientations and positions selected such that their longitudinal axes are parallel to a principle guided deposition axis of a guided deposition substrate. In some embodiments, guided deposition methods of the present invention provide a means of assembling and/or positioning carbon nanotubes in orientations and positions wherein their longitudinal axes are parallel to each other.

[0159] “Parallel to a principle guided growth axis” refers to a spatial configuration of one or more carbon nanotubes wherein the length of the carbon nanotube is substantially equidistant to the principle guided growth axis of a guided growth substrate for at least some points along the length of the nanotube. “Parallel to a principle guided deposition axis” refers to a spatial configuration of one or more carbon nanotubes wherein the length of the carbon nanotube is substantially equidistant to the principle guided deposition axis of a guided deposition substrate for at least some points along the length of the nanotube. As used in this context, the term parallel is intended to encompass some deviation from absolute parallelism. Nanotubes parallel to a principle guided growth or deposition axis may have parallel spatial orientations with deviations from absolute parallelism that are less than or equal to 20 degrees, preferably deviations from absolute parallelism that are less than or equal to 10 degrees for some applications, and preferably deviations from absolute parallelism that are less than 1 degrees for some applications. The present invention provides nanotube arrays and related methods of making nanotube arrays wherein at least 95% of the nanotubes in the array extend lengths that are parallel to each other and/or parallel to a principle guided growth or deposition axis with deviations from absolute parallelism of less than or equal to 20 degrees.

[0160] FIG. 1A provides a schematic flow diagram illustrating a method of the present invention for purifying carbon nanotubes, for example, by separation of a first subset of nanotubes having one or more selected physical or chemical properties from other nanotubes in a nanotube precursor layer. Aspects of this method are particularly useful for purifying carbon nanotubes on the basis of optical and/or electronic properties, such as optical absorption, electronic conductivity, interaction with an electromagnetic field, electric field, magnetic field, etc. In an embodiment, for example, the aspect of the invention provides a means of selectively removing or transferring metallic nanotubes from a precursor layer comprising a mixture of longitudinally aligned metallic and semiconducting carbon nanotubes. Aspects of the methods of the present invention are particularly well suited for purification of SWNTs, including layers and thin films containing SWNTs such as monolayer and submonolayer SWNT layers.

[0161] As shown in FIG. 1A, a precursor layer of substantially aligned carbon nanotubes is provided comprising a mixture of first carbon nanotubes (e.g., a first subset of nanotubes having one or more selected physical or chemical property) and second carbon nanotubes (e.g., a second subset different from the first subset), for example, providing as a layer or film of substantially aligned carbon nanotubes including both metallic and semiconducting carbon nanotubes. Next, the precursor layer is covered with a thermocapillary resist provided in thermal contact, and optionally in physical contact, with the carbon nanotubes, for example, in thermal contact with at least a portion of, and optionally all of, the first carbon nanotubes. The process further includes selectively heating the first carbon nanotubes to generate a thermocapillary flow of the thermocapillary resist away from the first carbon nanotubes, thereby exposing at least a portion of the first carbon nanotubes of the precursor layer. In an embodiment, for example, metallic nantoubes are selectively heated in a manner such that semiconducting nanotubes in the precursor layer do not undergo an equivalent increase in temperature. The process further includes separating at least a portion of the first carbon nanotubes, such as the exposed first nanotubes, from the second carbon nanotubes to generate a purified layer of carbon nanotubes. In some embodiments, the exposed first nanotubes are separated via removal from the precursor layer, for example via chemical degradation or transfer processing.

[0162] FIG. 1B provides a schematic flow diagram corresponding to a method of the present invention further illustrating various process approaches for selective heating the first carbon naontubes having one or more selected physical or chemical properties. As shown in this figure, selective heating is achieved in some embodiments via absorption of electromagnetic radiation (EMR), for example, via absorption of continuous or pulsed EMR from a laser source or a microwave source. Alternatively, selective heating is achieved in some embodiments via applying a voltage and/or electricfield so as to selectively generate current in the first carbon naontubes having one or more selected physical or chemical properties. In some embodiments, for example, a transistor or direct two terminal device structure is used for applying an electromagnetic field or voltage to the carbon nanotubes undergoing processing, thereby selectively generting an increase in temperature for the first carbon naontubes relative to the second carbon nanotubes. In an embodiment, for example, a voltage applied across the nanotubes and an electric field is simultaneously applied, for example, using a gate electrode positioned proximate to carbon nanotubes extending from source and drain electrodes.

[0163] FIG. 10 provides a schematic flow diagram corresponding to a method of the present invention further illustrating various process approaches for selective removal of the first carbon naontubes that undergo selective heating. In some embodiments, for example, exposure of the first nanotubes allows access for subsequent removal via a range of processes. As shown in this figure, exposed carbon nanotubes are removed in some embodiments by chemical degradation processing that optionally destroy the carbon nanotubes, for example, via etching, exposure to a plasma, chemical removal or ablation. Alternatively, selective removal is achieved in some embodiments via transfer processing that optionally does not result in degradation of the first carbon nanotubes, for example, via transfer printing (e.g., dry transfer printing) or via solution processing, such as by contacting the exposed nanotubes with a solution, dissolution and subsequent transfer away from the precursor layer. In some embodiments, for example, transfer is achieved via transfer printing via contacting the exposed first carbon nanotubes with an elastomeric stamp.

[0164] FIG. 1D provides a schematic flow diagram corresponding to a method of the present invention further illustrating various process approaches for generating a precursor layer comprising substantially aligned carbon nanotubes. As shown in this figure, a guide growth substrate is provided in some embodiments, and substantially longitudinally aligned carbon nanotubes are grown on a receiving surface of the guided drowth substate. Alternatively, the precursor layer comprising substantially longitudinally aligned carbon nanotubes is achieved in some embodiments via contacting the receiving surface of a guided deposition substrate with a solution containing suspended carbon nanotubes, which optionally undergo self assembly to form the precursor layer.

[0165] Devices and methods of making and using the devices will now be described with reference to the figures. For clarity, multiple items within a figure may not be labeled and the figures may not be drawn to scale.

[0166] Among the remarkable variety of semiconducting nanomaterials that have been discovered over the past two decades, single walled carbon nanotubes (SWNTs) remain uniquely well suited for applications in high performance electronics, sensors and other technologies. The most advanced opportunities demand the ability to form perfectly aligned, horizontal arrays of purely semiconducting, chemically pristine SWNTs. Here, we present strategies that provide this capability, in which nanoscale thermocapillary flows in thin film organic coatings serve as highly efficient means for selectively removing metallic SWNTs from electronically heterogeneous aligned arrays grown on quartz substrates. The low temperatures and unusual physics associated with this process enable robust, scalable operation, with clear potential for practical use. Detailed experimental and theoretical studies reveal all of the essential attributes of the underlying thermophysical phenomena. Demonstrations include use of purified arrays in transistors with mobilities and on/off switching ratios that can exceed ˜1000 cm²/Vs and ˜10,000, respectively, and with current outputs in the mA range; simple logic gates built using such devices represent first steps toward integration into circuits.

[0167] Exploiting the exceptional electrical properties^1,2 of arrays of SWNTs in advanced applications^3-9 requires an ability to meet demanding requirements on degrees of alignment and purity in semiconducting behavior. Because direct, selective growth of purely semiconducting SWNTs (s-SWNTs) remains a topic of continuing study, the synthetic strategies that offer the greatest near-term potential fall into two categories: (1) purify the SWNTs and then assemble them into arrays; and (2) assemble the SWNTs into arrays and then purify them. The first has the advantage that it can build on recently developed wet chemical methods (ultracentrifugation^10,11, chromatography^12-14 and others^15,16) for purification. The disadvantages are that the resulting SWNTs are typically short (˜1 μm), chemically modified and/or coated, and difficult to assemble into arrays with high degrees of alignment^15,17-19. The second approach overcomes these limitations through the use of chemical vapor deposition techniques that, when used with quartz substrates, can yield nearly perfectly linear (>99.9% of SWNTs within 0.01° of perfect alignment), aligned arrays of long (100 μm and up to millimeters) and chemically pristine SWNTs^3,20-23. The main difficulty is in removing the m-SWNTs from such arrays. Techniques based on optical²⁴, electrical²⁵, or chemical^26-28 effects involve some combination of drawbacks, including incomplete removal of the m-SWNTs, partial removal and/or degradation of the s-SWNTs, inability to operate on aligned arrays and/or reliance on uncertain underlying mechanisms. Among these methods, electrical breakdown is noteworthy because it operates directly on the basis of relevant distinguishing characteristics in charge transport²⁵. This scheme, however, has two critical disadvantages. First, the required high power operation (˜90 μW/μm for channel lengths >1 μm, increasing as channel length decreases to values >1 mW/μm)^29-31 leads to shifts in threshold voltage, avalanche effects³², band-to-band tunneling, failure in gate dielectrics, and significant heat sinking at the contacts²⁹, all of which can prevent proper operation of the process. More significantly, breakdown only removes the m-SWNTs in isolated, narrow regions (˜100 nm lengths), with positions that are not well controlled³⁴. As a result, the vast majority of the m-SWNTs remain in the arrays, thereby preventing generalized use in subsequently fabricated devices.

[0168] We introduce an approach for eliminating m-SWNTs in which thermocapillary effects in thin organic coatings allow their use as selective, self-aligned etch resists. Here, physical mass transport occurs by surface tension gradients generated through spatial variations in temperature³⁵ associated with selective heating in the m-SWNTs. We illustrate these concepts through the complete physical removal of all m-SWNTs from linear, horizontally aligned arrays that contain both m-SWNTs and s-SWNTs, without any measurable adverse effects on the latter. FIG. 2(i)a,b shows schematic illustrations and corresponding atomic force microscope images of the process applied to a heterogeneous collection of SWNTs grown on quartz. Arrays formed in this fashion consist of individual, isolated SWNTs, with very few multi-walled nanotubes or bundles of SWNTs, but with a distribution of diameters between ˜0.6 and ˜2.0 nm and a range of chiralities^23,31. The key element in the purification process is an ultrathin (˜25 nm) amorphous layer of a small molecule organic species, in this example α,α,α′-Tris(4-hydroxyphenyl)-1-ethyl-4-isopropylbenzene³⁶, deposited uniformly over the arrays of SWNTs by thermal evaporation. We refer to this film (FIG. 8) as a thermocapillary resist. Besides its favorable thermophysical properties, the particular material used here is well suited for present purposes because it combines hydroxyl and phenyl moieties to facilitate formation of uniform, continuous coatings on the surfaces of both the quartz and the SWNTs. This behavior is critical for its role as an effective etch resist at extremely small thicknesses.

[0169] Metal and dielectric layers patterned at the edges of an area of interest enable current injection primarily into only the m-SWNTs, due to controlled electrostatically induced increases in the heights and widths of the Schottky barriers at the source ends of s-SWNTs (FIGS. 1a, 10 and 31-33). These layers represent removable, transistor structures in which the gates extend beyond the source electrodes by a distance small (˜5 μm) compared to the separation between the source and drain (˜30 μm). Applying a positive voltage to the gate (˜20 V) and a negative voltage to the drain (−40 to −50 V), while holding the source at electrical ground leads to selective Joule heating only in the m-SWNTs, due to approximately unipolar p-type behavior in the s-SWNTs. (FIGS. S27 and 28 illustrate good stability in the current outputs.) This set of bias conditions produces small increases in temperature only in the vicinity of the m-SWNTs. The large thermal gradients associated with nanoscale localization of these heat sources, in turn, drive mass transport in the thermocapillary resist. In typical experiments (fields of V_DS/L_ch˜1.33-1.66 V/μm along the SWNTs for 5 min, with substrate heating to 60° C. in vacuum; V_DS is the drain-source bias and L_ch is the distance between these electrodes), the resulting flows yield trenches centered at the m-SWNTs and extending throughout the thickness of the thermocapillary resist (FIG. 1b). Although most experiments were performed in vacuum (1×10⁻⁴ torr), inert environments can also be used (e.g. dry nitrogen, or argon). Excluding oxygen can help to prevent electrical breakdown in extreme cases of hot spots along the lengths of the SWNTs with localized defects. Reactive ion etching (O₂/CF₄) after thermocapillary flow eliminates only the m-SWNTs. Removing the residual thermocapillary resist and the metal/dielectric structures leaves a purified array of s-SWNTs, in a configuration well suited for planar integration into diverse classes of devices and sensors.

[0170] A key feature of this process is its exceptional efficiency in removing the m-SWNTs completely and exclusively. Such operation is important because most envisioned applications of s-SWNTs in electronics require purity at the level of 99.99% or better. For present purposes, we define a SWNT as metallic (semiconducting) if the ratio between the on (I_on) and off (I_off) currents (i.e. on/off ratio) in a well-designed transistor structure that incorporates this SWNT is less than (greater than) ˜100. This definition places SWNTs that are sometimes referred to as quasi-metallic into the m-SWNT classification. (In all cases, we observe a clear distinction between the behavior of m-SWNTs and s-SWNTs defined in this way, for populations of SWNTs grown on quartz. In particular, of the hundreds of SWNTs studied here and elsewhere, none exhibit on/off ratios between ˜50 and ˜1000.)³⁷ Detailed electrical characterization (i.e. I_on and I_off before and after purification) and assessment of statistics (i.e. total numbers of SWNTs before and after) performed on significant numbers of devices (35 devices, each with an active area of 30×30 μm to enable full visualization by atomic force microscopy; 377 SWNTs in total) provide quantitative insights into the effectiveness. FIG. 2(i)c shows a representative transfer characteristic for a device before and after purification, measured in air using the same metal/dielectric structures that enable selective Joule heating. The results illustrate a dramatic reduction in I_off (from 0.7 μA to 2×10⁻⁵ μA), thereby improving the on/off ratio from 2.7 to 3×10⁴. All devices showed on/off ratios <10 (median=3.7) before and >2×10³ (median=6.6×10⁴) after purification, independent of the number of SWNTs removed (FIG. 1d). The relatively small numbers (<30) of SWNTs in each device used to examine the statistics lead to the conclusion that the observed on/off ratios correspond to complete removal (i.e. 100%) of the m-SWNTs.

[0171] Other results suggest that the process also preserves most or all of the s-SWNTs. First, of the 377 SWNTs present initially, 63% (i.e. 238 SWNTs) remain after purification. This outcome is consistent with the expected percentage (˜66%) of s-SWNTs in collections of SWNTs grown by chemical vapor deposition^3,38. Second, among 28 devices where the SWNT type can be determined from electrical behaviors measured before and after purification (i.e. those that incorporate SWNTs), all of the m-SWNTs and none of the s-SWNTs show trenches (for optimized conditions; see Supplementary Information, FIG. 7). Third, reductions in I_on induced by purification are modest; for the device shown in FIG. 1c the ratio of I_on after the process to its value before is I_on,a/I_on,b˜25%. The weighted average from all of the devices is I_on,a/I_on,b˜30%. These results can be interpreted by examining the dependence of I_on,a/I_on,b on the percentage of SWNTs removed (FIG. 1e). The trends are consistent with models that assume 100% preservation of s-SWNTs, expected populations of s-SWNTs and m-SWNTs, and ratios of conductances of m-SWNTs to s-SWNTs (in their on state) that are within an experimentally observed range of 6:1 and 2:1 (FIG. 9). Collectively, then, all observations suggest highly selective and efficient purification, in which all m-SWNTs are eliminated, and most or all s-SWNTs are preserved without degradation. Rigorous electrostatic analysis indicates mobilities of ˜1000 cm²/Vs for the s-SWNTs (See Supplementary Information for details, FIG. 24), similar to values previously reported from unpurified arrays^3,4.

[0172] Detailed experimental and theoretical studies reveal quantitative aspects of heat transport and thermocapillary flow. We start by examining the distributions of temperature generated during Joule heating and their role in the behavior of the thermocapillary resist. FIG. 2(ii)a shows a scanning Joule expansion microscope^39,40 image of thermal expansion that results from Joule heating in an array of SWNT, at a drain-source bias condition V(t)=V_DS cos(2πft) with V_DS=5 V and f=386 kHz. Here, Joule heating with power density Q(t)=Q₀[1+cos (4πft)]/2 yields AC thermal expansion at a frequency of 2f, according to E(t)=[E₁+E₀ cos (4πft)]/2. The components E₁ and E₀ correspond to DC and AC thermal expansion, respectively. The image signal corresponds to the peak-peak value of the AC expansion, E₀. FIG. 2(ii)b shows topographical images of the same array coated with thermocapillary resist after application of several increasing values of V_DS (direct current for 5 min; substrate temperature 60° C.). A key observation is that the distributions in expansion, and therefore temperature (FIG. 2a), correspond directly to the geometries of trenches that appear in the thermocapillary resist (FIG. 2b). For instance, trenches progressively form with increasing V_DS in an order consistent with the temperatures revealed by scanning Joule expansion microscopy, e.g. trenches at the second and fifth SWNT from the right appear first and last, respectively. Related effects can be observed along an individual SWNT, where trenches nucleate in areas of enhanced temperature (‘hot spots’; arrows in FIG. 2a and the top frame of FIG. 2b). These indications establish a clear, although qualitative, connection between temperature and operation of the thermocapillary resist.

[0173] The first step towards quantitative understanding is an experimentally validated model for nanoscale heat flow in this system. Raw data from measurements by scanning Joule expansion microscopy indicate relative temperature increases but not their absolute values. FIG. 2(ii)c shows a representative cross-sectional profile of E₀ for the case of a SWNT with length ˜3.5 μm, along with the corresponding scanning Joule expansion microscopy image (FIG. 11). The power density per unit length is Q(t) with Q₀ estimated to be ˜13 μW/μm based on the total input power into the device, which includes three SWNTs on an SiO₂/Si substrate. Analytical models of temperature distributions that treat the SWNT as line heat source with length L and an input power density, Q(t) can be developed (see Supplementary Information, FIG. 12). Boundary conditions involve continuous temperature and heat flow at all material interfaces except those with the SWNT, negligible heat flow at the top surface and a constant temperature at the base of the substrate. At the SWNT interface, discontinuous heat flow, Q(t), is assumed, as a means to introduce the source of Joule heating. The results, together with materials constants taken from the literature (see Table 1) and analytical treatments of the resulting thermal expansion, yield expansion profiles that have both peak magnitudes (E₀˜50 pm) and spatial distributions (characteristic widths ˜340 nm) consistent with the scanning Joule expansion microscopy results (˜40 pm and ˜320 nm, respectively), when Q₀˜13 μW/μm, the estimated experimental value. FIG. 2(ii)d shows the associated AC temperature increases (θ₀) and thermal gradients (dθ₀/dx), where θ(t)=[θ₁+θ₀ cos (4πft)]/2.

TABLE 1
Thermal and Mechanical parameters used in analytical and FE models.
			Coefficient of
	Thermal	Thermal	Thermal	Yong's
	Conductivity	Diffusivity	Expansion	Modulus	Poisson
Materials	(Wm−1K−1)	10−6(m2s−1)	10−6(K−1)	109(Pa)	Ratio
Si	120(ref5)	73	2.6(ref6)	165(ref7)	0.28(ref8)
SiO2	1.3(ref9)	0.84(ref9)	0.50(ref10)	64(ref7)	0.17(ref11)
Quartz	6.0(ref12)	—	—	—	—
PMMA	0.19(ref13)	0.11(ref14)	50(ref15)	3.0(ref16)	0.35(ref17)
Tc-resist	0.2(meas)	—	—	—	—

When applied to the case of DC heating (f=0 Hz), and quartz substrates, the same analytical model yields an expression for the rise in temperature of the surface of the thermocapillary resist, θ=T−T_∞ where T_∞ defines the temperature of the background,

$\begin{array}{cc}\theta \left(x,y\right)=\frac{1}{2k_s\pi }{\int }_{-L/2}^{L/2}\eta {\int }_0^{\infty }\frac{Q_0J_0\left(\xi \sqrt{{\left(\eta -y\right)}^2+x^2}\right)}{\cosh \left(\xi h_f\right)+\frac{k_f}{k_s}\sinh \left(\xi h_f\right)}\xi & \left(1\right)\end{array}$

Here, k_s and k_f are the thermal conductivity of the thermocapillary resist and quartz substrate, respectively, and h_f is the thickness of the resist. This solution, which is also consistent with 3D finite element analysis (ABAQUS), suggests small increases in temperature at the SWNTs (˜2-5° C.) for power densities needed to achieve trenches. The flows arise from large associated gradients in temperature (˜20° C./μm). (See Supplementary Information, FIG. 12). Studies of flow induced with heated tips in an atomic force microscope verify the low temperature operation. (See Supplementary Information, FIG. 16.)

[0174] The characteristics of this flow provide several attractive features for present purposes, one of which is immediately evident from inspection of FIG. 2a,b. At large V_DS (V_DS/L_ch>1 V/μm), the trenches associated with SWNTs that have pronounced hot spots exhibit uniform widths. Likewise, SWNTs that show vastly different temperatures at a given V_DS display similar trench widths at sufficiently large V_DS (V_Ds/L_ch>1 V/μm). FIG. 2(ii)e presents results for the second SWNT from the right, extracted from FIG. 2a and the bottom frame of FIG. 2b. Clearly, the variations (between the mean value and maximum value) in expansion measured along the length of the SWNT are much larger than those in the trench widths (W_Tc), as quantified by separations between the raised regions of the thermocapillary resist at the edges of the trench. This physics provides an ability to realize trenches with small, uniform widths even across large-scale arrays that incorporate m-SWNTs with wide ranges of conductances and diameters, and consequently, peak temperatures and thermal gradients. FIG. 2(ii)f shows the average W_Tc for a number of different, individual SWNTs as a function of Q₀. Similar values occur over ranges of power (˜10-40 μW/μm) that exceed those associated with optimized conditions for purification. This behavior is much different than that expected from other thermally driven processes, such as sublimation or ablation, which typically involve abrupt temperature thresholds (FIG. 19).

[0175] The governing equation of motion for thermocapillarity in systems where the dimension along the SWNTs can be considered infinite corresponds to unidirectional flow in which the thickness profile in the thermocapillary resist can be written h(x,t) with

$\begin{array}{cc}\frac{\partial \stackrel{\_}{h}}{\partial \stackrel{\_}{t}}+\frac{\partial }{\partial \stackrel{\_}{x}}\left[\frac{\stackrel{\_}{\tau }{\stackrel{\_}{h}}^2}{2\stackrel{\_}{\mu }}+\frac{{\stackrel{\_}{h}}^3}{3\stackrel{\_}{\mu }}\frac{\partial }{\partial \stackrel{\_}{x}}\left(\stackrel{\_}{\gamma }\frac{{\partial }^2\stackrel{\_}{h}}{\partial {\stackrel{\_}{x}}^2}\right)\right]=0& \left(2\right)\end{array}$

where, h=h/h_f, x=x/h_f, t=γ₁Q₀t/(μ₀k_fh_f), μ=μ/μ₀, γ=k_fγ/(Q₀γ₁), θ=k_fθ/Q₀, τ=δθ/δx is the thermocapillary stress, μ is viscosity at temperature T_c g is the viscosity at the background temperature T=T_∞ and γ is the surface tension, which often exhibits a linear dependence on temperature (i.e., γ=γ₀−γ₁θ). FIG. 3a shows the geometry. The appropriate initial condition is h(x, t=0)=1. The boundary conditions are, h(x=±∞, t)=1, and zero pressure,

$\frac{{\partial }^2\stackrel{\_}{h}}{\partial {\stackrel{\_}{x}}^2}\left(\stackrel{\_}{x}=\pm \infty ,t\right)=0.$

With Eq. (1) for the temperature, numerical solutions to this system yield h=h/h_f, based on assumptions that (a) at each point along x, the temperature throughout the thickness of the thermocapillary resist is equal to the temperature at its interface with the substrate and (b) flow in the thermocapillary resist does not change the temperature distributions. FIG. 3b shows results for the case of polystyrene⁴¹, which exhibits behaviors like the thermocapillary resist (see Supplementary Information, FIG. 18) but has a known temperature dependent surface tension; γ=50.40 −0.0738θmJ/m². For this example, μ=1, consistent with the small rise in temperature, and Q₀=16.7 μW/μm (from experiment). The trenches gradually widen and deepen with time, as the displaced material forms ridges at the edges. Topographical measurements of a representative SWNT coated with thermocapillary resist after Joule heating for various time intervals (V_DS/L_ch˜0.7 V/μm, 30° C. background heating), show similar behaviors and profiles (FIG. 3c, d). At longer times, wider trenches result, to the point where SWNTs can be clearly observed at the base (FIG. 3e). Although the specific time durations needed to form complete trenches (t˜1) yield computed values of W_Tc that are larger than those observed experimentally, the theory captures the essential time dependence. For example, FIG. 3f shows the measured time dependence of W_Tc for two SWNTs, where both roughly follow the expected theoretical behavior, namely W_Tc˜t^0.25 (see FIGS. 13-15). Another prediction of the theory is that, for a given time t=300 s, the value of W_Tc depends only weakly on Q₀, over a remarkably large range, i.e. from ˜10 μW/μm to ˜35 μW/μm (see Supplementary Information, FIG. 15). This finding is consistent with observations discussed in the context of FIG. 2(ii). Finally, besides capturing the underlying physics, these models also suggest that optimal materials properties for thermocapillary resists include large temperature coefficients of surface tension and low viscosities. Furthermore, decreasing the thickness reduces the trench widths. Empirical studies of various materials for thermocapillary resists (see Supplementary Information, FIG. 18) led to the selection of the molecular glass reported here.

[0176] The envisioned use of thermocapillary enabled purification is in a preparatory mode, where it serves as one of the several steps, such as substrate cleaning, SWNT growth, transfer and others that occur before device processing. Such a scheme decouples purification from any detailed consideration in component or circuit layout, and is made possible by the ability to eliminate entirely all of the m-SWNTs. Two approaches can be considered. In the first, one or a small number of electrode structures, each with large lateral extent as illustrated in FIGS. 4a-b, enable elimination of m-SWNTs over significant areas. Here processing occurs on hundreds or thousands of SWNTs at once, using pulsed currents to avoid cumulative heating (see Supplementary Information, FIG. 17). FIG. 4c shows the electrical characteristics of the structure in FIG. 4a before and after purification, where I_{on, a}/I_{on, b} is ˜20% and the on/off ratio after the process is ˜1×10³, similar to results achieved on small arrays discussed previously. Current outputs can reach the mA range, as shown in FIG. 4c and FIG. 29. Additional details and examples of outputs up to ˜3 mA appear in FIG. 30. FIG. 4d illustrates an alternative approach, in which smaller pairs of interconnected electrodes provide for purification in distributed regions, capable of lithographic alignment at a coarse level to areas of interest in a final application. Effects on I_on and I_off in this case are in the range of those achieved in other geometries (see Supplementary Information, FIG. 21, Table 2).

TABLE 2
Summary of conductance of 1 × 5
arrays of devices before and after TcEP.
Array #	Ion, b (A)	Ion, a (A)	Ion/Ioff ratio	Ion, a/Ion, b (%)
#1	4.50E−06	1.02E−06	1.06E+03	22.6
#2	5.28E−06	1.03E−06	6.60E+03	19.5
#3	4.99E−06	1.13E−06	2.46E+04	22.7
#4	7.18E−06	1.21E−06	9.26E+03	16.9
#5	1.20E−05	1.16E−06	4.38E+03	9.7
AVG	6.80E−06	1.11E−06	9.18E+03	18.3

The process can be applied to arrays of SWNTs that have both local (FIG. 20) and area averaged (FIG. 17) densities of a few per micron. Improved densities can be realized using transfer techniques.^42-44 Although high densities can be important in electronics, modest or low densities can be useful in sensors and other devices.

[0177] To simplify implementation, a re-usable bottom electrode structure can be exploited to eliminate cycles of processing that would otherwise be necessary for repetitive fabrication of top electrode structures described previously. As shown in FIG. 5a, a single, re-usable substrate provides a fully formed, bottom split gate structure for use in the purification process. Aligned arrays of SWNTs transferred to this substrate using techniques described previously^42-44 can be processed to remove m-SWNTs. The remaining s-SWNTs can then be transferred to a final device substrate. FIG. 5a schematically illustrates two cycles of this process. FIG. 5b,c present transfer characteristics of arrays of SWNTs before and after purification, performed with a single back gate structure in two separate cycles of use. Additional details appear in FIGS. 25 and 26.

[0178] Because the purification occurs on entire arrays of SWNTs, the resulting s-SWNTs can be easily integrated into nearly any type of component or circuit layout. Devices with short channel lengths (˜800 nm) defined using a near-field phase shift lithography technique⁵⁰ provide a demonstration, as shown in FIG. 6a,b. FIG. 6c presents electrical properties that are consistent with those of long channel devices when effects of contact resistance are included. The observed hysteresis has known origins that can be minimized using strategies described elsewhere^45-48. A simple logic gate, consisting of two transistors using arrays of s-SWNTs, provides an additional example of the utility of this process, as illustrated in FIG. 6d,e. FIG. 6f shows the voltage transfer characteristics and gain associated with this p-type inverter. The peak gain is ˜4, consistent with expectation for this design (see Supplementary Information, FIGS. 22-23).

[0179] In summary, the purification method introduced here provides scalable and efficient means for converting heterogeneous arrays of SWNTs into those with purely semiconducting character. An important advantage is that the processing steps are fully compatible with fabrication tools used for commercial manufacture of digital electronics and display backplanes.

[0180] Fabricating Top Electrode Structures.

[0181] Photolithography, electron beam evaporation (2 nm Ti, 48 nm Pd; AJA) and liftoff defined source and drain electrodes. Reactive ion etching (100 mTorr, 20 sccm O₂, 100 W, 30 s; Plasma-Therm) removed SWNTs everywhere except for regions between these electrodes. Prebaking (250° C., 2 hr, in a glove box) a spin cast (4000 rpm, 60 s) solution to a spin-on glass (SOG; Filmtronics; methylsiloxanes 215F, 15:1 diluted in IPA)⁴⁵ and then curing the material formed films of SOG (35 nm) uniformly across the substrate. Atomic layer deposition (80° C.; Cambridge NanoTech) created films of Al₂O₃ (30 nm) on top of the SOG. Photolithography (AZ 5214) and etching (6:1 BOE for 50 s) removed the SOG/Al₂O₃ bilayer from the region between the source/drain electrodes. Prebaking (110° C., 10 min) a spin cast (4000 rpm, 60 s) solution of polyvinyl alcohol (PVA; M_w between 89,000 and 98,000, 99%, hydrolyzed, Sigma-Aldrich; solvent: D.I. water) mixed with photosensitizer (ammonium dichromate, >99.5% at 40:1 by weight⁴⁹) followed by photolithographic patterning and postbaking (110° C., 30 min) defined a layer of PVA (˜400 nm) on top of and aligned to the SOG/Al₂O₃. Photolithography (AZ 5214), electron beam evaporation (50 nm Ti or Cr), and lift-off defined a gate electrode on top of this dielectric stack.

[0182] Thermocapillary flow and etching to remove m-SWNTs.

[0183] Thermal evaporation (0.5 Å/s) formed thin layers (25 nm) of the thermocapillary resist (α,α,α′-Tris(4-hydroxyphenyl)-1-ethyl-4-isopropylbenzene; TCI international). Applying a voltage between the source/drain electrodes (V_DS=−40 to −50 V, corresponding to fields of V_DS/L_ch ˜1.33-1.66 V/μm) while biasing the source/gate to +20 V under vacuum (˜10⁻⁴ Torr, Lakeshore) and holding the substrate temperature at 60° C., all for ˜5 min, yielded trenches in the thermocapillary resist at the locations of the m-SWNTs. Reactive ion etching (10 mTorr, 1 sccm O₂, 1 sccm CF₄, 75 W, 20 s; Plasma-Therm RIE) eliminated the m-SWNTs exposed in this manner, without affecting the s-SWNTs. Immersion in acetone for 30 min removed the thermocapillary resist, to complete the process.

[0184] Scanning Joule Expansion Microscopy.

[0185] Devices were wire bonded to a sample holder (Spectrum Semiconductor Materials) to allow contact mode atomic force microscopy (Asylum MFP 3D and Cantilever Asylum # Olympus AC240TS) while applying suitable biases to the electrode structures. A function generator (Agilent 33250A) provided the AC bias and the reference signal for lock-in (Stanford SR844) detection of the amplitude and phase of the signal associated with the thermal expansion. Measurements on quartz were performed with thick layers (˜100 nm) of thermocapillary resist deposited on arrays of SWNTs between two electrodes (i.e. two terminal devices, with L=30 μm, W=30 μm). The bias consisted of a sinusoidal voltage with amplitude of 5 V and frequency of 386 kHz. Measurements on SiO₂ (200 nm)/Si, used similar two terminal devices, but with spin cast overcoats of poly(methylmethacrylate) (Microchem. 950 A2) with thicknesses of ˜120 nm. The bias in such cases consisted of a sinusoidal voltage with amplitude of 3V and frequency of 30 kHz with the substrate electrically grounded.

[0186] Studying the Kinetics of Thermocapillary Flow.

[0187] Thermal evaporation formed thin layers of thermocapillary resist (˜25 nm) on two terminal devices (L=30 μm, W=100 μm) configured for electrical connection while in the atomic force microscope (Asylum research ORCA sample mount). Images collected by fast scanning (˜30 s acquisition times) defined the topography of a small region of interest. In between scans, application of electrical biases for durations, of 0.1 s at short times and increasing to 30 min at long times caused the trenches to increase in width by controlled amounts. A total of ˜400 scans, corresponding to the device under bias for a total, accumulated time of ˜8 hr, revealed the kinetics of trench formation, throughout and well beyond the time of interest.

[0188] Fabricating Reusable Bottom Electrode Structures

[0189] Photolithography and etching defined gate electrodes (2 nm Cr and 13 nm Pd). A bilayer of silicon nitride (STS 200 nm by plasma enhanced chemical vapor deposition) and SOG (35 nm)⁴⁵ served as a gate dielectric. Source and drain electrodes (2 nm Cr and 13 nm Pd) were formed using the same procedures as those for the gate completed the fabrication.

[0190] Finite Element Modeling of Heat Flow.

[0191] The 3D finite element model for the temperature distributions used eight-node, hexahedral brick elements in a finite element software package (ABAQUS) to discretize the geometry. The SWNT was treated as a volume heat source, with a zero heat flux boundary at the top surface of Tc-resist, and a constant temperature T_∞ the bottom of the quartz substrate.

[0192] Numerical Modeling of Thermocapillary Flows.

[0193] The equations of motion represent a pair of coupled partial differential equations

$\frac{\partial {\stackrel{\_}{h}}_1}{\partial \stackrel{\_}{t}}=\frac{\partial }{\partial \stackrel{\_}{x}}\left(-\frac{\stackrel{\_}{\tau }{\stackrel{\_}{h}}_1^2}{2\stackrel{\_}{\mu }}-\frac{{\stackrel{\_}{h}}_1^3}{3\stackrel{\_}{\mu }}\frac{\partial \stackrel{\_}{\gamma }}{\partial \stackrel{\_}{x}}{\stackrel{\_}{h}}_2-\frac{{\stackrel{\_}{h}}_1^3\stackrel{\_}{\gamma }}{3\stackrel{\_}{\mu }}\frac{\partial {\stackrel{\_}{h}}_2}{\partial \stackrel{\_}{x}}\right)\mathrm{and}$ $\frac{{\partial }^2{\stackrel{\_}{h}}_1}{\partial {\stackrel{\_}{x}}^2}-{\stackrel{\_}{h}}_2=0$

where h₁=h. The boundary conditions are h₁(x, t=0)=1 h₂(x, t=0)=0, h₁(x=±∞, t)=1 and h₂(x=±∞, t)=0. A Fortran routine (PDE_1D_MG) was used to solve these two partial differential equations directly.

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[0244] Individual SWNT Thermocapillary Trench Experiments.

[0245] Thermocapillary flows in thermocapillary resists (Tc-resists) were studied (5 min, 60° C. background heating) using devices that incorporate single or several SWNTs. Devices were fabricated in geometries to ensure that only 1 or 2 SWNTs were present in the channel, as confirmed by AFM. In the case of single SWNT devices, the electronic type could be determined directly from the electrical properties (on/off ratio >100, s-SWNT; on/off ratio <100, m-SWNT). For devices with 2 SWNTs that exhibited high on/off ratio, both SWNTs must be s-SWNTs. For similar devices with low on/off ratio before thermocapillary enabled purification (TcEP) and high on/off ratio after TcEP, one SWNT must be a m-SWNT and the other a s-SWNT. Devices with two m-SWNTs were not used for these experiments. Biases were applied to increase the resistance of the s-SWNTs (i.e. their “off” state, at +20 V_GS), resulting in relatively low (high) current levels for all s-SWNTs (m-SWNTs). As a result, all 2 SWNT devices fell into one of two cases: their currents were dominated by a single m-SWNT or they contained two s-SWNTs. For the second case, one s-SWNT is likely to dominate, but at worst, the s-SWNTs have roughly equal current levels in which case the data served as an upper limit for the actual current and could be as little as half that level. The large number of devices that were studied and the observation that most s-SWNTs showed current levels more than ten times below the threshold for trench formation suggest that assumptions concerning relative current distributions in s-SWNTs are unlikely to affect the broad conclusions. The thresholds were accurately defined by devices with just one SWNT. We performed systematic studies of trenches formed under a range of input powers for single s-SWNTs and single m-SWNTs. A range of outcomes for input powers between 0.1-30 μW/μm (SWNT length=30 μm) were observed by AFM (FIG. 7a). For all experiments, powers below 3.3 μW/μm led to no trenches. For powers between 3.3-10 μW/μm most devices exhibited trenches, but only partly along the lengths of the SWNTs. For all experiments with powers greater than 10 μW/μm, trenches with widths W_Tc˜250-300 nm, were observed along the entire lengths of the SWNTs. This analysis provides information on threshold powers for trench formation, which, via analytical modeling, can be correlated to peak temperatures of ˜2-5° C. By sorting these same results by input field and SWNT electronic type (FIG. 7b), optimized conditions can be established. At fields below the optimal range, the heating is insufficient to yield trenches along the entire lengths of all of the m-SWNTs; at higher fields, the most conductive s-SWNTs begin to show partial trench formation. However, for optimized conditions, all s-SWNTs yielded no trenches, while all m-SWNTs yield complete trenches, as required for proper operation of TcEP.

[0246] Deposition conditions for the Tc-resist and its properties.

[0247] FIG. 8a shows the chemical structure of the Tc-resist. The material was deposited via thermal evaporation. FIG. 8b shows AFM images of a film deposited on a SiO₂/Si substrate. The surface roughness is comparable to that of the underlying substrate, i.e. 2-3 A. Experiments that involved heated substrates (quartz or SiO₂/Si) with thin coatings of Tc-resist (˜25 nm thickness) showed an onset of dewetting between 80-120° C., depending on substrate hydrophobicity. Clean, hydrophilic surfaces yielded higher dewetting temperatures. In vacuum (˜1×10⁻⁴ torr), sublimation began at ˜100° C., as determined by experiments using lithographically patterned, calibrated resistive heaters of Pt (lengths ˜1-3 mm, widths ˜6-10 μm). Differential Scanning Calorimetry (dry nitrogen) yielded a specific heat of ˜1.5 J/C/cm³ (FIG. 8c, T_m=225° C., T_g=95° C., T_rc=155° C.). Time resolved, picosecond pump-probe experiments based on thermoreflectance¹ using relatively thick films (300 nm, FIG. 8d) yielded thermal conductivities of ˜0.2 W/m/K, similar to most organic thin films. Furthermore, similar experiments with relatively thin films (˜25, ˜50, ˜75 nm), suggest that the thermal interface resistance between quartz and the Tc-resist is ˜50-150 MW/m²/K.

[0248] Single SWNT Conductance Statistics.

[0249] The large number of SWNTs studied by TcEP on devices with small arrays of SWNTs provided statistics on the process. For each array, the number of SWNTs and the values of I_{on, b} and I_{on, a} (shown for a typical device, FIG. 9b) together with an assumption that all of the removed SWNTs are m-SWNTs and all of the remaining SWNTs are s-SWNTs, yields estimates for the average conductance of these two types of SWNTs, for each device. FIG. 9a shows a histogram of the conductances of individual SWNTs determined in this way. (We note that a device with 3 s-SWNTs and an average conductance of 50 kΩ/μm is counted 3 times.) The mean conductances for m-SWNTs and s-SWNTs (in their on state) are 17 kΩ/μm and 75 kΩ/μm, respectively. These distributions are in the range of those reported for single SWNTs studied previously²; with values of 35 kΩ/μm (m-SWNTs) and 55 kΩ/μm (s-SWNTs) for backgated devices (FIG. 9c)²; and 140 kΩ/μm (m-SWNTs) and 1000 kΩ/μm (s-SWNTs) for top gated devices². Using the experimentally observed ratios of numbers of m-SWNTs to s-SWNTs, and a ratio of mean conductances of ˜4:1, the assumption that TcEP preserves all s-SWNT is consistent with observations.

[0250] Partial Gate Device Properties.

[0251] The electrode geometries used for TcEP involved a partial gate structure shown schematically in FIG. 1a. This configuration results in reduced gate-drain fields, which minimize Schottky barrier tunneling, band-to-band tunneling and avalanche phenomena³. The operation avoids ambipolar conduction at the bias conditions needed for TcEP (characterization at conditions consistent with TcEP, 60° C. background heating, ˜1×10⁴ torr). These effects are clearly observed in transfer characteristics for devices based on an individual s-SWNT in partial gate (FIG. 10a) and full gate (FIG. 10b) layouts. Here, the same SWNT, same pair of source-drain electrodes, and dielectric were used for both devices. The only difference is the length of gate extension into the channel. Both configurations exhibit ideal device behavior at low bias (V_DS=−0.1 V). At high bias (V_DS<-10 V, L=30 μm), however, the full gate device shows pronounced ambipolar conduction, unlike the partial gate case. FIG. 9c illustrates the effect of source-drain bias and gate overlap (L_ov) on on/off ratio, where all measurements were performed on the same SWNT. The device with 5 μm gate overlap (i.e. the configuration used for TcEP) exhibits on/off ratios 2-3 orders of magnitude higher than the device with full overlap (L_ov=30 μm). FIG. 10d shows the ability of the partial gate configuration to maintain current levels several orders of magnitude lower than that of the full gate configuration, even for long bias durations (“off” state, V_DS=−40V, V_GS=+20V, 5 min, consistent with TcEP experiments).

[0252] Scanning Joule Expansion Microscopy.

[0253] FIG. 11a shows a scanning Joule expansion microscope (SJEM) image⁴ of an array of SWNTs (two terminal device, SiO₂ (200 nm)/Si substrate) covered with a 120 nm thick film of PMMA, collected at the condition of V(t)=V_DS cos (2πft) with V_DS=3 V and f=30 kHz and V_Gs=0 V. FIG. 11a shows the integrated expansion percentage (I.E.P.). To determine this quantity, we first located the maximum expansion along each measured cross-section perpendicular to the length of the SWNT. Next, we integrated these values along each SWNT, to get the integrated expansion (I.E.). The I.E.P. is the ratio of the I.E. to the sum of the I.E. for all three SWNTs, times 100%. Since the maximum expansion is proportional to the input power, the I.E.P. can be used to estimate the power input for each SWNT, from the measured total power into the device. FIG. 11c shows a 3D rendering of the SJEM signal for the SWNT associated with FIG. 2b. FIG. 11d shows a schematic of the SJEM measurement.

[0254] Computed temperature distributions associated with Joule heating in individual SWNTs. In this section, we describe procedures for determining the temperature distribution resulting from a SWNT embedded in a film of PMMA on SiO₂/Si substrate with power dissipation at the SWNT for an AC applied voltage. The temperature rise at the surface of the Tc-resist can be obtained by considering first the analytical solution for a disk heat source with radius r₀ at the interface between the Tc-resist and the SiO₂. Here, a cylindrical coordinate system is set such that the origin is coincident with the center of the heat source as shown in FIG. 12a,b. The heat transfer governing equation temperature in cylindrical coordinate is

$\begin{array}{cc}\frac{{\partial }^2T}{\partial r^2}+\frac{1}{r}\frac{\partial T}{\partial r}+\frac{{\partial }^2T}{\partial z^2}-\alpha \frac{\partial T}{\partial t}=0& \left(1\right)\end{array}$

where

$\alpha =\frac{k}{c\rho }$

is thermal diffusivity, k is thermal conductivity, ρ is density, and c is specific heat capacity. The subscripts 0, 1 and 2 denote Tc-resist, SiO₂ and Si, respectively. Setting θ=T−T_∞, where T_∞ is the remote temperature, the above equation is equivalent to

$\begin{array}{cc}\frac{{\partial }^2\theta }{\partial r^2}+\frac{1}{r}\frac{\partial \theta }{\partial r}+\frac{{\partial }^2\theta }{\partial z^2}=\alpha \frac{\partial \theta }{\partial t}& \left(2\right)\end{array}$
The boundary conditions are

z=−h₀(top surface)  

$\begin{array}{cc}-k_0\frac{\partial \theta }{\partial z}{|}_{z=-h_0}=0& \left(3\right)\end{array}$
z=0  

$\begin{array}{cc}{\theta }_{0^{+}}={\theta }_{0^{-}},-k_0\frac{\partial \theta }{\partial z}{|}_{z=0^{-}}=\{\begin{array}{cc}{Q}_1& 0\le r\le r_0\\ Q_{c1}& r_0<r<+\infty \end{array},-k_1\frac{\partial \theta }{\partial z}{|}_{z=0^{+}}=\{\begin{array}{cc}{Q}_2& 0\le r\le r_0\\ Q_{c1}& r_0<r<+\infty \end{array}& \left(4\right)\end{array}$

where Q₁ and Q₂ satisfy

$-Q_1+Q_2=\frac{P}{\pi r_0^2},$

P is the total power of the disk.

z=h₁  (3)

$\begin{array}{cc}{\theta }_{h_1^{+}}={\theta }_{h_1^{-}}\mathrm{and}-k_1\frac{\partial \theta }{\partial z}{|}_{z=h_1}=-k_2\frac{\partial \theta }{\partial z}{|}_{z=h_1}& \left(5\right)\end{array}$
z=h₁+h₂˜∞  (4)

θ_h1+h2=0  (6)

[0255] For a voltage V(t)=V₀ cos (ωt) with angular frequency ω=2πf, the Joule heating has angular frequency 2ω. The total power of the disk can then be obtained as P(t)=P₀[1+cos (2ωt)]/2, which yields a constant temperature rise (DC component) due to P₀/2 and a time oscillating temperature rise (AC component) due to P₀ cos(2ωt)/2. It should be noted that the DC component of temperature rise can be easily obtained by setting ω=0 in the solution of AC component.

[0256] The time oscillating temperature rise (AC component) has the same frequency as the power density, i.e. θ(r,z,t)=θ(r,z)exp(2ωti). Therefore, we have

$\begin{array}{cc}\frac{{\partial }^2\theta }{\partial r^2}+\frac{1}{r}\frac{\partial \theta }{\partial r}+\frac{{\partial }^2\theta }{\partial z^2}-q^2\theta =0\mathrm{where}q^2=\frac{2\omega }{\alpha }\mathrm{and}\theta =\theta \left(r,z\right).& \left(7\right)\end{array}$

[0257] Equation (7) can be solved via the Hankel transform, for which the following transform pair of the first kind is applicable,

φ(r,z)=∫₀^∞φ(ξ,z)J₀(ξr)ξdξ

φ(ξ,z)=∫₀^∞φ(r,z)J₀(ξr)rdr  (8)

where φ(r, z) is the original function, φ(ξ, z) is the transform, and J₀ is the 0^th order Bessel function of the first kind. Equation (7) then becomes

$\begin{array}{cc}\frac{{}^2\stackrel{\_}{\theta }}{z^2}-\left({\xi }^2+q^2\right)\stackrel{\_}{\theta }=0& \left(9\right)\end{array}$
Solving the above equation gives

θ=Aexp(z√{square root over (ξ²+q²)})+Bexp(−z√{square root over (ξ²+q²)})  (10)

where A and B are two unknown functions to be determined according to boundary and continuity conditions. The temperature rise is then obtained by

θ=∫₀⁼⁽Ae^−ξz+Be^ξz)J₀(ξr)ξdξ  (11)

Therefore, the temperature rise in Hankel space at each layer is obtained as

θ₀(ξ,z)=A₀exp(z√{square root over (ξ²+q₀²)})+B₀exp(−√{square root over (zξ²+q₀²)})  Tc-resist:

θ₁(ξ,z)=A₁exp(z√{square root over (ξ²+q₁²)})+B₁exp(−√{square root over (zξ²+q₁²)})  SiO₂ layer:

θ₂(ξ,z)=A₂exp(z√{square root over (ξ²+q₂²)})+B₂exp(−√{square root over (zξ²+q₂²)})  Si layer:

With BCs (3)-(6) in Hankel space, we can obtain the temperature at each layer. For example, A₀ and B₀ are given by

$\begin{array}{cc}{A}_0=\frac{\kappa +1}{\begin{array}{c}\left(1-\kappa \right)\left[1+\exp \left(-2h_0\sqrt{{\xi }^2+q_0^2}\right)\right]+\\ \left(\kappa +1\right)\frac{k_0\sqrt{{\xi }^2+q_0^2}}{k_1\sqrt{{\xi }^2+q_1^2}}\left[1-\exp \left(-2h_0\sqrt{{\xi }^2+q_0^2}\right)\right]\end{array}}\frac{P_0}{k_1\pi \xi \sqrt{{\xi }^2+q_1^2}}\frac{J_1\left(\xi r_0\right)}{2r_0}B_0=A_0\exp \left(-2h_0\sqrt{{\xi }^2+q_0^2}\right)\mathrm{where}\kappa =\frac{1-\frac{k_2}{k_1}\frac{\sqrt{{\xi }^2+q_2^2}}{\sqrt{{\xi }^2+q_1^2}}}{1+\frac{k_2}{k_1}\frac{\sqrt{{\xi }^2+q_2^2}}{\sqrt{{\xi }^2+q_1^2}}}\exp \left(-2h_1\sqrt{{\xi }^2+q_1^2}\right)& \left(12\right)\end{array}$

[0258] The temperature rise due to the disk heat source can be obtained by Eq. (11). For example, the temperature rise in the Tc-resist is obtained as

θ(r,z)=∫₀^+∞A₀[exp(z√{square root over (ξ²+q₀²)})+exp(−z√{square root over (ξ²+q₀²)}−2h₀√{square root over (ξ²+q₀²)})]·J₀(ξr)ξdξ  (13)

The surface temperature rise of the Tc-resist is then obtained by setting z=−h₀ as

θ(r)=∫₀^+∞2A₀exp(−h₀√{square root over (ξ²+q₀²)})·J₀(ξr)ξdξ  (13)

As r₀→0, we obtain the temperature rise due to a point heat source as

$\begin{array}{cc}{\theta }_F\left(r\right)=\frac{1}{4k_1\pi }{\int }_0^{+\infty }\frac{\left(\kappa +1\right)J_0\left(\xi r\right)\xi }{\begin{array}{c}\left(1-\kappa \right)\cosh \left(h_0\sqrt{{\xi }^2+q_0^2}\right)+\\ \left(\kappa +1\right)\frac{k_0\sqrt{{\xi }^2+q_0^2}}{k_1\sqrt{{\xi }^2+q_1^2}}\sinh \left(h_0\sqrt{{\xi }^2+q_0^2}\right)\end{array}}·\frac{P_0}{\sqrt{{\xi }^2+q_1^2}}\xi & \left(15\right)\end{array}$

[0259] For a point heat source at (0,η,0) with heat generation P₀=Q₀ ·dη and Q₀ as the power density, the integration of Eq. (15) with r=√{square root over ((η−y)²+x²)} gives the temperature rise at point (x, y) due to a line heat source as

$\begin{array}{cc}\theta \left(x,y\right)=\frac{1}{4k_1\pi }{\int }_{-L/2}^{L/2}\eta {\int }_0^{+\infty }\frac{\left(\kappa +1\right)J_0\left(\xi \sqrt{{\left(\eta -y\right)}^2+x^2}\right)\xi }{\begin{array}{c}\left(1-\kappa \right)\cosh \left(h_0\sqrt{{\xi }^2+q_0^2}\right)+\\ \left(\kappa +1\right)\frac{k_0\sqrt{{\xi }^2+q_0^2}}{k_1\sqrt{{\xi }^2+q_1^2}}\sinh \left(h_0\sqrt{{\xi }^2+q_0^2}\right)\end{array}}·\frac{Q_0}{\sqrt{{\xi }^2+q_1^2}}\xi & \left(16\right)\end{array}$

[0260] It should be noted that Eq. (16) gives the magnitude of time oscillating temperature rise, i.e., θ₀ in the main text is equal to 2θ(x,y). The total surface temperature rise can be obtained as θ(x,y,t)=θ(x,y)|_ω=0+θ(x,y)cos(4πft)=[θ₁+θ₀ cos(4πft)]/2 due to a line heat source with power density Q(t)=Q₀[1+cos (2ωt)]/2.

[0261] Here, boundary conditions involve continuous temperature and heat flow at all material interfaces except those with the SWNT, negligible heat flow at the top surface and a constant temperature at the base of the substrate. For the SWNT interface, discontinuous heat flow, is assumed, as a means to introduce the Joule heat source. The results, together with materials constants taken from the literature (see Table 1) and analytical treatments of the resulting thermal expansion, yield expansion profiles that have both peak magnitudes (E₀˜50 pm) and spatial distributions (characteristic widths ˜340 nm) that are remarkably consistent with the SJEM results (˜40 pm and ˜320 nm, respectively), when Q₀˜13 μW/μm, the estimated experimental value.

[0262] Computed Thermal Expansion at the Surface of a Thin Film Coating on a Heated SWNT on a Substrate.

[0263] Under the assumptions of (1) plane strain in y direction since the length of SWNT (˜30 μm) is much larger than its radius and (2) plane stress in z direction since the film is very thin (˜25 nm), the peak-peak value of AC surface thermal expansion (i.e., the out-of-plane displacement) of the Tc-resist can be obtained as

$\begin{array}{cc}{E}_0=\frac{1+v_0}{1-v_0}{\beta }_0h_0\theta \left(x,y=-h_0\right)& \left(17\right)\end{array}$

where v₀ and β₀ are the Poisson's ratio and coefficient of thermal expansion of the PMMA, respectively.

[0264] Computed Temperature Distribution for a System Consisting of a SWNT Undergoing Joule Heating with a Constant Bias, on a Quartz Substrate Coated with Tc-Resist.

[0265] Setting k₂=k₁=k, k₀, k_f, =k_f, h₀=h_f and ω=0, Eq. (16) gives the surface temperature of Tc-resist for Tc-resist/quartz under DC voltage as

$\begin{array}{cc}\theta \left(x,y\right)=\frac{1}{2k_s\pi }{\int }_{-L/2}^{L/2}\eta {\int }_0^{\infty }\frac{Q_0J_0\left(\xi \sqrt{{\left(\eta -y\right)}^2+x^2}\right)}{\cosh \left(\xi h_f\right)+\frac{k_f}{k_s}\sinh \left(\xi h_f\right)}\xi & \left(18\right)\end{array}$

[0266] where k_f and k_s are the thermal conductivity of Tc-resist and quartz, respectively and h₁ is the thickness of Tc-resist.

[0267] A 3D finite element model was established to study the temperature distribution in the system and validate the analytical model. Eight-node, hexahedral brick elements in the finite element software ABAQUS are used to discretize the geometry. A volume heat source was applied on the SWNT. The zero heat flux boundary was applied at the top surface of the Tc-resist, and a constant temperature T_∞ is applied at the bottom of the quartz substrate. The finite element simulations agree well with analytical modeling as shown in FIG. 12c for the surface temperature of the Tc-resist with k₀=0.2 W/m/K, k_f=6 W/m/K, Q₀=16.7 μW/μm and L=30 μm.

[0268] Effects of Thermal Interface Resistance.

[0269] The models above do not consider the effect of thermal interface resistance, which can in some cases affect the resulting temperature distributions. For the case of AC heating for relatively thick films (˜250 nm) for PMMA, the interface resistance has negligible effect (for ˜100 MW/m²/K for the SiO₂/PMMA interface, the result is a relatively small increase in peak temperature rise, ˜1%). For the case of thinner films of Tc-resist (˜25 nm) with DC heating, the surface temperature rise incorporating interface resistance can be obtained using Hankel transform as

$\begin{array}{cc}\theta \left(x,y\right)=\frac{1}{k_f\pi }{\int }_{-L/2}^{L/2}\eta {\int }_0^{\infty }\frac{Q_0{}^{-\xi h_f}\left(1+\frac{k_s\xi }{\zeta }\right)J_0\left(\xi \sqrt{{\left(\eta -y\right)}^2+x^2}\right)}{-\left(1+\frac{k_s\xi }{\zeta }-\frac{k_s}{k_f}\right){}^{-2\xi h_f}+\left(1+\frac{k_s\xi }{\zeta }+\frac{k_s}{k_f}\right)}\xi & \left(19\right)\end{array}$

where ζ is the thermal interface conductance. As ζ approaches to infinity, Equation (19) denigrates to Eq. (18). For ˜100 MW/m²/K for the Tc-resist/quartz interface, the result shows a ˜40% increase in peak temperature rise. However, this rise is not significant enough to affect any of the major conclusions associated with this study. Namely, that at the powers used to induce trenches by Tc-flow, temperature rises are small. Similarly, the qualitative aspects and scaling laws associated with the Tc-flow modeling are unaffected by these minor corrections.

[0270] Modeling of Thermocapillary Flow in TcEP.

[0271] The viscous flow of Tc-resist is essentially unidirectional and the evolution of film thickness h(x,t) can be obtained from a lubrication equation

$\begin{array}{cc}\frac{\partial h}{\partial t}+\frac{\partial }{\partial x}\left[\frac{\tau h^2}{2\mu }+\frac{h^3}{3\mu }\frac{\partial }{\partial x}\left(\gamma \frac{{\partial }^2h}{\partial x^2}\right)\right]=0.& \left(20\right)\end{array}$

where γ is the surface tension, which usually linearly depends on the temperature rise (i.e.,

$\gamma ={\gamma }_0-{\gamma }_1\theta ),\tau =\frac{\partial \gamma }{\partial T}\frac{\partial T}{\partial x}$

is the thermocapillary stress with T=T_∞+θ, and μ is viscosity. By introducing the following non-dimensional terms h=h/h_f, x=x/h_f, t=γ₁Q₀t/(μ₀k_fh_f²), μ=μ/μ₀, γ=k_fh_fγ/(q₀γ₁), τ=δθ/δx and θ=k_fh_fθ/Q₀, Eq. (20) can be written in non-dimensional form as

$\begin{array}{cc}\frac{\partial \stackrel{\_}{h}}{\partial \stackrel{\_}{t}}+\frac{\partial }{\partial \stackrel{\_}{x}}\left[\frac{\stackrel{\_}{\tau }{\stackrel{\_}{h}}^2}{2\stackrel{\_}{\mu }}+\frac{{\stackrel{\_}{h}}^3}{3\stackrel{\_}{\mu }}\frac{\partial }{\partial \stackrel{\_}{x}}\left(\stackrel{\_}{\gamma }\frac{{\partial }^2\stackrel{\_}{h}}{\partial {\stackrel{\_}{x}}^2}\right)\right]=0.& \left(21\right)\end{array}$

The Fortran solver PDE_1D_MG can be used to solve for h.

[0272] Experimental and Theoretical Time Dependence of Trench Evolution in TcEP.

[0273] The time dependence of trench evolution was studied for a small area (3×3 μm) within an array of SWNTs by collecting a sequence of AFM images (˜30 s), for different durations of applied bias (V_DS=0.66 V/μm, L=30 μm, 30° C. background heating). During imaging no bias was applied, thereby leaving the trenches in fixed geometries for the duration of the measurement. In between images, biases were applied, driving trench formation for controlled durations (durations varied depending on accumulated duration ranging from 0.1 s for very short accumulated duration, <10 s, to 30 min for very long accumulated duration, 6-8 hrs). The total time of trench formation was taken to be the sum of the durations for all preceding experiments. FIG. 13 shows representative images at various points in the evolution of trenches (FIG. 3c shows cropped images associated with the second trench from the left). At relatively short durations, trenches were shallow (<1 nm deep) and characterized by slight ridges in the Tc-resist on each side of the SWNT, over time evolving into fully formed trenches, which grow and eventually (hours) began to interact with trenches from adjacent SWNTs, limiting further growth. Data associated with analysis of time dependence was restricted to durations where trenches were isolated from one another (<2 hr). For the purposes of establishing reliable measures of trench evolution, the trench width, W_Tc, was defined as the width between the peak of the pile-up on either side of the trench (actual minimum widths, evaluated at the base of the Tc-resist, were much narrower). Analysis to determine the left and right side of the trench was performed in MATLAB, and involved identifying the first location to the left and right side of the trench where the slope fell below a certain threshold, 5×10⁻¹¹. FIG. 14a shows an AFM image for t=600 s with the identified left and right sides of the trench highlighted for the three central trenches. FIG. 14b shows cross-sectional profiles associated with the central trench at various points in the trench evolution and the identified left and right positions. FIGS. 3f and 15a show the resulting experimentally extracted W_Tc. Smaller trenches (W_Tc<150 nm, associated with t<10 min), were less distinct, and identifying the left and right positions was more difficult. While values of W_Tc were roughly accurate, there was significantly more error at shorter times than longer times. The short time values were not used for power law fitting (FIG. 15a). Power law fitting was performed in data ranges where the standard deviation was <10% of W_Tc. (For data outside of this range, standard deviation was W_Tc ˜20-50% of W_Tc). The data fit well to a power law with exponent 0.25 (The value for the constant of proportionality, A, are shown). FIG. 15b shows the predicted W_Tc based on modeled trench profiles (peaks in h(x,t)), which also fit well to a power law with exponent of 0.25 (The parameter A depends on various Tc-resist properties, several of which are unknown). FIG. 15c,d show the predicted W_Tc for power densities varying from 8.3-33.3 μW/μm for long durations and for durations that yield trench widths associated with those typical for TcEP. (Comparison to model can be difficult given the uncertainty in materials properties for the Tc-resist. Because t is normalized with respect to μ and γ, which are unknown, it is not possible to compare directly to t. Nevertheless, the computed W_Tc is only normalized by h₀, so it is meaningful to compare modeled t to ranges of experimental t that yield trenches of similar size to those measured experimentally). For long times, W_Tc varies with power density. At durations associated with experimental conditions, however, almost no variation is predicted. This relative insensitivity to power is consistent with experimental observation (FIG. 2e,f), where only ˜20% variations in W_Tc are typically observed. Such variations likely result from local changes in film viscosity associated with heating, or other effects not explicitly included in the model.

[0274] In addition, besides capturing the underlying physics, these models also establish a set of guidelines for the selection of optimal materials for Tc-resists, i.e. large temperature coefficients of surface tension and low viscosities yield narrow trenches within reasonable experimental times. Furthermore, decreasing the thickness reduces the trench widths. Empirical studies of various materials for Tc-resists (see FIG. 18) led to the selection of the molecular glass reported here.

[0275] Thermocapillary flows in Tc-resist, studied by heated AFM tips with integrated temperature sensors.

[0276] Heated atomic force microscope (AFM) tips with known temperatures contacted with the Tc-resist layer for various times, and with various applied powers, allow study of the effects of thermocapillary flow in a nanoscale system where temperature and other parameters are controlled (and known) more accurately than the case for SWNTs. The heated tip (radius <100 nm) was fabricated from doped single crystal silicon, and is capable of reaching temperatures of 1000° C. with a temperature calibration to within 5° C. for this entire range.¹⁸ Previous studies of viscous mass flow from a heated tip to a substrate revealed thermocapillarity to be an important driver of flow¹⁹. FIG. 16 shows Tc-resist layer deformation induced by tip heating for tip-substrate temperature differences between 5-45° C. and dwell times between 0.1-300 s on both an unheated Tc-resist layer and a Tc-resist layer heated to 50° C. The tip dwelled on the surface with tip forces below 20 nN and did not deform the surface when unheated. The results show that significant material flows radially away from the heated tip for Tc-resist layer temperatures far below the sublimation temperature, consistent with thermocapillary stresses induced by the temperature gradient around the tip.

[0277] Pulsed heating in TcEP for large scale arrays of SWNTs.

[0278] For arrays that contain large numbers of SWNTs (either at high densities or over large areas) the coupled heating of many SWNT leads to bulk, and sometimes large, increases in temperature. These effects can yield thermocapillary flow on larger length scales and in ways that are difficult to confine to the positions of the SWNTs (FIG. 17). Pulsed bias conditions (˜1-10 μs) can avoid these cumulative effects, to yield localized heating and thereby preserve well-behaved trenches even with large arrays of SWNTs and/or relatively high densities (up to 3 SWNT/μm studied here). FIG. 17, shows the resulting trenches for a localized region within a large area high density array (30 μm×1 mm, 2-3 SWNT/μm) for increasing duty cycles (10 to 100%) with a fixed pulse duration (10 μs). These data clearly show the gradual transition from narrow, well defined trenches associated with individual SWNTs to uncontrolled flow not correlated to SWNTs. For optimized application of pulsed TcEP (large area, high density arrays), 1-3 μs pulses (40V) were applied with 10 μs pulse periods.

[0279] Tc-Resist Material Selection.

[0280] There are numerous characteristics that are critical for an effective Tc-resist material. Basic requirements are that the material can be easily deposited in thin film configurations, where vacuum deposition is preferable to spin coating, since it easily yields uniform film thickness even in regions near the partial gate electrode structures, where substrate topography is highly nonuniform. The films must afford good coverage and adhesion to both the SWNT and the quartz substrate, and at the same time be sufficiently impermeable to O₂/CF₄ plasma to act as an effective etch resist. The unique chemistry of the Tc-resist material studied here combines hydroxyl and phenyl moieties which provide compatibility with both SWNT and oxide substrates. It is critical for films to exist in an amorphous phase, to avoid spatial nonuniformities in thermal properties (thermal conductivity, k), viscous flow properties (temperature coefficient of surface tension, Vi, and viscosity, μ) and thickness that can be associated with crystalline grains. FIG. 18a,b,c shows AFM associated with trench formation experiments with arrays of SWNTs and Tc-resists consisting of thin films of paraffin, TCNQ, and pentacene (similar results were achieved for TCTA and F4-TCNQ). All of these materials show features that roughly correlate to underlying SWNT heaters, but showed massive variations in resulting trenches over the area of the film. Films of TAZ and anthracene (deposited at −80° C.) yielded amorphous films, but, over the time scales associated with experiments and characterization, exhibited spontaneous crystallization. Other materials, such as polystyrene (M_w=288,000, FIG. S12d) or Alq3 provided high quality amorphous films, but significantly higher power densities (and/or higher background heating, T_∞>140° C.) were required to yield trenches. (In the case of Alq3, crystallization occurred at lower temperatures than those required for trenches to be observed, in reasonable experimental time scales). These power densities (or background heating) lead to bias requirements and/or operating conditions in which non-ideal device behaviors (e.g. non-negligible current through the s-SWNTs) limit the selectivity of the TcEP process. Models of thermocapillary flow suggest that such behaviors are due to either low temperature coefficients of surface tension or high viscosities. While both parameters play an important role in the flow (and γ₁ also plays a role in the trench profile), most materials exhibit γ₁ between ˜0.05 and ˜0.15 mJ/m²/° C., while viscosities can vary by many orders of magnitude. It is likely, then, that viscosity is the most significant parameter that determines whether materials yield trenches in experimentally practical time scales and with low power levels, without significant background heating. While the Tc-resist demonstrated here meets all of these criteria, advances could be obtained through the development of materials with similar properties but also with the ability for use at smaller thicknesses (e.g. 5-10 nm, rather than 25 nm). Reductions in thickness enable decreases in W_Tc (linearly with h_f) which, in turn, could allow application to arrays of SWNTs with high densities.

[0281] Processes Defined by Critical Temperatures.

[0282] The unique scaling (particularly power invariance) associated with thermocapillary flow is critical to the success of TcEP, because it allows uniform trenches in arrays of SWNT that incorporate significant variations in power densities among the various SWNTs. Although it is possible to envision approaches like TcEP but which rely on processes such as sublimation or ablation, their robust operation is limited by the existence of a critical temperature, T_C. In such cases, at temperatures below T_C, the resist will remain, while at temperatures above T_C, the film will be removed. Thermal models can provide key insights into the scaling of this type of process. FIG. 19a,b show temperature profiles and thermal gradients for a range of power densities similar to those measured experimentally. Both peak power and peak gradient scale linearly with power. A width associated with a process that relies on a critical temperature, Wc, can be determined (FIG. 19a). FIG. 19c,d show the predicted scaling for processes associated with critical temperatures of 2-10° C. It reveals that these processes yield no trench until a certain power density is reached. Afterward, the width increases dramatically with increasing power, to widths that would expose other SWNT in arrays of densities >0.1 SWNT/μm. This type of scaling is incompatible with desired operation. For higher T_C the range of powers that yield practical trench widths (several hundred nm) becomes larger. Here, the required power density to initiate trenches grows dramatically, which is also highly undesirable.

[0283] Effects of Trench Formation in Neighboring SWNTs.

[0284] For very high SWNT densities, non-ideal behavior in TcEP can occur if a trench associated with an m-SWNT exposes an s-SWNT in close proximity. The trench width provides an indicator for the density at which this type of behavior can be expected. In particular, for an array of SWNTs with regular spacing, the maximum density is defined roughly by the average trench width (trench width measured at the base of the Tc-resist ˜100 nm, where W_Tc is ˜250 nm). We note, however, that thermocapillary flow can be altered as neighboring trenches approach one another. At long times the pileup from two adjacent trenches coalesces, creating a narrow strip of Tc-resist in between them. It is unclear from the simple models here, which apply to isolated SWNT, how close the SWNTs can be before their trenches merge. As a result, the minimum spacing between trenches where Tc-resist remains in between them provides the best indicator of the maximum density that can be accommodated in TcEP, as implemented here. AFM measurements of trench formation in arrays with locally high densities suggest that neighboring trenches can be as close as 250 nm while still showing well-defined Tc-resist in between. FIG. 20 shows an AFM, cross-sectional height profile, and associated 3D renderings of such trenches. Here, isolated trenches are observed along the entire lengths of the trenches (˜8 μm).

[0285] Interconnected Arrays of SWNT for Large Area TcEP.

[0286] For applications where the collections of devices in a target application are known roughly, then it is practical to perform TcEP in local patches, as part of an interconnected array of electrodes. FIG. 21a shows five 1×5 sets of SWNT processed by TcEP in this manner. FIG. 21b,c show the transfer characteristics for one of the arrays before and after TcEP and the characteristics for all five devices after TcEP. Table 2 summarizes the results for all five arrays. For each array, after removing interconnects (lithography and etching), all of the devices (25 total) showed high on/off ratios (>1×10³). This result demonstrates the effectiveness of performing TcEP over large areas using this type of interconnection scheme.

[0287] Inverter Fabrication and Load Line Analysis.

[0288] A p-type inverter was fabricated from two devices based on arrays treated by TcEP. FIG. 22a shows optical micrographs associated with this process. Here, a common source electrode is used to perform TcEP on two arrays with interconnected drain electrodes. Following TcEP, the gate and dielectric layers were removed. For one transistor (the load TFT), the associated source and drain electrodes for TcEP served as electrodes for the final device. For the other (the driver TFT) the source electrode was extended to yield a reduced channel length (˜3.5 μm). Finally, new dielectric (SOG/HfO₂, 35/20 nm) and top gate (Ti, 70 nm) structures were defined, to complete the fabrication. The current level for the driver TFT increased roughly linearly with the reduction in channel length from 30 μm to 3.5 μm (expected ratio ˜8.5, measured ratio ˜9.5). This yielded for a current ratio between driver and load TFTs of ˜10. FIG. 22b,c shows the electrical properties of the driver and load TFTs. The measured voltage transfer curve (VTC) is consistent with that predicted from load line analysis (FIG. 23). Some variation between the measured and predicted VTC curves results from hysteresis in the load and driver TFTs. The measured voltage gain (˜4) is near expectation based on conventional diode-load inverter circuit design equation (˜3, A_v=g_m/g_{m_load}=(L_load/L_driver)^0.5)²⁰.

[0289] In addition, this demonstration hints that the TcEP scheme can be important for short channel devices and their circuit demonstrations. In particular short channel devices, such as the one shown in FIG. 6c, would difficult or impossible to fabricate reliably using a traditional method to eliminate the role of m-SWNTs, such as electrical breakdown, for two reasons: (1) heat sinking at the electrode contacts²⁹ progressively drives required powers to levels that reduce selectivity and leads to biases that can cause electrical breakdown in the necessarily thin gate dielectrics and (2) arrays of SWNT processed by breakdown in large device geometries lead to small discontinuities³⁴ in the m-SWNTs at positions that cannot be aligned, in determinate fashion, with the channels of subsequently fabricated devices.

[0290] Modeling of Electrical Properties of SWNTs in partial gate configurations, after TcEP.

[0291] To determine the mobility of s-SWNTs following TcEP, the transfer characteristics from the devices comprising −200 s-SWNTs with similar operating voltages were averaged and used as the basis of fitting to simulation results. In particular, self-consistent solutions to the Poisson and drift-diffusion equations²¹ were used to simulate a partial gate SWNT field effect transistors (PG-FET) with 1 nm diameter (average diameter expected for populations grown by this technique²) s-SWNT as channel. Dimensions and other parameters are based on experiments and shown in FIG. 24a. Solution of the three-dimensional Poisson equation captures the effect of contact dimensions on the electrostatics of PG-FETs; whereas solution of the drift-diffusion equation describes one-dimensional carrier transport along the s-SWNT. In addition to using analytical expressions for mobility and carrier densities, simulation also considers acceptor doping to capture the influence of (oxygen and water induced) negatively charged interface defects.

[0292] FIG. 24b shows measured and simulated drain to source current (I_DD) vs. gate voltage (V_G) characteristics of the PG-FET at different source-drain bias (V_DS) for the averaged s-SWNT response. The simulation shows good agreement with the values measured under similar bias conditions. (Measured values represent average characteristics for ˜30 PG-FETs with ˜200 s-SWNTs). As shown in FIG. 24c, the percentage difference between experiment and simulation, defined as (I_{DS_exp}−I_{DS_sim})/I_{DS_exp}×100% from V_GS˜0 V (i.e., the voltage where transconductance, g_m=dI_DS/dV_GS, is maximum) to V_GS=−20 V, is within ±5-7%. The variation reflects the uncertainty of device parameters used in the simulation. The average mobility throughout the devices, averaged over the quasi-Fermi level variation²², i.e.,

$\begin{array}{cc}{\mu }_{\mathrm{avg}}\left(V_{\mathrm{DS}},V_{\mathrm{GS}}\right)=\frac{{\int }_0^L\mu \left(x\right)\frac{Q_{\mathrm{Fp}}}{x}x}{{\int }_0^L\frac{Q_{\mathrm{Fp}}}{x}x}& \left(22\right)\end{array}$

is summarized in FIG. 24d. We find that μ_avg˜960-1050 cm²/V-sec. Variation of mobility with V_GS and V_DS follows the classical trend, i.e., decreases with both higher |V_GS|^{22, 23} and higher |V_DS|²². Such reduction of mobility at higher V_GS is routinely observed in s-SWNT's mobility measurements^{23, 24} and is related to the increase of average electric field along the SWNT (considered in simulation) and also to the non-parabolicity in SWNTs' band-structure²⁵ (ignored in simulation). The effect of contact resistance (˜28 kΩ) is observed to have negligible effect in extracted mobility for these long-channel length PG-FETs.

[0293] In addition, the average mobility (Eq. (22)) was extracted based on the following mobility equation (Eq. (23)). Mobility at position x, μ(x), along the nanotube is calculated using^{22, 23, 25}

$\begin{array}{cc}\mu \left(x\right)=\frac{{\mu }_{\mathrm{peak}}}{1+{\mu }_{\mathrm{peak}}\frac{Q_{\mathrm{Fp}}}{x}/v_s}& \left(23\right)\end{array}$

where μ_peak is the peak mobility, V is the potential at x, v_s is the saturation velocity. This position dependent mobility (Eq. (23)) is later used for calculating average mobility (μ_avg) at a particular V_GS, V_DS using²².

[0294] SEM and AFM Images at Each Stage of the TcEP Process, as Implemented with a Back Split Gate Structure (BSGS).

[0295] As a simplified version of TcEP, we demonstrated the feasibility of a re-usable electrode/gate structure, to eliminate cycles of processing that would otherwise be necessary for repetitive fabrication of top split gate structures used in the original scheme.

[0296] FIG. 25a shows an AFM image of the channel region of the BSGS (bottom split gate structure) immediately after transfer of an array of SWNTs. The AFM image in FIG. 25b shows selective formation of trenches for the entire channel length of 30 μm, by thermocapillary flow in an overlying layer of Tc-resist. The bias conditions to initiate this flow were similar to those for the corresponding top gate geometry, i.e, V_DS=−40V, V_GS=20V for 5 min at 60° C. in vacuum (1×10⁻⁴ torr). After dry etching to remove m-SWNTs, the Tc-resist is removed with acetone. The resulting channel appears in FIG. 25c. The red arrow highlights a pair of s-SWNTs throughout this process. This BSGS has W/L=30/30 μm.

[0297] Demonstration of Re-Use of a BSGS.

[0298] To demonstrate reusability, a BSGS was used for a 1^st TcEP cycle and then cleaned by O₂ plasma treatment (200 mTorr, 02 20 SCCM, 100 W, 20 min, Plasma-Therm RIE). New, as-grown arrays of SWNTs were then transferred to the same BSGS using PVA/thermal tape. After a 2^nd TcEP process, we observed expected operation, as shown in FIG. 26b. The behavior of the BSGS in this second cycle was the same as for the first. The successful multiple operation was confirmed by electrical measurements before and after TcEP for each of the two arrays of SWNTs, as summarized in FIG. 5 b, c.

[0299] Off-State Stability of Operation in Top Split Gate Structures.

[0300] For the purpose of selective metallic nanotube removal by TcEP process, current stability in the ‘off state’ condition (i.e. large negative gate biases) for the s-SWNTs is particularly important. To verify this stability, we measured current outputs in devices with several s-SWNT tubes at conditions corresponding to those used to induce thermocapillary flow (i.e, V_GS=20V, V_DS=−40V, T_sub=60° C., 1×10⁻⁴ torr). FIG. 27(b) shows that the current remains less than several nA throughout the experiment.

[0301] Off-State Stability of Operation in Top Split Gate Structures.

[0302] To evaluate on-state stability, we measured current output in the device of FIG. 28 at bias condition (V_GS=−20V and V_DS=−40V) for 5 min in vacuum (1×10⁻⁴ torr). The results of FIG. 28 indicate that the current in the on-state shows some variation in the first few tens of seconds, likely due to filling of charge traps near the SWNTs and in the gate dielectric, and then remains constant.

[0303] Full Characterization of Split Gate Devices with W/L(═1000/30 μm or 2000/30 μm) after TcEP.

[0304] For devices with large widths (W/L=1000/30 μm), I-V characteristics after TcEP reveal the maximum achievable current levels, as well as any variations in device switching behavior at high drain biases. In particular, we measured the device of FIG. 4(c), for which W/L=1000/30 μm, at drain biases up to V_DS=−40.1 V. Here, FIG. 29b indicates that the maximum output current which can be extracted is ˜1.5 mA. To further verify the width scalability of devices with purified arrays of s-SWNTs, we connected two devices with the same physical dimensions (W/L=1000/30 μm) to create an effective dimension of W/L=2000/30 μm, with current outputs of −3 mA as shown in FIG. 30b. These results correspond to the simultaneous operation of at least several hundred s-SWNTs. All characterization was performed in dry N₂ ambient.

[0305] On/Off Ratio as a Function of Drain Bias in Split Gate Devices with Large Widths.

[0306] The on/off ratios of devices shown in FIG. 4(a), (b), diminish somewhat at the most extreme bias conditions, due to effects that arise from band bending near the drain and associated band-to-band tunneling (FIGS. 32 and 33), but remains close to 100.

[0307] Electrostatic Behavior Associated with Operation at High Bias Voltage.

[0308] The values of on/off ratio (i.e., I_DS@V_GS=−20 V/I_DS@V_GS=20 V) in FIG. 10 and FIG. 6(c) suggest the existence of small bandgap (large diameter) semiconducting CNTs after metallic CNT removal. FIG. 10 is measured for a device that has a single semiconducting nanotube as a channel. Simulation of I_DS-V_GS for this device is consistent with a diameter of 1.74 nm (directly estimated by analysis of Raman spectra) for the SWNT and matches the on/off ratio measured by varying overlap length (L_OV) and V_DS (FIG. 32c). Low on/off ratio for the full-gate device configuration (L_OV=L; FIG. 32b) is due to larger band bending near the drain end of the nanotube (FIG. 33a) that induces band-to-band tunneling (BTBT)²² and high I_DS at V_GS=20 V. Band bending near the drain end is relaxed due to the extension of electrostatic gate control in the overlap region (FIG. 33c) and, therefore, BTBT and I_DS at V_GS=20 V is lower and on/off ratio is higher for the same nanotube in the partial-gate configuration (L_OV<L; FIG. 32a). For all L_OV values, band bending (FIG. 33a) and BTBT increases at larger |V_DS|, therefore, reduces the on/off ratio (FIG. 32c).

[0309] Forming Horizontally Aligned Arrays of SWNTs.

[0310] Photolithography (AZ 5214 positive photoresist), electron beam evaporation (0.6 nm Fe; AJA), and subsequent liftoff defined regions of catalyst in the geometry of strips oriented perpendicular to the preferred growth direction on ST-cut quartz substrates (Hoffman). Annealing in air at 950° C. for 1 hr at the pressure (1 atm)(quartz tube furnace with −1 inch outer diameter), cooling the furnace, purging it with hydrogen (300 sccm) at the pressure (1 atm), and then heating to 925° C. with ramping rate of 50° C./min prepared the iron catalyst for chemical vapor deposition. Introduction of growth gases (20 sccm H₂, 20 sccm Ar, bubbled through ethanol (T=0° C.) at 925° C. for 20 min yielded well aligned arrays of SWNTs.

[0311] Fabricating Devices that Incorporate a Single SWNT.

[0312] The fabrication procedures followed those described above. The use of arrays of SWNT grown at low density (0.1-0.2 SWNT/μm), and subsequently etched in patterns that removed all of the SWNTs except those in narrow strips (˜3 μm widths) yielded devices with small numbers of SWNTs. Electrical and AFM analyses identified a subset of such devices that incorporated only a single SWNT bridging the source and drain electrodes.

[0313] Removing the Gate Electrode and Dielectric.

[0314] Following TcEP, the purified SWNTs (i.e. consisting only of s-SWNTs) were protected by a patterned layer of photoresist (AZ 5214) prior to removal of the gate metal (for Ti, Transene, Inc; titanium etchant TFTN; for Cr, Transene, Inc; chrome mask ethant-CE-5M 9). Wet etching (H₂SO₄:H₂O₂=2:1, 60° C., 5˜10 s) removed the crosslinked PVA. Etching in buffered hydrofluoric acid (BOE 6:1, 30 s) removed the SOG/Al₂O₃ bilayer. Stripping the photoresist completed the process.

[0315] Fabricating Short Channel Devices.

[0316] Following removal of the partial gate transistor structure, phase shift lithography²⁷, electron beam evaporation (2 nm Ti, 25 nm Pd), and lift-off (facilitated by brief ultrasonication, −1 min) defined a narrow gap separating new source and drain electrodes on a purified array of s-SWNTs. PDMS stamps for phase shift lithography were cast and molded (Dow Corning, Sylgard) from a Si master, fabricated by photolithography (AZ 5214) and Bosch etching (etch/passivation, cycle time: 5 sec/5 sec, RIE power: 20 W/0 W, 35 sccm SF₆, 110 sccm C₄F₈, for constant ICP power of 600 W, etch rate: 1 μm/80 s) in SF₆ to a depth of −1 μm. Following liftoff, the dimensions of source and drain electrodes were further defined by photolithography (AZ 5214) and a combination of wet and dry chemical etching (Transene Pd etchant, 50 sec, followed by RIE, 40 sccm CF₄, 1.2 sccm O₂, 150 W, 30 sec; Plasma-Therm). Gate dielectric layer (˜30 nm) of HfO₂ was deposited by electron-beam evaporation followed by atomic-layer deposition of HfO₂(10 nm). Photolithography (AZ 2070), and sputtering (70 nm Ti, 150 W, 3 mTorr Ar; AJA International), followed by lift-off defined gate electrodes, to complete the devices.

[0317] Fabricating Inverters.

[0318] First, TcEP yielded two purified arrays of s-SWNTs. Photolithography (AZ 5214), electron beam evaporation (2 nm Ti, 48 nm Pd) and lift-off then patterned source and drain electrodes for the driver transistor (L=3.5 μm, W=30 μm). The electrodes associated with the TcEP processes were used for the load transistor (L=30 μm, W=30 μm). Previously described procedures²⁸ yielded SOG/HfO₂ (35 nm/20 nm) dielectrics for both transistors. Photolithography (AZ 5214), electron beam evaporation (100 nm Ti) and lift-off defined the gate electrodes.

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[0347] Aligned single walled carbon nanotubes (SWNTs) are well suited for applications in high dynamic range RF electronics, low-noise linear amplifiers, mixed-signal devices and sensors. During CVD growth of aligned tube arrays both metallic and semiconducting tubes naturally grow at a statistical ratio of 1:3. Many electronic device applications require arrays of purely semiconducting SWNTs. The presence of metallic nanotubes degrades the device electronic properties, impeding high performance. In the example above, we introduced nanoscale thermocapillary flow (NTF) processing in thermal resists for complete, selective removal of metallic SWNTs from CVD arrays. Here, we explore three distinct purification paths with a focus on complete process development, modeling and scalability. Microwave initiated NTF, laser initiated NTF, and direct laser ablation were assessed in detail. We have shown while all the techniques offer promise, microwave excitation is the most promising and can provide an efficient, highly scalable path for selective heating of metallic tubes via NTF enabling highly selective removal of the metallic tubes (99.999%). To build on this, we also suggest “scale-up” of direct microwave heating of m-SWNTs to initiate thermo-capillary enabled purification (TcEP) to enable purification of aligned 3 inch SWNT wafers.

[0348] We report completion of the exploration and development of three techniques for the selective elimination of metallic SWNTs from aligned nanotube substrates. FIG. 34 shows the general technical results based on the initial program objectives. As noted, the primary project goal was to identify a scalable technology which would enable selective elimination of metallic SWNTs. Three removal strategies were explored. Microwave initiated thermocapallary enabled purification (TcEP), laser initiated TcEP, and direct laser ablation, were studied in detail both experimentally and theoretically to assess the technical feasibility and scale-up potential of each. Results indicate that all of the techniques offer some level of selectivity enabling elimination of metallic tubes from the nanotube die. Importantly, the key finding of the program was that the microwave approach, due in part to our ability to use metal-semiconductor interactions to manipulate properties of the tubes during processing, shows in essence, perfect selectivity, i.e., complete removal of metallic nanotubes with no semiconducting nanotubes damaged or destroyed. This suggests it as the best scalable choice for full wafer processing. In this example we detail all three approaches, summarizing the experimental designs and findings, and accessing the purified die either spectroscopically or via the fabrication of transistors.

[0349] CNT transistors are an important technology area and have demonstrated an ability to provide highly linear, high performance device operation at low drive voltages. Technology development is enabled using single walled carbon nanotubes (SWNTs), an extremely powerful and versatile class of nanomaterials with a wide array of intriguing electrical properties [1]. They are being explored as the base paradigm for a wide range of device applications ranging from high performance RF electronics to flexible electronics [2]. As an electronics platform, SWNT transistors are being pursued for applications that include low-noise linear amplifiers and mixers where low power and high spurious-free dynamic range are very important. Aligned submonolayer films of SWNTs, grown by CVD represent the most promising materials platform for the applications under consideration. While there have been many demonstrations of impressive single tube devices, arrays, i.e., multi-tube structures (array transistors), are needed for the technology to mature. Key to the advance of high performance applications is the availability of ordered dense films of semiconducting material, with high purity (>99.9% s-SWNT[6]), at the wafer scale. Among all needs essential for this technology evolution; nanotube electrical purification has been the key challenge. There have been several attempts to develop controlled growth CVD conditions to achieve populations with enhanced s-SWNT content [7]. While conceptually these approaches could be ideal, to date, the achieved purity is rather limited, (current best practice >5% m-SWNTs remain), and is often not reproducible. The differences in the electronic characteristics of nanotubes are driven by very subtle changes in “structure” making “pure” direct growth extremely unlikely. Clearly a purification strategy that starts with highly aligned CVD based materials would have distinct advantages. Post growth purification has also been difficult. One strategy involves exploiting subtle differences in surface chemistry within SWNTs of different chirality in solution. Using chromatography or ultracentrifugation, the tubes are purified to generate the required semiconducting populations [8]. In addition, surface chemical methods and/or electrophoresis are utilized to sort suspended tubes as they are deposited onto a substrate. While extremely pure populations of SWNTs can be achieved in this manner, high purity requires multiple iterations due to the wide range of chiralities and diameters present in the starting population. While this approach can achieve electronic purity, generating parallel, aligned arrays of SWNTs is still problematic. While several approaches attempt to achieve post purification alignment, they are difficult and are generally non-scalable. Recently we developed a path to purification for CVD grown aligned materials based on utilization of a thermal resist which serves as an etch barrier for semiconducting tubes during processing. The demonstrated process uses nanoscale thermocapillary flows (NTF) in thin film organic thermal resists as a processing strategy for complete, highly efficient and selective removal of metallic SWNTs from aligned arrays of SWNTs grown on quartz substrates. The low temperatures involved and the ease of integration with current micro/nano-fabrication tools inherent with this process suggests it can serve as a robust technique for nanotube die purification. While thermocapillary enhanced purification (TcEP) was initially developed using selective joule heating of the m-SWNTs, detailed experimental and theoretical study has now shown that we can use other mechanisms to generate the selective heating needed to drive the underlying thermophysical phenomena. In this example, we show that laser irradiation and microwave excitation, in a coupled waveguide geometry, can lead to efficient, selective removal of metallic tubes via NTF. Moreover we have explored direct ablation of metallic nanotubes. After a thorough analysis and comparison we have concluded that microwave initiation is an optimal purification approach enabling 100% purity. We detail the system physics leading to this purification advance and show the performance of the resulting transistor arrays. We also define a path to “scale” microwave NTF methods for wafer scale manufacture. The approach is consistent with current manufacturing paradigm best practices and wafer processing protocols.

[0350] The electronic properties of single walled carbon nanotubes (SWNTs) make them uniquely suited for diverse applications in high dynamic range RF electronics, sensors and other device technologies. To realize the benefit of SWNT electronics, “scalable” process options consistent with manufacturing best practices are needed. In electronics, the program has emphasized large-scale carbon nanotube (CNT)-based memory, CNT-based logic devices, and CNT field-effect transistors with a goal of developing processes that are completely compatible with operations in a standard silicon foundry. Most high performance applications, require ordered dense films with high purity (>99% s-SWNT [6]) populations. Nanotube electrical purification is one of the fundamental barriers to technology development. This effort has removed the purification issue from the list of process needs.

[0351] As described above we utilized our innovative nano thermocapilary approach as a base development platform. A basic description of the joule heating based TcEP process is illustrated in FIG. 35 (left). Currently, 1) aligned arrays of SWNTs are fitted with removable electrodes to enable selective heating. 2) A thermal resist material is then deposited on the array and a bias current is applied to the array structure resulting in joule heating in the metallic tubes. Thermocapillary action induces the formation of an opening, i.e., a trench above the metallic tubes. This in essence, de-protects the metallic tubes allowing them to be selectively and exclusively removed in a simple O₂ etch process, completely compatable with conventional processing. Obviously, the impact on device performance is dramatic. The transfer curve on the right of FIG. 35 illustrates the increase on device on/off ratio. SWNT transistors with on/off ratios in excess of 10⁵ have been fabricated. Shown is a typical I_ON/I_OFF curve before and after m-SWNT removal. It is important to note that no damage to semiconductor SWNTs is observed using the TcEP process.

[0352] While this technique shows great promise, the direct joule heating approach as the NTF driver may face scalability challenges. For example, the addition of a partial gate structure to enable joule heating is a complex multistep process. FIG. 35b shows one simplified process example. Here a simple electromagnetic field is used to selectively heat the metallic tubes. Our work shows that differences in the electromagnetic absorptive properties of metallic and semiconducting tubes can be exploited for initiation leading to simplified purification. We developed, tested, and modeled, these alternative processes for initiating the selective NTF needed for purification. Feasibility and demonstration of CVD array purification has been achieved using both microwave and laser initiation, moreover direct laser ablation was explored. The work shows that the microwave technique is superior and has the most obvious path to manufacture, yet both options hold great promise. More generally the primary program deliverables are as follows:

• • [0353] 1. Both laser and microwave initiated TcEP processes were shown feasible and scalable, moreover they were demonstrated to produce CNT transistor arrays with device performance at or exceeding the program targets.
  • [0354] 2. For the microwave process, the “contact case” proved to be the best option for scale-up.
  • [0355] 3. Direct laser ablation was shown feasible.
  • [0356] 4. We developed models of the processes developed.
  • [0357] 5. We defined first generation resist specifications and a media model.

[0358] Microwave Initiated TcEP:

[0359] We developed the use of microwave initiation of the TcEP through to the fabrication of single CNT transistors and array devices. FIG. 36 shows the current microwave processing path. The thermal resist coated, aligned tube samples are mounted in a single mode microwave reactor and exposed at a fixed time and power. The radiation initiates the NTF de-wetting process with trenches opening above the metallic tubes which are subsequently removed using a O₂ plasma etch. The current process uses dipole antenna structures deposited onto the nanotube substrates to enhance the microwave field intensity at the tube positions, (FIG. 37). This feature allows for optimization of the NTF process at reasonable reactor powers. FIG. 37 shows a SEM image of the antenna structure with the SWNTs in the gap (right). An image of the microwave field distribution and a plot of the field intensity vs antenna gap width is also shown, (left, top). This gap can be tuned for process efficiency (left, bottom).

[0360] Model of Microwave Initiated NTF:

[0361] To support the experimental work we have in addition developed a comprehensive picture for the microwave initiation geometries explored. The two common geometrical variations of the microwave process that have been developed are shown in FIG. 38. They simply differ in how the microwave antenna engages the die. In the first configuration, (scheme 1), the electrodes are deposited directly on the tube substrate. This “contact case” geometry has consistently produced the lowest processing power thresholds, has resulted in the highest performing transistors, and has given us the largest processing window. All the devices, (both single and multi-tube), show high on/off current ratios, (10³-10⁴ or greater). The second geometry shown in FIG. 38, (scheme 2), is the “non contact” case. While this technique has proven to be more versatile, it clearly requires more microwave power. The implementation of this approach would allow the antenna structures to be removed. We have developed an equivalent circuit model to quantify these geometries. The base model is illustrated in FIG. 39. The schematic shows the combined geometries; the contact mode is of course the limit that D >0. The contact network shows the circuit with all the relevant parameters. Clearly the model has some very specific implications. 1) In both cases we are defining a heating process where metallic tube heating is driven by a microwave induced current. Importantly, the nature of the effective contacts, i.e., the metal/semiconductor (MS) interface to the tubes becomes increasingly important.

[0362] First, turning our focus fully to the contact case (FIG. 39, scheme 1). We focus here first for two reasons; 1) The contact case has shown the most success and 2) Adding antenna electrodes to a conventional die layout is not prohibitive. The contact case as stated above is the best, first, process scale-up path. FIG. 40 (top), shows the selectivity of the contact case, (Ti antenna). The selectivity cure shown indexes every tube on an exposed die and simply measures the trench depth at that location. A sharp step indicates high selectivity. In the ideal case the fraction of tubes forming “deep” trenches should be ˜33% consistent with expected growth statistics. Shallow trench formation is the hallmark of heating either semi-metallic or “doped” semiconducting tubes. FIG. 40 (bottom) illustrates the difference between antenna using Ti (41 nm) and those predominately Pd (40 nm), (Ti (1 nm)) is used here as a very thin adhesion layer). It should be noted that trenches need to be of order 15−20 nm to “de-protect” via reactive ion etch. Titanium shows some of the best results, but selectivity is sufficiently high using many metallic contact materials tested. FIG. 40 is a summary of the Ti contact results. Important to note is; a) the sharp distinction, i.e., you either get trenches or no trenches in Ti. Moreover, b) additional power appears to just deepens the trenches formed but does not change the selectivity, Important here is for Ti, shallow trenches are not detected. For example in the Pd case (FIG. 40, bottom), 300 W exposure results is some semiconducting tubes starting to form modest, shallow trenches continuously, ranging from 2-15 nm in depth, (as illustrated by the curvature in the red curve of FIG. 40). This is not seen in Ti at identical processing conditions, (black curve). As noted, the use of Ti seems to have taken the semi-metallic or doped semiconducting nanotubes “out of play”. This is an extremely important finding which greatly solidifies the scalability and precision of this process. Suggested is an important dependence of the antenna metal work function on the selectivity of the TcEP process. FIG. 41 shows the results for 3 metals with varying work functions. (Note: samples were studied using Pd (5.1 eV), Ti (˜4.33 eV), Mo (4.36 eV), Al (4.06), and Mg (3.7 eV) as the electrode materials. All early samples were Ti(1 nm)/Pd(40 nm) work function ˜5.0 eV.) The data shows the effect is clearly not due to work function only. FIG. 42 (left) indicates that something more subtle is in play. Here Mg electrodes are used, lowering the work function by more than 500 meV beyond Ti. Interestingly, we again derive a range of trench depths detected indicating that our selectivity is diminished. Ti, which has the most distinct selectivity, has its work function near the mid-gap of the semiconducting nanotubes. The relationship of the work function of the metal relative to the electron affinity of the tubes makes it a source of electrons for hole-doped semiconducting tubes and a sink for electrons in semi-metallic tubes. In fact the effect suggests the all tubes have been rendered either metallic or semiconducting with intrinsic properties buy the MS junction formed. From a device physics perspective; It is clear that changing the metal contact work function would modify the Schottky barrier present, changing the current/carrier dynamics. The view of this effect suggested by the model is shown in FIG. 42 (right). (Important here is, exploitation of this effect will also improve joule heating initiated TcEP.) FIG. 42 (left) shows trenches formed on the same sample, (the resist was deposited twice), where we have simply applied a low DC bias directly to the Ti antenna electrodes. Our model suggests that a work function of ˜4.3 eV results in barriers for both hole and electron transport (FIG. 42), resulting in all non-metallic SWNTs behaving as intrinsic materials. We have in essence eliminated semi-metallic behaving tubes. While we are still exploring the details of the mechanism, all needed process protocols have been explored from metal deposition optimization to μ-wave processing conditions. We have fully explored the work function space, (with Mg being the lowest), and also tested metals with a similar work function but with a difference in conductivity (Mo). Ti or Mo appear to be optimal choices. Mo, which has a work function nearly identical to Ti, was also used. As seen in FIG. 43 its selectivity curve results are similar to Ti (but you can clearly see the formation of very shallow trenches (sub 5 nm) in the thermal resist above some semi-metallic/semiconducting tubes.) FIG. 44 offers the clear explanation of this effect. We have not lost selectivity; the conductivity increase achieved with Mo lowers our needed excitation power. (Mo has a conductivity a factor of 8 higher than Ti.) Here again we form a distinct step function in the formation of full trenches at 250 W operation, but with only 15 minutes of irradiation. The increase in contact conductivity gives us a greater coupling of the microwave field to the nanotubes by making the contacts “better” antennas. This improvement greatly widens the operational window for the process. We are now optimizing the Mo deposition and general process and are processing transistors. In addition we are now pattering inter-digitated electrode structures to allow larger area irradiation. With these improvements we clearly establish microwave initiated TcEP as an efficient purification option.

[0363] Next, we will describe the results from the non-contact case. FIG. 45 shows the basic flow of the process. This approach enables processing of substrates without adding “permanent” antenna electrodes. As stated above, this approach requires more power from the microwave reactor but may offer more in device design flexibility. FIG. 46 shows a direct comparison between the contact and non-contact cases. Here, we have used 10 nm of SiO₂ as the spacer layer. In this experiment Ti/Pd electrodes are used for both, with identical exposure conditions. Deep trenches are formed in both cases. The non-contact structure does have a few shallow features, consistent with the need for higher exposure power. This is a limiting case, (i.e., minimizing d).

[0364] In practice a process similar to lamination is used. As shown in FIG. 47, the antenna mask is applied to the die using PDMS pillars as spacers (left image). The d in this case ranges from 500 nm-1 μm. The exposure results are shown in the micrographs. We use markers on the nanotube die to align the laminate antenna to the substrate. The middle image shows the result of a processed array die. The transfer function for a typical array transistor using this process is shown at the far right. Just as in the contact case, array transistor device performance far exceeds the program goals. The model for the non-contact case is shown in FIG. 48. As shown (bottom left), the model fits our observed trench profiles. The difference in mechanism here from the contact case is the heating current is generated from capacitive coupling of the microwave field to the metallic nanotubes. Importantly we see the same work function dependence observed as in the contact case (FIG. 49), suggesting optimization can be driven by contact case results.

[0365] Finally we illustrate the path to larger processed area. To enable large area irradiation we have utilized inter-digitated structures for the coupling antennas. FIG. 50 shows an example of a structure used. Shown is a simple electrode structure with 40 micron legs and 10 micron gaps. The structure acts as a series of coupled microwave transmission lines, with the spatial field pattern amplitude and phase dependent on the size and spacing of the whole structure. The SEM image on the right shows the structure deposited on a nanotube die. The tubes can easily be imaged in the gaps. FIG. 51 shows typical trenches formed with this basic structure. The top image is a SEM of one of the typical gap positions. Below are atomic force images of gap sections. (The scan range on the AFM is limited to about 90 microns.) The statistics of the trenches formed is consistent with that expected, (˜33% trench formation). Other interdigitated designs can be used and the metal used may be modified to control the e-field pattern and overall power. To fully optimize this approach in a processing environment one must design the lithography mask structure for the RF device envisioned, integrating the antenna design into the device layout footprint.

[0366] Laser Initiated TcEP:

[0367] We have also completed a full assessment of laser initiated purification. The basic process schematic is shown in FIG. 52. Here as in the microwave case we are utilizing differences in absorption in metallic and semiconducting tubes to selectively heat and initiate the nanocapillary flow in the resist. The spectral behavior of SWNTs in the region of interest is shown in FIG. 53. Shown is the density of states for both types of nanotubes along with the absorption spectra, (bottom). The bottom right plot shows the spectra on an expanded scale. In the wavelength range from 2-6 microns the semiconducting tube absorption is minimized relative to their metallic counterparts. We chose to operate at 2.5 microns because it was a point where the difference is large and the resist absorption is still very low. The exposure set-up is shown in FIG. 54. Here the nanotube die was exposed in an inverted geometry with the laser beam raster scanned along the die surface. The image on the right shows the exposure area with the exposure conditions described. The laser was focused to a diffraction limited spot and scanned to a length of 60 microns. (The absorption is ˜0.01 for a layer of nanotubes at current densities, (˜1 tube/micron)). FIG. 55 shows an AFM of an exposed die, as expected we form trenches above the metallic nanotubes, (verified using scanning Raman micro-spectroscopy). Statistical data on a number of nanotube die are shown in FIG. 56. Here more than 950 nanotubes have been irradiated with more than 360 continuous trenches formed. Again the number of trenches is consistent with that expected for the number of metallic tubes likely exposed. FIG. 57 shows a typical transfer function for fully processed transistors from the die. Again we obtain devices which operate well beyond the program target. Fully optimized, IR irradiation could be a viable processing option. One clear drawback is the selectivity. Thus far while small in number, we do generate trenches among a few semi-metallic and doped semiconducting tubes. These tubes of course are lost upon etching. It may be possible to treat substrates to mitigate this issue.

[0368] Laser Ablation: Direct Purification Via Ablation:

[0369] We explored and quantified the use of direct laser ablation of metallic nanotubes as a viable strategy. A platform based on a high peak power, near and far IR capability was developed (FIG. 59). The kHz repetition rate parametric amplifier system fitted with a difference frequency generator enabled exposure wavelength options ranging from 1−20 microns at high peak power. The optical layout of the laser exposure set-up was later modified to allow both pulsed and CW excitation. A nearly 1 Watt QCL (quantum cascade laser) developed by Daylight Photonics was used to explore the power scaling of the process. The system was retrofitted with an alignment and inspection microscope to enable precision alignment and in-situ characterization. The system was built with automated substrate motion control and laser power control to enable precision mapping. (These features led to the initial demonstration of selective laser ablation.) Moreover this system allowed us to explore the power and wavelength dependence of the process in detail. FIG. 60 shows an SEM image of an ablated array. Clearly some of the individual tubes are destroyed while others remain intact. (Note: at very high power, “all” tubes ablate.) FIG. 61 shows a direct power mapping of the ablation process at two different IR wavelengths, (3 μm and 3.5 μm). Here fluencies range from 10's to 100's of μWatts with near diffraction limited focus. Interestingly here the higher energy, i.e., shorter wavelength excitation seems to have a better ablation range, albeit with a higher threshold power. The extent of selectivity of the ablation mechanism is modest. While there is a clear range, i.e., a likely processing window, it seems factors other than simply electronic behavior impact the required power and the window is narrow. To probe this we attempted ablation with CW (continuous wave) exposure. Under all CW exposure geometries, no ablation was observed. We also attempted CW IR initiation of Tc flow to see if there was sufficient energy from CW sources to heat metallic tubes at all. (FIG. 62 illustrates the results using CW excitation driven TcEP.) Again very little heating occurred. This led us to detail the power question. Our early work suggests that to initiate TcEP via Joule heating requires of order 10μW/μm to drive the process. Power calculations suggest that our CW flux, may be nearly 2 orders of magnitude lower in absorbed peak power. For our pulsed laser cases our energies are comparable to, or greater than used in joule heating. More importantly, it appears that to initiate ablation we are at 30-50μW/μm, comparable to the joule heating limit. If high peak power is required, as the driver for the observed physics, the temperature jump experienced by the nanotubes, optically, may be much larger than we expected relative to the joule heating initiated process. This indicates the basic mechanism may be very different in these absorptive approaches. As noted, at this point, the ratio of ablated/un-ablated tubes suggests while we can find a range where we are likely selectively destroying metallic tubes, the selectivity window is modest.

[0370] Assessment of TcEP Resist:

[0371] Finally we explored issues relevant to the development of advanced resist materials for TcEP. The focus was to both develop a full predictive model of resist performance and to define a guide for the development of next generation materials. The current resist is shown in FIG. 63. Shown is the molecular structure for MG2OH, α,α,α′-Tris(4-hydroxyphenyl)-1-ethyl-4-isopropylbenzene, with its typical trench formation performance (right). We developed a model which captured all the relevant materials physics. The dependence of trench width on materials parameters such as viscosity and other thin film properties was detailed. The primary findings suggest that to fully optimize the resist there are two interrelated issues that need to be addressed and improved. First is the limiting width of the trenches formed. Here the density of tube die which can be purified with this method will be determined by the width of full trenches. Currently deep trenches range from 100-500 nm. At current CVD grown wafer densities (1-2 tubes/micron), this is sufficient. As we move to wafers at 5-10 tubes/micron, deep trenches need to be narrower. The path to narrower trenches is simply to apply thinner resist layers, but this leads to the second issue. A thinner resist layer leads to weaker etch protection. If our path to higher density performance is to use thinner layers, we need to improve substantially the etch resistance of our resist. For example, adding ring structure to the MG2OH framework or using Si containing materials could be a solution but care must be taken to keep proper viscoelastic properties. We have identified several classes of materials, such as low molecular weight polymers, including but not limited to (polystyrene) PS and (polymehtylmethacrylate) PMMA, which offer promise. By controlling molecular weight we control film viscosity and therefore thermocapillary kinetics.

[0372] We have shown that we can purify SWNT die to yield ˜100% semiconducting nanotubes using TcEP initiated by microwave and laser irradiation. We have shown that these die can be processed into high performance transistors. We have shown that the developed techniques, especially microwave initiation has paths to scale-up which will enable processing of full wafers. We note we have already begun the process of integrating and transferring this technology to a number of nanotube electronics efforts nationwide. Much of the momentum in SWNT device research has been stifled by the inability of device processers to purify nanotubes. This work removes this barrier.

• [0373] [1] Rutherglen, C., Jain, D., and Burke, P., Nature Nanotechnology (4), pg 811, (2009); Cao, Q. and Rogers, J. Advanced Materials, (21) pg. 29 (2009)
• [0374] [2] S. J. Kang, C. Kocabas, T. Ozel, M. Shim, N. Pimparkar, M. A. Alam, S. V. Rotkin and J. A. Rogers, “High-performance Electronics Using Dense, Perfectly Aligned Arrays of Single-Walled Carbon Nanotubes,” Nature Nanotechnology 2, 230-236 (2007).
• [0375] [3] C. Kocabas, S. Dunham, Q. Cao, K. Cimino, X. Ho, H.-S. Kim, D. Dawson, J. Payne, M. Stuenkel, H. Zhang, T. Banks, M. Feng, S. V. Rotkin and J. A. Rogers, “High-Frequency Performance of Submicrometer Transistors That Use Aligned Arrays of Single-Walled Carbon Nanotubes,” Nano Lett 9(5), 1937-1943 (2009).
• [0376] [4] A. A. Pesetski, J. E. Baumgardner, S. V. Krishnaswamy, H. Zhang, J. D. Adam, C. Kocabas, T. Banks and J. A. Rogers, “A 500 MHz Carbon Nanotube Transistor Oscillator,” Applied Physics Letters93, 123506 (2008).
• [0377] [5] C. Kocabas, H.-S. Kim, T. Banks, J. A. Rogers, A. A. Pesetski, J. E. Baumgardner, S. V. Krishnaswamy and H. Zhang, “Radio Frequency Analog Electronics Based on Carbon Nanotube Transistors,” Proceedings of the National Academy of Sciences USA 105(5), 1405-1409 (2008).
• [0378] [6] Lan, Y., Wang, Y., and Ren, Z. F., Advances in Physics; volume 60(4), pg. 533, (2011)
• [0379] [7] Ding, L. et al. Nano Letters 9, 800-805, doi:10.1021/nl803496s (2009); Zhou, C. et al. ACS Nano, ArticleASAP
• [0380] [8] Arnold, M. S., Green, A. A., Hulvat, J. F., Stupp, S. I. & Hersam, M. C., Nature Nanotechnology (1), pg. 60 (2006)

[0381] A schematic of the IR-based TcEP process is presented in FIG. 68. SWNTs were grown via CVD on ST-cut quartz. A 25 nm amorphous film of α,α,α′-Tris(4-hydroxyphenyl)-1-ethyl-4-isopropylbenzene, a small organic molecule, is deposited onto the substrate. This material, hereinafter referred to as the thermocapillary(Tc) resist, was chosen for its thermal properties, resistance to RIE, as well as its ability to form a uniform and continuous ultrathin film on SWNTs and quartz. In addition, the detailed mechanisms behind thermocapillary flow of this material have been thoroughly explored in previous publications. Background heating of 65° C. was uniformly applied to the substrate, decreasing the viscosity of the Tc resist and promoting thermocapillary flow. The SWNTs were exposed using a λ=2500 nm pulsed infrared laser with a pulse duration of 10 ns and repetition rate of 1 kHz focused to a 5 μm beam spot size. The beam was rastered back-and-forth over a distance of 60 μm orthogonally with respect to the direction of the aligned SWNTs at a rate of 0.4 μm/s. Selective IR absorption caused heating in the m-SWNTs, inducing thermocapillary flow of the Tc resist and forming trenches. RIE was used to etch m-SWNTs exposed after trench formation and the Tc resist was removed using organic solvents.

[0382] Laser power and rastering time was varied to optimize exposure dose and thereby selectivity. FIG. 69a shows the percentage of SWNTs that yielded trenches with respect to these two parameters. There are three distinct regions; Blue represents little to no trench formation, green shows 40-60% trench formation, and red indicates trenches formed by nearly all SWNTs. These are abrupt transitions between these regions, suggesting the presence of three distinct, stable conditions. In the blue region, heating is not sufficient for any trench formation. In the green region, m-SWNTs are heated to sufficient temperatures to allow for trench formation. In the red region, s-SWNTs also form trenches. Exposures in which the beam is rastered for 20 minutes or longer have little effect on selectivity. Trenches may become deeper or wider, but few new trenches form again suggesting stable, but phenomenologically distinct states. An optimal exposure condition of 3.5 mW laser power rastered for 120 minutes were chosen for all subsequent experiments.

[0383] FIG. 69b shows an AFM topography image of an isolated patch of aligned SWNTs on quartz patterned using photolithography and oxygen plasma etching. This patterning facilitates ease of counting. FIG. 69c shows the same device after Tc resist deposition and laser exposure at the optimized condition. Trenches have been formed by some, but not all SWNTs, indicating selectivity. Trenches formed are approximately 20 nm deep and 100 nm wide. Variation in trench length arises due to Gaussian power distribution of the laser beam profile and differences in absorption coefficient among species of m-SWNTs. FIG. 69d shows a higher magnification AFM scan of an exposed substrate, from which we can observe continuous and highly selective trench formation. Several SWNTs, presumably m-SWNTs, form continuous trenches in the exposed area while the remaining s-SWNTs do not exhibit any such trench formation. The variation in trench width along each SWNT can be attributed to the presence of small defects or kinks.

[0384] Raman spectroscopy was conducted to determine diameter and electronic type of SWNTs. Aligned arrays of SWNTs were grown on R-plane cut sapphire via CVD. Using sapphire substrates allows for direct assessment of SWNT diameter using the radial breathing mode (RBM) peaks, which are usually obscured by vibrational modes in quartz. In FIG. 69e, AFM images of a substrate before processing (top) and after Tc resist deposition and exposure (middle) correspond perfectly with its Raman spectra (bottom). Red and blue lines correspond to RBM signals from m-SWNTs and s-SWNTs, respectively. Raman signals from 39 individual SWNTs were acquired, 11 from m-SWNTs, and 28 from s-SWNTs. All 11 m-SWNTs yielded complete trenches while only 2 s-SWNTs yielded trenches, indicating excellent selective heating of m-SWNTs. Trenches formed by s-SWNTs could be caused by bundling with m-SWNTs, small band gap s-SWNTs, or heavily doped s-SWNTs.

[0385] Two-terminal devices were used to monitor device degradation during the laser exposure process. I-V measurements conducted before and after exposure for a representative device are shown in FIG. 69f. Current retention for this particular device was 95.4%. Histograms of I_DS at V_DS=2 V among 22 devices before and after exposure are shown in FIGS. 69g and 69h, respectively. Average current retention was 97.9%.

[0386] Thin film transistors integrating purified s-SWNTs after IR-based TcEP processing were fabricated. An optical microscopy image of the device is shown in FIG. 70a. Device dimensions are as follows: L_C=200 nm and W_C=40 μm. Representative transfer and output characteristics of a representative device are shown in FIGS. 70b and 70c respectively. I_ON/I_OFF ratio >10⁵ indicates complete removal of m-SWNTs. Switch ratios of 12 devices are plotted vs. the on-state currents. I_ON/I_OFF of no less than 10⁴ are measured and some devices exhibit switching ratios of nearly 10⁶.

[0387] FIG. 71 shows processes and outcomes of the microwave-based purification of large-area arrays of aligned SWNTs. (a) Schematic illustration of the process. Patterning well defined strips of Fe catalysts followed by CVD growth yields aligned SWNTs which consist of both metallic and semiconducting types. A second patterning defines the microstrip antennas (typically Ti) over the substrate which serve as means to selectively transfer the microwave radiation energy into m-SWNTs. The resulting heating induces the local flow of a thermo-evaporated thin layer (˜40 nm) of thermocapillary resist (Tc-resist) and opens trenches above the m-SWNTs. Reactive ion etching (RIE) subsequently etches away the exposed m-SWNTs while leaving arrays of s-SWNTs under the Tc-resist intact. (b) SEM and AFM images correspond to each step in the schematics, showing the mixtures of SWNTs before the purification, the trench formations on m-SWNTs and the s-SWNTs after the purification. (c) Statistics of the normalized trench depths h/H for more than 500 tubes, arranged in an ascending manner (x axis is the accumulated fraction of the SWNTs), showing that ˜36% of the SWNTs create trenches deep enough to etch away. This statistic matches that ˜⅓ of the SWNTs being metallic types. Inset represents the schematics of the geometry for extracting the trench depth, with key parameters defined. The SWNT, the Tc-resist and the substrate are grey, green and blue, respectively. (d), (e) Transfer curve and output characteristics for 40 transistors built with large-areas (˜40 mm in total width) of SWNTs after the purification. The transistors utilize the Ti microstrip antenna as the source and drain contacts, and achieve an on/off ratio ˜10³, and large output current-25 mA.

[0388] FIG. 72 shows the effectiveness of the microwave-based purification process. (a) Schematic illustration of various steps to verify the effectiveness of the purification process. Fabrication and measurements of transistors built on small arrays of SWNTs (number of SWNTs from 10 to 25) before and after the purification facilitates the direct comparisons. The source and drain of the transistor also serve as the antenna for the purification. The PMMA dielectrics make the top-gate easily removeable by acetone after the characterizations. Patterning new Ohmic contacts by Pd afterwards, and depositing SU8(20 nm)/HfO₂(5 nm) as new dielectric lead to transistors with low operational voltage and low hysteresis. (b)(c) Typical transfer curve and output characteristics (near the on state region) for a transistor before and after the purification. The on-off ratio increases from ˜3 to ˜8.5×10⁴, and the maximum output current retains ˜40% after the purification. (d) The maximum output current before and after (I_{max_b} and I_{max_a}, respectively) purification, as a function of the ratio (N_a/N_b) of the number of SWNTs after purification with respect to the one before purification. I_{max_b}/I_{max_a} ranges from 0.1 to 0.6, increasing with the rise of N_a/N_b, which suggests that the s-SWNTs are well protected. (e) Statistics of the on-off ratios of the transistors based on the SWNTs, before (black square) and after (red dot) the purification, respectively. The I_on/I_off increases from <10 to 1×10³˜10⁶, agreeing with the removal of all the m-SWNTs. (f) (g) Typical transfer curve and output characteristics of a transistor built on a small array of purified SWNTs (15 SWNTs), by using Pd as new contacts and SU8(50 nm)/HfO₂(5 nm) as dielectrics. The low hysteresis feature facilitates the extraction of the device mobility, which is ˜1600 cm²/V/s as shown in the insert graph.

[0389] FIG. 73 shows coupling between the microwave field, microstrip antenna and SWNTs, and the heating mechanism. (a) 3D FEM-simulation results of the electrical field distribution around the microdipole antenna. The incident microwave is assumed to be a TEM mode, propagating perpendicular to the antenna plane (Z axis), and with electrical field polarized along the length of the antenna (X axis). The simulation indicates the enhancement of the microwave field in the gap between the two antenna arms. (b) An equivalent circuit model for the antenna and SWNT structure. The antenna is treated as a voltage source with resistance of R_o+R_r, and inductance of X_A. The SWNT is assumed to be a metallic type, with a resistivity of r_s and inductance of L_k per unit length. Within the contact length L_c, strong coupling exists between the antenna and the SWNT, through a series of capacitance C_g (geometric capacitance) and C_g (quantum capacitance), and a shunt conductance G. In the exposed region between the two antenna arms (L₀), the coupling between the antenna and the SWNT is neglected for simplicity. (c) FEM simulated field enhancement with respect to the length of the antenna, indicating an approximately linear relationship within the length of interest. (d) Schematic illustration and AFM topography image of the case where the SWNT is in contact with both sides of the antenna arms. The plot below shows the trench depth profile along the length of the SWNT extracted from the AFM image (black square) and the heating profile calculated from the circuit model (red curve). The heating as well as the trench depth is relatively constant along the SWNT. (e) Schematic illustration and AFM topography image of the case where the SWNT is in contact with one side of the antenna arms. The extracted trench depth (black square) decreases starting from the left contact, all the way to the end of the SWNT, where the trench eventually diminishes. This trend can be well captured by the FEM simulation of the heating profile (red curve), by using the resistivity of the SWNT as the only fitting parameter. (f) Schematic illustration and AFM topography image of the case where the SWNT is separated from the antenna by an air gap with a constant distance of ˜1.1 um. The trench not only exists in between the two antenna arms, but also extends underneath the antenna. The trench profile can be well matched by the calculated heating profile from the circuit model, by using the resistance of the SWNT as the only fitting parameter.

[0390] FIG. 74 shows different metals as the antennas. (a) Average current per tube at 1 V, 5V, 10V and 20V, for different metals serving as the antennas. The DC voltage is applied across the dipole antenna bridged by small arrays of SWNTs for the measurements. Data of each metal type averages the results from more than 100 SWNTs. The average current decreases as the work-function of the metal decreases. (b)(c) Transport simulation of the average current per tube for different contacts. The simulation averages the current from SWNTs with different diameters (distribution taken from literature from the same group). For (b), it assumes that ⅓ of the SWNTs are metallic and the others are semiconducting. (c) shows the results from only s-SWNTs. The general trend matches with the experimental observations. As the work-function of the contacts decreases, the current in the s-SWNTs decreases, which is a result of the formation of a Schottky barrier at the contact region for s-SWNTs. The slight increase of the current for the Mg contact is due to a band to band tuning effect. (d)-(i) Experimental (square) and simulated (curve) statistics of the normalized trench depths for different metals as the antennas during the microwave process, (d) Pd, (e) Au, (f) Mo, (g) Ti, (h) Al, (i) Mg. The T_c film thickness (˜40 nm) and microwave conditions (250 W 73C 3h) are the same for all metal types. For metals with relatively high work-functions like Pd and Au, both the m-SWNTs and s-SWNTs create trenches (h>0); while for metals with low work-functions like Mo, Ti, Mg, a distinct gap in the statistics separate the m-SWNTs from the s-SWNTs. The Al antenna results in a continuous distribution of the trench depth, and the gap appears when the thickness of the film decreases to ˜20 nm. This suggests insufficient heating for the m-SWNTs, which is probably due to the poor wettability of Al to the SWNTs. The simulations match with the experimental results quite well, verifying that the Schottky barrier plays the key role for selectively heating the m-SWNT by using metals with low work-functions as the antennas.

[0391] FIG. 75 shows microwave purification based on removable antennas. (a) Schematic illustration of the purification process based on removable antennas. Patterning the antenna on a substrate and molding PDMS micropillars forms the antenna mask. Laminating the antenna mask to the quartz substrates with SWNTs results in sufficient heating to create deep trenches above the m-SWNTs during the microwave process. The micropillars hold the antenna mask and substrate together, with a constant distance in between. After the microwave process, the antenna mask can be easily peeled off, leaving SWNTs without any metal contacts. (b) Images correspond to each step shown in the schematics: SEM image of the SWNTs before the purification; optical image of the antenna mask after contacting the quartz substrate; AFM topography image of the trench formation and SEM image after the etching and washing away the T_c resist. (c) Transfer curve of a typical transistor based on the purified arrays via the removable antenna scheme. (d) Simulation of the heating power with respect to the resistivity of the SWNTs for different cases. Decreasing the distance, and increasing the dielectric constant of the materials between the antenna and the SWNTs can increase their capacitive coupling, resulting in a higher heating level.

[0392] Through selectively inducing Joule heating on m-SWNTs, the 2-terminal (2T) probing method provides another simple way for driving the thermocapillary flows for purification.

[0393] FIG. 76a shows a schematic illustration of this process. To do the purification, the SWNTs are first grown on the quartz substrate, followed by patterning strips of metal contacts on the SWNTs. Metals with relatively low work-functions with respect to the middle gap energy of the SWNTs, as well as good wettability to the SWNTs are typically good choices for the contacts. After the deposition of the thermocapillary resist (T_c resist), a DC voltage is applied across the metal contacts, which selectively induces Joule heating on the m-SWNTs, causing the flows of the T_c resist to open trenches above the m-SWNTs. Reactive ion etching is then used to etch away the exposed m-SWNTs, leaving the s-SWNTs well protected by the T_c resist. FIG. 76b shows the SEM image of a pristine array of SWNTs and the corresponding AFM topography image of the induced trenches. Such well-defined, uniform trenches along the SWNTs are the key for the successful removal. Statistics of the trench depth associated with each SWNT in a device with total 171 SWNTs are shown in FIG. 76c. The depths are arranged in an ascending manner (x axis is the accumulated differential fraction of the SWNTs), showing that ˜37% of the SWNTs create trenches deep enough to etch away. This statistic matches ˜⅓ of the SWNTs being metallic types.

[0394] FIG. 77a is the scheme to scale up the 2T probing method for the wafer scale purification. Here, interdigitated electrodes are patterned over the wafer. Those electrodes are linked together, resulting in electrical paths on the entire wafer. Since the thermocapillary flow is very sensitive to the temperature, it is important to control well the substrate temperature. However, when a wafer of SWNTs simultaneously run through current (especially when the density of the SWNTs is high >1 SWNT/μm), a substantial amount of Joule heating energy will cause the temperature rise, which may eventually result in dewetting of the Tc resist. Therefore, pulse operational mode for the voltage source needs to apply in order to get better thermal management, as shown in the image of FIG. 77b (Sunhun, Simon, Nature Nanotechnology, 2013).

[0395] Pulsed Biases for Forming Trenches in Large and/or High Density Arrays of SWNTs.

[0396] AFM trenches formed in Tc-resist for an array with 2-3 SWNT/μm associated with pulsed heating with increasing duty cycle (V_DS=−40V peak amplitude, period=10 μs, duration=1-10 μs, V_GS=+20V DC, 60 sec total stress duration, 50° C. background heating). For 10% duty cycle clearly defined trenches are observed. As the duty cycle increases, trenches become less clearly defined and flow is observed that does not correlate to the underlying SWNT positions. This results from delocalized heating associated with parallel operation in many SWNTs. Pulsed heating aids in localizing the flows needed for proper operation in TcEP.

[0397] Finally, to qualitatively explain the selectivity of the 2T probe method, FIG. 78a draws out the work-function of different types of metals, with respect to the valence and conduction band of the SWNT. S-SWNTs are usually found to be P type, therefore metals with low work-functions can form Schottky barriers to them, which will block the current flow (FIG. 78c). On the other hand, the metals with relatively high work-functions can form Ohmic contact with the s-SWNTs, which enables the current flow (FIG. 78b).

[0398] When implemented on the nanoscale, material flows driven by gradients in temperature, sometimes known as thermocapillary flows, can be exploited for various purposes, including nanopatterning, device fabrication, and purification of arrays of single walled carbon nanotubes (SWNTs). Systematic experimental and theoretical studies on thermocapillary flow in thin polymer films driven by heating in individual metallic SWNTs, over a range of conditions and molecular weights reveal the underlying physics of this process. The findings suggest that the zero-shear viscosity is a critical parameter that dominates the dependence on substrate temperature and heating power. The experimentally validated analytical models in this study allow assessment of sensitivity to other parameters, such as the temperature coefficient of surface tension, the thermal interface conductance, and the characteristic length scale of the heated zone.

[0399] Recent reports highlight the ability to use nanoscale, thermally driven processes of pattern formation for applications in ultralow power phase-change memory¹, nanolithography^2-4, purification of aligned arrays of SWNTs⁵ and others. In these examples, self-aligned structures in thin film coatings form as a result of local increases in temperature induced at the positions of Si or metal nanowires^2-4 or metallic SWNTs (m-SWNTs)^1,5. Some of these phenomena are reported to involve physical evaporation and/or chemical change in the films. In one case, data indicates a process of physical mass transport, or flow, that depends on temperature, gradients in temperature and physical/chemical properties of the film and substrate support. Such flows can occur in organic small molecule or polymer films at peak temperatures of just a few degrees, for sources of heat that have nanoscale dimensions. In one application, films coated onto aligned arrays of SWNTs undergo flow only at regions of selective current injection, and Joule heating, at the m-SWNT. This process creates openings that allow removal of the m-SWNTs by gas phase etching, in a manner that leaves the semiconducting SWNTs unaltered. A full understanding of this process is necessary for further optimization and use of this physics, not only in purification of SWNT arrays, but in nanolithography, device fabrication and other areas as well. Here, we report systematic experimental and theoretical studies that highlight, directly and indirectly, the essential aspects of nanoscale thermocapillary flows in films of polystyrene (PS), driven by Joule heating^1,5 in individual single walled carbon nanotubes (SWNTs). Quantitative agreement between experiment and theory establishes use of the models reported here for predictive assessment of the thermocapillary flow process. One key conclusion is that the viscosity^6,7 is a critical parameter that largely defines the influence of substrate temperature and rates of Joule heating on this process.

[0400] FIG. 79(a) provides a scanning electron microscope (SEM) image of an individual SWNT with a pair of metal electrode contacts. For studies reported here, ST-quartz wafers serve as substrates, with Ti/Pd (=2/40 nm) as contacts, separated by 30 μm.^5,8 For such devices formed with m-SWNTs, the voltage drops primarily along the length of the m-SWNTs, rather than at the contacts⁸. Spin casting thin films of PS on top of such devices and then applying a DC bias across the electrodes initiates nanoscale thermocapillary flow along the length of the heated m-SWNT, driven by the temperature dependent surface tension in the film, as described subsequently. FIG. 79(b) shows a typical trench that forms as a result. The trench width (W_Tc) is defined as the distance between the ridges that form in the PS on either side of the m-SWNT⁵. Studies involve PS (Sigma Aldrich, Inc) with M_w between 2.5 kg/mol to 30 kg/mol, dissolved in toluene to form a 0.8 wt % solution that is passed through a PVDF membrane filter with nominal pore size of 0.2 μm (Whatman) to remove any particulates or polymer aggregates. Typical film thicknesses are t_PS=30 nm±3 nm. Thermocapillary flow occurs on a temperature-controlled substrate (T_o=353 K) in a vacuum chamber (Lake Shore Cryotronics, Inc.) at a base pressure of ˜1×10⁻⁴ torr. The process involves applying a DC bias for 10 minutes while monitoring the current with a parameter analyzer (Agilent 4155C). An atomic force microscope (AFM; Asylum MFP 3D, tapping mode) yields images of the patterns of PS induced by thermocapillary flow. Soaking the sample in toluene, drying under a stream of nitrogen, and then baking on a hotplate (110° C. for 10 minutes) allows its re-use in multiple experiments.

[0401] FIG. 79(c) shows a collection of AFM images of trenches that form under identical overall conditions (i.e. average power dissipation per unit length of the SWNT, Q₀ ˜30 μW/μm, substrate temperature T₀=353 K and base pressure ˜1×10⁻⁴ torr for 10 min) using PS with M_w from 17.5 kg/mol to 2.5 kg/mol. The results show that W_Tc increases significantly with decreasing M_w, as summarized by the red symbols in FIG. 79d. The physics of this process is essentially unidirectional, such that the evolution of film thickness h(x,t) can be approximated by the one dimensional lubrication equation⁵,

$\begin{array}{cc}\frac{\partial h}{\partial t}+\frac{\partial }{\partial x}\left[\frac{\tau h^2}{2\eta }+\frac{h^3}{3\eta }\frac{\partial }{\partial x}\left(\gamma \frac{{\partial }^2h}{\partial x^2}\right)\right]=0& \left(1\right)\end{array}$

[0402] with the initial condition h(x,t=0)=h₀, where h₀ is the initial film thickness, and the boundary conditions h(x=±∞,t)=h₀ and δ²h/δx² (x=±∞,t)=0 (zero pressure). Here, γ is the surface tension, which usually depends linearly on the surface temperature T of film [i.e., γ=γ₀−γ₁(T−273)] where γ₀ is the surface tension at 273K and γ₁ is the temperature coefficient of surface tension,

$\tau =\frac{\partial \gamma }{\partial T}\frac{\partial T}{\partial x}$

is the thermocapillary stress, and η is the film viscosity. For polystyrene, γ₀ and γ₁ are taken as 47.4×10⁻³ N/m and 0.078×10⁻³ N/(mK)⁹, respectively, for all PS materials examined since γ₀ and γ₁ depend only slightly on M_w (less than 5% change for γ₀ and 20% change for γ₁ with M_w between 2 kg/mol to 30 kg/mol)⁹. The model suggests that low viscosity facilitates physical mass transport induced by spatial variations in surface tension due to temperature gradients created by Joule heating in the m-SWNT. The zero-shear viscosity, η, can be connected to M_w via the Vogel equation⁷,

$\eta =A{}^{\frac{B}{{\alpha }_f\left(T-T_{\infty }\right)}},$

where A is the structure factor, B/α_f is a constant⁷, and T_∞ is the Vogel temperature, respectively. Literature⁷ suggests that, B/α_f˜(1620±50) K, A=1.925×10⁻⁸M_w^1.25 Pa·sec, and T_∞=321.4−8.3×10⁴M_w⁻¹ K, both with M_w in g/mol. We use B/α_f=1640 K, chosen within the range defined by the literature, but with a specific value that leads to agreement between experiment and theory for the trench width (˜0.62 μm) at T₀=353K, Q₀=30 μW/μm and M_w=2.5 kg/mol after 10 minutes of heating. Calculated viscosities from the Vogel equation appear as blue symbols in FIG. 79d.

[0403] The temperature distribution for Eq. (1) can be approximated by the surface temperature⁵ of the film calculated as a result of heating of the m-SWNT, which can be written

$\begin{array}{cc}T\left(x\right)=\frac{1}{k_f\pi }{\int }_{-L/2}^{L/2}u{\int }_0^{\infty }\frac{Q_0{}^{-\xi h_0}\left(1+\frac{k_s\xi }{\zeta }\right)J_0\left(\xi \sqrt{u^2+x^2}\right)}{-\left(1+\frac{k_s\xi }{\zeta }-\frac{k_s}{k_f}\right){}^{-2\xi h_0}+\left(1+\frac{k_s\xi }{\zeta }+\frac{k_s}{k_f}\right)}\xi +T_0& \left(2\right)\end{array}$

where k_s and k_f are the thermal conductivity of PS and quartz, respectively, L is the length of the SWNT, ζ is the interface thermal conductance between PS and quartz, and J₀ is the 0^th order Bessel function of the first kind. Here, h₀=30 nm, k_f¹⁰=0.15 Wm⁻¹K⁻¹ and k_s¹¹=6 Wm⁻¹K⁻¹. Compared with that for the case of ζ=∞, the computed peak temperatures at the surface of the PS are only ˜35% higher for ξ=10⁸ W/(m²K) and ˜5% higher for 10⁹ W/(m²K), which are sufficiently small that they do not affect any of the major conclusions associated with this study. Therefore, all calculations in this example correspond to the temperature with ζ=∞, i.e.,

$\begin{array}{cc}T\left(x\right)=\frac{1}{2k_s\pi }{\int }_{-L/2}^{L/2}u{\int }_0^{\infty }\frac{Q_0J_0\left(\xi \sqrt{u^2+x^2}\right)}{\cosh \left(\xi h_0\right)+\frac{k_f}{k_s}\sinh \left(\xi h_0\right)}\xi +T_0,& \left(3\right)\end{array}$

[0404] Equation (1) is equivalent to a pair of coupled partial differential equations

$\frac{\partial h_1}{\partial \stackrel{\_}{t}}=\frac{\partial }{\partial x}\left(-\frac{\tau h_1^2}{2\eta }-\frac{h_1^3}{3\eta }\frac{\partial \gamma }{\partial x}h_2-\frac{h_1^3\gamma }{3\eta }\frac{\partial h_2}{\partial x}\right)\mathrm{and}\frac{{\partial }^2h_1}{\partial x^2}-h_2=0$

with h₁=h, initial conditions h₁ (x,t=0)=1 and h₂ (x,t=0)=0, and boundary conditions h₁ (x=±∞,t)=1 and h₂(x=±∞,t)=0. The Fortran solver PDE_1D_MG can be used to evaluated these equations (i.e., h₁ and h₂), to yield the evolution of the film thickness h(x,t). The dashed line in FIG. 79(d) shows the computed value of W_Tc for parameters equivalent to experiment: 10 minutes of heating at T₀=353 K and Q₀=30 μW/μm. The results agree remarkably well with experiment. The scaling trends arise mainly from variations in A, which yields a power law dependence of η on M_w (∝ M_w 1.25)⁷.

[0405] The values of T₀ and Q₀ are also important. FIG. 80(a) shows AFM images of results of thermocapillary flow in PS with M_w=2.5 kg/mol and Q₀=30 μW/μm for 10 min, with T₀ between 313 K to 353 K. The results show that W_Tc increases dramatically with increases in T₀. FIG. 80(b) shows effects of changing Q₀ from 8.4 to 151 μW/μm for T₀=353 K and PS with M_w=2.5 kg/mol at T₀=353 K. Clearly, as with T₀) W_Tc depends strongly on O₀. FIG. 81(a) summarizes a set of results similar to those of FIG. 80(a). The Arrhenius type scaling arises from the temperature dependence of η, as confirmed from results computed with Eqs (1) and (2). Likewise, FIG. 81(b) shows a collection of measurements like those of FIG. 80(b), which reveal scaling with Q₀. The trench width is nicely replicated with analytical solution without any fitting, thereby providing further indication that r_f is, to within experimental uncertainties, entirely responsible for the observed variations. We note that the calculations cease to be valid above a critical value h(x=0,t)=0.

[0406] In summary, the results presented here indicate that effects of temperature, power dissipation and molecular weight on nanoscale thermocapillary flow all arise primarily from associated variations in viscosity. The sensitivity to the temperature coefficient of surface tension (γ₁), the thermal interface conductance (ξ) are comparatively small, for values of these parameters that lie within ranges reported in the literature^7,9. For the conditions examined here, the maximum temperature gradient (dT/dx)_max, for a given Q₀, shows little dependence on the width of the heat source for values ranging from those corresponding to a SWNT (i.e. ˜1 nm) to ˜100 nm diameter range; at 1 μm, the gradient is reduced by nearly an order of magnitude. These and other insights can be developed from an examination of the physics implied by the experimentally validated models reported here. In particular, engineering design rules for control of flows associated with this type of thermally induced pattern formation can be defined. The immediate relevance is to recently described, low temperature approaches for purifying arrays of SWNTs, but can be extended to other areas in nanopatterning and device fabrication where such effects could be useful.

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[0418] All references throughout this application, for example patent documents including issued or granted patents or equivalents; patent application publications; and non-patent literature documents or other source material; are hereby incorporated by reference herein in their entireties, as though individually incorporated by reference, to the extent each reference is at least partially not inconsistent with the disclosure in this application (for example, a reference that is partially inconsistent is incorporated by reference except for the partially inconsistent portion of the reference).

[0419] U.S. Pat. No. 8,367,035, Issued Feb. 5, 2013, entitled “Methods of Making Spatially Aligned Nanotubes and Nanotube Arrays” relates generally to methods for making substantially longitudinally aligned arrays of carbon nanotubes and is hereby incorporated by reference in its entirety.

[0420] The following references relate generally to methods of synthesizing and purifying carbon nanotubes, and each is hereby incorporated by reference in its entirety: (1) A. M. Cassell, J. A. Raymakers, J. Kong, H. J. Dai, J. Phys. Chem. B 103(31), (1999), pp. 6484-6492; (2) M. Su, B. Zheng, J. Liu, Chem. Phys. Lett. 322(5), (2000), pp. 321-326; (3) B. Kitiyanan, W. E. Alvarez, J. H. Harwell, D. E. Resasco, Chem. Phys. Lett. 317(3-5), (2000), pp. 497-503; (4) J. H. Hafner, M. J. Bronikowski, B. R. Azamian, P. Nicolaev, A. G. Rinzler, D. T. Colbert, K. A. Smith, R. E. Smalley, Chem. Phys. Lett. 296(1-2), (1998) pp. 195-202; (5) H. M. Cheng, F. Li, G. Su, H. P. Pan, L. L. He, X. Sun, M. S. Dresselhaus, Appl. Phys. Lett. 72(25), (1998), pp. 3282-3284; (6) B. Zheng, Y. Li, J. Liu, Applied Physics A 74, 345-348 (2002); (7) C. Journet, W.K. Maser, P. Bernier, A. Loiseau, M. Lamy de la Chapelle, S. Lefrant, R. Lee, J.E. Fischer, Nature 388, 756-758 (1997); (8) A. Thess, R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert, C. Xu, Y. H. Lee, S. G. Kim, A. G. Rinzler, D. T. Colbert, G. E. Scuseria, D. Tomanek, J. E. Fischer, R. E. Smalley, Science 273, (1996) 483-487; (9) M. Holzinger, A. Hirsch, P. Bernier, G. S. Duesberg, M. Burghard, Applied Physics A 70, (2000) 599-602; (10) G. S. Duesberg, J. Muster, V. Krstic, M. Burghard, S. Roth, Appl. Phys. A 67, (1998), 117-119; (11) J. Liu, A. G. Rinzler, H. Dai, J. H. Hafner, R. K. Bradley, P. J. Boul, A. Lu, T. Iverson, K. Shelimov, C. B. Huffman, F. Rodriuez-Macias, Y. S. Shon, T. R. Lee, D. T. Colbert, R. E. Smalley, Science 280, (1998) 1253-1256; (12) A. G. Rinzler, J. Liu, H. Dai, P. Nikolaev, C. B. Huffman, F. J. Rodriguez-Macias, P. J. Boul, A. H. Lu, D. Heymann, D. T. Colbert, R. S. Lee, J. E. Fischer, A. M. Rao, P. C. Eklund, R. E. Smalley, Appl. Phys. A 67, (1998) 29-37; (13) Y. Feng, G. Zhou, G. Wang, M. Qu, Z. Yu, Chem, Phys, Lett, 375, (2003) 645-648; (14) T. Takenobu, M. Shiraishi, A. Yamada, M. Ata, H. Kataura, Y. Iwasa, Synthetic Metals 135-136, (2003) 787-788; (15) I. W. Chiang, B. E. Brinson, A. Y. Huang, P. A. Willis, M. J. Bronikowski, J. L. Margrave, R. E. Smalley, R. H. Hauge, J. Phys. Chem. B 105, (2001) 8297-8301. (16) U.S. Pat. No. 8,367,035; and (17) U.S. Patent Pub. No. 2011/0147715.

[0421] The terms and expressions which have been employed herein 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 invention claimed. Thus, it should be understood that although the present invention has been specifically disclosed by preferred embodiments, exemplary embodiments and optional features, modification and variation of the concepts herein disclosed may be resorted to by those skilled in the art, and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims. The specific embodiments provided herein are examples of useful embodiments of the present invention and it will be apparent to one skilled in the art that the present invention may be carried out using a large number of variations of the devices, device components, and methods steps set forth in the present description. As will be obvious to one of skill in the art, methods and devices useful for the present methods can include a large number of optional composition and processing elements and steps.

[0422] When a group of substituents is disclosed herein, it is understood that all individual members of that group and all subgroups, including any isomers, enantiomers, and diastereomers of the group members, are disclosed separately. When a Markush group or other grouping is used herein, all individual members of the group and all combinations and subcombinations possible of the group are intended to be individually included in the disclosure. When a compound is described herein such that a particular isomer, enantiomer or diastereomer of the compound is not specified, for example, in a formula or in a chemical name, that description is intended to include each isomer and enantiomer of the compound described individually or in any combination. Additionally, unless otherwise specified, all isotopic variants of compounds disclosed herein are intended to be encompassed by the disclosure. For example, it will be understood that any one or more hydrogens in a molecule disclosed can be replaced with deuterium or tritium. Isotopic variants of a molecule are generally useful as standards in assays for the molecule and in chemical and biological research related to the molecule or its use. Methods for making such isotopic variants are known in the art. Specific names of compounds are intended to be exemplary, as it is known that one of ordinary skill in the art can name the same compounds differently.

[0423] Many of the molecules disclosed herein contain one or more ionizable groups [groups from which a proton can be removed (e.g., —COOH) or added (e.g., amines) or which can be quaternized (e.g., amines)]. All possible ionic forms of such molecules and salts thereof are intended to be included individually in the disclosure herein. With regard to salts of the compounds herein, one of ordinary skill in the art can select from among a wide variety of available counterions those that are appropriate for preparation of salts of this invention for a given application. In specific applications, the selection of a given anion or cation for preparation of a salt may result in increased or decreased solubility of that salt.

[0424] It must be noted that as used herein and in the appended claims, the singular forms “a”, “an”, and “the” include plural reference unless the context clearly dictates otherwise. Thus, for example, reference to “a cell” includes a plurality of such cells and equivalents thereof known to those skilled in the art, and so forth. As well, the terms “a” (or “an”), “one or more” and “at least one” can be used interchangeably herein. It is also to be noted that the terms “comprising”, “including”, and “having” can be used interchangeably. The expression “of any of claims XX-YY” (wherein XX and YY refer to claim numbers) is intended to provide a multiple dependent claim in the alternative form, and in some embodiments is interchangeable with the expression “as in any one of claims XX-YY.”

[0425] Unless defined otherwise, all technical and scientific terms used herein have the same meanings as commonly understood by one of ordinary skill in the art to which this invention belongs. Although any methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present invention, the preferred methods and materials are described. Nothing herein is to be construed as an admission that the invention is not entitled to antedate such disclosure by virtue of prior invention.

[0426] Whenever a range is given in the specification, for example, a range of integers, a temperature range, a time range, a composition range, or concentration range, all intermediate ranges and subranges, as well as all individual values included in the ranges given are intended to be included in the disclosure. As used herein, ranges specifically include the values provided as endpoint values of the range. As used herein, ranges specifically include all the integer values of the range. For example, a range of 1 to 100 specifically includes the end point values of 1 and 100. It will be understood that any subranges or individual values in a range or subrange that are included in the description herein can be excluded from the claims herein.

[0427] As used herein, “comprising” is synonymous and can be used interchangeably with “including,” “containing,” or “characterized by,” and is inclusive or open-ended and does not exclude additional, unrecited elements or method steps. As used herein, “consisting of” excludes any element, step, or ingredient not specified in the claim element. As used herein, “consisting essentially of” does not exclude materials or steps that do not materially affect the basic and novel characteristics of the claim. In each instance herein any of the terms “comprising”, “consisting essentially of” and “consisting of” may be replaced with either of the other two terms. The invention illustratively described herein suitably may be practiced in the absence of any element or elements, limitation or limitations which is not specifically disclosed herein.

[0428] One of ordinary skill in the art will appreciate that starting materials, biological materials, reagents, synthetic methods, purification methods, analytical methods, assay methods, and biological methods other than those specifically exemplified can be employed in the practice of the invention without resort to undue experimentation. All art-known functional equivalents, of any such materials and methods are intended to be included in this invention. The terms and expressions which 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 invention claimed. Thus, it should be understood that although the present invention has been specifically disclosed by preferred embodiments and optional features, modification and variation of the concepts herein disclosed can be resorted to by those skilled in the art, and that such modifications and variations are considered to be within the scope of this invention as defined by the appended claims.

[0429] The following references relate generally to fabrication methods, structures and systems for making electronic devices, and are hereby incorporated by reference to the extent not inconsistent with the disclosure in this application:

Attorney			Publication	Publication
Docket No.	Application No.	Filing Date	No.	Date	Pat. No.	Issue Date
145-03 US	11/001,689	Dec. 1, 2004	2006/0286488	Dec. 21, 2006	7,704,684	Apr. 27, 2010
18-04 US	11/115,954	Apr. 27, 2005	2005/0238967	Oct. 27, 2005	7,195,733	Mar. 27, 2007
38-04A US	11/145,574	Jun. 2, 2005	2009/0294803	Dec. 3, 2009	7,622,367	Nov. 24, 2009
38-04B US	11/145,542	Jun. 2, 2005	2006/0038182	Feb. 23, 2006	7,557,367	Jul. 7, 2009
43-06 US	11/421,654	Jun. 1, 2006	2007/0032089	Feb. 8, 2007	7,799,699	Sep. 21, 2010
38-04C US	11/423,287	Jun. 9, 2006	2006/0286785	Dec. 21, 2006	7,521,292	Apr. 21, 2009
41-06 US	11/423,192	Jun. 9, 2006	2009/0199960	Aug. 13, 2009	7,943,491	May 17, 2011
25-06 US	11/465,317	Aug. 17, 2006	—	—	—	—
137-05 US	11/675,659	Feb. 16, 2007	2008/0055581	Mar. 6, 2008	—	—
90-06 US	11/782,799	Jul. 25, 2007	2008/0212102	Sep. 4, 2008	7,705,280	Apr. 27, 2010
134-06 US	11/851,182	Sep. 6, 2007	2008/0157235	Jul. 3, 2008	8,217,381	Jul. 10, 2012
151-06 US	11/585,788	Sep. 20, 2007	2008/0108171	May 08, 2008	7,932,123	Apr. 26, 2011
216-06 US	11/981,380	Oct. 31, 2007	2010/0283069	Nov. 11, 2010	7,972,875	Jul. 5, 2011
116-07 US	12/372,605	Feb. 17, 2009	—	—	—	—
213-07 US	12/398,811	Mar. 5, 2009	2010/0002402	Jan. 7, 2010	8,552,299	Oct. 8, 2013
38-040 US	12/405,475	Mar. 17, 2009	2010/0059863	Mar. 11, 2010	8,198,621	Jun. 12, 2012
170-07 US	12/418,071	Apr. 3, 2009	2010/0052112	Mar. 4, 2010	8,470,701	Jun. 25, 2013
38-04A1 US	12/564,566	Sep. 22, 2009	2010/0072577	Mar. 25, 2010	7,982,296	Jul. 19, 2011
71-07 US	12/669,287	Jan. 15, 2010	2011/0187798	Aug. 4, 2011	—	—
60-09 US	12/778,588	May 12, 2010	2010/0317132	Dec. 16, 2010	—	—
43-06A US	12/844,492	Jul. 27, 2010	2010/0289124	Nov. 18, 2010	8,039,847	Oct. 18, 2011
15-10 US	12/892,001	Sep. 28, 2010	2011/0230747	Sep. 22, 2011	8,666,471	Mar. 4, 2014
15-10A US	14/140,299	Dec. 24, 2013	—	—	—	—
19-10 US	12/916,934	Nov. 1, 2010	2012/0105528	May 03, 2012	8,562,095	Oct. 22, 2013
3-10 US	12/947,120	Nov. 16, 2010	2011/0170225	Jul. 14, 2011	—	—
118-08 US	12/996,924	Dec. 8, 2010	2011/0147715	Jun. 23, 2011	—	—
126-09 US	12/968,637	Dec. 15, 2010	2012/0157804	Jun. 21, 2012	—	—
50-10 US	13/046,191	Mar. 11, 2011	2012/0165759	Jun. 28, 2012	—	—
151-06A US	13/071,027	Mar. 24, 2011	2011/0171813	Jul. 14, 2011	—	—
137-05A US	13/095,502	Apr. 27, 2011	—	—	—	—
216-06B US	13/100,774	May 04, 2011	2011/0266561	Nov. 3, 2011	—	—
38-04A2 US	13/113,504	May 23, 2011	2011/0220890	Sep. 15, 2011	8,440,546	May 14, 2013
136-08 US	13/120,486	Aug. 4, 2011	2011/0277813	Nov. 17, 2011	—	—
151-06B US	13/228,041	Sep. 8, 2011	2011/0316120	Dec. 29, 2011	—	—
43-06B US	13/270,954	Oct. 11, 2011	2012/0083099	Apr. 5, 2012	8,394,706	Mar. 12, 2013
3-11 US	13/349,336	Jan. 12, 2012	2012/0261551	Oct. 18, 2012	—	—
38-04E US	13/441,618	Apr. 6, 2012	2013/0100618	Apr. 25, 2013	—	—
134-06B US	13/441,598	Apr. 6, 2012	2012/0327608	Dec. 27, 2012	—	—
28-11 US	13/472,165	May 15, 2012	2012/0320581	Dec. 20, 2012	—	—
7-11 US	13/486,726	Jun. 1, 2012	2013/0072775	Mar. 21, 2013	—	—
29-11 US	13/492,636	Jun. 8, 2012	2013/0041235	Feb. 14, 2013	—	—
84-11 US	13/549,291	Jul. 13, 2012	2013/0036928	Feb. 14, 2013	—	—
25-06A US	13/596,343	Aug. 28, 2012	2012/0321785	Dec. 20, 2012	8,367,035	Feb. 5, 2013
150-11 US	13/624,096	Sep. 21, 2012	2013/0140649	Jun. 6, 2013	—	—
38-04A3 US	13/801,868	Mar. 13, 2013	2013/0320503	Dec. 5, 2013	—	—
38-04A4 US	14/155,010	Jan. 14, 2014	—	—	—	—
125-12 US	13/835,284	Mar. 15, 2013	—	—	—	—
30-13 US	13/853,770	Mar. 29, 2013	—	—	—	—

[0430] Every formulation or combination of components described or exemplified herein can be used to practice the invention, unless otherwise stated.

[0431] All patents and publications mentioned in the specification are indicative of the level of skill of those skilled in the art to which the invention pertains. References cited herein are incorporated by reference herein in their entirety to indicate the state of the art as of their publication or filing date and it is intended that this information can be employed herein, if needed, to exclude specific embodiments that are in the prior art. For example, when compositions of matter are claimed, it should be understood that compounds known and available in the art prior to Applicant's invention, including compounds for which an enabling disclosure is provided in the references cited herein, are not intended to be included in the composition of matter claims herein.