WO2025183765A2

WO2025183765A2 - Remote-contact catalysis for high-purity semiconducting carbon nanotube array

Info

Publication number: WO2025183765A2
Application number: PCT/US2024/056736
Authority: WO
Inventors: Jing Kong; Jiangtao Wang
Original assignee: Massachusetts Institute of Technology
Current assignee: Massachusetts Institute of Technology
Priority date: 2023-11-24
Filing date: 2024-11-20
Publication date: 2025-09-04
Anticipated expiration: 2026-05-24
Also published as: WO2025183765A3

Abstract

Electrostatic catalysis in chemical synthesis is known to boost reaction rates and selectively produce certain reaction products. Earlier studies required external electric field (EEF) of more than 10 MV/cm and alignment of EEF with the reaction axis. Such large and oriented EEF is unfeasible for large-scale implementation. Disclosed herein is a method of spontaneously shifting the band energy at the tip of an individual single-walled carbon nanotube (SWCNT) in a high-permittivity growth environment, with its other end in contact with a low work function electrode, such as hafnium carbide or titanium carbide. By adjusting the band energy at a point where there is a substantial disparity in the density of states (DOS) between semiconducting (s-) and metallic (m-) SWCNTs, effective electrostatic catalysis for s-SWCNT growth is achieved. The disclosed method enables the production of high-purity (99.92%) s-SWCNT horizontal arrays with stable chirality twist, aided by weak EEF as a perturbation.

Description

REMOTE-CONTACT CATALYSIS FOR HIGH-PURITY SEMICONDUCTING CARBON NANOTUBE ARRAY This application claims priority of U.S. Provisional Patent Application Serial No. 63/602,551, filed November 24, 2023, the disclosure of which is incorporated herein by reference in its entirety. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT This invention was made with government support under W911NF-23- 2-0057 awarded by the U.S. Army Research Office, and FA9550-22-1- 0166 0292 awarded by the Air Force Office of Scientific Research. The government has certain rights in the invention. Field This disclosure describes a method of creating semiconducting single-walled carbon nanotubes (SWCNT). Background Electrostatic catalysis has garnered significant attention in recent years as a promising approach to improve the selectivity and accelerate the rates of chemical reactions by utilizing external electrical fields (EEF). This has opened up new possibilities for designing and tailoring reactions with precision, including catalytic processes such as Diels-Alder addition or Ullmann coupling reactions at single-molecule level. However, despite its potential, practical implementation of electrostatic catalysis on a large scale has been hampered by the required field strength of EEF, translating to extremely high voltage needed (10 MV for 1-cm sample), posing challenges for efficient and scalable applications. Furthermore, for the synthesis of materials with more complex structures either involving multiple reaction axis or multiple reaction steps, such an oriented EEF will not be effective. Therefore, there is a need for a method that overcomes these limitations and allows generation of semiconducting single walled carbon nanotubes. Summary Electrostatic catalysis in chemical synthesis is known to boost reaction rates and selectively produce certain reaction products. Earlier studies required an external electric field (EEF) of more than 10 MV/cm and alignment of the EEF with the reaction axis. Such a large and oriented EEF is unfeasible for large-scale implementation. Disclosed herein is a method of spontaneously shifting the band energy at the tip of an individual single-walled carbon nanotube (SWCNT) in a high-permittivity growth environment, with its other end in contact with a low work function electrode, such as hafnium carbide or titanium carbide. By adjusting the band energy at a point where there is a substantial disparity in the density of states (DOS) between semiconducting (s-) and metallic (m-) SWCNTs, effective electrostatic catalysis for s-SWCNT growth is achieved. The disclosed method enables the production of high-purity (99.92%) s-SWCNT horizontal arrays with stable chirality twist, aided by weak EEF as a perturbation. These findings highlight the potential of electrostatic catalysis in materials growth, especially for s- SWCNTs, and pave the way for the development of advanced SWCNT- based electronics and future computing. According to one embodiment, a method of forming high purity aligned semiconducting single-walled carbon nanotubes is disclosed. The method comprises creating single-walled carbon nanotubes (SWCNTs) on a substrate; contacting the SWCNTs with a low work function electrode in a high permittivity environment, wherein the contacting causes charge transfer and remote band bending along an entire length of the SWCNTs; and applying a weak external electric field (EEF) perturbation, wherein the weak EEF perturbation causes metallic SWCNTs (m-SWCNTs) to twist to semiconducting SWCNTs (s-SWCNTs), wherein the s-SWCNTs are stably semiconducting. In some embodiments, the SWCNTs that are created prior to applying the weak EEF perturbation are m-SWCNTs or networks of s-SWCNTs and m-SWCNTs. In some embodiments, the method also comprises preparing the substrate, wherein the substrate comprises a dielectric material having strips of the low work function electrodes, catalyst strips, and insulating strips deposited thereon. In certain embodiments, the catalyst strips are disposed on a first side of each low work function electrode, and the insulating strips are disposed on a second side of each low work function electrode, such that the SWCNTs grow from the first side of one low work function electrode toward the second side of an adjacent low work function electrode. In certain embodiments, the insulating strips prevent electrical shorting between two adjacent low work function electrodes through the SWCNTs. In certain embodiments, the catalyst strips are disposed on a first side and a second side of the low work function electrodes, such that the SWCNTs grow from the first side and the second side of one low work function electrode toward adjacent low work function electrodes. In certain embodiments, the insulating strips are disposed between adjacent low work function electrodes. In some embodiments, the low work function electrode has a work function of 4 eV or less. In certain embodiments, the low work function electrode is a metal carbide. In certain embodiments, the low work function electrode comprises hafnium carbide (HfC) or titanium carbide (TiC). In some embodiments, the high permittivity environment comprises a relative permittivity of greater than 10. In some embodiments, the weak EEF perturbation comprises an oscillating waveform having an amplitude between 200-V/cm and 200- V/mm. In certain embodiments, the oscillating waveform comprises a square wave or a sine wave. In some embodiments, the band bending causes electrostatic energy separation between m-SWCNTs and s-SWNCTs. According to another embodiment, a semiconducting single- walled carbon nanotube is disclosed, wherein the s-SWCNT is produced using any of the methods described above. In certain embodiments, the s-SWCNT comprises a diameter of less than 1.15 nm. In certain embodiments, the s-SWCNT comprises a diameter of less than 1.0 nm. According to another embodiment, an array of semiconducting single-walled carbon nanotubes is disclosed, wherein the array is produced using any of the methods described above. In certain embodiments, the array of s-SWCNTs have a diameter distribution of 0.95±0.04 nm. In some embodiments, the array of s-SWCNTs comprises a semiconducting purity of greater than 90%. Brief Description of the Drawings For a better understanding of the present disclosure, reference is made to the accompanying drawings, in which like elements are referenced with like numerals, and in which: FIGs. 1A-1G show band energy shift in single walled carbon nanotube in a high permittivity environment; FIGs. 2A-2N show remote band bending as a catalyst for selective growth of s-SWCNTs; FIGs. 3A-3I show the diametric evolution of the twisted SWCNTs under the effect of the remote band energy shift; and FIGs. 4A-4F are an electrical assessment of the s-SWCNT arrays grown with remote contact catalysis. Detailed Description This disclosure expands the scope of electrostatic catalysis to the growth of one-dimensional materials with a weak EEF perturbation. For example, the weak EEF perturbation may be a 200- V/cm square wave. In other embodiments, the weak EEF perturbation may be any voltage between 200-V/cm and 200-V/mm. Further, other waveforms may be used. For example, any oscillating waveform, such as a sine waveform or a sawtooth waveform may also be used. Thus, the weak EEF disclosed herein may be described as an oscillating waveform having an amplitude between 200-V/cm and 200-V/mm. An interesting phenomenon of remote-contact catalysis was found to occur at the far end of a single-walled carbon nanotube (SWCNT) during its synthesis when in contact with a low work function metal. In this disclosure, a low work function metal is defined as a metal having a work function of 4 eV or less. In the synthesis environment where the permittivity is high, band bending along the SWCNT not only occurs normally at the contact interface with the metal contact, but also extends to the remote end that may be tens of microns away. Such remote band-bending effectively shifts the Fermi level of the SWCNT, leading to a spontaneous electrostatic energy separation between metallic (m-) and semiconducting (s-) SWCNT during their catalytic growth. As a result, only a weak perturbation from an EEF is needed to initiate a stable chirality twist of an m-SWCNT to an s-SWCNT, resulting in highly selective production of s-SWCNTs. Band bending and charge transfer are well-known phenomena that occur at the interface of two materials with different work functions, such as between metals, between metals and semiconductors, or between metal nanoparticles and oxide substrates. Typically, the range of interface charge transfer and band bending inside the conventional metals is limited to the immediate vicinity of the contact interface due to the screening effect. The characteristic decay length of the band bending is about 0.1 nm. However, for materials with nanometer dimensions, the surface charge plays a more important role. FIG. 1A shows an illustration of the charge distribution between two metals with different work functions. A metal rod is on the right-hand side, contacted by a metal electrode on the left. W₁ and W₂ are the work function of the two metals. FIG. 1B shows the theoretical band bending at the interface between the two metals. When considering the charge redistribution at the outer surface of the two metals as shown in FIG. 1A, three factors should be taken into account: ^ the surface charge interaction through the dielectric, ^ the surface charge-band energy correlation, and ^ the surface charge conservation. To incorporate both electrostatics and band theory, a global potential (which encompasses all potentials outside, inside, and at the surface of the metal), denoted as ^^, is employed to describe the system. When the geometry and boundary potentials are fixed, the surface charge density (σ) is proportional to the environment dielectric constant, ^^^^ ^_^ ^^^^ in which ^^_^ and ^^_^ are the relative permittivity and vacuum డ_థ _{permittivity, respectively, െ} refers to the electric field డ^ perpendicular to the surface. the other hand, according to the band theory, for the ith metal, the surface charge density is proportional to the band energy shift Δ^^_^ (for a constant density of state at 0K approximation), ^_{^^ ൌ ^^ ∙ ^^^^^^^ ∙ Δ^^^ ൫2൯} where ^^ to the density of state per area and the work function the ith metal, respectively, and ^^_^^ is the potential inside the metal respect to the ground, െ^^^^_^^ is the Fermi level (or quasi-Fermi level when a external voltage is applied). The surface charge of conservation is expressed as: ^_{^ ^^^ ^^^^ ൌ 0 ൫4൯} ^ and ^^ represents the ith metal in the system. Since the global potential ^^ is the only variant defined, the model is based on electrostatics and incorporates band theory. Equations (1)-(4) establish the system's boundary conditions. FIG. 1C shows an illustration of an m-SWCNT contacted by a low work function metal in a high-permittivity environment. In this disclosure, a high-permittivity environment is one having a permittivity of 10 or greater. In certain embodiments, the permittivity may be 50 or greater. FIG. 1D shows the simulated band energy shift along the direction of the carbon nanotube (i.e., the z direction). The inset in FIG. 1D shows the remote band energy shift (i.e. at the remote end of the SWCNT) of the m-SWCNT as a function of various relative permittivity. The work function difference (i.e., between W₁ and W₂) and length of the m-SWCNT are fixed as 1 eV and 16 μm, respectively. To accurately simulate the charge distribution and band bending along the metal rod surface (e.g., an m-SWCNT or a metal nanowire), COMSOL is employed to establish an electrostatic model using cylindrical coordinates. As shown in FIG. 1C, the m-SWCNT (or metal nanowire) with a radius denoted as ^^_^ is positioned at _{^^ ൌ 0 along the positive direction of z axis, while the electrode} _{surface is located at ^^ ൌ 0 with the assumption that the inner} potential is zero. When a one-dimensional (1D) SWCNT is in contact with a low work function metal electrode (such as hafnium carbide having a work function of 3.5 eV) in a high-permittivity environment, the band energy along the tube entirely shifts with an additional remote band bending at the other end of the SWCNT, as shown in the circled region in FIG. 1D. Simulations reveal that the charge distribution and band energy shift Δ^^ along the m-SWCNT are strongly influenced by the relative permittivity ^^_^ of the environment, as seen in FIG. 1D and its inset. When ^^_^ is close to 1, the screening effect from free carriers in the SWCNT dominates and the band bending regions are limited to the immediate vicinity of the contact interface. However, when ^^_^ is more than ten, the band energy shift Δ^^ of the whole SWCNT becomes significant due to the strong interaction through the dielectric. The band bending at the remote end of the m-SWCNT (which will be referred to as the remote band energy shift, Δ^^ at the remote end) is formed because of the long aspect ratio. In the growth environment of the SWCNTs, the relative permittivity of the growth environment is typically close to 50 due to the presence of charged ions generated at high temperatures. For a better understanding of the remote band energy shift, the difference between a thick metal nanowire and an m-SWCNT was compared. FIG. 1E shows the remote band energy shift of an m-SWCNT or a metal (graphite) nanowire versus its diameter when contacted by a metal electrode. The relative permittivity, work function difference, and length of the m-SWCNT (or nanowire) are fixed as 50, 1 eV, and 16 μm, respectively. Unlike m-SWCNTs, metal nanowires in these simulations possess two end surfaces. Additionally, while the surface DOS of metal nanowire remains constant across different nanowire diameters, the surface DOS of m-SWCNT is inversely proportional to its diameter due to quantum confinement. The remote band energy shift for a 1D m-SWCNT is clearly noticeable (~0.4eV in this figure). Considering charge conservation and the fact that the total energy states of a thicker nanowire is much more than that in an m-SWCNT, the surface charge density as well as the remote band energy shift of the bulk metal are substantially reduced. On the contrary, the remote band energy shift does not vary significantly with m-SWCNT diameter, because of the inverse relationship between its DOS and diameter. As a result, pronounced and stable remote band energy shifts is expected to be primarily observed with SWCNTs in high-permittivity environments. Note that an m-SWCNT is used in this example for simplicity of the DOS near its Fermi level. However, the result is expected to be similar with an s-SWCNT during the synthesis process. In addition, it was found that the remote band energy shift is proportional to the work function difference between the m- SWCNT and the contacted metal, and slightly decreases with the length of the m-SWCNT. FIG. 1F shows the remote band energy shift with various contact work function differences. The relative permittivity and length of the m-SWCNT are fixed as 50 and 16 μm, respectively. The dotted line is a linear fitting to the simulated data. Besides, the band energy shift in the m-SWCNT is obviously affected by applying a weak EEF, because of the high permittivity and the large aspect ratio of m-SWCNT. FIG. 1G shows the simulated band energy shift under various EEF, respectively. The solid lines (of increasing thickness) show the band energy shift along the 16-μm m-SWCNT when +20 V/mm, 0 V/mm, and -20 V/mm EEFs are applied, respectively. The dashed lines (having corresponding thickness) correspond to the remote band energy shift values under various EEF as a function of the SWCNT length, thus the remote band energy shift at the nanotube tip end takes the minimal value with positive EEF, and has the maximum value with the negative EEF. It is worth noting that the EEF modulation becomes more effective when the m-SWCNT is longer. Such remote band energy shift turns out to be an effective electrostatic catalyst for the selective growth of s-SWCNTs. FIGs. 2A-2B illustrate a SWCNT with its tip end in a weak alternating square-wave EEF. Specifically, FIG. 2A is a schematic of the direction of the applied EEF perturbation, while FIG. 2B shows the waveform of this applied EEF perturbation. In this example, the growth mode of the SWCNTs is tip growth. FIG. 2C illustrates the density of states (DOS) of an m-SWCNT and s-SWCNT with its Fermi level shift under the applied EEF perturbation shown in FIG. 2A. E_s and E_m refer to the growth induced spontaneous charging level for s- and m-SWCNT, respectively. E_N is the Fermi level of the tubes without growth. In a typical CNT growth, the catalyst/SWCNT interface is charged, and the large difference of quantum capacitance between m-SWCNT and s-SWCNT separates the electrostatic energy plot of SWCNTs into two branches, as shown in FIG. 2D. FIG. 2D shows the calculated relative electrostatic energy of SWCNTs under zero (panel I), -20V/mm (panel II), +20V/mm (panel III) EEF without a remote band energy shift. The zero point of relative electrostatic energy is defined as the maximum value within the data frame. FIG. 2D was calculated under the assumption that all SWCNTs grow with the same rate. Compared with the high growth temperature (1073K), such energy difference between the m-SWCNTs and s-SWCNTs is not large enough to preferentially grow one type (either m- or s-) instead of another. Previously, it was found that the negative half cycle of an alternating EEF perturbation can be used to prompt the m- SWCNTs to change into s-SWCNTs due to the lower electrostatic energy of s-SWCNTs under negative EEF. This is shown in panel II of FIG. 2D, wherein under an EEF which causes a band energy shift of -0.08eV, the electrostatic energies of the s-SWCNTs becomes lower than m-SWCNTs. However, during the positive half cycle of the EEF, which is shown in panel III of FIG. 2D, because the electrostatic energies of m-SWCNTs are lower, the s-SWCNTs have a possibility to change back to m-SWCNTs. This is also illustrated in the twisting barrier change in FIGs. 2E-2G. FIG. 2E shows illustration of unstable chirality twist. FIG. 2F shows the evolution of the twisting barrier of s→m, m→m/s→s, and m→s with time under the alternating EEF shown in FIG. 2B. “s” and “m” indicate s-SWCNT and m-SWCNT, respectively. FIG. 2G shows a schematic of the twisting barrier variation causing unstable twist. In contrast, when a low work function metal is used to contact the SWCNT, the remote band energy shift effectively separates the electrostatic energies of s-SWCNTs and m-SWCNTs. FIG. 2H illustrates the DOS and energy level positions under 0, negative and positive EEFs while panels I-III of FIG. 2I present the electrostatic energies of the s- and m-SWCNTs under zero (panel I), -20V/mm (panel II), +20V/mm (panel III) EEF and with remote band energy shift of -0.30eV. Note that the electrostatic energies of s-SWCNTs are lower in all three panels. As a result, the twisting barriers are well separated, and each EEF switching will always prompt m-SWCNTs to be twisted into s-SWCNTs. FIG. 2J is an illustration of stable chirality twist, while FIG. 2K shows the evolution of the twisting barrier of s→m, m→m/s→s, and m→s with time under an alternating EEF. “s” and “m” indicate s-SWCNT and m-SWCNT, respectively. FIG. 2L shows a schematic of the twisting barrier variation causing stable twist under these conditions. Based on such understanding, the growth of aligned SWCNTs on a substrate was carried out. The substrate may be quartz, sapphire or another material that can be used to align the SWCNT. FIG. 2M is an illustration of the top view of the catalyst substrate layout that comprises low work function metal contacts, catalyst strips, and SiO₂ insulating layers arranged adjacent to one another, with the aligned SWCNTs on the substrate. In this configuration, the catalyst strips are disposed on a first side of each low work function metal contact, and the insulating layers are disposed on the second side of each metal contact. In this configuration, the SWCNTs grow toward the second side of the adjacent metal electrode. The insulating layers on the second side of each metal contact prevent shorting between adjacent metal contacts caused by SWCNTs contacting both metal contacts. Additionally, in this figure, the solid lines represent the semiconducting region and the dashed lines represent metallic dominant region. This figure shows the layout of the growth substrates (single crystal quartz) and the grown SWCNTs. Note that, if desired, the substrate layout may be different. For example, each metal contact may have a catalyst strip disposed on both its first side and its second side. In this way, the aligned SWCNTs may be grown in opposite directions from each of the low work function metal contacts. Further, the metal contacts may be spaced far enough apart so that two SWCNTs growing in opposite directions from adjacent metal contacts do not touch each other. In certain embodiments, the insulating layers may be disposed between adjacent metal contacts so that two SWCNTs do not touch. However, this configuration may be less efficient. FIG. 2N shows the scanning electron microscope (SEM) image of a corresponding growth result. This shows the stable twist of horizontally aligned SWCNTs from initially mixed metallic and semiconducting chiralities to only semiconducting chiralities. The upward and downward facing arrows indicate m-SWCNTs and s-SWCNTs, respectively. The scale bar is 2 μm. Thus, it can be seen that all the SWCNTs have been twisted into s-SWCNT which shows darker contrast under the SEM imaging. In fact, there are many ways to twist the chirality of the SWCNT during the synthesis, as long as an energy perturbation is input into the system. For example, a temperature change may be used as the energy perturbation. In addition to the observation of remote catalysis for selective growth of s-SWCNTs, interesting diametric evolution of the twisted SWCNTs under the effect of the remote band energy shift was also observed, which gives a very narrow distribution of the diameter when the remote band energy shift is strong. In order to measure the diameter of the SWCNTs effectively, SEM imaging technique was performed based on a previously developed method. For SWCNTs on an insulating substrate, under the electron beam illumination in SEM, the substrate becomes positively charged. The contrast of SWCNTs under SEM is determined by whether or not electrons are being compensated by a metal contact. Bright contrast indicates that the SWCNT is metallic and electrons are being compensated by its contact to a metal. Conversely, dark contrast indicates that there is no electron compensation, either because the SWCNT is semiconducting or because the SWCNT is not connected to a metal (and itself is not long enough to provide for the compensation). In this SEM imaging, a focused ion beam was utilized to deposit platinum (Pt) strips orthogonal to the aligned SWCNTs to observe the dark-contrast s-SWCNT better and to determine their diameters. This is illustrated in the right panels of FIGs. 3A- 3B, which show the schematic of the identification of s-SWCNTs under SEM by contacting with a metal strip. Specifically, the left panels of each figure show the aligned SWCNTs that are grown, wherein the bright segments are m-SWCNTs connected with the bottom low work function contact or the SWCNT networks before being twisted by the EEF, and the dark segments indicate uncertain SWCNTs after the twisting induced by EEF, in which the electrons cannot be compensated. After depositing the Pt strips across the uncertain SWCNTs, the electrons can transfer from the Pt strips to the uncertain SWCNTs within the length of bright segments (L_BS), as seen in the right panels of FIGs. 3A-3B. For the m-SWCNT/Pt contact, the electrons could transfer freely to the whole segment, resulting in a long L_BS. In contrast, for the s-SWCNT/Pt contact, the charge transfer was limited by the Schottky barrier, resulting in a relatively short L_BS. The length of Schottky barrier-limited charge transfer region L_BS is proportional to the diameter of an s-SWCNT. The contrast of uncertain SWCNTs and L_BS was classified into three groups. The first group had very dark contrast of SWCNTs with L_BS shorter than 1.5 μm, indicating the s-SWCNTs with smaller diameter and larger bandgap, as shown using arrows 1 in FIGs. 3A- 3B. The second group had lighter dark contrast of SWCNTs with L_BS between 1.5 μm to 3 μm, indicating the s-SWCNTs with larger diameter and smaller bandgap, indicated by the arrows 2 in FIG. 3B. The third group had bright contrast of SWCNTs with the L_BS longer than 3 μm, usually assigned to m-SWCNT segments that were not directly connected with the bottom electrode or the SWCNT network, as indicated by arrows 3 in FIG. 3B. The SWCNT network refers to the region where both m-SWCNT and s-SWCNT may exist. The arrows 4 in FIG. 3B point to the still uncertain SWCNT segments with lighter dark contrast that do not directly contact with the Pt strips. Based on the above knowledge, the effect of remote-contact catalysis with low work function contact under the alternating EEF was compared to the same growth of samples with no metal contact. FIGs. 3C-3D show the SEM images of s-SWCNTs grown with low work function contact, in which titanium carbide (TiC having a work function of 3.8eV) and hafnium carbide (HfC having a work function of 3.5eV) are used, respectively. After in-situ depositing the Pt strips, it was found that only short L_BS appear at the contact points for both TiC and HfC cases, showing stable electrotwist. In other words, there are no long bright segments. This means the m-SWCNTs were twisted to s-SWCNT, and the s-SWCNTs do not twist back to m-SWCNTs. In contrast, FIG. 3E shows that when no metal contact is being used, the long bright segments show that multiple s-SWCNTs were twisted back to m-SWCNTs, indicating obvious unstable electrotwist. These experimental observations are consistent with the theoretical understanding shown in FIGs. 2E-G and further verified the effects of the remote-contact catalysis. To compare with the effect of low work function contact, a high work function (Pt with a work function of 5.3eV) was used as a metal contact and observed similar unstable twist, as shown in FIG. 3F. This again confirms this understanding of the remote-contact catalysis. The scale bar for these graphs is 5μm. With the L_BS measurements along the growth direction of the SWCNTs, the diametric evolution effect upon continuous electrotwist under the alternating EEF was studied. FIG. 3G shows the scatter diagram of the Schottky barrier-limited charge transfer length L_BS of s-SWCNTs (contacted with Pt strips) versus the growth position starting from the low work function HfC contact edge. On the basis of the distribution of the data points, it was found that the diametric evolution can be divided into three regions. In region I, the growth position is closer than 8.5 μm (as measured from the low work function HfC contact edge), in which the diameters of s-SWCNTs are obviously thinner and have a narrower distribution. In region II, when the growth position is between 8.5 and 13.5 μm, the diameters of s-SWCNTs increase and have a broader distribution. In region III, the diameters of s-SWCNTs slightly increase further when the growth position is farther than 13.5 μm. This observation aligns with the calculations presented in FIG. 1G where the remote band energy shift exhibits more pronounced oscillations in response to the length of the SWCNT under a square-waveform EEF. The upper bound of the oscillation corresponds to the minimal remote band energy shift, the absolute value of which decreases with the length of the SWCNT as it grows. From FIG. 3H, it can be seen that the relative electrostatic energy separation between s-SWCNTs and m-SWCNTs decreases as the absolute value of the remote band energy shift decreases. Therefore, as the SWCNT grows longer, the relative electrostatic energy separation also decreases. From these and other test results, it can be seen that s-SWCNTs with smaller diameter have lower electrostatic energy, but the slope of decreasing (within a diameter range of 0.9-1.1 nm) is steeper in region I than in region II, and region III is the shallowest. As a result, the growth of s-SWCNTs with smaller diameter would be favorable. This tendency is also balanced by the energy cost in terms of the elastic energy of the very thin SWCNT wall, which will limit the decrease of the diameter of s- SWCNTs. According to this observation, the diameters are concentrated around 0.95 nm (see FIG. 3G) for region I. Such a comparison helps to understand the diameter broadening in region II and III, nevertheless, the overall diameters of the s-SWCNTs are less than 1.2nm in these regions. In FIGs. 3C-3D, it can be seen that the average length of L_BS at the s-SWCNTs/Pt contact in the case of HfC is shorter than that in the case of TiC, which means the diameters of s-SWCNTs using HfC contact are thinner than those using TiC contact. FIG. 3I shows the detailed comparison of diameter distributions with HfC-contact electrotwist, TiC-contact electrotwist, and without electrotwist, based on the corresponding SEM images in region I. It is evident that lower work function of the contact delivers a narrower distribution of s-SWCNT diameter. In the case of using HfC contact, the diameter distribution of as- synthesized s-SWCNTs is 0.95±0.04 nm, which shows a great potential in the diameter control. For example, it can be anticipated that with an in-situ SWCNT length monitoring during the growth process, one only needs to apply the EEF perturbation when the SWCNTs are growing in region I, and stop the EEF perturbation as the SWCNTs grow to longer distances. In this way, as shown in FIG. 3G, arrays of s-SWCNTs with diameters of 1.15 nm or less can be obtained. In some embodiments, if the length is limited, the diameters may be less than 1.1 nm or less than 1.0 nm. Furthermore, since the elastic energy within the SWCNT wall decreases at higher temperatures, the energy equilibrium point for the diameter can be adjusted by varying the growth temperature. The theoretical analysis and calculations are not only consistent with the experimental observation, but also reveal the great potential of remote-contact catalysis for the precise control of the structure of SWCNTs. To further verify the stability of the electrotwist with remote-contact catalysis and measure the semiconducting purity of the as-synthesized SWCNTs, arrays of field effect transistors (FETs) were fabricated with as-synthesized SWCNTs to perform the electrical assessment in large scale. The growth of s-SWCNT arrays was carried out on a patterned ST-cut single-crystalline quartz substrate that was annealed at 1000°C in an oxygen atmosphere for 10 hours. The substrate was prepared using a three-layer lithography process, as shown in FIG. 2M. The first layer comprises strips of contact metal and alignment marks (30 nm HfC by sputtering or 30 nm of other materials by e- beam evaporation). The second layer, which may be adjacent to the first side of the contact metal, and optionally partially overlap the contact metal, is then deposited by e-beam evaporation. This second layer is the catalyst strips, and may be 0.4 nm Fe catalyst strips. While iron is disclosed, it is understood that most metals may serve as the catalyst for SWCNT growth. The third layer, which may be adjacent to the opposite second side of the contact metal and may optionally overlap the contact metal is then deposited by e-beam evaporation. This third layer is an electrical insulator, which will prevent shortages between nearby contact metal strips after s-SWCNT growth. In one embodiment, the third layer is 30 nm SiO₂ strips, although other electrically insulating materials may be used. The growth was performed using a 2-inch sliding furnace (OTF-1200X-80SL, MTI corp.). The sample was placed on a fused silica substrate supported by two graphite rods, with the growth direction of the SWCNTs perpendicular to the graphite rods. After purging with 1000 sccm of Ar for 12 minutes, the pre-heated (800°C) furnace was rapidly slid over the sample to increase the growth temperature to 800°C within 8 minutes. The temperature was then stabilized for 5 minutes before switching to a feeding gas mixture of 360 sccm Ar, 40 sccm H₂, 200 sccm CH₄, and 0.1 sccm C₂H₄. It should be noted that the supersaturation of this feedstock was not sufficient to initiate SWCNT growth. After 8 minutes, the total flow rate was suddenly reduced to 6 sccm, increasing the heating time of the feedstock and resulting in further activation of the carbon precursor and higher supersaturation, which initiated the collective growth of the SWCNT array. This allows formation of the SWCNT network adjacent to the low work function metal. After an additional 40 seconds, a weak square-waveform electric field was applied between the graphite rods to induce electrotwist. After 2 minutes of growth, the furnace was slid away and the sample was quickly cooled in a flow of 1000 sccm Ar. Back-gated SWCNT-based FETs are fabricated with two different channel widths of W_ch = 5 µm (FIGs. 4A-4C) and W_ch = 50 µm (FIGs. 4D-4E). The devices with W_ch = 50 µm were used for purity estimation as more SWCNTs were included inside the wider channel. Except for the difference in channel width, all the devices in this study have a channel length (L_ch) of 2 µm and share the same fabrication recipes shown below. A silicon wafer with 90 nm thick dry thermal silicon oxide and prepatterned gold alignment marks was provided. The as-grown SWCNT arrays are transferred onto the SiO₂/Si substrate by PMMA based wet-transfer. SEM characterization was performed to find the orientation and offsets SWCNT arrays with respect to the prepatterned alignment marks. Next, electron beam lithography (EBL) was used to pattern source and drain metal pads and wires, which was conducted with the following sub steps: a) pre-bake the as-transferred SWCNT on SiO₂/Si at 180℃ for 5 minutes; b) spin-coat PMMA A4 at 2500 rpm and bake for 10 minutes; c) expose the sample with Elionix HS-50 ebeam writer using electron beam condition of 50 keV and 20 nA beam current; and d) develop the PMMA in 1:3 MIBK:IPA for 40 seconds at room temperature. The electron-beam evaporation and liftoff were used to deposit 1 nm Ti followed by 40 nm Pt (1 Å/s with a base pressure of 2E-6 Torr). Then, the active region was defined by patterning a bi- layer resist which includes a bottom layer PMMA A2 (spin-coated at 4500 RPM and baked at 180℃ for 10 minutes), followed by a top layer of MaN 2403 (spin-coated at 2500 RPM and baked at 90 ℃ for 1 minute). The MaN was patterned by EBL into 5 µm wide strip (or 50 µm for the devices with W_ch = 50 µm) covering the SWCNT FET channel and developed in 2% TMAH for 60 seconds. Oxygen plasma was used to etch through the PMMA and SWCNTs outside the active region and NMP (80℃ for 1 hour) was used to strip the PMMA and MaN. It should be noted that SEM imaging was carried out after each device fabrication steps to inspect the alignment of optically invisible SWCNT arrays, which inevitably degrade the electrical performance of s-SWCNTs but will not change its chirality. The schematic and SEM images in FIG. 4A (Scale bar: 5 µm) show one set of the as-fabricated back-gated FET devices based on one SWCNT array. Multiple contact electrodes are placed side by side along the growth direction to form a device set (each set contains 4-8 devices depending on the length of the SWCNTs) so that the SWCNTs before and after electrotwist are both characterized. FIG. 4B shows the phase image of electrostatic force microscopy (EFM) measurements on SWCNTs inside the device channel, with the height image of atomic force microscopy (AFM) being shown as a reference (Scale bar: 500 nm). When the tip bias (V_tip) is changed from 3V to -3V, a clear contrast change from dark to bright is observed on s-SWCNTs. In contrast, the m-SWCNTs before electrotwist remains bright despite whatever V_tip is applied. The corresponding transfer characteristic curves (I_ds-V_gs) are plotted in the inset of FIG. 4C and the extracted on/off ratios are plotted in FIG. 4C as a function of the device position. Along the growth direction, the first three SWCNT devices are conductive with on/off ratios of ~ 10 (plotted in solid lines), indicating the presence of m-SWCNTs at the early growth stage before the electrotwist. However, the fourth device shows p-type semiconducting behavior with on/off ratio of ~10⁵ and the rest of devices all exhibit on/off ratios of ~10⁴ (plotted in dashed lines). It is evident that all the SWCNTs in the channel become semiconducting after the electrotwist with remote-contact catalysis and stay semiconducting stably without being twisted back to metallic, which agrees with the change of SWCNTs contrast in the SEM image (as seen in FIG. 4A). The on/off ratio of the s-SWCNTs, which is inversely proportional to their diameter, also showed a consistent evolution with the diametric evolution as shown in FIG. 3G. Most of the devices change from metallic into semiconducting with on/off ratio >10³ at device position between 7 µm and 10 µm. The slight difference in twist position is attributed to the difference in growth speed at different substrate locations. To accurately estimate the electrotwisting yield and the semiconducting purity of produced SWCNT array, the electrical measurements were repeated over many SWCNT arrays with a much wider channel width (50 μm, to include more SWCNTs in one channel). FIG. 4D shows the on/off ratio mapping of 37 such device sets in one growth. For each device set index, similar FET measurements in FIG. 4C are repeated. Once the SWCNTs are twisted into semiconducting, they stay semiconducting and do not twist back to metallic under weak EEF perturbation. There are only two untwisted device sets at the substrate edge on this chip; a careful examination under SEM reveals three m-SWCNTs running through these two device sets. FIG. 4E shows the transfer curves of all the SWCNT devices where electrotwist was supposed to happen. Two transfer curves from these two untwisted device sets were taken respectively and were also shown in FIG. 4E. Based on all the electrical assessments, the actual semiconducting purity of synthesized SWCNTs was extracted to include ~3740 SWCNTs and estimated to be ~99.92%, which further proved both high efficiency and high stability of electrotwist with the remote-contact catalysis. In other words, the method described herein is able to produce an array of SWCNTs having a semiconducting purity of greater than 90%. In some embodiments, the semiconducting purity may be greater than 95%, 98%, 99% or 99.9%. FIG. 4F gives a comparison of the semiconducting purity and on/off ratio in this work to the previous reports for high-density SWCNTs. The residual m-SWCNT percentage in this study is significantly less while a high on/off ratio is maintained. The following section describes the techniques used to perform some of the analysis presented above. Analysis of the potential and electric field near the metal surface As shown in FIGs. 1A-1B, it is assumed that there is a charge distribution very close to a metal surface and interface caused by the band bending perpendicular to the surface. According to the band theory, the charge of a small cylinder with the base area of Δ^^ and the height of Δ^^ inside the metal is calculated as the following equation: Δ_{^^ ൌ െ^^ଶ ∙ ^^^^^^^ ∙ ^^^^^^^ ^ ^^ െ ^^^^ ∙ Δ^^ ∙ Δ^^ ൫5൯} in which ^^^^^^_^ is the density of state per volume (assumed to be constant with the range of surface potential). For convenience, _{^^^ ൌ ^^ is chosen. Hence,} Δ^^ ^_{^^^^^ ൌ} _{Δ^^ ∙ Δ^^ ൌ െ^^ଶ ∙ ^^^^^^^ ∙ ^^^^^^ ൫6൯} According to ^^^ଶ^^^^^^ ^^_^ ^^^^^ଶ _{ൌ ^^ଶ ∙ ^^^^^^^ ∙ ^^^^^^ ൫7൯} where ^^ represents The surface potential may be derived as below: ^_^ ^^ ^_{^ ^^ ൌ ^^ௌ exp ^െ} ^^ _{^ ൫8൯} in which ^^_ௌ indicates the surface potential of the very top of the surface. ^^ is defined as the decay length of surface charge, which is about 0.1 nm for most of usual metals. ^^_^ At the outer surface of the metal, the component of electric field perpendicular to the surface is: ^^^^^^^^ ^^ ^_{^ ௌ} ^^^^ ^^ The component of electric field parallel to the surface is: ^^^^_ௌ ^^^^ ∙_௭ Because the decay length ^^ is very small, the parallel component of electric field is usually 10^{ି^^} times smaller than the perpendicular component of that. Although the parallel component of electric field is extremely small, the existence of which is requisite to allow compatibility between classical electromagnetism and the band theory. Simulation of band bending along the m-SWCNT The simulation of the band bending along an m-SWCNT was implemented by using COMSOL. First, the cylindrical coordinate was used to establish the geometry of the m-SWCNT and the contact electrode as shown in FIG. 1C. For the sake of convenience, the electrode in the cylindrical coordinate was set as a disk with the z position of the top surface equaled to 0. The radius of the m- SWCNT (^^_^) was set as 0.65 nm, the length was set as a tunable parameter of ^^, and the z position of one end that contacted with the electrode was set as 0.34 nm with the consideration of the van der Waals gap. The external electrode was also included, of which _{the z position of the bottom surface was set as ^^ ൌ 60 ^^^^. Second,} the Laplace’s equation for the net-charge-free space and the boundary conditions were defined as following equations. Laplace’s equation: ∇_{ଶ^^ ൌ 0 ൫12൯} where ^^ refers to the potential for solving. The inner potential of the contact electrode: ^_{^|௭ୀ^ ൌ 0 ൫13൯} The inner potential of the external electrode: _{^^|௭ୀ^ ൌ ^^^^^௫ ൫14൯} in which ^^_^௫ is the defined external electric field. The boundary condition along the m-SWCNT wall: ^^^^ ^^_^^^_^ ฬ ^^^^ ^{^ୀ^} _{ൌ ^^ ∙ ^^^^^^ ∙ ^^^^^ ^ Δ^^^ ൫15൯} Take the ^_{^^^^^ ൌ 1.11 ൈ 10^଼ ^^ିଶ^^^^ି^ ൫16൯} Estimation of the relative permittivity of the growth environment For measuring the relative permittivity of the growth environment, a constant voltage was applied to the system, and the current was recorded. It was found that the measured current showed a bi-exponential decay, described by the following equation. ^_{^ ൌ ^^ ௧/௧ ௧} _{^ ^ ^^^^^ భ ^ ^^ /௧} _{ଶ^^ మ ൫17൯} _{in which ^^^ ൌ 13.8} _ൌ 62.5 ^^. The first exponential the charge current of the interface capacitor, and the other is due to the deactivation of the electrode interface. According to the equivalent circuit, the charging resistance (comprises of gas resistance ^^ and interface resistance ^^) is ^^ ^_{^ ^ ^^ ൌ ൌ 7 ^} ^^ _{.2 ൈ 10 ^^ ൫18൯} _^ where ^^ is the applied voltage, which is 1kV here, and the interface capacitance is: ^^ ^_{^ ^ ൌ 2.9 ൈ 10ି଼ ^^ ൫19൯} The electrode which the capacitance at room temperature can be estimated as: 2^^^^ ^^_^ ൌ _^^^_^^^௧ ln ^^^ _{ൌ 7.2 ൈ 10ି^ଶ ^^ ൫20൯} _ଶ/^^_^^ in which ^^_^^^௧ ^^_^ and ^^_ଶ refer to the furnace shield (100 mm), respectively. The capacitance between the measured value at high temperature and the estimated value at room temperature is due to the relative permittivity variation. Therefore, the relative permittivity at 800℃ and 1kV is: ^^ ^^_^,^^^ ൌ ^^ _{^ 4 ൈ 10ଷ ൫21൯} _^ It was noticed weaker than that at 1kV, and there is no obvious charging current. It indicates that the carrier density variate with different voltage. At 1kV, the gas resistance is: ^^ ^_{^ ൌ ^} _{^^ ൌ 1.2 ൈ 10 ^^ ൫22൯} _{^ ^ ^^^ ^} In our previous work, in situ electric measurement revealed that the growth of CNTs generated a voltage of 0.32V and a short circuit current of 5.0pA. Therefore, the gas resistance is: ^_{^ ^^} _{^ ൌ 6.4 ൈ 10 ^^ ൫23൯} Taking the Drude model into account, the resistivity is inversely proportional to the carrier density at zero voltage (^^_^): 1 ^_{^ ∝} Therefore, the carrier density at 1 kV is 5333 times higher than that at near 0 voltage. Now, consider the scaling law of the relative permittivity versus the carrier density. The Poisson’s equation inside the high temperature gas is: _{െ^^^∇ଶ^^ ൌ ^^^^^^^ െ ^^^ ൫25൯} where ^^ and ^^ are the positive and negative carrier density, respectively. ^^ is the charge number of each carrier which could be simplified as 1. The carrier spatial distribution follows the Boltzmann distribution, ^^^^ ^_{^ ൌ ^^^ exp ^} ^^^^ _{^ ൫26൯} _{where ^^^ is the charge} ∇_{ଶ^^^ ൌ} ^^_{ଶ sinh ^^^^^ ൫28൯} _^ ^_ఝ _{where ^^^ ൌ , and ^^ ൌ ^} ^ఌ _బ ^{^்} which is the Debye length. The ^் _{^ ଶ^} ^మ _^బ charge stored is: ^^^^ ^^ ^_{^ ൌ ^^^^^^^^ ∝ െ} ∝ ൫29൯ ^^^^ ^^_^ The charge is also proportional to the electric field that is inversely proportional to the Debye length, or: ^_{^ ∝} ^^ ൫30൯ ^^_^ Finally, the relation between the relative permittivity and the carrier density is as follows: 1 ^^_^ ∝ The intrinsic relative ^^ Identification of m- and s-SWCNTs under SEM and obtaining SWCNT diameter from L_BS. The diameter distribution of s-SWCNTs is calculated by depositing metal strips and evaluating their Schottky barrier length under SEM. The accelerating voltage, e-beam current and working distance for SEM imaging were 1.00 kV, 86 pA and 5.1 mm, respectively. The length of the bright segments (L_BS) is directly measured from the SEM images at places where metal is in contact with SWCNTs. The diameter has a linear relationship with L_BS through the equation L_BS ~ R exp (B/f), where R is the radius of SWCNT (half diameter), B is a constant and f is the doping fraction. It should be noted that in a previous work, Ti was used as the metal strip and calibrated for the bandgap evaluation, while in this study, Pt was used. Since the Schottky barrier length is highly dependent on the work function of metal, charge transfer length was correlated by depositing Pt strip and Ti strip on the same SWCNTs and measure their L_BS. Ti strips were patterned on as-grown SWCNTs via electron beam lithography (EBL), followed by deposition of 30 nm Ti and a standard lift-off process. The in-situ Pt deposition and SEM characterization were implemented by using FEI Helios 600 Dual Beam System (FIB/SEM). Calculation of the twisting barrier and relative electrostatic energy. The twisting barrier is defined based on the difference of electrostatic energy after and before the chirality twist as the following: _{^^் ൌ ^^^ െ} 1 2 _{^^^^^^௧^௧^^_^^௧^^ െ ^^^^^௧^௧^^_^^^^^^^ ൫33൯} where ^^_^ generated work, the electrostatic energy change was expressed as below: ^^^ଶ ^_{^^^ ^^ ൌ െ^ ଶ} _{^௧^௧ ^ ∙ ^^^^^^^ ∙ ^^^^ ൌ} ^^ _{∙ ^^^^ ∙ 3^^ ൫34൯} _^ in which ^^^^ ^^ and ^^_^^^^^ are the net charge around the catalyst region and the charge induced local electric field, respectively. In the actual growth process, due to the spontaneous charging of the carbon nanotubes during growth, the charge distribution around the catalyst and its local surroundings can be considered as a superposition of the equilibrium state of remote contact and the non-equilibrium state of growth induced potential. ^_{^ ൌ ^^ ∙ ^^^^ ∙ ^^^^ ൫36൯} The surface charge density, ^^, is given by the integration of the DOS over the energy range. The integration involves the contributions from both positive and negative energy states. For s-SWCNTs and m-SWCNTs, the Fermi levels are ^^_^ and ^^_^, respectively, as shown in FIG. 2C and 2H. ା^ ^_{^ ^^ ∙ DOS^^^^} ^ா _{ಿ ^^ ∙ DOS^^^^} _{^^ ^^ ^ ^^ ^^ ∙ ^^^^ ^ ^^ ∙ ^^^^}

where ^^ is the elementary charge, ^^ is Boltzmann's constant, and ^^ is the temperature (1000K). Electrical characterization of SWCNTs The as-fabricated SWCNT-based FETs are measured in atmosphere and room temperature using semiconductor parameter analyzer (Agilent 4155C). EFM measurements of SWCNTs inside the device channel were performed with a commercial AFM instrument (Asylum Research Cypher VRS AFM) under ambient conditions. Commercial rectangular silicon cantilever coated with a Pt layer with a resonant frequency of 75 kHz and a spring constant of 3 N/m (Multi75E-G, BudgetSensors, Bulgaria) was used for electrostatic force microscopy (EFM) imaging. The tip lift height is 0 nm and the tip voltage are set to -3V and 3V. The present disclosure is not to be limited in scope by the specific embodiments described herein. Indeed, other various embodiments of and modifications to the present disclosure, in addition to those described herein, will be apparent to those of ordinary skill in the art from the foregoing description and accompanying drawings. Thus, such other embodiments and modifications are intended to fall within the scope of the present disclosure. Further, although the present disclosure has been described herein in the context of a particular implementation in a particular environment for a particular purpose, those of ordinary skill in the art will recognize that its usefulness is not limited thereto and that the present disclosure may be beneficially implemented in any number of environments for any number of purposes. Accordingly, the claims set forth below should be construed in view of the full breadth and spirit of the present disclosure as described herein.

Claims

What is claimed is: 1. A method of forming high purity aligned semiconducting single-walled carbon nanotubes, comprising creating single-walled carbon nanotubes (SWCNTs) on a substrate; contacting the SWCNTs with a low work function electrode in a high permittivity environment, wherein the contacting causes charge transfer and remote band bending along an entire length of the SWCNTs; and applying a weak external electric field (EEF) perturbation, wherein the weak EEF perturbation causes metallic SWCNTs (m-SWCNTs) to twist to semiconducting SWCNTs (s-SWCNTs), wherein the s-SWCNTs are stably semiconducting.

2. The method of claim 1, wherein the SWCNTs that are created prior to applying the weak EEF perturbation are m-SWCNTs or networks of s-SWCNTs and m-SWCNTs.

3. The method of claim 1, further comprising preparing the substrate, wherein the substrate comprises a dielectric material having strips of the low work function electrodes, catalyst strips, and insulating strips deposited thereon.

4. The method of claim 3, wherein the catalyst strips are disposed on a first side of each low work function electrode, and the insulating strips are disposed on a second side of each low work function electrode, such that the SWCNTs grow from the first side of one low work function electrode toward the second side of an adjacent low work function electrode.

5. The method of claim 4, wherein the insulating strips prevent electrical shorting between two adjacent low work function electrodes through the SWCNTs.

6. The method of claim 3, wherein the catalyst strips are disposed on a first side and a second side of the low work function electrodes, such that the SWCNTs grow from the first side and the second side of one low work function electrode toward adjacent low work function electrodes.

7. The method of claim 6, wherein the insulating strips are disposed between adjacent low work function electrodes.

8. The method of claim 1, wherein the low work function electrode has a work function of 4 eV or less.

9. The method of claim 8, wherein the low work function electrode is a metal carbide.

10. The method of claim 8, wherein the low work function electrode comprises hafnium carbide (HfC) or titanium carbide (TiC).

11. The method of claim 1, wherein the high permittivity environment comprises a relative permittivity of greater than 10.

12. The method of claim 1, wherein the weak EEF perturbation comprises an oscillating waveform having an amplitude between 200-V/cm and 200-V/mm.

13. The method of claim 12, wherein the oscillating waveform comprises a square wave or a sine wave.

14. The method of claim 1, wherein the band bending causes electrostatic energy separation between m-SWCNTs and s- SWNCTs.

15. The s-SWCNT produced by the method of claim 1.

16. The s-SWCNT of claim 15, wherein the s-SWCNT comprises a diameter of less than 1.15 nm.

17. The s-SWCNT of claim 15, wherein the s-SWCNT comprises a diameter of less than 1.0 nm.

18. An array of s-SWCNTs produced by the method of claim 1.

19. The array of claim 18, wherein the array of s-SWCNTs have a diameter distribution of 0.95±0.04 nm.

20. The array of claim 18, wherein the array of s-SWCNTs comprises a semiconducting purity of greater than 90%.