Small Molecule Additives to Suppress Bundling in Dimensional‐Limited Self‐Alignment Method for High‐Density Aligned Carbon Nanotube Array

Semiconducting single‐walled carbon nanotube (CNT) is a promising candidate as a channel material for advanced logic transistors, attributed to the ultra‐thin 1‐nm cylindrical geometry, high mobility, and high carrier injection velocity. However, the presence of undesired CNT bundles in the CNT arrays for wafer‐scale device fabrication, even when utilizing the state‐of‐the‐art dimension‐limited self‐alignment (DLSA) method, poses challenges. These CNT bundles degrade the transistor gate's efficiency in controlling the flow of charge carriers in the CNT channel, leading to pronounced device‐to‐device variability. Here, a novel method is introduced to alleviate bundling in CNT arrays assembled via DLSA, by involving small molecule additive to screen the attractive van der Waals force between neighboring CNTs during the DLSA process, resulting in over 50% reduction in CNT bundling. Furthermore, a pioneering methodology for quantifying CNT bundles is presented and employed experimentally to assess bundles in dense CNT arrays assembled by DLSA using transmission electron microscopy. Both experimental data and molecular dynamics simulation reveal that CNT bundling originates from van der Waals attraction between CNTs, and the disturbed liquid‐liquid interface by accumulating excess polar molecules. These findings illuminate new pathways for realizing dense, bundle‐free CNT arrays.


Introduction
As silicon metal oxide semiconductor field effect transistors (MOSFETs) edge towards their fundamental physical limits, vacuum filtration, [15] evaporation, [16,17] Langmuir-Shaefer, [18] DNA fabricated trench assembly, [19] selective CNT deposition in pre-fabricated trenches, [20] tangential flow interfacial selfassembly (ta-FISA) [21] and dimensional-limited self-alignment (DLSA). [22]In particular, the 2D liquid crystal nematic assembly of densely aligned CNTs, utilizing the liquid-liquid interface (LLI), has demonstrated the capability to produce high-density monolayer CNT arrays on wafer scale.For instance, Jinkins, K. R. et al., developed ta-FISA to achieve aligned CNT arrays with a density over 50 CNTs μm −1 and reported the formation of CNT 2D liquid crystal nematic assembly at an LLI between water and chloroform. [21]Liu, L. et al., developed DLSA to assemble dense CNT arrays exceeding 250 CNTs μm −1 at a wafer scale using an LLI between 2-butene-1,4-diol and 1,1,2-trichloroethane, demonstrated the high-performance CNT FETs exhibiting an on-state current over 1 mA μm −1 at a bias of −1 volt. [22]he adaptability of LLI-based assembly methods is noteworthy, allowing for the deposition of dense CNT arrays on various surfaces, including silicon wafers with SiO 2 [22] coatings, quartz substrates, [23] and surfaces of self-assembled monolayer. [24]This versatility, influenced by the properties of the LLI and less dependent on substrate nature, suggests that LLI-based methods may offer advantages for diverse electronic applications, such as radio frequency transistors. [23]However, despite there has been abundant assembly progress reported by multiple groups, achieving the individualization of CNT, where each CNT exists in a separated and unbundled state within dense arrays, remains elusive for meeting the stringent demands of logic transistor technology.
In this work, we statistically assess the degree of individualization in dense CNT arrays assembled via the DLSA method using cross-section transmission electron microscopy (TEM) to determine the bundled CNT ratio within these arrays.To enhance CNT individualization, a novel method that leverages small molecule additives is introduced to screen the attractive van der Waals force between neighboring CNTs.This approach suppresses CNT bundling during assembly at an LLI using DLSA, resulting in a 50% reduction in bundling within dense CNT ar-rays and pointing to a potential pathway toward electronics-grade CNT arrays.Further insights from molecular dynamic simulation suggest that the thickness of the immiscible LLI changes due to polar interactions with small molecule additives, highlighting a key factor for the monolayer confinement of the dense CNT arrays in LLI-based assembly.

Assembly and Characterization Methods
To determine the degree of individualization in dense CNT arrays, we introduce a modified distance parameter, D x .As depicted in Figure 1a, D x denotes the center-to-center distance between neighboring CNTs projected on the X-axis in cross-section TEM images.Importantly, the presence of both close-packed CNT (where D x ≈ d CNT as shown in Figure 1a) and vertical stacked CNT bundles (D x < d CNT ) can degrade the gate control of a shortchannel transistor due to the screening effect from neighboring CNTs (Figure 1b). [6]Employing the D x parameter allows for precise characterization of the bundling ratio of CNTs in dense arrays, which we will dive deeper into later.
The dense aligned CNT arrays described in this work were assembled through a baseline dimensional-limited self-alignment (DLSA) method, as reported by Liu, et al. [22] The schematic of the assembly apparatus is shown in Figure 2a.Initially, assorted semiconducting CNTs are filtered out of the toluene solution, and repeatedly rinsed with toluene and THF to remove excess polycarbazole (PCz) polymers, then re-dispersed into 1,1,2trichloroethane (TCE) and placed in a quartz vessel.A target SiO 2 substrate for CNT array assembly is then vertically dipped into the CNT-TCE solution.10ul of 2-butene-1,4-diol (BD) is dropped near the target substrate to form a 2D LLI between the two immiscible solvents, leading to a one-dimensional liquid-liquidsubstrate interface (LLSI) along the target substrate.Within the TCE, CNTs, which are initially orientated randomly in 3D, accumulate at the LLI to separate two immiscible solvents to minimize the interfacial energy. [21,25]These CNTs at the LLI gradually form the 2D nematic liquid crystal assembly over time, for maximizing the configuration entropy, resulting in oriented CNT arrays. [26,27]Finally, the aligned CNT array is deposited on the slowly withdrawn target substrate with the global alignment guided by the one-dimensional LLSI.The as-deposited CNT array is then repeatedly rinsed with hot toluene, and THF and baked at 180 °C in air.Supporting Information Section 1 discusses the assembly process in more detail including semiconducting CNT sorting, excess polymer removal, DLSA assembly, and preparation of cross-section TEM.
To evaluate the quality of the CNT array, Figure 2b and Figure S2 (Supporting Information) show typical atomic force microscope (AFM) and scanning electron microscope (SEM) images of dense CNT arrays assembled using the DLSA method.Due to the lateral spatial resolution limitation of AFM and SEM, the CNT-CNT spacing is too small to identify individual CNTs.Consequently, from these images, insights into material quality are limited to the local degree of alignment and uniformity.For further characterization, high-resolution cross-section TEM images in Figure 2c clearly show the individual CNT positions, revealing the existence of close-packed and stacked CNT bundles in the dense CNT arrays despite local regions that are bundle-free.Additionally, Figure S3 (Supporting Information) illustrates that AFM inspection of CNT density versus CNT concentration in solution incorrectly appears to control CNT density, while closer inspection by cross-section TEM reveals every single feature in the AFM image consists of undesirable lateral close-packed or vertically stacked CNT bundles.Therefore, statistical cross-section TEM analysis is necessary to accurately report CNT density and undesirable bundle behaviors for dense CNT arrays.
To quantify the CNT bundle ratio using cross-section TEM, CNTs with D x smaller than the CNT diameter (d CNT ) plus one standard deviation () are categorized as bundled.In contrast, CNTs with D x larger than this threshold are considered individualized.The cumulative distribution function (CDF) of extracted D x is shown in Figure 2d, median D x is 1.84 nm with a standard deviation of 0.81 nm.The CDF of extracted d CNT is shown in Figure 2e, median d CNT = 1.44 nm and standard deviation  = 0.14 nm.Then, the key figure of merit of bundle ratio (# Bundled CNT/# Total CNT) can be obtained as 40.4%.This presents the first statistical and quantitative analysis reporting the CNT bundle ratio in dense CNT arrays.The statistical TEM analysis for D x and d CNT emerge as critical metrics for the electronics-grade CNT array.

Suppression of CNT Bundles in Unstable Suspension
In the following study, we spotlight two distinct scenarios leading to CNT bundling: 1) instability of CNT suspension in organic solvent and 2) the assembly at a disturbed LLI.
First, the bundles arising from unstable CNT suspension in TCE are investigated.A drop of CNT solution is spun coat on a SiO 2 substrate to deposit low-density CNT (<5 CNTs/μm) with random orientation.A representative AFM height image is shown in Figure 3a   respectively, match the CNT diameter measured by cross-section TEM.Notably, in condition II, a more pronounced distribution tail of ≈10.4% of the population is observed with an abnormal CNT diameter larger than a bundling threshold (> 2.03 nm).This can be attributed to CNT bundling during the suspension phase.In comparison, only ≈4.4% of the CNTs in condition I exhibited bundling.The bundle threshold for AFM measured CNT height is defined by the d CNT maximum (1.89 nm) plus one standard deviation (0.14 nm) measured by cross-section TEM in Figure 2d.
CNTs inherently tend towards bundling due to strong CNT-CNT van der Waals attraction.Various molecules, such as conjugated polymers and surfactants, can wrap around the CNT surface, mitigating the attraction and thus stabilizing suspensions in organic and aqueous mediums.Generally, the excess dispersants in CNT solution ensure more stable suspension with less aggregation over time. [28]However, as will be discussed in the following paragraph, the excess polymers are crucial to be removed before DLSA assembly, as they disturb the LLI.Utilizing high-viscosity solvents, including chloroform, dichloroethane, or 1,1,2-trichloroethane, can retard the bundling process with minimum excess polymer concentration. [29,30]However, according to our experimental results, this approach can only delay but not prevent CNTs from bundling.As a result, the dispersion of CNT with minimal excess polymer in TCE remains inherently unstable, positioning it as one of the contributors to CNT bundling.
To suppress the CNT bundling during suspension without relying on excess polymers, small molecule polycyclic aromatic hydrocarbons (PAHs) such as 1,10-phenanthroline and phenanthrene, have been reported as effective additives to screen the attractive van der Waals force by covering the exposed CNT surfaces. [28]This concept has been demonstrated to stabilize the dispersion of small-diameter (6, 5) CNT in toluene with minimal excess polymer.Small-diameter CNTs are typically less stable in suspension due to lower conjugated polymer wrapping efficiency. [31,32]Here, we extend this method for bundling suppression with large diameter CNT (d CNT = 1.44 nm compared to ≈0.78 nm for (6, 5) CNT) dispersed in TCE with minimal excess polymer.Two PAHs molecules are considered: phenanthrene (as condition III), which consisted purely of hydrocarbon atoms, and 1,10-phenanthroline (as condition IV), which incorporates two nitrogen atoms in place of carbon atoms, as depicted in Figure 3b insets.The concentration of PAHs additives is set to be one order of magnitude larger than CNT in TCE (500 μg mL −1 PAHs versus ≈50 μg mL −1 CNT) to maximize the adsorption of PAHs on exposed CNT surfaces.The CDF of AFM measured CNT height with PAHs additives are shown in Figure 3a.The tail of the distribution is summarized in Figure 3b and Table S1 (Supporting Information) showing the corresponding bundle ratio of CNT dispersed under conditions I to IV.With additives of PAHs in high-viscosity TCE solvent, the bundle ratio is suppressed from 10.4% (II) to 5.5% (III) and further to 4.4% (IV).

Suppression of CNT Bundles at Liquid-Liquid Interface
Mechanisms that occur during DLSA assembly account for the remainder of CNT bundles in baseline dense CNT arrays.As depicted in Figure S4 (Supporting Information), CNT accumulation at the LLI during assembly increases the local CNT concentration, leading to a higher probability of CNT meeting close x and e) corresponding bundle ratios extracted from cross-section TEM images.Black, blue, red, and grey color to CNT assembly with no additive, phenanthrene, phenanthroline, and PCz polymer additives, respectively.For CNTs with abnormally small D x are considered as CNT bundles.The bundling threshold is defined as median diameter plus one standard deviation (d CNT, median + ) extracted from cross-section TEM.
neighbors and hence promoting bundle formation.To investigate the bundling suppression strategy using PAHs additives in assembled dense arrays, CNTs suspended in TCE with phenanthrene and phenanthroline additives are employed in the DLSA process.The outcomes varied, as shown in the representative cross-section TEM images in Figure 4a,b.With phenanthrene additive, composed solely of hydrocarbons, a bundle suppression effect is observed.As shown in Figure 4d, a noticeable shift toward a larger D x value is observed for the cumulative distribution, indicating a higher degree of individualized CNTs.Extended collections of cross-section TEM images contributing to the CDF are presented in Figure S5 (Supporting Information).A comparison of corresponding bundle ratios in Figure 4e and Table S2 (Supporting Information) shows that the bundle ratio is reduced by half to 20.4% for dense CNT arrays with phenanthrene additive from 40.4% in the baseline results without additive.This result supports the hypothesis that CNT bundles form during the assembly process due to the same van der Waals force attraction as CNTs in suspension, exacerbated by smaller inter-CNT distances near the LLI.This study represents the first demonstration of CNT bundle suppression via van der Waals force screening during assembly.Furthermore, as detailed in Supporting Information section 6, polarized Raman spectroscopy confirms that the phenanthrene additive does not adversely affect the deviation of the alignment.
In contrast, dense CNT arrays assembled with phenanthroline additive lead to a noticeable shift in the cumulative distribution towards smaller D x value (Figure 4d) as measured by crosssection TEM.The bundle ratio rises to 58.6% (Figure 4e).Bilayer CNT arrays are frequently observed with CNTs appearing in the second layer, and only 2% of CNTs observed over 2 nd layer.These experimental results suggest an additional bundling mechanism, due to the interaction between LLI and PAHs additive, might sig-nificantly alter the results of CNT assembly and should be carefully investigated.
Similar bundle-exacerbated dense arrays are observed using CNTs in TCE, but with an intentional PCz polymer additive to increase the polymer to CNT mass ratio (M Polymer : M CNT ) to ≈10:1 for the DLSA process.The observation of strongly pronounced misalignment (Figure 4c and Figure S5d, Supporting Information) and the shift to smaller D x (Figure 4d) echo the bundled array with phenanthroline additive.While excess polymers can stabilize CNTs in suspension by screening the intertube attraction, the presence of nitrogen atoms in the carbazole backbone implies assembling CNTs with excessive PCz polymers at the LLI leads to a rise in CNT bundles and disturbed CNT alignment.

Molecular Dynamic Simulation of Liquid-Liquid Interface
Directly observing these effects through experiments is challenging due to the lack of in situ visibility into the complex interactions between the CNT liquid crystal and molecule additives at the LLI.Hence, molecular dynamic (MD) simulations are employed.Figure 5a depicts an MD simulation considering only TCE and BD, serving as a reference condition in the absence of PAHs additive, CNTs, or polymers.Figure 5b presents the molecular density as a function of distance along the z-axis, marked with green and red colors for TCE and BD, respectively.This density profile reveals a system consisting of two bulk solvents with nearly invariant molecular density across the z-axis, and one welldefined LLI with abrupt molecular density transition.The molecular density obtained from MD simulation is fitted by the hyperbolic tangent function, which has been reported for the liquidvapor interface. [33]In this function,  i represents molecular density, z 0 denotes the position of the Gibbs dividing surface, and d is the adjustable parameter related to the interfacial thickness.
Following a "90%−90%" criterion, the interfacial thickness of LLI (t LLI ) can be defined as the distance between two positions where the molecular densities of TCE and BD are 90% of their respective bulk densities. [34]An abrupt interface for the reference TCE and BD system is obtained with a t LLI of 5.2 Å.Few angstroms interfacial thickness agrees well with the typical thickness of oil-water interfaces, such as 2.0-4.6 Å for decane/water systems. [34]The t LLI in the binary liquid system with the additional PAHs additive is modeled in Figure 5c,d.The t LLI with phenanthrene additive only slightly increases to 5.7 Å, indicating a weak interaction of phenanthrene with the LLI, as illustrated in Figure 5e.This finding aligns with the experimental results.Demonstrates that by screening the attractive van der Waals force with phenanthrene, the bundle suppression effect can be extended to dense CNT arrays, because it does not disturb the sharp LLI.Conversely, the t LLI with phenanthroline additive significantly increases to 12.7 Å, which could be attributed to the two nitrogen atoms in the phenanthroline, strongly interacting with the LLI by forming the hydrogen bond with the hydroxy group in BD.As depicted in Figure 5f, the strong interaction between phenanthroline and BD disturbs the LLI on the nanometer scale, in the same way, that excess PCz polymer with nitrogen atom was observed to disturb the CNT assembly.
The simulated differences in t LLI closely mirror the observed CNT assembly behaviors under various experimental conditions.For scenarios where t LLI is substantially smaller than the diameter of CNTs (t LLI is ≈5-6 Å versus d CNT of ≈1.4 nm), a monolayer accumulation is enough to separate the immiscible liquids, leading to the formation of monolayer CNT arrays.In contrast, when the t LLI is of the same order as the CNT diameter (t LLI is ≈12.7Åversus d CNT is ≈1.4 nm), more CNTs inhabit within this expanded LLI, leading to the formation of a second CNT layer, which becomes a new interfacial energy minimum.This hypothesis appears to be in line with the experimentally observed trend to produce bilayer CNT arrays when the phenanthroline additive is incorporated.Overall, both experimental and simulation results reveal that the t LLI stands as a crucial determinant in optimizing the quality of the CNT array via the LLI-based assembly method.

Conclusion
In this work, the CNT bundle ratio in densely aligned CNT arrays is statistically quantified for the first time using cross-section TEM inspection.We identified two primary challenges contributing to CNT bundling: 1) unstable suspension in the absence of excess polymer, and 2) assembly at a disturbed liquid-liquid interface.To address these issues, PAHs additives were employed for the van der Waals forces screening, resulting in a notable 50% reduction in CNT bundling.Molecular dynamics simulations suggest the LLI interfacial thickness is affected by nitrogencontaining molecules (e.g., phenanthroline or PCz), pointing to a vital parameter for enhancing the liquid crystal nematic assembly via liquid-liquid-interfacial confinement.As we target advanced logic electronics, further improvement in the individualization of CNTs in dense arrays remains essential.Future research in CNT assembly should focus on achieving deterministic CNT placement and ensuring electronics-grade and wafer-scale uniformity.Additionally, clear opportunities exist to explore processes that preserve the pristine quality of initial CNT arrays during the transistor fabrication process (e.g., lithography, wet processing, PVD, and ALD) as highlighted in Figures S7 and S8 (Supporting Information) to realize practical high-performance, highly scaled CNT electronics.

Figure 1 .
Figure 1.a) Schematic to illustrate the definition of D x .Black circles represent CNTs.Orange arrows mark toward the center of each CNT with examples D x1 to D x4 illustrating D x in different scenarios.D x1 is the case for two well-separated CNTs with D x > d CNT .D x2 and D x3 are the cases for the CNT bundle with D x < d CNT .D x4 is the case for close compact CNT with D x ≈ d CNT .b) Projection of Sub-V T slope versus CNT D x for 12 nm L G top-gated FET from TCAD.

Figure 2 .
Figure 2. The densely, aligned CNT array assembled by dimension-limited self-alignment (DLSA).a) Schematic image for DLSA system for dense CNT assembly in this work.b) Top-view atomic force microscope (AFM) of dense CNT array.The scale bar is 500 nm.c) Cross-section transmission electron microscopy (TEM) images reveal that both well-separated CNT (top) and undesirable CNT bundles co-exist in the CNT array.The white arrow indicates the representative cross-section TEM of CNT.Yellow arrows indicate the CNTs on 2 nd layer of the array in bundles.The scale bar is 5 nm.Cumulative distribution plots of d)Dx and e) diameter extracted from dense CNT array through cross-section TEM images.For CNTs with abnormally small D x are considered as CNT bundles.The bundling threshold is defined as median diameter plus one standard deviation (d CNT, median + ) extracted from cross-section TEM.
inset.The CDF of individual CNT height measured by AFM is shown in Figure 3a.CNT solutions with two different conditions I and II are first investigated.Condition I comprises an as-purified CNT solution in toluene with polymer to CNT mass ratio (M Polymer : M CNT ) of ≈10:1.Condition II consists of CNT dispersed in TCE with minimal excess PCz polymer via vacuum filtration, which is a typical starting solution for the DLSA assembly, with an M Polymer : M CNT ratio of ≈1:1.Comparing the CDF of AFM measured CNT height for conditions I & II, median CNT heights of 1.41 and 1.44 nm are obtained,

Figure 3 .
Figure 3. Characterization of the CNT bundle ratio in bulk dispersions.a) Cumulative distribution function (CDF) of CNT height measured by AFM on low-density CNT network for condition I-IV.Grey, black, blue, and red color to conditions I, II, III, and IV, respectively.The inset displays a representative AFM image (scale bar is 500 nm), and a zoomed-in view of CDF tail.b) Corresponding bundle ratio for conditions I to IV. Condition I: as-sorted CNT dispersed in toluene with an abundance of excess polymer.Condition II: CNT dispersed in 1,1,2-trichloroethane (TCE) after the excess polymer removal process.Condition III: CNT dispersed in TCE with phenanthrene additive.Condition IV: CNT dispersed in TCE with phenanthroline additive.The distribution tails with abnormally large CNT height are defined as CNT bundles.The bundling threshold is defined as CNT maximum diameter plus one standard deviation (d CNT, maximum + ) extracted from cross-section TEM.

Figure 4 .
Figure 4. Characterization of CNT bundle ratio in dense CNT arrays.Representative cross-section TEM images for dense CNT array with a) phenanthrene, b) phenanthroline, and c) polycarbazole (PCz) polymer as additives.The scale bar is 5 nm.Yellow dashed lines are marked to highlight the non-monolayer CNT array.d) Cumulative distribution plot of CNT Dx and e) corresponding bundle ratios extracted from cross-section TEM images.Black, blue, red, and grey color to CNT assembly with no additive, phenanthrene, phenanthroline, and PCz polymer additives, respectively.For CNTs with abnormally small D x are considered as CNT bundles.The bundling threshold is defined as median diameter plus one standard deviation (d CNT, median + ) extracted from cross-section TEM.

Figure 5 .
Figure 5. Molecular Dynamic (MD) simulation of liquid-liquid interface (LLI).a) A snapshot of the binary liquid system in MD simulation.The corresponding molecular density of 1,1,2-trichloroethane (green) and 2-butene-1,4-diol (red) as a function of the z-axis b) without additive, with c) phenanthrene and d) phenanthroline additive.Schematic illustration of e) abrupt LLI with phenanthrene additive, and f) mixed LLI with phenanthroline additive.