Heating‑Enhanced Dielectrophoresis Yields Ultrahigh‑Density, Aligned Single‑Walled Carbon Nanotube Films

Background

Single‑walled carbon nanotubes exhibit strong one‑dimensional polarized properties, making directional alignment critical for high‑performance devices. Dielectrophoresis (DEP) is a powerful technique that aligns or separates CNTs and can be integrated into large‑scale fabrication workflows [1, 2]. While DEP has achieved high alignment densities [3, 4], many electronic and photonic applications—such as SWCNT field‑effect transistors (FETs) and optical waveguides—require multilayer, ultrahigh‑density films that current static DEP processes cannot deliver.

Traditional DEP studies focus on static parameters: electric‑field distribution, particle volume, and complex permittivities of particles and solvents [5]. Minor factors like particle concentration, substrate nature, and field duration have also been examined [6–9]. However, dynamic influences—convection driven by heating, solution viscosity, and other fluidic effects—have largely been overlooked.

In this work we introduce a heating‑enhanced (HE) dynamic DEP process that exploits intentional thermal convection to transport SWCNTs from beyond the DEP field into the groove vicinity. This results in a substantially higher alignment density than achievable without heating. Simulations suggest that convection can carry SWCNTs from more than 100 µm away into the DEP grooves, where they are captured by the DEP force. We also propose a novel way to assess the convection force by equating it with the DEP force at the boundaries of the gathering zones.

Methods

Ten milligrams of pristine HiPCO SWCNT powder were dispersed in 10 mL of 200 mg/mL sodium cholate (NaCh) in deionized water using 100 W ultrasonication. The mixture was ultracentrifuged at 25 k g for 60 min to remove bundles; the top 10× diluted layer contained individually dispersed SWCNTs.

Figure 1 shows the layout of a DEP chip and the cross‑section of a DEP groove. The chip was fabricated by growing a 300‑nm SiNx layer on silicon via PECVD, spin‑coating photoresist, UV exposure with a DEP mask, development, and sequential sputtering of 20‑nm Ti followed by 200‑nm Au. After acetone lift‑off, Au/Ti electrodes remained on the patterned area. Each DEP groove is 5 µm wide and 500 µm long; electrode widths are 500 µm.

Depiction of the DEP chip pattern and the schematic cross‑section of a DEP groove. The fabrication steps are summarized above.

DEP experiments used an AC potential of 20 Vpp at 10 MHz for 30 min. Two samples were prepared: sample A (room temperature, 20 °C) and sample B (heated from 20 to 100 °C using a heating plate). Ten µL of the SWCNT solution was applied to each chip. After the field application, the solutions were allowed to dry naturally.

Results and Discussion

Figure 2 presents SEM images of samples A and B. The red rectangles highlight magnified regions, while double‑headed arrows mark the widths of SWCNT gathering zones. Coffee‑ring features are indicated by the two arrows near the edge of each groove. In sample B, the SWCNT film aligns within the DEP groove, not by coffee‑ring deposition. The alignment density in sample B is markedly higher than in sample A, confirming the beneficial effect of heating. Compared with the best values reported in references [3] and [4], sample B’s density is superior.

SEM images of samples A and B. The red rectangles indicate magnified areas; double‑headed arrows show the widths of individual SWCNT gathering zones; two arrows denote coffee‑ring boundaries. Sample B demonstrates higher alignment density. Measured inter‑electrode resistances are ~20 MΩ for sample A and ~50 kΩ for sample B.

Assuming the 5 µm DEP groove width equals the length of each aligned SWCNT and that all SWCNTs share identical specific resistance and diameter, the resistance ratio directly reflects the number of aligned tubes:

$$\frac{R_A}{R_B}=\frac{S_B}{S_A}=\frac{N_B}{N_A}=\frac{20\text{ M}\Omega}{50\text{ k}\Omega}=400$$

Thus, the number of aligned SWCNTs in sample B is 400 times that in sample A, illustrating the dramatic density increase afforded by heating.

To analyze the HE‑DEP mechanism, we simulated the DEP force field using solid ellipsoid particles representing individual SWCNTs. The time‑averaged DEP force is given by [10, 11]:

$$\langle\mathbf{F}_{\text{DEP}}\rangle=\frac{\pi abc}{3}\varepsilon_m\text{Re}\left(\frac{\tilde{\varepsilon}_p-\tilde{\varepsilon}_m}{\tilde{\varepsilon}_m}\right)\nabla\left[\left|\text{Re}\left(\nabla\tilde{\phi}\right)\right|^2+\left|\text{Im}\left(\nabla\tilde{\phi}\right)\right|^2\right]$$

with $$\tilde{\varepsilon}_{p,m}=\varepsilon_{p,m}-\frac{j\sigma_{p,m}}{2\pi\nu},\quad \tilde{\phi}=\phi(x,y,z)e^{i2\pi\nu t}.$$

The parameters used for the 20 °C and 100 °C simulations are listed in Table 1. SWCNTs are modeled as 1 µm long, 1 nm radius rods—consistent with surfactant‑wrapped HiPCO SWCNTs.

The heating‑induced convection is complex, involving gravity, thermophoresis, viscous drag, buoyancy, Brownian motion, and more. For clarity, we consolidate all non‑DEP forces into a single “convection force.” Simulations show rapid thermal equilibration (≤0.2 s) when heating to 100 °C. Figure 4 displays the velocity field of natural convection at two time points separated by 120 s. Vortices span ~100 µm, matching the DEP groove depth, and convective flow transports SWCNTs from >100 µm away into the groove vicinity. The turbulence generated by temperature‑induced density differences further accelerates this transport, achieving millimetre‑per‑second velocities.

By equating the convection force to the DEP force at the boundary of the gathering zone (20–30 µm from the groove edge), we estimate the convection force to be on the order of 10⁻¹⁶ N—comparable to the local DEP force. The diminished viscous drag at 100 °C lowers the DEP force required to capture SWCNTs, explaining the unchanged gathering width despite the weaker DEP field.

Alternative explanations—such as concentration changes from solvent evaporation—do not account for the significant density increase observed only in the heated sample. Thus, the primary driver is the intense, temperature‑induced convection that shuttles dispersed SWCNTs into the DEP grooves where they are captured and aligned.

Conclusions

Heating‑enhanced dielectrophoresis dramatically boosts the alignment density of individual SWCNTs, achieving a 400‑fold increase relative to room‑temperature DEP. The process relies on vigorous convection that transports SWCNTs into the DEP groove vicinity, where the DEP force captures and aligns them. Our simulation framework offers a new approach to quantify the convection force. The resulting ultrahigh‑density SWCNT films promise substantial performance gains for future SWCNT‑based electronic and photonic devices.