Experiments show that carbon nanotubes transfer heat inefficiently at small scales, raising concerns for cooling and performance in nanoelectronic devices.
(Nanowerk Spotlight) Thermal energy in solid-state systems doesn’t flow as a smooth continuum but rather it moves through atomic vibrations known as phonons. At the nanoscale, where materials shrink to just a few atoms in width, heat transport is governed by the complex behavior of these phonons, especially when different types do not share energy efficiently.
In devices built from low-dimensional materials, this inefficiency can result in localized heating, reduced performance, and unexpected failure modes. As electronics push into the realm of nanowires, nanotubes, and atomically thin films, understanding how energy moves—and where it gets trapped—has become a central problem in designing efficient, reliable nanoscale systems.
One of the most persistent challenges in this area is characterizing the nonequilibrium between optical and acoustic phonons. Optical phonons absorb energy rapidly from electronic excitations but do not transport it efficiently. Acoustic phonons carry heat but rely on timely energy transfer from the optical branch. If this coupling is weak or delayed, energy builds up in the optical modes, distorting thermal measurements and limiting dissipation.
This mismatch is especially problematic in supported nanostructures, where standard techniques like Raman thermometry capture only the optical phonon temperature, masking what the rest of the system is doing.
Previous research has explored this problem in two-dimensional materials like graphene and transition metal dichalcogenides. But experimental studies on one-dimensional systems—such as single-walled carbon nanotubes—have been scarce. The unique geometry and vibrational spectrum of these systems introduce distinct phonon behaviors that can’t be extrapolated from planar materials.
Moreover, the coupling between a nanotube and its substrate adds another layer of complexity, affecting how heat exits the system. These challenges have limited both the modeling and direct measurement of phonon branch nonequilibrium in 1D materials.
Using a refined Raman spectroscopy technique, the authors measure the temperature difference between phonon branches under laser heating, revealing how phonon nonequilibrium scales with temperature and excitation size. Beyond offering a new methodology, this work delivers fundamental insights into heat transport in one-dimensional systems—insights that carry direct implications for the design of next-generation nanoelectronic devices and solid-state energy conversion technologies, where precise thermal control is crucial.
a) Schematic of the Raman experiment. A 532 nm laser irradiates the highly aligned SWCNT bundle supported on SiO2/Si substrate. The Stokes–Raman scattered light carries information about optical phonons under laser heating. b) A schematic diagram showing the optical–acoustic phonon temperature gradient under laser heating due to the OP–AP nonequilibrium. c) A 3D atomic force microscope (AFM) scan for sample #1 with the height shown on the scale to the right. The height is measured to be around 8 nm. d) The radial breathing modes (RBM), which are low-frequency phonon modes in SWCNT. The RBM is fitted to multiple Gaussian functions to extract the unique frequencies in the spectrum. (Image: reprinted from DOI:10.1002/advs.202509005, CC BY) (click on image to enlarge)
The researchers used a method called frequency-domain energy transport state-resolved Raman (FET-Raman), which allows separate detection of the temperatures associated with optical and acoustic phonons in aligned SWCNT bundles supported on a silicon dioxide substrate. By modulating laser heating at different frequencies, they extracted how temperature rise varies with time and excitation scale. This enabled them to isolate the temperature of optical phonons and infer the nonequilibrium relative to the heat-carrying acoustic phonons.
At 93 Kelvin, the temperature of the optical phonons was more than 75% greater than the rise observed in the acoustic phonons. At room temperature, this disparity was still present but reduced to about 33%. These measurements confirm that phonon–phonon energy exchange is highly temperature dependent. As temperature increases, anharmonic scattering processes become more active, allowing optical phonons to decay more readily into acoustic modes and reducing the temperature gap.
To quantify this behavior, the study introduced a parameter called GOA, the optical–acoustic phonon coupling factor. This describes how effectively energy is transferred between phonon branches per unit volume and per degree of temperature difference. At room temperature, GOA was approximately 0.21 times 10^{15} W m^{-3} K^{-1}, which aligns with previously reported values in 2D materials. At 93 K, the value dropped to just 5.8% of the room-temperature level, indicating a sharp decline in phonon coupling strength at cryogenic temperatures. The authors note that this suppression exceeds that of the interfacial phonon coupling that governs energy flow from the nanotube to the substrate.
They further examined the implications for interfacial thermal conductance—how efficiently energy crosses from the SWCNT into the silicon dioxide. Most energy in this system is transported by acoustic phonons, which interact more directly with the substrate. Because standard Raman measurements detect only optical phonon temperatures, using these measurements to estimate interfacial conductance can lead to error. The authors show that relying on optical phonon temperature alone underestimates interfacial thermal resistance by about 30% at room temperature.
To interpret this behavior and extend their findings across a wider temperature range, the authors applied the equivalent interfacial medium (EIM) model. This framework treats the interface not as a sharp boundary but as a disordered region characterized by localized vibrational states and finite energy transfer rates.
Using only two measurements of interfacial conductance, the EIM model accurately predicted its temperature dependence and agreed with published data across a range of systems. This modeling approach avoids the need for extensive experimental datasets and offers a compact way to represent interface effects in low-dimensional materials.
The team also investigated how the spatial scale of energy input influences phonon nonequilibrium. By changing the laser focus to adjust the heating area, they showed that smaller laser spots lead to larger temperature differences between phonon branches. A tighter laser spot confines energy within a smaller volume, limiting the distance over which acoustic phonons can distribute heat. When the spot radius was 0.37 microns, the optical–acoustic temperature difference was nearly 23% of the acoustic phonon temperature rise. Doubling the spot size reduced this ratio to 13%. This effect aligns with thermal diffusion models and highlights the role of spatial confinement in amplifying nonequilibrium.
The underlying mechanisms for these trends were also explored. Optical phonons in SWCNTs decay into acoustic phonons through anharmonic processes involving multiple phonon interactions. These decay rates depend on the temperature-dependent phonon population, which follows Bose–Einstein statistics.
At low temperatures, the reduced availability of target phonon states suppresses decay. Raman linewidth measurements in this study confirmed that optical phonon lifetimes decreased with temperature, consistent with stronger scattering at higher energies. The results were better described by four-phonon decay models than by simpler three-phonon interactions, particularly at room temperature.
Although the experiments were limited by modulation frequency constraints and some assumptions about internal phonon equilibrium, the methodology offers a clear step forward. GOA was calculated as an average parameter and does not resolve specific phonon mode interactions. Additional first-principle simulations could refine these estimates and assess how individual phonon branches contribute.
Moreover, the findings rest on measurements at two discrete temperatures. While the EIM model extends this data into a continuous trend, direct measurements at more points would provide stronger confirmation.
Still, the study offers an experimentally grounded view of how phonon nonequilibrium develops in a real, supported 1D system. It highlights that in low-dimensional materials, energy carriers do not always thermalize as expected. This has consequences not only for thermal measurements but also for how designers model and build nanoscale devices. Any system that assumes uniform phonon behavior risks overlooking critical bottlenecks in heat dissipation.
By establishing a method to measure and interpret phonon branch decoupling, the study enables more accurate characterization of nanoscale thermal transport. The findings are relevant for technologies that demand tight thermal control, including nanoelectronic transistors, photonic devices, and solid-state energy converters. In these systems, phonon dynamics determine efficiency, stability, and ultimately, device viability.
As materials science continues to explore new low-dimensional architectures, tools like FET-Raman and models like EIM will be essential for translating microscopic energy interactions into actionable design parameters.
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