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For multi-layered 2D materials, although its c-axis has a much lower thermal conductivity than the a-axis, its phonon mean free path has been confirmed to be very long, e.g., in the order of 100s nm at room temperature for multi-layered graphene. An anisotropic specific heat concept has been proposed in the past to explain this very long mean free path. This work carries out detailed atomistic modeling to quantify the anisotropic specific heat concept and reports the discovery of anisotropic temperatures in multi-layered 2D materials under ultrafast surface heating. Extremely fast c-phonon energy transport is discovered, and the non-Fourier effect is observed for both a-phonons and c-phonons. The energy coupling factor between these two modes of phonons is determined to be in the order of 1016 W K−1 m−3, with the specific number depending on the structure location. The anisotropic temperature concept is also quantitatively confirmed based on the lattice Boltzmann method simulation. The anisotropic temperature concept does not violate the physics that temperature is a scalar; rather, it is developed to distinguish the temperatures of phonons that travel in different directions. This concept is universally applicable to other 2D materials to describe the heat conduction in the in-plane and out-of-plane directions that feature different interatomic bonds. 

In the last two decades, tremendous research has been conducted on the discovery, design and synthesis, characterization, and applications of two-dimensional (2D) materials. Thermal conductivity and interface thermal conductance/resistance of 2D materials are two critical properties in their applications. Raman spectroscopy, which measures the inelastic scattering of photons by optical phonons, can distinct a 2D material's temperature from its surrounding materials', featuring unprecedented spatial resolution (down to the atomic level). Raman-based thermometry has been used tremendously for characterizing the thermal conductivity of 2D materials (suspended or supported) and interface thermal conductance/resistance. Very large data deviations have been observed in literature, partly due to physical phenomena and factors not considered in measurements. Here, we provide a critical review, analysis, and perspectives about a broad spectrum of physical problems faced in Raman-based thermal characterization of 2D materials, namely interface separation, localized stress due to thermal expansion mismatch, optical interference, conjugated phonon, and hot carrier transport, optical–acoustic phonon thermal nonequilibrium, and radiative electron–hole recombination in monolayer 2D materials. Neglect of these problems will lead to a physically unreasonable understanding of phonon transport and interface energy coupling. In-depth discussions are also provided on the energy transport state-resolved Raman (ET-Raman) technique to overcome these problems and on future research challenges and needs. 

Abstract Raman spectroscopy-based temperature sensing usually tracks the change of Raman wavenumber, linewidth and intensity, and has found very broad applications in characterizing the energy and charge transport in nanomaterials over the last decade. The temperature coefficients of these Raman properties are highly material-dependent, and are subjected to local optical scattering influence. As a result, Raman-based temperature sensing usually suffers quite large uncertainties and has low sensitivity. Here, a novel method based on dual resonance Raman phenomenon is developed to precisely measure the absolute temperature rise of nanomaterial (nm WS 2 film in this work) from 170 to 470 K. A 532 nm laser (2.33 eV photon energy) is used to conduct the Raman experiment. Its photon energy is very close to the excitonic transition energy of WS 2 at temperatures close to room temperature. A parameter, termed resonance Raman ratio (R3) Ω = I A 1g / I E 2g is introduced to combine the temperature effects on resonance Raman scattering for the A 1g and E 2g modes. Ω has a change of more than two orders of magnitude from 177 to 477 K, and such change is independent of film thickness and local optical scattering. It is shown that when Ω is varied by 1%, the temperature probing sensitivity is 0.42 K and 1.16 K at low and high temperatures, respectively. Based on Ω, the in-plane thermal conductivity ( k ) of a ∼25 nm-thick suspended WS 2 film is measured using our energy transport state-resolved Raman (ET-Raman). k is found decreasing from 50.0 to 20.0 Wm −1 K −1 when temperature increases from 170 to 470 K. This agrees with previous experimental and theoretical results and the measurement data using our FET-Raman. The R3 technique provides a very robust and high-sensitivity method for temperature probing of nanomaterials and will have broad applications in nanoscale thermal transport characterization, non-destructive evaluation, and manufacturing monitoring.