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Solving transient energy transport is crucial for accurately predicting the behavior of materials and devices during thermal cycling, pulsed heating, and transient operational states where heat generation and dissipation rates vary over time. Traditional methods, like the finite difference and element methods, discretize space and time and update temperature values at each grid point iteratively over time steps. Its straightforward implementation makes it popular for solving heat transfer problems. However, when high temporal and spatial resolutions or prolonged heating durations are required, the computational demand rises significantly, leading to significantly greater resource consumption. To address this, in this work we develop a new method termed Complex-modeling with Fourier Transform (CFT) that enables rapid and efficient simulations of transient energy transport problems. The CFT method decomposes the periodical heating problem into a complex-temperature energy transport problem with a single harmonic heat source. 1D and 3D transient heat conduction problems (conjugated with hot carrier transfer) are solved using the CFT method to demonstrate its effectiveness. The CFT method produces similar or higher accuracy results compared with the finite difference method, while the computational speed is increased by more than two orders of magnitude. We also developed a new method termed Complex-modeling with Fourier and Heaviside Transforms (CFHT) that can solve any transient energy transport problems with orders of magnitude speed increase. The CFT and CFHT methods developed in this work are applicable to linear problems that could involve mechanical, thermal, optical, and electrical responses. 

Abstract Interfacial thermal resistance plays a crucial role in efficient heat dissipation in modern electronic devices. It is critical to understand the interfacial thermal transport from both experiments and underlying physics. This review is focused on the transient opto-thermal Raman-based techniques for measuring the interfacial thermal resistance between 2D materials and substrate. This transient idea eliminates the use of laser absorption and absolute temperature rise data, therefore provides some of the highest level measurement accuracy and physics understanding. Physical concepts and perspectives are given for the time-domain differential Raman (TD-Raman), frequency-resolved Raman (FR-Raman), energy transport state-resolved Raman (ET-Raman), frequency domain ET-Raman (FET-Raman), as well as laser flash Raman and dual-wavelength laser flash Raman techniques. The thermal nonequilibrium between optical and acoustic phonons, as well as hot carrier diffusion must be considered for extremely small domain characterization of interfacial thermal resistance. To have a better understanding of phonon transport across material interfaces, we introduce a new concept termed effective interface energy transmission velocity. It is very striking that many reported interfaces have an almost constant energy transmission velocity over a wide temperature range. This physics consideration is inspired by the thermal reffusivity theory, which is effective for analyzing structure-phonon scattering. We expect the effective interface energy transmission velocity to give an intrinsic picture of the transmission of energy carriers, unaltered by the influence of their capacity to carry heat. 

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. 

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. 

Temperature dependent Raman intensity of 2D materials features very rich information about the material's electronic structure, optical properties, and nm-level interface spacing. To date, there still lacks rigorous consideration of the combined effects. This renders the Raman intensity information less valuable in material studies. In this work, the Raman intensity of four supported multilayered WS 2 samples are studied from 77 K to 757 K under 532 nm laser excitation. Resonance Raman scattering is observed, and we are able to evaluate the excitonic transition energy of B exciton and its broadening parameters. However, the resonance Raman effects cannot explain the Raman intensity variation in the high temperature range (room temperature to 757 K). The thermal expansion mismatch between WS 2 and Si substrate at high temperatures (room temperature to 757 K) make the optical interference effects very strong and enhances the Raman intensity significantly. This interference effect is studied in detail by rigorously calculating and considering the thermal expansion of samples, the interface spacing change, and the optical indices change with temperature. Considering all of the above factors, it is concluded that the temperature dependent Raman intensity of the WS 2 samples cannot be solely interpreted by its resonance behavior. The interface optical interference impacts the Raman intensity more significantly than the change of refractive indices with temperature. 

Abstract This work reports the dynamic behaviors of graphene aerogel (GA) microfibers during and after continuous wave (CW) laser photoreduction. The reduction results in one‐order of magnitude increase in the electrical conductivity. The experimental results reveal the exact mechanisms of photoreduction as it occurs: immediate photochemical removal of oxygen functional groups causing a sharp decrease in electrical resistance and subsequent laser heating that facilitates thermal rearrangement of GO sheets towards more graphene‐like domains. X‐ray and Raman spectroscopy analysis confirm that photoreduction removes virtually all oxygen and nitrogen containing functional groups. Interestingly, a dynamic period immediately following the end of laser exposure shows a slow, gradual increase in electrical resistance, suggesting that a proportion of the electrical conductivity enhancement from photoreduction is not permanent. A two‐part experiment monitoring the resistance changes in real‐time before and after photoreduction is conducted to investigate this critical period. The thermal diffusivity evolution of the microfiber is tracked and shows an improvement of 277 % after all photoreduction experiments. A strong linear coherency between thermal diffusivity and electrical conductivity is also uncovered. This is the first known work to explore both the dynamic electrical and thermal evolution of a GO‐based aerogel during and after photoreduction. 

Abstract Under photon excitation, 2D materials experience cascading energy transfer from electrons to optical phonons (OPs) and acoustic phonons (APs). Despite few modeling works, it remains a long‐history open problem to distinguish the OP and AP temperatures, not to mention characterizing their energy coupling factor (G). Here, the temperatures of longitudinal/transverse optical (LO/TO) phonons, flexural optical (ZO) phonons, and APs are distinguished by constructing steady and nanosecond (ns) interphonon branch energy transport states and simultaneously probing them using nanosecond energy transport state‐resolved Raman spectroscopy. ΔT_{OP −AP}is measured to take more than 30% of the Raman‐probed temperature rise. A breakthrough is made on measuring the intrinsic in‐plane thermal conductivity of suspended nm MoS₂and MoSe₂by completely excluding the interphonon cascading energy transfer effect, rewriting the Raman‐based thermal conductivity measurement of 2D materials.G_OP↔APfor MoS₂, MoSe₂, and graphene paper (GP) are characterized. For MoS₂and MoSe₂,G_OP↔APis in the order of 10¹⁵and 10¹⁴W m⁻³K⁻¹andG_ZO↔APis much smaller thanG_LO/TO↔AP. Under ns laser excitation,G_OP↔APis significantly increased, probably due to the reduced phonon scattering time by the significantly increased hot carrier population. For GP,G_LO/TO↔APis 0.549 × 10¹⁶W m⁻³K⁻¹, agreeing well with the value of 0.41 × 10¹⁶W m⁻³K⁻¹by first‐principles modeling.