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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. 

Upon laser irradiation, 2D materials experience a cascading energy transfer from electrons to optical phonons (OPs) and then to acoustic phonons (APs), resulting in a significant thermal non-equilibrium among energy carriers. This non-equilibrium presents challenges for Raman-based thermal characterization, as Raman scattering measures only OP temperature rise, while APs are the primary energy carriers. Despite recent efforts to address this issue, OP–AP thermal non-equilibrium in supported 2D materials remains poorly resolved. Here, we develop a method to distinguish the OP and AP temperature rises based on their different temporal thermal responses under laser irradiation: the OP–AP temperature difference responds almost immediately (∼a few to tens of ps), while the AP temperature rise takes longer to establish (∼tens of ns). Using energy transport-state resolved Raman, we probe the transient thermal response of Si-supported nm-thick MoS₂from 20 to 100 ns. We find that the OP–AP temperature difference exceeds 120% of the AP temperature rise under ∼0.439 µm radius laser heating. The intrinsic interfacial thermal conductance of the samples, based on the true AP temperature rise, varies from 0.199 to 1.46 MW·m⁻²·K⁻¹, showing an increasing trend with sample thickness.