Phonon branch-resolved electron-phonon coupling and the multitemperature model

Abstract

Electron-phonon (e-p) interaction and transport are important for laser-matter interactions, hot-electron relaxation, and metal-nonmetal interfacial thermal transport. A widely used approach is the two-temperature model (TTM), where e-p coupling is treated with a gray approach with a lumped coupling factor G ep and the assumption that all phonons are in local thermal equilibrium. However, in many applications, different phonon branches can be driven into strong nonequilibrium due to selective e-p coupling, and a TTM analysis can lead to misleading or wrong results. Here, we extend the original TTM into a general multitemperature model (MTM), by using phonon branch-resolved e-p coupling factors and assigning a separate temperature for each phonon branch. The steady-state thermal transport and transient hot electron relaxation processes in constant and pulse laser-irradiated single-layer graphene (SLG) are investigated using our MTM respectively. Results show that different phonon branches are in strong nonequilibrium, with the largest temperature rise being more than six times larger than the smallest one. A comparison with TTM reveals that under steady state, MTM predicts 50% and 80% higher temperature rises for electrons and phonons respectively, due to the "hot phonon bottleneck" effect. Further analysis shows that MTM will increase the predicted thermal conductivity of SLG by 67% and its hot electron relaxation time by 60 times. We expect that our MTM will prove advantageous over TTM and gain use among experimentalists and engineers to predict or explain a wide ranges of processes involving laser-matter interactions.

An Analytical Multiple-Temperature Model for Flash Laser Irradiation on Single-Layer Graphene

“…From a theoretical point of view, a few attempts have been presented to improve or simplify the TTM model [18,19]. Very recently [20], a more complex model was pointed out that replaced the standard TTM. The new model, named "Multiple-Temperature Model (MTM)", is more elaborated from theoretical point of view and provides a much better fitting of experimental data, e.g., in predicting the thermal field during laser-graphene interaction.…”

“…TTM uses the Quantum-Espresso package or/and EPW (Electron-Phonon coupling using Wannier functions) for simulations based on first principles density functional perturbation theory (DFPT) and an MTM [7]. The main goal of the current study is to develop a less sophisticated MTM using the Zhukovsky's formalism [20][21][22], thus producing innovation in current field.…”

Non-Equilibrium Thermal Transport: A Review of Applications and Simulation Approaches

“…It is an analogy of the coupling T e-p lat using RTA based on the assumption that the phonon-phonon scattering has negligible effect on phonon distribution and phase space. is the G pp,i phonon-phonon coupling factor between phonon branch and the i scattering lattice reservoir, which is calculated using RTA from the following equation: [104][105][106][107] (14) where is the relaxation time of phonon branch , and the scattering τ i i lattice reservoir's temperature is defined to ensure the energy T lat transfer among phonon branches is conserved: (15) Then by solving numerically, we can obtain the transient Eq. 12and steady state temperature profile of the system with resolved electron and phonon branch temperatures.…”

“…In many applications, such as laser-matter interaction and hot electron cooling, electrons and phonons can be driven into strong non-equilibrium due to selective electronphonon ( ) coupling and phonon-phonon ( ) coupling, and their e-p p-p respective temperature profiles significantly deviate from each other. [11][12][13][14] This phenomenon can significantly affect the heat transfer processes such as hot electron relaxation and thermal measurements in experiments, and has been drawing attention among the research community in both experimental and theoretical areas in the recent decade.…”

Role of phonon coupling and non-equilibrium near the interface to interfacial thermal resistance: The multi-temperature model and thermal circuit

“…The MTM with e-p coupling has been introduced in our previous works. 16,30 In this work, we aim at predicting the effect of non-equilibrium thermal transport on lattice ITC, and therefore we only focus on the lattice portion. The governing equation is…”