# First-principles predictions of high-order and nonequilibrium phonon thermal transport

First-principles method is a powerful approach to study atomic scale physics. With its introduction into thermal transport community, the \textit{ab initio} description of quantized lattice vibrations, phonons, achieved great success in predicting thermal transport properties in the past decade. Though such method is well established, recent theoretical and experimental efforts uncovered new physics and raised new challenges to our community. In particular, high-order phonon anharmonicity, which was assumed to be negligible, shows great impact on thermal transport. Highly nonequilibrium electron and phonon transport occurs in emerging materials with nonuniform temperature field and the equilibrium assumption is no longer valid. Finite temperature effect is found to change the potential landscape even in systems that are quite harmonic, and the previous quasi-harmonic approximation fails. These physical understandings are also closely related to applications that are being extensively studied today: high thermal conductivity materials in thermal management, hot electrons phenomenon in thermal photovoltaic, high temperature radiative properties in thermal barrier coatings, etc.

In this Dissertation, we seek to establish new physical understanding in thermal transport by studying four-phonon scattering, phonon nonequilibrium behavior, phonon renormalization scheme and their interplay in a wide range of solid state systems. For the benefit of the community, we develop an efficient open-source computational program, \textsc{FourPhonon}, and keep updating its core features to drive sustained scientific innovations. This program is capable of calculating phonon-phonon scattering rates up to the fourth-order and the lattice thermal conductivity of solids ($\kappa$).

The Raman peak position and linewidth provide insight into phonon anharmonicity and electron-phonon interactions in materials. For monolayer graphene, prior first-principles calculations have yielded decreasing linewidth with increasing temperature, which is opposite to measurement results. Here, we explicitly consider four-phonon anharmonicity, phonon renormalization, and electron-phonon coupling, and find all to be important to successfully explain both the $G$ peak frequency shift and linewidths in suspended graphene sample over a wide temperature range. Four-phonon scattering contributes a prominent linewidth that increases with temperature， while temperature dependence from electron-phonon interactions is found to be reversed above a doping threshold ($\hbar\omega_G/2$, with $\omega_G$ being the frequency of the $G$ phonon).

While the Raman spectra concerns one particular optical phonon mode, we move to consider $\kappa$ that is determined by full phonon spectrum. The thermal conductivity of monolayer graphene is widely believed to surpass that of diamond even for few-micron size samples and was proposed to diverge with system size. Here, we predict the thermal conductivity from first principles by considering four-phonon scattering, phonon renormalization, an exact solution to phonon Boltzmann transport equation (PBTE), and an unprecedented sampling grid. We show that at room temperature the thermal conductivity saturates at 10~$\rm\upmu m$ size and above and converges to 1300~W/(m$\cdot$K), which is lower than that of diamond. This indicates that four-phonon scattering overall contributes 57\% to the total thermal resistance and becomes the leading phonon scattering mechanism over three-phonon scattering. On the contrary, considering three-phonon scattering only yields higher-than-diamond values and divergence with size due to the momentum-conserving normal processes of flexural phonons.

Higher-order phonon scattering affects heat conduction and thermal radiation at high temperature to a larger degree than at room temperature. We establish a computational framework to compute temperature-dependent full spectrum optical properties and high temperature $\kappa$ of ceramics materials. From ultraviolet to mid-infrared region, light-matter interaction mechanisms in semiconductors progressively shift from electronic transitions to phononic resonances and are affected by temperature. Here, we present a parallel temperature-dependent treatment of both electrons and phonons entirely from first principles, enabling the prediction of full-spectrum optical responses. At elevated temperatures, \textit{ab initio} molecular dynamics (AIMD) is employed to find thermal perturbations to electronic structures and construct effective force constants describing potential landscape. Four-phonon scattering and phonon renormalization are included in an integrated manner in this approach. As a prototype ceramic material, cerium dioxide (CeO$_2$) is considered. Our first-principles calculated refractive index of CeO$_2$ agrees well with measured data from literature and temperature-dependent ellipsometer experiment.

The lattice thermal conductivity ($\kappa$) of two ceramic materials, CeO$_2$ and magnesium oxide (MgO), is then computed up to 1500~K using first principles and the PBTE with the same level of physics, and compared to time-domain thermoreflectance (TDTR) measurements up to 800~K. Our calculated thermal conductivities from the PBTE agree well with literature and our TDTR measurements. Other predicted thermal properties including thermal expansion, frequency shift, and phonon linewidth also compare well with available experimental data. Our results show that high temperature softens phonon frequency and reduces four-phonon scattering strength in both ceramics. The temperature scaling law of $\kappa$ is $\sim T^{-1}$ for three-phonon scattering only and remains the same after phonon renormalization. This scaling for three- plus four-phonon scattering is $\sim T^{-1.2}$ but is weakened to $\sim T^{-1}$ by phonon renormalization. This indicates that four-phonon scattering can play an important role in systems where measured $\kappa$ decays with temperature as $\sim T^{-1}$, which was conventionally attributed to three-phonon only. Compared to MgO, we find that CeO$_2$ has weaker four-phonon effect and renormalization greatly reduces its four-phonon scattering rates.

Phonon-phonon scattering, together with electron-phonon coupling, can often show strong selectivity and drive system out of thermal equilibrium. Measurements and a previous multitemperature model (MTM) resolving phonon temperatures at the polarization level have uncovered remarkable nonequilibrium among different phonon polarizations in laser irradiated graphene and metals. Here, we develop a semiconductor-specific MTM (SC-MTM) by including electron-hole pair generation, diffusion, and recombination, and show that a conventional phonon polarization-level model does not yield observable polarization-based nonequilibrium in laser-irradiated molybdenum disulfide (MoS$_2$). In contrast, appreciable nonequilibrium is predicted between zone-center optical phonons and the other modes. The momentum-based nonequilibrium ratio is found to increase with decreasing laser spot size and interaction with a substrate. This finding is relevant to the understanding of the energy relaxation process in two-dimensional optoelectronic devices and Raman measurements of thermal transport.

In summary, this Dissertation leverages first-principles method to explore thermal transport in emerging materials with a focus on high-order phonon scattering, phonon nonequilibrium behavior, and phonon renormalization. We reveal the importance of these effects in various phenomena including thermal conductivity, optical properties, Raman thermometry and thermal radiation control.

## History

## Degree Type

- Doctor of Philosophy

## Department

- Mechanical Engineering

## Campus location

- West Lafayette