Predicting interfacial thermal resistance by machine learning

Abstract
Various factors affect the interfacial thermal resistance (ITR) between two materials, making ITR prediction a high-dimensional mathematical problem. Machine learning is a cost-effective method to address this. Here, we report ITR predictive models based on experimental data. The physical, chemical, and material properties of ITR are categorized into three sets of descriptors, and three algorithms are used for the models. Those descriptors assist the models in reducing the mismatch between predicted and experimental values and reaching high predictive performance of 96%. Over 80,000 material systems composed of 293 materials were inputs for predictions. Among the top-100 high-ITR predictions by the three different algorithms, 25 material systems are repeatedly predicted by at least two algorithms. One of the 25 material systems, Bi/Si achieved the ultra-low thermal conductivity in our previous work. We believe that the predicted high-ITR material systems are potential candidates for thermoelectric applications. This study proposed a strategy for material exploration for thermal management by means of machine learning.

Introduction
Thermal transport across the interfaces of two different materials is a crucial issue in micro/nanoscale electronic, photonic, and phononic devices. A temperature discontinuity exists between the interface of dissimilar materials; this discontinuity can be described as interfacial thermal resistance (ITR) in the equation R?=?q/ΔT, where q is the heat flux and ΔT is the temperature difference at the interface. In nanostructured devices, in which the characteristic length scales are shorter than the phonon mean free paths, the transport mode is ballistic rather than diffusive, and ITR becomes the dominant factor of phonon transport as the length scale decreases. Practically, phonon transport in thin films is affected by a variety of interfacial properties, including roughness, binding energy, and the presence of impurities or intermediate layers of mixed atoms. Even when the interfaces are in perfect contact, phonon reflections occur across the boundary as a result of differences in the acoustic properties of adjacent materials. Thus, several characteristics contribute to ITR, making it difficult to describe or predict.

Methods such as acoustic mismatch model (AMM), diffuse mismatch model (DMM), and molecular dynamics (MD) are commonly used to predict ITR. In AMM and DMM, which were introduced by Khalatnikov in 1952 and Swartz and Pohl in 1989, respectively, phonons in the equilibrium state are modeled without accounting for the nonequilibrium distribution of phonons.1,2 AMM assumes that incident phonons at an interface undergo specular reflection or transmission, however, high-frequency or high-temperature phonons are scattered diffusely because of the interface roughness, leading researchers to develop more accurate methods to predict ITR. Prasher proposed the scattering-mediated acoustic mismatch model (SMAMM) and modified traditional AMM for weakly bonded atoms at an interface.3 DMM assumes that phonons are elastically scattered and lose their memory of transport modes at the interface. In addition, the transmission probability depends on the ratio of the phonon density of states (PDOS). Therefore, the assumption of elastically scattering will result in failure when inelastic phonons are present, as at the imperfect interfaces, where they create energy channels. In AMM and DMM models, properties including temperature, density, sound velocity (longitudinal and transverse), and unit cell volume, are used as descriptors. However, AMM and DMM result in large discrepancies between the predicted and experimental values, with correlation coefficients of 0.6 and 0.62, and with RMSE of 121.3 and 91.4 (10?9?m2K/W), respectively.4 Both AMM and DMM assume that the phonons are in equilibrium on each side of the interface; however, in systems where the layer thickness is smaller than the phonon mean free path (e.g., systems with multiple quantum wells and superlattices), the nonequilibrium distribution of phonons should be taken into account. Thus, AMM and DMM have important shortcomings that need to be addressed.

The effect of lattice mismatch at the interface on ITR can be evaluated by MD simulation. Equilibrium MD is more suitable for the analysis of transient response measurements, whereas nonequilibrium MD is applied for steady-state measurements. In classical MD, atomic motion is calculated from classical Newtonian mechanics rather than quantum theory, and the zero-point energy is assumed to be zero. In contrast, ab initio MD provides a higher accuracy than classical MD, however, the simulation time and particle numbers are restricted to allow the full quantum calculation of the electronic structure for every configuration of atoms. All trajectories of the system often need more information than that which is known.

Predicting the ITR for various material systems is a time-consuming process. Generally, the physical explanation with the different prediction methods mentioned above can be used only in specific cases. It is difficult to consider every property that might affect ITR in a single equation, particularly for interfacial conditions. Machine learning is a cost-effective and time-efficient method to address this high-dimensional problem. The machine learning has been implemented for thermal transport properties in many reported works. Xin Qian et al. developed Gaussian approximation potential models for analyzing the phonon dispersion stability.5 Shenghong Ju et al. designed the Si/Ge interfacial structure for controlling heat conduction through atomistic Green’s function and Bayesian optimization.6 Masaki Yamawaki et al. used Bayesian optimization for multifunctional structural design of graphene nanoribbons for thermoelectric materials.7 Our previous work also shows promising improvements of ITR predictive performance compared with the common-used AMM and DMM models through machine learning.4 And, the melting point, heat capacity, unit cell volume, density, and film thickness were proposed to be important descriptors for ITR prediction.4

In general, the larger dissimilarities of phonon properties lead to high ITR corresponding to the temperature. However, the inelastic interfacial scattering processes, which would be influenced by the interfacial quality, interfacial bonding, and phonon transmission coefficient, become important at and above the room temperature. Therefore, the physical and chemical properties which affect the interfacial quality should be carefully considered. Based on the thermophysical properties selection of our previous work,4 in this study, we will further discuss how we consider lots of important factors, especially the interfacial conditions, through machine learning. In the following, we will introduce how we evaluated the models, analyzed the predictions. The details of data collection, descriptor selection, and algorithms selection can be found in the Method section.

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