Modeling Thermal Transport Research Articles

Dissimilar thermal transport properties in κ-Ga2O3 and β-Ga2O3 revealed by homogeneous nonequilibrium molecular dynamics simulations using machine-learned potentials

The lattice thermal conductivity (LTC) of Ga2O3 is an important property due to the challenge in the thermal management of high-power devices. In this work, we develop machine-learned neuroevolution potentials (NEPs) for single-crystalline β−Ga2O3 and κ−Ga2O3 and demonstrate their accuracy in modeling thermal transport properties. Combining NEP-driven homogeneous non-equilibrium molecular dynamics simulations with tensor analysis, we determine the spatial distributions of LTCs for two Ga2O3 crystals, showing dissimilar thermal behaviors. Specifically, β−Ga2O3 shows isotropic thermal transport properties, with the LTCs along [100], [010], and [001] directions being predicted to be 10.3±0.2, 19.9±0.2, and 12.6±0.2 W/(m K), respectively, consistent with previous experimental measurements. For κ−Ga2O3, our predictions suggest nearly isotropic thermal transport properties, with the LTCs along [100], [010], and [001] being estimated to be 4.5±0.1, 3.9±0.1, and 4.0±0.1 W/(m K). The reduced LTC of κ−Ga2O3 vs β−Ga2O3 stems from its restricted low-frequency phonons up to 5 THz. Furthermore, we find that the β phase exhibits a typical temperature dependence slightly stronger than ∼T−1, whereas the κ phase shows a weaker temperature dependence, ranging from ∼T−0.5 to ∼T−0.7.

Deep learning interatomic potential for thermal and defect behaviour of aluminum nitride with quantum accuracy

Due to its exceptional physical properties, such as high thermal conductivity and mechanical strength, AlN has been widely used in high-power, high-temperature electronic, and optoelectronic devices. Molecular dynamics simulation is a powerful tool to study its thermal and defect properties. The selection of interatomic potentials plays an important role in the accuracy of calculation results. However, molecular dynamics simulations with various interatomic potentials have yielded different results when investigating the thermal and defect properties of AlN over the last few decades. In this paper, an interatomic potential (DP-IAP) model is developed using a deep potential (DP) methodology for AlN, with the training model's datasets derived from density functional theory (DFT) calculations. The DP-IAP demonstrates quantum-level accuracy in the calculation of the mechanical properties, thermal transport properties, and the defects formation and defects migration for AlN. The developed DP model paves the way for modeling thermal transport and defect evolution in AlN-based devices.

Competition between phonon-vacancy and four-phonon scattering in cubic boron arsenide by machine learning interatomic potential

Point defects can strongly suppress the thermal conductivity $\ensuremath{\kappa}$ of solid materials, which is crucial for a broad range of applications, such as thermal management of electronic devices and thermoelectrics. Understanding thermal transport in materials containing point defects often relies on atomistic simulations based on density functional theory (DFT) or empirical potentials (EPs). However, modeling thermal transport in defective materials using DFT is very computationally expensive or even prohibitive due to the breaking of crystal symmetry while EPs suffer from low accuracy. Recently, machine learning has been applied to the development of interatomic potentials, offering opportunities to model defective systems accurately and efficiently. Here, we present a Gaussian approximation potential (GAP) developed for crystalline cubic boron arsenide (c-BAs) with vacancies, which can achieve DFT-level accuracy in predicting its $\ensuremath{\kappa}$ and phonon transport properties at four orders of magnitude reduced computational cost, especially for phonon-vacancy and four-phonon scatterings. Particularly, we applied the GAP to investigate the effect of vacancies on the $\ensuremath{\kappa}$ of c-BAs by considering both three-phonon and four-phonon scattering. Special attention was paid to the competition between phonon-vacancy and four-phonon scattering, which tend to decrease and increase the temperature dependence of $\ensuremath{\kappa}$, respectively. Specifically, when the vacancy concentration is much lower than $0.07%$ $(2.56\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$, four-phonon scattering plays stronger roles in determining the temperature dependence of $\ensuremath{\kappa}$. As the vacancy concentration increases to $0.07%$, the temperature dependence of $\ensuremath{\kappa}$ becomes close to that considering only three-phonon scattering, indicating the comparable effect of phonon-vacancy and four-phonon scattering. As the vacancy concentration further increases, the phonon-vacancy scattering becomes more dominant and pushes the $\ensuremath{\kappa}$ towards a temperature-independent behavior. Our work deepens the understanding of the phonon scattering landscape in c-BAs with vacancies and will be helpful for tailoring its thermal properties. Atomistic simulations combined with machine learning interatomic potentials are expected to be able to greatly advance the understanding of thermal transport in defective materials.

Thermal transport in 3D printed shape memory polymer metamaterials

Shape memory polymers are gaining significant interest as one of the major constituent materials for the emerging field of 4D printing. While 3D-printed metamaterials with shape memory polymers show unique thermomechanical behaviors, their thermal transport properties have received relatively little attention. Here, we show that thermal transport in 3D-printed shape memory polymers strongly depends on the shape, solid volume fraction, and temperature and that thermal radiation plays a critical role. Our infrared thermography measurements reveal thermal transport mechanisms of shape memory polymers in varying shapes from bulk to octet-truss and Kelvin-foam microlattices with volume fractions of 4%–7% and over a temperature range of 30–130 °C. The thermal conductivity of bulk shape memory polymers increases from 0.24 to 0.31 W m−1 K−1 around the glass transition temperature, in which the primary mechanism is the phase-dependent change in thermal conduction. On the contrary, thermal radiation dominates heat transfer in microlattices and its contribution to the Kelvin-foam structure ranges from 68% to 83% and to the octet-truss structure ranges from 59% to 76% over the same temperature range. We attribute this significant role of thermal radiation to the unique combination of a high infrared emissivity and a high surface-to-volume ratio in the shape memory polymer microlattices. Our work also presents an effective medium approach to explain the experimental results and model thermal transport properties with varying shapes, volume fractions, and temperatures. These findings provide new insights into understanding thermal transport mechanisms in 4D-printed shape memory polymers and exploring the design space of thermomechanical metamaterials.

Thermal coupling-decoupling mechanism of heat transfer across van der Waals interfaces in n-eicosane

Progress toward improving thermal transport properties of n-eicosane, a promising phase change material for thermal energy storage near human body temperature, is hindered by lack of a general theoretical framework to model thermal interfacial conductance (TIC) of the van der Waals (vdW) force bonded molecular interfaces, which have little compositional/structural mismatch. Combining molecular dynamics simulations at temperatures up to the melting point and a time-domain analysis of interfacial heat currents in individual molecules, we unveil that (1) the heat flux across a molecular vdW interface has an alternating coupling-decoupling pattern at the single molecule level due to thermal fluctuations, and (2) the net heat transfer during the thermally coupled periods is orders of magnitude larger than that during the thermally decoupled periods. Furthermore, we demonstrate that a vdW interface's TIC correlates almost linearly with two atomistic-scale coupling-decoupling parameters: αc and σc, that represent the duration and strength of the thermal coupling, respectively. This thermal coupling-decoupling mechanism proposes a new paradigm that explicitly accounts for the effects of structural flexibility and dynamical fluctuation on heat transfer across molecular interfaces, and will likely provide new insights into modeling thermal transport properties in a wide-ranging soft materials, including self-assembled monolayers, paraffins or lipids.

Phononic transport and simulations of annealing processes in nanometric complex structures

Modeling thermal transport at the nanoscale is a difficult task, especially when external time-varying heating sources and the complexity of the studied systems make computational schemes that rely on accurate particlelike simulations nonaffordable. Alternative strategies based on corrections of the Fourier law could satisfy the trade-off between accuracy and computational efficiency, since they can be implemented in partial differential equation solvers. This continuum approach could also allow for the coupling between thermal transport and other evolving fields related to the generalized temperature field. Here we demonstrate that corrections due to the finite phonon mean free paths can be suitably included in annealing process simulations of three-dimensional nanosystems. Quantitative predictions can be obtained and readily compared with the experimental characterization of the processed samples.

Monitoring anharmonic phonon transport across interfaces in one-dimensional lattice chains.

Modeling thermal transport through interfaces has been one of the most challenging problems in nanoscale heat transfer. Although continuous theoretical efforts have been made, there has been no consensus on how to rigorously incorporate temperature effect and anharmonicity. In this paper, we adopt the self-consistent anharmonic phonon concept for nonlinear lattices to investigate phonon propagation within the materials as well as across interfaces based on equilibrium molecular dynamics simulations. Based on linear response theory, we propose an efficient method to calculate the frequency-dependent transmission coefficient in a nonlinear lattice. The transmission spectrum is extracted directly from velocity correlations, which naturally includes anharmonic effects. Phonon renormalization at finite temperature can also be easily handled using the proposed method. Our results are consistent with the atomistic Green's function method at the limit of weak anharmonicity. For nonlinear lattices under high temperatures, the anharmonicity is found to increase the cutoff frequency of the transmission coefficient due to phonon renormalization. Further analysis shows that the anharmonicity also promotes interfacial thermal conductance by causing the redistribution of the spectral flux of the excited vibrational waves during their propogation.

ATK-ForceField: a new generation molecular dynamics software package

ATK-ForceField is a software package for atomistic simulations using classical interatomic potentials. It is implemented as a part of the Atomistix ToolKit (ATK), which is a Python programming environment that makes it easy to create and analyze both standard and highly customized simulations. This paper will focus on the atomic interaction potentials, molecular dynamics, and geometry optimization features of the software, however, many more advanced modeling features are available. The implementation details of these algorithms and their computational performance will be shown. We present three illustrative examples of the types of calculations that are possible with ATK-ForceField: modeling thermal transport properties in a silicon germanium crystal, vapor deposition of selenium molecules on a selenium surface, and a simulation of creep in a copper polycrystal.

Solving Nongray Boltzmann Transport Equation in Gallium Nitride

Several studies have validated that diffusive Fourier model is inadequate to model thermal transport at submicron length scales. Hence, Boltzmann transport equation (BTE) is being utilized to improve thermal predictions in electronic devices, where ballistic effects dominate. In this work, we investigated the steady-state thermal transport in a gallium nitride (GaN) film using the BTE. The phonon properties of GaN for BTE simulations are calculated from first principles—density functional theory (DFT). Despite parallelization, solving the BTE is quite expensive and requires significant computational resources. Here, we propose two methods to accelerate the process of solving the BTE without significant loss of accuracy in temperature prediction. The first one is to use the Fourier model away from the hot-spot in the device where ballistic effects can be neglected and then couple it with a BTE model for the region close to hot-spot. The second method is to accelerate the BTE model itself by using an adaptive model which is faster to solve as BTE for phonon modes with low Knudsen number is replaced with a Fourier like equation. Both these methods involve choosing a cutoff parameter based on the phonon mean free path (mfp). For a GaN-based device considered in the present work, the first method decreases the computational time by about 70%, whereas the adaptive method reduces it by 60% compared to the case where full BTE is solved across the entire domain. Using both the methods together reduces the overall computational time by more than 85%. The methods proposed here are general and can be used for any material. These approaches are quite valuable for multiscale thermal modeling in solving device level problems at a faster pace without a significant loss of accuracy.

Multi-Scale Modeling of Self Heating Effects on Power Consumption in Silicon CMOS Devices

This work pursues a multi-scale modeling approach to combine interconnect and device level simulation in order to study the effects of carrier self-heating and thermal transport on device performance. More specifically, this work will focus on power consumption and heat dissipation in silicon CMOS technology. As device dimensions decrease to the nanometer scale, current density in the device active regions and the circuit interconnects increases [4]. This increase in current density leads to substantial increases in operating temperatures in critical regions of nano-scale electronic devices. We have already shown these effects in n-channel MOSFETs [2], and will continue to explore how this phenomenon affects p-channel MOSFETs and CMOS circuits. This paper presents the methodology used for the study, multi-scale results from the n-channel MOSFET simulations, and preliminary results from the device level p-channel MOSFET simulation. The modeling approach combines an electro-thermal device simulation with a thermal transport solver at the circuit level. The electrical simulation solves Poisson's equations self-consistently coupled with an ensemble Monte Carlo to determine internal electric fields and model electron and hole transport in the device [3]. The thermal simulation solves the energy balance equations for acoustic and optical phonons and uses the phonon energy to determine the lattice temperature [5]. The electro-thermal solver couples these two processes by introducing temperature dependent scattering to the carrier transport solver. Thermal transport can be modeled in a variety of ways: phonon Monte Carlo simulations are necessary for modeling extreme nano-scale and hot-carrier devices, energy balance modeling is used in this study to model thermal transport at the device level, and the Joule heating method commonly used in commercial device simulators is used in this study to model thermal transport at the interconnect level. The thermal modeling in the device and the interconnects is coupled using the device structure itself as an interface: the electro-thermal simulator provides Joule heating terms throughout the device to be used in the Joule heating simulator which in turn gives the temperature profile in the interconnects to be used as a boundary condition in the electro-thermal solver. These simulations are repeated in a self-consistent loop until convergence is achieved [2]. This modeling approach has been successfully applied to n-channel MOSFET devices and the results have been confirmed using a novel experimental approach. Two identical MOSEFTs in either common source or common drain configuration can be biased such that one device is in saturation and one device is in cut-off or sub-threshold region. The device in saturation heats up and the device in sub-threshold is used as a sensor; the temperature in the sensor can be determined using the subthreshold slope [2]. Confirming the simulation results with experimental results for the temperature in the subthreshold device substantiates the accuracy of the methodology for determining the temperature throughout the device [2]. This methodology, now verified by comparison with experimental results for n-channel MOSFETS, will be applied to the study of CMOS circuits.

Thermalization and Thermal Transport in Molecules.

The nature and rate of thermal transport through molecular junctions depend on the length over which thermalization occurs. For junctions formed by alkane chains, in which thermalization occurs only slowly, measurements reveal that thermal resistance is controlled by bonding with the substrates, whereas fluorination can introduce thermal resistance within the molecules themselves, although the mechanism remains unclear. Here we present results of quantum-mechanical calculations of elastic and inelastic scattering rates, the length over which thermalization occurs, and thermal conductance in alkane and perfluoroalkane junctions. The contribution to thermalization of quantum effects that give rise to many-body localization (MBL) in isolated molecules is examined. While MBL does not occur due to dephasing, thermalization is typically too slow to establish local temperature if the same molecule in isolation exhibits MBL. The results indicate limitations on the applicability of classical molecular simulations in modeling thermal transport in molecular junctions.

Modeling Thermal Transport in Heterogeneous Porous Media of PEM Fuel Cells Using Pore Network Model

Thermal and mass transport in the porous transport layers (PTL) of polymer electrolyte membrane (PEM) fuel cells is studied using a pore network model. The solid phase of the PTL is modeled as a network of solid cylinders and the pore phase is modeled as a network of hollow tubes. The two networks are coupled together at the nodes. The network of pores and solid-cylinders are generated independently using Weibull probability distribution function. In the current work, a new formulation of the thermal transport has been developed which incorporates the effect of compression under the lands of bipolar plate on thermal transport. The parameters of PTL used to model compression are obtained from experimentally obtained thermal conductivity values reported in literature. In this paper, a description of the model along with the technique of determining the parameters for compression and the effect of solid phase distribution on the thermal transport in the porous media of fuel cells is presented.

Modeling Thermal Transport in Heterogeneous Porous Media of PEM Fuel Cells Using Pore Network Model

Thermal and mass transport in the porous transport layers (PTL) of polymer electrolyte membrane (PEM) fuel cells is studied using a pore network model. The solid phase of the PTL is modeled as a network of solid cylinders and the pore phase is modeled as a network of hollow tubes. The two networks are coupled together at the nodes. The network of pores and solid-cylinders are generated independently using Weibull probability distribution function. In the current work, a new formulation of the thermal transport has been developed which incorporates the effect of compression under the lands of bipolar plate on thermal transport. The parameters of PTL used to model compression are obtained from experimentally obtained thermal conductivity values reported in literature. In this paper, a description of the model along with the technique of determining the parameters for compression and the effect of solid phase distribution on the thermal and mass transport in the porous media of fuel cells will be presented.

Predicting phonon properties and thermal conductivity from anharmonic lattice dynamics calculations and molecular dynamics simulations

Two methods for predicting phonon frequencies and relaxation times are presented. The first is based on quasiharmonic and anharmonic lattice dynamics calculations, and the second is based on a combination of quasiharmonic lattice dynamics calculations and molecular dynamics simulations. These phonon properties are then used with the Boltzmann transport equation under the relaxation-time approximation to predict the lattice thermal conductivity. The validity of the low-temperature assumptions made in the lattice dynamics framework are assessed by comparing to thermal conductivities predicted by the Green-Kubo and direct molecular dynamics methods for a test system of Lennard-Jones argon. The predictions of all four methods are in agreement at low temperature (20 K). At temperatures of 40 K (half the Debye temperature of Lennard-Jones argon) and below, the thermal-conductivity predictions from the two methods that use lattice dynamics calculations are within about 30% of those made using the more accurate Green-Kubo and direct molecular dynamics methods. The thermal-conductivity predictions using the lattice dynamics techniques become inaccurate at high temperature (above 40 K) due to the approximations inherent in the lattice dynamics framework. We apply the results to assess the validity of (i) the isotropic approximation in modeling thermal transport and (ii) the common assertion that low-frequency phonons dominate thermal transport. Lastly, we suggest approximations that can be made within the lattice dynamics framework that allow the thermal conductivity of Lennard-Jones argon to be estimated using two orders of magnitude less computing effort than the Green-Kubo or direct molecular dynamics methods.

Electron thermal transport in laser-target plasmas on the basis of Grad's 13-moment transport equations

Grad's 13-moment theory is used to model thermal transport in laser-produced plasmas where conditions are such that one may not assume that the plasma is collision-dominated. The equations are presented for a multi-fluid model in slab geometry and are solved numerically for various cases. Comparisons are made with classical theory and with simulations of collisionless plasmas. Results show that, although there are differences between 13-moment and classical predictions, the two theories agree on the general behaviour of the plasma. In particular, 13-moment theory fails to explain the heat-flux inhibition implied by some experimental observations. The theory has also been applied to model thermal transport in plasmas with a population of suprathermal electrons.

The ultraviolet luminescence of β-galliumsesquioxide

Quantitative descriptions of the structure-thermal property correlation have always been a challenging bottleneck in designing functional materials with superb thermal properties. In the past decade, the first-principles-based modeling of phonon properties using density functional theory and the Boltzmann transport equation has become a common practice for predicting the thermal conductivity of new materials. However, first-principles calculations of thermal properties are too costly for high-throughput material screening and multi-scale structural design. First-principles calculations also face several fundamental challenges in modeling thermal transport properties, for example, of crystalline materials with defects, of amorphous materials, and for materials at high temperatures. In the past five years or so, machine learning started to play a role in solving the aforementioned challenges. This review provides a comprehensive summary and discussion on the state-of-the-art, future opportunities, and the remaining challenges in implementing machine learning techniques for studying thermal conductivity. After a brief introduction to the working principles of machine learning algorithms and descriptors for characterizing material structures, recent research using machine learning to study nanoscale thermal transport is discussed. Three major applications of machine learning techniques for predicting thermal properties are discussed. First, machine learning is applied to solve the challenges in modeling phonon transport of crystals with defects, in amorphous materials, and at high temperatures. In particular, machine learning is used to build high-fidelity interatomic potentials to bridge the gap between first-principles calculations and empirical molecular dynamics simulations. Second, machine learning can be used to study the correlation between thermal conductivity and other relevant properties for the high-throughput screening of functional materials. Finally, machine learning is a powerful tool for structural design to achieve target thermal conductance or thermal conductivity. This review concludes with a summary and outlook for future directions for implementing machine learning in thermal sciences.