Engineering and understanding of thermal conduction in materials

Thermal conduction is a ubiquitous process that plays a critical role in many engineering applications, including power generation, energy harvesting and storage, thermal management of electronics, and materials processing. If the thermal conductivity of materials can be reduced and increased to extents that do not naturally exist, it will bring a significant impact to a wide range of applications. Such an effort would require proper experimental and simulation tools that can access the time and length scales associated with the propagation and scattering of energy carriers, such as atomic vibration, charge, and spin waves. Indeed, we have witnessed tremendous advances in the experimental and simulation methods for such time and length scales. Ultrafast laser-based thermal metrology could enable us to probe the thermal transport process at scales smaller than that of carrier scattering processes. Atomistic simulation methods combined with first-principles calculation make the prediction free from adjustable parameters. With the ab initio predictive power, the simulation identifies extraordinary phenomena and guides experimental efforts. Emerging machine learning techniques are a new workhorse that can advance the simulation methods even further.

The advances in both experimental and simulation methods have resulted in a better understanding of thermal transport processes and the rational engineering of materials with unprecedented thermal transport properties. The outcomes include ultrahigh thermal conductivity values of boron arsenide, ultralow thermal conductivity values even lower than the amorphous limit, and highly anisotropic thermal conductivity values. In addition, extraordinary thermal transport processes that are not governed by diffusive Fourier's law, such as ballistic and hydrodynamic thermal transport, have been extensively studied. While decades-old studies focused on dielectric materials where phonons are the dominant carriers, some of the recent studies explored a new realm where other carriers such as electrons and magnons have a complex interplay with phonons for thermal transport. Also, beyond the crystalline phase, thermal conduction in highly disordered and soft phases has received much attention. A prominent example is polymers with high thermal conductivity values. Considering all the exciting progress recently made in the field, it is a timely task to summarize the progress and discuss possible future directions. Thus, we have organized the Special Topic, “Engineering and Understanding of Thermal Conduction in Materials” in the Journal of Applied Physics.

Controlling defects has been an effective way to engineer thermal conductivity values. The inclusion of nanoparticles can be more effective than dislocations and grain boundaries in that they can strongly scatter low-frequency phonons, which are only weakly scattered by dislocations and grain boundaries. By inserting SiO₂ and diamond nanoparticles into nanograined thermoelectric materials, the thermal conductivity was significantly reduced.¹ In particular, the diamond is more effective than SiO₂ due to the large acoustic mismatch with the host thermoelectric material. The phonon–dislocation has been a topic of study for a long time, and Cheng et al.² contributed a comprehensive review of the existing theories for phonon–dislocation interactions with their perspectives. Introducing a porous structure is another effective way to suppress the thermal conductivity of materials. By introducing a porous structure, Wu et al.³ reported an extremely low thermal conductivity of β-Ga₂O₃, which is a promising thermoelectric material, though it has disadvantages of relatively high thermal conductivity. The record low thermal conductivity is even below the amorphous limit at room temperature. Also, a method for analyzing porous structures and thermal conductivity based on fractal theory is reported.⁴ The method was applied to aramid nanofiber, which is a promising thermal insulation material, discovering that the smaller pores can suppress thermal conductivity more than the larger pores when the porosity is kept the same. Highly disordered materials are remained poorly understood compared to the materials with a small degree of disorder. An extraordinary phenomenon expected in the highly disordered materials is Anderson localization which can lead to extremely low thermal conductivity. While the Anderson localization of photons and electrons has been studied extensively and clearly observed, the same phenomenon for phonons remains elusive. Ni and Volz provided a review on the past experimental and numerical studies of phonon Anderson localization.⁵ Semicrystalline polymers, with their electrically insulating and thermally conducting features, are considered next-generation materials for cooling electronics. The semicrystalline polymers consist of a crystalline lamella and a disordered amorphous region. Using the molecular dynamics simulation, He and Liu discovered that the interphase region has greater thermal resistance than the amorphous region, opposite to common perception.⁶ 

Modern nanostructured devices commonly have many interfaces and the understanding of thermal transport across interfaces is one of the key challenges in the field. Heterogenous interfaces including two-dimensional (2D) materials such as graphene are of particular interest due to the perceived widespread use of 2D materials in emerging electronic devices. Dong et al. report the numerical study of thermal transport across graphene–hexagonal boron nitride tilt grain boundaries showing that the lattice mismatch does not make a significant impact on thermal transport.⁷ The thermal transport across interfaces between graphene and light emitting diodes was also experimentally studied.⁸ The thermal annealing treatment reduces the wrinkles of graphene and thereby reduces the thermal interfacial resistance. The interface between magnetic and non-magnetic materials also received attention because a considerable portion of the energy is carried by spin waves in magnetic materials. Combining first-principles calculation, spin-lattice dynamics, and non-equilibrium Green's function method, Ge et al. calculated the thermal boundary conductance across a Co–Cu interface considering both phonons and magnons.⁹ The interface scattering of phonons was often assumed elastic under harmonic approximation, but recent studies report that the scattering process is inelastic and anharmonicity can play an important role. However, the extension of atomistic Green's function approach, one of the most widely used methods to simulate interfacial thermal conductance assuming harmonic approximation, to the anharmonic interactions is not trivial. Hopkins et al.¹⁰ developed a quasi-harmonic theory for phonon thermal boundary conductance that can be easily implemented in numerical studies and, hence, provide a useful tool for qualitative understanding of the anharmonic processes at interfaces.

Remarkable perspectives are promoted within the framework of “new materials.” These are the products of innovative combinations or modifications of known compounds and the results of theoretical predictions. Research on the high thermal conductivity of boron arsenide, rivaling that of a diamond at high temperature, is a prime example of successful material discovery guided by model prediction. An insightful and broad review on this topic is provided by Pan et al.¹¹ 2D materials have been emerging for more than a decade and their impact is mostly related to the versatility of their properties. It has been long known that graphene is not the only atomically layered material and a large set of compounds such as Sb₂C have yielded new ranges of properties including a high thermoelectric figure of merit ZT.¹² On the other hand, graphene-based compounds have also opened up new horizons, especially via the intercalation of new elements leading to unexpected outcomes such as the increase of interlayer bonding and the decrease of thermal conductivity.¹³ For long, superlattices have also been a building block of microdevices and the design of their most intrinsic acoustic wave mechanisms has led to the exploration of new wave-controlled thermal transport behaviors. The impact of phonon folding on heat transfer has been studied before but the acoustic stop-bands are usually spectrally too thin. Lee et al. demonstrated the use of tandem acoustic Bragg reflectors to manipulate anisotropy of thermal conductivity.¹⁴ We should also not forget the diverse top-down approaches allowing for the nanostructure and the design of thermal properties such as the one producing porous matrices of nanoparticle chains with ultralow thermal conductivity.¹⁵ 

While phonon heat transport has been investigated for decades, previously unexplored phenomena can now be observed due to the emergence of new fabrication and metrology capabilities. Hydrodynamic heat transport was recently proposed in analogy with fluids revealing the existence of non-Fourier effects at larger than mean-free path scales. The physical mechanism here relies on the predominance of momentum-conserving normal processes and several breakthrough measurements were performed including the one uncovering second sound at temperatures higher than 100 K.¹⁶ Those measurements, however, remain complex and the effects are weak, so accurate criteria should be established, for instance, to detect the Poiseuille flow of phonons.¹⁷ Even more elementary on the conceptual level, Anufriev et al. reviewed the recent experimental demonstrations of ballistic phonon transport in semiconductor nanowires and found different degrees of ballistic conduction in these experiments.¹⁸ They concluded that further studies are needed to clarify the ballistic effect in the nanowires.¹⁸ Nanowires have also become an excellent testbed to study phonon transport physics, ranging from classical size effect due to phonon boundary scattering to the intriguing superdiffusive effect of one-dimensional phonons confined in the nanowires.¹⁹ The latter has raised the exciting prospect of achieving super heat conductors.¹⁹ Finally, metrologies such as Brillouin Light Scattering²⁰ and Cyclotron²¹ stand more than ever in a key position to unravel the aforementioned emergent phenomena as well as the topological effects.

The last two decades have also witnessed the emergence of new experimental methods that enable the probing of thermal transport phenomena and the discovery of new physics. Laser-based pump-probe thermoreflectance technique, pioneered by Cahill in the early 2000,²² has been widely used in the nanoscale heat transfer community. The technique has seen continuous developments for new structures, materials, and applications. Hopkins et al. devised a thermoreflectance-based technique to detect sub-micrometer thermomechanical and thermochemical failure mechanisms of titanium metal under intense heat fluxes.²³ Using Fourier expansion analysis of thermoreflectance signal after period pulse heating, Mori et al. demonstrated a new technique to measure the thermal diffusivity of thin metal films.²⁴ Typical time-domain thermoreflectance (TDTR) needs a metal transducer layer such as Au and Al for laser absorption and thermoreflectance. Wu et al. proposed and demonstrated a transducerless TDTR measurement on semiconductors by utilizing direct laser absorption of above-bandgap photons and thermal response of the photogenerated carriers.²⁵ Transient grating spectroscopy (TGS) is another optical pump-probe technique that does not require a transducer. In a detailed tutorial written by Choudhry et al.,²⁶ the operational principle and instrumentation of a heterodyne TGS configuration were discussed and the applications of TGS in characterizing microscale thermal transport were reviewed. Besides the optical techniques, other methods have also seen significant development recently. Novel Schottky thermometry was utilized by Minnich et al. to characterize the self-heating effect in cryogenic high electronic mobility transistors, which are widely used in radio astronomy, deep space communications, and quantum computing.²⁷ Kuwano et al. reported a nanoparticle image velocimetry (nano-PIV) to characterize the motion of sub-micrometer particles in micro channels.²⁸ 

The new findings of thermal transport phenomena have been also driven by new simulation methods and theories, recently. This topic also features a few articles on the comprehensive review and perspectives for the theory and simulation methods that were recently developed. There have been several different ways to simulate thermal transport phenomena such as equilibrium and non-equilibrium molecular dynamics simulations, lattice dynamics calculation combined with first-principles calculation including higher order scattering processes, etc. Oftentimes, the results from those simulation methods disagree with each other, and thus, the fundamental assumptions and limitations of each method need to be discussed in a timely manner. Gu et al. provide a comprehensive comparison of the widely used simulation methods and discuss specific situations where each method fails.²⁹ Machine learning interatomic potential recently draws much attention because it can predict atomic force and energy at ab initio accuracy, while the computational cost is much cheaper than the direct ab initio simulation. The current status and challenges of the machine learning interatomic potential for molecular dynamics simulation are discussed, with particular emphasis on the challenge from a large atomic configurational space.³⁰ Last, calculating local heat flux from the atomic trajectory and force is a critical part of molecular dynamics simulation for thermal transport. Surblys et al. report a correct formalism of calculating local heat flux when the molecules are rigid or dynamically constrained.³¹ 

Ultimately, the new insights obtained from the thermal transport study could lead to new or improved technological applications, including energy conversion and storage, laser and light emitting diodes, and data storage. For example, Zhu et al. show marked enhancement in thermoelectric performance of N-type Bi₂Te₃ by Sb nano-precipitates, which are shown to lead to a low lattice thermal conductivity and high thermoelectric figure of merit ZT (>1.2 at 400 K).³² Prasher et al. presented an in-depth analysis linking nanoscale phonon physics to the performance of phase change materials for thermal energy storage (TES),³³ which leads to an important microscopic understanding of key metrics of TES such as supercooling and energy density. Wang et al. discussed magnons, an emerging class of heat carriers, and envisioned the potential applications enabled by spin-heat coupling such as in metrology and data storage, spin caloritronics, etc.³⁴ Garay et al. presented a comprehensive perspective on heat generation and the associated failure mechanisms in laser gain materials by examining the nano/microstructure effects on the optical, thermal, and mechanical properties of polycrystalline ceramics.³⁵ Hu et al. reviewed the fundamentals and recent development in the heat manipulation of photoluminescent materials in light emitting diodes and laser diodes.³⁶ 

All the articles in this Special Topic clearly show the significant progress made in the field during the last decade. We have now gained a deeper understanding of complex thermal conduction processes, including scattering by defects, propagation, and localization in highly disordered media, etc. and novel approaches to develop new materials with better engineered thermal properties. These efforts have been driven by the advanced experimental and simulation techniques that were recently developed. The innovations at the material level finally led to new technological applications. However, it is also clear that there still exists much room for further study. Many critical phenomena, for example, thermal conduction in disordered and soft materials and energy exchange between different types of thermal energy carriers, remained poorly understood. We believe a better understanding of these fundamental aspects will enable the rational approaches to further innovations in the field. We hope that this Special Topic will serve as a guidance for such efforts.

This Special Topic could not be possible without the authors who contributed their articles as well as numerous reviewers who provided constructive feedback with helpful suggestions. We are also grateful to Professor Pawel Keblinski, Associate Editor of the Journal of Applied Physics, for his strong support and the American Institute of Physics publishing staff for their help. S.L. acknowledges the support from the U.S. National Science Foundation (NSF) under Grant No. 1943807. R.C. acknowledges the support from the U.S. NSF under Grant Nos. 2005181 and 2024027.