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The secret of thermal boundary resistance: Why does the interface between materials affect heat transfer?
Thermal boundary resistance, or heat generation resistance, is the measure of the resistance to heat flow between the interfaces of two materials. This term is often used interchangeably with Kabiza drag, but the former more broadly encompasses the concept of thermal boundary resistance. At the interface between different materials, due to the differences in electronic and vibrational properties, when energy carriers (such as phonons or electrons, depending on the material) try to cross this interface, scattering occurs at the interface. This results in a certain amount of thermal resistance at the interface, which in turn leads to a significant temperature discontinuity at the interface when a constant heat flux is applied.
Understanding the thermal resistance at interfaces between materials is crucial to the study of thermal properties.
Thermal boundary resistance plays a key role not only in the development of microelectronic devices, but also has a significant impact in nanoscale systems where interfaces can greatly affect properties compared to bulk materials. For applications that require effective heat dissipation, such as microelectronic semiconductor devices, they urgently need interfaces with low thermal resistance due to the extremely high heat generation. According to the International Technology Roadmap for Semiconductors, devices with 8nm feature sizes are expected to generate up to 100,000 W/cm² of heat, and the required effective heat dissipation may be as high as 1000 W/cm², which is an order of magnitude higher than current devices.
In contrast, for applications that require good thermal isolation, such as jet engine turbines, an interface with high thermal resistance is required. These interface materials should remain stable at very high temperatures; metal-ceramic composites are a typical example of such an application. In addition, multi-layer systems can also achieve high thermal resistance, helping to expand application potential.
The existence of thermal boundary resistance is due to scattering of carriers at the interface, and the type of this scattering depends on the properties of the material.
At metal-metal interfaces, the scattering effect of electrons dominates the thermal boundary resistance because electrons are the main thermal energy carriers in metals. There are also two widely used prediction models, namely the acoustic mismatch model (AMM) and the diffusion mismatch model (DMM). The AMM model assumes that the interface is geometrically perfect and that the scattering of phonons through it is purely elastic, whereas the DMM assumes that the scattering at the interface is diffusive, which is true for rough interfaces at high temperatures.
Molecular dynamics (MD) simulation is a powerful tool to study interfacial thermal resistance. The latest MD research shows that the thermal resistance of the solid-liquid interface is reduced on the nanostructured solid surface, which is due to the increase of the solid-liquid interaction energy per unit area and the reduction of the solid-liquid interface. The vibration state density difference.
Theoretical Model
The main model for thermal boundary resistance is the phonon gas model, which includes the AMM and DMM mentioned above. These models assume that the interface behaves just like the bulk material on either side, but they completely ignore the complexity of mixed vibrational modes and phonon interactions. Energy is transferred from high-energy phonons in the hotter material to the colder material. Both the acoustic mismatch model and the diffusion mismatch model do not take into account inelastic scattering and multi-phonon interactions.
According to the acoustic mismatch and diffusion mismatch models, a key factor in determining thermal resistance is the overlap of phonon states.
These models provide upper and lower bounds for some aspects of the discussion, but their effectiveness in predicting specific materials is limited. The AMM and DMM models have fundamental differences in their treatment of interface scattering. The former assumes that there is no scattering at the interface while the latter assumes complete scattering, which directly affects the probability of phonon transmission at the interface.
Case Analysis
Liquid Helium Interface
The concept of resistance at the thermal interface was first proposed in 1936 in the study of liquid helium, and in 1941, Peter Kabiza conducted a systematic study of the thermal interface behavior of liquid helium. The acoustic mismatch model predicts a temperature dependence of T−3, but in fact it does not accurately capture the thermal conductivity of the liquid helium interface.
The abnormally low thermal conductivity of liquid helium interfaces is due to a variety of mechanisms that promote phonon transport.
Thermal conductivity at room temperature
Generally speaking, there are two types of heat carriers in materials: phonons and electrons. The free electron gas in metals conducts heat very efficiently, while heat conduction in all materials occurs via phonons. The lowest room temperature thermal conductivity measured to date is 8.5 MW m−2 K−1 in Bi/H-terminated diamond, and this measurement suggests that due to the intrinsic properties of the materials, they are sensitive to phonons and electrons. The coupling capability is extremely low.
Interface resistance of carbon nanotubes
The superb thermal conductivity of carbon nanotubes makes them an ideal candidate for making composite materials, but interface resistance affects their effective thermal conductivity. This area is poorly researched, and the few studies that have done have revealed the underlying mechanisms of this resistance.
We can see that thermal boundary resistance is a microscopic interface dynamic phenomenon, which has a profound impact on the thermal conductivity of materials. So, how will future material design affect thermal management technology in our daily lives?
