Interfacial thermal resistance

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Interfacial thermal resistance, also known as thermal boundary resistance, or Kapitza resistance, is a measure of resistance to thermal flow at the interface between two materials. While these terms may be used interchangeably, Kapitza resistance technically refers to an atomically perfect, flat interface whereas thermal boundary resistance is a more broad term.^[1] This thermal resistance differs from contact resistance (not to be confused with electrical contact resistance) because it exists even at atomically perfect interfaces. Owing to differences in electronic and vibrational properties in different materials, when an energy carrier (phonon or electron, depending on the material) attempts to traverse the interface, it will scatter at the interface. The probability of transmission after scattering will depend on the available energy states on side 1 and side 2 of the interface.

Assuming a constant thermal flux is applied across an interface, this interfacial thermal resistance will lead to a finite temperature discontinuity at the interface. From an extension of Fourier's law, we can write

${\displaystyle Q={\frac {\Delta T}{R}}=G\Delta T}$

where ${\displaystyle Q}$ is the applied flux, ${\displaystyle \Delta T}$ is the observed temperature drop, ${\displaystyle R}$ is the thermal boundary resistance, and ${\displaystyle G}$ is its inverse, or thermal boundary conductance.

Understanding the thermal resistance at the interface between two materials is of primary significance in the study of its thermal properties. Interfaces often contribute significantly to the observed properties of the materials. This is even more critical for nanoscale systems where interfaces could significantly affect the properties relative to bulk materials.

Low thermal resistance at interfaces is technologically important for applications where very high heat dissipation is necessary. This is of particular concern to the development of microelectronic semiconductor devices as defined by the International Technology Roadmap for Semiconductors in 2004 where an 8 nm feature size device is projected to generate up to 100000 W/cm² and would need efficient heat dissipation of an anticipated die level heat flux of 1000 W/cm² which is an order of magnitude higher than current devices.^[2] On the other hand, applications requiring good thermal isolation such as jet engine turbines would benefit from interfaces with high thermal resistance. This would also require material interfaces which are stable at very high temperature. Examples are metal-ceramic composites which are currently used for these applications. High thermal resistance can also be achieved with multilayer systems.

As stated above, thermal boundary resistance is due to carrier scattering at an interface. The type of carrier scattered will depend on the materials governing the interfaces. For example, at a metal-metal interface, electron scattering effects will dominate thermal boundary resistance, as electrons are the primary thermal energy carriers in metals.

Two widely used predictive models are the acoustic mismatch model (AMM) and the diffuse mismatch model (DMM). The AMM assumes a geometrically perfect interface and phonon transport across it is entirely elastic, treating phonons as waves in a continuum. On the other hand, the DMM assumes scattering at the interface is diffusive, which is accurate for interfaces with characteristic roughness at elevated temperatures.

Molecular dynamics (MD) simulations are a powerful tool to investigate interfacial thermal resistance. Recent MD studies have demonstrated that the solid-liquid interfacial thermal resistance is reduced on nanostructured solid surfaces by enhancing the solid-liquid interaction energy per unit area, and reducing the difference in vibrational density of states between solid and liquid.^[3]