Maximization of thermal conductance at interfaces via exponentially mass-graded interlayers

Abstract

We propose a strategy to potentially best enhance interfacial thermal transport through solid–solid interfaces by adding nano-engineered, exponentially mass-graded intermediate layers.

Phonon quarters-wave loss

“…While for the impedance increasing material, when reflected from the second boundary, both the first two waves will exhibit half-wave loss. Therefore, in the long-wave limit, the phonon wave will travel half wavelength closer than the one reflected from the first boundary, leading to destructive interference, and finally promote the thermal transport across the interface which is certainly coincident with simulations [39][40][41]. Since the wavelength is frequency dependent, in other frequency domains, more factors must be considered, such as the thickness of the interfacial medium, so that the constructive or destructive interference between the two waves reflected to the left region occurs.…”

A Review of Experimental and Computational Advances in Thermal Boundary Conductance and Nanoscale Thermal Transport across Solid Interfaces

“…However, a further increase in the thickness of the interfacial Si x Ge 1− x alloy region resulted in lower h K due to the dominant effect of alloy scattering intrinsic to the finite thickness interfacial region over the enhancement due to the reduction in the lattice and mass mismatch. Moreover, the functional form of the concentration profile of the intermixing region at the interface has also been shown to alter interfacial conductance …”

“…Another approach to enhance h K across interfaces is by altering the vibrational density of states at the interfacial region through engineering mass graded boundaries via intermixing of the species or by insertion of an interfacial film that bridges the vibrational properties of the two solids in contact. [65,90,103,137,[153][154][155] In comparison to a sharp and abrupt interface, the compositionally disordered (and mass graded) interfaces can demonstrate enhanced h K through vibrational impedance matching between the two solids along with opening new channels of heat transport via anharmonic interactions. For example, Hahn et al [156] have shown that an alloy of Si x Ge 1−x at the Si/Ge interface with a finite thickness of ≈0.5 nm can increase h K by ≈24%.…”

“…Moreover, the functional form of the concentration profile of the intermixing region at the interface has also been shown to alter interfacial conductance. [137,154] Although the majority of the work that have considered mass grading and compositional disorder at the interface have been computational, a few experimental works have also studied the effect of disorder on h K . Hopkins et al [65] studied Cr/Si interface for a variety of interfacial conditions and showed that h K is influenced by the thickness of the mixing region and the rate of compositional change in the mixing region.…”

Minimum and maximum conductance of a thin film layer bridged interface: the role of anharmonicity and layer thickness

“…As a result, the bridging layer, in the non-additive harmonic regime, decreases available modes and limits the possibility of enhancing conductance, G, for many combinations of materials. [13,14,17] The transition from the non-additive to the additive regimes depends on anharmonic phonon-phonon scattering processes, and thus on the length of the intermediate layer, L, on the strength of anharmonicity V 0 (the third order of the interatomic force constants) , and on the temperature, T. A comprehensive study on how phonons flow across bridged interfaces in different transport regimes, accessible by varying these parameters, is still missing. Such a study could clarify how different scattering processes determine the transition between additive and non-additive regimes and thus enable better thermal engineering of devices.…”