Directional Phonon Suppression Function as a Tool for the Identification of Ultralow Thermal Conductivity Materials

Abstract

Boundary-engineering in nanostructures has the potential to dramatically impact the development of materials for high- efficiency conversion of thermal energy directly into electricity. In particular, nanostructuring of semiconductors can lead to strong suppression of heat transport with little degradation of electrical conductivity. Although this combination of material properties is promising for thermoelectric materials, it remains largely unexplored. In this work, we introduce a novel concept, the directional phonon suppression function, to unravel boundary-dominated heat transport in unprecedented detail. Using a combination of density functional theory and the Boltzmann transport equation, we compute this quantity for nanoporous silicon materials. We first compute the thermal conductivity for the case with aligned circular pores, confirming a significant thermal transport degradation with respect to the bulk. Then, by analyzing the information on the directionality of phonon suppression in this system, we identify a new structure of rectangular pores with the same porosity that enables a four-fold decrease in thermal transport with respect to the circular pores. Our results illustrate the utility of the directional phonon suppression function, enabling new avenues for systematic thermal conductivity minimization and potentially accelerating the engineering of next-generation thermoelectric devices.

Efficient calculations of the Mode-Resolved ab-initio thermal Conductivity in nanostructures

“…In the case with infinite thickness, only polar discretization is needed thus we can plot S tk as a surface in 3D, as shown in the inset of Fig. 2(b) for the case with L = 50 nm; we note there are two main lobes, corresponding to the forward and backward direct paths [16]. In Fig.…”

“…To better understand the effect of the geometry on κ eff , it is convenient to define a suppression function, which is a measure on how much heat is carried in the nanomaterial compared to that from the bulk. Originally, this tool was conceived as a MFP-or frequency dependent function [27] and later was generalized to include directionality [16]. Here we define the mode-resolved suppression function as…”

“…To overcome this limitation, several approaches have been proposed; for example in the frequency-dependent BTE (FD-BTE), the BZ is made isotropic from a slice taken along a high-symmetry path, and then sampled in frequency space [12][13][14]. In a previous work, we developed a formalism, called the MFP-BTE, where the sampling is carried out in the MFPspace [15,16]. Recently, a deterministic approach based on the self-adjoint version of the BTE has been proposed [17].…”

Phonon Transport in Patterned Two-Dimensional Materials from First Principles

“…Within RTA, size effects occur when the pore-pore distance becomes comparable to the MFPs [45,46]; however, in light of the above discussion, boundary scattering may impact thermal transport even for larger feature sizes, should the off-diagonal terms of the collision operator be significant.…”

Diffusive Phonons in Nongray Nanostructures

“…However, for more complex geometries, one has to solve the space-dependent BTE, which gives κ eff /κ bulk = B 0 (Λ)S(Λ, Ω)dΛ, where f = 4π f (Ω)dΩ −1 is an angular average along the solid angle Ω, representing phonon direction. Generally, S(Λ, Ω), the "directional" suppression function [20], depends on K(Λ) itself [21]; thus the phonon suppression at a given Λ depends on the whole bulk spectrum. Consequently, the notion of diffusive and ballistic regimes has to be revisited in order to incorporate the coupling between phonons at different MFPs.…”