Determining phonon mean free path spectrum by ballistic phonon resistance within a nanoslot-patterned thin film

Abstract

At micro-to nano-scales, classical size effects in heat conduction play an important role in suppressing the thermal transport process. Such effects occur when the characteristic lengths become commensurate to the mean free paths (MFPs) of heat carriers that are mainly phonons for nonmetallic crystals. Beyond existing experimental efforts on thin films using laser-induced thermal gratings, this work provides the complete theoretical analysis for a new approach to extract the effective phonon MFP distribution for the in-plane heat conduction within a thin film or flakelike sample. In this approach, nanoslots are patterned on a suspended thin film. Phonons will transport ballistically through the neck region between adjacent nanoslots if the phonon MFPs are much longer than the neck width. The associated "ballistic thermal resistance" for varied neck dimensions can then be used to reconstruct the phonon MFP distribution within the film. The technique can be further extended to two-dimensional materials when the relaxation time approximation is reasonably accurate.

Two-step modification of phonon mean free paths for thermal conductivity predictions of thin-film-based nanostructures

“…In this work, a simple but accurate analytical model is developed, which extends our previous work on nanoporous films 14,20 to dry-etched nanowires and general thin-film-based nanoporous structures. The model predictions agree well with frequency-dependent phonon Monte Carlo (MC) simulations that incorporate the specularity of individual surfaces and the exact three-dimensional structures.…”

Nanostructured and Heterostructured 2D Materials for Thermoelectrics

“…[16] In contrast with patterns with periodic nanopores, an accurate characteristic length determined by the geometry is available for 2D structures with aligned nanoslots. [168], [169] This introduces unique opportunities in the design and optimization of such nanoconstriction structures for thermoelectric applications.…”

“…One important aspect of nanoslot-patterned thin films is that phonons with MFPs much longer than the neck width between adjacent nanoslots will travel ballistically away from the neck, leading to strongly suppressed thermal transport and an associated ballistic thermal resistance. [168], [170] If charge carriers in general have a much shorter MFP than phonons, bulklike electrical properties can be preserved and thus the overall ZT can be enhanced. This ZT enhancement is demonstrated in nanoslot-patterned Si thin films [169] using well-designed nanoslot patterns to adjust the characteristic length.…”

Measurement of the phonon mean free path spectrum in silicon membranes at different temperatures using arrays of nanoslits

“…The wafer had a top 145-nm-thick monocrystalline silicon layer with atomically smooth (σ = 0.2 nm) top and bottom surfaces [15,16] First, we deposited aluminum pads on the surface of silicon. Next, we used electron-beam Comparison of the predictions of the original seminumerical approach proposed by Hao et al [13] with those of our fully analytical method. Our Eq.…”

“…However, no experimental study attempted direct measurements of the phonon MFP spectra of thin mem-branes because setting up an MFP probing experiment on suspended membranes is challenging. Recently, Hao et al [13] proposed a semi-numerical procedure to extract accumulated MFP spectra from the thermal conductivity measured on membranes with arrays of narrow slits with varied width of the passage.…”