Specularity of longitudinal acoustic phonons at rough surfaces

Abstract

The specularity of phonons at crystal surfaces is of direct importance to thermal transport in nanostructures and to dissipation in nanomechanical resonators. Wave scattering theory provides a framework for estimating wavelength dependent specularity, but experimental validation remains elusive. Widely available thermal conductivity data presents poor validation since the involvement of infinitude of phonon wavelengths in thermal transport presents an underconstrained test for specularity theory. Here, we report phonon specularity by measuring the lifetimes of individual coherent longitudinal acoustic phonon modes excited in ultrathin (36-205 nm) suspended silicon membranes at room temperature over the frequency range ∼ 20-118 GHz. Phonon surface scattering dominates intrinsic Akhiezer damping at frequencies 60 GHz, enabling measurements of phonon boundary scattering time over wavelengths ∼72-140 nm. We obtain detailed statistics of the surface roughness at the top and bottom surfaces of membranes using HRTEM imaging. We find that the specularity of the excited modes are in good agreement with solutions of wave scattering only when the TEM statistics are corrected for projection errors. The often cited Ziman formula for phonon specularity also appears in good agreement with the data, contradicting previous results. This work helps to advance the fundamental understanding of phonon scattering at the surfaces of nanostructures.

Spectrally Resolved Specular Reflections of Thermal Phonons from Atomically Rough Surfaces

“…The most frequently used model to describe the specularity of phonon reflections is Ziman's model [13], and prior works draw conflicting conclusions on its validity for sub-THz phonons. For instance, Hertzberg et al [24] report that sub-THz acoustic phonons reflect more diffusely than predicted by Ziman's model using the surface roughness of their samples obtained from atomic force microscopy (AFM), while Gelda et al [22] report specular sub-THz phonon reflection consistent with Ziman's prediction with surface roughness obtained from transmission electron microscopy (TEM) characterization. Measurements for thermal phonons with frequencies around 10 THz have not been reported previously.…”

“…Experimentally, Pohl and co-workers originally investigated the nature of phonon reflections from surfaces over a temperature range of a few millikelvin to room temperature, observing qualitative evidence for partially specular scattering of phonons below 10 K [20,21]. More recently, Gelda et al [22] reported specular reflections of longitudinal phonons with frequencies less than 0.1 THz at room temperature in Si membranes and obtained good agreement with Ziman's specularity model. Heron et al [23] also reported agreement with Ziman's theory for acoustic phonons by measuring the thermal conductance of Si nanowires around 1 K. On the other hand, Hertzberg et al [24] reported that Ziman's theory underpredicts diffuse scattering of sub-THz phonons at the surfaces of Si nanosheets.…”

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

“…30 Experimental studies on the relationship between the surface roughness and the phonon specularity can be found elsewhere. [51][52][53] One major problem for phonon MC simulations lies in its poor computational efficiency, which limits the early frequency-dependent phonon MC studies to nanosized structures. 45 This challenge has been recently solved by a new deviational phonon MC technique, which was developed by Péraud and Hadjiconstantinou.…”

Peak thermoelectric power factor of holey silicon films

“…At these frequencies, phonon specularity at a typical cleanroom fabricated surface is expected to be < 1 (See Ref. [26], for example). Our calculations show 11 that at room temperature, boundary scattering affects S ph in silicon at limiting dimensions < 10 µm, and that S ph is likely completely quenched when the limiting dimension ∼100 nm.…”