(Invited) Phonon Coherence and Backscattering in Thermal Transport of Silicon Nanostructures
Authors: Lee Jaeho 
Published: February 2020

Understanding thermal transport at the nanoscale is critical for a broad range of semiconductor technologies involving nanoelectronics, phase change data storage, heat-assisted magnetic recording, solid-state lighting, and thermoelectric energy conversion. Past studies on the thermal conductivity of silicon materials have substantially contributed to establishing microscopic understanding of thermal transport. Classical theories based on the Boltzmann Transport Equation that treat phonons as incoherent particles have accurately described the size-dependent thermal conductivity in silicon thin films and high purity nanowires; these thermal conductivity reductions are due to mean free path suppression from boundary scattering. However, recent thermal conductivity measurements of silicon nanomeshes, which are thin membranes with a fabricated periodic mesh of nanoscopic holes, have called into question the validity of this particle-based Boltzmann Transport Equation approach when applied to periodic nanostructures. Phonons can display both wave-like and particle-like behavior during thermal transport. While the prospect of controlling phonon waves is attractive for potential phononic systems, experimental reports remain inconclusive on the relative importance of wave effects versus particle-based boundary scattering effects in the nanomesh. Although there are several mechanisms proposed to explain the thermal conductivity reduction in silicon nanostructures, possible phonon coherence (wave) and backscattering (particle) effects are often coupled, and previous experimental studies were unable to isolate the dominant mechanism. Here, we measure thermal conductivity of silicon nanomesh structures defined by electron-beam lithography to isolate these competing mechanisms of thermal conductivity reduction. By comparing nanomeshes with periodic and aperiodic holes of the same average dimension, our experimental design decouples the phonon coherence effect from boundary scattering effects. Similarly, by controlling the hole-to-hole pitch from 1 µm to 100 nm, our experiments evaluate the phonon backscattering effect. The thermal conductivity measurements are performed on monolithic silicon devices using an established technique that was first developed for nanowires. The measurement temperature is controlled from 325 K to 14 K; these low temperature measurements are crucial because the important phonon wavelength and the phonon mean free path are larger at low temperature, which facilitates observation of potential coherence and backscattering effects. We perform ray tracing simulations to rigorously capture the boundary scattering required for particle model thermal conductivity predictions. By comparing experimental results between samples and against particle model predictions, we show that phonon coherence effects are not necessary to describe thermal transport in the regime where the nanomesh pitch is greater than the phonon wavelength but smaller than the phonon mean free, and that the backscattering effect leads to the thermal conductivity reductions. The insights obtained from this work will be valuable in understanding phonon transport in complicated nanostructured geometries and advancing breakthroughs in silicon nanostructure-based thermoelectric devices