Phonon Mean Free Path Spectroscopy By Raman Thermometry

Abstract

In this work, we exemplify on a bulk silicon sample that Raman thermometry is capable of phonon mean free path (PMFP) spectroscopy. Our experimental approach is similar to the variation of different characteristic length scales $l_{c}$ during thermal reflectance measurements in the time or frequency domain and transient thermal grating spectroscopy. In place of $l_{c}$, we vary the laser focus spot size ($w_{e}$) and the light penetration depth ($h_{\alpha}$) during one-laser Raman thermometry (1LRT) measurements. For our largest $w_{e}$ values, the derived effective thermal conductivities $\kappa_{eff}$ converge towards the bulk thermal conductivity $\kappa_{bulk}$ for silicon. However, towards smaller $w_{e}$ values, we observe a pronounced increase for the $\kappa_{eff}$ values, which amounts up to a factor of 5.3 at 293K and even 8.3 at 200K. We mainly assign this phenomenon to quasi-ballistic phonon transport. As a result, we can compare our measured $\kappa_{eff}(w_{e})$ trends with the thermal accumulation function $\kappa_{cum}$ and its dependence on the phonon mean free path $l_{ph}$, which we derive from ab initio solutions of the linearized phonon Boltzmann transport equation (BTE). Since the variation of $w_{e}$ can be experimentally cumbersome, we also suggest varying $h_{\alpha}(\lambda)$ via the applied Raman laser wavelength $\lambda$ during 1LRT. In this regard, we present proof-of-principle 1LRT measurements, yielding a step-like $\kappa_{eff}(\lambda)$ trend for four different $\lambda$ values, which we also interpret in terms of quasi-ballistic phonon transport. Our results shall seed future PMFP spectroscopy based on 1LRT, which can directly be benchmarked against state-of-art theory by comparison of $\kappa_{\text{cum}}$ trends and not only $\kappa$ values, aiming to test our understanding of the intricate phonon transport physics.