Phonon mean free path spectroscopy by Raman thermometry

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 during thermal reflectance measurements in the time or frequency domain (TDTR and FDTR) and transient thermal grating (TTG) spectroscopy. In place of l, we vary the laser focus spot size (w) and the light penetration depth (h) during one-laser Raman thermometry (1LRT) measurements, enabling control over the size of the temperature probe volume V. For our largest w values, the derived effective thermal conductivities κ converge towards the bulk thermal conductivity κ for silicon, which we confirm by two-laser Raman thermometry and ab initio theory. However, towards smaller w values, we observe a pronounced increase for the κ values, which amounts up to a factor of 5.3 at 293 K and even 8.3 at 200 K. We mainly assign this phenomenon to quasi-ballistic phonon transport and discuss any prominent impact of other factors. As a result, we can compare our measured κ(w) trends with the thermal accumulation function κ and its dependence on the phonon mean free path l, which we derive from ab initio solutions of the linearized phonon Boltzmann transport equation (BTE). Since the variation of w can be experimentally cumbersome, we also suggest varying h(λ) via the applied Raman laser wavelength λ during 1LRT. In this regard, we present proof-of-principle 1LRT measurements, yielding a step-like κ(λ) trend for four different λ values, which we also interpret in terms of quasi-ballistic phonon transport. Interestingly, we find that our κ(w) scaling is opposite to previous TTG results, which can be explained by the actual physical quantity probed. For small w or h values, 1LRT mimics the situation of a local and/or surfacic heat source in a large matrix, which enables probing of real local κ values that exceed κ. From a theoretical point of view, this was first predicted by Chiloyan et al., (2020), who calculated κ(w) for different initial phonon distributions in good agreement with our data. To show the generality of our findings, we probed κ(w) not only for bulk silicon, but also germanium, which is in-line with our previous findings on GaN, see Elhajhasan et al., (2023). Our results shall seed future PMFP spectroscopy based on 1LRT, which can directly be benchmarked against state-of-art theory to probe the effect of, e.g., any nano-structuring by comparison of κ trends and not only κ values, aiming to test our understanding of the intricate phonon transport physics.