For higher temperatures, the temperature dependence deviates from linearity and fractons cannot be considered as the dominant mechanism. Our experimental results for highly porous Si at temperatures higher than 100 K [18] were fitted by models considering a simplified porous Si structure, as for example the phonon diffusion model by Gesele et al. [17] and the phonon hydrodynamic model by Alvarez et al. [48]. A comparison of our experimental results with the above models was made in [18]. Very good agreement with the phonon diffusion model was obtained for temperatures in the range 200 to 350 K, while a better qualitative description of the temperature dependence

of k in a larger temperature range (100 to 350 K) was obtained with the phonon hydrodynamic approach. We have to note here that LY3023414 nmr discrepancies CHIR-99021 cell line between the experimental results and the different theoretical models as the ones above are

mainly due to the very complicated structure of porous Si, which is not fully taken into account by the models. Nanostructured porous Si is composed of interconnected Si nanowires and nanocrystals, covered by a native oxide shell and separated by voids. The ratio of the native oxide compared to the Si core plays a critical OSI-027 order role in the determination of the mechanism of thermal conduction in the different temperature ranges, especially at cryogenic temperatures [49]. This is because of the different temperature dependence of vibrational modes in the two systems (the Si backbone and the shell oxide). Conclusions The thermal conductivity of 63% porosity nanostructured porous Si was measured for the first time in the cryogenic temperature range 5 to 20 K. A stable value as low as 0.04 W/m.K was obtained in this temperature range. We attribute the plateau-like behavior of our porous Si material at cryogenic temperatures to the presence of fractons, which are localized anomalous vibrational modes according to the scaling theory Celastrol of localization of Rammal and

Toulouse. We discussed in detail the specific fractal geometry of our porous Si system and its fractal dimensionality that supports the adoption of the fracton formalism. Literature results demonstrated the existence of the so-called Boson peak in the micro-Raman spectra of porous Si with a similar porosity than that of the porous Si layer used in this work. The existence of this peak in a material is in general considered as a signature of the presence of localized vibrational modes (‘fractons’ in a fractal lattice). In addition, literature results of Brillouin spectra of porous Si also showed localized vibrational modes that support our interpretation. Above the plateau and up to approximately 100 K, an almost linear increase with temperature was obtained for our highly porous Si material, as that obtained in amorphous materials and attributed to the anharmonic interaction between fractons and phonons.