Phonon Mean Free Path Spectra of Single Crystalline Silicon Thin Film

Fourier’s law, which is applied for heat conduction in bulk materials, becomes unsuitable for thermal transport at the nanoscale. Especially, when phonon mean free path (MFP) is longer than the characteristic length of a system, phonons in the system tends to be scattered significantly at the boundary, leading to the reduction of thermal conductivity. Therefore, nanostructuring is one of attractive ways to manipulate the thermal conductivity of material in some applications such as thermoelectric devices and thermal insulators. To predict the extent of thermal conductivity reduction <i>via</i> nanostructuring, it is significantly crucial to figure out the contribution of each MFP to thermal conductivity, which is phonon MFP spectrum. Thus, there have been numerous theoretical and experimental studies up to date. The 1^st principle calculation has been successful to predict the MFP spectrum for simple atomic structures such as Si, Ge, and etc. Among experimental approaches, the time-domain thermoreflectance and thermal grating method are representative for this research but have some limitations. The former adopts a metal transducer, which makes the analysis complicated, and the latter is limited in decreasing the size of grating, <i>i.e.</i>, the characteristic length, due to the diffraction limit of light. Also, most of previous works have studied only about bulk-scale materials, even though modern micro- or nanoelectronic devices are often based on thin film structures. In this work, nanoslots with various widths, which were patterned on a suspended silicon film using a focused ion beam system, provided different ballistic thermal resistances. Undesired damages such as amorphization and redeposition were minimized by employing sacrificial Al layers. The effective thermal conductivities of films including nanoslots were measured in a temperature range of 40–300 K using suspended devices, which were individually fabricated from silicon-on-insulator (SOI) wafer. From the measurement results, the phonon MFP spectrum was extracted by a convex optimization, using suppression function obtained by solving freqeuency-independent Boltzmann transport equation. Additionally, to better understand the measurement results, discrete ordinate method was used with inputs by first principle calculation. This study offers, for the first time, the phonon MFP spectrum for thin films using a non-optical experimental approach.