Phonon Mean Free Path Spectrum of Single Crystalline Silicon Thin Film

Abstract

With the advanced fabrication technology, the density of transistor keeps increasing and the design is getting more complexed. Fourier’s law, which is applied for heat conduction in bulk materials, becomes unsuitable for thermal transport at this micro- and nano-scale system. 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 modeling thermal management and designing thermoelectric materials. To predict the extent of thermal conductivity reduction via nanostructuring, it is significantly crucial to figure out the contribution of each MFP to thermal conductivity, which is knowon as phonon MFP spectrum. Thus, there have been numerous theoretical and experimental studies up to date. The 1st principle calculation has been successful to predict the MFP spectrum for simple atomic structures such as Si, Ge, and etc. However, it is challenging and time consuming to extend the same approach to nanostructures. Among experimental approaches, the TDTR (time-domain thermoreflectance) and TTG (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.e., 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, nanoslits with various widths, which were patterned on a suspended silicon nano-film using EBL (e-beam lithography) and RIE (reactive ion etching process), provided varied ballistic thermal resistances. The effective thermal conductivity values of nanoslit-films were measured in a temperature range of 40–300 K using micro-suspended devices, which were individually fabricated from SOI (silicon-on-insulator) wafer. Additionally, to better understand the measurement results, discrete ordinate method was used with inputs by 1st principle calculation. 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. This study offers, for the first time, the phonon MFP spectrum for Si thin film using a non-optical experimental approach.