Modified Ballistic-Diffusive Equations for Obtaining Phonon Mean Free Path Spectrum from Ballistic Thermal Resistance: II. Derivation of Integral Equation Based on Ballistic Thermal Resistance

Abstract

Rebuilding phonon mean free path (MFP) spectra from experimental data is integral to phonon MFP spectroscopy. However, being based on effective thermal conductivity, the current integral equation for this precludes the use of certain heat sources of convenient shapes, such as a cylindrical nanoline. Herein, to enable using diverse specimens exhibiting a ballistic effect, we develop a ballistic thermal resistance-based integral equation, utilizing the ease and accuracy of the modified ballistic-diffusive equations demonstrated in the companion paper. The availability of more diverse shapes of specimens will enhance further development and widen use of phonon MFP spectroscopy.