Measurement and analysis of ballistic-diffusive phonon heat transport in a constrained silicon film

Highlights: • The thermal resistance of a constrained Si film was measured with a suspended microdevice. • Corresponding thermal analysis was performed based on the MBTE. • FEA was used to solve the BTE numerically for a 3D model of the constrained Si film. • The effect of ballistic phonon transport was increased at temperatures below 100 K. -- Abstract: A suspended microdevice was fabricated to measure the ballistic thermal resistance of a constrained silicon film, which had a cross-section of 4.6 μm × 210 nm and a length of 22 μm. To better understand this phenomenon, the frequency dependent Boltzmann transport equation was numerically solved for a three-dimensional model using finite element analysis combined with the discrete ordinate method and the frequency dependence of phonons, and this was compared to the calculation results based on a previous study involving the analytical solution of the modified Boltzmann transport equation. The effect of ballistic phonons at a nanoconstriction with a width of 160 nm was also predicted using two theoretical methods in order to more clearly estimate the effect of ballistic phonons.