Temperature Profile for Ballistic and Diffusive Phonon Transport in a Suspended Membrane with a Radial Symmetric Heat Source

TL;DR

This paper compares ballistic and diffusive phonon heat transport in a suspended membrane with a radial heat source, showing how temperature profiles can distinguish these mechanisms and validating models with experimental data.

Contribution

It provides a theoretical comparison of ballistic and diffusive phonon transport in membranes and validates the ballistic model with experimental measurements.

Findings

Temperature profiles differ significantly between ballistic and diffusive transport.

Experimental data aligns qualitatively with the ballistic transport model.

Models can distinguish transport mechanisms based on temperature profiles.

Abstract

We have calculated the temperature profiles for phonon heat transport in a suspended membrane with a radially symmetric heat source in the two extreme cases of either fully ballistic or fully diffusive transport. Theoretical results confirm that it is possible to distinguish these two transport mechanisms from the radial temperature profiles alone. Models are also compared to experimental data measured with 40 nm thick, free standing silicon nitride membranes below 1 K by using tunnel junction (SINIS) thermometers. The measured temperature profile is qualitatively in agreement with the ballistic model.