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

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.