On calculating the radiated ballistic phonon power in phononic crystal membranes

摘要

Phononic crystals are periodically modified structures, where the phonon spectra (dispersion relations) are strongly modified due to interference, or Bragg reflections. In all practical cases, the resulting dispersion relations have to be calculated numerically, using for example the finite difference or the finite element method. We show that if one uses the results of finite element modeling directly in the calculation of phonon group velocities, a sizeable numerical error in the calculation of thermal conductance or radiated power can easily follow. We introduce here a sorting algorithm for the eigenfrequency surfaces to reduce this error, which arises from the discretization of the k-space points.