The impact of lattice type, period, porosity and thickness of two-dimensionalsilicon phononic crystals on the reduction of thermal conductance by coherentmodification of phonon dispersion is investigated using the theory ofelasticity and finite element method. Increase in the period and porosity ofthe phononic crystal affects the group velocity and phonon density of statesand, as a consequence, reduces the in-plane thermal conductance of thestructure as compared to unpatterned membrane. This reduction does not dependsignificantly on the lattice type and thickness of phononic crystals. Moreover,the reduction is strongly temperature dependent and strengthens as thetemperature is increased.
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