  The impact of lattice type, period, porosity and thickness of two-dimensional
silicon phononic crystals on the reduction of thermal conductance by coherent
modification of phonon dispersion is investigated using the theory of
elasticity and finite element method. Increase in the period and porosity of
the phononic crystal affects the group velocity and phonon density of states
and, as a consequence, reduces the in-plane thermal conductance of the
structure as compared to unpatterned membrane. This reduction does not depend
significantly on the lattice type and thickness of phononic crystals. Moreover,
the reduction is strongly temperature dependent and strengthens as the
temperature is increased.
