Investigation of full bandgaps in silicon phononic crystal membranes with tungsten and air inclusions

It has been observed experimentally that solid-solid PnCs have larger bandgaps for a wide range of hole radii and slab thicknesses than their solid-air counterparts. Here, we theoretically investigate the optimal hole radius and thickness parameters for full bandgap formation (accounting for all transverse and longitudinal modes) in PnCs formed from a Si matrix with a square-lattice of W inclusions. The plane-wave expansion technique was used to calculate the dispersion behavior for in-plane and out-of-plane transverse and longitudinal (flexural) modes, implementing a supercell method to account for the finite third dimension. The results are compared with those for a PnC composed of air holes in a Si matrix.