Surface acoustic waves in finite-depth air/silicon phononic crystals

Phononic crystals (PnCs) can stop surface acoustic waves (SAW) at the band gap frequency range efficiently. Traditional two-dimensional PnCs for SAW have inclusions extending infinitely into the half-space. In fact, experimental specimens with finite-depth inclusions still showed the gaps. In this paper, the PnCs with finite-depth holes on the surface of silicon substrate were analyzed systematically. Dispersion curves were calculated and various SAW modes were identified. The boundary condition based on Bloch´s theorem with real wave vectors can identify band structures and the one with complex wave vectors can analyze attenuation of SAWs in PnC. The evolution of acoustic bands, gap range, and attenuation was reported. Then PnC reflective gratings for SAW could be designed properly for high efficiency.