Analysis of Band Structures of Nanosized Phononic Crystals by Nonlocal Elastic Theory

Based on the nonlocal elastic continuum theory, the band structures of the nano-sized layered phononic crystals are analyzed by computing the localization factors and dispersion curves. Detailed calculations are performed for a nanosized HfO2–ZrO2 periodic layer stack. The size-effect on the band structures is examined. It is found that the nonlocal elastic continuum solution deviates from the classical elastic continuum theory and finally approaches the first-principle result as the thickness of each individual layer decreases. Due to the size-effect, there exists a cut-off frequency beyond which the waves cannot propagate through the system.