Quality Factor Comparison between Graphene and Sin with Triangular Lattice Phononic Crystal Structure Based on Dissipation Dilution Theory

Nanomechanical resonators attract interests both in fundamental and applied fields, offering outstanding mass and force sensitivity, relying on both the low mass m and high quality factor Q. However, the quality factor typically does not exceed the inverse of the material loss angle φ, related to resonant energy dissipation. Recently, some exceptions breaking the 1/φ limiting rule in a great extent have been reported in use of highly stressed silicon nitride material. Up to now it is interpreted that the pre-stress seems to ‘dilute’ the intrinsic energy dissipation according to Zener model. Dissipation dilution effect could be better if the device dimension is reduced, which implies that the smaller the resonator, the higher the quality factor. Single-layer graphene's thickness is 0.335 nm, which is one hundredth of silicon nitride’ typical thickness about 30 nm, indicating that the dissipation dilution effect of graphene could be much better than that of silicon nitride. Through theoretical calculation, the quality factor amplification coefficient defining the dissipation dilution effect quantitatively of graphene is 2272 times that of SiN. By COMSOL finite element simulation, we further confirm this conclusion. Take the first defect mode for example, the amplification coefficient of graphene and SiN is about 3.02 × 105 and 151 respectively, with the division result about 2004 times. As the overall size increases, the division results gradually converge to a stable value about 2260.