Design and implementation of graphene nano-electromechanical resonator via soft-clamped phononic crystals based on dissipation dilution theory
The low-quality factor at room temperature is the key bottleneck for employing graphene nano-electromechanical resonators for engineering and commercial applications.This phenomenon is challenging to explain convincingly using a dissipation mechanism dominated by ohmic loss.The mechanical loss remains a potential candidate for improving the stress tunable quality factor of graphene resonators.The dissipation dilution theory reveals the intrinsic energy distribution and dissipation mechanism for traditionally stressed silicon-based resonators with high-quality factors.This reasoning is considered for graphene-related two-dimensional materials dominated by mechanical loss.Based on Zener's model of elasticity,the energy distribution and dissipation characteristics of high-stress graphene are comparatively analyzed using the thin-plate and thin-membrane models.The results reveal that the bending energy at the boundary plays a dominant role in the total bending energy of the graphene resonator,and the thin-plate model is much more suitable for analyzing the energy dissipation characteristics of the resonator.By combining the dissipation dilution theory and bending stiffness characteristics of graphene,the dissipation dilution theoretical model of the graphene nano-electromechanical resonator is constructed,and the dissipation dilution mechanism of the soft-clamped phononic crystal(PnC)is proposed.The graphene nano-electromechanical resonator with a single-cell PnC soft clamp was constructed,considering the triangular lattice as the block to build the phononic crystal.The simulation confirms the existence of localized mode(LM),which has an amplification factor of the quality factor nearly five times higher than that of nonlocal modes.This proves the effectiveness of the PnC soft clamp design for improving the quality factor of the resonator.The mechanism of vibration energy localization and dissipation suppression of the PnC soft clamp is explained by analyzing the vibration amplitude and curvature distribution of the LM.The relationship between the amplification factor of the quality factor and the cell number of PnC is simulated and analyzed.Results demonstrated that only 2-3 layers of PnC are required to obtain a better localization effect,providing an important foundation for designing resonators.For the design scheme,an inverted-floating method is proposed for fabricating large-scale suspended graphene,and the focus ion beam(FIB)etch process is proposed for graphene PnC structure;they are successfully applied for the development of the PnC soft-clamped graphene nano-electromechanical resonator.The resonant test results showed that the quality factor of the PnC soft-clamped graphene resonator is 2.5 times that of the graphene drum resonator,verifying the effectiveness of the PnC structure in suppressing dissipation and improving the quality factor.The graphene dissipation dilution theoretical model and soft-clamped PnC dissipation dilution mechanism established in this paper offer a novel approach for examining the dissipation characteristics of graphene nano-electromechanical resonators.Additionally,the PnC soft-clamped graphene nano-electromechanical resonators provide a new platform and method for investigating the resonance characteristics and dissipation mechanisms of resonators.
graphenedissipation dilutionquality factorphononic crystalfocus ion beam
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