基于耗散稀释理论的声子晶体软支撑石墨烯纳机电谐振器设计与实现

Design and implementation of graphene nano-electromechanical resonator via soft-clamped phononic crystals based on dissipation dilution theory

室温品质因数低下是石墨烯纳机电谐振器走向工程应用面临的关键瓶颈,欧姆损耗难以完全解释石墨烯室温低品质因数以及品质因数应力调控现象.耗散稀释理论揭示了传统高应力硅基谐振器品质因数调控的内在能量及耗散机制,有望适用于石墨烯类二维材料体系.本文基于Zener滞弹性理论,对比分析高应力石墨烯薄板-薄膜模型下的能量分布与耗散特性,揭示边界处弯曲势能在总弯曲势能中的主导作用,指出薄板模型更适宜分析谐振器能量耗散特性.基于耗散稀释理论,结合石墨烯弯曲刚度特性,构建石墨烯纳机电谐振器耗散稀释理论模型,提出声子晶体软支撑耗散稀释机制.采用三角晶格晶胞构建声子晶体,并以此构建声子晶体软支撑石墨烯纳机电谐振器,仿真验证局域态的存在且其品质因数放大因子高于非局域态近5倍,证明了声子晶体软支撑设计提高品质因数的有效性.通过分析局域态的振幅与曲率分布,解释了声子晶体软支撑局域振动能量、抑制耗散的机制.仿真分析品质因数放大因子与软支撑声子晶体层数关系,研究发现仅需2~3层声子晶体即可实现较优局域效果,对谐振器设计具有重要指导意义.针对设计方案,提出了大规模悬空石墨烯背浮法制备工艺与石墨烯声子晶体软支撑结构FIB刻蚀工艺,成功实现了声子晶体软支撑石墨烯纳机电谐振器的制备.扫频测试结果表明,声子晶体软支撑石墨烯谐振器品质因数为圆形鼓膜石墨烯谐振器的2.5倍,验证了声子晶体软支撑结构抑制耗散提高品质因数的有效性.本文所建立石墨烯耗散稀释理论模型与声子晶体软支撑耗散稀释机制为石墨烯纳机电谐振器耗散特性研究提供了新思路,所研制声子晶体软支撑石墨烯纳机电谐振器为石墨烯纳机电谐振器谐振特性分析、耗散机制研究提供了新平台和新方法.

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 twodimensional 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 nanoelectromechanical 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 sof-clamped graphene nano-electromechanical resonators provide a new platform and method for investigating the resonance characteristics and dissipation mechanisms of resonators.