Zheng Xiande, Liu Ying, Qiu Jing, Liu Guanjun
College of Intelligence Science and Technology, National University of Defense Technology, Changsha 400713, China.
Nanomaterials (Basel). 2022 Aug 16;12(16):2807. doi: 10.3390/nano12162807.
Nanomechanical resonators offer brilliant mass and force sensitivity applied in many fields, owing to a low mass m and high-quality factor Q. However, in vibrating process, resonant energy is inevitably dissipated. Typically, quality factor does not surpass the inverse of the material loss angle φ. Recently, some exceptions emerged in the use of highly stressed silicon nitride material. As yet, it is interpreted that the pre-stress seems to "dilute" the intrinsic energy dissipation according to the Zener model. Is there any other material that could further break the 1/φ limit and achieve higher quality factors? In our previous research, through theoretical calculation and finite element simulation, we have proved that graphene's quality factor is two orders of magnitude larger than silicon nitride, on account of the extremely thin thickness of graphene. Based on this, we further optimize the structure of phononic crystals to achieve higher quality factors, in terms of duty cycle and cell size. Through simulation analysis, the quality factor could improve with a larger duty cycle and bigger cell size of triangular lattice phononic crystal. Unexpectedly, the Q amplification coefficient of the 3 × 5-cell structure, which is the least number to compose a phononic crystal with a central defect area, is the highest. In contrast, the minimal cell-number structure in hexagonal lattice could not achieve the brilliant dissipation dilution effect as well as the triangular one. Then we consider how overall size and stress influence quality factor and, furthermore, compare theoretical calculation and finite simulation. Lastly, we start from the primitive 3 × 5 cells, constantly adding cells to the periphery. Through simulation, to our surprise, the largest Q amplification coefficient does not belong to the largest structure, instead originating from the moderate one consisting of 7 × 13 cells.
纳米机械谐振器由于其低质量m和高品质因数Q，在许多领域具有出色的质量和力灵敏度。然而，在振动过程中，谐振能量不可避免地会耗散。通常，品质因数不会超过材料损耗角φ的倒数。最近，在使用高应力氮化硅材料时出现了一些例外情况。迄今为止，根据齐纳模型，预应力似乎“稀释”了固有能量耗散。是否有其他材料可以进一步突破1/φ的限制并实现更高的品质因数？在我们之前的研究中，通过理论计算和有限元模拟，我们已经证明，由于石墨烯的厚度极薄，其品质因数比氮化硅大两个数量级。基于此，我们进一步优化声子晶体的结构，以在占空比和晶胞尺寸方面实现更高的品质因数。通过模拟分析，对于三角晶格声子晶体，品质因数可以随着占空比的增大和晶胞尺寸的增大而提高。出乎意料的是，由3×5个晶胞组成的具有中心缺陷区域的声子晶体结构（这是构成声子晶体所需的最少晶胞数）的Q放大系数最高。相比之下，六边形晶格中的最小晶胞数结构无法像三角形晶格那样实现出色的耗散稀释效果。然后我们考虑整体尺寸和应力如何影响品质因数，并进一步比较理论计算和有限元模拟。最后，我们从原始的3×5个晶胞开始，不断地在其外围添加晶胞。通过模拟，令我们惊讶的是，最大的Q放大系数并不属于最大的结构，而是来自由7×13个晶胞组成的中等结构。
