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Probabilistic prediction of the quality factor of micro-resonator using a stochastic thermo-mechanical multi-scale approach

机译:随机热机械多尺度方法对微谐振器品质因数的概率预测

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摘要

As the size of the device is only one or two orders of magnitude higher than the size of the grains, the structural properties, such as the thermo-elastic quality factor (Q), of micro-electro-mechanical systems (MEMS) made of poly- crystalline materials exhibit a scatter, due to the existing randomness in the grain size, grain orientation, surface roughness. In order to predict the probabilistic behavior of micro-resonators, the authors extend herein a previously developed stochastic 3-scale approach to the case of thermoelastic damping. In this method, stochastic volume elements (SVEs) are defined by considering random grain orientations in a tessellation. For each SVE realization, the mesoscopic apparent elasticity tensor, thermal conductivity tensor, and thermal dilatation tensor can be obtained using thermo-mechanical computational homogenization theory. The extracted mesoscopic apparent properties tensors can then be used to define a spatially correlated mesoscale random field, which is in turn used as input for stochastic finite element simulations. As a result, the probabilistic distribution of the quality factor of micro-resonator can be extracted by considering Monte-Carlo simulations of coarse-meshed micro-resonators, accounting implicitly for the random microstructure of the poly-silicon material.
机译:由于器件的尺寸仅比晶粒的尺寸高一个或两个数量级,因此由微机电系统(MEMS)制成的结构特性(例如热弹性品质因数(Q))由于晶粒尺寸,晶粒取向,表面粗糙度方面存在随机性,多晶材料表现出分散性。为了预测微谐振器的概率行为,作者在这里将先前开发的随机三尺度方法扩展到热弹性阻尼的情况。在这种方法中,通过考虑镶嵌中的随机晶粒方向来定义随机体积元素(SVE)。对于每个SVE实现,可以使用热机械计算均化理论获得介观表观弹性张量,导热系数张量和热膨胀张量。然后,提取的介观表观特性张量可用于定义空间相关的介观随机场,该场又用作随机有限元模拟的输入。结果,可以通过考虑粗网格微谐振器的蒙特卡洛模拟来提取微谐振器的品质因数的概率分布,这隐含地考虑了多晶硅材料的随机微观结构。

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