To pave the way for system-on-chip MEMS confinement up to 50 GHz, the mechanical properties of a CMOS back-end-of-line (BEOL) are studied by analytic and finite element approaches. In particular, the two main directions of vertical and horizontal wave propagation are investigated. With respect to the symmetry of the BEOL, the movement through the nonperiodic horizontal layers is described by the Rayleigh-Lamb equation. It is shown that our finite element method (FEM) approach, preventing Brillouin zone folding, can be employed in simulations of these structures, since the results are in excellent accordance to the corresponding analytical solutions. The vertical propagation through the periodic stack on the other hand is subject to phononic crystal effects resulting in Bragg-like band gaps (BGs) for either a certain or every polarization. Factoring in both types of propagation, it is demonstrated by our FEM simulations how these BGs can be tailored to specific values through variations in the BEOL layers to improve the quality factor of monolithically integrated MEMS devices.

中文翻译：

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用于单片高 Q MEMS 谐振器限制的 CMOS 后端中的偏振无关带隙

为了为高达 50 GHz 的片上系统 MEMS 限制铺平道路，通过分析和有限元方法研究了 CMOS 后端 (BEOL) 的机械特性。特别地，研究了垂直和水平波传播的两个主要方向。关于 BEOL 的对称性，通过非周期性水平层的运动由 Rayleigh-Lamb 方程描述。结果表明，我们的有限元方法 (FEM) 方法可以防止布里渊区折叠，可用于这些结构的模拟，因为结果与相应的解析解非常吻合。另一方面，通过周期性堆叠的垂直传播受到声子晶体效应的影响，导致对于某个极化或每个极化产生类似布拉格的带隙 (BG)。