Touchdown and pull-in voltage behavior of a MEMS device with varying dielectric properties
Touchdown and pull-in voltage behavior of a MEMS device with varying dielectric properties
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DOI：
10.1137/040613391
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发表时间：
2005-01-01
影响因子：
1.9
通讯作者：
Ward, MJ
中科院分区：
文献类型：
--
作者：
Guo, YJ;Pan, ZG;Ward, MJ
分析了一个简单的MEMS器件的吸合电压不稳定性，该器件由一个支撑在刚性导电接地板上的薄电介质弹性膜组成。膜的上表面涂覆有薄导电膜。在代表薄器件的某个渐近极限中，数学模型由薄电介质膜的偏转的非线性偏微分方程组成。当电压V施加到导电膜时，介电膜朝向底板偏转。对于平板、圆柱和正方形区域，给出了鞍结分叉值V-* 的数值结果，V-* 也称为吸合电压，对于V > V-*，没有稳态膜偏转。当V > V-* 时，数值结果表明，薄膜的动态特性是薄介质膜接触下板无限长时间。结果给出了在薄介质膜的空间均匀和非均匀的介电常数分布。通过允许空间非均匀的介电常数pro。LE，它示出的吸合电压不稳定性可以延迟，直到更大的值的V和更大的吸合距离可以实现。给出了两类空间可变介电常数分布的吸合电压V-* 的解析界。特别是，严格的分析界V-1，这取决于类的介电常数亲。即，在V > V-1 > V-* 范围内，膜的挠度不存在稳态解，且发生有限时间触地。对V > V-1和V-* < V < V-1两种情况下的触地行为进行了数值计算，并给出了触地过程的渐近结构。即，给出了空间均匀和空间非均匀的介电常数分布。
The pull-in voltage instability associated with a simple MEMS device, consisting of a thin dielectric elastic membrane supported above a rigid conducting ground plate, is analyzed. The upper surface of the membrane is coated with a thin conducting film. In a certain asymptotic limit representing a thin device, the mathematical model consists of a nonlinear partial differential equation for the deflection of the thin dielectric membrane. When a voltage V is applied to the conducting film, the dielectric membrane deflects towards the bottom plate. For a slab, a circular cylindrical, and a square domain, numerical results are given for the saddle-node bifurcation value V-*, also referred to as the pull-in voltage, for which there is no steady-state membrane deflection for V > V-*. For V > V-* it is shown numerically that the membrane dynamics are such that the thin dielectric membrane touches the lower plate infinite time. Results are given for both spatially uniform and nonuniform dielectric permittivity profiles in the thin dielectric membrane. By allowing for a spatially nonuniform permittivity pro. le, it is shown that the pull-in voltage instability can be delayed until larger values of V and that greater pull-in distances can be achieved. Analytical bounds are given for the pull-in voltage V-* for two classes of spatially variable permittivity profiles. In particular, a rigorous analytical bound V-1, which depends on the class of permittivity pro. le, is derived that guarantees for the range V > V-1 > V-* that there is no steady-state solution for the membrane deflection and that finite-time touchdown occurs. Numerical results for touchdown behavior, both for V > V-1 and for V-* < V < V-1, together with an asymptotic construction of the touchdown pro. le, are given for both a spatially uniform and a spatially nonuniform permittivity profile.