556 radius 10.12 A micromirror optical actuator. A micromirror in the shape of a disk of 50 μm and thickness t - 1 µm is

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556 radius 10.12 A micromirror optical actuator. A micromirror in the shape of a disk of 50 μm and thickness t - 1 µm is supported at its center by a um nonconducting post made of SiO₂ (see Figure 10.52). The disk is coated with a thin aluminum deposition to create the reflecting surface and an aluminum layer is deposited on the substrate. The bottom of the disk is coated as well to create a continuous conducting surface. The actuation is Sensors, actuators, and their interfaces done electrostatically by applying a voltage V between the two aluminum surfaces. The distance between the two conducting layers is d - 3 µm. μm. Viewing the mirror as a thin disk made of silicon with a modulus of elasticity of 150 GPa and a Poisson ratio of 0.17, calculate the deflection of the edges of the mirror as a function of applied voltage. Neglect the thick- ness of the aluminum deposition.
Mirror Silicon Substrate 7