In Chapters 1 to 9, we developed theories to explain the mechanical and electrical behavior of MEMS, and described the static and dynamic responses of actuators by combining the theories. In MEMS, sensors are used to measure physical quantities that are usually converted to electrical signals. Combining the theories described in the foregoing chapters, we can develop governing equations for sensors and solve the equations for sensor responses. Since most MEMS sensors measure a force (equivalently, stress or strain) in response to a physical quantity that we wish to measure, we first describe force sensors and then deal with accelerometers and gyroscopes, which are sensors based on the measurement of inertial force. Even though we describe force sensors, accelerometers, and gyroscopes, theories regarding sensors are not limited to these sensors but can be extended to include sensors whose behavior can be described by the theories developed in the previous and present chapters.
10.1 FORCE AND PRESSURE SENSORS
Let us consider the elastic body in Fig. 10.1, where the elastic body is placed on a substrate and subjected to a force F. To maintain equilibrium, stresses inside the body are developed and the body is then deformed. If the body is linear, the stress (or strain) developed can be expressed as a function of the applied force F, the geometry, and material properties such as Young’s modulus and Poisson’s ratio. For example, if we measure the strain at point 1 ...