MATHEMATICAL PROOF WHY CRYSTALLOGRAPHIC PLANE (111) IS BETTER FOR MICROELECTROMECHANICAL SENSORS SENSING ELEMENTS.

In this research we have obtained mathematical relations between elastic constants, such as Young's modulus and Poisson's ratio, using single-crystalline silicon as an example. When the obtained relations are fulfilled, the influence of misalignment of the crystallographic directions and the coordinate axes associated with the sensing element of microelectromechanical sensors on the stress-strain state and natural frequencies of sensing element will be minimal. Therefore, the influence of such misalignment on the performance of microelectromechanical sensors will also be minimized. Elastic constants of the most commonly used crystallographic planes in microelectromechanical sensor’s design have been analyzed. It has been shown that the elastic constants of crystallographic plane (111) completely conform to the obtained relations, that makes use of crystallographic plane (111) preferable in terms of minimization of the effects of errors in orientation of coordinate axes relative to the crystal structure. [ABSTRACT FROM AUTHOR]