Modeling and designing quadratic membrane structures

Abstract

Membrane structures are one of the most common elements in microsystems. In order to perform system simulations, behavioral models of their bending lines have to be developed. These models may also be used as a basis for parameter extractions, which is a crucial task in the development of microsystems. But parameter extractions can only be performed, if the models used include all of the most important physical effects. Hence the physical basis of these models has to be very profound.Usually a distinction is made between small and large deflections [Engineering Mechanics Series, 2nd ed. (1959)] and only one of these cases is taken into consideration in today's behavioral models of membrane structures. Since some systems' range of operation includes both kinds of deflection, models are needed which take both cases into account. The paper presents the theoretical basis for this task. The solution is partially based on the results of [J. Microelectromech. Syst. 4 (4) (1995) 238] and the behavioral model only calls for one heuristic parameter that was introduced in [Int. Conf. Model. Simul. Microsyst. Puerto Rico, 1 (1999) 237]. All the other quantities are purely physical parameters. Evaluations of this model have been done using measured data of a capacitive pressure sensor. Finally design optimizations could be carried out in order to increase the sensor's sensitivity as much as possible.