Stochastic estimation of microactuator buckling

In order to make a robust design of microsystems, it is important to analyze the electrical, thermal and mechanical fields including the actual input parameters. These microdevices, which typically are made of brittle materials such as polysilicon, show wide scatter (stochastic behavior) in properties as well as substantial uncertainty in the shape and geometry because of manufacturing processes. These behaviors necessitate either costly and time-consuming trial-and-error designs or, more efficiently, the development of a probabilistic design methodology for MEMS. Computer aided MEMS simulations regarding performance, power consumption, and reliability is an important design task due to high prototyping costs. Since microbeams have a wide range of applications in MEMS actuation mechanisms, analysis of the thermomechanical behavior of these actuators is very important. In the present work, assessing meaningful uncertainties involved in thermally driven microbeams, the stochastic finite element model (SFEM) is developed and implemented. The analysis shows a large deviation in buckling temperature and thermal stresses for reasonable probability density functions of characteristic parameters. Although computationally significantly more expensive than deterministic electromechanical simulation, the work illustrates the requirement of stochastic modeling for true estimation of microsystems' performance