Design of Micromachined Ultrasonic Transducers for Variability with the Sample-Average Approximation Method

Inhalt:
Variability in the outcome of microfabrication processes may lead to a significant deviation in the performance of MEMS devices with respect to their nominal design. Seeking to design MEMS under such variable conditions, some authors have implemented techniques from stochastic programming, such as posynomial programming or a multi-objective genetic algorithm. Here we implement the technique of “Sample-Average Approximation” (SAA), which, unlike the previously mentioned methods, does not require an analytic formulation with posynomials nor knowledge from the gradient of the objective function. The formulation with SAA enables, thus, the implementation of a single-objective genetic algorithm such as CMA-ES, which can be seamlessly coupled to a numerical model (e.g. a finite-element simulation). We present the application of this methodology for the design of a micromachined ultrasonic transducer (MUT), which involves more constraints than the documented cases of resonators. By incorporating a holistic model of the MUT, we achieved a robust design that considers nonlinear effects (e.g. pull-in), technological constraints, acoustic loss mechanisms, and process variations.