A Limiting Model for MEMS with Heterogeneous Dielectric Properties
Idealized microelectromechanical systems (MEMS) consist of two dielectric plates: a rigid ground plate above which an elastic plate is suspended. The elastic plate deforms due to a Coulomb force induced by a voltage difference applied between the two components. Coating the ground plate with an insulating layer prevents direct contact between the plates.
Overview
Due to the presence of this layer, the MEMS device features heterogeneous dielectric properties, and the electrostatic potential solves a free boundary transmission problem in the non-smooth domain enclosed between the two plates. The shape of the domain itself is given by a partial differential equation governing the deflection of the elastic plate from rest, which, in turn, involves the electrostatic force exerted on it. By letting the thickness of the insulating layer go to zero, we derive a reduced model that retains the dielectric heterogeneity of the device. For this reduced model, we show the existence of a particular class of stationary solutions, which are additionally energy minimizers.
Presenters
Brief Biography
Katerina Nik is an assistant professor of Applied Mathematics and Computational Sciences (AMCS) in the Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division at KAUST. Her work focuses on partial differential equations that describe phenomena in biological growth processes, fluid dynamics, and mechanical engineering. She joined KAUST in 2024 after contributing to research at prominent European institutions.
Prior to joining KAUST, Dr. Nik worked as a principal investigator at the Austrian Academy of Sciences, supported by the APART-MINT Fellowship, which enabled her to lead innovative research in applied mathematics. Before this, she was a postdoctoral researcher at the Delft Institute of Applied Mathematics, TU Delft, where she collaborated with Professor Manuel Gnann's group. She also served as a postdoctoral researcher at the Faculty of Mathematics, University of Vienna, Austria, working with Professor Ulisse Stefanelli from 2020 to 2024.
Earlier in her career, she was a research and teaching assistant at Leibniz University Hannover (LUH), Germany, where she completed her doctorate in mathematics. Her academic contributions during this period focused on nonlinear dynamics and the modeling of complex systems.