Numerical modeling of 3‐D comb drive electrostatic accelerometers structure (method of levitation force reduction)

Abstract

Purpose -The purpose of this paper is to discuss the numerical modelling of 3D structure of micro-electro-mechanical systems (MEMS) accelerometers. The general idea being discussed is the method of levitation force reduction, as the main source of incorrect mathematical model of comb drive structure. Design/methodology/approach -Accelerometers design is a highly interdisciplinary area and, therefore, different methods and tools have to be exploited. Dynamic accelerometer behaviour modelling has been performed by use of a new object-oriented model (NOOM), based on complex computer field and mechanical models. Findings -The paper describes methods of levitation force reduction in electrostatic comb drive structures based on electrostatic structural models and finite elements method. Research limitations/implications -In the present work, the authors limit themselves to the electrostatic energy domains. Practical implications -Both, mechanical and electric models of accelerometers give the input data for defining the object-oriented model, based on Matlab-Simulink platform, fulfilling the general demand of dynamic behaviour simulation of comb drive structure. The proposed by authors methodology could give valuable contribution to MEMS design methodology. Originality/value -A new methodology has been successfully applied to calculation of levitation force in different geometries of comb drive. This methodology could be useful for multidisciplinary MEMS systems.

Optimal shape design of electrostatic microactuators: A multiobjective formulation

“…On the other hand, fostered by the development of new technologies, perspective applications of microactuators, or in general micro-electro-mechanical systems (MEMS), appear more and more in the market. Only in more recent times, however, has the design of MEMS been approached in a systematic way employing automated optimal design [1,8,15]: this trend shortens the gap between academic and industrial research. Following this approach, the design problem is set up as a problem of multivariable non-linear optimization of multiple objective functions subject to a set of constraints.…”

“…Analysing a full multiphysics model at the micro-scale level, encompassing electrostatic and mechanical phenomena, and more generally thermodynamics and fluid dynamics equations, might be computationally unpractical or even prohibitive in terms of cost. So, model complexity should be increased gradually; in this respect, an interesting method based on an object-oriented modelling was recently proposed [8].…”

“…the z-directed force density per unit voltage [NV −2 m −1 ]. Both f 1 and f 2 are subject to the solution of the field analysis problem.A prototype model of comb drive device used as an accelerometer[8], characterized by…”

Evolutionary Computing and Optimal Design of MEMS

“…elsewhere on the boundary, with thermal conductivity k = 401 W·m −1 ·K −1 , convection factor h = 5 W·m −2 ·K −1 and T ∞ = 298 K. It can be remarked that the right-hand side of (10) depends on the solution to (8), and-conversely-the lefthand side of (8) depends on the solution to (10) through (9); therefore, a coupled-field boundary-value problem originates. Finally, the Lamé's equation governing the vector displacement u is considered (λ + μ)∇ ∇ · u + μΔu = (3λ + 2μ)β∇T (12) with Lamé's constants λ = 95.149 × 10 9 Pa and μ = 44.776 × 10 9 Pa, corresponding to Young's modulus E = 120 × 10 9 Pa and Poisson's coefficient ν = 0.34, respectively; the thermal expansion coefficient is β = 16.5 × 10 −6 K −1 .…”

“…1), characterized by (w m , w f , h m , h f ) = (4, 4, 2, 2) (in micrometers), where w and h are width and height of the movable (m) and the fixed ( f ) electrodes, respectively, is assumed as the first case study [8]. The device exhibits 10 + 9 electrodes and the corresponding distribution of electric potential u is shown in Fig.…”