NUMERICAL ANALYSIS OF PULL-IN VOLTAGE OF FIXED-FIXED BEAM MEMS ACTUATOR INCORPORATING MATERIAL AND GEOMETRY VARIATIONS

Abstract

Microelectromechanical systems (MEMS) electrostatically actuated fixed-fixed beam actuators are ubiquitous in RF switches, tunable varactors, resonant sensors, and optical micro-mirrors. The pull-in instability, the critical electromechanical event at which the electrostatic attractive force irreversibly overcomes the elastic restoring force of the beam defines the safe operating voltage ceiling of every such device and is the primary design constraint in MEMS electromechanical engineering. This thesis presents a systematic coupled electromechanical finite element investigation of fixed-fixed beam MEMS actuators in COMSOL Multiphysics v6. Three structural materials- gold (Au, E = 79GPa), molybdenum (Mo, E = 329GPa), and tungsten (W, E = 411GPa) are investigated for three beam lengths (100μm, 150μm, and 230μm), with a fixed cross-section of 7μm × 0.5μm and an initial air gap of 0.9μm, yielding nine simulation configurations. For each configuration, parametric voltage sweeps at 0.1V increments deliver: (i) the pull-in voltage; (ii) the mid-span displacement versus voltage curve; (iii) the peak von Mises stress versus voltage curve; (iv) the full arc-length displacement and stress profiles at pull-in; and (v) three-dimensional volumetric displacement and stress field renderings at representative intermediate voltages. Pull-in voltages range from 0.68 V (Au, 230μm) to 10.0 V (W, 100μm), a 14.7 fold span. The scaling law Vpi ∝ E (1/2) · L (-3/2) is confirmed across all nine configurations with R² ≥ 0.997 in log-log regression. The universal one-third gap pull-in criterion (mid span displacement = g₀/3 = 0.167μm) is verified for all configurations. Arc-length von Mises stress profiles exhibit a characteristic triple-lobe pattern with primary peaks at the anchor junctions 2.4-2.8× higher than the mid-span plateau, identifying the anchors as the fatigue-critical hot spots. Peak stresses at pull-in range from 2.1 MPa (Au, 230μm) to 28.0 MPa (W, 100μm), yielding stress safety margins of 24× to over 144× against material yield strengths. Three-dimensional field maps confirm that electromechanical instability 5 is the universal failure mode. Results are validated against published analytical models and experimental data from the literature, with agreement within 5%. The thesis provides a comprehensive parametric design database and scaling law verification for fixed-fixed beam MEMS actuators that are directly actionable by MEMS designers and process engineers engaged in RF switching, inertial sensing, and optical MEMS applications.