Estimating residual stress, curvature and boundary compliance of doubly clamped MEMS from their vibration response

Abstract

Structural parameters of doubly clamped microfabricated beams such as initial curvature, boundary compliance, thickness and mean residual stress are often critical to the performance of microelectromechanical systems (MEMS) and need to be estimated as a part of quality control of the microfabrication process. However, these parameters couple and influence many metrics of device response and thus are very difficult to disentangle and estimate using conventional methods such as the M-test, static mechanical tests, pull-in measurements or dynamic mechanical tests. Here we present a simple, non-destructive experimental method to extract these parameters based on the non-contact measurement of the natural frequencies of the lowest few eigenmodes of the microfabricated beam, and knowledge of Young's modulus and plan dimensions of the beam alone. The method exploits the fact that certain eigenmodes are insensitive to some of these structural parameters which enable a convenient decoupling and estimation of the parameters. As a result, the method does not require complicated finite element analysis, is insensitive to the gap height and introduces no contact wear or dielectric charging effects. Experiments are performed using laser Doppler vibrometry to measure the natural frequencies of doubly clamped, nickel, RF-MEMS capacitive switches and the method is applied to extract the residual stress, beam thickness, boundary compliance and post-release curvature.

Residual Stress Extraction of Surface-Micromachined Fixed-Fixed Nickel Beams Using a Wafer-Scale Technique

“…Since the in-plane Young's modulus of the nickel beams shows a small a small variation (0.5%) across the wafer as stated before, we assume the Young's modulus is constant, and the error of the extracted residual stress due to the uncertainty of the Young's modulus is analyzed in Section V-B. stress are compared to the results obtained using a resonance frequency method reported in [32]. For 26 nickel beams which have the same structure and were fabricated with the same process as the beams studied in this paper, the extracted values of residual stress also follow a nearly normal distribution with a mean value of 1.6 MPa with a standard deviation of 5.1 MPa, which closely agree with our results.…”

“…In addition, the initial beam curvature is not included in the beam model which degenerated the accuracy of the results. The last category involves dynamic tests, in which the test structures are powered into vibration, and the fundamental resonant frequency [29], [30] or multiple eigenmodes [31], [32] are measured to determine the residual stress. However, in [29]- [31], the effects of anchor compliance and non-flat initial profiles of test structures are neglected.…”

“…However, in [29]- [31], the effects of anchor compliance and non-flat initial profiles of test structures are neglected. The initial profile of the testing beam is taken into account in [32] by a presumed arc shape, which might not follow the actual irregular beam profiles and may result in non-negligible errors of the extracted residual stress. In addition, the eigenmodes of the beam becomes less sensitive when boundary spring stiffness is small, and therefore, leading to larger errors of the predicted residual stress by the method in [32] for beams with small boundary stiffness.…”

Measurement and Isolation of Thermal Stress in Silicon-On-Glass MEMS Structures

“…The fourth method uses the stress–frequency conversion. The natural frequency of a doubly clamped beam changes with the axial stress in the beam and can be measured using a scanning laser Doppler vibrometer system or frequency sweeping instruments, and then the stress can be determined [ 15 , 16 ].…”

Design and simulation of a high tuning range MEMS digital varactor using SU-8

“…It is widely reported that MEMS bridges normally experience high stresses after fabrication process due to several factors including exposure to variable fabrication temperatures[73],[78]-[81].This causes the MEMS bridges to warp or buckle hence reducing the achievable downstate capacitance.…”