A simple analytical method for residual stress measurement on suspended MEM structures using surface profilometry

Abstract

This paper presents an analytical method to calculate residual stress and Young's modulus in clamped-clamped beams. These types of structures are a typical building block of many MEMS devices, and this guarantees accurate transferability of the measured parameters. The method is based on the determination of beam bending as a function of applied load by means of a surface profiler, and as a function of beam length. By modeling analytically both the elastic and the stress contribution to beam bending, it is possible to obtain both the stress value and Young's modulus by a simple fitting of the experimental data. Results are presented for electrodeposited gold beam arrays of different widths, but the method is in principle exploitable for every type of suspended film where the residual stress strongly influences the material properties. Accuracy and limitations of the method are also discussed.

On the electrostatic actuation of capacitive RF MEMS switches on GaAs substrate

“…The small discrepancy between the two values, 48.5 MPa and 55.3 MPa, of residual stress is likely due to the fact that the compressive thermal stress can be reduced by other temperature dependent components of gold internal stress, like grain growth or reorganization, which normally produces tensile stresses [20]. The values obtained here for the residual stress are comparable to those reported for electrodeposited gold beams typically used for MEMS switches [12].…”

“…Mechanical stylus surface profilers can be found in most clean rooms and are thus commonly used for topography measurements in MEMS with the valuation of the stress and Young modulus of the suspended membrane [12,13]. However, some degree of operator skill and care are required to avoid the damage of suspended membrane during the measurements with the stylus profilometer.…”

RF-MEMS switches for a full control of the propagating modes in uniplanar microwave circuits and their application to reconfigurable multimodal microwave filters

“…σ 2 = 58 MPa in the gold layer with a thickness t 2 = 1.8 µm and σ 1 = 62 MPa in the gold layer with a thickness t 1 = 3.5 µm, according to the membrane bi-layer structure (CPW and bridge layers) depicted in Fig. 6 (Mulloni et al 2013). Fig.…”

Comprehensive Solutions for the Response of Freestanding Beams With Tensile Residual Stress Subject to Point-Loading

“…thin films is to measure the load-deflection relationship of a freestanding structure, such as a thin beam or wire (e.g., membranes [1-4], microbeams [5,6] and wires [7,8]). Such methods are increasingly popular because a wide range of loads and displacements can be accessed using existing off-the-shelf systems, such as atomic force microscopes (AFM) [7][8][9][10][11][12][13], nanoindentation systems, profi]ometers, and instrumented microindenters [1- 6,14,15]. Further, the preparation of specimens amenable to one-dimensional modeling (i.e., beams and wires) is increasingly straightforward with emerging micro-and nanofabrication techniques [16,17].…”

“…There are a host of previous experimental studies and theoretical frameworks that utilize some aspects of the results presented here [1, [5][6][7][8][9][10]12,13,[19][20][21], The current work is a more comprehensive treatment of the response of point-loaded beams in the following respects. First, it includes an analysis that accounts for all levels of residual strain, across the full range of loads and displacements for moderate rotations.…”