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

This paper reports on the extraction of residual stress in surface-micromachined nickel thin films of electrostatically actuated fixed-fixed beams using a wafer-scale technique. The distribution of residual stress for 87 beams on a 4-in quarter wafer piece is presented. The residual stress (σ₀) is determined from the best fit of the displacement-voltage curves predicted by a computationally efficient model to the experimental data. The nondestructive and automated measurements are taken at room temperature and directly at the beam itself without any additional test structures. The model employed incorporates the nonideal effects of inclined supports, nonflat initial beam profiles, and fringing fields. The extracted residual stress values vary between -12.8 and 13.6 MPa (negative values are for compressive stresses and positive ones for tensile stresses). The residual stresses for these 87 beams follow a nearly normal distribution with a mean value of -1.7 MPa and a standard deviation of 5.9 MPa, which represents the variability of the residual stresses across the wafer. Detailed uncertainty analysis has been conducted, and it reveals that inaccurate modeling of the nonideal effects will result in significant errors in the extracted residual stress. Although demonstrated on nickel thin films, this technique can be applied to other metallic thin films.