Anelastic Stress Relaxation in Gold Films and Its Impact on Restoring Forces in MEMS Devices

In order to evaluate the importance of stress relaxation on device performance of capacitive RF MEMS switches, stress relaxation has been measured in 1.2-mum-thick Au films using a membrane bulge technique. When the residual stress in the films is small, the stress relaxation is fully recoverable and is well described by linear anelasticity (viscoelasticity) theory. A 27% reduction in the effective elastic modulus occurs over a three-day period under constant strain conditions at room temperature. The time dependence of the relaxation can be represented by a series of time constants with values extending from seconds to days. Linear superposition of the anelastic response can be used to accurately predict the stress under any time dependence of the strain. The prediction is accurate even during cyclic loading and unloading, and even when the strain is cycled at rates that are fast compared with any of the relaxation times. The restoring force available to open a capacitive RF MEMS switch is modeled for two different switch designs. The restoring force is shown to drop by approximately 7% or 20% at room temperature for the two cases presented.