Electrothermomechanical Finite-Element Modeling of Metal Microcontacts in MEMS

Three-dimensional fractal representations of surface roughness are incorporated into a finite-element framework to obtain the electrothermomechanical behavior of ohmic contacts in radio frequency (RF) microelectromechanical systems (MEMS) switches. Fractal surfaces are generated from the Weierstrass-Mandelbrot function and are representatives of atomic force microscope surface roughness measurements of contact surfaces in fabricated RF MEMS switches with metal contacts. A specialized finite-element scheme is developed, which couples the thermomechanical asperity creep deformations with the electromechanical contact characteristics to obtain predictions of contact parameters and their evolution as a function of time and loading. A dislocation-density-based crystal plasticity framework is also used to investigate microstructure evolution at microcontacts and its effects on contact parameters. Using this approach, simulations are made to investigate how surface roughness, initial residual strains, and operating temperature can affect asperity contact behavior. Based on these predictions, tribological design guidelines can be obtained to increase the lifetime of low-contact-resistance RF MEMS switches by limiting stiction and electrical resistance increase.