Time-Temperature Superposition Based Accelerated Aging Method for Packaged MEMS Resonators

SummaryThis manuscript introduces a new methodology to accelerate and predict stress-related aging in encapsulated MEMS resonators. This approach builds upon the time-temperature superposition principle that, in linear viscoelastic materials, relates the relaxation modulus (E(t,T)) at low temperature with the one measured at high temperature for a shorter range of time. The master curve shift factors derived from this correspondence permit us to reconstruct E(t,T) at room conditions from a relaxation profile that shrinks as a consequence of applying a staircase-like temperature. Thence, we use this technique to accelerate the aging of a MEMS resonator whose frequency is affected by package relaxation and, with the semi-analytical equation introduced in this manuscript, calculate the long-term drift. To validate this approach, a 4-step temperature function in log time scale is applied to a thickness-extensional MEMS resonator known as DBAR that is surrounded by mold compound in a QFN package.