A physical model to describe the distribution of adhesion strength in MEMS, or why one MEMS device sticks and another ‘identical’ one does not

In this paper a model is presented that describes the distribution of adhesion values typically experimentally observed for different MEMS devices that have been fabricated in the same way. This spread is attributed to the fact that different devices differ in the details of their surface roughness, even if these surface roughnesses are modeled as coming from the same ‘parent’ stochastic process. Using Monte Carlo simulations, the effect of surface roughness and relative humidity has been evaluated in detail, both on the expected mean value of the surface interaction energy between the MEMS surfaces, and the expected spread on this value from device to device. By comparing the new model to existing literature reporting this experimentally observed spread, we have found excellent agreement between the experimental spread observed, and the spread calculated with the theoretical model using Monte Carlo simulations. This work paves the way to detailed adhesion failure predictive modeling. It may be used to assess the reliability of MEMS designs that rely on contacting surfaces for their operation, but have a limited restoring force available to separate the surfaces when in contact