Study on the Pull-In Instability of Gold Micro-Switches Using Variable Length Scale Parameter

In this paper, the size dependent behavior of the gold micro-switches has been studied. This behavior becomes noticeable for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter. The size dependent effect is insignificant for the high ratio of the characteristic size to the length-scale parameter, which is the case of the silicon base micro-beams. On the other hand, in some types of micro-beams like gold base, the size dependent effect cannot be overlooked. In such cases, ignoring this behavior in modeling will lead to incorrect results. Some previous researchers have applied classic beam theory on their models and imposed a considerable hypothetical value of residual stress to match their theoretical results with the experimental ones. In this study, by obtaining the equilibrium positions or fixed points of the gold micro-beam, a considerable difference between the obtained fixed points using classic beam theory and modified couple stress theory has been shown. In addition, it has been shown that the calculated pull-in voltages using modified couple stress theory are much closer to the experimental results than those obtained by classic beam theory. Finally, it has been shown that considering a unique value of length scale parameter, especially for the smallest values of the beam thicknesses, may leads to inaccurate results and variable length scale parameter should be considered.