Effect of coating viscoelasticity on quality factor and limit of detection of microcantilever chemical sensors

Microcantilevers with polymer coatings hold great promise as resonant chemical sensors. It is known that the sensitivity of the coated cantilever increases with coating thickness; however, increasing this thickness also results in an increase of the frequency noise due to a decrease of the quality factor. By taking into account only the losses associated with the silicon beam and the surrounding medium, the,decrease of the quality factor cannot be explained. In this paper, an analytical expression is obtained for the quality factor, which accounts for viscoelastic losses in the coating. This expression explains the observed decrease of the quality factor with increasing polymer thickness. This result is then used to demonstrate that an optimum coating thickness exists that will maximize the signal-to-noise ratio and, thus, minimize the sensor limit of detection.