An analytical model for the response of a piezoresistive micro-cantilever to surface stress: Preliminary considerations for biochemical sensor design

Abstract

In this paper, we derive an analytical model to describe the response of longitudinal and transverse piezoresistors embedded in micro-cantilever biochemical sensors. This model estimates the relative change in resistance and sensitivity of the piezoresistive elements taking into consideration the biaxial stress profile induced by surface stress loadings, the dimensions of the piezoresistor, and its location within the cantilever. To demonstrate its applicability and usefulness, we utilize our model to construct an analytical model for a piezoresistor with a U-shaped configuration. The effect of variation in the piezoresistor and cantilever dimensions, as well as the piezoresistor location and Poisson’s ratio, on the relative change of resistance and sensitivity to the applied surface stress are examined. The analytical predictions show that low aspect ratio micro-cantilevered plates (i.e. wide cantilevers) are better suited for piezoresistors subject to surface stresses. Moreover, the analytical model results allow us to identify a set of preliminary piezoresistor dimensions to increase the sensitivity of p-type U-shaped piezoresistors embedded in rectangular micro-cantilevered plates. Limitations in the microfabrication techniques of piezoresistors are also discussed in the context of our model predictions. The model here presented can be readily extended to describe the response and sensitivity of other piezoresistor configurations such as a streamer.