An analytic model of thermal drift in piezoresistive microcantilever sensors

A closed-form semiempirical model has been developed to understand the physical origins of thermal drift in piezoresistive microcantilever sensors. The two-component model describes both the effects of temperature-related bending and heat dissipation on the piezoresistance. The temperature-related bending component is based on the Euler–Bernoulli theory of elastic deformation applied to a multilayer cantilever. The heat dissipation component is based on energy conservation per unit time for a piezoresistive cantilever in a Wheatstone bridge circuit, representing a balance between electrical power input and heat dissipation into the environment. Conduction and convection are found to be the primary mechanisms of heat transfer, and the dependence of these effects on the thermal conductivity, temperature, and flow rate of the gaseous environment is described. The thermal boundary layer value that defines the length scale of the heat dissipation phenomenon is treated as an empirical fitting parameter. Using the model, it is found that the cantilever heat dissipation is unaffected by the presence of a thin polymer coating; therefore, the residual thermal drift in the differential response of a coated and uncoated cantilever is the result of nonidentical temperature-related bending. Differential response data show that residual drift is eliminated under isothermal laboratory conditions but not the unregulated and variable conditions that exist in the outdoor environment (i.e., the field). The two-component model is then validated by simulating the thermal drifts of an uncoated and a coated piezoresistive cantilever under field conditions over a 24 h period using only meteorological data as input variables.