Analytical models of resonant rectangular cantilever type chemical sensors for applications in fluids

This paper demonstrates the analytical design and optimisation of piezoresistive rectangular cantilevers with particular concern for the geometric factors and associated influences of the displacement response functions through an increase in damping. Microcantilever sensors with a higher frequency response ultimately proved critical due to their response to forces that vary rapidly in time. The increase of the damping due to the fluid loading was shown to be mostly dependent upon the reduction of the cantilever dimensions. Such a scaling downward of dimensions has the profound additional benefit of leading to a marked reduction in response time. Reducing the dimensions of the cantilever provides tangible benefits include: the reduction of the total noise, the maximization of sensitivity to modulations in the Brownian fluctuations from analyst binding and the capacity to account for Brownian noise relative to Johnson noise.