Modeling and optimization of a side-implanted piezoresistive shear stress sensor

This paper presents the modeling and design optimization of a micromachined floating element piezoresistive shear stress sensor for the time-resolved, direct measurement of fluctuating wall shear stress in a turbulent flow. The sensor structure integrates side-implanted diffused resistors into the silicon tethers for piezoresistive detection. A theoretical nonlinear mechanical model is combined with a piezoresistive model to determine the electromechanical sensitivity. Lumped element modeling (LEM) is used to estimate the resonant frequency. Finite element modeling is employed to verify the mechanical models and LEM results. Two dominant noise sources, 1/f noise and thermal noise, were considered to determine the noise floor. These models were then leveraged to obtain optimal sensor designs for several sets of specifications. The cost function is the minimum detectable shear stress that is formulated in terms of sensitivity and noise floor. This cost function is subjected to the constraints of geometry, linearity, bandwidth, power and resistance. The results indicate the possibility of designs possessing dynamic ranges of greater than 85dB.