MODELING PIEZORESISTIVITY IN SILICON AND POLYSILICON

The piezoresistive effect of silicon is often utilized in sensors. Due to the crystalline nature of silicon, the sensitivity of the piezoresistive effect depends on many things including the direction and magnitude of the applied stress and the orientation of the crystallographic plane. A method of modeling the piezoresistive effect in silicon and poly crystalline silicon is presented. This mathematical model includes partial derivatives and linear algebra to combine basic electrical and mechanical equations to describe the change in resistivity as a function of stress. An experiment was used to verify the model. The analytical solution and experimental results agree. The model presented in this paper is adequate to predict the behavior of a piezoresistive sensor under uniform stress.