Analysis and Modeling of Piezoresistance Response.

A phenomenological model of piezoresistance was formulated to calculate the resistance change of a gage element subjected to mechanical deformation. This model incorporates the tensor nature of piezoresistivity, elastic-plastic gage response to include mechanical and electrical hysteresis, and dimensional contributions. The phenomenological model was used to analyze past data on Manganin and ytterbium. The stresses and strains in the gage element, needed for this analysis, were approximated from geometrical considerations. The results showed that the piezoresistance model was necessary to understand the gage response. However, many experimental results could not be adequately modeled. Improved analysis requires a rigorous determination of the stresses and strains in the gage element. A few well-defined experiments in support of the analysis, were performed to determine the effect of matrix stress rotation, gage strain states, and shear loading on gage response. The matrix stress rotation experiments gave definitive results and showed that the gage response was governed mainly by the matrix stress component normal to the foil. To understand these results, it is necessary to determine the gage stresses and strains.