Piezoresistance of Diffused Layers in Cubic Semiconductors

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Abstract
Piezoresistive characteristics of a diffused layer on the surface of a semiconductor having a cubic crystallographic structure are analyzed. The surface is assumed free of external forces, and the current component normal to the surface within the layer is assumed zero. The equations derived are useful in the design of diffused piezoresistive electromechanical transducers. The electric fields in the layer are related to the sheet current densities and the stresses by diffused piezoresistive coefficients, which are defined in integral form. These coefficients are functions of the fundamental piezoresistive coefficients, the crystal orientation, and the unstressed conductivity profile function in the layer, but are independent of the layer thickness. The coefficient of major interest is numerically evaluated as a function of surface impurity concentration for p‐type silicon and n‐type germanium‐diffused layers with Gaussian and complementary error function impurity distributions. Measurements on diffused samples are in agreement with the analysis. The magnitude of a nonlinearity in layer piezoresistance arising from the variations of the bulk coefficients with doping is estimated.