Nonlinearity of the piezoresistance effect of p-type silicon diffused layers

The nonlinearity of the piezoresistance effect of p-type layers diffused into the
{110}
silicon plane has been investigated. An expression which contains higher order stress terms and can treat the piezoresistance effect quantitatively has been derived. It has been found that third-order stress terms are sufficient to give a good approximation of the effect. The expression coefficients have been determined experimentally using a silicon cantilever on which p-type diffused layers having surface concentration values from 10
¹⁸
to 10
¹⁹
cm
^-3
are formed. Nonlinearity in the case where the longitudinal axis of the cantilever is perpendicular to the direction of current flow is greater than that in the case where it is parallel to the direction of current flow under both tensile and compressive stresses. Using the new expression, it has been confirmed that results of numerical analysis on the nonlinearity of trial silicon piezoresistive pressure sensors agree well with experimental results.