A kinetic formulation of piezoresistance in N-type silicon: Application tonon-linear effects

This paper is devoted to the theoretical study of the influence of the temp erature and of the doping on the piezoresistance of N-type silicon. In the first step the fractional change in the resistivity caused by stresses is c alculated in the framework of a multivalley model using a kinetic transport formulation based on the Boltzmann transport equation. In the second step shifts in the minima of the conduction band and the resulting shift of the Fermi level are expressed in terms of deformation potentials and of stresse s. General expressions for the fundamental linear; pi(11) and pi(12), and n on-linear, pi(111), pi(112), pi(122) and pi(123), piezoresistance coefficie nts are then derived. Plots of the non-linear piezoresistance coefficients against the reduced shift of the Fermi level or against temperature allow u s to characterize the influence of doping and temperature. Finally some att empts are made to estimate the non-linearity for heavily doped semiconducto r gauges.