This paper is devoted to the theoretical study of the influence of the
temperature 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 calculated 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 stresses. General expressions for the fundamental
linear, π11 and π12, and non-linear, π111, π112,
π122 and π123, piezoresistance coefficients are then derived. Plots of
the non-linear piezoresistance coefficients against the reduced shift of the Fermi
level or against temperature allow us to characterize the influence of doping and
temperature. Finally some attempts are made to estimate the non-linearity for heavily
doped semiconductor gauges.