Piezoresistive Properties of Heavily Dopedn-Type Silicon

The piezoresistance effect has been studied in $n$-type silicon over the impurity concentration range from approximately 1×${10}^{15}$ to 1×${10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$. From the analysis of the results, it is concluded that for Fermi energies up to 0.08 eV above the band edge, the total number of states below the Fermi level is correctly given by assuming that the band is parabolic with a density-of-states effective mass equal to that found in pure silicon. The qualitative dependence of the mobility anisotropy on impurity concentration and temperature is determined from the piezoresistance results. From the temperature dependence of the coefficient ${\pi }_{11}$, it is concluded that the deformation potential in $n$-type silicon increases by approximately 25% between 77 and 300°K. Finally, the ${\pi }_{44}$ coefficient is found to increase with increasing impurity concentration at the highest concentrations. This behavior is attributed to the Fermi level approaching the energy of the conduction band at the [100] zone boundary in silicon having an electron concentration of the order of 1×${10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$.