2ND-ORDER PIEZORESISTANCE COEFFICIENTS OF P-TYPE SI

A complete set of nine independent components of the second-order piezoresistance (SOPR) coefficients for p-type Si at 300 K are derived numerically. The electrical conductivity is calculated for the sixfold degenerate valence bands in Si with and without stress using a standard transport theory assuming the Maxwell-Boltzmann distribution and an energy-independent relaxation time. The calculated first- and second-order piezoresistance coefficients agree well with experimental ones for some current and stress directions. Using conductivities calculated for 30 combinations of current and uniaxial as well as biaxial stress directions, nine independent components of SOPR coefficients of p-type Si are optimized by the least-squares method. They are pi(111) = 34.4, pi(112) = -15.4, pi(122) = 11.7, pi(144) = 1.7, pi(144) = -12.0, pi(166) = 125.5, pi(661) = -9.7, pi(456) = -46.0, and pi(441) = 19.5 in 10(-8) MPa(-2) at 300 K.