First-order piezoresistance coefficients in heavily doped p-type silicon crystals

The first-order piezoresistance coefficients π11, π12, π44 were calculated for heavily doped p-type silicon crystals. The analytical calculation was carried out within the framework of the three-band model taking into account effect of anisotropy and influence of the spin-orbit split-off band (here the SO band) on shape of heavy and light hole bands as well as direct contribution of the SO band into magnitude of the piezoresistance coefficients. The letter is negligible for shear piezoresistance coefficient π44 but for values of piezoresistance coefficients π11 and π12 its contribution reaches 30%. In correspondence with experimental data the calculated values of piezoresistance coefficients π11 and π12 have opposite signs for scattering by acoustic phonons or by ionized impurities.There is a good agreement between our numerical results (for scattering by ionized impurities) and experimental data for shear piezoresistance coefficient π44 at temperatures 190–375 K. It has been obtained in wide range of impurity concentrations (5 × 1019–2 × 1021 cm−3).