Simulation of piezoresistivity inn-type single-crystal silicon on the basis of the first-principles band structure

We have simulated the piezoresistivity in $n$-type single-crystal bulk silicon based on the first-principles electronic band structure of model structures. Our simple procedure to calculate the piezoresistance coefficients is valid qualitatively and quantitatively for carrier electron transport in the multivalley conduction-band structure of $n$-type bulk silicon; the primitive longitudinal and transverse piezoresistance coefficients originate from the energy gap between the valleys, whereas the shear piezoresistance coefficient ${\ensuremath{\pi}}_{44}$ arises from a distortion of the band energy surface in the valleys and can be presented clearly as a negative constant. The distinction between the origins of longitudinal, transverse, and shear piezoresistivity can be followed as a dependence on a carrier concentration or temperature.