A model capturing the effect of general strain on the electron effective masses and band-edge energies of the lowest conduction band of silicon (Si) has been developed. Analytical expressions for the effective mass change induced by shear strain and valley shifts/splittings have been derived using a degenerate kp-theory at the zone boundary X point. Good agreement to numerical band-structure calculations using the nonlocal empirical pseudopotential method with spin-orbit interactions has been observed, as can be seen from the adjoining figure.
The model has been validated by calculating the bulk and inversion layer electron mobility under general strain. For this purpose the transport properties of strained Si have been investigated by solving the semiclassical Boltzmann equation using the Monte Carlo (MC) method employing fullband and analytical band models. The low-field electron mobility resulting from MC simulations using an analytical description of the electron bands and the fullband description coincide only for shear strain smaller than 0.5 percent. At larger shear strain the band deformation is so pronounced that fullband modeling is required. Through a rigorous modeling of the strain effect on the electronic band structure and MC simulations of the electron mobility, the limits of the linear piezoresistance model have been determined. In Si inversion layers on (001) oriented substrate with small body thickness, the effective mass change by shear strain has been shown to be the only mechanism able to enhance the electron mobility.