Tight-binding model for the transverse Shubnikov–de Haas effect in semiconductor superlattices

The oscillatory part of the conductivity along the confining planes of a superlattice miniband under a perpendicular quantizing magnetic field was calculated, assuming a tight-binding approximation for the miniband dispersion. The manifestation of the belly and neck cross sections of the Fermi surface is studied as a function of the broadening of the electronic energy levels, miniband widths, and energy minigaps. The effects of the deviation from the nearest-neighbor tight-binding approximation upon the line shape of the magnetoresistance are studied. The model presented allows for a quantitative description of the magnetoresistance spectra and is in good agreement with recent experimental observations on InAs_1-x{Sb}ₓ$/InSb doped superlattices and GaAs with a periodical planar doping of silicon.