Magnetic-field dependence of valley splitting in Si quantum wells grown on tilted SiGe substrates

摘要

The valley splitting of the first few Landau levels is calculated as a function of the magnetic field for electrons confined in a strained silicon quantum well grown on a tilted SiGe substrate, using a parametrized tight-binding method. More specifically, the valley splitting arising from the effect of misorientation between the crystal axis and the confinement direction of the quantum well is investigated. In the absence of misorientation (zero substrate tilt angle), the valley splitting slightly decreases with increasing magnetic field. In contrast, the valley splitting for a finite substrate tilt angle exhibits a strong and nonmonotonic dependence on the magnetic-field strength. The valley splitting of the first Landau level shows an exponential increase followed by a slow saturation as the magnetic-field strength increases. The valley splitting of the second and third Landau levels shows an oscillatory behavior. The nonmonotonic dependence is explained by the phase variation of the Landau-level wave function along the washboardlike interface between the tilted quantum well and the buffer material. The phase variation is a direct consequence of the misorientation. This result suggests mat when the misorientation effect is dominant, the magnitude of the valley splitting can be easily tuned by controlling the Landau-level filling factor through the magnetic field and the doping concentration.