  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 parameterized
tight-binding method. For a 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
non-monotonous 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
non-monotonous dependence is explained by the phase variation of the Landau
level wave function along the washboard-like interface between the tilted
quantum well and the buffer material. The phase variation is the direct
consequence of the misorientation between the crystal axis and the confinement
direction of the quantum well. This result suggests that the magnitude of the
valley splitting can be tuned by controlling the Landau-level filling factor
through the magnetic field and the doping concentration.
