Magnetotransport measurements and low-temperature scattering times of electron gases in high-quality Si/${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ge}}_{\mathit{x}}$ heterostructures

We report Shubnikov–de Haas and Hall measurements conducted on n-type modulation-doped Si/${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ heterostructures grown on relaxed ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ buffer layers. Hall mobilities up to 174 700 ${\mathrm{cm}}^2$/V s at T=0.35 K are achieved. We observe the lifting of both the spin and the valley degeneracies at rather low magnetic fields and well-defined quantum Hall plateaus at integer filling factors. The single-particle relaxation times ${\mathrm{\tau }}_{\mathit{s}}$ are of the order of 1 ps for all samples investigated. Assuming an effective transport mass of 0.19${\mathit{m}}_0$ for the electrons in the lowest, twofold-degenerate Si conduction band, the transport times ${\mathrm{\tau }}_{\mathit{t}}$ exceed ${\mathrm{\tau }}_{\mathit{s}}$ by more than an order of magnitude. This result clearly indicates that long-range impurity scattering is the dominant scattering mechanism in high-quality Si/${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ heterostructures.