Shubnikov–de Haas oscillations under hot-electron conditions in Si/${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ge}}_{\mathit{x}}$ heterostructures

The energy-loss rate of hot carriers in several modulation-doped Si/${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ heterostructures has been studied. The Ohmic properties of the Si/${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ samples, which were grown by ultrahigh-vacuum chemical-vapor deposition, were studied by Hall effect, conductivity, Shubnikov–de Haas, and quantum Hall effect measurements. For the samples with mobilities ranging from 1.3×${10}^4$ to 1.3×${10}^5$ ${\mathrm{cm}}^2$/Vs at T≊2 K the ratio of the transport time to the single-particle scattering time increases from 2.4 to 7.7. This result clearly indicates the change from dominant short-range to rather long-range scattering mechanisms in the higher quality Si/${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ge}}_{\mathit{x}}$ heterostructures. The dependence of the energy-loss rate (${\mathit{P}}_{\mathit{E}}$) on electron temperature (${\mathit{T}}_{\mathit{e}}$) was obtained from the damping of the Shubnikov–de Haas oscillations with applied electric field up to 5 V/cm. In the electron temperature range from 1.6 to 7 K, the functional dependence of ${\mathit{P}}_{\mathit{E}}$ does not change when the mobility of the samples is varied by a factor of 10, and thus ${\mathit{P}}_{\mathit{E}}$(${\mathit{T}}_{\mathit{e}}$) is unaffected by the nature of the elastic-scattering mechanisms within these limits. In this electron temperature range the dominant energy-loss mechanism is due to acoustic-phonon scattering via deformation-potential coupling. For a deformation-potential coupling constant of 9 eV, taking static screening into account, a quantitative agreement between experimental and calculated values of the energy-loss rate is obtained without any fit parameter.