Shubnikov-de Haas oscillations under hot-electron conditions in Si/Si1-xGex heterostructures

The energy-loss rate of hot carriers in several modulation-doped Si/Si1-xGex heterostructures has been studied. The Ohmic properties of the Si/Si1-xGex 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 1.3×104 to 1.3×105 cm2/Vs at T2 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/Si1-xGex heterostructures. The dependence of the energy-loss rate (PE) on electron temperature (Te) 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 PE does not change when the mobility of the samples is varied by a factor of 10, and thus PE(Te) 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. © 1994 The American Physical Society.