Monte Carlo study of the low-temperature mobility of electrons in a strained Si layer grown on a Si1-xGex substrate

A Monte Carlo approach is used to study the electron mobility in the Si/Si1-xGex system at low temperatures. The diffusion constant is evaluated in near thermal equilibrium simulations and is converted to the mobility by use of the Einstein relation for a degenerate two-dimensional electron gas. A modulation-doped structure is considered, where the doped Si0.7Ge0.3 layer provides channel electrons and is separated from the channel by an undoped Si0.7Ge0.3 spacer layer. The electron density is evaluated as a function of spacer width and doping concentration. Electrons are assumed to be only in the lowest subband. Acoustic-phonon scattering and remote impurity scattering determine the possible mobility that can be reached. We find mobility values of 2.5×105 cm2/V s at 4.2 K and 3.1×105 cm2/s at 1.5 K for an electron density of 7.5×1011 cm-2 (for typical choices of parameters: 10-nm spacer and 2×1018 cm-3 doping). Peak mobility values of 5.0×105 cm2/V s at 4.2 K and 7.6×105 cm2/s at 1.5 K are possible for wider spacer layer widths, with subsequently lower channel electron densities. The effects of surface roughness scattering, as well as other scatterers are discussed. These processes can be a mechanism to explain the difference between the above ideal mobility and the reported experimental data.