Electronic transport properties of a two-dimensional electron gas in a silicon quantum-well structure at low temperature

We calculate the static and dynamic transport properties of a two-dimensional electron gas in a Si quantum well of thickness a at zero temperature. Background doping, remote doping, and surface roughness are considered as the relevant scattering mechanisms. Multiple-scattering effects are included in the theory and the phase diagram for the metal-insulator transition is evaluated. Due to the anomalous wave-vector dependence of the polarizability the correction to the conductivity, which is linear in the temperature, is derived for quantum-well structures. The frequency dependence of the scattering rate is calculated. We compare our results on the mobility with recent experiments in superlattices of Si-${\mathrm{Si}}_{\mathrm{x}}$ ${\mathrm{Ge}}_{1\mathrm{-}\mathrm{x}}$ and discuss the upper limits of the mobility. For electron density n${>10\mathrm{}}^{12}$ ${\mathrm{cm}}^{\mathrm{-}2}$ and a>40 Å remote doping limits the mobility. But for n${<10\mathrm{}}^{12}$ ${\mathrm{cm}}^{\mathrm{-}2}$ homogeneous background scattering also becomes important. Surface roughness scattering becomes dominant only for thin quantum wells with thickness smaller than 40 Å.