Temperature and magnetic field dependence of the two-dimensional conductivity in ${\mathrm{Au}}_{\mathit{x}}$${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$/Si and Cu/Si multilayers

We have studied the temperature and magnetic field dependence of the conductivity of ${\mathrm{Au}}_{\mathit{x}}$ ${\mathrm{Si}}_{1\mathrm{-}\mathit{x}}$/Si (x=1, 0.54, 0.46, and 0.41) and Cu/Si multilayers. The individual layer thicknesses were from 9 to 20 Å and from 21 to 86 Å for metal and silicon layers, respectively. When silicon layers are thinner than about 40 Å, the onset of a coupling between the metallic layers through the silicon layers is observed. For thicker silicon layers, the two-dimensional electron localization and interaction models correctly account for the data. The analysis of magnetoresistance and conductivity data yields consistent results and thus allows us to derive the temperature and composition dependence of the relevant scattering rates.