Nonmetallic Conduction in Electron Inversion Layers at Low Temperatures

We have measured the resistance of electron inversion layers in Si metal-oxide-semiconductor field-effect transistors at low temperatures (∼50 mK) and low electric fields (∼0.1 V/m). At low values of $R_{\square }$ we observe logarithmic dependences of the resistance on both temperature and applied electric field which scale only on $R_{\square }$. We observe a gradual transition to an exponential dependence at $R_{\square }\gtrsim 10$ kΩ. The logarithmic dependences agree qualitatively but not quantitatively with current theories of localization.