Typically, the 2D resistivity ρ( n, T), where n is the 2D carrier density and T is the temperature, increases with increasing temperature by a substantial fraction in the 0.1 K–5 K regime at “intermediate” carrier densities before phonon effects become operational at higher temperatures. The observation of a strong apparent metallic temperature dependence of the 2D electrical resistivity in high-quality (i.e., low-disorder) semiconductor systems at low carrier densities has become fairly routine 1, 2, 3, 4, 5 during the last 20 years ever since the first experimental report of such an effective metallic behavior in high-mobility n-Si MOSFETs 6, 7. Experimentally verifiable predictions are made about the quantitative magnitude of the maximum possible low-temperature metallicity in 2D systems and the scaling behavior of the temperature scale controlling the quantum to classical crossover. We also discuss effects of interaction and disorder on the 2D screening properties in this context as well as compare 2D and 3D screening functions to comment why such a strong intrinsic temperature dependence arising from screening cannot occur in 3D metallic carrier transport. In this work, we derive a number of analytical formula, supported by realistic numerical calculations, for the relevant density, mobility, and temperature range where 2D transport should manifest strong intrinsic (i.e., arising purely from electronic effects) metallic temperature dependence in different semiconductor materials arising entirely from the 2D screening properties, thus providing an explanation for why the strong temperature dependence of the 2D resistivity can only be observed in high-quality and low-disorder 2D samples and also why some high-quality 2D materials manifest much weaker metallicity than other materials.

Low temperature carrier transport properties in 2D semiconductor systems can be theoretically well-understood within RPA-Boltzmann theory as being limited by scattering from screened Coulomb disorder arising from random quenched charged impurities in the environment.

Thomas fermi screening constant