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Although the two-dimensional electron gas (2DEG) in (001) Zn$_{1-x}$Mg$_x$O/ZnO heterostructures has been discovered for about twenty years, the origin of the 2DEG is still inconclusive. In the present letter, the formation mechanisms of 2DEG near the interfaces of (001) Zn$_{1-x}$Mg$_x$O/ZnO heterostructures were investigated via the first-principles calculations method. It is found that the polarity discontinuity near the interface can neither lead to the formation of 2DEG in devices with thick Zn$_{1-x}$Mg$_{x}$O layers nor in devices with thin Zn$_{1-x}$Mg$_{x}$O layers. For the heterostructure with thick Zn$_{1-x}$Mg$_{x}$O layers, the oxygen vacancies near the interface introduce a defect band in the band gap, and the top of the defect band overlaps with the bottom of the conduction band, leading to the formation of the 2DEG near the interface of the device. For the heterostructure with thin Zn$_{1-x}$Mg$_{x}$O layers, the absorption of hydrogen atoms, oxygen atoms, or OH groups on the surface of Zn$_{1-x}$Mg$_{x}$O film plays a key role for the formation of 2DEG in the device. Our results manifest the sources of 2DEGs in Zn$_{1-x}$Mg$_x$O/ZnO heterostructures on the electronic structure level., Comment: 6 pages, 6 figures

Ta-doped SnO$_2$ films with high conductivity and high optical transparency have been successfully fabricated using rf-sputtering method and their electrical transport properties have been investigated. All films reveal degenerate semiconductor (metal) characteristics in electrical transport properties. For the thick films ($t\sim 1\,\mu \rm{m}$ with $t$ being the thickness) deposited in pure argon, the electron-phonon scattering alone cannot explain the temperature dependent behaviors of resistivity, the interference effect between electron-phonon and electron-impurity scattering should be considered. For the $t\lesssim 36$ nm films, both conductivity and the Hall coefficient show linear relation with the logarithm of temperature ($\ln T$) from $\sim$100 K down to liquid helium temperature. The $\ln T$ behaviors of conductivity and Hall coefficient cannot be explained by the Altshuler-Aronov type electron-electron interaction effect, but can be quantitatively interpreted by the electron-electron interaction effects in the presence of granularity. Our results not only provide strong supports for the theoretical results on the electron-phonon-impurity interference effect, but also confirm the validity of the theoretical predictions of charge transport in granular metals in strong coupling regime., Comment: 7 pages and 6 figures