TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Properties: The mobility (mu) of carrier electron is 0.1-40 cm2/Vs. The carrier electron density (ne) and mobility (mu) of carrier electron satisfy the relations: mu less than or equal to 3.75nex10-20 and 0.2less than or equal to(nex10-20/mu).Preferred Oxide: The gallium-containing zinc oxide further contains an element (a) having covalent radius different from covalent radius of zinc atom, and content less than gallium content. The element (a) having covalent radius different from covalent radius of zinc atom, is element of 4 coordination excluding gallium and having ionic radius of 0.4-0.95 nm. The element (a) is XIII or XIV group element excluding gallium, preferably fluorine element or chlorine element.Preferred Film: Preferably, the zinc-oxide thin film has film thickness of 5000 nm or less, visible-ray transmittance (Tv) of 70% or more, and transmittance of light ray with wavelength of 500 nm of 70% or more. The solar radiation transmittance (Ts) and visible-ray transmittance (Tv) satisfies the relation: Tsless than or equal to1.4Tv-44, when film thickness is 30-350 nm. The solar radiation transmittance (Ts) and visible-ray transmittance (Tv) satisfies the relation: Tsless than or equal to1.4Tv-54, when the film thickness is 350-5000 nm. The transmittance in light ray of wavelength 750 nm is 88% or less, preferably 75% or less. The transmittance in light ray of wavelength 1000 nm is 80% or less, preferably 60% or less. The transmittance in light ray of wavelength 1200 nm is 65% or less, preferably 35% or less. The transmittance in light ray of wavelength 1500 nm is 40% or less, preferably 15% or less. The ratio of carrier electron-density x10-20/mobility of carrier electron is set to X, and the ratio (Tv/Ts) is set to Y. The film satisfies the relation: Ygreater than or equal to0.4X+1.06, when film thickness is 400 nm or more, and the relation: Ygreater than or equal to0.2X+0.98, when film thickness is 300 nm or less. The gallium-containing zinc-oxide thin film having gallium content of 0.25-5.5 wt.% is produced with oxygen flow rate of 0-10 sccm, and with gallium content of 5.5-25 wt.% is produced with oxygen flow rate of 0-13 sccm.