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The doping effects of Cu on the electrical conductivity of ZnO were studied in the simple binary system through the ac impedance spectroscopy. The Cu doping decreased the electrical conductivity of ZnO by several orders of magnitude. The Cu doping decreased the electrical conductivity of ZnO both in the grain and in the grain boundary. Hydrogen was introduced into the Cu-doped ZnO specimens by the ion implantation technique. The electrical conductivity of the hydrogen-implanted layer increased by about 9 orders of magnitude at most. The mechanism for such a hydrogen effect was also discussed.