Piezoelectric crystallime film on a substrate, which is a crystalline zinc oxide film with a c-axis perpendicular to the substrate surface, the crystalline zinc oxide film containing one copper compound selected from the group consisting of copper sulphide, copper telluride, copper selenide, copper selenate, copper phosphide and copper phosphate. The copper is present in the crystalline zinc oxide film in the form of its sulphide, telluride, selenide, selenate, phosphide or phosphate and in the concentration of 0.01 to 20.0 atomic percent. The piezoelectric crystalline film have high resistivity and a smooth surface so that they can be used in a wide range of low to high frequencies.