Proposed is a showerhead-cooler system of a semiconductor-processing chamber with uniform distribution of plasma density. The showerhead has a plurality of through gas holes that are coaxial with respective channels of the gas-feeding cooler plate. On the gas inlet side, the though passages of the showerhead are provided with unequal conical nozzles characterized by a central angle that decreases from the peripheral part of the showerhead to the showerhead center. Such design provides uniformity of plasma density. Furthermore, in order to protect the walls of the nozzle and the walls of the gas holes from erosion that may be caused by the hollow-cathode phenomenon, these areas are coated with a thin protective coating that is resistant to electrical breakdown and chemical corrosion.