Carbon nanotubes are formed on a surface of a substrate using a plasma chemical deposition process. After the nanotubes have been grown, a purification step is performed on the newly formed nanotube structures. The purification removes graphite and other carbon particles from the walls of the grown nanotubes and controls the thickness of the nanotube layer. The purification is performed with the plasma at the same substrate temperature. For the purification, the hydrogen containing gas added as an additive to the source gas for the plasma chemical deposition is used as the plasma source gas. Because the source gas for the purification plasma is added as an additive to the source gas for the chemical plasma deposition, the grown carbon nanotubes are purified by reacting with the continuous plasma which is sustained in the plasma process chamber. This eliminates the need to purge and evacuate the plasma process chamber as well as to stabilize the pressure with the purification plasma source gas. Accordingly, the growth and the purification may be performed without shutting off the plasma in the plasma process chamber.