Growth mechanism for spherical carbon particles in a dc methane plasma

The growth mechanism for spherical carbon particles of micron sizes observed in a vertically excited CH₄/Ar columnar plasma [F. Shoji, Z. Feng, A. Kono, and T. Nagai, Appl. Phys. Lett. 89, 171504 (2006)] is investigated theoretically, based on a model in which the particles are negatively charged in the plasma sheath region where they grow by capturing graphite onions with a diameter of ca. 10 nm and a positive charge. A balance of gravity and electric force keeps the particles in the sheath region during their growth. It is found that the particle radius initially increases linearly with time and then approaches a saturation radius, and that the center of gravity of the particle executes a simple harmonic oscillation about its balance position with a characteristic frequency of the order of 10 Hz determined by its specific charge, gravity, and sheath structure