BIAS VOLTAGE IN FINITE LENGTH, CYLINDRICAL AND COAXIAL RADIOFREQUENCY DISCHARGES

We obtain the ratio Va/Vb of the direct-current glow-to-electrode voltages at the powered (a) and grounded (b) electrodes in low pressure capacitive radio-frequency (rf) discharges having unequal electrode areas Aaand Abin finite length cylindrical and coaxial geometry. We use a transport model in the glow in which ions are generated by thermal electron ionization and are lost by ambipolar diffusion in the glow, with a constant diffusion coefficient. Three electrode sheath models are considered: collisionless ions, collisional ions with a constant mean free time, and collisional ions with a constant mean free path. Using these and the continuity of the rf current flow, we obtain the voltage ratio as a function of the electrode area ratio, the length-to-radius ratio of the cylinder, and, for coaxial systems, the ratio of inner-to-outer radii. The theory is in good agreement with experiments in cylindrical and coaxial geometry. © 1990, American Vacuum Society. All rights reserved.