AC Discharges with Unequal Area Electrodes

We begin by assuming that the ion current density to all internal surfaces is equal. Then, if we assume a collision-free sheath with the field being zero at the edge of the positive column, we can express the space charge-limited ion current as16 

Since the ion currents on each electrode have been taken equal, we can write 

replacing C2/C in Equation (12) from Equation (10) results in the desired relationship between V],/V2 and Ail/ 2- 

Clearly, there are many approximations in this model, so close agreement with experimental data should not be expected. It is interesting, however, to consider some relevant experimental data.17 In these experiments, peak-to-peak and DC bias voltages were measured for a 13.56-MHZ RF glow discharge confined within a reactor chamber with two electrodes of unequal area. Using a 

For these particular conditions, it can be seen that Vj/Vj = (A1/A2)n is a reasonable model, but that n s 4 only between At/A2 = 0.6 and 1.0. For smaller area ratios, we find n s 1. The data reported by Coburn and Kay18 were modified by the author by correcting the areas they used in their calculation. 

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