Comment on 'Sheath model for dual-frequency capacitive discharges'

Boyle et al (2004 J. Phys. D: Appl. Phys. 37 1451) introduced a sheath model for dual-frequency capacitive discharges. The electron sheath edge position s and the dc potential Φdc in the sheath are obtained with the assumption α/β >> 1 (where α/β is the ratio of the low-frequency electric field to the high-frequency electric field). However, α/β ≤ 4 is usually found in processing applications. Under this condition, we show that the Boyle et al model gives multiple values for the dc potential Φdc(x) at any given position x in the sheath. For this reason, we introduce a model without the assumption α/β >> 1. By comparing the results from the two models, it is found that, as the ratio α/β approaches 1, the sheath thickness sm and the sheath dc voltage Vdc obtained with the Boyle et al model are significantly underestimated.