Modeling the pressure dependence of DC bias voltage in asymmetric, capacitive RF sheaths

A semianalytical model for capacitively coupled radio frequency (RF) sheaths of asymmetric (unequal electrode area) systems has been developed. It can be applied in the high-frequency (ω > ω _pi) regime at different pressures. An analytical approximation to the pressure-dependent ion density profile is used. The time-varying electric field and potential within the sheath are obtained by solving Poisson´s equation. The current balance and zero net DC current conditions are applied to solve for the RF sheath parameters and DC bias voltage. The DC voltage ratio between the powered and grounded electrode sheaths increases as the pressure decreases, which results in a larger DC bias voltage at lower pressures