A unified boundary sheath/pre-sheath model for DC and RF driven low pressure discharges

Summary form only given. A unified theory is presented which describes, in one consistent framework, the boundary sheath and pre-sheath of low pressure gas discharges both for the case of DC and of RF excitation. The basis of the model is a simple, but sufficiently realistic macroscopic (fluid-dynamical) plasma description. It is assumed that the boundary sheath is thin compared to the total reactor dimensions, so that a planar formulation suffices. The electrons of the plasma are modeled in terms of a standard drift-diffusion equation with constant transport coefficients, inertia effects and ionization in the sheath are neglected. The ions are captured in a cold fluid description, with inertia effects included (because they may dominate the dynamics due to the high ion mass mass m), but any other than ambipolar diffusion neglected (because of the low ion temperature). The coupling electrical field is described by Poisson´s equation; magnetic fields are neglected. In a semi-analytical approach, the quoted equations are simplified by means of an asymptotic scale expansion, adopting the assumptions that i) the electron motion is fast compared to the frequency of the super-imposed electrical field, ii) the ion motion is slow, and iii) the thermal electron energy is small compared to the boundary sheath potential. These assumptions, which hold on the 10%-level in a typical processing plasma (meaning that the corresponding smallness parameters are about 0.1), allow to reduce the above equations considerably. As a result of the analysis, a single ordinary differential equation for the ion density /spl rho/=/spl rho/(x) is obtained.