Dynamics of sheaths in low pressure RF discharges

Abstract

Low-pressure RF discharges are widely used for materials processing. Typical parameters are pressure of 1-100 mtorr, frequency of 13.56 MHz, and RF voltage of 50-1000 V. A reasonably complete picture of the dynamics of these sheaths has been developed. Some typical results for a high-voltage sheath driven by a sinusoidal current source, under the assumptions of time-independent, collisionless ion motion and inertialess electrons, are: (1) the ion sheath thickness s/sub m/ is square root 50/27 larger than a Child's law sheath for the same DC voltage and ion current density; (2) the sheath capacitance per unit area for the fundamental voltage harmonic is 1.226 epsilon /sub 0//s/sub m/, where epsilon /sub 0/ is the free space permittivity; (3) the ratio of the DC to the peak value of the oscillating voltage is 54/125; (4) the second and third voltage harmonics are, respectively, 12.3% and 4.2% of the fundamental; and (5) the conductance per unit area for stochastic heating by the oscillating sheath is 2.98 ( lambda /sub D//s/sub m/)/sup 2/3/ ( epsilon /sup 2/n/sub 0//mu/sub e/), where n/sub 0/ is the ion density, lambda /sub D/ is the Debye length at the plasma-sheath edge, and u/sub e/=(8eT/sub e// pi m)/sup 1/2/ is the mean electron speed.<>