Spherical shell model of an asymmetric rf discharge

Journal Article · Thu Jun 01 00:00:00 EDT 1989 · J. Appl. Phys.; (United States)

DOI:https://doi.org/10.1063/1.343298· OSTI ID:6320494

Lieberman, M A

A spherical shell model is used to study ion transport and bias voltage formation in asymmetric, capacitive rf discharges, which have unequal areas A and glow-to-electrode voltages V at the powered (a) and grounded (b) electrodes. Ions are generated by thermal electron ionization and are lost by ambipolar diffusion in the glow. Resonant charge transfer with a constant cross section is assumed to dominate the ion transport. We obtain the density ratio scaling n/sub a//n/sub b/proportional(A/sub b//A/sub a/ )/sup 7//sup ///sup 24/, where n is the density at the glow-sheath edge. Three electrode sheath models are considered: collisionless ions, collisional (constant mobility) ions, and a constant-ion cross-section collisional law. Using these and the continuity of the rf current flow, we obtain the scaling of the electrode voltage ratio with the electrode area ratio: V/sub a//V/sub b/proportional(A/sub b//A/sub a/ )/sup q/. For typical rf materials processing discharges, the constant cross section law yields qapprox. =2.21. The effects of secondary electron ionization and local ionization near the sheaths due to stochastic heating are shown to further reduce the value of q.

• Research Organization: Department of Electrical Engineering and Computer Sciences and the Electronics Research Laboratory, University of California, Berkeley, California 94720
• OSTI ID: 6320494
• Journal Information: J. Appl. Phys.; (United States), Journal Name: J. Appl. Phys.; (United States) Vol. 65:11; ISSN JAPIA
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
AMBIPOLAR DIFFUSION
CHARGED PARTICLES
CONFIGURATION
DIFFUSION
ELECTRIC DISCHARGES
ELECTRIC POTENTIAL
ELECTROMAGNETIC RADIATION
IONS
MATHEMATICAL MODELS
RADIATIONS
RADIOWAVE RADIATION
SCALING LAWS
SHELLS
SPHERICAL CONFIGURATION
TRANSPORT THEORY