Dynamics of collisionless rf plasma sheaths

Abstract

The behavior of rf plasma sheaths has been the subject of much scientific study and also is technologically important for plasma etching and deposition in the manufacture of integrated circuits. This paper presents a semianalytic model of rf sheaths and describes an experiment that tested the model. An approximation to the first integral of the Poisson equation allows solving for the response of plasma sheaths to an imposed rf bias voltage. This approximation enables the plasma sheaths to be included within an electrical model of the plasma and external rf circuit components, and affords a prediction of the ion energy distributions impacting the electrodes, which are in contact with the plasma. The model is a significant advance beyond previous sheath models because it has no restriction on the ratio of the rf period to the ion transit time across the sheath. The model is applicable to those high-density, low-pressure plasmas in which the Debye length is a small fraction of the ion mean-free path, which itself is a small fraction of the plasma dimension. The experimental test of the model was conducted by comparing the predicted and measured rf potential, current, and power at the sheath adjacent to a capacitively coupled, rf-biased electrode in a plasma reactor with argon discharges sustained by an inductively coupled plasma source. The comparisons included both linear and nonlinear components of the rf electrical parameters. Results of the experiment were in substantial agreement with model predictions.

Ion energy distribution measurements in rf and pulsed dc plasma discharges

“…An analytical expression for E for all values of τ i /τ rf is also given by Sobolewski et al [29] which uses the rf sheath model described in [37]. This model is solved in terms of the ion plasma frequency at the sheath edge rather than the ion transit time.…”

Use of RF Bias in LAPPS (Large Area Plasma Processing System)

“…Various theories and experiments have explored these higher density regimes [7][8][9][10] In Ref. 8, we show that the characteristics of a collisionless rf sheath can be specified in terms of two dimensionless parameters, o^/a) and v os /c s .…”

“…io)-v e a e -Q c ioo-v e (10) Here Qe is the electron gyrofrequency and v e is the electron collision frequency. The substrate to be processed may or may not be a conductor, but it is mounted on an rf-biased platen which is a conductor, and which in the case of LAPPS is very large (typically 1 m).…”

Hydrodynamic Model of Plasma-Sheath for RF Discharges with and without Collision

“…[6][7][8] There are a few methods for modeling plasma-wall under applied RF potential. These include the bulk plasma model, the step-front-electron sheath model, and the asymptotic expansion method.…”