Ion energy distribution function in dual-frequency rf capacitively coupled discharges: analytical model

Area of Science:

• Plasma Physics
• Atomic and Molecular Physics
• Physical Chemistry

Background:

• Radio frequency (RF) discharges are widely used in plasma processing.
• Understanding ion energy distribution functions (IEDFs) is critical for controlling plasma-based manufacturing processes.
• Dual frequency (DF) discharges offer enhanced control over plasma parameters compared to single frequency discharges.

Purpose of the Study:

• To develop an analytical approach for calculating the IEDF in a collisionless DF RF discharge in argon.
• To analyze different frequency regimes within the DF discharge.
• To derive expressions for ion spectrum width and ion energies.

Main Methods:

• Analytical calculation of the IEDF.
• Discussion of three limit regimes for frequency relations.
• Derivation of analytical expressions for ion spectrum width, minimum, and maximum ion energies.
• Comparison with particle-in-cell Monte Carlo simulations and a semianalytical model.

Main Results:

• An analytical IEDF was obtained for the intermediate-frequency regime, relevant to plasma processing.
• Analytical expressions for ion spectrum width and energy limits were derived.
• The analytical theory shows good agreement with numerical simulations.

Conclusions:

• The developed analytical approach provides accurate IEDFs for DF RF discharges.
• The findings are applicable to optimizing industrial plasma processing technologies.
• The study validates the analytical model against numerical and semianalytical methods.