Fast 2D fluid-analytical simulation of ion energy distributions and electromagnetic effects in multi-frequency capacitive discharges

E. Kawamura, M. A. Lieberman, D. B. Graves

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42 Scopus citations


A fast 2D axisymmetric fluid-analytical plasma reactor model using the finite elements simulation tool COMSOL is interfaced with a 1D particle-in-cell (PIC) code to study ion energy distributions (IEDs) in multi-frequency capacitive argon discharges. A bulk fluid plasma model, which solves the time-dependent plasma fluid equations for the ion continuity and electron energy balance, is coupled with an analytical sheath model, which solves for the sheath parameters. The time-independent Helmholtz equation is used to solve for the fields and a gas flow model solves for the steady-state pressure, temperature and velocity of the neutrals. The results of the fluid-analytical model are used as inputs to a PIC simulation of the sheath region of the discharge to obtain the IEDs at the target electrode. Each 2D fluid-analytical-PIC simulation on a moderate 2.2 GHz CPU workstation with 8 GB of memory took about 15-20 min. The multi-frequency 2D fluid-analytical model was compared to 1D PIC simulations of a symmetric parallel-plate discharge, showing good agreement. We also conducted fluid-analytical simulations of a multi-frequency argon capacitively coupled plasma (CCP) with a typical asymmetric reactor geometry at 2/60/162 MHz. The low frequency 2 MHz power controlled the sheath width and sheath voltage while the high frequencies controlled the plasma production. A standing wave was observable at the highest frequency of 162 MHz. We noticed that adding 2 MHz power to a 60 MHz discharge or 162 MHz to a dual frequency 2 MHz/60 MHz discharge can enhance the plasma uniformity. We found that multiple frequencies were not only useful for controlling IEDs but also plasma uniformity in CCP reactors.

Original languageEnglish (US)
Article number064003
JournalPlasma Sources Science and Technology
Issue number6
StatePublished - Dec 1 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics


  • Multi-frequency sources
  • capacitive discharges
  • electromagnetic effects
  • fluid simulations
  • ion energy distributions
  • particle-in-cell simulations


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