Abstract
Nanoparticle charging in a capacitively coupled radio frequency discharge in argon is studied using a particle in cell Monte Carlo collisions method. The plasma parameters and dust potential were calculated self-consistently for different unmovable dust profiles. A new method for definition of the dust floating potential is proposed, based on the information about electron and ion energy distribution functions, obtained during the kinetic simulations. This approach provides an accurate balance of the electron and ion currents on the dust particle surface and allows us to precisely calculate the dust floating potential. A comparison of the obtained floating potentials with the results of the traditional orbital motion limit (OML) theory shows that in the presence of the ion resonant charge exchange collisions, even when the OML approximation is valid, its results are correct only in the region of a weak electric field, where the ion drift velocity is much smaller than the thermal one. With increasing ion drift velocity, the absolute value of the calculated dust potential becomes significantly smaller than the theory predicts. This is explained by a non-Maxwellian shape of the ion energy distribution function for the case of fast ion drift.
Highlights
The PIC-MCC model of a high frequency discharge plasma with nanoparticles is based on the electron and ion kinetic equations, including their interaction with dust and the Poisson equation
The simplest way for the direct definition of the currents is to count the number of events of electron and ion absorption by the dust particles with the cross sections (4) during the test particles motion simulation, with adjustment of the floating potential to minimize the difference in the electron and ion currents
Our method provides an accurate dust potential determination during the rf discharge simulation and can be used to test the validity of the traditional orbital motion limit (OML) approach (equations (7) and (8))
Summary
The PIC-MCC model of a high frequency discharge plasma with nanoparticles is based on the electron and ion kinetic equations, including their interaction with dust and the Poisson equation. In this model, the velocity distribution functions of electrons, fe(t, x, v), and ions, fi(t, x, v) (three-dimensional over velocity and one-dimensional in space) are obtained by solving the Boltzmann equations numerically,. Our model incorporates the cross sections of electron and ion absorption by negatively charged dust particles, taken from the orbital motion limit (OML) theory [9]: σed = πrd2(1 + eφd/εe), εe > −eφd, σed = 0, εe < −eφd,. We restrict our study to static dust and concentrate on the determination of the dust floating potential
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