Modeling Electronegative Plasma Discharges

Allan J. Lichtenberg, V. Vahedi, Michael A. Lieberman and T. Rognlien

EECS Department
University of California, Berkeley
Technical Report No. UCB/ERL M93/74
1993

A macroscopic analytic model for a three-component electronegative plasma has been developed. Assuming the negative ions to be in Boltzmann equilibrium, a positive ion ambipolar diffusion equation is found. The electron density is nearly uniform, allowing a parabolic approximation to the plasma profile to be employed. The resulting equilibrium equations are solved analytically and matched to an electropositive edge plasma. The solutions are compared to a simulation of a parallel-plane r.f. driven oxygen plasma for two cases: (1) p=50 mTorr, neo = 2.4x10 (15) m-3, and (2) 10 mTorr, new = 1.0x10 (16) m-3. In the simulation, for the low power case (1), the ratio of negative ion to electron density was found to be alpha sub 0 is almost equal to 8, while in the higher power case alpha sub 0 is almost equal to 1.3. Using an electorn energy distribution that approximates the simulation distribution by a two-temperature Maxwellian, the analytic values of alpha sub zero are found to be close to, but somewhat larger, than the simulation values. The average electron temperature found self-consistently in the model is close to that in the simulation. The results indicate the need for determining a two-temperature electron distribution self-consistently within the model.


BibTeX citation:

@techreport{Lichtenberg:M93/74,
    Author = {Lichtenberg, Allan J. and Vahedi, V. and Lieberman, Michael A. and Rognlien, T.},
    Title = {Modeling Electronegative Plasma Discharges},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1993},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2437.html},
    Number = {UCB/ERL M93/74},
    Abstract = {A macroscopic analytic model for a three-component electronegative plasma has been developed. Assuming the negative ions to be in Boltzmann equilibrium, a positive ion ambipolar diffusion equation is found. The electron density is nearly uniform, allowing a parabolic approximation to the plasma profile to be employed.  The resulting equilibrium equations are solved analytically and matched to an electropositive edge plasma. The solutions are compared to a simulation of a parallel-plane r.f. driven oxygen plasma for two cases: (1) p=50 mTorr, neo = 2.4x10 (15) m-3, and (2) 10 mTorr, new = 1.0x10 (16) m-3. In the simulation, for the low power case (1), the ratio of negative ion to electron density was found to be alpha sub 0 is almost equal to 8, while in the higher power case alpha sub 0 is almost equal to 1.3. Using an electorn energy distribution that approximates the simulation distribution by a two-temperature Maxwellian, the analytic values of alpha sub zero are found to be close to, but somewhat larger, than the simulation values. The average electron temperature found self-consistently in the model is close to that in the simulation. The results indicate the need for determining a two-temperature electron distribution self-consistently within the model.}
}

EndNote citation:

%0 Report
%A Lichtenberg, Allan J.
%A Vahedi, V.
%A Lieberman, Michael A.
%A Rognlien, T.
%T Modeling Electronegative Plasma Discharges
%I EECS Department, University of California, Berkeley
%D 1993
%@ UCB/ERL M93/74
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2437.html
%F Lichtenberg:M93/74