Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

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