# 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