Monte-Carlo simulation of cylindrical Langmuir probe sheaths

Makoto Goto, Min Sheng1), Toshiki Takahashi1), Naotaka Iwasawa2), Yoshiomi Kondoh1), and Tomio Okada3)

Department of Electronic Engineering, Hokuriku Polytechnic College, Uozu, Toyama 937-0856, Japan
1)Department of Electronic Engineering, Gunma University, Kiryu, Gunma 376-8515, Japan
2)Satellite Venture Business Laboratory, Gunma University, Kiryu, Gunma 376-8515, Japan
3)Department of Information Engineering, Maebashi Institute of Technology, Maebashi, Gunma 371-0816, Japan

The electric probe known as the Langmuir probe is commonly used to diagnose parameters (e.g. the electron temperature) for steady-state, isotropic, and unmagnetized plasmas. Besides measurements of the quiet plasmas, requirements to observe the plasma parameters of RF glow discharges for etching and sputtering applications have been increased recently, as the role of the plasma processing in the modern technologies is increasing. If a simulation study of the RF glow discharges predicts well experimental characteristics, the results provide useful information, such as the spatial variation of plasma parameters in the sheaths and plasma, and their temporal evolutions. This study is the bench mark to confirm good agreement of the simulation results with the experimental current-voltage characteristics of Langmuir probe, because of inevitable requirement for further applications of simulation codes established.
In the present study, the particle simulation is carried out for the cylindrical Langmuir probe in argon plasma. Orbits of both ions and electrons are traced, and the variation of potential in the sheath is self-consistently calculated by solving Poisson’s equation. The Monte-Carlo method is employed for computation of atomic collisions. The cross section for elastic scatterings between electrons and argon neutrals is introduced to calculate the collision frequency. The excitation processes for electron impact on argon are also considered; the cross sections for 25 excited states are summed up and the unified cross section is used in order to shorten the CPU time. Energy loss of electrons by the inelastic scattering is taken into account. The fine subslab technique and weight probability method are used [1, 2] and modified especially in plasma source region (object of measurements) so that high energy particles are generated and simulated over the simulation space and time. Electron energy distributions are obtained with a range of over 4 orders of magnitude and electron retarding current shows exponential curve over 3 orders in the simulation results of Maxwellian plasma source using 2000 particles in a slab. Not only the electron saturation current but also the ion saturation current is in good quantitative agreement with the probe theory and experimental measurements.

References

[1] M. Goto, Y. Kondoh, and M. Matsuoka, Jpn. J. Appl. Phys. 36 (1997) 4815.
[2] M. Goto and Y. Kondoh, Jpn. J. Appl. Phys. 37 (1998) 308.