Model of the cathode fall region in magnetron discharges

Abstract

Using a 1D, two-fluid description, the influence of the magnetic field on the plasma boundary region adjacent to the cathode target in a magnetron has been investigated. Assuming the transport of magnetically confined electrons above the 'race-track' to be dominated by diffusion and mobility, with plasma ions falling directly to the cathode, the spatial variation in the electron and ion densities and velocities in the sheath and pre-sheath have been determined, together with the electric field structure. By assuming an electric field remnant in the plasma, the fluid equations have been integrated through the space-charge sheath up to the cathode, allowing smooth joining of the sheath and pre-sheath regions. Modelling with both constant and spatially varying magnetic fields has shown that realistic secondary electron fluxes are predicted for only a limited range of initial discharge parameters, indicating that Bohm diffusion of electrons is the most appropriate transport mechanism.Sheath widths are found to decrease with increasing magnetic field strength at the cathode and increase with cathode potential. In the constant-B -field case and for deep sheath potentials (>10 electron temperatures equivalent), the sheath behaviour is consistent with the Child-Langmuir law. However, the inclusion of a grad B force in the spatially varying magnetic field case gives rise to electron densities in the sheath, a significant fraction of the ion density (>10%).

Estimating electron drift velocities in magnetron discharges

“…a glow discharge in the absence of a magnetic field. Much has been published about the magnetron's operational principles and properties [1][2][3][4][5][6][7][8][9][10][11][12] and therefore it is sufficient to focus here on some relevant details related to the closed electron drifts. …”

Electron transport in the downstream region of planar unbalanced magnetron discharge

“…Since the motions of charged particles near the cathode is complicated by the complex configurations of magnetic and electric fields, many efforts have been made to accurately understand the discharge phenomena near the cathode through experimental [5][6][7][8][9][10][11][12] and theoretical works. [13][14][15][16][17][18][19] In theoretical works, two approaches of fluid model [13][14][15] and particle-in-cell/Monte Carlo method [16][17][18][19] have performed but, the PIC/MC simulations have been preferably done in spite of heavy computational load because of the inadequacy of the fluid model in lowpressure discharges of few mTorr and then, have provided a lot of information. However, the fluid model is in itself of great value in supplying the perspective understanding about the effects of various discharge parameters.…”

Positive sheath behaviour in low pressure Argon plasma

“…Therefore, absolute A and B values from Eq. (6) are not studied in the present paper. In the future we plan to model both effects to perform a full analysis of the phenomenon and obtain information from fit of Eq.…”

“…Mathematician Degond published many work about this law since 1990 [4]. This law is used in many fields of physics [5][6][7], for example in semiconductor physics [8,9]. Recent studies focus on 2D or time dependent behaviour [5,10].…”