Hydrogenated Amorphous Carbon Deposition by Saddle-Field Glow Discharge
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anode
cathode
Figure 1. The saddle-field parallel electrode configuration.
e-
consisting of two wires [2]. It is referred to it as the saddle field-configuration. We use a wire grid anode. A fraction of the electrons approaching the anode can go through it and enter a second, symmetrical part of the discharge chamber attached to the anode from the other side. The electric field directs electrons to the anode from both sides ofthe anode. Electrons are then forced to oscillate about the anode increasing the number of ionization events per electron when compared with a solid, non transparent, anode. For diamond-like carbon film deposition we make both the anode and cathodes of a wire grid and the substrates are positioned behind the cathodes on electrically biased and heated substrate holders [3].
239 Mat. Res. Soc. Symp. Proc. Vol. 593 © 2000 Materials Research Society
2. MATHEMATICAL MODELING OF THE SADDLE FIELD GLOW DISCHARGE Electrons present in the chamber are accelerated by the electric field toward the anode from both sides. The anode transparency, T, gives the fraction of the electrons reaching the anode plane that penetrate the anode to emerge on the other side. Also, the probability of a very fast electron passing through the anode plane without changing velocity approaches T. The oscillating electrons undergo elastic and inelastic collisions with molecules of the gas. Inelastic collisions create secondary electrons leading to multiplication of electrons. Increasing the anode transparency increases the average path length of electrons and increases the average probability of ionization per electron. To find the distribution function for electrons we use the linear Boltzmann equation: • (0e - eft
I"fe (fioO)+ Se + Re.
(2)
m
Here F and V'are the position and velocity of the electron, m and e are the electron mass and elementary charge, (r-) is the electric field, and fe(?, V)d~d is the number of electrons inside the infinitesimal phase volume dd-V. l is the collision integral determined by the differential cross sections for elastic and inelastic electron-atom collisions [4]. Se(F, V) is the electron source, set by the current density of electrons at the cathode, Re(F,v) is the recombination rate determined by electrons-ion recombination. To obtain the ion distribution function, f, (F,v-)we use the Boltzmann equation:
E-
( +R,.
(3)
where Mis the ion mass, f,(f, V)dFdV is number ofions inside the infinitesimal phase volume dFdV and R, = Re. The system of integer-differential equations (2) and (3) can be solved by the Direct Monte Carlo Method if the cross sections for elastic and inelastic collisions, the functions Se(,ýV)andf(r-) and the boundary conditions are given [4,5]. In the very early stage of the discharge, shortly after the anode potential is applied, we can assume a uniform electric field exists between the anode and cathode. However, as the discharge develops a space charge is established and the field is modified. To find the steady state electric field in an established discharge we
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