Investigation of Plasma Induced Cluster Formation and Thin Film
Deposition
THE WORK DONE DURING THE PRESENT YEAR
Preface
The interest to monosilane ( SiH 4 ) plasma of glow discharge is stimulated by
widespread use of amorphous silicon films in microelectronics. The glow discharge t
occurs in plasma chemical reactors of low pressure during chemical vapour deposition
of hydrogenated amorphous silicon films (   Si : H4 ). Planar plasma chemical
reactors with two parallel electrodes (fig. 1) are often used for plasma enhanced
chemical vapour deposition of   Si : H4 thin films.
Fig. 1 Scheme of plasma enhanced chemical
vapour deposition reactor. RF discharge
source is connected with the set of plane
parallel electrodes. The mixture of gases
containing silane is situated between the
electrodes. Silane decays due to electron
impact. It results in deposition of amorphous
silicon hydride film. Here IMN is the high
frequency transformer.
Determination of simplest physical model.
Let us consider 1D model in order to get accustomed to the physics of the
process, employed models and methods of their numerical implementation.
1D model of radio frequency discharge includes hydrodynamical description of
electrons and ions. For electrons the transport equations for concentration and mean
energy are solved. For positive and negative ions the equations of hydrodynamics are
solved [32.
The distribution of potential  is described by Poisson equation:
Differential schemes
To solve the present equation system the simplest differential schemes were
selected that require minimal efforts while developing their parallel version.
Nevertheless it required a large number of test computations to find a steady
differential scheme for each equation since the equations are nonlinear.
Equations of the system for density and energy contain the second derivative of
these function with respect to spatial coordinate. It means that explicit schemes cannot
provide sufficient stability. An implicit scheme with weights was selected, the weight
parameter being determined on the example of a test problem of shock wave
propagation.
The equations are implemented by means of an explicit scheme with directed
differences:
In the same way the equation for negative ions concentration is implemented.
The equations for velocities of positive and negative ions are implemented by means
of the traditional explicit scheme with directed differences.
The equation of potential determination was traditionally solved by sweeping
method. It should be noticed that in order to make the schemes more simple central
differences were used for approximation of spatial derivatives whenever it was
possible.
Introduction of PIC method with collisions into the program.
Particle collisions are treated with Monte-Carlo method. Our scheme generally
follows the null collision method described in [16].
Couple interactions of particles are not considered. It is assumed that every
particle suffers a collision during time interval and thus scatters from initial direction
to some angle. In this model collision probability does not determine, either the
particle has suffered a collision or not, but gives a correction to the scattering angle of
the particle.
Let us introduce a spherical coordinate system. The direction of Z axis is
similar with initial direction of particle’s velocity, the scattering angle of the particle θ
gives the deviation of the new velocity vector from Z axis Azimuthal angle of the
spherical coordinate system φ (direction of scattering of the particle) is computed as a
random number with uniform distribution in the interval from 0 to 2π.
At every timestep the velocities of particles are recomputed with the above
listed formulae. During the period of time equal to 1 the initial velocity distribution
relaxes to Gaussian.
Refererences
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