Modelling of Complex Plasmas

Nowadays plasmas are used for various applications such as the fabrication of silicon solar cells, integrated circuits, coatings and dental cleaning. In the case of a processing plasma, e.g. for the fabrication of amorphous silicon solar cells, a mixture of silane and hydrogen gas is injected in a reactor. These gases are decomposed by making a plasma. A plasma with a low degree of ionization (typically 10_5) is usually made in a reactor containing two electrodes driven by a radio-frequency (RF) power source in the megahertz range. Under the right circumstances the radicals, neutrals and ions can react further to produce nanometer sized dust particles. The particles can stick to the surface and thereby contribute to a higher deposition rate. Another possibility is that the nanometer sized particles coagulate and form larger micron sized particles. These particles obtain a high negative charge, due to their large radius and are usually trapped in a radiofrequency plasma. The electric field present in the discharge sheaths causes the entrapment. Such plasmas are called dusty or complex plasmas. In this thesis numerical models are presented which describe dusty plasmas in reactive and nonreactive plasmas. We started first with the development of a simple one-dimensional silane fluid model where a dusty radio-frequency silane/hydrogen discharge is simulated. In the model, discharge quantities like the fluxes, densities and electric field are calculated self-consistently. A radius and an initial density profile for the spherical dust particles are given and the charge and the density of the dust are calculated with an iterative method. During the transport of the dust, its charge is kept constant in time. The dust influences the electric field distribution through its charge and the density of the plasma through recombination of positive ions and electrons at its surface. In the model this process gives an extra production of silane radicals, since the growth of dust is not included. Results are presented for situations in which the dust signi_cantly changes the discharge characteristics, both by a strong reduction of the electron density and by altering the electric field by its charge. Simulations for dust with a radius of 2 mu-m show that the stationary solution of the dust density and the average electric field depend on the total amount of the dust. The presence of dust enhances the deposition rate of amorphous silicon 2 at the electrodes because of the rise in the average electron energy associated with the decrease of the electron density and the constraint of a constant power input. This increase of deposition rate has also been observed in experiments by others. To study the behavior of dust in a less complicated environment, experiments in non-reactive plasmas have been carried out by a number of research groups. In these experiments the dust particles are injected through the electrodes in an argon discharge. These experiments have shown very interesting phenomena. Dust particles start to interact with each other in the discharge and form two-dimensional Coulomb clusters. These experiments often show an appearance of a void, a dustfree region in the discharge. Similar experiments have also been carried out under microgravity. These experiments have shown three-dimensional Coulomb clusters of dust particles also with the appearance of a void. Also rotating dust clouds (vortices) near the edges of the electrodes have been observed, that tend to rotate as long as the plasmas is on. To understand the behavior of the particles, we have developed a two-dimensional fluid model for a dusty argon plasma in which the plasma and dust parameters are solved self-consistently to study the behavior of dust particles. Simulations for dust with a radius of 7.5 mu-m show that a double space charge layer is created around the sharp boundary of the dust crystal. The inter-particle interaction is taken into account by means of an equation of state for the dust. A central dust-free region (void) is created by the ion drag force. The contribution of the thermophoretic force, driven by the temperature gradient induced by gas heating from ion-neutral collisions and heating of the dust particle material by the recombining ions and electrons, can be neglected in the quasi-neutral center of the plasma. Inside this void a strong increase of the production of argon meta-stables is found. This phenomenon is in agreement with experimental observations, where an enhanced light emission is seen inside the void

Fokker-Planck Equation for Boltzmann-type and Active Particles: transfer probability approach

Fokker-Planck equation with the velocity-dependent coefficients is considered for various isotropic systems on the basis of probability transition (PT) approach. This method provides the self-consistent and universal description of friction and diffusion for Brownian particles. Renormalization of the friction coefficient is shown to occur for two dimensional (2-D) and three dimensional (3-D) cases, due to the tensorial character of diffusion. The specific forms of PT are calculated for the Boltzmann-type of collisions and for the absorption-type of collisions (the later are typical for dusty plasmas and some other systems). Validity of the Einstein's relation for the Boltzmann-type collisions is analyzed for the velocity-dependent friction and diffusion coefficients. For the Boltzmann-type collisions in the region of very high grain velocity as well as it is always for non-Boltzmann collisions, such as, e.g., absorption collisions, the Einstein relation is violated, although some other relations (determined by the structure of PT) can exist. The generalized friction force is investigated in dusty plasma in the framework of the PT approach. The relation between this force, negative collecting friction force and scattering and collecting drag forces is established.+AFwAXA- The concept of probability transition is used to describe motion of active particles in an ambient medium. On basis of the physical arguments the PT for a simple model of the active particle is constructed and the coefficients of the relevant Fokker-Planck equation are found. The stationary solution of this equation is typical for the simplest self-organized molecular machines.+AFwAXA- PACS number(s): 52.27.Lw, 52.20.Hv, 52.25.Fi, 82.70.-yComment: 18 page

Modelling of Complex Plasmas

Nowadays plasmas are used for various applications such as the fabrication of silicon solar cells, integrated circuits, coatings and dental cleaning. In the case of a processing plasma, e.g. for the fabrication of amorphous silicon solar cells, a mixture of silane and hydrogen gas is injected in a reactor. These gases are decomposed by making a plasma. A plasma with a low degree of ionization (typically 10_5) is usually made in a reactor containing two electrodes driven by a radio-frequency (RF) power source in the megahertz range. Under the right circumstances the radicals, neutrals and ions can react further to produce nanometer sized dust particles. The particles can stick to the surface and thereby contribute to a higher deposition rate. Another possibility is that the nanometer sized particles coagulate and form larger micron sized particles. These particles obtain a high negative charge, due to their large radius and are usually trapped in a radiofrequency plasma. The electric field present in the discharge sheaths causes the entrapment. Such plasmas are called dusty or complex plasmas. In this thesis numerical models are presented which describe dusty plasmas in reactive and nonreactive plasmas. We started first with the development of a simple one-dimensional silane fluid model where a dusty radio-frequency silane/hydrogen discharge is simulated. In the model, discharge quantities like the fluxes, densities and electric field are calculated self-consistently. A radius and an initial density profile for the spherical dust particles are given and the charge and the density of the dust are calculated with an iterative method. During the transport of the dust, its charge is kept constant in time. The dust influences the electric field distribution through its charge and the density of the plasma through recombination of positive ions and electrons at its surface. In the model this process gives an extra production of silane radicals, since the growth of dust is not included. Results are presented for situations in which the dust signi_cantly changes the discharge characteristics, both by a strong reduction of the electron density and by altering the electric field by its charge. Simulations for dust with a radius of 2 mu-m show that the stationary solution of the dust density and the average electric field depend on the total amount of the dust. The presence of dust enhances the deposition rate of amorphous silicon 2 at the electrodes because of the rise in the average electron energy associated with the decrease of the electron density and the constraint of a constant power input. This increase of deposition rate has also been observed in experiments by others. To study the behavior of dust in a less complicated environment, experiments in non-reactive plasmas have been carried out by a number of research groups. In these experiments the dust particles are injected through the electrodes in an argon discharge. These experiments have shown very interesting phenomena. Dust particles start to interact with each other in the discharge and form two-dimensional Coulomb clusters. These experiments often show an appearance of a void, a dustfree region in the discharge. Similar experiments have also been carried out under microgravity. These experiments have shown three-dimensional Coulomb clusters of dust particles also with the appearance of a void. Also rotating dust clouds (vortices) near the edges of the electrodes have been observed, that tend to rotate as long as the plasmas is on. To understand the behavior of the particles, we have developed a two-dimensional fluid model for a dusty argon plasma in which the plasma and dust parameters are solved self-consistently to study the behavior of dust particles. Simulations for dust with a radius of 7.5 mu-m show that a double space charge layer is created around the sharp boundary of the dust crystal. The inter-particle interaction is taken into account by means of an equation of state for the dust. A central dust-free region (void) is created by the ion drag force. The contribution of the thermophoretic force, driven by the temperature gradient induced by gas heating from ion-neutral collisions and heating of the dust particle material by the recombining ions and electrons, can be neglected in the quasi-neutral center of the plasma. Inside this void a strong increase of the production of argon meta-stables is found. This phenomenon is in agreement with experimental observations, where an enhanced light emission is seen inside the void