Modeling, plasma

Nienhuis et al. [189, 191] have developed a self-consistent fluid model that describes the electron kinetics, the silane-hydrogen chemistry, and the deposition 

The main reason for using a 1D model is the reduction of the computational effort compared to the higher-dimensional models. This reduction to one dimension is acceptable because it is possible to study the sustaining mechanisms and the chemistry in the discharge with a ID self-consistent model. 

To verify the model and to establish in which process parameter space it is valid, a comparison is made with experimental data. These experimental data are the partial pressures of silane, disilane, and hydrogen and the growth rate, obtained during deposition of amorphous silicon. Data are compared for various combinations of the total pressure in the reactor, the electrical power, and the frequency of the power source. 

A sensitivity study of the influence of the elementary data (i.e., reaction coefficients, cross sections, and transport coefficients) has been performed to determine the importance of specific elementary data, so to guide further research in this area [189]. 

For each nonradical neutral j in the discharge volume Vo, the balance equation of their total number can be written as 

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B. Some Recent Developments Bohm-Pines Plasma Model,... 

Comparatively little space will therefore be devoted to some rather recent approaches, such as the plasma model of Bohm and Pines, the two-body interaction method developed by Brueckner in connection with nuclear theory, Daudel s loge theory, and the method of variation of the second-order density matrix. This does not mean that these methods would be less powerful or less impor-... 

An entirely different approach to the correlation problem is taken in the plasma model (Bohm and Pines 1953, Pines 1954, 1955), in which the electrons in a metal are approximated by a free-electron gas moving in a uniform positive background. According to classical discharge theory, such a plasma is characterized by an oscillatory behavior having a frequency... 

From the point of view of principles, it is interesting to note that the method based on the generalized form of Eq. III. 129 seems to be very closely connected both with Wigner s classical theory described in Section III.B and with Bohm and Pines plasma model (Krisement 1957). Following Krisement, we will replace the various trial functions flt /2,. . ., fn in Eq. III.9 by a single average function /, and Wigner s basic wave function (Eq. II1.7) takes then the simple form... 

Putting Wigner s theory in the simplified form (Eq. III. 130), Krisement was able to compare it with the results of the plasma model where, in a first approximation, Pines wave function may be written in the generalized form (Eq. III. 129) with... 

Bohm-Pines" plasma model seems at first sight to be very different from the expansion methods treated here, but in Section III.E(2b) it was shown that it is rather closely connected with the method using correlation factor. Similar to Wigner s formula, it probably gives reasonable values for the correlation energy for the... 

The plasma model itself gives an important contribution to the theory of systems containing highly mobile electrons, and particularly its treatment of the screening phenomena is of value. The model has been carefully described in some reviews, and here we would like to refer to Pines (1955). We note that the plasma model has essentially been constructed for treating metals, but it would be interesting to see whether the basic ideas could be applied also to other many-electron systems. 

Photochemical dissociation, 202 Photolyses, 200 Pine s wave function, 306 Plasma frequency, 306 Plasma model, 207, 304, 306, 318, 319, 323... 

Schwerdtfeger, P McFeaters, J.S., Stephens, R.L., Liddell, M.J., Dolg, M. and Hess, B.A. (1994) Can AuF be synthesized A theoretical study using relativistic configuration interaction and plasma modelling techniques. Chemical Physics Letters, 218, 362—366. 

In a silane-hydrogen discharge the feedstock gases SiHa and H2 take part in all the processes that occur. A large number of reactions have been proposed (see e.g. Kushner [190]). Nienhuis et al. [191] have performed a sensitivity analysis in their self-consistent fluid model, from which a minimum set of reactions have been extracted for a typical low-pressure RF discharge. Tables II and III list these reactions. They will be used in the plasma models described in subsequent sections. The review articles on silane chemistry by Perrin et al. [192] and on hydrogen by Phelps [193] and Tawara et al. [194] have been used. The electron collision data are compiled in Figure 13 [189]. 

In order to be able to explain the observed results plasma modeling was applied. A one-dimensional fluid model was used, which solves the particle balances for both the charged and neutral species, using the drift-diffusion approximation for the particle fluxes, the Poisson equation for the electric field, and the energy balance for the electrons [191] (see also Section 1.4.1). 

In this chapter the deposition of n-Si H by PECVD has been described. The chapter covers material as well as discharge issues. It tries to relate material and discharge properties in various ways. Plasma modeling provides a means to study in detail the physical and chemical processes that occur in the plasma. The presented models show a high degree of sophistication, but from the comparison with experimental data it is clear that especially the deposition model needs improvement. Also, a full 2D model most probably is not needed, as differences between ID and 2D modeling results are not very large. 

Plasma analysis reveals information on the products of chemical processes, and can be used to good effect as a feedback to plasma modeling. The role of ions has been thoroughly illustrated, and the important result that ion bombardment with moderate energy is beneficial for material quality has been quantified. 

I very much enjoyed the fruitful collaboration with Wim Goedheer and his group—Gert Jan Nienhuis, Peter Meijer, and Diederick Passchier—at the FOM Institute for Plasmaphysics Rijnhuizen, and thank him for supplying me with published and additional data used in the section on plasma modeling. 

Our lack of knowledge concerning the mechanisms of molecular recombination has serious consequences for plasma modeling. If the measured data are subject to three-body and field effects, then their application to low-density plasmas (e.g. space plasmas) is questionable. For this reason, studies that focus on recombination... 

The competitive equilibria based on the different plasma models cannot solely explain the in vivo behaviour of Gd111 complexes. The excretion of low molecular weight Gd111 chelates from the body is very rapid (e.g., t1/2 = 1.6 h for [Gd(DTPA)]2 ),M0 whereas the dissociation and trans-metallation of the Gd111 complexes is relatively slow. Therefore, the system is far from equilibrium and kinetic factors could substantially change the predicted amount of free Gd3+. 

This result gives in fact the mathematical limitation for the validity of the plasma approximation developed in the two preceding sections even with solvent molecules interacting with the ions, the plasma model will he valid in the limit of Brownian ions, provided that conditions (376) holds. 

According to two simultaneous hypotheses15,16, the principal component of the 7 of simple metals (from lithium to aluminum) originates in the shift in the zero-point energy of the plasma models of the system when one perfect crystal is broken into two separate crystals. Some simplifications and arbitrary assumptions lead finally to the relation... 

To explain the behavior of Gd3+ chelates and for a better understanding of their in vivo fate, it is necessary to know the equilibrium properties of the CAs in the plasma. Since the human plasma is a very complicated system, where a huge number of metal ions and ligands can form complexes of different types, a simplified plasma model must be used in order to approximate to the equilibrium situation, including the speciation of Gd3+. 

To characterize the kinetic stabilities of complexes, the rate constants should be used, determined for the exchange reactions occurring between the complexes and endogenous metal ions (e.g. Cu2+ and Zn2+). Similarly to the equilibrium plasma models, the development of a kinetic model is needed for a better understanding of the relation between the extent of in vivo dissociation and the parameters characterizing the rates of dissociation, the rates of distribution in the extracellular space and the rates of excretion of the Gd3+ complexes. 

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