Plasma reactor models

The wafer energy balance has to be solved simultaneously with the plasma reactor model since the etchant concentration, ion flux, and energy are needed as input to the wafer energy balance [98]. In turn, if the etch rate is temperature sensitive, the flux of product into the plasma (and in turn the plasma composition and output of the plasma reactor model) will depend on wafer temperature. Even for a temperature insensitive etch reaction, the wafer temperature will affect the gas density for an etch with controlled pressure (typical case). 

For any type of process which can be developed on an industrial scale, one must be able to plan all sorts of scaling on the economical and t hnical points of view. For this reason plasma torch or plasma reactor modeling has become an important study. For example Lonza Corp has proposed a study of the relative costs of different plasma torches that we have actualized (Table 11). In this paper we present an outline of the main plasma devices used in the ceramics field. 

Figure 2.1 shows a schematic diagram of the CVD equipment. A commercial low-pressure microwave (2.45 GHz) plasma reactor, Model AX5400 (ASTeX Coip., Wohurn, MA) was used (Fig. 2.2). This unit consists of a vacuum system, a microwave generating system and a gas supply system.

In practical applications, gas-surface etching reactions are carried out in plasma reactors over the approximate pressure range 10 -1 Torr, and deposition reactions are carried out by molecular beam epitaxy (MBE) in ultrahigh vacuum (UHV below 10 Torr) or by chemical vapour deposition (CVD) in the approximate range 10 -10 Torr. These applied processes can be quite complex, and key individual reaction rate constants are needed as input for modelling and simulation studies—and ultimately for optimization—of the overall processes. 

It is clearly shown, as already found by Penetrante and co-workers [33], Hoard and Balmer [34] and Dorai and Kushner [35], that the plasma reactor is able to produce oxygenates and RNO from RT to 400°C (673 K). Those species correspond to function 2 and they are necessary for the DeNO reaction according to the present model. 

Resist reactive-ion etching (RIE) was performed with a totally modified Tegal Model 400 plasma reactor. Ion-milling (IM) was accomplished with a Veeco three inch system. All resist RIE and IM etch rates are measured versus the rate of Si02 and PMMA as outlined above. 

Vanadium molecular size distributions in residual oils are measured by size exclusion chromatography with an inductively coupled plasma detector (SEC-ICP). These distributions are then used as input for a reactor model which incorporates reaction and diffusion in cylindrical particles to calculate catalyst activity, product vanadium size distributions, and catalyst deactivation. Both catalytic and non-catalytic reactions are needed to explain the product size distribution of the vanadium-containing molecules. Metal distribution parameters calculated from the model compare well with experimental values determined by electron microprobe analysis, Modelling with feed molecular size distributions instead of an average molecular size results in predictions of shorter catalyst life at high conversion and longer catalyst life at low conversions. 

Istadi and Amin, N. A. S. (2006). Hybrid Artificial Neural Network-Genetic Algorithm Technique for Modeling and Optimization of Plasma Reactor, Ind. Eng. Chem. Res., 45, pp. 6655-6664. 

Fig. 23. A methodology for modeling plasma reactors by braking the problem into smaller parts (top) From the reactor, to the feature, to the atomic scale, (bottom) Modules used for reactor scale model.

Plasma reactor simulations range from zero-dimensional (well-mixed) to three-dimensional. Well mixed [104-106] and one-dimensional models (including plug flow models [107, 108]) are best for sorting out the complicated gas and surface chemistry to arrive at a reduced reaction set for use in multidimensional simulations. Two-dimensional simulations can address the important aspect of reaction uniformity across the wafer radius. Three-dimensional simulations are useful for studying azimuthal asymmetries in the reactor due to non-axisymmetric power deposition, or non-axisymmetric gas inlets and pumping ports [109, 110]. 

Another critical need identified in Database Needs for Modeling and Simulation of Plasma Processing (Database, 1996) is the measurement of thermodynamic data for species of interest in plasmas (radicals and ions). Such data provide benchmarks for comparison with calculated potential energy surfaces, allow energetically unfavorable reaction pathways to be identified, and supply information necessary to estimate unknown reaction rates by transition state theory. Such thermodynamic information is a critical tool in understanding deposition and etching processes and in evaluating the optimum conditions for plasma reactors (Kruis et al, 1992). 

Model research operating conditions for a plasma reactor could comprise a 13.5 MHz RF generator for excitation with matching network and a power of 100 W, operating at a pressure of 2-50 Pa, with a gas flow rate of 8 0 cm min and contact time of 20 s—20 min... 

Moreover, Yamamoto et al. (Mahesh Akira, 2010) studied the decomposition characteristics and scale-up of the micro plasma reactor for the CO2 decomposition using simulation techniques. The plasma reactor configuration was modeled using the discharge and the recombination zones. In this study (Mahesh Akira, 2010), the plasma of the discharge zone is considered by the positive column and the cathode drop zone. Also, the conversion of CO2 and the energy efficiency of the reactor were evaluated. The plasma and the kinetic effects by reducing reactor diameter were analyzed separately. 

Modelling plasma chemical systems is a complex task, because these system are far from thennodynamical equilibrium. A complete model includes the external electric circuit, the various physical volume and surface reactions, the space charges and the internal electric fields, the electron kinetics, the homogeneous chemical reactions in the plasma volume as well as the heterogeneous reactions at the walls or electrodes. These reactions are initiated primarily by the electrons. In most cases, plasma chemical reactors work with a flowing gas so that the flow conditions, laminar or turbulent, must be taken into account. As discussed before, the electron gas is not in thennodynamic equilibrium... 

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