Microwave plasma modeling with COMSOL MULTIPHYSICS

Transcription

1 Microwave plasma modeling with COMSOL MULTIPHYSICS O. Geoffroy*, H. Rouch, INOPRO Telespace Vercors - 118, chemin des Breux F Villard de Lans * olivier.geoffroy@inopro.com Abstract: A microwave plasma simulation has been tested, and will be fitted and validated. Two types of assumptions were compared: in the first approach the plasma density depends directly from the electric field and some characteristic values of it; in the second approach plasma density and temperature conservation equations are solved. The last one was used for Nitrogen plasma. In case of SF6 and H2O plasma simulation quite simple kinetics models will be used, and fitted by comparison with experimental observations. The last part of this work is under progress. Keywords: plasma, process, industrial applications. 1. Introduction One of the most interesting simulation objective is to give predictive results showing geometrical or scale effects for industrial processes. This is commonly done taking in account neutral and non reactive CFD. This is also quite common but with less precision in combustion fields. This is also possible taking in account reactive effects even in case of lacking data [1], for example for MOCVD processes. In case of a research work, the main objective is usually to validate a kinetic model by comparison of simulation results with measurable experimental data. This is usually done for research reactor with simple geometry and by direct comparison of the unknown, for example gas composition or electronic density in case of plasma. We often Work on industrial application so we have to simulate real geometry and have no access to direct comparison but may validate the model by indirect comparison: growth rate, light emission for example. The main reason is the objectives we address which are usually not the physical processes knowledge (typically a research objective) but to improve productivity by studying all is around the process. The proposed methodology ( 2) follow this industrial goal and is apply to microwave plasma processes. After a description of the whole methodology, the solved equation are presented ( 3) and then the physical and chemical assumption for Hydrogen and Oxygen plasma, and then our results for these two cases ( 4). 2. Methodology Our general methodology to study real industrial equipments involving complex physical and chemical phenomenon consist of mixing predictive simulations and experience plan with experimental comparison. But doing simulation with unreliable data induce bad precision. That's why a great research effort to characterize physical and kinetics data is an important goal. Unfortunately industry usually don't want to pay it because of the too long return on investment. In the other hand the usual experience plan are specific to each process and doesn't include enough science knowledge. Because simulation is at the corner between these two job (research and industrial development), we propose to mix both. So we use all available models to simulate real equipment even if some data are missing. For these data we plan experimental comparisons to settle open parameters of the specific model. Of course the chosen model should not include too many uncertain parameters. This methodology has to be adapted to the industrial goal to give a good return on investment: that's why predictive is between comma at the beginning of this chapter. The precision and the predictive ability of simulations are themselves parameter of the project. The presented study is the first part of the application of this methodology to plasma processes. In the case of neutral chemistry the conservative equations and their boundary conditions are well known and have not to be adapted. The work is only on kinetics models which depend on expected precision and data which may be adapted from bibliography. In the plasma case, the physics itself is more complex and some choices have to be done on the conservation equation themselves. In this study we tested two possibilities for microwave plasma simulation corresponding to different simplification level.

2 The next step will be to use these models to simulate more complex chemistries, after choosing and adapting simplified kinetic models. Of course the interpretation of the results may be an hard challenge, but at this stage we have to include an experience plan methodology in the project, and the comparison with experimental results will be helpful. Even electron density measurements are difficult, so we plan to use relative data from more simple measurement to settle and validate the kinetic models. 3. Models 3.1 Geometry As mentioned in introduction the goal of this study is to validate the feasibility of microwave plasma modeling in a powerful way for industrial applications. The simulated geometry are very simple. The presented results for hydrogen were calculated on the same geometry than Funer [3]. The presented results for nitrogen plasma correspond to simple geometry (figure 1). From bottom to top of the figure 1 we can see the coaxial connection, the antenna zone, the plasma zone, the gas inlet and pumping. inlet pumping and temperature. The thermal equation are linked with the plasma model, in order to compute Joule heating in the reactor with: Q= 1 2 E2 The electromagnetic equation also relie on plasma model from its conductivity and permittivity, which are: =. 2 0 pe. en 2 i pe and en r =1 en 2 pe en 2. en 2 i. pe 2 2 en 2 where w are the excitation frequency, and Ven the electron-neutre collision frequency estimated with the Bohm velocity. 3. Plasma Models Two kind of models were used: A simple model from Füner, which relies only on the electromagnetic field to estimate the electron density. D e n e =. E E M n emin where E M is the necessary field for maintaining a discharge, and gamma has to be set by adjusting the modeling results to experimental observations. antenna A more common model based on Maxwellian distribution, with the hypothesis of drift-diffusion for the electronic density and temperature. For the electronic density, we use: Coaxial Figure 1. Axi symmetrical geometry used for plasma simulation. Axis is on the left, plasma inlet and pumping are on top boundary, 3.2 general Models Since the data relies on neutral density and temperature, we used a set of laminar Navier- Stokes and thermal equation for neutral velocity n e t = J e S e where the electron flux is Je = n e e E De ne and the source term is: S e = ij n e. n nj. K ij depending on the chemical reaction involved.

3 For convenience, we used the ambipolar diffusion approach, which neglect the convective term: n e t =S e D a n e We make some simplification in the energy continuum equation, in order to solve: t 3 2 n ek B T e Q e=p Joule P coll where the total energy flux is: Q e = 5 2 k B T e J e 5 2 k B D e n e T e with the Joule term source: Dirichlet conditions have show better stability for convergence. For the electronic temperature, Te was assumed to be constant at 0.5 ev, except on the axis where Neumann conditions are used. For electromagnetic field, perfect electric conductor where assumed everywhere, except for the power inlet, where port condition are used. 4. Results 4.1 Hydrogen plasma simulated by Funer model Here are presented the results of the model describe by Funer et al. [3] for Hydrogen plasma. The electric field (figure 2) and electron density (figure 3) are very similar to Funer results. P Joule =q e J e E and the loss term: P coll =n e.n n. H j K j 3 m e m n k B T e n n e The loss term need some data of the involved chemical reaction. The last term correspond to elastic collision and is negligible for Hydrogen plasma [3]. The results we present for Hydrogen use this assumption. The simulation for Oxygen and Nitrogen were done with this term, but we still have some convergence problem. then the presented results were obtain for an assumed electronic temperature field. 3.4 Properties The plate between antenna and plasma cavity is made of quartz, and we simulate a cupper antenna. The gaseous properties are from kinetic theory of gases [1], and the kinetics models for Hydrogen, Oxygen and Nitrogen from bibliography [2-7]. 3.5 Boundary Conditions For the electronic density, Dirichlet condition where used in the plasma domain on dielectric, and Neumann on the axis boundary. Some flux condition were tested on metal boundary, but Figure 2. Electric field at 5kW. The advantage of this model is the good convergence ability. One disadvantaged is the

4 sensibility to the gamma parameter. All the chemistry is in this parameter, then this approach is difficult to use for more complex chemistry. adapted to nitrogen. The velocity and neutral temperature field are firstly presented on figure 4 and 5. They are very similar for both the cases presented below. Figure 3. Electronic density in plasma cavity at 5kW. 4.2 Model comparison for Nitrogen plasma Figure 5. Neutral temperature field (K) for both models Figure 4. Velocity field (m/s) for both models Figure 6. Electric field (V/m) In the case of Nitrogen plasma we compare results from an am bipolar model with the results obtain by simulation with the Funer model Same remark can be done for the electric field presented on figure 6.

5 In the case of ambipolar model we still have some convergence problem due to energy equation, then we present results obtain with the assumed electronic temperature field of figure 7. parameters of Funer model. An evident conclusion is that all results are possible by using settling method on simple models. But another conclusion may be that this simple model may be use as an engineering tool despite it is uninteresting for research. Figure 7. Assumed electronic temperature field for ambipolar model simulation Figure 9. Electronic density from Funer model simulation for nitrogen plasma 5. Conclusions Our results show that simulation of microwave plasma are possible in a reasonable time. This may be apply in the same way on real geometries. In the case of the ambipolar model, the convergence is very sensitive to detail kinetic data, then the use of such model in 3D may be done carefully after a validation of the kinetic data and test of the convergence in 2D. Next step will be to apply this methodology to more complex chemistry, and validate simplified kinetic model derived from bibliography by comparisons with measurements. 8. References Figure 8. Electronic density from ambipolar model simulation for nitrogen plasma The electronic density obtain by ambipolar model (figure 8) and Funer model (figure 9) are similar, but this is the results of the settling of the 1. H. Rouch, MOCVD Research Reactor simulation, Comsol Conference P. Rummel, and T.A. Grotjohn, Method for modeling microwave plasma system stability, J. Vac. Sci. Technol., A 20(2), March / april (2002) 3. M. Füner, C. Wild, P. Koidl, Simulation and development of optimized microwave plasma

6 reactors for diamond deposition, Surface and Coatings Technology (1999) A.M. Gorbachev, V.A. Koldanov, A.L. Vikharev, Numerical modeling of a microwave plasma CVD reactor, Diamond and Related Materials 10 (2001) P. Mahalingam, D.S. Dandy, A plasma discharge model of a microwave plasma diamond CVD reactor, Dept. of Chemical Engineering (1999) 6. L. Latrasse, PhD thesis, Conception, caractérisation et applications des plasma microonde en configuration matricielle (2006)