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Combining a Legacy Cfd Code with an Evolutionary Algorithm to Perform Optimization Analysis of Chemical Vapor Deposition Systems

Theodora C. Xenidou, Andreas G. Boudouvis, and Nicolas C. Markatos. School of Chemical Engineering, National Technical University of Athens (NTUA), GR-15780, Athens, Greece

In Chemical Vapor Deposition (CVD) processes a thin solid film is deposited from gaseous precursors through chemical reactions on heated substrates (wafers). Although CVD is primarily a chemical process, the key issue in designing CVD reactors is to optimize their thermal and hydrodynamic behavior in such a way that, among other, the deposition rate is high and spatially uniform. Numerous studies have focused on developing simulation tools aimed towards optimizing thin films properties [1,2]. Fluid flow models that take into account mass, momentum and heat transfer effects, within both vertical and horizontal CVD reactors, have been developed. Computational Fluid Dynamics (CFD) modeling, however, is pointless without the inclusion of kinetic models describing the mechanisms of the film growth. The lack of reaction-rate data for many CVD precursors inhibits the use of CFD models for the accurate simulation and efficient design of novel CVD processes and precursors.

The development of kinetic models is a tedious, iterative process, where an approximate mechanism is extracted to govern the local concentrations of chemical species, so that the growth rate of the film can be predicted. Hence, the kinetic parameters that best fit the experimental data are determined. The validity of the proposed kinetic model is based on how thoroughly the parameter search has been conducted in the allowable range. The determination of the optimal kinetic parameters is complicated by the complexity and non-linearity of the model and the poor quality of the experimental data. Once the kinetic model is determined, the transport/kinetic model is further used to evaluate numerous reactors configurations and the effects of a wide range of process parameters on the CVD process outcome [3]. In particular, parametric analysis is usually performed by varying one process parameter at a time. Although significant conclusions can be obtained from each parameter continuation run, there will be no “global” solution to the design problem of the CVD reactor. Obviously, it would be more efficient to investigate the effect of more process parameters at a time on the CVD reactor performance [4].

To improve the effectiveness of CFD modeling in the design of novel CVD reactors and precursors, an approach using an Evolutionary Algorithm is developed. The approach requires the solution of two successive sub-problems: (1) the determination of the growth mechanism involving the estimation of the kinetic parameters from experimental measurements, and (2) the optimization of the growth process, concerning the identification of the appropriate CVD system, reactor shape and operating conditions, given the desired film quality. The first, single-objective reverse problem is directly connected with solving the question of precursors dissociation and of the chemical composition of the growing surface and of reactive gas phase. Langmuir-Hinshelwood type mechanisms are used to enhance the investigation of the competition for the occupation of surface sites between the precursor and other reactants. The maximum growth rate and its minimum spatial non-uniformity provide two competitive unambiguous criterions for the second optimization problem.

Using a legacy CFD code is practically a mandatory choice due to the complexity of the physico-chemical mechanisms along with three-dimensional effects and adverse geometry involved in typical CVD processes. A framework was developed for enabling a legacy finite-volume CFD code to perform systematic optimization studies of complex CVD systems. Most importantly, this is achieved without any alteration in the CFD code itself since this approach is built as a computational “shell” around the legacy CFD code, which is treated as an almost black box. Optimization results in different CVD systems are illustrated to demonstrate the effectiveness of the approach in single- and multi-objective problems. The application of the approach to novel CVD precursors is underway.


[1] R.P. Pawlowski, C. Theodoropoulos, A.G. Salinger, et al., "Fundamental models of metalorganic vapor phase epitaxy of gallium nitride and their use in reactor design", J. Crystal Growth, 221, 622-628 (200).

[2] S. Kommu, G.M. Wilson and B. Khomami, "A Theoretical/Experimental Study of Silicon Epitaxy in Horizontal Single-Wafer Chemical Vapor Deposition Reactors", J. Electrochem. Soc. 147(4), 1538-1550 (2000).

[3] T.C. Xenidou, A.G. Boudouvis, D.M. Tsamakis and N.C. Markatos, "An experimentally assisted computational analysis of tin oxide deposition in a cold-wall APCVD reactor", J. Electrochem. Soc. 151(12), C757-C764 (2004).

[4] A.G. Salinger, R.P. Pawlowski, J.N. Shadid and B. B. Waanders, "Computational analysis and optimization of a chemical vapor deposition reactor with large-scale computing", Technical report, Sandia National Laboratories. Albuquerque, New Mexico 87185 (2004).