613b

Cihan Oguz and **Martha Gallivan**. School of Chemical & Biomolecular Engineering, Georgia Institute of Technology, Ford Environmental Science & Technology Building, 311 Ferst Drive, Atlanta, GA 30332

Molecular simulation methods are widely used to predict properties of materials ranging from thin films to polymers. One method is Kinetic Monte Carlo (KMC) simulations [1], which are commonly employed for capturing the evolution of material systems with time. Each KMC simulation, being a stochastic realization of the probabilistic master equation, captures the microscopic details of a system together with the macroscopic properties. This leads to extremely high dimensional and noisy data. In addition, these simulations are not compatible with existing control and optimization tools and are hard to analyze because of the high dimension and the noise level. The main goal of this study is algorithm development for the computation of a simple dynamic model from the molecular simulation data.

We focus on the deposition of gallium arsenide (GaAs) thin films by molecular beam epitaxy (MBE) [2] to illustrate our model development approach. There are microscopic processes involved in this process including adsorption, desorption and diffusion of gallium (Ga) and arsenic dimer (As_{2}) species that take place at a time scale of femto to picoseconds. However, the surface morphology that shapes the overall film properties develops over a time scale of seconds [3]. We use simulation data from the full KMC model to extract a compact dynamic process model that relates the variable input (Ga flux) to the state of this system. Firstly, a set of simulations with different Ga flux profiles are run and the snapshots of the surface are recorded. Then, a spatial correlation function is used to characterize each recorded surface snapshot. As the next step, principal component analysis (PCA) is employed to reduce the dimensions of the data by eliminating the linear correlations between the variables in the spatial correlation function. Following this reduction step, self-organizing map (SOM) [4] groups similar surface structures. Finally, the implementation of the cell-to-cell mapping technique [5] provides the flux-dependent transitions between surface structure groups, hence our dynamic model. Using this dynamic model, the process is optimized by finding the desired film structure and minimizing the deposition time to reach that particular structure [6].

1. A. B. Bortz, M. H. Kalos and J. L. Lebowitz. New Algorithm for Monte-Carlo Simulation of Ising Spin Systems. Journal of Computational Physics, 17:10-18, 1975.

2. B. A. Joyce, D. D. Vvedensky, G. R. Bell, J. G. Belk, M. Itoh, and T. S. Jones. Nucleation and growth mechanisms during MBE of III-V compounds. Materials Science and Engineering B, 67:7–16, 1999.

3. P. Kratzer, E. Penev, and M. Scheffler. First-principles studies of kinetics in epitaxial growth of III-V semiconductors. Applied Physics A, 75:79–88, 2002.

4. T. Kohonen, Self-Organizing Maps. 2001, New York: Springer.

5. C. S. Hsu, Cell-to-Cell Mapping: A Method of Global Analysis for Nonlinear Systems. 1987, New York: Springer.

6. C. Oguz and M. A. Gallivan. Identification of a dynamic model for a thin film deposition process using a self-organizing map. Submitted to Proceedings of the 2006 IEEE International Joint Conference on Neural Networks (2006).

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