Deposition processes are an integral part of microelectronics fabrication. Due to continuous pressure on profit margins, recently there has been a move towards optimizing the process to reduce costs. One such deposition process is a thin film consisting of alternating GaAs/AlAs layers. Such a layered heterostructure is useful in microelectronic industry applications, such as Bragg reflectors [1]. In order to ensure adequate design for production, models should be developed that accurately capture the dynamics occurring in the deposition process. Additionally, the optimization process must meet both the physical goals for the deposition system and the optimization macroscale goals of quality, yield, cost, and time, since the expense and time of production for the process must not be prohibitive for use in industrial applications [2].

This work addresses an approach in determining the optimal conditions for the microscale goal of a smooth interface between the GaAs and AlAs layers. Control of these variables has traditionally been performed by measuring the flux at the interface based on changes in temperature and annealing time. The level of detail required to determine interface quality, however is too fine for macroscale transport equations. Therefore, Kinetic Monte Carlo (KMC) simulations were used to model the surface phenomena taking place at the required detail level. GaAs/AlAs is modeled using a simple cubic solid on solid model with no vacancies and no overhangs. Previous work by Grosse and Zimmerman is used for the rates of migration based on the number of nearest neighbors [3]. The KMC model also accounted for macroscale inputs consisting of temperature, annealing, and adsorption rate.

Characterization is necessary to provide for a quantitative method of evaluating the quality of the interfaces. The microscopic interface is characterized through step density, RMS roughness, and autocorrelation function (ACF). Step density is the preferred metric because it correlates experimental RHEED data with interface quality; step density can also be used to provide in-situ measurements for possible control systems. The surface step density and roughness are controlled during the growth and annealing phases, and they are used to characterize the interfaces, along with ACF. Based on this quantitative characterization of the GaAs/AlAs deposition, the process is then optimized with the objective to minimize the interfacial step density. The design problem is formulated as a dynamic optimization problem where the temperature of the thin film and the annealing time are the design parameters. This is achieved using a derivative-free optimization algorithm, due to the stochastic nature of the deposition process and the location of the interface (which implies that step density is non-differentiable and therefore traditional secant methods cannot be used.) The effects of temperature for the deposition of each layer and annealing time for both the GaAs and AlAs layers are described using the KMC model. Using the proposed interface characterization methods and formulation of the film growth, the GaAs/AlAs growth process was designed to produce layered heterostructures of low interfacial roughness at a reduced processing time and low process temperature.

[1] S.J. Chang, C.S. Chang, Y.K. Su, P.T. Chang, Y.R. Wu, K.H. Huang, and T.P. Chen, “Chirped GaAs-AlAs Distributed Bragg Reflectors for High Brightness Yellow-Green Light-Emitting Diodes,” IEEE Photonics Technology Letters, Vol. 9 Issue 2:182-184, 1997. [2] A. Varshney and A. Armaou, “Optimization of thin film growth using multiscale process systems,” American Control Conference, 2559-2565, 2005. [3] F. Grosse and R. Zimmermann, “Monte Carlo Growth Simulation for AlxGa1-xAs Heteroepitaxy,” J. Crystal Growth, 212:128-137, 2000.

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