Efficient Multiscale Dynamic Optimization of Thin-Film Growth Via Model-Reduction: Application to Gaas Epitaxial Growth
Amit Varshney, Pennsylvania State University, 23 Fenske Laboratory, Pennsylvania State University, University Park, PA 16802 and Antonios Armaou, The Pennsylvania State University, University Park, PA 16802.
The current trend of increasing device performance specifications and decreasing feature dimensions have necessitated the use of accurate process models for design, optimization and control of processes in the microelectronic industry. The corresponding mathematical models should accurately describe phenomena characterized by disparate length and time scales, spanning from macroscale and to the microscale. Due to the fact that continuum conservation laws are inapplicable for microscopic domains and atomistic simulations are computationally too expensive to be applied on macroscopic domains, hybrid multiscale models have been developed which combine the continuum description for macroscopic phenomena with atomistic description for microscopic phenomena. This work addresses the problem of dynamic process optimization of thin film growth when optimization objectives are defined over multiple length and time-scales. The above problem is intractable using conventional approaches because of the computational issues posed by the multiscale process model. The above problem is addressed by initially deriving approximate closed form mathematical descriptions for the continuum and the atomistic models. The development of computationally efficient descriptions is achieved through Karhuenen-Loeve expansion (KLE) at the macroscopic level and In-situ adaptive tabulation (ISAT) at the microscopic level. Subsequently, the reduced-order models are consistently linked to create a reduced-order multiscale model, which is employed during dynamic process optimization. The proposed methodology is applied towards the optimization of metal-organic vapor phase epitaxy of gallium arsenide (GaAs) using trimethyl gallium and arsine as precursors in a vertical showerhead reactor. Inlet concentration profiles and substrate temperature profiles are derived that simultaneously optimize the film growth rate (macroscopic objective) and minimize the surface roughness of the final thin film (microscopic objective).