Optimal design and operation of complex materials processing with application to microelectronics

Open Access
Behrens, Christopher Michael
Graduate Program:
Chemical Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
November 03, 2009
Committee Members:
  • Antonios Armaou, Thesis Advisor
  • multiscale methods
  • optimization
  • complex materials processing
  • computational efficiency
Spatially distributed multiscale systems have been recently developed to describe transport-reaction processes for phenomena which occur across length scales that differ by several orders of magnitude. The level of detail required to accurately describe the dynamic behavior of the system at smaller length scales cannot be provided by solely using a description from larger length-scales, whereas describing larger length-scale behavior using descriptions from smaller length-scale models would be infeasible due to the associated computational overhead required. Motivated by the above, multiscale models, which combine larger and smaller-length scale models that are intimately connected, have been developed. Continuous pressure on profit margins has resulted in the desire to improve efficiency to reduce costs, resulting in the need for optimization procedures. Increases in computational efficiency and optimization strategies have allowed for optimization of complex materials processing problems requiring multiscale models to be pursued. Multiscale optimization of such processes, however, is a problem with three levels of hierarchy in computation. In the lower hierarchy, potentially computationally intensive simulations may need to be performed to model the properties of interest at both smaller and larger length-scales. If bi-directional information is required, iterative convergence at all scales may be required; this serves as the intermediate hierarchy. Finally, optimization (gradient-based and black-box) algorithms require several function evaluations, which in this case is at the top of the hierarchy. With the need to perform numerous simulations, solving a multiscale optimization problem could quickly become intractable. One promising idea to circumvent this computational intractability is to obtain the necessary information from linear interpolations whenever possible instead of using costly simulations. This is the basic idea behind in situ adaptive tabulation (ISAT). Initially used in solving combustion chemistry problems, ISAT has been subsequently extended to stochastic systems and combined with black-box optimization for maximizing uniformity and minimizing surface roughness in a gallium nitride thin-film. Implementation and further refinement of these methods is investigated by modeling the deposition of a thin-film consisting of alternating gallium arsenide and aluminum arsenide layers (GaAs/AlAs.) This example uses macroscale “inputs” from the reactor description to determine properties such as temperature, flow rates, and concentrations, and mesoscale kinetic Monte Carlo (kMC) simulations to measure the previously characterized interfacial properties of the film. The objectives of this problem are to minimize the interfacial step-densities between GaAs and AlAs layers, while also minimizing the temperature and the time spent in-between depositing species (termed annealing time,) as well the macroscopic objective of reducing spatial non-uniformity. This problem only involves adsorption and therefore only requires uni-directional flow of information from the macroscale level to the mesoscale level. Based on this model, we explore the methodology needed to accelerate the computational process by implementing ISAT for each optimization trial. Using this methodology, a multiscale model for a GaAs/AlAs thin-film deposition process was developed for optimization of the interfacial properties, and used within an efficient optimization framework to identify optimal steady-state process conditions for the process. Finally, by implementing this methodology using the Nelder-Mead and Hooke-Jeeves pattern search algorithms, we were able to identify a range of optimal process conditions for minimizing the time with no organometallic flux at the wafer surface and for no organometallic flux at the inlet. With our methodology, we did so while reducing computation time and balancing improvements in step density and thickness uniformity with preferred processing conditions.