A parallel branch-and-bound algorithm for thin-film optical systems, with application to realizing a broadband omnidirectional antireflection coating for silicon solar cells

For the class of nondispersive, nonabsorbing, multilayer thinlm optical systems, this thesis work develops a parallel branch-and-bound computational system on Amazon's EC2 platform, using the Taylor model mathematical/computational system due to Berz and Makino to construct tight rigorous bounds on the merit function on subsets of the search space (as required by a branch-and-bound algorithm). This represents the rst, to the best of our knowledge, deterministic global optimization algorithm for this important class of problems, i.e., the rst algorithm that can guarantee that a global solution to an optimization problem in this class has been found. For the particular problem of reducing re ection using multilayer systems, it is shown that a gradient index constraint on the solution can be exploited to signi cantly reduce the search space and thereby make the algorithm more practical. This optimization system is then used to design a broadband omnidirectional antire ection coating for silicon solar energy. The design is experimentally validated using RF sputtering, and shows performance that is competitive with existing solutions based on impractical sophisticated nano-deposition techniques, as well as the more practical but also more narrowly applicable solutions based on texturing. This makes it arguably the best practical solution to this important problem to date. In addition, this thesis develops a mathematical theory for cheaply (in the computational sense) and tightly bounding solutions to parametric weakly-coupled semilinear parabolic (reaction-di usion) partial di erential equation systems, as motivated by the design of tandem organic solar cell structures (which are governed by the drift-di usion-Poisson system of equations). This represents the rst theoretical foundation, to the best of our knowledge, to enable guaranteed global optimization of this important class of problems, which includes, but is broader, than many semiconductor design problems. A serial branch-and-bound algorithm implementation illustrates the applicability of the bounds