A Parallel Branch-and-Bound Algorithm for Thin-Film Optical Systems, with Application to Realizing a Broadband Omnidirectional Antireflection Coating for Silicon Solar Cells, and a Mathematical Framework for Bounding Semilinear Parabolic PDEs
For the class of nondispersive, nonabsorbing, multilayer thin-film 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 first, to the best of our knowledge, deterministic global optimization algorithm for this important class of problems, i.e., the first algorithm that can guarantee that a global solution to an optimization problem in this class has been found. For the particular problem of reducing reflection using multilayer systems, it is shown that a gradient index constraint on the solution can be exploited to significantly reduce the search space and thereby make the algorithm more practical. This optimization system is then used to design a broadband omnidirectional antireflection 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. 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-diffusion) partial differential equation systems, as motivated by the design of tandem bulk heterojunction organic solar cells (governed by the drift-diffusion-Poisson system of equations). This represents the first 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 on a pair of simple examples.
Thesis Supervisor(s): Marc Baldo, George Verghese, Steven G. Johnson