Graduate Thesis Or Dissertation

 

Analysis of domain decomposition methods for the simulation of charge transport in semiconductor structures with heterojunctions Public Deposited

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  • Charge transport in a semiconductor structure with heterojunction is described by a multiscale partial differential equation model. This model can be used, e.g., for the design of more efficient solar cells. Phenomena at the heterojunction must be resolved at the angstrom scale while the size of the device is that of microns. The challenge is therefore to account for correct physics and to keep the model computationally tractable. Thus we use an approach introduced by Horio and Yanai in which the physics at the interface is approximated at the device scale, which is handled by tranditional drift diffusion equations, by unusual jump conditions, called thermionic emission equations. In this model the heterojunction region is approximated by an abrupt interface, resulting in a loss of continuity in the primary variables. The thermionic emission equations consist of a nonhomogeneous jump in the electrostatic potential and unusual Robin-like conditions for carrier transport. The data for these jumps is determined from an angstrom scale first principles calculation in the true heterojunction region. The continuum scale model lends itself well to a domain decomposition approach. In this thesis we present iterative substructuring methods developed for the drift diffusion system with thermionic emission transmission conditions and analyze the convergence of these algorithms.
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