| Summary: | Understanding the dewetting and solidification of thin films is key in the fabrication of thin film solar cells, as a device with low percentage of surface coverage will have a greatly diminished efficiency. In this thesis we use Rational Continuum Mechanics to propose a thermodynamically-consistent framework for classes of models describing the evolution of solidifying thin films.
Starting from the key laws of the conservation of mass and the first and second laws of thermodynamics, and employing the Coleman-Noll procedure, we derive a class of models for predicting the evolution of a thin liquid film in isothermal settings. We show that models existing in literature and derived using different techniques fit into these classes.
Invoking the same axioms we then consider non-isothermal settings, and first re-derive models for solidification in a bulk setting. Then we return to thin-film settings and derive a model for heat conduction in a rigid thin film by averaging the laws in the vertical direction to reduce the problem from d dimensions to d-1 dimensions, and then proposing a solution to the closure problem that arises due to fluctuations in the z direction. Culminating these techniques we discover, for the first time, a thermodynamically-consistent class of models for the solidification of thin films.
To allow proper numerical simulations, suitable choices for the constitutive relations within the new models are discussed. Simulations are discussed using linear finite elements for the spatial discretisation and energy-stable convex-splitting schemes as the time stepping algorithms. Parameters within the model are varied to investigate the effect they have on the dewetting of the thin film and the growth of holes, which gives implications on optimal manufacturing conditions for thin film solar cells.
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