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Crystallization of thin silicon layers on substrates is a key process in the manufacturing of various types of electronic devices. Let us consider photovoltaic wafers and thin-film transistors for flat screens. Although, the length scales for the silicon layers involved differ by several orders of magnitudes the principles of the crystallization process are the same. In both cases the solidification is driven by a complex interaction of thermal fluxes in lateral and normal direction. Dependent on the substrate temperature large regions of undercooled melt can be observed and the crystallization structure can change between columnar and dendritic. The paper deals with the application of the multi phase field method to simulate the crystallization of a liquid silicon film under the conditions of photovoltaic wafer production and the fast excimer laser recrystallization of thin amorphous silicon layers on glass. The leading mechanisms of crystallization into an undercooled melt with normal heat extraction will be examined by phase field simulation and a comparison with experimental data will be given with respect to crystallization velocities and resulting silicon microstructures. (c) 2006 Elsevier B.V. All rights reserved.