Interplay between facetting and confinement in directional solidification of silicon: A direct comparison between experiments and phase-field simulations

Abstract

We combine the analysis of experiments based on in situ X-ray imaging and phase-field simulations to get insight into the interplay between faceting and confinement effects in thin silicon samples during directional solidification from a monocrystalline seed. The phase-field model is parametrized by available experimental results, especially regarding the anisotropy functions for the surface energy and for the kinetic attachment coefficient. In the present work, a method is proposed to extrapolate 2D fully quantitative simulations results to 3D thin sample geometry. Two simple seed orientations along the 〈110〉 and 〈100〉 crystal directions are considered. For 〈110〉 direction, it is shown that confinement effects are weak so 2D simulations can be readily compared to the experiments. For 〈100〉 direction, much stronger confinement effects are identified and characterized by a confinement factor that is estimated from phase-field simulations of thin 3D systems. For both directions, the length of the side facets is shown to increase with the solidification velocity and an analytical expression including the confinement factor is obtained for the law relating both quantities. A very quantitative experiment-simulation agreement is obtained in each case.