Simulation of back-melting in Czochralski growth

We present a global and time-dependent model in order to predict the onset of remelting in Czochralski growth (such as occurs during shouldering when the change of growth angle is too fast). The numerical scheme selects automatically whether solidification or remelting must be considered, and the alternation of the two situations can be predicted accurately. As an example, the simulation of back-melting is carried out during the shouldering stage of a germanium crystal.