Float Zone Modelling: Transport Phenomena and Morphological Stability

A model is presented for a float zone established in a vertical sheet. Heat transfer between the system (melt, feed and crystal) and the surrounding environment (including the heating source) is assumed to take place via radiation. Asymptotic solutions for the temperature, concentration, and melt flow profiles and the melting, solidifying and melt/gas interfacial shapes are developed in the limit of small aspect ratio (zone half-width/length) and weak surface tension driven flows. We find that convective heat transport leads to melt back of the solidification front near the edges. Further, lateral solute segregation is due to both convective effects and curved solidification fronts. Increasing the flow or increasing the velocity of solidification leads to increased lateral solute segregation in melts that are not well mixed. Hence, flat solidification fronts may not yield flat concentration profiles. To reduce the level of convection, hot wall, low temperature gradient float zone techniques are also investigated. Morphological stability of the solidification front is of concern for such heating configurations. We present the results of a linear stability analysis in the limits of small segregation coefficient, slow velocities of solidification, and large surface heat transfer. It is found that shorter melt zones are less susceptible to long wavelength morphological instabilities.