Scaling analysis of convective solute transport and segregation in Bridgman crystal growth from the doped melt

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Abstract
Convective transport is well known to have a decisive influence on the macrosegregation encountered in metallic or semi-conductor crystals grown from an impure or doped melt. In the present paper, this problem is studied with the help of an order of magnitude analysis of the set of balance equations for mass, momentum and solute in the melt and at the growth interface. The different solute transport regimes are defined and the scaling laws of the solute boundary layer extent are obtained in each regime. Finally, the corresponding types of macrosegregation in the solidified crystal are derived. Our predictions compare favorably with the results of numerical simulations and ground-based as well as microgravity experiments. Thus our analysis provides a simple way to predict macrosegregation as a function of the physical properties of the system as well as the imposed experimental conditions : sample dimensions, growth rate, thermal gradients, gravity orientation and level. The extension of the method to other crystal growth situations is suggested