Modeling of dopant segregation in vertical zone-melting crystal growth

Abstract

Computer simulation is conducted to study the dynamic dopant segregation, both radial and axial, in vertical zone melting (VZM) crystal growth. Fluid flow and heat and mass transfer, as well as the dynamic evolution of interfaces, are simulated simultaneously using a robust finite-volume scheme. With the present scheme, excellent global dopant conservation is obtained, and it is not affected by meshes and convection. Gallium- and silicon-doped germanium growth are used as examples. Under normal gravity condition, due to the vigorous natural convection in the melt, the dopant is well mixed, and the axial segregation is close to that with complete mixing. With convection, the effective segregation coefficient attains a constant value quickly, and remains about the same for the rest of the growth. A scaling relationship of the solute boundary layer with the thermal Rayleigh number is also presented. Using a predoped zone, axial segregation is greatly reduced, but still affected by the change of melt volume. Due to the much larger segregation coefficient of silicon in germanium, axial dopant concentration of silicon reaches a pseudo-steady state quickly.