Theoretical analysis of the micro-pulling-down process for Ge xSi 1− x fiber crystal growth

Abstract

Theoretical analysis of the micro-pulling-down process for the growth of Ge x Si 1− x single crystal fibers is conducted using a finite-volume/Newton's method. Steady-state heat and nondilute solute transfer, melt flow, the melt/crystal interface, and the free surface as well as the grown fiber diameter are solved simultaneously. The effects of process parameters including the melt height, the die temperature, and the growth rate on the grown fiber diameter and solute distribution are investigated. Good agreement is found for the calculated meniscus shape and the grown fiber diameter with the observed ones. In the melt zone, due to the small physical dimension and the damping effect by Ge, buoyancy convection is negligible. However, Marangoni convection is dominant there and the solute segregation is thus affected. As the melt zone becomes shorter with the decreasing die temperature, a secondary flow is induced by the Marangoni convection leading to an inversion on radial segregation and a large depletion of Ge in the fiber core, which are consistent with the measurements.