Finite element analysis of horizontal silicon sheet growth from the melt

Abstract

A mathematical analysis of the continuous horizontal growth of crystalline Si sheets from the melt is presented. The assumption is made that heat removal is by radiation from a silicon melt surface covered with a carbon fiber net. This case corresponds to the horizontal carbon-fiber supported web (HSW) technique. The mixed initial and boundary value problem of heat conduction is formulated including the solidification mechanism. A numerical solution is obtained using a finite element program. The mesh and the time step width of the program are optimized for the state at the start of crystallization. The solution yields the increase of the silicon sheet thickness as a function of position and time. The pulling speed is determined as a function of the mean temperature gradient in the melt and of the length of the melt.