Thermal field is obtained for the Liquid Encapsulated Czochralski(LEC) process by Quasi-Steady State Model(QSSM). The heat transfer mechanism of the model includes the radiational heat transfer between the equipment components' surfaces and convectional heat transfer in melt flow of the crucible. Encapsulant layer is assumed to be totally opaque or transparent. Solutions of the model equations are obtained for the cases in which the crystal and crucible are stationary, as well as they rotate in opposite direction. The surface temperature of the heater satisfying the heat balance including the latent heat generation at the crystal and melt interface is obtained simultaneously with thermal field and velocity field. Surface temperature of the heater in the given radiative heat transfer configuration in the process has strong interaction with the radiational heat flow from the crystal surface and crucible inner wall. Thermal transparency of the encapsulant layer affects the temperature of the crystal near the interface, and the temperature of the heater surface and thermal field in the encapsulant region is dependent on the thermal transparency of encapsulant. Proposed model describing thermal field is easily applicable to next steps such as analysis of thermal stress in the growing crystal, based on assumption of cylindrical crystal geometry, but realization of the crystal and melt interface geometry in the model is indispensable to be used as a tool of process optimization.
