Semiempirical Model Would Control Czochralski Process

Semiempirical mathematical model proposed for control of growth of single crystals of silicon by Czochralski process. Expresses dependence of pulling rate and shape of liquid/solid interface upon important process variables; radius of growing crystal, temperature of crucible, level of melt, and height of exposed portion of crucible wall. Necessary to control shape of interface in manner consistent with other variables, to maintain radially uniform concentration of dopant, and reduce thermally induced stresses in vicinity of interface. Used to simulate complete growth cycles without requiring excessive computer time consumed by rigorous finite-element modeling.