A theoretical study of temperature distributions during Czochralski crystal growth

Abstract

A theoretical model is presented which enables temperature gradients during Czochralski crystal growth to be studied. For the first time the neck and the seed are included in such calculations; and, by using the model to study two elements which can be grown dislocation-free (viz. copper and silicon), it is shown that small changes in neck dimensions greatly affect metal crystal temperature gradients, but not semiconductor crystal temperature gradients. The seed dimensions are shown to be of minor importance in determining such gradients. When the radiated heat losses are high, the most effective way to reduce solid-liquid interfacial temperature gradients is to increase the diameter of the crystal; this implies that it may be easier to grow large crystals with low thermal stresses than small crystals.