The weight gain signal in Czochralski crystal growth

Abstract The force required to hold the crystal during Czochralski growth is analysed. The treatment accounts for (i) mass transfer between the melt and the crystal, (ii) capillary forces associated with the melt meniscus, (iii) buoyancy effects produced by a non-flat solid/melt interface, and (iv) the correction due to the fall of the bulk melt level. The new effects caused by a curved growth interface are discussed by linearizing around stationary growth conditions. Based on a congruent interface growth model we show that for crystal radii up to about one capillary length the effect of a curved interface is always negligible. For larger radii the effect is enhanced, but remains always a minor correction compared to the capillary force contributions. We show that what is commonly refered to as the “anomalous” component in the signal is not depending on the curvature of the interface.