A thermal-capillary dynamic model for Czochralski (Cz) growth of silicon si
ngle crystal is presented that accounts for convection in the melt, conduct
ion in the crystal, and radiation from the melt free surface and crystal. T
he shapes of the crystal/melt interface, moving crystal, and free surface a
re governed by the balance of energy and stresses. Decrease of the melt vol
ume as the crystal is grown is also considered A control algorithm based on
the adjustment of the pull rate and/or crucible wall temperature has been
developed The diameter of the crystal can remain constant or vary with time
based on the strategies implemented to control the growth process.