The nonlinear dynamic process of Czochralski crystal growth (CZCG) is studied by the perturbation method. The solutions of this method can be used to predict, quantitatively, how a crystal growth with constant crystal radius is perfectly controlled by the desired combination of crystal pull rate and bulk melt temperature. It is found that for growth under constant bulk melt temperature (pull rate), the pull rate (bulk melt temperature) will increase with increasing ambient Biot number and/or decreasing melt Biot number. Furthermore, if the melt cannot be supercooled, we can formulate the maximum pull rate analytically. The pull rate must not exceed this maximum value, otherwise the CZCG process will break down.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Inorganic Chemistry
- Materials Chemistry