CrysMAS, CGSim, and Elmer can be used to simulate some aspects of crystal growth with limited predictive capabilities. They are standalone tools used to study physical processes. They _might_ be useful to understand the general behavior of your laboratory system, but they cannot be used to fix your diameter control problem. In practice, diameter control of CZ-grown crystals is accomplished by feedback control software that manipulates pulling rate and heater power in response to real-time measurements of temperature and crystal diameter.

Dear Amirhossein Esmaeilkhanian in this context please have a look at the following potentially useful link which might help you in your analysis:

Quasi-Transient Calculation of Czochralski Growth of Ge Crystals Using the Software Elmer

Article Quasi-Transient Calculation of Czochralski Growth of Ge Crys...

This paper has been posted by the authors as public full text on RG. Thus you can freely download it as pdf file.

I hope this helps. Good luck with your work and best wishes, Frank Edelmann

dear Frank T. Edelmann

thanks for your full response. I'll check it ASAP.

Dear Andrew Yeckel

Do you have any idea about these software?

I think that using a simulation software can be helpful in some case. But you are right. Would you mind please helping me in this way.

Best regards

I do not use commercial or open source simulation software written by others. I do not have any advice whether such codes are usable or appropriate for your problem. Obtaining accurate, useful simulations of problems of this complexity is very time consuming, even for those with much experience in simulation. If you are trying to grow crystals of nearly constant diameter by the Czochralski method, I think you should study heuristic methods already developed by others.

Dear Andrew Yeckel

Thanks for your kind response. Would you mind please name some of these heuristic methods or write the Publication URL here for me. It is very important for me to have this constant-diameter single crystal.

Best regards

There is an enormous literature in this area. It is unlikely that any single publication will provide an easy answer to your problem. Please note that I am not a crystal grower, and I have never simulated a Czochralski system. Others are much more qualified than me in this area.