Physically-based, lumped-parameter models for the prediction of oxygen concentration during Czochralski growth of silicon crystals

Three-dimensional modelling of 300 mm Czochralski silicon crystal growth with a transverse magnetic field

“…10 CrysMas was used for 2D global simulation in a lumpedparameter model. 11 Collet and Li et al applied FEMAG for simulation of oxygen transport. 12,13 Some open-source codes such as OpenFOAM 11,[14][15][16] and Elmer 17 were also used in simulation of Cz silicon growth.…”

Research on diameter control of Czochralski Silicon Single Crystal based on PSO parameter tuning for RNN-PFDL-MFAC

“…In model predictive control (MPC), Rahmanpour et al [5] implemented MPC with run-to-run control to effectively simulate and control the Cz-si monocrystal process. Wang et al [6] used a lumped parameter model to predict Oxygen concentration levels during silicon crystal development, providing a reference for subsequent crystal control. Liu et al [7] developed a local 3-D heat and mass transfer model incorporating a transverse magnetic field for crystal growth and implemented PID control based on the model.…”