Modeling of Induction Heating in Oxide Czochralski Systems—Advantages and Problems

Abstract

Two mathematical models of induction heating for oxide Czochralski crystal growth systems are reviewed, and additional results of electromagnetic field and volumetric heat generation have been computed for both models using a finite element method (ENTWIFE package). In the first model, the eddy current in the RF coil (i.e., the self-inductance effect) has been neglected while for the second model, it is taken into account. For the calculations, the electrical current input and total voltage of induction coil are set to be 1000 A and 200 ν, respectively, with a frequency of 10 kHz; the heat generation in all metallic parts, that is, crucible, afterheater, RF coil, and chamber, has been calculated for a real Czochralski setup. It has been found that by including the self-inductance effect in the RF coil the results change dramatically. Also, it was shown that the spatial distribution of the heat generation in the crucible is more realistic in the second model than in the first model. Concerning the distribution of heat generation in all metallic parts (including the RF coil), the results for the first model are not reasonable, but they are acceptable for the second model.

Numerical study of induction heating in melt growth systems—Frequency selection

“…The mathematical model used for our numerical calculation has been described in detail elsewhere [15,17,18]. It can be summarized as follows.…”

Influence of coil geometry on the induction heating process in crystal growth systems

“…the cross section shape of turns). It shows the corner and edge effect which is a common occurrence in induction heating applications [1][2][3]8]. The total heat generation of the RF-coil is Q coil total ¼ 574 W. It means that about 7% of the total power generation of the system is produced in the RF-coil and 93% in the crucible and afterheater.…”

“…This surprising result arises from the electromagnetic end and edge effects (i.e. the distortion of electromagnetic filed in its end and edge areas) [1][2][3]8]. Because of large distance between the coil turns, these effects are more effective in the second configuration compared to the first one.…”

“…The heat transfer processes in crystal growth systems are quite sensitive to the geometry of the furnace, heat generation and orientation of the coil-crucible-afterheater-insulation [4][5][6]. Therefore, modeling of heat generation as well as heat and mass transfer processes is necessary for achieving a complete knowledge of the growth process in order to improve the quality of the grown crystals [1,7,8].…”

Simulation of temperature and flow fields in an inductively heated melt growth system

“…The heat transfer processes in an oxide CZ growth is quite sensitive to the geometry of the furnace, heat generation and orientation of the crucible-afterheaterinsulation [1][2][3][4][5]. Therefore, modeling of heat generation, and heat and mass transfer processes during the CZ growth is necessary for achieving a complete knowledge of the growth process in order to improve the quality of the crystal produced [6][7][8][9][10][11][12][13][14][15][16][17].…”