Global analysis of heat transfer in CZ crystal growth of oxide taking into account three-dimensional unsteady melt convection: Effect of meniscus shape

Global analysis of heat transfer in CZ crystal growth of oxide taking into account three-dimensional unsteady melt convection: Investigation of the coupling method between 2D and 3D models

“…The model used in this study was modified on the basis of our previous model [20][21][22]. For the convenience of readers, an outline of our previous model is given below.…”

“…As shown in refs. [20][21][22], the model was formulated by coupling a 2D global model and a 3D bulk flow model, interchanging data between the two models. The 2D global model is composed of energy equations for the melt, crystal, crucible, afterheater and other materials such as insulators and radiation shields.…”

“…For gaining correct information on the transport process inside the CZ furnace, a global model of heat transfer taking into account the three-dimensional unsteady melt flow is needed. Recently, some studies in this area were carried out by us [20][21][22]. In our global model, two existing models were combined: a global model of heat transfer based on the axisymmetric assumption, namely, a 2D global model [5] and an unsteady three-dimensional melt flow model, namely, a 3D bulk flow model [18], were combined by interchanging data between the two models as mentioned below.…”

3D unsteady computer modeling of industrial scale Ky and Cz sapphire crystal growth

“…Lately, there has been much interest in numerical modeling of oxide crystal growth. As a recent example in the literature, there are LiNbO 3 growth simulations using a coupling method between 2D and 3D models [4][5][6] with the account of crystal semitransparency in terms of the simplified P1 approximation. Some recent works on sapphire growth [7,8] contain 2D simulations during different stages of the growth, where radiation in the crystal, affecting much crystallization, is considered within an effective heat conductivity approach.…”

Dynamic global model of oxide Czochralski process with weighing control

“…However, unlike the semiconductor growth, the role of simulation in the development of the oxide crystal growth technology remains rather modest because the heat transfer in growing oxide crystals is much more complicated. Until now simulation of Cz oxide growth was limited to the static models when the shape of crystal is not varied in time and, consequently, the process of crystal pulling, as such, is not considered (for example [2][3][4][5][6][7]). At the same time, for semiconductor crystals, the dynamic simulation of the Cz process has long been proposed [8][9][10][11].…”