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MATHEMATICAL MODEL OF HEAT-MASS TRANSFER DURING CRYSTAL GROWTH PROCESS INCLUDING CLUSTER MODEL OF A MELT CONSTITUTION

Olga Naumenko
SSC RF Institute for Physics and Power Engineering, Sq. Bondarenko 1, Obninsk, 249033, Kaluga region, Russia

Michael Zabudko
SSC RF Institute for Physics and Power Engineering, Sq. Bondarenko 1, Obninsk, 249033, Kaluga region, Russia

Andrey Kartavykh
Institute of Chemical Microelectronics, Moscow, Russia

Michael Milvidsky
Institute of Chemical Microelectronics, Moscow, Russia

Abstrakt

The paper gives a brief analysis of current concepts about the processes of melt ordering and structural self - organization at the temperature close to melting point, including the interface area, when growing semiconductor single crystals. The experimental data confirm the existence of ordered growing units (clusters) in the melt under the conditions close to equilibrium crystallization. The conclusion is justified about the prospects of studying the processes of clusterization in the melt under the conditions of micro gravitation. A mathematical model of convection mass transfer is proposed as an independent tool. This model includes the equations of hydrodynamics, impurity transfer and convection flow in the interface in view of the medium cluster structure. Materials properties and the temperature are presented as a single - value function of enthalpy. For the first time the melt structural model near the crystallization front considers the availability of cluster formations which cause resistance to the melt flow. This resistance is described by analogy with a porous body by means of introduction of medium two - phase coefficient which depends on the enthalpy value in the assigned microvolume. The developed model allows the consideration of fundamental specific features of the processes of crystal growing from the melt. In particular, it enables heat and mass transfer to be calculated correctly both in the region core, and in the interface. The results of model testing are demonstrated, including the description of real orbital and ground processes of GaSb single crystal growing.

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