Abstract

A series of three-dimensional numerical simulations were performed to understand the thermal-solutal capillary-buoyancy flow of Ge1-xSix melts during Czochralski crystal growth with a rotating crystal or crucible. The crystal and crucible rotation Reynolds numbers in this work are 0∼3.5 × 103 (0∼4.4 rpm) and 0∼−2.4 × 103 (0∼−1.5 rpm), respectively. Simulation results show that if the thermal capillary Reynolds number is relatively low, the flow will be steady and axisymmetric, even though the crystal or crucible rotates at a constant rate. The critical thermal capillary Reynolds number for the initiation of the three-dimensional oscillatory flow is larger than that of pure fluids. As the crystal or crucible rotation rate increases, the critical thermal capillary Reynolds number first increases and then decreases. The dominant flow pattern after the flow destabilization is azimuthal traveling waves. Furthermore, a reversed evolution from the oscillatory spoke pattern to traveling waves appears in the melt. Once the crystal or crucible rotation rate is relatively large, the traveling waves respectively evolve to rotating waves at the crystal rotation and a spindle-like pattern at the crucible rotation. In addition, the maximum amplitude of solute concentration oscillation on the free surface initially decreases, but finally rises with the crystal or crucible rotation rate increasing.

Highlights

  • Single crystals of oxides and semiconductors mostly grow from melt, which takes on an important role in microelectronic and optoelectronic devices [1]

  • Rσ is fixed at −0.8, which ensures that much more attention is paid to the influence of the rotating crystal and crucible on the thermal-solutal capillary-buoyancy flow

  • When the capillary ratio is fixed at −0.8, the thermal capillary force is dominant, which induces flow movement from the crucible sidewall to the crystal edge along the free surface, as displayed in 7 of 15the

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Summary

Introduction

Single crystals of oxides and semiconductors mostly grow from melt, which takes on an important role in microelectronic and optoelectronic devices [1]. Pursued a similar direction by conducting experiments and 3D numerical simulations They reported that the solutal capillary and buoyancy forces, which are generated by the solute gradient as a result of the Soret effect, promote the destabilization of the thermal-solutal capillary-buoyancy flow in binary mixtures. The rotations lot of previous works focusing on the flow and the flow instabilityUnfortunately, have not yet paid attentionof and crucibles were alloys not taken into consideration, which is an essential industrial practice for tocrystals solute diffusion in binary [27,28,29,30] It is indispensable carry out numerical simulations the on the melt andcrystals the flow instability notthermal-solutal yet paid attention to solute diffusion in binary influences of flow rotating and crucibleshave on the capillary-buoyancy convections inalloys a Cz[27,28,29,30]. The present work is beneficial for improving crystal qualities in Cz crystal growth

Figure
Calculations’ Conditions and Numerical Method
Basic Flow
Critical Conditions for the Flow Destabilization
Characteristics the 3DofOscillatory
Overview of surface solute concentration of3D
Overview
Conclusions
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