열교환법에서 도가니 형상 변화가 사파이어 결정 온도와 고/액 계면 형태에 미치는 영향

Effects of the crucible shape on the temperature of sapphire crystal and the shape of melt/crystal interface in heat exchanger method

  • 발행 : 2004.08.01

초록

열교환법을 활용한 사파이어 단결정 성장 공정에서 도가니 형상 변화가 결정 온도와 고/액 계면 형태에 미치는 영향에 관해 고찰하기 위해 유한요소법, implicit Euler법, frontal 해석 연산을 활용한 수치해석을 수행하였다. 개발된 컴퓨터 시뮬레이션 기법은 고/액 계면의 형상이 반구 형상에서 평면 형상으로 전환되는 열전달 현상 해석에 효율적이다. 본 연구에서는 고/액 계면의 휨도를 개선하기 위해, 도가니 밑면의 다양한 형상을 고려하였으며, 도가니 형상은 공정 최적화 변수로 고려되어야 한다.

Numerical analysis which is based on finite element techniques, implicit Euler method and frontal solving algorithm was performed to study the effects of the crucible shape on the temperature of sapphire crystal and the shape of the melt/crystal interface in heat exchanger method. The computer simulation described here and effective to solving the heat transport phenomena with the transition of the interface shape from hemispherical to planar. In the work, various crucibles with differently shaped corners at their bottom are considered to improve the deflection of the melt/crystal interface. The shape of the crucible should be considered as one of the variables for the process optimization.

키워드

참고문헌

  1. Am. Ceram. Soc. Bull. v.73 Producing large sapphire for optical application F. Schmid;C. Khattak;D. Felt
  2. J. Crystal Growth v.225 Growth of the world's largest sapphire crystals C.P. Khattak;F. Schmid
  3. J. Crystal Growth v.26 Crystal growth using the heat exchange method (HEM) D. Viechnicki;F. Schmid
  4. Transport phenomena R.B. Bird;W.E. Stewart'E.N. Lightfoot
  5. Korean J. Chem. Eng. v.13 Analysis of moving boundary problem of growth of bismuth germanate crystal by heat exchanger method J.H. Wang;D.H. Kim;D.-S. Chung
  6. J. Kor. Ass. Crystal Growth v.7 Effects of natural convection on the melt/solis interface shape in the HEM process J.H. Wang;D.H. Kim
  7. J. Crystal Growth v.174 Modelling of crystal growth process in heat exchanger method J.H. Wang;D.H. Kim;J.-S. Huh
  8. J. Crystal Growth v.225 Numerical computation of sapphire crystal growth using heat exchanger method C.-W. Lu;J.-C. Chen
  9. Finite elements an introduction v.2 R.B. Becker;G.F. Carey;J.T. Oden
  10. An analysis of the finite element method G. Strang;G.J. Fix
  11. Transport phenomena in materials processing D.R. Poirier;G.H. Geiger
  12. Int. J. Num. Meth. Eng. v.10 Frontal solution program for unsymmetric matrices P. Hood
  13. Int. J. Num. Meth. Eng. v.11 Note on frontal solution program for unsymmetric matrices P. Hood