Numerical simulation study for the effect of static and rotating magnetic fields in liquid phase diffusion growth of SixGe₁-x single crystals




Yildiz, Emine

Journal Title

Journal ISSN

Volume Title



High quality semiconductor single crystals are the driving force behind today's rapidly growing electronic and communication industry. However, the growth of desired high quality crystals is difficult mainly due to the generation of defects and impurities in the grown crystal, and the segregation of species and strong convection in the liquid solution during growth. To minimize these undesirable effects, and to control segregation and convection, the use of magnetic fields (stationary, rotating, or traveling) has been widely considered. Static magnetic fields have been used to improve the quality of crystals by suppressing convection (Natural and/or Marangoni) and controlling the directional solidification and segregation of species. Rotating magnetic fields (RMF), on the other hand, have been used to obtain better mixing in the melt, better control for the heat and mass transport characteristics of the system and also for the shape of the growth interface. The objective of this thesis is to investigate the feasibility of using applied static vertical and rotating magnetic fields in Liquid Phase Diffusion (LPD) growth of SixGe1_x single crystals. To this end, a three-dimensional numerical simulation model was developed to study the heat, mass and momentum transfer characteristics of the Si-Ge solution under magnetic fields. The governing equations describing the fluid flow, heat and mass transport are solved numerically using the finite volume-based CFX software package of AEA Technology. In the simulation model, several complex user-defined subroutines have been developed to move the grid, to solve the scalar electric-charge balance equation for the electric potential distribution, and to include the magnetic body force terms. In addition, a command file is produced to define the physical properties of the solution and surrounding solids, and the numerical methods used, model topology, convergence criteria, and equation solvers. The results obtained from this study reveal that the use of a static vertical magnetic field is effective in suppressing natural convection. A magnetic field intensity of 0.3 Tesla is sufficient to provide significant suppression in the liquid Si-Ge solution. However, the static magnetic field does not provide the expected improvement on the growth interface shape. The use of RMF is, on the other hand, effective in creating a good mixing in the solution leading to more homogenous Si-Ge liquid. In addition, RMF is also very beneficial for creating a radially uniform solute distribution, thus flattening the growth interface for a stable growth.



semiconductors, crystal growth