Model And Numerical Simulation Of Solid-liquid Phase Transition In Czochralski Silicon Single Crystal Growth

Mono-crystalline silicon is the basic material of the semiconductor industry,which plays an important role in the development of integrated circuit technology and solar photovoltaic power generation industry.With the development of very large scale integrated circuits,more requirements are proposed for mono-crystalline silicon,and it is included in four aspects: high purity,high uniformity,low defect and large size.The Czochralski method is the main way of producing mono-crystalline silicon.The Czochralski mono-crystalline silicon growth is a phase transition process of polycrystalline silicon melt into solid silicon single crystal in a specific environment.The phase transition process is accompanied by the phenomenon of flow heat transfer,and the phase change interface shape affects the dislocation density in mono-crystalline silicon and the uniformity of resistivity,so it will affect the single crystal quality.Therefore,the research about solid-liquid phase change has very important theoretical significance and practical value to understand the physical phenomena in the process of phase transformation,to improve the crystal growth process parameters and the crystal quality,during the Czochralski mono-crystalline silicon growth.In this paper,a two-dimensional axisymmetric immersed boundary thermal lattice Boltzmann model is presented to study solid-liquid phase transition problems in Czochralski crystal growth.In immersed boundary method,the phase transition interface is considered to be an immersed boundary and is tracked explicitly by Lagrangian points.With regard to the temperature and velocity field of fluid,the lattice Boltzmann method is adopted.The temperature distribution of the crystal is calculated by the Finite difference method.Based on the above method,the crystal growth process with dynamic phase change interface is simulated successfully by the immersion boundary-lattice Boltzmann method.Under different crystal growth control parameters,the velocity and temperature distribution and phase change interface morphology were obtained.And the standard deviation and the average value are adopted to measure the flatness of the interface,and the control parameters corresponding to the flat phasetransition interface is obtained.The results show that the process of phase transition is related to the crystal pulling speed,the rotation parameter of crystal and crucible.Increasing the speed of crystal pulling can effectively improve the problem of the phase transition interface seriously convex to melt.In the case of only crystal rotation,the probelm of phase transition interface seriously convex to melt is improve,but the phase change interface is more volatile.When the rotation of the crystal and crucible together,a relatively flat phase change interface can be obtained,by adjusting the ratio of the rotation parameters of the crystal and crucible.And the function relation is obtained between the rotating parameters of the crystal and the crucible for flat phase change interface.The above results provide theoretical basis and experimental approach for improving crystal growth process parameters.