Modeling And Numerical Simulation Of Czochralski Crystal Growth Under Multi-physical Fields Coupling

Czochralski technology is one of the most common methods for producing silicon single crystal element of integrated circuits.With the increase of crystal size,the new requirements for crystal growth equipment,process level and single crystal quality have been put forward.There are many difficulties in the field of single crystal growth under the coupling of multi-physics fields,such as mechanism modeling and solution,optimization and selection of process parameters.Therefore,the establishment of crystal growth model under multi-fields action,model identification and reasonable optimization of process parameters will have important implications for clarifying crystal growth mechanism,optimizing process,guiding growth practice and reducing product cost.By using the method of numerical simulation and experimental research,this dissertation makes a further study of the modeling of silicon crystal growth under multi-physics fields coupling,the identification and optimization of key parameters,and the design and optimization of superconducting CUSP magnetic field.Firstly,for the difficult problem of modeling the heat flow coupling mechanism during the process of Czochralski silicon crystal,Lattice Boltzman method(LBM)is used to model and solve silicon crystal growth,and the melt flow and temperature distribution are studied.The evolution model of flow velocity momentum equation including thermal buoyancy and rotational inertia force,azimuth velocity momentum equation and energy equation are established.The flow velocity serves as the coupling term of momentum equation and energy equation,and solves the coupling problems of fluid dynamics and thermal dynamics simultaneously.Numerical simulation of the melt flow on the interaction of high Grashof number and high Reynolds number is carried out,and the force convection generated by rotation of crystal and crucible can effectively suppress the natural convection caused by heating,improve the uniformity of the temperature distribution of the melt and the crystal quality.The experimental results show that the proposed LBM model is correct and applicable to the research on the heat flow coupling of Czochralski crystal growth.Secondly,since the traditional LBM has the numerical stability in solving the thermosolutal mixing convection problem of single crystal silicon growth,an axisymmetric multiple relaxation time Lattice Boltzman Model(MRT-LBM)for Czochralski crystal growth is proposed.The melt flow velocity is solved by an axisymmetric rotational discrete D2Q9 model that constructed in the pseudo Cartesian coordinate system.The azimuth velocity,the melt temperature and the oxygen concentration are solved by three discrete D2Q5 models.The correctness of the proposed method and the efficiency and stability of the solution are validated by a large number of experiments.By analyzing the distribution of oxygen concentration under different CUSP magnetic field strengths,it is concluded that the applied magnetic field force can inhibit the melt convection and improve the oxygen concentration distribution.In particular,as the magnetic field strength increases,the oxygen concentration at the solid-liquid interface decreases,and the high oxygen concentration is suppressed at the crucible wall,which is beneficial to improve the oxygen content of the crystal.Thirdly,during the growth process of single silicon crystal with large size and electron level,due to the difficulty in process parameter selection,a hybrid strategy including Computational Fluid Dynamics(CFD),Group Method of Data Handling(GMDH)and an improved Non-dominated Sorting Genetic Algorithm(NSGA-?)is proposed,which is used for identifying the Czochralski silicon single crystal model and optimizing the process parameters.The three dimensional local model of crystal growth is established by CFD,and numerous process parameters are calculated.Taking the calculation results as the samples,the polynomial model of the object function is confirmed by the GMDH neural network algorithm.An improved NSGA-? is proposed to optimize the object function,and the Pareto optimal solution of the process parameters is obtained.The validity of the optimized result is verified by practical experiments,it is proved that the hybrid strategy is a new method for obtaining accurate process parameters of crystal growth,and it can be applied to solve multi-objective optimization problems of other complex and uncertain models.Finally,in order to meet the needs of the development of single silicon crystal with large size,the design,optimization and numerical simulation of the superconducting CUSP magnetic field for the crystal growth equipment are studied.Based on the basic theory of superconducting magnet,the coil structure of superconducting magnet is designed and calculated numerically.According to the design requirements,the number of coil layers,the distance between the upper and lower coils and the thickness of the magnetic shield are optimized.The numerical simulation of the magnetic field intensity on the melt convection,the free surface heat,the flow morphology and the control of the solid-liquid interface morphology are carried out respectively,and the corresponding results are analyzed.The above researches not only reveal the thermosolutal transport properties of crystal growth under multi-physics fields,but also provide a new way for model identification of key parameters and optimization of process parameters,offer guidance for understanding crystal growth mechanism and improving production process,and provide model reference and theory support for the process control of crystal growth as well.By using the method of numerical simulation and experimental research,this dissertation makes a further study of the modeling of silicon crystal growth under multi-physical fields coupling,the identification and optimization of key parameters,and the design and optimization of superconducting CUSP magnetic field.