Numerical Simulation And Process Optimization For The Growth Of ZnTe Crystal

ZnTe single crystal has potential application in many important areas,like green light emitting diodes?LEDs?,laser diodes?LDs?,solar cells,microwave devices and terahertz devices,etc.Obtaining ZnTe single crystal with high quality and large size is the prerequisite for its many applications.In order to guide the crystal growth experiments theoretically and to get ZnTe crystals with high quality,it is important to understand the growth mechanisms and to establish the relationship between the growth conditions and the growth results.In this thesis,a finite element numerical model is developed to simulate the transport phenomena and the growth interface morphology during the growth of ZnTe crystal from Te rich solution by the temperature gradient solution growth?TGSG?technique.Based on the numerical model,the growth interface and the crystalline quality are optimized by controlling the heat transfer.The effects of ACRT on the convections and mass transfer are studied from the view of convection control.A Maxwell-Stefan mass transfer model is established to study the multicomponent mass transfer during the growth of Cd_0.9Zn_0.1Te crystal.In order to simulate TGSG growth of ZnTe crystal,a finite element numerical model with the consideration of heat transfer,thermosolutal convection,solute segregation and non-isothermal phase transformation is developed.The values of several thermophysical parameters of ZnTe are estimated according to relevant literatures.The Galerkin finite element method is used to discretize the spatial portion of the governing equations.The resulting sets of nonlinear algebraic equations are solved using Newton's method.A dynamic mesh is used to guarantee the high efficiency of the discretization of the computational domain.Parameter continuation method is employed to analyze the effects of any parameter and to solve the nonlinear equations.The finite element numerical model is employed to simulate the transport phenomena and the growth interface morphology during the growth of ZnTe crystal by TGSG method.According to the simulation results,convections in front of the growth interface weaken or even disappear soon after the growth begins,making the mass transfer in this area nearly a pure diffusion process.Te-rich solution with high density and low growth temperature is inclined to accumulate near the central region of the growth interface,making the growth interface change into two distinct parts.High temperature gradient can significantly increase the growth rate and avoid the diffusion controlled growth to some extent,but can not avoid the distortion of the growth interface and the inhomogeneous growth.The growth rate in TGSG technique is only several millimeters per day.Therefore,the latent heat has little effect on the transport phenomena and the growth interface morphology,and is ignored.A cylindrical crucible pedestal consisting of a mullite sheath and a graphite core is designed,to optimize the growth interface during TGSG growth of ZnTe crystal.The effects of the radius of the graphite core on the growth are simulated.The results show that a pedestal made totally by graphite can make the convex or flat growth interface last for the longest growth distance.During the early stage of the growth,there are two clockwise vortexes in the solution.The lower one is close to the growth interface and the upper one occupies the rest of the solution.The lower vortex vanishes very soon,and a concentration gradient region forms in this area where the solute?ZnTe?transfers to the growth interface only by diffusion.The growth interface,which is convex first,becomes flat for the first half of the ingot,and turns concave after that.Distortion of the growth interface in the growth without the pedestal does not occur.The depth of the growth interface is far less than that in the growth without the pedestal.The optimized growth interface should be helpful to improve the grain size and the crystalline quality.ACRT parameters that may induce desirable forced convections according to P.Capper et al.'s approximate theory are estimated and employed in the simulation of the growth.It is found that the estimated ACRT parameters can not produce effective mixing of the solution,because the estimated maximum rotation rate is too low,and the constant rotation and the stop stages are too long.Suitable ACRT parameters are determined through modifying ACRT sequence in amounts of simulations.With the application of the trapezoid-wave ACRT sequence,the rotation of the ampoule accelerates and decelerates periodically in two opposite directions,the clockwise and counterclockwise Ekman flows appear and disappear alternately,and the dilute solution accumulates in front of the central part of the growth interface and then mixes into the bulk solution repeatedly.Solution in front of the growth interface can be well mixed only during the constant rotation stage when the clockwise Ekman flow exists.During the stop stage,however,a large amount of dilute solution will accumulate in front of the growth interface center.With the application of ACRT that can produce excessively strong clockwise and counterclockwise Ekman flows,constitutional supercooling will occur in front of the central part of the growth interface at the beginning of the stop stage,and in front of the peripheral part of the growth interface at the end of the constant rotation stage.By adjusting the acceleration of the ampoule rotation,such as lengthening the deceleration stage or decreasing the maximum rotation,appropriate Ekman flows can be obtained,to well mix the solution and avoid the constitutional supercooling.An appropriate ACRT sequence is provided,which can facilitate the mixing of the solution,avoid constitutional supercooling,and improve the growth interface morphology.Based on Maxwell-Stefan equations,a numerical model accounting for multicomponent mass transfer is developed to simulate the Bridgman growth of Cd_0.9Zn_0.1Te crystal.For the first time,theoretical values of the three Maxwell-Stefan diffusion coefficients in Cd_0.9Zn_0.1Te melt are estimated,i.e.,D_Zn,Te?2.3×10^-8 m²/s,D_Te,Cd?1.8×10^-8 m²/s andD_Zn,Cd?1.3×10^-8m²/s.The simulation result shows that in the early stage of the growth,the diffusions of Zn and Cd in the melt drive Te to diffuse up its concentration gradient.Later,when stable concentration gradients?in the melt near the growth interface and between the two vortices?of Te are formed,the distribution of Te is determined by a comprehensive effect of the concentration gradient of Te,the diffusions of Zn and Cd,and the convections.Increasing the crucible traveling rate will aggravate the segregation of Zn and Cd,and hence deteriorate the uniformity of Te in front of the growth interface.The effects of the Maxwell-Stefan diffusion coefficients indicate that during the melt growth of a ternary system,not only the diffusion coefficients but also the ratios between them have significant influence on the multicomponent mass transfer.