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The effect of the pulling rate on the melt–crystal interface shape and melt streamline is investigated.
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... geometry of CZ setup is shown in the schematic in Fig. 1. We assume that the growth furnace is axisymmetric and in a steady state, the fluid parts (i.e., the melt and argon) are incompressible Newtonian fluids following the Boussinesq approximation, all flows are laminar and the viscous dissipation is negligible. 12 2.1.1. Thermal field. For incompressible flow with the Boussinesq ...
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... to the asymmetric growth and dendritic growth of the crystal. 18,19 Table 9 shows the three categories of the optimal amount of pulling and rotation rate for the 5 cm crystal, and the rotation rate of the crucible for which the melt-crystal interface becomes flatter. Fig. 9 also shows the von Mises stress contours in these three situations and Fig. 10 illustrates a plot of the optimal values (the pulling rate, crystal rotation and crucible rotation) as a function of the crystal height. As the crystal height increases, the optimal values of the studied parameters and thermal stress pattern of the crystal change. Table 10 and Fig. 11 show the optimal values of crystal pulling, ...
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... the von Mises stress contours in these three situations and Fig. 10 illustrates a plot of the optimal values (the pulling rate, crystal rotation and crucible rotation) as a function of the crystal height. As the crystal height increases, the optimal values of the studied parameters and thermal stress pattern of the crystal change. Table 10 and Fig. 11 show the optimal values of crystal pulling, rotation rate, crucible rotation rate and the von Mises stress contours in the 17 cm crystal, respectively. Fig. 12 shows that situations with minimal stress create a lattice within the crystal whose lines are parallel or perpendicular to the crystal shoulder and the location of this lattice ...
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... rotation) as a function of the crystal height. As the crystal height increases, the optimal values of the studied parameters and thermal stress pattern of the crystal change. Table 10 and Fig. 11 show the optimal values of crystal pulling, rotation rate, crucible rotation rate and the von Mises stress contours in the 17 cm crystal, respectively. Fig. 12 shows that situations with minimal stress create a lattice within the crystal whose lines are parallel or perpendicular to the crystal shoulder and the location of this lattice does not change when the pulling rate and crystal or crucible rotation ...
Citations
... Therefore, it can be concluded that under stable melt flow structure conditions, the concavity of c-m interface increases continuously in the TSLAG crystal growth process. Moreover, for the same crystal height, a higher crystal rotation speed leads to a greater concavity of the c-m interface, which has been reported in studies on Cz crystal growth [17,18]. concave again. ...
... Therefore, it can be concluded that under stable melt flow structure conditions, the concavity of c-m interface increases continuously in the TSLAG crystal growth process. Moreover, for the same crystal height, a higher crystal rotation speed leads to a greater concavity of the c-m interface, which has been reported in studies on Cz crystal growth [17,18]. ...
Tb3Sc1.95Lu0.05Al3O12 (TSLAG) crystals are novel and high-quality magneto-optical materials with the most promising application as the core component of Faraday devices. Cracking is an obstacle to TSLAG crystal growth and is closely influenced by crystal thermal stress distribution. In this work, the evolution of thermal stress during TSLAG crystal growth in the initial Czochralski (Cz) furnace is numerically studied. The reasons for high thermal stress in TSLAG crystal are explained based on the results about the melt flow, the temperature distribution in the furnace, and the crystal/melt interface shape. A large crucible with a shallow melt is proposed to address the problem of significant variations in melt depth during TSLAG crystal growth. Based on the numerical results, the proposed design can stabilize the melt flow structure, suppressing changes in the crystal/melt interface shape and effectively improving thermal stress in the TSLAG crystal growth process, which contributes to precisely regulating the preparation of large-sized high-quality TSLAG crystals.
... Key words: crystal growth; lithium niobate crystal; crucible; temperature gradient; natural convection; crystal-melt interface 铌酸锂(LiNbO 3 , 简称 LN)晶体集压电、非线性、 电光、光折变等效应于一身，是一种综合性能优越 的人工晶体 [1][2][3][4] 。2017 年哈佛大学科研人员 [5] 撰文 认为，LN 单晶薄膜调制器具有传输损耗低、电光 调 制 速 率 高 、 可 以 与 互 补 金 属 氧 化 物 半 导 体 (Complementary metal-oxide semiconductor, 简 称 CMOS)工艺兼容等突出优点，这使得 LN 晶体在集 成光子学领域具有显著优势，提出"Now entering, Lithium Niobate Valley"(现在正在进入铌酸锂谷时 代)，引发了广泛关注 [6][7] 。常用的 LN 晶体为同成 分铌酸锂晶体(Congruent lithium niobate, 简称 CLN)， 采用熔体提拉法生长，然而，与硅(150 W·m -1 ·K -1 ) [8] 、锗(25 W·m -1 ·K -1 ) [9] 、蓝宝石(17.5 W·m -1 ·K -1 ) [10] 等晶体相比，CLN 晶体热导率较低，仅为 3.539 W·m -1 ·K -1 [11] Table 3 The axial temperature gradient at the crystal centre near the crystal-melt interface L /mm Gcrystal by using C-S /(℃·cm -1 ) ...
... Here, we describe the thermal and heat transfer modeling. The Navier-Stokes equations and continuity equation are expressed as the governing equations for heat transfer [10,11]: ...
... Thermal stress equation in the crystal has been described in detail elsewhere [11] and dislocation density ndisl in the grown crystal is calculated by disl T n br ...
Graphite crucibles are widely used in induced crystal growth systems. This study examines the impact of temperature variation on the electrical conductivity of the graphite crucible and its influence on the temperature field and melt flow in a Czochralski germanium crystal growth furnace using the two-dimensional finite element method. The in-depth analysis demonstrates that the temperature-dependence of electrical conductivity of the crucible is crucial in the growth process and the thermal field of the setup. Specifically, it is noted that temperature changes have a significant effect on the generation and distribution of induction heat, the temperature and melt flow field, the complex shape of the crystal-melt interface, as well as the stress and dislocations in the grown crystal. These findings highlight the intricate relationship between temperature, crucible conductivity, and the dynamics of the crystal growth process, providing insight into the subtle factors that impact the quality and properties of the resulting crystal.
Here, the radiative heat transfer inside a Czochralski furnace and the 3D thermal stress generated in a semitransparent Li2MoO4 crystal are deeply analyzed using anisotropic and temperature‐dependent elasticity and thermal expansion coefficients. The developed global numerical model takes into account induction heating, thermal conduction in all parts of the furnace, convection in the melt and the growth atmosphere, Marangoni convection at the free surface, radiation heat exchange between the furnace elements, internal radiation inside the semitransparent crystal and melt, and phase change at the growth interface. The contribution of each radiation mode is studied separately, then coupled together to clearly explain their roles in heat transfer, stress generation in the as‐grown crystal and in power consumption, and heat loss inside the furnace. Flow and temperature fields in the molten oxide and in the growth atmosphere as well as the thermal stress are presented and discussed for each case. Unrealistic cases are first considered where radiation exchange between the furnace elements and internal radiation in the assumed opaque crystal are neglected. For each case, the relation between temperature gradient and thermal stress is clearly demonstrated. Finally, the effect of the melt opacity on thermal stress is studied and related to temperature gradients in the crystal and at the free surface. The experimental observations are in good agreement. This work is devoted to analyze in detail the effect of radiative heat transfer between the elements of the furnace and internal radiation inside the Li2MoO4 (LMO) crystal and melt. Temperature gradients, 3D anisotropic thermal stress, and inductive heat loss are deeply discussed providing additional insight into the physical understanding of the transport phenomena involved in the Czochralski growth process.
