3D Anisotropic Stress Analysis during Kyropoulos Growth of Sapphire Single Crystal

Abstract

By using 3D finite element calculations, numerical simulations are performed to predict the thermal field as well as the thermal stress in a c-axis sapphire single crystal grown by Kyropoulos technique. The effects of additional resistive heating (placed under the crucible bottom) and crystal rotation are investigated and a comparison is made between the isotropic and anisotropic analysis. The anisotropy of the elastic constants and thermal expansion coefficients as well as their temperature dependence are considered in the anisotropy calculations while Young's modulus and the Poisson ratio are used in the isotropic analysis. Thermal stress is found to be smaller in the anisotropy analysis than that in the isotropic analysis and significant differences are found in their respective distribution patterns. Additional resistive heating acts to decrease both of the crystal-melt interface convexity and the von Mises stress. In addition, crystal rotation combined with additional resistive heating decreases significantly the thermal stress inside the sapphire crystal and along the melt-crystal interface. Therefore, optimizing the heating conditions and using a suitable crystal rotation rate seem to be favorable to control the growth interface shape and to reduce thermal-stress-related defects during the growth process.

Effect of the growth pulling direction on 3D anisotropic stress during different stages of semitransparent Li2MoO4 growth

“…As said above, the anisotropy of elastic constants and thermal expansion coefficients, as well as their temperature dependence, are mandatory for the exact computations of thermal stress, even for the axisymmetric shape of the crystal, since both of the anisotropy and temperature dependence affect considerably the distribution and intensity of thermal stress, as demonstrated by Miyazaki 19,20 , S. Zermout et al 21 and I.Lasloudji et al 22 .…”

“…Miyazaki et al 19,20 were the first who carried out a three-dimensional analysis of thermal stress field in LN and LT crystals, of about one inch in diameter, by using the temperature distribution obtained by global simulation of heat transfer for opaque assumed crystals. Taking into account the internal radiation, the anisotropy and the temperature dependence of both of elasticity and thermal expansion coefficients, the coauthors of this work computed the 3D thermal stress in semitransparent sapphire 21 and langatate crystals 22,23 . Zermout et al 21 compared numerically the isotropic and anisotropic analyses for a semitransparent sapphire crystal grown by Kyropoulos method.…”

“…Taking into account the internal radiation, the anisotropy and the temperature dependence of both of elasticity and thermal expansion coefficients, the coauthors of this work computed the 3D thermal stress in semitransparent sapphire 21 and langatate crystals 22,23 . Zermout et al 21 compared numerically the isotropic and anisotropic analyses for a semitransparent sapphire crystal grown by Kyropoulos method. They have shown that von Mises stresses are smaller and non-axisymmetric in the anisotropy analysis, where the coefficients are functions of temperature, compared to the isotropic one.…”

Numerical Modeling of Heat Transfer and Thermal Stress at the Czochralski Growth of Neodymium Scandate Single Crystals

“…Nevertheless, the steady‐state equilibrium analysis of thermal stresses during the growth of oxide crystals has recently received much attention. In particular for the semitransparent sapphire have recently been carried out 3D stress analyses, both for growing according to the Kyropoulos process [ 9 ] as well as according to Czochralski and the edge‐defined film‐fed (EFG) process. [ 10 ] In both articles the focus is on the use of anisotropic thermoelastic material properties, in ref.…”

“…[ 10 ] In both articles the focus is on the use of anisotropic thermoelastic material properties, in ref. [9] the relevant results are also compared with the results from isotropic data: significant differences were found in their respective distributions pattern.…”