Numerical Analysis of Thermal Stress in Semi‐Transparent Oxide Crystals Grown by Czochralski and EFG Methods

Abstract

Crystal growth of oxides is generally difficult since large curvatures of the growth interface in these systems generate high thermal stress, dislocations and crystal cracking. Three-dimensional numerical modeling is applied to investigate thermal stress distribution in sapphire and langatate La3Ta0.5Ga5.5O14 (LGT) semi-transparent crystals grown by Czochralski (Cz) and Edge-defined Film-fed Growth (EFG) techniques. The analysis of thermal stress distribution in a sapphire ingot grown in a Czochralski furnace shows high von Mises stresses distributed almost symmetrically on large areas in the crystal. Thermal stress computations for piezoelectric langatate crystals grown in a Czochralski configuration show non-symmetrical von Mises distribution with higher stress on one side of the ingot. These numerical results are in agreement with experimental results showing non-symmetrical cracking at the outer surface of the crystal. 3D modeling of multi-die EFG growth of white sapphire ribbons shows that the von Mises stress is almost constant when the number of ribbons is increased from two to ten. Two models are applied to simulate the internal radiative heat transfer in the sapphire crystals: P1 approximation and the Rosseland radiation model. Numerical results show that applying Rosseland formula introduces significant errors in temperature field calculations especially in the case of the EFG configuration.

Growth and characterization of the β-Ga2O3 (011) plane without line-shaped defects

“…26,27 Therefore, besides the group of dislocation that is parallel to the (011) plane, there are also some other slip groups existing in the β-Ga 2 O 3 bulk crystal, which would cause etch pits to appear on the (011)-oriented substrate. Higher thermal stress gathered on the surface induced higher dislocation density in the growing surface region, 28,29 as such the etch pits were aggregated at the edge of the wafer. The existence of defects or dislocations can affect the quality of the epitaxial layer and the performance of the device, which is one of the main reasons why the breakdown voltage of the device is much lower than the theoretical value.…”

Influence of growth process and crystal defects on sapphire brittleness

“…Numerical simulation of heat transfers and thermo-elastic stresses in multi-die EFG growth gives rather low stresses in the plates, 60 MPa, compared to 200 MPa during Czochralski growth of a 5 cm diameter crystal [67]. Anyhow this value is larger than the yield point at high temperature [47] and dislocations are formed.…”

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

“…For instance, for semitransparent oxidic crystals, Stelian et al. [ 12,13,10 ] have applied a 3D numerical modelling to investigate thermal stress distribution in sapphire and langatate semitransparent crystals grown by the Czochralski (CZ) and by the edge‐defined film‐fed growth (EFG) technique. As method for treating the internal radiation in sapphire crystals (optically thick) they applied the P 1 ‐approximation, which was successfully validated by comparing the computed shape of the solid–liquid interface to the experimental results.…”

“…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. [9] the relevant results are also compared with the results from isotropic data: significant differences were found in their respective distributions pattern.…”