Influence of internal radiation on the heat transfer during growth of YAG single crystals by the Czochralski method

Abstract

Heat and mass transfer taking place during growth of Y 3 Al 5 O 12 (YAG) crystals by the Czochralski method, including inner radiation, is analyzed numerically using a Finite Element Method. For inner radiative heat transfer through the crystal the band approximation model and real transmission characteristics, measured from obtained crystals, are used. The results reveal significant differences in temperature and melt flow for YAG crystals doped with different dopands influencing the optical properties of the crystals. When radiative heat transport through the crystal is taken into account the melt-crystal interface shape is different from that when the radiative transport is not included. Its deflection remains constant over a wide range of crystal rotation rates until it finally rapidly changes in a narrow range of rotation rates.

Numerical Modelling of the Czochralski Growth of β-Ga2O3

“…The importance of the internal radiation was already shown by Xiao and Derby [13] and, later, by Galazka et al [14]. The additional heat transport compared to an opaque crystal leads to conical interface deep into the melt.…”

An experimental and numerical effort to simulate the interface deflection of YAG

“…2 a real cone tip of the NaNO 3 -interface in contrast to the more ball-shaped interfaces found by numerical simulation of NaNO 3 (Fig. 4) or that of YAG [44]. Figs.…”

“…We indicate in Fig. 3a two points of interface deflections K=r calculated for YAG [44] in comparison to the K=r of NaNO 3 -crystals under various axial heat fluxes. For comparison of YAG and NaNO 3 we use an ''equivalent temperature gradient'', which is calculated for YAG, assuming that all heat in YAG is conducted by diffusion (l(solid)) and the appropriate grad z T (''equivalent grad z T'') although it is transported by radiation.…”

“…The idea of the experimental simulation of YAG-growth interfaces is as follows: the axial heat flux through the growing crystal q is composed of the diffusive heat flux q l and the radiant heat flux q r : The total heat flux through the crystal is q ¼ q l (solid)+q r : In YAG we have q r > q l : The YAG-melt is often assumed to be optically a black body [30,31,40,44]. In YAG-melt we therefore may have only diffusive heat transport (q l (melt)), which is strongly assisted by convection.…”

Transmission spectra of crystals at elevated temperatures for the calculation of internal radiant heat transport during crystal growth – Part 1: The spectrometer and its performance

“…Both measurements register the main Ndabsorption lines at the same spectral position and with sufficient spectral resolution for our purpose -to calculate Rosseland constants as by [8] for internal radiant heat transport calculations. Our measurement files have been used for such calculations for YAG-growth in [9]. Our transmission spectrometer gives a more noisy signal and the spectral resolution is less (approximately 50%) than that of the commercial spectrometer.…”