There are two existing methods of production of large-size Bi₄Ge₃O₁₂ (BGO) single crystals. The biggest known crystals now are produced by the low-thermal gradient Czochralski technology (LTG) [1]. At the same time, the conventional Czochralski method (Cz) has some advantages over LTG, such as lower Pt consumption for crucibles, higher yield of crystalline material due to cylinder shape of grown ingots, easy implementation on production-run equipment [2]. Therefore, optimization of BGO growth technology by Cz method is a topic of continuous interest.

One of existing drawbacks of the Cz method decreasing the production yield is a relatively big volume of the melt remaining in the crucible after growth. This is caused by heat transfer conditions in growth setups with induction heating [3], namely non-uniform crucible heating and BGO melt opacity. As a result, most of heat is released in side crucible walls, and crystallization interface (CI) is convex to the melt to the colder bottom crucible wall. This leads to contact of CI with crucible bottom and impossibility to crystallize about 40 % of the melt.

The present work is focused on solving this problem using the installation of additional passive heater. This heater is a metal disk installed under the crucible [4]. The disk is heated by the same induction coil as the crucible. Additional heating from below provides a higher temperature along the interface between the melt and the bottom crucible wall. This helps to create heat conditions when CI shape is nearly flat. This allows one to crystallize sufficiently bigger fraction of the melt and, at the same time, avoid crystallization inside the crucible leading to crucible deformation and lowering its lifespan. Definitely, the simplicity of technical implementation is a serious advantage of this approach. Contrariwise, heat power releasing from the lower heater is directly depends on power incoming to the induction coil, hence, independent control of lower heater power is impossible.  To skip this drawback, the dimensions and material of lower heater ensuring flat CI during growth process are determined using numerical modeling of global heat transfer in the growth setup.

Main goals of the current study are: (i) to reveal trends characterizing an influence of geometrical and physical parameters of the bottom heater on heat conditions of the BGO crystal growth; (ii) to determine optimal configuration of the parameters of the bottom heater, which allows one to receive nearly flat crystallization front through all growth stages.
Modeling is carried out by the Finite-Volume method using a CGSim program package [5]. The problem was solved in 2D axisymetrical approach using a quasistationary approximation.  Convection patterns in melt are determined on the base of Navier-Stockes equation for incompressible liquid using the Boussinesq approach with RANS turbulence model. The effects of thermal and forced convection, as well as Marangoni effect at free melt surface are accounted for. Spectral absorptivity was approximated by a three-band model radiation heat transfer in the crystal, calculated by the discrete ordinates method. Calculation of radiofrequency (RF) was based on solving Maxwell equations in quasistationary approach for linear, isotropic, and inhomogeneous media.

In particular, we have found the optimal electric conductivity of the bottom heater and the optimal diameter of the bottom heater. The computation results are in satisfactory agreement with experiment implementing the bottom heater for CI shape optimization at growth of BGO crystals with the diameter up to 80 mm by Cz method in crucibles with 96 mm inner diameter. The demonstrated approach can be used in optimization of Cz growth technology for other materials with opaque melt.

1.Yu.A. Borovlev, N.V. Ivannikova, V.N. Shlegel, Ya.V. Vasiliev, V.A. Gusev, J. Cryst. Growth, 229 (2001), pp. 305-311.

2. http://www.ezan.ac.ru/products/crystalgrowth/nika3/

3. K. Mazaev, V. Kalaev, E. Galenin, S. Tkachenko, O. Sidletskiy, J. Cryst. Growth, 311 (2009), Iss. 15, pp. 3933-3937.

4. V. Bondar, E. Galenin, Ia. Gerasymov, V. Nagornyak, O. Sidlestkiy, S. Tkachenko, Patent of Ukraine №88579, Oct. 26, 2009

5. http://www.str-soft.com/products/CGSim/

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