Numerical simulation during Kyropoulos growth of. sapphire crystals

Transcription

1 Numerical simulation during Kyropoulos growth of sapphire crystals Chun-Hung Chen a, Jyh-Chen Chen a,*, Chung-Wei Lu b, Che-Ming Liu c, Wen-Ching Hsu c, Szu-Hua Ho c a Department of Mechanical Engineering, National Central University, No.300, Jhongda Rd., Jhongli City, Taoyuan County 32001, Taiwan(R.O.C.) b Department of Information Management, Jen-Teh Junior College, Hou- Lung, Miao-Li 35664, Taiwan(R.O.C.) c Innovation Technology Researic Center, Sino-American Silicon Products Inc, No. 8, Industrial East Road 2, Science-Based Industrial Park, Hsinchu, Taiwan, (R.O.C.) ABSTRACT The finite element method is employed to simulate the temperature and velocity distribution during a large sapphire crystal growth process using Kyropoulos method. In the present study, the electromagnetic, thermal, and fluid field calculations are coupled to observe the shape of solid-melt interface. The energy input to the crucible by the electric magnetic field that RF coil produces, and the energy output through the heat-sink around the seed is modeled by the convection boundary conditions. The shape of solid-melt interface is strongly affected by the temperature gradient in the sapphire melt. Therefore, the effects of temperature gradient with various growth parameters; such as the position and numbers of RF coil, the properties of crucible, and the capacity of the heat-sink etc.; will be investigated. Keywords: numerical simulation; Kyropoulos; sapphire; finite element method

2 1. Introduction Sapphire single crystals are widely used in a variety of modern high-tech applications, from commercial and military optical systems to high power laser components, and semi-conductor substrates because of the combination of desirable optical and mechanical properties [1]. Amongcrystal growth methods, the Kyropoulos method (KY) is a good commercial method for growing the larger, high-optical-quality sapphire [2 4]. In an KY process, the material is heated above the melting point by a heating element, and, there after heat is extracted from the base of the crucible usinga heat exchanger, solidifying the melted material. The temperature of the furnace influences the temperature gradients in the melt, while the temperature of the heat exchanger affects the temperature gradients in the crystal [4]. Therefore, the thermal fields are highly dependent on the heat input from the furnace as well as the energy output through a heat exchanger. According to an experimental observation [3], the corners of the crucible are hot spots, and the crystal never grows out towards them until the amount of heat output reaches a certain value. The gradient solidification method (GSM) [5 7] and the temperature gradient technique (TGT) [8,9] are also developed to grow large-size single crystals. The main difference between the KY versus GSM and TGT is that the thermal field of the furnace in the GSM and TGT systems contains upward temperature gradients. 2. Theory 1 0 = jωσ A + ( μ A) 0 (1-1) In the equation, A is magnetic potential vector and ω is angular frequency and μ 0 is

3 permeability and σ is electrical conductivity. T ρ CP + ( k T + ρcptu) = Q (1-2) t C P In the equation, is specific heat, k is thermal conductivity, T is temperature in the melt, Q is the time, is the heat source and u is the velocity of melt. u = 0 (1-3) u 2 ρ η u + ρ( u ) u + p = F t (1-4) t p is the pressure of system and η is dynamic of viscosity and ρ is density of melt and F is volume force field such as gravity. We combind electromagnetic, thermal, and fluid field 3. Result Fig.1. Schematic diagram of KY systems Fig. 1 shows the model of the global analysis for sapphire single crystal growth using Kyropoulos method. Firstly, we use the COMSOL Multiphysics code which is based on the finite element method to simulate the two-dimensional model with its mesh is between 15,111 and 60,444

4 elements. We perform a heat and flow analysis to investigate the temperature distribution, flow field and melt/crystal interface in the sapphire growth process. Fig. 2(a). Temperature distribution of KY system Fig. 2(b). Electromagnetic of KY system

5 Fig. 2(c). Temperature contour distribution of KY system Fig. 2(d). Melt velocity distribution of KY system The global model analysis is coupled with the electromagnetic, thermal, and flow field in 2-D sapphire crystal growth. Fig.2(a) shows the temperature distribution and Fig.2(b) shows electromagnetic

6 distribution in the furnace. The RF coils induce the Ir crucible to produce a heat source and the heat is transferred from crucible to melt by conduction. Fig.2(c) shows the temperature distribution in the melt. Fig.2(d) shows the velocity distribution of the melt and the flow generated by the buoyancy force which is caused by the heating of the melt from the wall of crucible. (a) (b) (c) Fig. 3. (a)ir crucible;kheat sink=147w/mk. (b)mo crucible;kheat sink=147w/mk. (c) Ir crucible; kheat sink=200w/mk.

7 Fig.3 shows the effects of different crucible material on the melt/crystal interface. We can see the area of solidification in Fig. 3(a) is larger than that in Fig.3(b) at the same power and heat sink properties. Fig.3(c) shows the effect of different thermal conductivity of heat sink on the melt/crystal interface. Compare the Fig.3(a) to Fig.3(c), the heat sink thermal conductivity in Fig.3(c) is larger and more heat taken out. Therefore, the solidification area is larger. The heat sink plays as the key role in the crystal growth using the Kyropoulos method. Fig. 4(a) :+0.05m Fig. 4(a) :+0.00m Fig. 4(a) :-0.05m When the RF coil position is changed, we can observe the different shape of melt/crystal interface. Fig.4(a) shows the coil position raise 0.05m, Fig.4(b) shows the coil in the original position and Fig.4(c) shows the coil position down 0.05m. 4. Conclution

8 In our simulation, under the same heat sink, using the Mo crucible the crystal area is bigger than that is in Ir case. The crystal area is also larger with increasing the heat sink flux. When the RF coil position goes up at 0.05m, the temperature gradient is too small and this model may be better for crystal growth. In the future, we will use other parameters and study more detailed to develop a fine global furnace in the sapphire crystal growth using Kyropoulos method. References [1] C.P. Khattak, F. Schmid, Am. Ceram. Soc. Bull. 73, Vol.2, 1994, p. 39. [2] D. Viechnicki, F. Schmid, J. Crystal Growth 11 (1971) 345. [3] D. Viechnicki, F. Schmid, J. Crystal Growth 26 (1974) 162. [4] C.P. Khattak, F. Schmid, Adv. Opt. Mater. SPIE 505 (1984) 4. [5] A. Horowitz, S. Biderman, G. Ben-Amar, U. Laor, M. Weiss, A. Stern, J. Crystal Growth 85 (1987) 215. [6] S. Biderman, G. Ben-Amar, Y. Einav, A. Horowitz, U. Laor, M. Weiss, A. Stern, Infrared Technology XIII, Vol. SPIE 819, 1987, p [7] A. Horowitz, S. Biderman, D. Gazit, G. Ben-Amar, M. Weiss, J. Crystal Growth 128 (1993) 824. [8] J. Xu, Y. Zhou, G. Zhou, K. Xu, P. Deng, J. Xu, J. Crystal Growth 193 (1998) 123. [9] Y. Zhou, J. Crystal Growth 78 (1986) 32.

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