Single crystals of SiGe, especially Si_0.5Ge_0.5, attract the attentions as the post Si semiconductor substrates, and enable to produce high-speed and low energy devices, because both strained Si and Ge films grown on SiGe substrates have higher mobility than intrinsic Si and Ge substrates. For the production of homogeneous SiGe bulk single crystals, a lot of growth techniques have been developed. Recently, Kinoshita et al. [for instance, Journal of Crystal Growth, 349, 50(2012)] have developed the travelling liquidus-zone (TLZ) method to grow homogeneous SiGe crystals. In the TLZ method, Ge which is sandwiched by a Si seed and a Si feed is melted at around 1100°C above the melting point of Ge and at relatively low temperature gradients (5-15°C/cm) as shown in Figure 1. Since the solute Si is almost saturated throughout the molten zone in this method, the concentration profile coincides with that on liquidus line, and consequently, is uniquely determined following the temperature gradient in the zone. The crystal growth of SiGe occurs spontaneously due to interdiffusion of Si and Ge following their concentration gradients through the molten zone.

  Although homogeneous SiGe single crystals with a diameter of 2 mm were successfully grown by the TLZ method, the growth of larger diameter crystals was not succeeded yet, because free convection induced by the temperature and concentration gradients in the melt strongly affects the homogeneity of the crystals on the ground. In order to clarify the effect of free convection on the TLZ crystal growth of SiGe, therefore, the crystal growth experiments under a microgravity environment in International Space Station (ISS) have been planned and are being performed this year by JAXA.

  In this work, to understand transport phenomena in the TLZ crystal growth process of SiGe under microgravity in detail, a mathematical model for the crystal growth process of SiGe by the TLZ method has been developed, where the velocity field in the melt, the thermal field in the furnace, Si concentration field in the melt and crystal, and the melt/crystal interface shapes can be predicted numerically. Figure 2 shows the numerical results of temperature filed in the furnace (left side) and Si composition field in the molten zone (right side) during dissolution and crystal growth. The crystal diameter, temperature gradient of furnace and its moving speed are 10.2 mm, 9ºC/cm and 0.082 mm/h respectively. Firstly, the molten Ge dissolved the Si feed and seed, and consequently, the molten zone became longer (Figure 2(b)). At 400 min, the crystal began to grow (Figure 2(b)), and at 8000 min, grew up to 10.7 mm in length (Figure 2(d)). In this work, we investigated the effects of operational conditions, e.g., moving speed of furnace, thermophysical properties of crucible and crystal radius, on the spatial homogeneity of grown single crystals and the melt/crystal interface shapes which are macroscopic characteristics related to crystal quality.

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