# A Study on Heater Design for Crystal Growth of GaAs Ingot Using Growth Temperature Simulation
## 3 Design of Heater  
In this study, the design of a heater for ingot growth was performed. Through internal temperature measurement, the temperature simulation model was developed, and the optimized heater was designed. It was planned for a device that could control the temperature to grow while maintaining an ideal interface along the interface on the solid-liquid  
Figure 1: Each compartment of GaAs ingot. boundary and not form the concave interface. If a concave interface occurred, twins and polycrystals were formed due to differences between the growth direction and the thermal expansion area, so a temperature gradient condition was derived that could minimize it. The concave occurs during the ingot growth process. This study simulated the 4-inch GaAs ingot growth process through the temperature simulation and examined the application condition of the heater to determine the optimal heater position. It was constructed by a model for analyzing the VGF heater designed to predict heat transfer characteristics such as temperature distribution, thermal capacity, and insulation capability of VGF heaters, and the heat transfer analysis was carried out for them. The scope of heat transfer analysis for VGF heaters is from the heater winding, which is a heat source, to the heater's inside space where heat is transferred, GaAs, the quartz case, which is the heat transfer path from the heat source to GaAs, pBN, the ceramic block for external insulation, cerakwood, and ambient air that is a heat sink. The most important factor among the VGF heater's heat transfer characteristics is the heat value of respective heaters that could form the temperature distribution desired for GaAs in the vertical direction. In addition, the adequacy of the heat transfer path and the insulation capability of the external case should be examined. If the insulation capability against the outside is insufficient, there is a problem where the heat value required for heaters is excessive. If the design of the heat transfer path is improper, the temperature distribution in the vertical direction of GaAs is not formed as required [7; 8]. As in Figure 2, firstly, the heat generated from the heater winding is transferred by convection in the ambient air. In this way, heat transfer by convection occurs from the air with temperature rising to the surrounding wall surface. The heat transfer occurs by convection on the ceramic block, which is the external air direction, and the quartz wall surface, which is the GaAs direction, and they are solids, respectively, in which the heat is transferred by conduction. The heat transfer path from the heater winding, heat source, to the air, heat sink, in the horizontal direction is as in Figure 3. The heat resistance was defined using the following equation. \[R_{total}=\frac{1}{h_{hu}A}+\frac{ln(r_{c02}/r_{c01})}{2\pi L_{cb}K_{cb}}+\frac {ln(r_{cuz}/r_{cuz1})}{2\pi L_{cuz}K_{cw}}+\frac{1}{h_{amb}A} \tag{3}\]  
where is \(R_{total}\) is total heat resistance. \(h_{hu}\) is the heat transfer coefficient of air in a heater. \(K_{cb}\) is the thermal conductivity of ceramic blocks. \(L_{cb}\) is ceramic block thickness. \(K_{cw}\) is the thermal conductivity of cerakwood. \(L_{cw}\) is cerakwood thickness. \(r\) is radius. \(A\) is area. The heat transfer coefficient between the air and the VGF heater wall surface, between the air inside the heater and the cerakwood is a function of the shape and temperature difference, and it is very difficult to control it in terms of the design. To increase the insulation effect against the outside, therefore, we need a design to apply materials with low thermal conductivity and increase the thickness. The heat transfer path from the heater for melting GaAs is as in Figure 4, and the heat transfer coefficient between the air and the quartz wall surface is difficult to control, like external insulation. Therefore, the thickness of quartz, vacuum, and pBN, which are solid thermal resistance, should be considered to perform the design.