# A Study on Heater Design for Crystal Growth of GaAs Ingot Using Growth Temperature Simulation
## 2 Concept for Growth of GaAs Ingot  
The methods to manufacture GaAs crystal are classified into the VGF and the liquid encapsulated czochralski (LEC) growth ones. In the past, the crystal growth by LEC was in the mainstream due to the advantages of production yield rate and making a large diameter. Recently, however, the crystal growth by VGF has been in the current mainstream due to a demand for high-quality crystal ingots. The reason for preferring products manufactured by applying the VGF growth method in various fields is that they have the merit of having a long product life due to low defect density and low stress. The GaAs substrate for micro LEDs to be applied in this study should have low defect density, which has a direct effect on the performance of microelements. In general, the rate of defects such as twin and poly caused by temperature gradient, growth rate, and ambient environment change is very high. Therefore, a study was performed to improve the quality and productivity of products. It was needed to develop the equipment applying a heater that could reduce the defect rate by analyzing and learning the data such as growth temperature gradient, growth rate, and environment based on the existing accumulated technological data. In this study, the high-performance GaAs crystal growth method by controlling temperature gradient by growth compartment and growth rate was developed. The relation between the temperature gradient influencing growth and crystallinity is as follows. When the temperature gradient increases, thermal stress is received higher at the interface, so the dislocation density becomes larger, but the solid-liquid interface shape is leveled off. If the temperature gradient is smaller, thermal stress becomes lower, so the dislocation density decreases, but the solid-liquid interface shape becomes concave and it leads to the occurrence of twin or poly. And another big factor influencing growth is the growth rate. The theoretical relationship between temperature gradient and growth rate affecting this crystallinity is as follows [7,8]. \[\mathrm{f}=\ \frac{1}{\Delta Hv}(K_{s}\frac{dT_{s}}{dx}-K_{l}\frac{dT_{l}}{dx}) \tag{1}\]  
\[\mathrm{f}\simeq\frac{K_{s}}{2\Delta Hv}\frac{dT}{dx}=0.0288\frac{dT}{dx} \tag{2}\]where \(\Delta Hv\) is the latent heat of GaAs. \(K_{\rm s}\) is thermal conductivity of a solid state. \(K_{\rm f}\) is the thermal conductivity of the fluid state. \(\frac{dT_{\rm s}}{dx}\) and \(\frac{dT_{\rm f}}{dx}\) are a gradient of temperature. f could be derived from the equation above, but it takes a very long process time to apply the equation above into the actual process, so in this study, experimental data were used to apply a growth rate of about 6-10 times faster than the calculation formula to use in the process. This study used crystal factors as above to apply proper temperature gradient and growth rate depending on characteristics for each area to obtain a high-quality crystal. The conceptual diagram of the sectional shape of GaAs crystal manufactured by ingot growth is presented in Figure 1. In area A, because there is a frequent formation of twin or poly caused by the instability of solid-liquid interface shape, it needs to restrain it. This is the area that makes growth by minimizing thermal stress based on a large temperature gradient and corresponding theoretical calculation formula to level the solid-liquid interface shape more but also provide a growth rate that could keep planarization of the interface. In area B, the occurrence frequency of twin decreases noticeably compared to the cone area when growing the body after the cone's growth area, so it could increase the growth rate to reduce the process time significantly. If this growth rate changes widely, however, it brings about imbalances of the solid-liquid interface shape, which results in the formation of polycrystals or the increase of dislocation density caused by thermal stress.