# A Study on Heater Design for Crystal Growth of GaAs Ingot Using Growth Temperature Simulation
## 4 Numerical Analysis and Manufacturing of Heater  
Classical heat transfer analysis has limitations because the shape of the VGF heater designed is very complicated, so the numerical analysis method was used to carry out the heat transfer analysis. Since it is also needed to analyze the flux flow by natural convection, this analysis used ANSYS-CFX to perform the heat transfer analysis. For heat transfer analysis on VGF heaters, modeling for every component of the VGF heater was conducted, and elements with low importance were simplified. The grid generation of the models for each component of VGF heaters was carried out for finite element analysis. The solid components and the fluid components which could occur flux flow caused by natural convection were divided into models. For the fluid components, the boundary layer effect was considered to apply the structured grid to the interface part with the solid components. To save analysis time, the analysis model and grid generation were carried out for a quarter of the entire model. For the boundary condition for the heat source, heat flux was set on the surface area of the winding model so that the heat value of the heater winding should be within a maximum  
The heat transfer analysis on the designed VGF heater was carried out for the two-step solidification process of GaAs. The analysis was performed to make the temperature of the GaAs interface between liquid and solid become melting and freezing temperature by controlling the heat flux on the winding surface of eight heaters arranged in a vertical direction. Since the heat transfer analysis was carried out with steady conditions, the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & **Unit** & **Value** & **Remarks** \\ \hline Open total & \({}^{\circ}\)C & 20 & - \\ temperature & kPa & 101.325 & - \\ Open total pressure & kPa & 101.325 & - \\ Heater max heat flux & W/m\({}^{2}\) & 28,440 & At 550 W \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Each value of boundary conditions. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Index** & \(\rho\) **(kg/m\({}^{3}\))** & \(\mu\) **(Pa-s)** & **k (W/mK)** \\ \hline GaAs liquid & 5160 & 0.00279 & 54 \\ Vacuum & - & - & 0.004 \\ Air & & Ideal air model & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Properties of GaAs liquid and air. Figure 8: Boundary conditions of modeling. radiant heat transfer was not considered. The result of the heat transfer analysis is shown in Figure 9, which shows the temperature contour of GaAs. For temperature simulation, the heat value of respective heaters and the adequacy of the heat transfer path were examined, which could form the desired temperature distribution of GaAs in a vertical direction that is the most important factor in the heat transfer characteristics, and it was considered the insulation capability of the outer case. As a result of the temperature simulation, it made area A have a temperature gradient of 3 \({}^{\circ}\)C/Cm and the corresponding growth rate was about 2.8 mm/hr, but as an experimental result, even if reducing it to half, the solid-liquid interface was kept flat, and the heat stress decreased, so it was examined to obtain a high-quality crystal in this compartment. In area B, the growth rate increased to 2 mm/hr. To prevent the solid-liquid interface shape from continuing to be convex, the temperature gradient was reduced to 2.5 \({}^{\circ}\)C/Cm for planarization. In area C, the growth rate was increased to 3 mm/hr, and the temperature gradient was reduced to 2 \({}^{\circ}\)C/Cm again. In area C, it was applied to minimize the heat stress occurrence on the rear of the ingot. The shape of the equipment with the ingot growth furnace heater designed and finally manufactured heater is presented in Figure 10.  
The designed ingot growth furnace equipment was used to manufacture the final GaAs crystal through the GaAs ingot growth.