**1. Introduction**

With the development of the electronic information industry, semiconductor devices, integrated circuits and other high-tech fields have an increasing demand for electronicgrade (EG) high-purity polysilicon [1–3]. The modified Siemens process is the mainstream process for the production of high-purity polysilicon [4], accounting for more than 78% of the global production capacity [5]. The reduction process is the core process of the modified Siemens method. The principle of this method is that raw material with high purity, including trichlorosilane (TCS) and hydrogen (H2), enter the reactor through nozzles in the base plate, and a chemical vapor deposition reaction (CVD) occurs on the surface of polysilicon rods at a high temperature around 1323 K [6,7]. As a result, the diameters of the rods increase with the growth process. Compared with dozens of solar-grade (SG) polysilicon manufacturing enterprises, the number of electronic-grade polysilicon enterprises is very small, and the production is limited [8,9]. Electronic polysilicon has a very high requirement for product purity [10]. SG polysilicon has a minimum of 6 N or 99.9999% purity, while EG polysilicon has 9 N. The atomic fractions of acceptor impurities and donor impurities are usually below 50 ppt and 150 ppt, respectively, which puts forward a very high demand for the impurity control of the whole closed-loop process [11], resulting in extremely high costs.

Energy and material consumption in the reduction stage accounts for a remarkable proportion of the whole production process [12]. Some researchers have tried to decrease production costs from different directions. Luo [13] pointed out that the well-polished

<sup>1</sup> School of Chemistry and Chemical Engineering, Harbin Institute of Technology, Harbin 150001, China

substrate surface suggests an excellent radiation energy-saving capacity. Nie [14] used ceramic lining on a reactor vessel to emit thermal radiation and obtain smoother radialdependent temperature and thermal stress distributions. However, both of them increase the furnace cost for expensive materials or processing. Sun [15] studied the influence of the reaction temperature on the yield of silicon and power consumption under certain conditions for the production of electronic-grade polysilicon, which showed that higher temperatures are good for unit consumption but need to be as uniform as possible. Some researchers have studied deposition conditions from the perspective of electricity. Nie [16] presented an electrical heating model using alternating current (AC) for the silicon rods. The influences of the location of the silicon rods, AC frequency, the radius of the rod and wall emissivity on the temperature profile and current density were studied through the application of the developed model. Du [17] found that high-frequency current is conducive to reducing the temperature gradient and put forward the concept of the mixed-frequency heating process. The deposition conditions on the surface of the silicon rod in the reactor determine the polysilicon quality and deposition rate, which is hard to improve and related to many factors, such as the uniformity of rod surface temperature, gas flow rate, flow velocity along the rods and so on. Meanwhile, complex operating parameters, including the feed gas, electronic current, reactor shape and the layout of polysilicon rods, nozzles and outlet, can significantly influence the deposition conditions [18]. Since this stage is in a closed environment and the polysilicon rod surface has a very high temperature of around 1323 K during the deposition process [10,19], gas flow in the reactor and the temperature field distribution of the silicon rod surface are difficult to directly and precisely measure and characterize [20]. The PolySim software employed in this study was used as a numerical simulation tool to understand what happens inside the CVD reactor.

In order to improve the utilization rate of raw materials and reduce costs, a coupled furnace scheme is proposed, which means connecting several furnaces in series to change the amounts of raw materials or the flow rate. This concept is expected to achieve exhaust gas recovery, improve the overall conversion rate of raw materials and reduce material and energy consumption. Due to the reduction in raw materials from the first furnace to the next furnace, the feed material quantity needs to be changed to meet requirements for consistent deposition conditions. Usually, the gas inlet nozzles are fixed on the base plate, whose distribution directly determines the injection rate and flow rate of the raw materials supplied. Therefore, it is necessary to carry out simulation studies on furnaces with different characteristics of inlet gases. In this study, the original scheme, a high inlet gas flow velocity scheme and a high inlet gas flow rate scheme were studied and compared. By analyzing the deposition conditions on the surface of the silicon rods, the high flow rate base plate design was selected for the coupling equipment. The deposition characteristics and process parameter results of the coupling equipment were also simulated, which showed good prospects for the coupled reduction furnace scheme.

#### **2. Modeling Process**

The CVD furnace used for modeling is a bell jar type, and its main structure is shown in Figure 1a [21]. Numbers 1 to 13 indicate the base plate, electrodes, exhaust gas outlet pipes, mixed gas inlets, mixed gas inlet pipes, base plate coolant inlet pipes, base plate coolant outlet pipes, furnace coolant inlet pipes and outlet pipes, furnace, silicon rods, coolant interlayer and observation window. The 3D model was built and meshed using PolySim software, and the physical meaning of some parameters is shown in Figure 1b. After neglecting the irrelevant details, the key structures of the reactor, such as the inner wall, base plate, gas inlets, gas outlets and polysilicon rods, were abstracted, and the numerical domain required for the modeling of a CVD reactor was obtained. The main geometric parameters of the reactor are shown in Table 1. Due to the need for resistance heating, in actual production, the tops of the two silicon rods will be connected in series through a small segment of the silicon rods in the initial stage. However, in the model, it is simplified into a small segment with an arc shape (bridge part). In order to facilitate

the comparison of the physical field distribution inside the furnace chamber, a silicon rod diameter of 50 mm was preferentially set during 3D modeling.

**Figure 1.** Schematic diagram of bell-type polysilicon reduction furnace: (**a**) Profile; (**b**) Furnace shell and silicon rod.

**Table 1.** Geometrical dimensions of the model of 18-rod CVD reactor.


The reactor chamber was discretized by a mesh with different kinds of elements (hexahedral, polyhedral and prismatic) to adapt to different characteristics of different domains. To be specific, the prismatic element is used along the polysilicon rods, which allows the extrusion of cells along the cylinders. The boundary layer uses hexahedral structure meshes to provide cell size control, and the polyhedral element is used to discretize the dome due to its complex shape. The first unit of the furnace body boundary layer and the first unit of the silicon rod boundary layer are respectively set to 2 mm and 5 mm, and the transition factor is 1.4. A schematic diagram of the furnace body and silicon rods after meshing is shown in Figure 2. Due to similar settings of mesh generation, the different models have similar grids, which contain about 7 million cells, 19 million faces and 6 million nodes. The minimum orthogonal quality and the maximum aspect ratio are about 0.32 and 32, respectively, and the quality parameters of the grid meet the requirements.

**Figure 2.** Schematic diagram of furnace body and silicon rods: (**a**) 3D models; (**b**) grid structure.

To explore the requirements of the coupling scheme for the reduction furnace, it is necessary to conduct modeling comparisons from the perspective of increasing the flow rate and increasing the flow rate. In view of this, different base plates with different distributions of gas inlet nozzles were designed, while the overall shape of the equipment was not changed. As shown in Figure 3, the base plate has four rings, including outlet nozzles, silicon rods, inlet nozzles and inner silicon rods from the circumference to the center. Six inlet nozzles are evenly distributed on the nozzle ring, while different schemes have different inlet nozzle arrangements. In design A (original scheme), the inlet nozzles have two diameters of 7 mm and 11 mm, and these nozzles with two diameters are arranged at intervals. In design B (high flow rate scheme), the nozzle diameters are 4.2 mm and 7 mm. Considering the total cross-sectional area of each nozzle, the feed flow rate of scheme B remains unchanged, but the feed flow velocity is increased by 2.5 times. In design C (large flow scheme), the nozzle diameters are 9 mm and 15 mm. The feed flow rate increases twofold. It should be pointed out that the above calculation is simplified, which assumes that the outlet pressure of each nozzle is the same.

**Figure 3.** Diagram of base plate: (**a**) structure; (**b**) after meshing.

During the deposition process, large amounts of raw components for the reaction and enough electricity for heating are necessary. For controlling variables, the main process parameters and boundary conditions for modeling these designs are the same, such as electric current, the temperature of the wall, operating pressure, H2/Si mole ratio and so on, as shown in Table 2. In particular, in order to be close to the actual gas composition, there is some DCS (Dichlorosilane) in the raw material supply. The reduction furnace body is a double-layer structure, and the coolant in the middle layer absorbs the heat of the furnace wall and reduces its temperature. The furnace body is generally made of stainless steel, though some manufacturers use silver-plated materials. The boundary conditions are shown in Table 3. The furnace side wall and base plate are made of the same material in this study.





During the simulation, processes including turbulent flow (by k-eps model), heat transfer in the gas and inside the rods, radiation and electric current inside rods were modeled. Navier–Stokes equations were solved, together with equations for enthalpy and equations for k and epsilon, respectively. In addition, a surface-to-surface radiation model was used, also known as the view factor model. PolySim 3D was used to solve all of the above equations. The representative process time was selected when the silicon rod diameter was 50 mm so as to evaluate the growth conditions to the greatest extent. To achieve convergence, about 60,000 iterations are required. Residuals for solving equations are less than 0.0001. The heat and radiation imbalances are less than 1.5%, and the mass imbalances are less than 0.5%, which shows that the modeling results converge well. An internal visualizer of PolySim 3D was used to visualize 3D distributions of physical fields, including the temperature field, flow field and boundary layer in the reactor. The modeling results of design A were analyzed and compared with an experiment [22], and highly consistent results were obtained. In the previous study, under similar process conditions and furnace structure, the error of key parameters between the simulation results and the production results was about 4%. The accuracy meeting the requirements in design A provides reliable support for the simulation of the coupling mode.

## **3. Results and Discussion**
