**1. Introduction**

With the rapid development of the electronic information industry, silicon is a very important raw material for semiconductor manufacture, and electronic-grade polysilicon materials play a pivotal role [1,2]. Polysilicon has a high mobility in semiconductor circuits, and consequently it is widely used in such industries as semiconductors, integrated circuits and computer chips [3,4]. The polysilicon materials used in the semiconductor and electronic information industries are electronic-grade polysilicon, and are generally 99.9999% pure Si [5]. For a long time, the production technology for electronic-grade polysilicon has been monopolized by many countries. The demand for electronic-grade polysilicon in China is almost entirely dependent on imports, which are highly dependent on the international environment [6]. Because of my country's insufficient research on semiconductor materials, the purity of polysilicon has never reached the international level, and the lack of sufficiently pure silicon has become a key factor that directly hinders the development of my country's semiconductor industry.

The main processes for the production of polysilicon include chemical vapor methods and metallurgy [7]. The representative of the chemical vapor deposition methods are the modified Siemens method [8], and the fluidized-bed [9], silane [10] and gas-liquiddeposition methods [11]. The main metallurgical methods are the thermite reduction

**Citation:** Yang, Q.; Chen, F.; Tian, L.; Wang, J.; Yang, N.; Hou, Y.; Huang, L.; Xie, G. Boron Impurity Deposition on a Si(100) Surface in a SiHCl3-BCl3-H<sup>2</sup> System for Electronic-Grade Polysilicon Production. *Minerals* **2022**, *12*, 651. https://doi.org/10.3390/min12050651

Academic Editors: Kenneth N. Han, Shuai Wang, Xingjie Wang and Jia Yang

Received: 12 April 2022 Accepted: 12 May 2022 Published: 21 May 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

method and the regional hot-melt purification method, but the thermite reduction method is only suitable for use in a laboratory [12,13]. Since the development of the improved Siemens chemical vapor deposition method, no other method can produce the same purity in the product and the process [14], and hence this is currently the method mainly used in industry to produce polysilicon. However, there is an unavoidable problem in production by the improved Siemens method: distilled trichlorosilane (SiHCl3) and a small amount of boron trichloride (BCl3) enter the Siemens reduction furnace, causing a heterogeneous reaction on the surface of the silicon rod, which results in the doping of boron into the polysilicon [15]. However, research on boron impurities arising in the production of polysilicon by the improved Siemens method is still relatively weak, and research on this process is therefore of great significance.

The impurities in high-purity electronic-grade polysilicon come mainly from the boron impurity in the acceptor, and the content of this needs to be controlled below 0.33 ppb [15]. To control the B doping of polysilicon in chemical vapor deposition, it is important to reduce the content of impurity B in the product and improve its purity [16,17], and this requires in-depth and systematic research on B-doping in the polysilicon deposition process. To study the chemical vapor deposition rate, Jenkinson and Pollard experimented to explore the deposition rate of boron in a BCl3-H<sup>2</sup> system in a parallel flow reactor [18]. However, under these conditions, the boron deposition rate was limited by the transfer process of BCl3. To describe the kinetics and reaction mechanism of the BCl<sup>3</sup> hydrogenation process more accurately, Sezgi designed a collision-jet chemical vapor deposition reactor [19]. The role of the reactor was to minimize the impact of the transfer process on the boron deposition rate. On this basis, Sezgi further studied the kinetics of the process of boron chemical vapor deposition in the BCl3-H<sup>2</sup> system and obtained a deposition rate of B in the range of 75–1350 ◦C [20]. The Key Laboratory of Ultra-High Temperature Structural Composites of Northwestern Polytechnical University studied the influence of temperature on the kinetics of chemical vapor deposition during the preparation of Si-B-C ceramics. The results showed that the process is controlled by chemical reaction kinetics with an activation energy of 271 kJ/mol, the initial step of the deposition kinetics being BCl<sup>3</sup> (g) + H<sup>2</sup> (g) → HBCl<sup>2</sup> (g) + HCl (g) [21]. That study also proved that this step is one of the main reactions in the thermodynamic analysis of ZrB<sup>2</sup> synthesized using the ZrCl4-BCl3-H<sup>2</sup> system [22].

The doping mechanism of B in polysilicon chemical vapor deposition has been studied both domestically and abroad. To accurately and economically reflect the actual industrial situation, this study uses the method of simulation by quantum chemistry calculation to study the B-doping control mechanism in the process of polysilicon chemical gas deposition in a vacuum environment. The properties of different atomic positions of BCl<sup>3</sup> and SiHCl<sup>3</sup> on the Si(100) surface are calculated and analyzed using the first-principles method, and the most favorable state is determined by comparing the different adsorption energies. At the same time, the optimal adsorption density of states is calculated and the adsorption reaction mechanism is obtained.

#### **2. Calculational Methods**

On the basis of functional theory, the plane-wave method employing a supersoft pseudopotential was adopted, and a GGA-BLYP functional (a Becke–Lee–Yang–Parr functional incorporating the generalized gradient approximation) was used for the approximate calculation [23]. The DMol<sup>3</sup> module [24] in the Material Studio software package (Version 8.0, Accelrys Company, San Diego, CA, America) was used for the calculation of the gas-phase reaction, which includes the optimization of the SiHCl3, BCl<sup>3</sup> and H<sup>2</sup> molecules and the calculation of the energy and frequency. The CASTEP (Cambridge Serial Total Energy Package) module [25] was used to calculate the gas–solid reaction, involving mainly the calculation of the relevant parameters of the adsorption reaction of the adsorbed molecules on the surface of the basic model and a search for the transition state of the entire adsorption reaction. For the Si(100) surface, a 7-layer structure was adopted, with the cutoff energy

selected as 450 eV and the k-point grid set to 3 × 3 × 1 [26]. In the supersoft pseudopotential method, the convergence criteria of the pseudopotential have to be selected [27]. The convergence criteria for energy, force and maximum displacement are selected at the same time, with values chosen as energy (2 <sup>×</sup> <sup>10</sup>−<sup>5</sup> eV/atom), force (0.05 eV/Å) and maximum displacement (2 <sup>×</sup> <sup>10</sup>−<sup>3</sup> Å). The internal stress between atoms must be less than 0.1 GPa [28]. The path of the Brillouin zone was set to GFQZG, the complete LST/QST method was adopted for the transition state search, and a vacuum layer with a thickness of 12 Å was selected to eliminate interaction between the layers. The error in the surface energy was limited to 0.05 J/m<sup>2</sup> . The formula used to calculate the surface energy is shown in Equation (1) [29]:

$$
\sigma = \frac{E\_{slab} - nE\_{bulk}}{2A} \tag{1}
$$

where *Eslab* is the total energy of the unit-cell of the model, *Ebulk* is the energy of a single atom in the unit cell, *n* is the number of atoms in the unit cell, and *A* is the total surface area of the unit cell.

The mechanism of SiHCl<sup>3</sup> decomposition on the low index plane of the polycrystal silicon is performed the same as silicon [30]. Therefore, the adsorption energy (the change in the total energy before and after adsorption) of the SiHCl<sup>3</sup> and BCl<sup>3</sup> molecules on the surface of the Si(100) unit cell is calculated using Equation (2) [31]:

$$E\_{adsorption} = E\_{surface^\*} - E\_{surface} - E\_{molecules} \tag{2}$$

where *Eadsorption* represents the adsorption energy of BCl<sup>3</sup> or SiHCl<sup>3</sup> onto the surface of the Si(100) unit cell, *Esurface***\*** represents the energy of the adsorption base surface, *Esurface* is the energy of the surface without any interactions, and the total energy of the molecules before adsorption is represented by *Emolecules*.

Figure 1a shows the geometric structure of the model Si(100) unit cell. Its surface contains three types of Si atoms: top, bridge and acupoint Si atoms. To study the adsorption of related molecules on the polysilicon (100) surface, a complete unit cell surface must first be established. The thickness of the vacuum layer was set to 12 Å to avoid layer-to-layer interactions. In the process of establishing the model, in order to satisfy the stability of the model and the accuracy of the experiment at the same time, we did not impose any restrictions on the upper three layers of atoms but fixed the lower four layers of atoms. Simultaneously, to saturate the covalent bonds of each silicon atom in the bottom layer, two H atoms were added to each Si atom in the bottom layer, adding hydrogen atom at the bottom can increase the stability of the model, and the silica–hydrogen bond at the bottom is conducive to the stable convergence of the model, and the surface and nearsurface layer atoms were fully relaxed. The supercell chemical formula for the entire unit cell is Si83H9. After surface optimization, the optimization curve finally reached a stable convergence state, as shown in Figure 1b, which proved that the surface structure met the experimental requirements.

**Figure 1.** Model geometry and optimization curve of Si(100) surface. (**a**) is the Si(100) model geometry; (**b**) is the model optimization convergence curve.

#### **3. Results and Discussion**
