Effect of crucible rotation on the distribution of carbon, oxygen and nitrogen impurities in multi-crystalline silicon grown by directional solidification process – a numerical simulation analysis

M Avinash Kumar; M Srinivasan; P Ramasamy

doi:10.1088/2053-1591/ab3ecb

1. Introduction

Directionally Solidified (DS) multi-crystalline silicon has a huge share in PV market due to its low production cost, easy operation and high yield of large size ingots compared to mono-crystalline silicon produced from Czochralski (CZ) and other melt growth technique [1]. However, mc-silicon possesses low conversion efficiency compared to mono-silicon and so the research activities are mainly focused on engineering defects, dislocations, grain orientations, dopants and impurity incorporation in mc-silicon to improve its quality and efficiency [2]. In the DS process, ingot quality depends on various heat and mass transport parameters during the growth. Among those parameters, melt convection has the main role in impurity incorporation, temperature distribution, thermal stress, and melt/crystal interface shape while growing the crystal [3]. The impurity incorporation from feedstock and furnace elements during the growth of mc-silicon ingot should be controlled in order to improve the conversion efficiency of mc-solar cells [4]. The non-metallic Carbon, Oxygen and Nitrogen impurities and their interactions with silicon melt during solidification process have a huge impact on the solar cell efficiency and crystal quality [5]. To optimize these impurities incorporation and growth condition, it is necessary to control unsteady melt convection to have uniform melt mixing. The optimization of melt convection is essential to attain uniform mixing of the melt that leads to proper segregation and uniform distribution of impurities in as-grown ingot [6]. Using Accelerated Crucible Rotation Technique (ACRT), the uniformity in melt mixing is enhanced in which convective melt flow is controlled by accelerating and decelerating crucible periodically [7]. While rotating the crucible, Ekman layer flow is observed below the melt free surface causing radial flow along the horizontal direction and it varies with respect to change in rotation rate [8]. By applying ACRT, the growth rate and homogeneity in carbon concentration were reported for the growth of mc-silicon [9, 10]. Numerical results for precipitation of silicon carbide, silicon nitride and impurity transport from various furnace elements during solidification have been reported for the growth of mc-silicon [11–14]. In the present work, we have made a numerical simulation for impurity distribution in mc-silicon ingot grown at various crucible rotation rates in the DS system. The crucible rotation was applied from the beginning to the end of the solidification process and the distribution of impurities at various rotation rate was studied. The role of crucible rotation rate on the concentration of non-metallic impurities in mc-silicon ingot was analyzed using commercial numerical simulation software CGSim version 18.2.3 developed by STR group.

2. Numerical model of DS system

A global transient simulation was done to analyze the effect of rotation of crucible on impurity concentration in mc-silicon ingot. The simulations are done with the CGSim code used by numerous researchers for optimizing the crystal growth mechanism [15–17]. A two-dimensional axisymmetric model has been used in which the whole DS furnace is considered to be a two-dimensional structure and it is shown in figure 1. All heat and mass transport and convection of melt were calculated by two-dimensional finite volume method. The mesh generated in the geometry of DS furnace consists of the triangular and quadrangular grid. The mesh refinements are executed near the melt free region and crystal-melt interface. The silicon melt is considered as Newtonian fluid and very fine grids are generated to account the melt motion. The differential equation for heat and mass transport and impurity concentration are given below:

$\begin{eqnarray}&&\displaystyle \frac{\partial {\rho }_{i}}{\partial t}+{\rm{\nabla }}.\left({\rho }_{i}\,{\vec{u}}_{i}\right)=0\end{eqnarray} \tag{ 1 }$

$\begin{eqnarray}&&\displaystyle \frac{\partial \left({\rho }_{i}{\vec{u}}_{i}\right)}{\partial t}+\left({\vec{u}}_{i}\,.\,{\rm{\nabla }}\right){\rho }_{i}{\vec{u}}_{i}=-{\rm{\nabla }}{\rho }_{i}+{\rm{\nabla }}.{f}_{i}+\left({\rho }_{i}-{\rho }_{i,o}\right).\vec{g}\end{eqnarray} \tag{ 2 }$

$\begin{eqnarray}&&\displaystyle \frac{\partial ({\rho }_{i}{C}_{{p}_{i}}{T}_{i})}{\partial t}+{\rm{\nabla }}.\left({\rho }_{i}{C}_{{p}_{i}}{\vec{u}}_{i}{T}_{i}\right)={\rm{\nabla }}.\left({k}_{i}{\rm{\nabla }}{T}_{i}\right)\end{eqnarray} \tag{ 3 }$

$\begin{eqnarray}&&\displaystyle \frac{\partial \left({\rho }_{i}{C}_{j}\right)}{\partial t}+{\rm{\nabla }}.\left({\rho }_{i}{\vec{u}}_{i}{C}_{j}\right)={\rm{\nabla }}.\left({D}_{j}{\rm{\nabla }}{C}_{j}\right)\end{eqnarray} \tag{ 4 }$

$\begin{eqnarray}&&{\rho }_{g}=\displaystyle \frac{{p}_{0}m}{RT}\end{eqnarray} \tag{ 5 }$

Where, $t$ —time, $\rho$ —density, ${\rho }_{i,o}$ —reference density, ${C}_{p}$ —heat capacity, $\vec{u}$ —velocity vector, $T$ —temperature, $k$ —thermal conductivity, $p$ —pressure, $f$ —stress tensor, $\vec{g}$ —gravitational acceleration, $C$ —concentration, $D$ —diffusion coefficient, ${p}_{0}$ —reference pressure, $m$ —molecular weight, $R$ —universal gas constant. Subscript $i$ may be l or g, indicating the melt and argon gas respectively. And $j$ indicates the impurity atoms in melt and argon gas. From temperature distribution and velocity obtained from equations (1)–(3), the concentration of impurities in ingot is obtained from equation (4). To predict melt motion, one equation model associated with the RANS (Renolds Average Navier-Strokes) approach is used. Using the quasi-chemical approach the particle formation was modelled and the distribution of impurities was analysed.

**Figure 1.** The axisymmetric furnace geometry of Directional Solidification system.
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3. Impurity formation and segregation

The particle formations such as SiC, Si₃N_4, and Si₂N₂O are mainly formed from the graphite furnace elements, feedstock, and crucible coated with silicon nitrate. The carbon, nitrogen and oxygen impurities interact with the melt during solidification leading to particle formation and the reaction kinetics are given below,

$\begin{eqnarray*}&&S{i}_{\left(Liquid\right)}+C{}_{\left(Liquid\right)}\leftrightarrow Si{C}_{(Solid)}\end{eqnarray*}$

$\begin{eqnarray*}&&2S{i}_{(Liquid)}+\,2{N}_{(Liquid)}+{O}_{(Liquid)}\leftrightarrow S{i}_{2}{N}_{2}{O}_{(Solid)}\end{eqnarray*}$

$\begin{eqnarray*}&&3S{i}_{\left(Liquid\right)}+4{N}_{(Liquid)}\leftrightarrow S{i}_{3}{N}_{4(Solid)}\end{eqnarray*}$

The CO vapours originating from the graphite units reach the melt free surface and the oxygen dissolved in molten silicon is discharged into argon atmosphere within the furnace as SiO vapour.

$\begin{eqnarray*}&&C{O}_{(Gas)}\leftrightarrow {C}_{(Liquid)}+{O}_{(Liquid)}\end{eqnarray*}$

$\begin{eqnarray*}&&S{i}_{(Liquid)}+\,{O}_{(Liquid)}\leftrightarrow Si{O}_{(Gas)}\end{eqnarray*}$

In silicon melt, oxygen gets incorporated due to partial melting in the wall of quartz crucible and nitrogen gets incorporated due to silicon nitrate coating inside the quartz crucible.

$\begin{eqnarray*}&&Si{O}_{2(Solid)}\leftrightarrow S{i}_{(Liquid)}+2{O}_{(Liquid)}\end{eqnarray*}$

$\begin{eqnarray*}&&S{i}_{3}{N}_{4(Solid)}\leftrightarrow 3S{i}_{(Liquid)}+4{N}_{(Liquid)}\end{eqnarray*}$

In mc-silicon growth, the segregation of impurity is defined in terms of the ratio of impurity in silicon solid ( ${C}_{S}$ ) to silicon liquid ( ${C}_{L}$ ) which remains constant over a particular range of concentration. This ratio is said to be distribution coefficient or equilibrium segregation and it is denoted by ${k}_{0}$ as,

$\begin{eqnarray*}&&{k}_{0}={C}_{S}/{C}_{L}\end{eqnarray*}$

In terms of solidification fraction ( $g$ ), the distribution of impurities in solid is given as,

$\begin{eqnarray*}&&{C}_{s}={k}_{0}{C}_{0}{(1-g)}^{{k}_{0}-1}\end{eqnarray*}$

Where ${C}_{0}$ is the initial concentration of impurity in silicon melt.

Based on the segregation coefficient the impurity concentration in an ingot will get varied. If the segregation coefficient ${k}_{0}$ < 1, the impurities get segregated towards the top of an ingot and it will remain in molten silicon during solidification. If ${k}_{0}$ > 1, the impurity will be more soluble and it tends to segregate toward the bottom of an ingot. Segregation coefficient of some common impurities in silicon is given in table 1 [18].

Table 1. Segregation coefficient of common impurities in silicon.

Impurity	${{\boldsymbol{k}}}_{0}$
Al	0.002
As	0.3
B	0.8
C	0.07
N	0.0007
O	1.25
P	0.35
Sb	0.023
Cu	4 × 10⁻⁶
Fe	8 × 10⁻⁶

4. Results and discussion

Numerical simulations are done for the growth of mc-silicon with the application of crucible rotation rate of 3, 6, 9, 12 and 15 rpm throughout the growth process. The simulations are done separately for each rotation rate for the complete growth of mc-silicon ingot. The temperature gradient should be maintained by adjusting heater power and opening bottom insulation in order to achieve convex or planar interface during solidification [19]. The temperature distribution in melt should be optimized to control convective melt flow and the turbulence in convection is minimized by applying external body force on the crucible. The effect of rotation on carbon, oxygen and nitrogen concentration and distribution is observed for each mc-silicon ingot grown at different rpm. Carbon incorporation in the ingot is due to graphite elements in the furnace and it easily reaches the melt free surface thereby entering into the crystal lattice. From crucible wall, nitrogen and oxygen get incorporated into an ingot. The crucible is coated with silicon nitrate of coating thickness 0.0002 m and it acts as a separating layer between an ingot and the crucible [15]. The observations are done for an ingot grown at different rpm and variation in impurity concentration was analyzed.

4.1. Carbon concentration

Cbon is a major impurity that affects the conversion efficiency of solar cells. To control carbon concentration and improve uniformity in impurity distribution, crucible rotations are applied. The distribution of carbon in mc-silicon ingot grown by without applying crucible rotation and with crucible rotation of 3 and 15 rpm is shown in figures 2(a)–(c). For an ingot grown without any crucible rotation, the concentration of carbon is shown in figure 2(a) and it is observed that the concentration of carbon is high on the top of an ingot and has a maximum value of 2.45 × 10¹⁷ (atoms cm⁻³) near the melt free surface. When no crucible rotation is applied during the growth, the concentration of carbon varies along the axial and radial direction and inhomogeneity in impurity distribution is observed. There is no proper mixing of the melt inside the crucible causing the non-uniform distribution of impurity in a grown ingot. Without any crucible rotation, the melt/crystal interface seems to be w-shaped during the growth. The maximum concentration of carbon occurs at the convex part of the interface during the growth that segregates them toward the top of an ingot. The segregation coefficient of carbon is 0.07, so the presence of carbon will be higher in the melt during solidification of mc-silicon. Due to this, the carbon segregates on the top of an ingot at the end of the solidification process. As a result of w-shaped melt/crystal interface during the mc-silicon growth process, the solidification starts initially at the edges of an ingot. As the segregation coefficient of carbon is only 0.07, lower concentration of carbon was observed at the edges of the surface of an ingot. The higher concentration of carbon stays in the melt above the melt/crystal interface. And at the end of solidification process, the C concentration is always lower at the edges of the surface of the ingot. When crucible rotation of 3 rpm is applied, maximum value of carbon concentration in an ingot decreases to 2.26 × 10¹⁷ (atoms cm⁻³), for 6 rpm the value is 2.10 × 10¹⁷ (atoms cm⁻³), for 9 rpm the value is 1.95 × 10¹⁷ (atoms cm⁻³), for 12 rpm the value is 1.82 × 10¹⁷ (atoms cm⁻³) and for 15 rpm the value is 1.70 × 10¹⁷ (atoms cm⁻³). So with further increase in rotation rates, the maximum concentration value on the top of an ingot decreases causing the uniform distribution of impurities along the radial direction of an ingot. Figure 3 shows the distribution of carbon along the axial direction of an ingot grown at different rpm. When crucible rotation rate is increased from 3 rpm to 15 rpm, the concave part in the melt/crystal interface decreases and the radial uniformity of carbon concentration in an ingot is increased. Thus, the rotation rate has a significant impact on carbon concentration and uniformity in distribution by enhancing melt mixing. It enhances the uniformity in radial and axial directions thereby improving the efficiency of wafers sliced from a grown ingot. The concentration of carbon in an ingot is minimized by crucible covers or shield on top of the crucible thereby blocking impurity incorporation form surrounding graphite furnace elements [20].

**Figure 2.** The distribution of carbon concentration in mc-silicon ingot grown at (a) 0 rpm, (b) 3 rpm and (c) 15 rpm.
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**Figure 3.** The distribution of carbon along the axial direction of an ingot grown at different rpm.
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4.2. Oxygen concentration

Oxygen is one of the major impurities that directly influences the conversion efficiency of solar cells. Oxygen atoms usually originate from crucible wall during the solidification process and the concentration seems to be higher at the side surface of an ingot near crucible region. The distribution of oxygen in mc-silicon ingot grown by without crucible rotation and with crucible rotation of 3 and 15 rpm is shown in figures 4(a)–(c). An ingot grown without applying crucible rotation is shown in figure 4(a), the concentration of oxygen is higher at the sides of an ingot with the value of 2.51 × 10¹⁷ (atoms cm⁻³) due to irregular convective melt flow and poor melt mixing [13]. The oxygen has a higher segregation coefficient value compared to all other common impurities in silicon with the value of 1.25. Due to this, the concentration of oxygen will be higher in solidifying silicon compared to molten silicon during solidification and oxygen tends to stay in ingot after the complete growth process. When there is no crucible rotation during the growth process, there is a non-uniform distribution of oxygen along the axial and radial direction of a grown ingot. This inhomogeneity in oxygen concentration is optimized by applying crucible rotation and the oxygen is segregated towards the bottom of an ingot. When crucible rotation of 3 rpm is applied, the higher concentration region near the crucible wall segregated towards the center bottom of ingot due to the effect of crucible rotation on convective melt flow and high segregation coefficient. For 3 rpm, maximum value of oxygen concentration in an ingot decreases to 2.29 × 10¹⁷ (atoms cm⁻³), for 6 rpm the value is 2.25 × 10¹⁷ (atoms cm⁻³), for 9 rpm the value is 2.22 × 10¹⁷ (atoms cm⁻³), for 12 rpm the value is 2.20 × 10¹⁷ (atoms cm⁻³) and for 15 rpm the value is 2.19 × 10¹⁷ (atoms cm⁻³). When the crucible rotation of 3, 6, 9, 12 and 15 rpm is applied, the higher concentration region starts segregating towards the center bottom of an ingot with respect to increase in rotation rate. When there is no crucible rotation, the transport of oxygen decreases within the molten silicon thereby causing higher concentration near crucible bottom and crucible walls [21]. With application and increase in crucible rotation, the convective melt flow and the transport of oxygen in molten silicon increases causing decrease in oxygen concentration. The concentration of oxygen in the ingot decreases with increase in crucible rotation because some of the oxygen dissolved in molten silicon is discharged into argon atmosphere within the furnace as SiO vapour [22]. The silicon melt is in contact with the crucible. Due to dissolution of crucible, oxygen gets into the melt. Figure 4(a) pertains to 0 rpm and figure 4(b) pertains to 3 rpm. Due to rotation there is greater melt-crucible interaction, more dissolution and more oxygen. When solidification of the melt starts, due to higher segregation coefficient (1.25) more oxygen is seen at the bottom. Hence there is wider high-O region near the crucible bottom. Figure 5 shows the distribution of oxygen along the axial direction of an ingot grown at different rpm. The uniformity of oxygen concentration along the radial and the axial direction of an ingot increase with an increase in crucible rotation rates. If the value of segregation coefficient is near to one, the axial uniformity would be higher. The segregation coefficient of oxygen is near to one, so axial uniformity of oxygen is high compared to carbon and nitrogen. The higher concentration of oxygen often leads to dislocation generation, stacking fault and defects. Thus by applying crucible rotation, the uniform distribution of impurity increases thereby improving the quality and conversion efficiency of a grown ingot.

**Figure 4.** The distribution of oxygen concentration in mc-silicon ingot grown at (a) 0 rpm, (b) 3 rpm and (c) 15 rpm.
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**Figure 5.** The distribution of oxygen along the axial direction of an ingot grown at different rpm.
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4.3. Nitrogen concentration

The nitrogen usually originates from the crucible wall due to the coating of silicon nitrate and the higher concentration in an ingot occurs near the wall of crucible. The distribution of nitrogen in a grown mc-silicon ingot for without any crucible rotation and with various crucible rotation rates such as 3 and 15 is shown in figures 6(a)–(c). The segregation coefficient of nitrogen is very low with the value of 0.0007, so the concentration of nitrogen is minimum compared to carbon and oxygen and it stays in the melt during the solidification process. An ingot grown without any crucible rotation is shown in figure 6(a), the maximum concentration value of nitrogen in an ingot is 1.98 × 10¹⁵ (atoms cm⁻³) near the crucible wall. When no crucible rotation applied, there is a non-uniform distribution of impurities along the radial and the axial direction of a grown ingot. The higher concentration regions occur near the crucible wall and irregular distribution of nitrogen is observed within the ingot due to poor mixing of melt during the solidification process. This inhomogeneous distribution of nitrogen is optimized by applying crucible rotation thereby segregating the higher concentration region towards the bottom of an ingot. For 3 rpm, the maximum value of nitrogen concentration in ingot increases to 2.08 × 10¹⁵ (atoms cm⁻³), for 6 rpm the value is 2.10 × 10¹⁵ (atoms cm⁻³), for 9 rpm the value is 2.11 × 10¹⁵ (atoms cm⁻³), for 12 rpm and 15 rpm the value is 2.12 × 10¹⁷ (atoms cm⁻³). The concentration of nitrogen along the axial direction of an ingot is shown in figure 7. When crucible rotation of 3 rpm is applied, the maximum concentration region was observed to be transported towards the bottom of an ingot. This transport of the higher concentration of nitrogen towards the bottom of an ingot is due to external body force applied on molten silicon by means of crucible rotation during the solidification process. The higher concentration of nitrogen at lower half of an ingot is due to the silicon nitrate coating on the crucible but the radial uniformity of nitrogen in an ingot increases with an increase in rpm and the axial uniformity of ingot is also improved. This uniformity in nitrogen distribution is due to improved melt mixing with the application of rotation of crucible. As oxygen and nitrogen are originating from the crucible wall, they interact with molten silicon by forming precipitates such as Si₂N₂O and Si₃N₄. By applying crucible rotation, the precipitate formations can be controlled by optimizing convective melt flow and improving the mixing of melt. For better quality of the ingot, the higher concentration of nitrogen is not desirable because Si₃N₄ will concentrate at grain boundaries thereby causing generation of small grains. However, uniformity in nitrogen distribution with considerably low concentration is favourable for the growth of mc-silicon ingot [22].

**Figure 6.** The distribution of nitrogen concentration in mc-silicon ingot grown at (a) 0 rpm, (b) 3 rpm and (f) 15 rpm.
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**Figure 7.** The distribution of nitrogen along the axial direction of an ingot grown at different rpm.
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The obtained results show that the higher concentration of carbon on the top and the higher concentration of oxygen that segregated on bottom of an ingot decrease with increase in crucible rotation rate from 3 to 15 rpm. Carbon and nitrogen impurities stay in the melt during solidification due to low segregation coefficient and oxygen impurity remains in ingot due to high segregation coefficient thereby forming SiC, Si₃N₄ precipitates and Si₂N₂O on top of the ingot [12]. The transport of oxygen and nitrogen from crucible wall to the crystal is optimized by applying crucible rotation. The crucible rotation optimizes the heat convection in molten silicon and increases the transport of oxygen and nitrogen in silicon melt and prevents the accumulation of oxygen and nitrogen impurities near crucible contact regions. Without any crucible rotation, the higher concentration of oxygen and nitrogen get accumulated near the crucible walls. Thus the crucible rotation enhances the mechanism of impurity incorporation and distribution in the grown ingot.

5. Conclusion

Simulations are done for the growth of mc-silicon ingot and we have analyzed the distribution of carbon, oxygen and nitrogen impurities in an ingot grown at various crucible rotation rates. In the grown mc-silicon ingot, the uniformity in distribution of carbon, oxygen and nitrogen highly increases along the radial direction and axial direction of an ingot with the help of crucible rotation. The higher concentration of carbon gets slightly minimized and the uniformity in distribution in an ingot is achieved with crucible rotation. If the value of segregation coefficient is near to one, the axial uniformity would be higher. The segregation coefficient of oxygen is near to one, so axial uniformity of oxygen is high compared to carbon and nitrogen. The transport of oxygen and nitrogen from the crucible wall is optimized by the external body force applied to the crucible thereby controlling the convective melt flow. The concentration of nitrogen in an ingot is lower compared to carbon and oxygen and its higher concentration region was observed at the lower half of an ingot due to silicon nitrate coating on the crucible and the uniformity in distribution is observed with the application of crucible rotation. Thus, the application of crucible rotation enhances the melt mixing and its convective behaviour during the solidification process and increases the uniformity of impurity distribution in as-grown mc-silicon ingot.

Acknowledgments

This work was partly supported by the Ministry of New and Renewable Energy (MNRE), the Government of India (Order no: 31/58/2013-2014/PVSE & 15-01-2015).

Effect of crucible rotation on the distribution of carbon, oxygen and nitrogen impurities in multi-crystalline silicon grown by directional solidification process – a numerical simulation analysis

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Abstract

1. Introduction

2. Numerical model of DS system

3. Impurity formation and segregation