Effect of Cooling Rate on the Activation of Slip Systems in Seed CastGrown Monocrystalline Silicon in the [001] and [111] Directions
B. Gao,* S. Nakano, H. Harada, Y. Miyamura, and K. Kakimoto
ABSTRACT: To effectively reduce dislocation by controlling the cooling process, the effect of cooling rate on the activation of slip systems was studied in seed cast-grown monocrystalline silicon in the [001] and [111] growth directions. The results show that the cooling rate has a large effect on the activation of slip systems. In the [001] growth direction, a slow cooling rate either weakly activates 4-fold symmetric slip systems or does not activate them at all. In contrast, a fast cooling rate strongly activates the 4-fold symmetric slip systems. In the [111] growth direction, a slow cooling rate weakly activates the three 3-fold symmetric slip systems, while a fast cooling rate strongly activates the three 3-fold symmetric slip systems. The differences of the activation of the slip systems between the slow and fast cooling rates mainly cause differences in dislocation and residual stress. Irrespective of the crystal growth direction, it is mainly the radial flux that causes the difference between the fast and slow cooling rates. Therefore, the most effective method for reducing dislocation during the cooling process is to decrease the radial flux.
1. INTRODUCTION
The photovoltaic industry is in a phase of rapid growth, increasing by over 30% per year over recent years. The main challenge of today’s photovoltaic technology is the increase of solar cell efficiencies while still using cost-effective, highthroughput, and large-scale processes. To reduce the cost of production, a seed casting technique has been proposed to grow a complete single crystal of silicon in a whole ingot. The cost of producing monocrystalline silicon could be greatly reduced, and the conversion efficiency of wafers could be much higher than 18% for multicrystalline silicon wafers using the proposed seed casting technique. Solar cell efficiencies are generally governed by the concentration and type of impurities, and the density and electrical activity of extended defects such as grain boundaries and dislocations. Dislocations have been identified as one of the most efficiency-relevant defect centers in crystalline silicon for photovoltaic. The requirement for an increase of solar cell efficiencies necessitates a reduction of the crystal dislocations. Therefore, the dislocations generated by thermal stress during crystal growth have to be effectively suppressed for the production of highly efficient solar cells.
It is well-known that dislocation multiplication takes place during crystallization and the cooling process of the ingot. The multiplication process leads to a final, locally varying dislocation density at room temperature that depends on the thermal history of the crystalline material. Optimization of the crystallization and cooling processes can result in a reduction of the dislocation density. Many optimization studies have been performed to reduce dislocations by controlling the cooling process. However, the results are not consistent
Slow cooling was suggested for obtaining low dislocation density in GaP/Si heterostructures and in SiGe layers grown by liquid phase epitaxy. Fast cooling was suggested for obtaining low dislocation density in Pb and Si crystal growth from the melt. This discrepancy shows that the effect of the cooling process on the multiplication of dislocation is complex and different for different materials, growth furnaces, and growth processes. To better understand the relationship between the cooling rate and dislocation, it is essential to study the effect of the cooling process on the increase of dislocations from the perspective of activation of slip systems, since the generation of dislocations mainly originate from the activation of slip systems.
In this paper, we aim to clarify the following problems: What are the main differences of activated slip systems between fast and slow cooling rates for seed cast-grown monocrystalline silicon in the [001] and [111] directions? What is the most effective method to reduce dislocations when the cooling process is designed?
2. MODELS FOR DISLOCATION MULTIPLICATION
Thermal stress and dislocation multiplication have been studied by numerical simulations in various crystal growth processes. However, most of the simulations for the multiplication of the dislocation have assumed uniaxial creep or single slip, and ignored immobilization of mobile dislocations, the jog formation between different slip systems, and its influence on dislocation generation, or the internal stress due to short-range interactions from the total dislocation
Received: March 23, 2013 Revised: May 1, 2013
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activated or inactive, and those for the fast cooling is strongly activated.
After determining the effect of cooling rate on the activation of slip systems, it is essential to determine what type of cooling flux, axial or radial flux, dominates the activation of slip systems in group B . If radial flux mainly controls the activation of group B , it is possible to keep group B inactive by using a fast cooling rate, which is obtained by strengthening axial cooling flux. Figure 7 shows the history of dislocation during the fast cooling process in slice 3 of Figure 2a. The top layer is the section passing through the z axis, and the second layer is the cross-section perpendicular to the z axis. The vector shown in the top layer is the cooling flux, and the contours in the top layer are the magnitude of the radial flux. At the beginning of the cooling process (t = 4.0 h), the radial flux is low and the 4fold symmetric group B is inactive. However, at t = 5.083 h
the radial flux is high and the 4-fold symmetric group B is activated. Thus, the activation of group B could be caused by the increase of the radial flux. The magnitude of the axial flux at the edge of slice 3 is 732 at t = 4.0 h, 648 at t = 4.667 h, and 598 at t = 5.083 h. Thus, the activation of group B is not caused by the axial flux, because the axial flux gradually decreases and cannot activate group B . Therefore, it is the large radial cooling flux that activates the 4-fold symmetric group B along the edge in [001] growth for the fast cooling rate, which is the main difference between fast and slow cooling.
5.2. Crystal Growth in the [111] Direction. The crystal
growth direction was set to the [111] direction. The dislocation distributions inside the grown crystal at room temperature for the fast and slow cooling rates are shown in Figure 8, where Figure 8a shows the fast cooling rate and Figure 8b shows the slow cooling rate. Similar to the [001] growth direction, six slices are taken and labeled in Figure 8 for late discussions. Figure 8 shows that at the cylindrical surface for the slow
Figure 11. Comparison of the dislocation distributions on (111) slices of a [111] growth crystal for fast cooling (top layer) and slow cooling (bottom layer).
Figure 12. History of dislocation density during the fast cooling process in slice 6 of Figure 8a.
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cooling rate the dislocation density is less than that for the fast cooling rate. The maximum dislocation density in the [111] growth direction is much smaller than that in the [001] growth direction.
Following the same procedure as that for the [001] growth direction, the dislocation density generated by every slip system for slice 2 in Figure 8a is shown in Figure 9, and all of the dislocations generated by the 12 slip systems are superposed and shown in Figure 10. Figure 9 shows that the slip systems of 1, 2, 4, 5, 7, and 8 (group C ) are mainly activated at points along the edge, and in the interior, the slip systems of 3, 6, and 9 (group D ) are only activated at points along the edge, and the slip systems of 10, 11, and 12 (group E ) are mainly activated at points in the interior. The superposition of all of the dislocation densities generated by the 12 slip systems shows that the dislocation generated by group Cis composed of 3fold symmetry at the edge and 3-fold symmetry in the interior, the dislocation activated by group D is composed of 3-fold symmetry only at the edge, and the dislocation activated by group E is composed of 3-fold symmetry only in the interior. Therefore, the dislocation at the edge is due to the activation of groups C and D , and the dislocation at the interior is due to the activation of groups Cand E.
After obtaining the relationships between the dislocation and the corresponding activated slip system, the effect of cooling rate on the activation of slip systems can be determined from the dislocation distributions under different cooling rates. Figure 11 shows a comparison of the dislocation density for the six slices labeled in Figure 8. From slice 1 to slice 5, the distributions of dislocation density for the fast and slow cooling are similar, and all of the slip systems are activated. In slice 6, group D is inactive along the edge for the slow cooling rate, while it is activated for the fast cooling rate. From slice 1 to slice 6, the maximum dislocation along the edge for slow cooling is smaller than for fast cooling, and the dislocation density in the interior for the slow cooling rate is also smaller than for the fast cooling rate. Therefore, in the [111] growth direction the slip systems in groups C, D , and Efor the slow cooling rate are weakly activated, and those for the fast cooling rate are strongly activated.
Since the dislocation at the edge for the slow cooling rate is smaller than for the fast cooling rate, and the slow cooling rate has a smaller radial flux, it can be proposed that the radial cooling flux mainly activates groups C and D at the edge. Figure 12 shows the history of dislocation during the fast cooling process in slice 6 of Figure 8a. The top layer is the section passing through the z axis, and the bottom layer is the cross section perpendicular to the z axis. The vector shown in the top layer is the cooling flux, and the contours in the top layer are the magnitude of the radial flux. At the beginning of the cooling process (t = 4.0 h), the radial flux is low and there is no group C and D activation. However, at t = 5.083 h the radial flux is high and the 3-fold symmetric groups C and D are activated. Therefore, it is radial flux to activate dislocations along the edge in [111] growth that causes partial difference between fast cooling and slow cooling.
6. CONCLUSIONS
The symmetry of the crystal structure means that the slip systems of single crystal silicon can be divided into several groups: an 8-fold symmetric group A and a 4-fold symmetric group B for [001] growth direction; and the three 3-fold symmetric groups C, D , and Efor [111] growth direction.
In the [001] growth direction, the activated slip systems in group Amainly contribute an 8-fold symmetric distribution at the center and the edge, and the activated slip systems in group B mainly contribute a 4-fold symmetric distribution only at the edge. In the [111] growth direction, the activated slip systems in groups C and D mainly contribute a 3-fold symmetric distribution at the edge, and the activated slip systems in groups C and Emainly contribute a 3-fold symmetric distribution in the interior.
Cooling rate has an effect on the activation of the slip systems. In the [001] growth direction, a slow cooling rate either weakly activates the slip systems in group B or does not activate them at all, while a fast cooling rate strongly activates the slip systems in group B . In the [111] growth direction, a slow cooling rate weakly activates the slip system in groups C , D , and E , while a fast cooling rate strongly activates the slip system in groups C , D , and E. The differences of activated slip systems with slow or fast cooling rates mainly cause the differences in dislocation and residual stress.
Irrespective of the crystal growth direction, it is the radial flux that dominates the difference between the fast and slow cooling rates. Therefore, the most effective method for reducing dislocation during the cooling process is to reduce the radial flux.
■AUTHOR INFORMATION
Corresponding Author
*Tel: +81-92-583-7744. Fax: +81-92-583-7743. E-mail: gaobing@riam.kyushu-u.ac.jp.
Notes
The authors declare no competing financial interest.
■ACKNOWLEDGMENTS
This work was partly supported by the New Energy and Industrial Technology Development Organization (NEDO) under the Ministry of Economy, Trade and Industry (METI), Japan.
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