Multicrystalline sillicon using unidirectional solidification process is the most widely material for solar cells because of its cost-effectiveness and the mass productivity. However, dislocation density and residual stress are serious problems for solar cells because increasing of dislocation densities reduces the conversion efficiency of solar cells and increasing of residul stress causes the fracture of silicon ingot during the slicing process. It has been reported that dislocation densities rapidly increased during cooling process [1, 2]. Therefore, we have to optimize to temperature distribution in a silicon ingot during cooling process. We compared experimental and numerical results of residual strain, dislocation density and residual stress in a silicon ingot. Then, we evaluated the validity of numericalresults.

We investigated time-dependent dislocation multiplication in a silicon ingot. At first, thermal stress distribution in a silicon ingot was solved using temperature distribution in a silicon ingot. Then, we studied stress relaxation, creep deformation and the multiplication of the dislocations using Haasen-Alexander-Sumino model [3, 4]. 

We checked residual strain as a function of height from the bottom of the silicon ingot quantitatively. The numerical results show that a value of residual strain in a body of a crystal is order of 10^-5, and residual strain in the top and bottom areas of the silicon ingot is high (10^-4). This difference of residual strain between center area and edge area is due to outgoing thermal flux. Thermal flux in the top and bottom of the silicon ingot is large because conductive heat transfer in the bottom area and radiative heat transfer in the top area of the silicon ingot strongly affects to the residual strain. The value and distribution of residual strain obtained by numerical analysis are close to experimental data. Then, we can analyze residual strain quantitatively using this simulation. However, dislocation density of numerical analysis is not close to experimental data because we assumed a crystal as isotropic, and took into account dislocation multiplication only based on increase rate of mobile dislocation density.

References

[1] M. M’Hamdi, E. A. Meese, E. J. Øvrelid and H. Laux, Proceedings 20th EUPVSEC (2005) 1236.

[2] D. Franke, T. Rettelbach, C. Häβler, W. Koch and A. Müller, Sol. Energy Mater. Sol. Cells 72 (2002) 83.

[3] H. Alexander and P. Haasen, Solid State Phys. 22 (1968) 27.

[4] M. Suezawa, K. Sumino and I. Yonenaga, J. Appl. Phys. 51 (1979) 217.

• Legal notice:
  

  Copyright (c) Pielaszek Research, all rights reserved.
  The above materials, including auxiliary resources, are subject to Publisher's copyright and the Author(s) intellectual rights. Without limiting Author(s) rights under respective Copyright Transfer Agreement, no part of the above documents may be reproduced without the express written permission of Pielaszek Research, the Publisher. Express permission from the Author(s) is required to use the above materials for academic purposes, such as lectures or scientific presentations.
  In every case, proper references including Author(s) name(s) and URL of this webpage: https://science24.com/paper/29015 must be provided.

1. Modelling of unidirectional solidification of multicrystalline Si
2. Crystal growth of 50 cm square single crystal Si by directional solidification and its characterization
3. Ab initio Study of GaAs(100) Surfaces Under As₂, H₂, and N₂ Influence, as a Model for Vapor-Phase Epitaxy of GaAs_1-xN_x
4. Numerical Analysis of the Effect of Growth Rate Variations on Defect Formation in Czochralski Grown Silicon
5. Analysis of Argon Flow on Mass Transport in a CZ-Si Crystal Growth by Using Full Compressible Flow Solver
6. Quantitative analysis of correlations between the generation of dislocations and its influencing factors during cylindrical monocrystalline silicon growth
7. Effect of cooling rate on the activation of slip systems in seed cast-grown monocrystalline silicon in the [001] and [111] directions
8. Relationship between cooling flux direction and activation of slip systems of single -crystal silicon grown in [001] and [111] directions
9. Study of the effect of doped nitrogen and aluminum on polytype stability during PVT growth of SiC using 2D nucleation theory
10. Structural controllability of C clusters by template effect of SiC step
11. Influence of growth orientation on microstructure of AlN grown by solid-source solution growth (3SG) method
12. Numerical investigation of crystal growth process of bulk Si, SiC and nitrides