Search for content and authors

Evaluation of numerical analysis of residual strain and dislocation density  in a multicrystalline silicon for solar cells

Makoto Inoue 1Satoshi Nakano 2Karolin Jiptner 3,4Bing Gao 2Hirofumi Harada 3Takashi Sekiguchi 3Masayuki Fukuzawa 5Koichi Kakimoto 1,2

1. Kyushu University, Fukuoka, Japan
2. Kyushu University, Research Institute for Applied Mechanics, Kasuga 816-8580, Japan
3. National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki, Tsukuba 305-0044, Japan
4. Tsukuba Univ., Tsukuba 305-8577, Japan
5. Kyoto Institute of Technology, Kyoto 606-8585, Japan


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.


[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
  • Legal notice:

Related papers

Presentation: Oral at 17th International Conference on Crystal Growth and Epitaxy - ICCGE-17, General Session 2, by Satoshi Nakano
See On-line Journal of 17th International Conference on Crystal Growth and Epitaxy - ICCGE-17

Submitted: 2013-03-28 15:18
Revised:   2013-03-28 15:18