Keywords: four line bending test, finite elements, large displacement, monocrystalline silicon wafers, cleavage plane, size effect.

The development of clean energies is an important research line where photovoltaic solar energy arises as a reliable alternative. The main absorber material is Czochralski grown monocrystalline silicon. The growth process consists of melt feedstock where a seed is dipped and slowly withdrawn vertically whereby the liquid crystallises at the seed. The product obtained is a round cross section ingot which is cut into a pseudo-square for efficiency reasons and is sawn by moving a wire web, slicing it into hundreds of wafers.

It is estimated that the silicon wafer contributes to approximately 50% of the module cost, so it is clear that by cutting thinner wafers, the final cost will be decreased [1,2]. However, current tools employed during the solar cell production are not prepared to work with thinner wafers. Therefore, a study of the mechanical properties of monocrystalline silicon wafers is presented in the paper, as a first step to develop or modify existing tools.

To study mechanical properties, several dozens of wafers of different thicknesses have been tested. The four line bending test has been chosen so that edge and surface cracks could be taken into account [5]. In order to visualize the rupture process a HS camera able to record more than 1000 frames per second has been employed. The complete test setup and some frames recorded are shown in the full paper. In order to determine the mechanical properties, a numerical model has been developed and calibrated with test results. The finite element method study including large displacements and the sliding and friction between the wafers and the supports has been performed using the commercial packages ANSYS and ADINA.

In order to reduce the non-linear behaviour, tests dimensions have been modified for each wafer thickness. Different distances lead to stressed areas of different sizes, so a correction due to the size effect [3,4] has to be carried out. In this way, from different thicknesses and different test dimensions, a single failure curve is achieved.

Moreover, the fact that monocrystalline silicon wafers present cleavage planes which are the crystallographic fracture planes [5] has to be taken into account. In order to study their influence, three different types of wafers regarding the cleavage plane orientations have been prepared.

The global goal of the paper is to obtain a Cumulative Distribution Function of the mechanical strength of the wafers. Once the material is characterized through the resulting curve, it is possible to study new service situations or to develop new handling tools. The complete process to get the failure curve from different thicknesses, different test dimensions and different types of wafers according to the cleavage plane orientations is shown in the full paper.

1

A. Luque, S. Hegedus, "Handbook of Photovoltaic Science and Engineering", John Wiley & Sons Ltd, West Sussex, England, 2003.

2

J.C. Jimeno, V. Rodríguez, R. Gutiérrez, F. Recart, G. Bueno, F. Hernando, "Very Low Thickness Monocrystalline Silicon Solar Cells", Sixteenth European Photovoltaic Solar Energy Conference, Glasgow, Scotland, 2000.

3

W. Weibull, "A Statistical Theory of the Strength of Materials", Proceedings of the Royal Swedish Institute of Engineering Research Nr. 151, 1939.

4

M.A. García, A.F. Canteli, M. J. Lamela, E. Castillo, "A Design Model for Glass Elements based on the Statistical Distribution of Crack Sizes", Eighth Conference Exhibition of the European Ceramic Society. Istanbul, Turkey, 2003.

5

B. Cotterell, Z. Chen, J.B. Han, N.X. Tan, "The Strength of the Silicon Die in Flip-Chip Assemblies", Journal of electronic packaging, ASME, USA, 2003. doi:10.1115/1.1535934

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