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Research Papers

# The Effect of Microstructure, Thickness Variation, and Crack on the Natural Frequency of Solar Silicon Wafers

[+] Author and Article Information
S. Saffar

Department of Structural Engineering,
Norwegian University of Science and Technology,
Trondheim NO-7491, Norway

S. Gouttebroze

SINTEF Materials and Chemistry,
Oslo NO-0315, Norway

Z. L. Zhang

Department of Structural Engineering,
Norwegian University of Science and Technology,
Trondheim NO-7491, Norway
e-mail: zhiliang.zhang@ntnu.no

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received September 13, 2012; final manuscript received April 11, 2013; published online July 2, 2013. Assoc. Editor: Santiago Silvestre.

J. Sol. Energy Eng 136(1), 011001 (Jul 02, 2013) (8 pages) Paper No: SOL-12-1226; doi: 10.1115/1.4024248 History: Received September 13, 2012; Revised April 11, 2013

## Abstract

Vibration is one of the most common loading modes during handling and transport of solar silicon wafers and has a great influence on the breakage rate. In order to control the breakage rate during handling and facilitate the optimization of the processing steps, it is important to understand the factors which influence the natural frequency of thin silicon wafers. In this study, we applied nonlinear finite element method to investigate the correlation of natural frequency of thin solar silicon wafer with material microstructures (grain size and grain orientation), thickness variation and crack geometry (position and size). It has been found that the natural frequency for anisotropic single crystal silicon wafer is a strong function of material orientation. Less than 10% thickness variation will have a negligible effect on natural frequency. It is also found out that cracks smaller than 20 mm have no dominant effect on the first five natural frequency modes anywhere in the silicon wafer.

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## Figures

Fig. 1

Comparison of the natural frequency calculated by analytical solution and FEM for isotropic model with (a) FFFF boundary conditions and (b) SSSS boundary

Fig. 2

Comparison of the natural frequency between analytical solution and FEM for anisotropic model with SSSS boundary conditions

Fig. 3

maximum principle stress for first five shape modes of isotropic silicon wafers with FFFF boundary condition

Fig. 4

Example of grain size and material orientations for the models with 1, 2, 4, 8, 16, and 32 grains

Fig. 5

Effect of material orientation on the normalized frequency for single crystal silicon rotating (a) along z axis and (b) along x/y axis

Fig. 6

Effect of material orientation rotating along z axis on the normalized frequency for the wafer with 2 grains (grain 1 fixed at a = 0 deg, b = 15 deg, c = 30 deg, and d = 45 deg)

Fig. 7

Effect of material orientation rotating along x/y axis on the normalized frequency for the wafer with 2 grains (grain 1 fixed at a = 0 deg, b = 15 deg, c = 30 deg, and d = 45 deg)

Fig. 8

Effect of material orientation for 4, 8, 16, and 32 grains on the first five natural frequencies

Fig. 9

Effect of material orientation rotate on z axis for 4, 8, 16, and 32 grains on the first mode

Fig. 10

Frequency band for the first five natural frequencies

Fig. 11

The effect of thickness variation on the natural frequency of an isotropic model

Fig. 12

The effect of crack size on the natural frequency of an isotropic wafer model with a crack in the center

Fig. 13

The effect of crack position on the natural frequency with crack size = 20 mm

Fig. 14

The effect of crack position on the normalized frequency with crack size = 20 mm and different material orientation

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