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Research Papers

# Fracture Analysis and Distribution of Surface Cracks in Multicrystalline 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-0314, Norway

Z. L. Zhang

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

Usually, for the ith strength value Pf,i = (i − 0.5)/N, where N is the total number of measurements.

1Corresponding author.

Contributed by the Solar Energy Division of ASME for publication in the JOURNAL OF SOLAR ENERGY ENGINEERING. Manuscript received July 2, 2013; final manuscript received October 31, 2013; published online December 19, 2013. Assoc. Editor: Santiago Silvestre.

J. Sol. Energy Eng 136(2), 021024 (Dec 19, 2013) (9 pages) Paper No: SOL-13-1189; doi: 10.1115/1.4025972 History: Received July 02, 2013; Revised October 31, 2013

## Abstract

Solar silicon wafers are mainly produced through multiwire sawing. The sawing process induces micro cracks on the wafer surface, which are responsible for brittle fracture. Hence, it is important to scrutinize the crack geometries most commonly generated in silicon wafer sawing or handling process and link the surface crack to the fracture of wafers. The fracture of a large number of multicrystalline silicon wafers has been investigated by means of 4-point bending and twisting tests and a failure probability function is presented. By neglecting the material property variation and assuming that one surface crack is dominating the wafer breakage, 3D finite element models with various crack sizes (depth, length, and orientation) have been analyzed to identify the distribution of surface crack geometries by fitting the failure probability from the experiments. With respect to the 63% probability, the existing surface cracks in the wafers studied appear to have depth and length ratios less than 0.042 and 0.19, respectively. Furthermore, it has been shown that the surface cracks with depth in the range from 10 to 20 μm, length up to 10 mm and angles in the range of 30 deg–60 deg, can be considered as the most common crack geometries in wafers we tested. Finally, it has been found that the mechanical strength of the wafers tested parallel to the sawing direction is approximately 15 MPa smaller than those tested perpendicular to the sawing direction.

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## Figures

Fig. 1

Finite element model for (a) four-point bending (b) twisting

Fig. 3

Built model from the realistic MC silicon wafer

Fig. 4

Stress distribution in specimens under (a) von Mises stress for four-point bending and (b) shear stress for twisting

Fig. 5

J-integral versus time (displacement) for a crack with 1 mm length, 20 μm depth, and zero direction (in parallel direction to the sawing)

Fig. 6

Material parameters fitted for (a) four point bending and (b) twisting

Fig. 7

Failure probability versus displacement for (a) four point bending and (b) twisting

Fig. 8

Probability of existing crack at β = 0 deg for (a) four point bending and (b) twisting loading

Fig. 9

Probability of existing crack at β = 30 deg for (a) four point bending and (b) twisting loading

Fig. 10

Probability of existing crack at β = 45 deg for (a) four point bending and (b) twisting loading

Fig. 11

Probability of existing crack at β = 60 deg for (a) four point bending and (b) twisting loading

Fig. 12

Probability of existing crack at β = 90 deg for (a) four point bending and (b) twisting loading

Fig. 13

Crack geometry for the 63% probability of existing crack in wafers

Fig. 14

Failure probability of stress/force and displacement for (a) four point bending and (b) twisting

Fig. 15

Frequency distribution versus displacement (a) four point bending for both parallel the sawing and perpendicular to the sawing directions and (b) twisting test for both A and B directions

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