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Research Papers

Modeling the Tensile Strength and Crack Length of Wire-Sawn Silicon Wafers

[+] Author and Article Information
Claudia Funke

Institute of Experimental Physics, TU Bergakademie Freiberg, Leipziger Strasse 23, D-09596 Freiberg, Germany

Susann Wolf, Dietrich Stoyan

Institute of Stochastics, TU Bergakademie Freiberg, Prüferstrasse 9, D-09596 Freiberg, Germany

J. Sol. Energy Eng 131(1), 011012 (Jan 08, 2009) (6 pages) doi:10.1115/1.3028048 History: Received July 11, 2007; Revised May 07, 2008; Published January 08, 2009

Solar silicon wafers are mainly produced through multiwire-sawing. This sawing implies microcracks on the wafer surface, which are responsible for brittle fracture. In order to reduce the sawing-induced cracks, the wafers are damage etched after sawing. This paper develops a model for the impact of crack length manipulation on fracture stress distribution. It investigates the effect of damage-etching on the mechanical properties of solar silicon wafers. The main idea is to transform the fracture stress distribution into a crack length intensity function and to model the effect of etching in terms of crack lengths. The fracture stress distribution is determined statistically by fracture tests of wire-sawn and sawn and etched wafers. The Griffith criterion then enables the transition to crack lengths and crack length intensity functions. Two numerical parameters, called truncation parameter and scaling parameter, determine this relationship and enable a quantitative description of the effect of etching. They turn out to be dependent on etchant and geometry of load and thus tested crack population.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Fracture test setup: (a) biaxial fracture test; (b) four line bending test

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Figure 2

Weibull plot: (a) biaxial fracture test; (b) four line bending test. F denotes the Weibull distribution function explained by Eq. 2.

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Figure 3

Four line bending test, as-sawn wafer: (a) Empirical distribution function (○) and fitted Weibull distribution function FWS(σ) (—) obtained with Eq. 2; (b) corresponding flaw strength intensity function λWS(σ) obtained with Eq. 1

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Figure 4

Four line bending test: crack length intensity functions μW(l) obtained with Eq. 5; μ(l) in m−1; (—) μWS(l)≅as-sawn wafer; (-⋯-) μWE(l)≅wafer etched after sawing, etchant 2

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Figure 5

Four line bending test: flaw strength intensity functions λ(σ); (—) λWS(σ)≅as-sawn wafer, obtained with Eq. 1; (-⋯-) λWE(σ)≅sawn and etched wafer, etchant 2, obtained with Eq. 1; (---) λM(σ)≅Model, obtained with Eq. 13 with parameters a=0.9μm and b=5.2μm

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Figure 6

Four line bending test: empirical distribution functions for the data of as-sawn and sawn and etched, etchant 2 samples; fitted Weibull distribution functions FWS(σ) and FWE(σ) obtained with Eq. 2.

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Figure 7

Four line bending test: empirical distribution function (◇) for the data of the sawn and etched samples (etchant 2), fitted Weibull distribution function FWE(σ) (—) obtained with Eq. 2, and distribution function FM(σ) (-⋯-) obtained with Eq. 14 (approximation for the empirical data with the described length-transformation with parameters a=0.9μm and b=10μm)

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Figure 8

Biaxial fracture test: empirical distribution function for the data of the as-sawn and etched 2 samples (○), fitted Weibull distribution function F(σ) (-—) obtained with Eq. 2, and distribution function FM(σ) (-⋯-) obtained with Eq. 14 with estimated parameters

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Figure 9

Four line bending test: empirical distribution function for the data of sawn and etched samples (etchant 3), fitted Weibull distribution function FW(σ) obtained with Eq. 2, and distribution function FM(σ) obtained by means of Eq. 14 with estimated parameters

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