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Research Papers

Quantitative Infrared Photoelasticity of Silicon Photovoltaic Wafers Using a Discrete Dislocation Model

[+] Author and Article Information
T.-W. Lin

Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
1206 West Green Street,
Urbana, IL 61801
e-mail: lin142@illinois.edu

G. P. Horn

Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
1206 West Green Street,
Urbana, IL 61801
e-mail: ghorn@illinois.edu

H. T. Johnson

Mem. ASME
Department of Mechanical Science
and Engineering,
University of Illinois at Urbana-Champaign,
1206 West Green Street,
Urbana, IL 61801
e-mail: htj@illinois.edu

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 23, 2014; final manuscript received October 30, 2014; accepted manuscript posted November 5, 2014; published online November 14, 2014. Editor: Yonggang Huang.

J. Appl. Mech 82(1), 011001 (Jan 01, 2015) (10 pages) Paper No: JAM-14-1337; doi: 10.1115/1.4028987 History: Received July 23, 2014; Revised October 30, 2014; Accepted November 05, 2014; Online November 14, 2014

Residual stress and crystalline defects in silicon wafers can affect solar cell reliability and performance. Infrared photoelastic measurements are performed for stress mapping in monocrystalline silicon photovoltaic (PV) wafers and compared to photoluminescence (PL) measurements. The wafer stresses are then quantified using a discrete dislocation-based numerical modeling approach, which leads to simulated photoelastic images. The model accounts for wafer stress relaxation due to dislocation structures. The wafer strain energy is then analyzed with respect to the orientation of the dislocation structures. The simulation shows that particular locations on the wafer have only limited slip systems that reduce the wafer strain energy. Experimentally observed dislocation structures are consistent with these observations from the analysis, forming the basis for a more quantitative infrared photoelasticity-based inspection method.

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References

Figures

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Fig. 1

(a) Photo of a single crystal silicon PV wafer with the dashed lines indicating the four quadrants on the wafer. (b) Band-to-band PL image of wafer A. (c) Infrared photoelastic image of wafer A. The contour legends in (b) and (c) refer to different intensity scales.

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Fig. 2

(a) Stress field σ in the PV wafer containing dislocations can be found by superposition of (b) the thermal stress σ∧th in an ingot, (c) the dislocation stress σ∧d in an infinite medium, and (d) the correction stress σcorr in the wafer

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Fig. 3

Normalized radial and tangential thermal stress components versus the radial distance. The inset shows the schematic cross section of the ingot.

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Fig. 4

Schematic diagram of a PV silicon wafer (left) containing an array of the 60 deg dislocations on the (111) slip plane, which forms a −45 deg slip band when viewed along the x3-axis. The dashed lines (right), denoted ξA and ξB, are possible dislocation line directions that correspond to the slip direction b on the (111) slip plane.

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Fig. 5

Finite element model mesh used in the Comsol simulation

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Fig. 6

(a) Uncorrected stress σ120 and (b) corrected stress σ12 in the PV wafer

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Fig. 8

Simulated GFP image of the PV wafer (a) with the residual thermal stress only and with the slip band from (b) the (111) [1¯10] slip system, ξ = [01¯1] in quadrant I. (c) The (11¯1)[101¯] slip system, ξ = [011] in quadrant I. (d) The (111) [1¯10] slip system, ξ = [01¯1] in quadrant III. (e) The (111) [101¯] slip system, ξ = [01¯1] in quadrant I. (f) The (111) [1¯10] slip system, ξ = [101¯] in quadrant I.

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Fig. 7

(a) PL image of wafer B and (b) GFP image of wafer B

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Fig. 9

Accumulated slip band lengths measured on GFP images of 10 single crystal silicon PV wafers. The −45 deg slip bands correspond to the slip systems #1, #2, #3, #7, #8, and #9; the +45 deg slip bands correspond to the slip systems #4, #5, #6, #10, #11, and #12.

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Fig. 10

Resolved shear stress due to the thermal stress in the silicon ingot for (a) slip systems #1 and #7; (b) slip systems #2 and #8; (c) slip systems #3 and #9; (d) slip systems #4 and #10; (e) slip systems #5 and #11; and (f) slip systems #6 and #12

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Fig. 11

Strain energy in the wafer versus nominal dislocation density associated with the slip band from Fig. 8(b)

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