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

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.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Istratov, A. A., Hieslmair, H., Vyvenko, O. F., Weber, E. R., and Schindler, R., 2002, “Defect Recognition and Impurity Detection Techniques in Crystalline Silicon for Solar Cells,” Sol. Energy Mater. Sol. Cells, 72(1–4), pp. 441–451. [CrossRef]
Goodrich, A., Hacke, P., Wang, Q., Sopori, B., Margolis, R., James, T. L., and Woodhouse, M., 2013, “A Wafer-Based Monocrystalline Silicon Photovoltaics Road Map: Utilizing Known Technology Improvement Opportunities for Further Reductions in Manufacturing Costs,” Sol. Energy Mater. Sol. Cells, 114, pp. 110–135. [CrossRef]
Yang, C., Mess, F., Skenes, K., Melkote, S., and Danyluk, S., 2013, “On the Residual Stress and Fracture Strength of Crystalline Silicon Wafers,” Appl. Phys. Lett., 102(2), p. 021909. [CrossRef]
Hu, S. M., 1973, “Dislocations in Thermally Stressed Silicon Wafers,” Appl. Phys. Lett., 22(5), pp. 261–264. [CrossRef]
He, S., Danyluk, S., Tarasov, I., and Ostapenko, S., 2006, “Residual Stresses in Polycrystalline Silicon Sheet and Their Relation to Electron-Hole Lifetime,” Appl. Phys. Lett., 89(11), p. 111909. [CrossRef]
Haunschild, J., Glatthaar, M., Demant, M., Nievendick, J., Motzko, M., Rein, S., and Weber, E. R., 2010, “Quality Control of As-Cut Multicrystalline Silicon Wafers Using Photoluminescence Imaging for Solar Cell Production,” Sol. Energy Mater. Sol. Cells, 94(12), pp. 2007–2012. [CrossRef]
Trupke, T., Mitchell, B., Weber, J. W., McMillan, W., Bardos, R. A., and Kroeze, R., 2012, “Photoluminescence Imaging for Photovoltaic Applications,” Energy Procedia, 15(2011), pp. 135–146. [CrossRef]
Mchedlidze, T., Seifert, W., Kittler, M., Blumenau, A. T., Birkmann, B., Mono, T., and Müller, M., 2012, “Capability of Photoluminescence for Characterization of Multi-Crystalline Silicon,” J. Appl. Phys., 111(7), p. 073504 [CrossRef]
Fukuzawa, M., and Yamada, M., 2001, “Photoelastic Characterization of Si Wafers by Scanning Infrared Polariscope,” J. Cryst. Growth, 229(1–4), pp. 22–25. [CrossRef]
Yamada, M., 1993, “High-Sensitivity Computer-Controlled Infrared Polariscope,” Rev. Sci. Instrum., 64(7), p. 1815. [CrossRef]
Zheng, T., and Danyluk, S., 2011, “Study of Stresses in Thin Silicon Wafers With Near-Infrared Phase Stepping Photoelasticity,” J. Mater. Res., 17(01), pp. 36–42. [CrossRef]
Horn, G., Lesniak, J., Mackin, T., and Boyce, B., 2005, “Infrared Grey-Field Polariscope: A Tool for Rapid Stress Analysis in Microelectronic Materials and Devices,” Rev. Sci. Instrum., 76(4), p. 045108. [CrossRef]
Inzinga, R. A., Lin, T.-W., Yadav, M., Johnson, H. T., and Horn, G. P., 2011, “Characterization and Control of Residual Stress and Curvature in Anodically Bonded Devices and Substrates With Etched Features,” Exp. Mech., 52(6), pp. 637–648. [CrossRef]
Lin, T.-W., Elkhatib, O., Makinen, J., Palokangas, M., Johnson, H. T., and Horn, G. P., 2013, “Residual Stresses at Cavity Corners in Silicon-on-Insulator Bonded Wafers,” J. Micromech. Microeng., 23(9), p. 095004. [CrossRef]
Lin, T., Horn, G. P., and Johnson, H. T., 2013, “Characterization of Silicon Photovoltaic Wafers Using Infrared Photoelasticity,” SEM Annual Conference on Experimental and Applied Mechanics, Lombard, IL, June 3–5, Vol. 8, pp. 303–308. [CrossRef]
Ganapati, V., Schoenfelder, S., Castellanos, S., Oener, S., Koepge, R., Sampson, A., Marcus, M. A., Lai, B., Morhenn, H., Hahn, G., Bagdahn, J., and Buonassisi, T., 2010, “Infrared Birefringence Imaging of Residual Stress and Bulk Defects in Multicrystalline Silicon,” J. Appl. Phys., 108(6), p. 063528. [CrossRef]
Kaule, F., Wang, W., and Schoenfelder, S., 2014, “Modeling and Testing the Mechanical Strength of Solar Cells,” Sol. Energy Mater. Sol. Cells, 120(Part A), pp. 441–447. [CrossRef]
Ge, C., Ming, N., Tsukamoto, K., Maiwa, K., and Sunagawa, I., 1991, “Birefringence Images of Screw Dislocations Viewed End-On in Cubic Crystals,” J. Appl. Phys., 69(11), p. 7556. [CrossRef]
Hirth, J. P., and Lothe, J., 1992, Theory of Dislocations, 2nd ed., Krieger, Malabar, FL.
Groh, S., and Zbib, H. M., 2009, “Advances in Discrete Dislocations Dynamics and Multiscale Modeling,” ASME J. Eng. Mater. Technol., 131(4), p. 041209. [CrossRef]
Fivel, M. C., and Canova, G. R., 1999, “Developing Rigorous Boundary Conditions to Simulations of Discrete Dislocation Dynamics,” Model. Simul. Mater. Sci. Eng., 7(5), pp. 753–768. [CrossRef]
Cai, W., Arsenlis, A., Weinberger, C., and Bulatov, V., 2006, “A Non-Singular Continuum Theory of Dislocations,” J. Mech. Phys. Solids, 54(3), pp. 561–587. [CrossRef]
Khanikar, P., Kumar, A., and Subramaniam, A., 2011, “Image Forces on Edge Dislocations: A Revisit of the Fundamental Concept With Special Regard to Nanocrystals,” Philos. Mag., 91(5), pp. 730–750. [CrossRef]
Weygand, D., Friedman, L. H., Van der Giessen, E., and Needleman, A., 2002, “Aspects of Boundary-Value Problem Solutions With Three-Dimensional Dislocation Dynamics,” Model. Simul. Mater. Sci. Eng., 10(4), pp. 437–468. [CrossRef]
O'Day, M. P., and Curtin, W. A., 2004, “A Superposition Framework for Discrete Dislocation Plasticity,” ASME J. Appl. Mech., 71(6), p. 805. [CrossRef]
Ahrenkiel, R. K., Johnston, S. W., Metzger, W. K., and Dippo, P., 2007, “Relationship of Band-Edge Luminescence to Recombination Lifetime in Silicon Wafers,” J. Electron. Mater., 37(4), pp. 396–402. [CrossRef]
Ostapenko, S., Tarasov, I., Kalejs, J. P., Haessler, C., and Reisner, E.-U., 2000, “Defect Monitoring Using Scanning Photoluminescence Spectroscopy in Multicrystalline Silicon Wafers,” Semicond. Sci. Technol., 15(8), pp. 840–848. [CrossRef]
Fukuzawa, M., and Yamada, M., 2008, “Photoelastic Strain Measurement in GaP (100) Wafers Under External Stresses,” J. Mater. Sci. Mater. Electron., 19(S1), pp. 83–86. [CrossRef]
Mariani, J. L., Pichaud, B., Minari, F., and Martinuzzi, S., 1992, “Quantitative Determination of the Recombining Activities of 60 Deg and Screw Dislocations in Float Zone and Czochralski-Grown Silicon,” J. Appl. Phys., 71(3), p. 1284. [CrossRef]
Muižnieks, A., Raming, G., Mühlbauer, A., Virbulis, J., Hanna, B., and Ammon, W. V., 2001, “Stress-Induced Dislocation Generation in Large FZ- and CZ-Silicon Single Crystals—Numerical Model and Qualitative Considerations,” J. Cryst. Growth, 230(1–2), pp. 305–313. [CrossRef]
Jaeger, J., 1945, “On Thermal Stresses in Circular Cylinders,” Philos. Mag., 36(257), pp. 418–428. [CrossRef]
Hirsch, P. B., 1980, “The Structure and Electrical Properties of Dislocations in Semiconductors,” J. Microsc., 118(1), pp. 3–12. [CrossRef]
Zhao, C. W. W., Xing, Y. M. M., Zhou, C. E. E., and Bai, P. C. C., 2008, “Experimental Examination of Displacement and Strain Fields in an Edge Dislocation Core,” Acta Mater., 56(11), pp. 2570–2575. [CrossRef]
Hartman, K., Bertoni, M., Serdy, J., and Buonassisi, T., 2008, “Dislocation Density Reduction in Multicrystalline Silicon Solar Cell Material by High Temperature Annealing,” Appl. Phys. Lett., 93(12), p. 122108. [CrossRef]
Needleman, D. B., Choi, H., Powell, D. M., and Buonassisi, T., 2013, “Rapid Dislocation-Density Mapping of As-Cut Crystalline Silicon Wafers,” Phys. Status Solidi RRL, 7(12), pp. 1041–1044. [CrossRef]
Narasimhamurty, T. S., 1981, Photoelastic and Electro-Optic Properties of Crystals, Plenum, New York.
Biegelsen, D., 1974, “Photoelastic Tensor of Silicon and the Volume Dependence of the Average Gap,” Phys. Rev. Lett., 32(21), pp. 1196–1199. [CrossRef]


Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
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.

Grahic Jump Location
Fig. 5

Finite element model mesh used in the Comsol simulation

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
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.

Grahic Jump Location
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.

Grahic Jump Location
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

Grahic Jump Location
Fig. 11

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




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In