Skip to main content
SpringerLink
Log in

Light Scattering by Particles and Defects on Surfaces: Semiconductor Wafer Inspection

  • Conference paper
  • First Online:
Light Scattering from Microstructures

Part of the book series: Lecture Notes in Physics ((LNP,volume 534))

Abstract

Nonintrusive optical techniques for accurate sizing of discrete particles (or bubbles) suspended in continuous media have been studied for years and have reached, for some applications, an advanced stage of development. In contrast, a related problem of considerable importance that has received less attention is that of accurate characterization of _ne particles or other features/defects on and under surfaces. This capability is much needed in the _elds of semiconductor and integrated circuit fabrication, digital storage media manufacturing, and for research on contamination of optical components for both earth- and space-based applications. In this presentation, we show the development of theoretical based scattering modeling and comparisons between our experimental and theoretical studies of light scattering by features on and under surfaces relevant to semiconductor wafer inspection. The experimental work shown here involves measurements of angle-resolved light scattering signatures (for 64 scattering angles) from an individual spherical particle 0.482 μm in diameter on a bare Si wafer. Experiments and predictions show good agreement, and the models are being used in predicting the performance of wafer scanners for various experimental conditions and for assisting in the design of future-generation surface defect characterization instruments.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Semiconductor Industry Association (1997) The national technology roadmap for semiconductors. SIA, San Jose, CA

    Google Scholar 

  2. Lorenz, LV (1890) Upon the light refracted by a transparent sphere. Vidensk. Selsk. Shrifter 6:1–62

    Google Scholar 

  3. Mie, G (1908) Considerations on the optics of turbid media, especially colloidal metal sols. Ann D Physik 25:377–442

    Article  ADS  CAS  Google Scholar 

  4. Peltoniemi, JI (1996) Variational volume integral equation method for electromagnetic scattering by irregular grains. J Quant Spectrosc Radiat Transfer, 55:637–647

    Article  ADS  CAS  Google Scholar 

  5. Taflove, A (Winter 1995) Reinventing electromagnetics: Emerging applications for FD-TD computation. IEEE Comp. Science Eng 24–34

    Google Scholar 

  6. Patterson, JE, Cwik, T, Ferraro, RD, Jacobi, N, Liewer, PC, Lockhart, TG, Lyzenga, G, Parker, JW, Simoni, DA (1990) Parallel computation applied to electromagnetic scattering and radiation analysis. Electromagnetics 10:21–39

    Article  Google Scholar 

  7. Volakis, JL, Chatterjee, A, Gong, J, Kempel, LC, Ross, DC (1994) Progress on the application of the finite element method to 3D electromagnetic scattering and radiation. COMPEL 13A:359–364

    Google Scholar 

  8. Hage, JI, Greenberg, JM, Wang, RT (1991) Scattering from arbitrarily shaped particles: Theory and experiment. Applied Optics 30:1141–1152

    Article  ADS  CAS  Google Scholar 

  9. Harrington, RF (1968) Field computation by moment methods in electromagnetics. McGraw-Hill, New York

    Google Scholar 

  10. Livesay, DE, Chen, KM (1974) Electromagnetic fields induced inside arbitrarily shaped dielectric bodies. IEEE Trans. Microwave Theory Tech 22:1273–1280

    Article  Google Scholar 

  11. Goedecke, GH, O’Brien, SG (1988) Scattering by irregular inhomogeneous paricles via the digitized Green’s function algorithm. Appl Opt 27:2431–2438

    Article  ADS  CAS  Google Scholar 

  12. Purcell, EM, Pennypacker, CR (1973) Scattering and absorption of light by nonspherical dielectric grains. Astrophys J 186:705–714

    Article  ADS  Google Scholar 

  13. Draine, BT, Flatau, PJ (1994) The discrete-dipole approximation for scattering calculations. J Opt Soc Am A 11:1491–1499

    Article  ADS  Google Scholar 

  14. Lakhtakia, A (1993) Strong and weak forms of the method of moments and the coupled dipole method for scattering of time-harmonic electromagnetic fields. Int J Mod Phys C 3:583–603; errata (1993) 4:721-722

    Article  ADS  Google Scholar 

  15. Lakhtakia, A, Mulholland, GW (1993) On two numerical techniques for light scattering by dielectric agglomerated structures. J Res Natl Inst Stand Technol 98:699–716

    Google Scholar 

  16. Bobbert, PA, Vlieger, J (1986) Light scattering by a sphere on a substrate. Physica 137A:213–214

    ADS  Google Scholar 

  17. Assi, FI (1990) Electromagnetic wave scattering by a sphere on a layered substrate. Master’s Thesis, University of Arizona, Tucson, AZ

    Google Scholar 

  18. Lindell, IV, Sihvola, AH, Muinonen, KO, Barber, PW (1991) Scattering by a small object close to an interface. I. Exact-image theory formulation. J Opt Soc Am A 8:472–476

    Article  ADS  CAS  Google Scholar 

  19. Johnson, BR (1992) Light scattering from a spherical particle on a conducting plane: I. Normal incidence. J Opt Soc Am A 9:1341–1351

    Article  ADS  Google Scholar 

  20. Videen, G (1995) Light scattering from a particle on or near a perfectly conducting surface. Optics Comm 115:1–7

    Article  ADS  CAS  Google Scholar 

  21. Wojcik, GL, Vaughn, DK, Galbraith, LK (1987) Calculation of light scatter from structures on silicon Surfaces Lasers in Microlithography Proc. SPIE 774:21–31

    CAS  Google Scholar 

  22. Liswith, ML (1994) Numerical modeling of light scattering by individual submicron spherical particles on optically smooth semiconductor surfaces. Master’s Thesis, Arizona State University, Tempe, AZ

    Google Scholar 

  23. Yeremin, YA, Orlov, NV, Sveshnikov, AG (1995) The analysis of complex diffraction problems by the discrete-source method. Comp Math Phys 35:731–743

    Google Scholar 

  24. Ivakhnenko, VI, Eremin, YA (1997) Silicon wafer defects analysis. Nonaxisym-metrical model. In: Eremin, YA, Wriedt, T (eds) Electromagnetic and light scattering theory and applications: Proceedings from the 1st workshop on electromagnetic and light scattering: Theory and applications. Moscow State University, Moscow pp 132–134

    Google Scholar 

  25. Taubenblatt, MA (1990) Light Scattering from cylindrical structures on surfaces. Optics Letters, 15:255–257

    Article  ADS  CAS  Google Scholar 

  26. Taubenblatt, MA, Tran, TK (1993) Calculation of light scattering from paricles and structure by the coupled-dipole method. J Opt Soc Am A 10:912–919

    Article  ADS  Google Scholar 

  27. Schmehl, R (1994) The coupled-dipole method for light scattering for light particles on plane surfaces. Department of Mechanical and Aerospace Engineering, Arizona State University and the Institut für Thermische Strömungsmaschinen, Universität Karlsruhe, Germany

    Google Scholar 

  28. Nebeker, BM (1998) Modeling of light scattering from features above and below surfaces using the discrete-dipole approximation, Ph.D. Dissertation, Arizona State University, Tempe, AZ

    Google Scholar 

  29. Draine, BT, Flatau, PJ (1994) The discrete-dipole approximation for scattering calculations. J Opt Soc Am A 11:1491–1499

    Article  ADS  Google Scholar 

  30. Schmehl, R., Nebeker, BM, Hirleman, ED (1997) The coupled-dipole method for scattering by particles on surfaces using a two-dimensional fast Fourier transform technique. J Opt Soc Am A 14:3026–3036

    Article  ADS  Google Scholar 

  31. Nebeker, BM, Starr, GW, Hirleman, ED (1995) Light scattering from patterned surfaces and particles on surfaces. In: Lowell, JK, Chen, RT, Mathur, JP (eds) Optical characterization techniques for high performance microelectronic device manufacturing II: Proc SPIE 2638:274–284

    Google Scholar 

  32. Nebeker, BM, Schmehl, R, Starr, GW, Hirleman, ED (1996) Prediction of light scattering characteristics of particles and structures on surfaces by the coupled-dipole method. In: Jones, S (ed) Metrology, inspection, and process control for microlithography X: Proc SPIE. 2725:690–697

    Google Scholar 

  33. Nebeker, BM, Starr, GW, Hirleman, ED (1996) Prediction of light scattering from structures with particle contaminants. In: Stover, JC (ed) Flatness, roughness, and discrete defect characterization for computer disks, wafers, and flat panel displays: Proc SPIE. 2862:139–150

    Google Scholar 

  34. Weber, DC (1986) Light scattering by micron and submicron spheres on optically smooth surfaces. Master’s Thesis, Arizona State University, Tempe, AZ

    Google Scholar 

  35. Bawolek, EJ (1992) Light scattering by spherical particles on semiconductor surfaces. Ph.D. Dissertation, Arizona State University, Tempe, AZ

    Google Scholar 

  36. Warner, TL (1994) Characterization of light scatter by particles of various refractive indices on semiconductor surfaces. Master’s Thesis, Arizona State University, Tempe, AZ

    Google Scholar 

  37. Starr, GW (1997) Light scattering by submicron particles and defects on smooth and patterned surfaces. Ph.D. Dissertation, Arizona State University, Tempe, AZ

    Google Scholar 

  38. Starr, GW, Hirleman, ED (1996) Comparison of experimentally-measured differential scattering cross sections of PSL spheres on flat and patterned surfaces. In: Stover, JC (ed) Flatness, roughness, and discrete defect characterization for computer disks, wafers, and flat panel displays: Proc SPIE. 2862:130–138

    Google Scholar 

  39. Draine, BT, Goodman, J (1993) Beyond Clausius-Mossotti: Wave propagation on a polarizable point lattice and the discrete dipole approximation. Astrophys. J 405:685–697

    Article  ADS  Google Scholar 

  40. Lager, DL, Lytle, RJ (1975) Fortran Subroutines for the Numerical Evaluation of Sommerfeld Integrals unter Anterem, Rep. UCRL-51821. Lawrence Livermore Laboratory, Livermore, CA

    Google Scholar 

  41. Nebeker, BM, Starr, GW, Hirleman, ED (1998) Evaluation of iteration methods used when modeling scattering from features on surfaces using the discrete-dipole approximation. J Quant Spectrosc Radiat Transfer 60:493–500

    Article  CAS  ADS  Google Scholar 

  42. R. W. Freund, RW (1992) Conjugate gradient-type methods for linear systems with complex symmetric coefficient matrices. SIAM J Scient and Stat Comp 13:425–448

    Article  Google Scholar 

  43. Goodman, JJ, Draine, BT, Flatau, PJ (1991) Application of fast-Fourier-transform techniques to the discrete-dipole approximation. Optics Letters 16:1198–1200

    Article  ADS  CAS  Google Scholar 

  44. Bohren, CF, Huffman, DR (1983) Absorption and Scattering of Light by Small Particles. John Wiley and Sons, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Arizona State University, Box 876106, 85287-6106, Tempe, AZ, USA

    B. M. Nebeker & E. D. Hirleman

Authors
  1. B. M. Nebeker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. E. D. Hirleman
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departamento de Fisica Aplicada, Universidad de Cantabria, Avda, Los Castros s/n, 39005, Santander, Spain

    Fernando Moreno  & Francisco González  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nebeker, B.M., Hirleman, E.D. (2000). Light Scattering by Particles and Defects on Surfaces: Semiconductor Wafer Inspection. In: Moreno, F., González, F. (eds) Light Scattering from Microstructures. Lecture Notes in Physics, vol 534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46614-2_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-46614-2_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66937-1

  • Online ISBN: 978-3-540-46614-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation