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Applied Optics

Applied Optics


  • Vol. 30, Iss. 22 — Aug. 1, 1991
  • pp: 3210–3220

Roughness measurements of Si and Al by variable angle spectroscopic ellipsometry

Julio R. Blanco and Patrick J. McMarr  »View Author Affiliations

Applied Optics, Vol. 30, Issue 22, pp. 3210-3220 (1991)

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Rough surfaces of silicon and aluminum have been studied by rotating analyzer spectroscopic ellipsometry (RASE). The roughness of a silicon sample similar to that used for the RASE measurements was also studied by cross-sectional transmission electron microscopy. Total integrated scattering was measured on the aluminum specimens to obtain numerical estimates of the rms roughness. The ellipsometry measurements on these specimens were carried out at a number of angles of incidence in the 30–80° range and at a number of discrete wavelengths in the 300–650-nm spectral range. The RASE results were then analyzed using the Bruggeman effective-medium theory for the Si sample and scalar diffraction theory for the Al samples. This study shows that 70° is the optimum angle of incidence for characterizing the roughness of these Al surfaces using RASE. It also demonstrates the self-consistency of the Bruggeman theory with angular variation for the Si sample. The need for a vector diffraction theory for the interpretation of the rms roughness using ellipsometric angles Δ and Ψ is discussed.

© 1991 Optical Society of America

Original Manuscript: January 9, 1990
Published: August 1, 1991

Julio R. Blanco and Patrick J. McMarr, "Roughness measurements of Si and Al by variable angle spectroscopic ellipsometry," Appl. Opt. 30, 3210-3220 (1991)

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  1. S. O. Rice, “Reflection of electromagnetic waves from slightly rough surfaces,” Commun. Pure Appl. Math. 4, 351–378 (1951). [CrossRef]
  2. P. Beckman, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, London, 1963).
  3. O. Hunderi, D. Beaglehole, “Study of the interaction of light with rough metal surfaces, II. Theory,” Phys. Rev. B 2, 321–329 (1970). [CrossRef]
  4. I. Ohlídal, F. Lukeš, “Ellipsometric parameters of rough surfaces and of a system substrate-thin film with rough boundaries,” Opt. Acta 19, 817–843 (1972). [CrossRef]
  5. E. L. Church, J. Zavada, “Residual surface roughness of diamond-turned optics,” Appl. Opt. 14, 1788–1795 (1975). [CrossRef] [PubMed]
  6. V. Celli, A. Marvin, F. Toigo, “Light scattering from rough surfaces,” Phys. Rev. B 11, 1779–1786 (1975). [CrossRef]
  7. J. M. Elson, J. P. Rahn, J. M. Bennett, “Light scattering from multilayer optics: comparison of theory and experiment,” Appl. Opt. 19, 669–679 (1980). [CrossRef] [PubMed]
  8. J. M. Elson, “Theory of light scattering from a rough surface with an inhomogeneous dielectric permittivity,” Phys. Rev. B 30, 5460–5480 (1984). [CrossRef]
  9. T. Smith, “Effect of surface roughness on ellipsometry of aluminum,” Surf. Sci. 56, 252–271 (1976). [CrossRef]
  10. H. E. Bennett, J. M. Bennett, “Precision measurements in thin film optics,” Phys. Thin Films 4, 1–96 (1967).
  11. T. V. Vorburger, E. C. Teague, “Optical techniques for online measurements of surface topography,” Precis. Eng. 3, 61–67 (1981). [CrossRef]
  12. K. H. Guenther, P. G. Wierer, J. M. Bennett, “Surface roughness measurements of low-scatter mirrors and roughness standards,” Appl. Opt. 23, 3820–3836 (1984). [CrossRef] [PubMed]
  13. J. M. Bennett, “Scattering and surface evaluation techniques for the optics of the future,” Opt. News 11(7), 17–27 (1985). [CrossRef]
  14. Soe-Mie F. Nee, “Ellipsometric analysis for surface roughness and texture,” Appl. Opt. 27, 2819–2831 (1988). [CrossRef] [PubMed]
  15. F. Varnier, N. Mayani, G. Rasigni, “Statistical parameters for rough surfaces of thin films of CaF2 and Ag/CaF2,” Appl. Opt. 28, 127–134 (1989). [CrossRef] [PubMed]
  16. C. Granquist, O. Hunderi, “Optical properties of Ag-SiO2 cermet films: a comparison of effective-medium theories,” phys. rev. B 18, 2897–2905 (1978). [CrossRef]
  17. D. A. G. Bruggeman, “Berechnung verschiedener physikalischer Konstanten und Leitfahigkeiten der Mischkorper aus isotropen Substanzen,” Ann. Phys. Leipzig 24, 636–670 (1935). [CrossRef]
  18. D. E. Aspnes, A. A. Studna, “High precision scanning ellipsometer,” Appl. Opt. 14, 220–228 (1975); “Methods for drift stabilization and photomultiplier linearization for photometric ellipsometers and polarimeters,” Rev. Sci. Instrum. 49, 291–279 (1978). [PubMed]
  19. D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by SE,” Phys. Rev. B 20, 3292–3302 (1979). [CrossRef]
  20. D. E. Aspnes, A. A. Studna, “Preparation of high-quality surfaces on semi-conductors by selective chemical etching,” J. Vac. Sci. Technol. 20, 488–489 (1982). [CrossRef]
  21. D. E. Aspnes, J. B. Theeten, “Dielectric/semiconductor interface using spectroscopic ellipsometry,” Acta Electron. 24, 217–227 (1981–1982).
  22. D. E. Aspnes, A. A. Studna, “Optical detection and minimization of surface overlayers on semiconductors using spectroscopic ellipsometry,” Proc. Soc. Photo-Opt. Instrum. Eng. 276, 227–232 (1981).
  23. D. E. Aspnes, J. B. Theeten, F. Hottier, “Investigation of effective-medium models of microscopic surface roughness by spectroscopic ellipsometry,” Phys. Rev. B 20, 3292–0000 (1979). [CrossRef]
  24. J. R. Blanco, R. Messier, K. Vedam, P. J. McMarr, “Spectroscopic ellipsometry study of rf-sputtered a-Ge films,” Mater. Res. Soc. Symp. Proc. 38, 301–307 (1985). [CrossRef]
  25. P. J. McMarr, K. Vedam, J. Narayan, “Characterization of ion-implanted Silicon by Spectroscopic Ellipsometry and Cross section transmission electron microscopy,” Mater. Res. Soc. Symp. Proc. 27, 299–000 (1984); “Spectroscopic ellipsometry: a new tool for the nondestructive depth profiling and characterization of interfaces,” J. Appl. Phys. 59, 694–701 (1986). [CrossRef]
  26. S. Zollner, C. Lin, E. Schonherr, A. Bohringer, M. Cardona, “The dielectric function of AlSb from 1.4 to 5.8 eV determined by spectroscopic ellipsometry,” J. Appl. Phys. 66, 383–387 (1989). [CrossRef]
  27. K. G. Merkel, P. G. Snyder, J. A. Woollam, S. A. Alterovitz, A. K. Rai, “Characterization of multilayer GaAs/AlGaAs transistor structure by variable angle spectroscopic ellipsometry,” Jpn. J. Appl. Phys. 28, 1118–1123 (1989). [CrossRef]
  28. P. J. McMarr, “Characterization of surfaces, thin films, and ion-implanted silicon by spectroscopic ellipsometry,” Ph.D. dissertation (Pennsylvania State University, University Park, Pa., 1985).
  29. I. Ohlidal, F. Lukes, “Ellipsometric parameters of randomly rough surfaces,” Opt. Commun.5, 323–326 (1972).
  30. I. Ohlídal, F. Lukeš, “Calculation of the ellipsometric parameters characterizing a randomly rough surface by means of the Stratton-Chu-Silver Integral,” Opt. Commun. 7, 76–79 (1973). [CrossRef]
  31. I. Ohlídal, K. Navrátil, F. Lukeš, “Reflection of light by a system of nonabsorbing isotropic film-nonabsorbing isotropic substrate with randomly rough boundaries,” J. Opt. Soc. Am. 61, 1630–1639 (1971). [CrossRef]
  32. I. Ohlídal, F. Lukeš, K. Navrátil, “Rough silicon surfaces studied by optical methods,” Surf. Sci. 45, 91–116 (1974). [CrossRef]
  33. I. Ohlíidal, F. Lukeš, K. Navrátil, “The problem of surface roughness in ellipsometry and reflectometry,” J. Phys. C 38, 77–88 (1977).
  34. J. R. Blanco, P. J. McMarr, K. Vedam, “Roughness measurements by spectroscopic ellipsometry,” Appl. Opt. 24, 3773–3779 (1985). [CrossRef] [PubMed]
  35. J. R. Blanco, P. J. McMarr, K. Vedam, J. M. Bennett, “Study of surface roughness of Al and Si by spectroscopic ellipsometry,” in Multiple Scattering of Waves in Random Media and Random Rough Surfaces, V. V. Varadan, V. K. Varadan, eds. (Technomic, Lancaster, Pa., 1986).
  36. F. Varnier, G. Rasigni, J. P. Palmari, A. Llebaria, M. Rasigni, “Influence of some parameters on the surface profile restored from microdensitometer analysis of electron micrographs of surface replicas,” Appl. Opt. 23, 3705–3717 (1984). [CrossRef] [PubMed]
  37. B. G. Bagley, D. E. Aspnes, A. C. Adams, “Optical properties of LPCVD a-Si over the energy range 1.5 to 6.0 eV,” Bull. Am. Phys. Soc. 25, 12–13 (1980).
  38. G. Hass, “Über die optischen Konstanten dicker Aluminum und Silberschichten in Vakuum,” Optik 1, 8–10 (1946); G. Hass, J. E. Waylonis, “Optical constants and reflectance and transmittance of evaporated aluminum in the visible and ultraviolet,” J. Opt. Soc. Am. 51, 719–722 (1961). [CrossRef]
  39. H.-J. Hagemann, W. Gundat, C. Kunz, “Optical constants from the far infrared to the x-ray region: Mg, Al, Cu, Ag, Au, Bi, C, and Al2O3,” Deutsches Elektronen-Synchrotron SR-74/7 (May1974).
  40. O. S. Heavens, Optical Properties of Solid Films (Dover, New York, 1965), p. 200.
  41. R. W. Fane, W. E. J. Neal, “Optical constants of aluminum films related to the vacuum environment,” J. Opt. Soc. Am. 60, 790–793 (1970). [CrossRef]
  42. M. Badia, “Ellipsometric analysis of amorphous oxide film growth and crystalline oxide island development during thermal oxidation of aluminum,” Thin Solid Films 13, 329–331 (1972). [CrossRef]
  43. T. H. Allen, “Study of Al with a combined auger electron spectrometer-ellipsometer system,” J. Vac. Sci. Technol. 13, 112–115 (1976). [CrossRef]
  44. E. Shiles, T. Sasaki, M. Inokuti, D. Y. Smith, “Self-consistent and sum–rule tests in the Kramers–Kronig analysis of optical data: applications to aluminum,” Phys. Rev. A 22, 1612–1628 (1980).
  45. Z. Bodó, G. Gergely, “Intrinsic optical constants of aluminum,” Appl. Opt. 26, 2065–2067 (1987). [CrossRef] [PubMed]
  46. J. Narayan, O. W. Holland, “Solid-phase-epitaxial growth in ion-implanted silicon,” Phys. Status Solidi A 73, 225–236 (1982). [CrossRef]
  47. O. W. Holland, B. R. Appleton, J. Narayan, “Ion implantation damage and annealing in germanium,” J. Appl. Phys. 54, 2295–2301 (1983). [CrossRef]
  48. H. E. Bennett, “Scattering characteristics of optical materials,” Opt. Eng. 17, 480–488 (1978); P. C. Archibald, H. E. Bennett, “Scattering from infrared missile domes,” Opt. Eng. 17, 647–651 (1978).
  49. The portable instrument was built by Talandic Research Corp., 2793 East Foothill Ave., Pasadena, Calif. 91107 for the U.S. Army as part of a contract with the Naval Weapons Center (Jean M. Bennett was principal investigator). J. M. Bennett made this set of measurements as part of the demonstration to the Army that the instrument does indeed measure TIS.
  50. J. R. Blanco, P. J. McMarr, J. E. Yehoda, K. Vedam, R. Messier, “Density of amorphous germanium films by spectroscopic ellipsometry,” J. Vac. Sci. Technol. A 4, 577–582 (1986). [CrossRef]
  51. H. E. Bennett, J. O. Porteus, “Relation between surface roughness and specular reflectance at normal incidence,” J. Opt. Soc. Am. 51, 123–129 (1961). [CrossRef]
  52. R. M. A. Azzam, “Arrangement of four photodetectors for measuring the state of polarization of light,” Opt. Lett. 10, 309–311 (1985). [CrossRef] [PubMed]
  53. E. L. Church, J. M. Zavada, “Effects of surface microroughness in mirror absorption,” J. Opt. Soc. Am. 64, 1404A (1974); “Optical effects of surface roughness,” J. Opt. Soc. Am. 64, 574A (1974).
  54. J. L. Stanford, H. E. Bennett, “Enhancement of surface plasma resonance absorption in mirrors by overcoating with dielectrics,” Appl. Opt. 8, 2556–2557 (1969). [CrossRef] [PubMed]
  55. H. E. Bennett, J. M. Bennett, E. J. Ashley, R. J. Motyka, “Verification of the anomalous-skin-effect theory for silver in the infrared,” Phys. Rev. 165, 755–764 (1968). [CrossRef]
  56. J. M. BennettU.S. Naval Weapons Center, Michelson Laboratory, China Lake, CA 93555 (personal communication).

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