OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 21 — Jul. 20, 2012
  • pp: 5100–5110

Dual-modulator broadband infrared Mueller matrix ellipsometry

Liam J. K. Cross and Dennis K. Hore  »View Author Affiliations


Applied Optics, Vol. 51, Issue 21, pp. 5100-5110 (2012)
http://dx.doi.org/10.1364/AO.51.005100


View Full Text Article

Enhanced HTML    Acrobat PDF (963 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A broadband mid-infrared Mueller matrix ellipsometer is described based on two photoelastic modulators and a step-scan interferometer. The data are analyzed using a combination hardware–software double Fourier transformation. Obtaining spectra of the Mueller matrix elements requires that the infrared wavelength-dependent retardation amplitude of the modulators be known through calibration and subsequently incorporated into the data processing. The spectroscopic capability of the instrument is demonstrated in transmission and reflection geometries by the measured Mueller matrices of air, an anisotropic quartz crystal, and the ZnSe–water interface, each from 25004000cm1.

© 2012 Optical Society of America

OCIS Codes
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(120.3930) Instrumentation, measurement, and metrology : Metrological instrumentation
(120.4640) Instrumentation, measurement, and metrology : Optical instruments
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation
(260.5430) Physical optics : Polarization

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: January 30, 2012
Revised Manuscript: April 13, 2012
Manuscript Accepted: May 11, 2012
Published: July 12, 2012

Citation
Liam J. K. Cross and Dennis K. Hore, "Dual-modulator broadband infrared Mueller matrix ellipsometry," Appl. Opt. 51, 5100-5110 (2012)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-21-5100


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. L. L. Deibler and M. H. Smith, “Measurement of the complex refractive index of isotropic materials with Mueller matrix polarimetry,” Appl. Opt. 40, 3659–3667 (2001). [CrossRef]
  2. J. Bremer, O. Hunderi, K. Fanping, T. Skauli, and E. Wold, “Infrared ellipsometer for the study of surface, thin films, and superlattices,” Appl. Opt. 31, 471–478 (1992). [CrossRef]
  3. M. Schubert, Infrared Ellipsometry on Semiconductor Layer Structures (Springer, 2004).
  4. A. Röseler, “Spectroscopic ellipsometry in the infrared,” Infra. Phys. 21, 349–355 (1981). [CrossRef]
  5. A. Röseler, “IR spectroscopic ellipsometry: instrumentation and details,” Thin Solid Films 234, 307–313 (1993). [CrossRef]
  6. A. Röseler, Infrared Spectroscopic Ellipsometry (Wiley-VCH Verlag GmbH, 1990).
  7. T. Hofmann, M. Schubert, G. Leibiger, and V. Gottschalch, “Electron effective mass and phonon modes in GaAs incorporating boron and indium,” Appl. Phys. Lett. 90, 182110 (2007). [CrossRef]
  8. K. Q. Zhang and Y.-h. Yen, “Determining optical constants using an infrared ellipsometer,” Appl. Opt. 28, 2929–2934 (1989). [CrossRef]
  9. T. E. Tiwald, D. W. Thompson, J. A. Woollam, and S. V. Pepper, “Determination of the mid-IR optical constants of water and lubricants using IR ellipsometry combined with an ATR cell,” Thin Solid Films 313, 718–721 (1998). [CrossRef]
  10. B. Drevillon, “Spectroscopic ellipsometry in the infrared range,” Thin Solid Films 313, 625–630 (1998). [CrossRef]
  11. G.-Q. Xia, R.-J. Zhang, Y.-L. Chen, H.-B. Zhao, S.-Y. Wand, S.-M. Zhou, Y.-X. Zheng, Y.-M. Yang, and L.-Y. Chen, “New design of the variable angle infrared spectroscopic ellipsometer using double Fourier transforms,” Rev. Sci. Instrum. 71, 2677–2683 (2000). [CrossRef]
  12. E. Garcia-Caurel, E. Bertran, and A. Canillas, “Optimized calibration method for Fourier transform infrared phase modulated ellipsometry,” Thin Solid Films 354, 187–194 (1999). [CrossRef]
  13. R. T. Graf, F. Eng, J. L. Koenig, and H. Ishida, “Polarization modulation Fourier transform infrared ellipsometry of thin films,” Appl. Spectrosc. 40, 498–503 (1986).
  14. M. J. Dignam and M. D. Baker, “Analysis of a polarizing Michelson interferometer for dual beam Fourier transform infrared, circular dichroism infrared, and reflectance ellipsometric infrared spectroscopies,” Appl. Spectrosc. 35, 186–193 (1981). [CrossRef]
  15. A. Boosalis, T. Hofmann, J. Šik, and M. Schubert, “Free-charge carrier profile of iso- and aniso-type Si homojunctions determined by terahertz and mid-infrared ellipsometry,” Thin Solid Films 519, 2604–2607 (2011). [CrossRef]
  16. T. Hofmann, C. M. Herzinger, T. E. Tiwald, J. A. Woollam, and M. Schubert, “Hole diffusion profile in a p−p+ silicon homojunction determined by terahertz and mid-infrared spectroscopic ellipsometry,” Appl. Phys. Lett. 95, 032102 (2009). [CrossRef]
  17. V. Darakchieva, M. Schubert, T. Hofmann, B. Monemar, C.-L. Hsiao, T.-W. Liu, L.-C. Chen, W. J. Schaff, Y. Takagi, and Y. Nanishi, “Electron accumulation at nonpolar and semipolar surfaces of wurtzite InN from generalized infrared ellipsometry,” Appl. Phys. Lett. 95, 202103 (2009). [CrossRef]
  18. T. Hofmann, V. Gottschalch, and M. Schubert, “Dielectric anisotropy and phonon modes of ordered indirect-gap Al0.52In0.48P studied by far-infrared ellipsometry,” Appl. Phys. Lett. 91, 121908 (2007). [CrossRef]
  19. T. Hofmann, V. Gottschalch, and M. Schubert, “Far-infrared dielectric anisotropy and phonon modes in spontaneously CuPt-ordered Ga0.52In0.48P,” Phys. Rev. B 66, 195204 (2002). [CrossRef]
  20. T. Hofmann, M. Schubert, C. M. Herzinger, and I. Pietzonka, “Far-infrared-magneto-optic ellipsometry characterization of free-charge-carrier properties in highly disordered n-type Al0.19Ga0.33In0.48P,” Appl. Phys. Lett. 82, 3463–3465 (2003). [CrossRef]
  21. T. Hofmann, U. Schade, K. C. Agarwal, B. Daniel, C. Klingshirn, M. Hetterich, C. M. Herzinger, and M. Schubert, “Conduction-band electron effective mass in Zn0.87Mn0.13Se measured by terahertz and far-infrared magnetooptic ellipsometry,” Appl. Phys. Lett. 88, 042105 (2006). [CrossRef]
  22. J. Kircher, R. Henn, M. Cardona, P. L. Richards, and G. P. Williams, “Far-infrared ellipsometry using synchrotron radiation,” J. Opt. Soc. Am. B 14, 705–712 (1997). [CrossRef]
  23. T. Hofmann, U. Schade, C. M. Herzinger, P. Esquinazi, and M. Schubert, “Terahertz magneto-optic generalized ellipsometry using synchrotron and blackbody radiation,” Rev. Sci. Instrum. 77, 063902 (2006). [CrossRef]
  24. T. Hofmann, C. M. Herzinger, J. L. Tedesco, D. K. Gaskill, J. A. Woollam, and M. Schubert, “Terahertz ellipsometry and terahertz optical-Hall effect,” Thin Solid Films 519, 2593–2600 (2011). [CrossRef]
  25. T. Hofmann, C. M. Herzinger, A. Boosalis, T. E. Tiwald, J. A. Woolam, and M. Schubert, “Variable-wavelength frequency-domain terahertz ellipsometry,” Rev. Sci. Instrum. 81, 023101 (2010). [CrossRef]
  26. T. Hofmann, A. Boosalis, P. Kühne, C. M. Herzinger, J. A. Woolam, D. K. Gaskill, J. L. Tedesco, and M. Schubert, “Hole-channel conductivity in epitaxial graphene determined by terahertz optical-Hall effect and midinfrared ellipsometry,” Appl. Phys. Lett. 98, 041906 (2011). [CrossRef]
  27. S. Schöche, J. Shi, A. Boosalis, P. Kühne, C. M. Herzinger, J. A. Woollam, W. J. Schaff, L. F. Eastman, M. Schubert, and T. Hofmann, “Terahertz optical-Hall effect characterization of two-dimensional electron gas properties in AlGaN/GaN high electron mobility transistor structures,” Appl. Phys. Lett. 98, 092103 (2011). [CrossRef]
  28. B. Drevillon, J. Perrin, R. Marbot, A. Violet, and J. L. Dalby, “Fast polarization modulated ellipsometer using a microprocessor system for digital Fourier analysis,” Rev. Sci. Instrum. 53, 969–977 (1982). [CrossRef]
  29. G. E. Jellison and F. A. Modine, “Two-channel polarization modulation ellipsometer,” Appl. Opt. 29, 959–974 (1990). [CrossRef]
  30. M. W. Wang, F. H. Tsai, and Y. F. Chao, “In situ calibration technique for photoelastic modulator ellipsometry,” Thin Solid Films 455, 78–83 (2004). [CrossRef]
  31. B. J. Barner, M. J. Green, E. I. Saez, and R. M. Corn, “Polarization modulation Fourier transform infrared reflectance measurements of thin films and monolayers at metal surfaces utilizing real-time sampling electronics,” J. Am. Chem. Soc. 63, 55–56 (1990). [CrossRef]
  32. T. Buffeteau, B. Desbat, D. Blaudez, and J. M. Turlet, “Calibration procedure to derive IRRAS spectra from PM-IRRAS spectra,” Appl. Opt. 54, 1646–1650 (2000).
  33. M. J. Green, B. J. Barner, and R. M. Corn, “Real-time sampling electronics for double modulation experiments with Fourier transform infrared spectrometers,” Rev. Sci. Instrum. 62, 1426–1430 (1991). [CrossRef]
  34. R. Mendelson, J. W. Brauner, and A. Gericke, “External infrared absorption spectrometry of monolayer films at the air–water interface,” Annu. Rev. Phys. Chem. 46, 305–334 (1995). [CrossRef]
  35. T. Buffeteau, B. Desbat, and J. M. Turlet, “Polarization modulation FT-IR spectroscopy of surfaces and ultra-thin films: experimental procedure and quantitative analysis,” Appl. Spectrosc. 45, 380–389 (1991). [CrossRef]
  36. A. E. Dowrey and C. Marcott, “A double-modulation Fourier transform infrared approach to studying adsorbates on metal surfaces,” Appl. Spectrosc. 36, 414–416 (1982). [CrossRef]
  37. D. Blaudez, T. Buffeteau, J. C. Cornut, B. Desbat, N. Escafre, M. Pezolet, and J. M. Turlet, “Polarization modulation FT-IR spectroscopy of a spread monolayer at the air/water interface,” Appl. Spectrosc. 47, 869–874 (1993). [CrossRef]
  38. D. Blaudez, T. Buffeteau, J. C. Cornut, B. Desbat, N. Excafre, M. Pezolet, and J. M. Turlet, “Polarization modulation FT-IR spectroscopy of a spread monolayer at the air/water interface,” Thin Solid Films 242, 146–150 (1994). [CrossRef]
  39. T. Buffeteau, B. Desbat, S. Besbes, M. Nafati, and L. Bokobza, “Molecular orientation studies in polymer films by polarization modulation FTIR spectroscopy,” Polymer 35, 2538–2541 (1994). [CrossRef]
  40. L. A. Nafie, H. Buijs, A. Rilling, X. Cao, and R. K. Dukor, “Dual source Fourier transform polarization modulation spectroscopy: an improved method for the measurement of circular and linear dichroism,” Appl. Spectrosc. 58, 647–654 (2004). [CrossRef]
  41. D. Tsankov, T. Eggimann, and H. Wieser, “Alternative design for improved FT-IR/VCD capabilities,” Appl. Spectrosc. 49, 132–138 (1995). [CrossRef]
  42. F. A. Modine, G. E. Jellison, and G. R. Gruzalski, “Errors in ellipsometry measurements made with a photoelastic modulator,” J. Opt. Soc. Am. 73, 892–900 (1983). [CrossRef]
  43. E. Wold and J. Bremer, “Mueller matrix analysis of infrared ellipsometry,” Appl. Opt. 33, 5982–5993 (1994). [CrossRef]
  44. E. Compain, S. Poirier, and B. Drevillon, “General and self-consistent method for the calibration of polarization modulators, polarimeters, and Mueller-matrix ellipsometers,” Appl. Opt. 38, 3490–3502 (1999). [CrossRef]
  45. G. E. Jellison, C. O. Griffiths, D. E. Holcomb, and C. M. Rouleau, “Transmission two-modulator generalized ellipsometry measurements,” Appl. Opt. 41, 6555–6566 (2002). [CrossRef]
  46. R. Anderson, “Measurement of Mueller matrices,” Appl. Opt. 31, 11–13 (1992). [CrossRef]
  47. G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometry: experiment and calibration,” Appl. Opt. 36, 8184–8189 (1997). [CrossRef]
  48. G. E. Jellison and F. A. Modine, “Two-modulator generalized ellipsometry: theory,” Appl. Opt. 36, 8190–8198 (1997). [CrossRef]
  49. T. Hofmann, D. Schmidt, A. Boosalis, P. Kühne, R. Skomski, C. M. Herzinger, J. A. Woollam, M. Schubert, and E. Schubert, “THz dielectric anisotropy of metal slanted columnar thin films,” Appl. Phys. Lett. 99, 081903 (2011). [CrossRef]
  50. T. Hofmann, C. M. Herzinger, C. Krahmer, K. Streubel, and M. Schubert, “The optical Hall effect,” Phys. Status Solidi A 205, 779–783 (2008). [CrossRef]
  51. T. Hofmann, V. Darakchieva, B. Monemar, H. Lu, W. J. Schaff, and M. Schubert, “Optical Hall effect in hexagonal InN,” J. Electron. Mater. 37, 611–615 (2008). [CrossRef]
  52. J. H. W. G. den Boer, G. M. W. Kroesen, and F. J. de Hoog, “Spectroscopic rotating compensator ellipsometry in the infrared: retarder design and measurement,” Meas. Sci. Technol. 8, 484–492 (1997). [CrossRef]
  53. A. De Martino, E. Garcia-Caurel, B. Laude, and B. Drevillon, “General methods for optimized design and calibration of Mueller polarimeters,” Thin Solid Films 455, 112–119 (2004). [CrossRef]
  54. G. E. Jellison and F. A. Modine, “Two modulator generalized ellipsometer for complete Mueller matrix measurement,” U.S. patent 5,956,147 (21Sept.1999).
  55. R. J. Javeri, “Frequency subtractor,” U.S. patent 4,683,437 (28July1987).
  56. M. W. Wang, Y. F. Chao, K. C. Leou, F. H. Tsai, T. L. Lin, S. S. Chen, and Y. W. Liu, “Calibrations of phase modulation amplitude of photoelastic modulator,” Jpn. J. Appl. Phys. 43, 827–832 (2004).
  57. T. C. Oakberg, “Using a mechanical chopper with a PEM to measure vdc,” http://www.hindsinstruments.com/wp-content/uploads/Mechanical_Chopper_and_PEM.pdf.
  58. W. G. Spitzer and D. A. Kleinman, “Infrared lattice bands in quartz,” Phys. Rev. 121, 1324–1335 (1961). [CrossRef]
  59. H. R. Philipp, Handbook of Optical Constants (Academic, 1985), pp. 719–747.
  60. K. C. Jena, P. A. Covert, and D. K. Hore, “The effect of salt on the water structure at a charged solid surface: differentiating second- and third-order nonlinear contributions,” J. Phys. Chem. Lett. 2, 1056–1061 (2011). [CrossRef]
  61. K. C. Jena and D. K. Hore, “Water structure at solid surfaces and its implications for biomolecule adsorption,” Phys. Chem. Chem. Phys. 12, 14383–14404 (2010). [CrossRef]
  62. K. Hermansson, S. Knuts, and J. Lindgren, “The OH vibrational spectrum of liquid water from combined ab initio and Monte Carlo calculations,” J. Chem. Phys. 95, 7486–7496 (1991). [CrossRef]
  63. H. Ahlborn, X. Ji, B. Space, and P. B. Moore, “A combined instantaneous normal mode and time correlation function description of the infrared vibrational spectrum of ambient water,” J. Chem. Phys. 111, 10622–10632 (1999). [CrossRef]
  64. D. Segelstein, “The complex refractive index of water,” Ph.D. thesis (University of Missouri–Kansas City, 1981).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited