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Volumn 45, Issue 2, 2006, Pages 235-264

Unified analysis and mathematical representation of film-thickness behavior of film-substrate systems

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; POLARIZATION; SUBSTRATES; THICKNESS MEASUREMENT;

EID: 31344433972     PISSN: 1559128X     EISSN: 15394522     Source Type: Journal    
DOI: 10.1364/AO.45.000235     Document Type: Article
Times cited : (11)

References (40)
  • 2
    • 0036685387 scopus 로고    scopus 로고
    • High-precision system for automatic null ellipsometric measurement
    • H. Zhu, L. Liu, Y. Wen, Z. Lu, and B. Zhang, "High-precision system for automatic null ellipsometric measurement," Appl. Opt. 41, 4536-4540 (2002).
    • (2002) Appl. Opt. , vol.41 , pp. 4536-4540
    • Zhu, H.1    Liu, L.2    Wen, Y.3    Lu, Z.4    Zhang, B.5
  • 3
    • 0016486677 scopus 로고
    • Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry
    • R. M. A. Azzam, A.-R. M. Zaghloul, and N. M. Bashara, "Ellipsometric function of a film-substrate system: Applications to the design of reflection-type optical devices and to ellipsometry," J. Opt. Soc. Am. 65, 252-260 (1975).
    • (1975) J. Opt. Soc. Am. , vol.65 , pp. 252-260
    • Azzam, R.M.A.1    Zaghloul, A.-R.M.2    Bashara, N.M.3
  • 5
    • 31344466549 scopus 로고
    • Ellipsometry of transparent films on transparent substrate
    • R. M. A. Azzam, "Ellipsometry of transparent films on transparent substrate," Surf. Sci. 96, 67-80 (1980).
    • (1980) Surf. Sci. , vol.96 , pp. 67-80
    • Azzam, R.M.A.1
  • 7
    • 84975612631 scopus 로고
    • Selection of optimal angles for inversion of multiple-angle ellipsometry and reflectometry equations
    • W. H. Weedon, S. W. McKnight, and A. J. Devaney, "Selection of optimal angles for inversion of multiple-angle ellipsometry and reflectometry equations," J. Opt. Soc. Am. A 8, 1881-1891 (1991).
    • (1991) J. Opt. Soc. Am. A , vol.8 , pp. 1881-1891
    • Weedon, W.H.1    McKnight, S.W.2    Devaney, A.J.3
  • 8
    • 0027652561 scopus 로고
    • Accurate null polarimetry for measuring the refractive index of transparent materials
    • S. F. Nee and H. E. Bennett, "Accurate null polarimetry for measuring the refractive index of transparent materials," J. Opt. Soc. Am. A 10, 2076-2083 (1993).
    • (1993) J. Opt. Soc. Am. A , vol.10 , pp. 2076-2083
    • Nee, S.F.1    Bennett, H.E.2
  • 9
    • 0011778939 scopus 로고    scopus 로고
    • Jones-matrix analysis with Pauli matrices: Application to ellipsometry
    • S. Li, "Jones-matrix analysis with Pauli matrices: Application to ellipsometry," J. Opt. Soc. Am. A 17, 920-926 (2000).
    • (2000) J. Opt. Soc. Am. A , vol.17 , pp. 920-926
    • Li, S.1
  • 10
    • 0034292721 scopus 로고    scopus 로고
    • Theoretical study of method based on ellipsometry for measurement of complex permittivity of materials
    • F. Sagnard, F. Bentabet, and C. Vignat, "Theoretical study of method based on ellipsometry for measurement of complex permittivity of materials," Electron. Lett. 36, 1843-1845 (2000).
    • (2000) Electron. Lett. , vol.36 , pp. 1843-1845
    • Sagnard, F.1    Bentabet, F.2    Vignat, C.3
  • 11
    • 84975541719 scopus 로고
    • Ellipsometric function of a film-substrate system: Characterization and detailed study
    • M. S. A. Yousef and A.-R. M. Zaghloul, "Ellipsometric function of a film-substrate system: characterization and detailed study," J. Opt. Soc. Am. A 6, 355-366 (1989).
    • (1989) J. Opt. Soc. Am. A , vol.6 , pp. 355-366
    • Yousef, M.S.A.1    Zaghloul, A.-R.M.2
  • 12
    • 13044294967 scopus 로고
    • Thickness calculations for a transparent film from ellipsometric measurements
    • M. Ghezzo, "Thickness calculations for a transparent film from ellipsometric measurements," J. Opt. Soc. Am. 58, 362-372 (1968).
    • (1968) J. Opt. Soc. Am. , vol.58 , pp. 362-372
    • Ghezzo, M.1
  • 13
    • 0017947222 scopus 로고
    • Determination of the refractive index and thickness of a transparent film on a transparent substrate system from the angles of incidence of zero reflection-induced ellipticity
    • R. M. A. Azzam and A.-R. M. Zaghloul, "Determination of the refractive index and thickness of a transparent film on a transparent substrate system from the angles of incidence of zero reflection-induced ellipticity," Opt. Commun. 24, 351-353 (1978).
    • (1978) Opt. Commun. , vol.24 , pp. 351-353
    • Azzam, R.M.A.1    Zaghloul, A.-R.M.2
  • 14
    • 13044268601 scopus 로고
    • Inversion of the nonlinear equations of reflection ellipsometry on film-substrate systems
    • A.-R. M. Zaghloul, R. M. A. Azzam, and N. M. Bashara, "Inversion of the nonlinear equations of reflection ellipsometry on film-substrate systems," Surf. Sci. 5, 87-96 (1976).
    • (1976) Surf. Sci. , vol.5 , pp. 87-96
    • Zaghloul, A.-R.M.1    Azzam, R.M.A.2    Bashara, N.M.3
  • 15
    • 0020780822 scopus 로고
    • Method of numerical inversion of the ellipsometry equation for transparent film
    • Y. Yoriunie, "Method of numerical inversion of the ellipsometry equation for transparent film," J. Opt. Soc. Am. 73, 888-891 (1983).
    • (1983) J. Opt. Soc. Am. , vol.73 , pp. 888-891
    • Yoriunie, Y.1
  • 16
    • 18244368819 scopus 로고
    • Simultaneous and independent determination of the refractive index and the thickness of thin films by ellipsometry
    • K. Vedam, R. Rai, F. Lukes, and R. Srinivason, "Simultaneous and independent determination of the refractive index and the thickness of thin films by ellipsometry," J. Opt. Soc. Am. 58, 526-532 (1968).
    • (1968) J. Opt. Soc. Am. , vol.58 , pp. 526-532
    • Vedam, K.1    Rai, R.2    Lukes, F.3    Srinivason, R.4
  • 17
    • 0028317898 scopus 로고
    • Inverse profiling by ellipsometry: A Newton-kantorovitch algorithm
    • D. A. Tonova, "Inverse profiling by ellipsometry: A Newton-Kantorovitch algorithm," Opt. Commun. 105, 104-112 (1994).
    • (1994) Opt. Commun. , vol.105 , pp. 104-112
    • Tonova, D.A.1
  • 18
    • 0000469585 scopus 로고
    • An ellipso metric procedure for the characterization of very thin surface films on absorbing substrates
    • T. Easwarakhanthan, S. Ravelet, and P. Renard, "An ellipso metric procedure for the characterization of very thin surface films on absorbing substrates," Appl. Surf. Sci. 90, 251-259 (1995).
    • (1995) Appl. Surf. Sci. , vol.90 , pp. 251-259
    • Easwarakhanthan, T.1    Ravelet, S.2    Renard, P.3
  • 19
    • 0000746466 scopus 로고    scopus 로고
    • Numerical algorithm for spectroscopic ellipsometry of thick transparent films
    • S. Bosch, J. Perez, and A. Canillas, "Numerical algorithm for spectroscopic ellipsometry of thick transparent films," Appl. Opt. 37, 1177-1179 (1998).
    • (1998) Appl. Opt. , vol.37 , pp. 1177-1179
    • Bosch, S.1    Perez, J.2    Canillas, A.3
  • 20
    • 0032607461 scopus 로고    scopus 로고
    • Ellipsometric function of a film-substrate system: Detailed analysis and closed-form inversion
    • A.-R. M. Zaghloul and M. S. A. Yousef, "Ellipsometric function of a film-substrate system: detailed analysis and closed-form inversion," J. Opt. Soc. Am. A 16, 2029-2044 (1999).
    • (1999) J. Opt. Soc. Am. A , vol.16 , pp. 2029-2044
    • Zaghloul, A.-R.M.1    Yousef, M.S.A.2
  • 21
    • 23444440303 scopus 로고    scopus 로고
    • Closed-form inversion of the ellipsometric function of a film-substrate system: Absorbing-substrate optical constant
    • M. Elshazly-Zaghloul and A.-R. M. Zaghloul, "Closed-form inversion of the ellipsometric function of a film-substrate system: Absorbing-substrate optical constant," J. Opt. Soc. Am. A 22, 1630-1636 (2005).
    • (2005) J. Opt. Soc. Am. A , vol.22 , pp. 1630-1636
    • Elshazly-Zaghloul, M.1    Zaghloul, A.-R.M.2
  • 22
    • 0032284986 scopus 로고    scopus 로고
    • Ellipsometry as a sensor technology for the control of deposition processes
    • Institute of Electrical and Electronics Engineers
    • S. C. Warnick and M. A. Dahleh, "Ellipsometry as a sensor technology for the control of deposition processes," in Proceedings of the 37th IEEE Control System Society (Institute of Electrical and Electronics Engineers, 1998), Vol. 3, pp. 3162-3167.
    • (1998) Proceedings of the 37th IEEE Control System Society , vol.3 , pp. 3162-3167
    • Warnick, S.C.1    Dahleh, M.A.2
  • 23
    • 0036207595 scopus 로고    scopus 로고
    • Design, development, and testing of real-time feedback controllers for semiconductor etching processes using in situ spectroscopic ellipsometry sensing
    • I. G. Rosen, T. Parent, B. Fidan, C. Wang, and A. Madhukar, "Design, development, and testing of real-time feedback controllers for semiconductor etching processes using in situ spectroscopic ellipsometry sensing," IEEE Trans. Control Syst. Technol. 10, 64-75 (2002).
    • (2002) IEEE Trans. Control Syst. Technol. , vol.10 , pp. 64-75
    • Rosen, I.G.1    Parent, T.2    Fidan, B.3    Wang, C.4    Madhukar, A.5
  • 26
    • 84894012056 scopus 로고    scopus 로고
    • note
    • [x] is defined as the greatest integer that is ≤x (the step function).
  • 27
    • 84893985601 scopus 로고    scopus 로고
    • note
    • A domain [a, b] is divided into a sequence D(i) of disconnected subdomains if ∪D(i) = [a, b] and D(i) ∩(j) = {} ∀i ≤ j. Rearrangement may be ascending or descending.
  • 28
    • 84893992564 scopus 로고    scopus 로고
    • note
    • 1 = 1.
  • 29
    • 84894002997 scopus 로고    scopus 로고
    • note
    • 1/2) dφ.
  • 30
    • 84894004659 scopus 로고    scopus 로고
    • note
    • 1) the ratio of any term to the one before in the sequence of Eq. (39) is less than unity. Hence it is a convergent sequence.
  • 31
    • 84893998182 scopus 로고    scopus 로고
    • note
    • In general, a domain is called m simply connected if the boundary of the same consists of m distinct boundaries.
  • 32
    • 84894001999 scopus 로고    scopus 로고
    • note
    • A singular point of a function is isolated if the function is analytic at each point in some deleted neighborhood of that point.
  • 33
    • 84894001946 scopus 로고    scopus 로고
    • note
    • A limit of a function f(x) at a point x = ξexists if and only if limf(x)x→ξ-0 = limf(x)x→ξ+0 = f(ξ).
  • 34
    • 84893994996 scopus 로고    scopus 로고
    • note
    • The cases of internal and total reflection at any or both of ambient-film and film-substrate interfaces are, however, beyond the scope of this paper and are considered elsewhere.
  • 35
    • 84893995286 scopus 로고    scopus 로고
    • note
    • A binary relation ℛ on a set is called an equivalence relation on τ provided the following three properties hold: (1) For all a ετ, (a, a) ε ℛ. (2) For all a and b in τ, if (a, b) ε ℛ, then (b, a) ε ℛ. (3) For all a, b, and c in τ, if (a, b) ε ℛ and (b, c) ε ℛ, then (a, c) ε ℛ. A relation that satisfies (1) is called reflexive. A relation that satisfies (2) is called symmetric. A relation that satisfies (3) is called transitive.
  • 36
    • 84975576274 scopus 로고
    • On the calculation of thin-film refractive index and thickness by ellipsometry
    • rφ is described in detail in Refs. 3, 4, and 14. See also, D. A. Holmes, "On the calculation of thin-film refractive index and thickness by ellipsometry," Appl. Opt. 6, 168-169 (1967).
    • (1967) Appl. Opt. , vol.6 , pp. 168-169
    • Holmes, D.A.1
  • 37
    • 0016660424 scopus 로고
    • Polarizer-surface-analyzer null ellipsometry for film-substrate systems
    • One of the possible experimental techniques for scanning the A behavior of the ρ-CTC is to use the polarizer-surface-analyzer null ellipsometry described in detail in R. M. A. Azzam, A.-R. M. Zaghloul, and N. M. Bashara, "Polarizer-surface-analyzer null ellipsometry for film-substrate systems," J. Opt. Soc. Am. 65, 1464-1471 (1975).
    • (1975) J. Opt. Soc. Am. , vol.65 , pp. 1464-1471
    • Azzam, R.M.A.1    Zaghloul, A.-R.M.2    Bashara, N.M.3
  • 38
    • 23444440615 scopus 로고    scopus 로고
    • Design of reflection retarders by use of nonnegative film-substrate systems
    • A. R. M. Zaghloul, D. A. Keeling, W. A. Berzett, and J. S. Mason, "Design of reflection retarders by use of nonnegative film-substrate systems," J. Opt. Soc. Am. A 22, 1637-1645, (2005).
    • (2005) J. Opt. Soc. Am. A , vol.22 , pp. 1637-1645
    • Zaghloul, A.R.M.1    Keeling, D.A.2    Berzett, W.A.3    Mason, J.S.4
  • 39
    • 29144482027 scopus 로고    scopus 로고
    • Thin-film coatings: An ellipsometric function approach I. Nonnegative transmission systems, polarization devices, coatings, and closed-form design formulas
    • submitted to
    • A. R. M. Zaghloul, M. Elshazly-Zaghloul, W. A. Berzett, and D. A. Keeling, "Thin-film coatings: An ellipsometric function approach I. Nonnegative transmission systems, polarization devices, coatings, and closed-form design formulas," submitted to J. Opt. Soc. Am. A.
    • J. Opt. Soc. Am. A.
    • Zaghloul, A.R.M.1    Elshazly-Zaghloul, M.2    Berzett, W.A.3    Keeling, D.A.4
  • 40
    • 84975633842 scopus 로고
    • Simultaneous reflection and refraction of light without change of polarization by a single-layer-coated dielectric surface
    • R. M. A. Azzam, "Simultaneous reflection and refraction of light without change of polarization by a single-layer-coated dielectric surface," Opt. Lett. 10, 107-109 (1985).
    • (1985) Opt. Lett. , vol.10 , pp. 107-109
    • Azzam, R.M.A.1


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