Abstract

Using measurements of reflectance, transmittance, and the ellipsometric parameter Δ, we have determined the thickness, refractive index, and the absorption coefficient of various thin films and thin-film stacks. (Δ, the relative phase between the p- and s-polarized components, is measured for both reflected and transmitted light.) These optical measurements are performed with a specially designed system at the fixed wavelength of λ = 633 nm over the 10°–75° range of angles of incidence. The examined samples, prepared by means of sputtering on fused-silica substrates, consist of monolayers and trilayers of various materials of differing thickness and optical constants. These samples, which are representative of the media of rewritable phase-change optical disks, include a dielectric mixture of ZnS and SiO2, an amorphous film of the Ge2Sb2.3Te5 alloy, and an aluminum chromium alloy film. To avoid complications arising from reflection and transmission losses at the air–substrate interface, the samples are immersed in an index-matching fluid that eliminates the contributions of the substrate to reflected and transmitted light. A computer program estimates the unknown parameters of the film(s) by matching the experimental data to theoretically calculated values. Although our system can be used for measurements over a broad range of wavelengths, we describe only the results obtained at λ = 633 nm.

© 2001 Optical Society of America

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  1. A. Rothen, “The ellipsometer, an apparatus to measure thicknesses of thin surface films,” Rev. Sci. Instrum. 16, 26–30 (1945).
    [CrossRef]
  2. A. B. Winterbottom, “Optical methods of studying films on reflecting bases depending on polarization and interference phenomena,” Trans. Faraday Soc. 42, 487–495 (1946).
    [CrossRef]
  3. R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
    [CrossRef]
  4. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  5. R. M. A. Azzam, “Ellipsometry,” in Handbook of Optics (McGraw-Hill, New York, 1995), Vol. 2, Chap. 27.
  6. O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955).
  7. L. Ward, The Optical Constants of Bulk Materials and Films (Institute of Physics, London, 1994), Chap. 6, pp. 181–205.
  8. J. C. Kemp, “Piezo-optical birefringence modulators,” J. Opt. Soc. Am. 59, 950–954 (1969).
  9. S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
    [CrossRef]
  10. S. N. Jasperson, D. K. Burge, R. C. O’Handley, “A modulated ellipsometer for studying thin film optical properties and surface dynamics,” Surf. Sci. 37, 548–558 (1973).
    [CrossRef]
  11. G. J. Sprokel, “Photoelastic modulated ellipsometry on magnetooptic multilayer films,” Appl. Opt. 25, 4017–4022 (1986).
    [CrossRef] [PubMed]
  12. G. E. Jellison, “Two-channel spectroscopic polarization modulated ellipsometry: a new technique for the analysis of thin SiO2 films,” Thin Solid Films 206, 294–299 (1991).
    [CrossRef]
  13. J. Campmany, E. Bertran, A. Canillas, J. L. Andujar, J. Costa, “Error minimization method for spectroscopic and phase-modulated ellipsometric measurements on highly transparent thin films,” J. Opt. Soc. Am. A 10, 713–718 (1993).
    [CrossRef]
  14. T. E. Jenkins, “Multiple-angle-of-incidence ellipsometry,” J. Phys. D 32, R45–R56 (1999).
    [CrossRef]
  15. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Fortran (Cambridge U. Press, London, 1989), pp. 294–301.
  16. C. Peng, L. Cheng, M. Mansuripur, “Experimental and theoretical investigation of laser-induced crystallization and amorphization in phase-change optical recording media,” J. Appl. Phys. 82, 4183–4191 (1997).
    [CrossRef]

1999 (1)

T. E. Jenkins, “Multiple-angle-of-incidence ellipsometry,” J. Phys. D 32, R45–R56 (1999).
[CrossRef]

1997 (1)

C. Peng, L. Cheng, M. Mansuripur, “Experimental and theoretical investigation of laser-induced crystallization and amorphization in phase-change optical recording media,” J. Appl. Phys. 82, 4183–4191 (1997).
[CrossRef]

1993 (1)

1991 (1)

G. E. Jellison, “Two-channel spectroscopic polarization modulated ellipsometry: a new technique for the analysis of thin SiO2 films,” Thin Solid Films 206, 294–299 (1991).
[CrossRef]

1986 (1)

1973 (1)

S. N. Jasperson, D. K. Burge, R. C. O’Handley, “A modulated ellipsometer for studying thin film optical properties and surface dynamics,” Surf. Sci. 37, 548–558 (1973).
[CrossRef]

1969 (3)

J. C. Kemp, “Piezo-optical birefringence modulators,” J. Opt. Soc. Am. 59, 950–954 (1969).

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
[CrossRef]

1946 (1)

A. B. Winterbottom, “Optical methods of studying films on reflecting bases depending on polarization and interference phenomena,” Trans. Faraday Soc. 42, 487–495 (1946).
[CrossRef]

1945 (1)

A. Rothen, “The ellipsometer, an apparatus to measure thicknesses of thin surface films,” Rev. Sci. Instrum. 16, 26–30 (1945).
[CrossRef]

Andujar, J. L.

Azzam, R. M. A.

R. M. A. Azzam, “Ellipsometry,” in Handbook of Optics (McGraw-Hill, New York, 1995), Vol. 2, Chap. 27.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bashara, N. M.

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

Bertran, E.

Burge, D. K.

S. N. Jasperson, D. K. Burge, R. C. O’Handley, “A modulated ellipsometer for studying thin film optical properties and surface dynamics,” Surf. Sci. 37, 548–558 (1973).
[CrossRef]

Campmany, J.

Canillas, A.

Cheng, L.

C. Peng, L. Cheng, M. Mansuripur, “Experimental and theoretical investigation of laser-induced crystallization and amorphization in phase-change optical recording media,” J. Appl. Phys. 82, 4183–4191 (1997).
[CrossRef]

Costa, J.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Fortran (Cambridge U. Press, London, 1989), pp. 294–301.

Heavens, O. S.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955).

Jasperson, S. N.

S. N. Jasperson, D. K. Burge, R. C. O’Handley, “A modulated ellipsometer for studying thin film optical properties and surface dynamics,” Surf. Sci. 37, 548–558 (1973).
[CrossRef]

S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
[CrossRef]

Jellison, G. E.

G. E. Jellison, “Two-channel spectroscopic polarization modulated ellipsometry: a new technique for the analysis of thin SiO2 films,” Thin Solid Films 206, 294–299 (1991).
[CrossRef]

Jenkins, T. E.

T. E. Jenkins, “Multiple-angle-of-incidence ellipsometry,” J. Phys. D 32, R45–R56 (1999).
[CrossRef]

Kemp, J. C.

Mansuripur, M.

C. Peng, L. Cheng, M. Mansuripur, “Experimental and theoretical investigation of laser-induced crystallization and amorphization in phase-change optical recording media,” J. Appl. Phys. 82, 4183–4191 (1997).
[CrossRef]

Muller, R. H.

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

O’Handley, R. C.

S. N. Jasperson, D. K. Burge, R. C. O’Handley, “A modulated ellipsometer for studying thin film optical properties and surface dynamics,” Surf. Sci. 37, 548–558 (1973).
[CrossRef]

Peng, C.

C. Peng, L. Cheng, M. Mansuripur, “Experimental and theoretical investigation of laser-induced crystallization and amorphization in phase-change optical recording media,” J. Appl. Phys. 82, 4183–4191 (1997).
[CrossRef]

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Fortran (Cambridge U. Press, London, 1989), pp. 294–301.

Rothen, A.

A. Rothen, “The ellipsometer, an apparatus to measure thicknesses of thin surface films,” Rev. Sci. Instrum. 16, 26–30 (1945).
[CrossRef]

Schnatterly, S. E.

S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
[CrossRef]

Sprokel, G. J.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Fortran (Cambridge U. Press, London, 1989), pp. 294–301.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Fortran (Cambridge U. Press, London, 1989), pp. 294–301.

Ward, L.

L. Ward, The Optical Constants of Bulk Materials and Films (Institute of Physics, London, 1994), Chap. 6, pp. 181–205.

Winterbottom, A. B.

A. B. Winterbottom, “Optical methods of studying films on reflecting bases depending on polarization and interference phenomena,” Trans. Faraday Soc. 42, 487–495 (1946).
[CrossRef]

Appl. Opt. (1)

J. Appl. Phys. (1)

C. Peng, L. Cheng, M. Mansuripur, “Experimental and theoretical investigation of laser-induced crystallization and amorphization in phase-change optical recording media,” J. Appl. Phys. 82, 4183–4191 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Phys. D (1)

T. E. Jenkins, “Multiple-angle-of-incidence ellipsometry,” J. Phys. D 32, R45–R56 (1999).
[CrossRef]

Rev. Sci. Instrum. (2)

A. Rothen, “The ellipsometer, an apparatus to measure thicknesses of thin surface films,” Rev. Sci. Instrum. 16, 26–30 (1945).
[CrossRef]

S. N. Jasperson, S. E. Schnatterly, “An improved method for high reflectivity ellipsometry based on a new polarization modulation technique,” Rev. Sci. Instrum. 40, 761–767 (1969).
[CrossRef]

Surf. Sci. (2)

S. N. Jasperson, D. K. Burge, R. C. O’Handley, “A modulated ellipsometer for studying thin film optical properties and surface dynamics,” Surf. Sci. 37, 548–558 (1973).
[CrossRef]

R. H. Muller, “Definitions and conventions in ellipsometry,” Surf. Sci. 16, 14–33 (1969).
[CrossRef]

Thin Solid Films (1)

G. E. Jellison, “Two-channel spectroscopic polarization modulated ellipsometry: a new technique for the analysis of thin SiO2 films,” Thin Solid Films 206, 294–299 (1991).
[CrossRef]

Trans. Faraday Soc. (1)

A. B. Winterbottom, “Optical methods of studying films on reflecting bases depending on polarization and interference phenomena,” Trans. Faraday Soc. 42, 487–495 (1946).
[CrossRef]

Other (5)

R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).

R. M. A. Azzam, “Ellipsometry,” in Handbook of Optics (McGraw-Hill, New York, 1995), Vol. 2, Chap. 27.

O. S. Heavens, Optical Properties of Thin Solid Films (Butterworth, London, 1955).

L. Ward, The Optical Constants of Bulk Materials and Films (Institute of Physics, London, 1994), Chap. 6, pp. 181–205.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Fortran (Cambridge U. Press, London, 1989), pp. 294–301.

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Figures (13)

Fig. 1
Fig. 1

We deposited a 25-nm-thick film of complex refractive index n + ik = 4.5 + 1.75i on a hemispherical glass substrate (n 0 = 1.5). The probe beam has λ = 633 nm and is incident at θ = 60°. To avoid complications arising from reflections and losses at the substrate bottom, the hemispherical surface is assumed to be antireflection coated.

Fig. 2
Fig. 2

Variations of the reflection and transmission characteristics of the sample of Fig. 1 at λ = 633 nm and θ = 60° when the film’s refractive index n is varied from 4.0 to 5.0. The changes are relative to the nominal values obtained with n = 4.5.

Fig. 3
Fig. 3

Variations of the reflection and transmission characteristics of the sample of Fig. 1 at λ = 633 nm and θ = 60° when the film’s absorption coefficient k is varied from 1.5 to 2. The changes are relative to the nominal values obtained with k = 1.75.

Fig. 4
Fig. 4

Variations of the reflection and transmission characteristics of the sample of Fig. 1 at λ = 633 nm and θ = 60° when the film thickness d is varied from 20 to 30 nm. The changes are relative to the nominal values obtained with d = 25 nm.

Fig. 5
Fig. 5

Diagram of an ellipsometric system based on a variable retarder and a differential detection module. The beam emerging from the polarizer is collimated and linearly polarized along the X axis. The variable retarder’s axes are fixed at ±45° to the X, Z plane of incidence, whereas its phase shift is varied continuously from 0° to 360°. The light beam is incident on the sample, and the reflected beam is focused by a low-N.A. lens in the reflection path. The reflected beam is monitored by a differential detector consisting of a Wollaston prism (oriented at 45° to the plane of incidence) and two identical photodetectors. The sum of the detector signals S 1 + S 2 contains information about the sample reflectivities R p and R s , whereas their normalized difference (S 1 - S 2)/(S 1 + S 2) yields the relative phase (ϕ rp - ϕ rs ).

Fig. 6
Fig. 6

Computed plots of the sum and (normalized) difference signals in the system of Fig. 5 for the sample shown in Fig. 1. The horizontal axes depict the relative phase imparted to the beam by the variable retarder. The beam emerging from the polarizer has unit optical power, the detectors’ conversion factor is unity, the incidence angle is θ = 60°, and the focusing and collimating lenses have a N.A. of 0.025. (a) The assumed system is perfect. (b) Two examples of imperfect system behavior.

Fig. 7
Fig. 7

Diagram of the measurement system used in our experiments. The He–Ne laser is aligned with the aid of the pellicle beam splitter, the retroreflector, the telescope, and the camera. The air-gap attenuator placed immediately after the laser controls the amount of light that reaches the sample, and the reference detector is used to cancel out laser power fluctuations. The photoelastic modulator (PEM) is tilted slightly to eliminate the harmful effects of multiple reflections. The sample is immersed in an index-matching fluid in a container with a fused-silica window, through which the beam must pass to reach the sample. An immersed air-gap mirror reflects the beam out of the tank and into the differential detection module, which consists of a Wollaston prism and a pair of identical photodetectos. The lens that focuses the beam (through the Wollaston) onto the detectors also prevents the index-matching fluid from entering the detection module. The sample mount can be rotated by two separate mechanisms. In the reflection mode of operation the goniometer rotates the sample and the detection arm in a θ–2θ configuration. In the transmission mode, the detection arm is positioned behind the sample, whereas the sample mount is rotated into position by a small motor.

Fig. 8
Fig. 8

Variations of the sum (S 1 + S 2) and difference (S 1 - S 2) signals of detectors A and B with the driving voltage of the PEM. The driving voltage is proportional to the induced phase shift between the p and s components of polarization. (a) Reflection mode; angle of incidence on the sample is θ = 20°. (b) Reflection mode, θ = 55°. (c) Transmission mode, θ = 20°.

Fig. 9
Fig. 9

Experimental and theoretical results obtained for the 60.4-nm-thick ZnS-SiO2 dielectric layer on a fused-silica substrate. The light is incident on the sample from the film side, and the horizontal axis corresponds to the angle of incidence θ. (a) Reflectivity R p , R s , and transmissivity T p and T s . (b) Differential signal (S 1 - S 2) measured in both reflection and transmission. (c) Phase difference (ϕ rp , ϕ rs ) and (ϕ tp , ϕ ts ) for reflected and transmitted beams. The circles mark the experimental data points and the curves represent theoretical best fits to the data.

Fig. 10
Fig. 10

Same as Fig. 9 but for sample 2, which is an 18.4-nm-thick aluminum alloy film deposited on a fused-silica substrate.

Fig. 11
Fig. 11

Same as Fig. 9 but for sample 3, which is a trilayer stack deposited on a fused-silica substrate.

Fig. 12
Fig. 12

In a nulling ellipsometer the collimated beam of light emerging from the source is linearly polarized along the direction ρ p by a rotatable polarizer. The QWP’s axes are typically at ±45° to the X, Z plane of incidence. Thus the beam incident on the sample has equal amounts of p and s polarization, with the relative phase between these two components depending on ρ p . Reflection from the sample induces a phase shift (ϕ rp - ϕ rs ) between the p and s components, which we can cancel out by adjusting the polarizer’s orientation. Subsequently, the analyzer in the detection arm is rotated to extinguish the light transmitted to the detector. In the null condition the value of ρ p yields the sample’s phase shift (ϕ rp - ϕ rs ), whereas the analyzer angle ρ a yields the ellipsometric parameter ψ r , which is related to the amplitude ratio |r p |/|r s | of the reflection coefficients.

Fig. 13
Fig. 13

Computed detector signal S versus the orientation angle ρ a of the analyzer in the nulling ellipsometer of Fig. 12 with the sample of Fig. 1. Different curves correspond to different values of the polarizer angle ρ p . The total optical power of the unpolarized (or circularly polarized) beam emerging from the source is unity, the detector’s conversion factor is 4, the incidence angle is θ = 60°, and the focusing and collimating lenses have a N.A. of 0.025. (a) The assumed system is perfect. (b) There are departures from ideal behavior, namely, the polarizer and analyzer have a 1:100 extinction ratio, the angle of incidence is off by 1°, and the QWP’s retardation is 87° although its axes are 1° from the ideal 45° orientation.

Tables (1)

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Table 1 Refractive Indices of the Fused-Silica Substrate and Fluid at Various Wavelengths (nm)

Equations (1)

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χ=NW1+W2+W3+W4-1i=1NW1Rpical-Rpiexp2+Rsical-Rsiexp2+W2ΔSRical-ΔSRiexp2+W3Tpical-Tpiexp2+Tsical-Tsiexp2+W4ΔSTical-ΔSTiexp.

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