Abstract

The effective medium approximation (EMA) has been widely applied to model the effect of a solid sample with surface roughness in spectroscopic ellipsometry (SE). There are two specific cases to utilize the EMA model. One is utilizing the EMA model to perform the inversion of the optical constants of solid samples from the SE measurements. Another is utilizing the EMA model to estimate the thickness of the rough layer at solid surface from the SE measurements under the condition in which the optical constants of samples are known. For the first case, the thickness of the rough layer is usually assumed to be the root mean square (rms) roughness as measured by atomic force microscopy (AFM). We theoretically investigate the error of the EMA model to estimate optical constants for different surface morphologies and materials. Because the EMA model only accounts for the height irregularities of rough surfaces but neglects the effect of the lateral irregularities on electromagnetic scattering from rough surfaces, it is difficult to obtain high-precision results for optical constants. Moreover, the inversion error of optical constants by using the EMA model is difficult to evaluate. In the second case, the thickness of the rough layer is estimated by using the EMA model from the SE measurements, called the EMA model roughness. We show that the EMA model roughness generally has a deviation from the rms roughness as measured by AFM. Some correlated relationships are established between the EMA model roughness and the morphological parameters of rough surfaces. It is found that these relationships have similar forms but not identical coefficients for different materials. The results from this work may facilitate a better understanding and utilization for the EMA model in SE.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
OSA Recommended Articles
Investigation of ellipsometric parameters of 2D microrough surfaces by FDTD

J. Qiu, D. F. Ran, Y. B. Liu, and L. H. Liu
Appl. Opt. 55(20) 5423-5431 (2016)

Simulation of depolarization effect by a rough surface for spectroscopic ellipsometry

Kyung Hoon Jun, Joong Hwan Kwak, and Koeng Su Lim
J. Opt. Soc. Am. A 20(6) 1060-1066 (2003)

References

  • View by:
  • |
  • |
  • |

  1. M. Losurdo and K. Hingerl, Ellipsometry at the Nanoscale (Springer, 2013).
  2. V. Sirtori, L. Magagnin, E. Saglia, and P. L. Cavallotti, “Calculation model of rough gold optical constants,” Surf. Sci. 554(2–3), 119–124 (2004).
    [Crossref]
  3. C. A. Fenstermaker and F. L. McCrackin, “Errors arising from surface roughness in ellipsometric measurement of the refractive index of a surface,” Surf. Sci. 16, 85–96 (1969).
    [Crossref]
  4. J. C. Stover, Optical Scattering: Measurement and Analysis (McGraw-Hill, 1995).
  5. D. Bergström, J. Powell, and A. F. H. Kaplan, “A ray-tracing analysis of the absorption of light by smooth and rough metal surfaces,” J. Appl. Phys. 101(11), 113504 (2007).
    [Crossref]
  6. R. W. Collins, I. An, H. Fujiwara, J. C. Lee, Y. W. Lu, J. Y. Koh, and P. I. Rovira, “Advances in multichannel spectroscopic ellipsometry,” Thin Solid Films 313–314, 18–32 (1998).
    [Crossref]
  7. J. Koh, Y. W. Lu, C. R. Wronski, Y. L. Kuang, R. W. Collins, T. T. Tsong, and Y. E. Strausser, “Correlation of real time spectroellipsometry and atomic force microscopy measurements of surface roughness on amorphous semiconductor thin films,” Appl. Phys. Lett. 69(9), 1297–1299 (1996).
    [Crossref]
  8. P. Petrik, L. P. Biro, M. Fried, T. Lohner, R. Berger, C. Schneider, J. Gyulai, and H. Ryssel, “Comparative study of surface roughness measured on polysilicon using spectroscopic ellipsometry and atomic force microscopy,” Thin Solid Films 315(1–2), 186–191 (1998).
    [Crossref]
  9. H. Fujiwara, M. Kondo, and A. Matsuda, “Real-time spectroscopic ellipsometry studies of the nucleation and grain growth processes in microcrystalline silicon thin films,” Phys. Rev. B 63(11), 115306 (2001).
    [Crossref]
  10. D. Franta and I. Ohlídal, “Comparison of effective medium approximation and Rayleigh–Rice theory concerning ellipsometric characterization of rough surfaces,” Opt. Commun. 248(4–6), 459–467 (2005).
    [Crossref]
  11. A. Yanguas-Gil, B. A. Sperling, and J. R. Abelson, “Theory of light scattering from self-affine surfaces: Relationship between surface morphology and effective medium roughness,” Phys. Rev. B 84(8), 085402 (2011).
    [Crossref]
  12. J. Qiu, D. F. Ran, Y. B. Liu, and L. H. Liu, “Investigation of ellipsometric parameters of 2D microrough surfaces by FDTD,” Appl. Opt. 55(20), 5423–5431 (2016).
    [Crossref] [PubMed]
  13. I. Ohlídal, J. Vohánka, M. Čermák, and D. Franta, “Optical characterization of randomly microrough surfaces covered with very thin overlayers using effective medium approximation and Rayleigh–Rice theory,” Appl. Surf. Sci. 419, 942–956 (2017).
    [Crossref]
  14. H. Arwin and D. E. Aspnes, “Determination of optical properties of thin organic films by spectroellipsometry,” Thin Solid Films 138(2), 195–207 (1986).
    [Crossref]
  15. H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley & Sons, 2007).
  16. E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

2017 (1)

I. Ohlídal, J. Vohánka, M. Čermák, and D. Franta, “Optical characterization of randomly microrough surfaces covered with very thin overlayers using effective medium approximation and Rayleigh–Rice theory,” Appl. Surf. Sci. 419, 942–956 (2017).
[Crossref]

2016 (1)

2011 (1)

A. Yanguas-Gil, B. A. Sperling, and J. R. Abelson, “Theory of light scattering from self-affine surfaces: Relationship between surface morphology and effective medium roughness,” Phys. Rev. B 84(8), 085402 (2011).
[Crossref]

2007 (1)

D. Bergström, J. Powell, and A. F. H. Kaplan, “A ray-tracing analysis of the absorption of light by smooth and rough metal surfaces,” J. Appl. Phys. 101(11), 113504 (2007).
[Crossref]

2005 (1)

D. Franta and I. Ohlídal, “Comparison of effective medium approximation and Rayleigh–Rice theory concerning ellipsometric characterization of rough surfaces,” Opt. Commun. 248(4–6), 459–467 (2005).
[Crossref]

2004 (1)

V. Sirtori, L. Magagnin, E. Saglia, and P. L. Cavallotti, “Calculation model of rough gold optical constants,” Surf. Sci. 554(2–3), 119–124 (2004).
[Crossref]

2001 (1)

H. Fujiwara, M. Kondo, and A. Matsuda, “Real-time spectroscopic ellipsometry studies of the nucleation and grain growth processes in microcrystalline silicon thin films,” Phys. Rev. B 63(11), 115306 (2001).
[Crossref]

1998 (2)

P. Petrik, L. P. Biro, M. Fried, T. Lohner, R. Berger, C. Schneider, J. Gyulai, and H. Ryssel, “Comparative study of surface roughness measured on polysilicon using spectroscopic ellipsometry and atomic force microscopy,” Thin Solid Films 315(1–2), 186–191 (1998).
[Crossref]

R. W. Collins, I. An, H. Fujiwara, J. C. Lee, Y. W. Lu, J. Y. Koh, and P. I. Rovira, “Advances in multichannel spectroscopic ellipsometry,” Thin Solid Films 313–314, 18–32 (1998).
[Crossref]

1996 (1)

J. Koh, Y. W. Lu, C. R. Wronski, Y. L. Kuang, R. W. Collins, T. T. Tsong, and Y. E. Strausser, “Correlation of real time spectroellipsometry and atomic force microscopy measurements of surface roughness on amorphous semiconductor thin films,” Appl. Phys. Lett. 69(9), 1297–1299 (1996).
[Crossref]

1986 (1)

H. Arwin and D. E. Aspnes, “Determination of optical properties of thin organic films by spectroellipsometry,” Thin Solid Films 138(2), 195–207 (1986).
[Crossref]

1969 (1)

C. A. Fenstermaker and F. L. McCrackin, “Errors arising from surface roughness in ellipsometric measurement of the refractive index of a surface,” Surf. Sci. 16, 85–96 (1969).
[Crossref]

Abelson, J. R.

A. Yanguas-Gil, B. A. Sperling, and J. R. Abelson, “Theory of light scattering from self-affine surfaces: Relationship between surface morphology and effective medium roughness,” Phys. Rev. B 84(8), 085402 (2011).
[Crossref]

An, I.

R. W. Collins, I. An, H. Fujiwara, J. C. Lee, Y. W. Lu, J. Y. Koh, and P. I. Rovira, “Advances in multichannel spectroscopic ellipsometry,” Thin Solid Films 313–314, 18–32 (1998).
[Crossref]

Arwin, H.

H. Arwin and D. E. Aspnes, “Determination of optical properties of thin organic films by spectroellipsometry,” Thin Solid Films 138(2), 195–207 (1986).
[Crossref]

Aspnes, D. E.

H. Arwin and D. E. Aspnes, “Determination of optical properties of thin organic films by spectroellipsometry,” Thin Solid Films 138(2), 195–207 (1986).
[Crossref]

Berger, R.

P. Petrik, L. P. Biro, M. Fried, T. Lohner, R. Berger, C. Schneider, J. Gyulai, and H. Ryssel, “Comparative study of surface roughness measured on polysilicon using spectroscopic ellipsometry and atomic force microscopy,” Thin Solid Films 315(1–2), 186–191 (1998).
[Crossref]

Bergström, D.

D. Bergström, J. Powell, and A. F. H. Kaplan, “A ray-tracing analysis of the absorption of light by smooth and rough metal surfaces,” J. Appl. Phys. 101(11), 113504 (2007).
[Crossref]

Biro, L. P.

P. Petrik, L. P. Biro, M. Fried, T. Lohner, R. Berger, C. Schneider, J. Gyulai, and H. Ryssel, “Comparative study of surface roughness measured on polysilicon using spectroscopic ellipsometry and atomic force microscopy,” Thin Solid Films 315(1–2), 186–191 (1998).
[Crossref]

Cavallotti, P. L.

V. Sirtori, L. Magagnin, E. Saglia, and P. L. Cavallotti, “Calculation model of rough gold optical constants,” Surf. Sci. 554(2–3), 119–124 (2004).
[Crossref]

Cermák, M.

I. Ohlídal, J. Vohánka, M. Čermák, and D. Franta, “Optical characterization of randomly microrough surfaces covered with very thin overlayers using effective medium approximation and Rayleigh–Rice theory,” Appl. Surf. Sci. 419, 942–956 (2017).
[Crossref]

Collins, R. W.

R. W. Collins, I. An, H. Fujiwara, J. C. Lee, Y. W. Lu, J. Y. Koh, and P. I. Rovira, “Advances in multichannel spectroscopic ellipsometry,” Thin Solid Films 313–314, 18–32 (1998).
[Crossref]

J. Koh, Y. W. Lu, C. R. Wronski, Y. L. Kuang, R. W. Collins, T. T. Tsong, and Y. E. Strausser, “Correlation of real time spectroellipsometry and atomic force microscopy measurements of surface roughness on amorphous semiconductor thin films,” Appl. Phys. Lett. 69(9), 1297–1299 (1996).
[Crossref]

Fenstermaker, C. A.

C. A. Fenstermaker and F. L. McCrackin, “Errors arising from surface roughness in ellipsometric measurement of the refractive index of a surface,” Surf. Sci. 16, 85–96 (1969).
[Crossref]

Franta, D.

I. Ohlídal, J. Vohánka, M. Čermák, and D. Franta, “Optical characterization of randomly microrough surfaces covered with very thin overlayers using effective medium approximation and Rayleigh–Rice theory,” Appl. Surf. Sci. 419, 942–956 (2017).
[Crossref]

D. Franta and I. Ohlídal, “Comparison of effective medium approximation and Rayleigh–Rice theory concerning ellipsometric characterization of rough surfaces,” Opt. Commun. 248(4–6), 459–467 (2005).
[Crossref]

Fried, M.

P. Petrik, L. P. Biro, M. Fried, T. Lohner, R. Berger, C. Schneider, J. Gyulai, and H. Ryssel, “Comparative study of surface roughness measured on polysilicon using spectroscopic ellipsometry and atomic force microscopy,” Thin Solid Films 315(1–2), 186–191 (1998).
[Crossref]

Fujiwara, H.

H. Fujiwara, M. Kondo, and A. Matsuda, “Real-time spectroscopic ellipsometry studies of the nucleation and grain growth processes in microcrystalline silicon thin films,” Phys. Rev. B 63(11), 115306 (2001).
[Crossref]

R. W. Collins, I. An, H. Fujiwara, J. C. Lee, Y. W. Lu, J. Y. Koh, and P. I. Rovira, “Advances in multichannel spectroscopic ellipsometry,” Thin Solid Films 313–314, 18–32 (1998).
[Crossref]

Gyulai, J.

P. Petrik, L. P. Biro, M. Fried, T. Lohner, R. Berger, C. Schneider, J. Gyulai, and H. Ryssel, “Comparative study of surface roughness measured on polysilicon using spectroscopic ellipsometry and atomic force microscopy,” Thin Solid Films 315(1–2), 186–191 (1998).
[Crossref]

Kaplan, A. F. H.

D. Bergström, J. Powell, and A. F. H. Kaplan, “A ray-tracing analysis of the absorption of light by smooth and rough metal surfaces,” J. Appl. Phys. 101(11), 113504 (2007).
[Crossref]

Koh, J.

J. Koh, Y. W. Lu, C. R. Wronski, Y. L. Kuang, R. W. Collins, T. T. Tsong, and Y. E. Strausser, “Correlation of real time spectroellipsometry and atomic force microscopy measurements of surface roughness on amorphous semiconductor thin films,” Appl. Phys. Lett. 69(9), 1297–1299 (1996).
[Crossref]

Koh, J. Y.

R. W. Collins, I. An, H. Fujiwara, J. C. Lee, Y. W. Lu, J. Y. Koh, and P. I. Rovira, “Advances in multichannel spectroscopic ellipsometry,” Thin Solid Films 313–314, 18–32 (1998).
[Crossref]

Kondo, M.

H. Fujiwara, M. Kondo, and A. Matsuda, “Real-time spectroscopic ellipsometry studies of the nucleation and grain growth processes in microcrystalline silicon thin films,” Phys. Rev. B 63(11), 115306 (2001).
[Crossref]

Kuang, Y. L.

J. Koh, Y. W. Lu, C. R. Wronski, Y. L. Kuang, R. W. Collins, T. T. Tsong, and Y. E. Strausser, “Correlation of real time spectroellipsometry and atomic force microscopy measurements of surface roughness on amorphous semiconductor thin films,” Appl. Phys. Lett. 69(9), 1297–1299 (1996).
[Crossref]

Lee, J. C.

R. W. Collins, I. An, H. Fujiwara, J. C. Lee, Y. W. Lu, J. Y. Koh, and P. I. Rovira, “Advances in multichannel spectroscopic ellipsometry,” Thin Solid Films 313–314, 18–32 (1998).
[Crossref]

Liu, L. H.

Liu, Y. B.

Lohner, T.

P. Petrik, L. P. Biro, M. Fried, T. Lohner, R. Berger, C. Schneider, J. Gyulai, and H. Ryssel, “Comparative study of surface roughness measured on polysilicon using spectroscopic ellipsometry and atomic force microscopy,” Thin Solid Films 315(1–2), 186–191 (1998).
[Crossref]

Lu, Y. W.

R. W. Collins, I. An, H. Fujiwara, J. C. Lee, Y. W. Lu, J. Y. Koh, and P. I. Rovira, “Advances in multichannel spectroscopic ellipsometry,” Thin Solid Films 313–314, 18–32 (1998).
[Crossref]

J. Koh, Y. W. Lu, C. R. Wronski, Y. L. Kuang, R. W. Collins, T. T. Tsong, and Y. E. Strausser, “Correlation of real time spectroellipsometry and atomic force microscopy measurements of surface roughness on amorphous semiconductor thin films,” Appl. Phys. Lett. 69(9), 1297–1299 (1996).
[Crossref]

Magagnin, L.

V. Sirtori, L. Magagnin, E. Saglia, and P. L. Cavallotti, “Calculation model of rough gold optical constants,” Surf. Sci. 554(2–3), 119–124 (2004).
[Crossref]

Matsuda, A.

H. Fujiwara, M. Kondo, and A. Matsuda, “Real-time spectroscopic ellipsometry studies of the nucleation and grain growth processes in microcrystalline silicon thin films,” Phys. Rev. B 63(11), 115306 (2001).
[Crossref]

McCrackin, F. L.

C. A. Fenstermaker and F. L. McCrackin, “Errors arising from surface roughness in ellipsometric measurement of the refractive index of a surface,” Surf. Sci. 16, 85–96 (1969).
[Crossref]

Ohlídal, I.

I. Ohlídal, J. Vohánka, M. Čermák, and D. Franta, “Optical characterization of randomly microrough surfaces covered with very thin overlayers using effective medium approximation and Rayleigh–Rice theory,” Appl. Surf. Sci. 419, 942–956 (2017).
[Crossref]

D. Franta and I. Ohlídal, “Comparison of effective medium approximation and Rayleigh–Rice theory concerning ellipsometric characterization of rough surfaces,” Opt. Commun. 248(4–6), 459–467 (2005).
[Crossref]

Petrik, P.

P. Petrik, L. P. Biro, M. Fried, T. Lohner, R. Berger, C. Schneider, J. Gyulai, and H. Ryssel, “Comparative study of surface roughness measured on polysilicon using spectroscopic ellipsometry and atomic force microscopy,” Thin Solid Films 315(1–2), 186–191 (1998).
[Crossref]

Powell, J.

D. Bergström, J. Powell, and A. F. H. Kaplan, “A ray-tracing analysis of the absorption of light by smooth and rough metal surfaces,” J. Appl. Phys. 101(11), 113504 (2007).
[Crossref]

Qiu, J.

Ran, D. F.

Rovira, P. I.

R. W. Collins, I. An, H. Fujiwara, J. C. Lee, Y. W. Lu, J. Y. Koh, and P. I. Rovira, “Advances in multichannel spectroscopic ellipsometry,” Thin Solid Films 313–314, 18–32 (1998).
[Crossref]

Ryssel, H.

P. Petrik, L. P. Biro, M. Fried, T. Lohner, R. Berger, C. Schneider, J. Gyulai, and H. Ryssel, “Comparative study of surface roughness measured on polysilicon using spectroscopic ellipsometry and atomic force microscopy,” Thin Solid Films 315(1–2), 186–191 (1998).
[Crossref]

Saglia, E.

V. Sirtori, L. Magagnin, E. Saglia, and P. L. Cavallotti, “Calculation model of rough gold optical constants,” Surf. Sci. 554(2–3), 119–124 (2004).
[Crossref]

Schneider, C.

P. Petrik, L. P. Biro, M. Fried, T. Lohner, R. Berger, C. Schneider, J. Gyulai, and H. Ryssel, “Comparative study of surface roughness measured on polysilicon using spectroscopic ellipsometry and atomic force microscopy,” Thin Solid Films 315(1–2), 186–191 (1998).
[Crossref]

Sirtori, V.

V. Sirtori, L. Magagnin, E. Saglia, and P. L. Cavallotti, “Calculation model of rough gold optical constants,” Surf. Sci. 554(2–3), 119–124 (2004).
[Crossref]

Sperling, B. A.

A. Yanguas-Gil, B. A. Sperling, and J. R. Abelson, “Theory of light scattering from self-affine surfaces: Relationship between surface morphology and effective medium roughness,” Phys. Rev. B 84(8), 085402 (2011).
[Crossref]

Strausser, Y. E.

J. Koh, Y. W. Lu, C. R. Wronski, Y. L. Kuang, R. W. Collins, T. T. Tsong, and Y. E. Strausser, “Correlation of real time spectroellipsometry and atomic force microscopy measurements of surface roughness on amorphous semiconductor thin films,” Appl. Phys. Lett. 69(9), 1297–1299 (1996).
[Crossref]

Tsong, T. T.

J. Koh, Y. W. Lu, C. R. Wronski, Y. L. Kuang, R. W. Collins, T. T. Tsong, and Y. E. Strausser, “Correlation of real time spectroellipsometry and atomic force microscopy measurements of surface roughness on amorphous semiconductor thin films,” Appl. Phys. Lett. 69(9), 1297–1299 (1996).
[Crossref]

Vohánka, J.

I. Ohlídal, J. Vohánka, M. Čermák, and D. Franta, “Optical characterization of randomly microrough surfaces covered with very thin overlayers using effective medium approximation and Rayleigh–Rice theory,” Appl. Surf. Sci. 419, 942–956 (2017).
[Crossref]

Wronski, C. R.

J. Koh, Y. W. Lu, C. R. Wronski, Y. L. Kuang, R. W. Collins, T. T. Tsong, and Y. E. Strausser, “Correlation of real time spectroellipsometry and atomic force microscopy measurements of surface roughness on amorphous semiconductor thin films,” Appl. Phys. Lett. 69(9), 1297–1299 (1996).
[Crossref]

Yanguas-Gil, A.

A. Yanguas-Gil, B. A. Sperling, and J. R. Abelson, “Theory of light scattering from self-affine surfaces: Relationship between surface morphology and effective medium roughness,” Phys. Rev. B 84(8), 085402 (2011).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

J. Koh, Y. W. Lu, C. R. Wronski, Y. L. Kuang, R. W. Collins, T. T. Tsong, and Y. E. Strausser, “Correlation of real time spectroellipsometry and atomic force microscopy measurements of surface roughness on amorphous semiconductor thin films,” Appl. Phys. Lett. 69(9), 1297–1299 (1996).
[Crossref]

Appl. Surf. Sci. (1)

I. Ohlídal, J. Vohánka, M. Čermák, and D. Franta, “Optical characterization of randomly microrough surfaces covered with very thin overlayers using effective medium approximation and Rayleigh–Rice theory,” Appl. Surf. Sci. 419, 942–956 (2017).
[Crossref]

J. Appl. Phys. (1)

D. Bergström, J. Powell, and A. F. H. Kaplan, “A ray-tracing analysis of the absorption of light by smooth and rough metal surfaces,” J. Appl. Phys. 101(11), 113504 (2007).
[Crossref]

Opt. Commun. (1)

D. Franta and I. Ohlídal, “Comparison of effective medium approximation and Rayleigh–Rice theory concerning ellipsometric characterization of rough surfaces,” Opt. Commun. 248(4–6), 459–467 (2005).
[Crossref]

Phys. Rev. B (2)

A. Yanguas-Gil, B. A. Sperling, and J. R. Abelson, “Theory of light scattering from self-affine surfaces: Relationship between surface morphology and effective medium roughness,” Phys. Rev. B 84(8), 085402 (2011).
[Crossref]

H. Fujiwara, M. Kondo, and A. Matsuda, “Real-time spectroscopic ellipsometry studies of the nucleation and grain growth processes in microcrystalline silicon thin films,” Phys. Rev. B 63(11), 115306 (2001).
[Crossref]

Surf. Sci. (2)

V. Sirtori, L. Magagnin, E. Saglia, and P. L. Cavallotti, “Calculation model of rough gold optical constants,” Surf. Sci. 554(2–3), 119–124 (2004).
[Crossref]

C. A. Fenstermaker and F. L. McCrackin, “Errors arising from surface roughness in ellipsometric measurement of the refractive index of a surface,” Surf. Sci. 16, 85–96 (1969).
[Crossref]

Thin Solid Films (3)

R. W. Collins, I. An, H. Fujiwara, J. C. Lee, Y. W. Lu, J. Y. Koh, and P. I. Rovira, “Advances in multichannel spectroscopic ellipsometry,” Thin Solid Films 313–314, 18–32 (1998).
[Crossref]

P. Petrik, L. P. Biro, M. Fried, T. Lohner, R. Berger, C. Schneider, J. Gyulai, and H. Ryssel, “Comparative study of surface roughness measured on polysilicon using spectroscopic ellipsometry and atomic force microscopy,” Thin Solid Films 315(1–2), 186–191 (1998).
[Crossref]

H. Arwin and D. E. Aspnes, “Determination of optical properties of thin organic films by spectroellipsometry,” Thin Solid Films 138(2), 195–207 (1986).
[Crossref]

Other (4)

H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley & Sons, 2007).

E. D. Palik, Handbook of Optical Constants of Solids (Academic Press, 1985).

M. Losurdo and K. Hingerl, Ellipsometry at the Nanoscale (Springer, 2013).

J. C. Stover, Optical Scattering: Measurement and Analysis (McGraw-Hill, 1995).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1 FDTD simulations of the SE parameters (Ψ, Δ) of Si compared with the EMA model calculations: σ = 0.05 μm; ζ = 0.1 μm, 0.2 μm, 0.4 μm, respectively.
Fig. 2
Fig. 2 Relative mean square error (RMSE) of the SE parameters calculated by the EMA model as a function of the relative roughness: (a) σ = 0.05 μm; σ/ζ = 0.75; (b) σ = 0.05 μm; σ/ζ = 0.125.
Fig. 3
Fig. 3 Relative errors of the Fresnel equations and the EMA model to obtain the complex refractive index as a function of the parameter σ/ζ for different materials in the case of n = 3.4294, σ = 0.05 μm and σ/λ = 0.0125: (a) k = 0; (b) k = 2 and (c) k = 5, respectively.
Fig. 4
Fig. 4 Relative errors of the Fresnel equations and the EMA model to obtain the complex refractive index as a function of the parameter σ/ζ for different materials in the case of k = 2, σ = 0.05 μm and σ/λ = 0.0125: (a) n = 2; (b) n = 3.4294 and (c) n = 5, respectively.
Fig. 5
Fig. 5 Scaling of the EMA model roughness with the parameter σ2/ζ for three materials with different extinction coefficients: (a) k = 0; (b) k = 2 and (c) k = 5, respectively. (n = 3.4294, σ/λ = 0.0125)
Fig. 6
Fig. 6 Scaling of the EMA model roughness with the parameter σ2/ζ for three materials with different refractive indices: (a) n = 2; (b) n = 3.4294 and (c) n = 5, respectively. (k = 2, σ/λ = 0.0125)
Fig. 7
Fig. 7 Scaling of the EMA model roughness with the parameter σ2/ζ corresponding to the cases in Table 2.

Tables (4)

Tables Icon

Table 1 Relationships between the EMA model roughness and morphological parameters of rough surfaces.

Tables Icon

Table 2 Relative errors of the Fresnel equations and the EMA model to obtain the complex refractive indices with different morphologies of rough surfaces. (n = 5.57, k = 0.387).

Tables Icon

Table 3 Thickness of rough layer estimated by the EMA model from SE measurements corresponding to the eighteen cases in Fig. 3 (n = 3.4294, σ = 0.05 μm, σ/λ = 0.0125).

Tables Icon

Table 4 Mathematical relationships between the thickness estimated by the EMA model and the morphological parameters for different materials.

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

H( p )H( p + q ) = σ 2 exp[ ( q 2 / ζ 2 ) ]
ρ=tanΨexp(iΔ)= r p r s =( E rp E ip )/( E rs E is )
f ε n ε eff ε n +2 ε eff +(1f) ε v ε eff ε v +2 ε eff =0
RMSE= 1 2 [ ( ψ FDTD ψ EMA ψ FDTD ) 2 + ( Δ FDTD Δ EMA Δ FDTD ) 2 ] ×100%
nik= { [ (1ρ) sin 2 θ (1+ρ)cosθ ] 2 + sin 2 θ } 1/2
α= | N N | | N | ×100%

Metrics