Skip to main content
SpringerLink
Log in

Fast and Reliable Measurement of Thin Film Thickness Profile Based on Wavelet Transform in Spectrally Resolved White-Light Interferometry

  • Regular Paper
  • Published:
International Journal of Precision Engineering and Manufacturing Aims and scope Submit manuscript

Abstract

We describe an improved version of spectrally resolved white-light interferometry that enables us to measure thin film thickness profile in a faster and more reliable way. Both the interferometric phase and the spectral reflectance of thin films are monitored at the same time in order to obtain accurate thickness and top surface height of thin films, leading to the complete reconstruction of the 3D tomographic profile of thin films. To do that, information related to the layers of thin films and top surface height of thin films must be decoupled and, based on wavelet transform, allowing it to be achieved without introducing two troublesome measurement steps or spectral carrier frequency. The experimental results for a prepared specimen showed that thin film thickness profile could be determined within an error range of 9 nm compared to well-known techniques. Due to the rigorous approach used in the proposed method, it is well suited for the in-line high-speed inspection of microelectronic devices produced in large quantities as is done in the semiconductor and flat-panel display industries.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

h :

top surface height of thin film deviated from reference plane

d :

thickness of thin film

I :

intensity of interference sampled on specimen

φ :

total phase distribution along spectral wavenumber

ψ :

phase variation due to multiple reflections within thin film layer

I 0 :

spectral intensity of two beams directly reflected from reference mirror and specimen

I 1 :

visibility function resulting from interference

k :

spectral wavenumber

R :

total reflection coefficient

A :

real part of total reflection coefficient

B :

imaginary part of total reflection coefficient

r 01 :

Fresnel reflection coefficients of top boundaries of thin films

r 12 :

Fresnel reflection coefficients of bottom boundaries of thin films

N :

refractive index of thin films

R ref :

spectral reflectance of reference specimen

G ref :

spectral density of reference specimen

G sam :

spectral density of unknown film thickness sample

R sam :

spectral reflectance of unknown film thickness sample

W :

continuous wavelet transform of signal

ψ*:

mother wavelet

a :

scale parameter that represents dilation of daughter wavelet

b :

translation factor that shifts peak of daughter wavelet

f b :

bandwidth parameter of Morlet wavelet

f 0 :

wavelet frequency of Morlet wavelet

References

  1. Kim, S.-W. and Kim, G.-H., “Thickness-Profile Measurement of Transparent Thin-Film Layers by White-Light Scanning Interferometry,” Applied Optics, Vol. 38, No. 28, pp. 5968–5973, 1999.

    Article  Google Scholar 

  2. Kim, D., Kim, S., Kong, H. J., and Lee, Y., “Measurement of The Thickness Profile of a Transparent Thin Film Deposited Upon a Pattern Structure with an Acousto-Optic Tunable Filter,” Optics Letters, Vol. 27, No. 21, pp. 1893–1895, 2002.

    Article  Google Scholar 

  3. Hwang, Y.-M., Yoon, S.-W., Kim, J.-H., Kim, S., and Pahk, H.-J., “Thin-Film Thickness Profile Measurement Using Wavelet Transform in Wavelength-Scanning Interferometry,” Optics and Lasers in Engineering, Vol. 46, No. 2, pp. 179–184, 2008.

    Article  Google Scholar 

  4. Ghim, Y.-S., Rhee, H.-G., Yang, H.-S., and Lee, Y.-W., “Thin-Film Thickness Profile Measurement Using a Mirau-Type Low-Coherence Interferometer,” Measurement Science and Technology, Vol. 24, No. 7, Paper No. 075002, 2013.

    Google Scholar 

  5. Ghim, Y.-S. and Kim, S.-W., “Fast, Precise, Tomographic Measurements of Thin Films,” Applied Physics Letters, Vol. 91, No. 9, Paper No. 091903, 2007.

    Google Scholar 

  6. You, J.-W., Kim, S., and Kim, D., “High Speed Volumetric Thickness Profile Measurement Based on Full-Field Wavelength Scanning Interferometer,” Optics Express, Vol. 16, No. 25, pp. 21022–21031, 2008.

    Article  Google Scholar 

  7. Ghim, Y.-S. and Kim, S.-W., “Spectrally Resolved White-Light Interferometry for 3D Inspection of a Thin-Film Layer Structure,” Applied Optics, Vol. 48, No. 4, pp. 799–803, 2009.

    Article  Google Scholar 

  8. Ghim, Y.-S. and Kim, S.-W., “Thin-Film Thickness Profile and Its Refractive Index Measurements by Dispersive White-Light Interferometry,” Optics Express, Vol. 14, No. 24, pp. 11885–11891, 2006.

    Article  Google Scholar 

  9. Jo, T., Kim, K., Kim, S., and Pahk, H., “Thickness and Surface Measurement of Transparent Thin-Film Layers Using White Light Scanning Interferometry Combined with Reflectometry,” Journal of the Optical Society of Korea, Vol. 18, No. 3, pp. 236–243, 2014.

    Article  Google Scholar 

  10. Kim, K., Kim, S., Kwon, S., and Pahk, H. J., “Volumetric Thin Film Thickness Measurement Using Spectroscopic Imaging Reflectometer and Compensation of Reflectance Modeling Error,” Int. J. Precis. Eng. Manuf., Vol. 15, No. 9, pp. 1817–1822, 2014.

    Article  Google Scholar 

  11. Kwon, S., Kim, N., Jo, T., and Pahk, H. J., “Critical Dimension Measurement of Transparent Film Layers by Multispectral Imaging,” Optics Express, Vol. 22, No. 14, pp. 17370–17381, 2014.

    Article  Google Scholar 

  12. Deng, Y., Wu, Z., Chai, L., Wang, C.-Y., Yamane, K., et al., “Wavelet-Transform Analysis of Spectral Shearing Interferometry for Phase Reconstruction of Femtosecond Optical Pulses,” Optics Express, Vol. 13, No. 6, pp. 2120–2126, 2005.

    Article  Google Scholar 

  13. Watkins, L., Tan, S., and Barnes, T., “Determination of Interferometer Phase Distributions by Use of Wavelets,” Optics Letters, Vol. 24, No. 13, pp. 905–907, 1999.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Seoul National University, Gwanak-ro 1, Gwanak-gu, Seoul, 08826, Republic of Korea

    Min-Gab Kim & Heui-Jae Pahk

Authors
  1. Min-Gab Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Heui-Jae Pahk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Heui-Jae Pahk.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, MG., Pahk, HJ. Fast and Reliable Measurement of Thin Film Thickness Profile Based on Wavelet Transform in Spectrally Resolved White-Light Interferometry. Int. J. Precis. Eng. Manuf. 19, 213–219 (2018). https://doi.org/10.1007/s12541-018-0024-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12541-018-0024-0

Keywords

Search

Navigation