OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 11 — May. 21, 2012
  • pp: 12184–12190
« Show journal navigation

Uncertainty improvement of geometrical thickness and refractive index measurement of a silicon wafer using a femtosecond pulse laser

Saerom Maeng, Jungjae Park, Byungsun O, and Jonghan Jin  »View Author Affiliations


Optics Express, Vol. 20, Issue 11, pp. 12184-12190 (2012)
http://dx.doi.org/10.1364/OE.20.012184


View Full Text Article

Acrobat PDF (930 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We have proposed a modified method to improve the measurement uncertainty of the geometrical thickness and refractive index of a silicon wafer. Because measurement resolution based on Fourier domain analysis depends on the spectral bandwidth of a light source directly, a femtosecond pulse laser having the broad spectral bandwidth of about 100 nm was adopted as a new light source. A phase detection algorithm in Fourier domain was also modified to minimize the effect related to environmental disturbance. Since the wide spectral bandwidth may cause a dispersion effect in the optical parts of the proposed interferometer, it was considered carefully through numerical simulations. In conclusion, the measurement uncertainty of geometrical thickness was estimated to be 48 nm for a double-polished silicon wafer having the geometrical thickness of 320.7 μm, which was an improvement of about 20 times that obtained by the previous method.

© 2012 OSA

1. Introduction

A well-known method to measure the geometrical thickness of a silicon wafer is to use two separate contact or noncontact sensors on both sides of the wafer. The difference between the two readings gives the geometrical thickness of the wafer [1

1. Y. Zhang, P. Parikh, P. Golubtsov, B. Stephenson, M. Bonsaver, J. Lee, and M. Hoffman, "Wafer shape measurement and its influence on chemical mechanical planarization," in Proceedings of the First International Symposium on Chemical Mechanical Planarization, I. Ali and S. Raghavan, eds. (The Electrochemical Society, Pennington, New Jersey, 1997), pp. 91-96.

,2

2. M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A New method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(Part 1, No. 1A), 38–39 (1999). [CrossRef]

]. For higher measurement precision, several research works based on optical interferometry have been proposed and realized [3

3. G. Coppola, P. Ferraro, M. Iodice, and S. De Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer,” Appl. Opt. 42(19), 3882–3887 (2003). [CrossRef] [PubMed]

5

5. G. D. Gillen and S. Guha, “Use of Michelson and Fabry-Perot interferometry for independent determination of the refractive index and physical thickness of wafers,” Appl. Opt. 44(3), 344–347 (2005). [CrossRef] [PubMed]

]. In 2010, KRISS also proposed and demonstrated a novel measurement method for extracting the geometrical thickness from the optical thickness using the optical comb of the mode-locked pulse laser [6

6. J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express 18(17), 18339–18346 (2010). [CrossRef] [PubMed]

]. This method had advantages, including high-speed measurement, separate determination of the refractive index and the geometrical thickness in a single operation, and traceability to the length and time standards. Measurement uncertainty was estimated to be about 1 μm, which can restrict potential applications requiring higher accuracy.

2. Basic principle

A spectrum of interference signal corresponding to an optical path difference, L can be expressed as Eq. (1),
I(f,L)=I0(f){1+cos(2πfLc)}=I0(f){1+cosφ(f,L)}
(1)
where I(f, L) is the intensity of interference spectrum, I0(f) is the spectrum of the light source, f is the optical frequency, c is the speed of light, and φ(f, L) is the phase to be measured. After taking the DFT (discrete Fourier Transform) of I(f, L), one peak in positive time domain can be found at the position of L/c, which represents the period of the interference signal in the spectral domain. The time resolution in Fourier domain, Δt, depends on the spectral bandwidth of the light source, N∙Δf , which is given by
Δt=1NΔf
(2)
where Δf is the sampling interval of the interference spectrum, N is the sampling number. A 10 times larger spectral bandwidth makes the time resolution 10 times higher, which leads to improvement of the combined uncertainty. To get the phase information corresponding to the optical path difference L, only the peak located in positive time domain is selected with a sampling window, and then inverse-Fourier transformed. The phase φ(f, L) can be extracted by taking the imaginary part of the logarithmic function of the inverse Fourier transform result, I'(f, L) like Eq. (3).

φ(f,L)=Im{ln(I(f,L))}
(3)

Finally, the optical path difference, L can be determined through the linear fit of φ(f, L) as shown in Eq. (4).

L=c2πdφdf=dφdk
(4)

3. Experiments and uncertainty evaluation

T=L2(L3L1)
(5)
N=L2T
(6)

Figure 3
Fig. 3 Fourier transformed results of two interference spectra, (a) Ray 1 and (b) Ray 2.
shows the Fourier transform results of the two interference spectra of Ray 1 and Ray 2 in Fig. 1, which were obtained by using the OSA with 215 sampling points and a sampling resolution of 0.003 nm in the spectral range of 1500 nm to 1600 nm in wavelength. As mentioned before, to make the interference of L2 dominant, the optical intensity of the reference arm was adjusted by tilting the reference mirror, M1 in Fig. 1 before inserting the silicon wafer. By reducing the optical intensity of the reference arm, an interference term having information of L2 became dominant to almost 60% of L3 in terms of peak amplitude, while LB - LA and LB + N·T - LA became relatively weak. The optical intensity of the reference arm was reduced to about 10% of the maximum intensity, which was measured by a conventional optical power meter. In addition, the peak for L2 also could be recognized practically by blocking the reference path and the LC path in Fig. 1.

Table 1

Table 1. Measurement results of a silicon wafer

table-icon
View This Table
| View All Tables
shows the measurement results of 10 repeated measurements. The averaged T and N of the silicon wafer were measured to be 320.699 μm and 3.621, respectively. Also, the standard deviation of T was calculated to be 26.7 nm, which is an improved result by about one order of magnitude in comparison with the precedent task.

Uncertainty for the refractive index of air was roughly about 10-6 under general laboratory conditions, which was a minor factor because of the short OPDs. Moreover, for L2, the uncertainty was not considered because of common path interferences between front and back surfaces of the silicon wafer. Wavelength uncertainty came from the wavelength accuracy of the OSA in use. According to the technical performance, the wavelength uncertainty of the OSA was given as 0.01 nm in the wavelength range of our use.

The combined uncertainty of the T, u(T) can be expressed as
u(T)=i=13(TLi)2u2(Li)+2i=12j=i+13(TLi)(TLj)u(Li,Lj)
(7)
where, i and j are integer numbers and u(Li, Lj) is a covariance between Li and Lj, which can be estimated by use of Eq. (8) using a correlation coefficient, r(Li, Lj).

u(Li,Lj)=r(Li,Lj)u(Li)u(Lj)
(8)

The correlation term, the second term of Eq. (7) was estimated to be 269 nm with the correlation coefficient of 0.99. Therefore, the combined uncertainty of the T of the silicon wafer, u(T) was determined to be 48 nm (k = 1) when measuring a silicon wafer having a T of 320.7 μm. The uncertainty of refractive index N is easily calculated from that of T using Eq. (6).

4. Conclusion

Acknowledgement

This work was supported in part by the National Program: Development of Application Technologies of Physical Measurement Standards (2012), KRISS.

References and links

1.

Y. Zhang, P. Parikh, P. Golubtsov, B. Stephenson, M. Bonsaver, J. Lee, and M. Hoffman, "Wafer shape measurement and its influence on chemical mechanical planarization," in Proceedings of the First International Symposium on Chemical Mechanical Planarization, I. Ali and S. Raghavan, eds. (The Electrochemical Society, Pennington, New Jersey, 1997), pp. 91-96.

2.

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A New method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(Part 1, No. 1A), 38–39 (1999). [CrossRef]

3.

G. Coppola, P. Ferraro, M. Iodice, and S. De Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer,” Appl. Opt. 42(19), 3882–3887 (2003). [CrossRef] [PubMed]

4.

P. Maddaloni, G. Coppola, P. De Natale, S. De Nicola, P. Ferraro, M. Gioffre, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer,” IEEE Photon. Technol. Lett. 16(5), 1349–1351 (2004). [CrossRef]

5.

G. D. Gillen and S. Guha, “Use of Michelson and Fabry-Perot interferometry for independent determination of the refractive index and physical thickness of wafers,” Appl. Opt. 44(3), 344–347 (2005). [CrossRef] [PubMed]

6.

J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express 18(17), 18339–18346 (2010). [CrossRef] [PubMed]

7.

G. Nam, C.-S. Kang, H.-Y. So, and J. Choi, “An uncertainty evaluation for multiple measurements by GUM, III: using a correlation coefficient,” Accredit. Qual. Assur. 14(1), 43–47 (2009). [CrossRef]

8.

D. F. Edwards and E. Ochoa, “Infrared refractive index of silicon,” Appl. Opt. 19(24), 4130–4131 (1980). [CrossRef] [PubMed]

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(140.3538) Lasers and laser optics : Lasers, pulsed

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: March 7, 2012
Revised Manuscript: April 19, 2012
Manuscript Accepted: May 2, 2012
Published: May 14, 2012

Citation
Saerom Maeng, Jungjae Park, Byungsung O, and Jonghan Jin, "Uncertainty improvement of geometrical thickness and refractive index measurement of a silicon wafer using a femtosecond pulse laser," Opt. Express 20, 12184-12190 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-11-12184


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Y. Zhang, P. Parikh, P. Golubtsov, B. Stephenson, M. Bonsaver, J. Lee, and M. Hoffman, "Wafer shape measurement and its influence on chemical mechanical planarization," in Proceedings of the First International Symposium on Chemical Mechanical Planarization, I. Ali and S. Raghavan, eds. (The Electrochemical Society, Pennington, New Jersey, 1997), pp. 91-96.
  2. M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A New method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys.38(Part 1, No. 1A), 38–39 (1999). [CrossRef]
  3. G. Coppola, P. Ferraro, M. Iodice, and S. De Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer,” Appl. Opt.42(19), 3882–3887 (2003). [CrossRef] [PubMed]
  4. P. Maddaloni, G. Coppola, P. De Natale, S. De Nicola, P. Ferraro, M. Gioffre, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer,” IEEE Photon. Technol. Lett.16(5), 1349–1351 (2004). [CrossRef]
  5. G. D. Gillen and S. Guha, “Use of Michelson and Fabry-Perot interferometry for independent determination of the refractive index and physical thickness of wafers,” Appl. Opt.44(3), 344–347 (2005). [CrossRef] [PubMed]
  6. J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express18(17), 18339–18346 (2010). [CrossRef] [PubMed]
  7. G. Nam, C.-S. Kang, H.-Y. So, and J. Choi, “An uncertainty evaluation for multiple measurements by GUM, III: using a correlation coefficient,” Accredit. Qual. Assur.14(1), 43–47 (2009). [CrossRef]
  8. D. F. Edwards and E. Ochoa, “Infrared refractive index of silicon,” Appl. Opt.19(24), 4130–4131 (1980). [CrossRef] [PubMed]

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.

Figures

Fig. 1 Fig. 2 Fig. 3
 
Fig. 4 Fig. 5
 

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited