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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 17 — Aug. 16, 2010
  • pp: 18339–18346
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Thickness and refractive index measurement of a silicon wafer based on an optical comb

Jonghan Jin, Jae Wan Kim, Chu-Shik Kang, Jong-Ahn Kim, and Tae Bong Eom  »View Author Affiliations


Optics Express, Vol. 18, Issue 17, pp. 18339-18346 (2010)
http://dx.doi.org/10.1364/OE.18.018339


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Abstract

We have proposed and demonstrated a novel method that can determine both the geometrical thickness and refractive index of a silicon wafer at the same time using an optical comb. The geometrical thickness and refractive index of a silicon wafer was determined from the optical thickness using phase information obtained in the spectral domain. In a feasibility test, the geometrical thickness and refractive index of a wafer were measured to be 334.85 μm and 3.50, respectively. The measurement uncertainty for the geometrical thickness was evaluated as 0.95 μm (k = 1) using a preliminary setup.

© 2010 OSA

1. Introduction

Silicon is an indispensable element of, and a foundation layer in, semiconductor wafer manufacturing. It is essential to know the geometrical thickness of a silicon wafer accurately for quality control and process management of the manufacturing process. In the emerging field of semiconductor packaging, which is realized by stacking multiple interconnected wafers, the geometrical thickness of a silicon wafer needs to be controlled as one of the most important parameters, because a variation in the thicknesses of each wafer layer can lead to serious problems, such as disconnections or undesired connections between chips, circuits, and wafers.

In general, the geometrical thickness can be measured using two types of metrological technique: contact and noncontact. Contact-type measurements use a stylus, and this is the most widely used method because of its ease of operation. However, it can damage the polished surface of a silicon wafer, and can scratch the surface. Noncontact-type measurements have been employed as an alternative method to avoid damage caused by mechanical contact. One of the noncontact methods uses dual focused laser lights on the front and back surfaces, based on the confocal principle. The geometrical thickness is measured by detecting the focusing positions on both surfaces. The repeatability of such measurements is reported to be < 1 μm in the range 30 μm to 10 mm [1

1. D. Schurz, W. W. Flack, and R. L. Hsieh, “Dual side lithography measurement, precision and accuracy,” Proc. SPIE 5752, 97–105 (2005).

]. Similarly, optical interferometers have also been adopted instead of dual focusing lenses for high precision measurements of wafer thickness [2

2. M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5856, 334–343 (2004). [CrossRef]

]. Although interferometry is a sensitive displacement measuring technique, rigorous alignment is required for developing its strong point, its high precision. In the same manner, capacitive sensors installed on the front and rear sides of a wafer can be utilized by monitoring the variation in an induced current. Such methods using dual detectors have the advantages of a simple setup and easy handling. However, they need careful alignment of the dual detectors. They need to be isolated from both electromagnetic and background noise, because the geometrical thickness is derived from other physical properties, such as the current, voltage, and intensity distribution in the case of noncontact methods, except for interferometry. Ultrasonic wave inspection and X-ray imaging have also been used for this application, but it has many practical difficulties because of the harsh handling conditions required [3

3. J. Pei, F. L. Degertekin, B. V. Honein, B. T. Khuri-Yakub, and K. C. Sarawat, “In-situ thin film thickness measurement using ultrasonics waves,” Proc. Ultrasonics Symposium, 1237–1240 (1994).

,4

4. Z. H. Lu, J. P. McCaffrey, B. Brar, G. D. Wilk, R. M. Wallace, L. C. Feldman, and S. P. Tay, “SiO2 film thickness metrology by x-ray photoelectron spectroscopy,” Appl. Phys. Lett. 71(19), 2764–2766 (1997). [CrossRef]

]. A propagation medium, usually water, is needed for ultrasonic waves, because ultrasonic waves are absorbed easily in air. Therefore, a wafer needs to be soaked in water to be measured using ultrasonic waves. Since hard X-rays with a wavelength of 0.1 nm to 0.01 nm can penetrate solid objects, they are employed for nondestructive inspections, such as in diagnostic radiography and crystallography, and because of the high photon energy of X-rays, shielding has to be considered for safety.

In this paper, we demonstrate a novel method that can measure both the geometrical thickness and the refractive index of a silicon wafer at the same time. To measure these properties of a silicon wafer, infrared light with a wavelength near to 1.5 μm was selected as the light source, because this wavelength could penetrate the silicon wafer and also be reflected from the surface of the silicon wafer. The optical comb generated by the phase modulation of a seed laser was exploited for the spectral domain analysis. Using the phase values obtained in the spectral domain, which is based on spectral interferometry [11

11. K.-N. Joo and S.-W. Kim, “Refractive index measurement by spectrally resolved interferometry using a femtosecond pulse laser,” Opt. Lett. 32(6), 647–649 (2007). [CrossRef] [PubMed]

,12

12. Y.-S. Ghim and S.-W. Kim, “Spectrally resolved white-light interferometry for 3D inspection of a thin-film layer structure,” Appl. Opt. 48(4), 799–803 (2009). [CrossRef] [PubMed]

], the geometrical thickness was determined over a time period without using any mechanical moving parts or knowledge on the refractive index of the wafer. This led to high-speed measurements, and it did not require either soaking the wafer or the need to shield the measurement system. Since the optical thickness is determined using the optical wavelength, it can be traceable to the definition of meter. A single operation can minimize mechanical errors, environment errors, and vibration. A double-sided polished wafer having a nominal geometrical thickness of 335 μm was measured or the feasibility test was performed.

2. Thickness and refractive index measurements

The intensity of the interference signal having an optical path difference (OPD) of Δ can be expressed by
I(Δ)=I0(1+γcos(2πcΔf))
(1)
where, I0is the background intensity of the light source in use, γ is the visibility, c is the speed of light in a vacuum, and f is the optical frequency of the light source. In general, an interferometer using a monochromatic light needs additional steps, such as translating a reference mirror to obtain the OPD of the phase value of a sinusoidal signal. When a light source having wide-spectral bandwidth is used, the OPD can be extracted directly from the period of the interference signal obtained in the spectral domain. Since the period, P, of the interference signal is in the spectral domain, then the value of P can be determined from a discrete Fourier transform (DFT), the OPD, and the value of Δ is given by [12

12. Y.-S. Ghim and S.-W. Kim, “Spectrally resolved white-light interferometry for 3D inspection of a thin-film layer structure,” Appl. Opt. 48(4), 799–803 (2009). [CrossRef] [PubMed]

,13

13. L. M. Smith and C. C. Dobson, “Absolute displacement measurements using modulation of the spectrum of white light in a Michelson interferometer,” Appl. Opt. 28(16), 3339–3342 (1989). [CrossRef] [PubMed]

]

Δ=cP
(2)

In our work, an optical comb was adopted as a wide-spectrum light source having a frequency stability of 10−8–10−9 to realize high-speed measurements. The wavelength of the light source was chosen in the infrared regime near to 1550 nm, so that the light could partially pass through a silicon wafer for noncontact measurements.

Figure 1
Fig. 1 Optical layout of the measurement system. (EDFA: Er doped fiber amplifier, BS: beam splitter, M: mirror, CL: collimation lens, OSA: optical spectrum analyzer)
shows the optical layout of the measurement system. The light source consisted of a distributed feed-back (DFB) laser (Toptica, DL DFB), two erbium-doped fiber amplifiers (Luxpert, LXI2000), and a comb generator (OptoComb, WTAS-01). The DFB laser was a seed laser with a typical linewidth of 500 kHz to 4 MHz at 5 μs, which corresponds to 10−8~10−9 in terms of frequency stability. The optical comb was generated by the modulating phase of an amplified seed laser having an optical power of 20 mW. The spectral bandwidth of the light source was ~20 nm, with the center wavelength at 1540.2 nm, shown as Fig. 2(a)
Fig. 2 Spectrum of the optical comb in use: (a) full spectrum of the optical comb, (b) spectrum in the wavelength range 1535 to 1545 nm.
. The pulse train emitted from the light source had a repetition rate of 25 GHz with a pulse duration of 0.5 ps. Figure 2(b) shows the spectrum of the optical comb in the wavelength range of 1535 to 1545 nm. The mode spacing was equal to the repetition rate of 25 GHz, which corresponded to ~0.2 nm in terms of the wavelength. The repetition rate was locked to a Rb-reference clock (Novatech, 2975AR) having a frequency stability of 10−11 at 10 s. The pulses emitted from the light source were divided by a beam splitter (BS), and then reflected from the reference and the front and rear sides of a silicon wafer and a mirror. The reflected light was recombined and formed the interference signal composed of the reference and the front side, the reference (M1) and the rear side, the reference and the mirror (M2), and other interference, including the interference between the front and the rear sides of the wafer. The interference signals were detected using an optical spectrum analyzer (OSA) for the spectral domain analysis.

The interference signal traveling along Ray 1 in Fig. 1 contains information about the optical path difference, which is expressed as L1 + T + L2 – L0 (≡ A). The light traveling along Ray 2 passes through the silicon wafer and a part of the light is reflected from the front and rear surfaces of the silicon wafer. The interference signal traveling along Ray 2 in Fig. 1 also contains information on several optical path differences, which correspond to L1 – L0 (≡ B), L1 + N·T – L0 (≡ C), where N is the refractive index of the silicon wafer, L1 + N·T + L2 – L0 (≡ D), and other interference, which is too weak to be observed. Finally, the thickness and refractive index, T and N, can be determined from Eq. (3) and Eq. (4).

T=(CB)(DA)
(3)
N=(CB)/T
(4)

To extract optical path differences, the values of A, B, C, and D from the interference signals traveling along Rays 1 and 2 in a single operation, and the two optical spectra of the interference signals traveling along Rays 1 and 2 were measured using an OSA. Since the value of the OPD could be determined from Eq. (2), the obtained interference spectra were Fourier-transformed to obtain their periods.

Each interference spectrum was sampled from in the wavelength range 1535 to 1555 nm within 8196 points, which led to a wavelength resolution of ~0.004 nm. Within the wavelength range used, the wavelength uncertainty of the OSA (Agilent 86142B) was about 0.01 nm after calibration using stabilized light sources.

Table 1

Table 1. Measurement Results of a Silicon Wafer

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shows measurement results obtained from a double-sided polished wafer. The thickness and the refractive index of the silicon wafer were measured to be 334.85 μm and 3.50, respectively. The standard deviation of the geometrical thickness and refractive index of the silicon wafer from 10 repeated measurements were 0.49 μm and 0.004, respectively. Even if the measurement resolution was not the best among the other techniques mentioned in Section 1, our technique has the advantage of measuring both the geometrical thickness and the refractive index of the silicon wafer at the same time in a single operation. In the near future, we plan to improve the performance of the measurement system by extending the spectral bandwidth of the light source. This can be achieved using a femtosecond pulse laser with a photonic crystal fiber.

3. Discussion and summary

The measurement resolution of the geometrical thickness was achieved by determining the period of the interference signal in the Fourier domain. Since the periods were obtained using a discrete Fourier transform (DFT), the measurement resolution depended on the spectral bandwidth of the interference spectrum. In this work, the resolution of the DFT was 2.64 × 10−13 s, the reciprocal of the spectral bandwidth of the light source used was 3.80 THz, which could resolve the optical thickness to 40 μm. For better resolution, the indices of the peak locations in the Fourier domain were calculated to the third decimal place using a second-order curve fitting of the interference spectra within the full-width half maximum values of the peaks, which corresponded to a length of 0.05 μm. In addition, 8196 zeros were added to the raw spectrum data to improve the peak detection resolution in the Fourier domain. We expect to improve this by exploiting a femtosecond pulse laser with a spectral bandwidth that can be extended to several hundred nanometers using the nonlinear self-phase modulation effect. For example, a measurement resolution of 5 nm can be achieved by simply replacing the light source with a femtosecond laser having a spectral bandwidth of 300 nm.

Table 2. Uncertainty Evaluation

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The measurement uncertainty of the geometrical thickness was evaluated according to ISO/IEC 98-3 (GUM). The uncertainty of the refractive index of air is usually 10−6 under laboratory conditions. The uncertainty of the wavelengths of the OSA was 0.01 nm in the wavelength range 1480 to 1570 nm. The contribution to the uncertainty from these two uncertainty sources was around 10 nm in length for T = 334.85 μm. The uncertainty of the optical path differences of A, B, C, and D was mostly contributed by the uncertainty of the DFT algorithm and the measurement repeatability. The uncertainty of the DFT algorithm was evaluated using computer-generated ideal interference spectra. The ideal spectra had optical path differences of 0.5 to 3.5 mm with a step of 0.1 mm, whose errors after the DFT calculations were < 0.10% when optical path difference was > 1.0 mm. The errors increased to 0.70% for shorter optical path differences below 1.0 mm, because the interference spectrum had only a few periods within the spectral bandwidth of the light source, 20 nm. By adjusting the position of the reference, the mirror, and the silicon wafer, the optical path differences of A, B, C, and D could be > 1.0 mm to minimize the error caused by the DFT algorithm. In this work, the values of A, B, C, and D were selected to be 1.30 mm, 2.32 mm, 1.15 mm, and 0.47 mm, respectively.

The uncertainty attributed to random effects was evaluated by repeated measurements of A, B, C, and D. Therefore, the uncertainty of the optical path differences of A, B, C, and D was estimated to be 1.06 μm, 0.97 μm, 0.73 μm, and 1.17 μm, respectively. Since A, B, C, and D are partially correlated, the correlation terms were taken into account in evaluating the uncertainty of T. Because the uncertainties of the optical path differences were almost the same, the correlation coefficient, r, can be approximated by [14

14. 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]

]
r=uB(x)2/(uA(x)2+uB(x)2)
(5)
where uA(x)and uB(x) denote Type A and Type B uncertainties for the input quantity, x.

The correlation coefficient was calculated to be 0.80. From Eq. (1), with the correlation coefficient, the uncertainty of the coupling between A, B, C, and D was determined to be –1.75 μm. Finally, the uncertainty of the geometrical thickness was evaluated to be 0.95 μm (k = 1) for a 334.85 μm silicon wafer. In this study, the most dominant uncertainty factor was the DFT algorithm used. The uncertainty can be decreased by increasing the sampling number and the length of the raw data through adopting a mode-locked femtosecond pulsed laser that has a wide spectral bandwidth. The measurement repeatability can be improved by stabilizing the environmental conditions.

In this paper, a new method for measuring both the geometrical thickness and the refractive index of a silicon wafer at the same time was proposed and realized. It required no additional measurement steps, such as rotating or translating the sample, which led to high-speed measurements. In general, optical path differences should be close to zero for a light source having a wide spectrum due to its short coherence length. However, by adopting a mode-locked laser instead of a wide spectral light source, we could observe periodic interference signals because of pulse-to-pulse interference, which meant that there was interference between the different pulses. This makes a flexible measuring system equivalent to a nonequal path interferometer. Moreover, in the spectral domain, the optical path differences could be obtained, even if the pulses do not meet in the time domain. The optical comb can be considered as a combination of monochromatic light sources having well-defined wavelengths. It is similar to an extension of multiwavelength interferometry. Based on this principle, the geometrical thickness could be determined from the four optical path differences in the interferometer, which are measured in the spectral domain analysis. The geometrical thickness of a double side polished wafer was measured to be 334.85 μm, with a measurement uncertainty of 0.95 μm (k = 1). The uncertainty of the DFT algorithm, which is the most dominant uncertainty factor, can be reduced by adopting a mode-locked femtosecond pulse laser having a spectral bandwidth of several hundred nanometers.

Acknowledgement

This work was supported in part by the National Program: 3-dimensional Profile Measurement Technology on Microscopic Integrated Structures, KRISS.

References and links

1.

D. Schurz, W. W. Flack, and R. L. Hsieh, “Dual side lithography measurement, precision and accuracy,” Proc. SPIE 5752, 97–105 (2005).

2.

M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5856, 334–343 (2004). [CrossRef]

3.

J. Pei, F. L. Degertekin, B. V. Honein, B. T. Khuri-Yakub, and K. C. Sarawat, “In-situ thin film thickness measurement using ultrasonics waves,” Proc. Ultrasonics Symposium, 1237–1240 (1994).

4.

Z. H. Lu, J. P. McCaffrey, B. Brar, G. D. Wilk, R. M. Wallace, L. C. Feldman, and S. P. Tay, “SiO2 film thickness metrology by x-ray photoelectron spectroscopy,” Appl. Phys. Lett. 71(19), 2764–2766 (1997). [CrossRef]

5.

A. Hirai and H. Matsumoto, “Measurement of group refractive index wavelength dependence using a low-coherence tandem interferometer,” Appl. Opt. 45(22), 5614–5620 (2006). [CrossRef] [PubMed]

6.

M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and M. Hashimoto, “Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry,” Opt. Lett. 23(12), 966–968 (1998). [CrossRef]

7.

A. Hirai and H. Matsumoto, “Low-coherence tandem interferometer for measurement of group refractive index without knowledge of the thickness of the test sample,” Opt. Lett. 28(21), 2112–2114 (2003). [CrossRef] [PubMed]

8.

Y. Hori, A. Hirai, K. Minoshima, and H. Matsumoto, “High-accuracy interferometer with a prism pair for measurement of the absolute refractive index of glass,” Appl. Opt. 48(11), 2045–2050 (2009). [CrossRef] [PubMed]

9.

D. F. Murphy and D. A. Flavin, “Dispersion-insensitive measurement of thickness and group refractive index by low-coherence interferometry,” Appl. Opt. 39(25), 4607–4615 (2000). [CrossRef]

10.

D. I. Farrant, J. W. Arkwright, P. S. Fairman, and R. P. Netterfield, “Measuring the thickness profiles of wafers to subnanometer resolution using Fabry-Perot interferometry,” Appl. Opt. 46(15), 2863–2869 (2007). [CrossRef] [PubMed]

11.

K.-N. Joo and S.-W. Kim, “Refractive index measurement by spectrally resolved interferometry using a femtosecond pulse laser,” Opt. Lett. 32(6), 647–649 (2007). [CrossRef] [PubMed]

12.

Y.-S. Ghim and S.-W. Kim, “Spectrally resolved white-light interferometry for 3D inspection of a thin-film layer structure,” Appl. Opt. 48(4), 799–803 (2009). [CrossRef] [PubMed]

13.

L. M. Smith and C. C. Dobson, “Absolute displacement measurements using modulation of the spectrum of white light in a Michelson interferometer,” Appl. Opt. 28(16), 3339–3342 (1989). [CrossRef] [PubMed]

14.

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]

OCIS Codes
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.6200) Instrumentation, measurement, and metrology : Spectrometers and spectroscopic instrumentation
(130.3060) Integrated optics : Infrared
(140.3538) Lasers and laser optics : Lasers, pulsed

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: July 9, 2010
Revised Manuscript: August 2, 2010
Manuscript Accepted: August 2, 2010
Published: August 12, 2010

Citation
Jonghan Jin, Jae Wan Kim, Chu-Shik Kang, Jong-Ahn Kim, and Tae Bong Eom, "Thickness and refractive index measurement of a silicon wafer based on an optical comb," Opt. Express 18, 18339-18346 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-17-18339


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References

  1. D. Schurz, W. W. Flack, and R. L. Hsieh, “Dual side lithography measurement, precision and accuracy,” Proc. SPIE 5752, 97–105 (2005).
  2. M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5856, 334–343 (2004). [CrossRef]
  3. J. Pei, F. L. Degertekin, B. V. Honein, B. T. Khuri-Yakub, and K. C. Sarawat, “In-situ thin film thickness measurement using ultrasonics waves,” Proc. Ultrasonics Symposium, 1237–1240 (1994).
  4. Z. H. Lu, J. P. McCaffrey, B. Brar, G. D. Wilk, R. M. Wallace, L. C. Feldman, and S. P. Tay, “SiO2 film thickness metrology by x-ray photoelectron spectroscopy,” Appl. Phys. Lett. 71(19), 2764–2766 (1997). [CrossRef]
  5. A. Hirai and H. Matsumoto, “Measurement of group refractive index wavelength dependence using a low-coherence tandem interferometer,” Appl. Opt. 45(22), 5614–5620 (2006). [CrossRef] [PubMed]
  6. M. Haruna, M. Ohmi, T. Mitsuyama, H. Tajiri, H. Maruyama, and M. Hashimoto, “Simultaneous measurement of the phase and group indices and the thickness of transparent plates by low-coherence interferometry,” Opt. Lett. 23(12), 966–968 (1998). [CrossRef]
  7. A. Hirai and H. Matsumoto, “Low-coherence tandem interferometer for measurement of group refractive index without knowledge of the thickness of the test sample,” Opt. Lett. 28(21), 2112–2114 (2003). [CrossRef] [PubMed]
  8. Y. Hori, A. Hirai, K. Minoshima, and H. Matsumoto, “High-accuracy interferometer with a prism pair for measurement of the absolute refractive index of glass,” Appl. Opt. 48(11), 2045–2050 (2009). [CrossRef] [PubMed]
  9. D. F. Murphy and D. A. Flavin, “Dispersion-insensitive measurement of thickness and group refractive index by low-coherence interferometry,” Appl. Opt. 39(25), 4607–4615 (2000). [CrossRef]
  10. D. I. Farrant, J. W. Arkwright, P. S. Fairman, and R. P. Netterfield, “Measuring the thickness profiles of wafers to subnanometer resolution using Fabry-Perot interferometry,” Appl. Opt. 46(15), 2863–2869 (2007). [CrossRef] [PubMed]
  11. K.-N. Joo and S.-W. Kim, “Refractive index measurement by spectrally resolved interferometry using a femtosecond pulse laser,” Opt. Lett. 32(6), 647–649 (2007). [CrossRef] [PubMed]
  12. Y.-S. Ghim and S.-W. Kim, “Spectrally resolved white-light interferometry for 3D inspection of a thin-film layer structure,” Appl. Opt. 48(4), 799–803 (2009). [CrossRef] [PubMed]
  13. L. M. Smith and C. C. Dobson, “Absolute displacement measurements using modulation of the spectrum of white light in a Michelson interferometer,” Appl. Opt. 28(16), 3339–3342 (1989). [CrossRef] [PubMed]
  14. 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]

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