Open Access
Add to BibSonomy
Abstract
We propose a snapshot spectroscopic ellipsometry and its applications for real-time thin-film thickness measurement. The proposed system employs an interferometric polarization-modulation module that can measure the spectroscopic ellipsometric phase for thin-film deposited on a substrate with a measurement speed of around 20 msec. It requires neither moving parts nor time dependent modulation devices. The accuracy of the proposed interferometric snapshot spectro-ellipsometer is analyzed through comparison with commercial equipment results.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
For the last a few decades, thin film and nano-pattern measurement technology has been playing an important role in process monitoring and control of semiconductor manufacturing industry. Direct thin film measurement techniques based on scanning imaging technique such as SEM and AFM have their own distinct advantages of general tomographic solution with high precision [1–3]. However, such methods possess inherent shortcomings of destructiveness of measured sample and time-consuming measurement process. Therefore, they are usually not suitable for real-time in-line monitoring. For such industrial demands on high speed and non-destructive nano-metrology solutions, various optical approaches have been suggested for mass-production semiconductor manufacturing process monitoring fields due to their non-destructiveness and fast measurement capabilities [4–8]. Among them, the most precise and robust optical measurement solution for thin film and periodic nano-pattern structure measurements has been spectroscopic ellipsometry (SE) [9–11].
In spectroscopic ellipsometry, optical and geometrical properties of thin films and nano-pattern can be obtained by measuring the change of the polarization state of the light reflected from the measured object. Determination of the changed state of polarization is essential in ellipsometry. The change of the polarization state after reflection is directly associated with the measured ellipsometric parameters Ψ and Δ which depend sensitively on film thickness, nano-pattern shape and the refractive index of the film materials. Nowadays, various different type of commercialized spectroscopic ellipsometer system with highly reliable and precise measurements is available in the market. Most of them, however, require complicated mechanical rotation of a polarizer or a wave plate, or electric phase modulation devices to measure the state of polarization of the reflected light. In that reason, SE technology has not been regarded as a suitable solution for real time in-line monitoring and there always has been an increasing demand on faster spectroscopic ellipsometry solutions. Recently, various new designs of spectroscopic ellipsometer based on interferometry have been reported by some different groups [12–20]. And also, some attempts for simultaneous film thickness and 3D profile measurements based on interferometry have been demonstrated [21–23]. More recently, our group proposed an interferometric spectro-polarization measurement technique based on dual interfered spectra scheme for spectral Stoke vector measurements [24,25].
In this work, we describe a novel interferometric snapshot spectro-ellipsometer and its application for thickness measurement of thin film objects. The proposed system can provide a compact, low-cost, high speed solution, and it allows one to characterize thin film structures accurately in real-time speed. This system is strongly robust to the external vibration since it is based on a snapshot scheme which has no moving parts. After describing the unique design of the proposed interferometric snapshot spectro-ellipsometer, detail theoretical background on spectral ellipsometric parameter extraction procedures is explained. Lastly, the snapshot capability is demonstrated experimentally by using thin-film objects with different thickness.
2. Theoretical analysis
2.1. Instrumentation
The schematic of the proposed interferometric spectro-ellipsometer setup is portrayed in Fig. 1. It requires no moving parts to extract the spectroscopic ellipsometric parameters. It features four simple parts; a collimating optics with a Tungsten-Halogen lamp as a broadband light source, a reflective measured object part, an interferometric polarization-modulation module based on a Mach-Zehnder interferometric scheme, and a perpendicular linearly polarized dual-spectrum sensing module. The broadband light source is connected to the optical fiber and passes through the collimating optics to generate a linearly polarized input beam to the reflective thin film object. The object is placed at an incidence angle of 45 degrees for the feasibility setup. The reflected beam enters the modified Mach-Zehnder interferometer part employing two cube type non-polarizing beam splitters, two reflection plane mirrors, two knife-edge right-angle prism mirrors, and two linear polarizers. The interfered wave modulated by the two polarizers passes to the dual spectrum sensing module. The dual spectrum sensing module comprised of a non-polarizing beam splitter, two perpendiculars linearly polarized Glan-Thompson polarizers, two parabolic mirrors, two multimode optical fibers with a diameter of 1000μm and two 2047-pixel array sensor spectrometers with the spectral measurement range from 395 nm to 648 nm.
Fig. 1 Schematic of the proposed interferometric snapshot spectroscopic ellipsometer with the real-time spectral ellipsometric phase measurement capability.
The optical path difference between the arms of the Mach-Zehnder interferometer is set to around 30 to 50μm, and it creates the high spectral carrier frequency used for extracting the spectral phase information. Once the optical path difference in the interferometric part is set at a certain condition to generate the spectral interference fringes, it remains fixed throughout the entire measurement process.
2.2. Measurement method
In spectroscopic ellipsometry, characteristics of a reflection surface determine the polarization state of the reflected optical field and we extract important information such as film thickness, material refractive index and periodic nano-pattern 3D shape by analyzing the measured ellipsometric parameters. Let us represent the linearly polarized input light wave to the reflective object as Ein and the complex wave obtained after the reflection by the SiO2 thin-film deposited on Si wafer as a complex reflection coefficient rSiO2/Si, as follows.
Here, k is a wave number defined by 2π/λ, and j denotes complex operator which obeys the following rules j2 = −1. u and v represent the amplitude of the incident beam along x- and y- axis, respectively. η and ξ represent the phase of light waves in x- and y-axis, respectively. |rp,sSiO2/Si| and δp,sSiO2/Si , respectively, are the reflectance and the phase change on reflection for p- and s- polarizations.The reflected light wave passes through the interferometric polarization-modulation module, and the output optical fields are represented as follows [25].
Here, ED(k) and EM(k) represent the complex wave traveling through the direct path where no polarization modulation occurs and the modulation path with the two linear polarizers, respectively. The optical path difference between zD and zM generates the high-frequency spectral interference by which the input complex wave vector of the thin-film object is extracted. B1 and B2 correspond to the Jones matrix of the non-polarizing beam splitters used in the Mach-Zehnder interferometer. M1, M2, M3, and M4 represent the Jones matrix of the 4 reflection mirror surfaces utilized in the direct path with their complex reflection coefficients cM1, cM2, cM3, and cM4, respectively. M’1 and M’2 denote the Jones matrix of the reflection mirrors utilized in the modulation path, cM’1 and cM’2 represent their complex reflection coefficients, respectively. Multiplication of the complex reflection coefficients of mirror surfaces in the direct and modulation paths are defined as α = cM1cM2cM3cM4, and β = cM’1cM’2, respectively. P1(90°) and P2(45°) are referred as Jones matrices of the linear polarizers P1 and P2 with rotation angles of 90° and 45°, respectively. The polarizer P1 aligned with the rotation angle of 90° mainly modulates the light outgoing from the Mach-Zehnder interferometer, which enables the proposed scheme to work [25]. The role of the polarizer P2 oriented at 45° is not critical to the overall performance of the proposed scheme. However, we get lower contrast of the spectral interferometric signals when the polarizer P2 is not used. To maximize the spectrally interfered signals contrast, we set P2 to be around 45°.The interference between the beams of the interferometric polarization-modulation module can be resolved by the dual spectrometers as the interfered spectra IpSiO2/Si(k) and IsSiO2/Si(k) expressed as,
AndHere, EDx,y(k) and EMx,y(k) denote x- and y- components of the complex waves ED(k) and EM(k), respectively. γp(k) and γs(k) represent the spectral coherence functions. ΦpSiO2/Si(k) and ΦsSiO2/Si(k) correspond to the total phase functions for the SiO2 thin film deposited on Si wafer for p- and s- polarizations. ϕp and ϕs signify unknown additional phase shift terms generated by the spectral interferometric polarization-modulation module used simultaneously for the p- and s- spectral polarization channels, respectively.To measure the spectral ellipsometric parameter Δ(k), first we need to record the dual interfered spectra IpSiO2/Si(k) and IsSiO2/Si(k). Here, some modification is made to obtain a new sinusoidal shape by measuring |EDx|, |EMx|, |EDy| and |EMy| that can provide more reliable analysis. For p- and s- polarization channels, we modify the interfered spectra by subtracting |EDx|2 and |EMx|2 (|EDy|2 and |EMy|2, resp.) from the IpSiO2/Si(k) (IsSiO2/Si(k), resp.). Then the result is divided by 2|EDx||EMx| (2|EDy||EMy|, resp.) as follows.
To attain the s-polarized modified spectral data, Eq. (7) can be used just by replacing the subscript p- with s-. The next step is to apply the Fast Fourier Transform (FFT) algorithm [25,26] to the both modified spectra IpSiO2/Si(k)mod and IsSiO2/Si(k)mod. Then, we move to the spectral frequency domain for filtering out the DC component and windowing the spectral frequency domain data containing the object information. Lastly, inverse Fast Fourier Transform algorithm is applied for the windowed spectral frequency domain data which can provide subsequently the wrapped phase function ΦpSiO2/Si(k) (ΦsSiO2/Si(k), resp.). We can obtain the final spectral phase difference between the p- and s-channel for the SiO2 thin film object as follows.2.3. Calibration and spectral ellipsometric phase extraction
The proposed measurement method must be calibrated to obtain accurate results. It is calibrated by using the same spectral ellipsometric phase difference between p- and s-polarization of a bare Si wafer at the same incidence angle of 45 degrees. Equations (9) and (10) represent the interfered spectra IpSi(k) and IsSi(k) for the bare Si wafer object measured simultaneously by the dual spectrum sensing module, respectively.
Following the measurement procedure described in the previous subsection, we obtain the wrapped total phase functions ΦpSi(k) and ΦsSi(k). And then, we can calculate the spectral phase difference for the bare Si wafer as follows.Here, we see that the extracted spectral phase difference for the bare Si wafer configuration still has some unknown factors which are impossible to extract since they are inherent systematic errors caused by complicated polarization effects of all optical components used in the entire system. However, we can remove those unknown factors by subtracting Eq. (11) from Eq. (8) as depicted as follows.Note that C(k) contains no systematic unknown errors which are included in A(k) and B(k) although it contains the spectral ellipsometric phase difference term of the bare Si wafer. Finally, however, we can extract Δ(k) by subtracting the measured ΔSimeasured(k) of the bare Si wafer by using a commercial SE system as follows.3. Experimental results
To prove the feasibility of the proposed interferometric snapshot spectroscopic ellipsometry, we have conducted experiments by using a Si bare wafer and three different SiO2 thin film samples with different thicknesses deposited on silicon wafers as illustrated in Fig. 1. For the calibration step, we first placed the bare Si wafer at an incidence angle of 45° (as shown in Fig. 1). The dual spectra IpSi(k) and IsSi(k) are recorded by the interferometric polarization-modulation module. Figure 2(a) shows the simultaneously captured dual interfered spectra of the bare Si wafer. The modified spectra IpSi(k)mod and IsSi(k)mod described in Eq. (7) are illustrated in Fig. 2(b). By using the Fast Fourier transform method, we have extracted the wrapped total phase functions ΦpSi(k) and ΦsSi(k) as illustrated in Fig. 3(a). Figure 3(b) represents the spectral phase difference between the p- and s- polarized waves for the bare Si wafer which is defined as B(k) in Eq. (11). B(k) is measured only one time as a pre-preparation step for thin film thickness measurements.
Fig. 2 Raw spectral intensity data for bare Si wafer (p-polarized: solid line and s-polarized: dotted line)
Fig. 3 Spectral phase functions of Si wafer: (a) wrapped total phase functions ΦpSi(k) and ΦsSi(k) (p-polarized: solid line and s-polarized: dotted line), and (b) phase difference B(k) for the bare Si wafer.
As described, the bare Si wafer measurement can be regarded as a calibration step. Now, spectroscopic ellipsometric parameter measurement of any thin film object is ready. By replacing with SiO2 thin film object (with nominal thicknesses of 100nm, 200nm, and 500nm) for the same incidence angle, we measure the dual interfered spectra IpSiO2/Si(k) and IsSiO2/Si(k) simultaneously as illustrated in Fig. 4.
Fig. 4 Measured interfered dual-spectra for SiO2 films deposited on Si wafer: (a) 100nm, (b) 200nm, and (c) 500nm. (p-polarized: solid line and s-polarized: dotted line)
According to Eq. (13), Fig. 5 shows the measured spectral phase difference Δ(λ) from the center area of the three SiO2 thin film samples. The measurement accuracy of the proposed system is estimated through comparisons with results obtained by a commercial SE system. Figure 5 demonstrates that the proposed snapshot spectro-ellipsometry can provide a highly accurate Δ(k) measurement capability. The measurement time of 20msec suggested in this paper for extracting the spectroscopic ellipsometric parameter Δ(k) includes all processing time required for averaging and signal processing steps. Through this procedure, the proposed snapshot SE can provide the spectroscopic ellipsometric parameter Δ(k) with a precision of around 1 degree.
Fig. 5 Comparison of measured Δ(λ) for the SiO2 thin film objects with nominal thickness: (a) 100nm, (b) 200nm, and (c) 500nm (Solid lines correspond to the results obtained by using the proposed snapshot SE system, and dotted lines represents those measured by using a commercialized SE system).
To determine the thickness of the SiO2 thin film on a Si wafer, we used the multi-reflection theory based on the iterative Levenberg-Marquardt fitting algorithm [27] as illustrated in Fig. 6. The thicknesses of the SiO2 films calculated by this algorithm for all three samples are listed in Table 1.
Fig. 6 Least square fitting results for the Δ(λ) measured by using the proposed snapshot SE system for: (a) 100nm, (b) 200, and (c) 500nm.
Table 1. Thicknesses measurement results of the SiO2 thin film samples by a commercial SE and the proposed snapshot SE system.
Figure 5 shows that the proposed interferometric snapshot spectroscopic ellipsometer system can provide a highly accurate and reliable measurement capability for thin film thickness measurement application. The slight discrepancies comes mainly due to the lack of precise rotation angle alignment of the polarizing optics used in the proposed system since all the polarizing optics alignment has been performed manually in this work. Moreover, a slight systematic error can be caused by the signal processing performed in the spectral Fourier-domain.
4. Conclusion
High speed interferometric snapshot spectro-ellipsometer system with a real-time spectral ellipsometric phase measurement capability and its application for thin-film thickness measurements has been described. The proposed scheme provides a real time spectro-ellipsometric phase measurement solution for visible wavelength range. Highly stable system repeatability and high measurement speed makes the proposed system ideal for real-time process monitoring and control in various industrial applications.
Funding
National Research Foundation of Korea (NRF) grant funded by the Korean Government (MSIP) (2015R1A5A1037668 and 2015R1A2A2A11001529).
References and links
1. A. J. Gonzales and E. M. Philofsky, “Applications of scanning electron microscopy to thin film on semiconductor devices,” Proc. IEEE 59(10), 1429–1433 (1971). [CrossRef]
2. R. F. M. Lobo, M. A. Pereira-da-Silva, M. Raposo, R. M. Faria, O. N. Oliveira Jr, M. A. Pereira-da-Silva, and R. M. Faria, “In situ thickness measurements of ultra-thin multilayer polymer films by atomic force microscopy,” Nanotechnology 10(4), 389–393 (1999). [CrossRef]
3. A. K. Petford-Long and A. N. Chiaramonti, “Transmission electron microscopy of multilayer thin films,” Annu. Rev. Mater. Res. 38(1), 559–584 (2008). [CrossRef]
4. E. Chason and T. M. Mayer, “Thin film and surface characterization by specular X-ray reflectivity,” Crit. Rev. Solid State Mater. Sci. 22(1), 1–67 (1997). [CrossRef]
5. G. E. Jellison Jr., “The calculation of thin film parameters from the spectroscopic ellipsometry data,” Thin Solid Films 40, 290–291 (1996).
6. G. Tompkins and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User's Guide (Wiley, 1999).
7. D. Roy, “Optical Characterization of Multi-layer Thin Films Using the Surface Plasmon Resonance Method: A Six Phase Model Based on the Krestchmann Formalism,” Opt. Commun. 200(1-6), 119–130 (2001). [CrossRef]
8. W. Yang, J. Hu, R. Lowe-Webb, R. Korlahalli, D. Shivaprasad, H. Sasano, W. Liu, and D. S. Mui, “Line-profile and critical dimension measurements using a normal incidence optical metrology system,” in Advanced Semiconductor Manufacturing 2002 IEEE/SEMI Conference and Workshop (IEEE, 2002), pp. 119–124.
9. R. M. A. Azzam and N. M. Bashara, Ellipsometry, and Polarized Light Amsterdam, (North-Holland, 1987).
10. I. Ohlidal and D. Tranta, “Ellipsometry of thin film systems,” in Progress in Optics, 41, E. Wolf (Ed.) (1987).
11. H. Fujiwara, Spectroscopic Ellipsometry: Principles and Applications (John Wiley & Sons, 2007).
12. H. Hazebroek and A. Holscher, “Interferometric ellipsometry,” J. Phys. Educ. 6, 822–826 (1973).
13. C. H. Lin, C. Chou, and K. S. Chang, “Real time interferometric ellipsometry with optical heterodyne and phase lock-in techniques,” Appl. Opt. 29(34), 5159–5162 (1990). [CrossRef] [PubMed]
14. L. R. Watkins, “Interferometric ellipsometer,” Appl. Opt. 47(16), 2998–3001 (2008). [CrossRef] [PubMed]
15. K. Oka and T. Kato, “Spectroscopic polarimetry with a channeled spectrum,” Opt. Lett. 24(21), 1475–1477 (1999). [CrossRef] [PubMed]
16. T. Wakayama, Y. Otani, and N. Umeda, “One-shot birefringence dispersion measurement based on channeled spectrum technique,” Opt. Commun. 281(14), 3668–3672 (2008). [CrossRef]
17. A. Taniguchi, K. Oka, H. Okabe, and M. Hayakawa, “Stabilization of a channeled spectropolarimeter by self-calibration,” Opt. Lett. 31(22), 3279–3281 (2006). [CrossRef] [PubMed]
18. G. E. Jellison Jr and F. A. Modine, “Two-channel polarization modulation ellipsometer,” Appl. Opt. 29(7), 959–974 (1990). [CrossRef] [PubMed]
19. B. S. Stutzman, H. Huang, and F. L. Terry Jr., “Two-channel spectroscopic reflectometry for in situ monitoring of blanket and patterned structures during reactive ion etching,” J. Vac. Sci. Technol. B 18(6), 2785–2793 (2000). [CrossRef]
20. D. Kim, H. Kim, R. Magnusson, Y. J. Cho, W. Chegal, and H. M. Cho, “Snapshot phase sensitive scatterometry based on double-channel spectral carrier frequency concept,” Opt. Express 19(24), 23790–23799 (2011). [CrossRef] [PubMed]
21. S. W. Kim and G. H. Kim, “Thickness-profile measurement of transparent thin-film layers by white-light scanning interferometry,” Appl. Opt. 38(28), 5968–5973 (1999). [CrossRef] [PubMed]
22. D. Kim, S. Kim, H. J. Kong, and Y. Lee, “Measurement of the thickness profile of a transparent thin film deposited upon a pattern structure with an acousto-optic tunablefilter,” Opt. Lett. 27(21), 1893–1895 (2002). [CrossRef] [PubMed]
23. P. Hlubina, D. Ciprian, J. Lunácek, and M. Lesnák, “Dispersive white-light spectral interferometry with absolute phase retrieval to measure thin film,” Opt. Express 14(17), 7678–7685 (2006). [CrossRef] [PubMed]
24. D. Kim, Y. Seo, M. Jin, Y. Yoon, W. Chegal, Y. J. Cho, H. M. Cho, D. G. Abdelsalam, and R. Magnusson, “Stokes vector measurement based on snapshot polarization-sensitive spectral interferometry,” Opt. Express 22(14), 17430–17439 (2014). [CrossRef] [PubMed]
25. D. Kim, Y. Seo, Y. Yoon, V. Dembele, J. W. Yoon, K. J. Lee, and R. Magnusson, “Robust snapshot interferometric spectropolarimetry,” Opt. Lett. 41(10), 2318–2321 (2016). [CrossRef] [PubMed]
26. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72(1), 156–160 (1982). [CrossRef]
27. J. A. Woollam, “Overview of variable angle spectroscopic ellipsometric (VASE), part I: basic theory and typical applications,” in Optical Metrology, Vol. CR72 (SPIE Press, 1999).
