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In this investigation, we propose a dual low coherence scanning interferometer as the novel concept to measure large height steps on the topographic surface of a specimen and the thickness profile of a transparent optical plate. Dual low coherence characteristics by the tandem interferometric configuration can generate several discrete correlograms for the measured surfaces, which provide the possibility to reduce the scanning length of typical low coherence scanning interferometry significantly. Also, the spectrally-resolved interferometric method is combined to monitor the distance gaps between correlograms caused by the dual low coherence. To verify the proposed interferometry, a large height step specimen and a silicon wafer were used and the 3D surface and thickness profiles were rapidly and successfully measured. In addition, the technique which can identify each correlogram by the insertion of dispersive plates are suggested in this paper.
© 2016 Optical Society of America
1. Introduction
Low coherence scanning interferometry (LCSI) [1–3] is beneficial to measure 3D topographic surface profile of a specimen on which discontinuous height steps and textures are distributed compared to well-known monochromatic phase shifting interferometry (PSI) [4]. In addition, LCSI is applicable to obtain optical and geometrical thicknesses of a transparent optical plate based on the localized correlogram because of the low coherence characteristics [5–7]. In case that the discontinuous surface height step is relatively higher or the optical plates are thicker, however, the drawback of LCSI becomes significantly revealed; it fundamentally needs scanning mechanism. Because of the scanning procedure to detect correlograms, LCSI takes long time to reconstruct 3D surface and thickness profiles of the specimen.
Previously, sub-sampling [8] and lateral scanning [9] techniques have been proposed to improve the measurement speed of LCSI. Beyond the maximum scanning step size determined by Nyquist sampling theory, a sub-sampling technique adopts the longer scanning step size and extracts the envelop peak and phase peak positions of correlograms. Although the correlogram is distorted by the sub-sampling, Fourier analysis [8] can provide reliable measurement results without any modification of the hardware and measurement algorithm. As the measureable lengths are longer, for example thicknesses of the optical windows or wafers longer than a few millimeters, however, sub-sampling is not enough to reduce the data and acquisition time. On the other hand, lateral scanning [9] uses the tilted reference flat surface or tilted measurement probe to detect correlograms without the longitudinal scanning procedure. Based on the synchronization between the lateral motion and the sampling of the correlogram, height information corresponding to a single line can be obtained rapidly. However, it still takes long time for lateral scanning to measure surface profile of an area opposed to the typical LCSI which can measure 3D surface profile at once.
In this investigation, we propose a novel concept to measure large height steps on the topographic surface of a specimen and thickness of a transparent optical plate using LCSI. The whole system consists of two interferometers, i.e. a tandem low coherence scanning interferometric configuration, typically used for the group refractive index measurements in the previous researches [10, 11]. Opposed to the previous researches, however, the tandem interferometer is adopted to generate dual low coherence in this research and dual low coherence characteristics from the optical source part generate several discrete correlograms for the measured surfaces, which provides the possibility to reduce the scanning length of LCSI significantly. Also, spectrally-resolved interferometric method is used to monitor the distance gaps between these correlograms in real time. Moreover, each correlogram can be identified by the insertion of dispersive plates and the 3D surface profile of the specimen can be successfully reconstructed.
2. Dual low coherence scanning interferometer (DLCSI)
A dual low coherence scanning interferometer (DLCSI) mainly has two parts: the optical source part to generate the dual low coherence and LCSI part to measure 3D surface and thickness profiles of a specimen in the optical configuration as shown in Fig. 1. In the optical source part, a broadband light source is used and the temporally low coherent beam is split into two by a beam splitter (BS1). The beams are reflected off by the mirrors (M1 and M2) and the optical path difference (OPD) between two beams can be adjustable by the manually moving stage attached to M1. It is noted that the refractive index of air can be assumed as 1 and the OPD becomes the geometrical path difference (ΔL). Then, the small amount of the recombined beam is reflected by a beam sampler (BSP) and detected by a spectrometer for the acquisition of the spectral interferogram corresponding to ΔL. By the spectrally-resolved interferometric technique [12, 13], ΔL can be rapidly extracted by the Fourier method and monitored in real time. In this case, the beam from the optical source part has dual low coherence characteristics because of ΔL and is incident to LCSI part for measuring surface profiles. LCSI part is constructed as a Michelson-type interferometer and the specimen is attached to a motorized stage for longitudinal scanning.
Fig. 1 Optical configuration of DLCSI which consists of optical source part and LCSI part; BS1 and BS2, beam splitter; M1 and M2, mirrors; BSP, beam sampler; FL, focusing lens; BE, beam expander; MR, reference mirror; S, specimen; IL, imaging lens.
In DLCSI measuring a single surface, the intensity (IDLCSI) detected by a single pixel of a CCD camera according to the scanning distance (z) can be expressed as
where I0 is the mean intensity and h is the height of the surface. kc is denoted as (2π/λc) where λc is the center wavelength of the optical source. By the fundamentals of LCSI, the second term of the right part in Eq. (1) represents the correlogram generated when the optical path length of the reference arm is close to that of the measurement arm in the LCSI part. On the other hand, the third and fourth terms indicate the additional correlograms caused by the dual low coherence and they are symmetrically located at ± ΔL from h as shown in Fig. 2(a). It is noted that G1, G2 and G3 means the envelop functions of the correlograms.Fig. 2 (a) Correlograms of DLCSI and (b) comparison between typical LCSI and DLCSI when measuring a large height step sample.
When DLCSI is applied to measure the large height step (H) as shown in Fig. 2(b), the scanning distance can be significantly reduced. Compared to the typical LCSI which needs the scanning distance longer than H, DLCSI only needs (H-ΔL) because the upper surface is measured by the center correlogram and the lower surface is measured by one of the side correlograms. Adjusting ΔL by the manual stage in Fig. 1, (H-ΔL) can be minimized and DLCSI can obtain the 3D surface profile with the scanning distance corresponding to the coherence length of the optical source approximately a few tens of micrometers only. Even though the height of discrete surface texture reaches up to an order of millimeters, DLCSI can measure the surface profile with relatively short scanning distances and the measurement time can be significantly reduced. Also, the same principle can be adopted for measuring the surface and thickness profiles of a transparent optical plate and rapid measurements can be achieved.
3. Experiments
In order to verify the performance of DLCSI, a large discontinuous height step specimen and a silicon (Si) wafer were used for the measurements of 3D surface and thickness profiles. As an optical source, a super-luminescent diode (SLD) which has 1020 nm center wavelength and 50 nm bandwidth was used and the specimen was moved by a micro-stepping motorized stage with the sub-sampling of 650 nm sampling period to obtain the correlograms. Near infrared (NIR) light source is suitable for measuring various specimens such as topographic samples, optical plates and Si wafers because of the partial transparency to those specimens [14].
3.1 3D surface profile measurements of a large height step specimen
The large height step specimen was prepared with 3 gauge blocks which has different lengths (1, 2 and 3 mm) and they are aligned on the flat surface of another gauge block as show in Fig. 3(a). Because the length difference of the gauge blocks is 1 mm, ΔL of the optical source part was set close to 1 mm and the spectral interferogram was obtained as shown in Fig. 3(b). From the Fourier method [13], ΔL was extracted as depicted in Fig. 3(c) and it was calculated as 0.998 mm. Then, the correlograms on the different gauge blocks were detected in the scanning range of 50 μm as shown in Fig. 3(d) and it was confirmed that DLCSI was able to reduce the scanning distance from a few millimeters to a few tens of micrometers and the measurement time.
Fig. 3 (a) A large step height specimen which consists of 3 gauge blocks, (b) spectral interferogram obtained by the spectrometer for ΔL = 0.998 mm, (c) Fourier transformed result of (b) and (d) correlograms on 3 gauge blocks in the scanning range of 50 μm.
Figure 4 shows the 3D surface profile measurement result by DLCSI. By approximately 50 μm scanning, each gauge block surface was reconstructed as illustrated in Fig. 4(a). Because of the low numerical aperture (NA) of the imaging lens (IL), the edge portions between gauge blocks were not measured and each gauge block surface was inclined due to the tilts occurred in specimen preparation and the alignment of M1 and M2. In Fig. 4(a), the mean heights of 3 surfaces were close to each other as expected and the real 3D surface profile of the specimen was reconstructed using ΔL monitored during the measurement as shown in Fig. 4(b). As the result, the mean heights of the gauge blocks were 0.9996 mm, 1.9993 mm and 2.9959 mm, respectively and they are within the uncertainty range of the gauge blocks provided by the manufacturer. Each surface has approximately 73 nm PV (peak to valley) value and 9.6 nm Sa (arithmetical mean height of the surface) value. Table 1 summarizes the measurement results of gauge blocks.
Fig. 4 (a) 3D surface profile measurement result of 3 gauge blocks and (b) reconstructed surface profile with ΔL.
Table 1. Summary of measurement results of gauge blocks
3.2 Surface and thickness profile measurement of a Si wafer
DLCSI was also applied to measure dimensions of a silicon wafer using the transparent characteristics of NIR light. An undoped double-sided polished (DSP) wafer which has 475 ± 25 μm thickness was used as a specimen and ΔL of the optical source part was adjusted similar to the optical thickness of the wafer considering the group refractive index of Si (3.869) [15].
As shown in Fig. 5(a), the spectral interferogram corresponding to ΔL was obtained and it was 1.752 mm. Based on the dual low coherence characteristics, the front and rear surfaces of the wafer generated each 3 correlograms according to the scanning distance as shown in Fig. 5(b) and properly selected correlograms corresponding to the front and rear surfaces (④ and ⑤) were used for the measurement. In this case, ④ indicates the side correlogram of the front surface and ⑤ is the center correlogram of the rear surface. Due to the dispersion of Si, the correlograms of the rear surface were broadened compared to those of the front surface and their signal strengths were remarkably reduced by the low transmittance of Si.
Fig. 5 (a) Spectral interferogram obtained by the spectrometer for ΔL = 1.752 mm and (b) 6 correlograms from the front and rear surfaces of the wafer by the dual low coherence.
There are two benefits to measure a DSP Si wafer using DLCSI. First, the scanning distance can be significantly reduced. In typical LCSI, the scanning distance should be longer than the optical thickness of the wafer (an order of millimeters), but it becomes only 100 μm to avoid the overlap between two correlograms. Then, the measurement can be completed rapidly. Second, the signal strengths of both correlograms can be balanced and the CCD camera saturation or signal-to-noise ratio (SNR) problems, typically occurred in practice, are mitigated. In typical LCSI, the front and rear surfaces were detected by ② and ⑤, respectively, but the strength difference between two correlograms is relatively huge. On the other hand, the side correlogram of the front surface used in DLCSI has half the signal strength of the original one, and then two correlograms have comparable signal strengths as shown in Fig. 5(b). Figure 6 shows the measurement results of the DSP Si wafer for Fig. 6(a) front surface, Fig. 6(b) rear surface and Fig. 6(c) thickness profiles. It was confirmed that each surface profile was successfully measured by DLCSI and the wafer was dimensionally reconstructed as shown in Fig. 6(d). Each surface has approximately 11.3 nm, 18 nm and 15 nm as Sa values, respectively.
Fig. 6 Measurement results of the DSP Si wafer (a) front surface, (b) rear surface, (c) thickness profiles and (d) reconstructed wafer.
4. Discussion
The main advantage of DLCSI is to reduce the scanning distance when measuring the surface profile of large height step specimens and the thickness profiles of optical plates. However, the application of DLCSI should be careful because of the alignment of M1 and M2 in Fig. 1 and identification of correlograms. Basically, the side correlograms as shown in Fig. 2(a) are generated by two beams reflected off by M1 and M2, respectively and the relative tilt between two mirrors propagates 3D surface profile measurements of DLCSI. In this experiment, the alignment of two mirrors were confirmed by maximizing the visibility of the spectral interferogram. When measuring a flat mirror as a specimen, however, surface profiles reconstructed by 3 correlograms still had different slopes because of the remained tilt. From the flat mirror experiment, therefore, the relative tilt was measured and the result was utilized to compensate the surface distortion of other specimens. In addition to the amount of the relative tilt between two mirrors, another important issue is its stability for the reliable measurements. In order to overcome this limitation, the optical source part should be constructed with the thermally stable material and the relative tilt should be compensated with pre-implemented flat mirror experiments.
The second consideration is the identification of each correlogram in Fig. 2(a) because it can produce the ambiguity to reconstruct the original surface profiles using ΔL. For example, Fig. 4(b) was reconstructed with the preliminary knowledge such as the locations of the specific gauge blocks. However, the surface profiles can be mismatched to each other if there is no preliminary knowledge. The center correlogram can be distinguished from the side correlograms by the signal strength, of course, but it is not the general case because the signal strength is strongly dependent on the specimen. To identify each correlogram, dispersion which induce the broadening of the correlogram [16] can be a good motive and it can be implemented by the insertion of dispersive plates (DP) in the optical source part and LCSI part as shown in Fig. 7(a). In this case, the center correlogram is broadened by DP2 because of the unbalanced interferometric configuration of LCSI. In case of side correlograms, the broadening effect is different from each other, i.e. one is broadened twice compared to the center correlogram, but the other has no change due to the dispersion balance if the thickness and material of DP1 and DP2 are exactly same. Furthermore, one of the side correlogram can be dim if the dispersion is severe.
Fig. 7 (a) Modified DLCSI to identify each correlogram, (b) 3 correlogram identified by the dispersion effect.
In this research, 20 mm thick BK7 plates were used to verify the identification of correlograms and it was confirmed that each correlogram was broadened as expected. The coherence lengths of the center and the side correlograms, defined by the widths when the contrast were 1/e of the maximums, were 16.9 μm, 10.4 μm and 35.1 μm, respectively, as seen in Fig. 7(b) while the original one has 10.4 μm. From the Ref. [17], the broadened coherence lengths should be 13.6 μm, 20.3 μm, respectively and the deviations between the theoretical and measured values were originated from the assumption of the Gaussian spectrum of the theoretical model and surface reflections of dispersive plates. Although the practical coherence broadening effect differs from the theoretical expectation, each correlogram can be clearly identified. Based on the correlogram identification, previous two kinds of specimen were measured with the same procedure and the same results were obtained.
When the dispersive plates are used for the identification of correlograms, another important issue is the dispersion effect on the contrast of the correlogram and accuracy of LCSI. Dispersion of unbalanced LCSI can broaden the correlogram aforementioned, deteriorate the contrast of the correlogram, delay the correlogram and induce the phase shift between the phase and envelop peak positions [17]. If the signal strength of the correlogram is sufficiently larger than the intensity noise level, then the loss of contrast is not so significant problem. However, the delay of the correlogram and the phase shift should be compensated with preliminary theoretical and experimental results.
5. Conclusion
In this investigation, we proposed and verified a dual low coherence scanning interferometer (DLCSI) as the new concept to measure large height steps on the topographic surface of a specimen and thickness of a transparent optical plate using LCSI. Based on the dual low coherence characteristics, three discrete correlograms corresponding to each measured surface provided the possibility to reduce the scanning length of LCSI significantly. Also, spectrally-resolved interferometric method was used to monitor the distance gaps between these correlograms. In order to verify the performance of DLCSI, a large height step specimen and a Si wafer were used and the 3D surface and thickness profiles were successfully measured. In addition, the method which can identify each correlogram by the insertion of dispersive plates were suggested in this paper.
Funding
This study was supported by research fund from Chosun University, 2016.
References and links
1. L. Deck and P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33(31), 7334–7338 (1994). [CrossRef] [PubMed]
2. 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]
3. I. Shavrin, L. Lipiäinen, K. Kokkonen, S. Novotny, M. Kaivola, and H. Ludvigsen, “Stroboscopic white-light interferometry of vibrating microstructures,” Opt. Express 21(14), 16901–16907 (2013). [CrossRef] [PubMed]
4. K. Creath and P. Hariharan, “Phase-shifting errors in interferometric tests with high-numerical-aperture reference surfaces,” Appl. Opt. 33(1), 24–25 (1994). [CrossRef] [PubMed]
5. P. A. Flournoy, R. W. McClure, and G. Wyntjes, “White-light interferometric thickness gauge,” Appl. Opt. 11(9), 1907–1915 (1972). [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] [PubMed]
7. H.-J. Lee and K.-N. Joo, “Optical interferometric approach for measuring the geometrical dimension and refractive index profiles of a double-sided polished undoped Si wafer,” Meas. Sci. Technol. 25(7), 075202 (2014). [CrossRef]
8. P. de Groot and L. Deck, “Three-dimensional imaging by sub-Nyquist sampling of white-light interferograms,” Opt. Lett. 18(17), 1462–1464 (1993). [CrossRef] [PubMed]
9. A. Olszak, “Lateral scanning white-light interferometer,” Appl. Opt. 39(22), 3906–3913 (2000). [CrossRef] [PubMed]
10. 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]
11. H. Matsumoto, K. Sasaki, and A. Hirai, “In situ measurement of group refractive index using tandem low-coherence interferometer,” Opt. Commun. 266(1), 214–217 (2006). [CrossRef]
12. J. Schwider and L. Zhou, “Dispersive interferometric profilometer,” Opt. Lett. 19(13), 995–997 (1994). [CrossRef] [PubMed]
13. K.-N. Joo and S.-W. Kim, “Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser,” Opt. Express 14(13), 5954–5960 (2006). [CrossRef] [PubMed]
14. Y. G. Kim, Y. B. Seo, and K.-N. Joo, “Low cost wafer metrology using a NIR low coherence interferometry,” Opt. Express 21(11), 13648–13655 (2013). [CrossRef] [PubMed]
15. M. A. Green, “Self-consistent optical parameters of intrinsic silicon at 300K including temperature coefficients,” Sol. Energy Mater. Sol. Cells 92(11), 1305–1310 (2008). [CrossRef]
16. S. Diddams and J.-C. Diels, “Dispersion measurements with white-light interferometry,” J. Opt. Soc. Am. B 13(6), 1120–1129 (1996). [CrossRef]
17. P. Pavliček and J. Soubusta, “Measurement of the influence of dispersion on white-light interferometry,” Appl. Opt. 43(4), 766–770 (2004). [CrossRef] [PubMed]
