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Abstract
In this study, an optical method that allows simultaneous thickness measurements of two different layers distributed over a broad thickness range from several tens of nanometers to a few millimeters based on the integration of a spectroscopic reflectometer and a spectral-domain interferometer is proposed. Regarding the optical configuration of the integrated system, various factors, such as the operating spectral band, the measurement beam paths, and the illumination beam type, were considered to match the measurement positions and effectively separate two measurement signals acquired using both measurement techniques. Furthermore, for the thickness measurement algorithm, a model-based analysis method for high-precision substrate thickness measurements in thin-film specimens was designed to minimize the measurement error caused by thin films, and it was confirmed that the error is decreased significantly to less than 8 nm as compared to that when using a Fourier-transform analysis. The ability to undertake simultaneous thickness measurements of both layers using the proposed system was successfully verified on a specimen consisting of silicon dioxide thin film with nominal thicknesses of 100 nm and 150 nm and a 450 µm-thick silicon substrate, resulting in the exact separation between the two layers. From measurement uncertainty evaluation of a thin-film, a substrate in a thin-film specimen, and a single substrate, the uncertainties were estimated to be 0.12 nm for the thin-film, 0.094 µm for the substrate in a thin-film specimen, and 0.076 µm for the substrate. The measurement performance of thicknesses distributed on multi-scale was verified through comparative measurements using standard measurement equipment for several reference samples.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In the semiconductor and display industries, most high-tech and multi-functional devices are manufactured through thin-film deposition processes on a substrate [1–3]. As thickness uniformity as well as the thickness itself in such devices are directly related to device performance capabilities, it is crucial to measure the physical thicknesses of both thin films and substrates precisely to prevent yield reductions which can arise when the performance of thin-film devices is degraded [4–20]. Moreover, given that there are manufacturing processes in which the thicknesses of the thin-film and the substrate change in unison, such as the thermal oxidation process and patterning processes for holes or sidewalls, simultaneous thickness measurements of both thin film and substrates are very important for quality control of such manufacturing processes [21–24].
In thin-film devices, thin-film thicknesses range from a few nanometers to a few micrometers, whereas the substrate thickness is in the range of a few hundreds of micrometers to a few millimeters, indicating a considerable thickness difference for a maximum thin-film-to-substrate thickness ratio of 106. However, no currently existing measurement techniques can handle such a wide thickness range in a single measurement, which means that individual measurement techniques depend on the specific thickness range due to practical limitations caused by the optical characteristics of the measurement system used, such as the spectral resolution, detectable wavelength range, and wavelength dispersion, among others [25–27]. For this reason, spectroscopic ellipsometry (SE) and spectroscopic reflectometry (SR) are typically used for thickness measurements of thin films [28–46]. SE is suitable for measuring sub-nanometer-thick thin films by analyzing the amplitude ratio and the phase difference between reflection coefficients of vertically and horizontally polarized light reflected from the thin film [31,32]. However, it is inevitable that such a measurement system will become more complicated while also requiring additional measurement time due to the use of polarization-dependent characteristics. On the other hand, SR can be applied to thin-film thickness measurements exceeding a few tens of nanometers by simply analyzing the reflectance spectrum regardless of the polarization state, which enables a simple configuration and rapid measurements [33–46]. For substrate thickness measurements, various optical techniques of low-coherence interferometry (LCI), chromatic confocal microscopy (CCM), and spectral-domain interferometry (SDI) have been studied [47–71]. LCI can measure the thicknesses of relatively thick substrates through mechanical scanning along the optical axis, but this process unavoidably increases the measurement time. The other two techniques of CCM and SDI use spectral information acquired using a spectrometer, which is useful for in-line measurements. However, the measurable thickness range is limited by the spectral bandwidth and resolution in principle [52–71]. In terms of measurement precision, SDI is superior to the other two techniques during substrate thickness measurements, as it determines the thickness by analyzing the spectral phase acquired without any scanning process [56–71].
In this study, an optical method is proposed for the simultaneous thickness measurement of a thin-film and a substrate distributed over an extremely broad thickness range, and this achievement is realized by integrating two different techniques applicable to the thickness range corresponding to each layer. After considering several factors, such as configuration flexibility, the measurement speed, the measurement range, and the measurement precision, among others, SR and SDI were selected for the thickness measurements of thin films and substrates, respectively. For an efficient integration of the two techniques in a single optical system, various optical requirements were reflected in the integrated measurement system, in this case the coupling and separation of two different sets of spectral information, optical path sharing, and beam shape matching. To verify the proposed method during the simultaneous thickness measurements of a thin film and substrate with a significant thickness difference, a thin-film specimen consisting of a silicon dioxide (SiO2) layer and a silicon wafer was tested through specimen scanning. For a quantitative analysis of the thickness measurement performance, uncertainty estimations were conducted for both a thin film and a substrate on a thin-film specimen as well as a single substrate. Moreover, the measurement reliability of the thicknesses distributed on multi-scale was verified through comparative measurements of six reference samples calibrated using standard measurement equipment.
2. Measurement methods
Figure 1 shows schematic descriptions of the beam paths in SR and SDI modes when using coaxial illumination to simultaneously measure the thicknesses of both layers at an identical point on a thin-film specimen. The thickness and the complex refractive index of each layer are denoted by T1 and Ñ1 for the thin film and by T2 and Ñ2 for the substrate, respectively. To prevent the mixing of the measurement signals of the two modes, the light reflected from the specimen and that transmitted through the specimen are measured by SR and SDI, respectively.
Fig. 1. Descriptions of beam propagation paths in SR and SDI: (a) measurement and reference beams in SR (blue) and SDI (red), (b) detailed measurement beam paths in SR, and (c) detailed measurement beam path in SDI.
First, the thin-film thickness (T1) is determined by fitting the theoretical reflectance spectrum to the experimental reflectance spectrum, which is basic measurement principle of SR. The theoretical reflectance of the thin-film specimen is derived by modeling multiple reflections and transmissions at both interfaces of the thin–film layer, as shown in Fig. 1(b), which results in the theoretical reflectance spectrum (RT(T1;λ)) in Eq. (1) [72]. In Eq. (1), r01 and r12 are the Fresnel reflection coefficients for the air (0th layer)-to-thin-film (1st layer) and the thin-film-to-substrate (2nd layer), respectively, λ is the wavelength. The Ñ1 is referenced from the well-known refractive index value of the corresponding thin film material [73–75]. On the other hand, the experimental reflectance spectrum (RE(λ)) is determined by measuring two different intensity spectra: an intensity spectrum (IN(λ)) reflected from the reference substrate without any thin film and an intensity spectrum (IE(λ)) reflected from the thin-film specimen. The experimental reflectance spectrum (RE(λ)) of the thin-film specimen itself is obtained by dividing the intensity spectrum (IE(λ)) of the thin-film specimen by the intensity spectrum (IN(λ)) of the reference substrate and multiplying this by the theoretically calculated reflectance spectrum (RN(λ)) of the reference substrate according to Eq. (2), as the intensity spectrum of the thin-film specimen contains not only the reflectance characteristics of the thin-film specimen itself but also the spectral characteristics of the light source and all of the corresponding optical components. As a result, the thin-film thickness is determined as an optimal thickness value which makes the total sum (eSR(T1)) of the squared differences between the theoretical (RT) and experimental (RE) reflectance spectra the smallest, as indicated in Eq. (3), where, λl and m represent the lth wavelength and the total number of discrete wavelengths, respectively.
Figures 2(a) and 2(b) show the theoretically generated interference spectrum and the measured one, respectively. For an efficient comparison between the two interference spectra, both datasets with different envelopes are normalized to the same scale, as shown in Fig. 2(c). As a result, the substrate thickness T2 is determined as the optimal thickness, which makes the total sum (eSDI(T2)) of the squared differences between the theoretical (I'T) and experimental (I'E) interference spectra the smallest, as indicated in Eq. (5). As shown in Fig. 2(d), the theoretical and experimental spectra showed the uniform degree of coincidence for the entire spectral range in terms of the squared differences.
Fig. 2. Theoretical and experimental interference spectra: (a) theoretical interference spectrum including the DC signal (IT(T2;λ)), (b) experimental interference spectrum including the spectral intensity distribution of the light source (IE(λ)), (c) normalized theoretical and experimental interference spectra (I'E(λ) and I'T(T2;λ)), and (d) partial range of the normalized theoretical and experimental interference spectra enlarged horizontally (wavelength range 1540 nm–1560 nm).
Fig. 3. Numerical simulation results of the substrate thickness measurement errors via a Fourier analysis and a model-based analysis.
3. Experiments
Figure 4 shows the optical layout and experimental system to simultaneously measure the thicknesses of both a thin-film and a substrate constituting a thin-film specimen, operating in two different measurement modes of SR and SDI at the same time. Considering the measurement principle of each mode, the SR mode utilizes the visible band to measure the thickness of a thin film, as the reflectance of the thin-film specimen changes significantly in the visible band due to large dispersion compared to that in the near-infrared band, which is advantageous for measuring very thin film thicknesses on the order of tens of nanometers. As a light source in the SR mode, a Tungsten-Halogen lamp (Thorlabs, SLS201/M), which covers a wide wavelength range from 300 nm to 2600 nm, was used. As a detector in the SR mode, a visible spectrometer (Thorlabs, CCS200/M) operating in a wavelength range of 200 nm to 1000 nm with a spectral resolution of 0.25 nm and a spectral accuracy of less than 2 nm was used. On the other hand, as a light source in the SDI mode, a superluminescent diode (SLD, Thorlabs, SLD1005S) having a spectral bandwidth of 50 nm at a center wavelength of 1550 nm was used, because the silicon wafers mainly used as a substrate material in most semiconductor devices are partially transparent in this particular near-infrared band. As a detector in the SDI mode, a near-infrared spectrometer (Ibsen Photonics, I-MON 512 USB) operating in a wavelength range of 1510 nm to 1600 nm with a spectral resolution of 0.2 nm and a wavelength accuracy of 5 pm was used. Given that no optical components can cover a broad wavelength range from the visible to the near-infrared, a dichroic beamsplitter was used to realize an integrated measurement system to match the measurement positions of two measurement modes through the sharing of coaxial illumination paths, transmitting visible light in the wavelength range of 420 nm to 900 nm and reflecting near-infrared light in the wavelength range of 990 nm to 1600 nm. Furthermore, SR was designed to use a collimated beam simply to share the measurement path with the transmission-type SDI, which is also effective for stable reflectance measurements insensitive to variations of the specimen position along the optical axis. The paths shown in blue in Fig. 4(a) represent the optical paths of the SR. The light emitted from the visible lamp travels to the specimen after reflection at a visible beamsplitter (BS1) and transmission through a dichroic beamsplitter (DM1). The light reflected from the specimen is detected by the visible spectrometer after transmission at the DM1 and BS1. As shown in Fig. 4(a), SDI was realized as a transmission-type Mach-Zehnder configuration, and the paths shown in red represent the optical paths of SDI. The light emitted from the near-infrared SLD is divided into reference light propagating counterclockwise and measurement light propagating clockwise by the first near-infrared beamsplitter (BS2). After reflection from the dichroic beamsplitters (DM1 and DM2), the two beams are recombined by the second near-infrared beamsplitter (BS3) and the interference spectrum is acquired by the near-infrared spectrometer.
Fig. 4. Optical configuration and photos of the proposed measurement system: (a) optical configuration of the proposed system, (b) photos of the experimental setup (CL1 and CL2: collimation lenses in the SR mode, CL3 and CL4: collimation lenses in the SDI mode, BS1: visible beamsplitter, BS2 and BS3: near-infrared beamsplitters, DM1 and DM2: dichroic beamsplitters).
Figure 4(b) represents the experimental setup of the proposed measurement system. To verify the simultaneous thickness measurement performance of a thin film and a substrate, a thin-film specimen was fabricated, as described in Fig. 5. The thin-film specimen consists of a double-sided polished silicon wafer substrate with a nominal thickness of 450 µm and a single layer of SiO2 thin film. The thin film was etched using a patterned photomask with the same image shown in Fig. 5(a), resulting in two levels of thicknesses of 100 nm and 150 nm of the thin film, as shown in Fig. 5(b). For thickness distribution measurements of both layers, the thin-film specimen was scanned laterally over an area of 90 mm (x) × 120 mm (y) with equal steps of 1 mm, and the thicknesses of thin film and the substrate were simultaneously measured ten times repeatedly at a single point. The total measurement time at a single point was estimated to be approximately 0.4 s. Figures 6(a) and 6(b) show the measurement results of the thickness distributions of the thin film and the substrate, which were plotted through post-processing of linear interpolation between adjacent sampling points for effective visualization of thickness distribution maps. According to the thickness profiles in Figs. 6(c) and 6(d), the thin-film thickness profile clearly shows two distinct thickness levels of 100 nm and 150 nm, as designed in Fig. 5(b), whereas the substrate thickness profile shows gradual thickness variation unlike thin-film thickness profile. These results confirm that the thicknesses of a thin film and a substrate constituting a thin-film specimen can be measured simultaneously without mutual interference.
Fig. 5. Description of the thin-film specimen: (a) photo of the specimen from the top view and (b) cross-section of the specimen along the white dashed line in Fig. 5(a).
Fig. 6. Measurement results of thickness distributions of the thin-film specimen: (a) thin-film thickness distribution obtained in the SR mode, (b) substrate thickness distribution obtained in the SDI mode, and cross-sectional thickness profiles of (c) the thin film and (d) the substrate along the black dashed lines in Figs. 6(a) and 6(b).
4. Discussions
4.1 Uncertainty evaluation of a thin-film specimen
For reliability evaluation of the thickness measurement using the proposed method, the uncertainty evaluations were performed on the thin-film specimen in Fig. 5 according to the Guide to the expression of Uncertainty in Measurement (GUM) [76,77]. In the SR mode, the thickness measurement uncertainty of a thin film on a thin-film specimen is determined from two major uncertainty components related to measurement reproducibility and the spectrum analysis process shown in Table 1. First, measurement reproducibility can be calculated from the repeatability and long-term stability components according to several International Organization for Standardization (ISO) guidelines, in this case ISO 5725-1, ISO 5725-2, ISO 5725-3, ISO 21748, and ISO 21749 [78–82]. Through repeated measurements over 10 days, 100 times a day, the uncertainties for the repeatability and long-term stability were estimated to be approximately 0.006 nm (the square root of the average daily variance) and 0.045 nm (the standard deviation of daily mean values), respectively, resulting in a standard uncertainty of 0.045 nm for measurement reproducibility. Second, the uncertainty related to the spectrum analysis process was estimated from the theoretical model of the reflectance spectrum in Eq. (1), which consists of four different uncertainty components, as shown in Table 1. For an accurate estimation of the uncertainty from the reflectance spectrum expressed as a nonlinear function based on the four uncertainty components, a Monte Carlo simulation was conducted instead of using the law of uncertainty propagation for the approximated linear function [77,83]. First, the uncertainty related to the sample tilt angle was calculated and found to be approximately 0.007 nm under the assumption that the sample can be aligned with a tilt angle of less than ±1° due to mechanical tolerances. Second, the uncertainty according to a wavelength accuracy of the visible spectrometer was estimated to be 0.004 nm considering a spectral resolution of 2 nm. Third, the uncertainty stemming from the intensity stability of the light source was calculated to be 0.034 nm with the intensity stability at less than 2.2%, as measured through 100000 repeated measurements. Fourth, the uncertainty by the refractive index accuracy was calculated and found to be 0.009 nm, referring to the refractive index errors reported in the literature [73,74]. As a result, the standard uncertainty related to the spectrum analysis process was calculated to be approximately 0.036 nm. Finally, the combined uncertainty of the thickness measurement of the thin film with the thickness of 93.66 nm using the SR mode was estimated to be 0.058 nm (k = 1). According to the uncertainty budget in Table 1, the most dominant uncertainty factor in thin-film thickness measurements was found to be the long-term stability, meaning that the measurement locations may differ slightly due to the repeated loading and unloading of the samples during entire evaluation period.
Table 1. Uncertainty budget of the thickness measurement of a thin-film on a thin-film specimen using the SR mode of the proposed method (T1 = 93.7 nm)
In the SDI mode with the model-based analysis, the measurement uncertainty of the substrate thickness in a thin-film specimen is determined from two major uncertainty components related to measurement reproducibility and the spectrum analysis process, as shown in Table 2. First, the estimation of the measurement reproducibility was done identically to that for the previous thin-film case, and the standard uncertainty related to the reproducibility of repeated measurements over 10 days was estimated to be 0.033 µm. Second, the uncertainty related to the spectrum analysis process was estimated from the theoretical model of the interference spectrum in Eq. (4), which consists of five different uncertainty components, as shown in Table 2. With a calibrated wavelength-meter and a wavelength tunable laser, the spectrometer in the SDI mode was calibrated by using more than 30 wavelengths with a help of polynomial fitting. In order to accurately calculate the uncertainty by the model-based analysis of the interference spectrum defined as a nonlinear function with the five uncertainty components, a Monte Carlo simulation was conducted [77,83]. First, the uncertainty related to the wavelength accuracy of the near-infrared spectrometer was calculated simply using the manufacturer specifications of the spectrometer, because the calibration uncertainty of the spectrometer was much less than the wavelength accuracy provided from the manufacturer. In Monte Carlo simulation, the wavelength errors were randomly added to each wavelength values within the wavelength accuracy of ±5 pm assuming the rectangular probability distribution. Second, the uncertainty stemming from the intensity stability of the light source was estimated using a maximum value among the peak-to-valley values of intensity variations measured through 100000 repeated acquisitions for each wavelength. Third, the measurement uncertainty of the thin film thickness was estimated to be approximately 0.058 nm in case of the thin-film thickness of 93.7 nm, as described in Table 1. Fourth, the uncertainty by the accuracy of the refractive index of the thin film was calculated from the refractive index errors reported in the literature [73]. Fifth, the measurement uncertainty of the refractive index of the substrate, which is the silicon wafer in this case, can be estimated through the measurement process of a reference substrate using the Fourier analysis-based SDI mode. As shown in Table 2, it was found that the contribution of the measurement uncertainty of the substrate refractive index to the measurement uncertainty of the substrate thickness was the most dominant. As a result, the combined uncertainty of the substrate thickness measurement through the SDI mode using the model-based analysis in a thin-film specimen was estimated to be approximately 0.047 µm (k = 1), which is comparable to that of thickness measurement using the Fourier analysis-based SDI mode.
Table 2. Uncertainty budget of the substrate thickness measurement in a thin-film specimen when using the model-based analysis of the proposed method (T2 = 450.5 µm)
4.2 Uncertainty evaluation of a single substrate
For reliability evaluation of the substrate thickness measurement using the Fourier analysis-based SDI mode, the uncertainty evaluation was performed on a silicon wafer substrate with nominal thickness of 475 µm, which was used as the reference substrate for SR mode. As mentioned in chapter 2, the thickness of a single substrate can be measured using the Fourier analysis-based SDI mode. In this case, the measurement uncertainty of the substrate thickness is determined from two major uncertainty components related to measurement reproducibility and the thickness analysis process shown in Table 3. The estimation of the measurement reproducibility of the SDI mode was done identically to that in the previous two cases, and the standard uncertainty related to the measurement reproducibility was estimated to be 0.018 µm. Next, the uncertainty related to the thickness analysis process can be estimated from the combination of the uncertainties of the three different OPDs (L1, L2, and L3 in Table 3) used for thickness measurements in the SDI mode. The uncertainty for each OPD consists of the uncertainty components of the discrete Fourier transform (DFT) algorithm, the wavelength accuracy of the spectrometer, and the refractive index of air. First, the uncertainty for the DFT algorithm was derived from the OPD measurement error using the DFT algorithm for an ideally generated interference spectrum. Second, the uncertainty for the wavelength accuracy of the near-infrared spectrometer was calculated through a Monte Carlo simulation [77,83]. The uncertainty was determined to be half of the 95% coverage interval for the OPDs analyzed from ideal interference spectra generated by considering the wavelength accuracy of the spectrometer. The value related to the wavelength accuracy of the spectrometer, 5 pm was provided from the manufacturer specifications, and it represents the accuracy of the wavelength value assigned to each pixel considering wavelength fit resolution, wavelength linearity, wavelength drift, and so on. Third, the uncertainty for the refractive index of air was estimated using the Edlén equation considering typical laboratory environmental conditions (pressure, temperature, relative humidity, and CO2 concentration) [84]. Lastly, the uncertainty by coupling between the three OPDs in thickness measurements was also considered to eliminate the effect caused by the redundancy of systematic errors from identical uncertainty sources [85]. As a result, the uncertainty related to the thickness analysis process was estimated to be 0.034 µm. Finally, the combined uncertainty of the thickness measurement of the silicon wafer in the Fourier analysis-based SDI mode was estimated to be 0.038 µm (k = 1).
Table 3. Uncertainty budget of the thickness measurement of a silicon wafer in the Fourier analysis-based SDI mode of the proposed method (T2 = 477.3 µm)
4.3 Performance evaluation using thickness reference samples
In this study, six thickness reference samples (SP1, SP2, SP3, SP4, SP5, and SP6 in Fig. 7) with different nominal thicknesses were tested using the proposed method to verify the thickness measurement performance over an extremely broad thickness range. As shown in Fig. 7, SP1 and SP2 are SiO2 thin-film samples; SP3, SP4, and SP5 are glass substrates; and SP6 is a double-sided polished silicon wafer. The nominal thicknesses of the thin films (SP1 and SP2) and substrates (SP3, SP4, SP5, and SP6) are 50 nm and 100 nm, and 130 µm, 200 µm, 700 µm, and 475 µm, respectively. For the performance evaluation of each measurement mode of the proposed system, SP1 and SP2 were tested in the SR mode, while SP4, SP5, and SP6 were tested in the SDI mode. The SP3 sample was measured in both modes, as it is within the common thickness measurement range. The measurable ranges of the thin-film and substrate thickness using both modes can be estimated considering the spectral characteristics of the spectrometers in use like wavelength range, optical resolution, and detector sensitivity. In our case, the measurable range of the thin-film and substrate thickness were calculated to be approximately 50 nm-to-200 µm in SR mode and 100 µm-to-3 mm in SDI mode, respectively. To verify the reliability of the thickness measurement results using the proposed method, all samples were measured by standard measurement equipment in use at KRISS (Korea Research Institute of Standards and Science) in advance, which are a spectroscopic ellipsometer for thin-film thickness measurements and contact-type thickness measuring equipment for substrate thickness measurements. In Table 4, the measurement results of all the thickness reference samples were summarized. The expanded uncertainties and En-values of the measured values for all six samples were also evaluated. In the uncertainty evaluation process, the uncertainty components related to measurement reproducibility were evaluated only for SP1 and SP6, taking into account the similarity of the measurement modes. For this reason, the uncertainties of measurement reproducibility in case of SP2 and SP3 referred to that of SP1 for SR mode. Likewise, the reproducibility terms in case of SP3, SP4, and SP5 referred to that of SP6 for SDI mode. Considering the uncertainty budgets of the measured values, it can be said there is no thickness dependence of the uncertainty of the thin-film and substrate thickness, because most of uncertainties were originated from the uncertainties of long-term stability, the intensity instability of the light source, and the material refractive index, as shown in Tables 1 and 2, which are irrelevant to the thickness itself. According to the measurement results, the measured thickness values of all samples, which represent mean values of 100 repeated measurements, are in good agreement with the certified values within the expanded uncertainties of the comparative measurement equipment. As a result, it was confirmed that both measurement modes integrated in the proposed measurement system can provide reliable thickness measurements over a broad thickness range from the thin film to the substrate level.
Table 4. Measurement results of the certified samples
5. Conclusion
In this study, an optical measurement system based on an integration of two different techniques, SR and SDI, was proposed and realized for the simultaneous measurement of the thicknesses of a thin film and a substrate constituting a thin-film specimen. With regard to the optical configuration and thickness measurement algorithm, various factors, such as the separation of measurement signals, a technique-dependent wavelength band, wavelength-dependent specifications of the optical components, and optical paths arrangement were considered to implement the proposed single measurement system effectively. In the optical configuration, the measurement beams from two different methods were configured as collimation beams for simultaneous thickness measurements of both layers at the same position, which were then integrated and separated using a dichroic optical component. More importantly, a model-based analysis of the interference spectrum was designed and conducted to minimize the effect of the thin-film on the substrate thickness measurements in thin-film specimens compared to the conventional Fourier analysis method. To verify the simultaneous thickness measurement performance of the proposed method when used to measure a thin film and substrate, a thin-film specimen consisting of a thin layer of SiO2 material and a silicon wafer with a nominal thickness of 450 µm was fabricated and measured within an area of 90 mm (x) × 120 mm (y). From the thickness distribution measurement results, it was confirmed that the two thickness measurement results were successfully separated without significant coupling. Moreover, the measurement performance and reliability of the proposed method were verified in two ways. First, as a quantitative evaluation of the measurement performance, the uncertainty evaluations were performed on a thin-film thickness measurement using the SR mode, a substrate thickness measurement of a thin-film specimen using model-based analysis in the SDI mode, and a substrate thickness measurement using the Fourier analysis-based SDI mode, which resulted in 0.12 nm (k = 2) for a thin film thickness of 93.7 nm, 0.094 µm (k = 2) for a substrate thickness of 450.5 µm in a thin-film specimen, and 0.076 µm (k = 2) for a silicon wafer thickness of 477.3 µm. Second, six thickness reference samples with various thicknesses were measured with the proposed method, and it was concluded that all measured thicknesses by the proposed method were in good agreement with the certified values within their expanded uncertainties. Considering both the uncertainties from the proposed method and from standard measurement equipment, the thickness measurement results are in good agreement within the uncertainty of each measurement system. In conclusion, the proposed method is expected to be widely utilized as a metrological tool capable of thickness measurements in wide dynamic range in the semiconductor and display industries.
Funding
Korea Research Institute of Standards and Science (21011040).
Disclosures
The authors declare no conflicts of interest.
Data availability
No data were generated or analyzed in the present research.
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