1. Introduction

Thin films are essential components of advanced semiconductor products, e.g., in photovoltaic and flexible display industries [1,2]. Along with the increasingly matured ultra-thin film manufacturing processes based on selective atomic layer deposition [3], a sub-nanometer accuracy, real-time film measurement technique regarding film thickness t and refractive index n_λ is becoming emergently demanded for online ultra-thin film quality inspection, process optimization, and yield control [4]. Among the many existing thin-film measurement technologies, optical methods could be the most promising for non-destructiveness, high sensitivity, and fast speed. Optical methods determine thin film parameters by measuring the intensity, phase, frequency, state of polarization (SOP), or a combination of the optical responses through a thin film. Typical thin-film optical methods include spectral reflectometry (SR) and spectral ellipsometry (SE). With different light wavelength configurations, SR and SE have become industry standards in many film measurement applications with varying thicknesses from hundreds of micrometers to only a few nanometers [5].

SR could be the most successful technique for inline film measurements due to its millisecond-per-frame fast-sensing speed and portable hardware setup. It acquires the reflectance spectra of a target sample by calculating the ratio of reflected light intensities to incident intensities for measurement. However, optical reflectance is insensitive to the parameter variation of ultra-thin films smaller than 50∼100 nm, resulting in SR being ordinarily difficult to measure ultra-thin film [6] thickness and optical constants simultaneously. Besides, SR typically adopts co-axis optical fibers for normal incidence and reflectance control, which limits the lateral resolutions of inspection. Micro-SR has been developed using a high-NA (numerical aperture) objective for micro-spot imaging. However, micro-SR fuses angle-varying reflectance in a single spectrum, degenerating measurement accuracy [7,8].

SE, which determines thin film parameters by measuring SOP spectra, e.g., ψ, Δ, reflected or transmitted from a target sample, has shown extremely high sensitivity and accuracy. The state-of-art precision of SE in film-thickness measurement has achieved a typical value of 0.1 Å [9]. SE uses oblique optical configurations for illumination and polarization analysis, where a series of intensity spectra are taken at different polarization-analyzing settings in a time sequence. This principle results in SE and micro-spot-focusing SE [10] being limited to a lateral resolution of usually >20 µm and sensitive to sample vibrations due to limited measuring speed [11]. Therefore, SE usually is difficult to apply in real-time inline measurement on factory floors. Channeled spectropolarimetry (CSP) [12–14] has been developed recently to break through the speed bottleneck of SE measurement. CSP extracts Stokes or Mueller SOP parameters using Fourier analysis from a single-shot, thick-waveplate-modulated spectrum. Hence, the speed of measurement can be as fast as a camera’s shutter. Interferometric spectral ellipsometry (ISE) [15] has reported a 200 Hz snapshot ultrafast record of SOP measurement. ISE incorporates a film-reflected polarized interferometric spectrum with a carrier frequency by using an interferometer module [16,17]. Hence, the p/s-spectral phase difference of a film can be extracted from an interferogram via Fourier analyses. However, these Fourier analysis-based techniques may suffer from accuracy-limit problems due to spectral aliasing [13].

Beam profile reflectometry (BPR) [18] and its polarized form, known as angle-resolved ellipsometry (ARE) [19,20], have been developed to achieve micro-scale resolution thin-film measurement with a featured advantage of snapshot sensing capability. ARE is a kind of micro-ellipsometry that uses a high-NA objective lens for coaxial sample illumination and SOP spectral imaging. Thus, a micrometer-scale observation spot can be obtained through a pin-hole spatial filter for high-resolution measurements. By introducing continuous modulation of SOP and Mueller matrix modeling [20–22], ARE has been widely studied in complex film measurement with large surface roughness and other advanced applications [23]. Due to complicated optical configurations, however, exact calibration of ARE is still an intractable challenge to investigate, including the mapping of BFP radii to incident angles [24] and the polarization abbreviation of a high-NA objective [22]. Over the last few years, ARE has been intensively studied and modified to various forms for advanced applications. However, the application of which to ultra-thin films has not been demonstrated. For example, Dong integrated BPR with spectral reflectance imaging to construct angle-resolved hyper-spectra (ARS) for single-shot film measurement [25], though reflectance is known to be sensitivity-limited for ultra-thin films. He also showed that using a simple linear fitting, the ARS in both angular and wavelength domains could simultaneously determine film thickness and optical constants without falling in local minima. Ghim further applied a pixelated polarizing camera to polarized ARS acquisition for multilayer film measurement [26]. The obtained spectra exhibited significant deviations from the ground-truth due to the limited extinction ratios of a polarized camera. Lee combined BPR microscopic imaging with multi-order retarder modulation to achieve real-time film-thickness measurement [27]; but the method was not designed for simultaneous thickness and refractive index measurement. Choi considered using a digital light processor and RGB camera separately for multi-channel ARS acquisition and film measurement [28,29], where the refractive index was not investigated due to limited spectral channels. Lee, Chen, and Kim [30–32] further considered modifying BFP imaging into different configurations of orthoscopic illumination for high-resolution imaging ellipsometry development. Therefore, investigation of advanced methods for simultaneous thickness and refractive-index measurement of ultra-thin films in real-time is still challenging and yet to be explored.

In this paper, we follow the technical advancement of former researchers and develop a modified ARS, known as polarized angle-resolved spectral (PARS or polarized ARS) reflectometry, for simultaneous thickness and refractive-index measurement of ultra-thin films. PARS has a co-axial optical design for single-shot micro-spot inspection based on an alternative, cost-effective configuration by masking the slit of a spectrometer using a dual-angle analyzer. Specifically, an ARS image is captured for film measurement by radially filtering the back-focal-plane image of a high-NA objective through a dual-angle analyzer and chromatic disperser. Thus, film parameters are fitted accurately from an ARS image in both angular and wavelength domains. PARS has no mechanical movement devices and completes a measurement within milliseconds and thus is expected to apply in in-line film monitoring. Our experiments demonstrated the real-time measurement capability of the proposed method by simultaneously measuring the thickness and refractive indices of ultra-thin films through a single ARS shot.

2. Method

2.1 Hardware configuration

The proposed PARS reflectometry is illustrated in Fig. 1(a). It includes a broadband light source, a measuring probe, and an acquisition unit. The broadband light from a source is collimated and polarized through a 45°-placed linear polarizer relative to the x-axis. Then the light changes the propagation direction through a beam splitter and incidents to the sample at various angles through a high-NA objective lens. The numerical aperture of the objective determines the range of incident angles. In the study, an objective of NA 0.9 was used, resulting in approximately an incident angle range of [-64°, 64°]. The objective collects the light of various angles reflected from the sample, the back-focal-plane (BFP) information of which is then imaged to an imaging spectrometer with a 0°-placed entry line-slit through relay lenses and a dual-angle polarization analyzer. The analyzer was made by attaching two cross-polarized thin-film linear polarizers side-by-side. Thus, the light reflected from the BFP of a film sample enters the cross-polarized polarizers half-by-half for subsequent spectral analysis. Thin-film polarizers based on absorption dichroism are suggested for polarization analysis, which means the orthogonal polarization components of a light beam are strongly absorbed while the other transmits.

 

Fig. 1. Principle of the PARS reflectometry. (a) System configuration, (b) SOP of the incident (red) and reflected (green) light at the BFP, and (c) corresponding ray-tracing details, (d) top-view of the dual-angle analyzer and (e) an obtained PARS image.

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For any BFP location as presented in Fig. 1(b), its radius r corresponds to an angle of reflectance (and incidence), and its azimuthal angle corresponds to a specific SOP of reflectance. Figure 1(c) illustrates the high-NA objective-resulted ray tracing behaviors and how an incident angle $\theta $ corresponds to a BFP radius. In the acquisition unit, a customized dual-angle polarizer comprised of two symmetrically-placed orthogonal polarizers illustrated in Fig. 1(d) is used to filter specific SOPs of reflected light. Finally, the filtered light projects to the entry line-slit of an imaging spectrometer at the conjugate BFP for analysis. A polarized, angle-resolved hyper-spectrum of reflection, as presented in Fig. 1(e), is finally obtained for film analysis. For example, all film parameters t, n_λ, and k_λ of each illumination wavelength λ can be simultaneously determined by minimizing a sum-of-squares cost function in the form of:

2.2 Incidence angle calibration

Exact mapping from BFP radii to incident angles is fundamental to unbiased PARS measurement using a commercial imaging spectrometer. To this problem, Abbe’s sine condition of low-aberration objectives in the form of $r = c \cdot \sin \theta $ has been widely accepted. c can be simply calibrated using a pre-measured incident angle and its corresponding BFP radius: $({{r_c},{\theta_c}} )$, such that $c = {r_c}/\sin {\theta _c}$. In the study, ${\theta _\textrm{c}}$ was selected using the Brewster angle of a standard material block, under a boundary reflection of which ${r_\textrm{c}}$ corresponds to the minimum-intensity, p-polarized BFP positions.

Specifically, a semi-infinite K9-glass optical flat was used as the standard material. Its optical constants were initially measured using a commercial ellipsometer. Figure 2(a) presents an angle-resolved hyper-spectrum of p-polarized reflected light for the calibration, where a linear polarizer instead of the dual-angle polarizer in Fig. 1 was 0°-placed relative to the x-axis as the analyzer. Please note that the central small-angle area of the PARS image is eliminated because we only focused on the large incident angle area, where the Brewster angle of the used reference materials locates, for the incident angle calibration. Then, local quartic polynomial fitting was performed on each single-wavelength angular spectrum for minimal search. A quartic fitting was used because the spectral asymmetry near the minima has been reported [24], a lower-degree (e.g., quadratic) polynomial fit of which cannot adapt to the asymmetrical characteristics, while a large-degree polynomial may over-fit noise.

 

Fig. 2. Incident angle calibration analysis. (a) p-polarized ARS (portion) of a K9-glass optical flat; (b) minimal-intensity fitting of each angular spectrum at different wavelengths; and (c) cross-validation of the calibrated Brewster angles using K9 and fused silica glasses.

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The minimal-intensity positions, e.g., ${\rho _{1,\lambda }}$ and ${\rho _{2,\lambda }}$, thus correspond to the Brewster angle. Hence, the incident angle mapping function regarding a pixel position of ${\rho _\lambda }$ is expressed as:

Two optical flats made of K9 and fused silica were used to conduct the calibration for cross-validation. The calibrated results at each wavelength are plotted in Figs. 2(b),(c). It is found that along with the decreasing of wavelengths, the Brewster angle-corresponded BFP radius of an optical flat gradually increases. Please note that Fig. 2(a) shows that the Brewster angle-corresponded minimal intensity locations are difficult to identify due to low signal-to-noise ratios within the range of <500 nm. Thus, only the ARS image in the range of 500∼700 nm as seen in Fig. 2(b) was used for incident angle calibration. For the ARS image range of <500 nm, the incident angle mapping coefficients used the one calibrated at 505 nm. Considering that the refractive index functions of the used glasses are slowly varied within a visible wavelength range, we broke the incident angle calibration problem down to small wavelength segments of about 25 nm for individual linear fitting. Within each fragment, a goodness of fit was calculated, and an average of them in about 0.9999 was finally obtained. The separately fitted lines in Fig. 2(c) verified that the dispersion of the incident angle calibration is weak.

2.3 Film parameter analysis

The Jones matrix method [5] is widely used in optical SOP analysis, using which the output electric field vector ${E_{out}}$ in the spectrometer of Fig. 1 can be expressed in the following form:

In this study, the polarizer angle $\beta $ was fixed to 45°, and the observing angle $\mathrm{\Omega}$ was set to 0°. Hence, Eq. (3) leads to the following output intensity equation:

As presented in Fig. 1(d), the dual-angle analyzer has polarization angles of 0° and 90°, respectively, on the left and right of the optical axis. Therefore, as shown in Fig. 1(e), an obtained PARS image consists of angularly symmetrical p- and s-polarized intensity spectra on the left and right. By pre-calibrating the input intensity ${I_{\textrm{in}}}$ using a standard material, e.g., a bare single crystal silicon wafer from Filmetrics (TS-SiO₂-6-Multi, with a native oxide layer of 1.85 nm) in the study, an angularly symmetric p-/s-reflectance spectra R_ps-ARS, including R_p-ARS and R_s-ARS at each half, can be easily obtained using

3. Experiment setup

A visible-range PARS reflectometry like Fig. 1(a) was carefully constructed to validate the proposed method. The broadband white light source used was a halogen fiber optic illuminator (OSL2 from Thorlabs). The collimating lens and imaging relay lens used were double-cemented achromatic lenses. The polarization state generator used a Glan-Taylor polarizer (PGT6315, Union Optic) while the polarization state analyzer was made by attaching two cross-polarized thin-film linear polarizers side-by-side. The objective lens was an Olympus M-plan, semi-apochromatic, 100× objective with a NA of 0.9. The imaging spectrometer was Horiba iHR320 with a spectral resolution of 0.798 nm within 350–900 nm. The imaging sensor of the spectrometer was a 26 µm-pixelated CCD array with an incident angle dimension of 256 pixels and a wavelength dimension of 1024 pixels. The exposure duration of the spectrometer was set constantly to 10 ms.

Seven ultra-thin film samples with unknown refractive indices were measured, and each sample was repetitively measured ten times for accuracy verification. The samples were mono-layer SiO₂ films from Filmetrics with different thicknesses within 10-2000nm deposited on a monocrystalline-Si substrate. The accuracy and precision of measurement were then evaluated against an industrial reference SE: J. A. Woollam M-2000.

4. Results

Our calculation process, referring to the suggestion of ISO 23131-3 (draft), is a step-wisely refined fitting for thickness t and refractive index n. Since the refractive index n of SiO₂ changes slowly within the visible range (suggested by existing databases), an approximated simplification was used. In the study, for example, an initial fit of t_ini and constant n_ini within the visible rage was obtained at first. Then a refined fit of t and n was conducted by introducing a Cauchy dispersion model ($n = A + \frac{B}{{{\lambda ^2}}}\; + \frac{B}{{{\lambda ^4}}}\; $) instead of a constant, where t_ini and n_ini were used as the initial values of t and A, respectively.

The correctness of the PARS reflectometry was analyzed first. The measured PARS images of samples no. 1 (12.5 nm) and 6 (1000 nm) are presented in Fig. 3 and Fig. 4, where ψ-ARS have been symmetrically extended to be equalized to R_ps-ARS regarding the number of image pixels. For comparison, the theoretical PARS calculated using the results of M-2000 are also plotted. The figures show that the measured PARS signals coincide well with the theoretical models in both angular and wavelength dimensions. It is noted that the experimental R_ps-ARS images show non-distortion at the symmetrical centers, though the p- and s-light through individual polarizers converge at the angular symmetry centers with incident angles of near 0°.

 

Fig. 3. Theoretical and measured PARS signals of a 12.5 nm SiO₂ film (Sample 1). (a),(b) PARS images of dual-angle polarized reflectance R_ps and ψ, respectively; (c),(d) typical PARS curves extracted at the wavelength and incident angle dimension, respectively.

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Fig. 4. Theoretical and measured PARS signals of a 1000 nm SiO₂ film (Sample 6). (a),(b) PARS images of dual-angle polarized reflectance R_ps and ψ, respectively; (c),(d) typical PARS curves extracted at the wavelength and incident angle dimension, respectively.

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Film thickness and refractive indices were calculated by fitting all measured PARS images, including p-PARS, s-PARS, and ψ-PARS, using Eq. (1). In Table 1, film thickness results are summarized. The results show that the PARS system has an RMS (root-mean-square) systematic error of 1.1 nm.

Table 1. Film thickness error analysis through 10 repetitive PARS measurements (unit: nm)

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The consistency of measured thicknesses and reference values is presented in Fig. 5(a), which shows high goodness of 0.9999 of a linear fit within a measurement range of 10 nm to 2000nm. It can also be found that the random error varies along with the measured film thickness. The sensitivity-varying phenomenon coincides with most rotating-analyzer/-polarizer ellipsometers. The sub-nanometer precision indicates that PARS has higher measurement sensitivity than commercial SRs. Robust fitting algorithms and systematic calibration methods need to be investigated in the future to make PARS competitive with commercial SEs.

 

Fig. 5. Comparison of measured thicknesses (left) and refractive index spectra (right) of different film samples using PARS and a commercial SE.

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The time cost of a single measurement includes a PARS image exposure of 0.01s and an image fitting calculation of ∼0.4s in MATLAB. By applying C language and GPU parallel computation, the computational time cost is expected to drop off to a millisecond level in the future.

The measured refractive index spectra from different film samples are plotted in Fig. 5(b). The results show that the PARS-measured refractive indices from films thicker than 50 nm are close to the reference value obtained from a 1 µm-thickness film and a commercial SE. For ultra-thin films with a thickness close to or less than 50 nm, the PARS-measured spectra obviously deviate from the reference. This could be attributed to the reduced compactness or relatively large surface roughness of initially deposited films [33]. In addition, the optical thickness $nt$ as an entirety influences the ellipsometric responses of reflectance instead of t alone. A Taylor approximation $nt = {n_0}{t_0} + {n_0}\delta t + {t_0}\delta n$ indicates that when ${t_0}$ is small, a slight variation $\delta n$ compromises with a negative, equivalent variation $\delta t$; while if ${t_0}$ is large, a small variation $\delta n$ compromises with a large negative variation $\delta t$, indicating that the optical reflectance sensitivity increases if a film gets thicker. Therefore, for ultra-thin film measurement, a significant error may happen when trying to isolating n from t or vice versa. In the ARS cases, thickness t keeps constant when measuring using different wavelengths and at different incident angles. Hence, the measured t is relatively more accurate, while n deviates significantly from the bulk materials.

5. Discussion

5.1 PARS errors

Significant spectral errors can be observed at the reflectance peaks or pits at the large-incident angle areas (see red and black curves in Fig. 4(d) corresponding to >45°) and short-wavelength areas (see orange and brown curves in Fig. 4(e) corresponding to <500 nm). The spectral error in Fig. 3,4 coincides with the results in [25] where larger errors were observed. These could be attributed to the inaccurate incident angle calibration below 500 nm, as seen in Fig. 2, where the incident angle calibration results below 500 nm were omitted due to large measuring noise. Also, large incident angle calibration uncertainties in large angle areas may distort PARS. A variation analysis in [29] shows that the angle calibration uncertainty increases along with the increasing of incident angles and may approach 0.7° using an objective of NA 0.95. Besides, the limited distinction ratio of the analyzer may weaken the spectral peaks and pits at, respectively, the constructive and destructive interference positions. ψ-ARS shows larger errors than R_ps-ARS because the division-based ψ calculation enlarges the error of R_ps. This results in that film parameter determination using ψ or Δ may produce larger errors than R_ps though ψ or Δ are supposed to be more sensitive to film parameters. Therefore, film measurement through a combination use of R_ps and ψ is recommended in this study.

5.2 PARS advantages

The presented results above show that the proposed PARS reflectometry can accurately measure film thickness without knowing its refractive indices. Compared to general SR adopting a normal incident structure, our PARS reflectometry has significant accuracy advantages in measuring ultra-thin films of less than 100 nm. An important reason is that the PARS reflectometry simultaneously analyzes two-dimensional reflectance and ellipsometry information in both wavelength and angular domains in a single-shot measurement.

Figure 6 presents logarithmic cost functions of two extracted single-angle wavelength-domain spectra and the PARS of an ultra-thin film in a solution space of thickness and refractive index. The cost function maps show that the PARS method has an obvious, unique global solution (corresponding to the smallest search area of dark) that convergence can easily approach without requiring an accurate initial-value setting. This explains how the additional angular information of PARS significantly improves the convergence accuracy of multi-parameter fitting in film measurement.

 

Fig. 6. Cost functions of a wavelength-domain spectrum at an incident angle of (a) 0°, (b) 60°, and a whole PARS (c) for a 10 nm SiO₂ film on a c-Si substrate regarding film thickness and refractive index.

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5.3 PARS selection

Selection of a proper PARS in Eq. (7) for multi-parameter fitting influences film measurement accuracy. This study used a combination of p-, s- and ψ-PARS images to determine film parameters. Now we compare the proposed method with Dong’s [25] method, where only p-PARS information was used. By re-using the previously obtained PARS data, the comparative study analyzed the absolute measurement errors of film thicknesses and uncertainty of refractive indices. The error statistics are plotted in Fig. 7, where only five repetitive experiment results are presented for space-saving purposes. The results show that fitting from multiple PARS images can significantly improve film parameter determination accuracy compared to fitting from p-PARS only.

 

Fig. 7. Error analysis for the thickness (top) and refractive index (bottom) measurement of a 12.5 nm (left) and 50 nm (right) SiO₂ films by fitting different PARS images.

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In comparison to Ghim’s method based on a pixelated polarization camera [26], our method based a normal camera combined with a dual-angle polarizer brings in the merits of lower cost and possibly higher accuracy of measurement. This is because thin-film polarizers are cost-effective and have higher-extinction-ratios than a pixelated polarizer. By placing the dual-angle analyzer at 0° or 90°, R_ps and ψ are measured; and if placed at 45° or 135°, Stokes parameters S₀ and S₂ are obtained. The latter supposes to be also sensitive to ultra-thin film measurement.

Another simulated cost function analysis of different SOP variables, including R_p, R_s, ψ, S₂, Δ, and their combinations were conducted. As presented in Fig. 8, we must point out that Δ has the best sensitivity and convergence speed; however, the solving uncertainty in simultaneous multi-parameter (thickness and refractive index) solving is unsatisfying as seen that the blue convergence area is larger than that of R_p, ψ. R_p, ψ, and their combinations with R_s have relatively less sensitivity and convergence speed but with the smallest uncertainty in multi-parameter solving. This indicates that simultaneous estimation of film thickness and refractive index using R_p, ψ, and their combinations with R_s may have the smallest errors. ${S_2}$ including the terms of sin2ψcosΔ has a moderate sensitivity and the worst uncertainty of multi-parameter solving. An SOP combination analysis indicates that R_ps+ψ may provide the best solving accuracy over R_ps+Δ and R_ps+ S₂.

 

Fig. 8. Simulated cost functions of different SOP ARS for a 10 nm SiO₂ film with a refractive index of 1.46. (a)-(e) Cost functions of R_s, ψ, S_2, $\mathrm{\Delta }$, and R_p, respectively; (f)-(h) cost functions of combined SOP variables.

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5.4 Polarization error calibration

The polarization characteristics of the optical components, e.g., the beam splitter and high-NA objective lens, were ignored in the study, though they should be calibrated and corrected in high-accuracy SOP measurement. In facts, in the SOP measurement studies in [25–29], the polarization errors of beam splitters and objective lens were ignored without producing significant measurement errors. Another evidence is presented in the following through an SOP cost function analysis.

Firstly, the SOP ARS including R_p, R_s, ψ, S_2, $\mathrm{\Delta }$, and their combinations were simulated, and their cost functions regarding the measurement of an ultra-thin film are presented in Fig. 9. For comparison, a small polarization error in the Jones matrix form of $Je = [{\tan 40^\circ {e^{i5^\circ }},\tan 0.5^\circ {e^{i0.5^\circ }};\tan 0.5^\circ {e^{i0.5^\circ }},1} ]$ similar to [34] was then added to the ARS simulation, and the corresponding cost functions were analyzed. The comparison results in Fig. 9 show that $\mathrm{\Delta }$ results in significant convergence error in film measurement, providing a small system error. It indicates that $\mathrm{\Delta }$ is very sensitive to system errors, a small of which results in significant errors in film parameter determination. In contrary, the ARS of R_p, R_s, ψ, and their combinations show limited convergence error, and thus they are relatively insensitive to small system polarization errors in film measurement. Therefore, an ARS reflectometer can provide relatively accurate film measurement when limited systematic polarization errors are ignored.

 

Fig. 9. Simulated cost functions of different SOP ARS for a 10 nm SiO₂ film with a refractive index of 1.46 when a small polarization error induced by a beam splitter presents. Dashed crosses indicate the locations of the true solution.

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6. Conclusion

We propose a polarized angle-resolved spectral reflectometry for simultaneous thickness and refractive-index measurement of ultra-thin films. The technology simultaneously obtains angle-resolved spectra of p- and s-polarized reflectance at the back-of-plane of a high-NA objective in a single shot through a dual-angle analyzer and image spectrometer. Hence, multiple film parameters can be simultaneously fitted from the hyper-spectrum in both angular and wavelength domains in a reliable sense. A preliminary form of the proposed system was built, and seven thin-film samples of various thicknesses were measured against a commercial spectral ellipsometer. The results show that the proposed method has achieved sub-nanometer accuracy and precision in film-thickness measurement within a measuring range of 10 nm to 2000nm without knowing its refractive indices. The simultaneously obtained refractive index spectra coincide well with the reference except when measuring ultra-thin films of less than 50 nm. This could be attributed to the reduced compactness of ultra-thin films obtained from an initial deposition process. The mathematical foundations of the claimed accuracy advantage against existing reflectometry have also been discussed.

With the advantage of a compact hardware configuration, micrometer-scale spatial resolution, sub-nanometer accuracy, and single-shot sampling speed, we expect the proposed method to be a potential and powerful tool for millisecond-per-frame real-time, in-line ultra-thin film monitoring in semiconductor industries.