We have developed an extreme ultraviolet (EUV) scatterometer based on the analysis of coherent EUV light diffracted from a periodic array with nano-scale features. We discuss the choice of appropriate orders of the high harmonics generated coaxially along with the intense Ti:sapphire laser pulses for high resolution spatial performance. We describe an inverse-problem methodology for determining the structural parameters, and present preliminary measurement results confirming the functionality of the scatterometer. A rigorous coupled-wave analysis measurement algorithm was developed to extract accurately and quickly the relevant constitutive parameters from a measured diffraction pattern using a library-matching process.
© 2016 Optical Society of America
Device and integrated-circuit technology has rapidly evolved over the last decade, aiming toward ever-smaller three-dimensional (3D) structures. The 3D nanoscale nature of these structures presents considerable challenges for standard metrology techniques, especially when involving features smaller than 22 nm .
Critical-dimension scanning electron microscopy (CD-SEM) is suitable for imaging at the CD level, but its sensitivity to the 3D structure height, layer recess, or side-wall angle (SWA) is limited. CD small-angle X-ray scattering (CD-SAXS) has been identified as a potential solution for measuring nanoscale lithographic features using sub-nanometer-wavelength radiation in a transmission geometry. Brighter X-ray sources are necessary for applying this technique, presently confined to the laboratory, to high-volume manufacturing (HVM). CD atomic-force microscopy (CD-AFM) measurements are limited by the need to displace a probe over the entire measurement area. This limits the scope of measurable target features to the available probe dimensions, expressed in terms of probe width, probe length, and maximum angle of lateral extension [2–6]. With decreasing feature size and an increasing demand for precise measurements of nano-scale structures, scatterometry offers the best current optical technology for CD measurement and control. This technique is best suited to measuring shape profiles and vertical dimensions, and resolves some of the limitations of CD-SEM, CD-SAX, and CD-AFM. It is a versatile metrological technique based on analyzing light diffraction from periodic structures in terms of the CD and other profile properties [7–9]. Scatterometry is a model-based approach that involves comparing light-scattering measurements against theoretical “signature” scatter patterns. The theoretical model uses a rigorous grating theory to determine the series of diffraction efficiencies that correspond to discrete iterations of various grating parameters. The inverse problem is solved by using a library of pre-generated scatter signatures. After raw signatures are measured, the library is searched to find the best match to the data.
Two major types of scatterometry are designed for measuring small features on patterned wafers [10–12]. Angle-resolved scatterometry involves single-wavelength readings at various angles, which therefore requires special hardware for varying the measurement angle. Specular spectroscopic scatterometry measures the zero-order diffraction response at a fixed incident angle but for multiple wavelengths. The direct use of conventional spectroscopic ellipsometer (SE) and spectroscopic reflectometer (SR) systems requires complicated and costly components such as polarizers, analyzers, and spectrometers.
In advanced semiconductor geometries with feature lengths less than tens of nanometers, there is typically only one diffraction order (known as the zeroth order) if the measurement wavelength range is fixed in the visible or UV regime. Scattering data is unable to resolve lineshapes where the CD is much smaller than the incident wavelength. Thus, as the feature size decreases continuously, shorter measurement wavelengths are needed for scatterometry to resolve detailed features in structures smaller than 100 nm [13–15]. The short wavelengths of extreme ultraviolet (EUV) radiation are advantageous, as they give rise to several diffraction orders of scattering from features of the order of tens of nanometers. The increased sensitivity also allows the accurate extraction of topographic profile information from nanoscale periodic structures. This present paper discusses the use of polychromatic high-harmonic generation (HHG) in the EUV range for the purpose of novel applications of model-based EUV scatterometry. Compared to synchrotrons and X-ray free-electron lasers, which also serve as short-wavelength light sources, high-harmonic beams display a high degree of spatial coherence, albeit on a small scale . The HHG source is assessed to be a very promising for needs of the tabletop sources of coherent radiation in EUV, and soft X-ray spectral regions. Their unique characteristic multiple-order output can be tailored to single or multiple orders as required for experiments .
We extend earlier scatterometry work by employing harmonic emission consisting of a few harmonic orders, namely 15-50 nm in the EUV range, to illuminate periodic structures for diffractive imaging. In contrast to variable-angle and specular spectroscopic scatterometries, the proposed EUV scatterometer is designed to measure the intensity of non-zero-order diffraction at a fixed incident angle and at multiple laser-like wavelengths. The periodic structures within the sample form an optical grating and disperse the HHG onto a CCD camera. The well-separated higher-order diffraction beams are more informative than the zero-order diffraction beam, which propagates simply along the specular direction. This type of non-zero-order diffraction information, coupled with a very efficient rigorous coupled-wave analysis (RCWA), can achieve a detailed reconstruction of the profile of nanoscale periodic gratings. Conventional scatterometry is susceptible to correlation between critical measurement parameters and reduced sensitivity to their measurement. In this paper, however, describes the use of yet two more methods for breaking correlations and increasing sensitivity—include the use of non-zeroth order (m = + 1 and m = −1) diffracted light and polychromatic wavelengths of HHG. For many structures, this flexibility significantly increases parameter sensitivity and reduces parameter correlation. A novel approach to extracting a CD profile, viewed as an optimization problem, is to find a profile whose simulated orders of diffraction match the measured response, thus enabling 3D-structure profile reconstruction.
2. EUV source and scatterometer design
2.1 EUV source
The EUV source is driven by a table-top femtosecond laser developed by the EUV team of the National Tsing Hua University (NTHU). A pump laser (25 fs pulse duration, 0.5 mJ pulse energy, 1 kHz repetition rate at central wavelength 800 nm) was focused onto an argon-filled gas cell for HHG . The output coupled EUV beam contains many superimposed harmonics. This situation is desirable for EUV scatterometer applications, where nano-scale periodic geometrical structures serve as an optical grating to separate the harmonics for measurement by a CCD camera. Previous research showed that high-order harmonics can be tailored and confined to only a few orders, depending on the experimental requirements, by an appropriate choice of gas species and pressure, laser-focus position, the laser-beam intensity and diameter, and the interaction geometry [19, 20].
2.2 Scatterometer design
To conduct a preliminary test, the EUV scatterometer design used for polychromatic EUV diffraction adopted the simplest possible experimental geometry. This lens-free system records diffracted EUV light from a periodic grating pattern, allows aberration-free imaging, and offers a very large depth of focus. The experimental geometry is outlined in Fig. 1. The EUV scatterometer system consists of a pinhole for collecting incident light, an Ar gas cell, three Al filters, a pair of Kirkpatrick-Baez (K-B) mirrors, a grating-structure sample, and a back-illuminated CCD camera. The argon-filled gas cell enables HHG in the bright line region of 15-50 nm. Al filters, consisting of three 200-nm-thick Al layers, were inserted into the pump light. The K-B mirror pairs focused the high-harmonic (HH) beam to spot sizes below 100 μm. The sample was placed at a 45° angle of incidence near the focus of the EUV beam. The sample holder was mounted onto a piezoelectric x-y-z-θ stage, with range ± 21 mm, linear resolution 1 nm, and rotational resolution 2° × 10−4. A deep-cooled 16-bit resolution CCD camera (Andor iKon-L 2048 X 2048) with pixel size 13.5 μm × 13.5 μm was placed 15.7 cm away from the sample to capture the diffraction pattern, oriented with its surface nearly normal to the zero-order diffraction of the beam. Positive and negative orders of diffraction occurred on both sides of the zero-order beam, at angles specified by Eq. (1). The CCD camera recorded the diffraction and scattering-intensity images straightforwardly, without requiring any intermediary imaging optics, thereby providing intensity information in frequency space. The 3D-structure profile parameters were evaluated using the diffraction intensities derived from the periodic patterns, and reconstructed via the characteristic-signature library matching process discussed below.
2.3 Sample details
A gold-coated reflection grating (1200 lines per millimeter) was used for HHG wavelength calibration.
Two different rectangular reflection gratings, etched by the single-crystal silicon substrate, were studied:
- •The first had a density of approximately 1200 lines per millimeter, with a nominal groove depth of 200 nm and the substrate is a square of size 12.5 mm.
- •The second had a density of approximately 7200 lines per millimeter, with a nominal groove depth of 50 nm and the substrate is a square of size 12.5 mm.
3. Theoretical model of the diffraction spectrum
3.1 Basic theoretical model for the grating response
A monochromatic ray of wavelength λ is assumed to be incident at an angle θi onto a grating surface, and is diffracted over a set of discrete angles θm, depending on the grating pitch d. These quantities are related by the grating equation:
When monochromatic light is incident onto a grating, it is diffracted in directions corresponding to m = 0, ± 1, ± 2, ± 3, etc. The grating equation shows that the angles of the diffracted orders depend only on the pitch of the grating and not on its shape. A parallel polychromatic beam incident on a grating also disperses the light, with each wavelength satisfying the grating equation. Each wavelength in the input-beam spectrum is diffracted in a different direction, producing a spatially separated spectrum. The EUV radiation emission consists of distinct spectral components given by high-order harmonics of the fundamental frequency, and displays collimated laser-like characteristics. Thus, the wavelengths of the high-order harmonics generated and the accurate grating pitch were confirmed by the spatial distributions captured by the CCD camera, based on the known incident angle and the sample-CCD distance.
3.2 Theoretical model of grating diffraction in the EUV range
We used rigorous coupled wave theory, one of the most versatile and robust models used for computing diffraction effects in mono- and multi- layer gratings [21–24]. It uses film stack information (optical refractive indices, and thickness values) and the grating parameters (height and profile characteristics) to theoretically predict diffraction from the measured structure. The complex refractive indices of the grating structure and substrate materials in the EUV range are calculated based on the CXRO (Center for X-ray Optics) database. Certain approximations are used in RCWA to predict the grating efficiency accurately for a wide variety of grating profiles over wide spectral ranges. The distribution of the incident field power at a given wavelength, diffracted by the grating sample into the various orders, depends on many parameters, including the incident power, the incidence and diffraction angles, the (complex) refractive index of the grating material, and the grating profile. The extraction of the latter can be viewed as an optimization problem, yielding the best agreement between theory and measurement, to enable 3D-structure profile reconstruction.
Figures 2(a) and 2(b) show the simulated reflection of an Au-coated grating target for incident wavelengths 500 and 29 nm, and for a fixed incidence angle θi = 45°, depth 10 nm, and 90° side-wall angles respectively. The grating CD was changed from 10 to 60 nm with a fixed pitch 100 nm. As expected, only the zero-order case (m = 0) exists when using 500 nm incident wavelength. Also, the diffraction signal is insensitive to CD variations in the range 10-60 nm. Figure 2(b) shows how the CD changes the diffraction efficiency continuously, both at the zero- and first-diffraction orders when the incident wavelength is 29 nm. An appropriate choice of measurement wavelength is therefore necessary to obtain a strongly sensitive diffraction signal and thus a sufficient signal-to-noise ratio for grating pitches. Note that the reflectivity intervals of the vertical axis in Figs. 2(a) and 2(b) are the same for the purpose of sensitivity comparison, despite showing an approximately eight-fold difference. Rectangular line profiles are here assumed for computational efficiency. Although the example shown is for a simple structure, the analysis can be extended to any practical situation.
Figures 3(a) and 3(b) show the simulated reflectivity of an Au-coated grating target with incident wavelengths 500 and 29 nm, for a fixed incidence angle of 45°, a pitch of 100 nm (duty cycle 50%), and 90° side-wall angles. The grating depth was changed from 10 to 50 nm. As above, only zero-order diffraction (m = 0) is apparent when using the incident wavelength of 500 nm and the diffraction signal decreases slowly as the grating depth increases from 10 to 50 nm. Figure 3(b) also shows how the grating depth affects the diffraction efficiency dramatically, both in the zero- and first-orders, when the incident wavelength is 29 nm. Note that the scale increments on the vertical axis in Figs. 3(a) and 3(b) are the same, to allow a comparison of the sensitivities, despite their significantly different absolute values.
3.3 Theoretical model of grating-diffraction response of HHG
First-order high-harmonic emission at wavelengths in the range 15-50 nm was utilized for EUV scatterometry. Figures 4(a), 4(b), and 4(c) plot the theoretical first-order diffraction efficiencies from an Au-grating target for varying grating CDs, depths, and side wall angles respectively. Three HHG wavelengths 29, 27, and 25 nm are assumed when modeling each individual characteristic signatures of diffraction. We creates a full range (CD ranges from 40 to 60 nm, depth from 10 to 50 nm, side wall angle from 85° to 90°) within which to study the general characteristics of the diffraction signatures. The incident angle is 45°, the pitch 100 nm. Figure 4(a) shows the CD varying the diffraction efficiency of those three harmonics continuously. Figure 4(b) clearly indicates the characteristic response of HHG, especially in the case of shallow grating depths. Figure 4(c) shows the side wall angle varying the diffraction efficiency of those three harmonics slowly but with apparent difference of m = + 1 and m = −1 orders.
4. Measurement algorithm and library match process
As a first step toward verifying our EUV scatterometry concept, the experimental geometry was adjusted and simplified so as to measure only first-order diffraction intensity from a periodic grating in the case of multiple harmonic orders. A specific advantage of first-order diffraction measurements is that a high-harmonic source, by its nature, provides a high degree of spatial coherence. The diffraction pattern, which is the superposition of the diffraction images associated with each harmonic beam, can be analyzed subsequently to reconstruct the grating profile.
4.1 EUV spectra calibrations
Figure 5(a) shows the schematic arrangement of the EUV scatterometer operated in calibration mode, and Fig. 5(b) typical diffraction data. A gold-coated reflection grating with a density of 1200 lines per millimeter was used for calibrating the HHG wavelengths. The sample positioner was equipped with an x-y-z-θ stage to move and rotate the sample into the EUV beam focus. The beam focus was made to coincide exactly with the axis of rotation. The diffraction spectrum was projected onto a detector and recorded in a plane that was nearly perpendicular to the diffracted rays. Figure 5(a) outlines the geometrical arrangement of the calibration grating and CCD detector used in calibration mode. The EUV beam was incident at a nominal angle θi = 45.0° onto the gold-coated grating surface, and the sample was located at a nominal distance L = 157 mm away from the CCD surface. The beam was diffracted along discrete angles θ+1 and θ-1 by the grating with density 1200 lines/mm. Five of the wavelengths corresponding to the orders of n = 23th, 25th, 27th, 29th, and 31st HHG can be derived from the same grating equation, the only difference being the diffraction angles θ+1 and θ-1 (the arctangent of the distance between the diffraction peak and the CCD center Dn(m = ± 1), divided by the sample-CCD distance L). The upper section of Fig. 5(b) shows a typical diffraction image, as viewed in the CCD window, which allows the m = ± 1 diffraction intensities to be acquired simultaneously. The lower panel plots the total CCD counts, summed vertically along each column of pixels. The CCD sensor thus serves as a linear image sensor, like a photodiode array. This plot is more convenient for optimizing the HHG parameters, to achieve a high EUV flux before applying the grating equation.
The grating equation can be written as following form to describe first-order diffraction of HHG:
Table 1 shows the calculated HHG orders and wavelengths, based on the grating equation, Eq. (2). Some parameters (the grating pitch d, incident angle θi, fundamental wavelength λ0, and sample-to-CCD distance L) are common to the whole set of five independent grating equations. The greater the number of independent grating equations, the more parameters can be fitted. Thus, the fundamental wavelength, incident angle, and sample-to-CCD distance are confirmed to be 794.5 nm, 45.05°, and 157.4 mm, respectively. This minimizes the fitting errors on the HHG orders and wavelengths.
4.2 Library generation and matching process
The theoretical model uses rigorous grating theory to model the diffraction efficiencies of a given grating. To solve the inverse problem, once the HHG wavelengths are determined through the calibration process as discussed in section 4.1, a library of HHG scatter signatures spanning a range of CD values, grating depths, and side-wall angles is pre-generated. This library is then searched to find the best match to measured data. A common metric used for this purpose is the root-mean-square error (RMSE). It allows a comparison of the theoretical and measured diffraction efficiencies in individual orders of HHG. To eliminate pulse-to-pulse laser-intensity fluctuations, which can in turn cause HHG peak intensity fluctuations, the ratio of first-order (m = + 1 to m = −1) reflectivity is calculated and compared to the pre-generated library to obtain the best match. Figures 6(a), 6(b) and 6(c) show an example of modeling the ratio of first-order diffraction efficiencies, calculated from Figs. 4(a), 4(b) and 4(c). Figure 6(a), 6(b) and 6(c) show how the CD, depth, and side wall angle change the ratio of first-order diffraction efficiency of those three harmonics in a characteristic and sensitive way. The relative intensities of first-order diffraction depend sensitively on the detailed properties of the microscopic structure on the nanoscale.
5. Results and discussions
5.1 Etched Si grating with 1200 lines/mm
Figure 7(a) shows the schematic configuration of the EUV scatterometer operated in measurement mode, identical to that used in calibration mode. A measured diffraction image spectrum is plotted in Fig. 7(b). An etched silicon reflection grating with a pitch of 1200 lines per millimeter and a nominal depth of 200 nm was used for the first trial. The CCD exposure time was 5 s.
The most accurate measurements of diffraction intensities require many counts under the peaks. The intensity counts are integrated over a small angular range, and an estimated background which is 2% of the integrated counts is subtracted from the enclosed area. The relative counts for the different HHG orders provide a quantitative metric for use in matching during the library search, thus eliminating any measurement error caused by HHG input instability. Table 2 lists the detailed counts under each HHG diffraction peak and the best match results between measurement and modeling. Figure 8(a) shows the reconstructed grating profile based on the parameters including the CD, grating depth, and side-wall angle generated to get the best match; a cross-sectional SEM image is shown in Fig. 8(b). The model fit for a top CD of 371 nm, a bottom CD of 386 nm, and a grating depth of 202 nm shows satisfactory agreement with the cross-sectional SEM results.
5.2 Etched Si grating with 7200 lines/mm
An etched silicon reflection grating of density 7200 lines per millimeter and nominal depth 50 nm was used for the test. The distance between the grating and the CCD sensor, fixed at 157.4 mm in the current experimental setup, imposed a limit on the grating density. A high density produces a large diffraction angle, so that both of the m =± 1 beams cannot fit in the CCD window for a given incident angle. One solution is to rotate the sample so that both diffracted beams can be measured in turn, each with an appropriate incident angle. Figures 9(a) and 9(c) show the schematic arrangements for the EUV scatterometer designed to measure the m =+ 1 or −1 beam, with the EUV-beam incident angle set to 56.25° or 36.95°, respectively; the corresponding spectra are shown in Fig. 9(b) and 9(d). The CCD exposure time was 15 s. Table 3 lists the detailed counts under each HHG diffraction peak and the best match results between measurement and modeling. Figure 10(a) shows the reconstructed grating profile, based on parameters including the CD, grating depth, and side-wall angle that yielded the best match. A cross-sectional SEM result is given in Fig. 10(b). The model fit for a top CD of 66 nm, a bottom CD of 74 nm, and a grating depth of 49 nm shows satisfactory agreement with the cross-sectional SEM results.
We have developed an EUV scatterometer equipped with a laboratory EUV source for the purpose of high-harmonic generation (HHG) and serving as a stand-alone metrology tool. The m =+ 1 and −1 diffracted patterns were directly recorded by a CCD camera when the grating targets were illuminated with the EUV light. A novel approach involves reconstructing the grating profile by finding the best match, identified by considering the RMSE, between experimental data and pre-determined theoretical results stored in a library. One advantage of using the ratios of the m =+ 1 and −1 diffracted intensities of each harmonics is that any changes in the grating-target parameters due to EUV source variations essentially cancel out. This contributes toward the potential robustness of the electromagnetic modeling approach. Also, the wavelength of each harmonic was input into the RCWA model setup as a fixed constant, calibrated in advance using a well-characterized Au-coated grating. Based on our theoretical model and analysis algorithm, the experimental samples could be photomask or patterned wafer as long as their structures present in a periodic form. More results from the production samples will be presented in near future.
Future work will involve building a microscopic translation stage to adjust the distance between the grating target and the CCD sensor flexibly, to allow both the m =+ 1 and −1 diffracted beams to be collected simultaneously and with maximal spatial resolution. We estimate that increasing the grating frequencies from 1200 to 10000 lines/mm will require moving the grating target forward from its initial distance of 157.4 mm to approximately 30 mm. The presented data form a preliminary set of results, and a more detailed uncertainty analysis will be performed in the future. We will refine our current profile model by introducing the roundness of corners, the linewidth and line-edge roughness, local variations in the period, and other structural features.
MOEA (Ministry of Economic Affairs; grant no. 105-EC-17-A-01-05-0337) Taiwan.
The authors would like to thank the EUV/NTHU (Extreme UltraViolet/ National Tsing Hua University) team for providing the EUV source and the valuable discussions with respect to the EUV applications.
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