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Abstract
Optical coherence tomography (OCT) with the use of soft x-rays (SXR) and extreme ultraviolet (EUV) has been recently demonstrated [Fuchs et al. Sci. Rep. 6, 20658 (2016) [CrossRef] ; Fuchs et al. Optica 4, 903 (2017) [CrossRef] ]. This new imaging technique, named XCT, makes it possible to obtain cross-sectional and tomographic images of objects with nanometer spatial resolution. The article presents a newly developed laboratory system for XCT using a compact laser plasma light source operating in the SXR and EUV spectral ranges. The source is based on a gas puff target containing Kr gas or a Kr/Xe gas mixture irradiated with nanosecond laser pulses from an Nd:YAG laser. The use of the gas puff target enables efficient emission of SXR and EUV radiation without generating target debris associated with laser ablation when using a solid target. The system is equipped with an ellipsoidal mirror to collect radiation from the source and focus on the imaged object. The XCT measurements are made by processing the spectrum of the radiation reflected from the object recorded with a transmission grating spectrometer equipped with an identical focusing mirror and a CCD camera. The paper presents the characterization and optimization of the new XCT system and its application to the measurements of layered nanostructures.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical Coherence Tomography (OCT) is an interferometric imaging technique providing cross-sectional views of interfaces in the bulk of biological tissues or other objects using infrared and visible light. Since its invention in the early 1990s [1], OCT has been recognized as a very promising technology for biomedical imaging and optical biopsy [2]. Currently, OCT is a routinely used diagnostic technique in many different areas of biomedicine [3]. However, the capabilities of OCT have also been employed in various non-biomedical applications, including subsurface defect detection in materials [4,5], non-destructive examination of museum objects [6–8], non-contact metrology of LEDs [9,10], solar cells [11], and other electronic materials and components [12–18]. Recently, the OCT technique has been applied to the nondestructive analysis of automotive paints [19], coating thickness measurement on opaque materials [20,21], and three-dimensional subsurface defects detection in SiC and optical glasses [22,23].
A characteristic feature of OCT is that the axial resolution depends on the coherence length of the radiation source and the lateral resolution is limited by the focus spot size provided by the conventional imaging [24]. The coherence length is proportional to the wavelength and inversely proportional to the spectral width of a light source. Early OCT systems based on infrared and visible light sources had axial resolution of 10-15 µm [25]. However, thanks to advances in super-luminescent and laser light sources OCT systems can now achieve axial resolution of single micrometers. Moreover, a sub-micrometer axial resolution was demonstrated using a photonic crystal fiber in combination with a femtosecond Ti:sapphire laser generating extremely broadband continuum radiation [26,27]. This resolution of OCT systems is acceptable in typical medical and some non-medical applications, however, it may be insufficient for imaging smaller objects such as nanostructures as found in nanotechnology and nanoelectronics.
It has been demonstrated that the coherence length and thus the axial resolution of OCT can significantly be improved using radiation with a shorter wavelength in the soft X-ray (SXR) and extreme ultraviolet (EUV) spectral ranges [28]. The proof-of-principle experiments on this version of OCT, named XCT, have been performed with the use of broadband synchrotron radiation. Three-dimensional images of a silicon-based sample with different buried nanolayers of gold with the axial resolution of about 18 nm were obtained in the wavelength range from 12 to 40 nm (EUV). Using radiation in the wavelength range from 2.3 to 4.4 nm (SXR) the depth profile of a sample with buried nanolayers of platinum was reconstructed with a resolution of about 8 nm [28]. The ability of XCT to a non-destructive examination of nanolayer structures has been pointed out, however, the practical applicability of such a synchrotron-based technique, particularly in an industrial setting, is limited. The laboratory-scale XCT was demonstrated for the first time using a laser-driven EUV source based on high-order harmonic generation (HHG) [29]. The problem of producing strongly modulated spectra, typical for HHG-based sources, was solved by sweeping the driving laser wavelength [30] which allowed producing radiation in the wavelength range from 15 to 35 nm with broadband and sufficiently flat spectrum. Tomograms of a three-dimensional nanostructured sample with two laterally structured 5 nm thick gold layers buried in silicon at depths of about 230 nm 330 nm were obtained. The axial resolution, defined as the ability to resolve two layers, was approximately 24 nm and the lateral resolution was about 23 µm [29]. A single nanometer resolution XCT has been also demonstrated using a compact laser plasma soft X-ray source operating in the wavelength range from about 2 nm to 5 nm [31]. Depth profiles of a bulk multilayer structure made from 6 nm-thick silicon and 4 nm-thick molybdenum nanolayers with the axial resolution of 2 nm were obtained and the multilayer interfaces were detected up to a depth of about 100 nm [31]. In all these XCT experiments a variant of a common-path frequency-domain OCT scheme [32], was adapted to the specific conditions of XCT operating in the EUV and SXR spectral ranges [33]. The improved laboratory system for extreme ultraviolet coherence tomography with the use of a laser-driven source based on HHG and a high-resolution and highly sensitive reflection grating spectrometer has been recently developed [34]. The system was equipped with data acquisition and analysis tools as well as a setup for automated lateral scans. It allowed obtaining depth profiles of layered nanostructures with the axial resolution of about 16 nm, three-dimensional cross-sectional images with the axial resolution of about 38 nm and the lateral resolution of about 80 µm [34]. Recently, this system has been used for material-specific imaging of nano-layers allowing identification of the material of nanoscale structures inside of samples based on their spectral reflectivity [35].
In this paper, we present a new laboratory XCT system based on a compact laser plasma source operating in the EUV and SXR spectral regions. Radiation in the wavelength from 2 nm to 20 nm is generated in plasma produced as a result of irradiation of a Kr/Xe gas puff target with nanosecond laser pulses. The new system is equipped with two identical ellipsoidal mirrors. One mirror collects the radiation from the source and focuses it on the sample. The second mirror collects the radiation reflected from the sample and directs it to the spectrometer. The spectrum of the reflected radiation is recorded with a CCD camera and subjected to the XCT analysis. The new XCT system is described in Section 2 of the article. Section 3 presents the characterization measurements of the system, including the laser plasma source of SXR and EUV radiation and the focusing mirrors. The application of the new system for the XCT measurements of samples in the form of nano-layers is presented in Section 4. Section 5 of the article contains the final conclusions.
2. XCT laboratory system
A schematic of the laboratory XCT system based on a laser plasma source of soft X-rays and extreme ultraviolet is presented in Fig. 1. Components of the system are installed in a vacuum chamber consisting of two sections separated by a small diaphragm enabling differential pumping. In the first section elements of the laser plasma source are mounted. SXR and EUV radiation is emitted from a hot plasma produced as a result of irradiation of a gas puff target with nanosecond laser pulses from a commercial Nd: YAG laser (YG 980, Quantel, France). The laser generates pulses with the nominal parameters: time duration of 8-11 ns, maximum energy 1.6 J, repetition rate 10 Hz, and wavelength of 1064 nm. The laser beam is focused on the target using an aspherical lens (f = 25 mm, ½ inch in diameter).
The target in the form of a double-stream gas puff target is formed by pulsed injection of a small amount of working high-Z gas through a circular nozzle (0.4 mm in diameter) into an annular stream of helium gas created using a nozzle in the form of a ring surrounding the central circular nozzle. The inner diameter of the ring nozzle is 0.8 mm and the outer diameter is 1.5 mm. Both nozzles are supplied with gases under a pressure of up to 10 bar flowing from two solenoid-driven pulsed valves placed in a common body. The valve actuators are synchronized with the laser. The annular stream of helium confines the inner gas stream and makes it possible to obtain an elongated stream of the working gas with the density required for high absorption of laser energy. The use of the double stream gas puff target allows efficient emission of SXR and EUV radiation without the target debris production. Laser plasma sources based on the double-stream gas puff target approach have been used in a variety of applications, including metrology, processing materials, microscopy in the nanoscale, photoionized cold plasma studies, holography, and tomography, X-ray absorption fine structure spectroscopy, and radiobiology. In the previous work of the authors, it was shown that the use of pure Kr gas or Kr/Xe gas mixture (90:10) as working gas allows obtaining a broadband radiation spectrum in the SXR and EUV ranges required for XCT [36].
The valve system producing the gas puff target is mounted in the chamber with the use of three motorized linear stages which allow aligning the target in respect to the focused laser beam. In front of the plasma, a pinhole mask in the form of a linear array of laser-drilled pinholes with diameters of 200 µm, 100 µm, 75 µm, and 50 µm (P200D–P50D, Thorlabs, Sweden) is mounted at a distance of 17 mm. The pinholes limit the source size. The pinhole mask can be moved utilizing two motorized linear stages, which enables precise alignment of the pinhole with the plasma. Due to the relatively large amount of gas flowing from the valve during the source’s operation with repetition, the first section of the vacuum chamber is pumped with an oil-free rotary pump. The gas pressure in this section is about 10 mbar.
The sample to be imaged, the optics illuminating the sample, and collecting the radiation reflected from the sample are placed in the second section of the chamber which is pumped with the use of a turbopump providing a high vacuum of about 10−6 bar. The optical scheme of the XCT system is presented in Fig. 2. The beam of radiation illuminating the sample is formed by an ellipsoidal grazing incidence mirror which focuses the laser plasma radiation passing through the pinhole limiting the source size. The illuminating mirror creates an image of a pinhole on the sample which is reduced by about four times. An ellipsoidal mirror with the same parameters collects the radiation reflected from the sample and directs it to the grating spectrometer. In contrast to the illuminating mirror, the collecting mirror magnifies the image of the sample in the spectrometer also about four times. The angles between the normal to the sample surface and the axis of the beam irradiating the sample and the axis of the reflected beam are equal to 11.51°. The grazing incidence angle for the mirrors varies from 4.91° for the smaller diameter (exit diameter for the illuminating mirror and entrance diameter for the collecting mirror) to 2.96° for the larger diameter (entrance diameter for the illuminating mirror and exit diameter for the collecting mirror). The grazing incidence angles are larger than the critical angle for the Ni mirror at a radiation wavelength of about 1.2 nm. The mirrors were designed and manufactured by Rigaku, Inc. (Japan). Both mirrors are mounted with the use of 5D positioning stages, consisting of three linear stages and two rotation stages, allowing for precise alignment of the optics. For the sample, the stages were motorized which allowed it to be properly positioned under vacuum.
The spectrum of radiation reflected from the sample is measured with a 5000 l/mm grating spectrometer mounted to the exit flange of the vacuum chamber. The spectrum is recorded with a back-illuminated CCD camera with a chip of 1024 × 1024 pixels and a pixel size of 13 × 13 µm2 (i-Kon-M, Andor, UK). The CCD chip is placed at the same distance from the sample as the sample for the source (pinhole). In order to reduce the visible radiation of the laser plasma on the CCD array and to control the contribution of SXR or EUV radiation in the plasma radiation spectrum, a Zr or Ti filter in the form of a thin foil with a thickness of 200 nm is inserted in front of the spectrometer. The main parameters of the XCT system focusing optics, such as the mirror's length, the object and image distances, the entrance and exit diameters, magnification, the ellipsoid semiaxes, and the numerical apertures as well as the parameters of the spectrometer are given in Table 1. An overall view of the XCT system and the position of the ellipsoidal focusing optics inside the vacuum chamber is shown in Fig. 3.
Fig. 3. Laboratory system for optical coherence tomography (OCT) using a laser plasma source of soft X-rays and extreme ultraviolet (a), focusing optics mounted inside the vacuum chamber (b).
Table 1. Parameters of the XCT system focusing optics and spectrometer
3. XCT system characterization measurements
3.1 Source characterization
Laser plasma produced by irradiating a double-stream gas puff target with pure Kr gas or a Kr/Xe gas mixture as working gas with a nanosecond laser pulse was used as a source of SXR and EUV radiation in the new XCT system. The target parameters (gas backing pressure in the valve, delay times, and valve opening times) were optimized to obtain the maximum generation of radiation in the wavelength range of about 2 nm to 20 nm. It has been found that the optimal backing pressure of the working gas was 5.5 bar for Kr and 8 bar for Kr/Xe. The optimal backing pressure for the confining He gas was 6 bar in the case of the Kr target and 7 bar for the Kr/Xe target. The timing parameters were the same for both targets. The optimal valve opening delay time in respect to the laser trigger pulse was found to be 75 µs for the working gas and 100 µs for the confining gas. The valve opening time was equal to 925 µs for the working gas and 900 µs for the confining gas.
The spectral characteristics of the laser plasma radiation have been measured with the use of a grating spectrometer. The experimental arrangement for the spectral measurements is shown schematically in Fig. 4. The spectrometer is based on a 5000 l/mm transmission grating. In front of the grating, at a distance of 100 mm, there is a 100 µm slit, which is 885 mm away from the laser plasma. The spectra are registered with a back-illuminated CCD camera mounted at a distance of 210 mm from the grating. The time duration of the laser pulses measured with a fast photodiode was 10 ns, while the pulse energy - 900 mJ. Assuming a laser focus diameter of about 100 µm, the intensity of the laser radiation on the target was 1.2 × 1012 W/cm2.
Typical radiation spectra in the SXR and EUV range of the laser plasma produced from the Kr/Xe gas puff target and Kr target are shown in Fig. 5(a) and 5(b), respectively. The emission of laser plasma radiation depends on its electron temperature and density as well as on the ion charge in the plasma. The electron temperature of the plasma generated by irradiating the Kr or Kr/Xe gas puff target with nanosecond laser pulses can be estimated using the well-known collisional-radiative (CR) ionization plasma model proposed by Colombant and Tonon [37]. For the intensity of laser radiation of 1012 W/cm2 on the target, the electron temperature of this plasma is about 100 eV, while the average ion charge is about 10. As shown in Fig. 5(a), the measured spectrum of the Kr plasma in this wavelength range consists of characteristic spectral features of unresolved transition arrays (UTAs) resulting from a very large number of transitions in highly charged ions [38]. The dominating UTA in the EUV range near 10 nm is due to 3d-4p transitions in Kr X ions [39]. Less intense UTAs near 9 nm and 11 nm result from the same transitions in Kr XI and Kr IX ions [40]. Relatively intense spectral lines in the SXR range between 4 nm and 8 nm come from the 3d-4f and 3d-5f transitions in Kr XIII - Kr IX ions and the 3p-4s and 3d-4p transitions in Kr XIII -Kr XI ions [41]. The spectrum of the Kr/Xe plasma radiation shown in Fig. 5(b) is dominated by a very intense UTA near 11 nm, which is formed as a result of 4d-4f and 4d-5p transitions in Xe X and Xe XI ions [42–44]. The spectrum in the SXR range contains only UTAs derived from the emission of Kr ions.
As the spectrum of radiation reflected from the sample in the XCT system will be measured after the beam propagates through the Ti filter (in the case of measurements in the SXR range) or through the Zr filter (in the case of the measurement in the EUV range) the measured spectra have been corrected taking into account the filter transmission. The spectra for the Kr/Xe and Kr plasma, corrected in respect to the transmission of the Ti and Zr filters, are shown in Fig. 6.
Fig. 6. SXR and EUV radiation spectra of the Kr/Xe and Kr laser plasma corrected for the transmission of the Ti filter (a,b) and Zr filters (c,d).
Figures 6(a) and 6(b) present the spectra for both plasmas corrected for the transmission of the Ti filter. The contribution of the SXR radiation in the spectrum is greater compared to the EUV radiation for the Kr plasma. This plasma was used in further studies of the XCT system properties in the SXR range. The spectra presented in Fig. 6(c) and 6(d) show clearly that the Kr/Xe plasma generates significantly more EUV radiation compared to the Kr plasma. The Kr/Xe plasma was used in the further characterization studies of the XCT system in the EUV range.
The spatial characteristics of the source have been measured by imaging using a pinhole camera. A schematic of the experimental arrangement is shown in Fig. 7. The source was imaged onto a CCD camera with the use of a 25 µm pinhole in diameter placed at a distance of 537 mm from the source and 433 mm from the CCD. Thus, the demagnification of the pinhole camera was about 0.8 × . The source size was changed utilizing a pinhole mask in the form of an array of laser-drilled pinholes) with diameters of 200 µm, 75 µm, and 50 µm. The pinhole mask was mounted at a distance of 17 mm from the plasma using a translation stage. The source images were recorded with a back-illuminated CCD camera. The use of the Ti filter allowed to obtain images of the source in the SXR range, while the use of the Zr filter – in the EUV range.
Typical pinhole images of the source in the EUV and SXR spectral ranges are presented in Fig. 8. The source images in the EUV range (see Fig. 8(a)-(d)) were obtained for the plasma generated from the Kr/Xe target, while the SXR images (see Fig. 8(e)-(h)) for the plasma produced from the Kr target. The images were obtained without the use of a pinhole mask and with a mask with pinholes of various diameters. Plasma images obtained without the use of a mask (see Fig. 8(a) and 8(e)) are highly irregular and have an elongated shape along the propagation of the laser beam. The characteristic areas of high emission of radiation visible at the edges of the plasma images correspond to the gas density distribution in the target. Earlier studies have shown that the maximum gas density in a double-stream gas target occurs in areas where the central stream of working gas collides with the annular stream of He confining the central stream [45].
Fig. 8. Typical pinhole images of the plasma source in the SXR(a-d) and EUV(e-h) spectral ranges range without the use of a pinhole mask and using the mask with different pinhole diameters.
The regular and highly symmetric shapes of the plasma source can be obtained by the use of a pinhole mask. Figures 8(b)-(d) show the source images in the EUV range for the Kr/Xe target and Fig. 8(f)-(g) show the images in the SXR range for the Kr target obtained using a pinhole mask with pinholes of 200 µm, 75 µm, and 50 µm in diameter, respectively. The size of the source obtained with the pinhole mask is much smaller than that of the plasma. The diameter of the source corresponds to the diameter of the pinhole used. The measurements have shown that the use of a pinhole mask reduces the size of the source and significantly improves its shape, however at the cost of strong attenuation of the intensity of radiation.
3.2 Focusing optics characterization
The focusing optics applied in the XCT system play a key role in XCT imaging. It consists of two identical ellipsoidal mirrors, from the surface of which the radiation is reflected at the grazing incidence angle smaller than 5°. The illuminating mirror (see Fig. 1) collects radiation from the source and focuses the beam onto a sample. Theoretically, the diameter of the source is demagnified by a factor of four at the focal spot at the sample. The radiation reflected from the sample is collected by another ellipsoidal mirror (collecting mirror) and focused onto a transmission grating spectrometer. XCT images of the sample are obtained by analyzing the spectrum of the reflected radiation. By changing the position of the sample in a plane perpendicular to the axis normal to the sample, it is possible to scan the sample to obtain a 3D image (tomogram). The lateral resolution of the image depends on the diameter of the focal spot on the sample.
The characteristics of the focusing optics have been studied using the experimental setup presented in Fig. 9. The ellipsoidal mirror was mounted inside the vacuum chamber. A 5D positioning stage was used for the precise alignment of the mirror. The collected radiation from the source was focused onto a Ce:YAG scintillator creating a focal spot. The focal spot was observed through a glass window with the use of an optical CCD camera.
Images of the focal spots in the EUV and SXR spectral ranges obtained for different source sizes determined by the pinhole mask are presented in Fig. 10. The plasma was produced as a result of irradiation of the Kr/Xe gas mixture targets. Figure 10(a), (f) show the focal spot images for the case where the plasma is not obscured by the pinhole mask. Although the plasma is highly irregular in shape and elongated in the direction of the laser beam propagation through the gas target (see Fig. 8(a), (e)), the focal spots are regular in shape and circularly symmetrical. The size of the spot is smaller than the source size in the horizontal direction. Probably, it is caused by the limited aperture of the grazing incidence ellipsoidal mirror. The dimensions of the focal spots are a quarter to the diameters of the pinholes, however, their shapes are not so regular as expected. It may be due to the highly irregular shape of the plasma.
Fig. 10. Focal spot images in the EUV (a-e) and SXR (f-j) spectral ranges for different source sizes determined by the pinhole mask. (a,f) – without pinhole mask, (b,g) – 200 µm pinhole, (c,h) – 100 µm pinhole, (d,i) – 75 µm pinhole, (e,j) – 50 µm pinhole.
The vertical cross-sections of the focal spot images obtained in both spectral regions and their Gaussian fits are depicted in Fig. 11. Analysis of focal spot sizes points out that their FWHM’s reduce proportionally to the pinhole mask size. For 200 µm pinhole mask FWHM of the gaussian fit of a vertical cross section of focal spot corresponds to 50 µm which agrees with the demagnification value of ellipsoidal mirror.
Fig. 11. Gaussian fits of vertical cross-sections of the focal spot images with different sources sizes in the EUV (a) and SXR (b) ranges.
The absolute photon yield measurements of the focusing optics have been performed with the use of a calibrated photodiode (AXUV100G, Opto Diode, USA) [46]. A schematic of the experimental arrangement for the photon yield measurements is presented in Fig. 12. The photodiode was placed inside the vacuum chamber, at about 5 cm behind the focus of the ellipsoidal focusing mirror. As a result, all radiation passing through the focus of the mirror was collected by the detector.
The main challenge associated with gas puff target systems compared to synchrotron or solid target sources is the lower fluence and typically larger source size [47,48]. The plasma source is highly incoherent and non-directional in nature. The ellipsoidal optics according to its numerical aperture is capable to focus a small fraction of the radiation emitted from the source. In XCT techniques based on Fourier domain optical coherence tomography (FDOCT) the signal strength is depreciated by various factors of efficiency from the ellipsoid optics reflections, reflection from the sample, and the diffraction efficiency of the grating spectrometer. Hence it is very necessary in the case of tabletop plasma sources based on DGPT to evaluate the photon count at the focal spot produced by the ellipsoidal optics to determine the feasibility of such sources for photon-demanding applications such as the XCT.
The measurements were made for the plasma produced by irradiating a gas puff target made of pure Kr gas and a Kr/Xe gas mixture. The number of photons in the focus of the mirror was calculated using the measured radiation spectral distributions and the detector calibration data provided by the manufacturer. The results are presented in Table 2 showing the photon numbers in the focal spot for various plasma sizes and different gases in the EUV and SXR spectral ranges. It can be noted that Kr/Xe target is giving better fluence in both spectral regions. This is specific to the presented source set up and is related to the pump laser energy density.
Table 2. Photon numbers in the focus of the ellipsoidal mirror in the SXR and EUV spectral ranges for various plasma sizes and different gases
The method used to calculate photon counts in both extreme ultra-violet (EUV) and soft x-ray (SXR) spectral regions is based on the output voltage from a reverse-biased silicon p-n junction photodiode detector. The plasma is created at the DGPT for a few nanoseconds of duration. The number of photons N, received by an detector for a specific wavelength is given by
where v is the instantaneous voltage signal at the output of the detector, T is the integration time, R is the input impedance of the oscilloscope, e is the electron charge, and QE is the quantum efficiency of the detector at the specified wavelength. Since the plasma is a broadband source of radiation, the number of photons received by the detector is a function of energy and is related to the spectral characteristics of the gas puff target. The probability of a photon detected by the detector as a function of wavelength is given byThe quantum efficiency values of the detector QE were taken from the data provided by the photodiode manufacturer [46].
4. XCT measurements of layered nanostructures
The new XCT system based on a laser plasma source of SXR and EUV radiation and ellipsoidal focusing optics has been tested by inspection of layered nanostructures. In order to select a nanostructure design suitable for the tests, XCT simulations of various layered nanostructures were performed.
4.1 Simulations of layered nanostructures
A sample in the form of a layered structure with an appropriate reflectivity of radiation in the EUV and SXR ranges which is applied in the new XCT system has to be used for testing the new XCT system. The reflectivity in this range for such a sample depends on several factors. The refractive index contrast at the multilayer interfaces is one of the major factors which influences reflectivity. The depth resolution of XCT depends on the source bandwidth and hence the layer thicknesses must be designed accordingly. Another important factor is the absorption length of different materials. Since radiation in this range is strongly absorbed, the thickness of the layers made of metals or semiconductors ranges from a few nanometers to several dozen nanometers. Reflection and transmission simulations for several layered nanostructures consisting of four pairs of different materials with various combinations of metals and semiconductors were done using the transfer matrix method (TMM) [49]. The reflectance of radiation in the wavelength range from 8 nm to 12 nm from layered nanostructures consisting of four pairs of different materials with a thickness of the first layer 10 nm and the second layer 50 nm is shown in Fig. 13. The simulations showed that the samples made from the combination of Ag/C and Ag/Zr layers were characterized by the highest reflection in this spectral range. For technological reasons and the possibility of producing the nanolayers, the layered nanostructure consisting of four pairs of Ag/Zr layers with a 10 nm-thick Ag layer and 50 nm-thick Zr layer deposited on a silicon substrate was selected to test the new XCT system.
XCT computer simulations for the samples with the Ag/Zr layers were performed. The simulation results are shown in Fig. 14. A sample consisting of four pairs of Ag and Zr layers with a thickness of 10 nm and 50 nm is irradiated with radiation having a wavelength in the range of 10–20 nm at an angle of incidence of 11.5 degrees. The spectrum of the reflectivity of the sample on the wavelength and wavenumber scales are shown in Fig. 14(a) and 14(b), respectively. Figure 14(c) shows the reflectivity spectrum in the k domain with a Gaussian window applied. The window limits the influence of high frequency components on the Fourier transformed data presented in Fig. 14(d), depicting the reconstructed depth profile of the sample. The reconstruction procedure was described in previous papers [28,31].
Fig. 14. XCT simulation of the Ag/Zr layered nanostructure. The reflectivity of the Ag/Zr multilayer sample in the wavelength domain (a), k domain (b), gaussian window applied (c), and Fourier-reconstructed depth profile (d).
4.2 Sample reflectivity measurements
XCT measurements for samples in the form of Ag/Zr layered nanostructures were performed using the new XCT system presented in Fig. 2. Due to the higher intensity of the source radiation in the EUV range, the tests were carried out in this spectral range. Reflection spectra of the Ag/Zr sample were acquired to reconstruct the depth profile of the multilayers using Fourier analysis. The acquisition was done using 400 laser pulses at 5 Hz with an energy of 900 mJ and a 200 µm in diameter pinhole is used to spatially modify the EUV source. A Zr filter with a thickness of 200 nm is used to select EUV radiation in the range from 8 nm to 20 nm. The SNR at the spectrometer detector was improved by reducing the CCD temperature to -60° C and by acquiring and averaging the spectral images 10 times.
In order to align the collection mirror and to acquire the reference spectrum, the reflection of the radiation from a Si wafer was measured. Since the wafer is not a multi-layered structure the acquired spectra were just the reflection of incident radiation on its surface. The reflection spectral intensities of both the Ag/Zr multilayer sample and Si wafer are depicted in Fig. 15. The reflection from the Si wafer is much higher than the reflection from the sample. This can be explained due to the difference in roughness levels of Si wafer and Ag deposit on the multilayer sample. The specular reflection of the first layer of the sample determines the amount of reflected light at the spectrometer camera. The reflectivity for the Ag/Zr sample can be calculated as the ratio of the reflection spectral intensities for the Ag/Zr multilayer sample and Si wafer.
where Iinc(λ) and Iref (λ) are incident and reflected spectral intensity, as depicted in Fig. 15.4.1 XCT reconstruction
The characterization of source in terms of axial point spread function of the oct system is important to identify the cross talk and influence of source spectral shape in reconstructed depth profile. The source spectra which is a specular reflection of the radiation at the sample position is recorded. The point spread function of the OCT system is calculated using Fourier analysis of source spectra. The normalized source spectra and their corresponding calculated point spread function (PSF) inside the Zr sample are depicted in Fig. 16. It can be noticed that the FWHM of the PSF is 8 nm. Artifacts related to the non-gaussian structure of source spectra are also visible in the PSF.
The Fourier transform of the reflectivity spectra gives the depth profile of different layers with respect to the surface layer [29]. The discontinuities can occur at both ends of the reflectivity data due to the limited size of the detector. In order to reduce the ripple artifacts in the reconstructed profile, an approximation smoothening window function should be applied. A Kaiser-Bessel window function in the wavelength range from 12 nm to 18 nm was applied on the reflectivity data towards this end. The windowed reflectivity for the Ag/Zr sample is depicted in Fig. 17, together with the Kaiser-Bessel window function profile.
In post-processing of the reflectivity data to reconstruct the depth profile, it is remapped as a function of wavenumber k from that of the wavelength λ. The remapping must take into consideration of the dispersion effects which vary according to the materials and thicknesses of the layered sample. In a vacuum, k is related to λ as
Taking into consideration of dispersion in the dominant material Zr the relation changes to
where ${n_D}$ is the refractive index of dominant material and $\alpha $ is the angle of incidence with respect to the normal. Since the relation between them is nonlinear, the remapped reflectivity data should be resampled to have equidistant sampling points in wavenumber. In the simplified reconstruction method used here, the dispersion effects in the dominant material that is Zr, were taken into consideration, while neglecting those effects in the thin Ag layers. This approximation reduces the accuracy of the reconstructed depth profile. The dispersion effects dominantly affect the accurate reconstruction of the deeper layers. Fourier analysis of the resampled reflectivity data is performed to reconstruct the depth profile of the investigated sample.The reconstructed depth profile is depicted in Fig. 18. Since the period of the multilayer stack is 60 nm, one can see a peak at 59.4 nm in the reconstructed depth profile and is matching with the simulation results. The second period is also detected at about 110 nm. Other peaks of lower intensity below 30 nm that appeared in the reconstruction profile are artifacts from the source spectral shape. It should also be noted that only the first period is clearly visible in the reconstruction profile, the second period is detectable, but the third and fourth periods are invisible. Deeper layers in the sample is could not be reconstructed due to the fact that the high frequency fringes resulting from the reflection of radiation from them are not properly resolved at the spectrometer due to its lower resolution. This is due to the very strong absorption of radiation in this spectral range in the Ag and Zr nanolayers. The resolution of the XCT setup calculated from the source spectral characteristics turns out to be 22 nm. This is the reason why the Ag layers with 10 nm thickness were not separated in the reconstruction profile.
5. Conclusions
The paper presents a newly developed laboratory system for XCT using a compact laser plasma light source operating in the SXR and EUV spectral ranges. The source is based on a double stream gas puff target irradiated with nanosecond laser pulses from an Nd:YAG laser. The use of the gas puff target enables efficient emission of SXR and EUV radiation without target debris production. The system is equipped with two grazing incidence ellipsoidal mirrors to focus the radiation from the source on the imaged object and to collect the reflected radiation and direct it to the transmission grating spectrometer.
The source and optics characterization measurements have been performed for the source based on the gas puff target with pure Kr or a Kr/Xe gas mixture. The results of the study show that the use of a pinhole mask placed in front of the plasma source allows focusing the EUV and SXR radiation onto a sample in the spot with a diameter comparable to the diameter of the pinhole. It was found that the Kr plasma combined with the Ti filter is more preferable to be used as the SXR source while the Kr/Xe plasma combined with the Zr filter can be used as the EUV source. However, the photon number in the focal spot is about three times higher for EUV than for SXR.
The new system was tested by taking XCT measurements of the Ag/Zr layered nanostructure sample consisting of four pairs of 10 nm-thick Ag and 50 nm-thick Zr layers. The tests have been performed in the wavelength range from 10 nm to 20 nm. The studies have shown that the first and the second period of the layer structure can be visible demonstrating the depth range of about 110 nm. The depth range is determined by the resolution of the spectrometer. In future studies, a reflective grating spectrometer with a smaller source size can significantly increase the resolution of the spectrometer and thereby increase depth range. The spatial depth resolution was determined at about 22 nm for the given source characteristics and it was insufficient to resolve the Ag layers on the depth profile. Axial resolution can be increased by using a source with a shorter central wavelength and broader bandwidth. Further testing of the new system using shorter wavelength radiation and study of three-dimensional samples will be performed.
Funding
Narodowe Centrum Nauki (2016/23/G/ST2/04319); European Union Horizon2020 Programme Laserlab-Europe (871124).
Acknowledgements
Authors thank Gerhard Paulus and Silvio Fuchs from University of Jena for fruitful discussions on the project and Ladislav Pina from Czech Technical University in Prague for many years of collaboration in the field of X-ray optics.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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