Optical constants of magnetron sputtered Pt thin films with improved accuracy in the N- and O-electronic shell absorption regions

Pt thin films are widely used in optics operating in the extreme ultraviolet (EUV)/soft x-ray range, for example, as single-layer or bi-layer reflective coatings, as transmissive filters, or as the “absorber layer” in multilayer interference coatings, including magnetic multilayers.¹ Pt coatings exhibit high reflectance at grazing and normal incidence angles at EUV/soft x-ray photon energies² and have therefore been applied in synchrotron mirrors^3,4 and considered as mirror coatings for space-borne solar physics and astronomy telescopes.^5–9 The photon energies of the above applications include the Pt N- and O-electronic shell absorption edge regions, which extend from 50 eV to 800 eV. Accurate knowledge of the refractive index of Pt in this photon energy region is not only essential for the design and modeling of EUV/x-ray optics containing Pt, but for atomic physics and materials science research in general, especially considering the importance of Pt in catalysis and nanotechnology. At EUV/x-ray energies, the refractive index of materials is defined as

where 1 − δ and β represent the dispersive and absorptive portions of the photon energy-dependent refractive index, respectively. The terms δ and β are known as the optical constants.¹⁰ One of the most comprehensive and frequently accessed sources of EUV/x-ray optical constants by the scientific community is Ref. 11, which covers the photon energy range 30 eV-30 keV and is maintained and updated online¹² by the Center for X-ray Optics (CXRO) at Lawrence Berkeley National Laboratory (LBNL). In the CXRO database, measurements of Pt absorption dating from the 1900s to the 1980s have been compiled and interpolated with theoretical calculations; the dispersive part of the Pt refractive index is then calculated via the Kramers-Krönig relation. In the online version of the database,¹² the optical constants of about 15 elements have been updated with recent and more accurately measured photoabsorption values in the vicinity of absorption edges; however, Pt is not among them. More specifically, in the photon energy region of the Pt N- and O-electronic shell absorption edges, the Pt photoabsorption data compilation (and calculated dispersion values) in the CXRO database lacks fine structure details. Another compilation of Pt refractive index data based on reflectance and transmission measurements in the 0.1 eV-2 keV region, edited by Palik,¹³ also lacks fine structure in the Pt N- and O-edge regions. Both Refs. 11 and 13 use a combination of data obtained on bulk Pt and thin Pt films from various works. In the following, we note a few works where the Pt refractive index was determined experimentally in the photon energy regions of Pt N- and O-shell absorption: Haensel et al.¹⁴ obtained photoabsorption data on Pt thin films prepared by evaporation. Wehenkel and Gauthé¹⁵ also measured the absorption of Pt thin films via electron energy loss spectra. Birken et al.¹⁶ and Windt et al.¹⁷ determined experimentally both the absorptive and dispersive parts of the refractive index from reflectance data on Pt thin films prepared by evaporation. The Pt absorption values from Refs. 14 and 17 have been included in the CXRO database. More recently, Pt optical constants based on reflection electron energy-loss spectroscopy (REELS) data were published by Werner et al.¹⁸ 

This paper presents a new set of Pt optical constants deduced from reflectance and transmittance measurements in the 25–778 eV photon energy range, which includes the Pt N- and O-shell absorption edges. The new Pt optical constants are compared with existing databases and earlier experimental works, referenced in the previous paragraph. Highly resolved absorption-edge fine structure is revealed for the first time in the new Pt measurements.

The new experimental Pt values are combined with earlier data at photon energies below 25 eV and above 778 eV to construct a Pt optical constant data set in the full spectral range. The accuracy of the new data set is examined with electron sum rule tests.

Grazing Incidence X-Ray Reflectance (GIXR) measurements (discussed in Sec. II B) were performed at Laboratoire Charles Fabry (LCF) with a commercial diffractometer (Bruker^® Discover D8) equipped with a Cu Kα radiation source (photon energy E = 8048 eV), a collimating Göbel mirror, a rotary absorber, Söller and divergence slits, and a scintillator. The reflectance curve is obtained by scanning the grazing incidence angle while tracking the reflected beam (θ-2θ scan configuration). The mechanical angular accuracy and angular resolution are better than 0.01°. The GIXR data are fitted with a genetic algorithm by using the program Leptos^® in order to deduce several sample parameters: layer thickness, material density, and average interfacial roughness.

The GIXR apparatus at DTU-Space was also used in the measurements discussed in Sec. II B. It is a custom-built device operating at the same photon energy and geometry as mentioned above. The Cu Kα x-ray source was manufactured by Rigaku Corporation^®. The thin film stress measurement apparatus at DTU-Space, used in the measurements discussed in Sec. II B, was a Dektak 150 Stylus Profilometer by Brüker^®. The apparatus measures changes in the substrate curvature before and after thin film coating and applies Stoney's equation¹⁹ to determine the thin film stress.

The EUV/soft x-ray reflectance and transmittance measurements discussed in Secs. II B, III A, and III B were performed at beamline 6.3.2. of the Advanced Light Source (ALS) synchrotron at LBNL. Beamline 6.3.2. has a grating monochromator with a fixed exit slit and its general characteristics have been described in detail earlier.^20,21 A set of filters of various materials (with each filter selected specifically for each photon energy range) is used for wavelength calibration and 2nd harmonic and stray light suppression. For higher-order harmonic suppression, an “order suppressor” consisting of three mirrors at a variable grazing incidence angle (depending on energy range) and based on the principle of total external reflection is used in addition to the filters. The measurement chamber allows translation of the sample in three dimensions, tilt in two dimensions, and azimuth rotation of the sample holder. The available detectors include various photodiodes and a CCD camera (the latter for sample alignment), which can be rotated by 360° around the axis of the chamber. During the measurements discussed in this paper, a signal was collected with a GaAsP photodiode detector with 1° angular acceptance. The ALS storage ring current was used to normalize the signal against the storage ring current decay. The base pressure in the measurement chamber was 10⁻⁷ Torr. More detailed information on measurements at specific photon energy regions is given below.

The reflectance measurements in the photon energy range 83–188 eV for Pt thickness determination, discussed in Sec. II B, were obtained with the 200 lines/mm grating, a Be filter (83–111 eV), and a B filter (108–188 eV) for 2nd-harmonic and stray light suppression. The order suppressor consisted of 3 C mirrors at 14° (83–111 eV) and 8° (108-188 eV) grazing incidence angle. Photon energy was calibrated based on the L_2,3 absorption edge of a Si filter. The photon beam was 86% s-polarized.

The reflectance measurements for Pt optical constant determination in the photon energy range 25-95 eV, discussed in Sec. III B, were obtained with the 80 lines/mm grating (25-68 eV) and the 200 lines/mm grating (62–95 eV). A Mg filter (25–38 eV), Al filter (42–68 eV), Si filter (62–85 eV), and Be filter (91.84-95 eV) were used for 2nd-harmonic and stray light suppression. The order suppressor consisted of 3 C mirrors at 20° (25–38 eV), 18° (42–68 eV), and 14° (62–95 eV) grazing incidence angle. Photon energy was calibrated based on the L_2,3 absorption edges of an Al and a Si filter. The beam polarization ranged from 93% s-polarized at 25 eV to 89% s-polarized at 95 eV.

For the transmittance measurements discussed in Sec. III A, three gratings (80, 200, and 1200 lines/mm) were used in the monochromator to access the photon energy range 32-778 eV. At photon energies above 270 eV, a 2 mm-diameter pinhole was used in front of the reflectometer chamber to block scattered light from the 1200 lines/mm monochromator grating.

Photon energy calibration was based on the absorption edges of a series of filters (Al, Si, B, Ti, Cr) with a relative accuracy of 0.011% rms and could be determined with 0.007% repeatability. For 2nd harmonic and stray light suppression, a series of transmission filters (Mg, Al, Si, Be, B, C, Ti, Cr, Co) was used. The order suppressor consisted of three C or Ni mirrors at a grazing incidence angle ranging from 20° to 6°, depending on the photon energy range.

The Pt films used in the transmittance measurements were deposited at DTU-Space via DC-magnetron sputtering, using the deposition system described in Ref. 22. All depositions were done with a Pt cathode operated at 600 W with input Ar gas pressure of 2.9 mTorr and rate set to 88 sccm and a base pressure below 10⁻⁶ Torr. Each Pt film was deposited on a photoresist-coated, 100-mm diameter Si wafer substrate with (100) orientation and 525-550 μm thickness. After Pt deposition, the samples that were transported at CXRO/LBNL, where stainless steel support rings 8 mm in diameter with a 3 mm diameter opening, were glued onto the coated wafers using acetone-resistant glue. The samples were then soaked in acetone for a few minutes. This process results in producing free-standing Pt films mounted on the support rings, with a 3-mm-diameter area available for transmittance measurements. This method has also been implemented in the earlier work^23–26 to produce free-standing thin films for EUV/x-ray optical constant studies.

For atomic composition and thin film stress characterization purposes, two witness samples (for each transmittance sample) were also coated with Pt at DTU-Space. The witness substrates were Si wafer pieces, and during deposition, they were located next to the photoresist-coated Si wafer substrate used for the transmittance sample. Thin film stress measurements performed at DTU-Space determined that the stress of all Pt films discussed in this paper was in the −700 to −800 MPa range (compressive). The atomic composition of the Pt films deposited at DTU was determined via Rutherford Backscattering (RBS) measurements with 2.275 MeV He⁺⁺ ions and a backscattering angle of 160°, performed at EAG Labs (Sunnyvale, California), on a Pt witness sample of 48.4 nm thickness (determined experimentally at DTU-Space by fitting GIXR data). The atomic composition of the sample was thus found to be 99% Pt, 0.6% Fe, and 0.4% Ar, with Fe and Ar believed to have been incorporated in the film during deposition. The density of the Pt films deposited at DTU-Space was determined via fitting of GIXR data (obtained at DTU-Space and at LCF) on Pt transmittance and witness samples and was found to be 21.45 ± 0.20 g/cm³, which corresponds to the Pt bulk density. Four Pt samples (T1, T2, T6, and T7) were used in the transmittance measurements. The sample thicknesses and their surface and interface micro-roughness were verified experimentally (i) by GIXR measurements at DTU-Space, while the Pt thin films were on the photoresist-coated Si substrate (ii) by reflectance vs. photon energy measurements in the photon energy range 83–188 eV carried out at beamline 6.3.2. of the ALS at LBNL. It should be noted that these ALS reflectance measurements were aiming to determine only the Pt thickness and roughness, not the Pt optical constants (reflectance measurements for Pt optical constants are discussed in Sec. III B). The ALS reflectance measurements were performed at two different angles (65° and 85° from grazing) on Pt free-standing films, i.e., after removal from the photoresist coated Si substrate. Due to limitations in the geometry of the sample holder, the ALS reflectance measurements were performed with the photon beam incident on the Pt surface side, which was earlier (before removal from the substrate) in contact with the photoresist. The ALS reflectance data and corresponding models on two of the samples (T2 and T7) are shown in Fig. 1. All GIXR and ALS reflectance measurements were modeled using the IMD software package²⁷ and the results are summarized in Table I. For samples T1 and T6, the agreement between modeled Pt film thicknesses from GIXR and ALS data is excellent. In samples T2 and T7, the absence of well-defined interference fringes (due to the much larger Pt thickness) prevented modeling of the Pt thickness via GIXR measurements. In the ALS data, a residual photoresist layer (i.e., photoresist that has remained on the Pt surface after removal from the substrate) was derived on the surface of all samples. This photoresist layer was modeled as having a density of 1.42 g/cm³, consistent among all ALS reflectance measurements and an average thickness of 11.85 nm, determined among samples T1, T2, T6, and T7 (see Table I). The atomic composition of the residual photoresist layer was determined from the transmittance measurements discussed later in Sec. III A and was entered in the ALS reflectance data models. In sample T7, the Pt layer was too thick for interference fringes to be visible in the ALS reflectance or GIXR data. The ALS reflectance data on sample T7 were thus used only to model the residual photoresist layer density and thickness. The Pt thickness of sample T7 was determined using transmittance data (see Sec. III A). We estimate that the accuracy in the thickness determination of the Pt and residual photoresist layers is about ±1%.

The Pt sample used in the reflectance vs. incidence angle measurements in the 25–95 eV range at ALS beamline 6.3.2. for optical constants determination, discussed in Sec. III B, was deposited at CXRO in a DC-magnetron sputtering system with planar geometry, on a fused silica substrate with 25 mm diameter and 6 mm thickness. The density of the CXRO Pt coating was verified by GIXR measurements at LCF and was found to be 21.45 ± 0.20 g/cm³, the same as the Pt samples deposited at DTU-Space. The thickness of the coating was determined by fitting ALS reflectance and GIXR data and is discussed in detail in Sec. III B.

All GIXR and ALS reflectance data discussed in this work were modeled/fitted with the Fresnel equations for the reflected field intensities. Surface and interface roughness were assumed to have an error function profile in the models, as discussed in detail in Ref. 27. All fits to GIXR and ALS reflectance and transmittance data used material optical constant values from the CXRO database.¹² 

Figure 2 shows the transmittance measurement results on free-standing samples T6, T1, T2, and T7 with Pt thicknesses of 52.46, 54.13, 103.47, and 202.55 nm, respectively. The methodology used in this paper has also been implemented and described in detail in the earlier work.^23–26 The transmittance curves in Fig. 2 were obtained through the expression T = I/I₀ for the transmittance T of a film at a given photon energy, where I is the intensity transmitted through the film and I₀ is the intensity of the incident photon beam. Transmittance measurements were obtained in steps ranging from 0.1 to 0.5 eV, depending on the photon energy range. The position of the photon beam was monitored so that data would be collected from the same area on each sample at all photon energy ranges, resulting in measurement reproducibility better than 0.5%. Samples T1 and T6 have similar thicknesses; nevertheless, they were both measured (as is shown in Fig. 2) to demonstrate the reproducibility and consistency of our measurement methodology. The energy-dependent, absorptive portion β of the refractive index of the sputtered Pt thin film was obtained through the expression

where x is the thickness of the Pt layer, λ is the photon wavelength (related to the photon energy E by E = hc/λ), and T₀ is the transmittance from layers other than Pt, which may be present on the sample.

An example of the fitting procedure to determine β using Eq. (2) is shown in Fig. 3, for four different photon energies. In the plot of the measured transmittance T (on a logarithmic scale) vs. Pt thickness x at a given photon energy, the data points are fitted to a straight line whose slope is equal to 4πβ/λ. Furthermore, the point where the straight line intercepts the y-axis corresponds to the transmittance T₀ at Pt thickness x = 0, assuming that the thickness of the overlayer responsible for T₀ is nearly the same for all samples used in the measurements. The Pt thickness of samples T1, T2, and T6 was determined via the ALS reflectance and GIXR measurements discussed in Sec. II B and shown in Table I. The Pt thickness of sample T7 was adjusted around a nominal thickness of 200 nm, in order to maximize the regression factor of the transmittance-vs-thickness fits to the experimental data points, in the energy range 560 eV–770 eV (which is free of absorption edges). This method determined a Pt thickness of 202.55 nm for sample T7 and this thickness value resulted in a regression factor very close to 1 in the fits at all photon energies where transmittance data were obtained. The above-mentioned procedure to determine β for Pt using transmittance data from samples T1, T2, T6, and T7 was applied in the photon energy range 108–778 eV. At photon energies below 108 eV, data from samples T1 and T6 only were used, as the much thicker samples T2 and T7 produced transmitted signal values that were very “noisy” and thus unsuitable for use with the above method. For this reason, in the photon energy range 32–108 eV, β was determined via Eq. (2) from transmittance data on sample T6 only, using the layer parameters in Table I for the Pt layer and residual photoresist layer—the transmittance of the latter represents T₀ in Eq. (2). Similar results were obtained when β was determined from transmittance data on sample T1 only, in the range 32–108 eV.

As discussed in Sec. II A, the quantity T₀ in Eq. (2) was determined to be the result of a residual photoresist layer on each Pt sample. A plot of the results for T₀ vs. photon energy derived from the transmittance data on samples T1, T2, T6, and T7 discussed earlier in this section is shown in Fig. 4. It includes a curve calculated to model the experimental results for T₀, corresponding to a 11.85 nm-thick overlayer consisting of C:H:O = 1:1:1 with a density of 1.42 g/cm³. These values are consistent with the overlayer parameters determined by fitting ALS reflectance and GIXR data on samples T1, T2, T6, and T7, discussed in Sec. II A and shown in Table I. The model constructed for T₀ in Fig. 4 was employed to calculate T₀ in the photon energy range 32–108 eV, where β was determined from sample T6 only, via Eq. (2).

Figure 5 shows a plot of β vs. photon energy obtained by transmittance measurements in this work, compared with those from the CXRO database¹² and from Haensel et al.,¹⁴ the latter being the only earlier measurements we could find where the photoabsorption of Pt exhibits the splitting at the Pt N_6,7 absorption edge. Interestingly, although the data by Haensel et al. were part of the compilation included in the CXRO database, the Pt N_6,7 edge splitting is absent in the CXRO database, presumably due to the smoothing incurred by the combination of various data sets and the interpolation of data points with theoretical calculations. Figure 5 reveals significant differences between the present experimental Pt photoabsorption data and the CXRO values, especially at photon energies below 200 eV. The values from Haensel et al. are consistently higher (up to a factor of 2) than the present data, at photon energies above 70 eV.

Reflectance measurements were performed in the range 25–95 eV on the CXRO Pt sample discussed in Sec. II B, in order to determine the Pt optical constants with a method that is independent to the transmittance measurements discussed in Sec. III A. It should be noted that the reflectance method determines both δ and β experimentally, while the transmittance method determines only β experimentally and relies on additional absorption data sets from other works (at lower and higher energies) and on the Kramers-Krönig transformation, for δ. The photon energy range for the reflectance measurements was chosen to overlap with and extend the low-energy side of the transmittance measurements of Sec. III A, especially since in this work there was a lack of Pt samples that would be thin enough to produce useful transmittance data at low energies. Reflectance vs. incidence angle scans were performed at 85 different photon energies, in 2 eV or 0.2 eV increments, the latter in the region of the O₂ and N_6,7 absorption edges. In each reflectance scan, the incidence angle range was 1-88° in 1° steps. The experimental reflectance curves were fitted with the Fresnel equations for the reflected field intensities by means of a least-squares fitting algorithm.²⁸ First, reflectance vs. angle data at 5 photon energies were fitted for the Pt optical constants δ, β as well as for the thickness of the Pt layer, using the IMD software.²⁷ Regarding the fused silica substrate of the CXRO Pt sample, the tabulated density (2.19 g/cm³) and a surface micro-roughness of 0.2 nm rms (determined via surface metrology) were entered as fixed parameters in all fits. Based on the results of these 5 fits, the average thickness of the Pt layer was determined to be 31.37 nm with a standard deviation of 0.13 nm. The same procedure was applied to determine the micro-roughness of the Pt layer, by fitting reflectance vs. angle data at 9 different photon energies, resulting in a roughness of 0.58 nm with a standard deviation of 0.05 nm. These Pt thickness and roughness values were also confirmed by GIXR measurements at LCF. The Pt thickness and roughness values were then entered as fixed parameters in all 85 reflectance vs. angle scans, which were fitted for the optical constants δ, β of Pt using the Fresnel equations and custom-written software, to facilitate the efficient fitting of 85 scans. Six representative reflectance scans and their fits are shown in Fig. 6. The high quality of the fits is noteworthy, especially at low incidence angles, which largely determine the values of δ, β at each photon energy. The resulting values for β of Pt in the range 25–95 eV are plotted in Fig. 5, together with the values determined by transmittance in Sec. III A. The agreement between β values determined by reflectance and transmittance in this work is very good, which provides confidence in the data obtained by both methodologies. This is especially remarkable, if one takes into account that (i) optical constants (especially β) obtained by reflectance can be sensitive to surface roughness and contamination of the measured sample and (ii) the reliability of reflectance data fits may be diminished at photon energy regions, where β ≥ δ (such as the region 25-95 eV of the current Pt reflectance measurements) and especially near absorption edges, where the values of δ and β change abruptly.^28,29

Provided a set of photoabsorption values (β) is available in the full spectral range, i.e., from photon energies E → 0 to E → ∞, then δ can be calculated by the Kramers-Krönig relation^10,30

where P denotes the Cauchy principal value of the integral. Based on the results and analysis presented in Secs. III A and III B, a data set of new experimental values for β of Pt was constructed in the photon energy range 25–778 eV, containing the following: (i) in the region 25–31 eV, values determined from the reflectance measurements discussed in Sec. III B, (ii) in the region 32–108 eV, values determined from the transmittance measurements on sample T6 discussed in Sec. III A, and (iii) in the region 108–778 eV, values determined from the transmittance measurements on samples T1, T2, T6, and T7 discussed in Sec. III A. Outside the range 25–778 eV, β values from the earlier literature were employed, as follows: (i) In the region 10⁻⁴–0.09 eV, theoretical calculations by Rakic et al.³¹ based on the Lorenz-Drude model, (ii) in the region 0.1–21.4 eV, data compiled by Palik,¹³ (iii) in the region 811 eV–14.3 keV, tabulated values from CXRO,¹² and (iv) in the region 14.4 keV–433 keV, tabulated data from the National Institute of Standards and Technology (NIST).³² This approach, including the choice of data from the above references, was recently employed successfully to determine the optical constants of Cr.^33,Figure 7 shows a plot of the above-mentioned composite data set for β of Pt, demonstrating good continuity between the different sets of β values. These β values were employed to calculate δ via Eq. (3). The resulting δ values are plotted vs. photon energy in Fig. 8 (left column) alongside the corresponding β values in the right column and are compared with δ and β values from the earlier literature.^12,13,17,18 In Fig. 8 (top left), we note the good agreement between the new δ values determined directly via reflectance measurements (Sec. III B) and new δ values calculated from transmittance measurements via the Kramers-Krönig relationship [Eq. (3)]. The agreement is noteworthy especially considering that the Kramers-Krönig relationship may include errors contributed from β values in the entire spectrum. The new δ values exhibit pronounced differences with earlier data in the vicinity of the O_2,3 and N_6,7 edges—the splitting around the Pt N_6,7 edge is observed for the first time in the literature. In Fig. 8 (top right), we note again the agreement between β values from reflectance and transmittance measurements in this work and the significant differences with the earlier literature. Similarly, in Fig. 8 (bottom), both δ and β exhibit significant differences with earlier data, in the region 95–778 eV. The absence of fine structure around the Pt N_4,5 edge is evident in Fig. 8 (bottom) and in Fig. 5 (top). This has also been observed by Haensel et al.,¹⁴ who mention that the increased absorption taking place in that photon energy region (due to electronic transitions occurring at lower photon energies) may be masking the Pt N_4,5 transition. Finally, in Fig. 9, we present a comparison of the data from the present work with the data from Birken et al.,¹⁶ where the real and imaginary parts of the Pt dielectric function were determined experimentally via reflectance vs. incidence angle measurements using the same method as discussed in Sec. III B of this paper. The dielectric function ɛ of a material is defined as

therefore, from Eqs. (1) and (4), we obtain ɛ₁ = (1 − δ)² − β² and ɛ₂= 2(1 − δ)β.

Figure 9 demonstrates remarkable agreement between the results of this work and Ref. 16, for both real and imaginary parts of the Pt dielectric function, thus providing an additional validation of our measurements. Nevertheless, the photon energy spacing of the data points from Ref. 16 is not adequate to resolve the fine structure around the Pt N- and O-edges, which is present in the data from this paper.

The standard method to test the consistency of the composite set of β values used in the Kramers-Krönig relation [Eq. (3)] is to calculate the effective number of electrons (N_eff) contributing to the absorption processes in the atom at all photon energies from 0 to ∞ via the equation³⁴ 

where n_a is the atomic density of the material, m and e are the electron mass and charge, respectively, and ɛ₀ is the vacuum permittivity. If the β data are accurate in the entire spectral range, then Eq. (5) produces N_eff = Z* = Z − (Z/82.5)^2.37, which is the so-called f-sum rule, where Z* represents the atomic number Z corrected by the relativistic effect.¹¹ For Pt atoms, Z* = 77.12. Using the composite set of β values plotted in Fig. 7 and discussed above, including our new experimental data in the range 25 eV–778 eV, we obtain N_eff = 76.09 from Eq. (5). This result demonstrates a deficiency of only 1.03 electrons (1.3%) from the ideal 77.12 electrons and thus a very good overall consistency of our composite Pt photoabsorption data set. If we replace our experimental data in the range 25 eV–778 eV with the CXRO tabulated values,¹² we obtain N_eff = 76.19. The difference between the two N_eff results is 0.1 electrons, which represents 0.13% of the Z* value for Pt. This difference is too small and well within the error bars of both data sets; therefore, it is not meaningful towards assessing the accuracy of one data set vs. the other. For example, 1% uncertainty in the density of the Pt films in the photon energy region 25-778 eV would produce 0.36 electrons difference in N_eff in Eq. (5). Furthermore, it should be noted that Eq. (5) is useful toward pointing deficiencies in absorption data from the overall spectrum, without any specificity on localized photon energy regions. As can be seen in Fig. 5, our new experimental β values are higher than the CXRO tabulated values in some photon energy regions and lower in other regions, thus resulting in a near-zero net difference between the two sets, when the sum rule of Eq. (5) is applied. Reference 35 has proposed a method to evaluate optical constant data sets in specific photon energy regions, using “window functions.”

We have measured the optical constants (δ, β) of Pt via transmittance and reflectance measurements in the region of the Pt N- and O-shell absorption edges. We have combined our photoabsorption data with values from the literature at photon energies outside our measurement range and have employed the Kramers-Krönig transformation to produce a self-consistent set of (δ, β) values for Pt in the entire spectrum. Our experimental data demonstrate for the first time highly resolved fine structure in the region of the Pt O_2,3 and N_6,7 edges, resulting in differences of up to a factor of 2 compared to earlier published Pt optical constant values. The new (δ, β) values for Pt determined in this work are available upon request at regina.soufli@llnl.gov.

This work was supported by a NASA project (No. 13-APRA13-0091), by a STSM Grant from COST Action MP1203, by the Jean d’Alembert fellowship program from Université Paris-Saclay, and by Lawrence Livermore National Laboratory (LLNL)'s Professional Research and Teaching leave program. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344 and by the University of California Lawrence Berkeley National Laboratory under Contract No. DE-AC03-76F00098. The authors are thankful to Stefan Immler (NASA) and Marie-Anne Descalle and Stefan Hau-Riege (LLNL) for their support of this project.