Transmittance and optical constants of Ca films in the 4-1,000 eV spectral range

Luis Rodríguez-de Marcos1, Juan I. Larruquert1,* , Manuela Vidal-Dasilva1, José A. Aznárez1, Sergio García-Cortés1, José A. Méndez1, Luca Poletto2, Fabio Frassetto2, A. Marco Malvezzi3, Daniele Bajoni3, Angelo Giglia4, Nicola Mahne4, Stefano Nannarone4

1GOLD-Instituto de Óptica-Consejo Superior de Investigaciones Científicas Serrano 144, 28006 Madrid, Spain

2Institute of Photonics and Nanotechnologies-National Council for Research, via Trasea 7, 35131 Padova, Italy

3Dipartimento di Elettronica, Università di Pavia and Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia, Via Ferrata, 1, I27100 Pavia, Italy

4Istituto Officina dei Materiali Istituto Officina dei Materiali-Consiglio Nazionale delle Ricerche Laboratorio Tecnologie Avanzate e NanoSCienza, Area Science Park Basovizza, S.S. 14 Km 163.5, 34149 Trieste, Italy

j.larruquert@ csic.es

Abstract: The low expected absorption of Ca makes it an attractive material for multilayers and filters in the extreme ultraviolet (EUV) because most materials in nature strongly absorb the EUV. Few optical constant data had been reported for Ca. In this research, Ca films of various thicknesses were deposited on grid-supported C films and their transmittance measured in situ from the visible to the soft X-rays. The measurement range contains Ca M2,3 and L2,3 absorption edges. Transmittance measurements were used to obtain Ca extinction coefficient k. A minimum k of 0.017 was obtained at ~23 eV, which makes Ca apromising low-absorption material for EUV coatings. A second low-absorption band was found below Ca L3 edge at ~343 eV. k data andextrapolations were used to calculate the refractive index n using Kramers-Krönig relations. This is the first self-consistent data set on Ca covering awide spectral range including the EUV.

OCIS Codes: (260.7200) Ultraviolet, extreme; (120.4530) Optical constants; (350.2450) Filters, absorption; (230.4170) Multilayers; (310.6860) Thin films: optical properties

References and links

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Citation: Applied Optics, Vol. 54, Issue 8, pp. 1910-1917 (2015)

https://doi.org/10.1364/AO.54.001910

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1. Introduction

Ca is expected to have a relatively low absorption in a range between its plasmon wavelength (~7.75 eV) and its M2,3 absorption edge (~25 eV). Nature provides few materials with low absorption in the spectral range between ~12 and 25 eV (~50 and 103 nm), where most materials have either interband or intraband transitions that result in strong absorption. Hence materials with low absorption in this small-photon energy part of the extreme ultraviolet (EUV) are needed to be able to make efficient multilayer coatings and transmittance filters for applications such as instrumentation for space optics. To design optical coatings one needs the optical constants of the materials involved. Self-consistent optical constants of many materials, including some single elements of the periodic table like Ca, are not available. Materials with the common property of a moderately low absorption in the small-photon energy EUV have been fully characterized; they include the alkaline earths Mg1 and Sr2 and the whole set of the lanthanides metals, excluding radioactive Pm (La3, 4, Ce5, Pr6, Nd4, Sm7, Eu8, Gd4, Tb3,4, Dy4, Ho7,9, Er7,10, Tm11, Yb12,13, and Lu14), along with metals with close properties Sc15,16,17,18 and Y19.

For Ca there is a scant literature available on its optical constants. After initial experimental data performed with limited techniques to handle reactive Ca films20,21, Blanc et

al.22,23 measured reflectance and transmittance on various very thin films of Ca, from which they calculated absorption in the 0.5-5.5-eV range. Mathewson and Myers24 performed ellipsometry measurements in situ in the 0.75-3.65 eV range on Ca films deposited by evaporation in UHV; these data were used to calculate the optical constants. Potter and Green25 and Nilsson and Forssell26 measured the reflectance of Ca films in situ in the 6-30 eV and in the 2.1-11.5 eV range, respectively, and calculated the refractive index n and the extinction coefficient k using the Kramers-Krönig (KK) relations over the measured reflectance data, which were extended with extrapolations. Hunderi27 performed ellipsometry measurements in the 0.5-5.5-eV range at 80 K on Ca films that had been deposited on substrates at 200 K and later annealed to 425 K; these data were used to calculate the real part of the dielectric constant ε1 and the optical conductivity σ of Ca, from which n and k can be calculated. Few other papers report measurements of a single optical constant. Marfaing and Rivoira28 measured reflectance and transmittance with polarized light on films of thicknesses within a wide range, from which they calculated the imaginary part of the dielectric constant ε2 of Ca under the assumption of very thin films in the ~2.1-5.6-eV range. There are several papers measuring the absorption of Ca atoms in various EUV ranges29,30,31,32. Other than optical measurements, Langkowski33 measured electron energy-loss spectra (EELS) of Ca films in UHV in situ in the 2–54 eV range and calculated the complex dielectric function in the same range. Robins and Best34 and Kunz35 also measured EELS on Ca films but no optical constant was calculated. This completes the experimental literature that was found. Some optical constant data obtained with theoretical calculations have been reported. Lopez-Rios and Sommers36 calculated ε2 of Ca in the 2-9-eV range. More recently, Errea et al.37 performed theoretical ab initio calculations of the dielectric function of fcc Ca (along with Ca under pressure) in the 0-15-eV spectral range, although the plotted data is difficult to read above ~9 eV.

This paper provides self-consistent optical constants of Ca in a broad spectral range including the EUV that has not been covered in the past. The paper is organized as follows. Section 2 provides information on the experimental procedures. Section 3 displays the transmittance measurements on Ca films, the direct calculation of k and the calculation of n by means of the KK relations, along with the evaluation of the consistency of the derived optical constants.

2. Experimental techniques

4.1 Sample preparation

Ca film deposition was performed under ultrahigh vacuum conditions (UHV) and its transmittance was measured in situ at BEAR (Bending magnet for Emission Absorption and Reflectivity) beamline of ELETTRA synchrotron (Trieste, Italy). Since all materials in bulk are opaque to EUV radiation, self-supported C films were used as substrates. Ca films were deposited onto 5-nm thick C films supported on 117-mesh Ni grids with 88.6% nominal open area (pitch of 216 μm). The procedure to prepare the self-supported substrates was reported elsewhere17. A TriCon source38 was used to evaporate 99.9% purity Ca filling a small W crucible. The distance between crucible and sample was 200 mm. Deposition rate was ~3 nm/min for all films. A quartz crystal microbalance was used to monitor film thickness during deposition. Ca films were deposited onto room-temperature substrates. Near the grid-supported C film we placed a glass witness substrate that was simultaneously coated; the self-supported C substrate and the glass substrate were less than 10 mm apart from each other. The sample on glass was used to measure reflectance versus the incidence angle at the energy of 140 eV.

4.2. Experimental setup for transmittance and reflectance measurements

Transmittance measurements were performed at BEAR beamline with vertical slits of 100 µm above 24 eV and 450 µm below 24 eV; the monochromator spectral resolution E/ΔE varied between 500 and 2000, depending on slit widths. The suppression of higher orders was achieved using quartz, LiF, In, Sn, Al, and Si filters at specific ranges below 100 eV, and choosing a plane mirror-to-grating deviation angle in the monochromator setup that minimized the higher order contribution at energies above 100 eV. The detector was a silicon diode model SXUV-100 from IRD. The beam cross section at the sample was about 0.7×1.5 mm².

Measurements were performed in BEAR spectroscopy chamber39,40,41, which operates at a base pressure in the 1×10-8 Pa range. Samples were deposited in the preparation chamber, which is connected in vacuum with the spectroscopy chamber; this allows sample transfer between the chambers in UHV conditions. The base pressure in the preparation chamber before starting with evaporations was ~10-7 Pa. Although various previous degas processes of the Ca evaporant material were performed, pressure increased during film deposition, but this pressure increase was reduced over the samples: it went from 2x10-5 Pa for the first film down to 2x10-6 Pa for the last film. A similar behavior has been mentioned in the literature25 and the pressure increase was attributed to mainly H outgassing. After deposition, the sample was transferred to the spectroscopy chamber within few minutes.

We used three different self-supported C substrates for the different films. We started measuring the transmittance of each substrate prior to the deposition of Ca films. The first and second C substrates accumulated two successive Ca films of various thicknesses without breaking vacuum; the third C substrate only received one Ca film. Once the initial film of either first or second substrate had been measured, it was transferred back to the deposition chamber to deposit the second Ca film on top of the first one, and the sample was transferred again to the spectroscopy chamber for characterization of the two accumulated films. Transmittance measurements were performed onto samples at room temperature. For each film, uniformity evaluations were performed. At energies above 18 eV, fluctuations of the photon beam during transmittance measurements were recorded with a 100-V biased Au mesh and with the storage ring current; below 18 eV, only the ring current was available. Beam fluctuations were cancelled by normalizing the recorded beam intensity to the mesh current, or, when the latter was noisy, to the ring current.

3. Results and discussion

3.A Transmittance and extinction coefficient of CaFig. 1 displays the transmittance over the spectrum measured for the five film thicknesses,which have been normalized to the transmittance of the bare substrate. The following total Cafilm thicknesses were measured: 18.8 and 31 nm on the first substrate, 40.5 and 100 nm onthe second substrate, and finally 51 nm on the third substrate. Film thicknesses werecalculated using reflectance measurements versus angle of incidence at 140 eV. The angularpositions of the reflectance minima and maxima were fitted to obtain the thicknesses. Theenergy of 140 eV for reflectance measurements was selected to be far from the absorptionedges of Ca in order to be able to use Henke optical constants42,43 in the reflectancecalculation. Henke data were downloaded from the website of the Center for X-Ray Optics(CXRO) at Lawrence Berkeley National Laboratory44. For some film the fit was somewhatimprecise, so that a second method was used to refine the thickness, which is described asfollows. Transmittance depends on film thickness d and on k through Beer-Lambert law:

λπ−≈ kd4

T

T

s

fs exp (1)

where Ts and Tfs are the transmittance of the uncoated substrate and of the substrate coated with a Ca film, respectively, and λ is the radiation wavelength in vacuum. The approximate sign in Eq. (1) refers to the fact that reflectance at each interface has been neglected.

Reflectance can be neglected when both n-1 and k are close to 0, which is satisfied here in the large photon energy range, but not so well at small energies. When this approximation is valid, the normalized transmittance of film thicknesses d1 (T1) and d2 (T2) can be calculated from each other through:

1

2d

d

11

212 T

d

dkd4T =

λ

π−= exp (2)

which was used to refine the value of film thickness d2 using d1, T1, and T2. For this refinement, transmittance in the range above 360 eV was used.

FIG. 1. (color online) Log-log plot of the transmittance versus photon energy of Ca films with various thicknesses in nm, normalized to the transmittance of the

substrate

In fig. 1, two strong absorption bands are observed: a deep band with a transmittance minimum at 34.5 eV, that is attributed to Ca M2,3 edge, and a narrow band with a transmittance double minimum at ~351 eV, that corresponds to Ca L2,3 edge. Oscillations at ~285, ~100, and ~72.5 eV are attributed to the presence of some contamination of ubiquitous carbon and to the transparency onsets of Si and Al filters, respectively. Even though there is a clear trend for transmittance to decrease with increasing Ca film thickness, as expected, there are some undesired line crossings in Fig. 1. These crossings mainly occur in the low absorption ranges of Ca and might be due to the presence of some contamination; such contamination is expected to be small since its effect is not observable when Ca absorption increases. Present Ca has been investigated in the same laboratory and with the same methodology as other prior materials (Sr; Sc; Ce, Pr, Eu, Ho, Er, Tm, Yb, Lu), all of them also considered reactive. However, Ca seems to be the material the most influenced by the residual UHV atmosphere during the measurement period among the referred materials.

The transmittance measurements obtained at each photon energy for the various film thicknesses were used to calculate k using Eq. (1). When Eq. (1) is satisfied, k can be obtained at each wavelength/photon energy by fitting the slope of the logarithm of the normalized transmittance versus film thickness. When reflectance is not negligible, Eq. (1) was used

anyway in order to provide an approximate value for k, which was improved through an iteration process that will be described below. The aforementioned line crossings complicated the calculation of k. When possible, we used all the experimental data to calculate k. In some cases at small energies some data sets were discarded when they seemed not to be compatible with the other data; this had to be done for the two thinnest films in the range below 25 eV. In a further iteration process involving n (the calculation of n is described in the next sub-section), in the low energy range n was seen not to smoothly connect with literature data; this added to the modest consistency of small-energy transmittance data of Fig. 1 for the three samples in such a range. As a result we decided to replace our k data in the 4-8-eV range with the data of Nilsson and Forssell26, which could be smoothly connected with our data above 8 eV. Other than this, measured transmittance for the thickest film at the strong absorption range of 30-39 eV was not as small as what could be calculated from the transmittance of the other films when scaled to 100 nm thickness; this might be attributed to the presence of pinholes, which would be limiting the smallest attainable transmittance to ~0.1%. In consequence, the thickest film transmittance was not used in the 30-39-eV range.

Fig. 2. (color online) Log-log plot of the extinction coefficient of Ca as a function of photon energy, along with the data of Blanc et al.22,23, Mathewson

and Myers24, Nilsson and Forssell26, Potter and Green25, and Henke42,43

Fig. 2 displays the obtained k data in the measured range once the aforementioned iteration process had converged. Literature k data are also plotted in Fig. 2. Ca absorption edges are marked to help interpret the peaks; parasitic C K signal is still visible and it is indicated in the plot. Fig. 3 depicts the same data but limited to small energies. An interesting minimum of k of 0.017 is found at ~23 eV, below Ca M2,3 edge. This k can be considered a relatively low value at this range, which might enable transmission filters based on Ca or multilayer coatings based on Ca and a second material; however, the high reactivity of Ca may complicate its application in filters and multilayer coatings. Regarding this k minimum over the literature, the energy for the mentioned absorption minimum below M2,3 edge is only reached by Potter and Green, but their minimum is shifted towards smaller energies and is much wider. Langkowski33 calculated Ca optical constants from EELS data (not plotted in Figs. 2 and 3) but the referred minimum is shifted to smaller energies and to much larger k values. In our small energy range, the aforementioned use of the data of Nilsson and Forssell

assures a smooth connection. On the other hand, the peak of Blanc et al. is shifted to smaller energies and higher values of k. A good connection at 3.6-4 eV is obtained with the data of Mathewson and Myers and Hunderi (the latter not displayed). Above 30 eV we only found Henke’s semiempirical data42,43 for comparison; for these data, the nominal density of 1.55 g/cm3 was used for Ca.

Fig. 3. (color online) Log-log plot of the extinction coefficient of Ca versus small photon energies, along with the data of Blanc et al.22,23, Mathewson and

Myers24, Nilsson and Forssell26, and Potter and Green25

Fig. 4 depicts k at L2,3 edge, along with the semiempirical data of Henke et al. We have not found any previous optical data at this edge. The two main peaks at energies very close to those found in this research have been measured by appearance potential spectra45,46, XPS47, and x-ray absorption48. Refs 45 to 47 include a third and shorter peak at ~355 eV, which is not seen here, even though the present resolution of ~1000 at this energy should permit the observation of that peak, if present. In agreement to present results, the absorption spectrum of metallic Ca measured by Himpsel et al.48 displayed no extra feature at energies above L2.

Nyberg46 measured the appearance potential of metal Ca after exposure to controlled doses of oxygen; he found that L3 peak strongly decreases with respect to L2 with an O2 dose of 40 L (Langmuirs), and the whole picture is fully modified with larger doses. The present structure plotted in Fig. 4 seems compatible with Nyberg’s measurements with O2 doses between 0 and 20 L.

3.B The refractive index of Can of Ca was calculated with the KK relations:

( )'dE

E'E

'Ek'EP

21)E(n

022

∞

−π=− (3)

where P stands for the Cauchy principal value. In order to calculate n with Eq. (3) we need to know k over the whole spectrum. To do this, we extended the present k data with the available data in the literature and extrapolations. At smaller energies we used the data of Nilsson and Forssell26 (4-8 eV) and Mathewson and Myers24 (down to 0.75 eV) and we fitted a Drude model to k data in the small energy range of Ref. 24, which was used to extend k data to zero energy. On the large energy side we used Henke data42,43 up to 3·104 eV and for even larger

energies up to 4.3·105 eV we used the calculations of Chantler et al.49 Fig. 5 displays the set of k data gathered to perform KK analysis.

Fig. 4. (color online) The extinction coefficient of Ca versus photon energy at L2,3 edge, along with the semiempirical data of Henke42,43

Fig. 5. (color online) Log-log plot of k data gathered to perform KK analysis using the current data along with the data of Nilsson and Forssell26, Mathewson

and Myers24, Henke42,43, and Chantler et al.4949, along with extrapolated data with a Drude model

When reflectance is not negligible, calculating k with the slope method using Eq. (1) may result in uncertainties, as mentioned in the previous subsection. To avoid this problem, we calculated the optical constants in an iterative way, which was applied in the 8-160-eV range. In the first iteration, we obtained initial k values by plainly using the slope method. These values, along with k data in the rest of the spectrum, were used to obtain the refractive index n with KK analysis. Once a first set of data {n(E), k(E)} was available, we calculated the transmittance ratio of the C/Ca coated substrate to the C uncoated substrate with the well-known Fresnel coefficients. The calculated transmittance ratio was compared to the measured data, which enabled us to modify k. The modified value was considered a second estimate of k, which was used to obtain a second estimate of n by applying again the KK relations, and the iteration could be applied once and again. Three such iterations were performed until convergence was attained. The optical constants of the support C film had been previously calculated with the same procedure, which had been applied to transmittance measurements of an uncoated C substrate.

Fig. 6. (color online) Log-log plot of δ of Ca as a function of photon energy, along with the data of Blanc et al.22,23, Mathewson and Myers24, Nilsson and

Forssell26, Potter and Green25, and Henke42,43

Fig. 6 displays δ=1-n obtained with the above procedure. The agreement with Henke data is good in the whole range except at the edges, where Henke data is known to be inexact. Fig. 7 depicts n in the small energy range. There is a strong disagreement over the literature in the smallest energy range. The data of Blanc et al.22,23 departs from all others below ~3.2 eV, whereas the data of Nilsson and Forssell26 below ~2.6 eV looks inconsistent. By using k data of Nilsson and Forssell26 in the 4-8-eV range, as mentioned above, the deviation in n with the data of Mathewson and Myers24 and Nilsson and Forssell26 (the latter limited to 3 eV and above) is reduced with respect to what was initially obtained with our k data in this range, which is considered satisfactory taking into account the commented inconsistencies of our transmittance measurements mainly at small energies. Fig. 8 shows δ at L2,3 edge, along with Henke data, which may be the first experimental data available at this edge.

3.C Consistency of the optical constantsThe global consistency of the obtained optical constants can be evaluated with the sum-ruletests. The f sum rule connects the number density of electrons to k (or to other optical

parameters). The following equation is used to calculate the effective number of electrons per atom neff(E) contributing to k up to a given energy E50:

Fig. 7. (color online) Log-log plot of δ of Ca versus small photon energies, along with the data of Blanc et al.22,23, Mathewson and Myers24, Nilsson and

Forssell26, Potter and Green25, and Henke42,43

Fig. 8. (color online) δ=1-n of Ca versus photon energy at L2,3 edge, along with the semiempirical data of Henke42,43

( ) πε

=E

022

at

0eff 'dE)'E(k'E

eN

m4En

(4)

where Nat is the atom density, e is the electron charge, m is the electron mass, ε0 is the permittivity of vacuum, and is the reduced Planck’s constant. The high-energy limit given by Eq. (4) must reach Z=20, which is the atomic number of Ca; this number is slightly reduced to Z*=19.9451 when applying the relativistic correction. By integrating the present data, which are plotted in Fig. 5, we obtained a high-energy limit for Eq. (4) of 19.89, only a 0.26% smaller than the above Z* value. The agreement is excellent. In the calculation we used Ca nominal density of 1.55 g/cm3.

To check the consistency of n we use the inertial sum rule:

[ ] ,)(∞

=−0

0dE1En (5)

In order to evaluate the integral of Eq. (5), we use the following parameter50:

[ ]

∞

∞

−

−=ζ

0

0

dE1)E(n

dE1)E(n

(6)

Shiles et al.52 suggested that a good value of ζ should stand within ±0.005. With n data obtained in this research, we calculate ζ=-0.0034, which satisfies the inertial sum rule test. In conclusion, the two applied sum-rule tests suggest satisfactory consistency of present n and k data.

The data are available on request at the following e-mail address: j.larruquert@csic.es

4. Conclusions

The transmittance of freshly deposited Ca films of various thicknesses has been measured in the 4-1000-eV spectral range. Two strong absorption bands are observed: a deep band with a transmittance minimum at 34.5 eV, that is attributed to Ca M2,3 edge, and a band with a transmittance double minimum at ~351 eV, that corresponds to Ca L2,3 edge.

Transmittance measurements were used to calculate k at each photon energy in the above range. A minimum k of 0.017 is found in the small-photon energy EUV at 23 eV. This low absorption, which extends to the ~12-24-eV range, makes Ca one of the materials with smallest absorption in this range and hence a candidate for EUV filters and multilayer coatings. A second spectral range of interest of Ca for its low absorption is below its L3 edge, which is below ~343 eV. n of Ca was calculated with the KK relation over the present k data along with literature data and extrapolations. Two sum-rules tests were applied to the obtained optical constants and satisfactory consistency evaluation parameters were obtained. To our knowledge, this is the first self-consistent optical constant data set of Ca covering a wide spectral range, the first reported data above ~55 eV, and the first data obtained using optical measurements above ~30 eV.

Acknowledgments

We acknowledge support by the European Community - Research Infrastructure Action under the FP6 "Structuring the European Research Area" Programme (through the Integrated Infrastructure Initiative "Integrating Activity on Synchrotron and Free Electron Laser Science") through proposal numbers Ref. 2007655. This work was also supported by the National Programme for Space Research, Subdirección General de Proyectos de Investigación,

Ministerio de Ciencia y Tecnología, project number AYA2010-22032. L. Rodríguez-de Marcos and S. García-Cortés are thankful to Consejo Superior de Investigaciones Científicas (CSIC) for funding under the Programa JAE, partially supported by the European Social Fund. M. Vidal-Dasilva acknowledges financial support from an FPI fellowship number BES-2006-14047. We are very grateful to M. Fernández-Perea for her advice to organize the measurement procedure.