Regina Soufli

Franck Delmotte

Julia Meyer-Ilse

Farhad Salmassi

Nicolai Brejnholt

Sonny Massahi

David Girou

Finn Christensen

Eric M Gullikson

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

We are presenting an experimental, self-consistent determination of the optical constants (refractive index) of Pt using a combination of photoabsorption and reflectance data in the photon energy range 25 to 778 eV, which includes the N-and O-shell electronic absorption edges of Pt. We compare our new experimental values with Pt optical constant data sets from the literature. Our Pt optical constant values reveal highly resolved absorption-edge fine structure around the O2,3 and N6,7 edges in both the absorptive and dispersive portions of the refractive index, which were missing in earlier literature.

Introduction

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 energies [START_REF] Hunter | Reflectance Spectra of Single Materials[END_REF] and have therefore been applied in synchrotron mirrors [START_REF] Rehn | Vacuum Ultraviolet (VUV) and Soft X-Ray Mirrors for Synchrotron Radiation[END_REF][START_REF] Koide | Investigation of carbon contamination of synchrotron radiation mirrors[END_REF] and considered as mirror coatings for space-borne solar physics and astronomy telescopes [START_REF] Gull | Low earth orbit environmental effects on osmium and related optical thin-film coatings[END_REF][START_REF] Herzig | Long-duration orbital effects on optical coating materials[END_REF][START_REF] Pareschi | Astronomical soft x-ray mirrors reflectivity enhancement by multilayer coatings with carbon overcoating[END_REF][START_REF] Sakao | The soft x-ray photon-counting telescope for solar observations[END_REF][START_REF] Della Monica Ferreira | X-ray mirror development and testing for the ATHENA mission[END_REF] . 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

n = 1-+ i  (1)
where 1- and  represent the dispersive and absorptive portions of the photon energy-dependent refractive index, respectively. The terms ,  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. [START_REF] Henke | X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92[END_REF] , which covers the photon energy range 30 eV -30 keV and is maintained and updated online 12 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 lack 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 [START_REF] Lynch | Comments on the Optical Constants of Metals and an Introduction to the Data for Several Metals[END_REF] , also lacks fine structure in the Pt N-and O-edge regions. Both Ref. 11 and Ref. 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 [START_REF] Haensel | Optical absorption measurements of tantalum, tungsten, rhenium and platinum in the extreme ultraviolet[END_REF]

obtained photoabsorption data on

Pt thin films prepared by evaporation. Wehenkel et al [START_REF] Wehenkel | Optical absorption coefficient of nickel, palladium platinum and copper, silver, gold between 20 and 120 eV[END_REF] also measured the absorption of Pt thin films via electron energy loss spectra. Birken et al [START_REF] Birken | Investigations on the consistency of optical constants in the XUV determined by different methods[END_REF] and Windt et al [START_REF] Windt | Optical constants for thin films of Ti[END_REF]

Experimental setup

Measurement instrumentation

Grazing Incidence X-Ray Reflectance (GIXR) measurements (discussed in Section 2.2) 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 Section 2.2.

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 Section 2.2, 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 equation 19 to determine the thin film stress.

The EUV/soft x-ray reflectance and transmittance measurements discussed in Sections 2.2, 3.1 and 3.2, 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 [START_REF] Underwood | High-resolution, high-flux, user friendly VLS beamline at the ALS for the 50-1300 eV energy region[END_REF][START_REF] Gullikson | Recent developments in EUV reflectometry at the Advanced Light Source[END_REF] . A set of filters of various materials (with each filter selected specifically for each photon energy range) is used for wavelength calibration and 2 nd 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 manuscript, signal was collected with a GaAsP photodiode detector with 1 deg 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. For the transmittance measurements discussed in Section 3.1, 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 2 nd 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 deg to 6 deg, depending on photon energy range.

Sample preparation and characterization

The Pt films used in the transmittance measurements were deposited at DTU-Space via DCmagnetron sputtering, using the deposition system described in Ref. [START_REF] Jensen | Investigation of new material combinations for hard x-ray telescope designs[END_REF] . 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 m thickness. After Pt deposition, the samples 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 acetoneresistant 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 earlier work [START_REF] Gullikson | Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges[END_REF][START_REF] Soufli | Optical constants of materials for multilayer mirror applications in the EUV/soft x-ray region[END_REF][START_REF] Soufli | Absolute photoabsorption measurements of molybdenum in the range 60 to 930 eV for optical constant determination[END_REF][START_REF] Soufli | Optical constants of magnetron-sputtered boron carbide thin films from photoabsorption data in the range 30 to 770 eV[END_REF] to produce free-standing thin films for EUV/x-ray optical constants 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 manuscript 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/cm [START_REF] Rehn | Vacuum Ultraviolet (VUV) and Soft X-Ray Mirrors for Synchrotron Radiation[END_REF] , 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 microroughness 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 Section 3.2). The ALS reflectance measurements were performed at two different angles (65 and 85 deg 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 package [START_REF] Windt | IMD -Software for modeling the optical properties of multilayer films[END_REF] and the results are summarized in Table 1. 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. That photoresist layer was modeled as having a density of 1.42 g/cm [START_REF] Rehn | Vacuum Ultraviolet (VUV) and Soft X-Ray Mirrors for Synchrotron Radiation[END_REF] , consistent among all ALS reflectance measurements and an average thickness of 11.85 nm, determined among samples T1, T2, T6 and T7 (see Table 1). The atomic composition of the residual photoresist layer was determined from the transmittance measurements discussed later in Section 3.1 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 Section 3.1). 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 Section 3.2, 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/cm [START_REF] Rehn | Vacuum Ultraviolet (VUV) and Soft X-Ray Mirrors for Synchrotron Radiation[END_REF] , 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 Section 3.2.

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 constants values from the CXRO database 12 .

Pt optical constants results and discussion

Pt optical constants from transmittance measurements

Fig. 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 manuscript has also been implemented and described in detail in earlier work [START_REF] Gullikson | Absolute photoabsorption measurements of Mg, Al, and Si in the soft-x-ray region below the L2,3 edges[END_REF][START_REF] Soufli | Optical constants of materials for multilayer mirror applications in the EUV/soft x-ray region[END_REF][START_REF] Soufli | Absolute photoabsorption measurements of molybdenum in the range 60 to 930 eV for optical constant determination[END_REF][START_REF] Soufli | Optical constants of magnetron-sputtered boron carbide thin films from photoabsorption data in the range 30 to 770 eV[END_REF] . 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 energydependent, absorptive portion β of the refractive index of the sputtered Pt thin film was obtained through the expression:

T = T0 exp (-4πβx/) ( 2
)
where x is the thickness of the Pt layer,  is the photon wavelength (related to the photon energy

E by E = hc/) and T0 its the transmittance from layers other than Pt, that 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/. 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 Section 2.2 and shown in Table 1. The Pt thickness of sample T7 was adjusted around the 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 to 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 1 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 Section 2.1, 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, 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/cm [START_REF] Rehn | Vacuum Ultraviolet (VUV) and Soft X-Ray Mirrors for Synchrotron Radiation[END_REF] . 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 Section 2.1 and shown in Table 1. 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).

Pt optical constants from reflectance measurements

Reflectance measurements were performed in the range 25 -95 eV on the CXRO Pt sample discussed in Section 2.2, in order to determine the Pt optical constants with a method that is independent to the transmittance measurements discussed in Section 3.1. 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 Section 3.1, 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 N6,7 absorption edges. In each reflectance scan, the incidence angle range was 1 -88 degrees in 1-degree steps. The experimental reflectance curves were fitted with the Fresnel equations for the reflected field intensities by means of a leastsquares 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 [START_REF] Windt | IMD -Software for modeling the optical properties of multilayer films[END_REF] .

Regarding the fused silica substrate of the CXRO Pt sample, the tabulated density (2.19 g/cm [START_REF] Rehn | Vacuum Ultraviolet (VUV) and Soft X-Ray Mirrors for Synchrotron Radiation[END_REF] ) 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 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. 6 representative reflectance scans and their fits are shown in Fig. 6. The high quality of the fits is noteworthy,

Compilation of a new Pt optical constant data set

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

𝛿(𝐸) = - 2 𝜋 𝑃 ∫ 𝐸 ′ 𝛽(𝐸 ′ ) 𝐸 ′ 2 -𝐸 2 ∞ 0 𝑑𝐸 ′ , ( 3
)
where This has also been observed by Haensel et al [START_REF] Haensel | Optical absorption measurements of tantalum, tungsten, rhenium and platinum in the extreme ultraviolet[END_REF] , which 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 N4,5 transition. Finally, in Fig. 9 we present a comparison of the data from the present work with the data from Birken et al [START_REF] Birken | Investigations on the consistency of optical constants in the XUV determined by different methods[END_REF] , 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 Section 3.2 of this manuscript. The dielectric function ε of a material is defined as:

P
ε = ε1+i ε2 = n 2 (4)
therefore, from eqs. (1) and ( 4) we obtain: ε1 = (1-δ) [START_REF] Hunter | Reflectance Spectra of Single Materials[END_REF] -β 2 and ε2 = 2(1-δ)β. 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 (Neff) contributing to the absorption processes in the atom at all photon energies from 0 to  via the equation [START_REF] Smith | Finite-energy f-sum rules for valence electrons[END_REF] :

𝑁 𝑒𝑓𝑓 = 4𝑚𝜖 0 𝜋𝑛 𝑎 𝑒 2 ∫ 𝐸 ′ 𝛽(𝐸 ′ ) ∞ 0 𝑑𝐸′ (5)
where n is the atomic density of the material, m and e are the electron mass and charge respectively and ε0 is the vacuum permittivity. If the  data are accurate in the entire spectral range, then eq. ( 5) produces Neff = 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 [START_REF] Henke | X-ray interactions: photoabsorption, scattering, transmission, and reflection at E=50-30000 eV, Z=1-92[END_REF] . For Pt atoms, Z* = 77.12.

Using the composite set of  values plotted in Fig. 7 and discussed above, including our new experimental data in the range 25 eV -778 eV, we obtain Neff = 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 Neff = 76.19. The difference between the two Neff 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 Neff 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. Ref. [START_REF] Rodríguez-De Marcos | Tuning sum rules with window functions for optical constant evaluation[END_REF] has proposed a method to evaluate optical constants data sets in specific photon energy regions, using "window functions".

Conclusions

We

  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 energyloss 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.

  The reflectance measurements in the photon energy range 83 -188 eV for Pt thickness determination, discussed in Section 2.2, were obtained with the 200 lines/mm grating, a Be filter (83 -111 eV) and a B filter (108 -188 eV) for 2 nd -harmonic and stray light suppression. The order suppressor consisted of 3 C mirrors at 14 deg (83 -111 eV) and 8 deg (108-188 eV) grazing incidence angle. Photon energy was calibrated based on the L2,3 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 Section 3.2, 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 2 nd -harmonic and stray light suppression. The order suppressor consisted of 3 C mirrors at 20 deg (25 -38 eV), 18 deg (42 -68 eV) and 14 deg (62 -95 eV) grazing incidence angle. Photon energy was calibrated based on the L2,3 absorption edges of an Al and a Si filter. The beam polarization ranged from 93% spolarized at 25 eV to 89% s-polarized at 95 eV.

Fig. 5

 5 Fig.5shows a plot of  vs. photon energy obtained by transmittance measurements in this work,

  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 Section 3.1. 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 .

8 (

 8 Fig.8(bottom), both  and β exhibit significant differences with earlier data, in the region 95 -

Fig. 9

 9 Fig. 9 demonstrates remarkable agreement between the results of this work and Ref. 16, for both

  photoabsorption data with values from the literature at photon energies outside our measurement

Figure 1 :

 1 Figure 1: Reflectance data obtained at ALS beamline 6.3.2. (points) and IMD models 27 (solid

Figure 2 :Figure 3 :Figure 4 :Figure 5 :

 2345 Figure 2: Experimental transmittance results obtained at ALS beamline 6.3.2. on 4 free-standing

Figure 6 :Figure 7 :

 67 Figure 6: Measured reflectance vs. incidence angle data are plotted in lin-log scale at 6 different

Figure 8 :

 8 Photon energy (eV)

Figure 9 :

 9 Photon energy (eV)

Table 1 :

 1 Thin film parameters deduced from GIXR and reflectance data. ρ1, z1 and σ1 are the residual photoresist density, thickness and roughness at the vacuum / photoresist interface . z2, σ2 and σ3 are the Pt thickness and roughness at the photoresist / Pt and Pt / vacuum interfaces. A Pt density of 21.45 g/cm 3 was used in the models, determined by GIXR measurements.

	Reflectance
	Photon energy (eV)

Acknowledgements

This work was supported by NASA project 13-APRA13-0091, by a STSM Grant from COST Action MP1203, by the Jean d'Alembert fellowship program from Université Paris-Saclay and by 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), Marie-Anne Descalle and Stefan Hau-Riege (LLNL) for their support of this project.


Jennifer Rebellato
email: jennifer.rebellato@institutoptique.fr

Regina Soufli

Evgueni Meltchakov

Eric Gullikson

Sébastien De Rossi

Franck Delmotte

High efficiency Al/Sc-based multilayer coatings in the EUV wavelength range above 40 nanometers

In this work, we have developed new and highly efficient periodic multilayer mirrors Al/Sc, Al/Sc/SiC and Mo/Al/Sc with optimized reflectance at wavelengths between 40 nm and 65 nm. We have reached record values in measured peak reflectance: 57.5% at 44.7 nm and 46.5% at 51 nm, with Al/Sc/SiC at near-normal incidence. Furthermore, we have achieved the largest reported bandwidth with Mo/Al/Sc at 57 nm and the narrowest bandwidth with Al/Sc at 60 nm wavelength. These new and promising results demonstrate that Al/Scbased multilayer coatings are excellent candidates for future generations of EUV instruments for solar physics, EUV lasers and attosecond science, in a wavelength range that hasn't been fully explored.

Reflective multilayer interference optics have enabled the operation at normal incidence angles in the extreme ultraviolet (EUV) range for instrumentation (imaging and illumination mirrors, gratings, polarizers) for solar and planetary physics, plasma diagnostics, tabletop and free-electron lasers and highharmonic generation sources. EUV spectral features of the Sun's corona and photosphere are currently scanned by several spacebased telescopes equipped with such multilayer optics: SoHO, STEREO, SDO and soon Solar Orbiter (to be launched in February 2020). Most EUV imagers and spectrometers have been conceived to detect emission lines of Fe and He at wavelengths between 10 and 40 nanometers [1]. There are several interesting emission lines between 40 and 80 nm, for example Ne VII at 46.5 nm, He I at 58.4 nm and O V at 63 nm. However, few instruments have been developed to explore this portion of the EUV range due to technological limitations, most notably the absence of reliable refractive index values [2][3][4][5] that prevents the design and realization of efficient multilayer coatings. Earlier, Sc/Si-based multilayers were developed to operate at wavelengths longer than 40 nm, to take advantage of the low absorption of Sc in the spectral region below its M2,3 edge [6]. Corrosion-resistant, MgAl/SiC multilayers were also developed for 25-80 nm, [4,7] as well as Tb/Si and Gd/Si multilayers for the 60 nm wavelength region [5,8]. Al/Scbased multilayers were first proposed by our group [9]; we have also performed the first experimental demonstration of the improvement in reflectance with 3-material vs. 2-material multilayer systems [10]. In this paper, we are presenting the first EUV experimental demonstration of periodic multilayer coatings based on the Al/Sc material system. Samples were designed to peak near 44.7, 51.5 or 60 nm wavelengths and achieved record reflectance and bandwidth values. The results presented include grazing incidence X-Ray Reflectometry (XRR) at 8.05 keV and atwavelength, normal incidence measurements in the EUV range at the Advanced Light Source (ALS) synchrotron. Fig. 1. Calculated ideal peak reflectance (Rpeak) for Al/Sc, Al/Sc/SiC and Mo/Al/Sc multilayers from 30 to 60 nm wavelengths at normal incidence (θ = 0°). The number of periods in each multilayer has been chosen in order to saturate the peak reflectance in the entire wavelength range and is shown in the legend as a subscript. The choice of materials and the specific multilayer designs were based on calculations using a homemade Matlab code and the best available optical constant (refractive index) values from the literature, in the 30-65 nm wavelength region [2,[11][12][13]. It should be noted that the availability of reliable optical constants values in this wavelength range is sparse [2]. Fig. 1 shows the calculated "ideal" (zero interfacial roughness/diffusion) peak reflectance of the Al/Sc, Al/Sc/SiC and Mo/Al/Sc periodic multilayer systems at normal-incidence. The 3-material multilayers Al/Sc/SiC and Mo/Al/Sc were chosen because they have the potential for even higher peak reflectance than Al/Sc, with Al/Sc/SiC having the highest performance both above and below the Sc M2,3 edge (43.8 nm). In this study, we focus on wavelengths longer than the Sc M2,3edge. Close to the Sc-edge, where Sc absorption is the lowest, the difference in peak reflectance between Al/Sc, Al/Sc/SiC and Mo/Al/Sc is not so large. The advantage of using 3-material multilayers becomes more significant as the wavelength increases away from the absorption edge, where the material absorption increases as explored in our previous studies [10,14]. All multilayers were prepared at Laboratoire Charles Fabry with a magnetron sputtering system, which can accommodate up to four targets [10] and can be used either in a RF or a DC mode according to the deposited material. The substrates were Si wafer pieces in (100) crystal orientation with surface microroughness in the 0.2 nm range. We used pure Mo, SiC and Sc targets (better than 99.95% purity) and a Si-doped (1.5 wt. %) Al target. During the deposition process, we used a 2 mTorr Ar pressure in the deposition chamber.

The plasma discharge was established with a DC current of 0.1 A for the Sc target, 0.06 A for the Mo target, and a RF power of 200 W and 150 W for the Al and SiC targets, respectively. We protected all multilayers with a SiC top layer thicker than 3 nm. We have previously demonstrated that SiC capping layers are able to assure a good temporal stability of Al-based multilayers [15]. For Al/Sc and Mo/Al/Sc multilayers, we optimized the SiC top layer thickness (shown in Table 1 as dTop) in order to reach the highest reflectance.

All samples were measured by XRR at 8.05 keV (Cu Kα line, λ = 0.154 nm) on a Bruker Discover D8 diffractometer. We fit the XRR data with a genetic algorithm by using the program Leptos®, and optical constant values from the "Henke tables" [16]. These fits allow to determine the multilayer period, layer thickness and average values of layer interface roughness/diffusion. The fitted layer thickness values for the samples discussed in this work are summarized in Table 1. The sensitivity is estimated to be 0.01 nm for the period thickness and close to 0.1 nm for the individual layer thicknesses according to the Bragg peaks positions. Fig. 2 shows the XRR results from 3 representative samples, indicating good layer quality and periodicity for all 3 samples. The quality of each fit is ensured by the good agreement between simulated and experimental intensities of the successive Bragg peaks. The broadening of the higher-order Bragg peaks for the Mo/Al/Sc multilayer may indicate a non-negligible Mo-related interface effect that is still under study. The absence of pronounced peaks in the XRR data from the Al/Sc sample is due to the low optical contrast between Al and Sc at this wavelength. The interfacial roughness/diffusion values fitted from the XRR data were in the range 0.5-0.7 nm.

At-wavelength, absolute reflectance measurements of the samples were performed at the ALS synchrotron beamline 6.3.2 at Lawrence Berkeley National Laboratory. This beamline is designed for high-precision EUV optical metrology including reflectivity measurements [17,18]. The beamline has a spectral resolving power (λ/Δλ) of up to 7000, a wavelength accuracy of 2x10 -3 nm, and a reflectance accuracy of 0.1% (absolute). During the measurements, signal was collected with a Si photodiode detector. All samples were stored in a clean environment and measured 2-4 weeks after deposition. Fig. 3 shows the measured near-normal-incidence reflectance of Al/Sc, Al/Sc/SiC and Mo/Al/Sc samples, optimized to peak near 44.7 nm. The simulated values for each curve are also shown, using the IMD software [19] with optical constants from [11] for Al, [12] for Sc, [11] for Mo and [13] for SiC. The layer model used in IMD to simulate EUV reflectance was based on the model derived from the XRR fits and included the layer thicknesses and the interface roughness/interdiffusion values determined from the XRR measurements (Fig. 2 and Table 1). Some modifications to the XRR models were applied in order to better simulate the EUV data (Fig. 4). Based on earlier work [14], we have determined that a native oxide on top of the SiC capping layer modeled with an average 1.5 nm thick SiO2 layer is a good approximation. Also, we chose to keep a simple surface model without carbon contamination because of the lack of optical constant values for such a compound in the 40 -80 nm wavelength range. However, we added an interlayer between Al and Sc modeled by a "graded interface" function with the IMD software. The presence of such an interlayer of about 1-2 nm in thickness has been confirmed by Transmission Electron Microscopy analysis which will be discussed in an upcoming publication.

As shown in Fig. 3 and Table 2, Al/Sc and Al/Sc/SiC achieve measured peak reflectance (Rexp) close to their simulated peak reflectance value (Rsimu), with Al/Sc/SiC producing Rexp = 57.5% and a spectral bandwidth BWexp of 4.1 nm. Before this work, the highest reported Rexp at 44.7 nm at near-normal incidence was 56.6% (BWexp of 4.8 nm), from Sc/Si with Cr barrier layers [20]. Our results produce higher peak reflectance and narrower bandwidth. The Rexp of Mo/Al/Sc is 48.1% -it is not as close to its simulated reflectance value, which is attributed to lack of accuracy in Mo optical constants values in the 44.7 nm wavelength region, and probable interfacial effects related to the Mo layer that are not taken into account in our present Mo/Al/Sc model. Fig. 5. ALS synchrotron reflectance measurements and simulations (model) [19] in the EUV range for Al/Sc and Al/Sc/SiC multilayer samples at 5° from normal incidence. Fig. 5 shows the measured normal incidence reflectance of Al/Sc (Rexp = 42.4%) and Al/Sc/SiC (Rexp = 46.5%), optimized to peak near 51 nm. The simulated reflectance is also shown, using optical constants from [11][12][13]. The increase of reflectance and bandwidth with the addition of a 3 rd multilayer material is evident (Table 2), as has been discussed in our previous studies [10] and in the theoretical calculations plotted in Fig. 1. To our knowledge, no other experimental multilayer reflectance value has been reported at 51 nm so far. The closest wavelength found in the literature is 49 nm, with Rexp = 46.7% (BWexp = 4.9 nm), achieved with Sc/Si multilayers with Cr barrier layers [20]. The measured reflectance of our Al/Sc and Al/Sc/SiC samples, although it is amongst the highest reported in the literature, is appreciably lower than their simulated reflectance, indicating that the accuracy of available optical constants for Sc, Al and/or SiC is diminishing in the 51 nm region.

Fig. 6 shows the measured normal incidence reflectance of Al/Sc (Rexp = 27.2%) and Mo/Al/Sc (Rexp = 37.4%), as well as the simulated reflectance using optical constants from [11][12][13], optimized to peak near 60 nm. The effect of the 3 rd multilayer material and the lack of accurate optical constants mentioned in the previous paragraph are also evident here. In earlier literature, the following measured values have been reported in the 60 nm wavelength region: Rexp = 38.8% with AlMg/SiC at 55.7 nm (BWexp = 5.6 nm) [4], Rexp = 26.2% with Gd/Si at 62 nm (BWexp = 7.3 nm) [5], Rexp = 26.1% with Mo/Al at 58.4 nm (BWexp = 10 nm) [3], Rexp = 23% with Si/Tb at 60 nm (BWexp = 6.5 nm) [8]. It should be noted that, in addition to very high reflectance, we have achieved the largest reported bandwidth with a periodic multilayer (Mo/Al/Sc) at 57 nm with BWexp = 11.2 nm, as well as the narrowest bandwidth with Al/Sc at 60 nm wavelength with BWexp = 5.2 nm. Therefore, the Al/Sc-based multilayer coatings developed in this work may offer better out-of-band suppression at wavelengths near or longer than 60 nm, compared to the abovementioned multilayers from the literature. This is of particular importance for applications requiring high spectral selectivity, such as solar imaging and high-order harmonic selection. Table 2 summarizes the experimental and simulated peak EUV reflectance values and bandwidths discussed in this manuscript, and Table 3 compares our most significant experimental results with the best values reported in the literature. Sc/Cr/Si [20] AlMg/SiC [4] Si/Tb [8] In conclusion, despite being severely limited by uncertainties in the available optical constant values in the EUV range between 40 and 80 nm, we have reached record reflectance and selectivity performance with new Al/Sc-based multilayer coatings operating in the 40 -65 nm wavelength region. Further studies will be developed to understand in detail the structure and test the evolution of these multilayers through time and under different environmental conditions. These promising results are establishing Al/Sc-based multilayer coatings as leading candidates for future EUV instrumentation. The findings in this work also highlight the need for dedicated, accurate measurements of the refractive index of thin film materials, in order to capture the full potential of scientific discovery in this important wavelength region.

Fig. 2 .

 2 Fig. 2. Grazing incidence X-Ray Reflectometry measured and fitted curves at 8.05 keV for Al/Sc (9055), Al/Sc/SiC (9049) and Mo/Al/Sc (9051) multilayer samples.

Fig. 3 .

 3 Fig. 3. ALS synchrotron reflectance measurements in the EUV range for (a) Al/Sc, Al/Sc/SiC and (b) Mo/Al/Sc multilayer samples at nearnormal angles of incidence (indicated on the graph). The simulated (model) reflectance curves are also shown, using IMD [19].

Fig. 4 .

 4 Fig. 4. Schematic layer models of Al/Sc, Al/Sc/SiC and Mo/Al/Sc multilayers used to fit the reflectance data in the EUV range. N represents the total number of periods in each multilayer.

Fig. 6 .

 6 Fig. 6. ALS synchrotron reflectance measurements and simulations (model) in the EUV range for Al/Sc and Mo/Al/Sc multilayer samples at 5° from normal incidence. The simulations stop at 65 nm due to lack of optical constants values of Al and Mo in the 65-80 nm wavelength region.

Funding.

  Agence Nationale de la Recherche (ANR) (ANR-3113-EQPX-30005), Centre National d'Etudes Spatiales (CNES), Jean d'Alembert fellowship program from Université Paris-Saclay and LLNL's Professional Research and Teaching leave program.

Table 1 . Fitted values of layer thicknesses (dAl, dSc, dSiC(Mo), dTop) and multilayer period thicknesses (DML) for Al/Sc, Al/Sc/SiC and Mo/Al/Sc multilayers deduced from X-Ray Reflectometry at 8.05 keV. The number of periods in each multilayer is shown under "Structure", as a subscript.

 1

	#	Structure	dAl (nm)	dSc (nm)	dSiC(Mo) (nm)	dTop (nm)	DML (nm)
	9055	[Al/Sc]25	14.3	9.7	--	5.23	23.9
	9049 [Al/Sc/SiC]20 10.18 9.71	4.17	--	24.06
	9051 [Mo/Al/Sc]20 7.92 11.40	4.56	5.05 23.87
	9056	[Al/Sc]25	16	13.5	--	5	29.51
	9060 [Al/Sc/SiC]20 11.97 12.11	5.68	--	30.02
	8030	[Al/Sc]10	20.04 19.88	--	3.02 39.92
	9052 [Mo/Al/Sc]7 11.32 16.72	8.13	9.73 36.17

Table 2 . Simulated ( Rsimu, simu) and measured (Rexp, exp) peak EUV reflectance and peak wavelength for Al/Sc, Al/Sc/SiC and Mo/Al/SiC multilayers. The measured reflectance bandwidth (BWexp), defined as the full width at half-maximum is also listed.

 2

	Angle	#	Rsimu (%)	λsimu (nm)	Rexp (%)	λexp (nm)	BWexp (nm)
	θ = 2.5°	9055 9049	58.0 59.5	44.8 44.6	56.0 57.5	44.7 44.7	3.5 4.1
		9051	55.9	45	48.1	45.2	4.6
		9056	48.8	51.5	42.4	51.0	4.1
	θ = 5°	9060	52.4	50.8	46.5	51.0	5.6
		8030	37.2	62.8	27.2	60.6	5.2
		9052	40.7	58.8	37.4	57.3	11.2

Table 3 . Main results and comparison with literature values near normal incidence

 3

		Al/Sc-based multilayer values
	R exp	57.5%	46.5%	37.4%	27.2%
	λ exp	44.7 nm	51 nm	57.3 nm	60.6 nm
	BWexp	4.1 nm	5.6 nm	11.2 nm	5.2 nm
	Structure Al/Sc/SiC Al/Sc/SiC	Mo/Al/Sc	Al/Sc
			Literature values
	R exp	56.6%	46.7%	38.8%	23%
	λ exp	44.7 nm	49 nm	55.7 nm	60 nm
	BWexp	4.8 nm	4.9 nm	5.6 nm	6.5 nm
	Structure	Sc/Cr/Si
	Ref	[20]

Acknowledgments. The authors would like to thank Lan Nhi Nguyen for her contribution in the development of the Matlab code. All multilayer samples have been deposited as part of CeMOX (Couches Minces pour l'Optique X), a platform of LUMAT federation (CNRS FR2764), partially supported by grants from Région Ile-de-France. 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. Disclosures. The authors declare no conflicts of interest.


Cai Chen
email: cai.chen@ulb.be

A Chinese Ethnographer in DR Congo: Reflections on the Field and Fieldwork

Keywords: Chinese, DR Congo, fieldnotes, fieldwork, reflexivity

Why would a Chinese PhD student choose to conduct anthropological research in Congo? How did he secure access to the field? Do Chinese-Congolese couples exist, considering the "selfsegregation" of the Chinese in Africa? How does a Chinese ethnographer

[Part 1] Expatriation in Africa: The Genesis of a Research Project

First woman: What's that Chinese going to do in Congo? [with a ton of suspicion] Second woman: Maybe he wants to visit our beautiful country. [both laughing teasingly] On 14 December 2022, I took a flight from Brussels to Kinshasa to conduct a pilot fieldwork for my doctoral research. The above conversation took place between two Congolese women travelling together, as I stood in line to check in my luggage among a large group of black Africans and a few isolated white Europeans. This conversation was in French, the language I am fluent in, unlike others in Congolese local languages, of which I could barely make out the word Chinois (French term for Chinese). I feigned ignorance, outwardly pretending not to grasp the conversation, yet internally, I couldn't help wondering the underlying meaning behind the discussion.

I doubted that it was unusual for them to see a Chinese in Congo or travelling to Congo in my case, as David van Reybrouck ironically claimed that "[a] generation is growing up in Kinshasa today for whom a European is more exotic than a Chinese". 1 Moreover, I used to work and live in West Africa (i.e., Mali, Burkina Faso, and Niger) during 2016 and 2019. Based on my previous experiences, I knew that there was a large number of Chinese in the African continent, and it should also be the case in the Democratic Republic of Congo (hereafter 'Congo'). However, I kept asking myself, "Why was it still unusual for the Congolese diaspora to see me there-travelling to Congo from Brussels-and what did they think of me as a visibly Chinese among them?" On board, I was the only Chinese, indeed the only Asian-looking passenger on the plane. However, I had not expected to meet many of my compatriots, as I knew that Brussels is not a popular transit hub for passengers from China to Africa, compared to Addis Ababa and Istanbul among others. There may also be the impact of China's then zero-COVID policy until early 2023, but at the time it was much less difficult to leave China than to enter. Unlike previous trips that I had made to Africa as an expatriate working for a Chinese company, this time I went to Congo to conduct a pilot fieldwork for my PhD research project. I was a doctoral student in social anthropology at a Belgian university. As the plane slowly took off, I felt excited to be returning to Africa with a new role and the opportunity to discover another country, but without the fear, worry, and anxiety I had when I travelled abroad for the first time in my life at the age of 21 from Beijing (China) to Bamako (Mali) via Istanbul (Turkey).

Living and working in Africa was probably the most important turning point in my earlier life. Although I did not make a fortune there, after three years I was able to realize my dream of studying in Europe in an unexpected way. However, the influence of the material aspect of this experience was incomparable to that of the social environment in which I lived and the people with whom I interacted. It was in Mali that I began to pay attention to and became interested in the interpersonal relationships between people with different phenotypic traits (such as skin colour) and from different ethnic or racial backgrounds. Because of the classic Chinese pop song "Descendants of the Dragon" (longde chuanren), I always believed that I had "black eyes, black hair, and 'yellow' skin" like other Chinese. However, I was extremely confused when Malian children kept shouting "tubabu" ("white people" in the local language Bambara) at me as I walked through the streets of Bamako. In the same way, I learnt the equivalent term "nassara" in Ouagadougou (Burkina Faso). But I also heard the locals call me "petit Chinois" (little Chinese) instead. I have been asking myself and my local friends ever since: "How could I be mistaken for a white person? I am actually a 'yellow' person, and I look so Chinese, even with slanted eyes."

Studying social sciences in the superdiverse Europe (respectively in France, Romania, Spain and now Belgium) has brought me into a 'new world' and led me to many reflections about myself, my past, and the society. Taking my own "racial learning" 2 as an example, I have always been proud of being of the 'yellow race' (with different meanings in Mandarin) since my childhood because of the common mythical belief of the yellow lineage-we, Han Chinese, are descendants of the Yellow Emperor. Yellow was also the exclusive colour of the emperor in ancient China, representing power and majesty. Thus, in the Chinese context, 'yellow' transcends the simplistic phenotypical notion of skin colour. However, in the European context, 'race' is such a slippery term, and it seems politically incorrect to continue to be proud of my 'race'. 'Yellow' evokes connotations of the "yellow peril", a racist colour metaphor that portrays Asian people as a threat to the West.

[Part 2] Connecting with Chinese in DR Congo: Entering the Field Site I embarked on my PhD studies in October 2022. Despite my prior experience in Africa, Congo was still a new country to me. I questioned whether I could identify "at least 20 heterosexual couples […] and a minimum of 20 heterosexual Chinese/Congolese individuals who had intimate relationships with Congolese/Chinese", as outlined in my research project which I had submitted a few months earlier as part of my fellowship application. I initially intended to include same-sex relationships, but this plan has changed due to the challenges posed by the homophobic environment in both societies. To gain insights into the country and gather information about Chinese-Congolese couples, I mobilised a few strategies remotely, including (1) reaching out to acquaintances (former peers and professors) with living experience in DR Congo or connections matching the searched profile; and (2) using digital platforms (especially WeChat 1 groups and online forum) to identify potential informants.

I reached out online to my peers from my undergraduate French Studies program in China who had worked or were working in Congo as 'translators' 2 for Chinese state-owned enterprises. They all confirmed hearing rumours or gossip about such couples, yet none personally knew any. This did not surprise me, as being a 'translator' for a Chinese company in Africa typically involves restrictions on freedom of movement outside working hours and limited contact with the outside world due to security concerns. I was pleased to learn these rumours confirming the existence of Chinese-Congolese couples, even though I had no direct contact with them. Through these informal conversations, I also gathered some initial data on the perceptions of other Chinese individuals in Congo towards these 'mixed' couples. For instance, my younger schoolmate Tian 3 , who worked as a 'translator' for an infrastructure construction project in Lubumbashi for a year, shared with me: One of our [low-skilled] workers married a local [college] student. She's eight years younger than him and studied computer science. The woman's father seems to be a police officer. The man 'bought' his wife from the latter's family for a bride-price of $1,500. The Chinese man married her because he couldn't afford to marry a Chinese woman in China with the [poor] condition and [low] income of his family. Everyone found this story unbelievable and wondered how anyone [Chinese] could marry a local woman.

I also had a conversation with Professor Zhang, who was my French-Chinese interpretation instructor. Professor Zhang served at the Chinese embassy in the Republic of Zaire (Congo's name from 1971 to 1997) during the 1980s. His stories provided me with insights into the second wave of Chinese immigration to Congo under the regime of Mobutu Sésé Seko. In the late 1970s and early 1980s, thousands of Chinese, employed by state-owned enterprises or institutions such as hospitals and universities, were dispatched to Congo to work on cooperative projects funded by Chinese grants. According to Professor Zhang, almost all Chinese in Congo during that period were short-term contract migrants (3-4 years) who would return to China at the conclusion of the project. Consequently, Chinese-Congolese couples were not prevalent at that time. Nevertheless, with the deterioration of political stability, marked by two Congo civil wars since the 1990s, this influx of investment and Chinese labour came to a standstill.

Fortunately, with the assistance of another professor, I established contact with the first couple I would later meet and interview, and the Chinese woman became my 'gatekeeper'. When I mentioned my plans to work in Africa after graduation in 2016, Professor Wang, also a friend of mine, said, "If you ever go to Congo-Kin[shasa] and need any help, I have a female classmate who married a Congolese, and they are now living in Kinshasa." Thanks to Professor Wang's introduction, I connected with Liyuan via WeChat. Since I prefer introducing myself and my research project face-to-face, I didn't initially disclose my real purpose for going to Congo. Instead, I asked Liyuan for recommendations for my accommodation in Kinshasa.

Additionally, my 'translator' friends invited me to join several Congo-based WeChat discussion groups for the Chinese community. Through these groups, I obtained valuable information for my fieldwork from Belgium. These virtual spaces served as primary sites for my initial online participant observations among different groups of Chinese migrants in Congo, including the group for well-educated 'translators' and the Chinese 'marketplace' group, where individuals share business information and promote their goods or services.

I also searched online for potential Chinese gay informants before my pilot fieldwork. My previous research focused on young Chinese gay migrants in France, drawing on virtual ethnography. Building on this experience, I logged into the most famous Chinese homosocial forum of the 2010s (although much less popular now). This platform allowed users to connect and engage with homoerotic content such as pictures, videos, and novels. Navigating to the Friends Map section, categorized by Chinese cities and provinces, as well as other countries and regions in the world, I found a post updated on June 21, 2022, in the Africa subsection. The post read: "If there are any friends near DRC in Africa, you can connect to chat, eat, travel, and work together!" Connecting with Brother Li via QQ (another Chinese social media platform), I explained my upcoming field trip to Congo. Coincidentally, he was from the same municipality as me, deepening our connections and mutual trust.

Brother Li became another 'gatekeeper' for my fieldwork in Haut Katanga and Lualaba. Upon his suggestion, I booked a room in a Chinese restaurant, which includes three meals a day, for my stay in Kinshasa. He also assisted me in finding accommodation in Lubumbashi. Professor O. Kahola Tabu from the University of Lubumbashi offered me invaluable assistance by providing an official invitation, leading to the successful acquisition of a two-month visa for Congo. Only two months after the official start of my PhD studies, I embarked on my pilot fieldwork scheduled between December 2022 and January 2023 in Kinshasa and Lubumbashi.

Endnotes: [START_REF] Van Reybrouck | Congo: The Epic History of a People, trans. Sam Garrett[END_REF]. A widely used Chinese social media application both in China and among its diasporas. [START_REF] Lan | Diaspora and Class Consciousness Chinese Immigrant Workers in Multiracial Chicago[END_REF]. Their responsibilities extend beyond the basic translation of documents to include tasks such as purchasing, accounting, management, and human resources. However, both these enterprises and the individuals involved commonly use the term "fayu fanyi" (French translator) to designate those recruited primarily for their linguistic abilities. 'Translator' here is a convenient shorthand. On 14 December 2022, my Brussels Airlines flight landed on time at Kinshasa N'djili Airport. Upon arrival, I underwent a check for the Covid vaccination or PCR negative certificate before entering the airport's arrivals hall. While waiting in line for passport control, I noticed an immigration officer winking at me several times. It took me a moment to understand that this officer would 'help' me with the document check-an occurrence common among the Chinese in Africa, as I had confirmed with the owner of the restaurant, where I was going to stay in Kinshasa, the need for their service to 'pick me up' at the airport. However, I initially thought the airport pick-up service meant that someone-the driver-would be waiting for me at the exit with a piece of paper bearing my name. "Oh my God, I will have to pay a lot more for this extra service that I don't need because I speak fluent French and my travel document is in good order", I started getting worried. The immigration officer assisted me through the document check and directed me to another man who would help with finding my luggage and navigating through customs. The latter then escorted me to the car park, where I finally met the driver who would take me to my initial accommodation in Congo. All three of them expressed surprise, saying the same words when they met and spoke with me: "Oh, you speak French!" This thorough 'pick-up' service was arranged by (elder) Sister Lili, the manager and coowner of the restaurant. The restaurant with five guest rooms occupies the top floor of an eightstorey administrative building belonging to the Congolese state. On my first night in Kinshasa, I was without internet connection as there was no WIFI at the restaurant. The next morning, my first task was to go out and buy a SIM card, knowing that I could easily find them on the streets, much like in other African countries I had visited. In fact, just around the corner of the courtyard on the boulevard 30 juin, I quickly found a vendor without the need for much exploration. The small 'shop' was bustling in the morning, and I had to wait patiently. Suddenly, a man shouted at me: "Aie, Chinese! You should go where the expats are!". "Such hospitality in Kinshasa! It's my first day here and I just want to get a SIM card.", I replied. The man stared at me in surprise and then fell silent. The encounter left me feeling shocked, alienated, and othered. Reflecting on previous studies and my own lived experiences, I was reminded of the "self-segregation" of the Chinese in Africa. Nevertheless, I maintained a belief that there had to be various forms of people-to-people interaction between Chinese and Congolese, including intimate relationships.

After purchasing the SIM card, I headed straight back to my room. It was a Thursday, and the building was buzzing with activity. To reach the top floor, I needed to take the lift, but there were already three people-two women and a man-in the lobby awaiting its arrival. The building had three lifts in total, one on the right with the restaurant's name on the door, and two others on the left (only one was operational). Earlier that morning, I had used the lift reserved for the restaurant's customers and staff, which went directly to the top floor. As I entered the lobby, one of the lifts on the left opened its doors, and I rushed over to catch it. Just as I barely entered before the doors closed, one of the women spoke to me, pointing to the opposite side: "It's over there for the Chinese!" Confused, I asked, "Why?" She responded, "It's you Chinese who want it that way, and that lift there is only for Chinese!" I replied, "But this lift is already here, and I can take this one, right? Besides, it's my first day in Kinshasa, I just want to go to the top floor, to the Chinese restaurant." Surprisingly, she smiled and said, "Ah, you know how to express yourself in French. That's good! Not like other Chinese. Welcome to Congo!" When the lift finally reached the top floor and its door opened, I noticed the name of the restaurant on the opposite wall and a large red metal door on the left, marking the boundary of the 'Chinese space' in that Congolese public building. Upon returning to my room, I found myself pondering which spaces belonged to the Chinese or the so-called expatriates in Congo and how everyday interactions unfolded between them and locals, in particular considering the language barriers they often faced. It appeared, however, that the Chinese in Congo maintained good relations with local officials, as evidenced by the privileged airport pick-up service. Nevertheless, a sense of concern crept in, fearing that I might encounter difficulty in finding Chinese-Congolese couples. On my first day, the observed 'ethnic ghetto' and tensions between people inside and outside intensified this worry. Despite this, I remained eager to meet Liyuan and her Congolese husband, the only couple I knew at the time.

Liyuan met and married her Congolese husband, Héritier, in China. They have three children and have been residing in Kinshasa since 2007. Our meeting took place at her restaurant. Similar to her intercultural family, Liyuan aspires to make their 'unique' Chinese restaurant accessible not only to Chinese or other foreigners but also to Congolese, serving as a bridge between different cultures and cuisines. When I disclosed the purpose of my trip, she readily agreed to participate in my research. However, she added a note of caution, saying, "But our couplehood may be different from others and can't be representative." In fact, both Liyuan and Héritier are fluent in French and Chinese, holding at least a master's degree with academic training in social sciences. This background made it relatively easy for them to comprehend the nature of anthropological research and understand what researchers do or do not do with recorded interviews. For other Chinese and Congolese individuals that I encountered, I had to navigate the best approach to persuade them on one hand and continually negotiate my own identity and positionality in the field on the other.

"Visiting Kin Oasis, 'la cité chinoise'" by the author on 20 December 2022 [Part 4] A "Developed" Chinese: Negotiating Multi-faceted Field Relations

My initial fieldwork experience in Kinshasa proved to be extremely challenging. Despite Liyuan's assistance in reaching out to a Chinese man who had married a Congolese woman, my request for a meeting was declined. However, he agreed to respond to some questions through messages on WeChat. Additionally, not knowing anyone else in the city and grappling with the exorbitant cost of living in Kinshasa (where, for instance, a cappuccino cost me $7), posed significant challenges. This financial strain was particularly burdensome for an ethnographer whose fieldwork was not funded. Consequently, just ten days later, I made the decision to relocate to Lubumbashi, where I found a more affordable accommodation with the help of Brother Li.

On the eve of Christmas 2022, my Congo Airways flight, initially rescheduled and then delayed for over eight hours, finally took off from N'djili Airport at 1 am and landed in Lubumbashi at 4 am the next day. While domestic flights usually do not involve passport control upon arrival, I, as the only visibly Chinese passenger, was stopped by immigration. This occurrence did not surprise me, given the prior warnings from Liyuan, Brother Li, and my 'translator' friends. They had all reminded me to carry some change and cautioned about the targeted extortion of Chinese individuals by immigration officers at Lubumbashi airport, irrespective of the orderliness of their travel documents.

With a quick "Morning!" I handed over my passport and remained silent to see what was going to happen. The officer checked my document carefully, then looked at me, saying "makuta" (money in Kiswahili) with a "pay me" gesture. I was taken aback by the directness, a behaviour I hadn't encountered in other African countries. In response, I pulled out my invitation letter, pretending not to understand the word and the gesture. In French, I said, "Here you are, my invitation letter. Is this what you want?" Realizing that I was an invited researcher who spoke fluent French, she appeared surprised but persisted in attempting to solicit money, this time wishing me "Happy New Year!" Feeling increasingly unhappy and impatient, especially with an exhausted body at 4:30 am after the extensive delay of my flight, I replied, "No, no, today we say Merry Christmas! If you don't have any more questions, may I leave now?" Unpleasantly, the officer returned my passport and remarked, "You aren't like other Chinese!" Brother Li picked me up at the airport with his driver and took me to what he introduced as "a semi-open hotel of one of his friends, Sister Liu". When we arrived, it was already 5:30 am, and a power cut was in progress. Exhausted, I went straight to sleep. I'm not sure how many hours later, I was startled awake by the sudden opening and closing of the door and an African woman screaming, "Ah, there is someone in the room!" However, I simply rolled over and went back to sleep. Finally waking up around 11 am, I showered before venturing outside my room into the courtyard. I spotted a Congolese woman washing clothes near a door adorned with Spring Festival couplets-a typical 'Chinese' door. As she noticed me approaching, she greeted me in French. Jokingly, I replied, "Good morning, was it you who opened my door and interrupted my dream?" She burst into laughter and surprisingly responded, "Oh, I'm sorry, I didn't know anyone was there. Aie, how come you speak French so well? Are you French?" "No, I'm Chinese like others here, and this is a place for the Chinese, isn't it?", I replied. She explained, "Because you could speak French, and the other Chinese here only speak broken Chinese-style Kiswahili."

In the following days, all the Congolese workers in the courtyard-including two housekeepers, a security guard, and several drivers-shared with each other and told Congolese visitors that "this Chinese is different; he speaks French, greets, and talks to the Congolese; he studies in Brussels!" On separate occasions, my Congolese interlocutors commended me as a "developed" Chinese contrasting me with others they perceived as "poorly educated, badly dressed, speaking neither French nor English, and always ignoring people when they greet them". However, this perceived 'difference' elicited negative reactions from a group of Chinese traders and entrepreneurs also residing there. During our initial group meal, I revealed that I was a PhD student in Belgium on a scholarship (albeit a one-year one) and that I was interested in the lives of Chinese-Congolese couples. Regrettably, the fact that I was "funded by the Belgian government" was misinterpreted, leading to the assumption that I was "working for foreign forces" and "reporting on the indecent sexual relationships of the Chinese in Belgium's former colony".

As a PhD student residing in Europe, my social and cultural position accentuated the social distance with my Chinese interlocutors, many of whom come from rural or working-class backgrounds. They often referred to me as "daxue sheng" (college student), rather than using my name or "xiao chen" (Chen junior), a term reserved for the more privileged individuals with a university education in China. Despite this, coming from rural milieu myself, I was familiar with their sociability and language. To bridge the social gap, I made concerted efforts such as sharing meals, adjusting my language register, and even altering my hairstyle (from a trendy, slightly long haircut to a finger length) to foster a more authentic connection. Moreover, I extended my assistance with translation or IT needs. In contrast, the dynamics with those working as 'translators' in large Chinese companies were different, given that they all received higher education like me at the time and speak decent French.

"Chinese New Year Gathering" by the author on 21 January 2023

  [3]. All names in this series of blog posts are pseudonyms to preserve the privacy and anonymity of informants. "Arrived in Kinshasa. Santa too!" by the author on 14 December 2022 [Part 3] Segregated Interactions: Do Chinese-Congolese Couples Exist? "Dear passengers, it's 6:30 pm in Kinshasa [….]." [flight announcement]

Scholars in the North tend to conceptualise 'race' from the experiences of predominantly white societies. Why was I happy to be 'yellow' in China but not in Europe? Why could I be considered as part of the Whites in Africa? How do Africans perceive the Chinese and their 'differences' from 'real' Whites? It was with the great curiosity about the ideologies behind all these white-black-yellow encounters, that I decided to dedicate my self-initiated doctoral research to Sino-African ethnoracial dynamics in postcolonial Africa. Since I am studying in Belgium, which has historical links with Congo, and my supervisor specializes in conjugal mixedness, I chose to focus on a specific case study of Sino-Congolese intimate relationships, using the family as a primary site for exploring people-to-people interactions with China's growing presence in Congo.