Kewin Desjardins
email: kewin.desjardins@synchrotron-soleil.fr

Kadda Medjoubi

Pascal Mercère

Paulo Da Silva

Horia Popescu

Roland Gaudemer

M Sacchi

Adrien Besson

Rachid Belkhou

Stefan Stanescu

Sufal Swaraj

Stéphanie Pautard

Arafat Noureddine

Fabienne Orsini

Nicolas Jaouen

Back Side Illuminated scientific CMOS detector for soft X-ray Resonant Scattering and Ptychography

Keywords: X-ray detectors, sCMOS camera, 2D Soft

Huge progress have been done with the 3 rd generation storage ring, and more recently the ultimate storage ring under development suggest an unprecedent increase of x-ray brightness.

Unfortunately, as far as the detectors are concerned, progress has not been as fast and even more so in the range of soft x-rays. In particular for 2D detector the most commonly used detector are based on old CCD technology and the recent development of CMOS detector will be certainly crucial for 2D detector in the soft x-rays. With this goal we explore the possibilities and the the performance of a camera equipped with new mass-marketed scientific Complementary Metal Oxide Semiconductor Back Side Illuminated (sCMOS-BSI) integrated in vacuum environment for soft X-ray experiment at synchrotron. The 4 Mpix sensor reaches a frame rate up to 48 fps while suiting the necessary performances needed for X-ray experiments, in term of linearity (98 %), homogeneity (PRNU <1%) charge capacity (up to 80 ke-), readout noise (down to 2 e-rms) and adequate dark current (3 e-/s/px).

The sensor performances tests in the X-ray range have been performed at the SOLEIL METROLOGIE beamline. The Quantum Efficiency, the spatial resolution (24 lp/mm), the energy resolution (< 100 eV) and the radiation damage versus the X-ray dose (< 200 Gy) have been evaluated in the energy range from 40 eV to 2000 eV. In order to illustrate the capabilities of this new sCMOS-BSI sensor, several experiments have been performed at three soft x-ray beamline of the SOLEIL synchrotron: diffraction pattern from a pinhole at 186 eV, scattering experiment from nanostructured Co/Cu multilayer at 700 eV and Ptychoraphy imaging in transmission at 706 eV.

Introduction

In the last generation of synchrotron sources, the beamlines flux and beam coherence have been largely improved allowing to develop a large panel of sophisticated synchrotron radiation experiments. Nowadays, a lot of direct highly efficient detectors have been developed and are commercialized for hard X-ray application (Förster et al., 2019). They have demonstrated their high frame rates, high charge capacity, high efficiency and required high spatial resolution. However, a wide gap exists in the soft to tender X-ray domain (10 eV to 3 keV) where the experiments are not able to fully benefit from the performances offered by modern facilities. The detectors usually installed on the soft x-ray end-station are widely based on back-side illuminated CCD sensor such as the commercial cameras from Princeton© PI-MTE (https://www.princetoninstruments.com), GreatEye® GE-VAC (https://www.greateyes.de) or others equipped with cooled CCD-BSI. This kind of detector is compact enough, vacuum compatible (10 -9 mbar), presents performances largely demonstrated on laser based x-ray sources (Lambert et al, 2015), XFEL facilities (Pedersoli et al., 2011) or synchrotron beamlines (Chauleau et al, 2018). But these sensors suffers from severe readout speed limitation. Indeed, in order to limit the readout noise and so to guarantee a high signal to noise ratio allowing single photon sensitivity, the frame rate has to be limited to less than 1 frame per second. As an example, on SEXTANTS (Sacchi et al., 2013), the synchrotron SOLEIL's soft x-ray scattering beamline, they report a deadtime of 97.5%, due to the readout time in full-chip mode (typically 4 s over 0.1 s of X-ray collection), during Xray Fourier Transform Holography (FTH) experiments on the COMET end-station (Popescu et al, 2018). Nevertheless, some solutions have been implemented to tackle this problem: (i)

The fast-CCD (Denes et al., 2009) performs low readout noise with high frame rate (60 fps for 960 × 1920 pixels) by increasing the readout ports (ii) Other efforts have been done on Hybrid Pixel detectors (Jungmann-Smith et al., 2016, Wernecke et al. 2013) by decreasing the electronic noise level and optimizing the sensor entrance window allowing to profit of very high frame rate of new ASIC. (iii) Spectroscopic detector dedicated as pnCCD [START_REF] Strüder | High Speed Imaging and Spectroscopy with Low Energy X-Rays[END_REF]] could also be cited. (iv) the development of CMOS based sensor such Silicon-On-Insulator (SOI) technology (Arai et al, 2010) or DEPFET sensors [START_REF] Porro | [END_REF] for very high frame rate soft X-ray FEL applications, the CMOS PERCIVAL detector (Wunderer et al., 2014) again under development by a consortium of synchrotrons or also some developments teams effort as the Pipper MAPS technologies recently published (El Bitar 2019).

Recently, a new generation of large Back-Side Illuminated scientific CMOS sensor (sCMOS-BSI) has been developed [START_REF] Ma | Image Sensors and Imaging Systems[END_REF] and supplied by GPIXEL® (https://gpixel.com).

Especially designed in order to optimize the efficiency delivered in the visible light range (> 95% @ 550°nm), and keeping the good performances of the first generation of sCMOS (low readout noise, large full well capacity and high frame rate), this new cost efficient 4 Mpx sensor appears to be well suited for the soft x-ray applications, and has been already characterized for several use as soft x-ray resonant scattering [START_REF] Desjardins | AIP Conference Proceedings[END_REF] or Xray imaging spectroscopy [START_REF] Wang | [END_REF]. In this paper, we describe the integration of this sCMOS-BSI into an in-house vacuum compatible camera and its characterization. The performances have been measured on the METROLOGIE beamline (Idir et al, 2006) and are reported in the following sections. In particular, we have characterized the sCMOS-BSI camera dynamics (dark noise, readout noise, spatial uniformity, linearity and overall gain), the soft X-ray Quantum Efficiency in the energy range between 30 to 2000 eV, as well as the spatial, energy resolution and the radiation tolerance. We also report on different tests using this sCMOS-BSI camera: coherent diffraction pattern from a 5 µm pinhole at 186 eV at the METROLOGIE beamline, a soft X-ray Resonant Scattering experiment from nanostructure Co/Cu multilayer at 700 eV on SEXTANTS beamline and several soft X-ray ptychography reconstruction also at 706 eV on HERMES beamline (Belkhou et al, 2015).

Materiel

sCMOS GSENSE400BSI characteristics (Signal to Noise ratio in X-ray domain)

The integrated and characterized sensor is the GSENSE400BSI (figure 1a), a scientific CMOS Back Side Illuminated from GPIXEL® (https://gpixel.com). This sCMOS-BSI sensor Following these specifications, the Signal to Noise Ratio (SNR) of the GSENSE400BSI, defined by equation 1 (Janesick, J. R., 2007, (with equation 3.11 revised as discussed in stackexchange web forum)], has been calculated the different modes and compared to the other similar sensors in the X-ray domain (Figure 2). where S is the signal in (e-) equal to 𝑄𝐸 × 𝑁 × E ⁄ 3.65 with QE is the Quantum Efficiency depending of the beam energy E, N the number of photon, 3.65 eV is the electron-hole pair creation energy in silicon, F the Fano factor (~0.12 for silicon),  readout &  dark the temporal noises & DSNU and PRNU the spatial noises as given in table 1.

The figure 2 shows an example of the SNR for a X-ray beam of 500 eV and its comparison of each sensor. The spatial noise is excluded here (PRNU = 0 and DSNU = 0). In this figure

we also represent the photon detection limit (at 500 eV) corresponding to the full well capacity (in photon/mm²) taking into account the pixel area (see table 2 for all details). Now considering the HDR mode (dark noise of 3 e-/s/px, readout noise of 2 e-rms and FWC = 30 ke-) and the theoretical QE (as describe in the next paragraph, see §3.2), the limit of detection (SNR = 1) and the pixel saturation of the GSENSE400BSI sensor can be evaluated and the dynamic range (DR=FWC/limit) can be estimated in function of the beam energy (figure 3)

.

Figure 3 : Theoretical dynamic range of the GSENSE400BSI (HDR mode) considering the X-ray photon limits of detection (SNR=1) and the X-ray saturation limit (diamond red line).

X-ray camera design and software integration

In order to easily evaluate and integrate the sCMOS GENSE400BSI sensor on the soft Xray beamlines of SOLEIL synchrotron, we have adapted a TUCSEN® Dhyana95 camera, which has been totally disassembled and reassembled into a home-made mechanics ( Figure 4), to make it compatible as much as possible in vacuum environment (10 -6 mbar).

It can be noted that the components vacuum compatibility (cables, cooling, PCB board, …)

have not been the subject of in-depth studies for this first prototype assembly, whereas it is a crucial technical point which must be taken into account for the future detector that will be permanently installed on SOLEIL beamlines. Indeed, as seen during our series of tests, the cooled sensor could be quickly contaminated which could degrade its efficiency (Deiries et al, 2016). Then, following components are located in vacuum: sensor, sensor board, DAQ board (FPGA, power supply, data transfer, …) and a water-cooling circuit (> 12°C) has been made to maintain an optimal temperature of both the sensor (-20°C with 2 stages of Peltier cooler) and the electronic components. As typically done for such soft X-ray experiment, the To transfer and to record the images, this camera is connected via a USB3 interface through a dedicated UHV USB3 feedthrough to a classical Windows 64bit computer equipped with a Tango LIMA device (https://www.tango-controls.org) based on TUCAM API from TUCSEN®. Then, this camera keeps the same characteristics as the initial camera in term of SNR, readout speed (24Hz full frame), cooling and synchronization capacities.

Characterization tests results and discussion

X-ray experimental setup

As it has been already presented in the first DhyanaX prototype setup [START_REF] Desjardins | AIP Conference Proceedings[END_REF], this X-ray camera has been mounted in the reflectometer of the XUV branch of the METROLOGIE beamline at SOLEIL synchrotron. The beamline allows to select a photon beam in the soft X-ray range (30 eV -2000 eV) using several combination of gratings and mirrors to optimize the beamline transmission and energy resolution and a series of thin filters llowing to reduce the harmonics contamination in each configuration. The beam size could also be easily adjusted and a calibrated photodiodes (IRD® AXUV100, https://optodiode.com) can be used measuring, with less than 10% of uncertainty, the incident X-ray beam flux at each energy. With this configuration, the QE of two versions of GSENSE400BSI has been measured ( §3.2) over the full soft X-ray range. In addition, to characterize fully the detector, we have measured the spatial resolution at 1500 eV ( §3.3), the energy resolution ( §3.3) as well the sensor radiation hardness ( §3.4).

GSENSE400BSI soft X-ray Efficiency

Two versions of sCMOS GSENSE400BSI versions have been evaluated: the 𝑄𝐸 𝑚𝑜𝑑𝑒𝑙 (𝐸) = 𝑒 -𝑧 𝑆𝑖𝑂 ×𝜇 𝑆𝑖𝑂 (𝐸) × 𝑒 -𝑧 𝑆𝑖𝑁 ×𝜇 𝑆𝑖𝑂 (𝐸) × 𝑒 -𝑧 𝑛𝑒𝑢𝑡𝑟𝑎𝑙 ×𝜇 𝑆𝑖 (𝐸)

× (1 -𝑒 -𝑒 -𝑧 𝑑𝑒𝑝𝑙𝑒𝑡𝑒𝑑 ×𝜇 𝑆𝑖𝑂 (𝐸) )

(

where the z SiO and z SiN are the thickness material of the AR coating, 𝑧 𝑛𝑒𝑢𝑡𝑟𝑎𝑙 and z depleted are the thickness of the non-sensitive and sensitive silicon layer respectively. μSiO, μSiN and μSi are the attenuation coefficient for these different elements. To fit with the QE measurement results, the different parameters of the model (Equation 2)

have been adjusted. For the GSENSE400BSI-TVISB, the Silicon oxide thickness has been increased to 30 nm certainly due to the contamination and oxidation at its surface, the dead layer has been adjusted to 60 nm and the Si-Epi to 11 µm. Whereas the GSNESE400BSI-GP model fit correctly with the sensor parameters with a dead layer of 45 nm and a Si-Epi around 4 µm (and no-AR coating layer). Both measurements and models are reported in the figure 5.

Our result shows that the QE of the classical GSENSE400BSI is highly sufficient for a wide range of high flux synchrotron applications. In order to illustrate its low energy efficiency, a diffracted pattern image form a 5 µm diameter pinhole has been performed at an energy beam of 186 eV with the sCMOS GSENSE400BSI-TVSIB and the result is showed in figure 6. With twice the efficiency around 300 eV, the no-ARc sensor (GP version) could be a better choice for the so-called water window's region that include C, N and O K edge, but it should be noted that it will be at the price of using the thin Si-Epi layer sensor more sensible to radiation damage, as it will be shown in paragraph 3.4.

GSENSE400BSI spatial & energy resolution

The sCMOS GSENSEBSI400-TVISB spatial resolution has been checked using the ISO A 10% modulation transfer contrast is reached around 24 lp/mm, corresponding to a halfpitch resolution of 21 μm, in good agreement with the sensor pixel size (11 µm²). This resolution could be degraded for lower X-ray energy due to the lateral charge diffusion within the thick Epi-Silicon (~10 µm) and the neutral layer, but it was not the main object of our in this work. However, this effect will be discussed (figure 8b) in the next paragraph where we described the sensor energy resolution.

In order to characterize the energy resolution of the detector, a GSENSE400BSI-GP sensor has been exposed by a small part (out of focus) monochromatic X-ray beam of METROLOGIE beamline with very low flux (no more than 10 6 ph/s) in order to collect images of single isolated events. For each energy, a large series of cropped images (100 × 2048 pixels) has been acquired with the HDR mode and for a short exposure (20 µs, ~ 300 fps). This type of measurement, widely used in X-ray Spectroscopy Imaging and X-ray Spectroscopy astronomy (Lung et al., 1984) allows to work similarly as a counting detector with few photons per pixel per second. Then, for every dark-corrected image recorded, the single and isolated photon events (highlighted by blue circles in figure 8a) have been extracted and their amplitude cumulated to obtain a spectrum. This algorithm was carried out using in a MATLAB script isolated a pixel if its value is 95% greater than the sum of the 8 neighboring pixels. The result is displayed in figure 8b in which we superposed the normalized spectrums for energy from 100 eV to 1500 eV. In order to convert the spectra in eV the overall gain of 0.67 ADU/eV, calculated from this measurement, has been applied. The energy resolution is estimated by the full width at half maximum (FWHM) of the energy peaks [START_REF] Janesick | Scientific Charge-Coupled Devices[END_REF] and given in the figure 9 where the theoretical limitation given by the equation 3 below is also added for comparison:

𝐹𝑊𝐻𝑀 (𝑒𝑉) = 2.35 × 3.65 × √𝐹 × 𝐸/3.65 + 𝜎 𝑠𝐶𝑀𝑂𝑆 2 (3)
where F is the Fano factor (~0.1 for silicon), E the photon energy, 3.65 eV is the electronhole pair creation energy for X-ray absorption in silicon and 𝜎 𝑠𝐶𝑀𝑂𝑆 2 is the quadratic sum of noises of the sCMOS camera. We find an energy resolution that is slightly higher of 20 eV than the theoretical one, due to an excess noise in this camera prototype (with readout noise > 2 e-rms and higher offset and gain fixed-pattern noise). Furthermore, the sensor cooling was set to 16°C (only water cooling was operated and the Peltier stage was deactivated). In figure 9 is superposed a FWHM model fitting the datas with 𝜎 𝑠𝐶𝑀𝑂𝑆 2 of 6 e-rms. Also, the noise floor, represented in figure 8 by the tail on the energy peaks is reached for energy below 200 eV. As stated above, the effect is attributed to the spread charge created close to the surface into the thick Si and particularly in the non-depleted region.

GSENSE400BSI Radiation hardness

Considering the typical requirement for an X-ray detector needed at SOLEIL with energy of photon between 40 to 2000 eV and a monochromatic flux largely exceeded 10 12 ph/s/0.01%BW, radiation hardness has been evaluated on both sensors on the METROLOGIE beamline for different energies and X-ray fluences. The GSENSEBSI400-TVISB sensor has been locally exposed to a direct, collimated (< 200 × 200 µm²) and monochromatic X-ray beam of 160 eV, 560 eV, 1000 eV and 1600 eV and the GSENSE400BSI-GP only by a lower energy X-ray beam of 80 eV. For each energy, the delivered X dose has been increased by increasing the time of irradiation from few seconds to several hours (figure 10.a). The absorbed dose (D), i.e. the amount of energy absorbed per unit of mass of a given material (Ravotti, 2018), is basically calculated by using the following equation :

𝐷(𝑧) = μ 𝜌 × Φ/𝐴 × 𝑡 × 𝐸 (4)
with Φ is the considered X-ray photon flux, A is the surface exposed by the monochromatic X-ray beam with energy E, / the mass energy absorption coefficient (of Si) and t the exposure time.

The table 3 gives the absorbed dose evaluated on both the surface and the electronic layers of the sensor for different incident and different energies. We select characteristic energies over the wide soft x-ray energy range that allows to evaluate the radiation damage at the different layers on the sensor's thickness. Indeed, as shown in figure 11, the low x-ray photons are largely absorbed on the thin thickness of Epi-Si when the X-ray photons above 1000 eV goes through the Epi-Si and reach the electronic layer (figure 1b). Also, the photon beam at 80 eV could penetrate the thinner Epi-Si of the GSENSE400BSI-GP (4 µm) with a transmission about 0.1 %, against below 10 -5 % for the GSENSE400SI-TVISB (10 µm). As it can be found elsewhere (Clarke, 1994, Hancock et al., 1997), one of the radiation effect on the sensor manifests as an increased leakage current (pixel offset level), consequently we have compared the dark image after irradiations to the original one for the same exposure time, as showed in figure 10b. The mechanisms of these effects are complex and are not studied here but the results extracted from the figure 10.b are discussed. As described above, the low X-ray energies irradiation series (160 eV and 560 eV) with an absorbed dose up to 1

MGy into the surface layers of the GSENSE400TVSIB has no impact on the pixels offset level while the high energies X-ray irradiation series (1000 eV and 1600 eV) showed a significant increase of electronic offset level (for a lower dose) on the area irradiated (white spots on the right side of the dark image in figure 10.b). For these energies, the photons not absorbed by Epi-Si could penetrate deeply in the oxide and electronic layers of the CMOS sensor giving rise to a relatively important and persistent damage on the pixel (offset dark level remains high after few weeks at room temperature). It was similarly on the GSNES400BSI-GP with the 80 eV beam impact.

Then, the pixels dark level evolution (I dark after irration. -I dark0 ) has been compared to the dose on electronic layer for all irradiation series to extract an estimation of the limit of dose acceptable (figure12 by the sensor. The dark level increase, due to the dose, could be fitted with an empirical formula as:

𝐼 𝑑𝑎𝑟𝑘 -𝐼 𝑑𝑎𝑟𝑘0 = { 0, 𝐷 < 𝐷 𝑡ℎ 𝐾 × 𝑙𝑜𝑔 10 ( 𝐷 𝐷 𝑡ℎ
) , 𝐷 ≥ 𝐷 𝑡ℎ (5) where D is the dose on the electronic layer (equation 4), D th is the dose threshold and K a proportionality factor given the offset pixel evolution per (ADU/decade).

The fitted curve, in figure 12.a, for the two high energies measurement showed a limitation around D th = 200 Gy (20 kRad) and K = 125 ADU/dec. This dose threshold seems to be confirmed on the series of measurement performed on the thinner GSENSE400BSI-GP but with a higher dark evolution proportionality factor around 4000 ADU/dec, in figure 12.b.

If the dose limit seems not very high, it's very difficult to compare with other similar devices as this measurement is not easy to do or easy to exploit and so rarely published, nevertheless,

Experiments performed on Soft X-ray beamlines using the sCMOS GSENSE400BSI

@ 1000 eV, Limit = 2.3 10 11 ph/s/mm² (or 2.6 10 6 ph/s/pixel)

Soft X-ray Resonant Magnetic Scattering

The GSENSE400BSI camera has been firstly installed on the RESOXS (Jaouen et al, 2004) end-station of the SEXTANTS beamline at SOLEIL. In order to illustrate the capabilities of the detector, a soft X-ray (400 eV to 2000 eV) Resonant Magnetic Scattering (XRMS) (Chauleau et al, 2018) experiment on magnetic samples exposed to the soft X-ray beam was performed.

As mentioned above in this paper, high resolution, low noise and high charge collection capacity are strongly required for this type of acquisition and are achieved up to now with a direct CCD detection. The beamline routinely uses with users the Back-Illuminated CCD PIMTE from Princeton Instrumentation (4Mpixels e2V CCD 42-40, pixel size 13.5 µm, QE>90% @700 eV, FWC=100 ke-, electronic noise of 10 e-rms with 0.22 Hz). In order to experimentally compare the performances of the sCMOS camera with this CCD camera, soft X-ray scattering pattern from known a lithography prepared assembly of Xm*Xm square Co/Cu multilayer sample have been acquired. Unfortunately, the GSENSE400BSI camera has not been installed at the exactly same position compared to the CCD (figure 15). While the sCMOS was placed 1 m downstream from the sample, the CCD was placed closer, at distance of 25 cm, which, considering the sensor area, limits the angular aperture from 1.5° (sCMOS) to 6.3° (CCD). Despite these nooptimized test conditions, two similar acquisitions have been performed on the both sensor and following these characteristics: exposure time of 200 ms, accumulation of 100 images, HDR mode for GSENSE400BSI and ADC 1 MHz mode for the CCD. The resulting images represented in angle (𝜃) are given in figure 16 for the same scale. The beam was focalized into the CCD position and its divergence is few mrad, these explain why the diffracted spots are much wider and more separated for the sCMOS than for the CCD image. To compare these images, the spatial dimensions are transposing to the scattering vector q (𝑞 = 4𝜋 sin(𝜃) /𝜆, where 𝜃 is the angle between the direct beam and the detector axes and 𝜆 is the wavelength of the beam). The superposition of the one direction integrated diffraction peaks is presented in figure 17. It shows the similar distribution with a nice superposition of the peaks position but with a scattered intensity slightly different,

particularly close to the central peak (order 0). As the beam focalization, the aperture, the pixel size and the QE are not the same, the magnitude scattered intensity are not easy to compare directly. We plan to have a series of future experiments in the near future to obtain more experimental results about efficiency and SNR to compare to this well-known CCD BSI.

As first conclusion, we can conclude that similar image from sCMOS could be obtained for a total acquisition time of 20 s compared to the 8 min needed to record 100 images with the actual CCD, meaning a total time saved up to a factor 24 (limited by the exposure time). This gain will change drastically the time of acquisition of an image using Fourier Transform Holography that is typically of 1 h nowadays to few minutes in the near future. It will be really an important gain for imaging experiment when we have to scan an external parameter (magnetic field, electric field, temperature) or even more important for time-resolved experiments (Bukin et al, 2016). The capability to acquire image with such frame rate will also dramatically expand the time window available at SEXTANTS for soft resonant magnetic X-ray Photo Correlation Spectroscopy (XPCS) only obtain recently at NSLS2 using a fast CCD (Chen et al, 2019). Lastly, it will be also a real gain for soft X-ray resonant ptychography in reflection geometry that is nowadays limited only by the coherent flux and mechanical instabilities (Popescu et al, 2019). It is important also be noted that all these approaches will fully benefit, in terms of coherent flux and smaller beam size (using standard optics), from the new storage ring under development.

Soft X-ray ptychography reconstruction

In HERMES, a soft X-ray beamline dedicated for X-ray microscopy and equipped for Scanning Transmission X-ray Microscopy (STXM) at SOLEIL, a new dedicated set up for soft X-ray ptychography has been recently implemented to improve the spatial resolution capability of the beamline by replacing the 1D detector (scintillator photomultiplier tube, PMT) by the sCMOS GSENSE400BSI camera. So, the classical 2D sample scanning experiment consisting to measure the transmitted intensity is now consisting to measure the transmitted diffraction pattern recorded with the sCMOS camera.

In order to illustrate the capability of this new set-up, ptychography experiment was performed on a siemens star at 700 eV. During the experiment, diffraction patterns were collected by illuminating the sample at ? × ? positions on a rectangular grid with a grid spacing of ? nm. Thanks to the fast readout of the camera and its sensitivity, the experiment was performed in less than 10 min.

The figure 18 To confirm these nice performances obtained on easy construct able structure, several measured have been performed, the result obtained from magnetotatic bacteria (magnetosomes) is reported here. The images have been acquired using X-ray at 700 eV, the scan step is 20 nm. A region-of-interest (1024 px by 1024 px) has been selected on the sCMOS which allows to increase the frame rate up to 44 Hz (HRD mode) and so reduced the total acquisition to 10 mn. Again we presented, in the Figure 19

Summary and perspectives

A new camera based on the first world large production Back Side Illuminated scientific CMOS sensor GSENSE400BSI was developed and evaluated for soft X-ray application on several beamlines at SOLEIL synchrotron. The quantum efficiency is found to be sufficient for large field of application in the soft X-ray domain (QE > 50% for E > 400 eV) and the new no-ARC (antireflective layer) has already demonstrated a high quantum efficiency of > 90 % in the lower energy range and more importantly over the water window region. The readout noise (< 2 e-rms) and the full well capacity provide a good X-ray dynamical range and an interesting single photon detection capability without decrease of the readout speed performance. This sensor has a frame rate up to 48 Hz (on the standard mode) that allows to dramatically reducing the acquisition time for imaging application compared to the classical camera commonly used. The new version of acquisition board allows to upgrade the performance with a lower spatial noise with DSNU < 0.2e-and a PRNU of 0.3%. The soft Xray spatial and energy resolution has been confirmed with a limitation for low energy due to the low dead thickness and the thin Si-Epi layers.

As for similar synchrotron direct X-ray detector, the radiation hardness is a big challenge to keep good performances in the time with the high density of flux considered. The limit of dose of 200 Gy (20 kRad) and the corresponding fluence has been measured that will allow scientists to adapt the X-ray experimental conditions set-up in order to avoid damage of the sensor. A compact, cooled vacuum compatible camera prototype has been developed to be easily installed in the experimental end-stations of SEXTANTS and HERMES beamlines at SOLEIL. A first soft X-ray Resonant Scattering (REXS) acquisition from nanostructured multilayer sample has been performed on SEXTANTS beamline showing a good dynamical range with a total time saver of a factor 24 compare to their usual detector readout. A fully functional soft X-ray ptychography set-up based on this sCMOS camera has been used on the STXM end station at the HERMES beamline. Its performances and frame rate have been used to perform several reconstructions with spatial resolution down to ~6 nm.

Lastly, a new GSENSE400BSI sensor version combining a thicker Si-Epi with a high efficient process has been very recently tested by Harada team (Harada et al, 2020). It assures a very good efficiency (> 80 %) over a very large soft X-ray range and it will soon be massproduced by GPIXEL®. This new sensor will be very soon implemented on the second sCMOS HERMES camera to increase the set-up performances and particularly for the experiment at the so-called water window's carbon K-edge. Also, one other camera would be installed soon in the SEXTANTS COMET end-station in order to optimize the performance of acquisition time for magnetic imaging using Fourier Transform Holography.

Based on this first results and the scientist's community interest for this cost-efficient solution, a Canadian company specialist on high speed camera solution, Axis photonique [https://www.axis-photon.com] has started to produce this new soft X-ray sCMOS detector based on the SOLEIL prototype. Furthermore, others potential domains could be explored:

another synchrotron beamline application, as tender X-ray SAXS (> 1.2 keV) in SIRIUS beamline at SOLEIL, or for lower soft X-ray photon source based on femtosecond laser or for soft X-ray free electron laser (XFEL). In particular a test of our camera is already planned to take place in the next few months at FERMI.

To conclude, the first Back Illuminated sCMOS implementation reported in this paper could be considered as the beginning of a long series of new detector based on this technology.

is a 4

 4 PHOTOMETRICS®Prime95 (www.photometrics.com), the ANDOR® Sona (https://andor.oxinst.com) or others. These cameras take advantage of the sensor characteristic in term of readout noise (< 2 e-rms), relatively large Full Well Capacity (FWC up to 80 ke-), good performances in term of spatial noise (DSNU < 5 e-and PRNU < 1 %)

Figure 1 :

 1 Figure 1 : sCMOS GSENSE400BSI sensor (a) Sensor picture (Gpixel, http://gpixel.com) and (b) schematic cross section of the sensor

Figure 2 :

 2 Figure 2 : Signal to Noise Ratio estimation for GSENSE400BSI (Low Gain and High Gain), PIMTE CCDBSI (with ADC speed of 1MHz), PERCIVAL (Low Gain and High Gain) at 500 eV. The SNR of perfect detector is calculated for QE=1, noise = 0 eavec pixel size of 10 µm. The SNR of each detector are calculated from the details reported in table2and considering a dark noise given for 1 s of integration time. The saturation level of each compared sensors is given by dot, pentagon and star respectively for PERCIVAL, PIMTECCDBSI and GSENSE400BSI with a surface normalization.

  assembly has been designed to have a perfect tightness in parasite light with the possibility to add different visible filter (for example, carbon or alumina filter from Luxel®, https://luxel.com) in front of the sensor. It remains compact (10 cm × 11 cm × 12 cm) to fit with a vacuum chamber on beamline and their restrictive environment. Furthermore, an X-ray beam stop could be added in front of the camera and positioned with two linear piezo motorizations as shown in Figure 4 (Popescu et al 2019).

Figure 4 :

 4 Figure 4 : Mechanical design of GSENSE400BSI camera vacuum adaptation made at SOLEIL, so-called DhyanaX

  Figure 1 (b), is composed by a silicon epitaxial layer (Si-Epi) of 10 µm thick, 7 nm of SiO2followed by 63 nm Si3N4. This silicon nitride is on the top of the sensor, both layers serve as an anti-reflection coating (ARc) purpose and passivation layer (originally processed for visible applications). The second sensor tested has no anti-reflective coating (no-ARc) on the photo-sensitive area but has a thinner Si-Epi layer thickness around 4 µm. The method and measurement of the QE of the sensor have already been reported in the previous work(Desjardins 2019). The final result for both sensors is presented in figure5where the measurements have been superimposed with model results proposed in equation 2;

Figure 5 :

 5 Figure 5 : GSENSE400BSI-TVISB and GSENSE400BSI-GP Quantum Efficiency measurements compared to a theoretical model given by AR coating and Si-Epi absorption.

Figure 6 :

 6 Figure 6 : Circular integration of pinhole diffraction image from sCMOS GSENSEBSI400 obtained at 186 eV on METROLOGIE Beamline (100 accumulations of 100 ms dark-corrected images in HDR mode).

  knife slanted edge method (International Organization for Standardization [ISO], 2000). A silicon nitride support films has been used as edge slightly tilted (the edge angle was about 10° off of the pixel array alignment) and illuminated with X-ray beam at 1500 eV. The Modulation Transfer Function (MTF) has been calculated from cropped dark-corrected image (figure7) carried out by using sfrmat3 Matlab script[START_REF] Burns | SFRmat3 Script[END_REF]. The result is given in pair of line per mm in figure7.

Figure 7 :

 7 Figure 7 : MTF calculation from sCMOS GSENSEBSI400 slanted edge image at 1500 eV on METROLOGIE Beamline (1000 accumulation of dark corrected images of 100 ms).

Figure 8 :

 8 Figure 8 : (a) Example of image analyzed for X-ray energy beam of 1000 eV (blue circles are the pixel extracted). (b) Spectrums of single-event frequencies for X-ray photon energy of 100-1500 eV. The spectrums for 400 eV to 1500 eV have been voluntary cropped in low-energy range (down to 200 eV).

Figure 9 :

 9 Figure 9 : X-ray energy resolution of GSENSE400BSI-GP measurement results compared to the Fano noise limit and to the fit FHWM with σ sCMOS = 6 e-.

Figure 10 :

 10 Figure 10 : (a) Schematic representation of X-ray irradiation of GSENSEBSI400-TSVIB for 160 eV, 560 eV 1000 eV and 1600 eV (b) Part of GSENSEBSI400-TSVIB dark image (300 px by 1000 px) after irradiation (contrast voluntary increased)

Figure 11 :

 11 Figure 11 : Theoretical transmission versus the Si thickness for X-ray photon of 160 eV, 560 eV, 1000 eV and 1600 eV through the GSENSEBSI400-TVISB and of 80 eV through the GSENSEBSI400-GP.

Figure 12 :

 12 Figure 12 : Radiation tolerance evaluation of (a) sCMOS GSENSE400BSI-TVSIB and (b) sCMOS GENSE400BSI-GP by excess dark measurement after soft X-ray irradiation with beam of 560 eV, 1000 eV and 1600 eV and 80 eV, respectively. In dashed and red curves are the empirical model (equation 5).

  e2v reports a radiation tolerance of 10 kRad (100 Gy) on the classical CCD design [datasheet du CCD40-42, D. Burt et al, 2009]. From this value (D th = 200 Gy), we represent in figure 13 an estimation of the limit of fluence (number of photons/unit area/time) to avoid non reversible damage of the two sensors tested here.

Figure 13 :

 13 Figure 13 : Limit of fluence [ph/s/mm²] calculated for a limit the dose of 200 Gy on electronic layer of a GSENSE400BSI-TVSIB before damaging.

Figure 14 :

 14 Figure 14 : Exposure time limit calculated for a limit the dose of 200 Gy on electronic layer of a GSENSE400BSI-TVSIB (blue) and GSENSE400BSI-GP (red) before damaging.

Figure 15 :

 15 Figure 15 : Exposure time limit calculated for a limit the dose of 200 Gy with a flux of 10 s ph/s/(11 x 11 µm²) on electronic layer of a GSENSE400BSI.

Figure 16 :

 16 Figure 16 : SEXTANTS beamline synoptic for GSENSE400BSI camera test versus CCD installed. SEM image of the Co/Cu nanostrured sample of 530x1220nm rectange.

Figure 17 :

 17 Figure 17 : Dark corrected images of soft X-ray scattering from Co/Cu multilayer sample at 767 eV acquired with (a) the sCMOS GSENSE400BSI camera placed at 1 m behind the sample and (b) the PIMTE camera placed close to the sample (25 cm). Both images correspond to the accumulation of 100 images of 200 ms.

Figure 18 :

 18 Figure 18 : Superposition and normalized the sum of the pixels in central region of the images (figure 16) obtained with CCD camera (blue line) and sCMOS camera (red line) for X-ray energy photon of 767eV versus the scattering vector.

Figure 19 :

 19 Figure 19 : (a) STXM image with beam size spot of XXXXX and (b) Ptychography reconstruction of the Siemens star. (c) Example of a speckle pattern.

  .a, the lower resolution STXM classical image obtained with PMT while in the Figure.19.b, we showed the reconstructed ptychography image performed with the ePIE method implemented in a MATLAB script developed by the NANOSCOPIUM beamline[Medjoubi et al, 2018] and used by several SOLEIL beamlines. This reconstruction allows to clearly observe the bacteria (diameter of ? nm) with a very small space between two adjacent magnetosomes.

Figure 20 :

 20 Figure 20 : (a) Classical STXM image of magnetosomes at 706 eV. (b) Ptychography reconstruction of magnetosome. (c) Example of a speckle pattern

Table 1 Electro

 1

		Symbol Value	ref
	Gain	K	Low gain, High gain or HDR mode
		fps	24 Hz Full frame (HDR)
	Frame Rate		48 Hz Full frame (STD)
	Readout architecture		Rolling Shutter	GPIXEL datasheet (www.gpixel.com)
	Pixel Size	px	11 x 11 µm²
	Sensor size		4M -2048 × 2048 pixels (22.5 mm × 22.5 mm)
	Exp. times	t	20 µs -10s
	Binning		No
	Readout noise Dark noise Full Well Capacity Spatial pixel offset noise Spatial pixel gain noise	 read  dark FWC DSNU PRNU	< 2 e-rms (HDR & HG) & < 45 e-rms (LG) > 3 e-/s/pix (-20°C) 30 ke-(HDR), 1700 e-(HG) & > 80 ke-(LG) < 5 e-< 1 %	TUCSEN Dhyana95 datasheet (www.tucsens.com) Wang et al., 2017 Desjardins et al, 2019

-optical characteristics of the GSENSE400BSI sensor specifications and TUCSEN Dhyana95 camera measurements results

table 2 and considering a dark noise given for 1 s of integration time. The saturation level of each compared sensors is given by dot, pentagon and star respectively for PERCIVAL, PIMTECCDBSI and GSENSE400BSI with a surface normalization.

	QE (500 eV)	0.85	~ 0.8 (unpublished)	0.5 up to 0.8 (see §3.2)
	Readout noise	10 e-rms (1MHz ADC)	1600 e-rms (lowest gain) 15 e-rms (highest gain)	2 e-rms (HG) 38 e-rms (LG)
	Dark noise	0.02 e-/s/pixel (-50°C)	Supposed low (-40°C) (unpublished)	3 e-/s/pixel (-20°C)
	FWC	temporal noise 100 ke-	shot noise ~ 4 Me-/pixel (lowest gain) spatial noise 80 ke-(LG) 30 ke-(HDR) ~ 2000 e-(highest gain) 1600 e-(HG)
		PI-MTE CCD BSI
	Detector	(datasheet PIMTE2048B) [http://www.princeton.c	PERCIVAL (BSI) (Khromova et al, 2016)	GSENSE400BSI (Desjardins et al, 2019)
		om]
	Pixel size	13.5 x 13.5 µm²	27 x 27 µm²	11 x 11 µm²

Table 3 . Soft X-ray irradiation details

 3

	Energy	Incident flux ( Φ 0 ) on the sensor	TID on surface 1	TID on electronic layer 2
		(Total exposure time)
	1 The TID (absorbed dose) on the surface is estimated from equation 4 considering the anti-reflection layers

thickness attenuation and with μ/ρ extracted from NIST FFAST database (https://physics.nist.gov) 2 The TID (absorbed dose) on the electronic layer is estimated from equation 4 considering the antireflective layer and Epi-Si thicknesses attenuation and with μ/ρ extracted from NIST FFAST database (https://physics.nist.gov)

Acknowledgments

The authors wish to acknowledge Hao Yuan and Adam Hitchcock of the Department of

Chemistry and Biology McMaster University (Ontario, Canada) for providing us the greath helpful with Pytochography reconstruction

We also would like to acknowledge Ye(Evan) Tian from TUCSEN and Xinyang Wang from GPIXEL for the great help sharing all needed information for this work. Finally, we are very grateful to Zhang Jiang of Argonne National Laboratory for sharing the Matlab toolbox on Xray refraction of matter [Jiang 2020].


Maurizio Sacchi
email: maurizio.sacchi@insp.jussieu.fr

Nicolas Casaretto

Leticia Coelho

Mahmoud Eddrief

Jialin Ma

Carlo Spezzani

Franck Vidal

Hailong Wang

Jianhua Zhao

Yunlin Zheng

Threshold MnAs thickness for the formation of ordered α/β stripes in MnAs/GaAs(001)

Manganese arsenide layers epitaxially grown on GaAs(001) are known to feature a temperature dependent self-assembled microstructure of ordered stripes, alternating the ferromagnetic α and paramagnetic β phases. The surface dipolar fields generated by the α/β stripes have been used for achieving temperature controlled magnetization switching of a ferromagnetic overlayer. For this kind of application, it is advantageous to minimize the MnAs layer thickness. In this work we investigate, using x-ray scattering techniques, the presence of the ordered microstructure as a function of the MnAs layer thickness and we identify a minimum value of ~40 nm for the formation of ordered α/β stripes in MnAs/GaAs(001). These results have an impact for envisaging magnetization-switching applications that rely on the control of the temperature-or laser-driven surface dipolar fields in MnAs-based devices.

I. INTRODUCTION

Developing thermally induced magnetization switching (TIMS), where the temperature control of intrinsic material properties drives a deterministic reversal of the local magnetization, has potential for applications. For instance, the combination of materials with different temperature dependent magnetic properties has been used to switch the magnetization with a single laser pulse in rare-earth-transition-metal ferrimagnetic compounds, in a process that combines thermal effects with photon helicity dependent effects [START_REF] Kimel | Laser-induced ultrafast spin reorientation in the antiferromagnet TmFeO 3[END_REF][START_REF] Hassdenteufel | Thermally assisted all-optical helicity dependent magnetic switching in amorphous Fe(100-x)Tb(x) alloy films[END_REF][START_REF] Kirilyuk | Laser-induced magnetization dynamics and reversal in ferrimagnetic alloys[END_REF][START_REF] Mangin | Engineered materials for all-optical helicity-dependent magnetic switching[END_REF]. Controlling the local temperature by a laser pulse is also at the basis of heat assisted magnetic recording processes that were proposed to significantly lower the external field values necessary for switching a magnetic bit [START_REF] Thiele | FeRh/FePt exchange spring films for thermally assisted magnetic recording media[END_REF]. A different approach to TIMS makes use of substrates whose intrinsic magnetic properties feature regular spatial modulations generating local surface dipolar fields that can be controlled by tuning the temperature [START_REF] Marangolo | Method for changing the direction of magnetization in a ferromagnetic layer[END_REF]. The proof-of-principle of this approach made use of a thin ferromagnetic (FM) Fe layer deposited on a MnAs/GaAs(001) template. MnAs/GaAs(001) is a metal/semiconductor system where the interplay between epitaxial constraints and temperature-driven phase transitions gives rise to a peculiar morphological and magnetic behavior at ambient temperatures [START_REF] Tanaka | Epitaxial orientation and magnetic properties of MnAs thin films grown on (001) GaAs: Template effects[END_REF][START_REF] Schippan | Magnetic structure of epitaxially grown MnAs on GaAs(001)[END_REF]. At T~40 ºC, bulk MnAs features a first order transition between ferromagnetic α and non-magnetic β phases [START_REF] Rungger | Ab initio study of the magnetostructural properties of MnAs[END_REF][START_REF] Łażewski | Phonon mechanism of the magnetostructural phase transition in MnAs[END_REF][START_REF] Łażewski | Mechanism of the phase transitions in MnAs[END_REF]. In MnAs/GaAs(001) epitaxial films the two phases coexist over the temperature range ~10-40 ºC in the form of regular stripes [START_REF] Tanaka | Epitaxial orientation and magnetic properties of MnAs thin films grown on (001) GaAs: Template effects[END_REF][START_REF] Däweritz | Interplay of stress and magnetic properties in epitaxial MnAs films[END_REF] the period of which is determined by the MnAs thickness [START_REF] Tanaka | Epitaxial orientation and magnetic properties of MnAs thin films grown on (001) GaAs: Template effects[END_REF][START_REF] Schippan | Magnetic structure of epitaxially grown MnAs on GaAs(001)[END_REF][START_REF] Kaganer | Strain-mediated phase coexistence in MnAs heteroepitaxial films on GaAs: An x-ray diffraction study[END_REF] and by the presence of overlayers [START_REF] Vidal | Tuning the period of elastic MnAs/GaAs(001) α→β pattern by Fe deposition[END_REF]. It was shown that it is possible to control the Fe magnetization in Fe/MnAs/GaAs(001) by fine-tuning the temperature at ambient [START_REF] Sacchi | Thermal switching of the magnetization in an iron film on a magnetically active template MnAs/GaAs(001)[END_REF]. Element selective x-ray resonant magnetic scattering (XRMS) experiments demonstrated that various magnetic configurations of the Fe/MnAs system can be stabilized predictably by acting on the thermal cycle parameters and on the presence of a bias field [START_REF] Spezzani | Thermally induced magnetization switching in Fe/MnAs/GaAs(001): selectable magnetic configurations by temperature and field control[END_REF]. What one actually does by changing the temperature is to control the surface dipolar fields associated with the template magnetic microstructure, and, ultimately, vary the effective magnetic field acting on the overlayer. Time-resolved experiments showed the potential of this approach for fast magnetization switching, where the microstructure changes are triggered by a single femtosecond optical laser pulse [START_REF] Spezzani | Magnetization and microstructure dynamics in Fe/MnAs/GaAs(001): Fe magnetization reversal by a femtosecond laser pulse[END_REF][START_REF] Vidal | Dynamics of the MnAs α/β-striped microstructure and of the Fe magnetization reversal in Fe/MnAs/GaAs(001): an optical-laser pump -Free-Electron-Laser probe scattering experiment[END_REF].

The general motivation for this research is to develop a MnAs based two-layer systems for TIMS, where the overlayer magnetization can be switched by temperature control of the dipolar fields generated by the MnAs template. Up to now, TIMS was achieved by employing MnAs layers 100 to 200 nm thick, but our present understanding of the TIMS process in Fe/MnAs suggests that the advantage of using thinner MnAs layers is at least twofold. Firstly, the stripe period p is proportional to the film thickness t MnAs , with p ≈ 5 × t MnAs for a bare MnAs film [START_REF] Tanaka | Epitaxial orientation and magnetic properties of MnAs thin films grown on (001) GaAs: Template effects[END_REF][START_REF] Schippan | Magnetic structure of epitaxially grown MnAs on GaAs(001)[END_REF], therefore reducing t MnAs leads to narrower stripes that can generate stronger surface dipolar fields. A shorter period should also favor a better spatial definition of the TIMS process, since the size of the smallest bit of the overlayer that one can envisage switching independently is proportional to the period. Secondly, it was shown that a fluence threshold exists for laser induced switching, which corresponds to the complete transition of the MnAs film into the high temperature β phase [START_REF] Spezzani | Magnetization and microstructure dynamics in Fe/MnAs/GaAs(001): Fe magnetization reversal by a femtosecond laser pulse[END_REF][START_REF] Vidal | Dynamics of the MnAs α/β-striped microstructure and of the Fe magnetization reversal in Fe/MnAs/GaAs(001): an optical-laser pump -Free-Electron-Laser probe scattering experiment[END_REF]. Therefore a thinner MnAs template should make it possible to switch the overlayer magnetization using lower laser fluence, i.e. a reduced power. Finally, since the characteristic time for magnetization switching is determined by the return towards thermal equilibrium [START_REF] Lounis | Dynamics of laser induced magneto-structural phase transitions in MnAs/GaAs(001) epitaxial layers[END_REF], using a thinner template and a lower fluence will lead to a faster switching process.

In summary, reducing the MnAs layer thickness should allow for a faster laser-driven magnetization switching of smaller areas employing a lower power.

The controlled generation and disappearance of surface dipolar fields remains a pre-requisite for TIMS, which for MnAs implies the formation of regular α/β stripes. The occurrence of spatially modulated phase coexistence in thin films has been addressed in theoretical studies. In particular, the work of Sridar et al. [START_REF] Sridhar | Twinning in thin films -II. Equilibrium microstructures[END_REF], which was used for modelling the MnAs/GaAs(001) system [START_REF] Kaganer | Strain-mediated phase coexistence in MnAs heteroepitaxial films on GaAs: An x-ray diffraction study[END_REF], suggested that, for certain sets of parameters, the formation of regular stripes becomes unfavorable below a critical thickness of the film. Experimental studies exist on thin MnAs layers on GaAs(001), demonstrating that the crystal structure is well defined and relaxed for films a few nm thick [START_REF] Satapathy | In situ investigation of MnAs/GaAs(001) growth and interface structure using synchrotron x-ray diffraction[END_REF] and that the α/β phase coexistence as a function of temperature is observed already for very thin films [START_REF] Song | Effect of growth temperature on magnetic and electronic properties of epitaxially grown MnAs thin films on GaAs(100) substrates[END_REF]. Other studies [START_REF] Däweritz | Tailoring of the structural and magnetic properties of MnAs films grown on GaAs -Strain and annealing effects[END_REF][START_REF] Zdyb | Nanomagnetism studies with spin-polarized low-energy electron microscopy and x-ray magnetic circular dichroism photoemission electron microscopy[END_REF][START_REF] Ryu | Thickness-dependent magnetic domain change in epitaxial MnAs films on GaAs(001)[END_REF][START_REF] Fraser | Magnetization reversal in epitaxial MnAs thin films[END_REF][START_REF] Steren | Combined effects of vertical and lateral confinement on the magnetic properties of MnAs micro and nano-ribbons[END_REF] report, albeit with some contradictory results, images of the local magnetic order in thin (< 50 nm) MnAs layers.

Finally, the role of the layer thickness has been evoked also in connection with the electronic and magnetic properties of ~μm-sized laterally confined MnAs ribbons [START_REF] Steren | Combined effects of vertical and lateral confinement on the magnetic properties of MnAs micro and nano-ribbons[END_REF][START_REF] Fernandez Baldis | Anisotropic magnetic-field-induced phase transition in MnAs nanoribbons[END_REF]. In any case, none of these studies addressed specifically the formation of ordered α/β stripes versus thickness in the limit of very thin MnAs layers.

In this work we employ resonant soft x-ray scattering to study the ordered microstructure as well as the magnetic properties of thin MnAs films. We analyze MnAs/GaAs(001) layers with thickness in the 20-70 nm range. The main objective is to determine the minimum thickness capable of producing a regular microstructure of α/β stripes that can generate at precise and predictable locations the surface dipolar fields necessary for TIMS. Our work confirms the existence of a threshold thickness for stripe formation; we discuss its possible origin in the framework of previous results reported in the literature.

II. EXPERIMENTAL DETAILS

MnAs layers 20 to 70 nm thick were prepared by molecular beam epitaxy (MBE) on GaAs(001) at the State Key Laboratory of Superlattices and Microstructures of the Institute of Semiconductors (IoS) in Beijing, following a well-established protocol [START_REF] Sacchi | Uniaxial anisotropy and temperature driven magnetization reversal of Fe deposited on a MnAs/GaAs(001) magnetic template[END_REF][START_REF] Vidal | Sacchi Ultrafast structural dynamics along the β-γ phase transition path in MnAs[END_REF]. The samples were capped by ~4 nm of GaAs for protection against contamination. As a reference, we measured also two samples prepared at the Institut des NanoSciences de Paris (INSP) that were used in previous experiments, one 30 nm thick [START_REF] Steren | Combined effects of vertical and lateral confinement on the magnetic properties of MnAs micro and nano-ribbons[END_REF], the other 180 nm thick [START_REF] Lounis | Dynamics of laser induced magneto-structural phase transitions in MnAs/GaAs(001) epitaxial layers[END_REF]. All samples were characterized by x-ray diffraction (XRD) measurements at INSP, using the Cu-Kα 1 radiation from a rotating anode diffractometer equipped with a Ge(220) 2-reflection channel-cut monochromator. XRD data confirmed the growth of type-A MnAs layers [START_REF] Tanaka | Epitaxial orientation and magnetic properties of MnAs thin films grown on (001) GaAs: Template effects[END_REF], with the epitaxial relationship between MnAs and GaAs sketched in figure 1(a). Soft x-ray resonant scattering measurements were performed at the Circular Polarization beamline of the ELETTRA synchrotron (Trieste), using the IRMA scattering chamber [START_REF] Sacchi | Ultra-high vacuum soft X-ray reflectometer[END_REF].

The sample holder was equipped for temperature and magnetic field control. A photodiode with a 0.2 mm vertical aperture slit was placed on the detector arm at 150 mm from the sample. An in vacuum 2D detector, based on microchannel plates and a resistive anode, was mounted on a fixed flange (central scattering angle 2θ ≈ 32.5°) and allowed us to collect the diffuse intensity around the specular beam and the diffraction peaks originating from the regular stripe microstructure. Scattering measurements were performed in co-planar geometry [see figure 1(b)], tuning the soft x-ray energy to the Mn-2p resonance (~640 eV). In addition to providing a stronger diffraction signal from the ordered stripes, working at the Mn core resonance and using circularly polarized radiation allowed us to probe also the magnetic response as a function of temperature under the same experimental conditions.

The formation of regular stripes alternating the α and β phases was monitored by probing the scattered intensity around the specular beam either by using the 2D detector or by performing sample rocking scans using the slitted photodiode. In both cases, the regular stripes produce Bragg peaks the angular location of which depends on the stripe period p, on the x-ray wavelength λ, and on the incidence (ω) and scattering (2θ) angles. showing the incidence (ω), scattering (2θ) and off-specular (α) angles. k in and k out represent the vector momentum of the incoming and outgoing photons, q = k out -k in is the exchanged momentum with components q x and q z . (c) Schematic (q x ,q z ) chart, assuming p = 300 nm and λ = 1.94 nm. The thick black line at q x = 0 corresponds to specular reflectivity (ω/2θ scan with α = 0). The red dotted line represents a rocking curve (ω scan at 2θ = 32.5°). The blue dash-dot line corresponds to a detector scan (2θ scan at ω = 16.25°). The dashed vertical lines correspond to q x = ±2π/p = ±0.021 nm -1 . Large squares and circles locate the expected Bragg peaks on the rocking and detector scans, respectively.

Taking (x,y) as the sample surface and (x,z) as the incidence plane [see figure 1(b)], the exchanged momentum vector has components q x =(4π/λ)•sin(θ)•sin(α), q y =0 and q z =(4π/λ)•sin(θ)•cos(α), where α = ωθ is the sample off-specular angle. Figure 1(c) shows schematically in a (q x ,q z ) chart the location of Bragg peaks at q x =2π/p for a stripe period p = 300 nm, observed with a photon energy of 640 eV (λ=1.94 nm, Mn-2p resonance). On the same chart we have highlighted the lines corresponding to a detector scan and to a sample rocking scan. The former (blue dash-dot line) corresponds to a 2θ scan at fixed ω (in our case, to a 2D-detector acquisition), the latter (red dotted line) to a ω scan at fixed 2θ (i.e., to a q x scan at almost constant q z ). In our measurements we could also cover whole areas of the (q x ,q z ) chart by combing ω scans collected at different 2θ angles, using the slitted diode detector.

Table 1 lists all the samples addressed specifically in this study and compares their nominal

MnAs thickness values with those obtained by soft (synchrotron) and hard (Cu-Kα) x-ray reflectivity. In the following, we will refer to each sample by its nominal thickness value.

III. RESULTS

Figure 2 shows for all samples the temperature dependence of the Mn magnetization in a heating cycle, measured by Mn-2p resonant magnetic scattering. The magnetic signal is defined as the difference between the scattered intensity recorded for opposite magnetization/helicity orientations divided by their sum [START_REF] Spezzani | Thermally induced magnetization switching in Fe/MnAs/GaAs(001): selectable magnetic configurations by temperature and field control[END_REF]. 2 confirm also that all samples were aligned with their easy magnetization axis within the incidence plane, which is the correct azimuth for observing stripes-related Bragg peaks in our co-planar geometry.

Figure 3 shows the experimental results obtained for the reference 180 nm thick MnAs sample.

The 2θ scan at fixed  [2D-detector acquisition, figure 3(a,b)] shows the presence of Bragg peaks at q x ≈7 µm -1 corresponding to a period of ~900 nm, in perfect agreement with the Coming to the thin MnAs layers, figures 4-7 summarize the results for t MnAs between 20 and 70 nm.

Neither the rocking scans nor the 2D images in figure 4 show any Bragg peak at the expected position for t MnAs = 20 nm. In the (q x ,q z ) chart of figure 4(a), no additional intensity corresponding to the expected stripe period is observed at any q z value. The scattering measurements give a different picture for the thicker 50 nm and 70 nm samples.

Figure 6(a) shows a room-temperature (q x ,q z ) chart for t MnAs = 50 nm, featuring diffracted intensity at q x values around ±0.024 nm -1 , strongly enhanced at q z ≈ 0.85 nm -1 . Figure 6(b)

shows the 2D-detector diagrams measured at T = 23 °C and T = 55 °C, and the corresponding q x line profiles. Clear peaks are observed at room temperature, where both α and β phases are present, and they disappear when the sample is heated above the temperature for the transition to the β phase.

IV. DISCUSSION

From the ensemble of the results presented in figures 4-7, we conclude that there is a critical value of the MnAs layer thickness for observing the formation of ordered α/β stripes over the temperature region characterized by phase coexistence, and that this value is around 40 nm. In the following, we will correlate this finding with data reported previously by other authors and with the results of complementary x-ray diffraction measurements. First of all, one should mention that several studies exist that report magnetic images of thin MnAs layers obtained by either magnetic force microscopy (MFM) or by x-ray photoelectron emission microscopy (X-PEEM). Although none of them addresses the issue of stripe formation versus thickness explicitly, some of the reported results are worth discussing here.

In two of the early X-PEEM works on MnAs/GaAs(001), the magnetic images of a 37 nm [START_REF] Däweritz | Tailoring of the structural and magnetic properties of MnAs films grown on GaAs -Strain and annealing effects[END_REF] and of a 40 nm [START_REF] Zdyb | Nanomagnetism studies with spin-polarized low-energy electron microscopy and x-ray magnetic circular dichroism photoemission electron microscopy[END_REF] layer showed a clear array of nonmagnetic β stripes at room temperature.

These observations may help us setting an upper limit to the thickness at which ordered stripes are not formed anymore. One must notice, though, that the periods that can be extracted from the X-PEEM images are ~250 nm for the 37 nm sample (figure 1 of reference [START_REF] Däweritz | Tailoring of the structural and magnetic properties of MnAs films grown on GaAs -Strain and annealing effects[END_REF]) and ~350 nm for the 40 nm one (figure 3 of reference [START_REF] Zdyb | Nanomagnetism studies with spin-polarized low-energy electron microscopy and x-ray magnetic circular dichroism photoemission electron microscopy[END_REF]). These values exceed (the former only slightly) what is expected for a ~40 nm MnAs layer, suggesting that the thicknesses of these samples may had been underestimated.

A much lower value may be inferred from the MFM work of Fraser et al. [START_REF] Fraser | Magnetization reversal in epitaxial MnAs thin films[END_REF], which mentions the presence of α/β stripes with a period of 230 nm in a 10 nm thick sample. Unfortunately, no image is provided in the article to support this statement. Moreover, such a large period-to-thickness ratio seems unlikely.

A recent X-PEEM study [START_REF] Steren | Combined effects of vertical and lateral confinement on the magnetic properties of MnAs micro and nano-ribbons[END_REF] compared room temperature magnetic images for 30 and 50 nm thick samples (figure 3 of reference [START_REF] Steren | Combined effects of vertical and lateral confinement on the magnetic properties of MnAs micro and nano-ribbons[END_REF]). Regular non-magnetic β stripes running perpendicular to the easy magnetization direction are evident for the 50 nm thick MnAs layer, but they are absent in the 30 nm one. This observation, obtained by a completely different experimental method (X-PEEM), not only agrees with and supports the conclusions of our study, but also proves that these conclusions do not depend on the specific technique (XRMS) that we have employed.

Finally, it should be mentioned also that the investigation of both the magnetic domain structure [START_REF] Ryu | Thickness-dependent magnetic domain change in epitaxial MnAs films on GaAs(001)[END_REF] and of the electrical properties [START_REF] Fernandez Baldis | Anisotropic magnetic-field-induced phase transition in MnAs nanoribbons[END_REF] of MnAs films in the low thickness limit suggest a change in behavior across the 20 -50 nm range. These results may be related to microstructural changes and generally agree with our findings.

Based on the results of our work alone, we cannot provide a clear explanation for the absence of ordered stripes below a certain thickness of the MnAs layer. In the following, we will discuss some hypotheses.

The first one concerns a possible relationship with crystalline quality. The initial stages of the MnAs growth on GaAs(001) were addressed in previous works by following the structural evolution in situ [START_REF] Satapathy | In situ investigation of MnAs/GaAs(001) growth and interface structure using synchrotron x-ray diffraction[END_REF][START_REF] Hirayama | Initial stages of MnAs heteroepitaxy and nanoisland growth on GaAs(110) and (001)surfaces[END_REF]. It was shown in particular that the width of the rocking curves measured at scattering angles that match the MnAs Bragg peaks decreases when the layer thickness increases [START_REF] Jenichen | Structural properties of MnAs epitaxial films on GaAs: an in situ x-ray study[END_REF], a result that was associated with the improved grain size, crystal quality and long range order in the film. Therefore, it seems appropriate to question whether the ~40 nm critical value for observing ordered α/β stripes is related to the crystalline quality of the film.

A feature common to all our samples regardless of their thickness is the presence of both α and β phases at room temperature. Using Cu-K α radiation, we performed ω-scans (i.e., rocking curves) at 2θ values corresponding to the 006 Bragg peaks (in orthorhombic notation) of the α and β phases. Since the step height h between α and β stripes is proportional to the MnAs layer thickness (h is ~1% of t MnAs ), one can speculate that reducing the film thickness may make the diffraction peaks too weak to be observed by XRMS. Moreover, also the period p diminishes with t MnAs , and in the theoretical work of Kaganer and collaborators [START_REF] Kaganer | Strain-mediated phase coexistence in MnAs heteroepitaxial films on GaAs: An x-ray diffraction study[END_REF] it was predicted that the narrowing of the stripes could lead to a further smoothing of the steps between α and β domains, accompanied by the convergence towards a common value of the vertical lattice spacing for the two phases. This last prediction is at variance with our observation of clearly distinct 00l diffraction peak positions for α and β MnAs down to the thinnest layer that we measured.

Moreover, it is worth stressing that the X-PEEM observations mentioned above [START_REF] Steren | Combined effects of vertical and lateral confinement on the magnetic properties of MnAs micro and nano-ribbons[END_REF] are not affected by the step height h, since they rely only on the magnetic contrast between ferromagnetic α and paramagnetic β phases. Therefore, it seems unlikely that the disappearance of stripes in XRMS data and X-PEEM images when reducing the layer thickness below 40 nm can originate simply from the reduction of the steps height.

Another possible explanation for the existence of a threshold thickness compatible with experimental observations may come from the loss of the vertical homogeneity in the MnAs layer. Fu et al. [START_REF] Fu | Dimension effect on the in-depth phase transition of MnAs/GaAs(001): From a thin film to a nanorod[END_REF] report a transmission electron microscopy (TEM) study showing a depth dependent strain field in a 180 nm thick MnAs lamella, which may lead to an inhomogeneous phase transition. Another TEM work that analyzes the vertical magnetization profile in a 180 nm thick MnAs lamella [START_REF] Gatel | In depth spatially inhomogeneous phase transition in epitaxial MnAs film on GaAs(001)[END_REF] shows a reduced magnetization at the interfaces with the GaAs(001) substrate and with the capping layer, suggesting a temperature dependent inhomogeneous spatial distribution of the α phase in the layer depth. The impact of such observations would be enhanced for thinner films, where a loss of structural homogeneity in the vertical direction, combined with the smaller lateral size of the domains, may hamper the formation of regular α/β stripes. These observations should be tempered by two remarks: i) Fu et al. conclude that the TEM sample preparation may well be at the origin of the observed change in film properties; ii) inhomogeneous magnetization profiles in MnAs films were reported earlier, but they were attributed to the inhomogeneity of the magnetization vector orientation, rather than to its modulus [START_REF] Däweritz | Interplay of stress and magnetic properties in epitaxial MnAs films[END_REF][START_REF] Engel-Herbert | Understanding the submicron domain structure of MnAs thin films on GaAs(001): Magnetic force microscopy measurements and simulations[END_REF], which has only minor or no implication on the structural homogeneity. Finally, let us also remind that our structural and magnetic data show clearly that the α-phase persists over the same temperature range regardless of the layer thickness (figure 2), ruling out a premature disappearance of the α-phase with temperature in the thinner layers.

V. CONCLUSIONS

From the ensemble of our results we can draw two main conclusions. Firstly, the thickness of the MnAs film certainly matters in defining the presence or absence of regular α/β stripes at ambient temperature, with a threshold value that we determine to be around 40 nm. Secondly, the crystalline quality of the MnAs layer, at least as measured by the width of the rocking curves, does not seem to play a fundamental role, if any at all, in the definition of this threshold value.

On the one hand, these results will be very useful in the preparation of future experiments that use the MnAs/GaAs(001) system as the template material for the magnetization control of a ferromagnetic overlayer. In particular, they will be instrumental to envisaging any application that relies on the control of the temperature-or laser-driven surface dipolar fields for attaining magnetization switching. On the other hand, our results do not clarify the mechanisms leading to the existence of a critical thickness. Analyzed together with previously published results, though, they allowed us to discuss and possibly discard some hypotheses.

The most realistic picture for explaining the absence of ordered stripes in very thin MnAs layers seems to involve a loss of vertical structural coherence due to the simultaneous reduction of the thickness and of the lateral domain size. Although this view is not fully supported by experiments yet, it explains the results of all our XRMS measurements and also of previous experiments. Further X-PEEM and sectional TEM images may be helpful to validate this picture. On the theory side, an extension of the model calculations proposed in the seminal work of Kaganer et al. [START_REF] Kaganer | Strain-mediated phase coexistence in MnAs heteroepitaxial films on GaAs: An x-ray diffraction study[END_REF] and based on the work of Sridhar et al. [START_REF] Sridhar | Twinning in thin films -II. Equilibrium microstructures[END_REF] would provide a firmer theoretical support for understanding the absence of ordered α/β stripes in the low thickness limit of MnAs films on GaAs(001).

Figure 1 .

 1 Figure 1. (a) Epitaxial relationship between MnAs (orthorhombic notation) and GaAs(001) in type-A growth. (b) Sketch of the scattering geometry,

Figure 2 .

 2 Figure 2. Temperature dependent Mn magnetization curves in a heating cycle, normalized to 1 at T = -10 °C. Each curve represents the difference divided by the sum of the Mn-2p resonant scattering intensities collected for opposite orientations between the sample magnetization and the x-ray helicity. The applied field and the MnAs easy magnetization axis are oriented within the x-ray incidence plane.

  expected p ≈ 5 × t MnAs relationship. The association of the Bragg peaks with the formation of regular α/β stripes is further supported by the temperature dependence of their intensity over a heating cycle from 0 to 50 °C, shown in figure 3(c).

Figure 3 .

 3 Figure 3. Soft x-ray scattering results for the t MnAs =180 nm reference sample. All data were collected at 640 eV photon energy (λ=1.94 nm), corresponding to the Mn-2p resonance. (a) 2D detector acquisition with ω=16.25°. (b) Detector scan curve obtained by vertical integration of (a). (c) Temperature dependence of the 1 st order peak intensity.

Figure 4 (

 4 b) shows identical curves for data collected at 22 °C, where both α and β phases coexist (red squares) and at 55 °C, where the MnAs is β-only and no stripes are expected (black circles).

Figure 4

 4 (c) compares 2θ scans recorded at three temperature values in a heating-cooling sequence from 30 °C (α/β coexistence) to 77 °C (pure β phase) and back to 20 °C (α/β coexistence): no variation can be detected above the noise level.

Figure 4 .

 4 Figure 4. Resonant scattering results for the t MnAs = 20 nm sample. Dashed vertical lines locate the expected Bragg peak position for p = 5×t MnAs = 100 nm. (a) Room-temperature (q x ,q z ) chart obtained by a sequence of rocking scans performed at different 2θ values. The specular ridge is saturated. (b) Rocking curves at q z = 0.898 nm -1 measured at T = 22 °C and T = 55 °C. Their ratio (blue curve, ×5) is also shown. (c) 2D detector acquisitions ( = 18°) and corresponding q x line profiles measured at three temperatures in the sequence T = 30 °C → 77 °C → 20 °C.

Figure 5 .

 5 Figure 5. Scattering data for the t MnAs = 35 nm sample. (a) Rocking curves at T = 25 and 55 °C (2θ= 16°), and their intensity ratio (blue curve, ×5). (b) 2D detector acquisitions ( = 15.25°) and corresponding q x line profiles measured at T = -3 and +23 °C. The vertical lines locate the Bragg peak positions expected for a stripe period p = 5×t = 175 nm.

Figure 6 .

 6 Figure 6. Results of the scattering measurements at 640 eV photon energy for t MnAs = 50 nm. (a) Room-temperature (q x ,q z ) chart (the specular ridge is saturated). (b) 2D detector measurements ( = 16.25°) and corresponding q x line profiles at T = 20°C and T = 55 °C. The vertical lines locate the expected peak positions for p = 250 nm.

Figure 7 .

 7 Figure 7. Scattered intensity at 640 eV for the 70 nm MnAs sample. (a) Room-temperature (q x ,q z ) chart. (b) 2D detector diagrams ( = 16.25°) and corresponding q x line profiles measured at T = -7, 24 and 57 °C. The vertical lines correspond to the peak positions expected for p = 350 nm.

Figure 8 (

 8 figure 8(e) identifies samples prepared during a single growth session, showing that, depending on the growth conditions, very small w values can be obtained also for thin layers. The two samples of figure8(c,d) have similar thicknesses (35 and 30 nm): although they feature rather different rocking curve widths of 0.77° and 0.36°, stripes are absent for both of them. The samples of figure8(b,c), 50 and 35 nm thick prepared during the same growth session, feature almost identical rocking curve widths (w ≈ 0.75°), but behave differently in terms of stripe formation (see figures5 and 6).Overall, the ensemble of our data points unequivocally to the absence of a correlation between the crystalline quality of the MnAs layer, at least as measured by w, and the presence or absence of ordered α/β stripes.

Figure 8 .

 8 Figure 8. (a-d) Room temperature rocking curves (-scans) measured for four different samples with 2θ set at the 006 peaks of α (■) and β (○) MnAs. The w values reported for each sample correspond to the FWHM averaged for α and β peaks. (e) Summary of w values for a wider set of MnAs samples as a function of their thickness. Each symbol identifies a subset of samples prepared during a single growth session.

Table 1 .

 1 Sample list, showing the MnAs thickness nominal values and the experimental values determined by soft (SXR) and hard (HXR) x-ray reflectivity. The last two columns list the preparation laboratory and references.

	t nominal (nm)	t SXR (nm)	t HXR (nm)	Laboratory	References
	20	20	23	IoS
	35	35	34	IoS
	50	47	49	IoS
	70	70	72	IoS	[30]
	30	29	29	INSP	[27]
	180	180	179	INSP	[19]

ACKNOWLEDGEMENTS

We acknowledge Sincrotrone Trieste for granting beamtime to our project and the Circular Polarization beamline staff for assistance during the experiment. The research leading to these results has been supported by the project CALIPSOplus under Grant Agreement 730872 from the EU Framework Programme for Research and Innovation HORIZON 2020. We acknowledge the support from the National Natural Science Foundation of China under Grant No. U1632264.


Sophie Lemonnier
email: sophie.lemonnier@ifsttar.fr

Roland Bremond

Lara Desire

Thierry Baccino

] Brémond

] Désiré

Validation of a

published or not. The documents may come

Background

Method

Discussion

Variability intra-and inter-of participants and situations

Although test field experiments are costly, some advantages emerge. Among the benefits of generalizing a visual attention model to true driving situations, its applications to road safety, road design, driving assistance systems and traffic simulation become easier. In addition, such an experiment on the road produces a large database of behavioral data, ready for future analysis.

Expectancy

Results: data analysis in progress.

Model

Visual attention = Bottom-up (i.e. saliency) and Top-down processes (i.e. goal, task, expectancy; +++ in the literature).

The more complex the processes under study, the more necessary it is to have an ecological experimental setting.  Driving is an interesting task to study top-down models of visual attention [START_REF] Tatler | Eye guidance in natural vision : Reinterpreting salience[END_REF]. [START_REF] Wickens | Attentional models of multitask pilot performance using advanced display technology[END_REF] proposed a model of visual attention predicting in which areas of interest people get information. Visual attention depends on two TD parameters: expectancy and value of information. We are currently testing this model with driving field test.

These differences in terms of participants and crossroads environments help to generalize our results to many driving situations. (Smilek et al., 2006)

Itinerary includes 5 crossroads per road sign (i.e. give way, stop, priority). Some detours were necessary because of the constraints of the road network, which resulted in a 2 hours trip per participant. A benefit of this long trip is the fact that the participants cannot guess the hypothesis under study.

Traffic density

can only be controlled a posteriori, with some intra-modality variability (i.e. no, low, dense traffic).

Eye-tracking calibration is complicated, including variable duration, with expected consequences in terms of the participants' state of mind.

Surprising events

But also: the weather, the familiarity of the trip, interactions with other drivers, and more … all these factors contribute to the variability of the encountered situations.