Kai Gu

Thomas Maugey

Sebastian Knorr

Christine Guillemot

Omni-nerf: neural radiance field from 360°image captures

Keywords: Light field, omni-directional imaging, rendering, view synthesis, deep learning

This paper tackles the problem of novel view synthesis (NVS) from 360 • images with imperfect camera poses or intrinsic parameters. We propose a novel end-to-end framework for training Neural Radiance Field (NeRF) models given only 360 • RGB images and their rough poses, which we refer to as Omni-NeRF. We extend the pinhole camera model of NeRF to a more general camera model that better fits omni-directional fish-eye lenses. The approach jointly learns the scene geometry and optimizes the camera parameters without knowing the fisheye projection.

INTRODUCTION

The concept of 6 degrees of freedom (6DOF) video content has recently emerged with the goal of enabling immersive experience in terms of free roaming, i.e. allowing viewing the scene from any viewpoint and direction in space [START_REF] Broxton | Immersive light field video with a layered mesh representation[END_REF]. However, no such real-life full 6DOF light field capturing solution exists so far. Light field cameras have been designed to record orientations of light rays, hence to sample the plenoptic function in all directions, thus enabling view synthesis for perspective shift and scene navigation [START_REF] Shi | Learning fused pixel and feature-based view reconstructions for light fields[END_REF]. Several camera designs have been proposed for capturing light fields, going from uniform arrays of pinholes placed in front of the sensor [START_REF] Ives | Parallax panoramagrams made with a large diameter lens[END_REF] to arrays of micro-lenses placed between the main lens and the sensor [START_REF] Ng | Light Field Photography with a Handheld Plenoptic Camera[END_REF], arrays of cameras [START_REF] Wilburn | High performance imaging using large camera arrays[END_REF], and coded attenuation masks [START_REF] Miandji | Multi-shot single sensor light field camera using a color coded mask[END_REF]. However, these light field cameras have a limited field of view. On the other hand, omni-directional cameras allow capturing a panoramic scene with a 360 • field of view but do not record information on the orientation of light rays emitted by the scene.

Neural Radiance Fields (NeRF) have been introduced in [START_REF] Mildenhall | Nerf: Representing scenes as neural radiance fields for view synthesis[END_REF] as an implicit scene representation that allows rendering all light field views with high quality. NeRF models the scene as a continuous function, and is parameterized as a multi-layer perceptron (MLP). The function represents the mapping between the 5D spatial and angular coordinates of light rays emitted by the scene into its three RGB color components and a volume density measure. NeRF is capable of modeling complex large-scale, and even unbounded, scenes. With a proper parameterization of the coordinates and a welldesigned foreground-background architecture, NeRF++ [START_REF] Zhang | NeRF++: Analyzing and Improving Neural Radiance Fields[END_REF] is capable of modeling scenes having a large depth, with satisfying resolution in both the near and far fields.

First NeRF-based models need the camera pose parameters to map the pixel coordinates to the ray directions, and use COLMAP [START_REF] Schönberger | Structure-frommotion revisited[END_REF][START_REF] Schönberger | Pixelwise view selection for unstructured multiview stereo[END_REF] for the camera parameter estimation. An end-to-end framework, called NeRF-, is proposed in [START_REF] Wang | NeRF-: Neural Radiance Fields Without Known Camera Parameters[END_REF] for training NeRF models without pre-computed camera parameters. The intrinsic and extrinsic camera parameters are automatically discovered via joint optimisation during training of the NeRF model. The authors in [START_REF] Jeong | Self-Calibrating Neural Radiance Fields[END_REF] consider more complex non-linear camera models and propose a new geometric loss function to jointly learn the geometry of the scene and the camera parameters. Solutions are also proposed in [START_REF] Chen | MVSNeRF: Fast Generalizable Radiance Field Reconstruction from Multi-View Stereo[END_REF] and [START_REF] Chibane | Stereo Radiance Fields (SRF): Learning View Synthesis for Sparse Views of Novel Scenes[END_REF] to enable faster inference as well as using a sparser set of input views, and to enable generalization to new scenes.

Our motivation here is to be able to capture or reconstruct light fields with a very large field of view, in particular 360 • . We focus on the question: how do we extract omni-directional information and potentially benefit from it when reconstructing a spherical light field of a large-scale scene with a nonconverged camera setup?

To address this question, we propose a method for learning a 360 • neural radiance field from omni-directional images captured with fisheye cameras. We adapt the pinhole camera model of NeRF to a general camera model that fits omnidirectional fisheye lenses. Finally, we extend our approach to allow accurate camera parameter estimation (intrinsic and extrinsic) for omni-directional fisheye lenses. To evaluate our approach, we render photo-realistic panoramic fisheye views from 2 Blender scenes: an indoor "Classroom" scene and a larger scale scene "Lone Monk" of an atrium surrounded by buildings. With these datasets, we first evaluate how spherical sampling improves the performance of view synthesis compared to planar sampling. We prove that our model can learn the fisheye distortion from scratch with ground truth camera pose. We also assess the camera extrinsic parameter estimation, with a noisy initialization which simulates the case where the camera parameters are imperfect or measured with error. Finally, we train and evaluate our model on two real scenes captured by fisheye cameras.

NERF: BACKGROUND

In this section we briefly introduce the method of synthesizing novel views of complex static scenes by representing the scenes as Neural Radiance Fields (NeRF) [START_REF] Mildenhall | Nerf: Representing scenes as neural radiance fields for view synthesis[END_REF].

In NeRF, a scene is represented with a Multi-Layer Perceptron (MLP). Given the 3D spatial coordinate location X = (x, y, z) of a voxel and the viewing direction d = (θ, φ) in a scene, the MLP predicts the volume density σ and the viewdependent emitted radiance or color c = [R, G, B] at that spatial location for volumetric rendering. In the concrete implementation, X is first fed into the MLP, and outputs σ and intermediate features, which are then fed into an additional fully connected layer to predict the color c. The volume density is hence decided by the spatial location X, while the color c is decided both X and viewing direction d. The network can thus yield different illumination effects for different viewing directions. This procedure can be formulated as

[R, G, B, σ] = F Θ (x, y, z, θ, φ), (1)
with Θ = {W i , b i } being weights and biases of the MLP. The network is trained by fitting the rendered (synthesized) views with the reference (ground-truth) views via the minimization of the total squared error between the rendered and true pixel colors in the different views. NeRF uses a rendering function based on classical volume rendering [START_REF] Kajiya | Ray Tracing Volume Densities[END_REF]. Rendering a view from NeRF requires calculating the expected color C(r) by integrating the accumulated transmittance T along the camera ray r(t) = o + td , for o being the origin of cast ray from the desired virtual camera, with near and far bounds t n and t f . This integral can be expressed as

C(r) = t f tn T (t)σ(r(t)c(r(t), d)dt, (2)
where T (t) = exp(-t tn σ(r(s)ds). In practice, the integral is numerically approximated by sampling discretely along the ray.

While the original NeRF in [START_REF] Mildenhall | Nerf: Representing scenes as neural radiance fields for view synthesis[END_REF] requires the knowledge of the camera pose parameters, a pose-free solution has been introduced in [START_REF] Wang | NeRF-: Neural Radiance Fields Without Known Camera Parameters[END_REF] which estimates intrinsic and extrinsic camera parameters while training the NeRF model.

Assuming a pinhole camera model, the camera parameters can be expressed with the camera projection matrix

P = KR[I| -t]. (3)
I is a 3 identity matrix and K is the camera calibration matrix

K =   f x 0 c x 0 f y c y 0 0 1   , (4)
with the intrinsic camera parameters f x and f y as the focal length, which are identical for square pixels, and c x and c y as the offsets of the principal point from the top-left corner of the image. The extrinsic camera parameters in Eq. ( 3) contain the rotation and translation of the camera with respect to a 3-D world coordinate system and are expressed by the 3 × 3 rotation matrix R and the 3 × 1 translation vector t.

When these camera parameters are unknown, they need to be estimated. For camera rotation, the axis-angle representation is adopted in NeRF-:

Φ := αω, Φ ∈ R 3 ( 5
)
where α is the rotation angle and ω is the unit vector represent the rotation axis. Φ i can be converted to the rotation matrix R using the Rodrigues' formula [START_REF] Wang | NeRF-: Neural Radiance Fields Without Known Camera Parameters[END_REF]. With such parametrization, the i-th camera extrinsics can be optimized by searching for the parameters of Φ i and t i . To render the color of the m-th pixel p i,m = (u, v) from the i-th camera, we cast the ray r i,m from the image plane as

r i,m (t) = o + td, (6)
where

d = R -1 i   (u -c x )/f x -(v -c y )/f y -1   (7)
and o = t i using the current estimation of camera parameters

π i = (f x , f y , c x , c y , Φ i , t i ). (8)
Then, the calculated coordinate and direction of the sampled ray are fed into the NeRF model. The current estimated color value of the pixel is rendered by Eq. ( 2) and can be compared with the ground-truth color value by estimating the squared error. Finally, the parameters Θ of the NeRF model and the camera parameters π i are optimized jointly by minimising the photometric loss as described in [START_REF] Wang | NeRF-: Neural Radiance Fields Without Known Camera Parameters[END_REF] and [START_REF] Lin | BARF: Bundle-Adjusting Neural Radiance Fields[END_REF]. to omni-directional images, the key is to recover the true ray direction of pixel coordinates on the image plane. In order to do so, we need to model the projection of the fisheye lens onto the image plane. We can model these projections as relations between r d , the radial distance from the image center to the distorted image point, and θ, the incoming angle measured from the lens axis as depicted in Fig. 2. For the specific "equisolid" projection, the radial distance can be calculated as

r d = 2f • sin ( θ 2 ). (9)
Different projections exist for panoramic fisheye lenses [START_REF] Thoby | Photographic lenses projections: computational models, correction, conversion[END_REF]. In order to unify the description, we consider the sum of the 4 first terms of the infinite series as an odd-order polynomial representation of the incoming ray direction θ defined as

θ = θ d + k 1 θ 3 d + k 2 θ 5 d + k 3 θ 7 d , (10)
where

θ d = arctan ( r d f ), (11)
f is the focal length and k 1 , k 2 and k 3 are coefficients to fit the different fisheye projections. Given a pixel p with its pixel coordinates (u, v) on the image plane, the radial distance r d can then be expressed as

r d = (u -c x ) 2 + (v -c y ) 2 , (12)
where (c x , c y ) are the coordinates of the principle point. The actual direction of the ray of pixel p in the camera coordinate system can then be expressed as a vector d c = (x, y, z) T with

x = sin (θ) • (u -c x ) (13) y = sin (θ) • (v -c y ) (14) z = cos (θ). (15)
By applying a rotation and translation using the extrinsic parameters, the ray direction in world coordinates is then defined as

d = [R -1 |t]d c . (16)
The rotation matrix R can be parameterized by the axisangle representation Φ as described in Section 2.

When these camera parameters are not known, e.g. when using real world captures, they need to be estimated. For this,

Sample planes Sample spheres

Image plane

Optical axis

Fig. 3. Planar sampling vs. spherical sampling.

we follow the approach of NeRF-and SCNeRF [START_REF] Jeong | Self-Calibrating Neural Radiance Fields[END_REF] where the estimated parameters are:

π i = (f x , f y , c x , c y , Φ i , t i , k 1 , k 2 , k 3 ), (17)
i.e., extended by the parameters k 1 , k 2 and k 3 which approximate the projection as in Eq. [START_REF] Mildenhall | Nerf: Representing scenes as neural radiance fields for view synthesis[END_REF].

Assuming that the specific fisheye projection model is unknown, we initialize (k 1 , k 2 , k 3 ) to be (0, 0, 0), i.e., the pinhole perspective camera model. We then optimize the coefficients of the polynomial to fit the specific fisheye projection by minimizing the photometric loss as mentioned in Section. 2. With different combinations of (k 1 , k 2 , k 3 ) the polynomial distortion model can approximate fisheye lenses or mirrors with FOVs of up to 360 • .

Spherical sampling

In the original NeRF model, the pixels are rendered by sampling 5D coordinates (location and viewing direction) along the camera rays. For a camera ray r(t) = o + td with near and far bounds t n and t f , where o is the origin of ray and d is a vector giving the ray direction. The interval [t n , t f ] is originally partitioned into N evenly-spaced bins, and one sample is then uniformly drawn at random from each bin. Such a sampling pattern is equivalent to placing sampling planes parallel to the image plane as depicted in Fig. 3.

For fisheye lenses, however, the rays on the border are more sparsely sampled than the rays close to the optical axis, and the spacing tends to infinity when the angle of the incidence ray approaches 90 • (see Fig. 3). As the sampling is critical in the neural representation of the radiance field, such large bins have a high chance to skip thin objects in the scene and cause artifacts, i.e., resulting in degraded image quality.

Hence, we use a sampling on a sphere instead of the sampling on planes to resolve the above issue. For a ray direction d = (x, -y, -1) T , we define the normalized direction as

d n = ( x d , - y d , - 1
d ) T (18)
With this spherical sampling scheme, the rays at the border of the scene projected on an image have the same importance as the rays in the center. Thus, the spherical sampling offers a more uniform sampling of the whole scene. We therefore define the near and far bounds to be concentric spheres with radius t near and t f ar centered at the projection center. Similarly, we partition [t near , t f ar ] into N evenly-spaced bins. Hence, the bins for rays in all the directions are equal as shown in Fig. 3, and a ray is now expressed with

r(t) = o + td n . ( 19
)
Please note that the spherical sampling is not only preferred for fisheye lenses, but also improves the image quality for any wide-angle lenses.

EXPERIMENTAL RESULTS

Dataset

The dataset consists of four scenes, two synthetic scenes from the Blender demo "Classroom" (by Christophe Seux.) and "Lone Monk" (by Carlo Bergonzini) and two real scenes, the FTV-indoor-sit dataset captured in a big meeting room [START_REF] Maugey | Ftv360: a multiview 360 • video dataset with calibration parameters[END_REF] and a densely sampled scene in an office room, both captured with Samsung Gear360 cameras. Fig. 4 shows screenshots of the test scenes.

First, we deploy virtual fisheye and perspective cameras in the synthetic 3D scenes to create a dataset that samples the 3D scenes from different viewpoints. A pair of virtual cameras facing forward and backward are placed in a bounded cuboid at each vertex of the spatial grid to get full 360 • FOV. By subdividing the edge of the cuboid, we use different sampling of the space and therefore with a different number of cameras. In particular, we investigated two different sampling grids, namely 6x6x3 (108 view points) and 9x9x3 (243 view points) in each scene with fisheye and perspective camera pairs, which are our training datasets. Furthermore, we render a smooth path of 400 intermediate views in the sampled 3D space by varying rotation and translation for both camera types, which are our test datasets. Both training and test images have a resolution of 600x600 pixels. The fisheye views and perspective views are rendered with equisolid projection of 180 1. PSNR values obtained with different sampling methods and synthetic datasets. "FE" and "WA" denote fisheye and wide-angle perspective rendering, respectively. FOV, respectively. We demonstrate the performance of Omni-NeRF compared to SCNeRF using the synthetic datasets. Finally, we show that our model is capable of reconstructing real scenes. For configuration details of the dataset and camera setup, please refer to the provided supplementary material.

Fisheye and Spherical Sampling

Our first experiment aims to evaluate how spherical sampling improves the performance of view synthesis compared with planar sampling. For this, we train Omni-NeRF with synthetic data using ground truth camera parameters and different sampling schemes.

We use the hierarchical sampling strategy of NeRF and consider training and rendering with planar sampling of 128 and 256 coarse samples along the rays. For spherical sampling we use 128 coarse samples. Then, we allocate 128 fine samples biased towards the relevant parts of the volume for all the cases. The reported PSNR in Table 1 are averaged values over 400 test views of fisheye and perspective cameras. The table shows that spherical sampling outperforms the planar sampling for fisheye rendering with much fewer samples. For wide-angle perspective rendering, the spherical sampling achieves similar performance with only half the number of samples.

Fig. 5 shows small patches of rendered views with synthetic data. The rendered views with planar sampling show typical artifacts close to the border while the spherical sampling with same or a lower number of samples resolves the issue.

Fisheye distortion estimation

In our second experiment, we show that our model can learn the fisheye distortion from scratch using ground truth camera pose. And we also show that our model can optimize the camera parameters using noisy camera pose as initialization. We train our model and also SCNeRF on "Classroom" and "Lone Monk" datasets. We first investigate the estimation of radial distortion with different models, so we fix the extrinsics and intrinsics to their ground truth values and we initialize both models to correspond to pinhole projections. Fig. 6 shows how our model fit to fisheye projection.

We evaluate our model with the average PSNR of the test

We then add uniformly distributed random noise to the ground truth camera pose as initialization and optimize the noisy pose jointly with the projection model. we add random rotation angle ∆ θ ∼ U (-7.5, 7.5)(rad) along random axis, and translation ∆ t ∼ U (0.075, 0.075)(meter) along (x,y,z) axes for each training view. We train our model and SCNeRF with the same noisy initialization on the synthetic datasets. We report the result of different scenes using ground truth pose and noisy pose in Table 2 and visualize the projected ray error in Fig. 7. The result shows that our model, with the proposed polynomial representation of ray direction, can estimate the fisheye distortion accurately, with ground truth or noisy camera poses, while SCNeRF fails to learn the correct projection.

We finally train our model on real captured 360 data. The model has been initialized with imperfect camera pose parameters and projection model. Fig. 8 shows exemplary the reference views and rendered views using our model with 2 different scenes.

Discussion

We found that NeRF-and other differentiable camera models have a limited search range of camera parameters. For our non-planar and non-converging camera configurations, rough initialization is necessary. Due to the peculiarities of panoramic fisheye lenses, the camera usually captures some of the pixels of the camera mount or the photographer, leading to problems of inconsistency between frames, which have an impact on the scene reconstruction and parameter estimation.

CONCLUSION

We proposed Omni-NeRF, a NeRF-based method that reconstructs the scene with 360 • information from panoramic fisheye imaging. We optimized the parameterization for the estimation of wide-angle fisheye distortion and we stressed the importance of sampling in this case. We have shown that the spherical sampling improves the performance when training with panoramic fisheye or wide-angle perspective images. Furthermore, We have shown that our parametrization is better suited than the one of SCNerf when using panoramic fisheye lenses. We have also shown that NeRF can be used to reconstruct scenes with 360 • panoramic information, using a non-converged camera setup. Finally, we demonstrated that our method is also applicable to data collected with real 360 cameras, and that our model successfully reconstructs the scene. Since we are dealing with the problem of reconstructing large-scale scenes, the question of how to optimally deploy cameras in 3D space is worth further exploration.

  (a) 360 • fisheye images (b) Spatial camera grid

Fig. 1 .

 1 Fig. 1. Space sampling with 360 • cameras (fisheye camera pairs) in a spatial grid.

3 .Fig. 2 .

 32 Fig. 2. Distorted image projection.

Fig. 4 .

 4 Fig. 4. Overview of all the scenes

Fig. 5 .

 5 Fig. 5. Rendered views with planar (P) and spherical (S) sampling with different numbers of inputs, with the "Classroom" scene. (GT denotes ground truth, PSNR is shown on each sub-figure).

Fig. 6 .

 6 Fig. 6. We initialize the projection as pinhole camera and start to optimize the projection model. The figures show how our model (first row) and SCNeRF (second row) fit the fisheye projection during training. set and the mean absolute error (MAE) of angles e θ between estimated ray directions d and ground truth ray directions d of all valid pixels in the fisheye view, given by e θ = arccos ( d • d d d ).(20)

Fig. 7 .

 7 Fig. 7. Error of estimated ray directions. Please note that the scales of the two figures are different.

Fig. 8 .

 8 Fig. 8. Rendered view with Omni-NeRF trained for the FTVindoor-Sit [8] dataset and our office dataset. The model has been initialized with imperfect camera pose parameters and projection model.

  • FOV and perspective projection of 119 • .19 25.38 25.04 spherical(128) 28.69 25.18 28.45 25.03

	sample method	Classroom	Lone Monk
	(samples)	FE	WA	FE	WA
	planar(128)	22.46	24.77	15.13	24.68
	planar(256) 24.78 25Table

Table 2 .

 2 Comparison between SCNeRF and Omni-NeRF in terms of fisheye distortion estimation. We report the average PSNR of the smooth-path test set and the mean absolute error of estimated ray direcitions after a same amount of iterations.

		Classroom	Lone Monk
	Method	PSNR MAE PSNR MAE
	SCNeRF (gt. pose)	13.04	0.21	12.94	0.28
	Ours (gt. pose)	27.12 0.001 26.55 0.001
	SCNeRF (noisy pose) 13.74	0.13	13.92	0.21
	Ours (noisy pose)	21.65 0.004 24.68 0.003

• fisheye

ACKNOWLEDGEMENT

This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 956770.


Claire Bonnard

Julien Calmand

Jean-François Giret

International mobility of French Ph.D.s

Keywords: International mobility, higher education, academics, academic employment

This research investigates the determinants of international mobility of Ph.D.s upon graduation. It is based on a survey of 400 young Ph.D.s who graduated in France between 2003 and 2008, half of whom were still abroad more than six years after graduating. The impacts of personal, occupational and scientific characteristics on the successive mobility decisions after graduating were scrutinized. The findings show that motivations for going abroad relate principally to the difficulty in finding employment on the French labour market. The choices as to longer term expatriation are more fragmented and can be less readily unravelled. By contrast, readiness to return to France is often accounted for by family factors.

Introduction

The expatriation of graduates prompts a good deal of debate in developing and developed countries alike. It is often associated with the brain drain and entails a danger for countries that they will lose the skills required for their economies to be competitive. For expatriates, going abroad may by contrast turn out to be a real opportunity in terms of their careers [START_REF] Saint-Paul | The Brain Drain: Some Evidence from European Expatriates in the United States[END_REF]. The issue is of particular concern for Ph.D.s because in many OECD countries, certain scientific disciplines have largely encouraged people to travel abroad in particular for post-doctoral studies. According to an international survey implemented by an European consortium (IDEA consult 2013), around 30% of researchers were mobile for 3 months or more in the last 10 years following their Ph.D. graduation. While some young Ph.D.s return to their home country upon completing their post-doctoral courses, others remain abroad and join research centres, universities or firms in their host countries. However, there is little information about the numbers of expatriate Ph.D.s and their motives and career plans. By definition, surveys conducted in France such as the 'Generation' surveys of the Centre d'études et de recherches sur les qualifications (Céreq) do not question young Ph.D.s abroad. A 1996 Céreq estimation put the number of Ph.D.s still abroad three years after graduating at 7% [START_REF] Martinelli | A Brain Drain among Young PhDs: Mirage or Reality[END_REF]. However, the subsequent boom in postdoctoral courses, the growing difficulties for Ph.D.s in France on the labour market, and the growing internationalization of the scientific labour market all suggest that their numbers are currently underestimated. The report by the Observatoire de l'Emploi Scientifique (2009), taking up the findings of a CEPI researcher for the United States, is nuanced about the importance of expatriation for French researchers. The number of French Ph.D.s having emigrated to the United States between 1991 and 2000 and currently doing research there amounts to less than 1.5% of French researchers. Although this figure is up on that for the 1980s, France reportedly has the lowest ratio of any European country [START_REF] Tritah | Fuite des cerveaux européens: que nous disent les statistiques américaines?[END_REF]. Apart from the actual number of expatriate Ph.D.s, there is also the question of the motives for going abroad and future career plans. In public debate in France, there are two partly contradictory lines on these issues that bring out the limitations of higher education and the research sector. The first often concludes that the French system is unable to hold on to and make use of its finest minds1 . For various reasons France supposedly has difficulty in keeping its star scientists after training them [START_REF] Kohler | Les expatriés de l'enseignement supérieur français aux Etats-Unis[END_REF]. As suggested by [START_REF] Saint-Paul | The Brain Drain: Some Evidence from European Expatriates in the United States[END_REF] in the French case, the economic consequences of the brain drain could be considerably more negative if the expatriates are the most talented individuals. These key individuals are supposed to play a decisive role in the country's potential for growth and innovation. The second line of argument criticizes what is seen as an overly theoretical doctoral education in France that is disconnected from the needs of the knowledge economy. The system allegedly fails to provide highly qualified personnel capable of developing the national capacity for innovation. However, it may also be asked to what extent international mobility is related to the difficulties of Ph.D.s finding a place in the French labour market [START_REF] Calmand | L'éclatement des parcours professionnels des diplômés de doctorat en France[END_REF]. Unemployment for recent Ph.D. graduates in France is sensibly higher than in other developed countries [START_REF] Harfi | Les difficultés d'insertion professionnelle des docteurs[END_REF]. The scientific literature addresses these issues on the basis of migration theory, focusing especially on push and pull factors that might explain Ph.D.s' individual mobility motives [START_REF] Dongbin | International Doctorates: Trends Analysis on their Decision to Stay in US[END_REF]. This approach is favoured in this study, which aims to understand the determinants behind foreign mobility after obtaining a Ph.D. in France and then returning to France or remaining abroad three years after graduating. This research looks to provide some answers on the basis of a survey of 400 young Ph.D.s in France who graduated between 2003 and 2008 and having been abroad for more than three months after Ph.D. graduation. If the first mobility experience is generally a post-doc position, it can also correspond to other labour contracts. Our paper mainly focuses on academic mobility although early international mobility (prior and during the Ph.D.) may influence the subsequent mobility. The first section uses a review of the literature on the motives that may affect the international mobility of Ph.D.s, notably in the French case. Section 2 presents the survey and looks at factors that might explain the decision of young Ph.D.s to move abroad and to return. The third section concentrates on the possible trajectories of young Ph.D.s having moved abroad. The aim is to understand why some of them decide to stay abroad longer than they initially intended.

An analysis of the determinants of international mobility

Compared with other areas of employment of highly qualified personnel, in research occupations, international mobility is considered to be the norm for integration and occupational socialization [START_REF] Mahroum | Highly Skilled Globetrotters: Mapping the International Migration of Human Capital[END_REF]. Unlike in other sectors such as trade and industry, financial motives only partially drive mobility in this area. Scientific considerations and the prestige of the host institutions appear to prevail. However, it may be thought that the reasons for this type of mobility remain fairly diverse for young Ph.D.s looking for steady work on the labour market. For some of them, the aim is to return to their home countries and find tenured employment on the academic labour market [START_REF] Musselin | Towards a European Academic Labour Market? Some Lessons Drawn from Empirical Studies on Academic Mobility[END_REF]). Doing a post-doc, implying in most instances spending time abroad, is thought of as a 'near' requirement in some scientific disciplines for young Ph.D.s to get into research and enhance their résumés. Occupational and scientific interest and the absence of a buoyant labour market in France are reasons for such mobility. The influence of various professional or personal factors may, however, change over the course of the young Ph.D.'s career and explain a return to France or continued expatriation. Comparative studies of the insertion of young Ph.D.s in various developed countries emphasize how sluggish the French labour market is [START_REF] Auriol | Careers of Doctorate Holders: Analysis of Labour Market and Mobility Indicators[END_REF][START_REF] Harfi | Les difficultés d'insertion professionnelle des docteurs[END_REF]. Whereas the unemployment rate of young Ph.D.s three years after graduating was less than 2% in the United States in 2003, it stood at more than 10% over almost the same period in France. There are many explanations for these hardships and they are not exclusive. For one thing, as in many countries, young Ph.D.s wish to embark on academic careers; the Céreq surveys in France report that 70% of them give precedence to an academic career in the years after completing their Ph.D.s. However, unlike what happens in many countries, in France researchers or teaching and research staff find academic tenure very early on, in the few years after completing their Ph.D.s, and very seldom later on [START_REF] Musselin | Perspectives pour une analyse sociologique des marchés du travail universitaire[END_REF]. For another thing, recruitment in the non-academic sector, in R&D or outside R&D, is not favourable to young French Ph.D.s who are often in competition with graduates from the grandes écoles. This is particularly so in R&D where corporations prefer to recruit young engineers who are thought to be more versatile [START_REF] Beltramo | The Recruitment of Researchers and the Organization of Scientific Activity in Industry[END_REF]. Lastly, in other sectors in France, unlike in countries such as Germany, obtaining a Ph.D. is not seen as a prestigious achievement that is recognized in the career structure. The difficulties encountered on the French labour market are not the only professional reasons that motivate young Ph.D.s to be internationally mobile. Experience abroad is also a way of enhancing their scientific and non-scientific skills and networks, which [START_REF] Bozeman | Scientists' Collaboration Strategies: Implications for Scientific and Technical Human Capital[END_REF] define as scientific and technical human capital, including in it in particular the social skills required in research and innovation circles. In addition to providing an opportunity to perfect their foreign language skills, generally in English, post-doctoral periods allow young Ph.D.s to experience other working environments and to develop new research themes, new methods, new tools, and new empirical areas of study. By joining what are sometimes very different forms of research organization, they have to cope with new working environments and often autonomously. [START_REF] Kyvik | International Mobility among Nordic Doctoral Students[END_REF] identify three factors in the case of Norwegian Ph.D.s who went abroad to do research courses: direct aid in their research in terms, for example, of their fields of enquiry, the acquisition of new skills and knowledge, and more personal development such as proficiency in a foreign language or self-confidence. However, the question arises as to how such mobility is managed by employers and the public sector in these different countries. The contribution of these new skills upon returning to France is a factor that may encourage innovation and research if incentives to leave and then to return are consistent [START_REF] Cañibano | La gestion de la mobilité professionnelle des chercheurs : un défi pour les poli tiques de recherche et d'innovation[END_REF].The boom in post docs is not uniform, however, across the various disciplines and forms part of the scientific and technological development specific to each sector. Thus the transformation of research in biology, with the development of biotechnologies and research/industry relations has promoted the emergence in France of non-permanent jobs in research laboratories in the form of post docs [START_REF] Brunet | Le « post-doc » : transition professionnelle et précarisation du travail des scientifiques[END_REF]. Such post docs have become a requirement in these disciplines before steady employment in research circles can be found. Moreover, the question of the post-doc signal for access to academic careers is also important. The prestige of the host institution is a factor that has drawing power and may also explain the motives for going abroad or for not returning to France after the experience. It is decisive in scientific production, for example, through membership of prestigious research centres or partnerships in publications. Capacities for research and innovation in the host country will be decisive. Forced mobility of young Ph.D.s is often related to the difficulty in finding employment in their home countries upon graduating [START_REF] Morano-Foadi | Scientific Mobility, Career Progression, and Excellence in the European Research Area[END_REF]. It is important to look into the consequences of a post-doc stay abroad for access to employment in France. Despite the advantages in terms of signal and human capital, going abroad may contribute to the severing of the young Ph.D.s' ties with the national employment market and so to the loss of their social capital. This is related in part to the characteristics of the academic sector in France, where most recruitment is done locally in the form of lecturing positions [START_REF] Godechot | Comment les docteurs deviennent-ils directeurs de thèse?[END_REF]. Loss of contact may mean young researchers who have been abroad are deprived of valuable information about employment opportunities. Research findings in the academic sector [START_REF] Bonnal | Determinants of Access to Academic Careers in France[END_REF] and the private sector [START_REF] Recotillet | PhD Graduates with Post-doctoral Qualification in the Private Sector: Does it Pay Off?[END_REF]) relativize, though, the adverse effects of post docs on the careers of researchers or teaching and research staff in France and even indicate positive effects in some disciplines.

3. The motivations for young people to go abroad: lessons from a survey on Ph.D. graduates in France

The empirical part of this research is based on a survey of 400 Ph.D.s across all disciplines having been abroad for occupational reasons for more than three months. They obtained their Ph.D. in France between 2003 and 2008 and were surveyed in the second semester 2012.2 Three years after Ph.D. graduation, 57% of them are abroad. At the time of survey, 41% are still living abroad. 3 Part of the questionnaire is related to the determinants of international mobility and the skills developed by the Ph.D.s in their various jobs. The survey also collated information about the individual and social characteristics of young Ph.D.s, their disciplines, 4 publications at the time they graduated, financing, career path and geographical background upon completing their Ph.D. Information on the characteristics of the host country was also included in the data base for a better understanding of the mobility process. This survey is valuable in describing the process of international mobility after the Ph.D. but also for identifying the main factors explaining that mobility. The 400 Ph.D.s who responded to the survey had lived abroad for professional reasons for more than three months on at least one occasion. This mobility may initially correspond to post-doctoral position; it is the case for 80% of them. However, some of them are directly recruited in permanent position. As [START_REF] Kelo | Toward Improved Data on Student Mobility in Europe: Findings and Concepts of the Eurodata Study[END_REF] emphasize, the different types of international mobility are complex to define and do not provide the same measurement depending on whether, for example, we are interested in foreign students or students who experience international mobility in the course of their higher education. Our survey concerns Ph.D. students who graduated in France and then spent time abroad. Among the foreign students, only those who did not go back to their home country were kept in the sample, which amounted to about 6% of the final sample. On the contrary, foreign students who completed their Ph.D. in France and returned to their home country were excluded from the analysis. It corresponds to return mobility associated with specific strategies [START_REF] Teichler | Academic Mobility and Migration: What We Know and What We Do Not Know[END_REF]. Table 1, on Ph.D.s who were working abroad three years after graduating, proposes a first glimpse of the diversity of reasons for going abroad. The difficulties of young Ph.D.s on the labour market stands out as the main reason for going abroad. Leaving is explained for more than two in three young Ph.D.s by difficulties in finding a position in France at the start of their careers. 5 Next, the need to obtain professional experience abroad is a factor for 66% of Ph.D.s. Scientific reasons are also involved in the decision to go abroad for more than one in two young Ph.D.s, but they do not feature as the main reason. These initial observations nuance the hypothesis of a brain drain, with expatriation being for most young Ph.D.s a default choice, often forced on them by the shortage of jobs in the French labour market for higher education and research. By construction the survey provides more precise information about the geographical position of Ph.D.s three years after graduating and then at the time of the survey. Three years after graduating 57% of Ph.D.s in the sample were living abroad, and more than one in three of them in the USA and the UK. For Ph.D.s born abroad, 76% were no longer in France after three years. At the survey date, on average six years after graduating, about half of Ph.D.s were expatriates (62% for those born abroad). The occupational status of these young people was rather favourable. Close to 92% of young Ph.D.s were in employment at the date of the survey. Stability in that employment differed, however, even if it is difficult to compare employment contracts between different countries. Fewer than one in two young people abroad at the time of the survey had any kind of tenure compared with 80% for those Ph.D.s who had returned to France. The share of academic employment was slightly greater for Ph.D.s who had returned to France (81%) than for others (68%), who where by contrast more often employed in R&D. We characterize young people's academic profiles and motivations in terms of their geographic mobility. The survey identifies three groups: young people who returned to France within three years of graduating, those abroad three years after graduating but who subsequently returned to France, and expatriates, those still abroad at the date of the survey. The first group comprises Ph.D.s who had a comparatively short stay abroad. They have a fairly specific profile in terms of individual characteristics and academic and professional careers. Their academic career path is one in which the post-doc is just a temporary stage before taking up steady employment as a researcher or teaching and research staff. Most graduated in mathematics and physics and typically had a higher number of publications at the time they graduated, especially in foreign journals. More than half prepared their thesis work in three years and 90% in less than four years. They were also the most numerous at the time of graduating to plan working at university or in research and to have been employed as teaching staff during their Ph.D.s. A further indication of their wish to return to France rapidly is that most had applied for accreditation by the Conseil National des Universités (CNU)6 after their thesis and had been almost systematically accepted.

The second group is made up of Ph.D.s who were still abroad three years after graduating. Their academic profile is similar to that of the previous group.

Most received some form of public financing for their Ph.D. and did short theses, but more commonly in the life and earth sciences. Again very many of them, almost 80%, planned to work in academia or in research. They had a high level of scientific output, too, comparable with the first group in terms of the number of publications but, paradoxically, many had published less often in foreign journals. Very many of them had applied for national accreditation after graduating, which again was indicative of their wish to remain in France.

The third group, Ph.D.s still abroad at the time of the survey, stands more clearly apart from the previous ones. First the proportion of Ph.D.s born abroad7 is higher than in the other groups, which can be understood by the greater propensity to mobility of young people who have already had experience of mobility. In addition, they are more often male and the geographical areas frequented are more diverse (the proportion of Ph.D.s in Europe and North America is lower). Their career paths are less academic. Fewer than half had held temporary teaching positions, they had fewer publications at the time of graduating, and 20% fewer had done post-doc work. At the time of graduating, they were more numerous to want to work in research in business and their research positions were less often in the public sector. Only one in three of this group applied for CNU accreditation after graduating versus more than 70% in the other groups. In terms of their occupational position, three years after graduating, and at the time of the survey, there were as many of them in employment as their counterparts in France but far fewer in academic employment and fewer in tenured positions, being more often in non-tenured employment and post-doc work.

The effect of the different characteristics on the process of Ph.D. mobility can be tested more stringently by a ceteris paribus analysis. We analysed living and working abroad three years after graduating and then still being abroad at the survey date on the basis of individual characteristics and motivations and the host country (Table 2), and the characteristics of the host country (Table 3).

The results of estimations concerning individual characteristics (Table 2) emphasize the difficulty in predicting the movements of young Ph.D.s living abroad. Certain information may, however, provide an idea as to the motivations behind their chosen paths. Not applying for CNU accreditation upon graduating as a first step to securing an academic position in France seems to reveal that young Ph.D.s wish to be mobile. They are more often found abroad three years after graduating or at the survey date. The role of publications, which may be a signal of the Ph.D.s scientific quality, shows that Ph.D.s who had published little if at all at the time of graduating were slightly more likely to be abroad at the date of the survey. In other words, expatriation seems to concern Ph.D.s who published little. The discipline-related effect can be explained by professional strategies in the exact sciences, which are overrepresented in the sample. They are far more likely to experience international mobility but for a shorter period than other Ph.D.s. Conversely, our findings show that Ph.D.s in the human and social sciences are more likely to be abroad still three years after graduating. It might have been expected that the host country would have an impact on expatriation but this is virtually never the case excepted for UK. For example, the United States does not seem to hold on to French Ph.D.s any more than other countries. Individual characteristics are also barely discriminatory ceteris paribus. 10 Children of managerial-level parents were slightly more likely to be abroad three years after graduating, which may be because of an effect associated with financial resources or cultural capital, but the effect was no longer significant at the date of the survey. The effect of the Ph.D.'s nationality is not significant, all else being equal. Gender differences do not affect mobility strategies either, whereas it might have been hypothesized that men would be abroad for longer. Initial motives for going abroad seem, however, to determine the final situation more closely. Ph.D.s whose motivation was mainly to gain experience abroad in their career strategy are less likely to be expatriates. The result is the opposite for those Ph.D.s whose motives were the difficulty in finding a position in France and to lesser extent career advantages abroad. The difficulties that prompted them to leave France after their Ph.D. are also a curb on returning at the time of the survey. By contrast, scientific conditions abroad do not seem to influence Ph.D.s' choice to remain abroad. In addition, going abroad for post-doctoral position have any impact on the duration of expatriation. The results presented in Table 3 summarize the impact of the host country characteristics. Variables relating to research, innovation, or education in the host country have replaced the countries in the previous estimation. As these variables are closely correlated with each other, they were introduced separately but jointly with the individual characteristics. In accordance with the literature on the brain drain [START_REF] Docquier | Globalization, Brain Drain and Development[END_REF], the results highlight the effect of certain characteristics of the host country. For long stays, expatriation is more important when innovation and R&D are developed in the host country and the country has a substantial tradition of immigration. The results also highlight the hypothesis of upward mobility of Ph.D. graduates [START_REF] Teichler | Academic Mobility and Migration: What We Know and What We Do Not Know[END_REF], they move to a more favourable economic and scientific country. It is interesting to observe, however, that none of these host-country-related variables significantly accounts for Ph.D.s staying abroad three years after graduating. In other words, only comparatively long expatriation (six years) seems to depend on host country characteristics.

Desired mobility versus actual mobility

One of the challenges for the countries of origin of Ph.D.s is to come up with incentives for them to return after their experience abroad. The survey makes it possible to compare the mobility project as it was initially intended and the actual mobility of young Ph.D.s. They were asked more specifically about how long they had planned to stay abroad at the time when they first left.11 100 Note: 83% of Ph.D.s who went abroad changed their initial plans when the move was influenced by the desire to gain experience abroad (versus 74% on average, for all Ph.D.s who went abroad).

Table 4 shows that expectations were quite consistent with the position at the date of the survey since Ph.D.s who had returned to France by that date had anticipated a shorter median length of stay abroad than expatriates of 24 versus 36 months. Tables 5 and6 provide information on the causes that may explain a change of plan by young Ph.D.s by identifying those who stayed abroad for longer than they expected to when they first left. On average, Table 5 shows that 74% of young expatriates at the date of the survey had changed their plans and had therefore spent longer abroad than initially planned. However, this rate changes with the motivations for leaving: it is even higher when they left to gain experience abroad (83%). However, it is lower when they left for personal reasons (64%). Moreover, Table 6 shows that expatriate Ph.D.s tend to remain abroad longer than planned when the difficulties of returning to France can be explained by difficulties in finding employment. As in the previous section, the effect of these variables and the effect of individual characteristics can be analysed ceteris paribus. We examined the plans of young Ph.D.s before leaving in two steps. A linear regression of the expected time abroad was used first to identify the factors that may explain how the plan to move is formed (Table 7 column 1). Then a probit model was estimated to explain the change from the initial plan. The endogenous variable took the value 1 if the Ph.D. changed plans and stayed abroad longer than planned, and 0 otherwise (Table 7 column 2). In this instance, only Ph.D.s working abroad were concerned by the question. The findings show first that individual characteristics and host countries have little impact, as before. Motivations, on the other hand, do seem to have more structuring effects on the hoped for duration of stay as on staying abroad longer than planned. Ph.D.s hoping to work in research at the time of graduation and those who left to gain experience abroad expected a shorter stay abroad. Note: 83% of Ph.D.s who moved and were resident abroad at the survey date changed their initial plans when continued expatriation was motived by the difficulty in finding a position in France (versus an average of 74% for all Ph.D.s who went abroad). It can be supposed that these Ph.D.s went abroad primarily to enhance their résumé and wished to return to France rapidly, which is consistent with the need not to become cut off from the national networks in order to find academic employment in France. Conversely, Ph.D.s with no publications at the time of graduating anticipated staying abroad longer as did those who left for personal reasons. Those motivations also affected the change to their plans. Going abroad to gain experience or to look for better scientific conditions may lead on to remaining slightly longer than planned whereas personal reasons or career advantages prompt them not change their career plans. Lastly expatriate Ph.D.s also modify their plans when they think that it would be difficult for them to find a position in France or because they have found academic work abroad.

Conclusion

This study investigated the motivations for international mobility of young Ph.D.s in France. If student mobility is generally well documented, few are known in the literature about the mobility on researchers and scholars [START_REF] Cavalli | Preface[END_REF].The boom in post docs in recent years has led in certain disciplines to ever more frequent periods spent abroad after graduating. Some Ph.D.s return rapidly to France to try to find steady employment whereas other extend their time abroad and settle in their host countries. The survey of young Ph.D.s in France shows that it is difficult to liken such foreign stays to the generalized 'brain drain' phenomenon because, for example, professional conditions may be far more attractive or the scientific environment more stimulating. Most young Ph.D.s go abroad because they find it difficult to secure employment in France. This is often also why they extend their stay abroad. That does not mean that the situation abroad is not attractive to young Ph.D.s. More than half of them indicate that scientific conditions influenced their choice to move. Moreover, Ph.D.s tend to remain in the countries that have substantial R&D capacities and a tradition of immigration. It may be thought that recruitment strategies of certain host countries play a decisive role in international mobility [START_REF] Tremblay | Academic Mobility and Immigration[END_REF]. Policies for managing such mobility for home countries are also important, especially by providing incentives for young Ph.D.s who have gone abroad to return. It would be interesting in this context to examine more specifically how networks of young expatriates are built up throughout their careers and prove decisive for their further careers [START_REF] Burris | The Academic Caste System: Prestige Hierarchies in PhD Exchange Networks[END_REF]. Our findings might usefully be extended by re-questioning the Ph.D.s surveyed. On average, young Ph.D.s were questioned six years after graduating, which is still insufficient to determine whether some will not again change their mobility strategies. In many countries stabilization in academic employment, notably through securing tenure, occurs much later on in their careers than it does in France. Notes 1. . 2. They were questioned via an on-line survey conducted by Céreq and IREDU with support of APEC based on information collated from doctoral schools and Ph.D. associations. 3. Ph.D.s were interviewed about their situations three years after graduation and at the time of the survey. We do not have complete longitudinal information on their trajectory. 4. Table A in appendix presents the distribution by field of study. 5. This is also the case for the decision to stay abroad more than three years after completing their Ph.D. 6. This national qualification is a requirement for applying for positions as teaching and research staff in public-sector universities in France. 7. As previously mentioned, foreign students who returned to their home country were excluded. 8. Certain variables such as the type of financing for the Ph.D. or the wish to work in research at the time of graduating were introduced into the analysis and then removed because not significant. 9. More precisely, Ph.D.s were asked on the number of months they expected spend abroad before their mobility. As the survey was retrospective, it may be that young Ph.D.s reformulate their initial projects ex post and underor overestimate the length of time they planned to spend abroad. However, it is difficult to determine whether there is such a bias and its direction. 10. Only young Ph.D.s abroad three years after completing their Ph.D.s were questioned about their motives for leaving. Ph.D.s who returned to France less than three years after graduating did not answer the question because of the way the survey was constructed. 11. The Global innovation index is taken from the Global Innovation Index 2014 report. Other indicators are from World Bank data.

Table 1 .

 1 Motivations for going abroad (%).

	Motivations	Little if any influence Moderate influence Main influence	Total
	Need to have experience abroad	34	28	38	100
	Difficulty finding a position in France	35	21	44	100
	Better scientific conditions	40	29	31	100
	Career advantages	42	25	33	100
	Family and personal reasons	63	18	19	100
	Source: Iredu-Cereq survey.

Table 2 .

 2 Probability of living abroad as a function of young Ph.D.s' characteristics and motivations. ++, + positive impact of variable significant respectively at 1, 5, and 10%. Each variable was introduced separately instead of the host country in the estimation in Table2column 2. Individual characteristics introduced but not shown are the same as in Table2.

	Abroad three years	Abroad at date of
	after Ph.D.	survey

Table 4 .

 4 Expected length of stay abroad (before leaving).

	Expected stay (months)	Ph.D.s who returned to France	Expatriate Ph.D.s
	First quartile	12	24
	Median	24	36
	Third quartile	36	50
	Source: Iredu-Céreq survey.

Table 5 .

 5 Change of the initial plan to go abroad depending on initial motivations for leaving.

		Changed initial plans	Did not change initial	Total
		(74%)	plans (26%)
	Motivations for going abroad	(%)	(%)	(%)
	Difficulty finding a position in France	79	21	100
	Better scientific conditions	80	20	100
	Career advantages	73	27	100
	Need to gain experience abroad	83	17	100
	Family and personal reasons	64	36

Table 6 .

 6 Change of the initial plans to go abroad depending on motivations justifying still being abroad at the survey date.

		Changed initial	Did not change initial
		plans (74%)	plans (26%)
	Motivations relating to expatriation	(%)	(%)	Total (%)
	Difficulty finding a position in	83	17	100
	France
	Better scientific conditions	79	21	100
	Career advantages	76	24	100
	Family and personal reasons	70	30	100

Table 7 .

 7 Planned versus actual length of stay Planned stay abroad Column 1 shows the results of OLS regression on the number of months young people expected to spend abroad before leaving (a positive sign increases the number of months if significant). Column 2 shows the determinants of extending actual stays abroad compared with the planned length (probit model). Significance levels: *** 1%, ** 5%, * 10%.

	Planned stay	Extension of stay
	(months)	relative to
		planned length

The most often cited example is that of Gérard Debreu, the 1983 winner of the Nobel Prize for economics after becoming a US citizen in 1975, who was sorely disappointed by the French university system

They were questioned via an on-line survey conducted by Céreq and IREDU with support of APEC based on information collated from doctoral schools and Ph.D. associations.

Ph.D.s were interviewed about their situations three years after graduation and at the time of the survey. We do not have complete longitudinal information on their trajectory.

This is also the case for the decision to stay abroad more than three years after completing their Ph.D.

This national qualification is a requirement for applying for positions as teaching and research staff in public-sector universities in France.

As previously mentioned, foreign students who returned to their home country were excluded.

Only young Ph.D.s abroad three years after completing their Ph.D.s were questioned about their motives for leaving. Ph.D.s who returned to France less than three years after graduating did not answer the question because of the way the survey was constructed.

The Global innovation index is taken from the Global Innovation Index 2014 report. Other indicators are from World Bank data.

Certain variables such as the type of financing for the Ph.D. or the wish to work in research at the time of graduating were introduced into the analysis and then removed because not significant.

More precisely, Ph.D.s were asked on the number of months they expected spend abroad before their mobility. As the survey was retrospective, it may be that young Ph.D.s reformulate their initial projects ex post and under-or overestimate the length of time they planned to spend abroad. However, it is difficult to determine whether there is such a bias and its direction.

Notes on contributors

Claire Bonnard is associate professor in economics at University of Lille 1 and affiliated researcher at IREDU (Institute for Research in the Sociology and Economics of Education). Julien Calmand is researcher at Cereq and Ph.D. student in education at IREDU. Jean-François Giret if full professor in education at University of Burgundy and director of IREDU.

Appendix


Maxime Gayrard

Benedetta Marmiroli

Francois Chancerel

Philippe Decorse

Heinz Amenitsch

Jennifer Peron

Andrea Cattoni

Marco Faustini

Deep X-ray lithography on "sol-gel" processed noble metal mesoarchitectured films

teaching and research institutions in France or abroad, or from public or private research centers.

in the field of ultraviolet (UV) plasmonics as O 2 -resistant plasmonic photocatalyst. 10 Despite that, patterning strategies enabling integration into devices have not been reported (for Rh) or require multi-steps processes (for Ru). 1 In addition conventional processes are indirect, they rely on patterning of a sacrificial resist (polymer) followed by lift-off, electrodeposition and/or etching processes that can be very demanding for stable noble metals. Developing scalable and direct patterning strategies for noble metals would greatly simplify their integration in a number of devices. Besides polymeric resists, direct patterning was already demonstrated for Metal Organic Frameworks [11][12][13][14] or mesoporous oxides prepared by sol-gel process.

15-17

Among the various techniques, Deep X-Ray Lithography has proven to be very effective for the direct patterning of sol-gel precursors that were used as negative tone resists and further converted into oxides, typically by annealing. [17][18][19][20] For instance, X-Ray patterned Ti-based xerogels could be converted into crystalline TiO 2 by thermal treatment. 18 Generalizing the concept of "solgel process" beyond oxides by extending it to noble metals would enable direct patterning of metallic structures by X-Ray lithography. To do so, one must develop noble metal-based resists with two main requirements: (i) the resist should exhibit a solubility switch upon X-Ray exposure to allow for the development; (ii) the resist should directly be converted into metal by annealing. In addition, considering the high cost of the noble metal precursors, the process should be waste-free and should ideally allow for the recycling of the expensive resist by using environmental friendly solvents (such as H 2 O).

Here we show that mesostructured xerogels based on Ru and Rh (in presence of block-copolymers) act as effective negative tone resists for X-Ray lithography to obtain metallic nanostructures after annealing. Differently from previous reports on sol-gel derived transition metal oxides, we report for the first time on the radiation chemistry of underexplored "sol-gel" of noble metals. The key advantage of this "sol-gel" approach is that the materials can be shaped as polymeric resists by solution processing but can eventually be converted into metals. The general patterning strategy for noble metal xerogels is illustrated in Figure 1(a). The resist films are obtained from solutions containing the noble metal precursors (chlorides) and, a block-copolymer Pluronic F127. Differently from other noble metals chlorides such as gold, silver, platinum or palladium (that recrystallize after evaporation), in presence of block-copolymers Ru or Rh chlorides form homogenous films of optical quality after dip-coating (Figure S1). The dip-coating method is a waste free deposition technique, an important feature in case of costly noble metal precursors. 21 The film is then exposed to a synchrotron X-Ray radiation through a mask that induces a solubility change: the exposed materials become insoluble in polar solvents. The non-exposed material is developed in water. Water is also one of the solvents of the initial solution, and this is a key condition for the recycling of the initial noble metal precursors. The patterned insoluble materials can be annealed in reducing atmosphere (H 2 at 300°C) and directly converted in the corresponding noble metal.

A detailed study on structural and chemical evolution of the materials induced by the X-Ray exposure is presented for the case of Ru-based films. We first discuss the evolution of the structure. As in classical sol-gel process, self-assembly during evaporation (during the dip-coating step) results in the formation mesostructured hybrid materials composed of organic micelles surrounded by amorphous metallic complexes. 16 This was confirmed by GI-SAXS on a RuCl 3 /F127 film before exposure (Figure 1e). GI-SAXS measurement of the non-exposed material shows the characteristic diffraction pattern of the Im3m mesostructure (body center cubic arrangement). 17 After X-Ray exposure, in all the cases, a colour difference between the exposed and unexposed zones (latent image) is already visible by naked eye as exemplified in the optical photograph in Figure 1(b). The colour difference can be attributed to a structural modification of the films (such as a thickness decrease). We thus investigated in detail the effect of the X-Ray radiation dose on the structural properties of the films by UV-visible spectroscopic ellipsometry and GI-SAXS. The evolution of the relative thickness vs dose is shown in Figure 1(c). For all the films investigated hereafter, the initial thickness was around 100 nm. The relative thickness already significantly decreases at low doses and progressively reaches a contraction of 66% at higher doses. This decrease in thickness is characteristic of a densification of the material due to the X-Ray radiation. The densification can be due to the water loss or/and polymer degradation. The same study was performed for RuCl 3 films without F127 (Figure S2) and already at moderate exposure doses, RuCl 3 films exhibit a contraction of 30%-33%. This decrease can therefore be indeed attributed to the partial loss adsorbed water (more details will be shown later on). To gain better understanding, the evolution of the mesostructure after exposure at increasing doses was investigated by GI-SAXS (Figure 1f). The characteristic diffraction signal of the unexposed film progressively disappears upon X-Ray irradiation; we integrated the signal intensity along the in-plane 1-10 direction as a function of X-Ray dose (Figure 1d). The diffraction signal at q y = 0.42 nm -1 corresponds to a d-spacing of 14.9 nm which is in agreement with mesostructures containing F127 micelles. The strong decrease of the intensity already a low doses indicates a loss of the mesostructure, likely due to a chemical modification of the block-polymer micelles.

22

The chemical evolution during exposure was investigated by (i) GI-WAXS and XPS to characterized the noble metal precursor and (ii) infrared (IR) spectroscopic ellipsometry to probe the evolution of the polymer and H 2 O. The chemical evolution of the inorganic precursor vs X-Ray irradiation was first characterized by GI-WAXS. As shown in Figure S3, the GI-WAXS 2a and Figure S4). Since Ru(3d) core levels superimpose the C(1s) core level, the Ru(3p) region was analyzed. From Ru(3p) spectra plotted on Figure 2(a), we can see that Ru(3p) does not shift upon exposure time and remains at 463.1 eV, which is characteristic of Ru(III) species. Interestingly, the Cl/Ru for non-exposed sample is ∼3 confirming that the film presents a stoichiometry close to the initial precursor RuCl 3 in agreement with previous reports.

23, 24 Before exposure, noble metal precursors, that can be formally described as Ru(Cl) x (OH) y , are likely coordination xerogel based mostly on Cl ligands. 25 The peaks characteristic of the Cl 2p3/2 and 2p1/2 also remain located at 197.8 and 199.3 eV upon exposure (Figure S4), however a progressive decrease in Cl/Ru ratio is observed with increasing exposure time. The Cl/Ru decreases from ∼3 for non-exposed sample, down to 2.53, 1.46 and 0.71 with exposure doses of 168, 336 and 841 respectively. .This decrease of Cl content can be attributed to the formation of more hydroxylated species (-OH). XPS spectra in the O1s region (Figure S4) confirms the presence of H 2 O in nonexposed samples, with the O(1s) peak centered at 533 eV. Upon exposure, the contribution of water into the O(1s) peak disappears and the O(1s) peak is shifted to 531.5 eV which is characteristic of hydroxylated species. In contrast, no peaks centered at 529.3 eV characteristic of the M-O-M bond are observed. 23 This suggests that, differently from other sol-gel systems, the X-Ray irradiation does not promote condensation in the case of Ru.

We then perfomed IR ellipsometry as shown in Figure 2 and between 3200-3400 cm -1 can be attributed to the presence of water molecules in the film, due to residual water from the initial solution and/or due to humidity from the atmosphere. 26 The large O-H band at 3200-3400 cm -1 partially overlaps in the range 2850-2920 cm -1 with the CH 2 symmetric and asymmetric stretching bands of Pluronic F127. The band at ca. 1100 cm -1 can be attributed to the stretching of the C-O-C bonds in the PEO. 26 27 To confirm that, the k spectra of films of RuCl 3 and F127 (non-exposed) are also reported in Figure S5. After exposure at a low dose of 168 J-cm 2 , the drastic decrease of the O-H bands confirms the partial water loss while the characteristic peaks of the polymers are not visible. At high dose 841 cm -2 , the raw ellipsometric spectra do not present any visible absorption peak and are thus fitted with a Cauchy model for not absorbing materials (k=0). It is important to mention that the presence of residual polymer or water might fall below of the detection limit of the IR ellipsometer. However, it is reasonable to propose that X-Ray induces deconstruction of the film with two main effects: (i) loss of the mesostructure (as observed by GI-SAXS) that can be attributed to the fact that high energy X-Ray radiation provokes complete decomposition of F127 22 ; (ii) loss of the adsorbed water in agreement with the UV-vis ellipsometric analysis (Figure S2) and formation of hydroxocomplexes. What observed in this study is in agreement with the previous literature on sol-gel derived films. 28 The hard X-rays exposure to as-deposited solgel films produces hydrolysis of the precursors that is promoted by formation of free radicals. The free radicals H° Please do not adjust margins Please do not adjust margins and OH° are formed by dissociation of water molecules exposed to X-Ray radiation. Residual water is indeed always present in the hybrid films containing F127 and the hydrated noble metal precursors. Free radicals are also responsible of the decomposition of the organic matter in the films.

28

The film deconstruction during X-Ray exposure was also observed in the case of RhCl 3 films templated with F127.

Figure 3 shows the evolution of the relative thickness as function of the dose. As observed for Ru, the Rh-based films contract progressively (up to 62% at high values of dose) attributed to water loss and decomposition of F127. The loss of the mesostructure is also confirmed by the selected GI-SAXS patterns in the inset of Figure 3. The progressive decrease of the GI-SAXS signal is in agreement with the mechanism described for Ru-based films.

Coming back to the lithographic process, the combination of polymer decomposition, dehydration and partial hydroxylation is responsible of the solubility switch of the films. As mentioned above, to obtain an efficient negative tone resist for lithography, the exposed material must be insoluble while the unexposed material must be dissolved. The solubility contrast is thus crucial for the development step. We have tested the effectiveness of the development process on samples patterned through a mask. Examples of patterned samples before development are shown in Figure S6. The development step consisted in dipping the samples in H 2 O for about 30 s; the quality of the micropatterns was then evaluated by optical microscopy. The table in Figure 4(a) summarizes the results of the development for the two metal precursors Ru, Rh chlorides alone or in presence of blockcopolymers (F127) as function of the exposure doses. Several general trends can be observed. For all the systems, at low doses, the development is not efficient since the exposed material can re-dissolved in H 2 O. Oppositely, for high doses (that imply very long exposure time) the development is not optimal: overexposure induces a modification also in the unexposed material at the pattern edge that becomes less soluble after irradiation. Films made of RuCl 3 and RhCl 3 without F127 become insoluble too after irradiation. This is not surprising since more hydroxylated Ru complexes present poor solubility in water. 29 However, without F127, the solubility contrast (between the exposed and the unexposed zones) is not high enough to achieve effective development in H 2 O. For the RuCl 3 /F127 and RhCl 3 /F127 materials, 841 J-cm 2 is the optimal X-Ray dose to obtain an effective development in our conditions as exemplified in the optical micrographs in Figure 4(b) and 4(c). Similarly, the samples exposed at 841 Jcm 2 could be developed in other polar solvents such as ethanol (Figure S7). After development, the patterned noble metal xerogels can be converted into the respective metal by an annealing at 300°C under reducing atmosphere (H 2 /Ar) as illustrated in Figure 5 Please do not adjust margins Please do not adjust margins not dense but present porous nanoarchitectures. Indeed, during the reduction process, Cl/OH ligands are decomposed resulting in films that are composed by metallic nanoparticles forming a percolated network with voids. The formation of percolated nanoparticle layers (rather than isolated particles) is important for ensuring the metallic properties of the films (electrical and optical). To confirm, the optical properties of the films before and after reductive annealing have been probed by UV-vis spectroscopic ellipsometry.

The plots in Figure 5 (f) and (g) display the evolution of k as a function of the wavelength for Ru and Rh, respectively. In both cases, before annealing (after exposure at 841 J cm -2

) the film presents low values of k, especially at low wavelength in the visible range that are attributed to the presence of colored Ru and Rh complexes in the films. After reductive annealing, the value of k drastically increases especially in the near infrared region; this behavior is characteristic of the formation of metallic conducting films.

Conclusions

In conclusion, we demonstrated that, for the first time, sol-gel processed mesostructured xerogels composed on noble metal precursors (Ru and Rh-based) act as negative tone resists for X-Ray Lithography. The effect of the X-Ray radiation on the structure and chemical composition of the films was investigated by a set of techniques including GI-SAXS, Uv-vis and IR ellipsometries. Differently for other sol-gel based materials, no condensation take place but the X-Ray radiation induces the destructuration of the noble metal xerogels. We propose that block-copolymer decomposition, dehydration and partial hydroxylation are responsible for the solubility switch observed in the xerogels. We demonstrate that noble metal xerogels can directly be patterned by X-Ray lithography and converted into the corresponding metal by annealing. The process presents several advantages: it enables direct patterning and it minimizes wastes of the expensive noble metal precursors. Notably the development step is performed in water, a key requirement for the possible recycling of the resist. While in the present work we demonstrated the fabrication of micrometric patterns, DXRL theoretically enables patterning at the sub-micrometric scale. We believe that this report will trigger new fundamental research on X-ray assisted synthesis of nanostructured materials providing new possibilities for device fabrication at low cost. From a fundament point of view, this work expands the synthetic toolbox of sol-gel processed materials toward metals. We also provide new understanding in the radiation chemistry of noble Please do not adjust margins Please do not adjust margins metal materials, a relatively underexplored field that is also of high interest for a broader community working in catalysis and electrocatalysis. As a future research line, it would be interesting to investigate if and how the X-ray radiation is influencing the catalytic properties of the noble metal films.

Figure 1 (

 1 Figure 1 (a) Illustration of the patterning strategy of noble metal mesostructured xerogels. (b) Photograph of a Ru-based xerogel partially exposed to X-Ray radiation. (c) Evolution of the relative thickness of a RuCl 3 /F127 xerogel as function of the X-Ray dose. (d) Evolution of the scattering intensity as function of the qy for samples exposed to increasing doses. (e) GI-SAXS pattern of the unexposed RuCl 3 /F127 xerogel and, (f) evolution of GI-SAXS pattern of the sample at increasing exposure doses.

  (b). During an ellipsometric experiment, IR polarized light beam interacts with the film. This interaction changes the state of polarization of the reflected light which may be parametrized by the interference amplitude component Ψ and the phase difference Δ. Both Ψ and Δ values are very sensitive to photons absorptions due to vibrational modes at IR wavelengths. The Ψ and Δ spectra are then analyzed by the software "IR Wase" to obtain refractive index (n) and extinction coefficient (k) of the films. Figure 2(b) shows the evolution of k as function of wavelength for Ru-based films before and after X-Ray exposure. Before exposure, the RuCl 3 /F127 film shows many different features: the bands centered between 1650-1670 cm -1

Figure 2 (

 2 Figure 2 (a) XPS spectra recorded in the Ru(3p) region on films exposed at different doses and annealed in reducing atmosphere. (b) Evolution of the extinction coefficient k of a RuCl 3 /F127 film before and after exposure at different doses.

Figure 3

 3 Figure 3 Evolution of the relative thickness of RhCl 3 /F127 films as function of X-Ray dose. In the inset: corresponding GI-SAXS patterns

Figure 5

 5 Figure 5 (a) Illustration of the lithographic process toward metallic patterns; SEM micrographs of (b) (c) Ru and (d) and (e) Rh patterns. The corresponding EDX mapping and higher resolution view are reported in the inset (scale bar 50 nm). (f) and (g) Evolution of the extinction coefficient k for Ru and Rh-samples before and after annealing

O (a)

Acknowledgements

This work was supported by French state funds managed by the National Research Agency (ANR) through the MetaFleSS project, grant no. ANR-17-CE09-0027. M.F. acknowledges funding from the European Research Council (ERC) under European Union's Horizon 2020 Program (Grant Agreement no. 803220, TEMPORE). This project has also received funding from the EU-H2020 research and innovation program under grant agreement No. 654360 having benefitted from the access provided to ELETTRA Trieste, Italy, within the framework of the NFFA-Europe Transnational Access Activity. The infrared ellipsometry was funded by the Région Ile-de-France in the framework of DIM ResPore and by the French state within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02, within the framework of the Cluster of Excellence MATISSE. The XPS KAlpha+ was funded by the Région Île-de-France (convention SESAME n°16016303). ANR (Agence Nationale de la Recherche) and CGI (Commissariat à l'Investissement d'Avenir) are also gratefully acknowledged for their financial support through Labex SEAM (Science and Engineering for Advanced Materialsand devices), ANR-10-LABX-096 and ANR-18-IDEX-0001. We thank D. Montero and the Institut des Matériaux de Paris Centre (IMPC FR2482) for servicing FEGSEM & EDX instrumentation and Sorbonne Université, CNRS and C'Nano projects of the Région Ile-de-France for funding.

Conflicts of interest

There are no conflicts to declare.