Christophe Charrier
email: christophe.charrier@unicaen.fr

Gilles Lebrun
email: gilles.lebrun@unicaen.fr

Olivier Lezoray
email: olivier.lezoray@unicaen.fr

Image Quality Assessment with Manifold and Machine Learning

Keywords: Manifold learning, Machine Learning, SVM, Image quality, Human Visual System

A crucial step in image compression is the evaluation of its performance, and more precisely the available way to measure the final quality of the compressed image. In this paper, a machine learning expert, providing a final class number is designed. The quality measure is based on a learned classification process in order to respect the one of human observers. Instead of computing a final note, our method classifies the quality using the quality scale recommended by the UIT. This quality scale contains 5 ranks ordered from 1 (the worst quality) to 5 (the best quality). This was done constructing a vector containing many visual attributes. Finally, the final features vector contains more than 40 attibutes.

Unfortunatley, no study about the existing interactions between the used visual attributes has been done. A feature selection algorithm could be interesting but the selection is highly related to the further used classifier. Therefore, we prefer to perform dimensionality reduction instead of feature selection. Manifold Learning methods are used to provide a low-dimensional new representation from the initial high dimensional feature space.

The classification process is performed on this new low-dimensional representation of the images. Obtained results are compared to the one obtained without applying the dimension reduction process to judge the efficiency of the method.

INTRODUCTION

Nowadays, it is usual for anyone to take photos with digital cameras, to upload the images on computers, and to use some software to apply many image processing algorithms on these images (compression, blurring, ...). This is a simple and representative example of the growing of digital media that is everywhere. By the way, many Tera-bytes transit on the Internet. In order to reduce the amount of transmitted data, one typical applied processing on an image is compression, that allows to reach high compression levels, so that few data is to be further transmitted.

Image compression maps an original image into a bit stream suitable for communication over or storage in a digital medium. It consists in one or more of the following operations :

• Signal representation: the first and the most important element is the transform of the image to the most suitable domain. A frequential or spatial transform is applied to have an efficient image representation.

The goal is to concentrate energy in a few coefficient or to provide a useful data structure.

• Quantization: this conversion can operate on individual pixels (scalar quantization) or group of pixels (vector quantization). This operation is nonlinear and noninvertible: it is a lossy process. In our study, this conversion operates on a group of pixels by Vector Quantization (VQ).

• lossless compression: the compression is achieved by invertible code. The idea is to assign codewords with few bits to likely symbols and codewords with more bits to unlikely symbols so that the average number of bits is minimized.

A crucial step in image compression is the evaluation of its performance, and more precisely the available way to measure the final quality of the compressed image. There is a very rich literature on image quality criteria, generally dedicated to specific applications (optics, detector, compression, restoration, . . . ). The quality evaluation is divided into two topics: objective and subjective evaluation. The first topic gives place to two families of criteria: unweighted and weighted criteria. The first family corresponds to the traditional criteria known as mathematical measures, because they result from geometry (concept of distance) or from the signal processing (signal to noise ratio). These criteria do not give an estimate of the visual quality of the image. The second family of criteria takes into account the characteristics of the human visual system in particular by a weighting of the image of error. Lastly, the second topic relates to the psychophysical experiments allowing to add a subjective dimension in the quality evaluation process. Due to the time expensive aspect of this last topic, objective quality measures have been intensively investigated to quantify the quality of a compressed image.

The usually applied scheme consists in performing 1) a color space transformation to obtain decorrelated color coordinates and 2) a decomposition of these new coordinates towards perceptual channels. An error is then estimated for each one of these channels. A final quality score is obtained by pooling these errors in both spatial and frequential domain. The most common way to perform this pooling is to use the Minkowski error metric. Some studies 1 have shown that this summation does not perform well. The same final value can be computed for two different degraded images even if the visual quality of the two images is drastically different. This can be due to the fact that the implicit assumption of this metric is based on the independancy of all signal samples. It is commonly assumed that this is not true when one uses perceptual channels. This explains the reason why the Minkowski metric might fail to generate a good final score.

In our previous work, a machine learning expert, providing a final class number and its associated confidence probability, has been designed. [START_REF] Charrier | A color image quality assessment using a reduced-reference image machine learning expert[END_REF] The quality measure is based on a learned classification process in order to respect the one of human observers. Instead of computing a final note, our method classifies the quality using the quality scale recommended by the UIT. This quality scale contains 5 ranks ordered from 1 (the worst quality) to 5 (the best quality). The selected class of the proposed method represents the opinion score OS. This was done constructing a vector containing many visual attributes such as those defined by Wang et al. in their SSIM measure, [START_REF] Wang | A universal quality index[END_REF] and ones obtained computing a cortex filter based on a multi-channel decomposition, 4 and so on. Finally, the final features vector contains more than 40 attibutes.

Unfortunatley, no study about the existing interactions between the used visual attributes has been done so far. A feature selection algorithm could be interesting but the selection is highly related to the further used classifier. Therefore, we prefer to perform dimensionality reduction instead of feature selection. Linear dimensionality reduction methods have shown their limits and a lot a different nonlinear methods have emerged these last years. This is known as Manifold Learning and attempts at providing a low-dimensional representation from an initial high dimensional feature space.

The paper is structured as follows. In Section 2, we present the of features used to describe the quality of images. In Section 3, Manifold Learning methods are described. Section4 details how classification is performed with Support Vector Machines. Section 5 provides obtained results. Last Section concludes.

FEATURES VECTOR

This section describes the set of features used to describe the quality of images. Four types of attributes contained in that set are: 1) full-reference image SVH-based features and 2) full-reference image features, both for them a reference image is needed and 3) no-reference images SVH-based features and 4) no-reference images features, both for them no reference image is needed.

Full-reference image SVH-based features

When using full-reference image features, both original and degraded images are first subject to a transformation towards an antogonist luminance chrominance color space. From all existing opponent color spaces, the Krauskopf 5 one is selected. This coordinates system is computed from the LMS primaries that correspond to the HVS cone responses. Thus, from this color space one are able to take into account the spatial-frequency sensitivity of the SVH. Actually, it is well known that the HVS analyzes the visual input by a set of channels, each of them being selectively sensitive to a restricted range of spatial frequencies and orientations. Several psychophysical experiments have been conducted by different researchers to characterize these channels. Currently, concerning the luminance component the most used decompositions are from Daly, [START_REF] Daly | A visual model for optimizing the design of image processing algorithm[END_REF] Watson 6 and the Lubin's one. [START_REF] Lubin | Digital Images and Human Vision, ch. The use of psychophysical data and models in the analysis of display system performance[END_REF] are often used. The two first are characterized by a diadic radial selectivity (five one octave bandwidth channels) and a constant angular selectivity. The main difference is situated around the value of the bandwith: 30 degrees for Daly's model and 45 degrees for the Watson's one. Lubin's decomposition needs seven radial bands and four orientations.

In this paper, the cortex transform introduced by Daly 8 is used. Actually that transformation uses a radial frequency selectivity that is symmetric on a log frequency axis with bandwidths nearly constant at one octave. Their decompositions consist in one isotropic low-pass and three bandpass channels. The angular selectivity is constant and is equal to 45 degrees. Many different filters have been proposed as approximations to the multi-channel representation of visual information in the HVS. In this paper, a radial selectivity filter dom i (u, v) and a angular selectivity filter f an k,θ (u, v) are used that are combined to obtain the cortex filter mboxCortex k,θ,i (u, v) = dom i (u, v).f an k,θ (u, v), where u and v are the cartesian spatial frequencies, θ is the orientation and k represents the direction. Then, the image is then filtered by each one of the cortex filter to obtain a set of subimages a k,θ,i (u, v) defined by

a k,θ,i (u, v) = Cortex k,θ,i (u, v).S(u, v)
where S(u, v) represents the image spectrum.

Each one of those images corresponds to the structural content of the image with respect to the frequency and the orientation.

Contrast masking

Then, from each one of those filtered images, a contrast masking score is computed.

To obtain a good definition of the masking contrast, one have to take into account together the spatial and frequential resolution. Peli 9 has proposed such a model known as the limited band local contrast. This contrast is local since it quantifies the human observer's sentivitity to the luminance variation with respect to the local mean luminance. In addition, it is a limited band contrast since the degradation perception depends on its spectral location. When using the above mentionned cortex decomposition, one has to take into account both angular and radial to define the limited band local contrast such as:

c i,j (u, v) = L i,j (u, v) i-1 k=0 card(l) l=0 L i k,l (u, v) (1)
where L ij (u, v) and c i,j (u, v) respectively specifies the luminance and the contrast located to the coordinates (u, v) of the i th radial channel and the j th angular sector. card(l) represents the number of angular sectors of the k th radial band.

Then, the perceived errors are modeled by the contrast masking for one spatial frequency and orientation channel and one spatial location, into a single objective score for each one of the 31 filtered image.

From this step, 31 scores, labeled to as feature s i , are available and integrated within the feature vector.

full-reference image features 2.2.1 Structural criteria

In addition, the three criteria integrated in the metric proposed by Wang and Bovik 3 are added to the vector. These criteria are 1) a luminance distorsion, 2) a constrast distortion and 3) a structure comparison. The authors proposed to represent an image as a vector in an image space. In that case, any image distortion can be interpreted as adding a distortion vector to the reference image vector. In this space, the two vectors that represent luminance and contrast changes span a plane that is adapted to the reference image vector. The image distortion corresponding to a rotation a such a plane by an angle can be interpreted as the structural change.

The luminance comparison is defined as

l(I, J) = 2µ I µ J + C 1 µ 2 I µ 2 J + C 1 (2)
where µ I and µ J respectively represent the mean intensity of the image I and J, and C 1 is a constant avoiding instability when µ 2 I + µ 2 J ≈ 0. According to the Weber's law, the magnitude of a just-noticeable luminance change δL is proportional to the background luminance L. In that case, µ I = αµ J , where α represents the ratio of the luminance of the distorted signal relative to the reference one. The luminance comparison can be now defined as

l(I, J) = 2αµ 2 I + C 1 (1 + α 2 )µ 2 I + C 1 (3)
The contrast distortion measure is defined in a similar form:

cd(I, J) = 2σ I σ J + C 2 σ 2 I σ 2 J + C 2 (4)
where C 2 is a non negative constant, and σ I (resp. σ J ) represents the standard deviation .

The structure comparison is performed after luminance substraction and contrast normalization. The structure comparison function is defined as:

s(I, J) = 2σ I,J + C 3 σ 2 I σ 2 J + C 3 (5)
where

σ IJ = 1 N -1 N i=1 (I i -µ i )(J i -µ J )
, and C 3 is a small constant. s(I, J) can take negative values which is interpreted as local image structures inversion.

color criteria

Two local descriptors based on visual attention are used. [START_REF] Trémeau | Quantitative description of image distorsions linked to compression schemes[END_REF] Those descriptors are not ponctually defined in I(x, y) but with respect to the mean value µ(x, y) of neigborhood V of the pixel (x, y) . I M (ci) (x, y) and I m (ci) (x, y) respectively represent the maximal and minimal value of the c i axis within V for the image I at the pixel located to (x, y).

The two used features are:

1. local chrominance that measures the sensitivity of an observer to color degradation within a uniform area.

The calculation of this descriptor is performed in the L * a * b * color space.

2. local colorimetric dispersion that measures the spatio-colorimetric dispersion in each one of the two color images. This comparison which is performed over a neighborhood.

These descriptors have been defined according to the same scale ranging from 0 to 1 ; 0 corresponding to the most noticeable differences and 1 corresponding to the least noticeable difference.

No-reference image SVH-based features 2.3.1 Blockiness measures

The measure of blocking artefact has an important weight in the final judgment of the image quality. Blocking artefact results from a visible block structure appearing in reconstructed images. This is mainly due to the block-based compression algorithms used to compressed images.

Many techniques to quantify blockiness effects have been proposed. Yet, these techniques require to have access to the original image. In our case, three no-reference blockiness metrics have been used: 1) the Wang et al. one,, [START_REF] Wang | Blind measurement of blocking artifacts in images[END_REF] 2) the one developed by Vlachos 12 and 3) the blockiness measure as defined by Wu and Yuen. [START_REF] Wu | A generalized block-edge impairment metric for video coding[END_REF] Wang et al. model the blocky image as a non-blocky image interfered with a pure blocky signal. To estimate the blockiness of an image M B , they assume that the vertical M Bv and th horizontal M B h effects are of the same importance, and the relationship between M B and both M Bv and M B h effects is

M B = (M Bv + M B h )/2.
In order to define the two effects, they apply a 1-D FFT to the horizontal and vertical difference signals. From these signals, the average horizontal and vertical power spectra is computed. Peaks in these spectra are then identified by their locations in the spectra. The power spectra of non-blocky images is approximated by applying a median filter on these curves. The final blockiness measure is then computed as the difference between the resulting power spectra and the peaks location.

In the Vlachos's model, the used algorithm is based on the cross-correlation of subsmapled images. The original image is first decomposed in 8 × 8 size blocks. Every generated sub-image contains one specefic pixels from each original blocks. Eight sub-images are generated as follows: 1) four sub-images are generated from the four corner pixels of each blocks and 2) four other sub-images are constructed from four neighboring pixels in the top left corner of each block. Then, the cross-correlations from the former four sub-images are normalized by the computed cross-correlations of the latter four sub-images to score the blockiness measure.

For Wu and Yuen the blockiness measure is based on the vertical and horizontal differences between the columns and the rows all 8 × 8 boundaries. The mean and the standard deviation obtained from adjacent blocks to each boundary are respectively used to define weight respectively dedicated to perceptual luminance effects and texture masking effects. Then, the final blockiness measure is obtained from the latter measure normalized by the mean of the same measures computed at non-boundary columns and rows.

Blurriness measure

Blur in an image is due to the attenuation of high spatial frequencies in the image. It is characterized by a smearing of sharp edges and a general loss of details. This artefact commonly occurs during a compression process.

To measure the blurry effect on an image, one first have to detect edges. In order to detect edges in a color image, the Cumani edge detector 14 is used on the color image expressed in the Krauskopf space. Then an opening operator from mathematical morphology is applied on the resulting thresholded image in order to remove noise and non-important edges. Then, taking into account the gradient orientation, a measure of blurriness is performed along the actual local edges. To measure the width of a located edge, one used the Achromatic component and seeds obtained from the former edge image. Then both local maximum and local minimum are extracted from the achromatic image and correspond to luminance extrema closest to the edge seed. The difference between the location of those two extrema is computed to define the width of the edge. Finally the global blurriness measure is obtained by averaging the local blurriness measure over all detected edges.

No-reference image features

As no-reference image features, one has used three of the objectives features used by Gastaldo et al. to provide an objective assessment of JPEG compressed image using neural networks. [START_REF] Gastaldo | No-reference quality assessment of JPEG images by using CBP neural networks[END_REF] The three features are expressed from a color correlogram that allows us to have information about the spatial correlation of color changes with distance. The used features are:

1. Energy, that corresponds to a summation of all squared elements of the color correlogram,

DIMENSIONALITY REDUCTION

Given a set of visual attributes describing an image, we use a Manifold Learning method to project the data on a new low-dimensional space. Thus, nonlinear new discriminant features of the input data are yielded. The obtained low dimensional sub-manifold is used as a new representation that is transmitted to classifiers.

When data objects that are the subject of analysis using machine learning techniques are described by a large number of features (i.e. the data is high dimension) it is often beneficial to reduce the dimension of the data. Dimension reduction can be beneficial not only for reasons of computational efficiency but also because it can improve the accuracy of the analysis. Indeed, traditional algorithms used in machine learning and pattern recognition applications are often susceptible to the well-known problem of the curse of dimensionality, that refers to the degradation in the performance of a given learning algorithm as the number of features increases. To deal with this issue, dimension reduction techniques are often applied as a data pre-processing step or as part of the data analysis to simplify the data model. This typically involves the identification of a suitable low-dimensional representation for the original high-dimensional data set. By working with this reduced representation, tasks such as classification or clustering can often yield more accurate and readily interpretable results, while computational costs may also be significantly reduced. Dimensionality reduction methods can be divided into two sets wether the transformation is linear or nonlinear. We detail here the principles of two well-known linear and nonlinear dimensionality reduction methods: Principal Components Analysis (PCA) [START_REF] Saul | Spectral methods for dimensionnality reduction[END_REF] and Laplacian Eigenmaps (LE). 17 Let X = {x 1 , x 2 , • • • , x n } ∈ R p be n sample vectors. Dimensionality reduction consists in finding a new lowdimensional representation in R p with q ≪ p.

Principal Components Analysis

The main linear technique for dimensionality reduction, principal components analysis (PCA), performs a linear mapping of the data to a lower dimensional space in such a way, that the variance of the data in the low-dimensional representation is maximized. Traditionally, principal component analysis is performed on the symmetric covariance matrix C cov or on the symmetric correlation matrix C cor . We will denote C one of these two matrices in the sequel. From such a symmetric matrix, we can calculate an orthogonal basis by finding its eigenvalues and eigenvectors. Therefore, PCA simply consists in computing the eigenvectors and eigenvalues of the matrix

C: C = U ΛU T where Λ = diag(λ 1 , • • • , λ n ) is the diagonal matrix of the ordered eigenvalues λ 1 ≤ • • • ≤ λ n ,
and U is a p × p orthogonal matrix containing the eigenvectors. Dimensionality reduction is then obtained by the following operator h P CA : x i → (y 1 (i), • • • , y q (i)) where y k (i) is the i th coordinate of eigenvector y k . In the rest of this paper, we will denote h Cov P CA and h Cor P CA , dimensionality reduction performed with PCA of the covariance or the correlation matrix.

Laplacian Eigenmaps

Given a neighborhood graph G associated to the vectors of X, one considers its adjacency matrix W where weights W ij are given by a Gaussian kernel nearby sample vectors to be mapped to nearby outputs. This is achieved by finding the eigenvectors y 1 , y 2 , • • • , y n of matrix ∆. Dimensionality reduction is obtained by considering the q lowest eigenvectors (the first eigenvector being discarded) with q ≪ p and is defined by the following operator h LE :

W ij = k(x i , x j ) = e -
x i → (y 2 (i), • • • , y q (i)) where y k (i)
is the i th coordinate of eigenvector y k .

CLASSIFICATION METHOD

From all existing classification schemes, a Support Vector Machine (SVM)-based technique has been selected due to high classification rates obtained in previous works, [START_REF] Lebrun | Fast pixel classification by SVM using vector quantization, tabu search and hybrid color space[END_REF] and to their high generalization abilities.

The SVMs were developed by Vapnik et al. [START_REF] Vapnik | Statistical Learning Theory[END_REF] and are based on the structural risk minimization principle from statistical learning theory. SVMs express predictions in terms of a linear combination of kernel functions centered on a subset of the training data, known as support vectors (SV).

Given the training data S = {(x i , y i )} i={1,...,m} , x i ∈ R n , y i ∈ {-1, +1}, SVM maps the input vector x into a high-dimensional feature space H through some non linear mapping functions φ : R n → H, and builds an optimal separating hyperplane in that space. The mapping operation φ(•) is performed by a kernel function K(•, •) which defines an inner product in H. The separating hyperplane given by a SVM is: w • φ(x) + b = 0. The optimal hyperplane is characterized by the maximal distance to the closest training data. The margin is inversely proportional to the norm of w. Thus computing this hyperplane is equivalent to minimize the following optimization problem:

V (w, b, ξ) = 1 2 w 2 + C m i=1 ξ i (6)
where the constraint ∀ m i=1 : This optimization is a convex quadratic programming problem. Its whole dual [START_REF] Vapnik | Statistical Learning Theory[END_REF] is to maximize the following optimization problem:

y i [w • φ (x i ) + b] ≥ 1 -ξ i , ξ i ≥
W (α) = m i=1 α i - 1 2 m i,j=1 α i α j y i y j K (x i , x j ) (7)
subject to ∀ m i=1 : 0 ≤ α i ≤ C , m i=1 y i α i = 0. The optimal solution α * specifies the coefficients for the optimal hyperplane w * = m i=1 α * i y i φ (x i ) and defines the subset SV of all support vector (SV). An example x i of the training set is a SV if α * i ≥ 0 in the optimal solution. The support vectors subset gives the binary decision function h:

h(x) = sign(f (x)) with f (x) = i∈SV α * i y i K (x i , x) + b * (8)
where the threshold b * is computed via the unbounded support vectors [START_REF] Vapnik | Statistical Learning Theory[END_REF] (i.e., 0 < α * i < C). An efficient algorithm SMO (Sequential Minimal Optimization) [START_REF] Platt | Fast Training of Support Vector Machines using Sequential Minimal Optimization[END_REF] and many refinements [START_REF] Collobert | SVMTorch: Support vector machines for large-scale regression problems[END_REF][START_REF] Chang | LIBSVM: a library for support vector machines[END_REF] were proposed to solve dual problem. SVM being binary classifiers, several binary SVM classifiers are induced for a multi-class problem. A final decision is taken from the outputs of all binary SVM. [START_REF] Hsu | A comparison of methods for multiclass support vector machines[END_REF]

SVM model selection

Kernel function choice is critical for the design of a machine learning expert. Radial Basic Function (RBF) kernel function is commonly used with SVM. The most important reason is that RBF functions work like a similarity measure between two examples. As no a priori knowledge exists on the relative importance of each feature s k , the classical RBF function has been extended in order to reflect this fact and the kernel function has been defined as follow

K β (s i , s j ) = exp(- n k=1 β k (s k i -s k j ) 2 /r 2 ) (9)
where s k i is the k th feature of the i th image. To have efficient SVM inducers, a parameter tuning process has to be realized. This procedure is the so-called model selection. The selection of the SVM hyper-parameter (C), the radius of RBF function (r) has been realized by using cross-validation. In this paper, β k could only take binary values and modelize if the s k feature is used or not. When β k values are not fixed by human priors, they are determined by using a feature selection paradigm. The quality of a subset of features for the design of a binary SVM is measured by its recognition performance. This corresponds to a wrapper feature selection approach. [START_REF] Kohavi | Wrappers for feature subset selection[END_REF] SVMs being binary classifiers, multi-class decision using SVMs are usually implemented by combining several two-classes SVM decision. Several combination schemes of binary classifiers exist. [START_REF] Hsu | A comparison of methods for multiclass support vector machines[END_REF] In this paper, the common One-Versus-One (OO) decomposition scheme is used to create 10 binary classifiers. Let t i,j , ∀i ∈ [1, 5], j ∈ [2, 5] be a binary problem with t i,j ∈ {+1, -1}. The number 5 represents the final quality classes according to the ones recommended by the UIT. Let h i (•) be the SVM decision function obtained by training it on the i th binary problem. Table 4.1 gives binary problems transformation used in the OO scheme.

The binary problem transformation is the first part of a combination scheme. A final decision must be taken from all binary decision functions. Many combination strategies can be used to obtain the final decision. [START_REF] Hsu | A comparison of methods for multiclass support vector machines[END_REF] The majority vote criterion is the usual way to do this. Let V j (x) = n b i=1 LO 1 (h i (x), t i,j ) be the number of votes for class t 5,4 t 5,3 t 5,2 t 5,1 t 4,3 t 4,2 t 4,1 t 3,2 t 3,1 t 2,1

5 +1 +1 +1 +1 - - - - - - 4 -1 - - - +1 +1 +1 - - - 3 - -1 - - -1 - - +1 +1 - 2 - - -1 - - -1 - -1 - +1 1 - - - -1 - - -1 - -1 - 1
Table 1. Binary problems transformation used in a One-Versus-One combination scheme.

the class j, where n b is the number of binary decision function in a specific combination scheme, and LO 1 is a loss function defined as follows:

LO 1 (y 1 , y 2 ) = 0 if y 1 = y 2 1 else (10)
where m y2 corresponds to the number of images labelled to as class y 2 in the reference dataset. The multiclass decision function D using majority vote is:

D(x) = arg max 1≤j≤nc (V j (x)) (11)
(when conflicts exist, the SVM output is used to break it).

EXPERIMENTAL SETUP AND RESULTS

SVM classification results are obtained with JPEG2000 compressed versions of 12 images of the LIVE image database, for which 1) all the visual features have been computed and 2) the class selection of each human observer is available. The JPEG2000 compressed versions of the 13 remaining images constitute the test set, for which the same kind of information are available.

Figure 1 presents the 2D projection of the obtained results using the trial methods to reduce the initial dimension of the data. As we can observe, h Cor P CA seems to perform best than the two others tested dimension reduction techniques. Actually, the separation of the five quality classes is linearly separable in the first case, while using the two other projections classes are not linearly separable.

Considering this point of vue, the results obtained from h Cor P CA is the best candidate to be computed with the SVMs; it seems to be the best representation to be linearly separable. In order to confirm or not this assumption, the SVMs will be applied with the obtained results from the three dimension reduction methods: h Cov P CA , h Cor P CA and h LE .

Figure 2 presents the Mean Opinion Score (MOS) obtained from a set of human observers for each tested image versus its associated compression rate (bpp)-The MOS is not taken into account in the dimension reduction process. On the upper left corner, one notes a vertical set of points. Those points correpond to all the original images (with a compression ratio equal to 0) of the trial test for which the quality is judged as very good or as excellent. When observing the subfigure 1(a), the same remarks can be formulated. Thanks to the reduction of the dimension of the original features vector, one is able to reach a linear separation between classes, except for two classes : "Excellent" and "very good". This is probably due to the original images than can be interprated as noise.

Table 5 presents the recognition rate errors with respect to number of used features issued from the dimension reduction step. From this table one can observe that the recognition error rate is quite always minimized when the h Cor P CA is used to reduce the dimension of the data prior to apply SVMs, whatever the number of new vectors used. On note that the best error rate is given when one only uses one feature that yields to reach an error rate of 14.1% pm 7.8%. This means that the initial data are highly correlated. When other features are added to perform the SVM, the recognition rate error increases. This can be interpreted as the following: when one adds new features, in fact one adds noise, and thus the whole performance decreases. Nevertheless, when one compares the obtained results with the one obtained when the training phase is performed on the initial data (i.e., without applying the dimensionality reduction process as a prior step), the recognition rate is equal to 14.2% ± 7.1%. This means that, for the original attributes used to create the features vector characterizing a compressed image, the reduction of the dimension of this vector is not a significant step to improve the quality of the classification process. Nevertheless, using only one attribute, the data, and thus the results obtained at the end of the classification process become more easily understandable by a human being.

More generally, when a dimensionnality reduction process is expected as a prior step to a classification approach, one has to think about an existing correlation between the features of the initial vector.

2 .

 2 Information Entropy correponding to amount of information bringing by the color correlogram 3. Coefficient of homogeneity indicating the degree data approximates the Guttman implicatory scales. It measures the consistency of data matrices

||xi-xj || 2 σ 2 .

 2 Let D denote the diagonal matrix with elements D ii = j W ij and ∆ denote the un-normalized Laplacian defined by ∆ = D -W . Laplacian Eigenmaps dimensionality reduction consists in searching for a new representation {y 1 , y 2 , • • • , y n } with y i ∈ R n , obtained by minimizing 1 2 ij y iy j 2 W ij = T r(Y T ∆Y)with Y = [y 1 , y 2 , • • • , y n ]. This cost function encourages

  0 requires that all training examples are correctly classified up to some slack ξ and C is a parameter allowing trading-off between training errors and model complexity.

Figure 1 .Figure 2 .

 12 Figure 1. Obtained results from the three dimension reduction methods applied to the initial data. The colors are associated to the quality classes as follows: purple-5 (excellent), blue-4 (very good), green-3 (quite good), yellow-2 (bad) and red-1 ( very bad)

Table 2 .

 2 Recognition rate errors with respect to number of used features issued from the dimension reduction step.

	.166

CONCLUSION

In this paper a new approach to design a quality metric is proposed. This approach is based on a classification process such as the human being is supposed to proceed to judge the quality of an object. To apply the classification process, a vector of features has been generated. The selected features are chosen from fullreference image SVH-based features and full-reference image features, both for them a reference image is needed. In addition, no-reference images SVH-based features and no-reference images features (both for them no reference image is needed) are included in the initial features vector.

In order to reduce the number of features within the initial vector, a manifold learning process is applied to reduce the dimension of the vector that will be used during the classification process. Three techniques are tested: principal component analysis performed 1) on the symmetric covariance matrix and 2) on the symmetric correlation matrix, and 3) Laplacian Eigenmaps.

The obtained results shown that the PCA on the correlation matrix gives better results and yields to reach a recognition rate error close to 14%. Analysis tends to prove that the original attributes of the features vectors are highly correlated. In future works, new attributes will be designed, and original images will be removed from the trial images set.


Louise Fouquat

Xin Guan

Claude Botella

Geneviève Grenet

Philippe Regreny

Michel Gendry

Hemian Yi

Jose Avila

Matthieu Bugnet
email: matthieu.bugnet@insa-lyon.fr

Jose Penuelas
email: jose.penuelas@ec-lyon.fr

José Avila

José Penuelas

Insights into the Arsenic Shell Decapping Mechanisms in As/GaAs Nanowires by X-ray and Electron Microscopy

Keywords: III-V nanowires, core-shell, oxidation, annealing, in situ transmission electron microscopy, scanning photoelectron microscopy

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Introduction

III-V semiconducting nanowires (NWs) are promising for a large range of applications including solar energy harvesting [START_REF] Krogstrup | Single-nanowire solar cells beyond the Shockley-Queisser limit[END_REF][START_REF] Zhang | III-V nanowires and nanowire optoelectronic devices[END_REF][START_REF] Kornienko | Growth and photoelectrochemical energy conversion of wurtzite indium phosphide nanowire arrays[END_REF][START_REF] Vettori | Growth optimization and characterization of regular arrays of GaAs/AlGaAs core/shell nanowires for tandem solar cells on silicon[END_REF][START_REF] Vanka | InGaN/Si doublejunction photocathode for unassisted solar water splitting[END_REF], microelectronics [START_REF] Chuang | Ballistic InAs nanowire transistors[END_REF] and integrated photonics [START_REF] Mårtensson | Epitaxial III-V nanowires on silicon[END_REF][START_REF] Huang | Nanowires for integrated multicolor nanophotonics[END_REF][START_REF] Yan | Nanowire photonics[END_REF][START_REF] Hocevar | Growth and optical properties of axial hybrid III-V/silicon nanowires[END_REF][START_REF] Saxena | Optically pumped room-temperature GaAs nanowire lasers[END_REF][START_REF] Zhao | Three-dimensional quantum confinement of charge carriers in self-organized AlGaN nanowires: A viable route to electrically injected deep ultraviolet lasers[END_REF][START_REF] Ra | Full-color single nanowire pixels for projection displays[END_REF][START_REF] Bermúdez-Ureña | Plasmonic waveguide-integrated nanowire laser[END_REF][START_REF] Liu | Selective area epitaxy of AlGaN nanowire arrays across nearly the entire compositional range for deep ultraviolet photonics[END_REF][START_REF] Jaffal | InAs quantum dot in a needlelike tapered InP nanowire: a telecom band single photon source monolithically grown on silicon[END_REF][START_REF] Vukajlovic-Plestina | Fundamental aspects to localize self-catalyzed III-V nanowires on silicon[END_REF].

In most of these applications, an epitaxial shell or a passivation layer wrapping the III-V core of the NW is needed to modify their functional properties or to avoid the formation of surface recombination traps due to undesirable oxidation. Materials such as silicon and germanium [START_REF] Hauge | Hexagonal silicon realized[END_REF][START_REF] Fadaly | Directbandgap emission from hexagonal Ge and SiGe alloys[END_REF], aluminum [20,[START_REF] Krogstrup | Epitaxy of semiconductor-superconductor nanowires[END_REF], Fe3Si [START_REF] Hilse | GaAs-Fe3Si core-shell nanowires: Nanobar magnets[END_REF] and SrTiO3 [START_REF] Guan | GaAs core/SrTiO3 shell nanowires grown by molecular beam epitaxy[END_REF] have been used as shell-material wrapping of III-V NWs to enhance or optimize their properties. Nevertheless, growing such heterogeneous shells is challenging; in most cases the shell and the core must be deposited in separate reactors, which implies that the oxidation of the as-deposited III-V facets must be avoided when the NWs are transferred between the deposition chambers. The strategy to avoid oxidation must preserve the quality of the NW facets from the point of view of their crystallography, their morphology and their surface chemistry. Besides the obvious use of connected ultra-high vacuum (UHV) reactors [START_REF] Krogstrup | Epitaxy of semiconductor-superconductor nanowires[END_REF][START_REF] Hilse | GaAs-Fe3Si core-shell nanowires: Nanobar magnets[END_REF], various methods have been suggested to obtain clean III-V facets for an epitaxial shell growth, such as for example cleaning by atomic hydrogen [START_REF] Hjort | Direct imaging of atomic scale structure and electronic properties of GaAs wurtzite and zinc blende nanowire surfaces[END_REF][START_REF] Hjort | Surface morphology of Au-free grown nanowires after native oxide removal[END_REF]. Among them, the reversible capping by arsenic [START_REF] Guan | GaAs nanowires with oxidation-proof arsenic capping for the growth of an epitaxial shell[END_REF] presents several advantages. Firstly, As can be one of the constitutive element of III-V semiconductors, e.g., in GaAs or InAs, and consequently this approach does not require the introduction of any additional element, which could modify the nature of the surfaces. Secondly, the As decapping is obtained through heating at rather moderate temperature (less than 400°C), and can be performed in standard growth reactors or in situ in scanning tunneling microscopes (STM) [START_REF] Xu | Faceting, composition and crystal phase evolution in III-V antimonide nanowire heterostructures revealed by combining microscopy techniques[END_REF][START_REF] Capiod | Band offsets at zincblende-wurtzite GaAs nanowire sidewall surfaces[END_REF][START_REF] Díaz Álvarez | Nonstoichiometric low-temperature grown GaAs nanowires[END_REF][START_REF] Álvarez | Importance of point defect reactions for the atomic-scale roughness of III-V nanowire sidewalls[END_REF][START_REF] Schnedler | Composition modulation by twinning in InAsSb nanowires[END_REF]. Despite its practical importance, the physical mechanism behind the NW decapping has not been much studied, except by reflective high energy electron diffraction (RHEED) and xray photoelectron spectroscopy (XPS) [START_REF] Guan | GaAs nanowires with oxidation-proof arsenic capping for the growth of an epitaxial shell[END_REF], and STM [START_REF] Álvarez | Importance of point defect reactions for the atomic-scale roughness of III-V nanowire sidewalls[END_REF]. It has been shown that even if the capping protects the NW facets well enough for subsequent epitaxial shell growth, it may induce surface defects that require nanometer resolution analysis on a single NW, such as transmission electron microscopy (TEM), compared to characterization techniques operating at larger scales such as RHEED and XPS, which intrinsically probe a NW assembly. Therefore, the objective of this work is to combine thermal annealing using in situ TEM, and scanning photoelectron microscopy (SPEM) to determine how the morphology, the structure, and the surface chemistry evolve during the decapping of an As shell wrapping a single GaAs NW.

Results and Discussion

The RHEED pattern obtained after the growth of GaAs NWs of sample S1 (see experimental section) and shown in Figure 1(a) indicates that the epitaxial growth axis of the NWs, i.e., perpendicular to the surface of the substrate, is [111], confirming our previous observations [START_REF] Guan | GaAs nanowires with oxidation-proof arsenic capping for the growth of an epitaxial shell[END_REF]. The RHEED pattern exhibits spots related to both Zinc-Blende (ZB) and Wurtzite (WZ) phases, as described elsewhere [START_REF] Dursap | Crystal phase engineering of self-catalyzed GaAs nanowires using a RHEED diagram[END_REF][START_REF] Jakob | Quantitative analysis of timeresolved RHEED during growth of vertical nanowires[END_REF]. After the As capping, the RHEED pattern shown in Figure 1(b) does not exhibit spots related to GaAs, in agreement with the presence of an amorphous As shell that completely covers the GaAs NWs and hinders the RHEED signal from the core. The NWs are vertical with an approximate length of 1.7 μm and a density of about 4 NWs/µm 2 , as shown in the scanning electron microscopy (SEM) image of the As-capped sample S1 in Figure 1(c). These NWs are well separated and do not shadow each other, which is crucial to obtain a uniform and conformal As shell using MBE. Nearly all the As-capped GaAs NWs of sample S1 have a uniform core diameter of 80 nm. The NWs of sample S2 exhibit a similar structure with a core diameter of about 150 nm and a length of about 9.0 µm. The As-capped GaAs NWs were ripped from their native substrate. For TEM observations, sample S1 was deposited onto a micro-electro-mechanical system (MEMS) DENSsolutions Wildfire chip, optimized for in situ annealing within the TEM column. For SPEM and XPS measurements, sample S2 was deposited on a Si substrate with its native oxide removed.

The bright field TEM image and elemental maps shown in Figure 2 confirm the core-shell NW structure with a core diameter of about 80 nm, and a conformal and smooth amorphous As shell of about 40 nm thickness. The Ga droplet at the NW tip is not visible due to its exposure to As atmosphere, which induced the formation of a crystalline WZ GaAs segment of about 150 nm length. The origin of this ZB / WZ transition has been thoroughly discussed [START_REF] Dursap | Crystal phase engineering of self-catalyzed GaAs nanowires using a RHEED diagram[END_REF][START_REF] Rudolph | Direct observation of a noncatalytic growth regime for GaAs nanowires[END_REF][START_REF] Scarpellini | Ga crystallization dynamics during annealing of self-assisted GaAs nanowires[END_REF], and is thought to be resulting from the evolution of the Ga droplet contact angle during the growth [START_REF] Glas | Why does wurtzite form in nanowires of III-V zinc blende semiconductors?[END_REF][START_REF] Krogstrup | Impact of the liquid phase shape on the structure of III-V nanowires[END_REF][START_REF] Jacobsson | Interface dynamics and crystal phase switching in GaAs nanowires[END_REF][START_REF] Dursap | Wurtzite phase control for self-assisted GaAs nanowires grown by molecular beam epitaxy[END_REF].

After NW dispersion onto Si substrate, sample S2 was rapidly sealed into the UHV chamber of the ANTARES beamline at synchrotron SOLEIL [START_REF] Avila | a scanning photoemission microscopy beamline at SOLEIL[END_REF]. It should be noted that SPEM experiments could also be performed on vertical NW grown on their original substrate [START_REF] Jabeen | Contactless monitoring of the diameter-dependent conductivity of GaAs nanowires[END_REF][START_REF] Zeller | Scanning photoelectron spectro-microscopy: a modern tool for the study of materials at the nanoscale[END_REF],

however we dispersed the NWs on a substrate in order to measure individual NWs. Figure 3(a) shows the XPS spectrum of sample S2 acquired with a large spot size. Only the As 3d core levels are visible; the Ga 3d photoelectrons cannot escape the shell thickness because of their shorter mean free path. The position of the As 3d5/2 core level at about 41.4 eV is that of metallic As. The spin orbit splitting is clearly evidenced. Oxidation of the exposed As shell is also detected in small quantity at about 44.4 eV due to the exposition to air prior to insertion into the XPS chamber. However, the prevalence of metallic As attests of the efficiency of the shell protective role. The beam was then focused by means of Fresnel zone plates in order to obtain a pixel size of about 400400 nm². The SPEM image of Figure 3(b) shows that the NWs are well distributed on the surface and have the expected length. It should be noted that because the expected NW diameters (about 230 nm) are smaller than the pixel size, the NW diameter is overestimated in SPEM images. A series of four As 3d spectra have been extracted along the length of a single NW, in addition to one spectrum from the substrate as reference (Figure 3(c)).

The four spectra from the NW are similar (the doublet structure of the As 3d peak is well resolved and the As oxide is alike) and therefore demonstrate the NW homogeneity.

Comparable measurements have been obtained on several NWs.

For in situ TEM annealing of sample S1, the temperature of the SiNx membrane supporting the dispersed NWs was directly increased to 200 ºC, and then incrementally stepped by 5 °C every 30 s, up to 380°C. It should be mentioned that upon annealing, the structural evolution of GaAs NWs was observed to occur only in some NWs, while other NWs would undergo the same structural transformation after the temperature is raised tens or hundreds of degrees higher. It is thus apparent that the structural evolution of the NWs varies strongly as a function of the nature of the thermal contact between the nanowires and the SiNx membrane, which depends on various factors like the NW bending, important here for NWs as long as 1.7 µm, and the NW interface with the supporting membrane (e.g., presence of amorphous hydrocarbon species at the NW surface, oxidation of the NW facets, presence of defects like atomic steps, etc.). The decapping process on NWs grown in the same conditions as sample S1 was also performed in the MBE chamber, and followed by RHEED. The in situ TEM results reported in this manuscript show structural and chemical modifications of NWs where the temperature of the SiNx membrane, which is accurately measured directly by the 4-point probe DENSSolutions system in the TEM [START_REF] Van Omme | Advanced microheater for in situ transmission electron microscopy; enabling unexplored analytical studies and extreme spatial stability[END_REF][START_REF] Niekiel | Local temperature measurement in TEM by parallel beam electron diffraction[END_REF], is in agreement with the temperature measured during decapping in the MBE chamber.

Above 300 °C, the NW surface became rough, as the amorphous As shell turns polycrystalline (see Supporting Information Figure S1). This crystallization was previously reported to occur at 306 °C in thick layers of amorphous As by differential thermal analysis [START_REF] Šimečková | A study on the crystallization of amorphous Arsenic[END_REF], in good agreement with our observations. The homogeneous crystallization over the length of this NW suggests that it is lying flat on the SiNx membrane, providing a homogeneous thermal contact. This is different from the NW shown in Video V1 (see Supporting Information), where the slow progression of the crystallization front from top to bottom suggests that the thermal contact with the membrane is better at the top of the NW. While the crystallization of the NW in Video V1 seems to start from the outer part of the As shell, especially on the top left of the NW, which could be attributed to the fact that it constitutes a free surface, additional evidence should be provided to support this hypothesis. At around 310 °C, the crystalline As shell begins to disappear (Figure 4). At around 365 °C, the As shell is not visible anymore and the GaAs surface is clean and smooth. Recently, in situ heating experiments in the TEM have been realized to estimate activation energies of various phenomena in III-V NWs, such as GaAs replacement by Au [START_REF] Fauske | T In situ heat-induced replacement of GaAs nanowires by Au[END_REF][START_REF] Tornberg | Kinetics of Au-Ga droplet mediated decomposition of GaAs Nanowires[END_REF] or defect dynamics [START_REF] Gott | Defect Dynamics in Self-Catalyzed III-V Semiconductor Nanowires[END_REF]. The same method has been applied here to extract the activation energy of the present As desorption mechanism. From 300 to 380 °C, the diameter 𝐷 of the NW was measured in order to calculate the corresponding arsenic desorption velocity 𝑘 (see Supporting Information for details concerning the data measurement). This desorption velocity can be related to an activation energy Ea (see Figure 4b) equal to 2.32 eV, a value slightly smaller than the cohesive energy of As, which varies from Ec = 2.4 eV per As atom to Ec = 3.0 eV per As atom depending on the crystalline phase [START_REF] Albe | Modeling of compound semiconductors: Analytical bondorder potential for Ga, As, and GaAs[END_REF]).

Figure 5 shows the As 3d core level photoemission spectra measured on sample S2 before annealing, after a first annealing (30 min) at 400°C, and after a second annealing (30 min) at 440°C. It should be noted that this temperature is probably overestimated compared to the temperature measured during MBE growth. After the first annealing, the XPS spectrum does not display Ga 3d core level (see Figure S3), which means that the As capping is still wrapping the NWs. However, the As 3d core level does not exhibit As oxide (grey-filled area) anymore.

After the second annealing at 440°C, the As 3d core levels are strongly modified. A shift toward low binding energy is clearly evidenced, and a broadening is observed. This energy shift agrees well with a modification of the As environment from As-As to Ga-As, as expected after As shell desorption. The broadening of the As 3d peaks could be the consequence of residual As at the surface and/or surface defects. The fitting parameters are available in Supporting Information (Table S1).

Elemental maps extracted from EELS data after the in situ decapping in the TEM indicate the complete desorption of the As shell, as illustrated in Figure 6. Spectra on the nanowire show both Ga L23 and As L23 contributions at ~1120 eV and ~1330 eV, respectively, as shown in Figure S4. The O-K edge at ~530 eV is not detected on the NW, suggesting that the As shell protects the nanowire from oxidation. This is in good agreement with the As 3d core level XPS spectra (Figure 5(c)), which indicate a GaAs surface without traces of oxidation. However, the As 3d peaks are broad, which could be explained by the presence of surface defects such as AsGa antisite defects as observed by STM [START_REF] Álvarez | Importance of point defect reactions for the atomic-scale roughness of III-V nanowire sidewalls[END_REF]). Moreover, the high resolution TEM image in Figure 6 shows that the NW surface is crystalline, and strongly facetted, comparable to as grown NWs, opening the way for further epitaxial growth. These results can be compared with NWs that have been exposed to air, and which exhibit a thin amorphous oxide shell [START_REF] Guan | GaAs nanowires with oxidation-proof arsenic capping for the growth of an epitaxial shell[END_REF].

Conclusions

In summary, we combined in situ heating of core(GaAs)-shell(As) NWs in the TEM and synchrotron radiation scanning photoemission microscopy to explore the structural changes of GaAs nanowires capped with an As shell upon annealing, which is a conventional step towards the growth of oxide shells on III-V cores in NW geometry. The results unambiguously show that the As decapping is preceded by the crystallization of the initially amorphous As shell at ~300 ºC. Beyond this temperature, the arsenic shell desorbs with an activation energy of ~2.32 eV, leading to clean facets of the NW core, which supports the success of this approach to promote the subsequent epitaxial growth of an oxide shell. Two desorption phenomena were identified, which could correspond to As oxide desorption and metallic As desorption. This work demonstrates that the capping / decapping process is efficient to obtain clean GaAs nanowires surfaces (stable until 600 °C [START_REF] Gang | Microstructural evolution in self-catalyzed GaAs nanowires during in-situ TEM study[END_REF]), and could be suitable for other arsenide NWs such as InAs (stable until 380 °C [START_REF] Choi | Anisotropic atomistic evolution during the sublimation of polar InAs nanowires[END_REF]). The proposed method allows to obtain clean facets in the high vacuum of a TEM column, and UHV setups equipped with a heater, thus opening the way to surface science studies on arsenide NWs.

Experimental Section

Nanowire Synthesis

Self-catalyzed GaAs NWs were grown on epiready Si(111) substrates by molecular beam epitaxy (MBE). The substrates were cleaned with ethanol and acetone for 5 min in order to remove surface contaminations. After rinsing, the substrates were outgassed at 200°C under UHV for a few minutes and then transferred into the MBE chamber. The MBE chamber is equipped with a Ga Knudsen cell with an incident angle of 27.9° [START_REF] Vettori | Impact of the Ga flux incidence angle on the growth kinetics of self-assisted GaAs nanowires on Si (111)[END_REF] and an As valve cracked cell. GaAs NWs were grown using the VLS mechanism with Ga droplets as catalyst [START_REF] Colombo | Ga-assisted catalyst-free growth mechanism of GaAs nanowires by molecular beam epitaxy[END_REF][START_REF] Fontcuberta I Morral | Nucleation mechanism of gallium-assisted molecular beam epitaxy growth of gallium arsenide nanowires[END_REF].

Because no native silicon oxides were removed beforehand, the Si substrate temperature was increased to 530°C, and one monolayer (ML) of Ga was deposited on the substrate at an equivalent GaAs two-dimensional growth rate of 0.50 ML/s [START_REF] Tauchnitz | Decoupling the two roles of Ga droplets in the self-catalyzed growth of GaAs nanowires on SiO x/Si (111) substrates[END_REF][START_REF] Fouquat | X-ray photoelectron spectroscopy study of Ga nanodroplet on silica-terminated silicon surface for nanowire growth[END_REF]. Then, the substrate temperature was increased to 610°C to begin the growth of GaAs NWs by providing Ga and As fluxes simultaneously. The GaAs growth rate was fixed at 0.75 ML/s with a beam equivalent pressure (BEP) of Ga and As4 equal to 3.6 x 10 -7 Torr and 3.6 x 10 -6 Torr, respectively. During growth, the sample holder was continuously rotated to enhance the growth homogeneity. Two samples were fabricated: sample 1 (S1) was grown during 10 minutes, while sample 2 (S2) was grown during 100 minutes. As a result, S2 NWs are longer than S1 NWs but also thicker due to radial overgrowth during the VLS axial growth. After the Ga shutter closure, the sample was cooled down to room temperature (RT) under an As4 atmosphere to avoid GaAs decomposition.

The As capping procedure was initiated after the substrate cooled down to RT following the growth of GaAs samples S1 and S2. For the As-capping of the obtained NWs, the temperature of the As cracking-cell was increased up to 950°C to supply As2 instead of As4. The samples were exposed to As2 for about 2 hours. S1 was dedicated to the TEM experiments while S2 was dedicated to the SPEM/XPS measurements.

In situ TEM characterization

The TEM experiments have been performed in a FEI Titan ETEM G2, equipped with a spherical aberration corrector of the objective lens, a Gatan imaging filter (GIF) TRIDIEM for electron energy-loss spectroscopy measurements, and operated at 300 kV. The in situ annealing experiments were carried out using a dedicated Wildfire heating holder from DENSsolutions.

NWs were transferred to a MEMS chip with a Si3N4 membrane by mechanically scrapping NWs off their native silicon substrate. The EELS elemental maps were obtained after background subtraction and integration of the Ga-L23 (~1120 eV) and As-L23 edges (~1330 eV) using the Digital Micrograph (Gatan Microscopy Suite) software.

Synchrotron radiation scanning photoelectron microscopy

X-ray photoemission experiments were performed at the nano-XPS endstation of the ANTARES beamline of the SOLEIL synchrotron (Paris, France), equipped with Fresnel zone plates for focalization of the synchrotron radiation beam, with a spot size of ~600 nm in this work. The experiments were carried out at a photon energy of 100 eV and linear horizontal light polarization, with an angular resolution of ∼0.2º and an energy resolution of ∼30 meV [57]. The sample was kept at room temperature and the base pressure during all experiments was better than 210 -10 mbar. The advantage of the nano-XPS technique for the study of NWs is that the X-ray beam spot size is small enough ensuring that the XPS measured is obtained in a particular area of a single few µm-long NW.

Figure 1 .

 1 Figure 1. RHEED patterns (a) before the As capping, highlighting the presence of ZB (green arrows) and WZ phases (orange arrows), and (b) after the As capping. (c) SEM image of sample S1 after the growth.

Figure 2 .Figure 3 .

 23 Figure 2. (a) Bright field TEM image of the as grown As/GaAs NW. (b) STEM-ADF image acquired simultaneously with a STEM-EELS spectrum image leading to the elemental maps of (c) Ga, (d) As, and (e) Ga+As. Scale bar: 50 nm

Figure 4 .

 4 Figure 4. (a-f) Bright field TEM images of a single NW (sample S1) showing the desorption of the As shell, recorded at T = 300 ºC (a), 315 ºC (b), 330 ºC (c), 345 ºC (d), 360 ºC (e), 375 ºC (f). Scale bar: 100 nm. (g) Arrhenius plot extracted from the NW diameter evolution).

Figure 5 .

 5 Figure 5. XPS As 3d core level spectra measured on a typical NW before annealing (a), after the first annealing at 400°C (b), after the second annealing at 440°C (c). The photon energy was set to 100 eV. The grey curve corresponds to As oxide, the yellow curve to metallic As and the blue curve to As in GaAs.

Figure 6 .

 6 Figure 6. (a) STEM-ADF image acquired simultaneously with an EELS spectrum image leading to the elemental maps of (b) Ga, (c) As, and (d) Ga+As; scale bar: 100 nm. (e) High resolution TEM image of the NW after decapping of the As shell; scale bar: 1 nm. The yellow lines follow the facets and are guides for the eye. (f) FFT performed on the NW shown in (e).

Acknowledgements

This work has been partly funded by the French Agence Nationale de la Recherche, project BEEP (ANR-18-CE05-0017-01). The Chinese Scholarship Council (CSC) is acknowledged for its financial support. The TEM work has been carried out at the consortium Lyon-St-Etienne de microscopie (CLYM). The authors thank the NanoLyon platform for access to equipment and J. B. Goure for technical assistance. SOLEIL is acknowledged for providing beamtime at the ANTARES beamline (proposal 20170235).

Authors

Louise Fouquat -Univ Lyon, Ecole Centrale de Lyon, CNRS, INSA Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR 5270, 69130 Ecully, France Xin Guan -Univ Lyon, Ecole Centrale de Lyon, CNRS, INSA Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR 5270, 69130 Ecully, France Claude Botella -Univ Lyon, Ecole Centrale de Lyon, CNRS, INSA Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR 5270, 69130 Ecully, France Geneviève Grenet -Univ Lyon, Ecole Centrale de Lyon, CNRS, INSA Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR 5270, 69130 Ecully, France Philippe Regreny -Univ Lyon, Ecole Centrale de Lyon, CNRS, INSA Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR 5270, 69130 Ecully, France Michel Gendry -Univ Lyon, Ecole Centrale de Lyon, CNRS, INSA Lyon, Université Claude Bernard Lyon 1, CPE Lyon, INL, UMR 5270, 69130 Ecully, France Hemian Yi -ANTARES Beamline, Synchrotron SOLEIL & Université Paris-Saclay, L'Orme des Merisiers, Gif sur Yvette Cedex, France

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Associated content

The Supporting Information is available free of charge at S1: Measured binding energy. Figure S3: STEM-EELS analysis of a NW after decapping of the arsenic shell.

Author information

Notes

The authors declare no competing financial interest.