Thomas Chaigne

Ori Katz

Jérôme Gateau

Claude Boccara

Sylvain Gigan

Emmanuel Bossy
email: emmanuel.bossy@espci.fr

Improving Photoacoustic-guided Focusing in Scattering Media by Spectrally Filtered Detection

We experimentally and numerically study the potential of photoacoustic-guiding for light focusing through scattering samples via wavefront-shaping and iterative optimization. We experimentally demonstrate that the focusing efficiency on an extended absorber can be improved by iterative optimization of the high frequency components of the broadband photoacoustic signal detected with a spherically focused transducer. We demonstrate more than 8-fold increase in the photoacoustic signal generated by a 30 µm wire using a narrow frequency band around 60MHz. We numerically confirm that such optimization leads to a smaller optical focus than using the low frequency content of the photoacoustic feedback.

Focusing light, ideally down to the micrometer scale, is required in many biomedical and industrial applications such as optical microscopy and light delivery. However, light scattering in complex media such as biological tissue prevents focusing and imaging at depth with optical resolution. As a result, optical microscopy is currently restricted to rather superficial investigation, i.e hundreds of micrometers [START_REF] Ntziachristos | Going deeper than microscopy: the optical imaging frontier in biology[END_REF]. Nevertheless, in 2007, Vellekoop et al. have demonstrated focusing of coherent light to a diffraction-limited spot through highly scattering samples by wavefront shaping [START_REF] Vellekoop | Focusing coherent light through opaque strongly scattering media[END_REF]. By controlling the phase of the incident wavefront with a spatial light modulator (SLM), they demonstrated control over the scattered light complex interference speckle pattern. Iteratively optimizing a feedback signal from a chosen target position resulted in a diffraction limited, high-intensity focus at this point. Following this demonstration, wavefront-shaping has been exploited in numerous works to achieve various goals, from surpassing the diffraction limit in scattering media to allowing imaging through opaque layers [START_REF] Allard P Mosk | Controlling waves in space and time for imaging and focusing in complex media[END_REF]. In most of these works the feedback signal was obtained from a photodetector placed at the targeted location. However, to focus light inside a scattering sample in most practical scenarios, one cannot directly place such a detector at the target position. One promising approach to perform controlled focusing inside scattering media was presented by Kong et al.[4]. This approach is based on the photoacoustic effect in the transient regime, i.e. the generation of broadband ultrasonic waves subsequent to the absorption of a short optical pulse. The amplitude of the generated ultrasound waves is proportional to the local light intensity on the absorber. Furthermore, biological tissue already contain endogenous absorbers such as hemoglobin, and are only weakly scattering for ultrasound waves in the megahertz range. Hence, photoacoustics is an effective approach for localizing absorbing structures inside tissue, and monitoring the absorbed light intensity by detecting the emitted ultrasound waves with an external transducer [START_REF] Ntziachristos | Looking and listening to light: the evolution of whole-body photonic imaging[END_REF]. By optimizing such a photoacoustic feedback signal, it is possible to focus light through a scattering layer noninvasively , as demonstrated by Kong et al. [START_REF] Kong | Photoacoustic-guided convergence of light through optically diffusive media[END_REF]. Inside tissue, one will likely deal with extended absorbers (larger than the acoustic focus in at least one dimension), such as blood vessels [START_REF] Zhang | In vivo high-resolution 3d photoacoustic imaging of superficial vascular anatomy[END_REF]. As a consequence, the size of the optical focus after optimization is linked to the acoustic resolution, and the optical intensity enhancement over the probed volume is expected to drop in proportion to the number of speckle grains contained in the acoustic focus, and whose intensities are simultaneously enhanced [START_REF] Vellekoop | Demixing light paths inside disordered metamaterials[END_REF][START_REF] Chaigne | Controlling light in scattering media noninvasively using the photo-acoustic transmission-matrix[END_REF]. In this letter, we investigate the role of the center frequency and bandwidth of the ultrasound detection on the optical focusing capabilities (i.e. focus size and enhancement of the optical intensity on the target), considering the use of a single high frequency focused ultrasonic transducer and an extended absorber. We experimentally demonstrate a significant improvement in the photoacoustic signal enhancement by optimizing the high frequency components of the photoacoustic signal rather than the full band. We also confirm with numerical simulations that such spectral filtering leads to tighter optical foci compared to the ones obtained with optimization of the low frequency signal.

For our experimental investigation, we have implemented the following iterative optimization process to focus light using photoacoustic feedback. In this process, we sequentially shift the phase of a set of wavefront patterns that form a basis of the SLM pixels (i.e. the optical input modes). We record the modulation of the photoacoustic signal from the chosen position, and then keep the phase that maximizes it for each input mode(see Fig. 1). The optimization algorithm is using Hadamard basis vectors as the input basis instead of the canonical one (i.e. pixel-by-pixel), which allows for a larger modulation of the feedback signal and fast convergence [START_REF] Popoff | Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media[END_REF]. The experimental setup was presented in Fig. 1a: a 5ns pulsed laser beam (Continuum Surelite, 10 Hz repetition rate, 532nm wavelength, 10mJ pulse energy, a few millimeters of coherence length), was expanded to illuminate a phase-only SLM (Boston Micromachines Multi-DM with 140 segmented mirrors). The scattering medium was an optical diffuser (0.5 • circular light shaping diffuser, Newport). The SLM surface was imaged on the surface of the diffuser by a 4-f telescope. This ensured that the optical speckle size on the target remained constant for different SLM phase-patterns during the optimization [START_REF] Vellekoop | Exploiting disorder for perfect focusing[END_REF]. The absorbing target was a black 30µm diameter nylon wire (NYL02DS, 10/0, Vetsuture), embedded in an agarose gel placed at a distance of 5cm behind the scattering sample. The beam diameter on the diffuser and the distance between the diffuser and the absorber were set to obtain a speckle grain size of 25µm. The photoacoustic signal generated by the absorber was detected with a spherically-focused ultrasonic transducer (Sonaxis) having a center frequency f = 27M Hz and B = 26M Hz two-way -6dB bandwidth. The detector has an intrinsic focal zone with a transverse diameter of ∅ acoustic F c f D = 100µm, where F = 8mm is the focal length of the transducer, D = 4mm its diameter, c water = 1480m/s the speed of sound in water. It is worth noting that this transverse diameter is inversely proportional to the acoustic center frequency [START_REF] Gordon | Acoustic waves: devices, imaging, and analog signal processing[END_REF], and can therefore be controlled by approprate filtering. The absorber was placed perpendicular both to the laser beam propagation direction and the transducer axis, one portion being in the acoustic focus (see Fig. 1a). For each laser pulse and displayed SLM phase-pattern, the photoacoustic signal was measured by a computer-controlled oscilloscope (Lecroy Wavesurfer 104MXs-B), giving the temporal photoacoustic trace (Fig. 1, inset). The Fourier transform of the measured signal was computed and the RMS value in a selected bandwidth was used as the feedback signal for the iterative optimization algorithm. The feedback signal was normalized by the power of each pulse (as monitored by a photodiode) to compensate for the fluctuations of the laser.

To quantify the efficiency of the optimization, we define the enhancement η of the feedback signal as the ratio between the final optimized value of the feedback signal and the mean value of the feedback signal over the first iteration of the optimization. In previous works using direct detection of the light intensity at the target point [START_REF] Vellekoop | Demixing light paths inside disordered metamaterials[END_REF][START_REF] Popoff | Controlling light through optical disordered media: transmission matrix approach[END_REF], the enhancement η optical was given by:

η optical 0.5 × N SLM N modes , (1)
where N SLM is the number of controllable degrees of freedom, and N modes is the number of speckle grains or optical modes whose intensities are simultaneously optimized.

For the photoacoustic feedback optimization considered here, we expect to obtain a similar dependance on the number of simultaneously optimized speckle grains. These speckle grains correspond to the ones contained in the so-called acoustic cell [START_REF] Gateau | Improving visibility in photoacoustic imaging using dynamic speckle illumination[END_REF], i.e. the absorber portion that is contained in the focal volume of the transducer. Because these speckle grains are assumed to be invariant in the propagation direction, this number scales as: N modes ∝ ∅ acoustic ×∅ absorber ∝ f -1 , in the specific case of a linear absorber. To obtain larger signal enhancement, one has either to increase the number of degrees of control (N SLM ), which would require longer acquisition times, or reduce the number of optical modes inside the probed acoustic volume N modes . As the bandwidths of the transducer and photoacoustic signal are broad (spanning more than two octaves, see Fig. 1b), one could probe significantly smaller focal areas by highpass filtering the detected signals. Optimizing high spectral component of the photoacoustic response of the absorber thus allows to effectively reduce the detection volume, which would result in a smaller focal spot and an increased light delivery efficiency.

In addition to the above simple considerations, we em-phasize that specific characteristics of photoacoustic detection (compared to a direct optical detection) may affect the optimization process. First of all, the detected signal results from the coherent summation of the acoustic waves emitted by all absorbed speckle grain. Then, its frequency content relies on the source geometry, that is the spatial distribution of the illumination pattern. Moreover, the lateral detection profile of the transducer gives different weights to the speckle grains. This feature has been used in a recent paper to reach sub-acoustic resolution focusing after a genetic optimization process [START_REF] Conkey | Super-resolution photoacoustic imaging through a scattering wall[END_REF], but it is beyond the scope of our study. Despite these subtleties of photoacoustics, we still expect the photoacoustic feedback optimization to exhibit a similar trend concerning N modes , and thus the optimized frequency band. To experimentally demonstrate the influence of the spectral filtering, we optimized light delivery using different frequency bands. The calculated acoustic focal volumes corresponding to each band are illustrated in Fig. 1c, illustrating the shrinking of the focus size with increasing detected frequency. The optimization results are presented in Fig. 2: the optimization of the high frequency band leads to a higher enhancement of the feedback signal than the optimization of lower frequency bands or the full band of the photoacoustic signal. Specifically, the enhancement of the high frequency (48-65 MHz) photoacoustic signal is more than four times larger than the enhancement obtained during the optimization of the lower frequency content (5-12 MHz).

It is important to note that shrinking the focal zone of the transducer results in a lower measured signal as the probed area is smaller and thus contains less speckle grains, which is expressed in a reduced signal-to-noise ra-tio in the high frequency trace in Fig. 2c (blue trace). In addition, limiting the signal bandwidth ∆f affects also the axial resolution of the acoustic probing ∆z = c s /∆f , and would have to be taken into account in the case of densely packed absorbing targets in the axial direction.

To relate our experimental observations to the spatial confinement of the optical focus, we have numerically modeled our system and run the same optimization algorithm. A cylindrical absorber of 30µm diameter and 1mm length was simulated by considering photoacoustic point sources spaced by 2µm and excited by a 5 ns Gaussian laser pulse [START_REF] Irio G Calasso | Photoacoustic point source[END_REF]. The transducer geometry was modeled by discretizing the surface with 2.5µm steps.

The values for the discretization steps were chosen small enough to provide an accurate modeling, independent of the values themselves. The absorber was placed in the focal plane symmetrically to the transducer axis. The optical diffuser was modeled by a random phase mask (single scattering) so as to generate a speckle pattern with 25µm speckle grain size on the absorber, which is placed in the diffuser's far field. The speckle pattern was assumed to be invariant in the propagation direction, i.e. along the width of the wire. The discrepency between the speed of sound in nylon and water (c nylon = 2620m/s) was taken into account by scaling the diamenter of both the wire and the speckle grain by a factor c water c nylon . Simulations results were averaged over 100 different realizations of the scattering medium. The average evolution of the PA feedback signals are presented in Fig. 3a. The light intensity profiles obtained after optimization were averaged over the initial speckle realizations and are presented in Fig. 3c. We observe that the optimization of the high frequency content of the photoacoustic signal leads to a tighter optical focus, as expected.

Experiments and simulations follow the same trend (see Fig. 3b), but with a lower enhancement obtained experimentally. We attribute this fact to the lower experimental signal-to-noise ratio, especially for the high frequency bands, and to the experimental system stability.. We note that even the noise-free simulations do not exhibit the same behaviour than what would be obtained with a camera. This could be attributed to the fact that this approach does not take into account the geometry of the photoacoustic source. A smaller optical focus will indeed generate more high frequency than an extended one, which will affect the optimization of the filtered photoacoustic signal but not the optimization of the light intensity using a standard photodetector, even in the case where different weights would be attributed to different speckle grains.

In summary, we demonstrated that focusing light through scattering media by optimizing the photoacoustic response of an elongated cylindrical absorber can be improved optimizing the high frequency components of the photoacoustic signals. This type of elongated absorbing structures is an important model, relevant for mimicking blood vessels, a major endogenous source of photoacoustic constrast in tissue [START_REF] Zhang | In vivo high-resolution 3d photoacoustic imaging of superficial vascular anatomy[END_REF]. The enhancement of the high frequency photoacoustic feedback has been experimentally and numerically shown to be larger than the optimization of the low frequency or content. We relate this improvement to the reduction in the acoustic focal volume of the spherically focused transducer as the frequency increases. We numerically linked these observations to the spatial confinement of light after optimization, showing that a tighter optical focus is indeed obtained after optimization of the high frequency components rather than the low frequency band of the photoacoustic signal. Spectrally filtered signals were chosen over peak-to-peak values (usually computed for photoacoustic imaging) because it enables precise control of the focal volume of the transducer. Indeed the frequency weighting in the peak-to-peak value is expected to change during the optimization, changing dynamically the size of the focal spot, which is prevented in our approach. This new technique may become useful if one wants to achieve optical focusing inside scattering media, where the speckle grain size becomes indeed quickly small and diffraction limited. In such scenarios, one has to reduce the size of the acoustic focus as much as possible to get a measurable increase in the photoacoustic signal, using the smallest possible number of degrees of control (SLM pixels). The access to such spectrally controlled focus size does not have a direct counterpart in all-optical wavefront shaping experiments.

FIG. 1 .

 1 FIG. 1. (a) Experimental setup: a SLM shapes a nanosecond pulsed laser beam illuminating an absorbing wire through a scattering sample; a small portion of the beam is directed toward a photodiode (PD) to monitor the pulse to pulse intensity variation; a spherically focused acoustic transducer detects the photoacoustic signals generated by the absorber. The focal zone of the transducer is depicted by a blue elliptic region. (inset: a typical photoacoustic signal trace by the transducer). (b) Measured photoacoustic power spectrum (blue curve), and noise-floor of the detection system (dashedblack curve); the colored strips correspond to the frequency bands selected for optimization. (c) Typical dimensions of the acoustic foci corresponding to each frequency band: 5-12MHz (red), 45-52MHz (green) and 58-65MHz (blue). The black line depicts the absorbing wire.

FIG. 2 .

 2 FIG. 2. Evolution of the filtered photoacoustic feedback signals (RMS values) during their respective optimization (bb: broadband, 2-85MHz). The signals are normalized by the average of the signal over the first iteration of the optimization. 160 steps are needed, as this is the chosen Hadamard basis size, that spans the SLM pixels.

FIG. 3 .

 3 FIG. 3. Simulation results: (a) Evolution of the PA signals during the optimization process. (b) Enhancement of spectrally filtered PA signal after optimization over different frequency bands. Experimental results follow the same trend than simulations. (c) Light intensity profile along the absorbing wire after optimization of the PA signal (averaged over several realisations of the initial speckle pattern).


Thomas Chaigne

Jérôme Gateau

Ori Katz

Emmanuel Bossy
email: emmanuel.bossy@espci.fr

Sylvain Gigan
email: sylvain.gigan@espci.fr

Light Focusing and Two-Dimensional Imaging Through Scattering Media using the Photoacoustic Transmission-Matrix with an Ultrasound Array

We implement the photoacoustic transmission-matrix approach on a two-dimensional photoacoustic imaging system, using a 15 MHz linear ultrasound array. Using a black leaf skeleton as a complex absorbing structure, we demonstrate that the photoacoustic transmission-matrix approach allows to reveal structural features that are invisible in conventional photoacoustic images, as well as to selectively control light focusing on absorbing targets, leading to a local enhancement of the photoacoustic signal.

In biological tissue, light scattering limits the penetration depth of most optical imaging techniques to a few hundred micrometers [1]. In the last few years, wavefront shaping appeared as a powerful tool to compensate light scattering. By controlling the input wavefront with a spatial light modulator (SLM), Vellekoop and Mosk first demonstrated the focusing of coherent light through highly scattering opaque layers [2]. Popoff et al. then introduced the transmission-matrix approach, allowing imaging and focusing through highly scattering samples, by measuring the complex linear relations between many input and output optical modes [START_REF] Popoff | Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media[END_REF]. Many wavefront-shaping based techniques have been thoroughly investigated since [START_REF] Allard P Mosk | Controlling waves in space and time for imaging and focusing in complex media[END_REF], but most of the proposed approach relied on a feedback signal from a camera placed behind the scattering sample, i.e. at the target plane. Although the requirement for a direct optical access to the target was considered as the main limitation for applying wavefront shaping in practical scenarios, several approaches to overcome this apparent limitation have been investigated. These methods include using implanted guide-stars [START_REF] Vellekoop | Demixing light paths inside disordered metamaterials[END_REF][START_REF] Hsieh | Imaging through turbid layers by scanning the phase conjugated second harmonic radiation from a nanoparticle[END_REF], ultrasonic tagging of light [START_REF] Xu | Time-reversed ultrasonically encoded optical focusing into scattering media[END_REF][START_REF] Si | Fluorescence imaging beyond the ballistic regime by ultrasound-pulse-guided digital phase conjugation[END_REF][START_REF] Judkewitz | Speckle-scale focusing in the diffusive regime with time reversal of variance-encoded light (trove)[END_REF], and the photoacoustic effect [START_REF] Kong | Photoacoustic-guided convergence of light through optically diffusive media[END_REF].

Photoacoustic imaging has emerged in the past decade as a powerful hybrid modality to image optical-absorption contrast in turbid media [START_REF] Beard | Biomedical photoacoustic imaging[END_REF]. Because ultrasound waves are only weakly scattered, images can be obtained at penetration depth up to a few centimeters with a sub-mm resolution. By using the photoacoustic feedback from a single ultrasonic transducer, Kong et al. performed wavefront shaping to focus light on absorbers located behind a scattering sample [START_REF] Kong | Photoacoustic-guided convergence of light through optically diffusive media[END_REF]. The use of photoacoustic-guided wavefront shaping has then been extended to allow selective focusing at multiple absorbing targets using the photoacoustic transmission matrix [START_REF] Chaigne | Controlling light in scattering media non-invasively using the photoacoustic transmission matrix[END_REF]. Photoacoustic-guided wavefront-shaping has also been very recently performed using the large spectral bandwidth of photoacoustic signals [START_REF] Chaigne | Improving photoacoustic-guided focusing in scattering media by spectrally filtered detection[END_REF],

and it has been proposed as a mean to get sub-photoacoustic resolution [START_REF] Conkey | Super-resolution photoacoustic imaging through a scattering wall[END_REF]. In addition to providing a feedback signal for wavefront shaping, it appears that coupling photoacoustics and wavefront-shaping could also improve the quality of the photoacoustic images [START_REF] Antonio M Caravaca-Aguirre | High contrast three-dimensional photoacoustic imaging through scattering media by localized optical fluence enhancement[END_REF]. In all the above-mentioned works, one-dimensional photoacoustic "images" were acquired using a single spherically focused ultrasonic transducer, thus limiting the applicability of the technique to narrow fields-of-view and requiring mechanical scanning to obtain twodimensional images. In this Letter, we extend the photoacoustic transmission matrix method [START_REF] Chaigne | Controlling light in scattering media non-invasively using the photoacoustic transmission matrix[END_REF] to a two-dimensional photoacoustic imaging setup using a linear ultrasound array. Photoacoustic imaging using transducer-arrays is a well established technique which provides a two-dimensional photoacoustic image in a single laser shot. Commercial linear transducer-arrays are widely used in this domain because they enable imaging a whole plane, and benefit from technologies developed for ultrasonic measurements. By combining wavefront shaping and photoacoustic imaging with an ultrasound array, we propose to measure the photoacoustic transmission-matrix over a large field-of-view without scanning. With two-dimensional photoacoustic images, the photoacoustic transmission matrix describes the complex influence of the optical input modes (SLM pixels) on the acoustic output modes (defined as the acoustic cells [START_REF] Gateau | Improving visibility in photoacoustic imaging using dynamic speckle illumination[END_REF], i.e. the intersection between each acoustic resolution cell in the photoacoustic image and the absorbing structures [START_REF] Chaigne | Controlling light in scattering media non-invasively using the photoacoustic transmission matrix[END_REF]). We study the extended photoacoustic imaging capability provided by this matrix, which measurement involve illuminating the sample with multiple speckle patterns. Light focusing and photoacoustic imaging enhancement is demonstrated through scattering phantoms on several target positions on a complex absorbing structure.

The experimental setup is illustrated in Fig. 1. A laser pulse (Continuum Surelite, 532 nm wavelength, 5 ns pulse duration, 10 Hz repetition rate) is spatially shaped by an SLM (Multi-DM, Boston Micromachines, 140 segmented mirrors). The spatially-shaped pulse passes through a scattering sample (120 Grit ground glass diffuser, Thorlabs). The SLM plane is conjugated with the scattering surface by a 4-f telescope. This ensures that the optical speckle size on the target remains constant for different SLM phase-patterns [START_REF] Vellekoop | Exploiting disorder for perfect focusing[END_REF].

An third lens adds a curvature on top of the SLM phase pattern [START_REF] Chaigne | Controlling light in scattering media non-invasively using the photoacoustic transmission matrix[END_REF]. The scattered light illuminates a phantom containing an absorbing structure, embedded in an agarose gel with negligible optical scattering. In this study, we use a black leaf skeleton as the absorbing target (Fig. 2.a) [START_REF] Jose | Speed-of-sound compensated photoacoustic tomography for accurate imaging[END_REF][START_REF] Huang | Improving limited-view photoacoustic tomography with an acoustic reflector[END_REF]. This sample contains branching structures with multiple orientations and various spatial scales, ranging from 50µm to 200µm. This two-dimensional sample is located in the imaging plane and in the vicinity of the elevation focus of a linear ultrasound array (128 elements, 14.4 MHz center frequency and pulse-echo -6 dB bandwidth of 6.8 MHz, 0.1 mm pitch and elevation focus of 8 mm, Vermon, France), connected to a commercial ultrasound scanner (Aixplorer, Supersonic Imagine, France). The photoacoustic transmission matrix is measured using the protocol described in [START_REF] Chaigne | Controlling light in scattering media non-invasively using the photoacoustic transmission matrix[END_REF].

The influence of each of the controllable input modes (SLM pixels) on each of the photoacoustic image pixel is measured by varying the phase of each SLM pattern (in the Hadamard basis) from 0 to 2π in 8 steps. An unshaped part of the circular input beam serves as a fixed reference field [START_REF] Popoff | Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media[END_REF][START_REF] Chaigne | Controlling light in scattering media non-invasively using the photoacoustic transmission matrix[END_REF]. To increase the measurements SNR, the SLM input modes are in practice measured over a Hadamard basis set [START_REF] Popoff | Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media[END_REF]. A photoacoustic image is acquired for each input SLM phase pattern (as opposed to acquiring only a single one-dimensional time trace as in [START_REF] Chaigne | Controlling light in scattering media non-invasively using the photoacoustic transmission matrix[END_REF]). When varying each SLM input pattern phase from 0 to 2π, the intensities values of the photoacoustic images vary according to the cosine of the applied phase [START_REF] Beard | Biomedical photoacoustic imaging[END_REF]. The elements of the photoacoustic transmission matrix are obtained directly by analyzing these cosine modulation phases and amplitudes [START_REF] Beard | Biomedical photoacoustic imaging[END_REF]. To improve the SNR, we analyze the modulation of the maximum intensity values within areas of 125 × 125 µm 2 that match the acoustic resolution cell size, rather on single pixels, which are considerably smaller.

Once the photoacoustic transmission matrix is measured, it can be analyzed to obtained information about the scattering medium and the imaged object. Fig. 2 illustrates how the photoacoustic transmission-matrix approach can improve photoacoustic imaging. Figs 2.b and 2.c illustrate the images that would be obtained with the same imaging system using a uniform illumination. Here, these images were computed by averaging all the images acquired during the matrix measurement process. elongated absorbers emits acoustic energy mostly perpendicularly to their main orientation, and therefore only photoacoustic waves emitted from horizontal elements reach the ultrasound array. Because the transmission-matrix approach involves measuring a collection of photoacoustic images under several speckle illuminations, its analysis allows to reveal the hidden structures: by analyzing the modulation of the pixels values over the different photoacoustic images, it is possible to reconstruct hidden segments of the leaf skeleton, as shown in Fig. 2.d. More specifically, the modulus of the transmission-matrix elements was averaged over the input modes: I j =< |T i,j | > i , where I is the image displayed on Fig. 2.d, and T the photoacoustic transmission-matrix. The index j corresponds to a given pixel of the image and the index i corresponds to the input modes. We thus obtain a modulation image revealing all segments of the leaf skeleton independently of their orientation. This approach is very similar to that introduced by Gateau et al. [START_REF] Gateau | Improving visibility in photoacoustic imaging using dynamic speckle illumination[END_REF], where uncorrelated random speckle patterns were produced using a varying diffuser: images revealing invisible structures were obtained from the measure of the variance between the photoacoustic images obtained under the various random illuminations. This is made possible because the speckle illumination breaks up the elongated parts of the absorbing structure into small isotropic and high frequency sources. We emphasize that the image of Fig. 1.d is obtained without any additional measurement, all the information being contained in the transmission-matrix.

As demonstrated in [START_REF] Chaigne | Controlling light in scattering media non-invasively using the photoacoustic transmission matrix[END_REF], the photoacoustic transmission-matrix can be used to selectively focus light through a turbid sample. Here we investigate the light-focusing capability of the two-dimensional photoacoustic transmission-matrix for an arbitrary position on the absorbing structure. To this end, for each of the selected desired focusing positions, we use the transmission-matrix row corresponding to this output mode. We apply the corresponding conjugated phase pattern on the SLM, so that all input modes contribute constructively to maximize the photoacoustic signal at the target location [START_REF] Chaigne | Controlling light in scattering media non-invasively using the photoacoustic transmission matrix[END_REF]. The results of focusing on three arbitrary targets on the leaf skeleton fibers are shown in Fig. 3. Quantitatively, the signals of the reconstructed photoacoustic image were locally increased by a factor of 6.2 (red target, Fig. 3.b), 3.4 (blue target, Fig. 3.e), and 5.2 (green target, Fig. 3.h). This photoacoustic enhancement factor is defined as the ratio between the maxima over the targeted area (colored square, 125 × 125µm 2 ) of the enhanced (when applying focusing pattern on the SLM) and average (Fig. 2.c) photoacoustic images. These ratios are within the order of magnitude of the expected enhancement of the optical intensity, defined roughly as

0.5 × N SLM N speckles
, where N SLM is the number of SLM pixels and N speckles the number of optical speckles grains contained in the targeted acoustic cell [START_REF] Popoff | Measuring the transmission matrix in optics: an approach to the study and control of light propagation in disordered media[END_REF], which optical intensities are simultaneously enhanced. Here, the distance between the scattering sample and the absorbing structure yielded 25µm diameter speckle grains on the absorbing structure ( 1 √ 2 × FHWM of speckle autocorrelation). The size of the targeted acoustic resolution cells is 125 × 125µm 2 .

N speckle is thus assessed to be aroud 25, leading to an expected optical enhancement factor around 3. We compute N speckles as a ratio of areas, because the speckle are elongated in the light propagation axis. Moreover, the elevation resolution of the transducer-array is not taken into account here because the absorbing sample is fully contained in the elevation focal zone. In the focusing results presented in Fig. 3, we have selected noticeably bright points on the standard photoacoustic image (fig. 2.c) as target points, meaning that focus- ing was obtained only on rather horizontal veins of the leaf skeleton. However, using the photoacoustic transmission matrix, light focusing and control can be exerted on normally "invisible" vertical structures as well. In Fig. 4, we demonstrate such focusing on one such portion that is invisible on Fig. In summary, we have demonstrated that the implementation of the transmission-matrix approach on a two-dimensional photoacoustic imaging system enables to control light focusing over a large field-of-view without any mechanical scanning process, by parallezing the acquisition of the output modes. We experimentally demonstrate the selective focusing at arbitrary target points on a complex absorbing structure located behind a scattering sample. Moreover, we have shown that structures that are invisible in a standard photoacoustic image due to the limited-view configuration could be revealed by imaging the signals modulation when varying the input modes. In addition, we have demonstrated the capability to focus on these hidden segments using this modulation image to select the target points.

We note that the photoacoustic transmission-matrix method suits well the study of complex absorbing samples, as it enables a clear identification of the targets regardless of their orientation relatively to limited-view acquisition and allows to locally enhance photoacoustic signals.

Optical focusing was performed up to the acoustic resolution. Further studies are required to understand the effect of wavefront shaping below this current resolution limit. For practical application in deep-tissue imaging, two different challenges emerge. The first is related to the fast decorrelation of optical speckle patterns inside tissue. The use of higher repetition rate laser and higher damage threshold SLM would improve the speed of the transmissionmatrix measurement, which is currently limited to several tens of minutes. The second challenge is the ability to measure the small modulation of the photoacoustic signal from an acoustic-resolution cell containing a large number of optical speckles. One has thus to ensure that the number of optical speckles contained in an acoustic-resolution cell is as low as possible, by using either small absorbers, high frequency transducer, non-linear photoacoustic signal generation or an alternative analysis of the signal fluctuations. [1] Vasilis Ntziachristos. Going deeper than microscopy: the optical imaging frontier in biology.

Nature methods, 7(8):603-614, 2010.

[2] IM Vellekoop and AP Mosk. Focusing coherent light through opaque strongly scattering media. Optics letters, 32( 16):2309-2311, 2007.

  After each laser shot, the photoacoustically induced ultrasonic waves are measured simultaneously by all the elements of the array. The intensity fluctuations of the laser are monitored with a photodiode, and are used to normalize the measured photoacoustic signals. The acquired photoacoustic signals are averaged over 10 laser-pulses to improve the signal-to-noise ratio (SNR). The averaged signals are then filtered with a digital third-order Butterworth lowpass filter having a cutoff frequency of 25 MHz. The photoacoustic image is reconstructed with a standard backprojection algorithm[START_REF] Xu | Universal back-projection algorithm for photoacoustic computed tomography[END_REF], using a pixel size of 25 µm to match the sampling rate of the ultrasound scanner.

FIG. 1 .

 1 FIG. 1. Experimental setup: a 5-ns laser pulse is shaped by an SLM before passing through a scattering sample and illuminating an absorbing structure. Photoacoustic signals are detected with an ultrasonic linear array, driven by an ultrasound scanner.

  Fig. 2.c is the envelope of Fig 2.b, obtained by computing the modulus of the analytic signal representation of each column (z-axis) of image 2.b. From the photograph shown on Fig. 2.a, it is clear that Figs. 2.b and 2.c only reveals the horizontal (x-axis) structures of the sample. This feature is a standard artefact in photoacoustic imaging, due to the finite aperture of the transducer array [21]:

FIG. 2 .

 2 FIG. 2. Improved photoacoustic imaging using the transmission matrix: (a) Reference photograph of the absorbing leaf skeleton embedded in an agarose gel block. (b) A standard photoacoustic image equivalent to that obtained with uniform illumination: this image is obtained by averaging all the photoacoustic images acquired during the transmission matrix measurement, that correspond to the hundreds of speckle illuminations created by the successive SLM phase patterns. This image contains negative values because of the limited bandwidth of the imaging system and artefacts of the backprojection algorithm. The coloured circles indicate the position of the foci presented in the next figures. (c) Envelope image derived from (b), enabling a better visualization analog to that of conventional ultrasound images. (d) Modulation image: the value of each pixel gives the mean modulation depth of the photoacoustic signals (modulus of the transmission matrix), averaged over the input modes.

FIG. 3 .

 3 FIG. 3. Focusing on visible regions: (a) enveloppe of the mean photoacoustic image (zoom of Fig. 2.c). (b) enveloppe of the photoacoustic image when displaying specific focusing phase pattern on the SLM. (c) Enveloppe of the difference between the photoacoustic images corresponding to (b) and (a) (the difference is computed before the enveloppe). (d,e,f) and (g,h,i) are analog to (a,b,c) for different target positions. The colored squares indicate the areas over which the modulation of the photoacoustic signal was measured. The colors correspond to the positions marked on Fig.2.b.

  FIG. 4. Focusing on invisible regions: (a) enveloppe of the mean photoacoustic image (zoom of Fig. 2.c). (b) average of transmission-matrix modulus over the input modes (zoom of Fig 2.d). (c) enveloppe of the photoacoustic image when displaying specific focusing phase pattern on the SLM. (d) Enveloppe of the difference between the photoacoustic images corresponding to (c) and (b) (the difference is computed before the enveloppe).

  This work was funded by the European Research Council (grant number 278025), the Fondation Pierre-Gilles de Gennes pour la Recherche (grant number FPGG031), and the Plan Cancer 2009-2013 (project Gold Fever). O. K. acknowledges the support of the Marie Curie intra-European fellowship for career development(IEF).


Qirong Zhu

Barbara Paci

Amanda Generosi

Séverine Renaudineau

Pierre Gouzerh

Xihui Liang

Claire Mathieu

Cindy Rountree

Guillaume Izzet

Anna Proust 1

Nicholas Barrett 3

Tortech Ludovic

1

Conductivity via Thermally Induced Gap-States in a Polyoxometalate Thin Layer

We report a study of -[P 2 W 18 O 62 ] 6-, Wells-Dawson polyoxometalate layers deposited on ITO coated glass substrates. A variety of techniques has been used including atomic force microscopy for surface topography characterization, current mapping and current-voltage characteristics, X-ray photoemission spectroscopy for chemical analysis, UV-visible photoemission spectroscopy for determination of band line-ups and energy dispersive X-ray reflectivity for determination of layer thicknesses and scattering length densities. The conditions of film deposition and subsequent thermal annealing strongly affect the film characteristics. In particular, we show that nanostriped films a few tens of nm thick can be obtained in a reproducible manner and that such structuring is accompanied by the appearance of gap-states and by a switch from an insulating to a conductive state. Current-voltage characteristics demonstrate that highly ordered films of K 6 [P 2 W 18 O 62 ] allow electron flow only from ITO to [P 2 W 18 O 62 ] 6-, thus showing a rectifying effect. Finally, we integrate the POM layer into an organic photovoltaic device and show the conduction through it thanks to favorable band alignment between ITO, the gap states and the active photovoltaic layers.

Introduction

The heterostructure in an optoelectronic device is frequently described as an energy staircase favoring charge transport in the valence (holes) or conduction (electrons) bands through the device. Enhancement of charge carrier lifetime and mobility may be achieved by inserting appropriate interfacial layers (Ils) which therefore play a key role in improving power conversion efficiencies (PCEs) of organic light-emitting diodes (OLEDs) and organic photovoltaic (OPV) solar cells. [START_REF] Steim | Interface Materials for Organic Solar Cells[END_REF][START_REF] Ma | Interface Engineering for Organic Electronics[END_REF] A wide range of materials, including notably polymers and metal oxides, has been used for interfacial layer engineering in organic solar cells (OSCs). [START_REF] Yin | Interfacial Materials for Organic Solar cells: Advances and Perspectives[END_REF] With the development of inorganic interfacial layers and the implementation of novel architectures, organic electronics has now reached maturity and is primed for commercialization. However the complexity of such multilayer devices hinders in-depth understanding of interfacial electrical conduction so that optimization of charge transport and minimization of electron-hole recombination remain two key challenges in organic electronics. [START_REF] Yu | Metal Oxides for Optoelectronic Applications[END_REF][START_REF] Yip | Polymer Solar Cells That Use Self-Assembled-Monolayer-Modified ZnO/Metals as Cathodes[END_REF][START_REF] Yuan | Efficiency Enhancement in Organic Solar Cells with Ferroelectric Polymers[END_REF][START_REF] Kim | New Architecture for High-Efficiency Polymer Photovoltaic Cells Using Solution-Based Titanium Oxide as an Optical Spacer[END_REF][START_REF] Gilot | The Use of ZnO as Optical Spacer in Polymer Solar Cells: Theoretical and Experimental Study[END_REF] More generally speaking, metal oxides have a broad potential for applications not only in energy conversion and storage, [START_REF] Li | A Full-Sunlight-Driven Photocatalyst with Super Long-Persistent Energy Storage Ability[END_REF][START_REF] Wang | Oxygen defective metal oxides for energy conversion and storage[END_REF] but also in data storage. [START_REF] Ielmini | Resistive switching memories based on metal oxides: mechanisms, reliability and scaling[END_REF] In comparison with organic materials, they usually display better transport properties and stability in air, longer lifetimes and higher transparency, [START_REF] Sun | Air-Stable Bulk Heterojunction Polymer Solar Cells Using MoOx as the Anode Interfacial Layer[END_REF][START_REF] Cowan | Chemically Controlled Reversible and Irreversible Extraction Barriers Via Stable Interface Modification of Zinc Oxide Electron Collection Layer in Polycarbazole-Based Organic Solar Cells[END_REF][START_REF] Seo | Ultrathin TiO 2 Films on ZnO Electron-Collecting Layers of Inverted Organic Solar Cell[END_REF] but they often require relatively high temperature thermal annealing (higher than 200°C) that may be incompatible with organic electronic technology.

Within this context, polyoxometalates [START_REF] Pope | Heteropoly and Isopoly Oxometalates[END_REF][START_REF] Pope | Polyoxometalate Chemistry: An Old Field with New Dimensions in Several Disciplines[END_REF] (POMs) currently attract growing interest as an emerging class of materials in organic optoelectronics. They are polynuclear early transition metal-oxo anions that are molecular analogues of metal oxides. [START_REF] Klemperer | Metal oxide chemistry in solution: the early transition metal polyoxoanions[END_REF] More specifically, in view of their remarkable electrochemical [START_REF] Pope | Heteropoly and Isopoly Oxometalates[END_REF][START_REF] Sadakane | Electrochemical Properties of Polyoxometalates as Electrocatalysts[END_REF][START_REF] Ueda | Electrochemistry of Polyoxometalates: From Fundamental Aspects to Applications[END_REF] and photochemical [START_REF] Papaconstantinou | Photochemistry of Polyoxometallates of Molybdenum and Tungsten and/or Vanadium[END_REF][START_REF] Gómez-Romero | Polyoxometalates as Photoelectrochemical Models for Quantum-Sized Colloidal Semiconducting Oxides[END_REF][START_REF] Yamase | Photo-and Electrochromism of Polyoxometalates and Related Materials[END_REF] properties, they are interesting models for quantum-sized semiconducting oxides. Therefore, in addition to their application as catalysts, POMs -especially Keggin-and Wells-Dawson-type species -are increasingly used as molecular components in devices such as non-volatile memories, [START_REF] Busche | Design and Fabrication of Memory Devices Based on Nanoscale Polyoxometalate Clusters[END_REF][START_REF] Chen | Evolutionary Metal Oxide Clusters for Novel Applications: Toward High-Density Data Storage in Nonvolatile Memories[END_REF][START_REF] Hu | Inorganic-Organic Hybrid Polymer with Multiple Redox for High-Density Data Storage[END_REF] capacitors, [START_REF] Herrmann | Enhanced Capacitive Energy Storage in Polyoxometalate-Doped Polypyrrole[END_REF][START_REF] Balliou | Tungsten Polyoxometalate Molecules as Active Nodes for Dynamic Carrier Exchange in Hybrid Molecular/Semiconductor Capacitors[END_REF] OLEDs, [START_REF] Palilis | A water soluble inorganic molecular oxide as a novel efficient electron injection layer for hybridlight-emittingdiodes (HyLEDs)[END_REF][START_REF] Tountas | Water-Soluble Lacunary Polyoxometalates with Excellent Electron Mobilities and Hole Blocking Capabilities for High efficiency Fluorescentand Phosphorescent Organic Light Emitting Diodes[END_REF][START_REF] Ohisa | A Solution Processed Heteropolyacid Containing MoO 3 Units as a Hole-Injection Material for Highly Stable Organic Light-Emitting Devices[END_REF] and OSCs. In addition to molybdenum [START_REF] Sun | Air-Stable Bulk Heterojunction Polymer Solar Cells Using MoOx as the Anode Interfacial Layer[END_REF][START_REF] Vasilopoulou | The Influence of Hydrogenation and Oxygen Vacancies on Molybdenum Oxides Work Function and Gap States for Application in Organic Optoelectronics[END_REF][START_REF] Soultati | Solution-Processed Hydrogen Molybdenum Bronzes as Highly Conductive Anode Interlayers in Efficient Organic Photovoltaics[END_REF] and tungsten [START_REF] Vasilopoulou | Hydrogenated Under-Stoichiometric Tungsten Oxide Anode Interlayers for Efficient and Stable Organic Photovoltaics[END_REF][START_REF] Vasilopoulou | Fast Recovery of the High Work Function of Tungsten and Molybdenum Oxides via Microwave Exposure for Efficient Organic Photovoltaics[END_REF] oxides, POMsmainly Keggin- [START_REF] Palilis | Solution Processable Tungsten Polyoxometalate as Highly Effective Cathode Interlayer for Improved Efficiency and Stability Polymer Solar Cells[END_REF][START_REF] Jia | Highly Efficient Low-Bandgap Polymer Solar Cells with Solution-Processed and Annealing-free Phosphomolybdic Acid as Hole-Transport Layers[END_REF][START_REF] Zhu | A cost-effective commercial soluble oxide cluster for highly efficient and stable organic solar cells[END_REF][START_REF] Vasilopoulou | Annealing-Free Highly Crystalline Solution-Processed Molecular Metal Oxides for Efficient Single-Junction and Tandem Polymer Solar Cells[END_REF][START_REF] Vasilopoulou | Old Metal Oxide Clusters in New Applications: Spontaneous Reduction of Keggin and Dawson Polyoxometalate Layers by a Metallic Electrode for Improving Efficiency in Organic Optoelectronics[END_REF] and Wells-Dawson-type [START_REF] Vasilopoulou | Annealing-Free Highly Crystalline Solution-Processed Molecular Metal Oxides for Efficient Single-Junction and Tandem Polymer Solar Cells[END_REF][START_REF] Vasilopoulou | Old Metal Oxide Clusters in New Applications: Spontaneous Reduction of Keggin and Dawson Polyoxometalate Layers by a Metallic Electrode for Improving Efficiency in Organic Optoelectronics[END_REF] molybdates and tungstates and also a few lacunary [START_REF] Tountas | Low Work Function Lacunary Polyoxometalates as Electron Transport Interlayers for Inverted Polymer Solar Cells of Improved Efficiency and Stability[END_REF] and hybrid [START_REF] Tountas | A silanol-functionalized polyoxometalate with excellent electron transfer mediating behavior to ZnO and TiO2 cathode interlayers for highly efficient and extremely stable polymer solar cells[END_REF] species, have been used as cathode or anode interfacial layers in different architectures OSCs where they serve as electron or hole extraction layers, respectively, enhancing efficiency via energy level alignment.

While indium tin oxide (ITO) on glass is widely used as the top anode electrode in optoelectronic devices, up to now little consideration has been given to the insertion of a POM layer between ITO and the active layer. It is therefore necessary to study the properties of ITO/POM junctions. In a preliminary investigation we considered the behavior of a 140 nm thick layer of K 6 [P 2 W 18 O 62 ], hereafter noted K6-P2W18. [START_REF] Alaaeddine | Enhancement of Photovoltaic Efficiency by Insertion of a Polyoxometalate Layer at the Anode of an Organic Solar Cell[END_REF] Here, we report the results of a more detailed study. Layers of K6-P2W18 of different thicknesses have been deposited on ITO and characterized using various techniques, including conducting atomic force microscopy (c-AFM) to obtain topographic images and current maps, local spectroscopy to obtain currentvoltage characteristics and the electronic band diagram, X-ray (XPS) and ultra-violet (UPS) photoelectron spectroscopy to probe the chemical composition, and energy dispersive X-ray reflectivity (EDXR) to estimate the local charge density. We have also considered the lithium salt, Li 6 [P 2 W 18 O 62 ], and the acid form, H 6 [P 2 W 18 O 62 ], hereafter noted Li6-P2W18 and H6-P2W18, respectively, to study the influence of the POM counter-ion. We established the necessary conditions for obtaining highly structured POM layers. We found that the disorderorder transformation in thick layers is accompanied by the appearance of gap-states and by a transition from an insulating to a conductive state. The possible origin and the role of the gap states are discussed. Finally, the integration of a 46 nm K6P2W18 film as a hole transporting layer (HTL) in a conventional ITO/HTL/P3HT:PCBM/LiF/Al OSC confirmed the assumptions inferred from C-AFM, XPS and UPS studies.

Experimental section

Materials

ITO coated glass substrates (75 Ω cm -1 ) were purchased from Solems and silicon substrates from Siltronix. K O was obtained using the Drechsel method as reported in the Supporting Information. Poly(3-hexylthiophene) (P3HT), [6,6]-phenyl-C61-butyric acid methyl ester (PCBM, purity 99.5%), dimethyl sulfoxide (DMSO, purity 99.9%), 1,2-dichlorobenzene (ODCB, purity 99%), and lithium fluoride (LiF, assay 99.99%) were all purchased from Sigma-Aldrich. Aluminum (Al, purity 99.5%) was bought from GoodFellow. All the chemicals were used as received without further purification.

Preparation of substrates

All substrates were cleaned following the sequential process: (i) in the case of glass/ITO, the ITO electrode was defined using an adhesive tape to protect the desired track. The unprotected part was etched using a mixture of Zn powder and 38% w/w HCl; (ii) the adhesive tape was removed and the substrate was cleaned with ethyl acetate; (iii) wet cleaning was achieved by sequential ultrasonic baths using first alkaline detergent solution (5% v/v in deionized water), and then dichloromethane, ethanol and isopropanol (IPA), each for 10 min; (iv) the dried surfaces were exposed to UV-ozone treatment for 10 min. Once cleaned, the substrates were rapidly transferred into the glovebox for spin coating.

Preparation of POM films

The K6-P2W18 powder was dissolved in DMSO at a concentration of 100 mg/mL (2.2×10 -2 M) for thick films and 10 mg/mL (2.2×10 -3 M) for thin films. The Li6-P2W18 and H6-P2W18 powders were dissolved in DMSO at a concentration of 10 mg/mL (2.2×10 -3 M and 2.3×10 -3 M, respectively) for thin films. A 46 nm thick K6-P2W18 film was spin-coated from a 100 mg/mL solution in three steps: step 1 at 500 rpm for 30 s, step 2 at 900 rpm for 20 s and step 3 at 2600 rpm for 10 s. Thin K6-P2W18 (1.9 nm), Li6-P2W18 (2.2 nm) and H6-P2W18 (3.8 nm) films were spin-coated from 10 mg/mL solutions in two steps: step 1 at 500 rpm for 10 s and step 2 at 2600 rpm for 50 s. Then the spin-coating films were annealed on a hot plate at 140 C for 10 min in a nitrogen glovebox. Thicknesses were estimated by XPS taking in consideration the Beer-Lambert law and by AFM and scratch depth measurements (Figure S5).

Organic solar cell fabrication

A stacked (ITO/POM/P3HT:PCBM/LiF/Al) OSC was fabricated as follows. The POM film was first deposited onto ITO as described above, then a 100~150 nm active layer consisting of P3HT:PCBM (15 mg/mL of P3HT and 12 mg/mL of PCBM, blend in ODCB) was deposited onto the POM layer and subsequently annealed at 80 °C for 15 min under nitrogen in a glovebox. Then, the samples were placed into a high vacuum chamber (10 -7 mbar) for evaporation of LiF (1.2 nm, at a rate of 0.01 Å s -1 ) and Al (100-150 nm, at 0.5 Å s -1 ) through shadow masks defining active areas of 6 mm 2 .

Instrumentation

For surface morphology measurements, we used a Bruker ICON AFM in fast scan mode with a silicon tip (k = 4 N m -1 , radius = 5 nm). For C-AFM and local spectroscopy studies, we used an Agilent PicoLE AFM in current sensing mode with a Pt/Ir tip (k = 0.2 N m -1 , radius = 20 nm) by applying a specific bias. XPS measurements were performed in an ultra-high vacuum chamber (pressure lower than 10 -9 mbar) with a monochromatic Al Kα X-ray source (1486.7 eV) and a SPHERA-Argus analyzer (ScientaOmicron). The pass energy was 40 eV giving an overall energy resolution (photon bandwidth and spectrometer) of 0.4 eV. The binding energy scale was calibrated using the C 1s (C-C peak set at 284.8 eV). UPS data were obtained by using a HIS-13 He I source, h=21.2 eV (ScientaOmicron) and the work function was measured by applying a bias of -6.2 V to the sample during recording the photoemission threshold. The photo-electrical characterization of OPVs was performed using a xenon lamp, with a AMG1.5 filter calibrated at 80 mW cm -2 . EDXR measurements were performed to measure the film thickness, interface roughness and electron density. [START_REF] Albertini | Energy Dispersive X-Ray Reflectometry as a Unique Laboratory Tool for Investigating Morphological Properties of Layered Systems and Devices[END_REF] A polychromatic incident radiation produced by a W anode X-ray tube was used as probe (operating energy range: 10-55 keV), and an energy sensitive Solid State High purity Ge-single crystal detector accomplished the signal detection.

Results and discussion

AFM characterization of POM films

We began by investigating the effect of thermal annealing on the surface texture of 46 nm thick K6-P2W18 films grown on various substrates. Figures 1b-d show the AFM topography of 46 nm K6-P2W18 films on glass, silicon and ITO substrates, respectively. The K6-P2W18 solid film on the glass substrate is rough and irregular; moreover, cracks are visible (Figure 1b). On the silicon substrate, large height variations are observed across the film; the surface is highly heterogeneous (Figure 1c). In contrast, the ITO substrate provides a POM film with limited height variations and, in addition, promotes the formation of highly ordered strip domains, each of which is at an angle of 90° with respect to its neighbors (Figure 1d), while silicon or glass show no evidence of strip ordering. This structuring process is reproducible and the domain size can attain 100x100 m². Two line profiles, on and off the strip on a well-structured K6-P2W18 film surface (Figure S3) reveal that strips are crossing plateau and valley, which indicates that the ordering process is not restricted to surface texturing but involves the formation of an anisotropic bulk phase. Several K6-P2W18 films with a thickness from 2 to 150 nm have been grown on glass/ITO but well-structured films have only been observed for thicknesses between 46 nm and 150 nm (Figures S3 andS4). According to our results (Figure 1 and Figures S1 to S4), the necessary conditions for obtaining highly ordered strip domains oriented at 90° with respect to one another are i) use of a glass/ITO substrate, ii) deposition from a solution in DMSO, iii) thickness larger than 46 nm and iv) thermal annealing at 140°C for 10 min. The conductivity of an annealed 46 nm K6-P2W18 film was investigated by applying a negative bias of 600 mV between ITO and a platinum/iridium AFM tip. In such conditions, given the relatively large optical band gap (3.5 eV) of K6-P2W18 and the positions of the valence and conduction band edges, the film is expected to be insulating. However, the current map in Figure 1f reveals high conductivity in the ordered strips while the two rectangular domains without strips visible in Figure 1e are clearly insulating. Thus, the K6-P2W18 film switches from an insulating to a conductive state under structuration. As discussed above, strips represent a long range bulk structuring process. They therefore appears indispensable to provide conducting paths for charge transport in thick K6-P2W18 layers.

XPS characterization of POM films and POM/ITO interfaces

First, a full XPS core level analysis of a well-ordered 46 nm K6-P2W18 film grown on glass/ITO was carried out. The P 2p and K 2p spectra are shown in Figures S8 andS9. The XPS W core level spectrum (Figure 2a) was fitted after subtraction of a Shirley background, using symmetric 30% Gaussian/70% Lorentzian functions and a full width half maximum (FWHM) of 1.0 eV. The W 4f 7/2 and W 4f 5/2 peaks at 35.8±0.1 eV and 38±0.1 eV Binding Energy (BE) are typical for W in its highest oxidation state (W 6+ ). [START_REF] Fleury | Electrostatic immobilization of polyoxometallates on silicon: X-ray Photoelectron Spectroscopy and electrochemical studies[END_REF] There is no indication of W 5+ at the surface of the film. The O 1s spectrum of the film is shown in Figure 2b. The asymmetric peak was deconvoluted into three components located at 530.8, 531.7 and 532.8 eV BE, hereafter respectively referred to as O eq , O pol and O wat explained below. The relative proportions of O eq and O pol were angle dependent whereas that of O wat remained constant. The highest energy peak O wat is attributed to hydroxylated species, including most certainly residual water. It is worth mentioning that no measurable trace of solvent was detected (i.e. no sulfur 3p 1/2 3p 3/2 ). The two main components, O eq and O pol are associated with oxo ligands of the POM. There are nine non-equivalent types of oxo ligands in the Dawson structure (Figure 1a). The 18 O=W, the 36 OW 2 and the eight central oxygen atoms are chemically different from each other [START_REF] Filowitz | Oxygen-17 Nuclear Magnetic Resonance Spectroscopy of Polyoxometalates. 1. Sensitivity and Resolution[END_REF][START_REF] Pascual-Borràs | O NMR Chemical Shifts in Oxometalates: From the Simplest Monometallic Species to Mixed-Metal Polyoxometalates[END_REF][START_REF] Pascual-Borràs | O NMR Chemical Shifts in Oxometalates: From the Simplest Monometallic Species to Mixed-Metal Polyoxometalates[END_REF] and it is tempting to attribute the component with the lowest binding energy to the more basic bridging oxo ligands and the median one to the less basic terminal oxo bonds. However, this assignment would not account for the angular dependence of the spectrum. Thus, assuming a preferential orientation of the POMs based on the highly ordered structure of the layer, we favor an assignment in which these two peaks are attributed to equatorial and polar oxo ligands, respectively (hence, the notations O eq and O pol ).

We then studied layers thin enough to probe simultaneously the POM layer and the ITO substrate. In addition to a 1.9 nm K6-P2W18 film, we prepared a 2.1 nm Li6-P2W18 film and a 3.8 nm H6-P2W18 film for investigation of the effect of the counter-ion. XPS survey spectra of these three films and of ITO are shown in Figure S10 while the W 4f and O 1s core level spectra are shown in Figures 3a-f. Deconvolution of the XPS W 4f 7/2 spectra of 140°C annealed thin films of K 6 -P 2 W 18 (Figure 3b) and Li 6 -P 2 W 18 (Figure 3d) reveals two components at 34.5 and 35.8 eV BE, representative of 5+ and 6+ W oxidation states, respectively. [START_REF] Vasilopoulou | Old Metal Oxide Clusters in New Applications: Spontaneous Reduction of Keggin and Dawson Polyoxometalate Layers by a Metallic Electrode for Improving Efficiency in Organic Optoelectronics[END_REF] The W 5+ component represents 13% of the total intensity for the K6-P2W18 film (7% for the Li6-P2W18 film) and has a slightly larger FWHM (1.2 eV) than the W 6+ component. As no other reducing agent is present, we postulate that ITO spontaneously injects electrons into the POM layer. The percentages of W 5+ obtained from Figures 3d and3b indicate that approximately one and two electrons per POM have been transferred from ITO to the POM for the 1.9 nm and 2.1 nm films, respectively. On the other hand, no W 5+ is seen in XPS spectra of thick films, whether annealed or not (Figure S9a), which can be explained by the decrease in the concentration of negative carriers further away from the interface. The doping level, as evidenced by the W 5+ signal, is of the order of 10 21 cm -3 . Taking into account the band gap this would correspond to a depletion region of the order of 1 nm, similar to the electron inelastic mean free path. The effect of such doping is therefore expected to be detectable only in the very thin POM layers. The variation of the W 5+ concentration in function of the POM layer thickness is depicted in Figure 3g.

The reduction of K 6 -P 2 W 18 films at the interface with ITO may be compared with the spontaneous reduction of a (NH 4 ) 6 -P 2 W 18 film by aluminium. [START_REF] Vasilopoulou | Old Metal Oxide Clusters in New Applications: Spontaneous Reduction of Keggin and Dawson Polyoxometalate Layers by a Metallic Electrode for Improving Efficiency in Organic Optoelectronics[END_REF] The observed differences regarding the degree of reduction are due to the higher reducing power of Al in comparison with ITO. In addition to the signal from the ITO substrate, deconvolution of the XPS O 1s spectra of the thin films measured at the same angle (Figures 3a,3c,3e) revealed the same three components (O eq , O pol and O wat ) as for the thick film (Figure 2b). However, the intensity ratios differ (Table S1), highlighting the effect of the counter-ion on the structuration of the annealed POM layer, most probably on the in bulk orientation of the anions. The O eq /O pol ratio increases going from K + to Li + and then H + . Furthermore, assuming that the component at the highest BE (O wat ) only originates from residual water, this gives 12 H 2 O per POM for the K6-P2W18 and Li6-P2W18 layers, and 6 for the H6-P2W18 layer.

UPS characterization of POM films

To get further insight into the origin of the conducting nature of annealed POM films, we investigated their electronic structure using UPS. The valence band (VB) and the gap region up to the Fermi level of a well-structured 46 nm K6-P2W18 film on glass/ITO as well as those of bare glass/ITO are shown in Figure 4a. The position of the valence band maximum (VBM) as estimated from a linear extrapolation of the VB leading edge, is 3.3 eV with respect to the Fermi level for K6-P2W18 (Figure S7) and 2.9 eV ITO, thus there is a 0.4 eV valence band offset. In addition, we observed a photoemission signal between the VBM and the Fermi level, indicating the presence of filled gap states. By subtracting the ITO spectrum from that of the POM, we highlighted a signal specifically attributed to gap states in the POM layer (inset Figure 4b). It is worth noting that no gap state is observed in the absence of post-deposition annealing (see Figure S6). The most intense feature in the gap can be decomposed into two components which are fitted by Gaussian peaks located at 0.7 eV (peak 1) and 1.1 eV (peak 2) BE.

The spectra of the valence band (VB) and band gap region obtained for the 1.9 nm (K6), 2.2 nm (Li6) and 3.8 nm (H6) annealed films are presented in Figures 4c and4d. The VBM energy is 3.4 eV BE for K6-and Li6-P2W18, and 3.3 eV for H6-P2W18, (Figure 4c), indicating that alkali metal counter ions (K + and Li + ) shift the VBM to slightly higher energy compared to H + . In the same way as for the analysis of the UPS data for the thick (46 nm) POM layer (Figure 4b), the spectrum of the ITO substrate was subtracted from those of the thin POM layers (Figure 4e-g). The UPS spectrum of the H6-P2W18 film (Figure 4g) shows a clear decrease in the gap state intensity compared to the K6-P2W18 (Figure 4e) and Li6-P2W18 (Figure 4f) films. As in the case of the 46 nm K6-P2W18 film, two states referred to as 1 and 2, pinned at 0.7 eV and 1.1 eV BE below the Fermi level, can be resolved in the gap for the thin K6-P2W18 and Li6-P2W18 films whereas gap state 2 is almost absent for the acid form. These results are reported in Figure 4h. The films are conducting, with the exception of that based on H6-P2W18 which is almost insulating. We conclude that gap states, especially gap state 2, are at least in part responsible for the observed increase in conductivity of the films under annealing.

The existence and the role of gap states in semiconductors and their interfaces are well documented but their origin often remains unclear. In molecular semiconductors, they may result from contact with another material, thermal annealing, charge injection, defects or modifications of the crystal structure. [START_REF] Yang | Origin and Role of Gap States in Organic Semiconductor Studied by UPS: As the Nature of Organic Molecular Crystals[END_REF] In the present case the origin of gap states is particularly puzzling. Let us first consider the possibility of charge doping. As discussed above, electrons are injected from ITO into the POM film; however, the UPS (Figure 4b) and W 4f XPS (Figure 2) studies of annealed 46 nm K6-P2W18 films on ITO/glass substrate unequivocally show that the presence of gap states and W 5+ are not correlated. We can therefore exclude W reduction as the main cause for the existence of gap states in the thick films. Let us then discuss the possibility of structural defects in the Dawson structure. On the basis of IR data of catalytic studies, it has often been argued that reduction of POMs, especially polyoxomolybdates, is accompanied by the elimination of one or several bridging oxygens. [START_REF] Eguchi | An Infrared Study on the Reduction Processes of Dodecamolybdophosphates[END_REF] In this respect it may also been noted that unsaturated sites, namely defect structures when one or more metal-oxygen bonds around the same metal atom are broken while the latter remains connected to the defect site are commonly considered as reactive intermediates in the Mars-van Krevelen type oxidation reactions catalyzed by POMs, especially H 5 PV 2 Mo 10 O 40 . [START_REF] Efremenko | Computational Insight into the Initial Steps of the Mars-van Krevelen Mechanism: Electron Transfer and Surface Defects in the Reduction of Polyoxometalates[END_REF][START_REF] Khenkin | The Kinetics and Mechanism of Oxidation of Reduced Phosphovanadomolybdates by Molecular Oxygen: Theory and Experiment in Concert[END_REF] The existence of oxygen vacancies has been advanced to explain the observation of band gaps in SiO 2 /APTES/H 3 PW 12 O 40 /IPA stacks. [START_REF] Balliou | Tungsten Polyoxometalate Molecules as Active Nodes for Dynamic Carrier Exchange in Hybrid Molecular/Semiconductor Capacitors[END_REF] However, while the presence of oxygen vacancies is well-established in molybdenum and tungsten oxides, where they are associated with the appearance of new features below the Fermi level, [START_REF] Vasilopoulou | The Influence of Hydrogenation and Oxygen Vacancies on Molybdenum Oxides Work Function and Gap States for Application in Organic Optoelectronics[END_REF][START_REF] Vasilopoulou | Hydrogenated Under-Stoichiometric Tungsten Oxide Anode Interlayers for Efficient and Stable Organic Photovoltaics[END_REF] as yet no oxygen-defect POM has been reported. It should further be noted that thermal analysis of H 6 P 2 W 18 O 62 56,57 and K 6 P 2 W 18 O 62 [START_REF] Sambeth | A Theoretical-Experimental Study of Wells-Dawson Acid: An Explanation of Their Catalytic Activity[END_REF][START_REF] Comuzzi | The Solid-State Rearrangement of the Wells-Dawson K6-P2W18O62•10H2O to a Stable Keggin-Type Heteropolyanion Phase: A Catalyst for the Selective Oxidation of Isobutane to Isobutene[END_REF] demonstrates that the {P 2 W 18 O 62 } structure is stable up to 450 °C.

Accordingly, the possibility of oxygen vacancies in our Dawson structure may be reasonably ruled out. Thus, considering that no significant chemical change, except partial reduction of tungsten at the near interface ITO/POM, is anticipated for the POM, the origin of the gap states is rather to be found in the change in film structure upon annealing. This view is further supported by the effect of solvent (DMSO vs. DMF and H 2 O; see Figures S1 andS2) and that of the counter ions (Figures 3 and4). Residual water may also play a role in the process. The OFF/ON conductivity switching should therefore rather be seen as a self-doping effect induced by the thermal annealing, the bulk structuration and residual water (and solvent) constituting the layer.

UPS displays a clear signature of electronic states which could be responsible for the enhanced conductivity in the POM films grown on ITO after thermal annealing. However, it does not shed any light on the spatial distribution of conductivity in the POM layers. Based on the C-AFM topography (Figure 1e) and current (Figure 1f) maps, we suggest that long-range ordering enables efficient conduction pathways as depicted in Scheme S1.

Correlation between local I-V and gap states

UPS shows that two gap states are pinned 0.7 and 1.1 eV below the Fermi level (Figure 2b).

The position of the conduction band minimum (CBM) of K6-P2W18 can be deduced from the optical gap (Figure S13). In this way, band alignment between ITO and K6-P2W18 can be predicted. Local spectroscopy using C-AFM on a highly ordered K6-P2W18 film (Figure 5) was performed. In local spectroscopy, a positive bias on ITO would drive electrons from K6-P2W18 to ITO, while a negative bias on ITO would sweep electrons from ITO to K6-P2W18 (Figure 5a). The aim is to probe the electron transfer under an external applied bias, which also results in band bending at the ITO/POM interface. The electron transport process is revealed by an I-V characteristic, shown in Figure 5b where five regions can be identified: 0 V  V  1.5 V (area 1), V = 0 V (area 2), -0.9 V  V  -0.5 V (area 3), -1.6 V  V  -1.0 V (area 4) and V  -1.8 V (area 5). When the bias is negative, electrons are injected into the gap states. From +1.5 V to -3 V, band bending in bulk K6-P2W18 is gradually reduced and then reversed. Under negative bias, there are two different electron transfer mechanisms. The slopes of the I-V plot in areas 3 and 4 suggest an increase in electron mobility, which reflects the gap state enhancement of conductivity in the POM layer. The presence of gap states allows electrons to flow from ITO to K6-P2W18 (Figure 5c, areas 2 and 3). With a high enough negative bias (below -1.8 V, area 5) the I-V plot is parabolic at first and then becomes linear (see Figure S11), reflecting an ohmic contact and full overlap of the CBs of K6-P2W18 and ITO. In this case, the Fermi level and the gap states are shifted into the CB, which modifies the conduction of the K6-P2W18 layer by removing the energy barrier.

Energy band diagram and integration in solar cell

Highly ordered K6-P2W18 films on ITO show therefore a diode-like behavior. This suggests a charge transfer selectivity, only allowing electron flow from ITO to K6-P2W18 or, equivalently, hole injection from K6-P2W18 to ITO. The I-V characteristic from -1.8 V to 0 V demonstrates the role of the gap states in building an electronic bridge for hole injection into the ITO electrode at low bias. The ITO/POM band alignment can now be inserted into the overall band diagram of a POV stack, as shown in Figure 6a, demonstrating the potential of the POM gap states to act as an electronic bridge gate between the highest occupied molecular orbital (HOMO) of P3HT to the CB of the ITO electrode.

EDXR was carried out to characterize the obtained OPV stack before and after illumination.

The experimental conditions were optimized in order to enhance the bulk heterojunction (BHJ) signal; the P3HT-PCBM critical reflection edges and Kiessig fringes are well visible in Figure 6b. The K6-P2W18 reflection edge was also observed, but Kiessig fringes arising from K6-P2W18 were not detected since they are masked by the contribution of the polymeric blend. Analysis of the reflectivity edges and electron densities of each contributing layer is reported in Figure S12.

From the Parratt fitting 59 of the EDXR pattern in Figure 6b the morphological parameters of the P3HT-PCBM BHJ are deduced (thickness d = 163.8 nm, roughness  = 0.5 nm) in good agreement with the expected thickness given the film deposition conditions. The electron densities of K6-P2W18 and of the BHJ were obtained in the dark state, corresponding to: HTL ρ e = 3.04x10 -5 Å -2 and BHJ ρ e = 1.3x10 -5 Å -2 , in very good agreement with previously published P3HT:PCBM results. [START_REF] Albertini | Energy Dispersive X-Ray Reflectometry as a Unique Laboratory Tool for Investigating Morphological Properties of Layered Systems and Devices[END_REF] No thickness or roughness variations were observed for the BHJ upon illumination. However, some modification has occurred, indicating that illumination affects the electronic contrast at the interface. First of all, in the illuminated sample the first Kiessig fringe (0.04 A -1 ) of the HTL is now partially visible. Moreover, it is clear that the oscillation amplitude has changed, which is confirmed by the Parratt fitting procedure. Indeed, the electron density of the HTL is now  e = 3.20x10 -5 Å -2 , higher than in the dark state. On the other hand, the BHJ electron density is constant, thus suggesting that the observed increase of the electron density concerns the HTL-ITO system. Therefore, EDXR studies of the system {Glass/ITO/K6-P2W18/P3HT:PC60BM} detected an increase of the electron density at the K6-P2W18-ITO system under illumination. The excitons are generated under illumination and separated due to the P/N junction (P3HT:PCBM); the holes produced by the exciton separation are drained to the ITO while the absence of counter electrode induces the electrons accumulation in the POM responsible for the increase of the charge density. K6-P2W18 is a selective hole transport layer (blocking electron generated by the active layer under illumination). It can be denominated at the anodic ITO surface as a hole transport layer, HTL, thanks to the presence of gap states and N-Type semi-conductor characteristics. This provides confirmation of the hole injection phenomenon we observed from photoemission spectroscopy and local spectroscopy, i.e. the charge transfer between ITO/POM. The photovoltaic performance using the K6-P2W18 film in a conventional P3HT:PCBM stack is presented in Figure S14. The first observation about the current voltage curve is that the POM can be successfully used as hole transport layer adjacent to the ITO. The performance of the cells obtained demonstrated of an increase of the open circuit voltage from 0.44 to 0.52 V on insertion of the POM layer. This implies an improved hole transport channel by increasing the built-in voltage, due to the gap states. The resulting performance of the cells reach 2.5% of power conversion efficiency. There also appears to be a slight decrease of the current density attributed the resistivity of the POM layer. This may imply not only the ability of the POM to drain efficiently holes from the active layer to the ITO but also that the gap states play a crucial role in the charge transport.

Conclusion

AFM, XPS and UPS, local spectroscopy and EDXR analyses were performed on several annealed and unannealed P2W18 films with different thicknesses and different counter-ions (K + , Li + , H + ). We reproducibly obtained highly-structured K6-P2W18 films on glass/ITO provided that they are i) deposited from POM solutions in DMSO, ii) thick enough and iii) postannealed at 140 °C for 10 min. The formation of nano-stripes is accompanied by a switch from an insulating to a conducting state, the appearance of two gap states pinned at 0.7 and 1.1 eV below the Fermi level and also by an electron transfer from ITO to the POM layer -though this could not be directly demonstrated for thick films. We argue that the origin of gap states likely lies in the structuring process in which counter-ions and residual water play a crucial role. Gap states play a key role in the conduction mechanism(s). Integration of a structured K6-P2W18 film at the ITO anode of a {Glass/ITO/P3HT:PCPM/LiF/Al} stack confirms that it acts as a selective hole transport layer to ITO and results in an increase of the open circuit voltage from 0.44 V to 0.52 V. *E-mail: ludovic.tortech@sorbonne-universite.fr. Phone: +33169086556 *E-mail: anna.proust@sorbonne-universite.fr. Phone: +33144273034 *E-mail: nick.barrett@cea.fr. Phone: +33169083272

Figure 1 .

 1 Figure 1. (a) Schematic representation of the Wells-Dawson type polyoxoanion [P 2 W 18 O 62 ] 6-. (b), (c) and (d) AFM topographic images of 46 nm K6-P2W18 films grown on glass (b), silicon (c) and glass/ITO (d) substrates. Topography (e) and current mapping (f) (bias = -600 mV) of a highly ordered K6-P2W18 film on glass/ITO.

Figure 2 .

 2 Figure 2. Photoelectron spectroscopy of an annealed 46 nm K6-P2W18 film grown on a glass/ITO substrate: XPS W 4f (a) and O 1s (b) core-level spectra.

Figure 3 .

 3 Figure 3. (a-f) O 1s and W 4f XPS spectra of 1.9 nm K6-P2W18 (a,b), 2.1 nm Li6-P2W18 (c,d) and 3.8 nm H6-P2W18 (e,f) films. (g) Variation of the percentage of W 5+ as a function of layer thickness.

Figure 4 .

 4 Figure 4. (a) Valence band spectra of a thick (> 46 nm) annealed K6-P2W18 film on ITO, (b) extraction and deconvolution of the gap state signal, (c) Spectra of thin K6-, Li6-and H6-P2W18 layers on ITO, (d) zoom on the energy region of the gap states, (e-f-g) deconvolution of the gap state signal into two components for each of the three thin layers, (h) intensity ratio of the two gap state components as a function of counter ion.

Figure 5 .

 5 Figure 5. (a) Schematic diagram of local spectroscopy with AFM. (b) Current-voltage characteristic of a thick (46 nm) well-structured K6-P2W18 film grown on glass/ITO with applied bias ranging from -3 V to +1.5 V. (c) Corresponding energy staircase.

Figure 6 .

 6 Figure 6. (a) Global energy band diagram of a P3HT:PCBM photovoltaic cell with the K6-P2W18 thin film at the ITO interface, and (b) EDXR patterns of glass/ITO/K6-P2W18/P3HT:PCBM and best fits, black curve correspond to dark measurement and blue curve to the measurement performed under illumination.

  6 [-P 2 W 18 O 62 ]•14H 2 O 45 and Li 6 [-P 2 W 18 O 62 ].33H 2 O 46 were prepared according to procedures reported in the literature with only minor modifications. The acid form H 6 [-P 2 W 18 O 62 ].31H

  2

ACKNOWLEDGEMENTS

The authors would like to thanks the région Ile de France and the DIM Nano-K for funding the PhD grant to Qirong Zhu.

AUTHOR INFORMATION Corresponding Authors

SUPPORTING INFORMATION

Supplementary materials is available in the supplementary information describing: the synthesis of H6[-P2W18O62].31H2O, providing additional AFM topographical studies, describing UPS analysis of an unannealed K6-P2W18 layer, and local spectroscopy performed by AFM, EDXR analysis, giving complementary surface and electronic analysis performed by EDXR, and finaly presenting the characteristics of the OPV devices.