Ioanna Dimkou
email: ioanna.dimkou@cea.fr

Enrico Di Russo

Pradip Dalapati

Jonathan Houard

Nevine Rochat

David Cooper

Edith Bellet-Amarlic

Adeline Grenier

Eva Monroy

Lorenzo Rigutti

InGaN Quantum Dots Studied by Correlative Microscopy Techniques for Enhanced Light-Emitting Diodes

Keywords: InGaN, quantum dots, correlative microscopy, luminescence, laser-assisted atom probe tomography, cathodoluminescence and photoluminescence

InGaN/GaN nanostructures form the active region of III-nitride emitters (light emitting diodes, laser diodes, single photon emitters) in the visible spectral range. In order to understand the optical performance of these nanostructures it is necessary to obtain a direct correlation of alloy distribution and optical features. With this purpose in mind, laser-assisted atom probe tomography (La-APT) is a unique tool to visualize the three-dimensional distribution of chemical species at the nanometer scale. Recent advances in this technique also offer the possibility of recording simultaneously the photoluminescence spectrum of the specimen under investigation. Here, we report the results of a correlative study of a stack of InGaN/GaN quantum dots, combining high-resolution chemical and optical characterization by La-APT and in-situ micro-photoluminescence, compared to ex-situ cathodoluminescence.

We demonstrate that the structural information extracted from these techniques allows the precise modelling of these nanostructures, obtaining excellent agreement with the optical measurements. During the La-APT experiment, it was possible to resolve the emission of single quantum dots located in the 9 quantum dot layers closer to the substrate. Single quantum dot lines display a spectral shift during the experiment which is assigned to the relaxation of elastic strain due to material evaporation. Our study conveys an image of the Stranski-Krastanov InGaN/GaN quantum dots that is very different from the GaN/AlN systems. The thickness of the InGaN wetting layer is thicker than the part of the dots that protrudes above the layer, and the indium mole fraction in the wetting layer is lower than that in the dots. This perturbed Stranski-Krastanov growth is explained by the surfactant effect of indium, which favors planar growth.

INTRODUCTION

III-nitride semiconductors (AlN, GaN and InN) with wurtzite crystalline structure [figure 1(a)] are the keystone of blue and green optoelectronics. III-nitride ternary compounds present direct band gap which can be tuned from the near infrared to the ultraviolet C region (band gap tunable from 0.69 eV for InN to 6.2 eV for AlN) [START_REF] Vurgaftman | Band Parameters for Nitrogen-Containing Semiconductors[END_REF][START_REF] Gorczyca | Size Effects in Band Gap Bowing in Nitride Semiconducting Alloys[END_REF] , with the possibility of fabricating type-I heterostructures [figure 1(b)]. [START_REF] Tchernycheva | Systematic Experimental and Theoretical Investigation of Intersubband Absorption in GaN∕AlN Quantum Wells[END_REF][START_REF] King | InN/GaN Valence Band Offset: High-Resolution x-Ray Photoemission Spectroscopy Measurements[END_REF] In particular, few-nanometer-thick InGaN/GaN quantum wells (QWs) and quantum dots (QDs) form the active region of IIInitride emitters (light emitting diodes, laser diodes, single photon emitters). [START_REF] Nakamura | The Blue Laser Diode: The Complete Story[END_REF][START_REF] Pimputkar | Prospects for LED Lighting[END_REF][START_REF] Deshpande | Electrically Driven Polarized Single-Photon Emission from an InGaN Quantum Dot in a GaN Nanowire[END_REF][START_REF] Cho | Strongly Coherent Single-Photon Emission from Site-Controlled InGaN Quantum Dots Embedded in GaN Nanopyramids[END_REF] The localization of carriers in intentional (QDs) or unintentional [alloy fluctuations at the scale of the exciton Bohr radius ( 2.8 nm in GaN)] quantum confined systems may play a crucial role in their optical properties, having an impact on emission energies, oscillator strength, and eventually the recombination efficiency of the system. [START_REF] Chichibu | Spontaneous Emission of Localized Excitons in InGaN Single and Multiquantum Well Structures[END_REF][START_REF] Chichibu | Effective Band Gap Inhomogeneity and Piezoelectric Field in InGaN/GaN Multiquantum Well Structures[END_REF] Even in the case of QWs, structural factors like alloy fluctuations, extended defects or strain inhomogeneities can induce a weak three-dimensional (3D) confinement of carriers at the nanometer scale, [START_REF] Mancini | Multi-Microscopy Study of the Influence of Stacking Faults and Three-Dimensional In Distribution on the Optical Properties of m-Plane InGaN Quantum Wells Grown on Microwire Sidewalls[END_REF] which reduces the radiative lifetime, but also broadens the emission spectra and possibly enhances Auger recombination, [START_REF] Yang | The Influence of Random Indium Alloy Fluctuations in Indium Gallium Nitride Quantum Wells on the Device Behavior[END_REF][START_REF] Vaxenburg | The Role of Polarization Fields in Auger-Induced Efficiency Droop in Nitride-Based Light-Emitting Diodes[END_REF] contributing to the efficiency droop in light emitting diodes. [START_REF] Iveland | Direct Measurement of Auger Electrons Emitted from a Semiconductor Light-Emitting Diode under Electrical Injection: Identification of the Dominant Mechanism for Efficiency Droop[END_REF] Although the effect of indium fluctuations on the luminescence properties has been extensively discussed, a key challenge has been to correlate optical and structural properties to reach a full understanding of these 3D phenomena.

A similar situation occurs in the case of intentionally created QD structures, [START_REF] Moriwaki | Narrow Photoluminescence Peaks from Localized States in InGaN Quantum Dot Structures[END_REF] whose optical signature can only be predicted by getting access to the 3D structure and chemical distribution with a resolution close to the atomic scale. [START_REF] Park | Effect of InGaN Quantum Dot Size on the Recombination Process in Light-Emitting Diodes[END_REF][START_REF] Rigutti | Correlation of Microphotoluminescence Spectroscopy, Scanning Transmission Electron Microscopy, and Atom Probe Tomography on a Single Nano-Object Containing an InGaN/GaN Multiquantum Well System[END_REF] In the case of QDs synthesized following the Stranski-Krastanov growth method, most studies correlate typical optical properties with typical structural properties, since the dispersion of size, shape and composition in the QD ensemble sets a limit to precise modeling. The analysis is easier in the case of the GaN/AlN system [START_REF] Mancini | Carrier Localization in GaN/AlN Quantum Dots As Revealed by Three-Dimensional Multimicroscopy[END_REF] since interdiffusion is negligible and the QD facets and wetting layer thickness are well defined. [START_REF] Chamard | Strain Distribution in Nitride Quantum Dot Multilayers[END_REF] In contrast, the study of Stranski-Krastanov InGaN/GaN QDs [START_REF] Moriwaki | Narrow Photoluminescence Peaks from Localized States in InGaN Quantum Dot Structures[END_REF][START_REF] Damilano | Room-Temperature Blue-Green Emission from InGaN/GaN Quantum Dots Made by Strain-Induced Islanding Growth[END_REF][START_REF] Das | Growth and Characterization of Polar (0001) and Semipolar (11-22) InGaN/GaN Quantum Dots[END_REF][START_REF] Bartel | Recombination Dynamics of Localized Excitons in InGaN Quantum Dots[END_REF][START_REF] Park | Ultraviolet Light-Emitting Diodes with Self-Assembled InGaN Quantum Dots[END_REF] presents a major challenge, since little is known about their shape, the thickness of their wetting layer and the distribution of indium in the QD+wetting layer ensemble.

For the study of InGaN nanostructures, transmission electron microscopy (TEM) based techniques were called into question since the exposure to the imaging electron beam can induce alloy clustering. [START_REF] Smeeton | Electron-Beam-Induced Strain within InGaN Quantum Wells: False Indium "Cluster" Detection in the Transmission Electron Microscope[END_REF] In this direction, laser-assisted atom probe tomography (La-APT) is a valuable alternative providing 3D chemical information. [START_REF] Galtrey | Compositional Inhomogeneity of a High-Efficiency InxGa1-xN Based Multiple Quantum Well Ultraviolet Emitter Studied by Three Dimensional Atom Probe[END_REF][START_REF] Cadel | Depth Resolution Function of the Laser Assisted Tomographic Atom Probe in the Investigation of Semiconductors[END_REF] Furthermore, the possibility of analyzing the luminescence in situ during the La-APT measurement (the so-called photonic atom probe [START_REF] Houard | A Photonic Atom Probe Coupling 3D Atomic Scale Analysis with in Situ Photoluminescence Spectroscopy[END_REF] or PAP technique) allows linking the emission lines to the atomic layers that are evaporated. [START_REF] Mancini | Multi-Excitonic Emission from Stranski-Krastanov GaN/AlN Quantum Dots inside a Nanoscale Tip[END_REF] However, quantitative La-APT of III-nitrides faces some particular challenges since the result depends on experimental parameters such as the electric field at the sample surface, the laser pulse energy and the sample temperature. [START_REF] Russo | Compositional Accuracy in Atom Probe Tomography Analyses Performed on III-N Light Emitting Diodes[END_REF] Here, we investigate the correlation of the spectral emission properties of Stranski-Krastanov InGaN/GaN QDs with their structural and chemical features, even at the level of a single QD. The structure of the QDs is defined in detail by combining the chemical information extracted by La-APT, the distribution of QD size and shape measured by TEM and atomic force microscopy (AFM), and the superlattice period extracted from x-ray diffraction (XRD) measurements. The model of the QD structure is validated by the measured optical lines and those predicted by theoretical calculations. The study also reveals that the emission linewidth of the QD ensemble is mostly due to in-plane fluctuations of the indium content in the QDs and the dispersion of the QD diameter.

EXPERIMENTAL SECTION

Specimen growth. The sample under study consists of 40 periods of InGaN/GaN QDs deposited on commercial 3.5-m-thick GaN-on-sapphire templates by plasma-assisted molecular beam epitaxy (PAMBE). The QD height was 2.0±0.2 nm and the barrier thickness was  10 nm. The growth process was monitored by Reflection high-energy electron diffraction (RHEED). The substrate temperature was fixed at 597°C (calibrated by measuring the In desorption time, as described by S. Valdueza-Felip et al. [START_REF] Valdueza-Felip | High In-Content InGaN Layers Synthesized by Plasma-Assisted Molecular-Beam Epitaxy: Growth Conditions, Strain Relaxation, and In Incorporation Kinetics[END_REF] ), and the active nitrogen flux was adjusted to provide a growth rate of 0.52 monolayers per second (ML/s) under metal-rich conditions. For the generation of InGaN QDs, the Ga flux was fixed at 30% of the stoichiometric value, and the In flux was tuned close to the stoichiometry, as described in refs. [START_REF] Das | Growth and Characterization of Polar (0001) and Semipolar (11-22) InGaN/GaN Quantum Dots[END_REF][START_REF] Gačević | Internal Quantum Efficiency of III-Nitride Quantum Dot Superlattices Grown by Plasma-Assisted Molecular-Beam Epitaxy[END_REF] . Therefore, the growth proceeds under metal-rich conditions during the whole process, as schematically described in figure 1(c). The Stranski-Krastanov transition is due to an elastic relaxation process forced by the strong lattice mismatch [see figure 1(d)], in spite of the slightly metal-rich atmosphere and the well-known surfactant effect of In, which promotes planar growth. [START_REF] Neugebauer | Adatom Kinetics On and Below the Surface: The Existence of a New Diffusion Channel[END_REF] The InGaN growth time was 45 s, followed by a growth interruption of 15 s, during which roughening was observed in the RHEED pattern. For the deposition of the GaN barriers, the In shutter was closed and the Ga flux was fixed slightly above the stoichiometric value. Before the growth of the following QD layer, the Ga excess accumulated at the growth front is consumed with active nitrogen during 15 s. The substrate was rapidly cooled down after the deposition of the last QD layer, to enable characterization of the QD shape and density by AFM.

Surface and structural characterization. AFM measurements were performed using a Dimension Icon AFM system operated in the tapping mode using Bruker TESPA-V2 tips.

The periodicity and structural quality was analyzed by XRD in a Rigaku SmartLab diffractometer using a 2 bounce Ge(220) monochromator and a long plate collimator of 0.228° for the secondary optics.

To study the as-grown structure, a lamella specimen extracted from the sample was observed by scanning TEM (STEM) in an aberration-corrected FEI Titan 80-300 microscope operated at 200 kV, with high-angle annular dark field (HAADF) and bright field (BF) detectors. In order to minimize electron beam damage, STEM images were recorded in a sample region far from the area used for the alignment process. In this way, the region of interest was exposed to the electronic beam for less than one minute. This prevents electron beam damaging, which is expected to be significant only after several minutes (e.g. in Bennett et al. [START_REF] Bennett | Atom Probe Tomography Assessment of the Impact of Electron Beam Exposure on In x Ga 1-x N/GaN Quantum Wells[END_REF] the exposure time is 64 minutes).

In the case of the APT tips, BF-TEM analyses were performed on a FEI TECNAI microscope operated at 200 kV. Such TEM measurements are required to extract the APT 3D reconstruction algorithm, namely the shank angle and the initial tip curvature radius. The total exposure time was less than 30 seconds.

Optical spectroscopy. Photoluminescence (PL) measurements under continuous-wave excitation were obtained by pumping with a frequency-doubled solid-state laser (λ = 244 nm), with an optical power of 100 μW focused on a spot with a diameter of 100 μm. PL measurements under pulsed excitation used a Nd-YAG laser (266 nm, 2 ns pulses, repetition rate of 8 kHz). In both cases, samples were mounted on a cold-finger cryostat, and the PL emission was collected by a Jobin Yvon HR460 monochromator equipped with a UVenhanced charge-coupled device (CCD) camera.

Cathodoluminescence (CL) mapping was performed from room temperature to 4 K using an Attolight CL microscope. The acceleration voltage was 10 kV and the beam current was  5 nA. The luminescence was collected through an integrated microscope objective (NA : 0.7). By scanning the sample, the optical spectra of each pixel are recorded on a CCD camera through a dispersive spectrometer with 400 mm focal length (grating: 150 grooves/mm blazed at 500nm).

Sample preparation.

Needle-shaped tips required for atom probe tomography (APT) and TEM lamella specimens were prepared using both FEI Helios NanoLab 450S and Zeiss Crossbeam550 scanning electron microscope/focused ion beam (SEM/FIB). To extract the regions of interest, the as-grown sample was coated with a 500-nm-thick Pt layer using a GATAN PECS system, and Ga + ions were used for the lift-out and annular milling procedure. The annular milling procedure was performed with an acceleration voltage of 15 kV in a first stage, and then 2 kV for the final milling and cleaning stages, so that the thickness of the amorphized region is reduced. [START_REF] Blum | Atom Probe Sample Preparation[END_REF] Atom Probe Analysis. The samples were analyzed in a homemade laser-assisted wideangle tomographic atom probe coupled with a micro-PL (μPL) bench, also referred to as a photonic atom probe (PAP) as described in ref. [START_REF] Houard | A Photonic Atom Probe Coupling 3D Atomic Scale Analysis with in Situ Photoluminescence Spectroscopy[END_REF][START_REF] Rigutti | Optical Contactless Measurement of Electric Field-Induced Tensile Stress in Diamond Nanoscale Needles[END_REF] . Analyses were performed at 80 K and the evaporation of the specimen is controlled and triggered by means of  150 fs laser pulses at 260 nm, focused on a spot with a diameter around 1.5 μm. The repetition frequency of the laser was 300 kHz and the average power was 300 μW. The system was equipped with an 8cm-diameter multichannel plate/delay line detector (MCP/DLD). The flight length is  10 cm, corresponding to a field of view of 22° on the detector and of 35° on the tip. The detection rate was 0.0005-0.0025 event/pulse. The µPL spectra were acquired in-situ at 80 K. Excitation was provided by the same pulsed laser emitting at 260 nm, using a repetition frequency of 4 MHz to increase the number of counts in the detector. The incident power was tuned in the 25-1000 μW range.

The PL signal was collected and analyzed through a grating spectrometer with 320 mm focal length equipped with a liquid nitrogen-cooled CCD camera. The spectral resolution was approximately 0.3 nm.

For precise chemical analysis, we also used a CAMECA FlexTAP system. The APT analysis was performed at 50 K with a UV femtosecond laser emitting at 341 nm having a pulse energy of 0.2 nJ, laser spot size  10 µm, and repetition rate of 50 kHz. The field of view was set to 15°. Data were processed using the TAP3D software and homemade MATLAB codes. The 3D reconstruction was performed using a cone-angle algorithm. The reconstruction parameters (cone-angle = 7 o and tip curvature radius = 39 nm) were extracted from the STEM images of the specimen before performing La-APT.

Modeling. Three-dimensional calculations of the band diagram and electronic levels in the QDs were performed using the commercial Schrödinger-Poisson solver nextnano, [START_REF] Birner | Nextnano: General Purpose 3-D Simulations[END_REF] with the material parameters described in ref. [START_REF] Suski | Switching of Exciton Character in Double InGaN/GaN Quantum Wells[END_REF] . The modelled structure consisted of the 10 periods of InGaN quantum dots, with the dimensions and composition extracted by combination of XRD, AFM, STEM and La-APT data. In each layer, the QDs were defined as a hexagonal truncated pyramid with {10-13} facets, connected by a wetting layer. The 3D strain distribution was calculated by minimization of the elastic energy through the application of periodic boundary conditions along the <1-100> and <11-20> directions. For the calculation of the band profiles, the spontaneous and piezoelectric polarization, as well as the band gap deformation potentials, were taken into account. The energy location of the quantum levels and the electron and hole wavefunctions were calculated using the effective mass approximation. This approximation can result in significant deviations from the experiment when the electron levels are located deep into the conduction band due to the nonparabolicity of III-nitrides, [START_REF] Tchernycheva | Systematic Experimental and Theoretical Investigation of Intersubband Absorption in GaN∕AlN Quantum Wells[END_REF][START_REF] Kandaswamy | AlN Short-Period Superlattices for Intersubband Optoelectronics: A Systematic Study of Their Epitaxial Growth, Design, and Performance[END_REF] but it provides a good description of band-to-band transitions between near-band-edge levels. [START_REF] Suski | Switching of Exciton Character in Double InGaN/GaN Quantum Wells[END_REF]

RESULTS AND DISCUSSION

Description of the as-grown specimen. The heterostructure under study is a 40-period InGaN/GaN QD superlattice grown by plasma-assisted molecular beam epitaxy on a commercial 4-µm-thick GaN-on-sapphire template. Nominally, the heterostructure consists of  2-nm-thick InGaN QD layers separated by 10-nm-thick GaN barriers. An AFM image of the topmost QD layer (uncapped) is presented in figure S1 of the Supporting Information.

It shows a high density (mid-10 11 cm -2 ) of QDs with a height = 0.9±0.2 nm. Note that this value corresponds to the QD height above the wetting layer. From such AFM measurements, it is difficult to extract reliable measurements of the QD base diameter since the expected value (10-20 nm [START_REF] Gačević | Internal Quantum Efficiency of III-Nitride Quantum Dot Superlattices Grown by Plasma-Assisted Molecular-Beam Epitaxy[END_REF][START_REF] Das | Improved Luminescence and Thermal Stability of Semipolar (11-22) InGaN Quantum Dots[END_REF] ) is comparable to the dimension of the AFM tip (see figure S2 and associated discussion in the Supporting Information).

The BF-STEM image of the heterostructure in figure 2(a) shows the 40 periods of InGaN/GaN QDs. HAADF-and high-resolution BF-STEM images of the specimen observed along [1120] zone axis with higher magnification are presented in figure S3 of the Supporting Information. The wetting layer is not well defined due to the high density of dots with a diameter smaller than the thickness of the lamella specimen, 70±10 nm, which results in more than one dot being projected in the images. It is nevertheless possible to measure with atomic precision the height of the QD layer (including wetting layer), which is 8±1 monolayers (ML), i.e. 2.0±0.3 nm. The diameter of the QDs, estimated from the variations of contrast in the images, would be in the range of 12-17 nm.

Comparing the results of AFM and TEM, we can extract an estimation of the thickness of the wetting layer ( 1.1 nm). This value should be taken cautiously, since the AFM analysis is performed in an uncapped QD layer, and the capping process can lead to morphological changes in the QD structures. In the case of GaN/AlN QDs grown by molecular beam epitaxy (MBE), the geometry remains undisturbed during capping for growth temperatures below 730°C. At higher temperatures, we observed a reduction of thickness that was more severe in the case of plastic relaxation during the growth of the QD layer, i.e. QDs containing misfit dislocations. [START_REF] Gogneau | Influence of AlN Overgrowth on Structural Properties of GaN Quantum Wells and Quantum Dots Grown by Plasma-Assisted Molecular Beam Epitaxy[END_REF] In the case of InGaN/GaN grown by MBE, Figge et al. reported the complete dissolution of their InGaN QD structures when overgrown at 510°C. [START_REF] Figge | Quantum Dot Growth in the Limits of Stranski-Krastanov and Spinodal Decomposition: InGaN Quantum Dots[END_REF] However, their uncapped QDs contained around 80% of In and there was evidence of plastic relaxation. Other groups have reported stable QD luminescence for InGaN QDs grown by MBE and capped at significantly higher temperatures (550-640°C), [START_REF] Gačević | Internal Quantum Efficiency of III-Nitride Quantum Dot Superlattices Grown by Plasma-Assisted Molecular-Beam Epitaxy[END_REF][START_REF] Lefebvre | Effects of GaAlN Barriers and of Dimensionality on Optical Recombination Processes in InGaN Quantum Wells and Quantum Boxes[END_REF][START_REF] Adelmann | Self-Assembled InGaN Quantum Dots Grown by Molecular-Beam Epitaxy[END_REF] and no effect of capping was observed in the case of InGaN/GaN QDs grown by metalorganic vapor phase epitaxy when the GaN barriers are grown at the same temperature as the QDs. [START_REF] Zhu | Growth and Optical Characterisation of Multilayers of InGaN Quantum Dots[END_REF] In our case, TEM images show that the relaxation process is purely elastic and the GaN barriers were grown at the same temperature as the InGaN QDs.

Therefore, in a first approximation, we have considered that the QD height measured by AFM is also valid for capped QDs. The validity of this statement will be further discussed later.

To get access to the average superlattice period and strain state, we performed an XRD study. The reciprocal space map around the (10-15) x-ray reflection of the GaN/InGaN QD superlattice is reported in figure 2(b). The peak corresponding to the GaN substrate is located at the reciprocal lattice point -3.625 nm -1 and 9.625 nm -1 , where a and c are the in-plane and out-of-plane lattice parameters. The multiple peaks corresponding to the periodic heterostructure are aligned along Q x = -3.625 nm -1 , which demonstrates a pseudomorphic structure on GaN. Precise values of the superlattice period and lattice parameters were extracted from the θ-2θ x-ray diffractogram recorded around the (0002) reflection of GaN, depicted in figure 2(c). The experimental result is compared with a theoretical calculation using the Rigaku GobalFit software. The best fit is obtained assuming an average period of 12.6±0.1 nm, and modeling the QDs as an InGaN layer with a thickness of 1.6 nm and an average indium composition around 10%.

However, the values of InGaN layer thickness and alloy composition must be taken cautiously. The model assumes a pseudomorphic structure on GaN, with biaxial strain in the InGaN layers. In this situation, the out-of-plane strain is given by the expression

, where is the in-plane strain and and are elastic constants (we use here 106 GPa and 398 GPa for GaN, [START_REF] Polian | Elastic Constants of Gallium Nitride[END_REF] and 92 GPa and 224 GPa for InN, [START_REF] Wright | Elastic Properties of Zinc-Blende and Wurtzite AlN, GaN, and InN[END_REF] with a linear interpolation for the ternary alloy). This approximation is not valid in the case of QDs. [START_REF] Andreev | Theory of the Electronic Structure of GaN/AlN Hexagonal Quantum Dots[END_REF][START_REF] Sarigiannidou | Strain Distribution in GaN∕AlN Quantum-Dot Superlattices[END_REF][START_REF] Himwas | Enhanced Room-Temperature Mid-Ultraviolet Emission from AlGaN/AlN Stranski-Krastanov Quantum Dots[END_REF] Therefore, the fit in figure 2(c) tell us only that the QDs can be approximated by layers with a thickness of 1.6 nm and an average out-of-plane lattice parameter equivalent to that of In 0.1 Ga 0.9 N fully strained on GaN, without any conclusion about the indium mole fraction in the QDs.

The as-grown specimen was characterized by temperature-dependent CL, as illustrated in figure 2(d). The peak emission wavelength is around 413 nm at 5 K, and shifts to 422 nm at 300 K. The evolution of the CL integrated intensity normalized to its low temperature value as a function of the inverse temperature is displayed in figure 2(e). The slight increase of the luminescence from 5 K to 50 K can be explained by the improved transfer of carriers from the barriers to the dots when increasing the temperature. The integrated intensity remains constant in the range of 50 to 100 K and drops sharply for higher temperature due to the activation of nonradiative recombination paths. [START_REF] Leroux | Temperature Quenching of Photoluminescence Intensities in Undoped and Doped GaN[END_REF] The dashed line is a fit that assumes dominance of a monoexponential nonradiative process, so that the variation of the normalized intensity is described by (1) where is the integrated intensity at low temperature, A is a fitting parameter, E a is the activation energy of the nonradiative process, and kT is the thermal energy. In the figure, A = 11±3 and E a = 67±5 meV, which is comparable to the values reported in the literature. [START_REF] Das | Growth and Characterization of Polar (0001) and Semipolar (11-22) InGaN/GaN Quantum Dots[END_REF][START_REF] Gačević | Internal Quantum Efficiency of III-Nitride Quantum Dot Superlattices Grown by Plasma-Assisted Molecular-Beam Epitaxy[END_REF] The ratio of the room-temperature and low-temperature CL integrated intensities, which is generally considered as an estimation of the internal quantum efficiency, is 52%. The stability of the luminescence with temperature support our assumption that the QDs were not dissolved during the QD process (see comparison of InGaN/GaN QD and QW luminescence in Gačević, et al. [START_REF] Gačević | Internal Quantum Efficiency of III-Nitride Quantum Dot Superlattices Grown by Plasma-Assisted Molecular-Beam Epitaxy[END_REF] ).

To gain further insight on the origin of the CL linewidth, we have performed crosssection CL mapping of a cleaved edge of the sample, with the result displayed in figure S4 of the Supporting Information. Analyzing the CL spectra at different points along the growth axis and focusing on the emission from the InGaN QDs, we observe that the linewidth is rather constant along the structure (with full width at half-maximum FWHM  20 nm), and comparable to that obtained in the top-view configuration. There is a slight shift of the peak emission along the growth axis, but its value ( 2 nm) is of the order of the spectral resolution of the spectrometer (±0.8 nm) and significantly smaller than the linewidth.

Therefore, the spectral broadness of emission is due to in-plane QD inhomogeneties, rather than to a drift of the growth conditions.

At this point, we face some limitations hampering a proper correlation of optical and structural properties, and thus the achievement of a complete understanding of these 3D objects. AFM and TEM provide information on the QD height and density. In addition, XRD gives precise information on the periodicity of the structure. However, we only have a rough estimate of the lateral dimensions of the dots, and no reliable information on the indium distribution in the structure.

Characterization of the atom probe tomography (APT) specimen. In order to analyze

the InGaN/GaN QDs using La-APT, field emission tip specimens were fabricated by standard focused ion beam (FIB) based lift out followed by annular milling procedures.

Further details on the specimen preparation are described in the Experimental Section. The FIB process can cause several kinds of damage: 52 amorphization of the surface due, [START_REF] Bogdanowicz | Laser-Assisted Atom Probe Tomography of Semiconductors: The Impact of the Focused-Ion Beam Specimen Preparation[END_REF] Ga implantation and redeposition of milled material, and formation of voids and bubbles at the surface, which further agglomerate into metallic nano-blitters. [START_REF] Dhara | Mechanism of Nanoblister Formation in Ga+ Self-Ion Implanted GaN Nanowires[END_REF] In the case of InGaN, indium redistribution and evaporation is also possible. [START_REF] Wu | Focused Ion Beam Milled InGaN/GaN Multiple Quantum Well Nanopillars[END_REF] It is hence important to be rigorous in the characterization of the specimens before their introduction in the APT system, if results are to be extrapolated to the as-grown material.

FIB prepared tips were first observed in TEM, as illustrated in figure 3(a). The optical activity of the needle-like samples was then measured in the CL system. Figure 3(b) is a panchromatic CL map of the tip in (a), suggesting that the entire superlattice is optically active. Figure 3(c) displays the integrated CL spectrum at room temperature, which presents an emission line at 364 nm that originates from the GaN substrate, and a large band peaked at 422 nm that is assigned to recombination in the QDs. The evolution of the emission spectrum along the tip is shown in figure S5 of the Supporting Information. The peak wavelength and linewidth remain approximately constant along the tip (spectral shift smaller than 2 nm). The variation of the CL integrated intensity as a function of temperature is described in figure 3(d). The dashed line is a fit to eq 1 where A = 33±12 and E a = 38±10 meV, and the room-temperature to high-temperature integrated intensity rate is around 11%. The energy of the QD emission of the tip shape sample remained the same as the as-grown sample, which confirms that the FIB protocol did not introduce significant loss or rearrangement of indium in the specimen. However, the reduced activation energy and increased prefactor A points to a moderate enhancement of nonradiative recombination, due to the higher surface-to-volume ratio.

Tips were then introduced in a photonic atom probe (PAP) system that enables in-situ μPL spectroscopy measurements during the La-APT process, as described in the Experimental Section. In order to determine the best experimental conditions to perform simultaneous µPL and APT characterization, we have first measured in-situ µ-PL as a function of the laser pumping power, as show in in figure 4(a). During these preliminary measurements, we used a repetition rate of 3.8 MHz, adjusting the laser power in the range of 25 to 700 μW. In these spectra, it is possible to identify the narrow emission of the GaN substrate at 358 nm and a broad band peaked around 411 nm, which is assigned to the InGaN QDs. Plotting their intensity as a function of the laser power [figure 4(b)], the luminescence from GaN scales linearly. On the contrary, the intensity of the QD emission saturates for laser power higher than 300 μW. Figure 4(c) shows the evolution of peak wavelength of the luminescence from GaN and InGaN QDs as a function of the laser power. The FWHM of the emission is indicated as an error bar. The GaN line presents a red shift starting at 300 µW, with an increase of the FWHM. The behavior at high pumping power points to a local increase of the tip temperature, whose effect is dominant over a potential band-filling phenomenon. The spectral shift of the QD band is not so obvious due to the broad emission, but the FWHM increases clearly for laser power higher than 300 µW.

In view of these results, we decided to perform the APT experiment with a laser energy corresponding to the 300 µW experiment, which is the point where the tip starts warming up due to pumping. However, during the APT experiments coupled with μPL the laser frequency was reduced to 340 kHz to allow a time delay between pulses longer than the expected time of flight of the ions from the specimen during the APT process. [START_REF] Rigutti | Laser-Assisted Atom Probe Tomography[END_REF] The in-situ µPL emission during the PAP analysis of the last 15 InGaN/GaN QD layers is displayed in figure S6 of the Supporting Information. The PL was analyzed during the evaporation of the last 15 QD layers. As described for the preliminary experiments in figure 4, the peak at 358 nm is related to the carrier recombination in the GaN buffer, and the broad band around 411 nm was assigned to the carrier recombination in the InGaN QDs. The evolution of peak wavelength and FWHM of these QD lines (QD1, QD2, QD3)

during the evaporation of the tip is described in the figure 5(c), and figure 5(d) shows the evolution of the μPL line assigned to the GaN buffer (at 358 nm, shown in figure S6). The QD emission lines present a red shift of around 2 nm during the APT process of the last 9 QD layers. [START_REF] Rigutti | Optical Contactless Measurement of Electric Field-Induced Tensile Stress in Diamond Nanoscale Needles[END_REF] In contrast, the GaN line presents only a slight red shift of around 0.55 nm. The different behavior of QDs and GaN points out that the shift is not thermally induced but rather strain related. Strain is the result of mechanical stress, and it leads to a change of the semiconductor bandgap (which can be estimated using the band deformation potentials) and the generation of piezoelectric polarization. During the experiment, two sources of mechanical stress act on the QDs, namely the stress resulting from the lattice mismatch between GaN and InGaN and the stress induced by the electric field during the APT measurement. It is hence important to assess the magnitude of both sources of stress to know if the spectral shift is associated to the material properties or to the experimental conditions.

The stress associated with the lattice mismatch between GaN and InGaN results in a deformation of the lattice to minimize the elastic energy accumulated during the growth of the sample, as illustrated in figure S7 of the Supporting Information. In the case of the InGaN QDs, there is an in-plane compressive stress due to the growth of InGaN on top of GaN, and a uniaxial compressive stress along the c crystal axis (growth direction) due to the GaN that is in contact with the QD side facets. The stress along the c axis in the QDs can be calculated as (2) where are elastic constants and and are the in-plane and out-of-plane strain. With the values of strain in figure S7 ( and ), the stress is estimated at GPa. Note the negative sign, which indicates that the stress is compressive along c. In this strain configuration, using the deformation potentials from Vurgaftman and Meyer, [START_REF] Vurgaftman | Band Parameters for Nitrogen-Containing Semiconductors[END_REF] the InGaN band gap increases by  106 meV with respect to the relaxed value.

When evaporating the layers on top of a certain QD, the uniaxial stress imposed by the material surrounding the dot decreases, but the in-plane stress due to the GaN underlayer remains. Therefore, evaporation should lead to an expansion of the lattice along c (higher ). Keeping and releasing the uniaxial stress ( ) would lead to , resulting in an increase of the band gap by only  74 meV with respect to the relaxed value. In addition to this modification of the band gap, the increase of induces an enhancement of the piezoelectric polarization. These two phenomena explain a red shift during the APT process of the order of magnitude observed in figure 5(c).

The GaN PL signal in figure 5(d) stems from the GaN layer below the QD superlattice.

The topmost nanometers of this layer are strained by the presence of the InGaN QDs on top.

Our Nextnano calculations point out strain that can reach and ( 0.71 GPa) right below an InGaN QD. Using again the deformation potentials in ref. [START_REF] Vurgaftman | Band Parameters for Nitrogen-Containing Semiconductors[END_REF] , the strain increases the GaN band gap by  7.6 meV. This strain is fully relaxed when the InGaN material is evaporated, which should lead to a slight red shift of the PL signal, as experimentally observed.

On the other hand, during the APT experiment, a high positive voltage in the range of V DC = 5-10 kV is applied to the InGaN/GaN tip, which results in an electric field F at the tip that can be estimated by [START_REF] Wei | Measuring the Stress in Field-Emitting Carbon Nanotubes[END_REF] (3)

where k  7 is a geometrical factor and R is the curvature radius of the tip apex. Free carriers generated by laser illumination drift due to the electric field and holes accumulate at the needle apex screening the electric field inside the semiconductor material. However, the field induces a mechanical stress along the tip, which is given by (4) where is the vacuum permittivity. As we evaporate the sample, V DC increases and the radius of the tip, R, increases. Tracing those values, the average electric field when the apex evolves along the 9 deepest QD layers can be estimated to be in the range 8-10 MV/cm, corresponding to a field-induced stress in the range GPa to GPa. As the electric field points towards the detector, the stress is uniaxial, tensile, along the c axis of the semiconductor crystal. The field-related stress has the opposite direction of ; however, both and increase during the experiment ( becomes less negative and becomes more positive). However, it should be kept in mind that is at least 4 times smaller than in the QDs, and about half the value of in the GaN material right below the superlattice. Furthermore, is expected to increase only by 10% for an increase of the tip curvature radius of 5%. Therefore, we can conclude that it is the variation of the stress induced by the lattice mismatch that dominates the spectral shift of the PL during the APT measurement. This is further supported by the fact that, at the beginning of the experiment, there is no major difference in the PL peak energy with and without electric field.

It should be mentioned that the PAP requires the use of a fast APT detection system, at the expense of a lower detection efficiency and accuracy in assessing composition.

Therefore, in order to quantify the alloy composition within InGaN layers, La-APT measurements were performed using a CAMECA FlexTAP system, equipped with an advanced delay-line-detector (aDLD). [START_REF] Costa | Advance in Multi-Hit Detection and Quantization in Atom Probe Tomography[END_REF] The InGaN layers contain In-rich regions with a typical in-plane diameter of 15.4±1.4 nm and typical In-site fraction  13%, connected by the wetting layer, a thinner InGaN layer with an In-site fraction  6%. The shape and size of these In-rich regions correspond to InGaN QDs rather than to random alloy fluctuations. [START_REF] Rigutti | Coupling Atom Probe Tomography and Photoluminescence Spectroscopy: Exploratory Results and Perspectives[END_REF] This picture is confirmed by the complementary isosurface analysis of one of the QD layers [marked with a square in figure 5(e)], which is reported in figures 5(f) and 5(g). Figure 5(f) displays the isosurface corresponding to an In-site fraction of 14% (in red), representing a single QD. The diameter of the QD is 15.0±0.5 nm, with a height of 2.0±0.1 nm. On the other hand, the isosurface corresponding to an In-site fraction of 6% [displayed in figure 5(g)] shows a layer connecting neighboring QDs, consistent with the wetting layer. The combination of both isosurfaces provides a consistent representation of composition and morphology of both wetting layer and QD.

Modelling of the QD structure. At this point, combining the result of STEM, XRD, AFM and La-APT, we have a complete description of the QD structure, including the period of the superlattice (12.6 nm, from XRD), the height of the QDs (2.0 nm, from STEM), the QD height above the wetting layer (0.9 nm from AFM), and the In content of the QDs and of the wetting layer (13% and 6%, respectively, from APT). To validate these results, we have compared the optical emission with theoretical calculations of the electronic structure using the geometrical and chemical parameters listed above. A schematic description of the simulated structure is presented in figure 6(a), and a complete description of the modelled cell and conditions are described in the Experimental Section. In a first stage of the 3D simulations, we obtain the strain distribution in the structure. The in-plane and out-of-plane components of the strain are presented in figure S7 of the Supporting Information. In the center of the dot, the  zz / xx ratio is -0.284, which confirms a significant deviation from the biaxial strain configuration, where . Taking into account the In content and the calculation of the elastic strain, the results are consistent with XRD measurements: Assuming that the structure is well described by figure 6(a), and with an In 0.06 Ga 0.94 N wetting layer that is biaxially strained and In 0.13 Ga 0.87 N QDs with , the average lattice parameter in a period of the superlattice is approximately the same as in an InGaN/GaN QW superlattice with the same thickness and pseudomorphic, 1.6-nm-thick In 0.1 Ga 0.9 N QWs, i.e. the structure used for the XRD calculation presented in figure 2(c). The consistency of the results with the structural characterization data supports our initial assumption that the fact of capping the QDs with GaN does not introduce a significant perturbation of their morphology.

Taking the strain distribution into account, the band diagram of the 3D structure was The correlation of µPL in-situ APT and of the structural parameters issued by TEM has also been performed at the level of a second tip as described in figure S8 of the Supporting Information, and confirming the reproducibility of the results and the homogeneity of the sample.

In summary, the excellent agreement between the theoretical calculations and the experimental optical features show that the model extracted from structural and chemical characterization provides a good description of this InGaN/GaN QD system. This model conveys an image of the InGaN/GaN QDs that is very different from the Stranski-Krastanov growth in the InGaAs/GaAs or GaN/AlN systems, where the dots and wetting layer can be distinctly and separately visualized. On the contrary, in the structure under study, the thickness of the wetting layer is thicker than the part of the QDs that protrudes above the layer. The dots look resemble rather the coexistence of a thickness undulation and a local increase of the In mole fraction. This perturbed Stranski-Krastanov growth is caused by the presence of indium at the growth front, with a surfactant effect that favors planar growth. [START_REF] Neugebauer | Adatom Kinetics On and Below the Surface: The Existence of a New Diffusion Channel[END_REF][START_REF] Chen | Surface Structures and Growth Kinetics of InGaN(0001) Grown by Molecular Beam Epitaxy[END_REF] However, these nanostructures behave optically as quantum dots, with an enhanced stability of the luminescence at high temperature thanks to their capability to confine free carriers a three-dimensional volume with a size comparable that of the exciton in InGaN.

CONCLUSIONS AND PERSPECTIVES

To conclude, we have performed a correlative microscopy study of a stack of self-assembled

Figure 5 (

 5 a) shows a zoomed view of the emission of the QDs acquired at different stages of the tip evaporation. The legend indicates the number of QD layers that were left in the tip when the PL spectra were recorded. Figure5(b) shows the 3D APT reconstruction of the indium signal when only 5, 3 and 2 layers remain in the specimen, as an example. In figure5(a), the initial luminescence peak of the whole tip appears broad, as it results from the overlap of the emission of multiple QDs. The spectra do not display major variations during the evaporation of the 5 topmost QD layers (shown in figureS6). However, during the evaporation of the last 10 layers, the total emission intensity decreases, as expected from the reduction of the tip volume containing multiple QDs. As only a few dots remain in the tip, the spectra present a multi-peak structure due to fluctuations of the size and the indium content of the QDs. 17 When only 5-2 layers are left, we can identify the signature of single InGaN QDs. The QD signal disappears when there is still one InGaN layer, which means that most probably that first InGaN layer does not contain any dot. Dashed lines in figure5(a) are Lorentzian fits that identify the QDs contained in layer 2: a first line (QD1) is located at 422.7 nm with FWHM = 1.2 nm, and a second emission line (QD2) peaks at 417.36 nm with FWHM = 0.87 nm. A third peak (QD3) that disappeared after evaporation of layer 3 was located at 413.2 nm with FWHM = 1.3 nm.

Figure 5 (

 5 e) shows the indium site fraction map obtained through the analysis of 18 InGaN QD layers present in a 3D APT reconstruction.

  figures 6(b). The electron and hole quantum confined levels are calculated in a QD in the

  InGaN/GaN (2 nm / 10 nm) QDs embedded in a needle-shaped atom probe specimen fabricated by FIB. Comparative optical characterization of the as-grown sample and the atom probe specimen shows that there was no loss or rearrangement of indium during the FIB process. This allows the extrapolation of the characterization results to the as-grown sample. To get a complete view of the QDs, we have performed spectroscopic (in-situ mocro-photoluminescence and ex-situ cathodoluminescence) and structural (XRD, AFM, STEM and APT) measurements, to get a full view of the sample at the nanometer scale.During APT measurement of the 9 QD layers closer to the substrate, it was possible to resolve single QD emission lines. The spectral red shift observed in these single quantum dot lines during the APT process was assigned to the relaxation of elastic strain due to the material evaporation. Theoretical modeling of the QDs considering the experimental values of their size and indium distribution predicts room temperature photoluminescence at 426 nm, in excellent agreement with the measured spectra. Furthermore, the spectral linewidth of the as-grown sample is explained as due to in-plane fluctuations of the QD In content and diameter. These results confirm the relevance of PAP studies to provide a complete view of the InGaN QDs, and shows the potential of this technique for the analysis of nanostructured materials.In terms of nanomaterials, a conclusion of this study is that Stranski-Krastranov InGaN/GaN QDs look like a thickness undulation and a local increase of the In mole fraction. The thickness of the wetting layer is comparable to the QD height, and the indium content in the wetting layer is significantly lower than the indium content in the QDs. The nanostructures behave optically as quantum dots, but these structural parameters can have an important impact on the design of the active region of a light emitting device, since they affect the band diagram and carrier transport properties.In particular, we have shown that PAP can be used in samples containing a large set of nanoscale emitters in order to isolate the optical emission of few of them by a controlled reduction of the optically active volume induced by field evaporation. Furthermore, the technique allows the correlation of the 3D image of the chemical composition of a few light emitters contained in a nanoscale object with their spectral signature. This opens perspectives for the application of this technique to super-resolution studies, to discriminate the optical emission of neighboring quantum dots, or to strictly correlative studies, in which the 3D chemical map of a single quantum dot is correlated with its optical signature.■ ASSOCIATED CONTENT*Supporting Information: The supporting information includes AFM measurements of the as-grown sample, HAADF and BF STEM images of the InGaN/GaN QD superlattice, crosssection CL mapping of a cleaved edge of the as-grown sample, study of the variation of the CL spectrum along the APT specimen, the µPL spectra recorded in situ during the La-APT characterization of InGaN/GaN QDs, and a calculation of the distribution of the in-plane ( xx ) and out-of-plane ( zz ) strain in the InGaN QD stack.

Figure 1 Figure 1 .

 11 Figure 1

Figure 2 Figure 2 .

 22 Figure 2

Figure 3 Figure 3 .

 33 Figure 3

Figure 4 .

 4 Figure 4. µPL measurements performed before the La-APT evaporation of InGaN/GaN QDs with different laser power. The experiment was performed at 80 K and the frequency and wavelength of laser were 300 kHz and 260 nm, respectively. (b) Intensity of the GaN and QD PL lines as a function of the laser power, extracted from (a). (c) Peak wavelength of the GaN and QD PL lines as a function of the laser power. The FWHM is indicated as an error bar.

Figure 5 Figure 5 .

 55 Figure 5

Figure 6 Figure 6 .

 66 Figure 6

■ ACKNOWLEDGEMENTS

This work was co-funded in the framework of RIN IFROST, and CPER BRIDGE projects by European Union with European Regional Development Fund (ERDF) and by Region Normandie. This study was performed on the NanoCharacterisation PlatForm (PFNC), and supported by the "Recherches Technologiques de Base" Program of the French Ministry of Research.


Davide Andrea Guastella
email: davide.guastella@irit.fr

Cesare Valenti
email: cesare.valenti@unipa.it

Estimating Missing Information by Cluster Analysis and Normalized Convolution

Smart city deals with the improvement of their citizens' quality of life. Numerous ad-hoc sensors need to be deployed to know humans' activities as well as the conditions in which these actions take place. Even if these sensors are cheaper and cheaper, their installation and maintenance cost increases rapidly with their number. We propose a methodology to limit the number of sensors to deploy by using a standard clustering technique and the normalized convolution to estimate environmental information whereas sensors are actually missing. In spite of its simplicity, our methodology lets us provide accurate assesses.

I. INTRODUCTION

The increasing demand for better public services offered by modern cities requires ad hoc support for technologies, all tied together into the so-called smart city concept, that embraces different multidisciplinary fields as informatics, urban and social sciences, politics as well as economics. Nonetheless, the concept of a smart city remains strongly ambiguous; it has been growing from empirical experience and lacks a systemic theoretical study [START_REF] Dameri | Searching for Smart City definition: a comprehensive proposal[END_REF].

A study commissioned by the European Union defines smart city initiatives as multi-stakeholder municipally based partnerships aimed at addressing problems of common interest with the aid of information and communications technologies, which underpin the smart classification [START_REF] Manville | Mapping Smart Cities in the EU[END_REF]. Dameri [START_REF] Dameri | Searching for Smart City definition: a comprehensive proposal[END_REF] analyzed five areas of study concerning the smart city: intelligent city, digital city, sustainable city, technocity and well-being city. Technocity concerns mainly efficiency and effectiveness improvements of the infrastructures, whereas digital city refers to the representation of several aspects of a real city. These two aspects are not of primary interest for this paper, which will focus on the following definitions:

• an intelligent city is able to produce knowledge and to translate it into unique and distinctive abilities; this city is smart because it is able to create intellectual capital and to ground development and well-being on this intellectual capital; • a sustainable city aims to become a "green city" by using technology to reduce pollution, to produce energy and to improve the buildings efficiency; • a well-being city produces the best quality of life for citizens, but also to create regional attractiveness both for people and for business. Technology is just part of the means used to reach these goals, but also culture, climate, history and monuments are considered as important success factors.

These concepts do not represent disjoint areas of analysis and still share some common aspects. Moreover, a system to support a smart city (in terms of both hardware and software) must satisfy the following conditions:

• openness: the system must be able to work with intermittent devices. For example, if we consider devices such as the smart-phones, there is no guarantee that these are always available; • heterogeneity: observations from heterogeneous devices usually produce large volumes of data that must be pruned and correlated in order to generate a valuable knowledge; • large-scale: due to the amount of (physical and virtual) entities involved in smart cities and the huge amount of data to process, there is a need for efficient data storing and manipulation techniques. Moreover the data must be always available to the final user; • unpredictability: it concerns robust systems able to continuously self-adapt to changes that may occur in a highly dynamic environment; • privacy: non-intrusiveness is considered a key point when collecting data in a smart city.

All these challenges must be addressed when the mobility of ubiquitous and heterogeneous devices introduce different accessibility scenarios with a high level of complexity. Ambient systems represent a key solution to integrate different technologies and provide an IoT infrastructure to be aware of the environment, doing pervasive computing and profiling through human-centric computer interactions [START_REF] Viterbo | Ambient intelligence: Management of distributed and heterogeneous context knowledge[END_REF].

Wang et al. [START_REF] Wang | Multi-agent control system with information fusion based comfort model for smart buildings[END_REF] suggested a multi-agent check system where a heuristic intelligent optimization is used to achieve a high level of comfort (with respect to temperature, illumination and the CO 2 concentration) with the minimum power consumption.

Costantini et al. [START_REF] Costantini | DALICA: Agent-Based Ambient Intelligence for Cultural-Heritage Scenarios[END_REF] defined a multi-agent system approach to control cultural sites such as museum or archaeological sites and to disseminate personalized information to users according to their location.

Ballatore et al. [START_REF] Ballatore | Design and development of personal geoservices for universities[END_REF] realized a system for querying the buildings in a campus to send users information such as room and equipment availability or scheduled classes in courses.

Saldaña-Pérez et al. [START_REF] Saldaña-Pérez | RRMA Referenced Routing Model to Generate a Semantic Service of Navigation in Mobile Devices[END_REF] described a model to provide semantic instructions to move around places through geospatial analysis, semantic processing and mobile technologies. The route starts from the mobile position and proposes points of interest and visual aids along the road.

As a matter of fact, today there is a growing interest to support technologies to support not only smart cities, but also smart regions [START_REF] Vuppalapati | Smart dairies-enablement of smart city at gross root level[END_REF]. Moreover, the deployment of applications in large scale environments is a difficult task due to a variety of constraints (e.g. energy, communication, computing capacities, mobility, autonomy) [START_REF] Olaru | A Context-Aware Multi-Agent System as a Middleware for Ambient Intelligence[END_REF], [START_REF] Piette | Deployment and configuration of applications for ambient systems[END_REF]. Smart tourism supports systems that bind together technologies and systems in different cities to provide specific services to the final user. The method developed by Rivera et al. [START_REF] Rivera | Semantic recommender system for touristic context based on linked data[END_REF] makes use of preferences, like recommended points of interests and opinions by other users (obtained from the web 2.0 by means of social media), activities declared during vacations, the maximum distance the user is able to walk to provide better touristic itineraries. Sabatucci et al. [START_REF] Sabatucci | Adopting a middleware for self-adaptation in the development of a smart travel system[END_REF] developed a smart travel system that acts as a tour operator, combining travel components ondemand to create a holiday package that takes into account user preferences such as budget availability, places of interest and activities to perform.

Among the variety of methods to complete missing information or to handle sparse data, classical methods based on regression analysis use different coefficients for each missing data and take into account a fixed number of data [START_REF] Xia | Forest climatology: estimation of missing values for bavaria, germany[END_REF], [START_REF] Ferrari | Missing data imputation of climate datasets: Implications to modeling extreme drought events[END_REF]. The model predictive control is based on a mathematical model that describes the environment and it is used to make predictions in smart buildings to reduce their energy consumption while ensuring the occupants' comfort at the same time [START_REF] Oldewurtel | Use of model predictive control and weather forecasts for energy efficient building climate control[END_REF]. Another approach, based on artificial neural networks, was proposed for missing environmental information [START_REF] Zanetti | Estimating evapotranspiration using artificial neural network and minimum climatological data[END_REF], although it needs to specify a precise architecture as well as the activation function. These parameters greatly depend on the case study. Vice versa, normalized convolution is an efficient approach that requires very low computational power and requires just a few parameters that can be pre-defined easily.

This paper focuses on a simple yet effective methodology to estimate missing environmental information by cluster analysis and normalized convolution (see fig. 1). We verified the proposed approach on a real weather dataset, freely available on the Internet, showing good results for applications on a regional scale. The paper is organized as follows: section II faces the problem of clustering by using a hierarchical approach together with deciding automatically the optimal number of clusters; section III describes the normalized convolution technique, used the extrapolate missing information; section IV reports the experimental setup, enhances the hierarchical clustering by means of the Voronoi diagram and discusses the final results; section V summarizes the applicability of the proposed methodology and describes research perspectives.

II. AGGLOMERATIVE HIERARCHICAL CLUSTERING

In a clustering problem we are given a dataset of "points" and the goal is to partition this dataset into a finite set of disjoint subsets (i.e. clusters) C such that the union of all subsets covers the whole dataset. A high quality clustering is one in which the points in any particular subset are more similar to each other than the points in other subsets [START_REF] Kobren | A hierarchical algorithm for extreme clustering[END_REF].

One common technique for clustering is known as agglomerative hierarchical clustering; this approach starts considering each single point into a single cluster and then it iteratively merges the closest pair of clusters according to some similarity criteria until all points belong to one cluster. The main drawbacks of this approach are that the points that have been incorrectly grouped at an early stage cannot be reallocated subsequently and different similarity measures among the clusters can lead to completely different results [START_REF] Gan | Data Clustering: Theory, Algorithms and Applications[END_REF].

The hierarchical methods group training points into a typical tree structure known as dendrogram which represents a sequence of nested cluster constructed top-down or bottomup. The root of the tree represents the cluster that includes the whole dataset of points while each leave has one point. By cutting the tree at a certain level we obtain a clustering into disjoint groups (fig. 2) [START_REF] Rafsanjani | A Survey Of Hierarchical Clustering Algorithms[END_REF].

A major challenge in cluster analysis is determining the optimal number of clusters. There are two principal approaches to face this problem. One common technique depends on plotting an optimization parameter against a number of clusters and on choosing the number which corresponds to a large change in the parameter value. A second method seeks large changes in inter-group fusions where fusion distances are generally determined with the aid of the dendrogram. Both these techniques depend on the determination of relatively large changes in an index rather than its minimization or maximization and therefore require human interpretation and subjective analysis of what should be considered a "large change" [START_REF] Davies | A Cluster Separation Measure[END_REF]. In the gap statistic method [START_REF] Tibshirani | Estimating the number of clusters in a data set via the gap statistic[END_REF] we suppose that we clustered the set of points into k clusters C 1 , C 2 , . . . , C k . Let

D n = i,j∈Cn d ij
be the sum of pairwise distances for all points in C n and let

W k = k n=1 D n 2||C n ||
be the variance that represents be the dispersion of the points within the k clusters. The idea of gap statistic is to compare the dispersion of the points within each of the k clusters to its expectation under an appropriate null reference distribution [START_REF] Tibshirani | Estimating the number of clusters in a data set via the gap statistic[END_REF].

III. NORMALIZED CONVOLUTION

Dealing with irregularly sampled data due to the presence, for example, of noise or instrumental error is quite common in many scientific fields, such as astrophysics, geoscience, oceanography, telecommunications, remote sensing and medical imaging. In general, performing operations on incomplete or irregularly sampled data is a non-trivial task and therefore it is often required to reconstruct the irregularly sampled data or resample it onto a regular grid. These operations can be carried out through direct methods, which can involve the computation of irregularly sampled data in the frequency domain and the inverse transform to obtain a regularly spaced signal [START_REF] Marvasti | Nonuniform Sampling. Theory and Practice. Information Technology: Transmission, Processing and Storage[END_REF], [START_REF] Greengard | Accelerating the Nonuniform Fast Fourier Transform[END_REF], [START_REF] Chen | Finite Fourier Frame Approximation Using the Inverse Polynomial Reconstruction Method[END_REF]. Normalized convolution is a non-direct methodology widely used for filtering incomplete or uncertain data which is based on the separation of both data and operator into a signal part and a certainty part. A map indicates the presence degree of a sample in a given position and, in particular, a binary map would indicate just the absence or presence of the signal. This approach was described for the first time by Knutsson and Westin for digital image analysis with a simple and fast implementation [START_REF] Knutsson | Normalized and differential convolution[END_REF].

Let S be the positive map that represents certain samples of bi-dimensional data I. The kernel, centered in the origin, have the original and general form

K x,y = r -α cos β πr 2R if r < R 0 otherwise
where r = (x 2 + y 2 ). Usually, the parameters α = 0 and β = 2 are used, thus obtaining the bi-dimensional raised cosine depicted in figure 3.

To avoid over-smoothing the output signal, K should be big enough to contain just some pixels of the input signal. Vice versa, if the distance between the nearest samples in S is greater than the size R of K, then the reconstructed image will contain gaps. Without a priori information, R is automatically set to the minimal distance among the available samples to reduce artifact effects along discontinuities: at least one point lies always within the radius [START_REF] Albanese | Genetic Normalized Convolution[END_REF]. Fig. 3. Graphic representation of the typical smoothing kernel, as described in [START_REF] Knutsson | Normalized and differential convolution[END_REF].

It is noteworthy that the normalized convolution can be calculated through efficient lookup tables if we accumulate the contribution of the few known samples according to the reflected kernel's values about its center (fig. 4), instead of directly calculating the scalar product at each unknown point. Instead, this latter approach is preferable if we are interested in a single missing point, without considering the rest of the signal (fig. 5).

A variant of this algorithm is known as adaptive normalized convolution and it modulates both the size and the shape of the kernel K, according to the position of certain samples [START_REF] Pham | Normalized Averaging Using Adaptive Applicability Functions with Applications in Image Reconstruction from Sparsely and Randomly Sampled Data[END_REF], [START_REF] Pham | Robust Fusion of Irregularly Sampled Data Using Adaptive Normalized Convolution[END_REF]. In this case, implementing an optimized and efficient custom convolution routine can be quite difficult: a different filter should be arranged for each point of the output image and an estimate of the gradient of the whole signal is used to determine this proper kernel. Obviously, this gradient itself is just an approximation since it has to be computed from available samples specified by S. Actually, we preferred not to use this approach because it requires a considerable amount of computational time and usually its performances does not justify the enhancement of the final result due to the very few known samples.

IV. MATERIALS AND METHOD

To evaluate the correctness of the proposed methodology we considered the freely available temperatures in degree Celsius recorded by Arpae-SIMC, a weather service of the Emilia-Romagna region in Italy which provides weather warnings to the Italian Civil Protection Department. Beyond climatological data, Arpae-SIMC provides tools, products and indicators to evaluate the impact of storms on the coast [START_REF] Bressan | Sensitivity of sea-level forecasting to the horizontal resolution and sea surface forcing for different configurations of an oceanographic model of the Adriatic Sea[END_REF]. About 48% of this region consists of plains while 27% is hilly and 25% is mountainous. We considered the average daily air temperatures at 2 meters of altitude, collected in 196 days from September 8 2017 to April 25 2018 by 80 weather stations. Actually, since we do not make a temporal analysis, we have not considered the days when some stations were not operational between those two dates. That is, the minimal form of this dataset consists in an array of 196×80 numerical values. The exact geographic locations of these stations were corrected to the Cartesian plane through the Mercator projection [START_REF] Monmonier | Rhumb lines and map wars: a social history of the Mercator projection[END_REF].

The main steps of the proposed methodology are depicted in figure 1. At first, a Voronoi tessellation [START_REF] Okabe | Spatial Tessellations -Concepts and Applications of Voronoi Diagrams[END_REF] is calculated according to the actual positions of the stations: this delimits their rough relevance areas (fig. 6a). Given a station, its Voronoi tile is a convex polygon that includes all points closer to that station than to any other station. This way, each tile contains exactly one station. The Voronoi tessellation can be calculated efficiently by mathematical morphology [START_REF] Guastella | Cartoon filter via adaptive abstraction[END_REF].

Actually, some stations (especially if close to each other) can show similar detected temperature; a hierarchical clustering technique groups together these stations and therefore their corresponding tiles. The hierarchical clustering tree is created starting from the information I of the dataset and then the optimal number k of clusters is computed by using the gap statistic method. Stations belonging to the same cluster and in adjacent Voronoi tiles are grouped together: this refines the original clustering by separating eventual stations which act in the same manner though are too far one from each other (fig. 6b). These new tiles are no more convex in general and contain stations with a similar behavior, normally due to the local orography. The certainty map S needed by the normalized convolution stores just the positions of the stations. In order to estimate the temperature value in a missing position, it is sufficient to apply the normalized convolution on the information map I from the dataset and on the certainty map S, limited to the cluster containing the position (fig. 7).

All experiments were carried out on an entry level machine, equipped with i7-7820HQ, 32GB RAM and Windows 10. Our algorithm was coded in Matlab language without particular optimizations; nonetheless it takes about a second to cluster the whole dataset and it is practically instantaneous in computing the normalized convolution. It should be noted that the clusters should be computed from time to time and while it is appropriate for a server to update the cluster periodically, the normalized convolution can be efficiently calculated even by low-end mobile devices. That is, the certainty map S can vary not only according to the response provided by the fixed stations, but it can be refined also through extemporaneous surveys.

To verify the correctness of the results we considered a leave-one-out cross validation: for each experiment a precise station has been removed at a time, in order to evaluate the estimation from the remaining stations. Figure 8 shows the average error and the standard deviation of each station during the considered 196 days. The average overall error is just -0.03°. The same normalized convolution can be effectively applied to determine the reliability of the proposed method on the entire lattice: it is sufficient to propagate the average error of each weather station to measure the correctness of the extrapolated measurements in any point without a real station (fig. 9).

V. CONCLUSION AND PERSPECTIVES

This paper introduces a simple and effective non-supervised methodology for estimating missing environmental information in a large scale context through cluster analysis and -3.3°0.0°+1.9°F ig. 9. Expected error through normalized convolution. Most stations do not introduce any error (green); some stations report warmer values than the real temperatures (yellow); only one station indicates a lower temperature (blue). We highlight that this colder station (#80 in fig. 8) is due to the absence of neighboring stations for a correct evaluation. normalized convolution. We believe the method could be further improved: for example, we considered a standard off-line hierarchical clustering algorithm while on-line techniques [START_REF] Pensa | Hierarchical co-clustering: off-line and incremental approaches[END_REF] could update dynamically the clustering tree each time the system receives new information (e.g. mobile devices equipped with proper sensors). Also geographical characteristics of the stations such as altitude can be used to provide a better grouping in the Voronoi diagram.

The proposed methodology is scale-independent, since it makes no assumption on the spatial distribution of the stations. Moreover, it is applicable to a variety of sensors and it does not require any intervention by the user. Although we considered only temperatures from a real regional dataset, the methodology is general enough to be applied to a variety of environments. Indeed, we plan to use the same approach to determine technologies that could be employed in the smart-campus context of the University of Toulouse III Paul Sabatier [START_REF] Gleizes | neOCampus: a Demonstrator of Connected[END_REF]. As a matter of facts, more and more researchers consider universities as great places to experiment innovative services and techniques for smart buildings. Installing and maintaining a large number of different sensors to monitor all parameters of the campus is quite expensive.

According to the quantitative results, our methodology already provides satisfactory temperature estimations by considering a reduced subset of weather stations, while the clustering step is suggested from time to time to process the whole dataset. To improve the performances it would be possible to cluster data streams by accessing the input information via a few linear scans; these algorithms do not store large amount of data by processing only a very limited subset of data [START_REF] Guha | Clustering data streams[END_REF]. This idea is due to emerging smart applications which involve massive data such as traffic, services and environmental data. We plan to investigate in our future works different techniques

Fig. 1 .

 1 Fig. 1. Sketch of the main steps of our methodology.

Fig. 2 .

 2 Fig. 2. Colors represents the clusters obtained by thresholding the dendrogram at 0.6 (the dashed line).

  If we indicate by {S • I} the pointwise product of S and I and by {K * I} the usual convolution with a kernel K, then normalized convolution is defined by N C(I, S, K) = {K * S • I} / {K * S} In other words, to reconstruct the data I from its samples specified in S, we just have to weight {K * S • I} by the confidence {K * S} of the results generated.

Fig. 4 .

 4 Fig. 4. If very few sensors (marked in red) are available, it is convenient to calculate the values in all remaining points by indirect contributions of the actual temperatures: their precalculated products by the kernel are simply added to accumulation arrays.

Fig. 5 .

 5 Fig. 5. If we are interested in estimating the temperature in just one point (marked in green), the straightforward implementation of the convolution remains the fastest solution.

Fig. 6 .

 6 Fig. 6. Superimposition of the Voronoi diagram (a) and subsequent clusters (b) on the map of Emilia-Romagna (obtained through Open-StreetMap [33]). Red dots indicate the weather stations.

Fig. 7 .

 7 Fig. 7. Only the stations within the same cluster (in detail) contribute to the normalized convolution, similarly to figure 5.

Fig. 8 .

 8 Fig. 8. Error bar of deduced temperatures (degree Celsius) for each station, computed through the leave-one-out process.

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	38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

-4 -2 0 2 Weather station Average error and standard deviation

to produce missing information, in order to carry out a comparative analysis.

VI. ACKNOWLEDGEMENT

This work was supported partially by the neOCampus initiative (neocampus.org) from the University Toulouse III Paul Sabatier [35].