Mathilde Guiltat

Marie Brut

Sébastien Vizzini

Anne Hémeryck
email: anne.hemeryck@laas.fr

A Hemeryck

Dioxygen molecule adsorption and oxygen atom diffusion on clean and defective Aluminum (111) surface using first principles calculations

Keywords: Oxidation, aluminum, DFT, diffusion, kinetics, defects

First principles calculations are conducted to investigate kinetic behavior of oxygen species at the surface of clean and defective Al(111) substrate. Oxygen island, aluminum vacancy, aluminum sub-vacancy, aluminum ad-atom and aluminum terraces defects are addressed.

Adsorption of oxygen molecule is first performed on all these systems resulting in dissociated oxygen atoms in main cases. The obtained adsorbed configurations are then picked to study the behavior of atomic oxygen specie and get a detailed understanding on the effect of the local environment on the ability of the oxygen atom to diffuse on the surface. We pointed out that local environment impacts energetics of oxygen atom diffusion. Close packed oxygen island, sub-vacancy and ad-atoms favor oxygen atom stability and decrease mobility of oxygen atom on the surface, to be seen as surface area for further nucleation of oxygen island.

Introduction

Aluminum oxides have been subject to wide number of studies focused on growth mechanisms, thermal and diffusion barrier coating properties, insulating interfaces, surface reactivity as catalysis among others [START_REF] Schiller | Reactive dc high-rate sputtering as production technology[END_REF][START_REF] Sproul | New routes in the preparation of mechanically hard films[END_REF][START_REF] Heuer | Alumina Scale Formation: A New Perspective: Alumina Scale Formation: A New Perspective[END_REF] because they are of major interest for highly applicative fields such as corrosion of aluminum-based alloys, surface preparation through thermally grown oxides, high-k oxides integration in microelectronics [START_REF] Lee | Characteristics of high-k Al2O3 dielectric using ozone-based atomic layer deposition for dual-gated graphene devices[END_REF][START_REF] Li | Characterization of Al2O3 ceramic coatings on 6063 aluminum alloy prepared in borate electrolytes by micro-arc oxidation[END_REF]. Knowing the high potential breakthroughs and reduced domestic and technological costs that could arise from the mastering and tailoring of aluminum oxide growth, this topic is still of concern.

Today, oxide growth remains a not well-understood and a not controlled phenomenon: experimental and theoretical investigations reveal that aluminum oxidation is highly complex and depends on external temperature [START_REF] Heuer | Alumina Scale Formation: A New Perspective: Alumina Scale Formation: A New Perspective[END_REF], substrate surface properties [START_REF] Benka | Oxidation of aluminum studied by secondary electron emission[END_REF][START_REF] Zhukov | Oxygen adsorption on Al(111)role of surface pretreatment in governing oxidation[END_REF][START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF][START_REF] Monkhorst | Special points for Brillouin-zone integrations[END_REF], crystal orientations [START_REF] Henkelman | Methods for finding saddle points and minimum energy paths[END_REF][START_REF] Sheppard | Optimization methods for finding minimum energy paths[END_REF][START_REF] Jacobsen | Electronic structure, total energies, and STM images of clean and oxygen-covered Al (111)[END_REF][START_REF] Reichel | The effect of substrate orientation on the kinetics of ultra-thin oxide-film growth on Al single crystals[END_REF], exhibits several ranges of velocity in growth mode [START_REF] Cai | Tuning the Limiting Thickness of a Thin Oxide Layer on Al(111) with Oxygen Gas Pressure[END_REF][START_REF] Cabrera | Theory of the oxidation of metals[END_REF], through native oxide growth to thermally grown oxide. But the growth velocity and formed oxide layer are highly dependent on the early stages of oxidation starting from first adsorption of oxygen species on the substrate to oxygen island formation and oxide nucleation. In addition, surface reactivity of aluminum oxides for further studies on polymer or organic coating to prevent corrosion, or multi-layered directly integrated materials, are hot and highly addressed topics using handmade model system usually built by assembling two material bulks which do not mimic realistic interface [START_REF] Costa | Atomistic Modeling of Corrosion Resistance: A First Principles Study of O 2 Reduction on the Al(111) Surface Covered with a Thin Hydroxylated Alumina Film[END_REF][START_REF] Wallin | Ab initio studies of Al, O, and O 2 adsorption on α -Al 2 O 3 ( 0001 ) surfaces[END_REF][START_REF] Santos | Elucidating the high-k insulator α-Al2O3 direct/indirect energy band gap type through density functional theory computations[END_REF][START_REF] Koberidze | Effect of interface geometry on electron tunnelling in Al/Al 2 O 3 /Al junctions[END_REF][START_REF] Pilania | Revisiting the Al/Al2O3 Interface: Coherent Interfaces and Misfit Accommodation[END_REF][START_REF] Brune | Interaction of oxygen with Al(111) studied by scanning tunneling microscopy[END_REF][START_REF] Lanthony | On the early stage of aluminum oxidation: An extraction mechanism via oxygen cooperation[END_REF][START_REF] Lanthony | Formation of Al/CuO bilayer films: Basic mechanisms through density functional theory calculations[END_REF][START_REF] Guo | Dissociation and reconstruction of O2 on Al (111) studied by First-principles[END_REF]. Having a realistic model-system of aluminum oxide achieved as a thermally grown oxide from the early steps of oxidation process is thus from a critical interest also for these applications and model systems.

In a recent paper, we show that kinetics are the main issue in the formation of oxygen island on the aluminum surface, which will be the center of oxide nucleus formation through a barrierless extraction mechanism [START_REF] Brune | Interaction of oxygen with Al(111) studied by scanning tunneling microscopy[END_REF][START_REF] Lanthony | On the early stage of aluminum oxidation: An extraction mechanism via oxygen cooperation[END_REF]. The aim of this paper is to get insights on the kinetics of the primary steps formation of oxygen islands [START_REF] Lanthony | On the early stage of aluminum oxidation: An extraction mechanism via oxygen cooperation[END_REF] and where and how oxygen island will begin to form, by exposing a bare Al(111) surface to oxygen molecule with a particular focus given on the subsequent behavior of adsorbed oxygen species as a function of its local structure when considering increasing coverage and influence of presence of defects using a first-principles calculations approach.

Previous theoretical and experimental approaches of primary stages of oxygen molecule adsorption on Al surfaces reveal a systematic dissociation on the clean Al(111) surface, [START_REF] Benka | Oxidation of aluminum studied by secondary electron emission[END_REF][START_REF] Guo | Dissociation and reconstruction of O2 on Al (111) studied by First-principles[END_REF][START_REF] Kuschel | Ion-enhanced oxidation of aluminum as a fundamental surface process during target poisoning in reactive magnetron sputtering[END_REF][START_REF] Popova | Comparative study of Al (111) oxidation with O 3 and O 2[END_REF][START_REF] Arranz | Characterization of the surface and interface species formed during the oxidation of aluminum[END_REF][START_REF] Hasnaoui | Nanoscale oxide growth on Al single crystals at low temperatures: Variable charge molecular dynamics simulations[END_REF][START_REF] Ciacchi | Hot-Atom O2 Dissociation and Oxide Nucleation on Al(111)[END_REF][START_REF] Zhukovskii | On the mechanism of the interaction between oxygen and close-packed single-crystal aluminum surfaces[END_REF][START_REF] Honkala | Oxygen molecule dissociation on the Al (111) surface[END_REF][START_REF] Komrowski | Oxygen Abstraction from Dioxygen on the Al(111) Surface[END_REF][START_REF] Oner | On the role of long-range elastic interactions for the Al(1 1 1) oxide nucleation kinetics[END_REF][START_REF] Sasaki | Dissociation process of O 2 on the Al (111) surface[END_REF][START_REF] Schmid | Oxygen adsorption on Al (111): low transient mobility[END_REF][START_REF] Kiejna | Stability of oxygen adsorption sites and ultrathin aluminum oxide films on Al (111)[END_REF][START_REF] Sasaki | Adsorption of the oxygen to the Al (111) surface[END_REF]. This dissociation is due to a charge transfer inside the dioxygen molecule leading to the partial occupancy of the anti-bonding orbitals: the molecule goes through different electronic states known as O à O 2 -à O 2 2- [START_REF] Ciacchi | Hot-Atom O2 Dissociation and Oxide Nucleation on Al(111)[END_REF][START_REF] Honkala | Oxygen molecule dissociation on the Al (111) surface[END_REF][START_REF] Komrowski | Oxygen Abstraction from Dioxygen on the Al(111) Surface[END_REF][START_REF] Libisch | Origin of the Energy Barrier to Chemical Reactions of O 2 on Al(111): Evidence for Charge Transfer, Not Spin Selection[END_REF]. In the literature, the dissociation occurs on the surface that could lead to abstraction mechanism giving rise to monomer on the surface [START_REF] Komrowski | Oxygen Abstraction from Dioxygen on the Al(111) Surface[END_REF], or could result in the separation of oxygen atoms in close neighborhood between one and three Al interatomic spacing [START_REF] Schmid | Oxygen adsorption on Al (111): low transient mobility[END_REF] or by more than 80 Å [START_REF] Brune | Interaction of oxygen with Al(111) studied by scanning tunneling microscopy[END_REF][START_REF] Österlund | Dissociative sticking of O 2 on Al (111)[END_REF], thus appearing still as an unclear issue. Actually, isolated oxygen atom are observed on aluminum surface and explained by the high-energy release incoming from the adsorption of molecular oxygen. This high-energy release appears to give an enhanced velocity to adsorbed oxygen atom on the surface that will consequently exhibit a high mobility on the surface and long scale displacement. This high mobility observed right after the dissociation will result in a 'hot atom' behavior as referred in many experimental publications [START_REF] Arranz | Characterization of the surface and interface species formed during the oxidation of aluminum[END_REF][START_REF] Schmid | Oxygen adsorption on Al (111): low transient mobility[END_REF][START_REF] Österlund | Dissociative sticking of O 2 on Al (111)[END_REF][START_REF] Trost | Interaction of oxygen with Al (111) at elevated temperatures[END_REF]. However, this cannot be observed in first-principles calculations because non-adiabatic effects are not taken into account, whereas they cannot be neglected [START_REF] Komrowski | Oxygen Abstraction from Dioxygen on the Al(111) Surface[END_REF]. But oxygen atoms diffuse on the surface forming close-packed oxygen islands thanks to thermal activated moves and favorable energy interaction. This point is relevant and stimulates few discussions about activation barriers that drive oxygen island formation [START_REF] Brune | Interaction of oxygen with Al(111) studied by scanning tunneling microscopy[END_REF][START_REF] Lanthony | Formation of Al/CuO bilayer films: Basic mechanisms through density functional theory calculations[END_REF][START_REF] Guo | Dissociation and reconstruction of O2 on Al (111) studied by First-principles[END_REF][START_REF] Oner | On the role of long-range elastic interactions for the Al(1 1 1) oxide nucleation kinetics[END_REF][START_REF] Chakarova | Monte Carlo simulation of initial Al (111) oxidation[END_REF][START_REF] Oner | Al (111) oxidation kinetics in the submonolayer regime; experiment and Monte Carlo simulations[END_REF][START_REF] Yourdshahyan | Adiabatic potential-energy surfaces for oxygen on Al(111)[END_REF][START_REF] Lanthony | Elementary Surface Chemistry during CuO/Al Nanolaminate-Thermite Synthesis: Copper and Oxygen Deposition on Aluminum (111) Surfaces[END_REF], because of the difficulty to estimate the activation barrier experimentally. Large scale modeling approaches based on Monte Carlo methodologies have been developed to simulate primary steps of oxidation in order to take into account kinetics [START_REF] Oner | On the role of long-range elastic interactions for the Al(1 1 1) oxide nucleation kinetics[END_REF][START_REF] Chakarova | Monte Carlo simulation of initial Al (111) oxidation[END_REF][START_REF] Oner | Al (111) oxidation kinetics in the submonolayer regime; experiment and Monte Carlo simulations[END_REF][START_REF] Oner | Monte Carlo simulation of the chemisorption kinetics and initial oxide formation on Al(111)[END_REF]. Furthermore, structural defects can also have a drastic effect on the activation barriers that could affect kinetics of the oxygen islands formation and also their number and size on the surface. Defects are observed experimentally on the surface [START_REF] Brune | Interaction of oxygen with Al(111) studied by scanning tunneling microscopy[END_REF][START_REF] Trost | Interaction of oxygen with Al (111) at elevated temperatures[END_REF][START_REF] Polatoglou | Vacancy-formation energies at the (111) surface and in bulk Al, Cu, Ag, and Rh[END_REF], but have not been subject of studies to our knowledge, whereas it is clear that when environment changes locally, it will impact the chemical dissociation and adsorption mode of the oxygen molecule [START_REF] Lanthony | On the early stage of aluminum oxidation: An extraction mechanism via oxygen cooperation[END_REF][START_REF] Sasaki | Adsorption of the oxygen to the Al (111) surface[END_REF][START_REF] Kiejna | Stability of oxygen adsorption sites and ultrathin aluminum oxide films on Al (111)[END_REF][START_REF] Chakarova | Monte Carlo simulation of initial Al (111) oxidation[END_REF][START_REF] Oner | Monte Carlo simulation of the chemisorption kinetics and initial oxide formation on Al(111)[END_REF][START_REF] Zhdanov | Simulation of the first stage of oxide formation on Al (111)[END_REF][START_REF] Frederick | A vibrational characterisation of the O/Al(111) system: a reassignment of HREELS data[END_REF][START_REF] Jeurgens | Growth kinetics and mechanisms of aluminum-oxide films formed by thermal oxidation of aluminum[END_REF].

With such non-elucidated points about kinetics and surface defects influence, we combine a study on molecular oxygen adsorption with atomic oxygen behavior investigation, on clean and defective Al(111) surfaces for a complete overview. The main focus will be the investigation of the ability of oxygen atom to move on the surface as a function of its local environment and see how activation barriers of oxygen atom diffusion are affected. Among considered defects, we investigate aluminum vacancy, aluminum sub-vacancies, aluminum ad-atoms, and aluminum steps defects. This paper based on Density Functional Theory based calculations (DFT) is organized as follows: Adsorption of oxygen molecule on Al(111) is first addressed, then thermodynamics and kinetics of atomic oxygen are discussed with an increasing oxygen coverage by considering isolated oxygen atom and an existing oxygen atoms island [START_REF] Yourdshahyan | Adiabatic potential-energy surfaces for oxygen on Al(111)[END_REF][START_REF] Carbogno | Signatures of nonadiabatic O 2 dissociation at Al(111): First-principles fewest-switches study[END_REF][START_REF] Neuburger | On the viability of single atom abstraction in the dissociative chemisorption of O2 on the Al(111) surface[END_REF]. This has to be considered because oxygen island has to be first formed on the surface to allow oxide to grow [START_REF] Benka | Oxidation of aluminum studied by secondary electron emission[END_REF][START_REF] Brune | Interaction of oxygen with Al(111) studied by scanning tunneling microscopy[END_REF][START_REF] Lanthony | On the early stage of aluminum oxidation: An extraction mechanism via oxygen cooperation[END_REF][START_REF] Ciacchi | Hot-Atom O2 Dissociation and Oxide Nucleation on Al(111)[END_REF][START_REF] Oner | On the role of long-range elastic interactions for the Al(1 1 1) oxide nucleation kinetics[END_REF][START_REF] Lanthony | Elementary Surface Chemistry during CuO/Al Nanolaminate-Thermite Synthesis: Copper and Oxygen Deposition on Aluminum (111) Surfaces[END_REF]. In the second part of the paper, the adsorption of oxygen molecule is performed as detailed in the first part for Al(111) containing defects: vacancy, sub-vacancy, ad-atom, terrace. Kinetics of isolated oxygen atom moving on these defective surfaces is then discussed.

Computational Details

Calculations are based on Density Functional Theory (DFT) [START_REF] Kiejna | First-principles study of surface and subsurface O structures at Al(111)[END_REF] with the Perdew-Burke-Ernzerhof functional in the Generalized Gradient Approximation (PBE-GGA) [START_REF] Perdew | Generalized gradient approximation made simple[END_REF] as implemented in VASP 5.3 (Vienna Ab initio Simulation Package) [START_REF] Kresse | Ab initio molecular dynamics for liquid metals[END_REF][START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF][START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | Ab initio molecular-dynamics simulation of the liquid-metalamorphous-semiconductor transition in germanium[END_REF]. We used a plane wave basis set for the Kohn-Sham Bloch functions, with a cut off energy of 400 eV to account for valence electrons. Ions are relaxed with a conjugate-gradient algorithm. The sampling of the Brillouin zone was performed using a Monkhorst-Pack [START_REF] Monkhorst | Special points for Brillouin-zone integrations[END_REF] mesh of 2x2x1 k-points. The nudged elastic band (NEB) method [START_REF] Henkelman | Methods for finding saddle points and minimum energy paths[END_REF][START_REF] Sheppard | Optimization methods for finding minimum energy paths[END_REF][START_REF] Henkelman | A climbing image nudged elastic band method for finding saddle points and minimum energy paths[END_REF] was used to determine activation barriers along reaction paths of atomic oxygen species. The aluminum (111) slab is built as an orthorhombic supercell of (4x2) surface unit cells. A vacuum zone of 15 Å is added following the z-axis, in order to model the surface. The system contains 96 atoms distributed in 6 layers of 16 atoms corresponding to slab dimensions of 11.43 x 9.90 x 25.00 Å 3 . Al atoms at the bottom of the cell are kept fixed during geometry optimizations, reproducing thereby the bulk behavior. All other atoms are free to relax.

This slab is used throughout the paper in order to study both atomic and molecular oxygen species adsorption. Adsorption is performed by considering atomic oxygen in a singlet state whereas molecular oxygen is initially set in a triplet state, with a spin state free to relax. In all adsorption mechanism, oxygen species are placed at 2 Å above the Al(111) surface and then are fully relaxed. Considering the simulated coverage and surface dimensions, the used slab has been validated as large enough to avoid any interaction between periodic slabs during both adsorption and diffusion investigations.

Using this (111) oriented aluminum surface-model (Figure 1), the deposition of dioxygen molecule and oxygen atom on both clean surface and defective surfaces are performed. For each surface, the defect formation energies have been calculated as ∆H f = E defective_bulk ± E Al -E clean_bulk where E defective_bulk is the total energy of the defective bulk (see Figure 1), E Al is taken as the reference energy of the atomic aluminum calculated from the bulk and E clean_bulk is the energy of perfect Aluminum slab (111). The studied Al(111) surfaces are:

-A perfect Al(111) surface considered as the reference system -Defective surfaces containing Al Vacancy and Al sub-vacancy defects schematized as #1 and #2 on Figure 1a. Formation energies of such defects are respectively 0.80 eV and 0.87 eV [START_REF] Polatoglou | Vacancy-formation energies at the (111) surface and in bulk Al, Cu, Ag, and Rh[END_REF]. Other defective surfaces contain Al ad-atom defect, the formation energies are 0.85 eV when generated from a kink site at the edge of a terrace defect as will be discussed in the following and 1.79 eV if formed as a Schottky defect. In the following, the reaction energies ∆H are calculated as follows :

∆H = E total -E O -E bulk
With :

-E total the total energy of the system in a given adsorbed configuration.

-E O the reference energy of an atomic oxygen calculated from ½ of the molecular oxygen or of an molecular oxygen depending on the considered adsorbed specie.

-E bulk the reference energy of smooth or defective Aluminum slab.

Oxygen behavior on clean aluminum surface

Dioxygen molecule adsorption

Primary calculations are focused on the adsorption of molecular oxygen species on perfect aluminum surface [START_REF] Brune | Interaction of oxygen with Al(111) studied by scanning tunneling microscopy[END_REF][START_REF] Guo | Dissociation and reconstruction of O2 on Al (111) studied by First-principles[END_REF][START_REF] Ciacchi | Hot-Atom O2 Dissociation and Oxide Nucleation on Al(111)[END_REF][START_REF] Zhukovskii | On the mechanism of the interaction between oxygen and close-packed single-crystal aluminum surfaces[END_REF][START_REF] Trost | Interaction of oxygen with Al (111) at elevated temperatures[END_REF][START_REF] Yourdshahyan | Adiabatic potential-energy surfaces for oxygen on Al(111)[END_REF][START_REF] Carbogno | Signatures of nonadiabatic O 2 dissociation at Al(111): First-principles fewest-switches study[END_REF][START_REF] Katz | Abstractive dissociation of oxygen over Al(111): A nonadiabatic quantum model[END_REF][START_REF] Brune | Surface migration of "'hot'" adatoms in the course of dissociative chemisorption of oxygen on Al(111)[END_REF]. Several starting orientations and positions for the dioxygen molecule have been tested and all the final positions are provided on Figure 2. Initial configurations of the dioxygen molecule have been chosen with the respect of the surface topology (above topmost atom or fcc site or hcp sites) by considering either horizontal or vertical orientations centered or shifted from the center of adsorption sites. As previously reported in literature, the adsorption mechanism of dioxygen is dissociative, barrierless and brings a great energy gain of ∆H = -9.85 eV [START_REF] Guo | Dissociation and reconstruction of O2 on Al (111) studied by First-principles[END_REF][START_REF] Sasaki | Adsorption of the oxygen to the Al (111) surface[END_REF].

Starting positions are in Figure 2a: number given inside this starting position is provided to establish the correlation with final positions given in Figure 2b. As can be observed, several starting different configurations can result in a same final configuration. Circles with two rings represent vertical molecules; two circles and a stick represent the horizontal ones. The more stable position contains two adsorbed oxygen atoms on close fcc sites, as first neighbors (d = 2.90 Å) and referred as #1 in Figure 2b. This final configuration is obtained when the dioxygen molecule is placed horizontally, centered or shifted (along the xaxis), above the Al surface and associated with a reaction enthalpy large of ∆H = -9.85 eV.

Other stable position exhibits one oxygen atom on a fcc site and the other on a hcp site also in close vicinity (d = 3.31 Å), where oxygen atoms are second neighbors. This position is reached when the dioxygen molecule is placed vertically or parallel (along the y-axis) on the surface aluminum between the two final sites, or vertically put above a hcp site. The energy gain for this position is ∆H = -9.32 eV. The third more stable position is obtained with the dioxygen molecule placed horizontally (along the x-axis) and centered above a hcp site: here one oxygen atom is adsorbed on a fcc site and the other on a hcp site on third neighbor. The energy gain for this position is ∆H = -9.16 eV. Here, we notice that oxygen atoms are in hcp and fcc sites as observed in #2 but further from each other. This indicates a supplementary favorable interaction existing when oxygen atoms are in close neighborhood as in configuration #2 which does not exist anymore in configuration #3. This favorable interaction is attributed to a larger electrostatic interaction coming from higher charge transfers between adsorbed oxygen atoms and their surrounding aluminum atoms, stabilizing the system when the two oxygen atoms are adsorbed as first neighbors. A fourth stable position is obtained when the dioxygen molecule is placed above a fcc site, vertically or parallel (along the x-axis) resulting in two oxygen atoms adsorbed on two hcp sites as first neighbors. We notice here that hcp is a less stable position compared to fcc site when comparing this final adsorbed configuration with the most stable one, i.e. two adsorbed oxygen atoms on fcc sites. This adsorbed position corresponds to ∆H = -9.06 eV. The last position and also the less stable observed in this study is obtained when one oxygen atom is on hcp site and the other on fcc site at a distance of d = 2.40 Å, which is a smaller distance compared to the most favorable adsorbed configuration. Here, the two oxygen atoms are too close and a repulsive energy destabilizes the system. This last position is obtained with the dioxygen molecule placed horizontally (along the y-axis), centered above a hcp and a fcc site. The energy gain is ∆H = -8.96 eV.

In conclusion, fcc sites are the most stable on the Al(111) surface and first neighbor interactions are favorable.

But considering high energy released during the adsorption, it is shown that oxygen atoms once dissociated and adsorbed on the surface will migrate rapidly due to this extra energy that will enhance their mobility on the surface as 'hot atom' behavior [START_REF] Ciacchi | Hot-Atom O2 Dissociation and Oxide Nucleation on Al(111)[END_REF][START_REF] Honkala | Oxygen molecule dissociation on the Al (111) surface[END_REF][START_REF] Schmid | Oxygen adsorption on Al (111): low transient mobility[END_REF][START_REF] Sasaki | Adsorption of the oxygen to the Al (111) surface[END_REF][START_REF] Österlund | Dissociative sticking of O 2 on Al (111)[END_REF][START_REF] Brune | Surface migration of "'hot'" adatoms in the course of dissociative chemisorption of oxygen on Al(111)[END_REF]. At this stage, one can consider that atomic specie exists on the surface also as an isolated adsorbed state as observed experimentally [START_REF] Trost | Interaction of oxygen with Al (111) at elevated temperatures[END_REF] and a detailed study on oxygen species as an isolated atom has to be considered.

Atomic Oxygen adsorption

Considering previous conclusions, the dissociation of dioxygen molecule on Al( 111) is observed at the primary steps of adsorption. In this context, a careful study has been conducted on the behavior of a single oxygen atom on the Al(111) surface: -as an isolated atom moving on the surface and -as a function of larger coverage since favorable interaction between oxygen atoms when adsorbed in close neighborhood has been discussed above. The study is carried out with the goal to get insights on kinetics of oxygen diffusion and discussing clustering effects on the surface.

The stability of the isolated atomic oxygen on all possible existing configurations hcp, fcc, top and bridge sites is first studied. Figure 3a illustrates the adsorption of a single oxygen atom above the four characteristic sites of the (111) fcc-like surface, respectively top, bridge, fcc and hcp, referred as T, B, F and H [START_REF] Lanthony | On the early stage of aluminum oxidation: An extraction mechanism via oxygen cooperation[END_REF][START_REF] Lanthony | Formation of Al/CuO bilayer films: Basic mechanisms through density functional theory calculations[END_REF][START_REF] Guo | Dissociation and reconstruction of O2 on Al (111) studied by First-principles[END_REF][START_REF] Schmid | Oxygen adsorption on Al (111): low transient mobility[END_REF]. Only two sites are stabilized where fcc site (∆H = -4.82 eV) appears as energetically favored by -0.40 eV compared to the hcp site (∆H = -4.41 eV) in a good agreement with the dissociated adsorbed states in fcc and hcp configurations (#1 vs #4 in Figure 2b). The atomic study confirms that top and bridge configurations as adsorbed states do not exist on Al(111) surface and finally result in fcc adsorbed state. Nevertheless, we performed constraint relaxations by keeping frozen x and y coordinates of the oxygen atom in both bridge and top positions on order to estimate the potential energy surface. These calculations reveal that top position is less favorable by 0.16 eV compared to the bridge configuration. The bridge configuration will thus be used as the saddle point to characterize the most probable minimum energy path of oxygen atom diffusion between fcc and hcp sites. Activation barriers are calculated below.

To go further and get clues on the kinetics associated to the diffusive behavior of an isolated oxygen atom, we characterize the diffusion between the two observed stable adsorption sites fcc and hcp in close neighborhood. The minimum energy path is illustrated on the Figure 3b and the associated activation energy is given on Figure 3c. From the fcc site, oxygen atom must overcome an activation barrier large of 0.72 eV to move from fcc site toward hcp one (Figure 3c). The backward migration reaction from hcp to fcc site is characterized by an activation barrier of 0.30 eV. Both the disparity when regarding sites stability and the lower activation barrier from hcp to reach a more stable fcc site lead us to conclude that fcc site is favored [START_REF] Jacobsen | Electronic structure, total energies, and STM images of clean and oxygen-covered Al (111)[END_REF][START_REF] Brune | Interaction of oxygen with Al(111) studied by scanning tunneling microscopy[END_REF][START_REF] Trost | Interaction of oxygen with Al (111) at elevated temperatures[END_REF][START_REF] Kerkar | Adsorption site determination for oxygen on AI(111) using normal incidence standing X-ray wavefield absorption[END_REF].

Increasing Coverage: Migration toward formation of oxygen islands

The same study focused on the atomic oxygen migration is performed with an increasing coverage of oxygen atoms by considering already formed oxygen island on the surface in order to investigate in details the favorable interaction effect on the ability of oxygen atom to diffuse on the surface. This favorable interaction has been revealed in the molecular adsorption study.

First, a static investigation is first performed: the energies of two oxygen atoms deposited on fcc sites on close first neighborhood (d = 2.90 Å) or distant by 5.73 Å from each other are compared: We respectively obtained -9.85 eV and -9.66 eV for adsorption energies. The -0.19 eV difference between these adsorption energies can thus be explained by the favorable interaction existing between oxygen atoms stabilizing the system with a contribution of -0.10 eV per atom. As an interacting energy term exists, we evaluate its effect on the ability of oxygen atom to diffuse from a close-packed three oxygen atoms island moving to an isolated state between different configurations (see Figure 4a):

A. The triangle, as a close-packed compact configuration, where oxygen atoms are located on sites #1, #2 & #3 on Figure 4a. In this configuration, the adsorption energy is -15.06 eV. The contributing interaction energy to the value is estimated to be -0.60 eV, with six interaction terms to be considered similarly to the contribution of -0.10 eV per atom as previously calculated.

B. The L-shape, where atoms located on sites #1, #2 and on sites #2, #5 are first neighbors but atoms located on sites #1, #5 are distant by 4.99 Å. In this configuration, the adsorption energy is large of -14.83 eV. This lower adsorption energy is obtained due to a reduced interaction energy (estimated at -0.37 eV).

This energy difference corresponds to the broken bonds compared to the triangle configuration, indicating that oxygen atom has no more interaction with the other oxygen atom located as its second neighbor. where one oxygen atom is isolated from the two oxygen atoms adsorbed on close sites. Sites #1, #2 are first neighbors. Here, the adsorption energy is the weakest with -14.70 eV. The interaction energy is -0.24 eV, revealing only two oxygen atoms in interaction, and a third isolated one.

These configurations confirm the favorable interacting energy between oxygen atoms when adsorbed as first neighbors. This energy can be quantified and is large of -0.2 eV per pair of interacting oxygen atoms. This observation enables us to assume that oxygen island will be favorably formed on the surface on Al(111) substrate.

Considering those configurations, we explore the migration of one oxygen atom leaving a compact triangle configuration (A) to reach an isolated state (D). This path is explored as a multi-steps reaction by moving one oxygen atom of the A configuration step-by-step through fcc and hcp sites as identified previously. This multi-steps migration path is depicted on The first diffusion from #3 to #4, corresponding to a displacement from fcc to hcp, highlights an activation barrier of 0.95 eV. Compared to the single oxygen atom migration in Figure 3c,

we observe an increase of the activation barrier large of 0.20 eV indicating that compact configurations are favored, thanks to a favorable oxygen-oxygen interaction. Starting from configuration (A), it will not be favorable to dissociate triangle configuration and few oxygen atoms will be able to leave compact adsorbed structure because of the high activation barrier of 0.95 eV expect under high temperature condition.

In the following, we observe that the migration of oxygen specie moving around an existing island has the same behavior as an isolated oxygen: when oxygen atom moves from site #4 to site #5 the same activation barriers (0.30 eV and 0.73 eV) are observed as the ones determined in Figure 3c. This shows that an interaction between two oxygen atoms has shortrange influence: oxygen atom on position #4 does not see anymore the oxygen atom located on position #1 as confirmed by the total energy discussed before.

From the L-shape, when moving atom is adsorbed on site #5, two different pathways are investigated: -where oxygen atom can move around the island (from #5 to #7) to form the line configuration or -where oxygen atom can leave the island (from #5 to #8) as the described isolated oxygen configuration. When oxygen atom diffuses from #5 to #7, through #6, activation barriers are the same as those observed in the case of isolated atom as in migration from #4 to #5 in Figure 4a and b, confirming the short range interaction between oxygen atoms. Oxygen atom will thus have the same ability to diffuse as an isolated state as when moving around an oxygen island.

On the contrary and interestingly, when oxygen atom is moved away from an oxygen island, a raise in the activation barrier is observed from the hcp to fcc sites: the activation barrier from #6 to #8 increases to the value of 0.48 eV and a destabilization of the final configuration by 0.18 eV is observed.

As previously conducted [START_REF] Lanthony | On the early stage of aluminum oxidation: An extraction mechanism via oxygen cooperation[END_REF], dragging an oxygen atom outwards from a larger oxygen atoms island (from four oxygen atoms), lead to a rise of the activation barrier to 1.22 eV, 0.27 eV higher than the migration between positions #3 and #4 in the case of three oxygen atoms island. This energy increase reaches 1.30 eV for five oxygen atoms island and more.

Considering kinetics and energetics, these calculations reveal the tendency of oxygen atom to form close-packed oxygen island on the surface of Al(111) at low coverage. Nevertheless, interestingly we observe that oxygen atom exhibits the same kinetics to move around the oxygen island without going away as the ones observed as isolated state. These conclusions are experimentally observed, with the formation of geometrical clusters at low coverage in agreement with highly symmetrical Al(111) pattern [START_REF] Brune | Interaction of oxygen with Al(111) studied by scanning tunneling microscopy[END_REF].

Oxygen specie adsorption on defective Aluminum surfaces

Aluminum surface containing a vacancy

A similar detailed study is realized on a defective surface containing a vacancy on the topmost surface symbolized by a white circle on Figure 5: on this defective surface, molecular oxygen specie is adsorbed above the vacancy and atomic oxygen behavior is investigated from adsorbed state. 3. Configurations #3 and #6 result in dissociated oxygen atoms with one oxygen atom adsorbed on a surface site surrounding the vacancy and the other one inserted underneath the topmost layer. Both configurations characterized by an insertion inside the vacancy defect exhibit different adsorption energies large of -0.80 eV that can be explained by the obtained adsorption sites: in one case the oxygen atom on the surface is on fcc and the second is located inside the vacancy as on hcp site (#3), in the other case one oxygen atom is adsorbed on hcp on the surface and the other is adsorbed inside the vacancy between a fcc and a hcp site (#6). The difference on the energetic gains observed between #3 and #6 income in one hand from the higher stability of the fcc site on the surface compared to hcp site even close to a vacancy and on the other hand mainly because of the destabilization of the configuration #6:

actually the oxygen atom inside the vacancy is on a bridge-like configuration, a non stable configuration, as will be discussed below, which only exists when another oxygen atom is nearby.

Interestingly, we observe that energy gain large of -9.53 eV of the configuration #1 is more favorable compared to the adsorption on perfect surface with the configuration #2 on the Figure 2 at -9.32 eV. This shows that vacancies stabilize oxygen atoms and so this kind of defect is more favorable than the clean surface.

To investigate the stability of the neighboring fcc or hcp adsorption sites at the neighborhood of a vacancy, we relax the atomic oxygen specie by placing it above a vacancy. In the following we also perform a static study based on final adsorption configurations observed in Figure 5c. Results for the atomic oxygen are given in Table 3.

It is mainly observed that the oxygen atom relaxes favorably in either fcc or hcp sites on the surface layer as first neighbors of the vacancy. The stability of fcc sites is not affected by the presence of an existing vacancy even if oxygen atom is located as first and second neighborhood from this vacancy (See configuration a on Figure 5c). The oxygen adsorption energy is nearly the same as on the clean surface with ∆H = -4.85 eV. On the other hand, hcp sites are affected, since a stabilization of the oxygen atom is obtained with an adsorption energy large of ∆H = -4.65 eV and -4.53 eV when oxygen atom is placed on a hcp site in close neighborhood of vacancy, compared to -4.41 eV for the clean surface. This energetic gain regarding the stability of the hcp site nearby a vacancy defect explains the energy gain observed in configuration #1 on Figure 5a andb. Interestingly, we observe that the bridge configuration is stabilized when oxygen atom is adsorbed above the vacancy and close to hcp site.

The last position is obtained with the oxygen atom adsorbed inside the vacancy, above a hcp site inside the vacancy (See configuration d on Figure 5c). It is placed in the center of a triangle formed by two aluminum atoms of the surface and the one in the bottom layer, so its position is slightly underneath the surface layer. It is the less stable with ∆H = -4.36 eV.

Furthermore interestingly, we do not succeed in getting a bridge configuration stabilized between a fcc site and the vacancy, this one reaching an adsorbed fcc configuration as in Figure 5c. As well we do not succeed in inserting an oxygen atom on a fcc site inside the vacancy as reached when molecular adsorption occurs: an oxygen atom directly inserted on a fcc position inside the vacancy between the topmost layer and the sub-surface layer, based on the observation of the final configuration #6 on Figure 5b leads to a surface reconstruction:

the oxygen atom goes on a fcc surface site configuration and a sub-vacancy is created, where an aluminum atom of the sub-surface layer moves toward the topmost layer, healing the surface. Here, we notice that the spontaneous adsorption of oxygen atom as inserted into the vacancy by replacing missing aluminum atom is never observed. Even if the oxygen atom is directly placed into the site of the missing aluminum atom, we observe that the oxygen atom adsorbed in a as-like fcc site in the sub-surface layer with an energy gain of -4.13 eV, lower compared to other adsorbed configurations on the surface.

In the following part, we also study the influence of a vacancy on the atomic migration of oxygen atom in close vicinity of the vacancy. NEB calculations with oxygen atom moving around the vacancy have been performed and are shown in Figure 6. The studied migration starts from a hcp site in direct contact with the vacancy in #1 on Figure 6a to reach a fcc site named #2. The encountered migration barrier is large of 0.55 eV to go far from the vacancy toward a fcc site #2. This energy barrier is larger by 0.25 eV compared to the case of clean surface (Figure 3b), due to the stabilization of the hcp site in the vicinity of the vacancy (see Figure 5c). Then from fcc site #2, oxygen atom will migrate around the vacancy on a hcp site nearby as #3 and #4, through a determined activation barrier of E ac = 0.69 eV. The migration around the vacancy will be favored energetically, with the position #4 more stable by -0.08 eV compared to #3, so that an oxygen atom located on #3 will preferentially go back toward #2 with an energetic barrier E ac = 0.27 eV, compared to going away from the vacancy (E ac = 0.34 eV). Then from #4, oxygen atom can move toward the fcc site #5 with E ac = 0.41 eV. When oxygen atom is located on site #5, it is surrounded by activation barriers of nearly 0.72 eV, which are the same obtained as on clean part of the surface. It confirms here the local effect of the vacancy only on the stability of hcp site and not on the fcc. Then, in position #6 oxygen atom still feels the vacancy since its stability is more stable by -0.10 eV compared to the one on clean surface. Here, the diffusion will be easier to leave the vacancy area (E ac = 0.22 eV) than to maintain a diffusion process around the vacancy to the position #5 (E ac = 0.40 eV).

We observe that vacancy will stabilize hcp sites directly located in the close area of the vacancy and will notably slow down the diffusion of the oxygen atom when it is adsorbed on the neighboring sites. A stabilization of the hcp site large of -0.25 eV as first neighbor and -0.15 eV as a second neighbor associated to an increase of the activation barrier large of 0.25 eV were observed. Once the oxygen atom leaves the close neighborhood of the vacancy, its diffusion ability tendency is the same as the clean surface.

Aluminum surface with vacancy in sub-surface layer

The sub-surface vacancy defect is formed by removing one oxygen atom of the sub-surface layer, i.e. under a hcp site of the surface. In the following pictures, the sub-vacancy is symbolized with a white dashed line circle in Figure 7. eV compared to adsorption on clean surface (see Figure 7). Here, we note that a change in energy is associated to the presence of a vacancy in sub-surface layer that stabilizes hcp site right above the sub-vacancy. This energy gain is accompanied by a diminution of 0.02 Å to 0.10 Å of the O-Al bond. Finally, the configuration #3 remains the less stable because of the proximity of the two oxygen atoms. This is highlighted with bond deformation where bonds between the oxygen atoms are longer by ~0.02 Å while the other ones are shortened by 0.05 Å to 0.10 Å.

To get a better understanding of sub-surface vacancy and discriminate the role of each kind of surface site, an atomic oxygen specie has been placed directly above several fcc and hcp sites distinct from each other by their distance from the vacancy from first neighbor to third neighbor. These sites are classified by ∆H on the Figure 7c. The most stable site is the fcc in second neighbor (configuration a on Figure 7c) with ∆H = -4.87 eV where oxygen atom adsorbed on this site does not feel sub-surface vacancy as the adsorption energy is the same as the one observed on clean surface. On the contrary, fcc site near the sub-surface vacancy is slightly destabilized by 0.10 eV (b on Figure 7c). The major observation is the drastic change in the oxygen atom stability right above the sub-vacancy on the hcp site. A large energy gain of -0.40 eV is observed compared to clean surface. In this configuration, hcp site features the same stability as the fcc site. This stabilization of the hcp site is also slightly observed for further hcp sites (∆H = -4.46 eV compared to -4.41 eV).

Migration of the oxygen atom in close vicinity and above the sub-vacancy is plotted on Figure 8. The starting considered point is the hcp site right above the sub-surface vacancy (position c). As predicted in the stability discussion, this site is as stable as a fcc site, and results in a large increase of the diffusion barrier from 0.30 eV to 0.60 eV compared to clean surface.

Others barriers are similar to the surface barriers observed for clean surface, with small shifts because of the electronic perturbation of the sub-vacancy and destabilization of fcc site around this defect. A deep change in the hcp stability has been observed due to the presence of sub-surface vacancy. Here hcp site becomes isoenergetic with fcc sites, which will drastically slow down oxygen atom migration on the surface. Because of the reduced diffusion of oxygen atom on this surface topology, sub-surface vacancy area can become a center for oxygen island formation.

Al ad-atom on aluminum surface

We investigate the effect of an aluminum ad-atom on the surface. To do so, we first discuss the existence of such a defect and how an aluminum ad-atom can be formed on the aluminum surface. A Schottky defect requires a high formation energy of 1.79 eV. Furthermore, Aluminum (111) surfaces are also characterized by terraces and kinks [START_REF] Brune | Interaction of oxygen with Al(111) studied by scanning tunneling microscopy[END_REF][START_REF] Trost | Interaction of oxygen with Al (111) at elevated temperatures[END_REF] from where aluminum ad-atom can be generated. In the following we investigate the formation of an adatom from a kink site. In this paragraph, a larger slab, four times bigger (64 atoms per layer) than the one previously used was created to avoid limits of calculations due to periodic conditions. A kink defect was simulated by removing half of the aluminum atoms from a (-1-11) vicinal plane as densest atomic planes (Figure 9a). The Al atom located at the kink site has been constrained to move away from the terrace using a drag method by keeping fixed one coordinate along the migration path (y-axis) while other coordinates are allowed to relax, until the isolation of the aluminum atom from the border of the terrace (Figure 9). In order to check both the minimum energy path and the saddle point identified by the drag method, the activation barriers have been validated by a NEB calculation. A static study on the adsorption of atomic oxygen atom has been conducted to investigate the probability of presence of atomic oxygen atom at the edge of terrace defect. These calculations show that at the bottom of the step, the adsorption energies are -3.99 eV and -4.63 eV on the hcp and fcc sites respectively and at the top and at the edge of the terrace, the adsorption energies are -4.48 eV and -4.77 eV on the hcp and fcc sites respectively. The general observed trend is that the calculated adsorption energies are less favorable than adsorption of oxygen atom on perfect part of the surface without terrace. These results do not show any favorable adsorbed sites for oxygen atoms at the border of a terrace defect indicating a low presence of oxygen species close to such defects.

On an aluminum ad-atom defect, molecular oxygen is adsorbed. Here again, fully dissociated configurations are the most stable (#1 Figure 10b) where both oxygen atoms are located on close fcc sites with ∆H = -9.81 eV. On this configuration the ad-atom moves far from its initial position to a second neighbor site as explained by the low diffusion energy of the aluminum atom of E ac = 0.03 eV and by the lower interaction energy between ad-atom and Al surface compared to oxygen atom with Al surface. The starting configuration leading to this stable state is when molecular oxygen is placed in the far vicinity (second neighbor) of the adatom, enabling the molecular oxygen to react with the clean part of the surface. We can notice that in this configuration ∆H is the same as the dissociated molecular dioxygen on clean surface, so there is no interaction between the ad-atom and the oxygen atoms in this configuration as second neighbors. Configurations #7 and #8 are not dissociated states associated to the smaller obtained ∆H where oxygen molecule is adsorbed on top configurations on the ad-atom.

Finally, many of the tested configurations when molecular oxygen is placed in the close neighborhood of the ad-atom lead to non-fully dissociated and bridging configurations where ad-atom is linked to the surface using also aluminum-oxygen-aluminum bonds in addition to Al-Al bonds: Configurations #2, #3, #4, #5 & #6 are also dissociated with at least, one oxygen atom bridged to the ad-atom. We can notice that in many of the observed final configurations, ad-atom is located on bridge configuration (configurations #2, #5, #6).

Configuration #6 is less stable because of the oxygen atom remaining as on top metastable position above the ad-atom.

To conclude, we observe that adsorption of oxygen molecule on ad-atom defect is not as favorable energetically as on clean part of Al(111) surface, since oxygen atom will bond with the ad-atom and will form bridged adsorbed state on the surface. To reach those specific bridged states, adsorption on ad-atom must occur on close neighborhood, with an oxygen molecule located above the ad-atom. Furthermore a destabilization of the aluminum ad-atom is observed when oxygen molecule approaches this area (adsorption #1) due to the low interaction of the aluminum ad-atom with the surface compared to the great interaction of oxygen atom with the surface and the already mentioned high velocity of ad-atom on the surface. Here the ad-atom prefers to move away further from the arriving oxygen molecule, to let it react with a clean part of the surface. Furthermore considering the low probability of Al ad-atom to be generated on the surface estimated at 10 -15 using the transition state theory [START_REF] Hémeryck | A kinetic Monte Carlo study of the initial stage of silicon oxidation: basic mechanisms-induced partial ordering of the oxide interfacial layer[END_REF] with an average value of formation energy of 0.85 eV and at room temperature. This probability is also dependent on the surface state of the substrate since it is related to the presence of kink sites. Moreover, if one considers a molecular flux of oxygen species [START_REF] Hémeryck | A kinetic Monte Carlo study of the initial stage of silicon oxidation: basic mechanisms-induced partial ordering of the oxide interfacial layer[END_REF], the probability to react with a specific site on the surface is of the order of 10 -4 when considering room temperature and a given pressure of 0.000133 Pa [START_REF] Trost | Interaction of oxygen with Al (111) at elevated temperatures[END_REF]. Considering these assumptions, the probability of an oxygen molecule to react with ad-atom defect appears to be low in the order of 10 -20 compared to other possible surface mechanisms. Ad-atom defects will nevertheless affect the stability of oxygen atom on Al(111) surface: because of the low interaction of aluminum atom on the surface and the high mobility of this ad-atom when isolated on the surface, an oxygen atom diffusing close to the ad-atom will trap this latter to form stable Al-O bonds as a bridged configuration. Indeed, we observe that configuration with one oxygen atom stabilized as bridge with an ad-atom (Figure 10c andd) has the same stability as adsorbed on hcp (-4.37 eV) as on clean Al(111). Then when moving oxygen atom on the surface, ad-atom diffuse with the oxygen atom keeping the favorable interacting energy. This behavior has already been reported in previous study [START_REF] Migaou | A perfect wetting of Mg monolayer on Ag (111) under atomic scale investigation: First principles calculations, scanning tunneling microscopy, and Auger spectroscopy[END_REF]. We also perform calculations on coupling a vacancy and an Al ad-atom on the surface mimicking a surface Schottky defect. As the main results fit with what has been highly detailed above, we do not enter in details for this specific case. Interestingly, we notice in some adsorptions that dissociation of oxygen molecule destabilizes ad-atom as seen above, and the high mobility of the Al isolated atom will lead to the regeneration of the surface as a barrierless mechanism with the ad-atom healing the vacancy. This process is highly favorable with large enthalpies of around -10 eV, -11 eV.

V. Conclusion

In this paper we propose a detailed and exhaustive study of oxygen species adsorption and behavior at the surface of perfect and defective Al(111) surfaces. A list of configurations, behaviors and their associated energies is provided with a particular focus given on the variation of kinetics in diffusion of oxygen atom when evolving in close neighborhood of structural defects. This study enables us to have a better understanding on what happens on the Al(111) surface during oxygen deposition or on how oxygen specie reacts with aluminum substrate when taking into account a more realistic surface, i.e. containing defect. Oxygen atom will preferentially migrate on the Al(111) surface using typical fcc to hcp sites through thermal activated mechanism calculated as 0.72 eV and 0.30 eV from fcc to hcp and from hcp to fcc respectively. We observe that once small oxygen islands begin to form on the surface, oxygen atom mobility is reduced because of the interaction energy that will favor oxygen species clustering on the surface. The vacancy and sub-vacancy defects will drastically modify kinetics by slowing down the diffusion of oxygen atom in the vicinity of such defects but their effect is only effective on a local neighborhood of the defects. Hcp sites are stabilized becoming as stable as fcc sites, resulting in possible sites for oxygen island nucleation. On the contrary, terraces do not seem to stabilize oxygen atom, which will prefer to proceed and diffuse on clean part of the aluminum substrate.

Figure 1 :

 1 Figure 1: a) Schematic top view of Al(111) used throughout the paper where hcp, fcc, vacancy, subvacancy and ad-atom are represented. This color scheme will be used throughout the paper into the schematics. Grey circles represent aluminum atom. White circles are for vacancies and dark grey one are for ad-atoms. b) is provided to highlight fcc sites represented by green triangles and the hcp ones in purple, on top view. c) is a side view of the three topmost layers of our simulation slab to explain fcc and hcp use as epitaxial and anti-epitaxial growth sites.

Figure 2 :

 2 Figure 2: Schematic top views of dioxygen molecule deposited on smooth aluminum surface. a) starting positions above the surface and b) final dissociated and adsorbed configurations where identical numbers belong to the same molecule. Molecules with identical numbers on starting positions lead to the same final configuration in b. Energy gains of configurations 2b are provided in Table1.

Figure 3 :

 3 Figure 3: a) Schematic top view of oxygen atoms deposited on clean Al(111) surface. Oxygen atoms are schematized by red circles and aluminum atoms are grey. b) Activation barrier associated to the migration of one oxygen atom on the clean Al(111) surface between the hcp and fcc sites.

C

  . The line configuration, where oxygen atoms are adsorbed on sites #1, #2 & #7 with sites #1, #2 and #2, #7 are shown as first neighbors and sites #1, #7 are distant by 5.77 Å, with an adsorption energy of -14.88 eV. The interaction energy is -0.42 eV, which is close to the previous one, where no-interaction exists between the furthest oxygen atoms of the line configuration. D. So-called Isolated oxygen configuration (adsorbed states on sites #1, #2, #8),

Figure 4 :

 4 Figure 4: here, oxygen atoms located on sites #1 and #2 are kept fixed and the oxygen atom

Figure 4 :

 4 Figure 4: a) Top view of the migration of one oxygen atom around an island composed of two other oxygen atoms. b) Top views of fcc configurations reached during the migration. c) Minimum Energy Path corresponding to the migration of the Figure a). The red line corresponds to the red oxygen migration. The orange one corresponds to orange oxygen migration.

Figure 5 :

 5 Figure 5: a) Schematic top views of dioxygen molecule deposition on the aluminum surface containing a vacancy schematized by a white circle and b) final dissociated and adsorbed configurations where identical number on each dissociated oxygen atoms belongs to the same molecule. Molecules with identical number on starting positions lead to the same final configuration. Adsorption energies of those configurations are provided in Table 2. c) Schematic top view of the deposition of atomic oxygen on the aluminum surface containing a vacancy. Identical letters are oxygen atoms with the same adsorption energy given in Table3.

# 5 )

 5 exhibit bridge position where only one oxygen atom is bonded to two aluminum atoms around the vacancy. The bridge configuration is obtained when adsorption occurs above the vacancy defect and close to an available hcp surface site. The first conclusion is that vacancy stabilizes bridge configurations whereas the configuration was not reachable on non-defective surface. Configuration #5 is obtained with the molecule placed in the same way as the molecule #7, but above a hcp site of the vacancy, in line with Al-Al bond and with a neighboring surface fcc site. Such a position leads to the molecule dissociation above the vacancy where each oxygen atom goes on a bridge position, on the closest neighboring hcp sites of the aluminum surface.

Figure 6 :

 6 Figure 6: a) Top view of migration pathway of the oxygen atom on the aluminum surface next to the vacancy b) Energies associated to the oxygen migration pathway.

Figure 7 :Table 4 : 37 Table 5 : 44 For

 7437544 Figure 7: a) Schematic top views of the dioxygen molecule deposition on the aluminum surface containing a sub-vacancy schematized by a white circle and b) final dissociated and adsorbed configurations where identical number belongs to the same molecule. Final adsorption energies are provided in Table 4. c) Schematic top view of the deposition of atomic oxygen on the aluminum surface containing a sub-vacancy. Letters are oxygen atoms classification in function of ∆H given in Table 5. Table 4: Energy gain after the adsorption of the dioxygen molecule close to a sub-vacancy, in relation with the Figure 7b. Positions (#) 1 2 3

Figure 8 :

 8 Figure 8: a) Top view of the diffusion path of the atomic oxygen close and above the aluminum surface with the sub-surface vacancy located below the position c. b) Minimum Energy path associated to the atomic oxygen migration path in a). The grey zone corresponds to the surface area above the subvacancy defect

Figure 9 :

 9 Figure 9: Formation of an aluminum ad-atom from a surface step at a kink site a) Top view and b) Side view of the step defect with the drag applied in y-axis, on an aluminum located at a kink site c) Energy barrier associated to the drag method.When looking at Figure9, we observe that ad-atom birth occurs through a migration barrier of

Figure 10 :Table 6 :

 106 Figure 10: a) Schematic top views of dioxygen molecule deposited on the aluminum surface containing an ad-atom schematized by a grey circle and b) final adsorbed configurations where identical number belongs to the same molecule. Molecules with identical number on starting positions lead to the same final configuration. c) Schematic top views of atomic oxygen deposition on the aluminum surface and d) final adsorbed configurations where identical letter belongs to configurations with the same adsorbed energy. Table 6: Energy gain after the adsorption of the dioxygen molecule close to an adatom, in relation with the Figure 10b. Positions (#) 1 2 3 4 5 6 7 8

Table

1. Table 1: Energy gain after the adsorption of the dioxygen molecule, in relation with the Figure 2.

	Positions (#)	1	2	3	4	5
	∆H (eV)	-9.85	-9.32	-9.16	-9.06	-8.96

Table 2 : Energy gain after the adsorption of the dioxygen molecule above the vacancy, in relation with the Figure 5b.

 2

	Positions (#) 1	2	3	4	5	6	7
	∆H (eV)	-9.53	-9.43	-9.31	-9.16	-8.85	-8.67	-3.90

Table 3 : Energy gain after the adsorption of the oxygen atom close to a vacancy, in relation with the Figure 5c.

 3

	Positions (#)	a	b	c	d
	∆H (eV)	-4.85	-4.65	-4.53	-4.36
	In the case of molecular oxygen adsorption above the vacancy defect, at a first glance, one
	can observe that only one starting configuration leads to a non-dissociative adsorbed case (#7
	on Figure 5b) when initially molecular oxygen is placed above the vacancy site, in line with a

Al-Al bond centered above a fcc site inside the vacancy site. The final non-dissociated state is a metastable state with ∆H = -3.90 eV as a bridge configuration where oxygen molecule is adsorbed as a peroxy bridge on two aluminum atoms around the defective site. A dissociative adsorption is observed in all other tested cases. Other remarkable configurations (#2, #4 and

Table 7 : Energy gain after the adsorption of the atomic oxygen close to an ad-atom, in relation with the Figure 11b.

 7

	Positions (#)	a	b	c

Acknowledgment

The authors would like to thank Alain ESTEVE and Mehdi DJAFARI ROUHANI from LAAS-CNRS for discussions. The computer simulations were performed using HPC resources from CALMIP (Grant 1418).


Adem Lale

Nicolas Videau

Abdelhakim Bourennane

Frédéric Richardeau

Samuel Charlot

Mixed monolithic

Keywords: Buck converter, full bridge converter, orthogonal switching cell, parasitic inductance, monolithic intgration, reverse conducting IGBT, IGBT, diode

come

I. INTRODUCTION

Currently commercialized conventional power modules are generally realized using 2D hybrid packaging technology in which two-terminal power dies such as Insulated Gate Bipolar Transistor (IGBT) and PiN-diode are bonded on their backside and interconnected using wire bonds. A power module is made of a great number of two-terminal dies that are interconnected by wire bonds. Power modules are therefore bulky and their mass fabrication is limited in productivity. Moreover, due to the fact that the power dies are soldered on their backside, the midpoints of the converter's phase legs are placed on the circuit board. As a result, the circuit board is directly subjected to voltage variations during switching phases which is source of the undesirable common mode current through the circuit board. Moreover, wire bonds in power modules are source of parasitic inductance [START_REF] Tanimoto | High junction temperature and low parasitic inductance power module technology for compact power conversion systems[END_REF][START_REF] Li; Tolbert | Stray Inductance Reduction of Commutation Loop in the P-cell and N-cell-Based IGBT Phase Leg Module[END_REF] that induces high turn-off voltage overshoot, which not only add electrical stress on the power dies, but also result in switching losses and thus affect the overall efficiency.

To improve reliability, electrical performance and reduce cost of power modules, significant breakthrough can be achieved by the monolithic integration of the 2D-multiphase module within a minimum number of multi-terminal dies that are judiciously packaged. Within the context of integration and miniaturization, the reverse conducting Insulated Gate Bipolar Transistor (RC-IGBT), as described in Fig. 1(a) and (b), is considered as the elementary brick for converter integration. The RC-IGBT monolithically integrates an IGBT and an antiparallel freewheeling PiN diode. The structure of the RC-IGBT was extensively studied in literature [START_REF] Yi | Snapback-free reverse-conducting IGBT with low turnoff loss[END_REF][START_REF] Vemulapati | Reverse conducting-IGBTs initial snapback phenomenon and its analyticalmodelling[END_REF]. Using this device, the authors have recently proposed a vertical quasi-monolithic integration of power converter called two-chip approach as well as an ultra-compact single chip approach [START_REF] Khadiry | New Monolithic Multi-poles Converter Device for Medium Power Applications[END_REF] aiming at reducing fabrication costs, improving electrical performance and reliability. Different approaches for converter integration were described in literature in order to reach similar objectives. However, they are either limited in performance (lateral integration with vertical insulation trenches [START_REF] Green | Fully Isolated High Side and Low Side LIGBTs in Junction Isolation Technology[END_REF]) or require a complex technological process for their realization (molecular bonding of two wafers [START_REF] Benaissa | A vertical power device conductive assembly at wafer level using direct bonding technology[END_REF]). The initial objective of the dualchip integration [START_REF] Imbernon | Flexible technological process for functional integration[END_REF] approach was to integrate the high-side part of the power converter within a single multi-terminal power chip named a "common anode" chip and the low-side part within another multi-terminal power chip named "common cathode" power chip as illustrated in Fig. 2(a). Each power chip is composed of a great number of quasi-parallel connected RC-IGBTs that share the same N -drift region as shown in Fig. 2b). The number of RC-IGBTs within each chip depends on the number of converter phases. Within the common cathode chip, each RC-IGBT section must be electrically insulated from the neighbouring RC-IGBT sections as illustrated in Fig. 3c). To that end, a vertical P + wall that crosses vertically the silicon wafer and surrounds entirely each RC-IGBT section is used. However, the technological realization of the P + wall is clearly complex and an intensive process development is in progress today. To overcome the necessity of using a P + wall insulation that crosses vertically and entirely the silicon wafer, the authors propose in this paper original three multi-terminal power chips. Moreover, it will be demonstrated that the judicious packaging of these three multi-terminal chips allows to obtain switching cells of identical quality as those obtained using the two terminal approach.

The paper is organized as follows: the first section presents the "three-chip" power converter integration approach, the second section focuses on the packaging of the three multiterminal chips on a PCB, and the last section details the different characterization techniques employed to the estimation of the commutation loop stray inductance.

II. PRINCIPLE OF THE THREE-CHIP INTEGRATION APPROACH

As detailed in Fig. 3 (a), (b) and (c), the whole row of high side Reverse-Conducting Insulated Gate Bipolar Transistors (RC-IGBTs) is integrated within a single multi-terminal chip named "common anode" while the low-side RC-IGBTs row is integrated within two distinct monolithic multi-terminal power chips: the low-side insulated gate bipolar transistors are integrated within one single multi-terminal power chip while the low-side power PiN diodes are integrated within another multi-terminal power chip as shown in Fig. 4. This allows overcoming the technological complexity encountered for the realization of the P + wall that crosses vertically the silicon wafer within the common cathode chip [START_REF] Imbernon | Flexible technological process for functional integration[END_REF] that makes its process of realization complex [START_REF] Khadiry | Multiphase Power Converter Integration in Si: Dual-Chip and Ultimate Monolithic Integrations[END_REF][START_REF] Sanchez | Realization of vertical P+ walls through-wafer for bi-directional current and voltage power integrated devices[END_REF]. For the purpose of validating the operating modes of the different chips using 2D Sentaurus TM simulations, dielectrically filled trenches were used within the frame of this study.

The optimized targeted packaging for the three-chip approach is shown in Fig. 3(b). The chips are packaged so that to minimize the length as well as the apparent surface of the commutation loops. So then, the unique high-side multiterminal common anode chip is positioned at the centre and on its one side is placed the low-side multi-terminal IGBT power chip and on the opposite side the low-side multi-terminal diode power chip. In this way, as it is detailed in section §IV dedicated to packaging and characterization, the parasitic commutation loop inductance is reduced to that of a single set of wire bonds, instead of two series connected sets encountered in the case of conventional packaging. Moreover, the circuit board effect is reduced due to the fact that this latter is not directly subjected to dv/dt disturbances during switching phases. For buck and boost chopper applications, one of the low-side two multi-terminal chips becomes useless and the packaging can be reduced to only two multi-terminal power chips.

III. SENTAURUS TM MIXED-MODE SIMULATION RESULTS

The main geometrical and physical parameters of the diffusion regions used in the IGBT and diode sections are those set by the IGBT process-flow of the micro and nanotechnology platform at LAAS-CNRS [START_REF] Imbernon | Flexible technological process for functional integration[END_REF]. The drift region thickness is chosen so that the devices are able to withstand 600 V. In Fig. 5 and6, the simulation conditions correspond to a static state: when one diagonal section of the bridge is in onstate the other is in off-state, a current source of 100 A/cm 2 simulates an inductive load. The common anode concept was already validated in previous works of the authors [START_REF] Khadiry | Multiphase Power Converter Integration in Si: Dual-Chip and Ultimate Monolithic Integrations[END_REF] and is not described in this paper. In Fig. 5(a) and Fig. 6(a), 100A current flows through one section of each chip while the other

N-! P+ P+ P P N+ N+ N+ N+ Anode P+ N+ N+ P+ P+ N+ Gate! Cathode Cathode Gate! Gate! N+ Anode Cathode Gate V DC IGBT 1 IGBT 2 IGBT k D 1 D 2 D k N 1 N 2 N k

Common anode chip

Mul9-diode chip The multi-terminal chips were assembled to form a 3-chip inverter. A 600V DC supply is applied at the input and a 100A DC current supply simulate the load. The results obtained using mixed-mode Sentaurus TM simulations are provided in figure 7.

RC-IGBT K RC-IGBT 2 RC-IGBT 1 Mul9-IGBT chip

IGBT 1 IGBT 2 IGBT K RC-IGBT 1 D 1 D 2 D K N 1 N 1 N 2 N 2 N K N K Low side

IV. THREE-CHIP VERSUS REFERENCE ASSEMBLY

A. Realized and characterized converter assemblies

The reference two-phase converter assembly makes use four Reverse Conducting-IGBTs. The targeted packaging for the full bridge converter circuit given in Fig. 8 (b), according to the proposed three-chip approach, is shown in Fig. 9 (d). The IGBTs chip (flipped) is positioned on one side (left-side in this case) of the common anode chip while the diodes chip is positioned on the other side (right-side in this case) of the common anode chip. Due to the fact that the realization of the proposed IGBT and diode Si multi-terminal chips is being in progress, the realized converter assemblies are buck type converters composed of fast two-terminal Si and SiC MOSFET dies as well as SiC diode dies (Table II) from commercial providers. These assemblies allow one to characterize the switching loop inductance. To evaluate the improvements brought by the proposed approach, generic layouts ere designed for the reference as well as 3-chip two-phase converters. Silicon as well as silicon carbide chips were used. As compared to Fig. 4, the RC 1 and RC 2 of Fig. 9(c) form the common anode chip, IGBT1 and IGBT2 form the multi-terminal IGBT-chip while D1 and D2 form the multi-terminal diode-chip. The optimized layout of the conventional converter results in a coplanar commutation loop of 130mm 2 surface while the optimized 3-chip converter leads to an orthogonal 3D-commutation loop of 26mm 2 surface (ratio: 1/5).

B. Switching loop modelling during low-side switch turn-off

The use of a very small (negligible) gate resistance allows hard and fast turn-off switching. Consequently, the duration of Miller effect can then be neglected [START_REF] Rossignol | Switching optimization of WBG power devices on inverter leg "dv/dt -switching energy" trade off and comparison using directly the gate resistance or an additional feedback gate-drain capacitor[END_REF] and the switching cell can be modelled by the electrical circuit given in figure 10. From the equivalent circuit of the switching cell composed of medium and high frequency loops (Fig. 10b), the peak overvoltage across the power device (MOSFET in this case) at turn-off can be expressed as follows:

DC + C 1 RC-IGBT 1 DC - N 1 C 2 RC-IGBT 2 N 2 C HV RC-IGBT 3 RC-IGBT 4 C 1 IGBT 1 D 1 RC-IGBT 1 DC + DC - N 1 C 2 IGBT 2 D 2 RC-IGBT 2 N 2 C HV C K = C K-IGBT IGBT K D K RC-IGBT K DC + DC - N K IGBT-Loop C K = C K-diode IGBT K D K RC-IGBT K DC + DC - N K Diode-Loop (
Eq. ( 1)

(a) (b) (c) (d)
The term (a) represents the transfer of energy stored in the busbar inductance L Beq to the decoupling ceramic capacitors C dec . Terms (b) and (d) represent the different effects of commutation loop stray inductances: (b) gives back the transfer of energy stored in the inductance loop L SCeq to the C oss capacitance of the device, while (d) represents the relation between the turn-off di/dt and the inductive over-voltage across the device. A detailed analysis shows that during the dv/dt sequence just before the over-voltage, the current loop flows through the C oss part and the transition capacitor of the diode. Then, the equivalent current loop in series with de device is reduced by a factor K = C T /(C T +C oss ). It should be noted that the term (a) is predominant at medium frequencies (< 50 MHz) while (b) is predominant at high frequencies (> 50 MHz) due to low values of L SCeq compared with L Beq and of C oss compared with C dec . Moreover, it can be noted that due to the low value of C oss for fast WBG device such as Mosfet SiC, term (b) is higher than term (d) by a ratio near to 20 (ex. numerical application: 5nH, 100pF, 1000A/µs, 30A, K = 0.5). Thus, it appears that the gate resistor and the channel control are not directly influent parameters to manage the HF phenomena. Parameters of the circuits such as stray inductances and capacitors values are clearly more influent on the over-voltage stress. Finally, term (c) easily reflects the forward dynamic recovery of the diode, mainly for Si-PiN diode that exhibits slow commutation behaviour in this work.

C. Double-pulse time-domain characterization of the switching loop

The used circuit is a buck-type converter composed of a high speed switching power device and a freewheeling diode. The operating principle consists in applying to the gate of the power device two consecutive short pulses. The first pulse is of duration (t1) relatively long allows the establishment of the load current, the second pulse of shorter duration (t 3 ) and aims at enabling the observation of oscillations in the output voltage waveform across the MOSFET at turn-off (figure 11(b)). The stray inductance can then be deduced from the measurement of the oscillation frequency of the voltage waveform across the power device at turn-off. The analysis of the components that compose the amplitude and oscillation-frequency, of the voltage waveform at turn-off, enables one to determine the parameters of the switching cell. From eq. ( 1), the High frequency term (HF) allows to determine the pair (L SCeq , C oss ), medium frequency (MF) term allows to characterize the pair (L Beq , C dec ). Conventional as well as proposed 3-chip converters were realized using either Si-dies or SiC-dies and were characterized. The turn-off waveforms of Si and SiC assemblies, summarized in tables II and III, are provided in Fig. 12 and Fig. 13. The analytical expressions used to estimate the inductances values at medium and high frequencies are given in tables IV and V, respectively. Table IV is organized as follows: part (A) presents the medium-frequency (MF) measurements as well as calculations carried-out to estimate the busbar inductance (L Beq ), part (B) presents L Beq values obtained for the reference (classical) Si and SiC assemblies, and part (C) presents L Beq values obtained for Si and SiC assemblies based on the proposed 3-chip approach. Table V is organized as follows: part (A) describes high-frequency (HF) measurements as well as calculations carried-out to estimate the switching cell inductance (L SCeq ), part (B) presents L SCeq values obtained for the reference (classical) Si and SiC assemblies, and part (C) presents L SCeq values obtained for Si and SiC assemblies based on the proposed 3-chip approach.

Fig. 1 .Fig. 2 .

 12 Fig. 2. (a) The dual-chip integration approach, cross-sectional view of the: (b) common anode three-terminal structure, (c) common cathode threeterminal structure [8].

Fig. 3 .Fig. 4 .

 34 Fig. 3. (a) Principle of integrating a multiphase converter composed of Kphase legs using the 3-chip approach , (b) Schematic illustration of the 3-chip packaging.

Fig. 5 .

 5 Fig. 5. 2D mixed-mode Sentaurus TM simulation results for the multi-IGBT chip: (a) total current density, (b) equipotential lines.

Fig. 7 .

 7 Fig. 7. 2D Mixed-mode Sentaurus TM simulation result for a two phase inverter application.

  Fig. 8. Two-phase converters: (a) Reference using four RC-IGBTs , (b) According to the proposed 3-chip approach.

Fig. 9 .

 9 Fig. 9. Layout of converter on the PCB board: (a) coplanar commutation loop for the reference assembly, (b) orthogonal commutation loop for the 3chip, (c) illustration of the IGBT and diode power loops.

Fig. 10 .

 10 Fig. 10. (a) The switching cell model including parasitic elements and (b) its circuit model at turn-off.

Fig. 11 .

 11 Fig. 11. (a) test bench for electrical characterizations, (b) Electrical circuit in Buck-Type topology, (c) double short-pulse control signal.

  Gate drive voltage = +18V/-18V, External gate resistance Rg in the range [0Ω, 10Ω] Buck-Type circuit (with stray inductances) Gate drive voltage =+19V/-2.5V, External gate resistance Rg in the range [0Ω, 10Ω] (a) (b) Fig. 12. Turn-off voltage waveforms for conventional (reference) (a) Siconverter assembly, (b) SiC converter assembly. TABLE II. DOUBLE-PULSE CHARACTERIZATION: SI AND SIC "PROPOSED" Gate drive voltage = +18V/-18V, External gate resistance Rg in the range [0Ω, 10Ω] Buck-Type circuit (with stray inductances) Gate drive voltage =+19V/-2.5V, External gate resistance Rg in the range [0Ω, 10Ω] . Turn-off voltage waveforms for the proposed (a) Si-converter assembly, (b) SiC converter assembly.

Analytical expressions 1 )"

 1 5A/div] V dsk V d [20V/div] 0% V sk [20V/div] Time Base 400ns/div 2xδV dsk 1/F HF Time Base 40ns/div @R gExt. 10Ω/100V-11.7A @R gExt. 0Ω/150V-26A δV dsk HF = 6V F HF = 113.5MHz δV dsk MF = 1.6V F MF = 1.56MHz dV/dt = 6.3kV.µs -1 % δV dsk HF = 24.5V F HF = 113.5MHz dV/dt = 24kV.µs -1 % Zoom Vgs [10V/div] INDUCTANCE VALUE: MEASUREMENT AND CALCULATED (SEE (A), (B) AND (C) BELOW) A) Busbar characterization (Medium-Frequency loop) methods (Equivalent localized physical quantities: Lbeq, Cdec) Realized measurements Measurements using an impedance analyzer, Agilent 4294A + dedicated PCB Probe 42941A 2) Time-domain measurements: carried-out using an oscilloscope TEK DPO4104B 1GHz/5GSamp.s -1 + Passive voltage probes TPP1000 1GHz (Deskew mode + Hi/Average x4 mode) From time-domain measurements, two techniques were used to calculate Lbeq: Technique (a) From the voltage ripple (damping neglected --> giving a lower bound value): Technique (b) From the oscillation period (damping neglected --> giving an upper bound value): 2x60 nF (at 100V) 2x45 nF (at 150V) ESL = 0.8 nH ESLeq = 0.4 nH Cfilter (fp) : EPCOS 2x3.3 uF/ 400V/ESLeqMAX= 9 nH Lbeq MEASURE = 10.03nH at 10MHz

  (a) and (b) below. It can also be calculated using technique (c) below. a) From the voltage ripple (damping neglected --> giving a lower bound value):

TABLE IV .

 IV

	HIGH FREQUENCY STRAY INDUCTANCE VALUE:
	MEASUREMENT AND CALCULATED (SEE (A), (B) AND (C) BELOW)
	A) Switching-cell characterization (High-Frequency loop)
	(Equivalent localized physical quantities: Lsceq, ESLdec, Coss)
	Realized measurements	Analytical expressions
		From time-domain measurements, one
		can calculate Lsceq. Indeed, Lsceq can be
	1) Measurements using an	calculated by a combination of
	impedance analyzer Agilent 4294A	techniques
	+ dedicated PCB Probe 42941A
	2) Time-domain measurements:
	carried-out using an oscilloscope
	TEK DPO4104B 1GHz/5GSamp.s -1
	+ Passive voltage probes TPP1000
	1GHz (Deskew mode + Hi/Average
	x4 mode)

ACKNOWLEDGMENT

This research work received financial support from the French National Research Agency (ANR). The project name is "ConvPlUS", ANR-13-JS09-0008-01, using the technological support of RENATECH-LAAS and 3DPHI platforms.

V. CONCLUSION Multi-terminal power dies suitable for the 3-chip integration approach of multi-phase power converter integration were proposed and validated by Sentaurus TM 2D simulations. A partial flip-chip packaging process was set-up. Converters assemblies composed of Si as well as SiC dies were realized and characterized for commutation loop stray inductance estimation. The switching cell inductance was determined from measurements using an impedance analyzer and also from time domain measurements using the doublepulse technique. A comparison between the value of the switching loop inductance in the reference (classical) assembly and that in the proposed 3-chip assembly shows that a reduction by a factor of about two is obtained by the 3-chip approach (it is about 10.7 nH with the classical and about 4.5 nH with the proposed 3-chip approach). To reduce further the stray inductance value of the switching cell, the realization of a Direct Lead Bonding (DLB) version based on the proposed 3-chip assembly is in progress.