Eva Izquierdo

Marion Dufour

Audrey Chu

Clément Livache

Bertille Martinez

Dylan Amelot

Gilles Patriarche

Nicolas Lequeux

Emmanuel Lhuillier

Sandrine Ithurria
email: sandrine.ithurria@espci.fr

Coupled HgSe colloidal quantum wells through a tunable barrier: a strategy to uncouple optical and transport band gap

Keywords: Nanoplatelets, Heterostructure, Narrow band gap materials, Band engineering

INTRODUCTION

Colloidal quantum dots have generated a large interest because of their tunable optical feature from UV to THz. [START_REF] Lhuillier | Infrared Photodetection Based on Colloidal Quantum-Dot Films with High Mobility and Optical Absorption up to THz[END_REF] In addition their bright luminescence make them appealing candidates for a broad variety of applications spanning from single photon source [START_REF] Brokmann | Colloidal CdSe/ZnS Quantum Dots as Single-Photon Sources[END_REF] , to light emitter for displays or even for laser [START_REF] Geiregat | Continuous-Wave Infrared Optical Gain and Amplified Spontaneous Emission at Ultralow Threshold by Colloidal HgTe Quantum Dots[END_REF][START_REF] Fan | Continuous-Wave Lasing in Colloidal Quantum Dot Solids Enabled by Facet-Selective Epitaxy[END_REF][START_REF] Lim | Optical Gain in Colloidal Quantum Dots Achieved with Direct-Current Electrical Pumping[END_REF] . In all these applications, the wavefunction engineering remains at a very basic level and mostly consists in band gap tunability thanks to quantum confinement. In this sense, colloidal heterostructure remains far below the maturity that is achieved with epitaxially grown heterostructure of III-V semiconductors. Quantum well infrared photodetectors [START_REF] Liu | Quantum Well Infrared Photodetectors[END_REF][START_REF] Levine | Quantum-well Infrared Photodetectors[END_REF] and quantum cascade structure used for detection [START_REF] Gendron | Quantum Cascade Photodetector[END_REF][START_REF] Hofstetter | Quantum-Cascade-Laser Structures as Photodetectors[END_REF] and lasing [START_REF] Faist | Quantum Cascade Laser[END_REF] are certainly the state of the art of wavefunction engineering. In such heterostructure, quantum states are coupled using phonon [START_REF] Faist | Quantum Cascade Laser[END_REF] or other scattering mechanisms [START_REF] Lhuillier | Interface Roughness Transport in Terahertz Quantum Cascade Detectors[END_REF] . A key step to the wavefunction engineering into colloidal systems was the introduction of wide band gap type I heterostructure to boost the photoluminescence efficiency [START_REF] Hines | Synthesis and Characterization of Strongly Luminescing ZnS-Capped CdSe Nanocrystals[END_REF] . Some other improvements were made by growing complex colloidal heterostructures with multi shell [START_REF] Soni | Simultaneous Type-I/Type-II Emission from CdSe/CdS/ZnSe Nano-Heterostructures[END_REF] or anisotropic shell [START_REF] Carbone | Synthesis and Micrometer-Scale Assembly of Colloidal CdSe/CdS Nanorods Prepared by a Seeded Growth Approach[END_REF][START_REF] Cassette | Colloidal CdSe/CdS Dot-in-Plate Nanocrystals with 2D-Polarized Emission[END_REF] . Type II heterostructures have also been proposed [START_REF] Piryatinski | Effect of Quantum and Dielectric Confinement on the Exciton-Exciton Interaction Energy in Type II Core/shell Semiconductor Nanocrystals[END_REF][START_REF] Chuang | Charge Separation and Recombination in CdTe/CdSe Core/shell Nanocrystals as a Function of Shell Coverage: Probing the Onset of the Quasi Type-II Regime[END_REF] for the design of long living exciton: in such system, one high work function material is combined with a lower work function material to obtain a colloidal p-n junction. In such material, one material confines the electron and the other the hole. Finally, one of the most (conceptually) complex attempt for wavefunction engineering in colloidal material was proposed by Cragg et al [START_REF] Cragg | Suppression of Auger Processes in Confined Structures[END_REF] who suggested that gradient interface heterostructures should be used to reduce Auger effect. Here, we try to bring wavefunction engineering into colloidal material to the next level and demonstrate that core/shell structure made of a CdSe core surrounded by HgSe wells can be grown and present transport properties which can be tuned independently from their optical features. In other words, we build an heterostructure for which the optical band gap is not the electrical band gap. This result is of utmost importance for narrow band gap materials dedicated to infrared (IR) detection. When it comes to detection in the IR range of the electromagnetic spectrum, transition energies are small and phonon activated carriers compete with optical excitation. As a result, the noise, rather than the signal itself becomes the main challenge. The noise magnitude is tightly bonded to the amount of dark current and thus to the dark carrier density. Designing a material for which the transport band gap is larger than the optical band gap is very promising to obtain near and mid IR devices based on colloidal materials. [START_REF] Lhuillier | Recent Progresses in Mid Infrared Nanocrystal Optoelectronics[END_REF] In this paper, we demonstrate the growth of 2D heterostructures made of a CdSe core surrounded by a shell of HgSe.

Weller group has already reported quantum well structures of spherical Cd/Hg/CdE (E = S or Te) nanocrystals [START_REF] Eychmüller | A Quantum Dot Quantum Well: CdS/HgS/CdS[END_REF][START_REF] Kershaw | Colloidal CdTe/HgTe Quantum Dots with High Photoluminescence Quantum Efficiency at Room Temperature[END_REF] . On these systems, it has been shown that the transition energy can be tuned by the core diameter of CdE (E = S or Te), the thickness of the well (mercury layer) and the thickness of the external shell. After the cation exchange on CdE quantum dots by mercury, the nanocrystals don't present any fluorescence. By adding Cd 2+ ions on Cd/HgE structures, the fluorescence significantly increases by charge carriers confinement in the HgE layer. This observation was confirmed by a theoretical approach on the probability of the presence of electrons and holes in the nanoparticles [START_REF] Schooss | Quantum-Dot Quantum Well CdS/HgS/CdS: Theory and Experiment[END_REF] .

CdSe 2D nanoplatelets (NPLs) are a special class of nanocrystals (NCs) [START_REF] Lhuillier | Two-Dimensional Colloidal Metal Chalcogenides Semiconductors: Synthesis, Spectroscopy, and Applications[END_REF][START_REF] Nasilowski | Two-Dimensional Colloidal Nanocrystals[END_REF] , which present no inhomogeneous broadening. A thickness, defined at the atomic scale, leads to narrower excitonic features compared to 0D spherical equivalent. Recently, Izquierdo et al [START_REF] Izquierdo | Strongly Confined HgTe 2D Nanoplatelets as Narrow Near-Infrared Emitters[END_REF] showed, that such narrow excitonic features could be extended to near-IR range by synthesizing HgTe and HgSe NPLs. The latter are obtained via a Hg 2+ cation exchange procedure conducted on thin CdSe and CdTe NPLs. So far only homomaterials of mercury chalcogenides have been reported. Here we extend the method and achieve a partial cation exchange on thicker NPLs. We bring evidence of a CdSe core embedded between two HgSe quantum wells. The electronic properties and transport properties of the formed heterostructures are then discussed. Finally, we finish the discussion by addressing the carrier relaxation dynamics using transient photocurrent measurements.

EXPERIMENTAL METHODS

Chemicals

Se powder (Sigma-Aldrich), Mercury acetate (Hg(Ac)2) (Aldrich, > 99.0%), Cadmium acetate (Cd(Ac)2) (STREM, 98 %), Cadmium oxide (CdO) (STREM, 99.99 %), Myristic acid (Fluka, > 98 %), Oleylamine (Acros, 80-90 %), Tributylphosphine (TBP) (Cytec), Oleic acid (OA) (Aldrich, 90%), Octadecene (ODE) (Aldrich, 90 %), n-Hexane (VWR, 99 %), Toluene (VWR, 99.8 %), Ethanol (VWR, 95-97 %), Methanol (Carlo Erba, 99.9 %), N-methylformamide (NMF) (Carlo Erba, 99 %), LiClO4 (Aldrich, 98 %), Polyethylene glycol MW = 6x10 3 g.mol -1 (PEG 6k) (Fluka).

Precursors

Cadmium myristate: In a 100 mL three neck flask, 2.56 g of CdO and 11 g of myristic acid are degassed under vacuum for 30 minutes at 70°C. Under argon flow, the mixture is heated up to 200°C for 30 minutes until the solution becomes colorless. Then, 50 mL of MeOH is added between 60°C and 70°C in order to solubilize the excess of myristic acid. The mixture is stirred for 30 minutes. At the end, the cadmium myristate is precipitated by using centrifuge tube through the addition of MeOH. The washing procedure is repeated at least three times. The cadmium myristate is dried overnight under vacuum. TOPSe (1M): In the glove box, 1.58 g of Se powder are mixed with 20 mL of trioctylphosphine and let stir until complete dissolution of Se in TOP. Selenide solution (0.1 M): In the glove box, 40 mg of NaBH4 are dissolved in 0.5 mL of NMF and 0.5 mL of ethanol. Then 24 mg of selenium powder are added. NaBH4 reduces the selenium powder in SeNa2 with the formation of H2. After ten minutes the reaction should be complete and the mixture should turn colorless.

Nanocrystals synthesis

Synthesis of 3 MLs CdSe NPLs: In a three neck flask, 240 mg of Cd(Ac)2 and 10 mL of ODE are degassed under vacuum for 10 min at room temperature. Under argon flow, the mixture is heated up to 200 °C. A solution of 400 µL of TOPSe at 1M, 200 µL of OA and 3.75 mL of ODE is injected drop by drop (5 mL.h -1 ). After the injection, the mixture is cooled down and precipitated with a mixture of 10 mL of hexane and 5 mL of ethanol. The NPLs are suspended in 10 mL of hexane. Synthesis of 4 MLs CdSe NPLs: In a 50 mL three neck flask 340 mg of Cd(myristate)2, 24 mg of Se and 25 mL of ODE are degassed for 30 minutes at room temperature. Under Argon flow, the temperature is raised to 240 °C. When the mixture reaches 200 °C, 100 mg of Cd(Ac)2 are introduced. The reaction is stopped after 10 minutes at 240 °C. The NPLs are precipitated through the addition of a mixture of 30 mL of hexane and 30 mL of ethanol. The NPLs are suspended in 10 mL of hexane. CdSe growth by c-ALD: 4 mL of 3 MLs NPLs solution is precipitated with ethanol and suspended in 2 mL of hexane. In the glove box, 20 µL TBP, 20 µL of EtOH and 150 µL of the sodium selenide solution are added to the NPLs. The solution is vigorously stirred up to the complete precipitation of the NPLs and a color change from yellow to orange is observed. Then 2 mL of NMF are added to resuspend the precipitated NPLs. The NPLs should be stable in NMF, if not sodium selenide solution and TBP should be added to the biphasic medium. The solution is taken out of the glove box and the hexane is removed. The NPLs in NMF are first washed with a mixture of 3 mL of hexane, 20 µL of TBP and 20 µL of EtOH and second with 3 mL of hexane and 20 µL of EtOH. To grow the half layer of Cd, 200 µL of a solution of Cd(Ac)2 in NMF at 0.1 M is added. The solution is vigorously stirred until it becomes red. Then the NPLs are transferred back to hexane thanks to oleylamine. The addition of MeOH facilitates the phase separation. Finally, the NPLs are precipitated and suspended in 6 mL of ODE. The crystallinity of the NPLs is improved with an annealing step. In 25 mL three neck flask, the NPLs in ODE, 50 mg of Cd(Ac)2, 70 µL of oleic acid and 70 µL of TBP are degassed for 20 minutes at room temperature. Under argon flow, the mixture is heated up at 230°C for 20-25 minutes until the refinement of the optical features. Finally, the NPLs are precipitated with EtOH and suspended in 8 mL of hexane. The same process is reproduced for each additional layer.

Cation exchange 3MLs HgSe NPLs:

In a flask, 2 mL of toluene, 20 µL of 3 MLs CdSe nanoplatelets (OD = 1 at 400 nm) and 3 µL of oleylamine are introduced. Then 15 µL of a freshly prepared solution at 0.08 M of Hg(Ac)2 in MeOH is introduced at room temperature (the ratio Cd:Hg is 1:1.2). The cation exchange is monitored by absorption spectroscopy (Figure S1 a.). When the first exciton has reached 735 nm, the nanoplatelets are precipitated and resuspended in hexane. Regarding the lateral sizes, the nanoplatelets precipitated without addition of a polar solvent. On TEM images (Figure S1 b. and c.), it can be observed that the NPLs morphology is preserved during the exchange process. Core-shell CdSe/HgSe NPLs: In a typical reaction, 3 µL of OAm and 15 µL of a freshly prepared solution at 0.08 M of Hg(Ac)2 in MeOH are introduced at room temperature in CdSe NPLs solution suspended in 2 mL of toluene. The cation exchange occurred with a typical time scale of 20 minutes, see Figure S2. Absorption at short wavelength gives some information on the amount and the composition of materials in solution [START_REF] Lhuillier | Corrigendum: Optical Properties of HgTe Colloidal Quantum Dots[END_REF] . After c-ALD growing, there are two more planes of Cd and Se on the NPLs, while keeping the lateral sizes unchanged. To have the same concentration of NPLs, if the starting 3 MLs CdSe NPLs solution (7 atomic planes) have an optical density of 1 at 400 nm, the OD of 5 MLs CdSe NPLs (11 atomic planes) should be 1.57 at 400 nm. Consequently with the same reasoning, the OD of 7 MLs (9 MLs or 11 MLs) CdSe NPLs solution should be 2.14 (respectively 2.71 or 3.28). For each population, the ratio of mercury and NPLs is identical. Consequently, the amount of Cd exchanged is the same, corresponding to 2 planes of cations on the external sizes of NPLs.

DISCUSSION

II-VI NPLs materials [START_REF] Lhuillier | Two-Dimensional Colloidal Metal Chalcogenides Semiconductors: Synthesis, Spectroscopy, and Applications[END_REF] present optical features free of inhomogeneous broadening which results from roughness free atomic surfaces in the confined direction. While for cadmium based semiconductors, large efforts have been dedicated to the growth understanding [START_REF] Riedinger | An Intrinsic Growth Instability in Isotropic Materials Leads to Quasi-Two-Dimensional Nanoplatelets[END_REF][START_REF] Chen | Symmetry-Breaking for Formation of Rectangular CdSe Two-Dimensional Nanocrystals in Zinc-Blende Structure[END_REF] , the growth of heterostructures with various materials [START_REF] Bouet | Synthesis of Zinc and Lead Chalcogenide Core and Core/shell Nanoplatelets Using Sequential Cation Exchange Reactions[END_REF] and spatial organizations (core/shell [START_REF] Ithurria | Colloidal Atomic Layer Deposition (c-ALD) Using Self-Limiting Reactions at Nanocrystal Surface Coupled to Phase Transfer between Polar and Nonpolar Media[END_REF] and core/crown [START_REF] Prudnikau | CdSe-CdS Nanoheteroplatelets with Efficient Photoexcitation of Central CdSe Region through Epitaxially Grown CdS Wings[END_REF] ), far less effort has been dedicated to narrower band gap materials. Recently, our group proposed to use cation exchange to indirectly synthesize HgTe and HgSe NPLs [START_REF] Izquierdo | Strongly Confined HgTe 2D Nanoplatelets as Narrow Near-Infrared Emitters[END_REF] . The procedure leads to a complete cation exchange and to pure mercury chalcogenides NPLs free of initial cadmium (ie final objects are neither alloys, nor gradients). As for cadmium chalcogenide NPLs, these nanoparticles crystallize in a zinc blende structure with the thickness along the [001] direction.

The softness of mercury chalcogenides and their ability to aggregate make the growth of heterostructure difficult and only few reports exist [START_REF] Schooss | Quantum-Dot Quantum Well CdS/HgS/CdS: Theory and Experiment[END_REF][START_REF] Choi | Major Electronic Transition Shift from Bandgap to Localized Surface Plasmon Resonance in Cd X Hg 1-X Se Alloy Nanocrystals[END_REF][START_REF] Shen | HgS and HgS/CdS Colloidal Quantum Dots with Infrared Intraband Transitions and Emergence of a Surface Plasmon[END_REF][START_REF] Robin | Surface Control of Doping in Self-Doped Nanocrystals[END_REF][START_REF] Sagar | Core/Shell Nanocrystals by Colloidal Atomic Layer Deposition[END_REF] . Here, we proceed in two steps to synthesize HgSe/CdSe/HgSe heterostructures. In a first step, we synthesize CdSe NPLs with variable thicknesses from 3 monolayers (MLs) to 11 MLs [START_REF] Chu | Electronic Structure Robustness and Design Rules for 2D Colloidal Heterostructures[END_REF] . Note that N ML NPLs refer to nanoparticles with N layers of anions and N+1 layers of cations in the thickness (2N+1 layers in total). The additional cadmium plane comes from the cadmium rich top and bottom faces. In a second step, these CdSe NPLs are exposed at room temperature to a precursor of mercury which allows proceeding to the partial cation exchange.

In the first step, we preliminarily synthesize 3 and 4 ML CdSe NPLs using already established procedures [START_REF] Ithurria | Colloidal Nanoplatelets with Two-Dimensional Electronic Structure[END_REF] , see Figure 1a andb. Then we use the colloidal Atomic Layer Deposition 30 (c-ALD) procedure to further increase the thickness of the NPLs and obtain NPLs with up to 11 MLs, see Figure 1c andd. The c-ALD procedure is well established to grow metal sulfide semiconductors thanks to the easy handling of sulfide precursors. A contrario, the growth of selenide based semiconductors is more sensitive, due to the easy oxidation of Se 2-in polyselenide. Thus, the growth of the Se layer was done by using fresh sodium selenide Na2Se solution obtained from the reduction of Se powder in presence of a strong reducing agent (NaBH4) [START_REF] Lhuillier | Electrolyte-Gated Field Effect Transistor to Probe the Surface Defects and Morphology in Films of Thick CdSe Colloidal Nanoplatelets[END_REF] . These selenide anions allow the transfer of NPLs in the polar N-methylformamide. Then, the additional Cd layer is grown through reacting the selenium rich NPLs with cadmium acetate. The NPLs are transferred back in a non-polar solvent with addition of oleic acid. Starting from N ML CdSe NPLs, a c-ALD process leads to N+2 ML CdSe NPLs.

The CdSe NPLs suspended in a non-polar solvent are exposed to mercury acetate complexed with oleylamine. By doing so, the cation exchange is only complete for 3 ML NPLs (see Supporting Information Figure S1). For all thicker NPLs (see Supporting Information Figure S2 andS3), we observe using energy dispersive X-ray spectrometry (EDX) and Rutherford Backscattering Spectrometry that the final NPLs still include cadmium (see Supporting Information Table S1 and S2, Figure S8). We also notice that for all these populations, the ratio of Hg/Cd is consistent with the amount expected for 4 planes of Hg. Hg cannot diffuse up to the center of the particle and it only diffuses over two layers on the surface of the NPLs. This hypothesis is further confirmed using high angle annular dark field (HAADF) scanning transmission electron microscopy (STEM) imaging, with a high Z contrast imaging, see Figure 1g. We clearly see two bright layers on the external planes of the NPLs due to Hg, while the inner part of the NPLs is less intense due to the lower electronic density of Cd (see Supporting Information Figure S5). Thus, it is possible to exclude the possibility to have either a gradient or an homogeneous HgCdSe alloy. The core/shell structure will be further confirmed by other techniques such as X-ray diffraction (XRD) and optical measurements. Such uncomplete cation exchange has already been observed in other systems such as PbS/CdS [START_REF] Sagar | PbS/CdS Core/shell Quantum Dots by Additive, Layer-by-Layer Shell Growth[END_REF] and CdTe/HgTe [START_REF] Smith | Bright and Compact Alloyed Quantum Dots with Broadly Tunable near-Infrared Absorption and Fluorescence Spectra through Mercury Cation Exchange[END_REF][START_REF] Smith | Mapping the Spatial Distribution of Charge Carriers in Quantum-Confined Heterostructures[END_REF][START_REF] Kershaw | Investigation of the Exchange Kinetics and Surface Recovery of CdxHg1-xTe Quantum Dots during Cation Exchange Using a Microfluidic Flow Reactor[END_REF] . It is more likely to happen when the host and replacing cations have the same level of oxidation and comparable sizes. In addition CdSe and HgSe share the same zinc blende crystal structure with really close lattice parameters, aCdSe= 0.605 nm and aHgSe= 0.608 nm (See Figure S6 for X Ray Diffraction (XRD)). Moreover, the mercury is larger than cadmium, which leaves less room for the interstitial insertion. In NPLs the top and bottom facets, which can represent ≈95% of the total surface, are cation rich and stabilized by carboxylates. In order to induce cation exchange, it is necessary to create local cation vacancies on these surfaces. Here, the introduction of oleylamine and methanol which have a good affinity for cations, can remove few cadmium atoms from the surface. Then, as it has been proposed by Hens and coworkers [START_REF] Sagar | PbS/CdS Core/shell Quantum Dots by Additive, Layer-by-Layer Shell Growth[END_REF] for cadmium in PbS NCs, the mercury can diffuse over few layers. This low diffusivity has also been observed in spherical CdTe NCs and was estimated at the submonolayer level [START_REF] Kershaw | Investigation of the Exchange Kinetics and Surface Recovery of CdxHg1-xTe Quantum Dots during Cation Exchange Using a Microfluidic Flow Reactor[END_REF] . In NPLs, the top and bottom facets are, chemically, strictly equivalent, hence have the same reactivity. Here, the mercury diffusion is limited to exactly 2 planes in the [001] direction of the thickness. Thus a total of 4 planes of cadmium are exchanged and the diffusion of mercury is limited to 4Å.

The XRD patterns show that after exchange (see Figure S6), the zinc blende crystalline structure is not affected. CdSe core NPLs present XRD patterns shifted compared to their theoretical positions. This is explained by the surface ligands which induce strain in the crystals. Oleate ligands lead to an extension of the lattice parameter in the lateral dimensions and a contraction in the thickness. [START_REF] Antanovich | A Strain-Induced Exciton Transition Energy Shift in CdSe Nanoplatelets: The Impact of an Organic Ligand Shell[END_REF] As the thickness of the CdSe NPLs increases, the diffraction peaks are approaching their theoretical positions. After cation exchange, the peaks end up to positions close to those expected for the bulk. Since HgSe and CdSe have the same lattice parameters, the incorporation of HgSe in or on CdSe should not bring new stress in the material. Nevertheless, CdSe and HgSe have different bulk moduli of around 60 GPa 44 and 50 GPa [START_REF] Kumazaki | Elastic Constants and Inoicity of Semimetallic HgSe[END_REF] , which means that the "softness" of HgSe allows absorbing ligands stress. Thus the shift observed after cation exchange may originate from the nature of the external layer at the interface between the solid and the ligands. These results are also pledging for a core/shell structure, here after noted HgSe/CdSe/HgSe NPLs. Here the DRX, EDX data and TEM suggest that the interface between the core and the shell is abrupt. This is further confirmed with the optical properties.

The electronic structure of the NPLs can be investigated thanks to absorption spectroscopy. In Figure 2a, we plot the absorption spectra for each NPL thickness before and after Hg cation exchange. For the CdSe NPLs (highlighted by a green band in Figure 2a), we see a clear shift of the excitonic feature from 460 nm for the 3 ML NPLs to 666 nm for the 11 ML NPLs, as the NPL thickness increases in accordance with a decrease of the (dieletric) confinement. In Figure 2b, the energies of the heavy hole and light hole to electron transitions are plotted as function of the thickness given in number of MLs for CdSe NPLs (green dots). For the HgSe/CdSe/HgSe heterostructures, on the other hand, the absorption spectra show that the band edge energy is almost unchanged regardless of the thickness of the CdSe core barrier and appears around 750 nm (1.65 eV) with two excitonic peaks (highlighted with a red band in Figure 2a and Figure 2b). The absorption spectra of the HgSe/CdSe/HgSe heterostructures also reveal a second feature (the blue band in Figure 2a) at higher energy which depends on the core thickness. The energy of this feature reasonably fits the band edge energy of CdSe NPLs for which 3 MLs would have been removed, see Figure 2b. Indeed, when 10 ML CdSe NPLs are exchanged with mercury, the obtained NPLs are, regarding our notation, HgSe(1ML)/Se/CdSe(6MLs)/Se/HgSe(1ML). The selenium planes which separate the CdSe and HgSe quantum well belong to both materials. Thus the CdSe core is equivalent to 7 ML CdSe NPLs (total of 15 planes: 7 planes of cadmium alternated with 8 planes of selenium) while the HgSe shell is equivalent to 1.5 ML HgSe quantum well (2 planes of mercury alternated with 2 planes of selenium), see Figure 1e and Figure 2b. Hereafter in this article, the exchanged NPLs coming from the N MLs CdSe will be named N MLs HgSe/CdSe/HgSe NPLs.

Figure 2 (a.) Absorption spectra of the CdSe NPLs before (black curve) and after cation exchange (red curve) for different thicknesses of the initial objects. The green band represents the variation of the first two transitions in CdSe NPLs. The red band (resp. blue band) represents the transitions at lower energies (resp. higher energies) in the exchanged NPLs (b.) Energies of the two band edge features (red peaks) and from the bluer features (labelled blue peaks) for exchanged NPLs and from the two first exciton transitions for the CdSe NPLs. The black arrows show the equivalent CdSe core quantum well after cation exchange. Energy band profile and associated wavefunction for a HgSe/CdSe/HgSe heterostructure with 6 MLs thickness (c.) and 11 MLs (d.).

To further elucidate the observed spectra, the energy and alignment of the formed heterostructure needs to be discussed. HgSe as bulk material is a semimetal (ie there is no band gap), CdSe is a semiconductor with a 1.7 eV band gap. From photoemission, it was determined that the valence band offset between HgSe and CdSe is 0.6 eV. [START_REF] Eich | Photoemission Investigation of MBE-Grown HgSe/CdSe Heterostructures[END_REF] The energy band profile of the formed heterostructure is typically given for two NPLs thicknesses in Figure 2c and2d. We then solve numerically the 1D time independent Schrödinger equation, see Supporting Information for details, to obtain the electronic spectrum of the formed heterostructure. The method is basic since it neglects mirror charge effect [START_REF] Benchamekh | Tight-Binding Calculations of Image-Charge Effects in Colloidal Nanoscale Platelets of CdSe[END_REF] , dielectric confinement [START_REF] Rajadell | Excitons in Core-Only, Core-Shell and Core-Crown CdSe Nanoplatelets: Interplay between in-Plane Electron-Hole Correlation, Spatial Confinement, and Dielectric Confinement[END_REF][START_REF] Achtstein | Electronic Structure and Exciton-Phonon Interaction in Two-Dimensional Colloidal Cdse Nanosheets[END_REF] and band non parabolicity but useful to obtain qualitative dependence due to confinement. Our simulation predicts a quasi-type II band alignment, with a hole confined in HgSe and 1Se electron state delocalized over the heterostructure, see Figure 2c. and d. At first sight, the delocalized character of the electron wavefunction might appear in contradiction with the lack of dependence of the interband energy with the size of the CdSe barrier. However, the 1Se state is almost resonant with the top of the CdSe bulk band gap (100-200 meV above) which provides to the 1Se state only a little of the CdSe character. As a result, the electronic state is only poorly delocalized over the whole heterostructure and energetically behaves as if the electronic state was confined in HgSe.

Finally the blue structure observed in the HgSe/CdSe/HgSe heterostructure spectrum is the result of the 1Dh to 1Se transition, see blue arrow on Figure 2c and2d. Indeed the 1Dh state has a maximum density of presence in the CdSe barrier, which provides this transition a strong CdSe character and explains the good matching between the energy of the blue features of the heterostructure with the transitions of 3 ML thinner CdSe NPLs (see black arrows in Figure 2b). At this point, we have designed an heterostructure, with a band edge energy marginally (only the broadening) affected by the presence and size of the central CdSe tunnel barrier. In the following, we demonstrate that this barrier is nevertheless playing a central role onto the electronic properties of thin film of NPLs. To evidence that, we investigate the transport properties of an array of HgSe and HgSe/CdSe/HgSe NPLs. To obtain conductive film of NPLs we first performed a ligand exchange from acetate/oleylamine insulating ligands to short S 2- anions [START_REF] Nag | Metal-Free Inorganic Ligands for Colloidal Nanocrystals: S2-, HS-, Se2-, HSe-, Te2-, HTe-, TeS32-, OH-, and NH2-as Surface Ligands[END_REF] through a well-established phase transfer procedure. Once deposited on electrodes, the NPL films are used as the channel of an ion gel gated electrolytic transistor [START_REF] Lhuillier | Investigating the N-and P-Type Electrolytic Charging of Colloidal Nanoplatelets[END_REF] . This method combines several advantages such as air operability, gating of thick film and low bias operation due to the large electrolyte capacitance. A scheme of the setup is shown in Figure 3a. The transfer curves of the NPL films are given in Figure 3b and S9. All NPLs present a n-type character, with a rise of the conductance upon electron injection. However the threshold voltage strongly raises while the CdSe barrier thickness is increasing, see Figure 3c. Only the pure HgSe NPLs present a negative threshold voltage, which is the expected behavior for degenerately doped semiconductor (ie when the Fermi level is, in or close, to the conduction band). Once a CdSe barrier is present, the threshold voltage becomes positive, which is typical behavior for wide band gap barrier with a Fermi level deep into the band gap. This reduction of doping is strongly impacting the film conductance and we observe a reduction of the conductance by five orders of magnitude as the NPLs thickness increases from 3 MLs to 11 MLs, see Figure 3d ande. Assuming an Arrhenius law for the temperature scaling of the conductance ( )

T k E G b a / exp - 
, we obtain a difference between the electrical gap and the transport gap given by 3MLs HgSe 11MLs HgSe/CdSe/HgSe photoconductive properties of the film. Thin HgSe NPLs are quasi non photoresponsive, see Figure 3d. On the other hand, in presence of a CdSe barrier, a clear photoconductance signal is measured (see Figure 3e), with an increase of the conductance by a factor 50 under illumination. While the presence of the barrier was leading to marginal effect on the absorption spectrum, its impact on transport is drastic. By finely controlling the doping of the system, through the CdSe barrier, it switches from narrow band gap semiconductor behavior, with strong conductance and weak photoresponse to a typical behavior expected for wide band gap material. In other words, we have built a system whose optical properties are set by the narrow band gap HgSe layers, but behaves as the wide band gap CdSe core from a transport point of view. One key question is then to determine if these properties result from the heterostructure or the presence of a mixture of CdSe and HgSe NPLs. In other words, would a mixture of CdSe and HgSe NPLs act the same way as the heterostructures? In figure S10 of supporting information, we have mixed in a 1:1 ratio 3ML HgSe and 3ML CdSe NPLs. The measured photomodulation is weak (< 2) and the transistor characteristic is leading to a negative threshold. Thus we can conclude that a mixture of NPL is actually behaving as the most conductive material (ie the narrow band gap one). This allows us to conclude that the enhanced performances obtained for the heterostructure is really an original properties of the heterostructure which can be further used to uncouple the optical from the transport band gaps. To finish, we discuss the dynamics of carriers into these heterostructures. So far, these NPLs do not present photoluminescence (PL) and traditional time resolved PL cannot be used to probe carrier relaxation. Other methods such as transient absorption and time resolved photoemission 52 can be used as alternative probe. Here, we rather choose to study the photoconductive properties of the material through time resolved transient photocurrent measurements [START_REF] Martinez | Probing Charge Carrier Dynamics to Unveil the Role of Surface Ligands in HgTe Narrow Band Gap Nanocrystals[END_REF] . After a fast ns UV laser excitation, we follow the rise and decay of the photocurrent on a GHz oscilloscope of a film of NPLs, see Figure 4a for a scheme of the setup. The rise of the current is typically limited by the light pulse. This rise is first followed by a fast decay during the first ns whatever the sample. Then a dependent thickness decay appears at longer time scales, see Figure 4b. We observe that the thicker the NPLs are, the faster they respond (see Figure 4c). HgSe NPLs present a long tail of photocurrent, which expands up to 1 ms after pulse (black curve on Figure 4b). Recently it was proposed, in narrow band gap HgTe NCs that such tail is the signature of multitrapping process. [START_REF] Martinez | Probing Charge Carrier Dynamics to Unveil the Role of Surface Ligands in HgTe Narrow Band Gap Nanocrystals[END_REF] After excitation, the carriers can either recombine or get trap. Once trapped, the dynamics of the system is driven by the trapped carriers release time. And the deeper the traps are, the longer the release lasts. The faster dynamics observed in the heterostructures suggests a limited role of traps. This is consistent with our previous observation that transport is driven by the CdSe core and is thus less sensitive to the external traps thanks to the presence of the HgSe shell.

CONCLUSION

We have grown a 2D heterostructure combining both a wide band gap and a narrow band gap material. These HgSe/CdSe/HgSe heterostructures are obtained thanks to a cation exchange happening on exactly two cationic layers on the equivalent top and bottom facets of CdSe NPLs. The interface between the two materials is topotaxial. By carefully choosing the two materials and hence the effective mass of their carriers, it is possible to make the optical feature only determined by the narrow band gap material, in spite of the quasi-type II band alignment. Even more interestingly is the fact that transport properties are driven by the wide band gap core material. We observe that in presence of a CdSe barrier, the heterostructures present an electrical gap which can be wider (by 300 meV) than its Tables of Contents:

Figure 1 (

 1 Figure 1 (a.) Scheme of a 4ML thin CdSe NPL and (b.) TEM image of 4 ML thin CdSe NPLs. (c.) Scheme of a 10ML thick CdSe NPL and (d.) TEM image of 10ML thick CdSe NPLs. (e.) Scheme of a 10ML HgSe/CdSe/HgSe heterostructure. (f.) TEM and (g.) high resolution TEM in dark filed mode of a 10ML HgSe/CdSe/HgSe heterostructure.

Figure 3 (

 3 Figure 3 (a.) Scheme of an electrolytic transistor where a thin film of NPLs is used as channnel. (b.) Transfer curve (drain current vs gate bias) for HgSe/CdSe/HgSe heterostructures of various thicknesses. As the conductivity of the sample strongly changes, the curves have been normalized to better illustrate the shift of the threshold voltage. Non normalized data are given in Figure S9 (c.) Threshold voltage for transistor made of HgSe/CdSe/HgSe heterostructures as a function of the thickness of the NPL. (d.) I-V curve of a film of 3ML HgSe NPLs measured at room temperature under dark condition and under illumination (λ=532 nm-P=0.13 mW). (e.) I-V curve of a film of 11ML HgSe/CdSe/HgSe heterostructures measured at room temperature under dark condition and under illumination (λ=532 nm-P=0.13 mW).

.

  This corresponds to an increase of the electrical gap of 300 meV with respect to the optical gap. The effective increase of the band gap also dramatically impacts the NPLs

Figure 4 (

 4 Figure 4 (a.) Scheme of the transient photocurrent setup. (b.) Normalized transient photocurrent signal for CdSe-HgSe heterostructures of different thicknesses. (c.) Transient photocurrent decay time as a function of the NPLs thickness.

optical gap. This strategy is extremely useful for future development of IR active layer based on NCs for infrared photodetection where dark current is a key limitation.

ACKNOWLEDEGMENTS

This work has been supported by the Region Ile-de-France in the framework of DIM Nano-K (grant dopQD). This work was supported by French state funds managed by the ANR within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02, and more specifically within the framework of the Cluster of Excellence MATISSE and also by the grant Nanodose and H2DH. EL thanks the support ERC starting grant blackQD (grant number 756225). GP thanks the Equipex TEMPOS referenced 10-EPQX-0050. We acknowledge the use of clean-room facilities from the "Centrale de Proximité Paris-Centre".

Supporting informations

Supporting information include details about absorption kinetics from CdSe to HgSe 3 ML NPLs; TEM images of NPLs before and after cation exchange; absorption spectra from 6 to 11 ML NPLs; X-ray diffraction patterns of NPLs; energy dispersive X-ray spectroscopy (EDX); Rutherford Backscattering Spectrometry, numerical simulation; ligand exchange and fabrication of field effect transistors; time resolved measurements


Charles Cornet

Simon Charbonnier

Ida Lucci

Lipin Chen

Antoine Létoublon

Angela Alvarez

Karine Tavernier

Tony Rohel

Rozenn Bernard

Jean-Baptiste Rodriguez

J.-B Rodriguez

L Cerutti

E Tournié

Y Léger

M Bahri

G Patriarche

L Largeau

A Ponchet

P Turban

N Bertru

Zinc-blende group III-V/group IV epitaxy: Importance of the miscut

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I. INTRODUCTION

The monolithic integration of both Zinc-Blende and Wurtzite III-V semi-conductors respectively on (001) and (111) group-IV substrates (such as Si or Ge), is nowadays one of the most promising approach for the development of integrated photonic devices, or efficient energy production and storage applications [START_REF] Cornet | Integrated Lasers on Silicon[END_REF][START_REF] Cotal | [END_REF][3]. More specifically, (001) substrates are generally preferred over (111) ones, as they are expected to ease the post-growth processing of group III-V/ group IV devices [START_REF] Cornet | Integrated Lasers on Silicon[END_REF]. On the other hand, crystal defects generated in III-V epilayers grown on group IV substrates may be numerous and detrimental for devices operation. Especially, antiphase domains (APDs) which are related to the polar on non-polar epitaxy (i.e. to the two different ways for the III-V atoms to be allocated at the group IV substrate surface) strongly impact the structural, and electronic properties of grown III-V semiconductors. The easiest solution to avoid or mitigate the formation and propagation of antiphase boundaries (APBs) through the device itself is to grow the III-V materials on misoriented group IV (001) substrates. But the post-growth processing of such misoriented (vicinal) III-V/IV wafers remains tricky [START_REF] Cornet | Integrated Lasers on Silicon[END_REF], especially when the miscut angle reaches 1° or more. Recently, many research groups tried to reduce or even suppress the miscut of the used group-IV wafer. [4,5] But a clear view on the relationship between miscut, APBs generation, and APBs propagation is still missing.

Indeed, the use of a vicinal substrate is often motivated by the ability to promote the double step formation at the group IV surface [6], avoiding the monoatomic layer translation of the III-V crystal which may appear due to the presence of single steps at the substrate surface, theoretically generating an APB. With this picture in mind, K. Volz et al. explained their results about epitaxial GaP/Si by considering a 2D III-V growth mode on the substrate [7] (Note that the difference between a 2D growth mode and a flat 3D one is difficult to make experimentally).

On the other hand, the recent work by I. Lucci et al. proposes an alternative model [8] based on Density Functional Theory calculation and the extensive characterization of a variety of GaP/Si, AlSb/Si and AlN/Si samples. This model can be summarized as follow: (i) There is only a partial wetting between III-V semiconductors and Si, thus leading to the formation of pure 3D Volmer-Weber growth mode, as experimentally confirmed by some other studies [9,10]. AlSb/Si islands have even been found to be at their equilibrium shape. [9] This model can be generalized to the epitaxy of III-V on Ge, based on the surface energy involved and the experimental results found in the literature [11]. (ii) APBs are generated during the coalescence of 3D islands having different phases, as also suggested in pioneering works on III-V/Ge [11]. The size of individual monodomain islands can be much larger than the distance between steps (the terrace width) [8], which suggests that the step itself cannot be the main cause for the APDs generation. (iii) Elastic energy does not have a significant impact on the island morphology at the coalescence growth step (and therefore does not impact the APD distribution), as most of the islands are already A c c e p t e d m a n u s c r i p t plastically relaxed (even for GaAs/Si [12]) at this stage (or unstrained in the particular case of the quasi-lattice-matched GaP/Si system). (iv) The epitaxial relationship is defined locally at the nucleation site which further governs the phase distribution.

Meanwhile, extensive works were performed about the dislocation-free GaP/Si model case. A clear correlation between the Si local surface dimer orientation and the subsequent epitaxial III-V phase was established (See for instance ref. [13] or [14] and references therein). This led the authors to support the idea of a step-induced generation of APBs. Although these observations may seem in contradiction with the model involving the nucleation of monodomain islands described previously, the connection will be established later on in this work. Finally, many groups tried to favor the so-called APB annihilation by playing with the III-V growth parameters. It was noticed that the V/III ratio and growth temperature play an important role in this process [15,16], suggesting a significant contribution of kinetic effects at this stage.

In this work, we aim to clarify the impact of the miscut on the generation of antiphase domains during the heteroepitaxy of group III-V semiconductors on group IV substrates. We first investigate the influence of the miscut on the initial APD distribution, in the low and large miscut regimes. It is then proposed that the growth rate imbalance between the two III-V phases is the main driving force for the APD burying. The possibility to leverage this mechanism in the case of very low miscut substrates is finally discussed.

II. THE INITIAL PHASE DISTRIBUTION

Before any other consideration, the link between the initial phase distribution in the III-V layer (i.e. the phase distribution after the growth of only a few nanometers) and the group IV substrate surface properties should be made. In this section we first review the results of the literature about phase distributions in III-V/IV materials systems, and show how it connects to the substrate properties, and especially to the miscut. We then infer the important physical parameters that characterize the initial phase distribution, and their link with the group IV substrate surface properties.

A. The critical miscut

In order to clarify the impact of the miscut on the initial distribution of III-V islands phase we first analyze the results of the literature. In the following, all the works reported here use a miscut along the [110] direction. For low miscut Si substrates (typically <1°), Beyer et al. [14] have demonstrated that the APD distribution in the GaP crystal reproduces well the distribution of steps at the Si surface. For large miscut (typically >1°), on the contrary, many studies report on APD sizes significantly larger than the average terrace width. For the MOCVD growth of GaP on 2°-off Si (corresponding to an average terrace width of 3.89 nm), 9 to 26 nm-large APDs were observed [17]. For the MBE growth of GaP on 4°-off Si (average terrace width of 1.94 nm), a complete analysis of the APD distribution led to the conclusion that the APD lateral width typically falls in the 10 to 58 nm range [16]. Finally, APDs with an average width of 12 nm were found for the MBE growth of GaP on 6°-off Si substrates (average terrace width of 1.29 nm) [8,18,19]. Additionally, on Si-6°-off substrates again, 10-50 nm large islands were determined for the MBE growth of AlSb/GaSb on Si [9]. From all these results, it therefore appears that the APDs morphology are somewhat related to the steps distribution at the group-IV surface only when the III-V growth is performed on low miscut substrates. It is markedly not the case when the III-V growth is performed on large miscut group IV substrates, because the average APD width is systematically larger than the terrace width.

Also, only a partial wetting of the group-IV surface by the III-V is theoretically expected and experimentally observed [8,9]. Therefore, it is reasonable to postulate that the III-V growth on group IV substrate starts with the formation of monodomain III-V 3D islands, whose phase is defined directly by the surface dimer orientation at the nucleation site. In the case of low miscut group IV substrates (see Fig. 1(a)), terraces are large, and several III-V islands with the same phase can therefore grow on the same terrace. After coalescence of these islands, the APD distribution thus mimics the terrace distribution: the APBs will approximately follow the monoatomic step edges initially existing at the group IV substrate surface. But it is only an approximation, as before coalescence individual islands may grow over a Si monoatomic step while staying monodomain, as schematically represented in Fig. 1(a). Thus, for low miscut substrates, the lateral size of APDs is expected to be directly related to the average lateral size of the substrate surface terraces. The APD distribution is therefore "terraces-driven".

By contrast, large miscut group-IV substrates result in narrow terraces. The typical size of the monodomain III-V islands is in that case larger than the width of terraces (see Fig. 1(b)). This leads to a "nucleation-driven" APD distribution, where the lateral size of the APDs after coalescence is mainly related to the distance between two neighboring islands of opposite phases.

The frontier between the terraces-driven and the nucleation-driven APD generation regimes corresponds to the situation where the average width of the terraces at the group IV substrate surface equals the average distance between two neighboring islands of opposite phases along the miscut direction. The corresponding miscut angle is named hereafter the "critical miscut". The value of the critical miscut depends on the initial density of nucleation sites and therefore directly depends on the nature of the III-V material, as well as on the growth conditions at the nucleation stage. composed of monoatomic steps. We note here that this trend is also valid for a Ge surface. In fact, terrace widths for a given miscut angle are only marginally different for Ge compared to Si at the scale of the process described here. The average distance between two neighboring islands along the miscut direction d1D can be calculated from the island density d measured experimentally by considering a Poisson distribution of the III-V islands positions at the group-IV surface [20] :

𝑑 1𝐷 = 1 𝜋√𝑑 (1)
The average distance between two neighboring islands along the miscut direction was extracted for different III-V/IV systems studied in the literature using equation ( 1): GaSb/Si [21], AlSb/Si [21], GaP/Si [8], InP/Si [22], GaAs/Si [23,24] and GaAs/Ge [11]. In these works, islands are observed well after the nucleation step. Therefore, the island density is not expected to change during the growth, and would remain the same for thicker layers at the coalescence step. The values extracted here can thus be used to derive the critical miscut corresponding to the growth conditions reported in these papers. To this end, the average distance between two neighboring islands calculated for each of the reference above are plotted with colored dots on the "Terrace-width vs Miscut angle" curve in Fig. 1(c). directions as a function of the miscut angle for Si or Ge surfaces composed of monoatomic steps. Colored dots correspond to the 1D average distance between islands reported for different III-V/group IV systems, from refs. [8,11,[21][22][23][24]. The vertical dashed arrows indicate the corresponding critical miscuts.

Dashed arrows in Fig. 1(c) represent the critical miscuts between the two APD generation regimes for each material system for the corresponding growth conditions. Red and blue miscut ranges are highlighted in Fig. 1(c) and are regions where terraces-driven and nucleation-driven APD distribution are respectively likely to occur. Of course, in addition to the growth conditions used during the nucleation, number of parameters could have an impact on the critical miscut, including the actual number of steps at the surface and the growth technique chosen (e. g. Molecular Beam Epitaxy (MBE) or Metal-Organic Chemical Vapor Deposition (MOCVD)). Nevertheless, except in some extreme epitaxial conditions [25], most of the previous works report island surface densities in the [10 9 -10 11 ] cm -2 range, which allow concluding that the critical miscut is in the [0.1-1] ° range for common group III-V/group IV heterogeneous associations.

B. The antiphase domain initial distribution

Overall, the initial APD distribution (very near the III-V/group IV interface) can be fully characterized by two parameters. First, the III-V crystal mean phase can be characterized by a single number ranging from -1 to +1 [18,26]. Here, considering APBs propagating vertically, a mean phase of 0 means an equal number of atoms in the main phase and antiphase domains. The island nucleation being a stochastic process, the mean phase is directly related to the area ratio between the two different group IV substrate terraces local surface dimer orientations. Note that for a given III-V crystal mean phase, many different monoatomic or biatomic group IV steps possible configurations may be considered. Inversely, a given average density of monoatomic steps at the substrate surface is not enough to predict the mean phase of the III-V crystal, as the in-plane distribution of monoatomic steps can significantly change the mean phase of the III-V crystal. Therefore, the achievement of statistically-dominant biatomic steps distribution at the surface certainly helps to promote a near to single phase domain configuration (i.e. a mean phase of +1 or -1) in III-V layers [27].

The second important parameter is the mean lateral extent of APDs, which is related either to the terrace width below the critical miscut, or to the nucleation islands density above the critical miscut. Here, it should be mentioned that the concept of critical miscut was introduced by considering a perfect monoatomic step lattice at the group IV surface. But, depending on the strategy used to prepare the group IV substrate (e.g. chemical preparation or homoepitaxy), the A c c e p t e d m a n u s c r i p t real step distribution can be quite different from the ideal one. Especially, for low miscut substrates, a fine control of the miscut angle and the miscut direction in addition to a proper homoepitaxial or passivation strategy is needed to reach the perfect terraces-driven APD distribution regime over the whole sample [14].

III. EXPERIMENT

On the basis of the general framework given in sec. I establishing the link between the group IV substrate surface and the initial III-V phase distribution, the evolution of such a phase distribution with the III-V thickness can then be discussed. To this aim, structural properties of thick III-V layers grown on different Si substrates with low and large miscuts were studied and compared.

In Fig. 2, a comparison between similarly thick III-V layers grown on low and large miscut group IV substrates is shown. Growth and microscopy details are given in the supplemental materials [20]. First, cross-sectional Transmission Electron Microscopy (TEM) images of two comparable samples mainly composed of GaSb (with a thin AlSb nucleation layer) grown on freshly prepared [28] Si 0.3°-off toward the [110] direction (Fig. 2(a)) and 6°-off toward the [110] direction (Fig. 2(b)) are shown. In these images, bright and dark areas correspond to the main phase or antiphase domains contrasts, although the presence of other defects may contribute as well. At first sight, it can be seen that APDs are overall larger and taller for the low miscut case than for the large miscut case.

More specifically, the two images show two distinct features: (i) the presence of very small APDs very near the interface, with a typical width than 20nm, and a height smaller than 50 nm, which corresponds to the size of the individual islands formed initially [8]. These small APDs are numerous for large miscut samples, although some small APDs can also be seen in the low miscut case. (ii) Some large APDs, with a width typically larger or much larger than 20 nm, and a vertical extent larger than 50 nm which correspond to the APD distribution after the burying of the previously discussed small APDs. This apparent bimodal distribution may be related to the adatom diffusion length needed for APD burying, which will be discussed later on in this paper.

Regarding the initial APD distribution, i.e. near the III-V/Si interface, it can be seen that while the GaSb growth on 6°-off Si leads to very small dark and bright areas observed all along the interface in the III-V region, the growth on low miscut substrate gives rise to large singlephase areas between two APBs. Indeed, in the low miscut case, following a direction parallel to the III-V/Si interface in close vicinity to the interface, single-phase areas are observed over 40 nm and even beyond, while for the large miscut case, single-phase areas extend at the maximum over 15 nm laterally. This observation is in good agreement with the previously proposed explanation of the impact of the miscut on initial APD distribution.

For samples grown on 6°-off substrate, few large APDs are still visible (see e.g. the one highlighted with dashed line in Fig. 2(b)), but they are on average smaller than the one found in samples grown on (001) substrates (see e.g. the one highlighted with dashed line in Fig. 2(a)). Furthermore, a monodomain GaSb layer is finally reached for the vicinal case, while APBs are propagating until the surface for the nominal one, as shown in the supplemental materials [20]. But a meaningful quantitative assessment cannot be given from these pictures, because other defects, such as dislocations [29], introduce a superimposed contrast which complicates the analysis. A more ideal case can be found with the quasi-lattice-matched GaP/Si system. Crosssectional Transmission Electron Microscopy (TEM) images of two comparable samples (with the same growth conditions) mainly composed of GaP grown on freshly prepared [30] Si (001) (0 +/-0.5°) substrate (Fig. 2(c)) and 6°-off along the [110] direction (Fig. 2(d)) are shown. It is useful to recall that the exactly oriented nominal group IV (001) substrate is a theoretical case, not achievable by substrate manufacturers. In practical cases, a residual and A c c e p t e d m a n u s c r i p t often uncontrolled miscut should always being considered [7]. Bright and dark contrasts are again attributed to domains with different phases. A statistical analysis was performed over a cumulated width of 4 µm along the [110] direction (see examples of TEM images in the supplemental materials [20]). Values collected for the APDs width and heights are given in Fig. 2 (e) and (f). APBs emerging at the surface observed for the (001) case are not considered for this analysis. A perfect deconvolution between small APDs and large APDs populations is not achievable, but the images as well as the statistics clearly show that small APDs, near the III-V/Si interface are more numerous and smaller on 6°off substrates, which tends to confirm the impact of the Si terraces width in the low miscut limit. We also confirm quantitatively that large APDs are much larger on the nominal substrate, and propagate farther in the sample. Finally, Fig. 2(c) also points out that APBs induce roughness and faceting [31] with consequences well after their annihilation. Indeed, it can be seen on the three APBs shown in Fig. 2(c) that the flatness of the free surface is directly related to the distance to the highest point of the buried APD. After a given thickness, the (001) surface is recovered, as shown for the central APD of Fig. 2(c). A thin buffer layer is therefore needed after APBs annihilation to smoothen the surface.

Overall, these images confirm the central role of the miscut on the initial APD distribution, but also point toward the importance of the miscut on the subsequent III-V growth steps.

IV. PHASE DISTRIBUTION EVOLUTION

The experimental observations of sec. III demonstrate that the initial phase distribution discussed in sec. II evolves during the growth and may lead in some cases to monodomain III-V crystals. In the following, we first investigate how and at which condition the miscut enables burying the antiphase domains. We then introduce, and calculate for GaAs/Si, the growth rate imbalance coefficient, the value of which determines the dominant phase that will develop in the sample and the rate at which it will occur.

A. Antiphase domain burying

The role of the miscut in the so-called APB annihilation process still needs to be clarified. Numbers of situations were reported in the literature ranging from annihilation achieved on large miscut group IV substrates [26] or nominal substrates with a residual miscut (<0.2°) [7], by MBE [16], or by MOCVD [17]. In these references, and in the Fig. 2 TEM images, various APBs profiles are observed, with single or many facets composing the APB. A more precise idea of the mechanisms involved during the "annihilation process" can be obtained by imaging the morphology of the surface precisely at the moment where one domain becomes statistically dominant over the other one. To this aim, a 200-nm thick GaP layer was grown on a Si (001) -6°-off substrate (see the supplemental materials [20] for growth details). The growth conditions have been chosen such that GaP would become purely monodomain for a thickness of about 300 nm. The sample was then transferred to a Scanning Tunneling Microscope (STM) chamber [20,32] for further surface investigation at the atomic scale. The STM image obtained is shown in Fig. 3(a). The local crystallographic directions of the two different GaP phases can be distinguished at the atomic scale by the surface reconstructions, as shown in Fig. 3(a) inset. Interestingly, the surface is covered by elongated domains either along the [110] direction of the Si substrate, or along its [START_REF] Cornet | Integrated Lasers on Silicon[END_REF][START_REF] Cotal | [END_REF][3][4][5][6][7][8][9][10] direction. Since GaP domains are always elongated along their own [-110] local direction, the two phases are therefore easily distinguishable, even at the microscopic scale.

With this in mind, one can now study in Fig. 3(a) the way one domain dominates the other. Especially, it can be seen that the GaP domains having their [-110] direction parallel to the [110] direction of the Si substrate seem to coalesce through the continuous growth of material over the other phase, leading to the formation of larger single phase domains at the surface. We note here that for given growth conditions, and similar substrates, the dominant phase is consistently the same at the wafer level, as shown in the supplemental materials [20]. Based on this analysis, it is now clear that the annihilation of APBs is simply the result of the antiphase domains burying. This important finding implies that the two different domains have different growth rates despite the fact that they are made of the same material. This is somehow surprising since the two domains have the same (001) surfaces at the growth front, and we propose in the following that the substrate miscut plays at this point an important role.

B. The growth rate imbalance

In this paragraph, we explain how the miscut breaks the symmetry between the two different III-V domains. Fig. 3(b) illustrates the impact of the substrate miscut (along the [110] direction in this example) on the III-V layers grown atop. For the sake of simplicity, a (2x4) surface reconstruction is schematically represented at the top surface of the III-V semiconductor (the atomic reconstruction of the steps is not shown). It clearly appears that for one III-V domain, the miscut is transferred along the [110] direction, while it is transferred to the [-110] direction for the other domain. Consequently, one domain will predominantly form A-steps (when their edges are parallel to the group V dimers, which is the case for the yellow domain in Fig. 3(b)), whereas the other domain will form B-steps (blue domain in Fig. 3(b)) [33]. The incorporation rate on A-and B-steps being different [34,35], the growth rates of domains having different phases is thus also expected to be different. It is important to mention that the situation discussed here only applies to the case of vicinal (001) III-V surfaces. Facets of A c c e p t e d m a n u s c r i p t higher-index are not considered here, although large stable facets (see for instance the presence of (114) ones for GaP/Si in ref. [31]) may develop (depending on the material system and/or the substrate miscut), especially at the APD edges. The presence of these facets certainly has an impact on the growth rates of each domain, but is not expected to modify the conclusion drawn in the present work In the following, we will call α and β the two different phases of the III-V crystal having respectively more A-steps and B-steps at the surface. The phase α results from the III-V nucleation on a Tα terrace at the Si surface, while the phase β results from the III-V nucleation on a Tβ terrace at the Si surface. Tα and Tβ are Si terraces with orthogonal surface dimers orientations. The determination of the growth rate imbalance between the αand the βphases is therefore of interest, as the early of APDs is requested for highly integrated photonics [START_REF] Cornet | Integrated Lasers on Silicon[END_REF] while the propagation of APBs is of interest for some non-linear photonic [26] or water splitting applications [3]. The growth of III-V semiconductors on miscut surfaces may follow two different growth modes, namely step-flow growth or 2D-nucleation ones, or a combination of both [36]. Especially, for given growth conditions, with a very low miscut, the distance between steps at the surface is so large that the growth mostly depends on the diffusion length of adatoms at the surface and 2Dnucleation growth mode arises. For larger miscuts, the incorporation of group-III atoms at the step-edges becomes dominant over all the other contributions, and the step-flow regime is thus favored. This regime corresponds to the situation where the distance between steps is lower than the diffusion length of group-III adatoms, which highly depends on the temperature. [36] The typical values of the diffusion lengths given for group-III adatoms on a III-V planar surface are in the [0.5-1] µm range [15], implying that the miscut at which step-flow growth mode may occur is typically larger than [0.01-0.03]°, depending on the material system and growth conditions. In the present case, a pure 2D nucleation growth mode would result in the same growth rates for the α-and βphases because the step-edges are only marginally involved in that case. Some fraction of step-flow is therefore required to observe a growth rate difference between αand βphases. Therefore, one can conclude that burying of APDs is only possible if the substrate has at least a projected miscut of 0.03° precisely along a given [110] or [START_REF] Cornet | Integrated Lasers on Silicon[END_REF][START_REF] Cotal | [END_REF][3][4][5][6][7][8][9][10] direction. Beyond this value, the respective growth rates of phases α and β only depend on the incorporation rates at steps A and B.

We now introduce the growth rate imbalance coefficient Cα/β defined as:

Where Vgα and Vgβ are the crystal growth rates of the phases α and β. R°A, R°B, EA and EB, are respectively the amplitudes and energy barriers for direct incorporation at steps A and B, as defined in refs. [34,35]. kB is the Boltzmann constant, and T the growth temperature. Therefore, the growth rate imbalance coefficient is a simple ratio between the growth rate of phases α and β, which we can calculate as the ratio of direct step incorporation rate per site for each phase. Therefore, if Cα/β is lower than unity, the β phase will grow faster than the α one. On the contrary, if Cα/β is larger than 1, the α phase will become dominant. If Cα/β equals to one, the growth rates are the same and APBs will propagate to the surface. Interestingly, the development of the α-or βphases and the rate at which it occurs does not depend on the miscut angle. Indeed, the areal density of steps at the surface of αand βphases is the same, whatever the miscut value. APD burying is therefore expected to occur in the same way on low and large miscut group IV substrates, but with different initial phase distributions.

The determination of the growth rate imbalance coefficient requires a solid knowledge of the growth rates or direct step incorporation rates per site for each phase. Experimental determination of the incorporation rates was proposed in the pioneering works of Shitara et al. for MBEgrown GaAs, by using reflection high-energy electron diffraction [34,35]. From these data (see supplemental materials for the parameters used [20]), the growth rate imbalance coefficient Cα/β was calculated as a function of the temperature, for various V/III ratio. The results, shown in Fig. 4, are relevant to the MBE growth of GaAs on Si or Ge substrates (and to some extent to the MOCVD GaAs/Si or GaAs/Ge growth).

Fig. 4 shows that for most growth conditions, the β phase will grow faster than the α one, except at high growth temperature (>600°C) and low V/III ratio [START_REF] Cotal | [END_REF], where the α phase will be favored. It can also be noticed that the lower the V/III ratio, the more the Cα/β coefficient becomes sensitive to the growth temperature (slopes of the Cα/β(T) curves are larger for V/III=2 or 2.5, as compared to the ones for V/III=4.3 or 6.8). As a consequence, in the temperature range shown in Fig. 4, the largest value of Cα/β is reached for the highest temperature (620°C) and a low V/III ratio (2.0). In that case, Cα/β is larger than unity and the α phase growth is thus favored. On the other hand, the lowest value of Cα/β is reached for the lowest growth temperature (540°C) and still a low V/III ratio (2.5), and the β phase will become dominant. This explains the experimental observations given by I. Lucci et al. [31]. In this previous work, thick GaP/Si samples were grown, resulting in a single domain GaP in the central part of the wafer, while at the edges of the 2" wafer, another GaP single domain with opposite phase was observed. The local increasing of the temperature at the edges of the wafer has certainly allowed changing the dominant phase.

It is also interesting to see that, for a given growth temperature (high enough), the V/III ratio may allow to tune the dominant phase at will. This is illustrated in the inset of Fig. 4, where the Cα/β coefficient was plotted as a function of the V/III ratio for GaAs at a growth temperature of 620°C. By increasing the V/III ratio, the dominant phase changes from α to β. The trends described for GaAs in Fig. 4 are expected to be similar for other III-V semiconductors and thus provide a guide for the growers. A precise determination of the direct step incorporation rates for the different materials systems is however still needed to precisely optimize the heterogeneous group III-V on group IV epitaxy on purpose. The hydrogenation of the surface during MOCVD III-V growth may also significantly impact the step incorporation rates imbalance. We note here that the growth rate imbalance coefficient may also be measured directly for most III-V/IV systems by using direct plan-view imaging on different samples with different thicknesses or crosssectional imaging on a single sample.

FIG. 4: Growth rate imbalance coefficient Cα/β as a function of 1000/T for various V/III ratio used in the case of GaAs/group IV epitaxy, determined from ref. [34,35]. The corresponding temperature range is between 540°C and 620°C. The orange area indicates the conditions where the α III-V phase grows faster, while the blue area indicates the conditions where the β III-V phase grows faster. Inset shows the evolution of the imbalance coefficient as a function of the V/III ratio for GaAs grown at 620°C on a group IV substrate.

C. Discussion

The consequences of this antiphase domain burying process description are numerous but we would like to highlight the most important ones. First of all, the mean phase of the initial APD distribution does not impact on the final phase of the layer. Even if the initial Tα/Tβ surface ratio is at 80/20, subsequent growth conditions favoring the β phase will lead to a monodomain β-phase crystal after a sufficient thickness. Second, the thickness at which a single domain III-V semiconductor is recovered mainly depends on the initial APD mean lateral extent, and the growth rate imbalance coefficient Cα/β. A large initial APD, as the one observed on nominal substrates in Fig. 2(a) and (c) or in ref. [7], will obviously require a larger deposition thickness to be buried (see fig. 2 e) and f)). In the same way, large A c c e p t e d m a n u s c r i p t deposition thicknesses will be needed before complete APD burying if growth conditions resulting in Cα/β close to unity are chosen. Third, the general morphology (and "facets") of APDs is governed by the initial APD distribution as well as by the growth rate imbalance coefficient Cα/β. APBs lying on high-index crystallographic planes certainly reflect a strong growth rate imbalance, i.e. Cα/β much larger or lower than 1. On the contrary, vertical propagation of APBs indicates a Cα/β coefficient close to 1 or a too low miscut angle, at least locally. This is especially what is currently observed when the growth is performed on standard commercially-available low miscut group IV substrates, where the miscut is not precisely controlled, or when the thermal or chemical substrate preparation does not allow to homogenize the miscut at the wafer scale. We also note that the use of [010] or [100] offcut directions will create the same step density in both directions within one domain, leading therefore to a Cα/β equals to 1, whatever the growth conditions used in this specific case.

Of course, this general picture does not allow to predict the APB structure at the atomic level, which may be locally impacted by charge compensation effects or temperatureinduced kinks, as described by Beyer et al. [37]. Last, from this description it can be understood why burying of APDs can be achieved even on low, but controlled, miscut substrates, if the growth conditions, and especially V/III ratio and growth temperature are carefully chosen to promote growth rate imbalance. Here, we point out that a successful APD burying achieved on a low miscut group-IV substrate requires the precise control of both the miscut angle (larger than 0.03° to keep the step flow growth mode) and the miscut direction, homogeneously at the substrate surface, so that the growth rate imbalance is achieved everywhere in the sample, despite some local miscut direction or angle fluctuations. Thus, the thermal and/or chemical preparation of the group IV wafer prior to the III-V growth, which determines the homogeneity of the miscut and the step distribution at the substrate surface, is undoubtedly the key parameter to achieve a high quality hetero-epitaxial III-V/IV material.

V. CONCLUSIONS

In conclusion, the relationship between the group-IV substrate miscut, and the initial III-V antiphase domain distribution mean phase, and mean lateral size during III-V/group IV epitaxy was clarified. The central role of the miscut in the antiphase domain burying was established. Especially, the miscut was found to induce a growth rate imbalance between the two III-V crystal phases. On this basis it was shown how burying of antiphase domains is possible for low miscut substrates. The detailed description of the group-IV substrate miscut impact on epitaxially grown III-V structural properties opens new prospects for the development of highly integrated photonics or energy production/storage applications.

Figure 1 (

 1 Figure 1(c) represents the evolution of the average terrace width as a function of the miscut angle, for a silicon surface

FIG. 1 :

 1 FIG. 1: Sketch of (a) the terraces-driven phase distribution in III-V islands grown on low miscut group IV substrates, and of (b) the nucleation-driven phase distribution in III-V islands grown on large miscut group IV substrates. Blue and yellow colors are used to indicate the different surface dimer orientations and phases of both group IV terraces and III-V islands. L indicates the mean size of III-V islands. (c) Average length of terraces along the [110] or [1-10]

FIG. 2 :

 2 FIG. 2: Cross-sectional Transmission Electron Microscopy images of thick (a) GaSb/Si(001) 0.3°-off, (b) GaSb/Si(001) 6°-off, (c) GaP/Si(001) and (d) GaP/Si(001) 6°-off samples along the [110] direction. For GaSb/Si (a&b), the Si substrate is the black area at the bottom of the images. For GaP/Si (c&d), the Si substrate is the bright grey area at the bottom of the images. The white bar represents 100nm for each TEM image. Dashed lines are guide to the eyes showing typical APBs shape in the sample. Corresponding antiphase domains width (e) and height (f) distributions are quantitatively represented for GaP/Si samples on both nominal and vicinal substrates.

FIG. 3 :

 3 FIG. 3: (a) Plan-view STM image of a 200 nm-thick GaP deposition on Si (001) -6°-off (400*400 nm2, vertical color scale: 0-13.9nm), during the APB annihilation step. The 19*19 nm 2 inset shows the atomically-resolved morphology of the GaP dominant phase. Dashed lines are guide to the eyes showing local different GaP phases. (b) Illustration of

A c c e

  p t e d m a n u s c r i p t

The authors acknowledge Dr. R. Le Guével and A. de Verneuil for fruitful discussions on the statistical analysis of experimental data for the determination of the critical miscut. Pr. K. Volz and Dr. J.-C. Harmand are also acknowledged for the interesting discussions about III-V/ group IV epitaxial processes. The authors acknowledge RENATECH (French Network of Major Technology Centers) within Nanorennes for technological support. This research was supported by the French National Research Agency ANTIPODE Project (Grant no. 14-CE26-0014-01), ORPHEUS Project (Grant no. ANR-17-CE24-0019-01) and Région Bretagne.