N Foy

E Chevallier
email: eddy.chevallier@u-picardie.fr

H Zerari

D Zehouani

D Favry

ELECTRICAL PROBING OF A STEEL ROUGH INTERFACE UNDER SHEAR STRESS

Keywords: Experiments in tribology, Physics of friction, Contact and adhesion, Electrical contact resistance

We present in this work the experimental results of shear stress applied to a rough metallic interface. This interface was test using a weak DC current, measures of the voltage evolution were done on each end of the system while an increasing shear stress was applied. From these measurements we deduce the evolution of the interface electrical resistance to attempt to highlight the contact area evolution. Results show that the interface resistance follows a non-monotonic behavior: it first increases to a maximum and then decreases until the contact breaks. The evolution of the interface resistance is related to the evolution of the contact area, the non-monotonic behavior is interpreted as different deformation regimes in the spots of contact.

INTRODUCTION

The contact between two rough surfaces is occurs in tiny contact spots [START_REF] Greenwood | Contact of nominally flat surfaces[END_REF] where their number, distribution, shape or size -i.e. their geometrical properties -depends on the roughness, the nature of materials, and the stress applied on the contact interface. A direct assessment of relevant parameters acting on the contact zone is difficult because of its discrete nature, so that real contact consists in a distribution of individual N micro-junctions, each one with its own surface Sk (k = 1, 2, …, N) leading to a total area Ar (Ar = ΣSk) much smaller than the apparent contact area [START_REF] Bowden | The Friction and Lubrication of Solids[END_REF][START_REF] Ovcharenko | In situ and real-time optical investigation of junction growth in spherical elastic-plastic contact[END_REF][START_REF] Krick | Optical in situ micro tribometer for analysis of real contact area for contact mechanics, adhesion, and sliding experiments[END_REF]. Actually, Ar follows two major behaviors: (i) it is proportional to the applied normal load [START_REF] Bowden | The Friction and Lubrication of Solids[END_REF][START_REF] Dieterich | Direct observation of frictional contacts: New insights for statedependent properties[END_REF][START_REF] Rubinstein | Detachment fronts and the onset of dynamic friction[END_REF][START_REF] Yashima | Normal contact and friction of rubber with model randomly rough surfaces[END_REF][START_REF] Archard | Elastic deformation and the laws of friction[END_REF][START_REF] Persson | On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion[END_REF][START_REF] Pastewka | Contact between rough surfaces and a criterion for macroscopic adhesion[END_REF][START_REF] Yastrebov | From infinitesimal to full contact between rough surfaces: Evolution of the contact area[END_REF], and (ii) it logarithmically increases with time -as known as geometric aging or creep - [START_REF] Dieterich | Direct observation of frictional contacts: New insights for statedependent properties[END_REF][START_REF] Ben-David | Slip-stick and the evolution of frictional strength[END_REF][START_REF] Baumberger | Solid friction from stick-slip down to pinning and aging[END_REF].

To probe properly the interface and find relevant criteria of any influences from undergone stresses, the measurement of any appropriate physical quantities sensitive to the mechanical state is required. The measurement of electrical -or thermal -resistance corresponds perfectly to the requirements since it derives from the mechanical conditions imposed on the interface. The behavior of the interface resistance versus an applied normal stress is a wellknown effect [START_REF] Persson | On the nature of surface roughness with application to contact mechanics, sealing, rubber friction and adhesion[END_REF][START_REF] Zeroukhi | Dependence of the Contact Resistance on the Design of Stranded Conductors[END_REF][START_REF] Arrazat | Discrete Analysis of Gold Surface Asperities Deformation under Spherical Nano-Indentation towards Electrical Contact Resistance Calculation[END_REF][START_REF] Tekaya | Influence de la dimensionnalité et de la complexité d'un réseau sous compression mécanique sur les transports électrique et thermique dans les milieux granulaires métalliques -De l'interface individuelle aux propriétés collectives[END_REF][START_REF] Holm | Electric Contacts -Theory and Applications[END_REF][START_REF] Tabor | The Hardness of metal[END_REF][START_REF] Foy | Modélisation et simulation multi-physique des interfaces multi-contacts métal/métal[END_REF][START_REF] Jonckheere | Assessment of the real contact area of a multi-contact interface from electrical measurements[END_REF]. So, it is therefore legitimate to assume that the interface resistance have also its own dependence versus an applied shear stress.

In [START_REF] Eisner | The effect of a tangential force on the contact of metallic bodies[END_REF] Courtney-Pratt and Eisner made an experimental study about the mechanical evolution of a spherically ended cone, bearing on a plane and undergoing a tangential force. In their study electrical measurements were made to probe the mechanical evolution of the sphere/plan contact between two polished metals of the same kind. Thus, they showed that the contact conductance seems to be proportional to the square of the shear force, for 2 polished platinum and steel. Due to the presence of an oxide layer, the model describing the behavior of noble metals did not make possible to correctly describe the behavior of steel.

The present paper appears as a complement on the electrical aspect of the study made in [START_REF] Eisner | The effect of a tangential force on the contact of metallic bodies[END_REF]. Using cylindrical polished steel samples, we focus on the influence of shear stress on the interfacial electrical resistance in order to understand the mechanical behavior of this contact interface. The experimental protocol and samples preparation were specially made in order to understand and focus on the mechanical behavior of multi-contact interfaces. Thus, emerging a behavior law between real contact area and shear stress for metallic interfaces would directly affect the slipping properties of rough contact and so, the way we use and understand tribological models.

MATERIAL AND METHODS

Apparatus

To study the contact interface, we use a pair of hand polished cylindrical samples made of steel (ISO683-1 C45 / AISI-SAE 1045) which were placed in a dry frictional contact arrangement in which a DC current flows (fig. 1). The applied current arrives and leaves from a small zone behind each of the samples where a wire was fixed by a silver conductive paint. Samples were sized to have a homogeneous current distribution in the bulk (fig. 2) to ensure that only the contact spots influence electrically the measure. The voltage at each end of the set was then measured during the increasing of the shear stress. The electrical probing was done by the "4 points" method using a Keithley SourceMeter 2611A wired to a computer to acquire the data.

As shown on figure 1, the lower cylinder was adhered to the table and the upper one was driven horizontally through a wire attached in the plane of the contact interface. The normal load was applied using labelled masses and the tangential force (shear stress) is applied through a pulley by an increasing mass piloted by a sandglass which delivers 6.36E-3 N/s. A sandglass was use here because of its very regular flow, which ensures a reliable application of shear on the system.

Samples preparation

Our samples were manually prepared using sandpaper to abrade the surface, then to polish them, and to finish with a 500-mesh sandpaper. For each measurement, the concerned surfaces were systematically finished and degreased with acetone before being in contact.

To know the initial surface state of the samples, a map profilometry was made with a "DektakXT Stylus Profiler" from Brucker with a 2µm stylus at 3mg of load; also EDX measures were made with a "Quanta 200 FEG scanning electron microscope" from FEI Company. The first analysis shows the overall shape of the contacting surfaces and their roughness while the second one the chemical composition of the material. The figure 3a, shows an example of a typical profile of the surface, 3b a typical map and 4 an example of an EDX spectra with the percentage content of elements in the surface.

Since our samples were manually prepared, the contact surface presents a curvature which can be fitted by a sphere (fig. 3a) and so, the contact between our samples is a kind of sphere/sphere contact, where the spheres have a very large radius (~4m). From the mechanical parameters we can estimate, using the Hertz's model, the contact zone around 0.15mm² under a normal load of 1N.

Protocol

Right after the initial contact, the following specific protocol is applied:

[0 to 180s]: interface relaxes (creep phenomenon [START_REF] Dieterich | Direct observation of frictional contacts: New insights for statedependent properties[END_REF][START_REF] Baumberger | Solid friction from stick-slip down to pinning and aging[END_REF][START_REF] Tekaya | Influence de la dimensionnalité et de la complexité d'un réseau sous compression mécanique sur les transports électrique et thermique dans les milieux granulaires métalliques -De l'interface individuelle aux propriétés collectives[END_REF][START_REF] Tekaya | Electron tunneling in metallic beads systems and slow electric relaxation[END_REF]).

[180s to 210s]: an increasing current is applied from 0 to 1.5A. [210s to 240s]: the current decreases from 1.5A to 0.25A. [240s to 300s]: the current is maintained to its probing value 0.25A. [300s to contact break-up] shear and voltage measurements begin.

The increasing/decreasing current permits to ensure the creation of contact spots, to discard thermal influences, to break a possible oxide layer, and mainly to discard Branly effect [START_REF] Tekaya | Influence de la dimensionnalité et de la complexité d'un réseau sous compression mécanique sur les transports électrique et thermique dans les milieux granulaires métalliques -De l'interface individuelle aux propriétés collectives[END_REF][START_REF] Tekaya | Electron tunneling in metallic beads systems and slow electric relaxation[END_REF][START_REF] Tekaya | Influence of surface topology on the electrical response of many bead assemblies[END_REF]. This last effect, actually not well understood, consists mainly of a transition to a more conductive state usually related to micro-contacts nucleation. This phenomenon, mainly observed in granular media, is also observed in contact interfaces when a DC current is directly applied, leading to a significant drop of the electrical resistance by several orders of magnitude.

To ensure a good statistics of measurements, we repeat each measurement at least five times, keeping carefully the same experimental conditions. Also, to ensure the nonappearance of an oxide layer, all measurements were done one after the other and less than five minutes after polishing and cleaning the samples.

RESULTS

For different normal loads , we determine the evolution of the interface resistance vs. shear stress ( was directly get from the voltage divided by the applied constant current value). In all experiments the interface resistance, first increases with increasing shear to reach a maximum and then decreases until the contact breaks. Figure 5 focuses on the resistance evolution of a contact undergoing a normal load around 1N and highlights the gap ∆ of resistance between the initial value (at = 0) and the maximum reached one (∆ = -).

The existence of this gap, being reproducible, raises questions about the mechanical behavior of the contact interface. Thus, to compare each measurement, we plotted the evolution of ⁄ vs. ⁄ (= ) on the figure 6. In each case, the maximum is reached at a value close to the half of the static friction coefficient (µs ≈ 0.38), which is determined from the linear fitting on the figure 7.

The normal load has a clear effect on the top of the maximum in each measurement. To highlight its behavior we plot on figure 8 the evolution of ∆ ⁄ vs. . If we exclude the first point, we can fit the data by a power law "y = ax b " where a = 1.339 and b = -1.984. The curve "y = 4/(3x 2 )" has been added to estimate the proximity of the fit. This result leads to conclude that the normal load gradually erases the observed bump from the increment of the interface resistance by following a behavior close to the one from equation 01.

∆ ≈ 4 3 • 1 (eq. 01)
The decrement of the interface resistance seems to be also influenced by the normal load: the strongest the normal load, the faster the resistance decreases. If some curves remain smooth enough to be fitted, others presents breaks -i.e. signatures of micro-displacements -making uneasy the study of this part of the behavior.

From the Holm's model describing the contact resistance (eq. 02), and assuming that the contact is resume in one spot, we can deduce an associate circular area, of radius , for this one (eq. 03). Note that designates the resistivity of the considered material. = 2 (eq. 02)

= = 2 ! (eq. 03)
Using the same reasoning as for the resistance, we computed from eq. 03 the estimated values of ∆ ⁄ and then plotted those vs. on figure 9. For 1.5N of normal load, the gap between the initial assumed contact area and the minimum reached is about a drop of 60%. It would mean that a half of the initial contact area is lost by the shear effect.

DISCUSSION

In [START_REF] Eisner | The effect of a tangential force on the contact of metallic bodies[END_REF] the study of a steel interface was made under a normal load of 920 g wt (~10N) which is much bigger than the normal load we use. Their interpretation of the increasing conductance lies in the break of an oxide layer even if it have sense for normal load of around 10N, it does not explains why and how the conductance decreases before it increases for lower normal loads. A comparison between the results from [START_REF] Eisner | The effect of a tangential force on the contact of metallic bodies[END_REF] (fig. 10) and the present work (fig. 11) can possibly give a first element of answer. In both cases, the evolution of the static friction coefficient with the conductance is represented. The shape of our results is much closer to the shape of the results of the lubricated interface from [START_REF] Eisner | The effect of a tangential force on the contact of metallic bodies[END_REF]. Thus, the lubricant seems to emphasize an already present phenomenon which seems to not be fully related to an oxide layer break.

At the onset of slipping, old micro-junctions are replaced by smaller new ones [START_REF] Rabinowicz | The Nature of the Static and Kinetic Coefficients of Friction[END_REF]: slip inception is accompanied by a drop of real contact area [START_REF] Dieterich | Direct observation of frictional contacts: New insights for statedependent properties[END_REF][START_REF] Ben-David | Slip-stick and the evolution of frictional strength[END_REF][START_REF] Prevost | Probing the micromechanics of a multi-contact interface at the onset of frictional sliding[END_REF][START_REF] Sahli | Evolution of real contact area under shear and the value of static friction of soft materials[END_REF]. This effect is often considered to be the origin of the difference between static and dynamic friction forces [START_REF] Baumberger | Solid friction from stick-slip down to pinning and aging[END_REF]. For an elastomer, i.e. an elastic medium, the contact interface decreases with the shear stress due to the narrowing of the contact spots area [START_REF] Prevost | Probing the micromechanics of a multi-contact interface at the onset of frictional sliding[END_REF][START_REF] Sahli | Evolution of real contact area under shear and the value of static friction of soft materials[END_REF][START_REF] Sahli | Shear-Induced Anisotropy in Rough Elastomer Contact[END_REF][START_REF] Papangelo | Shear-induced contact area anisotropy explained by a fracture mechanics model[END_REF][START_REF] Mergel | Continuum contact models for coupled adhesion and friction[END_REF]. In the case of the present study, the interpretation of the increasing interface conductance just as an increasing of the contact area vs. shear stress goes against those previous assertions. Metals are mainly plastic media (and it is clearly showed in [START_REF] Eisner | The effect of a tangential force on the contact of metallic bodies[END_REF]) but they still have an elastic behavior for weak shear stresses. This is why for a weak shear stress the mechanical behavior of the interface can be more complex than it is. Thus, our interpretation is summarized as follow: first the contact spots react elastically to the shear stress and their area decreases ( increases), then the contact spots begin to react plastically and their area increases ( decreases). During the shearing of the interface, some contact spots break but the interface area continues to evolve until the shear stress is strong enough to surpass the adhesion force between the contact spots. The normal load assists the deformation of the contact spots, accessing them more rapidly to a plastic behavior. This explains why the measured electrical resistance gap ∆ decreases with the normal load . In the lubricated case of [START_REF] Eisner | The effect of a tangential force on the contact of metallic bodies[END_REF] the lubricant, which fills the porosities due to the roughness, creates a thickness which reduces the interpenetration of opposite surfaces, and so reduces the contact area. The lubricant acts against the normal load and so, the behavior of the interface looks like the behavior for weak normal load.

The evolution of ∆ (or ∆ ) with were well fitted as for the exception of the first point. This point is excluded to find the best fit for a maximum of data points. The relevance of its exclusion remains in coherence with the current models about the effect of the normal load [START_REF] Greenwood | Contact of nominally flat surfaces[END_REF]. However, between 1N and 1.5N, it seems that the gap is able to increase due to a complex coupling between normal and tangential stresses occurring in the contact. A future experimental campaign for weak normal loads would give answers about this hypothesis.

CONCLUSIONS

As prove a series of experimental peer-reviewed studies over recent decades, contact properties of multi-contact interfaces are not fully understood especially for shear stress responses. For instance, smooth metallic sphere/plane contact typically grow as shear stress increases [START_REF] Bowden | The Friction and Lubrication of Solids[END_REF][START_REF] Tekaya | Electron tunneling in metallic beads systems and slow electric relaxation[END_REF][START_REF] Brizmer | A model for junction growth of a spherical contact under full stick condition[END_REF], unlike in smooth elastomer-based sphere/plan contact [START_REF] Sahli | Evolution of real contact area under shear and the value of static friction of soft materials[END_REF][START_REF] Degrandi-Contraires | Sliding friction at soft micropatterned elastomer interfaces[END_REF][START_REF] Savkoor | The effect of tangential force on the contact of elastic solids in adhesion[END_REF][START_REF] Varenberg | Shearing of fibrillar adhesive microstructure: Friction and shearrelated changes in pull-off force[END_REF][START_REF] Waters | Mode-mixity-dependent adhesive contact of a sphere on a plane surface[END_REF] where it decreases. It is therefore relevant to assume from our results that the evolution of the contact area with shear is more complex than it appears in the previous cited situations.

In the present study we highlighted a particular behavior of the mechanical response of the interface to shear stress using an electrical probing. This method has proved its effectiveness through some patents [START_REF] Bourny | Monitoring the quality of a Communication channel supported by a sliding contact[END_REF][START_REF] Puille | Surveillance de l'état d'un dispositive de garniture mécanique[END_REF][START_REF] Bourny | Surveillance de l'état d'un dispositif de roulement[END_REF] and showed its ability to monitor the contact interface. Thus, we showed through its electrical response, the mechanical evolution of a metallic rough interface. This evolution follows a non-monotonic behavior and seems to show the distinction between two deformation regimes. Such a behavior would directly affect the understanding of the mechanical properties of contacting rough interface, the way we use current contact and friction models, and the physical meaning of the parameters of some friction law.

Note that we used only a DC current to probe the interface. So, because of the complexity of the physical situation, extend investigations based on the impedance response, i.e. impedance spectroscopy, would be an important step for a better understanding of the contact area evolution.

FIGURES Fig. 1 .

 1 FIGURES

Fig. 2 .

 2 Fig.2. Current distribution into the contacting cylinders (I=250mA, unit in A/m²).

Fig. 3a .

 3a Fig.3a. Global shape of contact surface.

Fig3b.

  Fig3b. Map of a part of contact surface.

Fig. 4 .

 4 Fig.4. Chemical analysis of contact surface.

Fig. 5 .Fig. 6 .

 56 Fig.5. Evolution of the interface resistance versus the applied shear under a normal load around 1N.

Fig. 7 .Fig. 8 .

 78 Fig.7. Linear fitting of the critical value of shear (contact breaking) versus the applied normal load. The static friction coefficient is estimated around 0.38.

Fig. 9 .

 9 Fig.9. Evolution of ∆ ⁄ versus the normal load.

Fig. 10 .

 10 Fig.10. Friction coefficient vs. contact conductance from [21]: ○ dry contact, • lubricated contact.

Fig. 11 .

 11 Fig.11. Friction coefficient vs. normalized contact conductance, for different normal loads. The value of ∆# # ⁄ is directly deduced from ∆ ⁄ since # = 1 ⁄ .

ACKNOWLEDGMENTS

Thanks a lot to the Physics Department at the University of Picardie Jules Verne. Thanks to Clément Puille from the LPMC for the map gotten by the DektakXT Stylus Profiler. Thanks to Arash Jamali from the electron microscopy platform "Hub de l'énergie" for the EDX analysis. Thanks to Julien Scheibert from the LTDS for discussions. Thanks to Tania B. Garcia Ramos from the LPMC for her time on the English corrections.


Nicole Beddelem

Stéphanie Bruyere

Franck Cleymand

Sebastien Diliberto

Christophe Longeaud

Sylvain Le Gall

Roselyne Templier

Patrice Miska

Bérangère Hyot
email: berangere.hyot@cea.fr

Stéphanie Bruyère

Sébastien Diliberto

Structural and functional properties of Zn(Ge,Sn)N2 thin films deposited by reactive sputtering

Keywords: Zinc tin germanium nitride alloys, Sputtering, Optical bandgaps, Tunable optical bandgap, Optoelectronic applications

Introduction

InGaN-based semiconductor materials are used in current commercial colored blue and green Light Emitting Diodes (LEDs) [START_REF] Crawford | LEDs for Solid-State Lighting: Performance Challenges and Recent Advances[END_REF]. The In content in the InGaN alloys enables tuning the band gap energy (Eg) within the range set by the two binary compounds InN (Eg=0.69 eV) and GaN (Eg=3.51 eV) and achieving the desired emission wavelength. Hence, InGaN alloys provide a class of semiconductors whose bandgap can, in principle, span the entire visible spectrum and beyond. However, the large lattice mismatch between InN and GaN results in phase segregation and the synthesis of homogeneous high quality crystals with more than 20% Indium [START_REF] Duxbury | Indium segregation in InGaN quantum-well structures[END_REF][START_REF] Liliental-Weber | Compositional modulation in InxGa1-xN: TEM and X-ray studies[END_REF] to produce an emission in the red range of the color 2 spectrum is not straightforward. Numerous works to achieve efficient red LEDs based on InGaN alloys are still ongoing. This bottleneck motivates the search for alternatives to current III-nitride semiconductors for optoelectronics applications.

The Zn-IV-N2 compounds (where IV=Ge, Sn) closely related to the III-N compounds have similar electronics and optical properties to InGaN, as for example direct bandgaps and large optical absorption coefficients [START_REF] Lahourcade | Structural and optoelectronic characterization of RF sputtered ZnSnN2[END_REF][START_REF] Punya | Quasiparticle band structure of Zn-IV-N2 compounds[END_REF]. Those alloys appear to be analogous to III-N compounds with the group III elements (In or Ga) replaced by a combination of group II element (Zn) and a group IV element (Sn or Ge). Calculations [START_REF] Punya | Electronic and lattice dynamical properties of II-IV-N2 semiconductors[END_REF][START_REF] Limpijumnong | Electronic Structure and Optical Properties of ZnGeN2[END_REF][START_REF] Punya | Band offsets between ZnGeN2, GaN, ZnO, and ZnSnN2 and their potential impact for solar cells[END_REF] performed using density functional theory for the ZnSnxGe1-xN2 alloys have predicted that the band gaps span the range 1.4-3.1 eV which includes the full visible spectrum. Recently, the concept of type II ZnGe(Sn)N2/InGaN quantum well LEDs design [START_REF] Han | Designs of blue and green light-emitting diodes based on type-II InGaN-ZnGeN2 quantum wells[END_REF][START_REF] Rolles | New Architecture of ZnGeN2/In0.16Ga0.84N Type-II Quantum Well-Based Green Emitting LED[END_REF][START_REF] Rolles | Design of Efficient Type-II ZnGeN2/In0.16Ga0.84N Quantum Well-Based Red LEDs[END_REF][START_REF] Gorai | Red light emitting diodes based on the type-II InGaN-ZnSnN2/GaN quantum wells[END_REF] was proposed and revealed that the red emission can be reached with low In content (less than 20%) with an increased radiative recombination rate (better quantum efficiency) compared to the classical type I In-rich (35% In) InGaN quantum wells needed to reach the red emission [START_REF] Hwang | Development of InGaN-based red LED grown on (0001) polar surface[END_REF].

We describe here the preparation of ZnSnxGe1-xN2 thin films grown by reactive co-sputtering and report on their structural and optoelectronic properties. Sputtering is a technique used in research and industry to grow thin films offering a wide range of possibilities concerning the choice of the material to be deposited and the experimental conditions. Co-sputtering enables the growth of alloys from separate targets and the presence of a reactive gas such as nitrogen in the sputtering chamber makes it possible to grow nitrides. It is therefore a good technique to start the study of a rather unexplored material system such as ZnSnxGe1-xN2.

Experimental methods

Thin film samples are deposited by reactive co-sputtering at a base pressure of 10 -6 Pa (10 -8 mbar) from separate Zn, Sn, and Ge targets. Each target is 99.99+% pure and the sputtering gas is 99.9999% pure nitrogen. A nitrogen flow of 30 sccm is used with a constant pressure of 1.3 Pa controlled by a gate regulation valve. The Ge target is connected to a Radio Frequency (RF) source and the Zn and Sn ones to a Direct Current (DC) source. The cathodes are confocal with a target to substrate distance of approximately 10.5 cm. The substrate-holder is a rotating inconel molyblock on which the substrates are fixed and heated at 200°C. The growth time is 45 min. By varying DC currents and RF power for each growth, films whose colors range from pale orange to dark brown are synthesized. The richest Sn samples appear metallic. Four types of substrates (glass, silicon, sapphire and GaN template substrates) are used for the subsequent analysis depending on the constraints of each characterization method. No thermal treatment or chemical etching is performed on the substrates. Under the growth conditions used, it can be safely assumed that the nature of the substrates has little influence on the thin film growth regime. The analyzes performed on the different substrates can be reasonably compared.

The sample compositions determined by energy-dispersive X-ray spectroscopy (EDX) analysis are reported in Table 1 and Fig. 1. A quanta 600 scanning electron microscope (SEM) from FEI with a 100 mm 2 AXS detector from Bruker are used for the EDX analyzes. P/B-ZAF method is used to quantify the elements Zn, Ge, Sn and nitrogen at 10 kV and 20 kV at different places on the samples. An average is carried out on the two energies and at the different places. The zinc concentration is indeed 50 at% for all the samples and we see a linear variation of the Sn and Ge concentration from 0 to 50 at%. The whole range of composition of the alloy from x=0 to x=1 N2 alloy is obtained.

Zn (A)

Sn (A) Ge (W) For cross-sectional observations of the structure of the samples, a HITACHI S-5500 SEM is used. Atomic force microscopy (AFM) measurements are made on a D3100 equipment from Bruker in TappingMode TM mode with a RTESPA-150 tip. The crystallinity of the samples is analyzed by X-ray diffraction (XRD) in Bragg-Brentano configuration (θ-2θ scans). X-ray analyses are done on a D8 Advance diffractometer from Bruker with Cu Kα radiation (λ = 1.5406 Å). Transmission electron microscopy (TEM) observations are done on a ARM200 microscope from Jeol. The cross-section TEM sample preparation is made by focused ion beam (FIB) in a Helio Nanolab 600i SEM FIB from FEI. Before introduction into the FIB, sample is metallized with carbon. A Pt strip (first using electron beam then followed by ion beam) is then deposited to protect the sample before starting the milling (with Ga + ions) of the trench. The final sample is about 3 µm long for less than 100 nm thick. Fourier transform infrared spectroscopy (FTIR) and Raman spectroscopy methods allow to study the interatomic vibrations and the different types of bonds. FTIR spectra are acquired from 60 to 4000 cm -1 on a Nicolet TM 8700 FT-IR from Thermo Scientific under nitrogen flux. From 30-600 cm -1 the transmission spectra are acquired with a Globar source, a "Solid Substrate" type beam splitter and a DTGS-PE detector. From 400-4000 cm -1 , the transmission spectra are acquired with a Globar source, a KBr beam splitter and a DTGS-KBr detector (cooled with liquid nitrogen). The acquired spectra are then superimposed on the common range (400-600 cm -1 ) in order to obtain a continuous spectrum from 60 to 4000 cm -1 . Raman spectroscopy is made on a Labram HR spectrometer from HORIBA Jobin Yvon.

The source is a 532 nm laser, the focal length is 80 cm, the diffraction grating is 1800 or 1200 gr/µm and the CCD detector is cooled with liquid nitrogen. UV-Vis-NIR spectroscopy is used to probe the optical properties of the alloys. The measurements are made on a UV-Vis-NIR spectrophotometer, Cary7000 from Agilent. Electrical measurements are made on a K617 from Keithley with a two-point probe. A voltage of 100 V is applied between two coplanar electrodes (in silver paste) separated by 1 mm. The length of the electrodes is 7 mm. The sample is placed on the cold finger of a cryostat that can cover the temperature range 100-450K.

Results and discussion

SEM cross-sectional images (Fig. 2) give a view on the growth structure that appears columnar whatever the concentration of tin. The typical widths of the columns are of the order of 100 nm but the surface morphology of the Ge-rich columns appears to be more faceted than the Sn-rich ones, which exhibit softer domes. Different roughness parameters determined by AFM measurements on ZnGeN2 and ZnSnN2 films confirm these observations (Table 2). The average roughness (Ra) and the root mean squared roughness (Rq) values are clearly lower for ZnSnN2 and the values of opposite sign for the skewness parameter (Sk) which characterizes the heights distribution asymmetry reveal a softer surface topography for ZnSnN2. The kurtosis parameter (Ek) close to 3 measured on ZnSnN2 indicates also a more rounded shape for the ZnSnN2 domes. As it will be discussed below, the XRD patterns show that the ZnGeN2 layer is polycrystalline without preferred crystalline orientation whereas ZnSnN2 crystallizes with the preferential [001] out of plane orientation.

The combination of all these elements (SEM, AFM, XRD) tends to show that the deposit regime for ZnGeN2 is situated between Zone Ic and Zone T (Fig. 3) according to the structure zone model described by Mahieu et al. [START_REF] Mahieu | Biaxial alignment in sputter deposited thin films[END_REF]. For ZnSnN2 the growth structure appears rather located in Zone II revealing a higher relative temperature T* (described as the ratio between the substrate temperature Ts and the melting point of the material Tm). However all the films are deposited at the same substrate temperature which means that the melting point of ZnSnN2 should be much lower than that of ZnGeN2. In addition, theoretical calculations predict a lower formation energy for ZnSnN2 than for ZnGeN2 [START_REF] Lambrecht | Heterovalent ternary II-IV-N2 compounds: perspectives for a new class of wide-band-gap nitrides[END_REF][START_REF] Paudel | First-principles study of phonons and related ground-state properties and spectra in Zn-IV-N2 compounds[END_REF] which means that the crystalline growth synthesis of ZnSnN2 is energetically less expensive than that of ZnGeN2. This is in agreement with our observations shown above. Films seem to crystallize according to a hexagonal structure [START_REF] Lahourcade | Structural and optoelectronic characterization of RF sputtered ZnSnN2[END_REF]. The three peaks (100), ( 002) and (101) around 2θ=35° are characteristic of this structure. ZnSnN2 films appear to be better crystallized than ZnGeN2 films with more intense peaks. We observe also in Fig. 4b a linear dependence in peak positions with the Sn content of the films, in agreement with Vegard's law. The deduced lattice parameters are reported in Table 3. The linear shift in Sn content indicates an apparent lack of phase separation in the material. We also observe in an evolution of the preferred crystalline orientation with Sn concentration; ZnSnN2 shows a strong crystalline orientation along the c axis (presence of (002) and (004) reflections) whereas several crystalline orientations appear in ZnGeN2. To quantify the degree of preferential crystalline orientation, the texture coefficient of Harris (TC) [START_REF] Manzano | Thermoelectric properties of Bi2Te3 films by constant and pulsed electrodeposition[END_REF] is calculated and reported in Fig. 5a. [001] is indeed the preferential orientation in Sn-rich samples whereas Ge-rich samples don't seem to crystallize into a peculiar orientation. A second series of samples was fabricated exactly with the same growth conditions (Fig. 5b). Again Sn-rich films exhibit a strong preferred orientation along the [001] direction. But Ge-rich samples appear to crystallize differently from the first series. These observations are in agreement with the structure zones identified above. In the Ic-T Zone, for ZnGeN2 growth, atoms merely have the needed energy to nucleate crystalline seeds. The energy supply is not enough to allow atomic diffusion from seed to seed and each grain grows along its own and initial crystalline orientation. Crystalline orientations of the Ge-rich samples appear to be random from one sample to another. With Sn incorporation, the structure zone is moving towards Zone II where atoms can diffuse from one grain to another to recrystallize the layer. The thin layer tends towards its most stable thermodynamic state with a preferential out of plane orientation, the c axis ([001] direction in our case). Mössbauer spectroscopy is a powerful tool to obtain information about the chemical environment of tin atoms [START_REF] Alnjiman | Chemical environment and functional properties of highly crystalline ZnSnN2 thin films deposited by reactive sputtering at room temperature[END_REF]. The Mössbauer spectra of three samples of ZnSnxGe1-xN2 (with x=0.2, x=0.7 and x=1) recorded at 300 K are depicted in Fig. 7. The experimental curves are fitted with a single doublet and the values of the corresponding isomeric shift (IS) and quadripolar splitting (QS) are reported in Table 4. An IS of 1.06 mm/s is characteristic of Sn 4+ ions in tetrahedral configuration. So, whatever the composition of the alloy, the tin appears to be located in a single crystallographic site. The decreasing value of QS with Sn content could mean a reduction in the deformation of the tetrahedrons in agreement with a better crystallinity of the Sn-rich samples with more regular and less distorted crystalline cells. These observations tend to confirm the tendency of a homogeneous nature of Zn(Ge,Sn)N2 alloying. FTIR spectra acquired on the samples deposited on silicon substrates are reported in Fig. 8a. For all x values of ZnSnxGe1-xN2, they are fitted using five Gaussians to identify the vibration modes. An evolution of the FTIR peak positions as a function of the composition is visible in Fig. 8b. Only few studies [START_REF] Shang | ZnGeN2 and ZnGeN2:Mn 2+ phosphors: hydrothermal-ammonolysis synthesis, structure and luminescence properties[END_REF][START_REF] Beddelem | Study of amorphous Zinc Germanium Nitride thin films grown by reactive co-sputtering[END_REF] report on the clear analysis of FTIR peaks of ZnGeN2. Shang et al. [START_REF] Shang | ZnGeN2 and ZnGeN2:Mn 2+ phosphors: hydrothermal-ammonolysis synthesis, structure and luminescence properties[END_REF] reported 3 peak families. The peak at ∼ 750 cm -1 can be attributed to Ge-N bonds [START_REF] Zanatta | Nitrogen in the amorphous-germanium network: From high dilution to the alloy phase[END_REF]. In the case of ZnSnxGe1-xN2 alloy, the progressive shift of this vibration mode towards small wavenumbers with increasing Sn content (∼ 650 cm -1 for ZnSnN2) could be the signature of the substitution of Ge atoms by heavier Sn atoms and the formation of the Sn-N bonds in the alloy. The peaks in the far IR show the same evolution, from 280 cm -1 to 200 cm -1 , and could also be attributed to a Ge-N bond evolving towards a Sn-N bond. The less pronounced evolution (< 50 cm -1 ) of the vibration mode at ∼ 600 cm -1 seems consistent with the hypothesis of a Zn-N-Ge bond [START_REF] Paudel | First-principles study of phonons and related ground-state properties and spectra in Zn-IV-N2 compounds[END_REF] changing to Zn-N-Sn bond during the formation of the quaternary alloy. Finally, the peak at ∼ 500 cm -1 attributed to Zn-N [START_REF] Nazir | Synthesis and characterization of zinc and cadmium complexes with deoxyalliin[END_REF] bond shouldn't change in position in the ZnSnxGe1-xN2 material. But it also appears to shift slightly towards smaller wavenumbers with increasing Sn content. In presence of tin, it can be assumed that the different chemical environment can cause a progressive shift of the Zn-N vibration mode. Raman spectroscopy on the different alloys tends to support this behavior as displayed on Fig. 9. The optical modes shift towards the low frequencies when heavier Sn atoms are substituted to Ge in the alloy. This is consistent with previous FTIR measurements. The Raman peaks don't appear well defined.

The sputtered alloys rather have the signature of a phonon-glass-like revealing densities of state widen by defects and disorder. The phonon densities of state calculated by Paudel et al. [START_REF] Paudel | First-principles study of phonons and related ground-state properties and spectra in Zn-IV-N2 compounds[END_REF] for ZnGeN2 and ZnSnN2 crystals are reported in Fig. 10 (a andd). To compare with experimental data, Lambrecht et al. [START_REF] Lambrecht | Structure and phonons of ZnGeN2[END_REF] simulate the Raman spectra by convoluting the spectra with a Gaussian broadening (Fig. 10b ande). The spectra consist of three main regions, a region which is basically a folding of the acoustic branch (between 130 and 340 cm -1 for ZnGeN2 and between 100 and 280 cm -1 for ZnSnN2), a lower optical branch, called the transverse optic region (between 470 and 700 cm -1 for ZnGeN2 and between 430 and 640 cm -1 for ZnSnN2) and an upper optical branch we are tempted to call longitudinal optic region (between 760 and 860 cm -1 for ZnGeN2 and between 660 and 750 cm -1 for ZnSnN2). The low frequency region contains two peaks which can be correlated with the corresponding experimental peaks at about 130 cm -1 and 275 cm -1 for ZnGeN2 (respectively 100 cm -1 and 230 cm -1 for ZnSnN2). According to Lambrecht et al. [START_REF] Lambrecht | Structure and phonons of ZnGeN2[END_REF], the second experimental peak appears higher in intensity in part because there is a strong overlap with the second harmonics of the first peaks. Our experimental spectra for ZnGeN2 and ZnSnN2 are reported for comparison once again in Fig. 10 (c andf). The next broad region shows three peaks in the theory for ZnGeN2, 480, 560 and 660 cm -1 . In the experiment, one sees a broader spectrum with very little pronounced modes at 465, 540, 650 cm -1 . However for ZnSnN2, the two predicted peaks at 470 and 590 cm -1 can be easily correlated to the two experimental peaks observed in the 400-600 cm -1 region. Finally, at higher frequency we find a peak at about 780 cm -1 for ZnGeN2 while the experiment shows a peak at 800 cm -1 . For ZnSnN2, the theoretical peak is predicted to be at 700 cm -1 while the experimental spectrum shows a peak at 655 cm -1 . Given the complexity of the spectra and the difficulty in identifying the modes in our polycrystalline samples, the agreement between experiment and theory is rather satisfactory. The Raman spectrum of ZnSnN2 shows better resolved optical modes than ZnGeN2 revealing a better crystal quality of the samples, which is consistent with the previous XRD measurements. Fig. 11a shows the dependence of the resistivity measured on the ZnSnxGe1-xN2 samples deposited on glass substrates and measured at 120, 300 and 420K using a two-point probe. ZnGeN2 sample exhibits a resistivity of 2.10 9 Ω.cm (at 300 K) while ZnSnN2 sample shows a resistivity of several order of magnitude lower (30 Ω.cm). Thus, an increase in the Sn content produces a strong decrease in the resistivity of the ZnSnxGe1-xN2 alloys. Ge-rich ZnSnxGe1-xN2 samples (0 ≤ x ≤ 0.5) exhibit a typical semiconducting behavior with an almost exponential increase in resistivity as temperature decreases.

Typically, the resistivity of ZnGeN2 varies on several orders of magnitude, between 7.10 5 Ω.cm and 4.10 10 Ω.cm when temperature decreases from 400 to 120 K. This behavior is consistent with the insulating character previously reported for sputtered ZnGeN2 films [START_REF] Misaki | Epitaxial growth and characterization of ZnGeN2 by metalorganic vapor phase epitaxy[END_REF]. On the contrary, ZnSnN2 shows a rather "metallic" behavior; its resistivity barely changes with temperature (but shows a slight and linear increase as the temperature decreases) and is of the order of 30 Ω.cm. The strong decrease in resistivity with increased Sn concentration can be attributed to a decrease in the band gap (as discussed in the next paragraph) and to an increase in the number of thermally activated carriers in the conduction band of the alloys. Furthermore, the substitution of Ge by Sn may increase the number of electrons available for conduction because Sn is less electronegative than Ge and hence Sn is a better electron donor than Ge. The presence of small grains (less than 100 nm), grain boundaries and defects in sputtered samples likely dominates the mobility term. And thus the resistivity of the samples reflects the carrier concentrations in the films. Other groups report the resistivity values of sputtered ZnSnxGe1-xN2 alloys [START_REF] Shing | Semiconducting ZnSnxGe1-xN2 alloys prepared by reactive radio-frequency sputtering[END_REF]. They observe the same tendencies with Sn content and temperature but measure different absolute values for resistivity. For example, samples prepared by Shing et al. [START_REF] Shing | Semiconducting ZnSnxGe1-xN2 alloys prepared by reactive radio-frequency sputtering[END_REF] with the same Sn concentration show a much lower resistivity than ours (for example, for x=0.4, we measure a resistivity of 10 3 Ω.cm and Shing et al. report a resistivity of about 10 Ω.cm). Alnjiman et al. [START_REF] Alnjiman | Chemical environment and functional properties of highly crystalline ZnSnN2 thin films deposited by reactive sputtering at room temperature[END_REF] report values of 0.23 Ω.cm for highly crystallized ZnSnN2 samples and Fioretti et al. [START_REF] Fioretti | Combinatorial insights into doping control and transport properties of zinc tin nitride[END_REF] obtain a resistivity in the 0.03 and 50 Ω.cm range. These differences in resistivity appear to be strongly dependent on the sputtering conditions used. The final composition, microstructure of the samples and their crystal quality are undoubtedly key factors.

Arrhenius plots (log of resistivity versus inverse temperature) were plotted for the samples (not shown here). For 0 ≤ x ≤ 0.7, the slopes of the linearly fitted data yielded activation energies Ea for the carriers. According to the discussion above and according to Hall measurements described in literature, it seems reasonable to think that ZnSnxGe1-xN2 alloys are intrinsically n-doped materials [START_REF] Lahourcade | Structural and optoelectronic characterization of RF sputtered ZnSnN2[END_REF][START_REF] Alnjiman | Chemical environment and functional properties of highly crystalline ZnSnN2 thin films deposited by reactive sputtering at room temperature[END_REF][START_REF] Fioretti | Combinatorial insights into doping control and transport properties of zinc tin nitride[END_REF][START_REF] Qin | Semiconducting ZnSnN2 thin films for Si/ZnSnN2 p-n junctions[END_REF]. Hence, Ea corresponds to the difference in energy between the Fermi level and the bottom of the conduction band. The evolution of Ea is shown in Fig. 11b. Ea decreases for increasing x values until it becomes difficult to determine above x = 0.7 because the resistivity of tin-rich samples decreases very rapidly.

A low Ea means that the majority charge carriers (electrons in our case) fill states very close of the conduction band. The decrease in activation energy as the Sn content increases agrees with the higher conductivity observed for the Sn-rich samples, consistent with a reduced activation energy required for thermal excitation of carriers into the conduction band.

UV-Vis-NIR transmittance and reflectance measurements were used to probe the optical properties of the alloys. In the visible part of the spectrum, the incorporation of Sn in the alloy induces a red shift in the transmission onset compared to ZnGeN2 thin films (Fig. 12a). As it will be discussed in the next paragraph, this behavior is related to a shift in absorption into the red region with bandgap energies smaller for Sn-rich alloys compared to Ge-rich alloys. A focus in the IR region (λ>1000 nm) shows that the sum of the transmittance and reflectance measurements is close to 100% for the Ge-rich samples (Fig. 12b). So there is no absorption below the bandgap of the alloy. But for Sn-rich samples, T+R is less than 100%, revealing a strong absorption phenomenon below the gap (at λ ∼ 2250 nm for ZnSnN2). This absorption may be due to the presence of free carriers in Sn rich samples (as discussed above) and give rise to plasmon resonance effects. From equation 1 describing the plasmon frequency [START_REF] Jullien | Influence of the nanoscale structural features on the properties and electronic structure of Al-doped ZnO thin films: an X-ray absorption study[END_REF]:

λ p 2πc ε 0 m* Ne 2 1/2 (1)
where N is the free carrier density and m* the free carrier effective mass, ε0 the vacuum permittivity, c the speed of light, we can determine the corresponding value of the free carrier density for ZnSnN2. An electron concentration N in the 3.10 19 -2.10 20 cm -3 range is obtained (for 0.15me<m*<1me where me is the mass of the free electron and 0.15me is the calculated effective mass for electrons in ZnSnN2 [START_REF] Punya | Quasiparticle band structure of Zn-IV-N2 compounds[END_REF]).

These values are consistent with the ones determined by Hall Effect measurements on sputtered ZnSnN2) [START_REF] Lahourcade | Structural and optoelectronic characterization of RF sputtered ZnSnN2[END_REF][START_REF] Alnjiman | Chemical environment and functional properties of highly crystalline ZnSnN2 thin films deposited by reactive sputtering at room temperature[END_REF][START_REF] Fioretti | Combinatorial insights into doping control and transport properties of zinc tin nitride[END_REF]. The fitted gaps are 2.12 eV for ZnSnN2 and 3.04 eV for ZnGeN2. But the rather soft Tauc plots allow only a subjective determination of the gaps with uncertainties expressed by the error bars in Fig. 13. Despite these uncertainties in the exact values of the gaps, it is safe to say that the gap is around 2.0 eV for ZnSnN2 and that of ZnGeN2 is around 3.1 eV. These values are close to those measured by other groups for sputtered films, around 2 eV for ZnSnN2 [START_REF] Lahourcade | Structural and optoelectronic characterization of RF sputtered ZnSnN2[END_REF][START_REF] Alnjiman | Chemical environment and functional properties of highly crystalline ZnSnN2 thin films deposited by reactive sputtering at room temperature[END_REF][START_REF] Narang | Bandgap tunability in Zn(Sn,Ge)N(2) semiconductor alloys[END_REF] and around 3.1 eV for ZnGeN2 [START_REF] Kikkawa | RF-sputter deposition of Zn-Ge nitride thin films[END_REF]. Fig. 13 shows the change in optical band gap as a function of composition, with the band gap ranging from 2 to 3 eV and thereby allowing access to the entire bandgaps between ZnSnN2 and ZnGeN2. To investigate the band gap bowing of the ZnSnxGe1-xN2 alloy, the determination of the optical gap E04 [START_REF] Stenzel | Oxide Coatings: Porous and Dense Films[END_REF], corresponding to α=10 -4 cm -1 is more robust and its variation as a function of the composition x is shown in Fig.

Conclusions

In this work, we have presented a structural, electrical and optical investigation of the ZnSnxGe1-xN2 for 0 ≤ x ≤ 1 by gradually substituting germanium with tin. Films are fabricated using reactive sputtering. Compared to InGaN alloys which are difficult to synthetize as homogeneous alloys, without phase segregation, across the full range of [In]/[Ga] ratio, ZnSnxGe1-xN2 seem to form advantageously a continuous alloy for 0 ≤ x ≤ 1. The linear evolution of the lattice parameters according Vegard's law as well as the linear variation of the peak positions of the different vibration modes identified by FTIR spectroscopy indicate that the ZnSnxGe1-xN2 alloying is achievable without phase separation. Moreover, whatever Sn content in ZnSnGeN2, Mössbauer spectroscopy, evidences that tin ions are Sn 4+ ions in a single tetrahedral configuration and confirms the continuous nature of alloying. Samples exhibit semiconducting properties, including optical band gaps and decreasing in resistivities with temperature. The resistivities of ZnSnN2 are a few tenths of Ω.cm and resistivities of ZnSnxGe1-xN2 alloys increased exponentially with decreased Sn content, whereas sputtered ZnGeN2 thin film exhibited a quasi-insulating behavior. The experimental observations have also shown that the band gap in ZnSnxGe1-xN2 is tunable from 2.1 eV to 3.04 eV with a nearly linear dependence on the composition. Thus, ZnSnxGe1-xN2 materials offer a solution for bandgap tunability in nitride semiconductors, and may enable enhanced functionality such as long wavelength (green and red) light emitters and light absorbers for solar cells. To enable these future applications, additional experimental work on doping and band offset in alloys will be needed to move towards device integration where theoretical works have already suggested promising optoelectronic device architectures with tunable wavelengths. [START_REF] Narang | Bandgap tunability in Zn(Sn,Ge)N(2) semiconductor alloys[END_REF]. The green curve shows the band gap bowing for Inx Ga1-xN reported by Wu et al. [START_REF] Wu | Small band gap bowing in In1-xGaxN alloys[END_REF].

Table captions:

Table 1 : DC currents and RF power applied on each of the Zn, Sn and Ge source respectively to grow ZnSnxGe1-xN2 samples. For all samples, Zn concentration is close to 50 at% with a progressive evolution of Ge and Sn concentration. All the composition range from x=0 to x=1 of the ZnSnxGe1-xN2 alloy is obtained. Si substrates are used for EDX analysis.

Table 2 : Roughness parameters of ZnGeN2 and ZnSnN2 samples determined by AFM measurements. The presented parameters are maximum surface roughness (Rmax), average surface roughness (Ra), root mean squared surface roughness (Rq), skewness (Sk) and kurtosis (Ek).

Table 3 : Lattice parameters (a and c) of ZnSnxGe1-xN2 with a hexagonal indexing.

Fig. 1 :

 1 Fig. 1 : Composition of the samples (deposited on Si substrates) as a function of the current of the Sn cathode.

Fig. 2 : 2 :

 22 Fig. 2 : SEM images of ZnSnxGe1-xN2 samples from x=0 to x=1 (deposited on Si samples). (a) Crosssectional images. (b) Images acquired with a tilt angle of 5°. ZnGeN2 ZnSnN2 Rmax 82 nm 53.9 nm Ra 5.6 nm 4.8 nm Rq 7.15 nm 6.1 nm Sk 0.5 -0.5 Ek 4.9 3.3 Table 2 : Roughness parameters of ZnGeN2 and ZnSnN2 samples determined by AFM measurements. The presented parameters are maximum surface roughness (Rmax), average surface roughness (Ra), root mean squared surface roughness (Rq), skewness (Sk) and kurtosis (Ek).

Fig. 3 :

 3 Fig. 3 : Schematic overview of the structure zone models of sputter deposited films discussed by Mahieu et al. The figure comes from ref [14].

Fig. 4a

  Fig.4apresents XRD θ-2θ scans for ZnSnxGe1-xN2 films with various compositions grown on sapphire. Films seem to crystallize according to a hexagonal structure[START_REF] Lahourcade | Structural and optoelectronic characterization of RF sputtered ZnSnN2[END_REF]. The three peaks (100), (002) and (101) around 2θ=35° are characteristic of this structure. ZnSnN2 films appear to be better crystallized than ZnGeN2 films with more intense peaks. We observe also in Fig.4ba linear dependence in peak positions with the Sn content of the films, in agreement with Vegard's law. The deduced lattice parameters are reported in Table3. The linear shift in Sn content indicates an apparent lack of phase separation in the material. We also observe in an evolution of the preferred crystalline orientation with Sn concentration; ZnSnN2 shows a strong crystalline orientation along the c axis (presence of (002) and (004) reflections) whereas several crystalline orientations appear in ZnGeN2. To quantify the degree of preferential crystalline orientation, the texture coefficient of Harris (TC)[START_REF] Manzano | Thermoelectric properties of Bi2Te3 films by constant and pulsed electrodeposition[END_REF] is calculated and reported in Fig.5a.[001] is indeed the preferential orientation in Sn-rich samples whereas Ge-rich samples don't seem to crystallize into a peculiar orientation. A second series of samples was fabricated exactly with the same growth conditions (Fig.5b). Again Sn-rich films exhibit a strong preferred orientation along the [001] direction. But Ge-rich samples appear to crystallize differently from the first series. These observations are in agreement with the structure zones identified above. In the Ic-T Zone, for ZnGeN2 growth, atoms merely have the needed energy to nucleate crystalline seeds. The energy supply is not enough to allow atomic diffusion from seed to seed and each grain grows along its own and initial crystalline orientation. Crystalline orientations of the Ge-rich samples appear to be random from one sample to another. With Sn incorporation, the structure zone is moving towards Zone II where atoms can diffuse from one grain to another to recrystallize the layer. The thin layer tends towards its most stable thermodynamic state with a preferential out of plane orientation, the c axis ([001] direction in our case).

Fig. 4 :

 4 Fig. 4 : (a) XRD θ-2θ scans for ZnSnxGe1-xN2 films with various compositions grown on sapphire. (b) Linear relationship between 3 peak positions ( (100), (002) and (101) reflections ) and the alloy composition. x 0 0.2 0.4 0.7 0.9 1 a (Å) 3.22 3.25 3.30 3.35 3.39 3.41 c (Å) 5.22 5.27 5.32 5.40 5.47 5.51 Table3: Lattice parameters (a and c) of ZnSnxGe1-xN2 with a hexagonal indexing.

Fig. 5 :

 5 Fig. 5 : Texture coefficient of Harris (TC) calculated for 2 series of alloys (a and b) with identical deposition parameters.Columnar grain structure, observed by SEM, was confirmed by bright-field TEM. A representative image taken from a ZnGeN2 film cross section is shown in Fig.6. The width of the columns is ranging between 50 and 80 nm on film top surface. The diffraction pattern acquired on the columnar area reveals a polycrystalline structure and matches very well the simulated diffraction pattern for a hexagonal structure with lattice parameters a=3.23 Å and c=5.25 Å. We see clearly the first three rings corresponding to (100), (002) and (101) planes, which is consistent with XRD analysis.

Fig. 6 :

 6 Fig. 6 : (a) Bright field TEM of a ZnGeN2 film cross section deposited on GaN substrate. (b) Experimental (left) and simulated (right) diffraction pattern. A hexagonal structure with lattice parameters a=3.23 Å and c=5.25 Å is considered for the simulation.

Fig. 7 : 4 :

 74 Fig. 7 : Experimental (black) and simulated (red) 119 Sn Mössbauer spectra of ZnSnxGe1-xN2 (deposited on Si substrates). x IS (mm/s) QS (mm/s) 0.2 0.7 1 1.06 1.06 1.06 0.97 0.93 0.90 Table 4 : Hyperfine parameters of ZnSnxGe1-xN2 (Isomeric Shift and Quadripolar Splitting).

Fig. 8 :

 8 Fig. 8 : (a) Plots of the FTIR measurements for ZnSnxGe1-xN2 (deposited on Si samples). (b) Evolution of the FTIR peak positions as a function of the composition.

Fig. 9 :

 9 Fig. 9 : Measured Raman spectra for ZnSnxGe1-xN2 (deposited on Si samples).

Fig. 10 :

 10 Fig. 10 : Raman spectra and calculated phonon density of states of ZnGeN2 and ZnSnN2. (a) and (d) Calculated density of states according to Paudel et al. [16] and Lambrecht et al. [23] (b) and (e) Calculated density of states: Gaussian broadened. (c) and (f) our measured Raman spectra. In agreement with previous papers [24-26], the results presented above highlight the continuous nature of ZnSnxGe1-xN2 alloying films for 0 ≤ x ≤ 1. The linear evolution of the lattice parameters according to Vegard's law, the linear variation of the position of the different chemical bonds identified by FTIR spectroscopy and the continuous evolution of the Raman modes indicate a progressive substitution of Ge by Sn without phase separation.

Fig. 11 :

 11 Fig. 11 : (a) Resistivity of ZnSnxGe1-xN2 thin films (deposited on glass) and measured at 3 temperatures (120, 300 and 420 K). (b) Activation energies corresponding to the slope of the linearly fitted part of Arrhenius plots (log of resistivity versus inverse temperature).

Fig. 12 :

 12 Fig. 12 : (a) Transmittance (T) of the ZnSnxGe1-xN2 films (deposited on sapphire substrates) in the UVvisible-SWIR range. The arrow in the visible part of the spectrum indicates the red shift in the transmittance as the Sn content increases. (b) Transmittance (T) + Reflectance (R) in the SWIR range. λp reveals a plasmon resonance in ZnSnN2 in the IR region. To investigate the optical properties of the alloys, particularly close to the absorption onset of the materials, we plot the absorption coefficient α (not shown here) deduced from UV/Vis transmittance data by the equation α = -1 / d ln (Tfilm), with d the film thickness and Tfilm ∼ Texperimental/Tsusbtrate. The absorption exhibits an obvious red shift as the Sn composition increases. For direct band gap

14 .Fig. 13 :

 1413 Fig. 13 : Dependence of the optical band gap Eg of the ZnSnxGe1-xN2 films. The inset corresponds to the Tauc plot to determine the band gap of ZnGeN2. The rather soft Tauc plots obtained on the other compositions allow only a subjective determination of the gap with uncertainties expressed by the error bars.

Fig. 14 :

 14 Fig. 14 : Bowing parameter b determined from the measured E04 bandgaps of ZnSnxGe1-xN2 (black curve). The red and blue curves correspond to the values determined experimentally and theoretically by Narang et al. [31]. The green curve shows the band gap bowing for Inx Ga1-xN reported by Wu et al. [34].

Figure captions:Fig. 1 :Fig. 2 :

 12 Figure captions: Fig. 1 : Composition of the samples (deposited on Si substrates) as a function of the current of the Sn cathode. Fig. 2 : SEM images of ZnSnxGe1-xN2 samples from x=0 to x=1 (deposited on Si samples). (a) Crosssectional images. (b) Images acquired with a tilt angle of 5°.

Fig. 3 :

 3 Fig. 3 : Schematic overview of the structure zone models of sputter deposited films discussed by Mahieu et al. The figure comes from ref [14].

Fig. 4 :Fig. 5 :

 45 Fig. 4 : (a) XRD θ-2θ scans for ZnSnxGe1-xN2 films with various compositions grown on sapphire. (b) Linear relationship between 3 peak positions ( (100), (002) and (101) reflections ) and the alloy composition.Fig. 5 : Texture coefficient of Harris (TC) calculated for 2 series of alloys (a and b) with identical deposition parameters.

Fig. 6 :

 6 Fig. 6 : (a) Bright field TEM of a ZnGeN2 film cross section deposited on GaN substrate. (b) Experimental (left) and simulated (right) diffraction pattern. A hexagonal structure with lattice parameters a=3.23 Å and c=5.25 Å is considered for the simulation.

Fig. 7 :

 7 Fig. 7 : Experimental (black) and simulated (red) 119 Sn Mössbauer spectra of ZnSnxGe1-xN2 (deposited on Si substrates).

Fig. 8 :

 8 Fig. 8 : (a) Plots of the FTIR measurements for ZnSnxGe1-xN2 (deposited on Si samples). (b) Evolution of the FTIR peak positions as a function of the composition.

Fig. 9 :

 9 Fig. 9 : Measured Raman spectra for ZnSnxGe1-xN2 (deposited on Si samples).

Fig. 10 :

 10 Fig. 10 : Raman spectra and calculated phonon density of states of ZnGeN2 and ZnSnN2. (a) and (d) Calculated density of states according to Paudel et al. [16] and Lambrecht et al. [23] (b) and (e) Calculated density of states: Gaussian broadened. (c) and (f) our measured Raman spectra.

Fig. 11 :

 11 Fig. 11 : (a) Resistivity of ZnSnxGe1-xN2 thin films (deposited on glass) and measured at 3 temperatures (120, 300 and 420 K). (b) Activation energies corresponding to the slope of the linearly fitted part of Arrhenius plots (log of resistivity versus inverse temperature).

Fig. 12 :

 12 Fig. 12 : (a) Transmittance (T) of the ZnSnxGe1-xN2 films (deposited on sapphire substrates) in the UVvisible-SWIR range. The arrow in the visible part of the spectrum indicates the red shift in the transmittance as the Sn content increases. (b) Transmittance (T) + Reflectance (R) in the SWIR range. λp reveals a plasmon resonance in ZnSnN2 in the IR region.

Fig. 13 :

 13 Fig. 13 : Dependence of the optical band gap Eg of the ZnSnxGe1-xN2 films. The inset corresponds to the Tauc plot to determine the band gap of ZnGeN2. The rather soft Tauc plots obtained on the other compositions allow only a subjective determination of the gap with uncertainties expressed by the error bars.

Fig. 14 :

 14 Fig. 14 : Bowing parameter b determined from the measured E04 bandgaps of ZnSnxGe1-xN2 (black curve). The red and blue curves correspond to the values determined experimentally and theoretically by Narang et al.[START_REF] Narang | Bandgap tunability in Zn(Sn,Ge)N(2) semiconductor alloys[END_REF]. The green curve shows the band gap bowing for Inx Ga1-xN reported by Wu et al.[START_REF] Wu | Small band gap bowing in In1-xGaxN alloys[END_REF].

Table 1 :

 1 DC currents and RF power applied on each of the Zn, Sn and Ge source respectively to grow ZnSnxGe1-xN2 samples (time growth is 45 minutes). For all samples, Zn concentration is close to 50 at% with a progressive evolution of Ge and Sn concentration. All the composition range from x=0 to x=1 of the ZnSnxGe1-xN2 alloy is obtained. Si substrates are used for EDX analysis.

	x

Thickness (nm) at% Zn at% Sn at% Ge

Table 4 :

 4 Hyperfine parameters of ZnSnxGe1-xN2 (Isomeric Shift and Quadripolar Splitting).

Acknowledgements

This work was funded by the Région Lorraine and the European Regional Development Fund.

Patrice Miska passed away in November 2018 before we finished to write this article. We have done our best with respect to his memory.