Marion Urvoy
email: murvoy@ifremer.fr

Claire Labry

Daniel Delmas

Layla Creac'h

Creac'

Microbial enzymatic assays in

Keywords: Microbial enzymatic activities, Fluorimetry, Inner Filter Effect, Biogeochemical studies

come

Introduction

Extracellular enzymes are mostly produced by heterotrophic prokaryotes that hydrolyse polymeric organic matter into units smaller than 600 Dalton, transportable across their cell membranes [START_REF] Payne | Microorganisms and nitrogen sources : transport and utilization of amino acids, peptides, proteins, and related substrates[END_REF]. Although they are the only entity capable to significantly affect both dissolved and particulate organic matter (Chrost 1990), other organisms can release extracellular enzymes as well. For instance, phytoplankton, phototrophic prokaryotes, metazoa and macroalgae are able to contribute to the pool of alkaline phosphatases [START_REF] Hoppe | Phosphatase activity in the sea[END_REF][START_REF] Niell | Phosphatase activity of benthic marine algae. An overview[END_REF][START_REF] Labry | Phytoplankton and bacterial alkaline phosphatase activities in relation to phosphate and DOP availability within the Gironde plume waters (Bay of Biscay)[END_REF].

Microbial enzymes play a major role in the ocean: they initiate the mineralization of complex organic matter through the microbial loop, transforming both dissolved and particulate organic matter into living biomass, dissolved organic carbon or carbon dioxide. The activity and specificity of extracellular enzymes therefore affect global carbon and nutrient cycling, carbon flow through aquatic food web as well as carbon export to the deep ocean [START_REF] Azam | The Ecological Role of Water-Column Microbes in the Sea[END_REF][START_REF] Azam | Microbial control of oceanic carbon flux: The plot thickens[END_REF][START_REF] Bidle | Phytoplankton-Bacteria Interactions: Ectohydrolytic Enzymes and Their Influence on Biogeochemical Cycling[END_REF]). As hydrolysis is considered the limiting step of organic matter utilization, any factors affecting enzyme activity might affect the entire mineralization pathway. As such, enzymatic assays are widespread and degradation capacity has been investigated in relation to diverse factors, such as for instance: substrate composition and size, microbial community structure or environmental conditions [START_REF] Azam | The Ecological Role of Water-Column Microbes in the Sea[END_REF][START_REF] Chróst | Microbial Ectoenzymes in Aquatic Environments[END_REF][START_REF] Kirchman | Microbial Ecology of the Oceans: Second Edition[END_REF].

Measurements of enzyme activity are typically carried out using fluorogenic molecules consisting of a substrate moiety covalently linked to a fluorophore (or fluorochrome). Non-hydrolysed substrate has a low background fluorescence, while upon hydrolysis the fluorescence spectra of the released fluorophore is considerably modified, allowing its selective detection (Fig. 1). The most commonly used molecules include 4-Methylumbelliferone (MUF) linked to monosaccharides (glycosidase assays) or phosphate groups (phosphatase assays) and 7-Amino-4-methylcoumarin (MCA) linked to amino acids (protease assays) [START_REF] Arnosti | Microbial extracellular enzymes and their role in dissolved organic matter cycling[END_REF][START_REF] Hoppe | Significance of exoenzymatic activities in the ecology of brackish water: measurements by means of methylumbelliferyl-substrates[END_REF][START_REF] Kirchman | Microbial Ecology of the Oceans: Second Edition[END_REF]. Enzymatic activity is determined by following the increase in fluorescence over time and using standards of known fluorophore concentration. Even though the use of simple substrate analogs suffers from limitations [START_REF] Arnosti | Microbial extracellular enzymes and the marine carbon cycle[END_REF][START_REF] Steen | Substrate specificity of aquatic extracellular peptidases assessed by competitive inhibition assays using synthetic substrates[END_REF], they have been widely used thanks to their sensitivity and ease of use [START_REF] Chróst | Microbial Ectoenzymes in Aquatic Environments[END_REF].

A.

B. (protease substrate, dashed lines) and MCA (product, solid lines) over emission (gray lines) or excitation wavelength (black lines). To obtain excitation spectra of MCA and LLMCA, emitted light was respectively collected at a wavelength of 440 and 410 nm while excitation wavelength varied. To obtain emission spectra, emitted light was collected over a range of wavelength while excitation wavelength was set to 350 and 325 nm for MCA and LLMCA, respectively. em: emission, ex: excitation.

Vertical lines represent excitation and emission wavelengths used during enzymatic assays.

However, several biases might affect result interpretation and impede inter-study comparison. The first one is a measurement artifact intrinsic to fluorimetry known as the Inner Filter Effect (IFE), which has been completely overlooked in the literature assaying enzymatic activity in environmental water samples. With conventional spectrofluorometers, a fluorescent molecule is excited by a light source at a specific wavelength, selected by a monochromator. The emitted fluorescence is collected at right angle with respect to the incident beam and detected by a photomultiplier at the emission wavelength, also selected by a monochromator [START_REF] Valeur | Molecular fluorescence, principles and application[END_REF]. The IFE reduces the fluorescence signal due to the absorption of exciting (excitation IFE) or emitted light (emission IFE), which affects the relationship between fluorophore concentration and fluorescence intensity [START_REF] Kao | A comparison of fluorescence inner-filter effects for different cell configurations[END_REF][START_REF] Valeur | Molecular fluorescence, principles and application[END_REF][START_REF] Eccleston | Fluorescence-Based Assays[END_REF], see Fig. 2 for a conceptual representation). IFE can result from the fluorophore itself or any other light-attenuating molecules naturally present in the analysed sample. The predominant effect, excitation or primary IFE, is caused by the absorption of the exciting light, which is attenuated as it progresses through the solution, inefficiently exciting the fluorophore.

Absorption can be performed by the hydrolysis product, but also by the non-hydrolysed substrate. For instance, in the case of phosphatase assays, both MUF-Phosphate (MUF-P, alkaline phosphatase substrate) and MUF (hydrolysis product) absorb exciting light at the routinely used excitation wavelength (λex = 364 nm, Fig. 1). Substrate absorption seems minimal and is often completely neglected by investigators, but it can be significant in enzymatic assays performed with a high substrate to product ratio. Excitation IFE is favored by the use of concentrated solutions (absorbance > 0.1), which are almost inevitable in enzymatic assays [START_REF] Valeur | Molecular fluorescence, principles and application[END_REF][START_REF] Eccleston | Fluorescence-Based Assays[END_REF]. IFE is likely to occur with the conventional right angle geometry as detection system collects light on an area restricted to the center of the cuvette: light might be absorbed before even reaching the collection area [START_REF] Kao | A comparison of fluorescence inner-filter effects for different cell configurations[END_REF][START_REF] Valeur | Molecular fluorescence, principles and application[END_REF]). Different cell configurations, such as front face illumination, were specifically developed in order to avoid this and reduce IFE. Long optic path systems (i.e. 1 cm cuvette) are especially affected by IFE, although shorter optic path systems such as microtiter plate spectrofluorometers can be impacted as well [START_REF] Pinto | Enzyme kinetics: The whole picture reveals hidden meanings[END_REF][START_REF] Marathe | Determination of Neuraminidase Kinetic Constants Using Whole Influenza Virus Preparations and Correction for Spectroscopic Interference by a Fluorogenic Substrate[END_REF]. The age and efficiency of the exciting lamp can also play a role in the occurrence of this effect [START_REF] Valeur | Molecular fluorescence, principles and application[END_REF].

A secondary IFE might also arise if the emitted light is re-absorbed by surrounding molecules.

Absorption by the fluorophore itself depends on its Stokes shift, which is the difference between emission and excitation maxima [START_REF] Eccleston | Fluorescence-Based Assays[END_REF]. A small Stokes shift implies that absorption and emission spectra strongly overlap, so the emitted light might be absorbed by non-excited fluorophore molecules, decreasing the measured signal. For molecules with large Stokes shift, such as MUF and MCA, emission IFE is not likely to occur [START_REF] Fonin | Fluorescence of dyes in solutions with high absorbance. Inner filter effect correction[END_REF].

The IFE has been described before in biochemical studies using substrate analogs [START_REF] Liu | Use of a fluorescence plate reader for measuring kinetic parameters with inner filter effect correction[END_REF][START_REF] Palmier | Rapid determination of enzyme kinetics from fluorescence: Overcoming the inner filter effect[END_REF][START_REF] Puchalski | Assessment of inner filter effect corrections in fluorimetry[END_REF]) but, to our knowledge, has never been considered in the context of marine studies. [START_REF] Sebastián | Alkaline phosphatase activity in marine oligotrophic environments: Implications of single-substrate addition assays for potential activity estimations[END_REF]reported a reduction of the reaction velocity by excess of substrate when assaying high substrate concentrations. . However, they did not mention a possible IFE.

The second bias is linked to the wide differences in substrate concentrations used, for both Michaelis-Menten kinetics and single point assays. Before performing a single point enzymatic assay, kinetic parameters (maximum velocity -Vmax -and Michaelis affinity constant -Km) should ideally be determined with a kinetic experiment using several substrate concentrations. However, there are wide differences in maximum substrate concentration used in the literature. They vary between 0.1 and 300 µM for alkaline phosphatase activities (APA) assayed with MUF-P (see Table 1 for references) and between 25 and 1000 µM for exoproteolytic activities (EPA) assayed with L-Leucine-MCA (LLMCA, see Table 2 for references). Insufficient maximum substrate concentration can affect parameters determination as the saturation of enzymatic active sites might not be reached.

As kinetics are laborious, time consuming, expensive and require large sample volume, they are often set aside in favor of single point assays, using a single substrate concentration. A huge variability in the concentrations used is also noticed: between 0.1 and 250 µM for APA assayed with MUF-P (see Table 1 for references) and between 2.5 and 1000 µM for EPA assayed with LLMCA (see Table 2 for references). Those differences may be related to the existence of different perspectives in the current oceanographic community. Trace substrate concentration (< 1 µM) might be used in order to determine enzymatic rates and substrate turnover in conditions as close as possible to those prevailing in situ. This is opposed to a more conventional approach using a saturating substrate concentration, several times higher than the enzymes Km which allows the determination of maximal velocity rate [START_REF] Chróst | Microbial Ectoenzymes in Aquatic Environments[END_REF][START_REF] Hoppe | Phosphatase activity in the sea[END_REF]. Single point assays using low substrate concentration results in several issues. (i) The substrate might not greatly exceed the enzyme concentration, which is a necessary condition to satisfy the steady-state assumption made by Michaelis-Menten. (ii) Slow product formation leads to fluorometric sensitivity issue [START_REF] Chróst | Microbial Ectoenzymes in Aquatic Environments[END_REF]). (iii) Those assays are subject to higher errors as velocities correspond to the first order part of the Michaelis-Menten equation, which is the most variable region.

In consequence, small pipetting errors could result in large differences in estimated activity. (iv) At low concentration, naturally occurring substrates might compete with the fluorogenic substrate analog, leading to significantly underestimated activities [START_REF] Chróst | Microbial Ectoenzymes in Aquatic Environments[END_REF]). Consequently, measured activities might be dependent on natural substrate concentration, potentially altering results and preventing intra and inter-study comparison. The accumulation of these experimental biases might lead to severely misestimated enzymatic activities.

The purpose of this study is to address these issues by quantifying their effect on fluorometric enzymatic assays. First, we will show how to detect the IFE occurrence, its effect on enzymatic measurements and how it can be corrected. Secondly, we will address the effect of the substrate concentration ranges upon the determination of kinetic parameters of pure enzymes, phytoplankton cultures and natural bacterial communities. We will finally argue in favor of using saturating substrate concentrations when performing single point assays, which allows the determination of the enzymatic equipment of the cells, rather than the in situ degradation rate.

Material and procedures

Reagents and solutions

All chemical products were purchased from Sigma-Aldrich.

Substrate solutions. Stock solutions of 10 mM 4-Methylumbelliferyl-phosphate (MUF-P) and 40 mM L-Leucine-7-amido-4-methylcoumarin (LLMCA) were prepared in half a volume of 2-methoxyethanol, dissolved using sonication and volume was adjusted to final concentration with Milli-Q water (Millipore purification system). Working solutions from 0.5 to 500 µM for MUF-P and from 3.9 to 1000 µM for LLMCA were obtained by successive dilutions of stock solutions in Milli-Q water and stored at -20 °C.

Product solutions. Stock solutions of 2 mM 4-Methylumbelliferone (MUF) and 4 mM 7-Amino-4methylcoumarin (MCA) were prepared as described previously and used to prepare standards, as described in the following section.

Competitors for inhibition tests. Stock solutions of 4.2 mM Glucose-6-phosphate (G6P), 10 mM Leucyl-glycine (Leu-gly), 10 mM L-Leucyl-glycyl-glycine (Leu-gly-gly) and 10 mM Hexaglycine (Hexagly) were made in Milli-Q water, serially diluted to appropriate concentrations and stored at -20 °C.

IFE detection

Standards preparation. As non-hydrolysed substrate may affect fluorescence measurement, calibration curves of each product (MUF and MCA) were prepared in various concentration of substrate (MUF-P and LLMCA, respectively). Substrate concentrations are the ones used when determining enzymatic parameters. In practice, standards of MUF ranging from 8 nM to 2 µM were prepared in Milli-Q water or MUF-P concentration ranging from 0.5 to 500 µM, resulting in 12 calibrations for APA. Buffered formaldehyde (18%, pH 8) was added to each standard to respect assay dilution conditions (3.3% final concentration), as formaldehyde was used here to stop APA (C. Labry unpubl.).

Standards of MCA ranging from 20 nM to 2 µM were prepared in Milli-Q water and in LLMCA concentration ranging from 3.9 to 500 µM resulting in 9 calibrations for EPA. 10% sodium dodecyl sulfate (SDS) was added to each standard to respect assay dilution conditions (1% final) as it is used to stop EPA. This is particularly important for EPA as 1% SDS was shown to result in a 20% increase in MCA fluorescence [START_REF] Delmas | SDS-preservation for deferred measurement of exoproteolytic kinetics in marine samples[END_REF]. All standards were stored at -20 °C.

Fluorometric measurements. In this study, we compared classical cuvette readings with Flow Injection Analysis (FIA) reading [START_REF] Delmas | Exoproteolytic activity determined by flow injection analysis: its potential importance for bacterial growth in coastal marine ponds[END_REF]. Briefly, FIA is a liquid chromatography injection system (without the chromatographic column), connected to a Kontron SFM25 fluorescence spectrometer with a 1 mm optic path. This system allows a quick, sensitive and reproducible sample processing [START_REF] Delmas | Exoproteolytic activity determined by flow injection analysis: its potential importance for bacterial growth in coastal marine ponds[END_REF]. The use of a carrier fluid (here a 0.1 M buffered borate solution adjusted to pH 10.5 and delivered at 1 mL min -1 ) provides the possibility of setting the pH during fluorescence reading, independently from the pH of incubation. This is important as MUF fluorescence yield greatly varies with pH and is maximum at pH > 10 (Chróst and Krambeck 1986). For cuvette readings, pH was adjusted to 10 by adding 0.98 and 0.20 mL of a 0.5 M pH 12 buffered borate solution per 4 mL sample (containing preservative) for APA and EPA respectively. Measurements were carried out in a 1 cm cuvette using two spectrofluorometers, SFM25 and Perkin Elmer LS50.

All measurements were performed with a 90° angle illumination. Excitation and emission wavelength were respectively 364 nm and 460 nm for APA and 380 nm and 440 nm for EPA.

Michaelis-Menten kinetics

Michaelis-Menten kinetics were carried out on various samples to evaluate the impact of IFE and of substrate concentration ranges on kinetic parameters determination.

Sample preparation. Tested samples were either purified enzymes, phytoplankton cultures or natural microbial communities. Purified enzymes from Escherichia coli and shrimp (acquired from Sigma/Aldrich) were diluted to a stock concentration of 10 mU mL -1 in Milli-Q water and stored at 4

°C. For each activity assay, stock enzyme was diluted to 250 µU mL -1 in 0.2 µm filtered natural seawater (Whatman Nucleopore filters).

Alexandrium minutum and Thalassiosira weissflogii were precultured in F/4 medium [START_REF] Guillard | Studies of marine planktonic diatoms[END_REF] and inoculated in phosphate-free F/4 medium for 3 days at 18 °C, under a 12:12 light cycle (120 µmol photons m -2 s -1 ). Activities were measured on total fraction comprising algal-attached and dissolved enzymes.

Natural seawater was collected from the Brest station of the Service d'Observation en Milieu LITtoral program (SOMLIT, French marine monitoring network, http://somlit.epoc.u-bordeaux1.fr).

and filtered through 0.8 µm Whatman Nucleopore filters to remove eukaryotes and larger cells.

Incubations. In order to determine kinetic parameters, 2 mL samples were incubated in the dark with 50 µL substrate solutions, with final concentrations ranging from 0.5 to 500 µM for MUF-P and from 1.95 to 1000 µM for LLMCA). Incubation time for each type of sample was previously determined so that less than 25% of the substrate was hydrolysed, in order to measure initial linear velocity. Natural bacterial communities were incubated at in situ temperature (between 12 and 16 °C), purified enzymes and phytoplankton cultures at 20 °C. At the end of the incubation, reaction was stopped by adding 18% buffered formaldehyde (pH 8, 3.3% final concentration) for APA or 10% SDS for EPA (1% final concentration). Samples were then frozen at -20 °C until fluorescence measurement, which was performed as previously described. These preservatives stop enzymatic activities and allow storage at -20°C for deferred sample analysis, if necessary, without any changes on the kinetic parameters (APA:

C. Labry unpubl., EPA: Delmas and Garet 1995).

Controls.

As natural seawater and substrates (MUF-P and LLMCA) do produce fluorescence, a blank sample was prepared for each substrate concentration by directly mixing samples, substrate and reaction inhibitor (formaldehyde for APA, SDS for EPA) and immediately freezing them at -20 °C. Blank fluorescence was then subtracted from sample fluorescence and results were converted to degradation rates using product standards diluted in Milli-Q water.

Statistical analysis. Affinity constant (Km) and maximum velocity (Vmax) and their standard deviations were calculated using nonlinear least squares regression of the data fitted to the Michaelis-Menten equation, using R ("nls" function in the "stats" package). Non-linear regression seems to be the best method to estimate kinetic parameters [START_REF] Chróst | Microbial Ectoenzymes in Aquatic Environments[END_REF]).

Inhibition tests

To assess the effect of natural competitors on APA and EPA of natural bacterial samples, we monitored the fluorescence emitted by 3 mL seawater sample amended with 75 µL substrate (0.125 to 2 µM of MUF-P, 0.125 and 2 µM of LLMCA) in a 1 cm optic path cuvette (SFM25 spectrofluorometer) during short periods of time (2 to 10 min). A molecule competing with the substrate analog was then added and fluorescence was monitored using the same procedure. The competitor used for APA was G6P (75 µL, final concentration from 50 nM to 1.5 µM), a natural compound involved in bacterial metabolism which is susceptible to be present in both natural environments and cultures. For EPA, three competitors were tested: Leu-gly, Leu-gly-gly and Hexagly (30 µL, final concentration of 8 and 16 µM). Fluorescence increased linearly over time and the presence of competitors visibly affected the slopes, which correspond to reaction velocities. pH was not adjusted during this measurement as slopes were not converted to actual velocities. Slopes were corrected for the dilution due to competitor's addition.

Assessment and discussion

Influence of IFE on activity assays

IFE occurs when exciting or emitted light is absorbed, decreasing the fluorescence signal and resulting in underestimated enzymatic activities. It includes all light-attenuating processes, caused by the fluorogenic substrate analog itself or by any other chromophores naturally present in samples. This study is limited to IFE caused by fluorogenic substrate as it is important during enzymatic assays using large concentration of substrate, but IFE resulting from natural organic matter may also affect fluorometric assays [START_REF] Kothawala | Inner filter correction of dissolved organic matter fluorescence[END_REF]. IFE resulting from natural compounds should theoretically be corrected using calibration curves prepared in the same matrix as the samples (for instance 0.2 µm filtered seawater).

Detection of IFE caused by fluorogenic substrate

MUF-P/MUF and LLMCA/MCA have similar excitation and emission spectra, characterized by a large

Stokes shift, meaning that emission IFE should not occur. However, both non-hydrolysed substrates and hydrolysis products can absorb exciting light and produce an excitation IFE.

The occurrence of an excitation IFE from fluorescent products was tested by measuring calibration standards of products (MUF and MCA) diluted in Milli-Q water. If this effect occurs, the released product will absorb exciting light, with a greater impact at high product concentration. Consequently, the emitted signal will not be linear over the product range of concentration. As the curves obtained were linear (determination coefficient for linear fitting: R² > 0.999, data not shown) for the three instruments (FIA-SFM25, SFM25 and LS50), it appears that there is no IFE from the product between 0 and 2 µM, for both MUF and MCA.

Excitation IFE resulting from non-hydrolysed substrates can be detected by measuring fluorescence of the reaction product in varying substrate concentrations. If an IFE occurs, we expect that a given substrate concentration will affect the fluorescence of all product concentrations in a similar way. The linearity of the relationship between fluorescence and product concentration would be unaffected.

However, the IFE would increase with increasing substrate concentration which would result in a reduction of the calibration slope.

Figure 3 shows the results obtained for APA (no IFE detected, Fig. 3a,c,e) and EPA (IFE detected, Fig. 3b,d,f) with LS50 spectrofluorometer. Without IFE, the slope of those calibration curves is independent from MUF-P concentration (slope = -6.77 x 10 -6 , correlation coefficient r = 0.236, df = 10, not significant, Fig. 3c) as MUF-P substrate does not affect fluorescence reading. The intercept is linearly proportional to this concentration (slope = 0.25, r = 1.000, df = 10, significant at 0.1%, Fig. 3e),

reflecting the natural fluorescence of the substrate. These results also show the necessity of using a blank for each substrate concentration assayed. When an IFE occurred, the slope of the calibration curves decreases with increasing LLMCA concentration (slope = -4.37 x 10 -5 , r = 0.742, df = 8, significant at 5%, Fig. 3d): as exciting light is absorbed, it becomes limiting and the fluorochrome is not fully excited.

As expected, this effect is more pronounced at higher concentration of LLMCA, affecting calibration curve slopes in a greater manner. For similar reasons, the intercept does not vary linearly at high LLMCA concentrations (Fig. 3f).

Overall, no IFE was detected when assaying APA with all three tested instruments. An IFE was detected for proteases assays performed using cuvettes (SFM25 and LS50) but not using FIA-SMF25.

The absence of IFE using FIA-SFM25, compared to the cuvette systems, might be due to both the sample dilution by hydraulic system (as sample is diluted about 10 times by carrier fluid) and by the 10 times shorter optic path, resulting in 100 times less substrate interfering with light flux. A greater overlap of fluorescence spectra, as well as different samples dilution (see following discussion), might favor the occurrence of IFE with the EPA assays compared to the APA assays.. Those results illustrate the fact that this effect greatly depends on the type of substrate, concentrations and equipment used and should be regularly tested for each assay protocol.

Calibration of MUF shows no IFE as the slope of each calibration is not dependent on MUF-P concentration (c) and intercept varies linearly with MUF-P concentration (e). Calibration of MCA exhibits an IFE as the slope of each calibration varies significantly with LLMCA concentration (d) and intercept does not vary linearly above 60 µM of LLMCA (f). r: correlation

coefficient. Error bars (c, d, e, f) represent 95% confidence interval of the fitted parameters.

Consequences and correction of IFE

To assess the consequences of the detected IFE on natural samples, we carried out a kinetic measurement of natural bacterial communities EPA. The samples were measured using both FIA-SFM25 and cuvette operated LS50 with pH correction.

With FIA-SFM25, unweighted hyperbolic regression gave a Vmax of 3386 ± 198 nM h -1 and a Km of 275 ± 40 µM. When carried out with LS50 for which IFE occurs, Vmax only reached 2668 ± 154 nM h -1 and Km equalled 205 ± 32 µM, hence a respective difference of 21 and 26% on each parameter (Fig. 4a). The correlation between the two measurements shows that, for the tested spectrofluorometers, the IFE appears at a LLMCA concentration of 125 µM (Fig. 4a), which roughly corresponds to a rate of 1000 nM h -1 .Below this threshold, the two spectrofluorometers results correlate well (slope of 1.05, Fig. 4b) whereas above, cuvette measurements yield lower activities (slope of 0.70, Fig. 4b). This threshold value is close to the 150 µM self-quenching threshold observed by [START_REF] Saifuku | A novel fluorometric ultramicro determination of serum leucine aminopeptidase using a coumarine derivative[END_REF] in the original method of LLMCA assay.

IFE can be avoided by using diluted solutions, shorter optic path, horizontal over vertical slits, a change in lamp geometry or in excitation/emission wavelengths [START_REF] Valeur | Molecular fluorescence, principles and application[END_REF][START_REF] Eccleston | Fluorescence-Based Assays[END_REF][START_REF] Fonin | Fluorescence of dyes in solutions with high absorbance. Inner filter effect correction[END_REF]). However, it is not always possible to modify those parameters and this effect cannot always be avoided. In such cases, it should be corrected either experimentally or mathematically. If mathematic corrections are available, they can be quite complicated to implement (see [START_REF] Fonin | Fluorescence of dyes in solutions with high absorbance. Inner filter effect correction[END_REF][START_REF] Puchalski | Assessment of inner filter effect corrections in fluorimetry[END_REF] for references). To experimentally correct the IFE in a simple way, each fluorescence value obtained with a given substrate concentration was converted into a concentration using the calibration curve of product prepared in the same given substrate concentration, instead of the usual calibration curve prepared in Milli-Q water. For instance, the values measured when assaying EPA with 1000 µM of LLMCA were converted using the MCA standards prepared in 1000 µM of LLMCA. The corrected values with LS50 are: Vmax = 3267 ± 183 nM h -1 and Km = 288 ± 40 µM, hence a respective difference of 4 and 5% on each parameter, which is within standard error inherent to fluorometric measurement and model fitting.

Importance of protocol and equipment used

We would like to draw specific attention to the fact that IFE greatly depends on protocol as well as equipment used.

The first methodological key point would be the preparation of calibration curves, which are necessary to correctly assess and correct IFE. As this effect is dependent on dilution, calibration solutions should be prepared in the exact same manner as the samples. In our protocol, all samples were diluted 1.2 times by the preservative (formaldehyde or SDS), which was consequently also added to the standards. Preservative is, to our knowledge, almost never amended in calibration solutions.

The second methodological key point concerns the pH adjustment when fluorescence is measured using cuvette. Our samples were further diluted by buffered borate amendment (1.24 times for APA, 1.05 times for EPA) to adjust pH to 10, which maximizes MUF and MCA fluorescence and allows the comparison between FIA and cuvette measurements. As such, IFE is minimized in our protocol. This is especially true for APA, for which larger volumes of buffer were necessary to reach pH = 10. However, in the literature, it is often unclear if pH adjustment is performed when using cuvettes or microplates. If not, IFE could be much more severe.

Another methodological key point would be the choice of excitation wavelength. For instance, [START_REF] Christie | Saccharide Binding to Transition Metal Ion Free Concanavalin A[END_REF] noted that an excitation wavelength of 350 nm was necessary to overcome an IFE that was observed at 320 nm (maximum excitation wavelength) with MUF-α-D-mannopyranoside and MUF-α-D-glucopyranoside with a spectrofluorometer using cuvette. This is especially important for MCA as an excitation wavelength of 360 nm (maximum of excitation) will favor IFE due to a bigger absorbance by LLMCA (Fig. 1).

The occurrence of IFE strongly depends on the equipment used. For instance, Briciu-burghina et al.

(2015) encountered a pronounced IFE in 1 cm optic path cuvette using MUF-β-D-glucuronide substrate, whose fluorescence spectra resemble MUF-P spectra, for which we found no IFE. This could be due, for example, to differences in cell geometry, slits orientation, fluorescence observation angle, lamp power and age [START_REF] Valeur | Molecular fluorescence, principles and application[END_REF][START_REF] Eccleston | Fluorescence-Based Assays[END_REF][START_REF] Fonin | Fluorescence of dyes in solutions with high absorbance. Inner filter effect correction[END_REF]).

Microplate spectrofluorometer have been increasingly used as they allow high throughput assays and limit the substrate volume, although the small incubation volume and long incubation time may lead to bottle wall-effects (higher enzyme and substrate adsorption). IFE seems less likely to occur with those set-ups thanks to front-face optics and small optic path. However, studies using 96-wells microplates have shown its occurrence with MUF derivative substrates. For instance, [START_REF] Pinto | Enzyme kinetics: The whole picture reveals hidden meanings[END_REF] reported an IFE using MUF-galactoside, without specifying the importance of the effect. [START_REF] Marathe | Determination of Neuraminidase Kinetic Constants Using Whole Influenza Virus Preparations and Correction for Spectroscopic Interference by a Fluorogenic Substrate[END_REF] found an IFE using 2'-(4-methylumbelliferyl)-α-D-N-acetylneuraminic acid, which was an important interference in their assay. Even though microplates are less prone to IFE, its occurrence should be checked in every spectrofluorometer.

Influence of substrate concentration range on kinetic parameters determination

To illustrate the effect of substrate concentration range on kinetic parameters determination, we conducted APA measurements on purified enzymes (E. coli and shrimp), phytoplankton cultures (A.

minutum and T. weissflogii) and natural bacterial populations. Several fittings were consecutively made on each kinetics to determine V n max and K n m each time eliminating the highest concentration of substrate (Smax). This process aims to illustrate the impact of substrate concentration range by decreasing the maximum concentration used from Smax = 500 µM (n = 11 points) to Smax = 2 µM (n = 3). The resulting variation of parameters is due to fitting artifact. It should be noted that only an apparent Km can be determined, as natural substrates might be present in the medium, competing with the substrate analog.

Figure 5 shows the results obtained for the purified E. coli APA. Both V n max and Km increase (respectively + 61% and + 157%) when Smax increases from 2 µM to 60 µM. Both parameters then tend to plateau at higher Smax, reaching what can be considered as their "true" value when Smax = 500 µM (V t max= 952 nM h -1 and K t m= 6.5 µM), even though K n m still seems to vary consequently. The threshold concentration of 60 µM roughly corresponds to 10 K t m. This value is generally recommended as a saturating concentration even though it deviates from true enzyme saturation since "only" 91% of active sites are occupied, as dealing with concentrated solutions can be complicated [START_REF] Bisswanger | Enzyme assays[END_REF] . In order to compare the results of consecutive fittings performed on different enzymes, kinetic parameters (V n max and K n m) were normalized by the "true" kinetic parameters (V t max and K t m) determined using the largest substrate concentration range (Smax = 500 µM). Figure 6 presents the normalized velocities (V n max / V t max) plotted against the normalized maximum substrate concentration (Smax / K t m), which allows to observe the impact of Smax independently from the enzyme's affinity. It clearly shows the same pattern as before: V n max greatly varies with low Smax, then tends to stabilize around the correct parameter estimation at higher Smax (> 25 K t m). Normalized Km follows the exact same pattern (data not shown).

20 This experiment illustrates the consequences of the use of insufficient Smax to determine kinetic parameters. Both low and high substrate concentration are necessary to correctly fit all parts of the Michaelis-Menten equation (0 and 1 st order, [START_REF] Chróst | Microbial Ectoenzymes in Aquatic Environments[END_REF]). The width of the range depends on the enzyme affinity, since enzymes with low Km are easily saturated and the curve's plateau will be reached even at low Smax. High affinity enzymes (low Km) are usually thought to occur in oligotrophic environments since they are supposed to process substrates at very low concentrations [START_REF] Chróst | Environmental Control of the Synthesis and Activity of Aquatic Microbial Ectoenzymes[END_REF][START_REF] Rath | Ectoenzymatic activity and bacterial dynamics along a trophic gradient in the Caribbean Sea[END_REF]). However, even in those environments, Smax should be carefully chosen. For instance, all five studies determining enzymatic parameters in oligotrophic environments listed in Table 1 contained at least one experiment where Km was equal or greater than Smax. In contrast, enzymes are considered to have lower substrate affinity (high Km) in eutrophic environments [START_REF] Chróst | Environmental Control of the Synthesis and Activity of Aquatic Microbial Ectoenzymes[END_REF][START_REF] Rath | Ectoenzymatic activity and bacterial dynamics along a trophic gradient in the Caribbean Sea[END_REF], so substrate ranges should be even wider. Similar results were obtained for EPA (not shown).

As the variation of kinetic parameters results from a fitting artifact, it should logically occur for all enzymatic kinetics.

Effect of natural substrates competition at trace concentration of analog substrate

Substrate concentration used for single point assays varied from 0.1 µM to 250 µM for APA assayed with MUF-P (see Table 1 for references) and from 2.5 to 1000 µM for EPA assayed with LLMCA (see Table 2 for references). Low substrate concentrations are usually used in oligotrophic conditions, in order to mimic mean environmental conditions. However, in such assays, naturally occurring substrates might compete with the analog substrate. To illustrate this effect, we performed APA assays on natural seawater microbial communities using trace substrate concentrations of MUF-P (0.125 -2 µM, similar to those in studied literature) amended with different concentrations of G6P (0.1 -1.5 µM). G6P was arbitrarily chosen to mimic dissolved organic phosphorus (DOP), the natural substrate of phosphatases.

Concentrations were chosen to be representative of DOP concentration in natural environments: it usually ranges from 0 to 0.2 µM in open ocean surface waters [START_REF] Ridal | Dissolved organic phosphorus concentrations in the northeast subarctic Pacific Ocean[END_REF]Karl and Björkman 2015) while coastal and estuarine waters often contain more than 0.25 µM DOP (Karl and Björkman 2015;[START_REF] Labry | High alkaline phosphatase activity in phosphate replete waters: The case of two macrotidal estuaries[END_REF], with values sometimes exceeding 2 µM [START_REF] Rinker | Dissolved organic phosphorus in the Mississippi River plume during spring and fall 2002[END_REF].

Activities were measured as slopes of fluorescence over time (in mV min -1 ) and expressed as percentage of maximum activity, measured without inhibitors, for each substrate concentration (Fig. 7).

With a MUF-P concentration of 0.125 µM, G6P concentrations of 0.1, 0.2, 0.6 and 1.5 µM decrease MUF-P hydrolysis by 11, 18, 22 and 38%, respectively. Inhibition patterns are quite similar with 0.25, and 0.5 µM MUF-P, while those effects are lower at 1 µM and tend to disappear at 2 µM MUF-P (1-8% reduction). As measurement are carried out in seawater, naturally occurring DOP is also competing for the enzymes' active sites, so the actual effect of G6P might be underestimated. However, results clearly show that competition depends on the ratio of competitor to MUF-P and is not susceptible to happen at saturating concentration of MUF-P. Although G6P was used as a single competitor, samples often contain a mixture of compounds with their own affinity and inhibition constant, affecting enzymatic assays in different ways. The competitor's affinity for the enzyme (hence its effect on measurement) might especially vary for polymeric substances given their huge diversity (peptides or carbohydrates for example). We conducted similar tests on EPA, amending 8 and 16 µM Leu-Gly, Leu-Gly-Gly or Hexagly to 0.125 and 2 µM LLMCA. Although high, those competitor concentrations are representative of natural environments as combined dissolved amino acids may vary from 0.2 to 8 µM in oligotrophic to coastal waters [START_REF] Keil | Dissolved combined amino acids in marine waters as determined by a vapor-phase hydrolysis method[END_REF]. As a result, 8 µM of Leu-Gly, Hexagly and Leu-Gly-Gly generated an inhibition of 18, 19 and 34%, while 16 µM generated respectively 25, 33 and 41% of inhibition (Fig. 8a). Those results might be explained by the fact that measurements using peptidase substrates actually represent the concerted action of many distinct enzymes, as suggested by [START_REF] Steen | Substrate specificity of aquatic extracellular peptidases assessed by competitive inhibition assays using synthetic substrates[END_REF], who performed competition experiments between 12 amino acid-p-nitroanilide compounds and 3 fluorogenic substrates (LLMCA, L-arginine-MCA, Lproline-MCA). As expected, the use of higher concentration of LLMCA (2 µM) reduced the inhibition:

8 µM of Leu-GLy, Hexagly and Leu-Gly-Gly generated 5, 10 and 8% inhibition respectively while 16 µM generated 6, 23 and 16% of inhibition respectively (Fig. 8b). Several other studies have shown the competition between natural and fluorogenic substrates when assaying APA (see for instance Chróst 1990;[START_REF] Fernley | Studies on Alkaline Phosphatase -Inhibition by phosphate derivatives and the substrate specificity[END_REF][START_REF] Hoppe | Significance of exoenzymatic activities in the ecology of brackish water: measurements by means of methylumbelliferyl-substrates[END_REF], EPA [START_REF] Hoppe | Significance of exoenzymatic activities in the ecology of brackish water: measurements by means of methylumbelliferyl-substrates[END_REF][START_REF] Somville | A method for determining exoproteolytic activity in natural waters[END_REF][START_REF] Christian | Ectoaminopeptidase specificity and regulation in Antarctic marine pelagic microbial communities[END_REF] or glycosidases [START_REF] Hoppe | Significance of exoenzymatic activities in the ecology of brackish water: measurements by means of methylumbelliferyl-substrates[END_REF][START_REF] Somville | Measurement and study of substrate specificity of Exoglucosidase activity in eutrophic water[END_REF], which confirms our results showing that natural substrates may significantly alter the measured enzymatic activites at low analog substrate concentrations.

This issue arises from the legitimate need to measure in situ degradation rates. However, as natural substrates compete with the fluorogenic analog, those measurements are unreliable and depend on sample composition, which completely impedes inter-study comparison. It raises questions regarding what we really are interested in quantifying when measuring enzyme activity rates. Single point assays using a saturating substrate concentration (> 10 Km) allow the determination of a potential degradation rate (Vmax). This can be considered as a determination of enzyme concentration [START_REF] Billen | Protein Degradation in Aquatic Environments[END_REF]. When it is normalized by the biomass or number of cells, it reflects the enzymatic equipment of the cells. Those measurements are comparable across studies and allow, for instance, to study the regulation of enzyme synthesis in response to environmental trophic conditions. In any case, fluorogenic substrate assays should be interpreted cautiously in terms of real substrate utilization, keeping in mind that activities are measured with respect to naturally occurring substrates [START_REF] Billen | Protein Degradation in Aquatic Environments[END_REF].

Conclusion and recommendations

The starting point of this study was the comparison of existing literature on enzymatic activity measurement in aquatic environments. We noticed substantial divergences in existing methodologies, the most notable one being the difference in substrate concentrations used for assays. Furthermore, the occurrence of IFE, a fluorometric artifact, has never been considered despite being likely to occur, especially at saturating concentrations of substrate. Those factors might alter results and therefore, investigation of past articles and inter-study comparison should be carried out cautiously. In this study, we tried to highlight several methodological key points of enzymatic assays, illustrating them with APA and EPA, although results should apply to all fluorometric enzymatic assays.

(1) We would like to emphasize the possible occurrence of IFE, a fluorometric artifact that has been completely ignored in environmental water studies until now, despite having the potential to significantly affect measurements. In this study, it was not detected for APA assays but occurred for EPA assays with the two cuvette based spectrofluorometers tested, at a LLMCA threshold concentration of 125 µM. This effect can also occur with microplate readers, to a lesser extent.

IFE depends on sample dilution and the equipment used and can be corrected by using appropriate calibration curves.

(2) Ideally, before any single substrate assay, a kinetic analysis should be performed to determine the apparent Km and to choose a saturating concentration. In practice, this step is laborious.

However, when such experiments are carried out, a wide substrate concentration range (up to several hundred micromolar) should be used in order to reach the enzyme's active sites saturation and correctly fit both first and zero-order part of enzyme reaction. The maximum substrate concentration should be at least 10 Km to ensure that most enzymes are sufficiently saturated.

(3) Finally, when performing a single substrate assay, saturating substrate concentrations (> 10 Km) should be preferred, rather than trace concentrations mimicking natural conditions. Indeed, this latter approach might not fulfill Michaelis-Menten conditions (i.e. excess substrate compared to enzyme concentration) and may lead to higher uncertainties. Furthermore, it is highly dependent on both natural substrate concentrations and composition, as natural substrate might compete with the substrate analog for the enzyme active sites. Up to 34% and 38% inhibition was observed in the present study inhibition tests with natural substrates for EPA and APA, respectively.

All these methodological issues must be addressed in order to correctly measure enzymatic rates and allow inter-study comparison. Excitation spectra of MUF and MUF-P were obtained using a constant emission wavelength (460 nm) while excitation wavelength varied. Emission spectra were obtained using a constant excitation wavelength (364 nm) with variable emission wavelength. (B) Normalized fluorescence spectra of LLMCA (protease substrate, dashed lines) and MCA (product, solid lines) over emission (gray lines) or excitation wavelength (black lines). To obtain excitation spectra of MCA and LLMCA, emitted light was respectively collected at a wavelength of 440 and 410 nm while excitation wavelength varied. To obtain emission spectra, emitted light was collected over a range of wavelength while excitation wavelength was set to 350 and 325 nm for MCA and LLMCA, respectively. em: emission, ex: excitation.

Figure captions

Vertical lines represent excitation and emission wavelengths used during enzymatic assays. of APA assays conducted on various samples (purified enzymes from shrimp and E. coli, cultures of T.

weissflogii and A. minutum and natural bacterial communities). Each dot represent a non-linear fitting done on the same kinetic experiment data, but iteratively reducing Smax, which is represented normalized on the X-axis. Velocities are normalized by the "true" V t max obtained at Smax = 500 µM and substrate concentrations are normalized by the "true" K t m obtained at Smax = 500 µM.

Fig. 1 .

 1 Fig. 1. (A) Normalized fluorescence spectra of MUF-P (alkaline phosphatase substrate, dashed lines) and MUF (product, solid lines) over emission (gray lines) or excitation wavelength (black lines). Excitation spectra of MUF and MUF-P were obtained using a constant emission wavelength (460 nm) while excitation wavelength varied. Emission spectra were obtained using a constant excitation wavelength (364 nm) with variable emission wavelength. (B) Normalized fluorescence spectra of LLMCA

Fig. 2 .

 2 Fig. 2. Conceptual illustration of excitation IFE (also termed primary IFE) and emission IFE (also termed secondary IFE)using a right angle geometry, one of the most common for cuvette system.

Fig. 3 .

 3 Fig. 3. Detection of IFE using calibration curves of MUF (a, c, e) and MCA (b, d, f), with cuvette operated LS50 spectrofluorometer. Calibration curves (a, b) were determined from solutions prepared in varying concentration of nonhydrolysed substrate (MUF-P, LLMCA). On panel a and b, only four calibration curves are shown to facilitate readability although 12 and 9 curves were respectively measured for APA and EPA. All calibrations are displayed on other panels.

Fig. 4 .

 4 Fig. 4. (a) Kinetics of natural bacterial communities EPA measured using FIA-SFM25 (black line) or with LS50 (using cuvette, grey line). (b) Correlation between EPA measured with LS50 (using cuvette) and using FIA-SFM25. Dashed line highlights the substrate concentration threshold.

Fig. 5 .

 5 Fig. 5. Evolution of kinetic parameters (V n max, K n m) of purified E. coli alkaline phosphatase over the maximum substrate concentration (Smax) used. Several fittings were done on the same assay data, iteratively removing the highest substrate concentration. Correlation coefficient indicated significant results for n > 4 (at 0.1%).

Fig. 6 .

 6 Fig.6. Normalized Vmax (V n max / V t max) over normalized maximum substrate concentration (Smax / K t m) of APA assays conducted on various samples (purified enzymes from shrimp and E. coli, cultures of T. weissflogii and A. minutum and natural bacterial communities). Each dot represent a non-linear fitting done on the same kinetic experiment data, but iteratively reducing Smax, which is represented normalized on the X-axis. Velocities are normalized by the "true" V t max obtained at Smax = 500 µM and substrate concentrations are normalized by the "true" K t m obtained at Smax = 500 µM.

Fig. 7 .

 7 Fig. 7. APA measured using trace MUF-P concentrations with various concentrations of G6P, a natural non-fluorescent competitor. Results are given in mV min -1 and normalized by the maximum activity obtained for each MUF-P concentration (without competitor).

Fig. 8 :

 8 Fig. 8 : EPA measured using 0.125 µM LLMCA (a) or 2 µM LLMCA (b), with various concentrations of Leu-Gly-Gly, Leu-Gly or Hexagly, acting as competitors (C). Results are measured in mV min -1 and normalized by the maximum activity obtained without competitor.

Fig. 1 .

 1 Fig. 1. Fig. 1. (A) Normalized fluorescence spectra of MUF-P (alkaline phosphatase substrate, dashed

Fig. 2 .

 2 Fig. 2. Conceptual illustration of excitation IFE (also termed primary IFE) and emission IFE (also

Fig. 3 .

 3 Fig. 3. Detection of IFE using calibration curves of MUF (a, c, e) and MCA (b, d, f), with cuvette

Fig. 4 .

 4 Fig. 4. (a) Kinetics of natural bacterial communities EPA measured using FIA-SFM25 (black line) or

Fig. 5 .

 5 Fig. 5. Evolution of kinetic parameters (V n max, K n m) of purified E. coli alkaline phosphatase over the

Fig. 6 .

 6 Fig. 6. Normalized Vmax (V n max / V t max) over normalized maximum substrate concentration (Smax / K t m)

Fig. 7 .

 7 Fig. 7. APA measured using trace MUF-P concentrations with various concentrations of G6P, a natural non-fluorescent competitor. Results are given in mV min -1 and normalized by the maximum activity

Fig. 8 .

 8 Fig. 8. EPA measured using 0.125 µM LLMCA (a) or 2 µM LLMCA (b), with various concentrations of Leu-Gly-Gly, Leu-Gly or Hexagly, acting as competitors (C). Results are measured in mV min -1 and

Table 1 .

 1 Literature examples showing phosphatase activity assay conditions used in different environments. All

measurements were carried out using 4-Methylumbelliferyl phosphate (MUF-P) substrate.

Table 2 .

 2 Literature examples showing exoproteolytic activity assay conditions used in different environments. All measurements were carried out using L-Leucine-7-amido-4-methylcoumarin (LLMCA) substrate.

Table 1 .

 1 Literature examples showing phosphatase activity assay conditions used in different environments. All measurements were carried out using 4-Methylumbelliferyl phosphate (MUF-P) substrate.

Table 2 .

 2 Literature examples showing exoproteolytic activity assay conditions used in different environments. All measurements were carried out using L-Leucine-7-amido-4-methylcoumarin (LLMCA) substrate.

Acknowledgments

This work was supported by the French National Program for Coastal Environment (EC2CO) and by the ISblue project, Interdisciplinary graduate school for the blue planet (ANR-17-EURE-0015), cofunded by a grant from the French government under the program "Investissements d'Avenir". We wish to thank M. Latimier for the preparation of phytoplankton cultures.


Marta Agati
email: marta.agati@gmail.com

Maxime Vallet
email: maxime5vallet@gmail.com

Sébastien Joulié

Daniel Benoit
email: daniel.benoit@st.com

Alain Claverie
email: alain.claverie@cemes.fr

Sébastien Joulie
email: sebastien.joulie@cemes.fr

Chemical phase segregation during the crystallization of Ge-rich GeSbTe alloys

Keywords: Phase Change Materials, GST alloys, transmission electron microscopy, phase separation, crystallization

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

1.

Introduction

The microelectronic industry is currently facing new challenges linked to the miniaturization of electronic devices and to the increase of system functionality delivered in the same size package [START_REF] Burr | Phase change memory technology[END_REF]. In this context, Phase-Change Memories (PCMs) have emerged among the most promising candidates to overcome the future technological nodes prospected for non-volatile memory technology [START_REF] Burr | Phase change memory technology[END_REF][START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF][START_REF] Wełnic | Reversible switching in phase-change materials[END_REF][START_REF] Burr | Recent Progress in Phase-Change Memory Technology[END_REF]. Lately, PCM technology has demonstrated suitability to scaling as well as integration in large arrays with impressive data retention and endurance [START_REF] Burr | Phase change memory technology[END_REF][START_REF] Burr | Recent Progress in Phase-Change Memory Technology[END_REF]. The working principle of PCMs relies on the phase transition between an amorphous (high resistive) state and a crystalline (low resistive) state, which can then be associated to the binary states of an electronic memory [START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF]. Furthermore, multilevel data storage concepts, exploiting intermediate resistance states, have been demonstrated to be feasible using PCMs [START_REF] Burr | Recent Progress in Phase-Change Memory Technology[END_REF][START_REF] Nirschl | Write Strategies for 2 and 4bit Multi-Level Phase-Change Memory[END_REF][START_REF] Bedeschi | A Bipolar-Selected Phase Change Memory Featuring Multi-Level Cell Storage[END_REF][START_REF] Oh | Parallel multi-conned (PMC) cell technology for high density MLC PRAM[END_REF][START_REF] Gyanathan | Two-bit multi-level phase change random access memory with a triple phase change material stack structure[END_REF]. The need to combine rapid switching speed and large resistivity difference between the two states has driven the interest towards the Ge-Sb-Te (GST) compounds [START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF]. Figure 1 shows the ternary phase diagram relative to GST compounds.

Pseudo-binary (GeTe)x-Sb2Te3 alloys as well as GeTe are located along the tie line, which represents the line of compounds which exhibit congruent melting [START_REF] Bastien | Etude des matériaux à changement de phase pour application dans le domaine des PCRAM-Verres infrarouges pour l'optique spatiale[END_REF]. Congruent melting exists as long as the solid phase AB and its melt have the same composition. Far from this tie line, phase separation should be expected as a result of the amorphous-to-crystal transition [START_REF] Bastien | Etude des matériaux à changement de phase pour application dans le domaine des PCRAM-Verres infrarouges pour l'optique spatiale[END_REF][START_REF] Shelimova | Composition and Properties of Layered Compounds in the GeTe-Sb2Te3 System[END_REF]. Actually, several papers report on other GST materials which do not seem to show phase separation although not belonging to the tie line, such as Ge4SbTe5 [START_REF] Woltgens | Exploring the limits of fast phase change materials[END_REF][START_REF] Wamwangi | Crystallization kinetics of Ge4Sb1Te5 films[END_REF], Ge2Sb1Te4 [START_REF] Wetnic | Controlling Material Properties in new Phase Change Alloys beyond the pseudobinary line[END_REF], Ge1.5Sb2Te4 [START_REF] Wetnic | Controlling Material Properties in new Phase Change Alloys beyond the pseudobinary line[END_REF], GeSb6Te10 and GeSb8Te13 [START_REF] Shelimova | Composition and Properties of Layered Compounds in the GeTe-Sb2Te3 System[END_REF]. However, these materials are located very close to the tie line, as we can see in Fig. 1. On the other hand, although not far from the tie line, Ge2Sb2Te4 is quite unstable and decomposes into the Ge1Sb2Te4 and Ge2Sb1Te4 phases [START_REF] Wetnic | Controlling Material Properties in new Phase Change Alloys beyond the pseudobinary line[END_REF][START_REF] Wełnic | Phase change materials: From structures to kinetics[END_REF][START_REF] Van Eijk | Investigation of local distortions in the rocksalt structure of Ge2Sb2Te4[END_REF]. Among the GST materials located along the tie line, Ge2Sb2Te5 is the compound offering the best compromise between crystallization speed [START_REF] Yamada | Rapid-phase transitions of GeTe-Sb2Te3 pseudobinary amorphous thin films for an optical disk memory[END_REF] and high amorphous stability (i.e., high crystallization temperature) [START_REF] Abrikosov | An investigation of the structural diagram of Sb2Te3-GeTe[END_REF]. For this reason, countless studies have focused on the investigation of Ge2Sb2Te5 properties [START_REF] Bastien | Etude des matériaux à changement de phase pour application dans le domaine des PCRAM-Verres infrarouges pour l'optique spatiale[END_REF]. Ge2Sb2Te5 exists in two phases: a metastable face-centered-cubic (FCC) structure, which forms at a temperature T~150°C [START_REF] Yamada | Rapid-phase transitions of GeTe-Sb2Te3 pseudobinary amorphous thin films for an optical disk memory[END_REF], and a stable hexagonal structure, which forms above T~300°C [START_REF] Zheng | Surface Energy Driven Cubic-to-Hexagonal Grain Growth of Ge2Sb2Te5 Thin Film[END_REF]. In the FCC phase, a FCC sub-lattice containing only Te atoms (anion sites) is intercalated with another FCC sub-lattice containing a solid solution of Ge and Sb atoms as well as vacancies (cation sites). The amount of vacancies has been calculated to be a little less than 20% at [START_REF] Yamada | Structure of laser-crystallized sputtered thin films for use in optical memory[END_REF].

In the hexagonal structure, atomic (basal) planes of Te atoms alternate with Ge and Sb planes [START_REF] Matsunaga | Structures of stable and metastable Ge2Sb2Te5, an intermetallic compound in GeTe-Sb2Te3 pseudo-binary systems[END_REF]. GST alloys such as Ge2Sb2Te5, GeSb4Te7 [START_REF] Abrikosov | An investigation of the structural diagram of Sb2Te3-GeTe[END_REF], GeSb2Te4 [START_REF] Abrikosov | An investigation of the structural diagram of Sb2Te3-GeTe[END_REF], Ge3Sb2Te6 [START_REF] Shelimova | Composition and Properties of Layered Compounds in the GeTe-Sb2Te3 System[END_REF], Ge4Sb2Te7 [START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF][START_REF] Shelimova | Composition and Properties of Layered Compounds in the GeTe-Sb2Te3 System[END_REF], Ge6Sb2Te9 [START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF], Ge8Sb2Te11 [START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF] have been previously reported in literature and have been plotted here. Close to the tie line, Ge4SbTe5 [START_REF] Woltgens | Exploring the limits of fast phase change materials[END_REF][START_REF] Wamwangi | Crystallization kinetics of Ge4Sb1Te5 films[END_REF], GeSb6Te10 [START_REF] Shelimova | Composition and Properties of Layered Compounds in the GeTe-Sb2Te3 System[END_REF], GeSb8Te13 [START_REF] Shelimova | Composition and Properties of Layered Compounds in the GeTe-Sb2Te3 System[END_REF], Ge2SbTe4 [START_REF] Wełnic | Phase change materials: From structures to kinetics[END_REF], Ge1.5Sb2Te4 [START_REF] Wełnic | Phase change materials: From structures to kinetics[END_REF] and Ge2Sb2Te4 [START_REF] Wetnic | Controlling Material Properties in new Phase Change Alloys beyond the pseudobinary line[END_REF][START_REF] Wełnic | Phase change materials: From structures to kinetics[END_REF] have also been reported. Ge-rich materials may be defined as those compounds which are located in the region right to the vertical black line passing through the Ge2Sb2Te5 alloy.

Unfortunately, the crystallization temperature of Ge2Sb2Te5 is not high enough to allow its use in several classes of applications (such as automotive and aerospace applications) where the device is exposed to temperatures higher than 150°C, thus inducing undesired phase transitions in the PCM. For some other applications, the information needs to be recorded before the soldering process, the latter being carried out at ~260°C, thus potentially altering the code integrity. Ge-rich GST materials have recently appeared as a good solution for PCM-based devices requiring elevate working temperatures [START_REF] Aoukar | Dépôt de matériaux à changement de phase par PE-MOCVD à injection liquide pulsée pour des applications mémoires PCRAM[END_REF][START_REF] Coué | Electrical characterization & TEM analyses of the physical mechanisms governing reliability of Ge-rich Phase-Change Memories[END_REF]. Gerich GST materials usually refer to those compounds which contain more Ge than needed to satisfy the 225 stoichiometry. These compounds are located on the right of the Ge2Sb2Te5 phase in the ternary phase diagram shown in Fig. 1. The performances of PCMs based on Gerich GST alloys have been also tested, demonstrating high data retention over an extended temperature range [START_REF] Sousa | Operation fundamentals in 12Mb Phase Change Memory based on innovative Ge-rich GST materials featuring high reliability performance[END_REF][START_REF] Zuliani | Overcoming temperature limitations in phase change memories with optimized GexSbyTez[END_REF]. Moreover, N-doping has been shown to further increase the crystallization temperature, leading to better endurance, and to reduce the undesired drift phenomenon affecting the low resistance state [START_REF] Navarro | Trade-off Between SET and Data Retention Performance Thanks to Innovative Materials for Phase-Change Memory[END_REF][START_REF] Navarro | N-doping Impact in Optimized Ge-rich Materials Based Phase-Change Memory[END_REF][START_REF] Kiouseloglou | A Novel Programming Technique to Boost Low-Resistance State Performance in Ge-Rich GST Phase Change Memory[END_REF].

Actually, the chemical compositions of these materials are defined in the "asdeposited" state and thus correspond to amorphous layers of homogeneous compositions.

Whether or not these compositions and homogeneity remain unaltered during multiple cycling of a device and how the resulting structure can explain the observed properties are still open questions. In a PCM device, the amorphous-to-crystalline transition is promoted by electrical pulses which heat up a thin layer of GST material. Previous pioneering works have evidenced that chemical phase separation between Ge and some GST phase results from thermal annealing of full sheet deposited layers and from cycling of GST devices [START_REF] Sousa | Operation fundamentals in 12Mb Phase Change Memory based on innovative Ge-rich GST materials featuring high reliability performance[END_REF][START_REF] Zuliani | Overcoming temperature limitations in phase change memories with optimized GexSbyTez[END_REF][START_REF] Navarro | Trade-off Between SET and Data Retention Performance Thanks to Innovative Materials for Phase-Change Memory[END_REF][START_REF] Navarro | N-doping Impact in Optimized Ge-rich Materials Based Phase-Change Memory[END_REF][START_REF] Privitera | Atomic diffusion in laser irradiated Ge rich GeSbTe thin films for phase change memory applications[END_REF].

Nonetheless, an exhaustive analysis of the processes which take place during the crystallization of Ge-rich materials is still missing. While expected, the phase segregation probably occurring prior or during the crystallization of Ge-rich materials and the formation of stable crystalline compounds have not been studied in detail. Unpredicted variations of the local composition of the material during cycling can represent a source of failure and compromise the memory device endurance [START_REF] Padilla | Voltage polarity effects in Ge2Sb2Te5-based phase change memory devices[END_REF][START_REF] Crespi | Modeling of atomic migration phenomena in phase change memory devices[END_REF]. It is thus of primary importance to investigate the changes of chemical composition which affect Ge-rich GST alloys during thermal annealing leading to their crystallization.

In this paper, we report a detailed study of the different and successive phenomena which take place during thermal annealing of a N-doped Ge-rich GST alloy. For this, we have studied thoroughly the structural and chemical characteristics of samples annealed at different and increasing temperatures. The microstructure of the layers was analyzed using Transmission Electron Microscopy (TEM) techniques and automated crystal orientation mapping (ASTAR), while their chemical composition was analyzed using high angle annular dark field scanning TEM (HAADF-STEM) imaging and STEM energy dispersive X-ray (STEM-EDX) mapping. We show that a chemically homogeneous amorphous Ge-rich GST material undergoes phase separation during annealing and finally transforms into a composite material based on the two most stable crystalline phases offered by the constituents, Ge and Ge2Sb2Te5 crystals.

Experimental

A N-doped and highly Ge-enriched GST (E-GST, with [Ge] > 30%) film, with a thickness of 100 nm, was deposited by physical vapor deposition on a Si (100) substrate.

Then, an ultra-thin (14 Å) Ti-rich TiN layer was deposited on the E-GST surface prior to the deposition of a 20 nm-thick TiN encapsulating layer. The wafer was cut into different samples and annealed in a horizontal Carbolite furnace under atmospheric pressure and N2 flux, at different temperatures and times. In a previous paper [START_REF] Agati | In-situ transmission electron microscopy studies of the crystallization of N-doped Ge-rich GeSbTe materials[END_REF] we have shown that the onset of the phase change occurs at temperature T~380°C. For this reason, thermal annealing were performed at temperatures equal or larger than 380°C, i.e. at 380°C for 1 hour, 400°C for 30 minutes, 450°C for 30 minutes and 500°C for 30 minutes. TEM specimens were prepared in cross-section by traditional mechanical polishing followed by ion beam thinning (asdeposited, annealed 380°C/1 hour and annealed 400°C/30 minutes samples) or by focus ion beam (FIB) techniques (annealed 450°C/30 minutes. and 500°C/30 minutes specimens). The use of FIB for these latter samples annealed at higher temperatures was required due to the formation of blisters on the surface of these samples during annealing, which hampers the bonding of two samples face to face. A scanning electron microscope (SEM) image of these blisters is provided in the supporting information, Fig. S1(a). To understand the origin of these blisters, a FIB lamella was prepared at the edge of such a blister [Fig. S1(a)]. TEM analyses on this sample [Fig. S1(b)] revealed that the blisters are formed from the exfoliation of the TiN layer. Based on our experience [START_REF] Cherkashin | Cracks and blisters formed close to a silicon wafer surface by He-H co-implantation at low energy[END_REF], we believe that the blisters form as a result of N-exodiffusion from the E-GST film and N2 gas accumulation and pressurization below the TiN layer during high enough temperature annealing. Specimen preparation and SEM analyses were carried out using a FEI Helios Nanolab 600 dual-beam FIB and SEM. TEM conventional imaging, selected area electron diffraction (SAED), high resolution TEM (HRTEM) and HAADF-STEM analyses were performed using an aberration corrected FEI TECNAIF20, equipped with a FEG source. STEM-EDX and ASTAR (TEM orientation imaging) analyses were performed using a Philips CM20-FEG TEM. STEM-EDX analyses were performed using a Microanalyser QUANTAX XFlash detector with a 30 mm² active area and an energy resolution of 127 eV, while EDX quantification was performed by exploiting the Esprit 1.9 software. ASTAR imaging was performed using the Nanomegas Digistar ACOM system [START_REF] Moeck | High spatial resolution semi-automatic crystallite orientation and phase mapping of nanocrystals in transmission electron microscopes[END_REF]. In HAADF-STEM imaging, the Rutherford-scattering of electrons is maximized and diffraction-contrast effects are smoothed out. Since the Rutherford cross-section is proportional to Z 2 (where Z is the atomic number), the contrast of HAADF-STEM images is related to differences of the mean atomic number from one region to the other and hence to the local material composition [START_REF] Williams | Transmission Electron Microscopy: A Textbook for Materials Science[END_REF]. In Fig. 3(b), we again note the same nanometric "objects" as those observed in BF-TEM, but this time they appear in black. This evidences that they originate from regions of smaller atomic density. Finally, the contrasts observed both in the BF-TEM and the HAADF-STEM images evidence that annealing at 380°C for one hour results in fluctuations of the chemical composition of the material and this while staying in the amorphous phase.

Results

We consider afterwards the E-GST annealed at 400°C for 30 minutes. A typical BF-TEM image of this sample is shown in Fig. 4(a) along with its associated SAED pattern in Fig. 4(b). As discussed in our previous work [START_REF] Agati | In-situ transmission electron microscopy studies of the crystallization of N-doped Ge-rich GeSbTe materials[END_REF], this pattern evidences the coexistence of two crystalline phases which sequentially form during annealing: cubic Ge and FCC-GST.

Since the structure of FCC-GST crystals only marginally varies with stoichiometry along the congruent line, the exact composition of these GST crystals cannot be inferred from such diffraction patterns. The BF-TEM image shows the presence of very small crystals (3 nm, as indicated by the red arrow in Fig. 4(a)) as well as larger crystalline regions (dimensions of ~30 nm) in the layer. HRTEM images, as the one shown in the inset of Fig. 4(a), reveal that the small crystalline grains are interspersed within some amorphous phase. The structural characteristics of the small crystals and of the larger crystalline regions have been further studied using dark field (DF) imaging. To confirm our findings, we have analyzed the composition of these films using STEM-EDX.

Figure 6(a-f) is a set of STEM-EDX maps taken on the same sample and showing the spatial distribution of the elements within the layer. While nitrogen is still homogenously distributed across the layer, Ge, Te and, to a lesser extent, Sb have been redistributed during annealing.

Clearly, there exist regions, typically of several tens of nanometers wide, which are Gedepleted while they show an increased concentration of Te. The Sb map, although less contrasted, shows the same features than the Te map. This set shows that amorphous homogeneous Ge-rich GST undergoes some phase separation during annealing at 400°C [START_REF] Privitera | Atomic diffusion in laser irradiated Ge rich GeSbTe thin films for phase change memory applications[END_REF]. Compared to those shown in Fig. 6, these maps show that the Te and Sb-rich regions are now larger in size and that the contrast between the Ge-rich and Te-rich regions is higher. This indicates that phase separation continued during annealing at 450°C and led to the growth of the two types of regions we have evidenced. The oxygen map also confirms that oxygen has largely redistributed from the Si/E-GST interface towards the layer and preferentially getters in the Ge-rich regions. At this stage, it is very tempting to try to deduce the actual composition of the grains showing the FCC-GST structure from the STEM-EDX data. This would require that different grains do not overlap in the image i.e., that the specimen thickness is equal or smaller than the grain size. This has been achieved on samples annealed at 500°C for 30 minutes. As said above, since there is little overlap between the Ge matrix and the GST crystals in the sample annealed at 500°C for 30 minutes, STEM-EDX can be used to measure locally, on specific grains, the actual composition of the GST crystals. The ratios Ge/Te, Sb/Te and Ge/Sb can be used to infer its stoichiometry, as long as Te atoms are located only on the anionic sites, while the cationic sites can host Ge, Sb atoms or vacancies in different proportions which define the actual stoichiometry of the GST alloy. Table 1 shows the ratios which are expected for the different known phases of GST. Table 2 reports the experimental values we have measured on the different GST grains found in the film annealed at 500°C for 30 minutes. The experimental error is also reported.

Table 1. Ge/Te, Sb/Te and Ge/Sb characteristic ratios of the different GST phases shown in Fig. 1.

GST

Stoichiom.

Ge/Te Sb/Te Ge/Sb Ge/Te σ(Ge/Te) Sb/Te σ(Sb/Te) Ge/Sb σ(Ge/Sb) Crystal-1 0,5 0,3 0,5 0,2 1,0 0,7

Crystal-2 0,6 0,3 0,7 0,3 0,8 0,5

Crystal-3 0,6 0,3 0,7 0,3 0,9 0,5

Crystal-4 0,7 0,3 0,6 0,3 1,0 0,7

Crystal-5 0,8 0,3 0,5 0,2 2 1

Crystal-6 0,8 0,4 0,7 0,3 1,1 0,7

Crystal-7 0,7 0,3 0,6 0,3 1,2 0,8

Crystal-8 0,7 0,3 0,5 0,2 1,3 0,9

Crystal-9 0,8 0,4 0,7 0,3 1,2 0,8

Crystal-10 0,7 0,3 0,6 0,3 1,1 0,7

First, the Ge/Sb ratio which is experimentally measured most often close to 1 allows one to rule out a large number of GST stoichiometries. In particular, Ge-rich GST phases do not fulfill this criterion. The well-known 225 stoichiometry provides a better agreement although the larger than predicted Ge/Te and Sb/Te ratios we have measured may be an indication that some of the vacancies normally sitting on the cationic sub-lattice have been filled with Ge and Sb atoms.

Discussion

Summarizing our results, we have evidenced that homogeneous Ge-rich GST alloys are stable up to 380°C. At this temperature, chemical inhomogeneities (Ge-rich, Ge-poor) at the nanoscale start to appear while the material is still in the amorphous phase. Ge atoms diffuse and segregate in regions of nanometric dimensions. The nucleation of pure Ge nanocrystals occurs only after longer annealing times, once this phase separation has been consolidated [START_REF] Agati | In-situ transmission electron microscopy studies of the crystallization of N-doped Ge-rich GeSbTe materials[END_REF]. Annealing at 400°C favors this segregation further and allows the crystallization of two phases: large (several tens of nanometers) crystals exhibiting a cubic GST structure are found, surrounded by a high density of cubic Ge nanocrystals, as also reported previously by Privitera et al. [START_REF] Privitera | Atomic diffusion in laser irradiated Ge rich GeSbTe thin films for phase change memory applications[END_REF]. Annealing at 450°C results into an increase of the sizes of both types of crystals. Finally, after annealing at 500°C, the layer is totally crystalline.

In general, the GST crystals are large (up to one hundred of nanometers), surrounded and isolated from each other by a matrix of Ge nanocrystals. Interestingly, these Ge grains appear to have gettered the oxygen atoms initially present in the native oxide at the Si/E-GST interface.

Quantitative chemical analysis shows that the material has transformed into two pure and well identified phases, the cubic Ge and a cubic GST phase, most probably, the FCC-Ge2Sb2Te5. However, the Ge/Te and Sb/Te ratios we have measured, slightly larger than expected for a regular Ge2Sb2Te5, might indicate that this material is doped, with Ge and Sb atoms at sites normally vacant on the cationic lattice (20%). It is important to note that, despite the high temperature involved, the GST phase we evidence is still cubic, as demonstrated by the HRTEM images, and not hexagonal as expected after annealing above the cubic-to-hexagonal transition temperature of the Ge2Sb2Te5 i.e., 300-350°C [START_REF] Zheng | Surface Energy Driven Cubic-to-Hexagonal Grain Growth of Ge2Sb2Te5 Thin Film[END_REF]. It is thus suspected that this transition is hampered by the environment, the Ge phase and probable stress at the interfaces. However, it is not unreasonable to think that the delicate balance between Ge and Sb atoms and vacancies on the same sub-lattice may be affected by such strong out-of-equilibrium conditions (more than 150°C above the transition temperature). The observation of voids, precipitates of vacancies, in the layer reveals that, at some point, the crystals have expulsed vacancies, in support of our hypothesis for a "doped" Ge2Sb2Te5 phase.

Most importantly, our results show that the crystallization of a Ge-rich GST material proceeds through different steps. First, chemical fluctuations of the initially homogeneous amorphous phase take place, driven by Ge diffusion, and lead to Ge segregation. Then, Ge crystallization occurs and forms Ge nanocrystals. The observation of oxygen gettering on these nanocrystals, probably on their facets, may explain why they do not grow so much in size but instead stay small and nucleate in huge density. Once these crystals are formed, they drive Ge diffusion from the surrounding matrix towards them, hence decreasing the Ge concentration in the matrix. Experimentally, it is only after many Ge nanocrystals have been formed that the first GST crystals nucleate. This observation strongly suggests that a too high local concentration of Ge hampers the crystallization of the GST phase. In other words, the Ge concentration increases the energy barrier height for the amorphous to crystalline transition of GST. It is only after a region has been "purified" from Ge that it can crystallize as a GST phase.

All our observations support the idea that the change of properties which are sought for memory applications i.e., higher thermal stability and increase of "transition temperature", are not intrinsic properties of some precise Ge-rich phases, but result from kinetic factors.

Indeed, phase segregation phenomena are energetically expensive processes which involve long range diffusion of atomic species, what explains the need for longer incubation times for crystallization as well as higher thermal stability of the amorphous phase when the Ge content is increased.

While selecting doped GST alloys on the basis of the classical graphs showing the variations of the resistivity as a function of the annealing temperature is certainly pertinent for enlarging the application domains of PCMs [START_REF] Sousa | Operation fundamentals in 12Mb Phase Change Memory based on innovative Ge-rich GST materials featuring high reliability performance[END_REF][START_REF] Zuliani | Overcoming temperature limitations in phase change memories with optimized GexSbyTez[END_REF][START_REF] Navarro | Trade-off Between SET and Data Retention Performance Thanks to Innovative Materials for Phase-Change Memory[END_REF], our results show that Ge-rich alloys decompose and crystallize as a two-phase material. Thus, such graphs evidences that, given the volume of material probed by the measurement and the annealing ramp-up rate, the time spent at some temperature and below was sufficient for the system to undergo phase separation between Ge and Ge2Sb2Te5.

Conclusion

Using a variety of TEM based techniques, we have investigated the changes which affect the structure and composition of Ge-rich GST alloys during thermal annealing. We show that, although Ge-rich GST materials can be grown as amorphous layers of homogeneous compositions, the primary effect of annealing is to activate phase separation between stable Ge and GST phases. This phase separation starts at 380°C while the material is still amorphous. and later leads to the nucleation of the first Ge nanocrystals. Increasing the annealing temperature to 400 and then 450°C allows the crystalline Ge phase to grow by driving the excess Ge out of the matrix and finally to the formation of large (30-50 nm) crystals with the FCC-GST structure. After annealing at 500°C for 30 minutes, the layer has fully crystallized and consists of a population of large (50-100 nm) FCC-GST crystals with a stoichiometry close to 225 buried in a matrix composed of small Ge nanocrystals.

This study evidences that the superior properties of Ge-rich alloys i.e., higher thermal stability and larger crystallization temperature, do not result from the intrinsic properties of some Ge-rich crystalline phase but from kinetic factors, and involves long range diffusion of atomic species, first and foremost Ge. The crystallization kinetics of such two-phase materials is diffusion limited and requires adequate combinations of temperatures and times to occur.

Fig. 1 .

 1 Fig. 1.Ternary phase diagram for GST compounds. The tie line is indicated in magenta color and intercepts the alloys exhibiting congruent melting. GST alloys such as Ge2Sb2Te5, GeSb4Te7[START_REF] Abrikosov | An investigation of the structural diagram of Sb2Te3-GeTe[END_REF], GeSb2Te4[START_REF] Abrikosov | An investigation of the structural diagram of Sb2Te3-GeTe[END_REF], Ge3Sb2Te6[START_REF] Shelimova | Composition and Properties of Layered Compounds in the GeTe-Sb2Te3 System[END_REF], Ge4Sb2Te7[START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF][START_REF] Shelimova | Composition and Properties of Layered Compounds in the GeTe-Sb2Te3 System[END_REF], Ge6Sb2Te9[START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF], Ge8Sb2Te11[START_REF] Wuttig | Phase-change materials for rewriteable data storage[END_REF] have been previously reported in literature and have been plotted here. Close to the tie line, Ge4SbTe5[START_REF] Woltgens | Exploring the limits of fast phase change materials[END_REF][START_REF] Wamwangi | Crystallization kinetics of Ge4Sb1Te5 films[END_REF], GeSb6Te10[START_REF] Shelimova | Composition and Properties of Layered Compounds in the GeTe-Sb2Te3 System[END_REF], GeSb8Te13[START_REF] Shelimova | Composition and Properties of Layered Compounds in the GeTe-Sb2Te3 System[END_REF], Ge2SbTe4[START_REF] Wełnic | Phase change materials: From structures to kinetics[END_REF], Ge1.5Sb2Te4[START_REF] Wełnic | Phase change materials: From structures to kinetics[END_REF] and Ge2Sb2Te4[START_REF] Wetnic | Controlling Material Properties in new Phase Change Alloys beyond the pseudobinary line[END_REF][START_REF] Wełnic | Phase change materials: From structures to kinetics[END_REF] have also been reported. Ge-rich materials may be defined as those compounds which are located in the region right to the vertical black line passing through the Ge2Sb2Te5 alloy.

Figure 2 (

 2 Figure 2(a) shows a bright field (BF) TEM image of the as-deposited E-GST film. The

Fig. 2 .

 2 Fig. 2. (a) BF-TEM image of as-deposited E-GST and its SAED in the inset. The chemical composition is homogeneous across the film, as evidenced by the STEM-EDX maps of (b) Ge, (c) Sb, (d) Te, (e) N. The presence of a thin Si oxide layer at the Si/E-GST interface is evidenced in (f).

Figure 3 (

 3 Figure 3(a) shows a BF-TEM image of the sample annealed at 380°C for 1 hour. The

Fig. 3 .

 3 Fig. 3. (a) BF-TEM image and (b) HAADF-STEM image of E-GST annealed at 380°C for 1 hour, both showing the same nanometric contrast. The SAED shown in the inset of (a) indicates that the film is in the amorphous state.

Fig. 4 .

 4 Fig. 4. (a) BF-TEM image of the E-GST annealed at 400°C for 30 minutes and (b) the corresponding SAED. (c) DF image obtained by selecting the diffraction spot indicated by the red circle. A typical HRTEM image of this sample is also shown in the inset of (a).

Figure 4 (

 4 c) is a DF image obtained by selecting the GST spot in the SAED pattern, as indicated by the red circle in Fig. 4(b). As this spot is very close to the diffraction ring characteristic of the Ge phase, the DF image results from both contributions. Under such conditions, the images show faintly visible small nanocrystals homogeneously dispersed across the E-GST layer and larger and defective crystalline regions of irregular shapes.

Figure 5 (

 5 Figure 5(a) shows the BF-TEM image of one of these large crystalline regions.Figure

Fig. 5 .

 5 Fig. 5. (a) BF-TEM image showing a crystalline region in E-GST annealed at 400°C. The corresponding DF images taken (b) by selecting the FCC-GST diffraction spot and (c) along the Ge ring are also shown.

Fig. 6 .

 6 Fig. 6. (a) Superposition of the STEM-EDX maps of (b) Ge, (c) Sb, (d) Te, (e) N and (f) O relatively to E-GST annealed at 400°C for 30 minutes.

Figure 7 (

 7 Figure 7(a) is a typical BF-TEM image of the layer annealed at 450°C for 30 minutes.

Fig. 7 .

 7 Fig. 7. (a) BF-TEM image of the E-GST annealed at 450°C for 30 minutes. (b) Typical HRTEM image of the same sample.

Fig. 8 .

 8 Fig. 8. (a) BF image of a crystalline zone of E-GST annealed at 450°C for 30 minutes and its SAED in the inset. (b-d) Series of DF images.

Figure 9 (

 9 Figure 9(a-f) shows the chemical mapping obtained by STEM-EDX on this sample.

Fig. 9 .

 9 Fig. 9. (a) Superposition of the STEM-EDX maps of (b) Ge, (c) Sb, (d) Te, (e) N and (f) O relatively to E-GST annealed at 450°C for 30 minutes.

Figure 10 (

 10 Figure 10(a) shows a BF-TEM image of this sample. After such an annealing, the

Fig. 10 .

 10 Fig. 10. (a) BF-TEM image of E-GST annealed at 500°C for 30 minutes and its SAED in the inset. (b) HRTEM of a large GST crystal: the stacking sequence abcabc… evidences the cubic structure.

Fig. 11 .

 11 Fig. 11. (a) ASTAR map of the E-GST annealed at 500°C for 30 minutes. (b) Superposition of the STEM-EDX maps of (c) Ge, (d) Sb, (e) Te, (f) N and (g) O relatively to the same sample. As a reference, the arrows in (a) and (b) indicate the same crystal.

Table 2 .

 2 Ge/Te, Sb/Te and Ge/Sb ratios measured by quantitative STEM-EDX analysis on the different GST grains observed in the ASTAR and STEM-EDX maps shown in Fig.11, corresponding to the sample annealed at 500°C for 30 minutes.

Acknowledgements

The authors would like to thank the people in charge of the TEM and FIB facility at CEMES, in particular C. Marcelot and R. Cours for their precious technical support. This work was partially funded by Minefi through the Nano2017 initiative and by the Labex NEXT (n° ANR-10-LABX-0037) in the framework of the "Programme des Investissements d'Avenir".

ASTAR imaging was used to provide orientation mapping of the different crystals found in the sample annealed at 500°C for 30 minutes. This technique is based on a collection of precession electron diffraction patterns acquired at each point by scanning the electron beam over the sample. In our case, each acquired electron diffraction pattern was compared numerically with those theoretically corresponding to pure Ge and Ge2Sb2Te5. The resulting ASTAR map is shown in Fig. 11(a) and displays large Ge2Sb2Te5 crystals in yellow surrounded by Ge crystals in blue. This analysis firstly shows that, after annealing at 500°C for 30 minutes, the E-GST is fully crystallized. However, since the structures corresponding to the different GST materials lying on the congruent line shown in Fig. 1 cannot be sorted out based only on their diffraction patterns, one cannot conclude on which GST alloy has crystallized. For this reason, we have investigated the chemical composition of the GST grains using STEM-EDX on the same region of the sample imaged by ASTAR. Chemical maps are shown in Fig. 11(b-g). The contrast between the Ge-rich and the Te and Sb-rich regions is very high. This is due from one hand to the thin thickness of the sample but also to the full separation of the two Ge and GST phases. Comparing these chemical maps with the ASTAR image of Fig. 11(a), one can see that the initially homogeneous layer has transformed into a layer of 50-100 nm wide GST crystals embedded in a Ge crystalline matrix.