Anne-Laure Barthelemy

Victor Certal

Guillaume Dagousset

Elsa Anselmi

Luc Bertin

Laurence Fabien

Bruno Salgues

Philippe Courtes

Christian Poma

Youssef El-Ahmad

Emmanuel Magnier
email: emmanuel.magnier@uvsq.fr

Optimization and Gram-scale Preparation of S-Trifluoromethyl-Sulfoximines and Sulfilimino iminiums, Powerful Reagents for the Late Stage Introduction of the CF 3 Group

Keywords: Trifluoromethyl, Sulfoximines, Sulfilimino iminiums, Sulfilimines, DSC measurements

come

INTRODUCTION

The introduction of a fluorine atom or perfluoroalkylated moieties into an organic compound can lead to profound changes in its physical, chemical or biological properties due to the peculiar intrinsic properties of the fluorine atom. 1 Indeed, fluorine exhibits a high electronegativity (4.0 on the Pauling scale), a small atomic radius (1.47 Å) and induces a strong C-F bond (about 116 kcal/mol). This is the reason why nowadays about 20% of pharmaceuticals and 50% of agrochemical compounds contain at least one fluorine atom. 2 However, the number of natural organic compounds containing a fluorinated moiety is quite limited. 3 This implies that access to organofluorine compounds is essentially based on the development of practical fluorination or fluoroalkylation reactions, and always requires new methodologies. The toolbox that chemists now possess contains more and more fluorinating and perfluoroalkylating reagents which are stable, selective and easy to handle. Among them, the electrophilic reagents of Umemoto and Togni (Figure 1) have probably been the most popular. 4 In addition, a third class of compounds in this family, the fluorinated sulfoximines, should not be omitted and have received increasing attention in the last decade. [START_REF] Bizet | Fluorinated sulfoximines: syntheses, properties and applications[END_REF] Indeed, these aza-analogs of sulfones are fluoroalkylating reagents with flexible reactivity, via nucleophilic, electrophilic or radical pathways. The Shibata reagent is the most known member of this family, but in our laboratory, we have also discovered other types of sulfoximine-based reagents as well as a very peculiar structure, a sulfilimino iminium, which has successfully been used for the efficient production of the trifluoromethyl radical. The synthesis of NH S-perfluoroalkylated sulfoximines was quite cumbersome, using harsh and dangerous conditions, until our group described, in 2009, a three-step methodology for the preparation of such compounds. 7 A slight adaptation of the reaction conditions allowed access to sulfilimino iminiums.

Consequently, because of the increasing use of sulfoximines as reagents, large-scale production appeared to be essential. We describe in this article a gram-scale, divergent synthesis of sulfoximine and sulfilimino iminium. Each step of our previous methodologies has been reconsidered and improved. Differential Scanning Calorimetry (DSC) measurements of both the reaction mixtures and the isolated molecules are described in order to ensure the maximum safety of the process. Total costs of the synthesis are also discussed.

RESULTS AND DISCUSSION

The synthesis of these reagents starts from the phenyl trifluoromethyl sulfoxide 1, which is treated with acetonitrile in the presence of triflic anhydride, leading, via a Ritter-type reaction, to The phenyl trifluoromethyl sulfoxide 1 is commercially available but quite expensive (at least 78 € per gram). However, compound 1 can be easily prepared following our previously described one-pot procedure starting from sodium trifluoromethanesulfinate (Langlois reagent) and benzene. [START_REF] Magnier | Straightforward one-pot synthesis of trifluoromethyl sulfonium salts[END_REF] A reappraisal of our protocol is presented herein (Scheme 2). The production of compound 1 has been scaled up to 78 g without major issues and with a good yield of 73% (Table 1, entry 3) after purification by distillation.

Scheme 2: Synthesis of the sulfoxide 1 This reaction occurs without solvent which causes two major issues: elevation of the temperature of the reaction and difficulty in stirring the reaction mixture. It is noteworthy that the addition of trifluoromethanesulfonic acid to sodium trifluoromethanesulfinate leads to a pasty mixture and to a rapid increase in temperature that can rise to 80°C. On a 10 g scale (Table 1, entry 1), magnetic stirring gives a reasonably homogeneous mixture and the exothermic phenomenon is not problematic. With larger quantities of reagents (Table 1, entries 2-3), mechanical stirring is required to obtain good dispersion and a homogeneous medium. Otherwise, the formation of aggregates proves deleterious to the yield. The triflic acid should be added portion wise (at least by thirds) to minimize temperature elevation. An additional cold-water bath is required to maintain the temperature of the reaction mixture (controlled by a thermometer) below 50°C. After 19 hours of stirring at room temperature, the reaction is poured onto ice (10 g of ice for 1 g of sodium trifluoromethanesulfinate) to control the exothermicity of the quenching. The thermal stability of this compound was explored by DSC analysis (Figure 2). The phenyl trifluoromethyl sulfoxide 1 exhibits good thermal stability with decomposition from 205°C, proving the safety of the previously described reaction conditions and purification. It is important to underline that purification of the sulfoxide 1 is not necessary for the next steps.

Synthesis of the intermediary sulfilimine 3.

The second step is a Ritter-type reaction between the sulfoxide 1 and acetonitrile in the presence of trifluoromethanesulfonic anhydride. The procedure described by our group in 2009 7a has been adapted to a larger scale using acetonitrile as reagent and solvent, increasing its quantity from 1.5 to 11 equivalents.

Scheme 3: Synthesis of the intermediary sulfilimine 3

It should be noticed that a low temperature (-15°C) is necessary to control the first step and to obtain an optimal formation of the intermediate sulfilimine 3. This experimental observation was supported by DSC analysis of the reaction media just after the addition of trifluoromethanesulfonic anhydride and also after full conversion of the sulfoxide 1. The DSC analysis of the reaction medium after the dropwise addition of trifluoromethanesulfonic anhydride (Tf2O) shows an endothermic peak at 20°C followed by an exothermic peak from 55°C, revealing the instability of the reaction medium (Figure 3). Moreover, after full conversion of sulfoxide 1, it was shown that the medium is quite unstable with an exothermic peak starting at 15°C (Figure 4). Therefore, the temperature of the reaction should be maintained under -15°C to preserve an acceptable thermal stability. For this purpose, the reaction can be simply stored in a freezer for 18 hours, as the absence of stirring does not negatively impact the yield of the transformation. It should be underlined that there is an interaction between triflic anhydride Tf2O and acetonitrile (Figure 5), regardless of the number of equivalents, with a thermal phenomenon, which contributes to the one of the reaction (Figure 4). and in order to control the exothermicity of the reaction quench, it is necessary to pour the crude mixture onto ice (10 g of ice for 1 g of sulfoxide 1). The pure N-acetylated sulfilimine 3 shows a DSC profile with a decomposition starting from an onset temperature of 145°C (Figure 6), far from the process temperature. On a large scale, an excellent overall yield is obtained for the production of 33 g of sulfoximine 4 (Table 2, entry 3). The scale up can be achieved without major issues. To facilitate the oxidation step on scale-up, potassium permanganate was slowly added as a solid to the solution of intermediate sulfilimine 3 in water and acetonitrile. It is important to note that no intermediate purification is required and the final product was simply filtered through a pad of silica. Pleasingly, we noticed a substantial improvement in the yield on increasing the scale of the reaction. Both steps were analyzed by DSC. The oxidation medium exhibits an exothermic peak from 125°C, revealing a good thermal stability of the mixture (Figure 7) under the reaction conditions. The DSC profile of the isolated products were also explored. It is noteworthy that both compounds 4' and 4 exhibit an autocatalytic behavior (sharp peak) with an important exothermic peak. Indeed, the N-acetylated sulfoximine 4' decomposes with an energy exceeding 600 J/g from 265°C (Figure 9). 5 starts from the trifluoromethyl sulfoxide 1, and the first step is a Ritter-type reaction between the sulfoxide 1 and acetonitrile in the presence of triflic anhydride. The major difference is the quench reagent. This time, the addition of dimethylamine delivers the desired sulfilimino iminium 5 (Scheme 5).

Scheme 5: Synthesis of the sulfilimino iminium 5

In our previous protocol, 7b the dimethylamine was added in pure form. The use of a commercial solution of dimethylamine in THF (2M) is more convenient and was added dropwise at -15°C (Table 3, entry 1). At the end of the addition, the temperature of the reaction was allowed to rise slowly to room temperature. During the scale-up of the reaction conditions, we realized that the introduction of 4 equivalents of dimethylamine led to a very dilute reaction medium, and we assumed that fewer equivalents could afford the desired product with a similar yield. When 2.6 equivalents of dimethylamine in THF are introduced, the desired sulfilimino iminium 5 is obtained with a good yield of 76 % (Table 3, entry 2), similar to the yield with 4 equivalents (Table 3, entry 1). The production of sulfilimino iminium 5 has been scaled up to 40 g with a good yield of 64 % (Table 3, entry 3). From a practical point of view, the purification of compound 5 by chromatography on silica is quite cumbersome, using a lot of solvent and time. Changing the purification method quickly became essential during the scale-up of the synthesis. Sulfilimino iminium 5 is insoluble in diethyl ether. Therefore, compound 5 can be placed on a pad of Celite ® (10 g of Celite ® per gram of sulfoxide), impurities are removed by washing the Celite ® with diethyl ether and the desired product is then recovered by washing the celite ® with dichloromethane. If some impurities remain, the obtained solid can be washed again with diethyl ether. It is important to mention that the use of a newly opened bottle of high quality trifluoromethanesulfonic anhydride is crucial for the success of the reaction.

The thermal stability of sulfilimino iminium 5 has also been explored by DSC analysis (Figure 11). After an endothermic phenomenon corresponding to the melting of 5 around 64°C, an exothermic peak is observed from 120°C with an energy at 412 J/g revealing its good thermal stability under the process temperature. Financial estimation for reagent production.

We have been able to produce 78 g of sulfoxide 1, 33 g of sulfoximine 4 and 40.5 g of sufilimino iminium 5. We decided to determine the cost of the production of such batches. To estimate the cost, the reagents, the solvents used for reactions and extraction, and the solvents, Celite ® or silica used for purifications have been taken into account (Tables 4, 5 and6) but the cost of manpower has been overlooked. Globally, the cost per gram of these reagents is highly reasonable.

CONCLUSION

The production of sulfoxide 1, sulfoximine 4 and sulfilimino iminium 5 has been optimized and performed on a multi-gram scale. DSC analyses, performed on only a few milligrams of substance, allowed us to investigate the thermal stabilities of the intermediates and final species. It is noteworthy that we are confident that these quantities do not represent an upper limit, and that larger quantities could be obtained in good yields with such optimized conditions. Moreover, the overall costs of these reagents are highly reasonable. These efficient conditions clearly pave the way to easy syntheses of such reagents in any laboratory for further applications, and should contribute to the popularization of their use.

EXPERIMENTAL SECTION

Synthesis of the ((trifluoromethyl)sulfinyl)benzene 1

A dry 1 L, three-necked, round-bottomed flask equipped with a thermometer and a mechanical stirrer was charged with sodium trifluoromethanesulfinate (90 g, 0.58 mol) and dried under vacuum for 24 hours prior to use. The flask is placed in a cold-water bath and trifluoromethanesulfonic acid (315 mL, 3.56 mol) is added, under argon, in three portions with vigorous stirring (around 100 mL each), in order to keep the temperature under 50°C. After the addition, the reaction is stirred for 20-30 minutes until the temperature decreases to room temperature. Then, benzene (90 mL, 1.01 mol) is added in one portion and the solution is stirred at room temperature for 19 h under an inert atmosphere. The reaction is quenched by pouring the reaction medium on ice (900 g), extracted with dichloromethane (3 x 100 mL), and washed with a saturated solution of NaHCO3 (3 x 60 mL). The organic phase is dried over MgSO4, filtered and concentrated under reduced pressure. The product is purified by distillation under reduced pressure (78 -80°C at 15 mmHg) to afford 1 (78.1 g, 73%, colorless oil).

1 H NMR (300 MHz, CDCl3) δ (ppm): 7.76 (d, J = 7.4 Hz, 2H), 7.70 -7.49 (m, 3H). 13 C NMR ( 75MHz, CDCl3) δ (ppm): 135.6 (q, J = 1.72 Hz), 133.6, 129.61, 125.9, 124.7 (q, J = 335 Hz, CF3).

19 F NMR (282 MHz, CDCl3) δ (ppm): -75.0 (s, 3F).

Imino(phenyl)(trifluoromethyl)-λ 6 -sulfanone 4

In a dry 500 mL two-necked round-bottomed flask equipped with a dropping-funnel and a thermometer, a solution of phenyl trifluoromethyl sulfoxide 1 (40 g, 206.0 mmol) in dry acetonitrile (120 mL, 2.28 mol) is cooled to -15°C under argon. Tf2O (52 mL, 309.1 mmol) is introduced into the dropping-funnel and added dropwise to the solution, keeping the temperature around -15°C. The solution is then left at -15°C for 18 h under argon in a freezer. The reaction is quenched by pouring the reaction media on ice (400 g), extracted with dichloromethane (3 x 80 mL), and washed with a saturated solution of NaHCO3 (3 x 40 mL). The organic phase is dried over MgSO4, filtered and concentrated under reduced pressure.

To a solution of this crude product in acetonitrile (160 mL) and water (40 mL) is added KMnO4 (32.56 g, 206.0 mmol) portion wise. The reaction is stirred at room temperature for 18 hours, diluted with H2O (150 mL) and a saturated solution of Na2S2O4 is added until complete discoloration of the solution. The product is extracted with dichloromethane (3 x 70 mL), and the organic phase is dried over MgSO4, filtered and concentrated under reduced pressure.

The crude product is dissolved in acetonitrile (184 mL) and HCl 6M (67.2 mL) is added. The reaction is stirred at room temperature for 18h. Then, water (100 mL) is added and the organic phase is extracted with dichloromethane (3 x 50 mL), washed with a solution of saturated NaHCO3

(3 x 20 mL), dried over MgSO4, filtered and concentrated under reduced pressure. The product is filtered on silica (200 g) using petroleum ether/ethyl acetate 8/2 as eluent to afford the desired sulfoximine 4 (32.8 g, 76 %, white solid). In a dry 500 mL two-necked round-bottomed flask equipped with a dropping-funnel and a thermometer, under argon, a solution of phenyl trifluoromethyl sulfoxide 1 (30 g, 154.5 mmol) in dry acetonitrile (87.1 mL, 1.67 mol) is cooled to -15°C. Tf2O (39.1 mL, 232.4 mmol) is added dropwise, keeping the temperature around -15°C. The solution is then left at -15°C for 18 h under argon in a freezer. A solution of Me2NH (2M in THF, 200.9 mL, 401.8 mmol) is added dropwise to the reaction, keeping the temperature at around -15°C, under an inert atmosphere. Then, the reaction mixture is allowed to warm to room temperature slowly. The reaction is stirred at room temperature for 18h, under an inert atmosphere. The reaction is quenched by addition of 100 mL of water and the product is extracted with dichloromethane (3 x 120 mL). The organic phase is dried over MgSO4, filtered and concentrated under reduced pressure. The crude residue is placed on Celite ® (300 g) and the solid is washed three times with diethyl ether to remove impurities.

Then, the deposit is washed three times with dichloromethane to recover the desired product 5

(40.5 g, 64 %, brownish solid).

6

 6

Figure 1 :

 1 Figure 1: Electrophilic or radical perfluoroalkylating reagents

a

  Scheme 1: Synthetic scheme of the preparation of trifluoromethyl-sulfoximines and sulfilimino

Figure 2 :

 2 Figure 2: DSC analysis of the phenyl trifluoromethyl sulfoxide 1

Figure 3 :

 3 Figure 3: DSC analysis of the reaction medium after the addition of Tf2O

Figure 4 :

 4 Figure 4: DSC analysis at full conversion of sulfoxide 1

Figure 5 :

 5 Figure 5: DSC analysis of the interaction between Tf2O and acetonitrile (Tf2O/MeCN = 1/2 v/v)

Figure 6 :

 6 Figure 6: DSC analysis of the N-acetylated sulfilimine 3

Figure 7 :

 7 Figure 7: DSC analysis of the oxidation reaction medium

Figure 8 :

 8 Figure 8: DSC analysis of the hydrolysis reaction medium

Figure 9 :

 9 Figure 9: DSC analysis of the intermediate 4'

Figure 10 :

 10 Figure 10: DSC analysis of the sulfoximine 4

Figure 11 :

 11 Figure 11: DSC analysis of sulfilimino iminium 4

  1 H NMR (300 MHz, CDCl3) δ (ppm): 8.15(d, J = 7.5 Hz, 2H), 7.84 -7.72 (m, 1H), 7.63 (dd, J = 8.5, 7.1 Hz, 2H), 3.53 (s, br s, 1H).13 C NMR (75 MHz, CDCl3) δ (ppm): 135.6, 131.6, 130.7, 129.6, 121.0 (q, J = 333 Hz, CF3).19 F NMR (282 MHz, CDCl3) δ (ppm): -70.3 (s, 3F). (Z)-N-methyl-N-(1-((phenyl(trifluoromethyl)-λ 4 -sulfanylidene)amino)ethylidene)methaneminium 5

Table 1 : Multigram synthesis of phenyl trifluoromethyl sulfoxide 1

 1

	Entry	Benzene	CF3SO2Na	TfOH	Sulfoxide	Yield
	1	10 mL	10 g	35 mL	7.6 g	61 %
	2 a	50 mL	50 g	176 mL	41.9 g	68 %
	3 a	90 mL	90 g	315 mL	78.1 g	73 %

a Use of a mechanical stirrer

Table 2 :

 2 Multigram synthesis of phenyl trifluoromethyl sulfoximine 4

	Entry Sulfoxide	Tf2O	MeCN	KMnO4	HCl 6M	Sulfoximine	Yield
	1	5 g	6.5 mL	15 mL	4.07 g	8.4 mL	2.7 g	50 %
	2	20 g	26 mL	60 mL	16.28 g	33.6 mL	14.3 g	66 %
	3	40 g	52 mL	120 mL	32.56 g	67.2 mL	32.8 g	76 %

Table 3 :

 3 Multigram synthesis of sulfilimino iminium 5

	Entry	Sulfoxide	Tf2O	MeCN	Me2NH in THF	Compound	Yield
	1	2.0 g	2.6 mL	5.8 mL	20.6 mL/ 4 eq	3.0 g	71 %
	2	15.0 g	19.5 mL	43.6 mL	100.0 mL/ 2.6 eq	24.3 g	76 %
	3	30.0 g	39.1 mL	87.1 mL	200.9 mL/ 2.6 eq	40.5 g	64 %

Table 4 :

 4 Financial estimation for the synthesis of sulfoxide 1 Negotiated prices with chemical suppliers.b Exchange rate on 01/21/19, 13:15 UTC.

	Reagent	Chemicals cost a	Quantity Cost (€)
	Benzene	20.79 € / 500 mL	50 mL	2.08
	CF3SO2Na	£ 83.00 / 100 g	50 g	47.00 b
	TfOH	193.98 € / 1 kg = 590 mL 176 mL	57.87
	Dichloromethane (Extraction) 8.10 € / 5 L	300 mL	0.49
	Total cost for the production of 42 g of sulfoxide 1		107.43
	Total cost for the production of 1 g of sulfoxide 1		2.56 (2.91 $) b

Table 5 :

 5 Financial estimation for the production of sulfoximine 4

	Reagent	Chemicals cost a	Quantity	Cost (€)
	Sulfoxide 1	2.56 € / 1 g	40 g	102.4
	Tf2O	£ 270.0 / 1 kg = 596 mL 52 mL	26.61 b
	Acetonitrile	13.70 € / 2.5 L	119 + 344 mL 2.54
	KMnO4	59.90 € / 500 g	32.55 g	3.90
	HCl 37 %	5.57 € / 2,5 L	33.6 mL	0.07
	Dichloromethane (Extraction) 8.10 € / 5 L	1 L	1.62
	Silica (Purification)	11.80 € / 1 kg	200 g	2.36
	Petroleum ether (Purification) 8.35 € / 5 L	2.1 L	3.51
	Ethyl acetate (Purification)	10.0 € / 5 L	0.4 L	0.8
	Total cost for the production of 33 g of sulfoximine 4		142.93
	Total cost for the production of 1 g of sulfoximine 4		4.33 (4.91 $) b

a Negotiated prices with chemical suppliers.

b

Exchange rate on 01/21/19, 13:15 UTC.

Table 6 :

 6 Financial estimation for the production of sulfilimino iminium

5 Reagent Chemicals cost a Quantity Cost (€)

	Dichloromethane (Purification) 8.10 € / 5 L	0.6 L	0.97
	Total cost for the production of 40.5 g of sulfilimino iminium 5	135.94
	Total cost for the production of 1 g of sulfilimino iminium 5		3.36 (3.81 $) b
	a Negotiated prices with chemical suppliers. b Exchange rate on 01/21/19, 13:15 UTC.
	Sulfoxide 1	2.56 € / 1 g	30 g	76.8
	Tf2O	£ 270.0 / 1 kg = 596 mL 39.1 mL 20.05 b
	Acetonitrile	13.70 € / 2.5 L	87.1 mL 0.48
	Me2NH in THF (2M)	74.00 € / 500 mL	200.9 mL 29.7
	Dichloromethane (Extraction) 8.10 € / 5 L	360 mL	0.58
	Celite ® (Purification)	399.00 € / 25 kg	300 g	4.79
	Diethyl ether (Purification)	21.40 € / 5 L	0.6 L	2.57

H NMR (300 MHz, CDCl3) δ (ppm): 8.07[START_REF] Pégot | Perfluoroalkylated Bis (sulfilimine) s and Bis (sulfoximine) s by a Ritter-Type Reaction[END_REF] J = 7.9 Hz,

2H),7.89 -7.75 (m, 1H), 7.70 (dd, J =

ACKNOWLEDGMENT

We thank the CNRS and French Ministry of Research for their financial support. We also acknowledge Dr. Karen Wright for the careful reading and improvement of the English, Dr. F.

Metz from Solvay-Rhodia Lyon for the gift of chemicals and the French Fluorine Network for its support.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.


The Pandemic Response Shows How Workers Defend the Interests of All Humanity

By

Hadrien Clouet Maxime Quijoux Translation by Nathan French : https://jacobinmag.com/2020/05/coronavirus-covid-france-factory-workers-laborppe-masks Across France, workers are insisting that they be allowed to make masks and ventilators rather than continue with business as usual. Their initiatives show that when workers, not stock prices, decide what's being made, production can serve the needs of society as a whole.

A box containing disposable protective masks stands among boxes of products by 3M and Honeywell at the Rhenus logistics center during the coronavirus crisis on April 16, 2020 in Grossbeeren, Germany. Sean Gallup / Getty

Coronavirus has become a global crisis; official figures tell us that more than 3 million people have already been infected (some estimates put the number ten times higher), and more than a quarter of a million have died. In the bid to contain the virus's spread and reduce the strain on hospitals, over 3 billion people are on lockdown. In this context of crisis, many analysts have pointed to errors in initial risk assessments, against a backdrop of structural unpreparedness and budget cuts. Government pronouncements regarding masksinitially considered ineffective, before they were deemed essentialspeaks to the contradictions and fluctuations in public discourse on the pandemic.

Yet the focus on government actionas symbolized by the daily ritual of televised press conferences offering updates on the situationshould not obscure the initiatives and the work that is being done by other social actors. As shown in the weekly tracking from French statistics agency DARES, the country's labor market has been deeply affected by the stateimposed lockdown: since the second week of April, 11 million workers in France have filed unemployment claims, mainly among small and middle-size businesses (83 percent in firms with under 250 workers).

In this context, the divisions that structure the labor market seem to have been aggravated. As

France comes out of one of its largest workplace conflicts in historyalso coming after the gilets jaunes proteststhe world of labor is experiencing a new series of social tensions. They are not very audible because opportunities for collective action are limited by COVID-19 precautions; the spread of partial unemployment, remote work, and layoffs has also largely atomized workers. But how are these social tensions structuredand are they likely to have an effect beyond the current health crisis?

Even though the data is scarce and fragmented, some do point to major conflicts traversing the world of labor todayones that assume an unprecedented role and visibility during the current crisis. For instance, if the coronavirus crisis highlights the failure of public policies to "rationalize" public health costs, it also reveals the extent and failure of an economic model centered on the profit motive "embedded" in other social realities, in this case, public health.

As well as the capital-labor conflicts over the production of sanitary equipment, this crisis highlights a reality of the world of labor that is often less considered among the general public: namely the "professional consciousness" of workers and trade unionists, concerned with their health, viable economic production, as well as objectives of general interest. In this sense, it constitutes an observatory for the differentiated practices between firms, depending on the degree of social democracy in action.

The Crisis and the Economic Logic Behind It

The principles and practices of political economy that guide globalization are now well documented. For the last forty years, there have been countless reports and sociological surveys on the economic, social, and ecological effects of a system of exchange founded on the principles of increasing productivity and short-term profit, which sacrifices even profitable enterprises, if their margin is lower than other potential and accessible investment projects. However, the coronavirus crisis shines a harsh light on the objective oppositions within this system: private proprietors' time frames and economic aims don't coincide with the health needs of the general population. Worse still, there are successive examples of certain kinds of production being terminated, even though they are much needed in a health crisis like the current one. The demands of average profit rates and their timescales have undermined the industry supplying the public health system, as three recent examples illustrate.

The Gerzat site, in the center of France, has long produced oxygen cylinders, which are much needed by hospitals (or by fire departments, in the case of large fires). Even though it was the only site of production in Europe for this resourceand a shortage of oxygen cylinders is not hitting Italy (after Iran and China)the British company Luxfer decided to close the site in order to induce delays on the market and thereby increase the company's profit margins. As the shortage of these oxygen bottles becomes more and more acute, there is a clear gap between the expectations of shareholders and the needs of the general populationeveryone is a potential stakeholder. Faced with this situation, employees are currently occupying the site to keep the production of these oxygen cylinders going: if workers' employment is always part of their confrontation with employers, the need to provide sanitary equipment is also just as important.

One such line of division can be found at the Plaintel factory. Situated in the west of France (Brittany), this is the only French site producing FFP masks: thanks to their high filtration level, these offer professionals the best antibacterial and anti-aerosol protection. The state has moved to build up stocks of these masks. However, the acquisition of Sperian Protection by the Honeywell group in 2010 meant the integration of the factory into a global corporation. The first layoffs came very quickly, followed by strategic firing, and finally the total liquidation of the plant during summer 2018, which meant the last thirty-eight employees losing their jobs. Yet a financial audit concluded that the site was still profitable. Thus, we see that the closure was motivated by the desire to increase dividend per share as well as the total market valuation of the Honeywell group. Faced with this closure, it was impossible for the employees of the Plaintel factory to hold on to any fixed capital because Honeywell quickly moved to dismantle the machines and send them away to be scrapped. Therefore, the reasons for the closure owed not to profitability at the Plaintel factory so much as its profitability as compared to other parallel factories owned by the Honeywell group.

In addition, the Péters Surgical site in Bobigny, in the Paris suburbs, will close in June 2020, meaning the dismissal of sixty of its 134 employees -in spite of a net profit of €6 million in 2018 as well as €600,000 in grants from CICE [tax credits]. This site produces feeding tubes that are unique in Europe because they are produced with a sheath that protects nursing staff from possible splashes. They are currently sought by hospitals around the continent. However, profit margins can be increased by transferring production to India rather than adapting to new European standards for medical production.

Crisis Management and Speculation

With the general shortage of appropriate sanitary equipment (such as respirators, tests, and protective masks), a speculative dynamic is emerging at the heart of public crisis planning. Not only has the shareholder logic limited the availability of resources needed to fight the pandemic, it has also created a situation marked by soaring prices for sanitary equipment.

Competition is raging between public buyers (the state, communities, and health infrastructures) eager to obtain the necessary equipment to combat COVID-19. Online auction sites are frequented by private and public purchasing centersand the use of this mode of transaction lengthens by several weeks the time needed to secure access to the required equipment. These sites also deprive certain communities of any protection at all, because administrators are unable to get authorization fast enough to keep up with real-time auctions.

In this unstable environment, prices are soaring and the black market is expanding. An increasing proportion of equipment is acquired through direct contracts, which can mean behind-the-scenes arrangements, disguised favoritism, or even embezzlement. There are many examples of middlemen who buy sanitary equipment wholesale directly on the airport tarmac at a competitive price in order to resell it elsewhere. Many American investment banks are already pushing medical providers to raise their prices, taking advantage of a "captive" clientele who cannot simply wait for more competitive prices.

When private firms move to provide their employees with protective equipment, they make it harder for the public sector to access masks. For example, Airbus recently reopened its sites, at the price of having to order twenty thousand masks, in addition to stocks already procured and the thousands of orders throughout the chain of subcontractors. This shows how the desire for private activity at all costs helps to cause shortages of equipment for caregivers.

Consequently, faced with shortages, thousands of employeesor their relativesturn to homemade solutions: they save material, disregard expiration dates, reuse materials despite recommendations to the contrary, or even manufacture and disinfect equipment (such as masks) themselves. Could this time spent be a new kind of surplus value extracted from workers during this crisis?

Overwork and Health Costs

As well as causing problems for the medical industry, a logic of speculation and shareholder advantages puts strain on hospitals by mobilizing a workforce in cramped and face-to-face conditions. Amazon illustrates this perfectly, given the explosion in the rates of profits related to the delivery of video games, office supplies, and electronics. This has the corollary of spreading the virus to yet more workers, in turn increasing the numbers who hospitals have to find beds for.

Therefore, a section of the workforce is mobilized for tasks that have questionable public utility and contribute to the congestion of health services. Far from restricting the mobilization of the workforce, recent government decisions increase the exposure of the workforce to coronavirus by authorizing deregulation of working-hour limits as well as permitting work on Sundays in sectors of the economy supposedly "necessary to the continuation of social life." This opens a new field of interpretation and controversy whose resolution will last long after the decisions bosses now make.

Last, we can hypothesize that the pandemic will have health consequences of a more classic psychological and physiological order. These stem from workers being permanently online and contactable, and the general suspension of paid holidays and breaks in certain sectors under these same government directivesnot to mention the intensification of work for caregivers. Employers are now demanding that employees convert their time in confinement into paid holidays, preferring the eating-up of paid holidays rather than "partialunemployment" claims. In certain situations, the extortion of work takes an unprecedented form: employees are asked to work from home and declare "partial-unemployment" status, while they are actually declared by their firm as being on paid leave. There are two consequences to all of this. First of all, salaried work is swapped for work from home, without compensation. Second, the real break time normally given to employees disappears. In coming months, this will weigh heavily on workers and, consequently, the medical sector.

Employers' expectations, notably within large firms, thus conflict with multiple recommendations made by health professionals as well as the medical system's own capacity to treat new patients. The confrontation between this type of decision and union recommendations highlights a dichotomy between the interests of capital and of labor. Far from reducible solely to questions of employment and income, this sense of professional consciousness appears to be closely linked with a sense of public interest, which currently contributes to helping the struggle for health.

Professional Consciousness and General Interest

In recent decades, the sociology of work has been used to highlight neoliberal policies' harmful effects on working conditions and employment in both the private and public sectors.

The sociology of trade unionism has long followed a similar trajectory. Faced with failed mobilizations and the collapse of union membership, specialists in this field have highlighted the weakening of workers' main defenses against employer and state efforts to enforce the dominant economic logic.

But for at least a decade, trade unionism has been far from inactive. As shown by the work of Rémy Ponge, the federations have taken up, for example, occupational health issues, in particular mental health issues and musculoskeletal disorders (MSD). Thanks to fruitful collaborations with academics as well as consulting firms, we are seeing the proliferation of initiatives working to better our knowledge about the health effects that work has on employees. In the late 2000s, the CGT launched an important investigation into working conditions at Renault. In collaboration with psychologists and doctors, trade unionists are trying to reformulate the relationship to worknot only to improve working conditions, but also to transform the existing frameworks of union mobilization. Solidaires is probably the trade union that pulled off the action best known to the wider public: following the privatization of France Télécom, its post and telecoms wing Sud-PTT was the first to raise the alarm to the suicides that hit the firm. Sud-PTT was one of the key actors in the court process that took place last year and resulted in the conviction of company management. More generally, trade union organizations participate in regular awareness-raising work through the French shop-floor councils: the "Comités Social et Économique" (CSE). Amid today's great anxiety, this long-term activist work is now influencing many workers' own conduct. Facing an absence of employment protections, many protest movements are appearing. After the first day of confinement, some employees of the Atlantic shipyards refused to restart work. At the post office, one out of five post carriers exercised their right to withdraw from work, with unions denouncing safety measures that were reduced to "a bottle of water, a package of tissues, and a garbage bag" as well as management pressure on workers. Management was forced to reconsider the organization of work, reducing the number of postal rounds per day as well as closing many post offices. But beyond the minimum protection measures, many trade unions are launching petitions urging for the cessation of nonessential work and the requisition of medical equipment.

Three weeks after the start of the quarantine, in some sectors such as the automotive industry, employee representatives are still opposing the resumption of work for the same reasons, even though negotiations seem to be succeeding in some places, where wages are paid if employees surrender vacation days. However, the sanitary problems posed by COVID-19 do not only concern workers with strong professional integration. Facing the total absence of barrier measures and social distancing, employees at Amazon have also joined in the call to close non-vital activities. After management's rejection of workers' right to withdraw from their posts during the pandemic, the Solidaires union brought the case to the judicial tribunal in Nanterre, filing a complaint over the endangering of employees. The tribunal ordered Amazon to scale down its activity in France; faced with this decision, the company decided to close its warehouses for several days. Better still, their struggle has surpassed the national framework as Amazon employees in both Europe and America are supporting it. Even the most precarious workers, such as those doing bike delivery, are calling for the suspension of deliveries from which they get their income. Recently, Gregor Gall has reminded us of workers' reactions to COVID-19 around the world.

Professional Consciousness Is Helping the Fight Against COVID-19

Far from Épinal's image of struggling trade unionists, many works have shown union activists' ability to show creativity and make new proposals: whether in the service industry or in more traditional industrial sectors, trade unionists, including the most radical, are continuously making proposals to management, not only on matters about working conditions, but also about investment strategies. As Guillaume Gourgues showed with regard to the worker-occupied LIP factory, the Collectif du 9 août with regard to Molex, and indeed our own work on the workplaces taken under worker management in Argentina and France, these workers demonstrated not only their welter of economic and legal ingenuity in saving their workplaces from the threat of closure and the short-term logic that had gone before, but often forcefully asserted their own social utilityplacing it within a wider socioeconomic perspective. Unlike large multinationals, employees and their representatives have a much better understanding not only of their work activity, but also of its usefulness and role in a given field. France's government is aware of this and receives representatives from the CFDT, CGT, FO, CFE-CGC and the CFTC via video conference several times a weekbut limits them to the role of sources of information and a mechanism to issue alerts.

In this crisis, we find many examples of this professional conscience. The most emblematic concerns hospital workers. The sheer extent of the COVID-19 crisis results from public health policies which hospital personnel have been combating for years. In France, 2019 saw a continuous strike that brought together all grades of health care professionals, in a movement that built on older collective protests. As Pierre-André Juven, Frédéric Pierru, and Fanny Vincent remind us, this movement above all displayed a vision alternative to the budget cuts pursued in hospitals for some three decadesinsisting that public hospitals are a productive investment and not just a cost. Since the beginning of the lockdown, there have been countless media interventions by care staff denouncing the deplorable conditions in which they work but also demanding a radical paradigm shift in the public health system. Emmanuel Macron himself adopted "welfarist" tones at the beginning of the lockdown, calling for the defense of public hospitals for all.

Many other groups of workers have taken spectacular initiatives to back up the fight against the epidemic, notably in production facilities outside the influence of finance capital or where unions have a strong organizational presence. While no French collective has taken measures as radical as in Tunisia (where workers decided to quarantine themselves in order to make masks for the population) or in Argentina (where companies under workers' management have launched various solidarity initiatives like making masks and hydro-alcoholic gel for their neighborhoods), actions serving the public good or showing solidarity have, in fact, rapidly emerged. In the Creuse département, seamstresses in technical unemployment responded to a home-help association's appeal by providing them with masks. Their initiative rapidly expanded to include making prototype disposable overalls for hospital staffproof of both the existence of an on-the-ground solidarity network and the reconversion of highskilled work. Similar initiatives have come to light elsewhere in France. Initiatives have also been launched based on union activism. In Marseilles's quartiers nord there has been similar territorial-level solidarity: workers on strike at a McDonald's decided to use their workplace as a base for providing aid to the poorest, using cool chambers in order to stock free food.

But probably the most emblematic example of this professional conscience resides in the current project to restart the Plaintel sitethe mask factory cited above, closed for reasons of shareholder advantage. Since early April, a "Co-op for the General Interest" project has been developed by union figures, workers, associations, and elected representatives at the local level. Defending a company model where power is shared between different stakeholdersworkers, local administration, consumers, clientsthey hope to subordinate production to the interests of the collectivity.

The Power of Cooperative Working

It is hardly surprising that that these initiatives "from below" rapidly turn to cooperative forms that perfectly espouse the sought-after balance between social utility and economic imperatives. Despite its limited means, the co-op movement is already very present across France's territory via its regional unions. In some parts of France, they are major sources of employment (like ACOME in Normandy, owned by its 1,300 employees). These firms also have a strong inclination to support solidarity initiatives, as we see in the current context of health crisis. In the Marseille region, staff at the SCOP-TI tea factoryrecovered by its workers after a well-known strugglerevised their work organization even before the lockdown, distancing their work posts, systematically cleaning the premises, and organizing to avoid teams crossing in shared living spaces. Then, on the recommendation of a workplace doctor, they distributed protection material to care centers; "a little over 1,000" masks, overalls, full-body suits, and hygiene caps were sent to hospitals in Aubagne and Marseille. In Rennes, a recently established undertakers' co-op set up a whole series of measures as both mutual aid for its own employees (such as masks), but also for the families of the dead, so that they could attend the funerals. Many co-op employers' federations, like in the building trade, are asking authorities to tighten restrictions on which businesses stay open.

Unlike the big financialized capitalist corporations, these employers are trying to limit their activity in order to lower the tension between public health care (at the territorial level) and market shares (between individual businesses). Indeed, such efforts seem very widespread among the various French co-ops. The proximity between management and workers led to drastic protection measures right from the first days of the pandemicor even pulling down the shutters, prioritizing the health risk above the financial one. Their participation in stable territorial websthrough their local rootedness and recognizabilityallows them to collect, stock, and redistribute health protections to many inhabitants of the surrounding area.

Finally, the solidaristic notions present in the workplace, uniting collectives of workers, demand some concrete expression in a moment of crisis. Companies' ability and will to invest their efforts in the health care crisis seems closely linked to their workers' commitment to their work and their control over the means of production.

Putting Workers in Charge

The initiatives outlined in this article are not necessarily representative of employers or workers in general. Since the beginning of the crisis, we have also seen employers' organizations defend their workers' conditions, sparking major tensions with the government. Even a large firm like LVMH -headed by Bernard Arnault, one of the world's richest men has reoriented part of its activity to producing hydro-alcoholic gel (though some might be so rude as to suggest that this hardly compensates for the mass-scale tax evasion in which the firm has indulgedand its share of responsibility for low health care budgets). Similarly, the translation of work hierarchies into the lockdown situation has produced very varied relationships to work itself: when managers keep working, their exposure to virus is limited by remote work, while shop-floor and service workers often have no fallback other than to stop working entirely. Often this form of inequality is intersected by another, much more powerful one: the total shutdown of many unskilled jobs done by artisans and blue-collar workers. It is difficult for them to take a leading role in making proposals and offering practical efforts to combat the epidemic.

But the health crisis also reminds us that power relations within companies are a matter for us all. They obviously concern the workers in each business, but they are also reflected across the whole territory, in the form of the sanitary resources and potential contamination that results from them.

We might even assert, rather bluntly, that the greater the workers' power (through unions, or co-ops), the greater the "social" direction of its activity. While the data we have for now is temporary and full of holes, the materials we can study suggests that individuals are better equipped to help fight the crisis when they have better professional consciousness. Not only because the workers know their workplaces betteri.e., both the conditions in which they work and the possibility of transforming thembut also because they know the local productive ecosystem and can "account" to other actors at the local level. Thus, the insertion of co-op activity within wider webs of relations, and their management's responsibility to the personnel, lead to the mobilization of specific networks sometimes inaccessible to large corporations detached from their immediate environment.

The appropriation of the means of production is not just an economic principle that alters the aims and rationale of work. Rather, it is also a reliable, prudent, and long-term principle ensuring good hygiene and health care. In this sense, the "class struggle" highlighted here does not necessarily have to do with its ancestral model, but it can also bring together economic actors (as in the case of co-ops) who share similar definitions of the sense to give production. This means respect for workers and work itself, providing for the general interest, and planning for long-term need over short-term profits.


R Makarem

F Cristiano

D Muller

P F Fazzini

An improved STEM/EDX quantitative method for dopant profiling at the nanoscale November 7, 2019

In this paper, an improved quantification technique for STEM/EDX measurements of 1D dopant profiles based on the Cliff-Lorimer equation is presented. The technique uses an iterative absorption correction procedure based on density models correlating the local mass density and composition of the specimen. Moreover, a calibration and error estimation procedure based on linear regression and error propagation is proposed in order to estimate the total measurement error in the 1 dopant density. The proposed approach is applied to the measurement of As profile in a nanodevice test structure. For the calibration, two crystalline Si specimens implanted with different As doses have been used and the calibration of the Cliff-Lorimer coefficients has been carried out using Rutherford Back Scattering measurements. The As profile measurement has been carried out on a FinFET test structure, showing that quantitative results can be obtained in the nanometer scale and for dopant atomic densities lower than 1%. Using the proposed approach, the measurement error and detection limit for our experimental setup are calculated and the possibility to improve this limit by increasing the observation time is discussed.

Introduction

One of the key issues for the miniaturization of semiconductor nanodevices is the precise control of their doping [START_REF] Vandervorst | Dopant/carrier profiling for 3dstructures[END_REF]. In new generation devices, the doping spatial distribution must be controlled with a precision higher than 1 nm while atomic concentrations below 1% have to be measured. This is a particularly critical issue for the characterization of nanodevices and 3D transistors (Colinge, 2008), where standard techniques such as as Secondary Ion Mass Spectroscopy (SIMS) cannot be used. This calls for the use of high resolution techniques. Scanning transmission electron microscopy (STEM) associated with Energy Dispersive X-ray spectroscopy (EDX) is an excellent candidate due to its versatility (several dopants can be mapped) and its high spatial resolution. Moreover, the current availability of probe spherical aberration correction, high brightness sources, and high angle silicon drift detectors (SDD) make this technique even more attractive since a high signal to noise ratio can be obtained with the characteristic resolution of STEM imaging techniques. Atomic elemental mapping of alloys can be obtained using commercially available microscopes [START_REF] Kothleitner | Quantitative Elemental Mapping at Atomic Resolution Using X-Ray Spectroscopy[END_REF].

In spite of all these advances, using STEM/EDX to obtain quantitative information on the doping distribution in a nano-device is still a challenging task. Quantitative analysis is complicated by the presence of measurement artifacts [START_REF] Goldstein | Scanning Electron Microscopy and X-Ray Microanalysis[END_REF] [START_REF] Williams | Transmission Electron Microscopy: A Textbook for Materials Science[END_REF]) that can safely be ignored for high concentrations impurities, but become critical for low concentration dopants (concentration lower than 1%) since the artifact contribution can be of the same order of magnitude as the signal to be measured. More specifically the artifacts complicating doping profiling with STEM/EDX can be divided into two categories:

• The artifacts arising from the detector design such as escape peaks, sum peaks, peak deformations due to partial charge collection and the absorption of X-rays in the detector surface and window [START_REF] Goldstein | Scanning Electron Microscopy and X-Ray Microanalysis[END_REF]. The effect of these artifacts are negligible in modern SDD devices, thanks to the careful design minimizing the size of the dead layers in the active surface and the fact that the constructors take into account the absorption in the detector using a quantum efficiency function [START_REF] Alvisi | The determination of the efficiency of energy dispersive X-ray spectrometers by a new reference material[END_REF].

• The artifacts arising from the physical interactions (absorption, fluorescence ...) of X-rays emitted in the specimen with the specimen itself and other elements in the column [START_REF] Williams | Transmission Electron Microscopy: A Textbook for Materials Science[END_REF]. This problem is unavoidable and can affect the accuracy of the obtained results, especially when measuring dopant concentration. Particular attention must be paid to the effect of the absorption of X-rays in the specimen. A rigorous treatment of the effects of self-absorption on the measured composition calls for the employ of an iterative approach since the absorption effects clearly depend on the specimen composition [START_REF] Watanabe | Absorption Correction and Thickness Determination Using the ζ-factor in Quantitative X-Ray Microanalysis[END_REF].

In this paper we will present a modified [START_REF] Cliff | The quantitative analysis of thin specimens[END_REF] method in order to deal with the second kind of artifacts and to obtain quantitative dopant profiling in a nanoscale device structure. The method has been applied on specimens prepared by Focused Ion Beam, in order to reduce the influence of secondary X-rays produced by fluorescence or back scattered electrons, and is based on the iterative correction of X-rays absorption effects in the specimen. In order to obtain reliable results the k-factors have been calibrated using Rutherford Back Scattering (RBS) measurements and the total experimental error has been calculated using standard error propagation techniques. The method has then been applied to the measurement of As dopant profiles in a FinFET structure,

The main novelties of this approach is the use of RBS data to calibrate the k-factors and that the specimen local density has been calculated using physical models. The knowledge of the local density is used to correct the absorption effects without any in-situ measurement of the electron beam current, which is an advantage with respect to other techniques such as the ζ-factor [START_REF] Watanabe | The quantitative analysis of thin specimens: a review of progress from the Cliff-Lorimer to the new ζ-factor methods[END_REF] or cross-section method [START_REF] Macarthur | Quantitative Energy-Dispersive X-Ray Analysis of Catalyst Nanoparticles Using a Partial Cross Section Approach[END_REF]. The main difference between this techniques and other tech-niques not requiring an in-situ measurement is that specific peaks family can be selected for each element (while at least two must be used in the technique proposed by [START_REF] Morris | Proceedings EMAG '79 Brighton[END_REF] and [START_REF] Qiu | Calibration of thickness-dependentk-factors for germanium X-ray lines to improve energy-dispersive X-ray spectroscopy of SiGe layers in analytical transmission electron microscopy[END_REF]) and there is no need to use several specimen tilt angles (as in the technique proposed by [START_REF] Morris | Proceedings EMAG '79 Brighton[END_REF]). The main disadvantage of this approach when compared with the other techniques is that the specimen must have a constant thickness, that the thickness must be measured with other techniques, and that no direct information can be obtained on the specimen density.

Materials and Methods

In this section the experimental techniques and the data analysis methods used in this work will be presented.

First of all, the specimens that have been used for the calibration of the k-factors and for doping measurements will be described, then some experimental details on the STEM/EDX measurements will be given and, finally, the techniques we used for data quantification will be detailed.

Description of the samples

To be able to measure arsenic doping concentration in silicon nanodevices, we have designed some calibration specimens obtained by ionic implantation of arsenic in monocrystalline silicon wafers. Two specimens were used to check the precision of the calibration on different concentrations. Both were implanted using an acceleration voltage of 21KeV but with a different dose amounting, respectively, to 9.4 • 10 15 cm -2 and 1.8 • 10 15 cm -2 . It has to be noted that due to the high dose, the implanted wafers are amorphized in the implantation region. The implantation parameters have been chosen by simulating the implantation profile using the SRIM (Stopping and Range of Ions in Matter) Monte Carlo simulation software [START_REF] Ziegler | The Stopping and Range of Ions in Matter[END_REF].

The simulation results corresponding to the two different doses are shown in Figure 1(a). It can be noted that the value of the concentration peak amounts to 5 • 10 21 cm -3 (equivalent to 10% atomic As concentration) for the higher dose implant and to 10 21 cm -3 (2% atomic As concentration) for the lower dose implant. An absolute measurement of the arsenic concentration of the implanted samples has been obtained in bulk specimens by Rutherford backscattering spectroscopy (RBS) measurements [START_REF] Chu | Backscattering Spectrometry[END_REF] using He + ions accelerated at 1.5 MeV. The detector resolution and solid angle have been obtained on a SiO 2 reference specimen using a detector collection angle of 10°. For the As concentration measurements an elevation angle of 60°has been used. By using RBS, the atomic concentration profiles (atoms/cm 3 ) of arsenic in the two calibration specimens have been obtained. The final error on the concentration measurement is in the order of 10% while the spatial resolution of the technique is 4 nm. The RBS results were used to calibrate the k-factors, as explained in section 2.3.3. Since the resolution of the RBS measurements is comparable with the resolution obtained by STEM/EDX, the alignment of the two set of data for the calibration can be easily obtained by aligning the As concentration peaks.

To show the applicability of the proposed measurement technique to nanodevices, a FinFET test structure, with a channel width of 35 nm and a height of 100 nm has been used (see Figure 1(b)). In this specimen an As plasma implant followed by a high temperature thermal annealing (higher than 900°C) have been used to obtain a conformal distribution [START_REF] Vandervorst | Dopant/carrier profiling for 3dstructures[END_REF] of the doping profile in the source and drain regions of the device.

Specimen preparation and TEM observations

TEM observations have been performed on cross sectional lamellas fabricated using a FEI Helios 600i dual beam focused ion beam (FIB) [START_REF] Ke | TEM sample preparation by FIB for carbon nanotube interconnects[END_REF].

A lift-out procedure has been used to transfer the specimen on a supporting copper grid. A platinum layer has been deposited onto the wafer surface before the creation of the lamella to minimize curtaining effects. To avoid any kind of ionic damage near the surface, platinum deposition has been carried out in two consecutive steps by using electron beam-induced deposition followed by ion beam-induced deposition. There are several advantages in using FIB specimen preparations for EDX analysis. As discussed in the introduction, the use of a lamella reduces the emission of secondary X-rays by fluorescence and the backscattering in comparison with specimens prepared by other techniques like mechanical grinding followed by ion thinning (see figure 2). Moreover, the use of FIB guarantees that the specimen thickness is constant all over the observation region, located near to the capping Pt layers. Finally, FIB preparation has been used in the case of the FinFET structure to select a precise specimen region such as the implanted regions shown in figure 1. Electron energy loss spectroscopy [START_REF] Malis | EELS log-ratio technique for specimen-thickness measurement in the TEM[END_REF] has been used to estimate the value and uniformity of the specimen thickness.

For the three specimens a value of 150 nm with negligible variations in the observation region has been obtained. The STEM/EDX measurements have been carried out using a JEOL ARM cold FEG microscope equipped with a probe spherical aberration corrector. For the EDX measurements, a CENTURIO-X detector with a take-off angle of 24.3 degrees and a collection angle of 0.98 steradians has been used.

In order to exploit the 1D geometry of the observed samples the specimens have been oriented as in Figure 3. The reason of this choice is that, if we consider the detector size as negligible, the X-rays reach the detector passing through a slice of homogeneous density.

Figure 3: Schematic illustration of the detector position and of X-ray path, when the detector is placed on a plane perpendicular to the variation direction of the doping profile.

2D STEM/EDX maps of the observed region have been used to measure the dopant profile in the x direction. First of all an EDX spectrum has been acquired for each pixel of the 2D map. Then the JEOL Analysis Station program 1 has been used to subtract the Bremsstrahlung background noise pixel by pixel and to calculate the integrated intensities of the characteristic peaks for the various elements in order to obtain 2D intensity maps. The uni-dimensional intensity profiles have then been obtained from the 2D intensity maps by lateral integration in the y direction (see figure 3). Observations have been carried out for all observed specimens in the same experimental conditions. The FIB lamella was placed on the side of the central finger of a three post Omniprobe lift-out grid2 . A JEOL analytical double tilt holder with material removed on the detector side, designed to minimize penumbra effects, was used. The z position of the holder was adjusted in order to have the specimen at eucentric eight and a tilt angle of 10°around the holder axis (α-tilt, see figure 3) has been used in order to further minimize penumbra effects. In the particular case of 1D objects, this does not induce any deformation of the concentration profile.

Quantification Method

As already mentioned, for the quantification of the specimen composition we have used an approach based on Cliff-Lorimer factors. Data treatment has been carried out using the scientific programming language GNU Octave3 .

The starting point for our quantification method is the Cliff and Lorimer equation giving the mass fractions of a specific element i [START_REF] Williams | Transmission Electron Microscopy: A Textbook for Materials Science[END_REF]:

f M i = k i:F i ,F i 0 I i:F i N A j=1 k j:F j ,F i 0 I j:F j (1)
where N A is the total number of elements in the sample f M i is the mass fraction of the i th element and I i:F i is the intensity of the characteristic peak associated to the F i family and k i:F i ,F i 0 is the k-factors relative to the element i and a common reference element i 0 that, by definition, has a unitary k-factor

(k i 0 :F i 0 ,F i 0 = 1).
The total intensity I i:F i of the family F i for a specific element is obtained by adding the intensities I i:F i ,k of the N F i lines (Kα, Kβ...) belonging to the family chosen for the element i. Each specific line of the family is associated to an energy E i:F i ,k . While mass fractions are easily obtained by EDX, atomic concentrations (in atoms/cm 3 ) are customary in semiconductor literature. The following formula can be used to convert mass fractions to atomic fractions f A i or concentrations c A i :

f A i = f M i /m i j f M j /m j , c A i = ρ M f M i m i N AV (2)
where ρ M is the mass density of the specimen, m i is the atomic mass of the i element and N AV = 6, 02214076 • 10 23 mol -1 is the Avogadro number.

Iterative absorption calculation

In a homogeneous material of constant thickness, the peak intensity I * (E)

after self-absorption of X-rays of energy E and initial intensity I(E) can be calculated as follows [START_REF] Williams | Transmission Electron Microscopy: A Textbook for Materials Science[END_REF] :

I * (E) = 1 -e -µ(E)ρ M t/ sin(α) µ(E)ρ M t/ sin (α) I (E) = T • I (E) (3)
where µ(E) is the mass absorption coefficient of the material, t is the material thickness, ρ M is its mass denisty, α is the take-off angle which is equal to 34.3°in our case. In the previous formula we have also defined the transmission factor T to simplify further notation. For an alloy, µ(E) ( [START_REF] Eibl | New method for absorption correction in high-accuracy, quantitative EDX microanalysis in the TEM including low-energy x-ray lines[END_REF]) must be calculated as follows:

µ E, f M i = N AT i=1 µ i (E) f M i (4)
where µ i (E) is the mass absorption coefficient associated to the i th atom.

In this work the value of µ i (E) for the various elements has been calculated using the EPQ library implementation of the model proposed in [START_REF] Heinrich | Mass absorption coefficients for electron probe microanalysis[END_REF]. For that, the Java interface features of Octave have been used to access the EPQ library routines.

As already observed, equation 3 can only be used for homogeneous specimens of constant thickness. In our case both conditions hold because of the choice of the specimen orientation (see figure 3) and of the FIB specimen preparation (section 2.1) used in this work. Equation 3 can be used to implement an iterative approach provided that the relation between the local density and the local composition (expressed in the form

ρ M f M i )
is known. This is the approach used in this paper and various models that can be used to evaluate ρ M are discussed in section 2.3.2). In this case the transmission factor is a function of the energy and the mass fractions and can be written as

T (E, f M i ).
For the iterative procedure the initial mass fractions f M i 0 are calculated from the measured intensities by neglecting absorption and are used as a starting point. For each iteration the transmission factor is calculated using the set of mass fractions f M i n obtained in the previous iteration. For a peak located at an enrgy E this can be written:

[T (E)] n = T (E, f M i n-1 (5)
At each iteration the value of the absorption corrected intensities is cal- )] n and the corresponding absorption corrected mass fractions are evaluated from the corrected intensities using equation 1.

culated as follows [I(E)] n = I * E / [T (E
This same technique is applied at each position x of the profile and for each intensity line of the selected peak families. At the end of the iterations the absorption corrected mass fractions f M i (x) are obtained . The stopping criterion is that the relative variation of the mass fractions between two subsequent iterations is below a tolerance that can be chosen by the user

f M i n -f M i n-1 / f M i n < .

Mass density calculation

For a given material, the application of the iterative procedure requires to establish the appropriate relation between the specimen local mass density ρ M (x), and the local elements mass fractions f M i (x). In this section two formulas will be derived for the amorphous SiAs alloy (a-SiAs) used for the calibration and for the As implanted crystalline silicon (c-SiAs) composing the FinFET test structure.

To derive the formula for a-SiAs, it must be noted that the covalent radii for silicon and arsenic have a close value, R Si = (111 ± 2)pm and R As = (119 ± 4)pm, while the value of their atomic masses greatly differs (m Si = 28.0855 g • mol -1 and m As = 74.9216 g • mol -1 ). Hence, a possible approximation to evaluate the density consists in neglecting the difference in atomic radius, so that the mass density can be easily calculated starting from the mass density of amorphous Si and evaluating the mass difference obtained when an As atom replaces a Si atom. If we define the local atomic fractions for the two elements f A As (x) and f A Si (x) and we take into account that for a binary alloy we have

f A Si (x) = 1 -f A As (x)
we can write:

ρ M SiAs (x) = ρ M a-Si 1 + m As m Si -1 f A As (x) (6)
Where ρ M a-Si = 2.285 g • cm -3 is the amorphous Si mass density [START_REF] Custer | Density of amorphous Si[END_REF]. This equation is a function of the As atomic fraction but it can be easily expressed as a function of the mass fractions using equation 2:

ρ M a-SiAs = ρ M a-Si 1 + (m As -m Si ) f M As (x) m As -(m As -m Si ) f M As (x) (7)
We will refer to this approximation in the following as the "same radius approximation". The problem of this approach is that it overestimates the mass density of a-SiAs for high arsenic concentrations as shown in figure 4.

A better approximation can be obtained by using a formula that has been originally derived for solids that do not present any kind of ordering (also known as ideal amorphous solids (IAS)) [START_REF] Stachurski | Fundamentals of Amorphous Solids: Structure and Properties[END_REF]:

ρ M a-SiAs = ρ M a-As f V As + ρ M a-Si f V Si (8)
where ρ M Si and ρ M As are the mass densities of amorphous Si and amorphous As respectively while f V As and f V Si are the volume fractions of the two elements. We will refer to this approximation in the following as the "amorphous solid approximation". The main hypothesis behind the derivation of this formula is that the volume occupied by an atom of each element does not depend on the alloy concentration. A direct consequence of this hypothesis is that the structure around an individual atom must not depend on the alloy concentration.

The atomic arrangement in amorphous As and amorphous Si is very similar. This can be shown by evaluating the ratio s = V S /V A between the atomic volume V A and the atom size V S . The volume V A is by definition the inverse of the atomic density ρ A = ρ M /m of the material while the atom size can be calculated by using a spherical approximation (V S = 4/3 πr 3 ) and the covalent radius r. The values of s for amorphous silicon and amorphous arsenic can be calculated by using the value of a-As and a-Si densities reported in literature (ρ M a-As = 4.7 g/cm 3 , see [START_REF] Greaves | Amorphous arsenic[END_REF]). The obtained values (s Si = 0.28 ,s As = 0.26 ) are close, confirming that the packing of the two structures is almost the same. It can then be assumed that the volume occupied by Si and As atoms is almost the same in SiAs for any concentration value which is precisely the assumption used to derive equation 8. Using the same reasoning it can be shown that the "amorphous solid approximation" also holds for pseudomorphic alloys such as SiGe. For this kind of structures the crystalline structure of pure and binary alloys are exactly the same (for example crystalline Si, Ge and SiGe all have a diamond structure). Moreover the variation of the lattice parameter with concentration is on the order of some percent. It can then again be assumed that the atomic volume does not vary with the alloy concentration and equation 8 can be used. This example is particularly important since in the case of SiGe the validity of equation 8 can be proved by a direct calculation of the alloy density based on the alloy crystal structure and Vegard's law, which is an excellent approximation of the lattice parameter for SiGe alloys [START_REF] Kasper | Test of Vegard's law in thin epitaxial SiGe layers[END_REF].

The volume fractions used in equation 8 can be expressed as a function of the mass fractions as follows:

f V i = f M i ρ M i / j f M j ρ M j (9)
Then we finally obtain the equation relating the alloy mass density to the mass fractions measured by EDX:

ρ M a-SiAs = f M As ρ M a-As + f M Si ρ M a-Si -1 (10)
The density function obtained using the "amorphous solid approximation" is shown in figure 4. It can be observed that this approximation gives better results for high arsenic concentrations while the two approximations are almost equivalent for low As concentrations (see figure 4). Equation 10has been used to quantify As doping in a-SiAs.

Finally it is important to note that the "same radius approximation" can be used for low doped crystalline Si since in the case the alloy consists in a almost unperturbed Si lattice where some Si atoms are replaced by As atoms.

In this case the expression of the density is given by equation 7 where ρ M a-Si is replaced by the density of crystalline Si ρ M c-Si = 2.32 g/cm 3 [START_REF] Stachurski | Fundamentals of Amorphous Solids: Structure and Properties[END_REF]. This density equation has been used to quantify As doping in the FinFET test structure.

Model calibration and error estimation

In this section we will discuss the calibration procedure used for the k-factors and how we have calculated the total error on the composition measurement.

First, for the comparison between EDX rand RBS results, it is necessary to transform the experimental arsenic atomic density concentrations c A As/RBS (x)

measured by RBS into mass fractions. This is the best strategy to use since in this way the k-factors can be obtained by weighted linear regression.

Equations 2 and 10 can be combined to obtain the value of the arsenic mass fractions measured by RBS:

f M As/RBS = m As c A As/RBS (x) N AV ρ M Si + m As c A As/RBS (x) (1 -ρ M Si /ρ M As ) (11)
The value of the k-factors for a specific peak family F As can then be obtained by linear regression.

To estimate the error on ∆k As:F As on the calibrated value of k As:F As ,F Si we have assumed that the statistical distribution of the measured intensities follows a Poisson law. In this case the error on the measurement of the intensity I is given by ∆I(x) = I(x) and the relative error is given by

I = ∆I I = 1 √ I .
The best fit value for k As:F As can be obtained by using a weighted least squares approach [START_REF] Wasserman | All of nonparametric statistics[END_REF]. This is equivalent to minimize the expression :

R = i 1 w(x i ) f M As/RBS (x i ) 1 -f M As/RBS (x i ) -k As:F As ,F Si I As:F As (x i ) I Si:F Si (x i ) 2 (12)
where {x i } is the set of positions where the densities have been experimentally measured. In order to favor the most precise points the weighting factors w(x i ) have been chosen to be equal to the relative experimental error associated to

I As:F As (x i ) I Si:F Si (x i ) .
By using error propagation laws we can then write:

w(x i ) =   1 I As:F As (x i ) + 1 I Si:F Si (x i )   . ( 13
)
The best fit value of k As:F As and the associated statistical error ∆k As:F As have been calculated using the standard formula for parameter error estimation in weighted least square regression [START_REF] Wasserman | All of nonparametric statistics[END_REF] and adding the contribution of the errors on RBS measurements by using error propagation formulas [START_REF] Taylor | Introduction To Error Analysis: The Study of Uncertainties in Physical Measurements[END_REF].

When performing a quantitative measurement, it is important to evaluate the total measurement error. In our case three kind of errors must be taken into account:

1. The fore-mentioned statistical errors ∆I i:F i (x) on the measured intensities. The contribution of these errors to the arsenic mass fraction can be calculated, using standard error propagation techniques, to be

∆ I f M As (x) = k As:F As ,F Si [I Si:F Si (x)∆I As:F As (x) + ∆I Si:F Si (x)I As:F As (x)] [I Si:F Si (x) + k As:F As ,F Si I As:F As (x)] 2 (14)
2. The error ∆k As:F As ,F Si on the calibrated value of the k-factor. The contribution of this error on the arsenic mass fraction can be calculated to be :

∆ k f M As (x) = I As:F As (x)I Si:F Si (x)∆k As:F As ,F Si [I Si:F Si (x) + k As:F As ,F Si I As:F As (x)] 2 (15)
3. The experimental error on the specimen thickness ∆t. In this case it is not possible to apply the error propagation formula to evaluate the error since the dependence of f M As (x) on t is given by the previously discussed iterative calculation. In this case the contribution to the total error has been estimated using the following formula

∆ t f M As (x) = f M As (x) t+∆t -f M As (x) t-∆t 2 (16)
calculated for a thickness t.

The final error is given by:

∆ f M As (x) = ∆ I f M As (x) 2 + ∆ k f M As (x) 2 + ∆ t f M As (x) 2 (17)
As already discussed, all dopant concentrations have been expressed using the atomic concentrations c A As (x). For that we have used equation 2 to calculate the absorption corrected As distribution c A As (x) from the corrected intensities f A As (x). The error on c A As (x) for the case of a-SiAs have been calculated using the following formula, that can be derived using equations 10 and 2:

∆ c A As (x) = (18) N AV m As ∆ f M As (x)      ρ M a-SiAs (x) + f M As (x) ρ M a-Si η 1 -η f M As (x) 2      where η = 1 - ρ M a-Si ρ M a-As
and ρ M a-SiAs (x) is the value of the density when

f M As (x) = f M As (x).
The same procedure can be applied to obtain the concentration error to be used in the case of FinFETs. In this case using equation 7 it can be shown that:

∆ c A As (x) = (19) N AV m As      ρ M c-SiAs (x) + ρ M c-Si m As (m As -m Si ) m As -(m As -m Si ) f M As (x) 2 f M As (x)      ∆f M As (x)
where ρ M c-SiAs (x) is the value of the density when f M As (x) = f M As (x) (see eq. 7).

Results and discussion

In this section we will present the results obtained using the previously described improved quantification technique. The discussion will be divided in two parts. First we will describe the calibration results and then we will show how we have performed dopant profiling on a FinFET test structure.

Calibration results

The calibration techniques described in section 2.3.3 have been applied to the a-SiAs calibration specimens described in section 2.1. Several characteristic peak families have been used: the K peaks for silicon, and either the K or the L peaks for arsenic. The absorption correction procedure described in section 2.3.1 has been used to calculate the absorption corrected intensities I Si:K , I As:K and I As:L . Then linear regression techniques have been used to calculate the value and corresponding uncertainty of:

• the k-factor K As,Si:K,K = k As:K,K associated to the K family of peaks of arsenic when the K family of peaks of silicon is used as reference • the k-factor K As,Si:L,K = k As:L,K associated to the L family of peaks of arsenic when the K family of peaks of silicon is used as reference In order to minimize the error on the k-factors we have carried out the calibration on the specimen with a 10% atomic As peak concentration. The reason of this choice can be easily understood by observing that under the fore-mentioned hypothesis that the X-ray count has a Poisson distribution the relative error is minimized for higher peak intensities. This implies a lower variance on the intensity values and a lower error on the best-fit values of the k-factors.

The comparison between the results obtained by RBS and the doping concentration measured by EDX before and after calibration of the k-factors are reported in figure 5 . This has allowed us to obtain the following best fit coefficients for the microscope used in this experiment: K As,Si:K,K = 2.2 ± 0.1 , K As,Si:L,K = 1.9 ± 0.1.

The convergence of the iterative algorithm has also been checked by inspecting the modification of the measured concentration after several iterations (see figure 6). In our case the tolerance has been chosen to be equal to 1%, to be sure that the error related to the iterative calculation was lower than the experimental error. It is clear from the figure that the region that is most affected by absorption effects is the peak region, and that the algorithm converges after one iteration. This can be explained by the fact that in thin specimens, such as those observed by TEM, the absorption effect is small enough to be corrected by just one iteration.

In order to check the validity of our procedure and the applicability of these coefficients to arsenic distributions with lower concentrations, we have used the previously obtained values of the k-factors to measure the doping concentration in the specimen with a 2% atomic As peak concentration. The results are shown in figure 7 where the experimental errors on the EDX measurements are also reported.

First of all it must be observed that the experimental error is larger for higher concentrations. This is due to the hypothesis that X-ray intensities Figure 6: Absorption corrected concentrations obtained after a variable number of iterations. In (a) the full profile is shown while in (b) a zoom on the high density region is displayed. The profiles corresponding to iterations 2 to 10 are superimposed and a single curve is visible. follow a Poisson distribution. This implies that the absolute error on the measured intensity increases with the intensity while the relative error decreases. The error on doping concentration follows the same trend since it directly depends on the error on the measured intensity. This means that, in the doping distribution peak, the measured value of doping concentration is more precise (i.e. has a lower relative error) than the values in the distribution tail, even if larger error bars appear in the graph.

Figure 7 clearly shows that the results obtained using the K peaks of arsenic are more accurate than those obtained using the L peaks. This is still more evident for low concentrations (i.e. in the rightmost tail of the doping profile). In the peak region there is a larger discrepancy between the AsK and RBS data that can be explained by noting that, as already discussed, the measured intensities in the peak region are affected by a larger absolute statistical variation.

The origin of this discrepancy arises from the lack of precision on the measured intensity of the L peaks of arsenic. This is due to the position of the L peaks, located in the low energy region of the spectrum. In this region, the subtraction of the Bremsstrahlung noise is more difficult since the noise is higher and there are neighboring peaks associated to oxygen and carbon [START_REF] Williams | Transmission Electron Microscopy: A Textbook for Materials Science[END_REF]. Another advantage of K peaks with respect to L peaks is that they are less affected by absorption effects [START_REF] Williams | Transmission Electron Microscopy: A Textbook for Materials Science[END_REF] even if caution must be paid to use these peaks when the observed specimens are thinned bulk specimens [START_REF] Maclaren | Silica Glass Segregation in 3 wt% LiF-Doped Hot-Pressed Y2si2o7[END_REF] and not FIB lamella as in our specific case .

For low As concentrations, such as those we are measuring this kind of problem becomes critical since the Bremsstrahlung and peak intensities can be of the same order of magnitude. This means that a small error in the the background noise interpolation has a strong impact on the measurement of As concentration. We have thus decided to use the arsenic K peaks for all the measurements reported in the following. This choice can also be supported by the fact that K-peaks are less affected by absorption

Doping profile in a nano-device

To check the applicability of our method to real nanodevices we have carried out some measurements on the FinFET test structure described in section 2.1. For that an EDX hyper-map has been acquired. Some intensity maps and profiles extracted from the hyper-map are shown in figure 8. In order to be able to apply the same measurement geometry illustrated in section 2.3 and in figure 3 we have decided to study the distribution of one of the vertical walls of the FinFET structure and the specimen has been specifically oriented for the acquisition as in figure 9(a). The quantification method described in the previous section has then been applied to the silicon and arsenic K peaks profiles. The final result is shown in figure 9(b) where the doping profile on the lateral wall and the corresponding errors are shown.

For density calculation, the formula of equation 7 has been used. It has to be noted, that, strictly speaking, this formula is not rigorously applicable in the peak regions, where density exceeds arsenic solid solubility in crystalline silicon [START_REF] Pichler | Intrinsic Point Defects, Impurities, and Their Diffusion in Silicon[END_REF]. In this regions a large fraction of the As atoms are not located in substitutional positions but they form, instead, different kind of electrically inactive clusters. At the high annealing temperature used in this work As atoms form two preferential types of clusters (see again [START_REF] Pichler | Intrinsic Point Defects, Impurities, and Their Diffusion in Silicon[END_REF] The results clearly show that a doping profile on a nanodevice can be obtained with this technique and that the obtained experimental error is low enough to be able to appreciate the concentration variations in the profile.

Finally it is interesting, in the context of doping profile measurement by STEM/EDX to try to understand what is the detection limit for arsenic concentration in a nano-device. To estimate the lowest measurable arsenic concentration we have used a simple approach based on the experimental results. It is easy to understand that a density measurement cannot be distinguished by zero if zero is included in the confidence interval (i.e. it is between c -∆c and c + ∆c). The obtained result obviously depends on the chosen confidence level [START_REF] Taylor | Introduction To Error Analysis: The Study of Uncertainties in Physical Measurements[END_REF](a Student coefficient equal to 1 has been chosen in this paper). The analysis of the profiles shown in figure 9 clearly shows that doping concentration is always above the concentration limit. The concentration limit can be obtained from the calibration data shown in 7(a) and can be estimated to be 7.7 10 19 cm -3 . This is not an absolute estimation: the value of the detection limit clearly depends on the measured doping peaks intensity since the error on the intensity (see equation 14 and 15) can be improved by increasing the hyper-map exposition times. The formulas given in this paper can be used to calculate the error associated to a specific set of measured intensities but it is impossible to deduce a theoretical lowest limit since the maximum exposition time depends on many experimental factors such as the stability of the specimen to drift and its resistance to electron irradiation. Moreover this estimation neglects the influence of counting artifacts (such as those arising from secondary fluorescence in the specimen holder or microscope apertures) that we have checked to be absent in our case but could not be negligible in general.

Yet a target intensity value can be estimated. To give an example of this procedure, we have estimated the exposition times needed to obtain a given detection limit using the specific parameters of our experimental setup.

More specifically we have used the values of the count per seconds measured in our setup to calculate the time needed to obtain different values of the detection limit. For the calculations we have supposed that the value of the counts-per-seconds does not change with time. The intensity rate measured in our setup amounts to 600 cps, corresponding to the total average count rate of X-rays belonging to the K peaks of Si and As. The obtained detection limit variation with measuring time are shown in table 1.

As density detection limit Measuring time (live time)

1 10 19 cm -3 51 minutes 5 10 18 cm -3 1 h and 43 minutes 1 10 18 cm -3 8 hours and 55 minutes Table 1: Estimated measuring time (live time) needed to obtain higher detection limits for a 600 cps count rate.

It can clearly be observed that in our case it is difficult to considerably improve the detection limit just by increasing the measuring times, since the presence of specimen drift, beam damage and current instability (in our case a cold Field Emission Gun gun is used) limit the measuring time to a few tens of minutes.

There is another possible way to improve the detection limit. To improve background removal, bremsstrahlung subtraction can be applied on cumulative spectra instead of pixel by pixel on the STEM/EDX map (as described in section 2.2). This can be done by creating a cumulative spectrum for each point of the 1D profile by integration in the y direction or by directly acquiring cumulative spectra on a 1D profile . Unluckily we were unable to test this approach due to limitations of the EDX acquisition,/analysis software we have used.

There is another possible way to improve the detection limit. Due to the limitations of the software we have used for peak integration we have been forced to apply background substract on the spectrum collected at each individual position of the STEM/EDX map (as described in section 2.2).

The precision of the background subtraction can, in principle, be improved by working on a cumulative spectrum, created for each point of the 1D profile by integrating in the y direction. This possibility should be exploited when using a system capable to perform lateral integration of the spectra in a EDX map or of the direct acquisition of cumulative spectra on a 1D profile.

Conclusions

In this paper we present an improved methodology to obtain dopant profile in nanodevices. With the proposed quantification method, absorption effects can be accounted for in a rigorous way and without using in-situ beam current measurement. For that an algorithm for the self-consistent calculation Using the proposed approach a doping profile has been obtained on a Fin-FET test structure with a spatial resolution on the nanometer range and a resolution limit lower than 1%. Finally the detection limit for dopant concentration has been evaluated and the exposition times needed to improve it have been calculated using the measured count rates. It is evident from this estimation that, due to instabilities of the experimental setup, the resolution limit cannot be drastically improved by just increasing the measuring time.

Figure 1 :

 1 Figure 1: (a) Implanted doping distribution simulated with SRIM for As implant in silicon with an energy of 21keV; (b)Bright field STEM image of the cross section of the FinFET sample.

Figure 2 :

 2 Figure 2: Schematic illustration of the influence of the specimen geometry on EDX artifacts (secondary X-rays created by fluorescence and backscattered electrons) in specimens prepared using: a) FIB. b) mechanical thinning.

Figure 4 :

 4 Figure 4: Mass density a function of the As mass fraction calculated with two different approximations. The experimentally determined value of the mass density ρ M As of amorphous arsenic is shown in the plot.

Figure 5 :

 5 Figure 5: Plot of the measures As concentration c A As (x) before (a) and after (b) calibration of the k-factors. In both insets the values obtained by using the AsK and AsL peaks are reported and compared with the values obtained by RBS. The standard values of the k-factors provided by the EDX analysis is used in (a) while the calibrated k-factors are used in (b). The absorption correction procedure described in this paper has been applied to all the profiles obtained by EDX.

Figure 7 :

 7 Figure 7: Plot of the measured As concentration c A As (x) using (a) K peaks for Si and As and (b) K peak for Si and L peaks for As. In both cases the obtained values are compared with the values obtained by RBS.

Figure 8 :

 8 Figure 8: Bright field STEM images(a) and EDX intensity maps (b-c) obtained on a FinFET device. The K peaks have been used both for oxygen and arsenic to obtain the peak intensity maps shown in (b) and (c) from the EDX hyper-map. Intensity profiles obtained using a laterally averaged line-scan are superimposed to maps ((b) and (c)). The direction and position for the line-scan as well as the lateral integration width are shown in figure (a), (b) and (c).

  ): As 4 clusters consisting of 4 As atoms placed in the four inner position of a diamond structure, and As 2 V clusters consisting in 2 substitutional As atoms coupled with a Si vacancy. From the point of view of density calculations there is a negligible difference between subsitutional As atoms and the preferential clusters and equation 7 can still be used to describe the density in the peak region.

Figure 9 :

 9 Figure 9: (a) Schematic image illustrating the geometry used to obtain the doping profile and (b) doping profile with experimental error obtained by applying the quantification method.

  of absorption effects has been proposed and the relations between the local density and the local composition of the specimen has been established using a physical model. To calibrate the model parameters, EDX and RBS results have been compared in two different specimens. The k-factors for As in Si and the associated error have been measured using linear regression tech-niques. The results show that a reliable calibration can be obtained by using the intensities of the silicon K and arsenic K peak families. The error on the measured doping concentration has also been estimated combining the different sources of experimental error using error propagation techniques.

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