<figure><img src="image_56.png" /><figcaption>FIG. 6. Temporal evolution of the emission intensity of Fe and NO-γ(0,2). The spectra were recorded at the beginning of the discharge (after venting).</figcaption></figure>

the literature data for outgassing mechanisms under the influence of temperature, we can assume that hydrogen and water vapor desorb from the grids while the walls would only be the source of hydrogen. The decrease in the intensity of the emission lines of species containing only nitrogen is mainly explained by the strong variations in the electrical parameters during this step. Indeed, during this first period (cf. Fig. 4), the composition of the gas varies enormously because of the slowness of the degassing which results from the thermal equilibrium of the reactor. However, thermal outgassing cannot fully explain our experimental results. Indeed, hydrogen lines emission is continuously decreasing whereas it should increase at least at the beginning of the desorption process as observed by Czerwiec *et al.*³³ It is interesting to note that the NH line intensity first increases. Hence, some reactive nitrogen species

like N, vibrationally excited species N₂(v), or metastable states of N₂ must be probably involved in surface reactions with the OH radicals resulting from the adsorption of water on stainless steel. Such surface reactions would be able to produce NO and NH from the water vapor adsorbed on the wall or on the screen.

The continuous increase in iron emission during the first three stages leads us to believe that the preponderant surface in these surface reactions must be the grid itself. It is indeed from the grid that the iron atoms are sputtered. It is very probable that oxides form at the surface of the active screen, thus limiting the iron sputtering efficiency. As the possibility to observe the fourth positive system of N₂, obtaining stable iron emission over time could be a potential indicator of cleanliness of the reactor.

One very important thing that should not be forgotten is the fact the discharge is periodically cut off. In plasma nitriding processes, the pulsed unipolar power supply allows a periodic cutting of the discharge in order to prevent electric arcs from developing. Long duration arcs can deteriorate the active screen in the ASPN process. Active nitrogen species can react on surfaces with adsorbed oxygen species only during the part of the cycle during which voltage is applied to the active screen. In the temporal post-discharge (t<sub>off</sub>), the active nitrogen species disappear quite quickly during this period and no longer react with the species adsorbed on the surfaces. The time for this cutoff is short enough not to have any influence on the temperature of the walls and the screen. Thus, the thermal desorption of the species containing oxygen and hydrogen continues during the cutoff period. The reactivation of the plasma, therefore, takes place in a polluted atmosphere at the end of each electrical cycle.

## B. The D³Σ⁺u state of N₂: Observations and population mechanisms

As presented before, the fourth positive system seems to be correlated to the reactor cleanliness, by contrast to the emission

<figure><img src="image_57.png" /><figcaption>FIG. 7. Emission spectra of nitrogen plasma in the spectral range of 242–262 nm under unclean (a) and clean (b) conditions at 0.5 mbar.</figcaption></figure>

<figure><img src="image_58.png" /></figure>
<figure><img src="image_59.png" /><figcaption>FIG. 8. (a) Emission spectra recorded in the range of 242–262 nm for a gas mixture composed of 80% N₂–20% H₂ at 0.5 mbar. The spectra were recorded at the beginning of the discharge (after venting). (b) Temporal evolution of NO-γ(0,2) band intensity in 80% N₂–20% H₂ plasma following by pure nitrogen discharge without venting.</figcaption></figure>

bands of NO, which are clearly linked to reactor contamination. During the decontamination phase, the decrease in NO emission intensity reveals the fourth positive system. At this moment, it could be interesting to study the population mechanisms of both excited species (NO and N₂).

In this case of NO emission, it could be supposed that NO excited state (A³Σ⁺ at about 5.5 eV) is produced by a direct electronic impact. Electrical characteristics [cf. Fig. 5(a)] are relatively constants; it can be assumed that emission intensity is proportional to the NO concentration.

<figure><img src="image_60.png" /><figcaption>FIG. 9. Potential energy curves for X¹Σ⁺g, A³Σ⁺u, B³Πg, C³Πu, and D³Σ⁺u states of N₂. Potential curves are calculated assuming Morse potential and by using spectroscopic constants given by Lofthus and Krupenie³¹ for X¹Σ⁺g, A³Σ⁺u, and B³Πg, C³Πu and by Lewis et al. for D³Σ⁺u.³⁰</figcaption></figure>

For the case of the fourth positive system, population mechanisms remain relatively unknown. Figure 9 presents the potential energy curves of the N₂ electronic state observed in ASPN plasma. Potential curves are calculated assuming Morse potential and by using spectroscopic constants given by Lofthus and Krupenie³⁰ for X¹Σ⁺g, A³Σ⁺u, and B³Πg, C³Πu and by Lewis et al. for D³Σ⁺u.²⁹ D³Σ⁺u is shown in dashed line, because the potential curve is not well known. As depicted in Fig. 9, this state requires 14 eV to be populated from the ground state. The origin of populating the D³Σ⁺u state asks question. Several mechanisms can be considered such as excitation by electronic impact from the fundamental state (R1) and from the metastable state A³Σ⁺u (R2) and by pooling reaction (R3).

$$N_2(X^1\Sigma_g^+) + e^- \rightarrow N_2(D^3\Sigma_u^+), \qquad (R1)$$

$$N_2(A^3\Sigma_u^+) + e^- \rightarrow N_2(D^3\Sigma_u^+), \qquad (R2)$$

$$N_2(A^3\Sigma_u^+) + N_2(A^3\Sigma_u^+) \rightarrow N_2(D^3\Sigma_u^+). \qquad (R3)$$

The production of N₂(D³Σ⁺u) by the pooling reaction is unlikely as the energy difference between A and D states (6 eV) is larger than the energy of A state (cf. Fig. 9). A production by electronic impact from the metastable state of N₂ (cf. R2) is also unlikely because (i) the density of state A³Σ⁺u is in the range of 10¹¹–10¹² molecules cm⁻³ (see Ref. 34) and (ii) according to Franck–Condon principle, electronic transitions are promoted between state which inter-molecular distance does not suffer large change, which is not the case of A³Σ⁺u and D³Σ⁺u state with, respectively, 1.286 56 and 1.1081 Å [potential curve is not well known, but rₑ was estimated from the relationship given by Lofthus and Krupenie: rₑ(cm⁻¹) = 1.551 677 86√1/Bₑ, with Bₑ (cm⁻¹) being the
equilibrium rotational constant, $B_e = 1.961 \text{ cm}^{-1}]^{30}$. On the contrary, X (1.097 696 8 Å$^{30}$) and D states own a similar intermolecular distance. Hence, the production of $N_2(D^3\Sigma_u^+)$ from $N_2(X^1\Sigma_g^+)$ by electron-impact excitation appears likely, suggesting an electron population with at least 14 eV. Absolute optical-emission function for the fourth positive system band (0,ν′) is given by Filippelli et al.$^{28}$ They found that D-B emission reaches a maximum for 14.1 ± 0.3 eV just after the threshold energy and excitation cross section from $X(ν'' = 0)$ to $D(ν' = 0)$ equal to $1.27 \times 10^{-19} \text{ cm}^2$.

If we assume that electrical characteristics and $N_2$ concentration are constants, the emission intensity of the fourth positive system remains also constant during the decontamination process. Observation of this system is linked to the NO decrease due to the reactor decontamination. We can conclude that the fourth positive system is a good cleanliness indicator in pure nitrogen discharge.

## V. CONCLUSION

In the present paper, contamination by oxygen species was observed in pure nitrogen through the observation of NO-γ in the so-called active screen plasma nitriding process operating under the pulsed unipolar power supply. This contamination was observed by OES when the discharge is initiated in pure nitrogen immediately after venting the reactor. The temporal evolution of the emission intensity of $N_2$, $N_2^+$, NO, OH, H, NH, and Fe species was monitored in the spectral range of 200–900 nm. Observation of the fourth positive system of $N_2$ (only the $ν' = 0$ progression) and NO-γ bands in $N_2$ plasmas was reported. To our knowledge, the fourth positive system of $N_2$ was not yet observed in such plasmas applied to nitriding.

It was found that the emission of oxygen-containing species (NO and OH) decreases with time, while Fe emission intensity increases with time. Contamination of the reactor surfaces results from water vapor adsorption during reactor venting in order to place the samples to be nitrided. Desorption can be different from the active screen and from the wall, because of temperature differences: higher than 500 °C on the active screen and around 100 °C on the sample placed on the center. The result is a long decay of the NO-γ band emission. After decontamination, the fourth positive system of $N_2$ could be observed. Such a not commonly observed system can be used as a tool to control reactor cleanliness in pure nitrogen discharge for nitriding applications. Emission of iron lines consequential to active screen sputtering was found to be correlated to the evolution of the NO-γ system. This is due to the removal of oxide pollution by ions bombardment of the cathodic screen. A way to test the cleanliness of the reactor could be to realize pure nitrogen plasma and to verify that NO-γ bands were not observed. Following this test, hydrogen could be introduced into the mixture and treatment begins in a clean atmosphere.

## ACKNOWLEDGMENTS

This work was performed in the frame of the research project RESEM 2020, managed by the Institut de Recherche Technologique Matériaux Métallurgie Procédés (IRT M2P), and financially supported by the French program Plan d'Investissement d'Avenir (PIA). We acknowledge G. Cernogora of LATMOS laboratory,

Université de Versaille Saint Quentin en Yvelines, for his help in understanding the population mechanism of $N_2(D^3\Sigma_u^+)$.

## DATA AVAILABILITY

The data that support the findings of this study are available from the corresponding author upon reasonable request.

## REFERENCE

¹S. Li, J. Medrano Jimenez, V. Hessel, and F. Gallucci, *Processes* **6**, 248 (2018).

²P. Peng, C. Schiappacasse, N. Zhou, M. Addy, Y. Cheng, Y. Zhang, K. Ding, Y. Wang, P. Chen, and R. Ruan, *ChemSusChem* **12**, 3702 (2019).

³L. Lin, H. Xu, H. Gao, X. Zhu, and V. Hessel, *J. Phys. D: Appl. Phys.* **53**, 133001 (2020).

⁴E. Rolinski, “Plasma assisted nitriding and nitrocarburizing of steel and other ferrous alloys,” in *Thermochemical Surface Engineering of Steels*, edited by E. J. Mittemeijer and M. A. J. Somers (Woodhead Publishing, 2014), p. 413.

⁵A. Pavlik, G. Marcos, M. Coulibaly, M. Vincent, T. Czerwiec, and T. Philippon, *Tribol. Int* **146**, 106232 (2020).

⁶T. Czerwiec, H. Michel, and E. Bergmann, *Surf. Coat. Technol.* **108-109**, 182 (1998).

⁷J.-P. Lebrun, in *Proceedings of 10th International Congress IFHTSE* (Brighton, UK, 1996), p. 169.

⁸J. Georges, U.S. patent 5,989,363 (November 23, 1999).

⁹J. Georges, Heat Treat. Met. **28**, 33 (2001).

¹⁰H.-J. Spies, I. Burlacov, K. Borner, and H. Biermann, *Int. Heat Treat. Surf. Eng.* **8**, 1 (2014).

¹¹C. X. Li, *Surf. Eng.* **26**, 135 (2010).

¹²S. Corujeira Gallo and H. Dong, *Surf. Coat. Technol.* **203**, 3669 (2009).

¹³I. Burlacov, K. Börner, H.-J. Spies, H. Biermann, D. Lopatik, H. Zimmermann, and J. Röpcke, *Surf. Coat. Technol.* **206**, 3955 (2012).

¹⁴D. Kovács, J. Dobránszky, and A. Bonyár, *Results Phys.* **12**, 1311 (2019).

¹⁵A. Nishimoto, K. Nagatsuka, R. Narita, H. Nii, and K. Akamatsu, *J. ASTM Int.* **8**, 103286 (2011).

¹⁶A. Itoh, Y. Ishikawa, and Y. Kawabe, *J. Vac. Sci. Technol. A* **6**, 2421 (1988).

¹⁷Y. H. Shin, K. J. Lee, and K. H. Chung Jhung, *Vacuum* **47**, 679 (1996).

¹⁸D. Kovács, J. Dobránszky, T. Fodor, V. Takáts, and A. Bonyár, *Surf. Coat. Technol.* **394**, 125638 (2020).

¹⁹D. L. Crintea, U. Czarnetzki, S. Iordanova, I. Koleva, and D. Luggenhölscher, *J. Phys. D: Appl. Phys.* **42**, 045208 (2009).

²⁰J. Walkowicz, *Surf. Coat. Technol.* **174-175**, 1211 (2003).

²¹K. S. Suraj, P. Bharathi, V. Prahlad, and S. Mukherjee, *Surf. Coat. Technol.* **202**, 301 (2007).

²²L. Petitjean and A. Ricard, *J. Phys. D: Appl. Phys.* **17**, 919 (1984).

²³M. Hannemann, S. Hamann, I. Burlacov, K. Börner, H.-J. Spies, and J. Röpcke, *Surf. Coat. Technol.* **235**, 561 (2013).

²⁴S. Hamann, K. Börner, I. Burlacov, H.-J. Spies, and J. Röpcke, *J. Phys. D: Appl. Phys.* **48**, 345204 (2015).

²⁵H. Michel, T. Czerwiec, M. Gantois, D. Ablitzer, and A. Ricard, *Surf. Coat. Technol.* **72**, 103 (1995).

²⁶H. Uyama and O. Matsumoto, *Plasma Chem. Plasma Process.* **9**, 13 (1989).

²⁷O. Matsumoto, M. Konuma, and Y. Kanzaki, *J. Less Common Met.* **84**, 157 (1982).

²⁸A. R. Filippelli, S. Chung, and C. Lin Chun, *Phys. Rev. A* **29**, 1709 (1984).

²⁹B. R. Lewis, K. G. H. Baldwin, A. N. Heays, S. T. Gibson, J. P. Sprengers, W. Ubachs, and M. Fujitake, *J. Chem. Phys.* **129**, 204303 (2008).

³⁰A. Lofthus and P. H. Krupenie, *J. Phys. Chem. Ref. Data* **6**, 113 (1977).

³¹Y. Ishikawa and T. Yoshimura, *J. Vac. Sci. Technol. A* **13**, 1847 (1995).

³²J. P. Joly, F. Gaillard, E. Peillex, and M. Romand, *Vacuum* **59**, 854 (2000).

³³T. Czerwiec, K. Anoun, M. Remy, and H. Michel, *Mater. Sci. Eng. A* **139**, 276 (1991).

³⁴A. Ricard, *Plasma Reactifs* (SFV Editions, 1995).
# Stainless steel patterning by combination of micro-patterning and driven strain produced by plasma assisted nitriding

Gregory Marcos a,*, Stephane Guilet b, Franck Cleymand a, Tony Thiriet a, Thierry Czerwiec a

## ARTICLE INFO

**Article history:**

Received 20 September 2010
Accepted in revised form 10 January 2011
Available online 20 January 2011

**Keywords:**

Patterning
Nitriding
Strain
Stainless steel
Stress

## ABSTRACT

Plasma-assisted nitriding treatments on austenitic stainless steel at low temperature produce the so called "expanded austenite". The expansion of the nitrided layer that occurs from the initial surface of the substrate in a direction perpendicular to the surface is used here as a mean to produce patterned surfaces by selective nitrogen diffusion through masks. Using grids, a network of well defined square dots can be obtained. In this communication, the results of nitriding treatments on austenitic stainless steel substrates previously covered by a patterned silicon oxide layer are presented. The interactions mechanisms at the interface between fixed silicon oxide mask with several different shapes (circular and square dots) and the expanded austenite are also described. The role of nitrogen diffusion, consistent with the experimental conditions and the mask characteristics, is shown to be very important. Depending on the size of the dots, it leads to a simple uniform mask deformation or to a significant mask deformation with strong distortions at the edges. This phenomenon is noted as a toroidal-shell shape distortion. Optical cross-section seems to prove that it is only the result of the vertical force due to the austenite expansion induced by nitrogen diffusion just under the mask edges.

© 2011 Elsevier B.V. All rights reserved.

## 1. Introduction

Thermochemical diffusion treatments such as nitriding, carburizing and nitrocarburizing are commonly used to improve surface properties of austenitic stainless steels [1]. These materials are of great technological interest in industries like aeronautic where corrosion resistance and toughness are primary requirement. Even if the debate is still open, it is now well accepted by the scientific community that below 420 °C, a plasma-assisted nitriding (PAN) treatment of austenitic stainless steel forms a peculiar phase usually called expanded austenite and noted γN in this communication. The γN phase is a metastable nitrogen supersaturated solid solution with a disordered fcc structure and a distorted crystal lattice [2]. Appearing from the surface towards the bulk according to nitrogen diffusion, this phase is hard and wear resistant. The good tribological properties are due to the high nitrogen content (from 20 to 35 at.%) which is possible to introduce in the nitrided layer, inducing high compressive residual stresses (from 1 to 5 GPa).

Recently, novel perspectives were found to use PAN treatment as a mean to perform surface patterning [3]. Surface patterning or surface texturing is a very active field of research according to many applications such as wetting [4,5], adhesion [6], self-cleaning [7] or tribological performances [8,9]. In this innovative approach, extrusion

phenomenon of expanded austenite through a mask allows obtaining networks of dots. But the result is strongly dependant on mask properties (well adherent/not adherent, size features and geometry) and experimental conditions. These interactions between mask and expanded austenite are the subject of this paper.

## 2. Experimental set-up and characterisation techniques

Samples used in this communication are AISI 316L stainless steel cylinders (13 wt.% Ni, 17 wt.% Cr, 67 wt.% Fe, 2 wt.% Mo, 0.5 wt.% Si, 0.2 wt.% Mn, and 0.02 wt.% C) cut from a cylindrical rod (20 mm of diameter) and with a thickness of 5 mm. Table 1 summarizes the experimental conditions used to perform PAN treatments. C1 employs a pulsed direct current glow discharge (GD) system working under rough vacuum [10]. For C2 and C3, a multi-dipolar electron cyclotron resonance system (MDECR) was used [11]. Profiles of the treated surfaces are done using a SURFASCAN 3S profilometer. Data analysis using the Mountains Map© software provides roughness parameters according to the norm ISO 4287:1997. The atomic force microscope (AFM) images presented in this paper were obtained by a Veeco device. Images have been taken in retrace direction and no significant effects have been noticed in relation with the scanning direction. Images were taken in intermittent contact mode (also called tapping® mode) and the results are presented in height mode.

The main steps of process 1 for surface patterning are the following ones (see ref [3] for the complete protocol). A copper TEM grid is simply put (not stuck) on a sample polished to a mirror-like finish

<footnote>a Institut Jean Lamour, Ecole des Mines de Nancy, Parc de Saurupt, CNRS UMR 7198, CS 14234, 54042 NANCY Cedex, France</footnote>

<footnote>b Laboratoire de Photonique et de Nanostructures, CNRS UPR 20, Centrale de Technologie - Procédés Plasmas, Site Alcatel de Marcoussis, Route de Nozay, 91 460 MARCOUSSIS, France</footnote>

<footnote>* Corresponding author.
E-mail address: gregory.marcos@ijl.nancy-universite.fr (G. Marcos).</footnote>
<table><caption>**Table 1**
Experimental conditions.</caption><thead><tr><th>Condition</th><th>Nitriding device</th><th>Gas mixture</th><th>Pressure (Pa)</th><th>Temperature (°C)</th><th>Substrate bias (V)</th><th>Duration (h.)</th></tr></thead><tbody><tr><td>C1</td><td rowspan="2">Pulsed dc discharge</td><td>90% N<sub>2</sub>-<br/>10% H<sub>2</sub></td><td>300</td><td>450</td><td>-490 to<br/>-500</td><td>0.5 to 8</td></tr><tr><td>C2</td><td>60% N<sub>2</sub>-<br/>40% H<sub>2</sub></td><td>5.75</td><td>400</td><td>-50</td><td>1</td></tr><tr><td>C3</td><td>MDECR</td><td>90% N<sub>2</sub>-<br/>10% H<sub>2</sub></td><td>2</td><td>410</td><td>Floating</td><td>4</td></tr></tbody></table>

(diamond 3 µm). The PAN treatment is realized in a MDECR plasma reactor in experimental conditions C2 (Table 1).

The main steps of process 2 for surface patterning are the following. In a clean room, plasma enhanced chemical vapour deposition (PECVD) technology was used for deposition of a 500 nm thick silicon oxide layer on AISI 316L samples previously mirror like polished and cleaned in methanol. On this silicon oxide layer, a 1.4 µm thick AZ5214 photoresist was deposited by spin-coating. A specific mask containing different features (large squares of 200 µm and series of circular discs with different diameters from 3 to 15 µm) was used to perform UV photolithography. A step of dry etching of the silicon layer through the thus patterned photoresist was performed in a SF<sub>6</sub>/CHF<sub>3</sub> plasma mixture. At the end, the residual photoresist was removed in oxygen plasma cleaning. The PAN treatment is realized in a MDECR plasma reactor in experimental conditions C3 (Table 1).

### 3. From surface deformation to surface patterning

The evolutions of some roughness parameters ($R_t$, $R_p$, and $R_v$) is represented in Fig. 1 as a function of the square roots of nitriding time. These experimental data have been obtained in pulsed dc plasma nitriding, however similar results are also gained from MDECR nitriding experiments. The three roughness parameters linearly increase with the square roots of nitriding time. This is the signature of a progressive transformation of the surface state, according to the thermochemical diffusion process. This evolution is well visible on the scanning electron microscopy (SEM) picture (Fig. 1), where some grains appear more elevated than others. This characteristic, defined by the $R_t$ parameter, shows that this surface displacement is mainly anisotropic due to the residual stress induced by the nitriding treatment. A mechanical model that links stress and strain is proposed in reference [10]. It takes into account the compositional strain due to the isotropic introduction of nitrogen in austenitic phase. As the nitrided layer is attached to the rest of the substrate, a biaxial

compressive stress develops to elastically deform the layer in order to compensate the effect of the compositional strain. By mechanical considerations, it is possible to assume that this distortion is fully anisotropic, perpendicular to the plane of the substrate. With the model, we deduce the expression of this displacement (noted $\Delta x$):

$$ \Delta x = e_N \frac{\langle \epsilon_t \rangle}{1 + \langle \epsilon_t \rangle} \quad (1) $$

In this formula, $e_N$ is the total thickness of the nitrided layer and $\langle \epsilon_t \rangle$ is the mean total strain (compositional strain + elastic strain). According to the treatment conditions, $\Delta x$ varies from a few hundred nanometers to a few microns. We use this expansion property to perform surface patterning on AISI 316L samples.

Fig. 2 presents the results obtained in experimental conditions C2 with the patterning process 1. The topography, realised by profilometry after grid removal, shows the formation of a network of square dots with 200 µm in lateral dimension and heights ranging from 220 nm to 275 nm. These zones correspond to the open spaces of the grid allowing the incoming reactive species from the plasma to diffuse into the sample. Fig. 2 also shows an optical cross-section view around one dot, realised according to the dashed line passing through a row of dots. The $\gamma_N$ phase layer is well visible, proving that the dots are clearly connected to expanded austenite. The height of the dots, measured from the untreated parts (the valleys associated to the masked zones), corresponds to the total displacement, in other words the extruded part of the nitrided layer. As the obtained nitrided layer has a thickness $e_N$ of around 2.3 µm, by using the relation (1) we deduce the displacement $\Delta x$ to be between 130 and 170 nm. This is in good agreement with the data measured by profilometry.

### 4. Expanded austenite through a fixed patterned mask

Fig. 3.a is an optical view of the patterned masks we used in the patterning process 2 before the nitriding step. In the centre, series of cylindrical dots appear surrounded by four big square dots. The AFM image presented in Fig. 3.b shows well defined features corresponding to the initial mask geometry. The top of dots appears to be strictly parallel to the substrate surface. Fig. 4 shows AFM image in height mode in the vicinity of a big square dot together with two circular dots. Profile obtained perpendicularly to the border of a big square dot (white line in Fig. 4) is also represented in Fig. 4. The height calibration of this profile is done by considering that the centre of the big square is not affected by any deformation due to the expanded austenite and remains flat. Thanks to this assumption, we have drawn in bold lines the initial dots position in Fig. 4. By this way, it is possible to rebuild the expansion of austenite and dots at the end of the nitriding process. From a general point of view, one notes from Fig. 4, a disturbed topography with a strong deformation in the direction perpendicular to the surface of the sample. Concerning the non-masked zones and referring to the properties of expanded austenite, this behaviour is in agreement with the result described in the previous section. Expanded austenite develops differently according to the observed zones: the vertical expansion ranges from 200 to 900 nm. It is difficult to explain these differences in expansion levels. Although condition C1 and C2 are not the same, the maximum difference in expansion (700 nm) is in good agreement with the measured $R_t$ value. It seems that this phenomenon is connected to the grains orientation in which the expansion occurs. It is probably also necessary to take into account the space available for the expansion between the dots. Another possible explanation is a well known effect in the community working on dry etching process: the shadow effect. Such effect is connected to a geometrical reduction of the active species incident flux close to the mask. From Fig. 4, it can be seen that the maximum level of austenite expansion between the two circular

<figure><img src="image_61.png" /><figcaption>**Fig. 1.** (a): Evolution of roughness parameters ($R_t$, $R_p$, and $R_v$) as a function of the square root of nitriding treatment time together with a surface SEM picture showing the surface distortion after nitriding in conditions C1 (see Table 1).</figcaption></figure>
<figure><img src="image_62.png" /><figcaption>**Fig. 2.** (a): Topography of a patterned AISI 316L sample after a nitriding treatment in conditions C2 (see Table 1) together with an optical cross-section view of the dots in a nitrided zone.</figcaption></figure>

dots is smaller in the vicinity of dots as compared to the middle of the inter dots space.

Concerning the dots, a vertical displacement between 200 and 750 nm is measured. The behaviour of the dots is different according to their size. For the smallest ones (dimension lower or equal to 5 µm (not shown in Fig. 4), a perpendicular displacement of the whole surface is observed. As a consequence, at the end of the nitriding process, this family of dots has followed the local austenite expansion and their top is not deformed or just slightly bent. For the bigger cylindrical dots, a toroidal-shell shape develops on the top surface. From Fig. 4, it also appears as a deformation of the initial surface of the dots. This displacement phenomenon is particularly spectacular at the edges of the rectangular dot: an elevation of 650 nm is measured compared to the height of reference. The dots distortion seems to be directly connected to interaction phenomena between them and expanded austenite. It clearly appears when one locally compares the expansion of austenite and the elevation of dots.

In order to understand the nature of the interactions between the silicon oxide mask and expanded austenite, we had to consider

additional observations. Before the nitriding step, the dots are well adherent to the substrate. The deposition process is controlled in such a way that there are no voids at the interface between the silicon oxide layer and the austenitic substrate. We experimentally verify that the silicon oxide layer is not affected by a tempering at the nitriding temperature. So, dots distortion is only a consequence of the nitriding treatment.

From our point of view, two hypotheses can be suggested in order to explain the behaviour of the silicon oxide film after a nitriding treatment.

The first hypothesis involves lateral forces acting in a direction parallel to the surface on the dots edges. As a matter of fact, a nitriding treatment without mask induces the formation of high level of compressive stresses in the austenitic material [3]. With a mask, the mechanical behaviour of a discontinuous layer is more complicated to describe than those of a continuous layer. Nevertheless, it is possible to assume that nitrogen introduction in the free space between dots induces not only an expansion of the austenite in the direction perpendicular to the surface, but also a lateral expansion that in turns

<figure><img src="image_63.png" /><figcaption>**Fig. 3.** (a): Optical view of the patterned silicon oxide layer, and (b): 3-D view obtained by AFM showing a series of cylindrical dots and a corresponding 2-D profile that confirms a good reproducibility and reveals slightly tilted sides at around 10° with respect to the perpendicular direction.</figcaption></figure>
<figure><img src="image_64.png" /><figcaption>**Fig. 4.** Reconstructed two dimensional view of an AFM profile performed along the drawn line through square and cylindrical dots after a nitriding treatment in conditions C3 (see Table 1).</figcaption></figure>

produce lateral forces on the dots. Following such assumption, this lateral forces act on the dots edges and induce strong deformations of the silicon oxide layer with a bending at their top. After the nitriding treatment, when the patterned mask — expanded austenite system releases, a phenomenon like a debuckling can occur, the centre of the dot breaks down, thus creating the toroidal-shell shape of the dots. Within these hypotheses, this mechanical behaviour can be regarded as similar to the destabilisation of wrinkling patterns observed in other systems [12].

The second hypothesis involves a lateral diffusion of nitrogen during the nitriding treatment. Following this idea, nitrogen diffusion not only process in the open space between the dots, but also under the mask with a lateral penetration from a few hundreds of nanometers to several micrometers, according to the experimental conditions. The expanded austenite layer, created under the silicon oxide masks, exerts a force in a direction perpendicular to the surface that pushes the mask edges vertically.

Fig. 5 shows the SEM cross-section of a sample treated two times in experimental conditions C3. From this figure, it is obvious that nitrogen diffused under the dots during such a long nitriding time. Expanded austenite is thus formed under the silicon oxide mask by lateral nitrogen diffusion. According to the dot size and/or the process conditions (time, temperature, and gas mixture), two cases can be distinguished. For the dots with the smallest sizes (less than 5 µm after one nitriding treatment in condition C3 or 10 µm after one nitriding treatments in condition C3), it seems that nitrogen completely diffuses in the lateral direction under the mask. In such situation, the expanded austenite layer is thus continuous, from the zones not covered by the mash towards the masked zones. Under the mask, a relatively homogeneous vertical force is thus exerted by the expanded austenite layer on the mask. As a consequence, a vertical displacement of the dots occurs following the homogeneous expansion of the underneath austenite layer. It seems that this situation corresponds to that observed in Fig. 5. It must be noted that this mechanism seems to correspond to an elevation of the dots that fully cover one single grain. As a matter of fact, we suspect more complicated distortion when the dot covers more than one grain.

For bigger dots, in other words, for dots with a size larger than the lateral nitrogen diffusion length, expanded austenite only forms under the edges of the mask. The vertical force exerted by the expanded austenite layer on the mask is thus localized in the area under the edges of the mask. This can explain the toroidal-shell shape of big dots after nitriding.

The SEM cross-section of Fig. 5 shows that the second hypothesis seems to be relevant: dots distortion is mainly due to a mechanical effect induced by expanded austenite formed under the mask. Nevertheless, we did not succeed yet proving that there is no partial separation of the mask and the substrate during a nitriding treatment. So, the first hypothesis cannot be rejected. A modelling work, based on elastic stress evaluation of the dot on the substrate by applying the Föppl-Von Karman formalism to describe dot deformation will be undertaken to improve our knowledge of the deformation mechanisms [12] [13].

<figure><img src="image_65.png" /><figcaption>**Fig. 5.** Cross-section of a sample nitrided two times in condition C3 observed by SEM. Marble used as an etching reagent to reveal the microstructure.</figcaption></figure>
Conclusion

Below 400 °C, a low temperature nitriding treatment of austenitic
stainless steel produces high compressive residual stress induced by
the introduction of a large amount of nitrogen. As a result, an
expansion of the nitrided layer occurs from the initial surface of
substrate in a direction perpendicular to the surface. We use this
property to perform surface patterning by a selective diffusion of
nitrogen using grids as a mask. By this way, a network of well defined
square dots can be obtained. In this communication, we presented the
results of nitriding treatments on austenitic stainless steel substrates
previously covered by a patterned silicon oxide layer. In such a
configuration, interesting interactions between expanded austenite
and the attached silicon oxide mask with several different shapes
(circular and square dots) were observed. After a nitriding treatment,
strong dots distortions were obtained, particularly at the edges of the
dots with a larger size. Some explanations were proposed to justify
such behaviour. The role of elastic strain, due to the expanded
austenite phase formed by nitrogen diffusion under the mask, seems
to be of primary importance. A modelling work is in progress to bring
complementary information on the distortion of the dots. The method
we propose to perform surface patterning on austenitic stainless

steels opens the way to innovative applications, in particular for
mechanical devices. A better understanding of the patterning
mechanisms will allow a better control of the features realised by
the new surface texturation process presented here.

References

[1] T. Bell, Surf. Eng. 18 (2002) 415.

[2] Y. Sun, X.Y. Li, T. Bell, J. Mater. Sci. 34 (1999) 4793.

[3] T. Czerwiec, G. Marcos, T. Thiret, Y. Guo, T. Belmonte, IOP Conf. Ser. Mat. Sci. Eng. 5 (2009).

[4] Y. Xia, D. Qin, Y. Yin, Opin. Coll. Interface Sci. 6 (2001) 54.

[5] J.A. Blach-Watson, G.S. Watson, C.L. Brown, S. Myhra, Appl. Surf. Sci. 235 (2004) 164.

[6] D. Marchetto, A. Rota, L. Calabri, G.C. Gazzadi, C. Menozzi, S. Valeri, Wear 268 (2010) 488.

[7] M. Ma, R.M. Hill, Curr. Opin. Colloid Interface Sci. 11 (2006) 193.

[8] I. Etson, J. Tribol. 127 (2005) 248.

[9] A. Kovalchenko, O. Ajayi, A. Erdemir, G. Fenske, I. Etson, Tribol. Int. 38 (2005) 1241.

[10] T. Czerwiec, H. He, G. Marcos, T. Thiriet, S. Weber, H. Michel, Plasma Proc. Pol. 6 (2009) 401.

[11] A. Lacoste, T. Lagarde, S. Bechu, Y. Arnal, J. Pelletier, J. Plasma Sources Sci. Technol. 11 (2002) 407.

[12] F. Cleymand, J. Colin, C. Coupeau, Eur. Phys. J. App. Phys. 17 (2002) 173.

[13] F. Cleymand, C. Coupeau, J. Colin, J. Grilhe, Eur. Phys. J. App. Phys. 10 (2000) 3.
# Influence of the real dimple shape on the performance of a textured mechanical seal

<figure><img src="image_66.png" /></figure>

CrossMark

M. Adjemout<sup>a</sup>, A. Andrieux<sup>b</sup>, J. Bouyer<sup>a, *</sup>, N. Brunetière<sup>a</sup>, G. Marcos<sup>b</sup>, T. Czerwiec<sup>b</sup>

## ARTICLE INFO

### Keywords:

- Surface texture

- Mechanical seal

- Hydrodynamic lubrication

- Surface defects

## ABSTRACT

Surface texturing the friction faces of a mechanical seal reduces friction as well as leakage and wear, where dimples machined on the surface enhance the formation of a full lubricating film in the seal interface. Numerical simulation is used to determine the optimal surface texturing for the investigated operating conditions of the seal. The geometry of the dimples introduced in the model assume a perfect shape, but machining causes the dimple shapes to be imperfect in terms of the roughness in the dimples, absence of sharp angles, deformed boundaries, and so on. The effect of the real geometry must be considered to confirm that surface texturing will provide the desired results. In the present work, surface texturing is performed using low-temperature plasma coupled with a thermo-chemical surface treatment on stainless steel sealing rings. The real dimple shapes are analysed and considered within the hydrodynamic lubrication model. The influence of different types of defects is studied. It is shown that there is a limit above which surface imperfections dispel the texture's positive effects. Controlling the dimple shapes is important when performing surface texturing.

## 1. Introduction

A mechanical seal is a sealing device that is widely used in industry such as those utilizing pumps and compressors. It mainly consists of two rings (the stator and the rotor), where one of them is linked to the housing and the other to the shaft. The sealing function is ensured by the mating faces of these two rings, which constitute a mechanical seal. A thin fluid film that is a few microns thick is created in the gap between the rotating faces, which reduces the risk of contact, and therefore, the risk of wear. To preserve the main function of mechanical seals (that is, sealing), the induced leakage should be eliminated or minimized to an acceptable level. Thus, the optimal configuration of a mechanical seal is one that minimizes the friction as well as the leakage.

One of the main methods studied and discussed in tribology literature is the performance enhancement of mechanical seals through surface texturing. In 1966, Hamilton et al. [1] discovered the effect of surface texturing when studying roughness effects by means of artificial asperities possessing a cylindrical shape. The authors explained that each pillar is like a micro-bearing that assists in fluid film generation and friction reduction. A few years later, Anno et al. [2] showed that cavities can be more beneficial for mechanical seals because they preserved a low leakage rate and allowed hydrodynamic fluid film generation between

the seal faces. In 1997, Etsion et al. [3], showed that it was possible to increase a seal life when dimples were created on the seal surfaces with a laser texturing method. The possibility of enhanced performance in terms of lower friction and a higher critical load before seizure has been confirmed by several other studies [4–6]. However, the experimental results yielded a great dependence on texture geometrical parameters [6], such as the area ratio covered by the cavities, and the diameter and depth of the dimples. For certain parameters, it is possible to obtain worse performance with textured surfaces than with flat surfaces [7]. This is because the shapes of the dimples are unlimited [8], which highlights the need for an optimization process.

Numerical simulation offers a good solution for optimizing dimple shapes [8,9]. A recent review of Gropper et al. [10] revealed that several papers were dedicated to simulating the hydrodynamic lubrication of textured surfaces. Additionally, Etsion [11] provided some advice for solving the Reynolds equation, which governs fluid flows in the thin film when the surfaces are being textured. During this process, some pressure peaks are created at the trailing edge of cavities, whereas pressure decreases occur in the dimples. If the pressure decreases below a critical value, cavitation or film rupture could occur. It is important to model this phenomenon using a mass conserving algorithm to obtain relevant results, more particularly with seals, as shown by Qiu and Khonsari [12].

<footnote><sup>a</sup> Institut Pprime UPR 3346, CNRS, Université de Poitiers, Ensma, Dept. GMSC, 86962, Futuroscope, France</footnote>

<footnote><sup>b</sup> Institut Jean Lamour UMR 7198, CNRS, Université de Lorraine, Dept. CPSS, 54011, Nancy, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: jean.bouyer@univ-poitiers.fr (J. Bouyer).</footnote>
<figure><img src="image_67.png" /><figcaption>Fig. 1. A textured ring.</figcaption></figure>

<figure><img src="image_68.png" /><figcaption>Fig. 2. Geometric scheme of the model [13].</figcaption></figure>

$$F \frac{\partial}{\partial r} \left( \frac{r h^3}{\mu} \frac{\partial D}{\partial r} \right) + F \frac{\partial}{\partial \theta} \left( \frac{r h^3}{\mu r} \frac{\partial D}{\partial \theta} \right) = 6 V \left[ \frac{\partial h}{\partial \theta} + (1-F) \frac{\partial}{\partial \theta} (h D) \right] \quad (1)$$

$$\left\{ \begin{array}{l} D = p - p_{cav} > 0 \\ \rho = \rho_0 \\ F = 1 \end{array} \right. \quad \left\{ \begin{array}{l} p = p_{cav} \\ D = \frac{\rho}{\rho_0} - 1 < 0 \\ F = 0 \end{array} \right. \qquad (2)$$

Generally, perfect dimple shapes are considered in simulations by using very thin meshes [13]. However, the geometrical shape of real cavities on real textured surfaces is not perfect. Even if laser surface texturing was used, which is one of the most commonly used methods [14], there are many alternative techniques for performing surface structuration [15,16]. Each of these methods produces imperfect

dimples, where Ref. [17] demonstrated that the performance of textured surfaces greatly depended on their geometrical parameters. It is, therefore, necessary to consider shape imperfections to obtain accurate results. Although some researchers have simultaneously considered surface roughness and surface texture [10,17,18], very few have focused on the effects of dimples.

In the present work, the real dimple shapes are analyzed and introduced into a hydrodynamic model. The dimples are created through the ion etching of stainless steel sealing rings (Fig. 1). Once the surface texturing has been performed, a plasma-assisted, thermo-chemical surface treatment is applied to enhance the surface hardness and corrosion resistance [16]. An optimization of the size, shape, and distribution of the texture patterns were performed in previous studies [9,13] that used a triangular dimple shape. In contrast, this work investigates the influence of several types of defects: the roughness at the bottom of the dimples, the absence of sharp angles, and deformed boundaries.

## 2. Theoretical model

The previously mentioned model using two rings in relative sliding motion, which has been used in previous studies [9,13,17], is presented in Fig. 2. The upper ring is smooth and possesses an angular velocity $\omega$. The lower ring is fixed and textured. The periodicity permits that only one small radial domain be studied. Fig. 2 illustrates that this domain is located between the inner radius $R_i$ and the outer radius $R_o$. A periodic condition on the lateral boundaries is necessary to ensure domain continuity. The flow field is governed by the Reynolds equation, Eq. (1), and the cavitation phenomenon was accounted for using a mass-conservative algorithm, Eq. (2). Based on the work of Dobrica and Fillon [19], the Reynolds equation remains valid in the present application if the Reynolds number is lower than 5 and the dimple length to depth ratio is greater than 500.

$F$ is a switch variable indicating whether cavitation occurs, and $D$ is a universal variable that can represent either the fluid pressure $P$ or the fluid density $\rho$. The problem is supposed to be stationary, because the upper ring is perfectly smooth while the lower ring is textured. The finite volumes method was used to discretize the domain while a direct method was used to solve the discretized equations. A mesh convergence study was performed prior to this work [13].

## 3. Optimization studies

Before treating the influence of the real dimple shapes, a previous work by Adjemout et al. [9], which explores texture pattern optimization, is summarized in this section. Both local and global effects in this study [9] were investigated in regards to different textured shapes and orientations on the hydrodynamic performance of a mechanical seal. The results showed that an area density of 0.3 yielded the highest load carrying capacity for each textured shape, while the effective value of the depth

<figure><img src="image_69.png" /><figcaption>Fig. 3. Configuration with different triangular distributions on each radial band [9].</figcaption></figure>
<table><caption>**Table 1**
Parameters relating to seal geometry and operating parameters.</caption><thead><tr><td>Parameter</td><td>Symbol</td><td>Unit</td><td>Value</td></tr></thead><tbody><tr><td>Inner radius</td><td>R<sub>i</sub></td><td>mm</td><td>25.75</td></tr><tr><td>Outer radius</td><td>R<sub>o</sub></td><td>mm</td><td>28.75</td></tr><tr><td>Inner pressure</td><td>P<sub>i</sub></td><td>MPa</td><td>0</td></tr><tr><td>Outer pressure</td><td>P<sub>o</sub></td><td>MPa</td><td>2</td></tr><tr><td>Cavitation pressure</td><td>P<sub>cav</sub></td><td>MPa</td><td>-0.01</td></tr><tr><td>Viscosity</td><td>μ</td><td>Pa.s</td><td>0.001</td></tr><tr><td>Fluid density</td><td>ρ<sub>o</sub></td><td>kg/m<sup>3</sup></td><td>1000</td></tr><tr><td>Depth</td><td>h<sub>p</sub></td><td>μm</td><td>0.2</td></tr><tr><td>Velocity</td><td>Ω</td><td>rad/s</td><td>30–500</td></tr><tr><td>Closing force</td><td>F<sub>close</sub></td><td>N</td><td>1266</td></tr><tr><td>Depth of the dimples</td><td>h<sub>d</sub></td><td>nm</td><td>200</td></tr><tr><td>Density of the texture</td><td></td><td>%</td><td>30</td></tr></tbody></table>

<figure><img src="image_70.png" /><figcaption>**Fig. 4.** Texture produced by the ion etching method.</figcaption></figure>

ratio depended on the dimple's edge profile. In regards to the geometric shape and orientation, triangles placed in a base-to-base configuration (Fig. 3) produced the highest load carrying capacity. In the second part of this study [9], several implementations of triangular patterns, which were also placed in base-to-base configurations on the matting ring (Fig. 3), were performed to minimize friction and leakage from the mechanical seal system investigated herein.

The parametric study showed that the distribution of 7i-3o (or 7 dimples at the inner rim and 3 dimples at the outer rim) for artificial triangles on the radial column gave the smallest absolute leakage and an acceptable value for the coefficient of friction. Table 1 summarizes the

main data used in the numerical simulation. Note that our mechanical seal system was used to seal pressurized water at 20 bars and was operated at a nominal rotational velocity of 3000 rpm.

The performance of a mechanical seal, such as the radial leakage and viscous friction, were calculated and presented as a function of a duty parameter (Eq. (3)):

$$G = \frac{\mu \Delta r \omega R_m}{F_{\text{close}}} \qquad (3)$$

<figure><img src="image_71.png" /><figcaption>**Fig. 5.** Defects in the real dimple shape.</figcaption></figure>
<figure><img src="image_72.png" /><figcaption>Fig. 6. Example of a mask with square holes.</figcaption></figure>

<figure><img src="image_73.png" /><figcaption>Fig. 7. Roughness at the bottom of the dimples. (a) Addition of surface roughness in the dimples. (b) S1 and S2 are two orientations of the roughness.</figcaption></figure>

<figure><img src="image_74.png" /><figcaption>Fig. 8. Effect of the roughness on the leakage.</figcaption></figure>

## 4. Influence of the real dimple shapes on the seal behavior

To assist the reader in understanding the remainder of this study, the surface texturing process used herein is briefly described. Fig. 4 provides an overview of the main steps involved in texturing process. The texture was obtained by means of the ion etching method. In the reactor, a mask having holes with the desired shape pattern was used to limit etching to areas not protected by the mask. After etching, a thermo-chemical post-treatment was used to increase the hardness of the surfaces.

The real shape of the triangles obtained by ion etching on stainless steel was analyzed using white-light interferometry. Three main defects were identified and are discussed in this study: roughness inside the

dimples, rounded summits, and deformed boundaries. These defects are illustrated in Fig. 5.

The observed defects were directly due to the texturizing process. The masks were laser machined with a minimum spot size of 5 µm, which lead to inaccuracies in each hole's geometric boundaries (Fig. 6). Moreover, a type of diffusion occurred under the mask during the ion etching process, which produced additional defects.

The roughness in the dimples was due to the stainless steel's anisotropic response to ion etching, where grains with different crystallographic orientations yielded different etching rates. Thus, some height variations were observed in the bottoms of the cavities.

The main objective of this study was to investigate the effect of the real dimple shapes on the performance of the studied mechanical seal. To achieve this goal, the defects were introduced into the hydrodynamic model and a parametric study was carried out. Leakage, friction, and film thickness were analysed by varying the standard deviation of the roughness in the dimple, the curvature edges, and the curvature of the boundaries for the triangular dimples.

### 4.1. Roughness in the dimples

The effect of roughness in the dimples was considered by adding a controlled sample to roughen the surface at the bottom of the dimples (Fig. 7). The sample was measured on a real stainless steel surface obtained by carburizing treatment. A 200 µm × 200 µm square was cut from the original surface. Afterwards, this surface sample was introduced into each triangular dimple. In order to carry out the simulation in this section, the standard deviation (Sq) of the roughness was set to four different values: 10 *nm*, 20 *nm*, 40 *nm* and 60 *nm*. These values were based on measurements. The orientation of the roughness in the dimples was studied and is shown in Fig. 7.

Fig. 8 illustrates the effect of roughness at the dimple bottoms on the leakage when the duty parameter was varied. The result for configuration
<figure><img src="image_75.png" /><figcaption>Fig. 9. Effect of the roughness on the friction.</figcaption></figure>

<figure><img src="image_76.png" /><figcaption>Fig. 10. Effect of the roughness on the film thickness.</figcaption></figure>

<figure><img src="image_77.png" /><figcaption>Fig. 11. Effect of the roughness on the film thickness at $G = 2 \times 10^{-9}$.</figcaption></figure>

<figure><img src="image_78.png" /><figcaption>Fig. 12. Effect of the roughness on the leakage at $G = 3.3 \times 10^{-8}$.</figcaption></figure>

7i-3o (smooth dimples) serves as a reference. The leakage level increased with an increasing standard deviation (Sq) of the roughness in the dimples. As expected, the largest leakage value corresponded with the highest value of the standard deviation Sq = 60 nm. In this case, the leakage could be increased by 96% compared to the reference (7i-3o) for the highest value of the duty parameter (G). In this figure, the effect of the roughness orientation in the dimples on the fluid flow is also shown. The orientation S1 showed a trend of assisting the fluid flow from the outer to the inner radius, while the orientation S2 increased the fluid pumping from the inner to the outer radius. Significantly, the latter configuration leads to a 75% reduction in leakage. Fig. 9 shows the variation of the friction coefficient with the duty parameter. Neither the increase in standard deviation of the roughness nor its orientation in the dimples have an observable effect on the friction coefficient. The results of the film thickness are illustrated in Fig. 10. Similar to the friction coefficient, the findings showed that an increase in standard deviation of the roughness in the dimples had almost no effect on the film thickness. These results could be explained by the fact that the maximum value of the roughness height (Sq) is less than one third of the dimple depth ($h_d$), which is insufficient to modify the fluid flow.

To more clearly show the effect of roughness, the leakage at the maximum G value, as well as the film thickness at the minimum G value, are presented in Figs. 11 and 12 as a function of the ratio of the roughness height to the dimple depth. Those G parameter values were chosen to enhance the differences between the results. To obtain a dimensionless form of the parameters, the film thickness h and the leakage Q were respectively divided by the dimple depth $h_d$ and the reference leakage between two parallel plates $Q_r$:

$$Q_r = \frac{\rho \pi R_m h_d^3 P_o - P_i}{6\mu (R_o - R_i)} \quad (4)$$

As shown by Qiu and Raymaekers [18], when the ratio of the roughness height to the dimple depth was lower than 0.2, the load carrying capacity, and thus the surface distance, was only slightly modified (Fig. 11). Above this limit, as demonstrated with S2's roughness orientation, significant variations were observed because the highest asperity summits possessed similar heights to the surface outside of the dimple. The leakage, a parameter that is very sensitive to the film thickness distribution, displayed large deviations that were observed as the roughness height was increased from the initial value of zero (Fig. 12).

It should be noted that, in this section, the same surface sample was used on each dimple, which does not yield statistically representative results. Further analyses with variable surfaces on the dimple bottoms would be necessary to more accurately determine the effect of
<figure><img src="image_79.png" /><figcaption>Fig. 13. Triangular summit configurations.</figcaption></figure>

<figure><img src="image_80.png" /><figcaption>Fig. 14. Configurations used to study the effects of boundaries deformations.</figcaption></figure>

<table><caption>**Table 2**

Shape parameters of the deformed triangles.</caption><thead><tr><th>Shape/Parameter</th><th>a</th><th>b</th><th>n<sub>1</sub></th><th>n<sub>2</sub></th><th>n<sub>3</sub></th></tr></thead><tbody><tr><td>A</td><td>0.045</td><td>0.045</td><td>1.6</td><td>1.6</td><td>0.545</td></tr><tr><td>B</td><td>0.054</td><td>0.054</td><td>1.7</td><td>1.7</td><td>0.545</td></tr><tr><td>C</td><td>0.290</td><td>0.290</td><td>1.6</td><td>1.6</td><td>0.220</td></tr><tr><td>D</td><td>0.245</td><td>0.245</td><td>1.4</td><td>1.4</td><td>0.220</td></tr></tbody></table>

<figure><img src="image_81.png" /><figcaption>Fig. 15. Effect of the dimple shapes on the film thickness at $G = 2 \times 10^{-9}$.</figcaption></figure>

dimple roughness.

## 4.2. Deformed triangles

The second part of this parametric study focuses on defaults observed in triangular dimples, in the radius of curvature for each triangle's summit, and at the deformed boundaries. Simulations with triangles

possessing curved angles at their corners (e.g., using $R = 10 \ \mu m$ and $R = 20 \ \mu m$) were carried out and compared to a reference simulation comprised of perfect triangles (Fig. 13). As with the rest of this study, the local density was kept constant at 0.3 for each simulation. The analysis also illustrated the impact of dimples with deformed boundaries on the mechanical seal's performance. As shown in Fig. 14, four configurations were analyzed (labelled as A, B, C, and D). Configuration 7i-3o ($R = 20 \ \mu m$) served as a reference, and it corresponded to a triangle possessing curved corners with $R = 20 \ \mu m$. Note that the curvature of the corners for the other configurations were also set at $R = 20 \ \mu m$.

The deformed boundaries were obtained by applying the Gielis formula [20], which is given in polar coordinates by:

$$r(\theta) = \left( \left| \frac{1}{a} \cos\left(\frac{m}{4}\theta \right) \right|^{n_1} + \left| \frac{1}{b} \sin\left(\frac{m}{4}\theta \right) \right|^{n_2} \right)^{\frac{1}{n_3}} \quad (5)$$

The parameter *m* determines the number of sectors (for example, *m* = 3 represents a triangle). The parameters *a* and *b* determine the lengths of the major axes, while *n*₁, *n*₂ and *n*₃ control the shape of the three sectors. All parameter values are shown in Table 2. To quantify the magnitude of the defect, the dimple area $S_d$ was divided by the area within the circumscribed circle $S_c$ (Fig. 13) to yield the shape's area ratio. Increasing the radius of curvature for a triangle's summit, for instance, would increase this ratio.

The blue curve (diamond dots) in Fig. 15 presents the dimensionless film thickness as a function of the shape's area ratio. The maximum film thickness was obtained with a perfect triangular dimple. When the radius of curvature for the corners was increased creating rounded summits, the film thickness decreased to values as low as 36% of the initial value. This result was not surprising as a similar result was demonstrated in Ref. [9],
<figure><img src="image_82.png" /><figcaption>Fig. 16. Effect of the dimple shapes on the leakage at $G = 3.3 \times 10^{-8}$.</figcaption></figure>

where a load capable of enabling surface separation was not possible when circular dimples were used. Modifying a triangle's corners to increase its radius of curvature made the dimple shape closer to a circle as described by the area ratio $S_d/S_c$.

The green curve (triangle dots) in Fig. 15 presents the film thickness at the minimum $G$ value as a function of the dimple's shape ratio. When the sides of the triangles were bent outwards, such as with points A and B, a dimple shape became closer to that of a circle due to an increased shape area ratio. The opposite was obtained when the sides of the triangles were bent inwards, such as with points C and D. As for the radius of curvature for the corners, a decrease in film thickness was obtained when the defect produced a decreased shape ratio. For the configuration used to achieve point B, which possessed the largest shape area ratio, the seal surfaces were close to a contact condition, which could be critical for the seal reliability.

The effect of the deformed triangles on the leakage as a function of the shape area ratio is presented in Fig. 16 when $G$ is set at its maximum

value. The blue curve (diamond dots) displays results for the variations of the corners' radius of curvature. Even if the film thickness decreased when the radius of curvature was increased, an increased leakage was observed. This could be explained through increasing the corners' radius of curvature, which lead to an increased maximum pressure at the trailing edge of the dimples (Fig. 17-a). Thus, the slope of the pressure field in the untextured area (Fig. 17-b) changed slightly and increased the leakage. The green curve (triangle dots) shows the influence of the deformed boundaries. As in the case of the rounded summits, an increased shape area ratio leads to increased seal leakage.

Holistically, the shape area ratio, which is defined as the dimple area divided by the area of the circumscribed circle, appeared to be a simple method for quantifying the defects examined. Based upon these results, maintaining this parameter to values below 0.6 avoided a significant film thickness decrease or leakage increase.

## 5. Conclusions

The influence of the real shape of triangular dimples on a mechanical seal's performance was investigated using a hydrodynamic model coupled to a mass conserving cavitation model. The defects were selected among real problems encountered after surface texturing. In this case, surface texturing was performed with ion etching through a protecting mask. The impacts of the three main defects on the hydrodynamic performance of the mechanical seal were numerically analyzed, which led to the following conclusions:

* The roughness height and orientation at the dimple bottoms significantly impacted the leakage. At the highest duty parameter value, the leakage varied from -75% to +96% in relation to the reference value. The impact on the other parameters was weak.

* An increased radius of curvature for the corners displayed detrimental effects that depended on the duty parameter value. At high $G$ values, the radius of curvature increased the leakage by 68%, while at low $G$ values, face contact could occur.

* When the deformed dimples approached a circular shape, the global effect provided by the triangular dimple arrangement was progressively lost, and could lead to possible contact. Conversely, enhanced

<figure><img src="image_83.png" /><figcaption>Fig. 17. Effect of the radius of curvature for the corners on the (a) pressure fields and (b) pressure profiles for varying $R$ in the untextured area.</figcaption></figure>
performance could be obtained when the sides of the triangles were bent inwards towards the dimple center.

The shape defects were quantified by the shape area ratio. It was found that this parameter should remain below 0.6 to avoid significant deviation from an ideal dimple shape. Also, maintaining a dimple RMS roughness height below 0.2 times the dimple depth is advisable. Finally, the present work demonstrated that an accurate study requires that the real dimple shapes be accounted for in a numerical model.

## Acknowledgments

This work was supported by the ANR under the reference ANR-11-RMNP-0008. This work pertains to the French Government program "Investissements d'Avenir" (LABEX INTERACTIFS, reference ANR-11-LABX-0017-01).

## References

[1] Hamilton D, Walowit J, Allen C. A theory of lubrication by micro-irregularities. ASME J Basic Eng 1966;88:177-85.

[2] Anno J, Walowit J, Allen C. Load support and leakage from microasperity-lubricated face seals. In: 4th international conference on fluid sealing; 1969. p. 199-204.

[3] Etsion I, Halperin G, Greenberg Y. Increasing mechanical seals life with laser-textured seal faces. In: 15th international conference on fluid sealing; 1997. p. 3-11.

[4] Etsion I, Kligerman Y, Halperin G. Analytical and experimental investigation of laser-textured mechanical seal faces. Tribol Trans 1999;42:511-6.

[5] Yu X, He S, Cai R. Frictional characteristics of mechanical seals with a laser-textured seal face. J Mater Process Technol 2002;129:463-6.

[6] Wang X, Kato K. Improving the anti-seizure ability of SiC seal in water with RIE texturing. Tribol Lett 2003;14:275-80.

[7] Yan D, Qu N, Li H, Wang X. Significance of dimple parameters on the friction of sliding surfaces investigated by orthogonal experiments. Tribol Trans 2010;53: 703-12.

[8] Shen C, Khonsari MM. Texture shape optimization for seal-like parallel surfaces: theory and experiment. Tribol Trans 2016;59:698-706.

[9] Adjemout M, Brunetiere N, Bouyer J. Numerical analysis of the texture effect on the hydrodynamic performance of a mechanical seal. Surf Topogr Metrology Prop 2016;4, 014002.

[10] Gropper D, Wang L, Harvey TJ. Hydrodynamic lubrication of textured surfaces: a review of modeling techniques and key findings. Tribol Int 2016;94:509-29.

[11] Etsion I. Modeling of surface texturing in hydrodynamic lubrication. Friction 2013; 1:195-209.

[12] Qiu Y, Khonsari MM. On the prediction of cavitation in dimples using a mass-conservative algorithm. J Tribol 2009;131, 041702.

[13] Adjemout M, Brunetiere N, Bouyer J. Optimization of mesh density for numerical simulations of hydrodynamic lubrication considering textured surfaces. Proc Inst Mech Eng Part J J Eng Tribol 2015;229:1132-44.

[14] Etsion I. State of the art in Laser surface texturing. J Tribol 2005;127:248-53.

[15] Coblas D, Fatu A, Maoui A, Hajjam M. Manufacturing textured surfaces: state of art and recent developments. Proc Inst Mech Eng Part J J Eng Tribol 2015;229:3-29.

[16] Andrieux A, Marcos G, Michel H, Czerwiec T. Surface patterning of an austenitic stainless steel by different low-temperature thermochemical plasma-assisted treatments. IVC 19 2013, Paris, September 9-13, paper #PST/SE/TF-3-Or-12.

[17] Brunetiere N, Tournerie B. Numerical analysis of a surface-textured mechanical seal operating in mixed lubrication regime. Tribol Int 2012;49:80-9.

[18] Qiu M, Raymaekers B. The load-carrying capacity and friction coefficient of incompressible textured parallel slider bearings with surface roughness inside the texture features. Proc Inst Mech Eng Part J J Eng Tribol 2015;229:547-56.

[19] Dobrica M, Fillon M. About the validity of Reynolds equation and inertia effects in textured sliders of infinite width. Proc Inst Mech Eng Part J J Eng Tribol 2009;223: 69-78.

[20] Gielis J. A generic geometric transformation that unifies a large range of natural and abstract shapes. Am J Bot 2003;90:333-8.
<figure><img src="image_84.png" /></figure>

# Improving the surface durability of patterned AISI 316LM steels by nitriding treatment for dry friction sliding

A. Pavlik<sup>a,b,c</sup>, G. Marcos<sup>b,c,*</sup>, M. Coulibaly<sup>a,c</sup>, J. Vincent<sup>c,d</sup>, T. Czerwiec<sup>b,c</sup>, S. Philippon<sup>a,c</sup>

## ARTICLE INFO

### Keywords:

- Dry

- Sliding

- Texture

- Wear

## ABSTRACT

In this study, different configurations of hard micro-patterns on AISI 316LM samples are obtained by a dry etching step followed by plasma nitriding. A "ball-on-plane" tribometer was used for low velocity reciprocal dry friction tests in order to characterise the influence of configurations on asperity lifetime, friction coefficient and wear mechanisms. The distance between asperities plays a key role in friction and wear behaviours by acting on contact pressure and development of debris. For a given ball dimension, pattern configuration determines the debris management at the contact and along the wear track. With 100 µm spacing between asperities, most part of the debris are simply trapped. At 300 µm, wear mechanisms are more complex with a debris recycling by the ball.

## 1. Introduction

Surface patterning is a part of surface engineering that consists in the etching of surfaces with patterns organized in networks, with different dimensions (from nano to millimetre scale) and geometries depending on the required applications or functionalities. Large varieties of domains are concerned including optics, biology, mechanics, combinatorial chemistry for sensing analysis or synthesis, microfluidics, surface energy, microelectronics ... [1-9]. To provide the patterns, the technical solutions must adapt to the material to be structured (chemical composition, shape and size of the pieces) and to the expected features [10-12]. Four technical classes of patterning were proposed by Bruzzone et al. [12]: adding material, removing material, moving material and self-forming.

In the case of steels, the main used patterning technique is laser surface texturing (LST). This material ablation technique belongs to the removing material class [13-15]. The main disadvantages of this method are time-consuming processing due to the patterns made one by one and geometrical limitation [16,17].

Numerous articles report the benefits of textured surfaces for

tribological applications, particularly with respect to lubricated friction [17-20]. The effects of surface patterning on dry friction are less documented. However, the application challenges are significant for conventional mechanical applications such as machining [21] but also in microsystems and magnetic storage [22]. The nature of the textured surfaces is a determining parameter in dry sliding. Xing et al. [23] show that the laser textured TiC ceramics always exhibit higher coefficient of friction (COF) and excellent wear resistance compared with a smooth sample. Carrying out Si₃N₄ Pin-on-disk tests on micro-honeycomb structured metallic glass, Li et al. [24] show that the COF has a minimum value as the surface pitch dimension is modified. They explain this behaviour by a competitive effect between the contact area and local stress level.

Dry sliding on strip-like patterns obtained by LST has previously been investigated and reported by three teams [25-28]. Applied forces are relatively weak (1-5 mN) to avoid a fast wearout of texture induced by LST. Although steel surface texture is very vulnerable to wear during the sliding, literature [28] shows that an increasing hardness by martensitic formation improves its durability. In the present work, linear grooves causes a friction anisotropy during sliding [26,27].

<footnote><sup>a</sup> ENIM, University of Lorraine, Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3), UMR CNRS 7239, 7 rue Félix Savart, F-57070, Metz, France</footnote>

<footnote><sup>b</sup> University of Lorraine, Institut Jean Lamour (IJL), UMR CNRS 7198, Campus ARTEM, 2 allée André Guinier, BP 50840, F-54000, Nancy, France</footnote>

<footnote><sup>c</sup> University of Lorraine, Laboratory of Excellence Design of Alloy Metals for Low-Mass Structures (Labex DAMAS), 7 rue Félix Savart, F-57070, Metz, France</footnote>

<footnote><sup>d</sup> Université de Lorraine, CNRS, Arts et Métiers ParisTech, Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux (LEM3), UMR CNRS 7239, F-57000, Metz, France</footnote>

<footnote>* Corresponding author. University of Lorraine, Institut Jean Lamour (IJL), UMR CNRS 7198, Campus ARTEM, 2 allée André Guinier, BP 50840, F-54000, Nancy, France.</footnote>

<footnote>E-mail address: gregory.marcos@univ-lorraine.fr (G. Marcos).</footnote>
<table><caption>**Table 1**
Experimental conditions used in the MDECR device for the duplex treatments.</caption><thead><tr><th>Condition</th><th>Gas Mixture</th><th>Pressure (Pa)</th><th>Substrate Bias (V)</th><th>Temperature (°C)</th><th>Duration (h)</th></tr></thead><tbody><tr><td>C1 (patterning)</td><td>95%Ar - 5%H<sub>2</sub></td><td>2.5</td><td>- 400</td><td>Heating up to 400</td><td>10</td></tr><tr><td>C2 (surface activation)</td><td>20%Ar - 20%H<sub>2</sub></td><td>1</td><td>-100</td><td>Heating up to 400</td><td>0.33</td></tr><tr><td>C3 (nitriding)</td><td>80%N<sub>2</sub> - 20%H<sub>2</sub></td><td>1.9</td><td>- 50</td><td>400</td><td>8</td></tr></tbody></table>

Rosenkranz et al. [25] showed that all textured samples exhibited a lower kinetic COF than for smooth samples, with lower values for transverse oriented grooves than for longitudinal ones. To take into account the effect of friction anisotropy, Yu and Wang [26,27] defined the ratio of groove width to tip radius b/R as the relative pattern size. If this latter ratio is lower than $10^{-3}$, the COF decreases when the grooves are oriented perpendicularly to friction direction while, at the opposite, it increases for ratios b/R greater than $10^{-1}$. Wang et al. [28] investigated the effect of groove spacing on the dry tribological properties of textured stainless-steel sliding against Al₂O₃ ceramic ball, and found that the groove spacing had an influence on the friction and wear properties. The mean COF can be reduced or increased by modulating the groove spacing.

As mentioned further above, texture durability is a critical feature that has to be considered in patterning. Regarding steels, nitriding is a promising way to increase the durability. Below 420 °C, for an austenitic stainless steel, a plasma-assisted nitriding (PAN) treatment forms the so-called expanded austenite phase (γN). The γN phase is supposed to be a metastable nitrogen supersaturated solid solution with a disordered fcc-type crystalline structure and a distorted crystal lattice [29,30]. The favourable tribological properties of this phase are due to the high nitrogen content (from 20 to 35 at%), inducing high compressive residual stresses (from 1 to 5 GPa) [30]. The phase transformation to γN leads to an increase in the wear resistance of the nitrided surfaces and to a transition of wear mechanism from severe adhesive mode to mild abrasive type with tribo-oxidation [31–35]. Combining surface patterning and nitriding for tribological purposes is not so common [36, 37]. Borghi et al. [36] have performed such duplex treatment by laser patterning of nitrided ferritic steel, whereas Lin et al. [37] nitrided a non-deterministic pattern performed by electrochemical etching.

The aim of this work is to demonstrate the feasibility and to discuss the durability of metal patterns obtained by using a duplex treatment on austenitic stainless steels substrates. This duplex treatment combines a sputtering step and a following plasma-assisted nitriding. This functionalization process belongs to the removing material class and is an alternative to LST technologies [12]. The tribological properties of linear, unidirectional and homogeneous strip-like nitrided patterns are studied using a conventional “ball-on-plane” tribometer in reciprocal

dry sliding and ambient conditions. The number of ball motion cycles are set at a relevant value of 1000 cycles in order to study the wear resistance, in comparison with non-nitrided patterns. Two different spacings between consecutive surface asperities - 100 and 300 µm - were tested. These different spacing configurations enable to study the role of wear debris on the dry interaction process and their distribution along the contact track. From the experimental analysis, scenarios of wear mechanisms are proposed in the discussion.

## 2. Materials and methods

### 2.1. Duplex treatment

The tested samples are 4 mm thick discs made of austenitic stainless steel (AISI 316 LM; 17 wt% Cr, 13 wt% Ni, 2 wt% Mo, 0.5 wt% Si, 0.2 wt % Mn and 0.02 wt% C) provided from a cylindrical bar (diameter: 24 mm). Before treatment, each sample is mirror polished, cleaned in ethanol and dried. The whole nitriding stage is performed in a MDECR-type (Multi-Dipolar Electron Cyclotron Resonance) plasma reactor [38].

The surface patterning process is carried out by dry plasma etching induced by ion bombardment. The samples are placed on the substrate holder and covered by masks (thin metal plates of 250 µm of thickness) previously drilled by laser beam. Once the limit vacuum is established (around $10^{-4}$ Pa), a plasma mixture of Ar/H₂ is switched on under C1 conditions (see Table 1). A DC bias of –400 V is imposed to the substrate holder to create a strong ion bombardment inducing sputtering mechanisms of the samples through the masks. For C1 conditions, the etching rate is around 1 µm/h. During the process, the substrate temperature remains below 400 °C, prohibiting any microstructural modification of the stainless steel. Next, the cooling step is carried out under vacuum before the masks are removed from the patterned surfaces. In the rest of the paper, three textured patterns were designated by the spacing D and the asperity width W, e.g. W100-D300 pattern is a Duplex treated sample with a spacing between consecutive asperities of 300 µm and 100 µm width asperities (Fig. 1).

In order to harden the resulting patterns, a plasma-assisted nitriding treatment is applied [39]. A preliminary step of surface cleaning and activation is conducted under C2 conditions (Table 1). The DC bias

<figure><img src="image_85.png" /><figcaption>**Fig. 1.** Schematic illustration of Duplex treatment steps occurring in a MDECR-type plasma reactor. C1: patterning; C2: surface activation; C3: nitriding (see Table 1). D is the spacing between consecutive asperities, W is the asperity width and H is the asperity height.</figcaption></figure>
<table><caption>**Table 2**
Test conditions used for dry sliding experiments.</caption><thead><tr><th>Surface</th><th>PAN</th><th>Height (µm)</th><th>Sliding distance (cycles)</th><th>Frequency (Hz)</th><th>Stroke (mm)</th><th>Counterpart material</th></tr></thead><tbody><tr><td>Without texture</td><td>non nitrided</td><td>N/A</td><td>500</td><td>0.1</td><td>8</td><td>alumina</td></tr><tr><td>W240-D120</td><td>non nitrided</td><td>H = 10</td><td>500</td><td>0.1</td><td>8</td><td>alumina</td></tr><tr><td>W240-D120</td><td>non nitrided</td><td>H = 40</td><td>500</td><td>0.1</td><td>8</td><td>alumina</td></tr><tr><td>Without texture</td><td>nitrided</td><td>N/A</td><td>1000</td><td>0.1</td><td>8</td><td>alumina</td></tr><tr><td>W100-D100</td><td>nitrided</td><td>H = 11</td><td>1000</td><td>0.1</td><td>8</td><td>alumina</td></tr><tr><td>W100-D300</td><td>nitrided</td><td>H = 11</td><td>1000</td><td>0.1</td><td>8</td><td>alumina</td></tr></tbody></table>

<figure><img src="image_86.png" /><figcaption>**Fig. 2.** a) Mean friction coefficient evolution vs cycle number for dry sliding tests on textured W240-D120 AISI 316L samples, with asperity heights H = 0 µm (polished sample), 10 µm and 40 µm, sliding against alumina under a 5 N load. b) Local friction coefficient development for the 15th cycle of sliding (H = 10 µm).</figcaption></figure>

imposed to the substrate holder is sufficient to remove the surface contaminants (including possible oxide layer) but too low to damage the patterns. During this step, the samples are progressively heated to reach the nitriding temperature (400 °C). According to C3 conditions (Table 1), the time of nitriding treatment is 8 h. After that, the cooling step is achieved under vacuum.

## 2.2. Friction experiments

Friction tests are performed by a commercial “ball-on-plane” tribometer device (Anton Paar TRN) by reciprocating sliding motion setup at room temperature. Each experiment is carried out 3 times with a 6 mm diameter alumina ball counterpart. A constant applied normal load of 5 N is set for all the testing experiments. The ball slides against the steel plate at a 0.1 Hz frequency along 8 mm long sliding stroke. The total testing sliding length after 1000 cycles corresponds to a distance of about 16 m. A ball made of alumina is chosen due to its high chemical inertia and hardness similar to those of expanded austenite.

The aim of the present investigation is to further understand the mechanisms involved by the layout of the asperities and their effects on tribological properties of the chosen tribo-pair in dry conditions. For this purpose, the spacing between straight strip-like asperities transversally oriented with respect to the motion direction is set at 100 µm, 120 µm and 300 µm. Their maximum height after the patterning is around 10 µm for W100-D100 and W100-D300, and 40 µm for W240-D120. It should be noted that the sample W240-D120 is textured but not nitrided in order to study the durability depending on patterns height. Dry sliding tests were conducted according to the parameters given in Table 2.

The acquisition of the COF is provided by the own CPU of the “ball-on-plane” tribometer device from Coulomb’s law. All signals are

recorded at 400 Hz storage frequency and the COF mean value is extracted from data for each cycle of friction assuming a constant normal force. Due to the sinusoidal sliding velocity with static friction at both track tips and a maximum value (2.15 mm s⁻¹) in the central part of the track, the mean value of the COF was calculated from the data (see Fig. 2) obtained at the 4.8 mm long central part of the track.

## 2.3. The observations and measurements of the surface

The surface of the specimens was observed before and after friction tests using both optical and scanning electron microscopy (SEM). The optical microscope used, an Alicona Infinite Focus, is able to measure the surface topography using a method called Focus-Variation. The combination of a small depth of focus optical system, a motorised focus and image processing makes it possible to acquire the surface topography. A full focus 2D image can then be correlated from colour 3D and colours data. From the surface topography, 1D profiles of the functional surface after etching and nitriding can be obtained. A 20x lens were retained for the observations by optical microscopy. The measured area is 10.7 × 1.45 mm². In these conditions, the surface topography resolution is 2.7 µm in lateral and 28 nm in vertical directions. Profiles of the textured surface can be extracted from the 3D data. In a first time, profiles are obtained on non-worn surfaces in order to characterise the geometry of the patterns before and after the nitriding. In a second step, this method is used to analyse the wear profiles, comparing the worn and non-worn neighbouring surfaces. The profiles presented in this work are calculated for a line width of 70 µm.

For the structural, morphological, compositional observation and analysis, a ZEISS-SUPRA 40 field emission scanning electron microscope (FE-SEM with the unique VPSE detector) was used with secondary
<figure><img src="image_87.png" /><figcaption>Fig. 3. Optical micrographs of worn patterned surfaces of AISI 316L steel. a) W240-D120 after 500 cycles and Duplex treated AISI 316L samples. b) W100-D100 after 1000 cycles of sliding. c) W100-D300 after 1000 cycles of sliding.</figcaption></figure>

<figure><img src="image_88.png" /><figcaption>Fig. 4. Surface profiles of non-nitrided patterned surfaces. a) W100-D100 non-nitrided samples. b) W100-D100 duplex treated samples. c) W100-D300 non-nitrided samples. d) W100-D300 duplex treated samples.</figcaption></figure>
<figure><img src="image_89.png" /><figcaption>Fig. 5. Cross sections of Duplex treated samples. a) W100-D100. b) W100-D300.</figcaption></figure>

electron image resolution of between 1.0 nm (at 15 kV) and 2.1 nm (at 1 kV). The microscope is fitted with an energy division spectroscopy (EDS) detector.

## 3. Results

### 3.1. Tribological tests on non-nitrided structured samples

Fig. 2 shows recorded curves of the COF versus the number of cycles during dry sliding tests on non-nitrided patterned surfaces W240-D120 for different heights of asperities: 0 µm, 10 µm and 40 µm. In this work, the height of asperity is considered as 0 µm for mirror polished sample. The polished specimen COF follows a transient regime which rapidly occurs for the first 50 cycles (0.8 m), while the COF of textured samples is initially lower and characterised by several distinct regions. At the beginning of the test, the friction curve is relatively smooth with a slight increase in friction coefficient. After a critical sliding distance, a rapid raise in friction coefficient appears, associated to strong fluctuations.

Fig. 3a presents optical images of the non-nitrided surface W240-D120 top view after 500 cycles of sliding on the sample with 40 µm initial asperity height. Verification of worn surfaces at the end of the test revealed that tribological process on non-nitrided specimens leads to the total removing of asperities, thus attesting the low durability of austenitic stainless-steel patterns.

The low wear resistance of the non nitrided samples induces a premature wear, which leads to the complete removal of asperities and gives the same steady state COF in all tests, including those performed on the only polished samples. These results indicate that identical contact areas are expected after removal of asperities for all non nitrided samples.

### 3.2. Characterisation of structured samples

After PAN treatment, XRD analysis of nitrided patterns shows that no chromium nitride, nor ferrite are present in the nitrided layer.

For the sake of clarity, x and z-axis of surface profiles in Fig. 4 are presented at different scales. Fig. 4a and c show the square asperity shape obtained after 10 h of plasma sputtering through the masks, while Fig. 4b and d display the slight increase of asperity height and the rise of surface roughness after nitriding. In Figs. 5a and b, cross section images of the nitrided samples in the transverse plane with respect to the direction of asperity allow to identify the nitrided layer and the microstructure. To do this, the surfaces were polished and then electrochemically etched during 10 s in the oxalic acid. It can be seen that the whole surface is continuously protected by an expanded austenite layer. While the thickness of the nitrided layer is homogeneous on non-textured samples (21–23 µm), it is no longer so on textured surfaces. Thus, the thickness of the nitrided layer varies between 7 and

<figure><img src="image_90.png" /><figcaption>Fig. 6. SEM image of the top view of asperity on the Duplex treated W100-D100 surface before testing.</figcaption></figure>

10 µm for the W100-D300 nitrided samples and between 5 and 20 µm for the W100-D100 nitrided samples.

As a consequence, after the nitriding, the entire asperity volume consists of expanded austenite. In addition, SEM image of the top view on the Duplex surface of W100-D100 sample is shown in Fig. 6. In this image, cracks can be observed at the edges of asperities, as they are distributed along the direction of asperity borders.

This surface cracking is due to plastic deformations induced by the high content of nitrogen (from 12 to 35% at.) and the very high residual compressive stresses (1–5 GPa) in the expanded austenite layer [30]. The anisotropic character of strain associated to the high values of internal stress produces deformation at grain boundary, entailing a degradation of the state of the surface, observable to the naked eye (Fig. 6). Such plastic deformation is revealed by slip lines at the top of the nitrided layer (Fig. 6). It was shown that internal stress also induces a lattice rotation of a few degrees (<5°) of the nitrided layer [40]. After the plasma nitriding of 316L at 400 °C, Stinville et al. [41] observed that very small cracks appeared after 1 h of nitriding with some damage, preferentially at the grain boundaries. As a consequence of these phenomena, the surface roughness increased at the top of asperity and at the groove (Fig. 4b and d). Thus, the arithmetical mean deviation (roughness Ra) in the bombarded part between asperities increased from 0.03 to 0.3 µm.

In Fig. 4b, d and 5, it should be noted that protrusions of about 1.5 µm height are observable at the edges of asperities. Swelling of the nitrided layer occurs in the direction perpendicular to the surface of the sample. Generally, the volume occupied by the nitrided layer is larger than that of the matrix. As a consequence, a local deformation of the crystal lattice occurs induced by the building-up of in-plane compressive stresses. The surface perpendicular to the sample is free to move under the action of these internal stresses. This phenomenon is associated to
<figure><img src="image_91.png" /><figcaption>**Fig. 7.** Results of ball-on-plane sliding tests for nitrided surfaces - only nitrided and Duplex treated samples - against alumina ball counterpart under a load of 5 N. a) Mean friction coefficient (COF) evolution versus cycles number up to 1000 cycles of sliding. b) Local friction coefficients versus ball linear position for the 500th cycle of sliding.</figcaption></figure>

the swelling of the nitrided layer in the perpendicular direction to the surface of the sample. Marcos et al. [39] observed an inhomogeneous swelling from 200 to 300 nm at the edges of cylindrical silica dots after nitriding in conditions similar to the ones used in this paper. The main consequence of this high local deformation is cracking at the border of the protrusion on the top side of the asperity. Furthermore, let us remind that the top surface of the asperity is not affected by ion bombarding during the sputtering process since it is covered by the mask. Therefore,

the grains seem to be more deformed at the sputtered surface and some pits are distributed non-homogeneously. According to De Vre and Muir's work [42], defects are sensitive to plasma etching conditions. As a consequence, etching of defects is faster or slower than the bulk material, thus creating pits (see Fig. 6) or pillars.

<figure><img src="image_92.png" /><figcaption>**Fig. 8.** Optical microscope images (×20 magnification) of worn surfaces after 1000 cycles of sliding on nitrided surfaces. a) Only nitrided sample. b) W100-D100. c) W100-D300. The rectangular shapes in and outside the tracks show the selected zone for the profiles presented in Fig. 9.</figcaption></figure>
<figure><img src="image_93.png" /><figcaption>Fig. 9. Transversal profiles of raw and worn surfaces without cleaning, after 1000 cycles of sliding on Duplex treated samples. a,c) W100-D100. b,d) W100-D300.</figcaption></figure>

### 3.3. Tribological tests on duplex samples

The graph in Fig. 7a shows the curves of mean COF vs number of cycles during the sliding test for nitrided surfaces with or without patterns W100-D100 and W100-D300. It can be seen that Duplex treatment can reduce or increase COF (0.5 for W100-D100 and 0.7 for W100-D300) in comparison with the nitrided non structured sample (0.6).

The stabilisation period for Duplex samples is reached before the end of the test (at about 450 cycles for W100-D100 and 300 cycles for W100-D300). In contrast, the COF for nitrided sample does not still stabilise after 1000 cycles of sliding, reaching a final value of 0.63.

On the other hand, the local COF versus ball linear position, during the 500th cycle of sliding test, for all three tested samples, is presented in Fig. 7b. Here, it should be noted that only the development of local COF for the first half of the cycle is given, since it is quite the same for the second half. At this scale, some fluctuations with different periodicities and amplitudes can be observed. Concerning W100-D300 specimen, the

number of fluctuations corresponds to the number of asperities (20 asperities) involved in the contact during the sliding. Regarding W100-D100 sample however, the development of local COF is rather similar to the one of the only nitrided sample with no correlation between the numbers of fluctuations and asperities at the contact (40 asperities). It should be noted that the bandwidth of the data acquisition system is probably not suitable for such a measurement. Because of this reason, current study is based on the mean COF data. Nevertheless, it is interesting to note that for W100-D300 case, the amplitude of fluctuations is higher, with a value of about 0.3, than for both non-structured nitrided sample (≈0.1) and W100-D100 duplex sample (≈0.12).

For further examination, optical images of the top views of the worn nitrided surface are presented in Fig. 8. All images were obtained after the sliding tests without cleaning the wear track. Under an optical microscope, the wear tracks exhibited a brown appearance, typical of oxidised surfaces. Noticeably, the formation of debris is more important for Duplex samples than for simply nitrided one. It can also be noticed
<figure><img src="image_94.png" /><figcaption>**Fig. 10.** SEM images of the top view on the worn asperity surface. a) and b) Nitrided non-structured sample. c) and d) W100-D100 sample. e) and f) W100-D300 sample.</figcaption></figure>

that, for non-structured nitrided and W100-D300 samples, wear debris are localised at the tips of the track. Furthermore, for W100-D100 sample, debris are also located between asperities, while for the W100-D300 sample, most of the debris are located at the extremities of the track, with an overflow spreading about 1 mm on each side of the track. The debris are preferably accumulated in the zones where friction is static or quasi-static.

Fig. 9 shows profiles in the transversal plane to the asperities of the duplex surfaces before and after the friction test. In order to highlight the presence of wear debris, tested surfaces were not cleaned after the sliding tests. The profiles presented in Fig. 9 a,b were taken in the centre of the track as shown in Fig. 8c. After 1000 cycles, the geometry of asperities was modified - slightly rounded - only for W100-D300 sample and their mean height was reduced for both samples. For the sample W100-D100, grooves are filled up with the wear debris over a depth of around 6 µm. On the W100-D300 sample surface however, there are no visible traces of particles between asperities. This observation is well correlated with those displayed in Fig. 8. Also, the presence of debris at the tips of the track for both duplex surfaces is clearly visible at the profiles in Fig. 9 c,d. The mean asperity height losses are 1.8 ± 0.4 µm

and 2.4 ± 0.4 µm respectively for the samples W100-D100 and W100-D300, hence showing that the wear volume per asperity is greater for sample W100-D300 than for W100-D100 one. But in return, it should be noted that, as the number of asperities in contact against the alumina ball is not the same between the two types of duplex samples – from 40 to 20 asperities when switching from W100-D100 to W100-D300 sample – the total wear volume in relation to the whole set of rubbed asperities remains higher for the W100-D100 specimen than for the W100-D300 one.

In Figs. 3b and 9, it can be clearly noted that the protrusions observed at the edges of the asperities (see Fig. 4b, d and 5) are removed during the friction test. Fig. 3b shows very clearly that the protrusions observed at the edges of the asperities are levelled or destroyed during the friction test. It can be seen that, up to 70 µm of protrusion disappears on each side of the wear trace (direction to sliding) and on both edges of each asperity. Moreover, the presence of cracks on their base (see Fig. 6) implies that their destruction occurs very early after the sliding test beginning.

By using optical and SEM microscopes (see Figs. 8 and 10), the widths of the wear tracks are measured and evaluated at 120 ± 10 µm
<figure><img src="image_95.png" /><figcaption>Fig. 11. Optical microscope images of the worn surface top view of the alumina balls. a) Sliding against non-structured sample. b) Sliding against Duplex treated samples W100-D100. c) Sliding against Duplex treated samples W100-D300.</figcaption></figure>

for the non-etched nitrided surface, 210 ± 20 µm for W100-D100 pattern and 250 ± 30 µm for W100-D300 configuration.

Examining the worn cleaned surfaces of alumina balls by optical microscopy (see Fig. 11) allows to emphasise the material transfer, appearing as dark patches, from the nitrided surfaces to the ball after any sliding test. Moreover, the worn surfaces of the balls have rectangular shapes when sliding against duplex samples (Fig. 11b and c), in contrast with the round shape of worn spot of 60 µm radius observed with unstructured nitrided sample as counterpart (see Fig. 11a). The widths of the rectangular ball traces are 120 ± 10 µm for the W100-D100 sample and 330 ± 10 µm for the W100-D300 specimen, which almost correspond to the distance between asperities (D).

After cleaning, Fig. 3b and c clearly show that the bottom surface between asperities is not affected during the 1000 cycles of friction, since it remains similar to the surrounding surface of the untested wear track. Therefore, since this bottom surface was not subjected to wear, the ball is in fact in contact only with the surfaces of the top asperity. Consequently, the 16 mm sliding length per cycle observed for a flat non-patterned surface must be reduced to 8 mm for the W100-D100 sample and 4 mm for the W100-D300 one.

SEM analysis points out different wear and damage modes between treated samples. Concerning the nitrided non-patterned sample, Fig.. 10a and b show a smearing of the debris on the affected sliding surface [43]. Fig.. 10c and d reveal abrasive grooves with an average width of 3 µm, continuously distributed over worn asperity top surface of W100-D100 sample. With regard to W100-D300 sample, Fig. 10e and f display discontinuous abrasive traces on the wear track. Some cracks can also be observed perpendicularly to the sliding motion. It should be also noted some abrasion marks and debris on the worn surface of both duplex treated samples (especially on W100-D300 sample).

# 4. Discussions

## 4.1. Sliding on structured non-nitrided samples

The fast increase in the COF with respect to time (see Fig. 2) was also observed by Conradi et al. [44] on the same material and in the same tribological testing conditions. This phenomenon can be explained by the strong interaction induced by the deposition and smearing of wear particles in the contact zone. The particles are strongly interacting in the contact zone, as they tend to continuously agglomerate and collapse. Furthermore, wear particles are poorly shifted away and increase the ploughing component. In that case, the effect of the storage volume of the grooves to remove wear debris from the contact zone is very poor due to the non-durable character of the pattern [45]. As shown in Fig. 3a, the durability of the austenitic structured surface is not long enough to provide a persistent sliding with debris accumulation.

### 4.2. Sliding on nitrided and duplex samples

#### 4.2.1. Theoretical approaches

In order to explain the mechanical response to friction of the nitrided layers with or without texturing, two theoretical approaches are considered. The first one concerns the Hertz pressure, generated by the ball on a flat or textured surface. The second approach uses an energetic principle applied to the dynamics of the tribometer counter-ball on the textured layers.

By simply considering the static elastic contact between two isotropic and homogeneous bodies, it is possible to calculate Hertz pressure applied on the surfaces of nitrided samples [46,47]. The Young modulus and the Poisson ratio are respectively 380 GPa and 0.26 for the alumina ball [48], and 240–270 GPa [49–51] and 0.28 [52] for the

<figure><img src="image_96.png" /><figcaption>Fig. 12. Measurement of the radii of curvature for the patterned W100-D300 sample after 1000 cycles of sliding along transversal (a) and longitudinal (b) directions with respect to the sliding direction.</figcaption></figure>
<figure><img src="image_97.png" /><figcaption>**Fig. 13.** Trajectories of a counter-ball material point during the whole interaction time between the ball and an asperity edge from lower A to upper B position. X-axis corresponds to the sliding direction and z-axis designates the depth from the asperity top surface. a) Schematic representation of geometrical configuration of the contact in lower and upper positions. b) Trajectory for ball sliding against W100-D100, the black line, and W100-D300, the red line. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)</figcaption></figure>

nitrided austenitic stainless steel. Implementing the Hertz contact theory under the sphere-plate configuration leads to a maximum contact pressure of around 0.9 GPa. In order to estimate the Hertz pressure after 1000 cycles of sliding tests on duplex treated surfaces, the radii of curvature measurement in transversal and longitudinal directions with respect to the sliding direction are attempted. In the case of the W100-D300 sample (see Fig. 12), the contact surface against alumina ball is transversally concave (in asperity direction), with a radius of curvature $R_{22} = 3.8$ mm, and longitudinally convex (in the sliding direction), with a radius of curvature $R_{12} = 0.5$ mm. The maximum contact pressure is then evaluated to 2.1–2.2 GPa. Such a value should be considered as minimal, since the curvature radius $R_{12}$ decreases during the sliding test. The radii of curvature measurement are not possible to perform for the W100-D100 configuration, since the asperity keeps a square cross section shape at the end of the test (see Fig. 9a). However, the Hertz contact theory shows that the contact pressure should be greater than 2 GPa in the latter pattern configuration.

According to the energetic approach, the alumina ball kinematics on the textured samples are calculated from tribo-pair dimensions, assuming no wear and a perfect asperity strip shape. Fig. 13a schematically shows the contact between one asperity with the counter ball in its lower and upper positions. The results of the dynamic study indicate that the applied normal load ($F_N$) at the apparent contact surface is almost constant whatever the position and velocity of the ball with respect to the asperities and whatever the spacing between successive asperities. In every case of “ball-on-plane” sliding test, the normal load is equivalent to the 5 N nominal load set on the tribometer. The mechanical energy involved in the motion of the ball results from the works of normal and tangential forces. Since an experimental or theoretical estimation of the local tangential force is unreachable for this study, only the normal force work is considered. Hence, along the ball trajectory over a half distance between consecutive asperities (D/2) from lower to upper ball position (see Fig. 13), the work of normal load amounts to 2.10 $\mu J$ and 18.75 $\mu J$ respectively for W100-D100 and W100-D300 configurations. Assuming that, for the same sliding velocity, the tangential force applied on an asperity edge in contact with the counter ball is at least greater for the patterns with spacing $D = 300$ µm than for those with $D = 100$ µm, we can conclude that the mechanical energy involved during the entire time

of the interaction between the ball and asperity is much higher for the W100-D300 sample than for the W100-D100 one. Finally, the average mechanical power provided by the ball when sliding against an asperity edge can be calculated knowing the sliding velocity, which follows a time sinusoidal development. The results of this energetic model show that the average mechanical power is always higher for the W100-D300 patterns as compared to W100-D100 ones. In addition, the ratio of the higher to lower powers decreases with speed from 5 to 3 for an average speed ranging from the minimum value (0.2 mm/s) to the maximum value (2.5 mm/s).

### 4.2.2. Role of debris in friction

Luo et al. [35] clearly demonstrated the formation of a tribofilm in the case of the friction of alumina balls on non-textured expanded austenite. Fish-scale textures observed in the non-patterned nitrided samples in Fig. 10 are a typical sign of tribofilm presence [35]. According to these authors, the fish-scale patterns results from compacted wear powders forming a thin tribofilm on the worn surface. The wear debris are engaged in the sliding contact, leading to a mild three-body abrasive wear and tribo-oxidation [32–35] for thick nitrided layers. The self-mating sliding contacts between the worn surfaces and the transferred materials covering the ball surface give relatively high friction coefficients [35]. Furthermore, one of the consequences of the roughness induced by the anisotropic deformation of the surface grain during nitriding treatment [30] is to create reservoirs for debris. It results in a non-uniform tribofilm as it can be seen in Fig. 10a. Indeed, metallic debris, resulting from the shearing of particles on the worn surface [43], are present on the surface of a non-structured sample (Fig. 10b). It is known that adhesive bond between metals and ceramics is rather high [54]. Thus, debris shearing is usually taking place if the adhesion is strong.

To discuss the results obtained on duplex surfaces, it is important to consider how the debris are managed. An important factor is the distribution of the debris on the track during the friction test.

In the case of the W100-D100 configuration, a great part of the debris is accumulated in the topographic spacing between two consecutive asperities (see Figs. 8b and 9a). The maximum down positions of the ball is 0.42 µm in this case. This is almost the same case after 1000 cycles of
<figure><img src="image_98.png" /><figcaption>**Fig. 14.** EDX mapping of oxygen and aluminum distribution on the worn duplex surfaces. a, b, c) For W100-D100 configuration. d, e, f) For W100-D300 configuration.</figcaption></figure>

sliding since the geometry of asperities is still rectangular and the ball does not touch the bottom surface of the grooves. Even if some debris are attached to the ball, there is no contact either between the debris and the valley of the texture. When the ball arrives on an asperity, the rectangular profile allows a scraping of debris accumulated on the ball during the friction on the flat part of the asperities. So, most of the debris are removed from the contact and fall inside the grooves. Thus, the number of debris in the contact zone is considerably reduced, preventing the formation of a thick and continuous tribofilm. As it can be seen in Fig. 10c and d, the wear mechanism depicts an abrasive wear mode with a very different behaviour as compared to the only nitrided surface. Such an abrasive wear mechanism is not necessarily less severe than the three-body abrasive wear observed on the only nitrided sample [53]. As a matter of fact, the width of the wear track is more important for the W100-D100 configuration than for the simply nitrided one (Figs. 3 and 10). The ratio of the widths of the wear tracks is 1.75, while the ratio of the real sliding distances is 2. This can be explained by the very high Hertz pressures applied on the textured samples calculated by our theoretical model. So, the W100-D100 configuration gives very few benefits in terms of wear resistance.

However, except for the early beginning of the test, a significant gain in COF is obtained with the W100-D100 configuration compared to a simply nitrided layer. The ratio of W100-D100 to simply nitrided samples COFs is 0.8 after 500 cycles. This can be explained by the transition from an almost pure abrasive wear of the nitrided asperities, in W100-D100 configuration, to a more complex wear mode involving an interaction of the debris transferred by the ball and the tribofilm, in only nitrided configuration. This transition brings about an increase in COF according to Luo et al. [35].

In the case of the W100-D300 configuration, almost no debris are observed in the valleys between the asperities. They are accumulated at the wear track tips.

For this surface nitrided texture, the energetic model described further above estimates the counter ball maximum descent to 3.75 µm inside the grooves. As the shape of asperities is progressively rounded by wear mechanism during friction, this depth of ball penetration gets higher with the number of sliding cycles. Furthermore, even if asperities undergo severe wear, i.e. a height reduction, their final 7 µm height after

1000 cycles is not low enough to cause the contact on the bottom surface of the grooves. However, the ball penetration depth is sufficient to attach and transport the fallen debris along the wear track. For this reason, a carrying and a re-introduction of debris into the friction area - on the top of asperities - are observed for the W100-D300 pattern as compared to W100-D100 one.

Therefore, the number of debris in the contact zone of the W100-D300 sample is important and a thick and almost homogeneous tribofilm is formed as it is also the case for non-textured nitrided samples (Fig. 10). Wear is very severe for that configuration as it can be seen in Fig. 9 and by comparison of the higher width of the wear tracks with those of other configurations. By reference with the simply nitrided samples, the ratio between the widths of the wear tracks is 2, compared to the factor 3 obtained from the ratio of real sliding distances. Three reasons can explain such a severe wear. First, the very high Hertz pressures calculated by our theoretical model. However, only the Hertz pressure cannot explain the difference between W100-D100 and W100-D300 configurations. Secondly, it has been shown that, whatever the sliding speed, the average mechanical power provided by the ball to an asperity is higher for W100-D300 configuration than for W100-D100 one. Such reasoning is very well supported by the size of the wear traces measured on the ball in both configurations (120 × 260 mm for W100-D100 and 330 × 260 mm for W100-D300). The highest COF measured for the W100-D300 contribution is probably due to the fact that the highest mechanical power transferred from the ball contributes to the enhancement of particles shearing. The cracks observed on Fig. 10e and f indicate and confirm the plastic deformation of the tribofilm.

Fig. 14 shows the mapping of the distribution of chemical elements on the surfaces of the two duplex samples. Based on the presented data, it can be noted that the tribofilm is constituted by metallic oxides and is thicker and more homogeneous for W100-D300 configuration. In addition, incrustation of alumina particles through the worn surface is visible for this configuration, which is not the case on the surface of W100-D100 texture.

Concerning W100-D300 layout, the wear process is more complex and is a combination of several mechanisms: abrasion, adhesive friction, fatigue, and delamination through oxidation. All these processes
<figure><img src="image_99.png" /><figcaption>Fig. 15. Friction coefficient after the sliding on Duplex treated samples with ball cleaning, wear track cleaning, or both ball and track cleaning after 500 cycles. a) For W100-D100 configuration. c) For W100-D300 configuration. d) For W100-D300 configuration.</figcaption></figure>

together contribute to the increase in wear and average COF.

### 4.2.3. Sliding tests with surface cleaning

For a deeper understanding of the role of wear products in the friction processes, sliding tests were performed with a surface cleaning after 500 cycles of friction. Three sliding tests were carried out on both W100-D100 and W100-D300 samples. In the first case, both surfaces of alumina ball and duplex surfaces were subjected to cleaning. For the second and third tests, only one body of the tribo-pair was cleaned: on the one hand, ethanol cleaning was performed exclusively on the duplex surface, and on the other hand, only the ball surface was cleaned. The results are presented in Fig. 15.

The discrepancy between the three curves before the cleaning step illustrates the spreading of the experimental results. At the early beginning (less than 10 cycles), the mean COF is higher for W100-D100 configuration than for W100-D300 one. It corresponds to a running in period for which the formation and compaction of debris are faster than for W100-D100 layout. It is probably related to a different state of internal stress level in the protrusions located at the edge of asperities.

After cleaning, COF decreases for each configuration, but no longer

reaches its initial values. This can be explained by the evolution of the wear over time, including not only an increase in the real contact area, but also oxidation reactions on the same area. Based on the graphs presented in Fig. 15, it can be concluded that, for both samples, the reduction level in the COFs obviously depends on the cleaned surface area. Thus, the maximum COF reduction is reached when cleaning both surfaces, rather than only ball cleaning.

For both configurations, cleaning the ball has very little effect on the COF. The presence and management of debris on the trace of friction thus play a leading role on the behaviour of COF. By assuming a much thicker tribofilm for the W100-D300 configuration, its contribution to friction can be estimated. The difference between the minimum values of the COFs after cleaning is 0.1 for both configurations. Surprisingly, the COFs reach a lower limit value after cleaning the surface for the W100-D100 layout, unlike for the W100-D300 configuration. In this case, the efficiency of the debris storage is improved if some of the debris presented on the track are removed.
## 5. Conclusion

Within the frame of improving the dry sliding properties of steels, nitriding treatments were conducted on linear strip-like patterns etched in AISI 316LM samples in two configurations: W100-D100 and W100-D300, W being the width of asperity and D the distance between them, in micrometers. Such patterns were obtained by ion etching in a MDECR plasma reactor through masks. The same device was used for the low-temperature nitriding treatment (400 °C), which results in expanded austenite layers. Tribological tests were performed by ball-on-plane dry reciprocal sliding tests carried out with an alumina ball under a load of 5 N.

First of all, the durability of non-nitrided AISI 316 LM patterned samples is shown to be very low. The texture is completely destroyed after a few hundred cycles. We found a strong reduction of wear for all the nitrided textured samples. The height loss of asperities is measured after the sliding test by optical profilometer. It also reveals a different repartition of the wear debris along the tracks between both patterned configurations. Wear debris are found within the valleys of W100-D100 configuration, whereas negligible quantities of debris are observed in the valleys of W100-D300 configuration. In addition, debris accumulations occur at the tips of the wear tracks. Such accumulation is higher for the W100-D300 configuration. After nitriding, the average COF is found to be dependent on the configurations of the patterns. A duplex treatment increases the average COF for the W100-D300 samples and reduces it for the W100-D100 ones. These observations are linked to the wear mechanisms appearing to be different for the two patterns configurations: abrasive mode for the W100-D100, combination of abrasive, adhesive, fatigue and oxidation modes for the W100-D300.

Hertz pressure based model demonstrates high contact pressures for both patterned configurations. In combination with geometric data provided by the optical profilometer, the model allows to estimate the contact pressure for the W100-D300 configuration to be from 2.1 to 2.2 GPa. Furthermore, energetic model shows that the mechanical energy produced during the interaction of the ball against the asperity edges is higher on W100-D300 than for W100-D100 configuration.

Finally, this study demonstrates that the durability of patterned surfaces can be widely improved by a nitriding treatment. Our results also open new perspectives to tailor friction properties by an appropriate patterns geometry.

## Funding

This work is financially supported by the "Grand-Est" Region of France and Labex DAMAS, the Laboratory of Excellence 'DAMAS' (Design of Alloy Metals for low-mAss Structures).

## Credit authors statement

The research team at the IJL laboratory contributed to the realization of the duplex surfaces and their characterizations. The research team at LEM 3 laboratory contributed to the friction tests and to the study of the wear mechanisms.

## Acknowledgement

We are grateful to the service of University of Lorraine and Marjorie Antoni for proofreading our manuscript.

## References

[1] Kang CJ, Park SC. Semiconductor patterning technologies for nano devices. Curr Appl Phys 2008;8(6):656-8.

[2] Xia Y, Qin D, Yin Y. Surface patterning and its application in wetting/dewetting studies. Curr Opin Colloid Interface Sci 2001;6(1):54-64.

[3] Marchetto D, Rota A, Calabri L, Gazzadi GC, Menozzi C, Valeri S. Hydrophobic effect of surface patterning on Si surface. Wear 2010;268(3-4):488-92.

[4] Cui Z, Rothman J, Klaui M, Lopez-Diaz L, Vaz CAF, Bland JAC. Fabrication of magnetic rings for high density memory devices. Microelectron Eng 2002;61: 577-83.

[5] Etsion I, Sher E. Improving fuel efficiency with laser surface textured piston rings. Tribol Int 2009;42(4):542-7.

[6] Kovalchenko A, Ajayi O, Erdemir A, Fenske G. Friction and wear behavior of laser textured surface under lubricated initial point contact. Wear 2011;271(9-10): 1719-25.

[7] Zum Gahr KH, Mathieu M, Brylka B. Friction control by surface engineering of ceramic sliding pairs in water. Wear 2007;263(7-12):920-9.

[8] Ogaki R, Alexander M, Kingshott P. Chemical patterning in biointerface science. Mater Today 2010;13(4):22-35.

[9] Czerwiec T, Marcos G, Thiriet T, Guo Y, Belmonte T. Austenitic stainless steel patterning by plasma assisted diffusion treatments. In: IOP conference series: materials science and engineering, vol. 5. IOP Publishing; 2009, 012012. No. 1.

[10] Geissler M, Xia Y. Patterning: principles and some new developments. Adv Mater 2004;16(15):1249-69.

[11] Rajurkar KP, Levy G, Malshe A, Sundaram MM, McGeough J, Hu X, DeSilva A. Micro and nano machining by electro-physical and chemical processes. CIRP Ann 2006;55(2):643-66.

[12] Bruzzone AAG, Costa HL, Lonardo PM, Lucca DA. Advances in engineered surfaces for functional performance. CIRP Ann 2008;57(2):750-69.

[13] Wakuda M, Yamauchi Y, Kanzaki S, Yasuda Y. Effect of surface texturing on friction reduction between ceramic and steel materials under lubricated sliding contact. Wear 2003;254(3-4):356-63.

[14] Mourier L, Mazuyer D, Lubrecht AA, Donnet C. Transient increase of film thickness in micro-textured EHL contacts. Tribol Int 2006;39(12):1745-56.

[15] Greiner C, Schäfer M. Bio-inspired scale-like surface textures and their tribological properties. Bioinspiration Biomimetics 2015;10(4):044001.

[16] Duarte M, Lasagni A, Giovanelli R, Narciso J, Louis E, Mücklich F. Increasing lubricant film lifetime by grooving periodical patterns using laser interference metallurgy. Adv Eng Mater 2008;10(6):554-8.

[17] Fiaschi G, Di Lauro M, Ballestrazzi A, Rota A, Biscarini F, Valeri S. Tribological response of laser-textured steel pins with low-dimensional micrometric patterns. Tribol Int 2019. https://doi.org/10.1016/j.triboint.2019.01.007.

[18] Ito S, Takahashi K, Sasaki S. Generation mechanism of friction anisotropy by surface texturing under boundary lubrication. Tribol Int 2019.

[19] Panigrahi DK, Sarangi M. Tribological performance of positive deterministic textured surfaces in parallel sliding lubricated contacts: effect of texture size and height. Proc IME J J Eng Tribol 2020;1350650119897479.

[20] Adjemout M, Andrieux A, Bouyer J, Brunetière N, Marcos G, Czerwiec T. Influence of the real dimple shape on the performance of a textured mechanical seal. Tribol Int 2017;115:409-16.

[21] Kawasegi N, Sugimori H, Morimoto H, Morita N, Hori I. Development of cutting tools with microscale and nanoscale textures to improve frictional behavior. Precis Eng 2009;33(3):248-54.

[22] Bhushan B. Tribology and mechanics of magnetic storage devices. Springer Science & Business Media; 2012.

[23] Xing Y, Deng J, Wu Z, Wu F. High friction and low wear properties of laser-textured ceramic surface under dry friction. Optic Laser Technol 2017;93:24-32.

[24] Li N, Xu E, Liu Z, Wang X, Liu L. Tuning apparent friction coefficient by controlled patterning bulk metallic glasses surfaces. Sci Rep 2016;6:39388.

[25] Rosenkranz A, Reinert L, Gachot C, Mücklich F. Alignment and wear debris effects between laser-patterned steel surfaces under dry sliding conditions. Wear 2014; 318(1-2):49-61.

[26] Yu C, Yu H, Liu G, Chen W, He B, Wang QJ. Understanding topographic dependence of friction with micro-and nano-grooved surfaces. Tribol Lett 2014;53 (1):145-56.

[27] Yu C, Wang QJ. Friction anisotropy with respect to topographic orientation. Sci Rep 2012;2:988.

[28] Wang Z, Wang CW, Wang M, Zhao QZ. Manipulation of tribological properties of stainless steel by picosecond laser texturing and quenching. Tribol Int 2016;99: 14-22.

[29] Sun Y, Li XY, Bell T. X-ray diffraction characterisation of low temperature plasma nitrided austenitic stainless steels. J Mater Sci 1999;34(19):4793-802.

[30] Czerwiec T, Andrieux A, Marcos G, Michel H. Is "expanded austenite" really a solid solution? Mössbauer observation of an annealed AISI 316L nitrided sample. J Alloys Compd 2019;811:151972.

[31] Sun Y, Bell T. Sliding wear characteristics of low temperature plasma nitrided 316 austenitic stainless steel. Wear 1998;218(1):34-42.

[32] Li CX, Bell T. Sliding wear properties of active screen plasma nitrided 316 austenitic stainless steel. Wear 2004;256(11-12):1144-52.

[33] Lei MK, Zhu XM. Plasma-based low-energy ion implantation of austenitic stainless steel for improvement in wear and corrosion resistance. Surf Coating Technol 2005;193(1-3):22-8.

[34] De Las Heras E, Santamaría DG, García-Luis A, Cabo A, Brizuela M, Ybarra G, Corengia P. Microstructure and wear behavior of DC-pulsed plasma nitrided AISI 316L austenitic stainless steel. Plasma Process Polym 2007;4(S1):S741-5.

[35] Luo Q, Oluwafemi O, Kitchen M, Yang S. Tribological properties and wear mechanisms of DC pulse plasma nitrided austenitic stainless steel in dry reciprocating sliding tests. Wear 2017;376:1640-51.

[36] Borghi A, Gualtieri E, Marchetto D, Moretti L, Valeri S. Tribological effects of surface texturing on nitriding steel for high-performance engine applications. Wear 2008;265(7-8):1046-51.
[37] Lin N, Liu Q, Zou J, Guo J, Li D, Yuan S, Tang B. Surface texturing-plasma nitriding duplex treatment for improving tribological performance of AISI 316 stainless steel. Materials 2016;9(11):875.

[38] Lacoste A, Lagarde T, Béchu S, Arnal Y, Pelletier J. Multi-dipolar plasmas for uniform processing: physics, design and performance. Plasma Sources Sci Technol 2002;11(4):407.

[39] Marcos G, Guilet S, Cleymand F, Thiriet T, Czerwiec T. Stainless steel patterning by combination of micro-patterning and driven strain produced by plasma assisted nitriding. Surf Coating Technol 2011;205:S275-9.

[40] Rivière JP, Templier C, Declémy A, Redjal O, Chumlyakov Y, Abrasonis G. Microstructure of expanded austenite in ion-nitrided AISI 316L single crystals. Surf Coating Technol 2007;201(19-20):8210-4.

[41] Stinville JC, Villechaise P, Templier C, Riviere JP, Drouet M. Plasma nitriding of 316L austenitic stainless steel: experimental investigation of fatigue life and surface evolution. Surf Coating Technol 2010;204(12-13):1947-51.

[42] DeVre M, Muir G. Advances in GaN dry etching process capabilities. Plasma-Therm Technical Paper; 2010.

[43] Denape J, Berthier Y, Vincent L. Wear particle life in a sliding contact under dry conditions: third body approach. In: Fundamentals of tribology and bridging the gap between the macro-and micro/nanoscales. Dordrecht: Springer; 2001. p. 393-411.

[44] Conradi M, Drnovsek A, Gregorcić P. Wettability and friction control of a stainless steel surface by combining nanosecond laser texturing and adsorption of superhydrophobic nanosilica particles. Sci Rep 2018;8(1):7457.

[45] Hwang DH, Kim DE, Lee SJ. Influence of wear particle interaction in the sliding interface on friction of metals. Wear 1999;225:427-39.

[46] Bhushan B. Modern tribology handbook, two volume set. CRC press; 2000.

[47] Popov VL. Contact mechanics and friction. Berlin: Springer Berlin Heidelberg; 2010. p. 231-53.

[48] Totten GE. Handbook of lubrication and tribology: volume I application and maintenance. CRC Press; 2006.

[49] Menendez E, Templier C, Abrasonis G, Lopez-Barbera JF, Nogués J, Temst K, Sort J. A combinatorial study of the mechanical and magnetic properties of a gradually nitrided austenitic stainless steel single crystal. CrystEngComm 2014;16(17):3515-20.

[50] Tomas C, Stinville JC, Templier C, Villechaise P. Acta Mater 2012;60:1965-73.

[51] Baranowska J, Franklin SE, Pelletier CGN. Tribological behaviour and mechanical properties of low temperature gas nitrided austenitic steel in relation to layer morphology. Wear 2005;259(1-6):432-8.

[52] Ledbetter JM, Austin MW, Kim SA. Carbon and nitrogen effects on the elastic constants of a stainless steel at 4 K. Mater Sci Eng 1987;85:85-9.

[53] Varenberg M, Halperin G, Etsion I. Different aspects of the role of wear debris in fretting wear. Wear 2002;252(11-12):902-10.

[54] Luo Q. Tribofilms in solid lubricants. Encyclopedia of Tribology; 2013. p. 3760-7.
PAPER

# Etching of iron and iron-chromium alloys using ICP-RIE chlorine plasma

To cite this article: Guillaume Le Dain et al 2021 *Plasma Sources Sci. Technol.* **30** 095022

View the [article online](#) for updates and enhancements.

<figure><img src="image_100.png" /></figure>
# Etching of iron and iron-chromium alloys using ICP-RIE chlorine plasma

Guillaume Le Dain<fnref n="1" />, Feriel Laourine<fnref n="2" />,<fnref n="3" />, Stéphane Guilet<fnref n="3" />,
Thierry Czerwiec<fnref n="2" />, Grégory Marcos<fnref n="2" />, Cédric Noel<fnref n="2" />, Gérard Henrion<fnref n="2" />,
Christophe Cardinaud<fnref n="1" />, Aurélie Girard<fnref n="1" /> and Ahmed Rhallabi<fnref n="1" />,*

E-mail: ahmed.rhallabi@cnrs-imn.fr

Received 4 March 2021, revised 9 June 2021
Accepted for publication 22 July 2021
Published 28 September 2021

<figure><img src="image_101.png" /></figure>

CrossMark

## Abstract

The dry etching process of Fe, Cr and Fe-Cr alloys under a chlorine-based plasma is studied. The objective is to create new surface functionalities. The approach combines an experimental study of an ICP (Inductively Coupled Plasma) reactor with the development of a multi-scale etching model including kinetic, sheath and surface models. The results from plasma etching of substrates made of Fe, Cr and Fe-Cr alloys are presented. Optical emission spectroscopy and interferometry measurements show strong modifications of the plasma when Fe or Cr samples are present in the reactor. It is shown that Fe is easier to etch than Cr. The study highlights the role of chemical etching by the formation of volatile products such as $FeCl_3$. The Cr content in Fe-Cr alloys has a strong impact on both the lateral and vertical etch rates, as well as on the roughness along the profile. For Fe-Cr alloys, the experimental and calculated values of etch rate are very similar. The concept of hard zones is introduced to get a better agreement between simulation results and experimental ones. This good agreement demonstrates the capability of the developed simulator to implement new phenomena.

Keywords: plasma etching, plasma modelling, plasma characterization, surface
functionalization, metal alloys patterning, chlorine-metals interactions

(Some figures may appear in colour only in the online journal)

## 1. Introduction

The history of plasma etching began in the late 1960s when Irving set out to remove polymers using an oxygen plasma [1, 2]. Later, silicon etching using fluorine-based plasmas was developed [3–5]. In 1979, Coburn and Winters highlighted the ions to neutrals synergy mechanism, opening the way to reactive ion etching (RIE) processes to optimize the etch rates and the control of the etch profile[6]. From this period, etching processes were constantly optimized and have become considerably more complex to meet the needs of the micro technology sector. Nowadays, numerous materials can be plasma-etched [7]. However, developing a dry etching process

on substrates made of transition metals presents some difficulties due to very low vapour pressure for simple metallic compounds for temperatures lower than a few hundred degrees. The poor substrate/mask selectivity is also an issue. However, the patterning of metallic materials is currently arousing great interest due to its numerous applications in biology, mechanics, optics, microfluidics and microelectronics [8–11]. Stainless steels play a crucial role in sustainable development because they are durable, hygienic and recyclable. To create micrometric or submicron size patterns on stainless steel surfaces, it is important to better understand the etching of metals that compose these materials. The present study focuses on Fe and Cr substrates and Fe-Cr alloys, Fe and Cr being the main components of stainless steels [12–14]. The investigation of the interactions of these elements with the plasma is crucial in

<footnote n="1">¹ Université de Nantes, CNRS, IMN, 2 rue de la Houssinière, F-44322 Nantes, France</footnote>

<footnote n="2">² Université de Lorraine, CNRS, IJL, F-54000 Nancy, France</footnote>

<footnote n="3">³ Université Paris Saclay, CNRS, C2N, 10 Boulevard Thomas Gobert, F-91120 Palaiseau, France</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
the study and understanding of the main etching mechanisms (chemical and physical components). This work is developed according to two approaches: an experimental study using an inductively coupled plasma (ICP) reactor, and multiscale mod-elling. Both approaches feed jointly into the study of the inter-action mechanisms between the active species of the plasma phase and the etched surfaces.

Section 2 of this paper is a literature overview of metal etching, mainly Fe and Cr, using Cl-based plasmas, mainly Cl₂. The structure of the model is presented in section 3 and the experimental set-up is presented in section 4. Section 5 presents and discusses results on the etching of Fe and Cr. A study on the influence of the Cr content on the etching of Fe-Cr substrate is presented as well. This last study has not yet been reported in the literature.

## 2. Literature overview

One of the first studies dedicated to metal etching was con-ducted by Laegreid and Wehner [15], who measured the sput-tering yields of different metals. Their results present close sputtering yields for transition metals such as Cr, Fe or Ni, and higher sputtering yields for noble metals such as Ag or Au. The measured sputtering yields are higher for metals than for silicon or carbon. Behrisch and Eckstein's book [16] presents numerous results on the sputtering threshold energy of elements.

Recently, Altieri *et al* published a paper that summarizes different plasma mixture interactions with different metals, especially Cu, but also Co, Fe or TiN materials [17].

Other research works dealt with the etching of steel and metal alloys [18, 19]. Most of them were dedicated to plasma-wall interactions. Cunge *et al* studied the deposition of etching by-products of SiClₓ onto the reactor walls [20]. Until now, studies have shown that Cl-based plasmas are good can-didates for metal etching. Organic plasma mixtures can etch some metals, by pure ion bombardment processes or, in some cases, by forming volatile organometallic compounds, with CH₄ or C₃H₆O plasmas for example [21–23].

Plasma-surface interactions can be studied through a ther-modynamic analysis that focusses on the Cl/material chemical reactions [24]. It allows getting data about the volatility of cre-ated products and the most likely reactions occuring on the etched surface. The simulations can be performed with differ-ent gas mixtures, so it can be an asset if H₂ or O₂, for example, is added to another gas as this can form new volatile com-pounds. Altieri proved that Fe can form volatile compounds when it is exposed to Cl atoms in gaseous form [25].

For Cl₂ ICP plasma discharge, numerous studies exist, using trace rare-gas optical emission spectroscopy (OES) to determine the electron temperature Tₑ [26, 27]. From these studies, Tₑ is relatively stable, between 2 and 4 eV for a large range of power (10–1000 W) and pressure (5–20 mTorr). Fuller *et al* pointed out an increase in Tₑ with the argon per-centage in aCl₂/Ar mixture [28], as well as a slow decrease in Cl⁺ density [29]. Malyshev *et al* published numerous papers on the dissociation of Cl₂ [30] and the impact of substrate bias in plasma [31].

In addition, Efremov *et al* made comparisons between a global kinetic model and experiments for a Cl₂/Ar plasma mixture [32, 33], showing a decrease in electron density, from 10¹¹ cm⁻³ to 2 × 10¹⁰ cm⁻³, when the argon percentage varied from 0 to 100%.

Chanson *et al* developed a global model of Cl₂/N₂/Ar cou-pled to a Monte-Carlo cellular surface model for etching of InP [34]. They showed the effect of the nitrogen percentage on the elimination of the bowing of the sidewall.

With regard to Fe etching, Cho *et al* [35] demonstrated a rather high etch rate using IBr and ICl plasmas. They measured an etch rate of 100–150 nm min⁻¹ for Ni and Fe in some con-ditions. Andriesse *et al* [36] observed a strong increase in the Fe etch rate when the substrate temperature increased from 70 to 200 °C, while the etch rate slowly increased with bias from 0 to –75 V. X-ray photoelectron spectroscopy (XPS) analyses revealed the presence of Fe–Cl bonds, proving the chemical adsorption of Cl on the surface etched with Cl₂/BCl₃. Park *et al* [37] evaluated the effect of the Cl₂ percentage on the etch rate of Fe under Cl₂/Ar plasma. They observed a maximum etch rate at 50% Cl₂, and a strong increase in etch rate between 0 and 25% Cl₂. These results, in association with Andriesse's findings [36], show that Fe can be sensitive to chemical etch-ing with neutral Cl, with a dependence on the substrate tem-perature. FeCl₃ has a vaporization temperature of 316 °C at atmospheric pressure [38].

With regard to Cr, Ebbinghaus *et al* [39] showed the evo-lution of chloride, fluoride or oxychloride compounds of Cr, in terms of formation and volatility. Recently, Wu *et al* pub-lished a review of photomask plasma etching, with a section dedicated to Cr etching [40]. The first study dedicated to Cr etching was provided by Abe *et al* [41]. They analyzed the etching process using plasma mixtures with Cl₂ and O₂ and attributed it to the formation of CrCl₂O₂ volatile compounds (CrCl₂O₂ is volatile at room temperature [42]). Curtis *et al* [43] studied the evolution of Cr etching by varying the per-centage of O₂ in CCl₄/O₂ mixtures and observed a maximum Cr etch rate for 50% O₂. Staaks *et al* [44, 45] performed etch-ing of Cr using Cl₂/O₂ plasma, observing a maximum etch rate for 20%–40% O₂. By studying the substrate temperature impact, they showed a strong increase in the etch rate, from 5 to 40 nm min⁻¹ when the substrate temperature increased from –80 °C to 40 °C. This evolution can be due to chemical etching of Cr. The same behaviour was observed by Nakata *et al* [46] and Ichiki *et al* [47]. They also observed undercut etching for Cr and an etch rate ten times higher for a Cl₂/O₂ plasma mix-ture with a few % O₂ than for a pure Cl₂ plasma. Aydinoglu *et al* [42] observed a higher etch rate for a Cr₂O₃ substrate than for a Cr substrate under the same conditions. This was attributed to the presence of native oxide in Cr₂O₃. The pres-ence of a CrClₓOᵧ layer after plasma etching was confirmed by XPS analyses [48].

## 3. Model

The model developed in this study is based on a multiscale approach that includes three different modules to track the etched surface evolution as a function of the operating condi-
<figure><img src="image_102.png" /><figcaption>**Figure 1.** A flowchart of the model. The total simulation range applied for conditions close to those presented in table 3. In the conditions applied in this paper, the total simulation time is about 1–2 h, and the simulation time of each model is around 30 min. The spatial scale of the sheath model is the sheath length, so is around 1 mm, while the spatial scale of the surface model is 1 µm for the feature.</figcaption></figure>

tions: pressure, gas mixture, flow rates, power, bias and etching duration. This approach was already used for the simulation of InP etching with Cl₂/N₂/Ar plasma mixtures [34]. A multiscale approach has been developed by several authors [49–53].

Figure 1 shows our simulator flowchart in which the primary input data represent the machine parameters, such as RF power, pressure, gas flow rates, DC bias and reactor geometry:

* Plasma module: it allows calculating the densities and fluxes of neutral and charged species as well as the electron density $n_e$ and temperature $T_e$.

* Sheath module: it allows calculating the positive ion energy distribution function (IEDFs for different incident angles. Output data from the plasma module in terms of $n_e$, $T_e$ and positive ion flux fractions are introduced as input data in the sheath model. Indeed, $n_e$ and $T_e$ are required to evaluate the average sheath thickness using the Langmuir theory, while positive ion flux fractions are used to randomly select each ion type in the sheath entrance.

* Surface module: it allows calculating the steel etch profile evolution through a mask as a function of time. Output data from plasma and sheath modules in terms of Cl and positive ion fluxes and IEDFs, are introduced in the surface module as input data.

### 3.1. Kinetic model

The plasma kinetic model is applied to a Cl₂/Ar ICP. It is based on a zero-dimension (0D) global approach [54, 55] to

calculate the neutral and ion average densities and fluxes. It provides these values for the reactive species participating in the steel etching process. Details of the model formalism are given in [56, 57]. The reaction scheme was updated using data provided in [58, 59]. Indeed, a recent publication by Hamilton et al [60] presents new cross sections for the main reactions involved in Cl₂ molecule dissociation by electron impact. The mass balance equations, associated with each species (neutral and ion) considered in the reaction scheme, include the following mechanisms: reactions by electronic impact, neutral/neutral, neutral/ion and ion/ion volume reactions, radiative deexcitation by photon emission and surface reactions.

$$ \frac{\partial (n_j)}{\partial t} = x_j \frac{N_o}{\tau} - n_e n_j \sum_l k_l(T_e) + n_e \sum_{l,m} k_l(T_e)n_m \\ - n_j \sum_l k_l(T_{gas})n_m \\ + \sum_{l,m,i} k_l(T_{gas})n_i n_m - k_s^j(p, T)n_j \\ + \sum_r k_s^r(p, T)n_r - \frac{n_j}{\tau}. \quad (1) $$

The first term on the right hand side of this equation represents the injected gases, where $x_j$, $N_o$ and $\tau$ are the fraction of injected gas $j$, total gas density and residence time, respectively. In our case, $x_j \neq 0$ only for $j = \text{Cl}_2$ and Ar ($x_{\text{Cl}_2} + x_{\text{Ar}} = 1$). The second and third terms are the loss and production rates of species $j$ by electron impact. The fourth and the fifth terms are the loss and production rate, by volume reactions, respectively. The sixth and the seventh terms are the loss and production rates on the wall surface, and the last term is the loss rate by pumping. Here, $k_l(T_e)$ is the reaction coefficient of reaction $l$ by electron impact, $k_l(T_{gas})$ is the reaction coefficient of collision between $i$ and $m$ species and $k_s^j$ is the reaction coefficient on of species $j$ on the surface. All these reaction coefficients are listed in appendix A.

The reaction coefficients by electron impact are calculated by assuming a Maxwellian electron energy distribution function (EEDF). The calculation of such coefficients needs knowledge of their associated cross sections. Details are given in [61–65]:

$$ k_e(T_e) = \langle \sigma_e(\varepsilon) v_e \rangle = \int \sigma_e(\varepsilon) \sqrt{\frac{2\varepsilon}{m_e}} f(\varepsilon, T_e) d\varepsilon, \quad (2) $$

where $T_e$ is the electron temperature, $v_e$ is the electron velocity, $m_e$ is the electron mass, $f(\varepsilon)$ is the EEDF and $\varepsilon$ is the kinetic energy of the electrons.

For volume reactions, the rate coefficient can be written most of the time as follows:

$$ k_v(T_{gas}) = c_1 \left( \frac{T_{gas}}{300} \right)^{c_2} \exp \left( -\frac{c_3}{T_{gas}} \right), \quad (3) $$

where $c_1$, $c_2$, $c_3$ are constant, and $T_{gas}$ is the gas temperature in K. Here, $c_1$, $c_2$ and $c_3$ can be evaluated using thermo-kinetic data [66]. In our case, $c_3$ is usually equal to zero, $1 < c_2 < 3$ and $c_1$ is around $10^{-9} \text{ cm}^3 \text{ s}^{-1}$, while it is around $10^{-36} \text{ cm}^6 \text{ s}^{-1}$.
<figure><img src="image_103.png" /><figcaption>Figure 2. The initial and final profile provided by the surface model during Fe/Cr etching using pure Cl₂ plasma.</figcaption></figure>

for three body reactions. Gas temperature is calculated as a function of the gas pressure Pr and RF power $P_{RF}$ [67]:

$$T_{\text{gas}} = 300 + 1250 \left(1 - e^{(-91 \text{ Pr})}\right) + 400 \times e^{(-337 \text{ Pr})} \frac{1}{3.69} \ln \left(\frac{\alpha P_{\text{RF}}(V_{\text{D}})}{40V}\right), \quad (4)$$

where $\alpha$ is the fraction of absorbed power (estimated to be 0.75), $V_D$ is the volume of Donnelly's reactor and $V$ is the volume of the reactor considered in simulations [68].

For de-excitation reactions, we refer to Singh et al's works for the estimation of the average loss rate [69]. For surface reactions, we use a formalism developed by Chantry [70]. Note that surface reactions, especially those involving atoms, have been studied for different plasmas [71, 72]. The present plasma kinetic model does not take into account the desorbed particles from the etched surface. It is assumed that their concentrations are lower than those of the species produced from the injected gases. The complete reaction scheme is presented in appendix A.

An 0D model cannot study spatial variations that occur in the plasma sheath. Hence, the calculated output data, in terms of ion fluxes and electron temperature and density, are introduced as input data in the sheath model.

## 3.2. Sheath model

We use a sheath module to study the positive ion transport through the sheath. Located between the plasma and the substrate, the sheath zone is characterized by an electron depletion due to the high electron mobility in comparison to that of the positive ions. This induces a change in the electric field leading to the acceleration of positive ions across the sheath. When the DC bias increases, the electrical field in the sheath becomes stronger.

To determine the evolution of an electric field in the sheath, a simple analytic formula has been proposed by Manenschijn et al [73], assuming that the electric field is perpendicular to the substrate surface:

$$E(z, t) = V_{\text{CS}}(t) \frac{n}{l_s} \left(\frac{z}{l_s}\right)^{n-1}, \quad (5)$$

where $z$ is the axial coordinate ($z = 0$ at the sheath entrance), and $n$ is constant between 0.5 and 1. In our simulations, $n$ is estimated to 0.75. Here, $l_s$ is the sheath thickness, that depends on $T_e$ and $n_e$, and it is evaluated from the plasma model [74]. Here, the potential drop across the sheath ($V_{CS}$) depends on the DC bias [74].

To calculate the ion energy at the entrance of the sheath, we used a formula proposed by Kokkoris et al [75].

The simulation is based on a Monte-Carlo 3D algorithm. The considered positive ions are randomly selected regarding their fractions compared to the total positive ion flux. As an example, for a given ion, such as Cl⁺, with 33% of the total ion flux, the probability for the selection of it is 0.33. Then, the initial position and angle of each selected ion are randomly chosen at the entrance of the sheath. Its trajectory is then calculated using Newton's law and by knowing the electric field evolution versus the axial position and time [73]. When the ion reaches the substrate surface, its angle and energy are stored.

By following the trajectories of many ions (a high number of Cl₂⁺, Cl⁺ and Ar⁺ for a Cl₂/Ar discharge), $10^5$ to $10^6$ ions, the IEDFs for different incident angles can be determined (from 0°, normal to the surface, to 90°, parallel to the surface). The calculated IEDFs are introduced in the surface model as input data.

## 3.3. Surface model

The main part of this study uses a Monte-Carlo 2D cellular algorithm. Details can be found in several papers [56, 76–78]. The model simulates interactions between super-particles, which represent reactive neutrals and ions from plasma, and supersites, which represent surface atoms. The simulation area, composed of a substrate and mask, is represented in a 2D Cartesian coordinate system (x, y) (see figures 2 and 3). This pattern is taken as representative of all the features over the surface of a real sample.

The surface properties are set by the user: vertical and lateral dimensions of the whole considered system, mask thickness and aperture, mask sidewalls. This 2D simulated area is completely divided into square supersites, with dimensions provided by the user, which represents a finite number $N$ of
<figure><img src="image_104.png" /><figcaption>**Figure 3.** A description of successful treatment for a superparticle-surface interaction. Only one superparticle (neutral or ion) interacts at the same time. Redeposition, modification of desorption probability are treated after superparticle reaches surface. Neighbours affected by sputtering is ion-enhanced etching, which is described in section 3. The displacement there concerns the displacement of surface supersites until they reach the surface; they are not going into the substrate. It is a security procedure that is implemented to avoid the creation of voids between surface supersites and the surface; which is not physically relevant. After three adsorptions of Cl on the same site, Fe becomes $FeCl_3$ and disappears because it is gaseous.</figcaption></figure>

real atoms. N is determined using dimensions of supersites, the chemical composition of the substrate and atomic densities:

$$N = N_A(\delta^* 10^{-4})^3 \left( \% \text{Fe} \frac{\rho_{\text{Fe}}}{M_{\text{Fe}}} + \% \text{Cr} \frac{\rho_{\text{Cr}}}{M_{\text{Cr}}} \right), \quad (6)$$

where $N_A$ is Avogadro's number, $\delta$ is the lateral dimension of a supersite in $\mu$m, typically $3.231 \times 10^{-3} \mu$m, $\rho$ is the volumic mass and M is the molar mass.

For this study, Fe and Cr are the two main elements considered for the substrate, whereas the mask is made of silica.

Three types of solid supersites are therefore on the simulation area when a new simulation begins: Fe, Cr and $SiO_2$. The positions of Fe and Cr in the initial matrix are randomly generated regarding their fractions. The areas without atoms are represented by empty supersites with the same dimensions as the others.

The mechanisms describing interactions between plasma superparticles and surface supersites are based on survey methods. The principle is as follows: an interaction between
<table><caption>**Table 1.** Plasma-surface reactions between neutral superparticles and supersites. The (g) sign corresponds to gaseous species and the (s) sign to solid or surface species. Here, $P_{des}$ is a probability specific to each supersite and evolves with ion bombardment; its evolution is explained in table 2. Redeposition neutrals are sputtered sites.</caption><thead><tr><th rowspan="2">Reaction</th><th colspan="2">Probability</th></tr><tr><th>Initial</th><th>After ion bombardment</th></tr></thead><tbody><tr><td colspan="3"><strong>Chemical etching with neutrals</strong></td></tr><tr><td>Cl(g) + FeCl<sub>x</sub>(x = 0-1)(s) → FeCl<sub>x+1</sub>(s)</td><td>0.05</td><td>0.05 + P<sub>des</sub></td></tr><tr><td>Cl(g) + FeCl<sub>2</sub>(s) → FeCl<sub>3</sub>(g)</td><td>0.05</td><td>0.05 + P<sub>des</sub></td></tr><tr><td>Cl(g) + CrCl<sub>x</sub>(x = 0-1)(s) → CrCl<sub>x+1</sub>(s)</td><td>0.05</td><td>0.05 + P<sub>des</sub></td></tr><tr><td colspan="3"><strong>Neutrals redeposition</strong></td></tr><tr><td>FeCl<sub>x</sub>(g) + surface → FeCl<sub>x</sub>(x = 0-2)(s)</td><td>0.1</td><td>0.1 + P<sub>des</sub></td></tr><tr><td>CrCl<sub>x</sub>(g) + surface → CrCl<sub>x</sub>(x = 0-2)(s)</td><td>0.1</td><td>0.1 + P<sub>des</sub></td></tr><tr><td>SiO<sub>2</sub>(g) + surface → SiO<sub>2</sub>(s)</td><td>0.1</td><td>0.1 + P<sub>des</sub></td></tr></tbody></table>

a plasma superparticle (atom or ion) with a supersite is considered representative of the interactions between N species from the plasma and N surface sites of the same nature.

Figure 3 is an overview of different superparticle-surface site interactions considered in the model: adsorption/desorption, sputtering and redeposition. All of these processes are introduced in a probabilistic way. Table 1 gives the probabilities for Cl atom adsorption on Fe or Cr sites to form FeCl<sub>x</sub>(x = 1-3) or CrCl<sub>x</sub>(x = 1-2) compounds. Probabilities for redeposition of etched sites are thus listed. Srivastava et al underlined the possible role of unpaired electrons on the sticking coefficient of SiCl<sub>x</sub>(x = 1-4) compounds, which is lower for SiCl<sub>2</sub> or SiCl<sub>4</sub> onto reactor walls than for SiCl or SiCl<sub>3</sub> [79]. Deposition probabilities of FeCl and CrCl sites could thus be different to the deposition probabilities of FeCl<sub>2</sub> and CrCl<sub>2</sub>. On Fe sites, the successive Cl atom adsorptions lead to the formation of the FeCl<sub>3</sub> compound, that is volatile and thus spontaneously desorbs (see figure 4), while spontaneous desorption is not allowed for CrCl<sub>x</sub>(x = 0, 2). Indeed, the successive adsorptions of Cl onto Cr sites form only non-volatile CrCl<sub>2</sub>. If the adsorption process of the neutral reactive particle (Cl in our case) on the neighbouring site does not occur, the particle reflects, with a randomly generated direction, into another etched surface. Redeposition concerns only sputtered surface supersites. After sputtering, a direction is randomly selected using a sinusoidal probability distribution centred on the direction of the impinging/sputtering ion. Finally, after interactions, there is a displacement procedure in the model. It is a security procedure that moves the supersites on the sidewalls if empty sites are present. This is because some supersites are only sensitive to ion bombardment so, in the area under the mask, they cannot be etched. This can lead to the formation of supersites surrounded by voids, which is not relevant. So, displacement takes care of it and moves the supersites as prevention.

During ion bombardment, a large part of the incident energy is transmitted to the surface and produces sputtering mechanisms. This atom ejection creates defects on the surface, especially dangling bonds, and a part of the ion energy is transmitted to the non-ejected surface atoms. Due to these dangling bonds and energy, some surface atoms can desorb

<figure><img src="image_105.png" /><figcaption>**Figure 4.** Vapour pressure of chlorinated metals from Yaws handbook [97].</figcaption></figure>

according to thermodynamics. Moreover, the surface defects make it easier for the adsorption of reactive neutrals onto the surface. This enhancement of adsorption is calculated by the introduction of a probability, named $P_{des}$, initially equal to 0. $P_{des}$ is increased by 0.04 for the first neighbours that surrounded a sputtered site. This is taken into account in the model, as shown by the red rectangle in figure 3. Both FeCl<sub>x</sub>(x = 0-2) and CrCl<sub>x</sub>(x = 0-2) are sputtered or desorbed by ion bombardment.

Sputtering yields introduced in the model are listed in table 2. They are calculated using SRIM software [80] by varying the incident ion energy and angle (see figure 5). The same sputtering yield is taken for Fe and FeCl<sub>x</sub>(x = 0-2), and for Cr and CrCl<sub>x</sub>(x = 0-2). The right column of table 2 presents the sputtering data of hard zones. It is a specific concept used to describe the etching mechanisms for Fe-Cr alloys and is described in section 5. In the model, a hard zone represents the first Fe supersite neighbours of Cr supersites or the first Cr supersite neighbours of Fe supersites. Figure 6 shows the numerical treatment in the model that represents this phenomenon of hard zones. These hard zones are a procedure implemented in the model to simulate a strong reduction of the etch rate in some conditions. This reduction is assumed to be linked to a low ion/surface energy transmission, due to interactions between Fe and Cr elements. The effects are similar to those of etch inhibitors, studied and simulated by Kokkoris et
<table><caption>**Table 2.** Plasma-surface reactions between ionic superparticles and supersites. The (g) sign corresponds to gaseous species and the (s) sign to solid or surface species. SY means the sputtering yield; it is the sputtering yield calculated using SRIM software. E is the ion energy, A is the incident angle of the ion with respect to the surfqce normal. Spontaneous desorption appears after ion/surface interaction. As an example, a nFe site with two sputtered neighbours has a desorption probability of 0.08. Cl₂⁺ has the same sputtering yield as Cl⁺ as a first approximation.</caption><thead><tr><th>Reaction</th><th>Yield</th></tr></thead><tbody><tr><td><strong>Physical etching with ions</strong></td><td></td></tr><tr><td>(Cl⁺, Cl₂⁺) + FeClₓ (x = 0-2)(s) → FeClₓ (x = 0-2)(g)</td><td>SY<sub>Cl⁺→Fe</sub> ((E<sub>Cl⁺</sub> (eV), A<sub>Cl⁺</sub> (°))</td></tr><tr><td>(Cl⁺, Cl₂⁺) + CrClₓ (x = 0-1)(s) → CrClₓ (x = 0-2)(g)</td><td>SY<sub>Cl⁺→Cr</sub> ((E<sub>Cl⁺</sub> (eV), A<sub>Cl⁺</sub> (°))</td></tr><tr><td>(Ar⁺) + FeClₓ (x = 0-2)(s) → FeClₓ (x = 0-2)(g)</td><td>SY<sub>Ar⁺→Fe</sub> ((E<sub>Ar⁺</sub> (eV), A<sub>Ar⁺</sub> (°))</td></tr><tr><td>(Ar⁺)) + CrClₓ (x = 0-1)(s) → CrClₓ (x = 0-2)(g)</td><td>SY<sub>Ar⁺→Cr</sub> ((E<sub>Ar⁺</sub> (eV), A<sub>Ar⁺</sub> (°))</td></tr><tr><td><strong>Physical etching with ions, hard areas</strong></td><td></td></tr><tr><td>(Cl⁺, Cl₂⁺) + FeClₓ (x = 0-2)(s) → FeClₓ (x = 0-2)(g)</td><td>SY/5</td></tr><tr><td>(Cl⁺, Cl₂⁺) + CrClₓ (x = 0-1)(s) → CrClₓ (x = 0-2)(g)</td><td>SY/5</td></tr><tr><td>(Ar⁺) + FeClₓ (x = 0-2)(s) → FeClₓ (x = 0-2)(g)</td><td>SY/5</td></tr><tr><td>(Ar⁺)) + CrClₓ (x = 0-1)(s) → CrClₓ (x = 0-2)(g)</td><td>SY/5</td></tr><tr><td colspan="2">Spontaneous desorption (initial P<sub>des</sub> = 0)</td></tr><tr><td>Interaction site</td><td>Interaction site hard areas</td></tr><tr><td>P<sub>des</sub> = P<sub>des</sub> + 0.1</td><td>P<sub>des</sub> = P<sub>des</sub> + 0.05</td></tr><tr><td>1st neighbours</td><td>1st neighbours hard areas</td></tr><tr><td>P<sub>des</sub> = P<sub>des</sub> + 0.04</td><td>P<sub>des</sub> = P<sub>des</sub> + 0.002</td></tr></tbody></table>

<figure><img src="image_106.png" /><figcaption>**Figure 5.** Sputtering yields of elements by Cl⁺ ions, calculated using SRIM© software for different energy and incident angles.</figcaption></figure>

al [81, 82]. But the origin of these etch inhibitors is the deposition of species from the reactor walls, masks or electrodes for hard inhibitors and the deposition of species from plasma for soft inhibitors. The hard zones described in this study are thus different to these inhibitors. Hard zones are also different from the micromasking effect, which is rather due to the local redeposition of etched compounds. Such compounds are resistive to chemical etching [83, 84].

## 4. Experimental set-up

Experiments were performed in an ICP/RIE SENTECH SI500 plasma reactor, represented in figure 7, according to the different conditions given in table 3. The samples are placed on an Al₂O₃ substrate holder.

Studies on Fe and Cr pure elements were realized on 250 µm thick Fe sheets (99.5% pure) from Goodfellow and

<figure><img src="image_107.png" /><figcaption>**Figure 6.** A drawing of the numerical treatment of hard zones and its implications. The supersite surrounded by red is the interaction supersite. Modification of the desorption probability concerns the neighbours of the interaction supersite and itself. The area of interest is the area explored to research Fe or Cr presence.</figcaption></figure>

on 3 mm thick massive Cr substrates of produced in an evaporation machine. For the Fe-Cr alloys, studies were performed on 3 mm thick samples with 0, 1, 3, 5, 8, and 12 wt
<figure><img src="image_108.png" /><figcaption>**Figure 7.** A drawing of an ICP/RIE SENTECH reactor SI500 with the interferometer and optical emission spectroscope tools implemented.</figcaption></figure>

<table><caption>**Table 3.** The experimental conditions for etching plasmas in ICP/RIE SENTECH reactor. The % wt of Cr in Fe–Cr alloys are 0, 1, 3, 5, 8 and 12.</caption><thead><tr><th>Substrate</th><th>Fe or Cr</th><th>Fe–Cr alloys</th></tr></thead><tbody><tr><td>Power (W)</td><td>800</td><td>800</td></tr><tr><td>Pressure (mTorr)</td><td>5</td><td>5</td></tr><tr><td>Flow rate Cl<sub>2</sub> (sccm)</td><td>60</td><td>60</td></tr><tr><td>Flow rate Ar (sccm)</td><td>60</td><td>0</td></tr><tr><td>Bias (V)</td><td>-150</td><td>-150</td></tr><tr><td>Surface temperature (°C)</td><td>150 or 220</td><td>220</td></tr><tr><td>Duration (min)</td><td>2</td><td>2</td></tr></tbody></table>

(weight) % of Cr. Before etching, the Fe and Cr samples were mirror polished with SiC paper until 2400 granulometry, then with a diamond suspension containing grains of 3 µm then 1 µm. Samples were masked by Plasma-Enhanced Chemical Vapor Deposition (PECVD) with a 1 µm thick SiN mask. Fe–Cr alloys were also mirror polished and masked by PECVD with a 500 nm thick SiO₂ thin layer. All samples were patterned using optical lithography. After the etching step, the remaining SiO₂ and SiN masks were removed by SF₆/CHF₃ plasma, in the same reactor. Then, etch rates were calculated by dividing the average depths measured on every etched sample by the etching time.

The average etched depth is calculated over three steps height, measured on patterns after etching and removal of the remaining SiN/SiO₂ mask. These measurements were carried out using a contact profilometer (DEKTAK8) with a stylus of 5 µm.

Between each etching run, the ICP/RIE reactor was cleaned using a standard cleaning recipe consisting of three steps, as shown in table 4. OES measurements were performed during Fe and Cr etching through the reactor quartz windows. A TRIAX500 (Jobin-Yvon) equipped with a CCD detector with a diffraction grating with 1800 lines/mm was used for this study. The aperture of the entrance slit was 50 µm, the exposure time was 50 ms. Spectra were recorded over the wavelength range from 300 and 900 nm. The identification of the emission lines was performed using available databases [85, 86].

<table><caption>**Table 4.** The experimental conditions for the cleaning procedure for the ICP/RIE SENTECH.</caption><thead><tr><th>Step</th><th>1</th><th>2</th><th>3</th></tr></thead><tbody><tr><td>Flow rate Cl<sub>2</sub> (sccm)</td><td>20</td><td>0</td><td>0</td></tr><tr><td>Flow rate Ar (sccm)</td><td>10</td><td>0</td><td>40</td></tr><tr><td>Flow rate O<sub>2</sub> (sccm)</td><td>0</td><td>40</td><td>0</td></tr><tr><td>Pressure (mTorr)</td><td>3</td><td>3</td><td>3</td></tr><tr><td>ICP RF power (W)</td><td>500</td><td>500</td><td>300</td></tr><tr><td>Temperature (°C)</td><td>20</td><td>20</td><td>20</td></tr><tr><td>Duration (min)</td><td>20</td><td>15</td><td>5</td></tr></tbody></table>

Plasma electron density ($n_e$) was measured using a microwave interferometer (Miwitron MWI2650). Interferometry is a non-perturbative technique that allows determining the electron density from the phase shift of the microwave propagating through the plasma with respect to the incident wave. The interferometer used works at a frequency of 26.5 GHz, which fixes an upper limit at about $9 \times 10^{12} \text{ cm}^{-3}$ for $n_e$. The accuracy is of 0.1°, which corresponds to $10^9 \text{ cm}^{-3}$ in electron density for a plasma length of 55 mm [87].

## 5. Results and discussion

This section presents the results for Cl₂ plasma etching of Fe, Cr and Fe – Cr alloys. Section 5.1 is dedicated to the analysis of Cl₂ plasma properties evolution with pressure and power. This study presents results from the simulation and experimental results without introducing metallic samples into the chamber. Section 5.2 presents the effect of the metallic substate on the plasma properties using microwave interferometry and OES. Section 5.3 presents experimental etch rates of Fe and Cr, as well plasma surface interactions deduced from experiments. Section 5.4 exposes the simulation results, showing the effect of the Cl adsorption probability on the Fe etching evolution. Section 5.5 shows the comparison between experimental and simulated etch rates of Fe – Cr alloys. Finally, section 5.6 draws the effect of Cr content on the morphological properties of etched patterns as well as the etched product evolution.

### 5.1. Plasma properties: simulation results vs experimental results

Figure 8 shows the electron density evolution with RF power for 5 and 20 mTorr pressure. Electron density increases when the RF power increases because of higher ionization processes. However, for RF power lower than 500 W, a decrease in $n_e$ with the pressure is observed. In this power range, a significant part of the collisions is responsible for the negative ion production to the detriment of the production of free electrons. Such production is due to the dissociative attachment of Cl₂ by electron impact (reaction R₁₄). This can be explained by the fact that, for RF power lower than 500 W, the Cl₂ dissociation rate is rather low and then Cl₂ is still the dominant species favouring the attachment process (figure 9). Over 500 W RF power, the Cl₂ dissociation rate gets higher and higher as the power increases and Cl atom becomes the dominant species in the plasma. This favours the ionization of Cl,
<figure><img src="image_109.png" /><figcaption>**Figure 8.** Electron density evolution versus RF power for two different pressures and for initial condition presented in table 3, with neither metallic substrate nor bias.</figcaption></figure>

while the attachment process through the reaction R₁₄ (see appendix A) gets less important. We note that the satisfactory agreement between the simulation and the measurements is obtained for 5 mTorr pressure. An experimental estimation of the evolution of the Cl₂ dissociation rate can be obtained by optical actinometry, using xenon as an actinometer. An experimental estimation of the Cl₂ dissociation rate can be obtained by optical actinometry using xenon as an actinometer, the Xe I line at 823.1 (transition 5p⁵(²p°₃/₂)6s → 5p⁵(²p°₃/₂)6p) was used [88]. The energy of the upper level of the transition lies at 9.83 eV. Regarding chlorine atoms, the Cl I line at 837.6 nm (transition 3s²3p⁴(³p)4p → 3s²3p⁴(³p)4s was chosen since its upper level energy (10.4 eV), is close to that of the Xe I transition. Malyshev and Donnelly also reported that all Cl lines in the range 700 - 900 nm follow the same variation with increasing RF power [88]. Malyshev and Donnelly [88] also showed that under similar conditions than those used here, the plasma is strongly dissociated and that the contribution of dissociative excitation by electron impact on Cl₂ on Cl line emission is very low. As the excitation cross sections of Cl lines by electron impact from the ground state are unknown, it is estimated that the line ratio ICl/IXe is proportional to the density of atomic Cl, as carried out by Malyshev and Donnelly [88]. The dissociation rate, defined as [Cl]/[Cl₂], is then proportional to the ICl/IXe and is qualitatively compared to the calculated one in figure 9.

It is evident that the ion to neutral flux ratio plays an important role in the plasma etching. The non-linear dependence of the etch rate on this ratio was already pointed out because of the ion-neutral synergy in the etching process [89]. The physical etching under ion sputtering is more important than the fact that the ion to neutral flux ratio gets higher. In contrast, a low value of this ratio favours the pure chemical etching. Figure 10 presents the ion to neutral flux ratio versus the power for 5 and 20 mTorr pressure. For 5 mTorr, an almost linear variation in the ion to neutral flux ratio with RF power is observed. However, for 20 mTorr, as ne in figure 8, the ion to neutral flux ratio is relatively lower at 20 mTorr than at 5 mTorr for RF power less than 500 W, while the trend changes beyond 500 W. This change

<figure><img src="image_110.png" /><figcaption>**Figure 9.** Dissociation percentage versus RF power for two different pressures and for initial condition presented in table 3, with neither metallic substrate nor bias. Note that dissociation percentage is not estimated the same way for experiment and for simulation. Simulation data use the evolution of (1-nCl₂ (plasmaon))=nCl₂ (plasmaoff) ratio while experimental data use ICl/IXe ratio to estimate the dissociation percentage. ICl/IXe is multiplied by a constant value of 20 for each points for graphical scaling purpose. Only trends can be compared and not absolute values.</figcaption></figure>

<figure><img src="image_111.png" /><figcaption>**Figure 10.** The ion to neutral flux ratio versus RF power for the initial conditions presented in table 3 without substrate and without bias.</figcaption></figure>

is due to the increase in the ionization process of Cl to the detriment of the production of Cl⁻ by electron impact dissociative attachment of Cl₂. Therefore, the ionization of Cl by the production of Cl⁺ is well favoured because of the significant increase in the Cl₂ dissociation percentage (figure 9).

## 5.2. Impact of etched metals on plasma properties

Figures 11(a) and (c) show optical emission spectra obtained for reference Cl plasmas (Cl₂ 60 sccm, Xe 7 sccm at 4.8 mTorr, 800 W and -150 V of bias without substrate heating) with no metallic sample on the sapphire substrate holder. Xenon was introduced in a small quantity in the discharge as the actinometer to obtain estimate of the atomic Cl density. As expected in ICP chlorine plasma [90]. Most of the observed transitions belong to Cl I spectrum together with some line from Cl+, Cl2 and Cl2+. [90], These reference spectra were recorded just before the etching experiments.
<figure><img src="image_112.png" /><figcaption>**Figure 11.** Emission spectrum of a chlorine plasma. Pressure, RF Power and Cl2 flow rate are the same than the ones presented in table 3. $X_e = 7$ sccm, with neither metallic substrate nor bias, nor substrate heating. The reference plasmas without samples are: (a) for Cr and (c) for Fe. Plasmas during etching are, respectively, (b) Cr and (b) Fe.</figcaption></figure>

When metallic sample are placed on the substrate holder, spectra results reveal the presence of Cr I (figure 11(b)) and Fe I (figure 11(d)) lines in the plasma. This confirms the ability of chlorine ICP plasma to etch Fe and Cr

The spectra show a strong decrease in the emission intensities for Cl₂ plasmas with Fe samples. The line ratio $I_{Cl}/I_{Xe}$ however does not change much: it varies from 2.05 to 2.07 for the reference plasma and the plasma, respectively, with the presence of Cr, and from 1.67 to 1.74S for the reference plasma and the plasma, respectively, with the presence of Fe.

Electron density values determined by microwave interferometry are plotted in figure 12. The accuracy of phase variation is 0.1°, which gives an accuracy in $n_e$ measurement of $8.4 \times 10^8$ cm⁻³. The error due to spatial variations of $n_e$ in the plasma chamber was not estimated. Therefore, no error bars are included in figure 12. The number 1 indicates the reference density, in Cl plasma (conditions table 3), obtained just after reactor cleaning (see the detailed procedure in table 4), without introducing a metallic sample or heating. Data points 2 to 5 were measured after the introduction of a Cr substrate (temperature at 150 and 220°C; points 2 and 3) then an Fe substrate (points 4 and 5; same temperatures). Point 6 depicts a second reference point obtained just after Fe removal and before the reactor cleaning. These data show a drop in the electron density induced by the presence of the metallic sample. This drop is more significant for both Fe and the higher temperature. During etching, the formation and ejection of $FeCl_x$ ($x = 0-3$)

<figure><img src="image_113.png" /><figcaption>**Figure 12.** Electron density of Cl₂ plasmas for the conditions presented in table 3 with different substrate temperatures (150°C for points 2 and 4, 220°C for points 3 and 5). References of $n_e$ are given by points 1 and 6 (without substrate heating), before any etching (point 1) and after every etching (point 6).</figcaption></figure>

or $CrCl_x$ ($x = 0-2$) from the metallic sample will contaminate both the Cl plasma and the reactor walls. As shown previously, under the same conditions the etch rates of Fe are greater than Cr. Consequently, contamination induced by Fe-containing etchant products is expected to be more significant, worsening when the temperature rises. These species strongly modify the electrical parameters of the plasma, including the electron density. The pollution of reactor walls is also the cause of these trends. During the experiments, they become covered with etching products that can subsequently desorb and re-enter the plasma phase. This is why $n_e$ (figure 12, point 6, before reactor cleaning) does not rise to the initial value (point
<table><caption>**Table 5.** Etch rates in nm min⁻¹ of Fe and Cr estimated by experiment; the conditions are presented in table 3.</caption><thead><tr><th>Sample</th><th>Cl<sub>2</sub></th><th>Ar</th></tr></thead><tbody><tr><td>Fe</td><td>269 (±5)</td><td>40 (±1)</td></tr><tr><td>Cr</td><td>45 (±3)</td><td>26 (±2)</td></tr></tbody></table>

1), but is at a level close to that measured during the etching of Fe at 220 °C.

To explain this drop in electron density, two mechanisms are assumed. Firstly, the FeCl₃ species has a calculated electron affinity of 3.90 eV [91], a value that is even higher than those of Cl, which is 3.61 eV from the NIST database. It is possible that an electronic attachment process becomes more efficient, leading to the production of negative ions to the detriment of the electron population. Secondly, the polyatomic aspect of etchant products in the plasma phase would increase the power loss under excitation and dissociation by electronic impact of these etchant products. This would increase the effective creation energy of an electron–ion pair [92]. But due to a lack of etchant product data in terms of cross sections of reactions by electronic impact, it is difficult to confirm these hypotheses.

### 5.3. Experimental results: etching mechanisms of Fe and Cr

Pure Fe and Cr substrates were submitted respectively to argon and Cl ICP plasmas, under the conditions depicted in table 3. Etch rates are summarized in table 5. Under argon, the results are very close. In this case, the etching is due to pure sputtering mechanisms induced byAr⁺ ions. Calculations performed using SRIM software show that the sputtering yields of Fe and Cr are very similar. Under Cl plasma, etch rates increase more for Fe (×6.7) than for Cr (×1.7). According to the results of the kinetic model and from OES, Cl⁺ and Cl are, respectively, the major ionic and reactive neutral species, hence those participating in the etching mechanisms. Cl atoms can form FeClₓ(x = 1–3) species or CrClₓ(x = 0–2) species after surface adsorption of Cl. According to the data in figure 4, this process is expected to form FeCl₃, a volatile product for the present operating pressure and surface temperature. The formation of a gaseous compound by successive adsorption of Cl is known as chemical etching. Fe is thus exposed to both chemical and physical etching. On the other hand, chemical etching is not possible for Cr under the tested conditions: the process temperature being too low to form gaseous compounds (see figure 4). FeClₓ(x = 1–2) and CrClₓ(x = 1–2) compounds are sputtered by Cl₂⁺ and Cl⁺ ions, as well as Fe and Cr. FeClₓ(x = 0–2) and CrClₓ(x = 0–2) species can spontaneously desorb from the surface only in the areas exposed to ion bombardment. In these zones, the formation of dangling bonds at the surface improves the adsorption of neutral Cl onto FeClₓ(x = 0–2) and CrClₓ(x = 0–2) surface sites. This process is taken into account in the surface model.

### 5.4. Etching of Fe: impact of Cl adsorption. Simulation results

The used RF bias (–150 V) is higher compared to some ICP etching processes [20, 93–96]. Furthermore, the ion to

<figure><img src="image_114.png" /><figcaption>**Figure 13.** Trench profiles determined using modelling for different reflection probabilities for Cl → FeClₓ(x = 0–2) reactions: (a) Pads = 0.1, (b) Pads = 0.2, (c) Pads = 0.3 and (d) Pads = 0.4. The etching time is 2 min. The other operating conditions are presented in table 3. Dashed lines represent the etching depth estimated with the experimental etch rate for the pure Fe sample.</figcaption></figure>

<figure><img src="image_115.png" /><figcaption>**Figure 14.** Experimental and modelling etch rates of the Fe/Cr target with different %Cr. The operating conditions are presented in table 3.</figcaption></figure>

neutral flux ratio Γᵢₐₗs/ΓCl is relatively high (about 38%). In these conditions the physical etching is the dominant etching mechanism due to the efficiency of ion bombardment.

Both the energy and number of ions in seconds are really high in this kind of machine. As a first approximation, the sputtering yields of FeClₓ and CrClₓ(x = 1–2) are supposed equal to those of original sites of Fe and Cr. The adsorption of Cl on Fe sites accelerates the etching process. As explained in section 3, in the area exposed to ion bombardment, the adsorption probability of atomic Cl increases and spontaneous desorption of surface sites occurs.

Figure 13 shows the effect of the adsorption probability (Pads(Cl): 0.1 to 0.4) on the FeClₓ sites (x = 0–2) on the etch profile evolution. For a fixed etching time (2 min) of Fe, the simulations show that the trench is deeper when Pads(Cl) is maximum. The increase in this surface parameter enhances
<figure><img src="image_116.png" /><figcaption>**Figure 15.** Trench profiles determined using modelling for: (a) 0% wt Cr, (b) 8% wt Cr and (c) 20% wt Cr. The etching time is 2 min, and the other operating conditions are presented in table 3.</figcaption></figure>

the $FeCl_x(x = 0–2)$ formation. In the trench bottom, where the surface is submitted to the directional ion bombardment, high Cl adsorption improves the reactive ion etching processes. Moreover, as neutral species have an isotropic distribution, the increasing adsorption probability enhances $FeCl_x(x = 1–3)$ site formation along the trench sidewalls. These zones are thus subjected to an important chemical etching process due to the formation of $FeCl_3$ species desorbing from the surface. The consequence is the formation of undercut and bowing defects, as shown in figure 13.

### 5.5. Etching of Fe–Cr alloys: experiment and simulation

To analyze the effect of the chemical composition of Fe–Cr alloys on the etching processes under $Cl_2$ plasma, we have performed a simulation and experiment series by varying the % wt of Cr from 0 to 12 (see table 3).

Figure 14 shows that the increase in the % wt of Cr leads to a decrease in the etch rate of the Fe–Cr alloy. The experimental etch rates are 244, 129, 67 nm min⁻¹ for 0, 3 and 12 % wt of Cr, respectively. Both the simulation and the experiments show the same variation trend. However, the simulated etch rates are slightly higher than those obtained by experiment. The decrease in the etch rate is particularly sharp between 0 and 5% wt of Cr, then slows down to stabilize above 12% of Cr. This non-linear evolution indicates that the mechanisms involved are not limited to differences in etch rates between Fe and Cr.

To explain this result, it is necessary to consider the existence of a global phenomenon resulting from the simultaneous presence of Fe and Cr. We thus introduce the concept of hard zones to take into account this interaction effect between Fe and Cr on the etching mechanisms. These hard zones therefore have better resistance to etching. Since it is unlikely that chemical etching decreases as much with such low Cr contents, we assume that surface mechanisms linked to ion bombardment

<figure><img src="image_117.png" /><figcaption>**Figure 16.** Roughness and undercut measured in Fe/Cr targets, from model results with different % wt Cr. The operating conditions are presented in table 3.</figcaption></figure>

are affected by a lower transmission of ion/substrate energy. Thus, in these hard zones the sputtering yields decrease and the assistance provided by the ion bombardment to the surface desorption of compounds is less efficient. The physical origin of these hard zones states that the inclusion of Cr in Fe would increase the hardness of the material and modify the surface energy. The subsequent modification of surface energy will lead to a lower sputtering yield than for pure Fe or pure Cr. At the same time, the dislocation along the surface and the creation of defects are limited. This will impact the spontaneous desorption of Fe and Cr as well as the favorable adsorption of Cl atoms on the Fe/Cr surface. Once a sufficient Cr content is reached, the surface is covered by these hard areas and the etch rate settles down.

The surface model introduces this concept (see section 3 and table 2). Figure 14 clearly shows that the simulation results correlate well with the experiments, which supports our hypotheses. This accuracy has been obtained after the adjustment of numerical parameters in the model.

Figure 15 shows three simulated trenches obtained respectively for 0, 8 and 20% wt of Cr (see table 3 for operating
<figure><img src="image_118.png" /><figcaption>**Figure 17.** The number of supersites etched by different processes in Fe/Cr targets. The Fe case is presented in (a), while Cr is presented in (b). From the model results with different % Cr or % Fe. The operating conditions are presented in table 3. The d sign corresponds to desorption, while the sp sign corresponds to sputtering.</figcaption></figure>

conditions). The third result is particularly interesting since it is similar to the case of austenitic steels, that generally have a Cr content of around 16% wt. For pure Fe, even a global anisotropic aspect, the trench profile is characterized by the formation of lateral defects: bowing and undercut. Its depth is about 565 nm. The addition of Cr leads to the reduction (figure 15(b)) or even to the elimination of these defects (figure 15(c)).

At the trench bottom, the introduced hard zones induce the formation of a significant roughness (figure 15(b)), that is reduced when the percentage of Cr exceeds a certain threshold. From the results of figure 14, this threshold can be set at around 12%wt. As explained previously, the hard zones' existence lowers the sputtering yields, leading to the decrease in the vertical etch rate.

### 5.6. Etching of Fe-Cr: simulation results

In figure 16 the variations in the simulated etched surface roughness and undercut level versus Cr percentage are plotted. The lateral dimension of a supersite is 3.231 nm. The roughness is calculated in the trench bottom by averaging the height of the peaks and valleys on either side of a baseline. This surface parameter varies from 15 to 40 nm, that is 5 to 12 supersites. There is a maximum roughness for 3%wt Cr followed by a constant decrease until it reaches a value lower than that measured for pure Fe. A low Cr content induces the formation of hard zones that increase the roughness by locally decreasing the sputtering and spontaneous desorption. When their distribution begin to recover the surface on the trench bottom, the interaction processes become more homogeneous as well and the roughness decreases.

The undercut is almost constant Cr content less than 3% wt (around 50 nm) and decreases for Cr content greater than 3% wt up to 20% wt (22 nm for 20% wt of Cr). On the sidewalls, chemical etching is the dominant surface process because sputtering or assisted desorption are induced by ion bombardment that is almost directional. According to the sheath model, the angular shift is 2.5° around the normal to the sample surface. So, just under the mask, Cr sites cannot be etched. For sufficient content, the Cr sites homogeneously cover the trench sidewalls, creating a passivation layer that reduces the lateral

etching processes. This has a positive effect on the profile anisotropy.

With this model, it is possible to count the different occurrences during one etching process. The variations of desorbed sites from the Fe or Cr surfaces are plotted in figures 17(a) and (b). It shows the desorption of $FeCl_x(x = 0-3)$ and $CrCl_x(x = 0-2)$ due to chemical etching or ion bombardment. For the two figures, the d letter means spontaneous desorption (comprising chemical etching for $FeCl_3$), whereas sp means physical sputtering. A constant decrease in desorbed species is observed when the Cr content increases. For Fe in figure 17(a), etching is dominated by the formation of gaseous $FeCl_3$, while sputtering of $FeCl_x(x = 0-2)$ is consequent: Fe sites are the most sputtered, because they are numerous in the alloys considered, followed by FeCl and $FeCl_2$ sites. Desorption of non-volatile compounds $FeCl_x(x = 0-2)$ is very low. Furthermore, creation of gaseous $FeCl_3$ is favoured by the greater adsorption of Cl on $FeCl_x(x = 0-2)$ in the areas exposed to ion bombardment. This synergy makes understandable the dominance of $FeCl_3$ formation and sputtering of $FeCl_x(x = 0-2)$ in the etching processes.

Spontaneous desorption of non-gaseous $CrCl_x(x = 0-2)$ (see figure 17(b)) is very low in comparison, nearly equal to zero. In the reaction scheme introduced in the model, successive adsorptions of Cl atoms into the same supersite lead to the formation of stable $CrCl_2$.

For Cr (see figure 17(b)), etching is largely dominated by sputtering mechanisms, with a great proportion of sputtered $CrCl_2$ sites. Due to the low Cr content in the substrate, Cr is expected to always be surrounded by some Fe sites. Hence, for Cr in Fe-Cr alloys, adsorption is not favoured by ion bombardment but sputtering and spontaneous desorption are negatively affected by the phenomena of hard zones described in the previous section. Consequently, before its ejection from the surface due to ion bombardment, Cr transforms to $CrCl$, then $CrCl_2$.

## 6. Conclusion

This work presents a joint experimental and modelling study of dry etching of Fe-Cr alloys. An etching model of an Fe-Cr
<table><caption>**Table 6.** Species taken into account for pure Cl₂ plasma. Cl₂(A, C) corresponds to a³Π<sub>u</sub>, A¹Π<sub>u</sub>, b³Π<sub>g</sub>, c³Σ<sup>-</sup> and B¹Π<sub>g</sub> states. Cl₂(B) corresponds to C¹Δ<sub>g</sub>, D¹Σ<sup>+</sup> and e³Σ<sup>+</sup> states.</caption><thead><tr><th>Neutrals</th><th>Positive ions</th><th>Negative ions</th></tr></thead><tbody><tr><td>Cl₂(ν = 0–3), Cl₂(A, C), Cl₂(B), Cl, Cl(4s), Cl(4p), Cl(3d)</td><td>Cl₂<sup>+</sup>, Cl<sup>+</sup></td><td>Cl<sup>-</sup></td></tr></tbody></table>

<table><caption>**Table 7.** Reactions of dissociation and ionization for Cl₂ plasma.</caption><thead><tr><th></th><th>Reaction</th><th>Threshold energy (eV)</th><th>Reaction rate (cm³ s<sup>-1</sup>)</th><th>Reference</th></tr></thead><tbody><tr><td>R1:</td><td>e + Cl₂(ν = 0–3) → 2Cl + e</td><td>0.0</td><td>k₄ = 6.67 × 10<sup>-8</sup>T<sub>e</sub><sup>-0.1</sup> exp(-8.67/T<sub>e</sub>)</td><td>[60, 98]</td></tr><tr><td>R2:</td><td>e + Cl₂(ν = 0–3) → Cl₂(a³Π<sub>u</sub>) + e → Cl₂(A, C) + e</td><td>3.252</td><td>k₁₃ = 8.0 × 10<sup>-8</sup>T<sub>e</sub><sup>-0.55</sup> exp(-5.5/T<sub>e</sub>)</td><td>[60, 98]</td></tr><tr><td>R3:</td><td>e + Cl₂(ν = 0–3) → Cl₂(A¹Π<sub>u</sub>) + e → Cl₂(A, C) + e</td><td>4.348</td><td>k₁₄ = 1.0 × 10<sup>-7</sup>T<sub>e</sub><sup>-0.675</sup> exp(-7.0/T<sub>e</sub>)</td><td>[60, 98]</td></tr><tr><td>R4:</td><td>e + Cl₂(ν = 0–3) → Cl₂(b³Π<sub>g</sub>) + e → Cl₂(A, C) + e</td><td>6.498</td><td>k₂₀ = 4.0 × 10<sup>-8</sup>T<sub>e</sub><sup>-0.6</sup> exp(-10.2/T<sub>e</sub>)</td><td>[60, 98]</td></tr><tr><td>R5:</td><td>e + Cl₂(ν = 0–3) → Cl₂(c³Σ<sup>-</sup>) + e → Cl₂(A, C) + e</td><td>7.257</td><td>k₂₆ = 2.0 × 10<sup>-10</sup>T<sub>e</sub><sup>-0.6</sup> exp(-9.0/T<sub>e</sub>)</td><td>[60, 98]</td></tr><tr><td>R6:</td><td>e + Cl₂(ν = 0–3) → Cl₂(B¹Π<sub>g</sub>) + e → Cl₂(A, C) + e</td><td>7.537</td><td>k₁₅ = 3.0 × 10<sup>-9</sup>T<sub>e</sub><sup>-0.5</sup> exp(-11.0/T<sub>e</sub>)</td><td>[60, 98]</td></tr><tr><td>R7:</td><td>e + Cl₂(ν = 0–3) → Cl₂(C¹Δ<sub>g</sub>) + e → Cl₂(B) + e</td><td>7.790</td><td>k₂₇ = 5.0 × 10<sup>-10</sup>T<sub>e</sub><sup>-0.6</sup> exp(-10.0/T<sub>e</sub>)</td><td>[60, 98]</td></tr><tr><td>R8:</td><td>e + Cl₂(ν = 0–3) → Cl₂(D¹Σ<sup>+</sup>) + e → Cl₂(B) + e</td><td>8.228</td><td>k₁₆ = 5.0 × 10<sup>-10</sup>T<sub>e</sub><sup>-0.75</sup> exp(-12.0/T<sub>e</sub>)</td><td>[60, 98]</td></tr><tr><td>R9:</td><td>e + Cl₂(ν = 0–3) → Cl₂(e³Σ<sup>+</sup>) + e → Cl₂(B) + e</td><td>9.219</td><td>k₁₇ = 1.0 × 10<sup>-10</sup>T<sub>e</sub><sup>-0.5</sup> exp(-11.0/T<sub>e</sub>)</td><td>[60, 98]</td></tr><tr><td>R10:</td><td>e + Cl₂(ν = 0–3) → Cl₂(²Σ<sup>+</sup>)<sup>-</sup> → Cl + Cl<sup>-</sup></td><td>0.0</td><td>k₅₁ = 6.5 × 10<sup>-11</sup>T<sub>e</sub><sup>-1.4</sup> exp(-0.0/T<sub>e</sub>)</td><td>[61, 98, 99]</td></tr><tr><td>R11:</td><td>e + Cl₂(ν = 0–3) → Cl₂(²Π<sup>-</sup>)<sup>-</sup> → Cl + Cl<sup>-</sup></td><td>2.5</td><td>k₅₂ = 5.5 × 10<sup>-10</sup>T<sub>e</sub><sup>-1.3</sup> exp(-2.0/T<sub>e</sub>)</td><td>[61, 98, 99]</td></tr><tr><td>R12:</td><td>e + Cl₂(ν = 0–3) → Cl₂(²Π<sup>-</sup>)<sup>-</sup> → Cl + Cl<sup>-</sup></td><td>5.5</td><td>k₅₃ = 3.15 × 10<sup>-9</sup>T<sub>e</sub><sup>-1.4</sup> exp(-5.0/T<sub>e</sub>)</td><td>[61, 98, 99]</td></tr><tr><td>R13:</td><td>e + Cl₂ → Cl + Cl<sup>+</sup> + 2e</td><td>12.0</td><td>k₂ = 2.14 × 10<sup>-7</sup>T<sub>e</sub><sup>-0.07</sup> exp(-25.26/T<sub>e</sub>)</td><td>[57, 59, 62, 64, 98, 100]</td></tr><tr><td>R14:</td><td>e + Cl₂ → Cl<sup>+</sup> + Cl<sup>-</sup> + e</td><td>12.0</td><td>k₃ = 2.94 × 10<sup>-10</sup>T<sub>e</sub><sup>-0.19</sup> exp(-18.79/T<sub>e</sub>)</td><td>[57, 59, 61, 98, 100]</td></tr><tr><td>R15:</td><td>e + Cl₂ → Cl<sup>+</sup> + 3e → Cl<sup>+</sup> + Cl<sup>+</sup> + 3e</td><td>35.0</td><td>k₅₀ = 2.27 × 10<sup>-10</sup>T<sub>e</sub><sup>-1.92</sup> exp(-21.26/T<sub>e</sub>)</td><td>[57, 59, 62, 64, 98]</td></tr><tr><td>R16:</td><td>e + Cl₂ → Cl<sup>+</sup> + 2e</td><td>11.5</td><td>k₁ = 5.12 × 10<sup>-8</sup>T<sub>e</sub><sup>0.48</sup> exp(-12.34/T<sub>e</sub>)</td><td>[57, 59, 62, 98]</td></tr><tr><td>R17:</td><td>e + Cl → Cl<sup>+</sup> + 2e</td><td>13.5</td><td>k₆ = 3.17 × 10<sup>-8</sup>T<sub>e</sub><sup>0.53</sup> exp(-13.29/T<sub>e</sub>)</td><td>[57, 59, 63, 100]</td></tr></tbody></table>

alloy is developed. The model is composed of three modules: a plasma kinetic model, a sheath model and a surface model. With this multiscale approach, it is possible to predict the etch profile evolution of Fe–Cr alloys through the mask versus the external ICP parameters.

The substrate temperature influences the volatility of compounds because of the difference in the boiling temperatures of pure elements and the chlorinated compounds. Knowledge of vapour pressure for these compounds help establishing reaction scheme. The differences in Fe and Cr etch rates while exposed to Cl₂ or Ar plasma is due to the formation of volatile FeCl₃ compounds and CrCl₂ non-volatile compounds on the surface. This hypothesis has been reinforced by OES and interferometry measurements of Cl₂ plasma alone and during Fe and Cr etching. This corresponds to the data from the literature and to the evolution of the vapour pressure of chlorinated compounds. Fe and Cr are both sensitive to physical etching by ion bombardment, and chlorinated Fe and Cr species are created on the surface. The differences between surface energies of pure metals and chlorinated metals can increase the removal of these metals, hence the etch rate.

Based on the model results, a preponderance is established of chemical etching for Fe through the creation of gaseous FeCl₃ while sputtering of Fe and FeClₓ (x = 1–2) is high. For Cr, sputtering of CrCl₂ is dominant. For Fe, spontaneous desorption of non-volatile surface compounds is low while, for Cr, it is almost negligible.

The diminution of the etch rate by increasing the Cr percentage, measured by profilometry and estimated by simulation, is also explained by the creation of hard zones around Fe sites due to the presence of Cr sites. These hard zones strongly decrease the etch rate because the sputtering yield as well as spontaneous desorption probabilities decrease. Etching of steels using chlorinated plasma is an interesting way to functionalize steel surfaces with submicron patterns. As an immediate perspective, analyses of etched surfaces using XPS is needed to validate our hypothesis and improve both our model and our understanding of Cl plasma interactions with metal alloys.

## Acknowledgments

This study is financially supported by the French National Research Agency (ANR), through ANR-17-CE08-0029 project. This work was partly supported by the French RENATECH network.

## Data availability statement

All data that support the findings of this study are included within the article (and any supplementary files).

## Appendix A

In this section, we present the full reaction scheme taken into account by our model, modified from Chanson *et al* [56].
<table><caption>**Table 8.** Reactions between charged species, atoms and molecules for Cl₂.</caption><thead><tr><th>Reaction</th><th>Threshold energy (eV)</th><th>Reaction rate (cm³ s⁻¹)</th><th>Reference</th></tr></thead><tbody><tr><td colspan="4"><strong>Reactions electron-ion</strong></td></tr><tr><td>R18: e + Cl<sup>+</sup> → 2Cl</td><td>0.0</td><td>k<sub>34</sub> = 9.0 × 10<sup>-8</sup>T<sub>e</sub><sup>-0.5</sup></td><td>[57, 59, 100]</td></tr><tr><td>R19: e + Cl<sup>-</sup> → Cl + 2e</td><td>10.1</td><td>k<sub>9</sub> = 9.02 × 10<sup>-9</sup>T<sub>e</sub><sup>0.72</sup> exp(-4.88/T<sub>e</sub>)</td><td>[57, 59, 65, 100]</td></tr><tr><td>R20: e + Cl<sup>-</sup> → Cl<sup>+</sup> + 3e</td><td>28.6</td><td>k<sub>51</sub> = 3.62 × 10<sup>-9</sup>T<sub>e</sub><sup>0.72</sup> exp(-25.38/T<sub>e</sub>)</td><td>[57, 59, 65, 100]</td></tr><tr><td colspan="4"><strong>Reactions neutral-ion</strong></td></tr><tr><td>R21: Cl<sub>2</sub> + Cl<sup>+</sup> → Cl<sub>2</sub><sup>+</sup> + Cl</td><td>0.0</td><td>k<sub>35</sub> = 5.4 × 10<sup>-10</sup></td><td>[57, 59, 100]</td></tr><tr><td colspan="4"><strong>Reactions neutral-neutral</strong></td></tr><tr><td>R22: Cl<sub>2</sub> + 2Cl → 2Cl<sub>2</sub></td><td>0.0</td><td>k<sub>52</sub> = 3.5 × 10<sup>-27</sup> exp(810/T<sub>gas</sub>)</td><td>[57, 59]</td></tr><tr><td>R23: 2Cl + Cl → Cl<sub>2</sub> + Cl</td><td>0.0</td><td>k<sub>53</sub> = 8.75 × 10<sup>-28</sup> exp(810/T<sub>gas</sub>)</td><td>[57, 59]</td></tr><tr><td colspan="4"><strong>Reactions ion-ion, X is a non-chlorinated species</strong></td></tr><tr><td>R24: Cl<sup>-</sup> + Cl<sub>2</sub><sup>+</sup> → Cl<sub>2</sub> + Cl</td><td>0.0</td><td>k<sub>7</sub> = 5.0 × 10<sup>-8</sup>(300/T<sub>gas</sub>)<sup>0.5</sup></td><td>[57, 59, 100]</td></tr><tr><td>R25: Cl<sup>-</sup> + Cl<sup>+</sup> → Cl + Cl</td><td>0.0</td><td>k<sub>8</sub> = 5.0 × 10<sup>-8</sup>(300/T<sub>gas</sub>)<sup>0.5</sup></td><td>[57, 59, 100]</td></tr><tr><td>R26: Cl<sub>2</sub><sup>+</sup> + Cl<sup>-</sup> → 3Cl</td><td>0.0</td><td>k<sub>54</sub> = 5.0 × 10<sup>-8</sup>(300/T<sub>gas</sub>)<sup>0.5</sup></td><td>[59, 101]</td></tr><tr><td>R27: X<sup>+</sup> + Cl<sup>-</sup> → X + Cl</td><td>0.0</td><td>k<sub>55</sub> = 5.0 × 10<sup>-8</sup>(300/T<sub>gas</sub>)<sup>0.5</sup></td><td>[58]</td></tr></tbody></table>

<table><caption>**Table 9.** Excitation and de-excitation reactions for Cl₂.</caption><thead><tr><th>Reaction</th><th>Threshold energy (eV)</th><th>Reaction rate (cm³ s⁻¹)</th><th>Reference</th></tr></thead><tbody><tr><td colspan="4"><strong>Vibrational excitation</strong></td></tr><tr><td>R28: e + Cl₂(ν = 0) → Cl₂(ν = 1) + e</td><td>0.07</td><td>k<sub>36</sub> = 4.35 × 10<sup>-10</sup>T<sub>e</sub><sup>-1.48</sup> exp(-0.76/T<sub>e</sub>)</td><td>[57, 59, 100]</td></tr><tr><td>R29: e + Cl₂(ν = 0) → Cl₂(ν = 2) + e</td><td>0.14</td><td>k<sub>37</sub> = 8.10 × 10<sup>-11</sup>T<sub>e</sub><sup>-1.48</sup> exp(-0.68/T<sub>e</sub>)</td><td>[57, 59, 100]</td></tr><tr><td>R30: e + Cl₂(ν = 0) → Cl₂(ν = 3) + e</td><td>0.21</td><td>k<sub>38</sub> = 2.39 × 10<sup>-11</sup>T<sub>e</sub><sup>-1.49</sup> exp(-0.64/T<sub>e</sub>)</td><td>[57, 59, 100]</td></tr><tr><td>R31: e + Cl₂(ν = 1) → Cl₂(ν = 2) + e</td><td>0.07</td><td>k<sub>31</sub> = 1.04 × 10<sup>-9</sup>T<sub>e</sub><sup>-1.48</sup> exp(-0.73/T<sub>e</sub>)</td><td>[57, 59, 100]</td></tr><tr><td>R32: e + Cl₂(ν = 1) → Cl₂(ν = 3) + e</td><td>0.14</td><td>k<sub>32</sub> = 2.98 × 10<sup>-10</sup>T<sub>e</sub><sup>-1.48</sup> exp(-0.67/T<sub>e</sub>)</td><td>[57, 59, 100]</td></tr><tr><td>R33: e + Cl₂(ν = 2) → Cl₂(ν = 3) + e</td><td>0.07</td><td>k<sub>33</sub> = 1.04 × 10<sup>-10</sup>T<sub>e</sub><sup>-1.48</sup> exp(-0.73/T<sub>e</sub>)</td><td>[57, 59, 100]</td></tr><tr><td>R34: e + Cl₂(ν = 0-3) → Cl₂(ν = 0-3) + e</td><td>0.0</td><td>k<sub>21</sub> = 9.24 × 10<sup>-9</sup> exp(-11.15/T<sub>e</sub>)</td><td>[57, 59, 100]</td></tr><tr><td colspan="4"><strong>Excitation by electronic impact</strong></td></tr><tr><td>R35: e + Cl → Cl(4s) + e</td><td>9.1</td><td>k<sub>25</sub> = 2.0 × 10<sup>-8</sup> exp(-10.5/T<sub>e</sub>)</td><td>[57, 59, 100-102]</td></tr><tr><td>R36: e + Cl → Cl(4p) + e</td><td>10.5</td><td>k<sub>24</sub> = 3.0 × 10<sup>-8</sup> exp(-8.0/T<sub>e</sub>)</td><td>[57, 59, 100-102]</td></tr><tr><td>R37: e + Cl → Cl(3d) + e</td><td>11.2</td><td>k<sub>22</sub> = 2.0 × 10<sup>-8</sup> exp(-11.0/T<sub>e</sub>)</td><td>[57, 59, 100-102]</td></tr><tr><td>R38: e + Cl → Cl(5s) + e</td><td>11.4</td><td>k<sub>56</sub> = 4.0 × 10<sup>-9</sup> exp(-11.5/T<sub>e</sub>)</td><td>[101, 102]</td></tr><tr><td>R39: e + Cl → Cl(5p) + e</td><td>11.8</td><td>k<sub>57</sub> = 1.5 × 10<sup>-8</sup> exp(-11.77/T<sub>e</sub>)</td><td>[57, 59, 100-102]</td></tr><tr><td>R40: e + Cl → Cl(4d) + e</td><td>12.0</td><td>k<sub>23</sub> = 1.27 × 10<sup>-8</sup> exp(-12.0/T<sub>e</sub>)</td><td>[57, 59, 100-102]</td></tr><tr><td>R41: e + Cl → Cl(6s) + e</td><td>12.1</td><td>k<sub>58</sub> = 1.27 × 10<sup>-9</sup> exp(-11.0/T<sub>e</sub>)</td><td>[101, 102]</td></tr><tr><td>R42: e + Cl → Cl(5d) + e</td><td>12.4</td><td>k<sub>59</sub> = 7.00 × 10<sup>-9</sup> exp(-13.0/T<sub>e</sub>)</td><td>[57, 59, 100-102]</td></tr><tr><td colspan="4"><strong>Radiative de-excitation</strong></td></tr><tr><td>R43: Cl(4s) → Cl + hν</td><td>0.0</td><td>k<sub>39</sub> = 2.03 × 10<sup>6</sup></td><td>[69, 100]</td></tr><tr><td>R44: Cl(4p) → Cl + hν</td><td>0.0</td><td>k<sub>40</sub> = 3.3 × 10<sup>7</sup></td><td>[69, 100]</td></tr><tr><td>R45: Cl(3d) → Cl + hν</td><td>0.0</td><td>k<sub>41</sub> = 1.83 × 10<sup>6</sup></td><td>[69, 100]</td></tr><tr><td>R46: Cl(A, C)ouCl₂(B) → Cl₂ + hν</td><td>0.0</td><td>k<sub>43</sub> and k<sub>44</sub> = 4.74 × 10<sup>8</sup></td><td>[69, 100]</td></tr></tbody></table>

<table><caption>**Table 10.** Surface reactions for Cl₂.</caption><thead><tr><th>Reaction</th><th>β<sub>Cl</sub></th><th>Reaction rate (cm³ s⁻¹)</th><th>Reference</th></tr></thead><tbody><tr><td colspan="4"><strong>Neutrals-walls reactions, considering coefficient β at wall temperature</strong></td></tr><tr><td>Rs1: Cl + wall → 1/2Cl₂ + wall</td><td>0.13</td><td>k<sub>5230</sub> = <div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding: 0 5px;">D<sub>ab</sub></div><div style="padding: 0 5px;">λ<sub>0</sub><sup>2</sup> + <sup>2f<sub>0</sub>D<sub>ab</sub></sup>&frasl;<sub>λ<sub>th</sub></sub> + <sup>(2-β<sub>Cl</sub>)</sup>&frasl;<sub>βCl</sub></div></div></td><td>[100]</td></tr><tr><td>Rs2: Cl + wall → Cl(4s, 4p, 3d) + wall</td><td>0.13</td><td>k<sub>230</sub> = <div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding: 0 5px;">D<sub>ab</sub></div><div style="padding: 0 5px;">λ<sub>0</sub><sup>2</sup> + <sup>2f<sub>0</sub>D<sub>ab</sub></sup>&frasl;<sub>λ<sub>th</sub></sub> + <sup>(2-β<sub>Cl</sub>)</sup>&frasl;<sub>βCl</sub></div></div></td><td>[100]</td></tr><tr><td>Rs3: Cl(4s, 4p, 3d) + wall → Cl + wall</td><td>0.13</td><td>k<sub>235</sub> = <div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding: 0 5px;">D<sub>ab</sub></div><div style="padding: 0 5px;">λ<sub>0</sub><sup>2</sup> + <sup>2f<sub>0</sub>D<sub>ab</sub></sup>&frasl;<sub>λ<sub>th</sub></sub> + <sup>(2-β<sub>Cl</sub>)</sup>&frasl;<sub>βCl</sub></div></div></td><td>[100]</td></tr><tr><td>Rs4: Cl₂(A, C)ouCl₂(B) + wall → Cl₂ + wall</td><td>0.13</td><td>k<sub>236</sub> = <div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding: 0 5px;">D<sub>ab</sub></div><div style="padding: 0 5px;">λ<sub>0</sub><sup>2</sup> + <sup>2f<sub>0</sub>D<sub>ab</sub></sup>&frasl;<sub>λ<sub>th</sub></sub> + <sup>(2-β<sub>Cl</sub>)</sup>&frasl;<sub>βCl</sub></div></div></td><td>[100]</td></tr><tr><td colspan="4"><strong>Ions-walls reactions</strong></td></tr><tr><td>Rs5: Cl<sup>+</sup> + wall → Cl + wall*</td><td></td><td>k<sub>18</sub> = 2μ<sub>B,Cl</sub> + (<div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding: 0 5px;">h<sub>L</sub></div><div style="padding: 0 5px;">R</div></div> + <div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding: 0 5px;">h<sub>R</sub></div><div style="padding: 0 5px;">R</div></div>)</td><td>[54, 100]</td></tr><tr><td>Rs6: Cl<sub>2</sub><sup>+</sup> + wall → Cl₂ + wall*</td><td></td><td>k<sub>11</sub> = 2μ<sub>B,Cl₂</sub> + (<div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding: 0 5px;">h<sub>L</sub></div><div style="padding: 0 5px;">R</div></div> + <div style="display: inline-block; vertical-align: middle; text-align: center;"><div style="border-bottom: 1px solid black; padding: 0 5px;">h<sub>R</sub></div><div style="padding: 0 5px;">R</div></div>)</td><td>[54, 100]</td></tr></tbody></table>