TiN hard coating as a candidate reference material for surface metrology in chemistry: characterization and quantification by bulk and surface analyses techniques

: This study presents the synthesis and characterization of TiN hard coatings as a candidate reference material for surface metrology in chemistry. TiN coatings were grown on a silicon wafer with (111) orientation using dc reactive magnetron sputtering. X-ray diffraction confirms that the diffraction phase of TiN coatings is polycrystalline, electron microscopy demonstrates that the TiN coatings presents pyrami-dal-shaped grains ranging from sub-micrometer to nano-size scale and with an average thickness of 666 nm. According to micro Raman results, the presence of LO phonon modes confirms that the TiN coatings are crystalline in nature and no impurities are detected. The mechanical properties at the nanoscale are evaluated using resonance tracking acoustic force atomic microscopy. The chemical composition of the TiN reveals a close 1:1 atomic ratio. The ANOVA is used to evaluate the homogeneity of the TiN via a homogeneity test according to the ISO Guide 35:2017, while, regarding the chemical composition of the Ti, the Fisher’s test demonstrates that the batch can be considered as homogeneous.


INTRODUCTION
Surface metrology and nano-metrology worldwide play a key role for measurements of advanced and emerging materials. In this way, the National Center of Metrology (CENAM, for its initials in Spanish) in Mexico has actively participated in different international groups such as the Working Group on Surface Analysis of the Comité Consultatif pour la Quantité de Matière (CCQM, for its initials in French), in the "Versailles Project on Advanced Materials and Standards" (VAMAS), and the Asia-Pacific Economic Cooperation. In a Latin-American context, the CENAM has participated in the "Mexican Society of Materials", where several research institutes as well as private and government companies are included. A substantial growth in the industrialization of technology has allowed an increasing need for researching and developing reference materials (RMs) since the existing market for these materials is still very low (Mathia et al., 2011;Kim et al., 2021;Wolfgang et al., 2022;Ferrarini et al., 2022).
As it has been largely reported in literature, hard coatings are widely used due to their tribological, morphological and structural properties as well as their chemical composition. Among these hard coatings, CNx and nitride-based compounds (TiNC, TiC and TiN), they are all broadly used due to their good hardness, they have a hardness between 15 to 40 GP, thermal conductivity between 25 to 260 W/mK and wear resistance, modulus of elasticity between 180 to 370 GP, (Caicedo et al., 2006;Ipaz Caustumal and Zambrano, 2013). In this context, the titanium nitride (TiN) is a well-known compound since it is widely applied as a biocompatible material (Hussein et al., 2020), protective coating (Feng et al., 2017), electrodes (Mustapha and Fekkai, 2020) and diffusion barriers in microelectronics (Silva et al., 2020).
It was presumed that a TiN barrier layer with a random array of pinholes could be coupled with an adaptive coating layer to limit lubricant transport to the coating surface only through those holes, thus reducing the rate of lubricant depletion in the adaptive coating layer and prolonging the life of the coating during sliding wear at elevated temperatures, Muratore et al. (2007).
Other applications of TiN thin films for the metal industry are, eliminates galling, fretting, micro welding, seizing and adhesive wear, smooth operation of moving components, wear resistance on precision components, holds sharp edges or corners, cavitation erosion, erosion resistance, non-stick surface, most materials will not adhere to TiN, low friction, little dimensional impact, perfect for close tolerance parts, enhances corrosion resistance, Matthews (1985). Therefore, the understanding of the thermophysical and physicochemical properties for hard coatings become important in order to manage their features as a possible candidate in what RMs are concerned.
The need for RMs -according to international normative-has allowed the synthesis of hard coating via several approaches, ISO Guide 35 (2017); ISO 20579-4 (2018). For example, chemical vapor deposition (CVD), physical vapor deposition (PVD), vacuum-arc method and magnetron-sputtering (MS) are the techniques more widely used to deposit hard coatings. Among these techniques, MS is commonly used to deposit hard transition metal nitrides and oxides, which are used in a wide range of relevant industrial coatings.
The need to compare testing results between laboratories in different countries has favored the design and synthesis to provide reference materials, known as standard samples. Since the reliability of all testing results in surface metrology and nano-metrology are completely dependent on the availability of RMs. Consequently, this work has the objective of introducing the TiN hard coating as a candidate reference material for surface metrology. Along with this, the TiN hard coating is characterized by several bulk and surface techniques. In this work, the result of interaction between the factors and the products of these factors is evaluated with the analysis of variance (ANOVA). Also, ANOVA is applied to evaluate the homogeneity of the TiN hard coating.
Currently, another problem is the lack of calibration standards that globally maintain the reliability and reproducibility of measuring results. They provide an independent reference with respect to the location, measuring device and environment. This immanently important property is a vital prerequisite to ensure a constant and invariable quality of the producing industry and for process control. The limited number of available certified reference materials (CRMs) for thin film analysis and in parallel the growing market of novel thin film materials induces a growing gap of required calibration samples (Wolfgang et al., 2022).
One example of such advanced thin films is the compound semiconductor material Cu(In 1-x Ga x )Se 2 (shortly CIGS) which is used as an absorber material for thin film solar cells. The band gap of this CIGS material can be enhanced by increasing the Gallium (Ga) to Indium (In) ratio. Thus, by tuning the in-depth elemental distribution, the energy conversion efficiency of the device can be optimized. For such materials no certified reference materials are available to for instance use them as calibration samples for inline process control, real-time investigations during film deposition, or quality management (Marinenko et al., 2004;Ferrarini et al., 2022).

Materials
Initially, a magnetron-sputtering vapor deposition system (Intercovamex Sputtering V3) was optimized for the synthesis of TiN coatings, varying and optimizing the system parameters (power to use from 100 W to 500 W, working pressure 1×10 -3 Pa to 5×10 -3 Pa, Ti targets 98% to 99.99% of purity, nitrogen 99% purity flow from 4% to 16% mass percent in relation to the mixture of Ar/N 2 , distance between target and substrate from 4 cm to 6 cm, time of deposit from 5 minutes to 12 minutes and cleaning of substrates), the temperature of the substrate was the same as that of the MS chamber, it was not possible to measure it, the equipment does not have a plate rotation.
Initially, through the MS process samples of approximately 2.5 cm 2 were obtained from the silicon wafer. These were cut to obtain a batch of 19 films of TiN on silicon (111), with an area of ~ 0.5 cm 2 . The samples were labeled according to the experiment number, mounting a silicon substrate on the magnetron sputtering plate is as shown in Fig. 1, a) first, the glass object holder is placed, which is attached with the kapton tape and in the center the silicon adhered to one of its ends is placed, b) Obtaining the TiN film on the silicon substrate and on the glass object holder.
The homogeneity analysis was done by using four samples, the first and the last samples (M1 and M19) and two other samples were chosen randomly, according to the sampling theory (Rossbach and Grobecker, 1999;Chen et al., 2019).

Synthesis of the coatings
The hard coatings were prepared using a DC pulsed magnetron sputtering (Intercovamex Sput-tering V3) in stable regimen to sputtering titanium (target for Stanford Advance Materials, 7.5 cm diameter, 0.64 cm thick, purity >99.99 wt.-%) in N 2 (99.9%) and Ar (99.9%) mixed atmosphere. Before deposition, the chamber was pumped down to a base pressure below 3×10 -3 Pa, and then the samples were sputter-cleared with Ar + ions at 800 V for 20 min. The deposition pressure was 1×10 -5 Pa. After that, TiN hard coatings were deposited for 10 min under a mixed atmosphere, Ar + N 2 . The TiN hard coatings were deposited according to the following deposition parameters: Atmosphere: Ar:N 2 (9:1); Chamber pressure: 0.4 Pa; Bias voltage: 120 V; deposition time 10 minutes; Current of titanium target: 3 A with a 381 W power; distance between target and substrate 0.05 m. A wafer of silicon with (111) orientation.
The Si (111) substrates (99.9% of purity) of 2.5 cm were obtained from a single sided polished silicon dicing wafer, 12.7 cm of diameter, 1 mm of thickness and roughness <0.5 nm, then were cleaned with phosphate-free soap and then, these were rinsed in double-distilled water. After that, the substrates were ultrasonically cleaned in an aqueous mixture (50% Xylene and 50% ethyl alcohol) for 8 minutes. Once the sonication concluded, the substrates were immersed into analytical grade ethyl alcohol. Finally, the substrates were dried under a nitrogen gas atmosphere.

Characterization of the coatings
Microstructure and chemical composition of the obtained coatings were traced by electron probe micro-analyzer (EPMA) (Rojas-Chávez et al., 2018), using a JEOL JXA 8530F hyper probe, equipped with WDS and EDS detectors (Falcone et al., 2006;Fazel et al., 2020). The crystallographic phases were analyzed via X-ray diffraction technique (RIGAKU Dmax 2100 diffractometer), the radiation generating tube is made of Copper (Kα1=1.5406 A), The patternsX-ray diffraction were obtained with a grazing incidence angle of α= 2° and a scanning speed of 0.5°/min, step of 0.02°. sweep angle from 30° to 80°. The structural changes of the coatings were measured using Raman spectrometry (Thermo Fisher DXR equipment), the surface of the samples was focused with 50X objective, 50 scans were acquired for each analysis with a laser of 532 nm (green), pinhole of 50 μm, grid of 900 lines / mm (low resolution) and 9 mW of power (Spengler and Kaiser, 1976).
Resonance-Tracking Atomic Force Acoustic Microscopy (RT-AFAM) technique (Senthilkumar et al., 2005;Enriquez-Flores et al., 2012), was carried out on a commercial SPM system (Bruker/Veeco/Digital Instruments Nanoscope IV Dimension 3100 AFM). This AFM process was also performed with a closed-loop x-y nanopositioning stage (nPoint, Inc. NPXY100). A signal access module (SAM) accessory was used as well for interfacing the signal input/output to the AFM. The unfiltered photodiode signal input to a Stanford Research Systems SR844 high-frequency lock-in amplifier. The sweeping frequency excitation signal required was obtained by an HP/Agilent 33 120A function generator. Budget Sensors diamond-coated silicon probe, using 450 µm long with a 3.0 N/m spring constant and using a National Instruments DAQ NI-PCI-6133 card for data acquisition.
Nanoindentation, tests were done on an IBIS 2 Nanoindenter from Fischer-Cripps Laboratories, in a downward charge range of 30 mN to 12.5 mN with Vickers indenter.
The ANOVA was used to evaluate the homogeneity of the alloy via a homogeneity test according with the ISO Guide 35 (2017) and Ellison (2015), which was useful to evaluate the variability of data. Precision was estimated under repeatability conditions, whose value was obtained of 5% and -according to the results of the ANOVA-it was found that the material was homogenous (Martin and Games, 1977;Hartung et al., 2002).

X ray diffraction
The X-ray diffraction patterns in Fig. 2 indicates that the as-deposited TiN coating is highly crystalline. As it is shown in that figure, the TiN coating exhibits a NaCl-type crystal structure where five Bragg's reflections (111), (200), (220), (311) and (222) correspond to FCC-TiN. These planes were associated with the PDF file 65-0715. It is worth noting that the TiN coating shows a strong (220) preferred orientation.
The capability of the strategy used in this work is more noticeable when it is compared with other strategies used with the MS process. For example, even though Lu et al. modified the TiN preferred orientation (Lu et al., 2020), they reported a poor crystallinity for the FCC-TiN when the nitrogen content was modified. Moreover, Mustapha and Fekkai reported that the substrate has a good impact on the crystalline structure of the TiN, but it affects the appearance of the Bragg's reflections (Mustapha and Fekkai, 2020).
The crystal size, from the most prominent diffraction peak, of the as-deposited TiN coating was determined using the Scherrer equation, Cullity and Stock (2001): (1) where D hkl is the grain size in the direction perpendicular to the lattice planes, hkl are the Miller indices of the planes belonging to the diffraction peak that is being analyzed, k is the shape factor, λ = 1.54 Å is the X-ray wavelength, θ is the diffraction angle, and β hkl is the full width at half maximum (FWHM) of the diffraction peak (in rad), (Cullity and Stock, 2001;Xiao et al., 2007;Chen et al., 2019;Silva et al., 2020).

Structural and chemical analyses
TiN coatings were deposited by MS, the SEM images indicate that the as-deposited TiN film is crystalline, see Fig. 3a. Based on SEM results, in Fig. 3a, the thickness of the as-deposited TiN thin film was determined to be 0.66 ± 0.04 μm where the deviation of 0.04 μm corresponds to the calculated standard deviation, while the Ra roughness measured was 15.97 nm ± 5.5 nm. Thickness and roughness were obtained using a Bruker Contour model profilometer, GT InMotion 3D and the tool for visualization and analysis of SPM data. Based on the results of the thickness of the film, a deposit speed of 60 nm/min was obtained.
As it can be seen in Fig. 3b, the structure of the TiN coating is examined via electron microscpy, as clear- TiN hard coating as a candidate reference material for surface metrology in chemistry: characterization and quantification... ly shown in this figure, the TiN presents a pyramidal-shaped grains with texture associated to the surface roughness, as it has been reported in the literature (Fazel et al., 2020). That is to say, the surface of the TiN is relatively rough with a visually compact texture, see Fig. 3c. However, the morphology of TiN is ranging from the submicrometer to nano-size scale, just as it is shown in Fig. 3d. The average crystal size estimated was 117 ± 36 nm from these electron microscopy images, it was obtained by adding the two sides (1 and 2) of the crystals and then obtaining their average, Fig.  3c and 3d. Such results are in good agreement with the results obtained from Scherer's equation, crystal size found from 85 to 115 nm, Compared with the microstructure reported by Yang et al. (2020), the as-deposited TiN coatings obtained in this work had the same pyramidal-shape, but without the need to vary the N 2 flow rate (Lu et al., 2020;Das et al., 2021). Figure 4 shows the characteristic X-ray spectra obtained by WDS from the TiN film using the PETH, LiF and LDE2 crystals. The calibration of the crystals used for the elements of interest was done with titanium 99.99% purity and aluminum nitride 99.99% purity as references, both materials from Micro Analysis Consultants. The NIST certified reference material NIST SRM ® 2061 TiAl (NbW) Alloy for Microanalysis (Marinenko et al., 2004), was used as the control material, which has a certified chemical composition for Ti of 53.92 ± 0.34 mass %.  Elemental chemical composition for titanium and nitrogen was obtained from different areas on 3 different days, to evaluate repeatability and reproducibility at the surface and in the longitudinal section of the sample, to estimate the chemical composition different measurements have been carried out as highlighted in the images of Fig. 5: a) seven different areas; b) different points along the sample and c) the longitudinal section. see Fig. 5. Average chemical composition for each sample is presented in Table 1, the average was obtained from punctual and linear measurements (with a beam size of 1 µm and 20 points every 100 µm) and from the measured areas of approximately 1000 µm 2 .
As shown in Table 2, the homogeneity results obtained for the thickness of the films were performed via ANOVA, the samples M1, M8, M15 and M19 were measured in triplicates.
Regarding the chemical composition of the Ti, the ANOVA and Fisher's tests demonstrated that the batch can be considered as homogeneous. Such homogeneity was supported by the analysis of variance, considering F calculated =0.09 and F critical =4.07. Therefore, the reference material candidate presented in this work meets the proper homogeneity for the intended purpose in this study.
As shown in Table 3 and Table 4, the homogeneity results obtained for the thickness of the films were performed via ANOVA, the samples M1, M8, M15 and M19 were measured in triplicates.
According to the Fisher test, the homogeneity of the batch is met when the variances among the samples are satisfied. Using the null hypothesis, it can be expressed as Ho: F calculated < F critical . For this case, it was obtained F calculated = 0.45 and F critical = 4.07 which satisfies the null hypothesis.    Figure 6 shows the characteristic Raman spectra of samples M1 and M19 in the range of 100 to 900 cm −1 . Both spectra show strong peaks centered at 215, 328, 548 and 656 cm −1 . The characteristic peak at 215 cm -1 is assigned to transverse acoustic (TA) / longitudinal acoustic (LA) modes of TiN, while the peak at 548.71 cm −1 is assigned to transverse optic (TO) / longitudinal optic (LO) modes of TiN. It is worth noting that the presence of LO phonon modes confirms that the as-deposited TiN coatings are crystalline in nature (Spengler and Kaiser, 1976), which is in good agreement with the results determined by XRD and electron microscopy. Furthermore, the assigned peaks are in accordance with the reported Raman studies for TiN films (Spengler and Kaiser, 1976).

Mechanical properties
Figures 7 and 8, shows the results obtained via RT-AF-AM where fused silicon was used to calibrate the equip-ment. In this figure, topography, frequency, elasticity modulus and the histogram of the elasticity modulus of the as-deposited TiN coating are presented. Figure 7a and Fig. 8a shows the topography of the samples M1 and M19, respectively. Although the topography shows rounded grains with size distribution larger than 50 nm, it   is worth keeping in mind that the XRD and the electron microscopy images showed congruent results. Additionally, it was measured a Ra roughness of ~10 nm that corresponds to a very flat surface compared with the results reported by Fazel and coworkers (Fazel et al., 2020). The frequency is shown in Fig. 7b and Fig. 8b in the range of 5.15 × 10 5 -5.45 × 10 5 Hz, the image depicts regions of common resonance frequencies as domains distributed on the surface. It is important to mention that the frequency variations detected were related to the tip-sample contact stiffness. Such changes can be associated with the topography or due to the non-uniform distribution of the elastic modulus of the sample, as has been reported in literature (Enriquez-Flores et al., 2012). The resonance frequency of the widespread domains has a value of approximately 538 kHz.
In Fig. 7c and Fig. 8c, the elasticity modulus of the as-deposited TiN coating is shown. It was calculated from resonance frequency measurements, as has been reported in literature (Enriquez-Flores et al., 2012). In this figure, the elastic domains are observed, the highest value of elasticity modulus is ~203 GPa, which is shown in light orange color. In the edge of this elastic domain a small area with different domain is observed, this domain has an elasticity modulus of ~195 GPa which is shown in light green color. Moreover, in the edge of these domains, a third domain is observed with ~185 GPa of elasticity modulus, which is shown in blue color. One can infer that the three domains can make a structure that benefits the hardening of the as-deposited TiN coating; that is to say, the TiN coating has the same mechanical properties. The elasticity modulus, Fig. 7c and Fig. 8c, can be more easily interpreted by means of its histogram, see Fig. 7d and Fig. 8d.
The average indentation hardness (HIT) obtained was 17 ± 3.1 GPa. Hernández et al. (2011) obtained comparable nanohardness values of 17.6, 31.0 to 23.3 GPa, So far the experimental findings in the areas of chemical stability and mechanical properties show significant results to propose TiN as a reference material. Nonetheless, we suggest that further experimentation needs to be accomplished for that purpose, for example, analysis with other surface analysis techniques such as XPS for the evaluation of impurities, or analysis by wet method such as ICP-MS or ICP-MS.

CONCLUSIONS
− TiN coatings were grown over silicon (111) substrates using dc reactive magnetron sputtering under a mixed atmosphere, Ar+N 2 . In this study the composition, microstructure and mechanical properties were investigated. The main results are shown as follows: − The TiN coating exhibited a single FCC structure and it presented a strong (220) preferred orientation. The average grain size estimated from microscopy was in good agreement with the results obtained from Scherer's equation. In addition to this, the presence of LO phonon modes, detected by micro Raman, confirmed that the as-deposited TiN coatings were crystalline in nature, which was in good agreement with the experimental findings determined by XRD and EPMA. − RT-AFAM results showed that the TiN coating exhibited a nanostructure of elastic domains, being the principal elastic domain ranging from ~203 to ~208 GPa. However, the elastic domains performed like nanostructure arrangements for hardening should act as a barrier for plastic deformations, which confers a high hardness, which was similar to that reported for this type of thin films. − Elemental chemical composition for titanium was obtained as Ti 59.7% mass fraction. The ANOVA demonstrated the homogeneity of the TiN according to the ISO Guide 35:2017, while regarding the chemical composition of the Ti, Fisher's test demonstrated that the batch can be considered as homogeneous. − Therefore, we can state that the chemical homogeneity and microstructure properties make TiN coating an eligible material to continue with the process of certification as a reference material to evaluate the mass % of Ti in the thin films.