Acta Polytechnica CTU Proceedings https://doi.org/10.14311/APP.2024.50.0036 Acta Polytechnica CTU Proceedings 50:36–43, 2024 © 2024 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague SUBSTRATE EFFECT IN THE EVALUATION OF ELASTIC MODULUS OF THIN PVD COATINGS FROM NANOINDENTATION František Lofaj Slovak Academy of Sciences, Institute of Materials Research, Watsonova 47, 040 01 Košice, Slovakia correspondence: flofaj@saske.sk Abstract. The comparison of nanoindentation results on reactive HiTUS TiZrHf+ME-Ny (ME = Nb, V, Ta and VNbTa) and reactive DCMS NbMoTaW coatings showed that the influence of substrate stiffness is still not fully eliminated in the evaluation of indentation modulus. To obtain comparable results by keeping the systematic error resulting from the existing evaluation procedures the same, nanoindentation should be performed using the same test parameters, a method for depth profile acquisition, a data evaluation procedure, and coatings with similar thicknesses on the same type of substrate. Applying these rules to nanoindentation on TiZrHf+ME-Ny coatings showed that the addition of ME = Nb, V, Ta, and VNbTa caused some degradation of mechanical properties indicating negligible or even negative “cocktail effect”. Keywords: Thin PVD films, nanoindentation, substrate effect elimination, multi-element nitride coatings. 1. Introduction The nanoindentation testing on thin hard coat- ing/softer substrate (and vice versa) systems always generates “composite” values due to simultaneous loading and response from the coating and substrate. The problem can be solved using several different approaches. Possibly the first way to extract coat- ing hardness from the composite values and known as “10% (relative depth) rule”, was proposed by H. Bückle in 1959 [1]. It was suggested that the hardness val- ues obtained from the relative depths below 10% of the coating thickness should be used because the contribution from the substrate would still be very limited. Unfortunately, this rule fully corresponds to the H. L. Mencken quote: “For every complex prob- lem there is an answer which is clear, simple and wrong” [2]. It is only a rule of thumb with limited applicability to hardness measurements and its use for the determination of an indentation modulus is principally not correct [3, 4]. The reason is that the size of the plastic field under the indenter defined by the yield stress can be confined only to the coating within the limited penetration depth range whereas the elastic field would extend into the substrate with- out any limit. Moreover, the stress field is affected by the ratio between elastic moduli of the coating and substrate and even by their interactions [5, 6]. Since the “10% rule” is not able to reflect all these interactions, significant efforts were devoted to the re- finement of the analysis of nanoindentation data from thin coatings. Starting from the early 1990s, various theoretical models have been developed to solve the problem of substrate effect analytically. The common features of these solutions were that they considered indentation as a deformation of coating and substrate in series and that they were fitted to experimentally obtain hardness and indentation modulus (relative) depth profiles. Depending on the physical processes obtained in the solutions, three groups of the models can be distinguished: (1.) linear transition models involving the works of Jönsson&Hogmark [7], Burnett&Rickerby [8], Do- erner&Nix [9], He&Li [10], Chicot&Lesage [11], Puchi-Cabrera [12], etc.; (2.) energy models including works of Korsun- sky&Bull [13, 14], (3.) Gao’s model & its modifications including studies of Gao&Chiu [15], Menčík [16], Song&Pharr [17], Hay&Crawford [5] etc. Most of these models, were applicable only to the coating/substrate systems in which the elastic mod- ulus of the coating was less than twice that of the substrate [5]. However, very stiff coatings can pro- vide additional support against the deformation of the substrate. The additional and parallel influence of the coating on the substrate was introduced into the Song&Pharr’s model [17] by Hay&Crawford (H&C) [5]. H&C model applies to the systems with ≤ 10-fold ra- tio between the elastic moduli of coating and substrate and the range of relative indentation depths (plateau width) available for the extrapolation to zero depth was expanded well above 10% relative depth. The disadvantage is that the obtained indentation moduli are highly sensitive to the accuracy of the additional input parameters, especially Young’s modulus of the substrate and coating thickness. The results of theoretical works on nanoindentation in coating/substrate systems were reflected in the standardization efforts which were summarized in ISO 14577-4:2016 standard [18]. It prescribes that the true hardness and modulus of hard coatings on softer 36 https://doi.org/10.14311/APP.2024.50.0036 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 50/2024 Substrate effect in the evaluation of elastic modulus . . . Substrate Young’s modulus Poisson’s ratio HIT # EIT # E [GPa] ν [–] [GPa] [GPa] (0001) sapphire 435 [25] 0.29 [25] 27.57 ± 0.27 458.7 ± 3.3 tempered 100Cr6 steel 210 (190–210) [26, 27] 0.285 (0.27–.30) [27] 9.25 ± 1.0 250.0 ± 9.5 (111) Si wafer 187 (186.5) [28] 0.223 (0.22–0.28) [28] 13.07 ± 0.13 193.6 ± 1.2 Ti6Al4V alloy 114 [29] 0.342 [29] 5.20 ± 0.16 133.2 ± 2.2 Table 1. Mechanical properties of the substrates used in the calculations (E and ν, and measured by nanoindentation in CSM mode (HIT and EIT ). substrates can be determined by the extrapolation of the values from the plateau at the maximum of the corresponding profile to zero penetration depth (load). It should be noted that such a procedure does not explicitly involve any analytical solution and the way the corresponding depth profile was obtained. The simplest way to generate statistically reli- able hardness and modulus depth profiles is to per- form a sufficiently large number of individual load- ing/unloading tests until predefined depths in the range from less than 100 nm up to the depths approach- ing the coating thickness. Analogous depth profiles from the reduced number of indents can be obtained when several partial unloading/re-loadings are applied during the loading part of the loading/unloading tests. This mode is usually called “continuous multicycle” (CMC). Further advancement of CMC led to the “sinu- soidal loading” or “continuous stiffness measurements” (CSM) [19–22] mode which involves an overlap of continuous sinusoidal load with small (constant abso- lute or constant relative) amplitude and conventional continuous loading. The advantage of CSM mode is a much higher speed of the generation of the corre- sponding depth profiles with better accuracy from a smaller number of indents. Statistical reliability of CSM tests is further improved due to the reduction of thermal drift and low-frequency noise effects [21]. The disadvantage of CSM mode is the contribution of “plasticity error” causing deviations at lower fre- quencies, especially in the materials with high E/H ratio [22]. It is related to small plastic deformation added to the elastic deformation due to a higher total load at the end of the cycle than at its beginning. However, plasticity error can be corrected [21] or sig- nificantly reduced using an appropriate combination of amplitude, frequency and loading rate [22]. It can be also eliminated when using the so-called Quasi- CSM (QCSM) mode when sinusoidal oscillations are applied only to repeated, short dwell-time periods during a continuous loading cycle [23]. Regardless of the method depth profiles were ob- tained, ISO standard procedure should be used to deduce the corresponding coating properties with- out the influence of the substrate. Sinusoidal modes (CSM and CSMTF) seem to be easier, faster and more precise than CMC and loading/unloading tests. Moreover, the ISO procedure is already built in the evaluation software of sinusoidal modes including that on the H&C model and known as “CSM for thin films” (CSMTF) mode. However, a comprehensive comparison of the evaluation of nanoindentation re- sults considering different methods for depth profile generation, differences between conventional CSM and CSM treated based on the H&C model with the effect of substrate properties are still missing. Therefore, the current work aimed to quantify the differences in the obtained hardness and moduli from the depth profiles obtained using different modes and on the coating/substrate systems with different sub- strate’s Young’s moduli on the statistically sufficient set of coatings. The work is the extension of our pre- vious on 4 different substrates [24] from one up to six types of multi-transition metal-nitride ((TiZrHf+ME)- Ny, where ME = V, Nb, Ta and NbMoTaW-Ny) coat- ings with different stoichiometry spanning from pure metallic high entropy stabilized alloys (y = 0) up to stoichiometric nitrides (y = 1). 2. Materials and methods 2.1. Coating deposition The studied coatings were deposited by sputtering on four different substrates from six different compos- ite targets. The substrates involved polished single crystalline (111) Si and (0001) sapphire wafers, the polished discs of polycrystalline tempered 100Cr6 steel and Ti6Al4V alloy with different elastic moduli (see Table 1). The targets included TiZrHf, TiZrHfV, TiZrHfNb, TiZrHfTa, TiNbVTaZrHf and NbMoTaW discs with the diameters 76.2mm and thicknesses of around 6.35mm (Table 2). The TiZrHf-based nitride coatings were produced by reactive High Target Utilization Sputtering (model S500, Plasma Quest Ltd., UK) from the above targets under the sputtering conditions optimized earlier [30] and applying different flows of nitrogen, x (in standard cubic centimeters per minute, sccm), into the sputter- ing Ar atmosphere (120 sccm). The values of x were usually in the range 0–10 sccm when stoichiometric composition was achieved. The structure and com- position of these coatings were described earlier [30]. The metallic NbMoTaW coating was deposited us- ing balanced DC magnetron sputtering at 300W on a sapphire substrate heated to 500 °C at a floating bias. 37 František Lofaj Acta Polytechnica CTU Proceedings Target Ti Zr Hf Nb V Ta Mo W [%] [%] [%] [%] [%] [%] [%] [%] TiZrHf (99.6 %)# 33 33 34 – – – – – TiZrHfV (>99.5 %)* 32 18 18 – 32 – – – TiZrHfNb (>99.5 %)* 33 19 19 29 TiZrHfTa (>99.5 %)* 33 19 19 – – 29 – – TiNbVTaZrHf (>99.5 %)* 20 12 12 18 20 18 – – NbMoTaV (>99.9 %)* – – – 25 – 25 25 25 *Testbourne, Ltd.; # Porexi Table 2. The list of the targets and their nominal compositions used for the deposition of the studied nitride coatings. 2.2. Nanoindentation Nanoindentation tests were performed with freshly calibrated Berkovich diamond tip in G 200 (Agi- lent/KLA, USA) nanoindenter under load control with the constant strain rate of 0.05 s−1 using four tech- niques – loading/unloading, CMC, CSM and CSMTF. In both CSM cases, the frequency of 45Hz and the am- plitude of 2 nm were applied to reduce the contribution of plastic deformation during sinusoidal loading [22]. On each coating, two sets of 16 indents up to 600 (or 800) nm depth were carried out. The depth profiles were treated according to ISO 14577-4 with the lower limit of the plateau range of >80 nm determined by tip area calibration. The upper limit depended on the shape of the average depth profile and measurement mode: in the CSM case, the upper depth limit was often within 10% of the relative coating thickness whereas when Hay&Crawford correction [5] was con- sidered, it may exceed that depth due to improved consideration of substrate effect. The thicknesses of the coatings were measured using scanning electron microscopy (SEM, models Auriga Compact, Zeiss, Ger- many) on the fractured cross sections of the coatings deposited on Si wafers. 3. Results and Discussion 3.1. Depth profiles by different methods To compare the depth profiles generated using four different methods, only one TiZrHfVNbTa-xN coat- ing (x = 6 sccm N2) with stoichiometric (y = 1) composition and thickness of 1700 nm on the silicon wafer was used. Figure 1a shows the depth profile of the indentation modulus obtained using simple loading/unloading tests. Each value calculated us- ing Oliver&Pharr (O&P) method corresponds to the average from 10 indents and 9 different depths were employed to obtain the profile. The data were valid in the range above 80 nm. The extrapolation procedure from the plateau-like region from 80 nm up to 200 nm resulted in the indentation modulus, EIT = 295 ± 35GPa whereas the “10% rule” approach gave around 284GPa. The hardness values, HIT = 29.5 ± 2GPa were identical in both cases. (a). (b). Figure 1. Indentation modulus depth profiles ob- tained on TiZrHfVNbTa-xN coating (x = 6 sccm N2) on (111) silicon substrate using (A) – 90 simple load- ing/unloading tests; (B) – 30 tests with 6 partial unloadings in each test. The zone below 80 nm should not be considered due to indenter tip surface area calibration effects. 38 vol. 50/2024 Substrate effect in the evaluation of elastic modulus . . . Method EIT [GPa] EIT [GPa] HIT [GPa] HIT [GPa] ISO 10% rule ISO 10% rule loading/unloading 295 ± 35 ∼285 29.5 ± 2.0 29.5 CMC ∼300 (∼300) ∼28 ∼28 CSM 290 ± 15 ∼270–275 27.2 ± 2.6 27.2 CSM+H&C (CSMTF) 275 ± 15 ∼250 28.2 ± 2.7 28.2 Table 3. Summary of the indentation modulus and hardness values calculated using ISO and the “10% rule” procedures from the depth profiles by four different methods on 1700 nm thick TiZrHfVNbTa-xN coating (x = 6 sccm N2) deposited on (111) silicon substrate by reactive HiTUS. In the case of CMC tests (Figure 1b), 10 indents up to 100mN, 200mN and 250mN loads with 6 par- tial unloading in each test were performed. Each unloading was evaluated according to O&P method but the averaging was not performed due to variations in the depths during unloadings within each test. It resulted in relatively large scatter of the data and only rough estimate of the coating properties. The approx- imate indentation modulus was around 300GPa and hardness was 28GPa. Possible differences between ex- trapolation according to ISO standard and the “10% rule” were not observed due to excessive scatter of the data. In the case of CSM tests (Figure 2a), the average depth profile curve was smooth and large scatter was present only below 100 nm depths. The maximum at 100 nm was followed by a smooth decrease without a clear plateau. The calculation of the corresponding EIT depends on subjectively selected depth range lim- its. In the range from 100 nm to 150 nm, EIT = 290 ± 15GPa whereas only around 275GPa were obtained using the “10% rule” approach. The hardness profile exhibited a well-defined plateau up to 250 nm depth. Therefore, the same values of HIT of 27.2 ± 2.6GPa were obtained when applying ISO and the “10% rule” procedure. Figure 2b illustrates the effect of the cor- rection on substrate modulus and coating thickness included in H&C correction (CSMTF) on the modulus depth profile compared to the standard CSM profile. The differences are visible already in the 100–150 nm (“plateau”) depth region and increase with the increase of penetration depth. Subsequently, different inden- tation moduli (full arrows) were obtained from these regions in CSM (∼275GPa) and CSMTF (∼263GPa). The average values from 9 indents (after removal of the outcasts) based on ISO procedure resulted in the average EIT = 275 ± 15GPa. At 10% relative depth, the values were ∼270GPa and ∼250GPa, respectively. The hardness profile is not affected by the correction and it was HIT = 28.2 ± 2.7GPa. Table 3 compares the results of nanoindentation tests using four different methods for depth profiles and evaluated using ISO and the “10% rule” proce- dure. It should be emphasized that the results were obtained on the same and relatively thick (1700 nm) coating on silicon substrate, which eliminated possible effects of variations between coatings, substrates and (a). (b). Figure 2. An average (from ≤16 indents) indentation modulus depth profiles on TiZrHfVNbTa-xN coating (x = 6 sccm N2) on (111) silicon substrate using (A) – continuous stiffness measurements (CSM) tests; (B) – the comparison of EIT ) depth profiles from 1 indenta- tion test using CSM and CSM with the correction on substrate properties based on Hay&Crawford model (CSMTF). 39 František Lofaj Acta Polytechnica CTU Proceedings small thickness. The values of EIT (and HIT ) cal- culated according to ISO standard from the profiles obtained by different methods varied from 275GPa to 300GPa (and 27.2GPa to 29.5GPa), which was within the scatter of each measurement. Thus, all four methods are suitable for the determination of hardness and modulus profiles in coating/substrate systems. However, CSM-based methods are experi- mentally easier, faster, more effective and conservative, especially with the correction on substrate properties. The differences between EIT values calculated accord- ing to ISO and the “10% rule” procedures were also not very large and fully overlapped in HIT . However, it does not rehabilitate the “10% rule” approach be- cause the coating was relatively thick which could shield the substrate and prevent the collision of the calculation range with the lower limit of validity range. Therefore, additional measurements on thinner coat- ings were performed. 3.2. Coating thickness effect Analogous nanoindentation tests using CSM only were performed on the NbMoTaW coating with a thickness of 610 nm deposited using DC magnetron sputter- ing on (0001) sapphire substrate. Figure 3 compares the indentation modulus and hardness depth profiles in CSM and corrected CSM (CSMTF). The H&C correction introduced a reduction of the indentation modulus profile and plateau became more pronounced than in the case of CSM. It caused that the modulus could be calculated from the relative depth range from 16% to almost 30% which is well above 10% of the relative depth. The resulting value from CSM was higher by 35GPa than that (354 ± 11GPa) obtained from the corrected CSM profile. The calculation em- ploying the “10% rule” completely failed: the depth of 61 nm falls into the range where the tip-blunting effects are dominant and the data are invalid. The hardness profile from CSM (Figure 3b) was not af- fected by the correction and it was HIT = 30.7 ± 1.0GPa. Applying the “10% rule” to hardness also failed because of the same reason. Thus, Figure 3 even more clearly than the data in Table 3 demonstrates why the “10% rule” approach should be avoided in the determination of the mechanical properties of thin coatings from nanoindentation. 3.3. The effect of substrate modulus This study involved one stoichiometric TiZrHfVNbTa- xN coating approximately 1325 nm thick deposited by reactive HiTUS at x = 6 sccm N2 flow simultaneously on four different substrates listed in Table 1. Two mea- surements were performed using independently CSM and corrected CSM (CSMTF) methods on each sub- strate. The results summarized in Figure 4a indicate that EIT and HIT values from both measurements were within the scatter and they are reproducible. Besides that, systematic and substantial differences in the 20–50GPa range between apparent EIT values (a). (b). Figure 3. Depth profiles of (A) – indentation mod- ulus, (B) – hardness, obtained using CSM method during nanoindentation of 610 nm thin r-DCMS NbMoTaW coating. from CSM and corrected CSM (CSMTF) and in the 65–150GPa range the increase of the substrate modu- lus from Ti-alloy to sapphire. Thus, the influence of the substrate elastic modulus on the coating modulus evaluation was not fully eliminated both in CSM and in the H&C-modified CSM and its further refinement is necessary. On the contrary, hardness (Figure 4b) varied only from 27GPa to 36GPa with an average value of around 31.5GPa and the differences were mostly within the scatter of individual measurements. 3.4. Best practice recommendations The above results suggest that substrate influence in the evaluation of indentation modulus is still not fully eliminated and the current solutions, despite the incorporation of ISO 14577-4 procedure, generate systematic differences exceeding measurement scat- ter. In the case of the presence of systematic errors, the following rules can be recommended to produce 40 vol. 50/2024 Substrate effect in the evaluation of elastic modulus . . . (a). (b). Figure 4. The effect of substrate modulus on the calculated values of indentation modulus – (A), and hardness – (B), in CSM and independent corrected CSM (CSMTF) models. The data from CSMTF were intentionally offset for better visibility [24]. comparable values of indentation modulus in thin coating/substrate systems: • strictly follow ISO 24577-4 and principally avoid the “10% rule” despite its simplicity and small bias in hardness determination in sufficiently thick coatings; • use sharp tip and frequent tip area calibration to minimize the depth range in which the results are dominated by tip bluntness [31]; • the coatings with a thickness >1 µm are preferred; reliable results from thinner coatings require very sharp tips and better consideration of substrate effects; • use the same method for obtaining corresponding depth profiles (the CSM method with the optimized parameters seems to be suitable); • use the same evaluation method (Hay&Crawford correction brings some benefits but it is sensitive to substrate modulus and coating thickness. Moreover, (a). (b). Figure 5. The dependences indentation modulus – (A), and hardness – (B), in TiZrHf+ME-Ny (ME = V, Nb, Ta) on the flow of nitrogen added in the sputtering Ar atmosphere (and subsequently, stoichiometry, y) during reactive HiTUS deposition. the results may not be directly comparable with the earlier data); • use the same substrates with the well-defined elastic modulus; • at least two independent nanoindentation measure- ments should be performed on each coating to take into consideration coating uniformity as well as measurement accuracy and repeatability. 3.5. Application to measurement in TiZrHfVNbTa-xN coatings The recommendations from Section 3.4 were applied in the measurements and evaluation of the effect of V, Nb, Ta and nitrogen additions on mechanical prop- erties of TiZrHf-ME-Ny coatings. It should be em- phasized that although only the sapphire substrates and CSMTF method were employed to keep possible systematic errors the same, the resulting values are only relative and should be used only for comparison. The full lines in Figures 5a and 5b indicate the de- 41 František Lofaj Acta Polytechnica CTU Proceedings pendences in the reference TiZrHf-Ny (ME = 0) and TiZrHfVNbTa-Ny (ME = VNbTa) coatings, respec- tively, as a function of nitrogen flow. The broken lines correspond to TiZrHf+ME-Ny. The highest values in all systems were above certain critical flow of nitrogen which was around 6 sccm N2 when stoichiometry was achieved [30]. The curves in TiZrHf-Ny coatings were above all other curves and also the maximum EIT = 490GPa and HIT = 39GPa were obtained in this system. Despite limited reliability of the absolute values, good agreement with the properties reported for similar multi-transition metal nitrides produced by reactive DC magnetron sputtering [32] was obtained. The relative comparison indicates that the additions of ME = V, Nb, Ta and VNbTa caused small degra- dation of HIT and EIT which became more visible at higher nitrogen flows. The smallest degradation seems to be in the coatings with ME = Nb whereas it is the most pronounced in TiZrHfVNbTa-N system. Thus, the “cocktail effect” resulting from the additions of additional elements considered in the high entropy al- loys, seems to be negligible or might be even negative in TiZrHf-ME-Ny coatings. 4. Conclusions The results of the current study suggest that the influence of substrate stiffness is still not fully elimi- nated in the evaluation of indentation modulus which causes systematic differences exceeding measurement scatter between coatings deposited on sufficiently dif- ferent substrates (without consideration of substrate influence on coating growth and structure). 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Surface and Coatings Technology 389:125674, 2020. https://doi.org/10.1016/j.surfcoat.2020.125674 43 https://doi.org/10.1111/j.1747-1567.2010.00618.x https://doi.org/10.1111/j.1747-1567.2010.00618.x https://doi.org/10.1557/s43578-021-00131-7 https://doi.org/10.1016/j.actamat.2017.05.036 https://doi.org/10.1007/s10853-021-06448-2 https://doi.org/10.2478/pmp-2022-0005 https://valleydesign.com/sappprop/ https://www.matweb.com/search/datasheet.aspx?matguid=d0b0a51bff894778a97f5b72e7317d85&ckck=1 https://www.matweb.com/search/datasheet.aspx?matguid=d0b0a51bff894778a97f5b72e7317d85&ckck=1 https://www.astmsteel.com/product/52100-bearing-steel-aisi/ https://www.astmsteel.com/product/52100-bearing-steel-aisi/ https://www.universitywafer.com/mechanical-properties-monocrystalline-silicon.html https://www.universitywafer.com/mechanical-properties-monocrystalline-silicon.html https://www.universitywafer.com/mechanical-properties-monocrystalline-silicon.html https://blog.truegeometry.com/designs3D/Titanium_Grade_5_Metal20240605.html https://blog.truegeometry.com/designs3D/Titanium_Grade_5_Metal20240605.html https://doi.org/10.3390/ma16020563 https://doi.org/10.1016/j.tsf.2017.09.051 https://doi.org/10.1016/j.surfcoat.2020.125674 Acta Polytechnica CTU Proceedings 50:36–43, 2024 1 Introduction 2 Materials and methods 2.1 Coating deposition 2.2 Nanoindentation 3 Results and Discussion 3.1 Depth profiles by different methods 3.2 Coating thickness effect 3.3 The effect of substrate modulus 3.4 Best practice recommendations 3.5 Application to measurement in TiZrHfVNbTa-xN coatings 4 Conclusions Acknowledgements References