Effects of Residual Stresses on the Structures and Mechanical Behavior of ZrO_xN_y/V₂O₃ Nano-Multilayers

Abstract

Residual stress plays a crucial role in determining the structural reliability and mechanical performance of nano-multilayers. In the present study, nano-multilayers composed of ZrO_xN_y and V₂O₃ were deposited via magnetron sputtering, with the N:Ar flow ratio systematically varied during the process. Through the precise control of the deposition conditions, the compressive residual stress within the films was effectively reduced to approximately 0 GPa, thereby improving their mechanical robustness. It was observed that the optimization of the stress distribution was strongly influenced by the structural symmetry of the multilayer configuration. This symmetrical design not only mitigated stress accumulation but also ensured uniform mechanical response throughout the multilayer structure. The results from nanoindentation testing revealed a steady hardness value near 10.6 GPa. Furthermore, the maximum H³/E² and H/E ratios recorded were 0.054 GPa and 0.073, respectively, suggesting enhanced resistance to both plastic deformation and cracking.

1. Introduction

The mechanical behavior of thin films—including hardness, elastic modulus, and fracture toughness—is strongly influenced by residual stress [1,2,3]. These internal stresses, often generated during film growth, significantly affect the functional performance, structural reliability, and long-term durability of thin-film systems. In recent years, considerable research has focused on the complex interplay between deposition parameters, stress evolution, and structural characteristics, aiming to optimize film performance across a variety of applications, from microelectronics to protective coatings [4,5,6].

Residual stress in thin films is typically classified as tensile or compressive. Tensile stress, if excessive, can promote crack formation and propagation, compromising film integrity. Conversely, high compressive stress may lead to blistering, buckling, or interfacial delamination—especially in layered or substrate-constrained systems [7,8]. Therefore, precise control over the stress state is critical not only for achieving mechanical robustness but also for maintaining symmetry and uniformity within multilayer architectures. Liu et al. [8] observed a distinct transition from compressive to tensile stress in magnetron-sputtered Cu films as thickness increased from 100 to 2000 nm, with corresponding stress values shifting from −0.984 to 0.136 GPa. They also noted that larger grain sizes facilitated a more homogeneous stress distribution, thereby reducing localized failure risks. Similarly, Cheng et al. [9] investigating TiAlN films on Si substrates, reported a strong inverse correlation between residual stress and mechanical strength: as internal stress increased, hardness and elastic modulus declined from 18.96/210.16 GPa to 16.9/185.9 GPa, highlighting the detrimental role of excessive stress-induced asymmetry.

In multilayer systems, residual stress often exhibits more complex behavior due to interfacial interactions and strain mismatches between constituent layers. McDonald et al. [10] using X-ray diffraction (XRD) and the sin²ψ method, detected significant tensile stress in both Cu and Ni layers of Cu/Ni multilayers. Notably, Ni layer stress increased markedly with decreasing thickness (from ~880 to 1550 MPa), whereas Cu layers maintained relatively stable stress levels (~250 MPa) until a critical thickness of 10 nm, below which the stress abruptly declined. Bouaouina et al. [11] further demonstrated that carefully tuned compressive stress could enhance the mechanical strength of MoN films. These findings, along with studies on AlCrSiN/VN [12], TiN/CrN [13], and AlCrN/AlTiSiN [14] multilayers, confirm that residual stress—when properly engineered—can be a powerful tool to tailor mechanical properties. While nitride-based thin films and multilayers have been extensively studied, systematic investigations into nanoscale multilayer oxide or oxynitride systems remain relatively sparse. Particularly, little is known about how residual stress evolves in oxynitride/oxide heterostructures and how it impacts their mechanical response at the nanoscale. This gap is especially critical given the increasing use of such systems in optical, protective, and functional coatings where stress-induced failures can severely limit device performance. Understanding how residual stress evolves in such systems, and how it influences microstructural and mechanical properties at the nanoscale, is therefore both scientifically and technologically significant.

In the present study, ZrO_xN_y/V₂O₃ nano-multilayers were fabricated via reactive magnetron sputtering under varying N:Ar flow ratios. Deposition durations for both the template and modulation layers were carefully controlled to ensure consistent architecture and interface definition. The primary objective is to elucidate the correlation between residual stress states and the resulting microstructure, hardness, and elastic modulus of the multilayer stack. By understanding the stress–structure–property relationships in this system, we aim to provide insights that could guide the design of high-performance nano-multilayer coatings with tailored mechanical properties and enhanced reliability.

This work presents a novel investigation into the role of residual stress in tailoring the mechanical performance of ZrO_xN_y/V₂O₃ nano-multilayers that has received limited attention to date. By systematically varying the N:Ar flow ratio during reactive magnetron sputtering, this study offers the comprehensive analysis of stress–structure–property relationships in such multilayers, providing valuable insights for the design of mechanically robust, high-performance thin-film coatings.

2. Experimental Details

2.1. Film Deposition

ZrO_xN_y/V₂O₃ nano-multilayers were fabricated on silicon (100) substrates (dimensions: 10 × 20 × 0.65 mm³) using a JGP-450 high-vacuum dual-cathode magnetron sputtering system (Shenyang Scientific Instrument Co., Ltd., Chinese Academy of Sciences, Shenyang, China) with varying N:Ar flow ratios. High-purity zirconium (Zr) and vanadium dioxide (VO₂) targets (99.99 wt%, diameter: 75 mm, thickness: 3 mm) were served as the material sources for the ZrO_xN_y and V₂O₃ layers, respectively.

Prior to deposition, substrates were ultrasonically cleaned in acetone and ethanol (15 min each) to remove organic residues, then dried using high-purity N gas (99.9999 vol%). The cleaned substrates were mounted onto a rotating holder set to 3.8 rpm, ensuring uniform thickness distribution during deposition. The target-to-substrate distance was maintained at 50 mm. The sputtering chamber was evacuated to a base pressure of 4 × 10⁻³ Pa to minimize contamination. Ar (99.9999 vol%) was introduced as the working gas, and both targets were pre-sputtered in pure Ar atmosphere for 10 min to remove surface oxides and contaminants, stabilizing the deposition conditions. Layer thicknesses were controlled by substrate residence times on the targets—15 s for the template and 8 s for the modulation layers. N₂ and Ar gases were introduced separately via independent flow controllers. Full sputtering details are available in [15].

2.2. Characterization

Phase composition and crystallographic structure were analyzed by grazing incidence X-ray diffraction (GIXRD) using a Bruker D8 Advance diffractometer (Bruker AXS GmbH, Karlsruhe, Germany) equipped with a Cu Kα radiation source (λ = 0.1542 nm). Measurements were carried out over a 2θ range of 20–80°, under an operating voltage of 40 kV and a current of 40 mA. The grazing incidence mode was employed to enhance surface sensitivity and minimize substrate interference, ensuring that the diffraction signal predominantly originated from the thin films.

Cross-sectional morphology and layer thickness were examined using a field-emission scanning electron microscope (FE-SEM, FEI Quanta FEG 450, Thermo Fisher Scientific, Hillsboro, OR, USA) operated at 30 kV. SEM imaging provided insights into layer continuity, interface sharpness, and grain structure evolution under varying N:Ar flow ratios.

2.3. Mechanics and Testing

Mechanical properties, specifically hardness and elastic modulus, were evaluated using a Bruker TI-980 nanoindenter (Bruker Corporation, Billerica, MA, USA) equipped with a Berkovich diamond tip. The load–displacement data were analyzed using the Oliver–Pharr method [16], which enables the accurate extraction of mechanical parameters based on the elastic unloading response. To minimize substrate influence, the maximum indentation depth was strictly limited to 100 nm—less than one-tenth of the total film thickness. The tests were performed with a controlled maximum load of 13 μN and a thermal drift rate below 0.05 nm/s. For statistical reliability, six indentations were performed per sample, with a lateral spacing of ~30 μm between indents to avoid mutual interference.

Residual stress in thin films was determined via substrate curvature variations [11,17] by a film stress measuring instrument (FST1000, Shenzhen Supu Instrument Co., Ltd., Shenzhen, China). Such stress commonly arises from disparities in thermal expansion, structural arrangement, and mechanical properties between the coating and its substrate. In this work, a laser beam deflection setup was utilized for curvature-based stress assessment. Residual stress (σ) was computed via Stoney’s equation [3]:

$$\sigma \left(x,y\right)={\displaystyle \frac{E{d}_s^2}{6(1-v)d_f}}\times ({\displaystyle \frac{1}{R}}-{\displaystyle \frac{1}{R_i}})$$

(1)

considering film/substrate thicknesses d_s/d_f, silicon substrate properties (E = 131 GPa, ν = 0.28), and radii of curvature (R and R_i) before and after films [9]. To ensure accuracy and reproducibility, each sample was measured at three different positions along its longitudinal axis, and the average stress value was reported. The standard deviation among these measurements was typically below ±3%, and error bars were included in the stress-related figures to reflect this variation. This method provides a reliable and non-destructive means to evaluate intrinsic residual stress induced by deposition and compositional changes in the multilayer architecture.

3. Results and Discussion

3.1. Morphology and Structure

Figure 1 displays the SEM cross-sections of ZrO_xN_y/V₂O₃ nano-multilayers deposited under varying N:Ar flow ratios. Uniform thickness and defect-free, smooth surfaces are maintained across all samples. Without N, the films exhibit smooth morphologies with a few equiaxed grains near the top (Figure 1b). As N₂ is introduced, the structure evolves into columnar grains (Figure 1a,c–e), suggesting enhanced vertical grain growth promoted by N incorporation.

The total film thickness shows a non-monotonic dependence on the N:Ar ratio, increasing from 918 nm to a peak of 1305 nm at 20:30, followed by a slight decrease to 1201 nm at 30:30. This trend likely results from a balance between enhanced growth rates due to increased reactivity at low N content and reduced deposition efficiency caused by target poisoning at high N₂ flow rates [18]. These morphological and dimensional variations suggest that N incorporation significantly influences growth kinetics and film densification, which may affect residual stress evolution and mechanical response.

Crystallographic planes are described using Miller indices, which are a standard notation in materials science for identifying the orientation of atomic planes in a crystal lattice [19]. For example, the (111) plane refers to a family of parallel atomic planes that intersect the crystal axes in a specific, geometrically defined manner.

Figure 2 shows the GIXRD results for ZrO_xN_y/V₂O₃ multilayers grown at different N:Ar ratios. All films exhibit a dominant cubic ZrO₂ phase with strong (111) orientation, while (220) and (311) peaks remain weak. The FWHM of the (111) peak is broadest and the (200) peak is absent at 0:30 N:Ar. As N:Ar flow increases, the (111) peak sharpens and intensifies, indicating improved crystallinity. The (200) peak emerges and strengthens, revealing enhanced phase formation and texture development due to N incorporation. The absence of distinct V₂O₃ peaks is likely due to its thin layer thickness and low deposition rate, which limit the detectability by GIXRD.

Notably, a shift of the (111) peak toward lower angles with increasing N suggests lattice expansion, attributed to substitutional N incorporation, and associated compressive stress. This induces compressive residual stress linked to ionic mismatch, thermal expansion differences, and ion bombardment, reflecting both structural and stress-related changes in the multilayers [20,21].

Figure 3 depicts the elemental composition of ZrO_xN_y/V₂O₃ nano-multilayers deposited under varied N:Ar flow ratios. While Zr and V concentrations remain stable (~25.56 at.% and 3.32 at.%), N increases (0 to 2.96 at.%) and O decreases (72.43 to 68.21 at.%).

This behavior is attributed to the element-specific sputtering yields under Ar ion bombardment [22]. VO₂ dissociates into V and O due to thermal and ion bombardment effects, favoring V₂O₃ formation [23]. Excess O combines with Zr to form ZrO₂. As N:Ar ratios increase, coexisting N and O ions lead to ZrO₂ and minor ZrN phases. Due to O’s higher affinity and content, oxides dominate [24,25].

3.2. Lattice and Grain

Based on the GIXRD θ/2θ scan, lattice parameter d was determined using Equation (2) [26],

$$d={\displaystyle \frac{a}{\sqrt{h^2+k^2+l^2}}}$$

(2)

while average crystallite size t was estimated by the Scherrer formula Equation (3) [27],

$$t={\displaystyle \frac{0.9\lambda }{B\times \mathit{cos}\theta }}$$

(3)

Here, λ denotes the wavelength of Cu Kα radiation, B represents the full width at half maximum (FWHM) of the diffraction peak, and θ is the Bragg angle.

GIXRD analysis revealed a clear correlation between residual stress and lattice spacing (d), as described by Equation (2). As shown in Figure 4, the lattice spacing initially decreased from 2.943 Å to a minimum of 2.940 Å at the 10:30 N:Ar flow ratio, before increasing to 2.978 Å with further N enrichment. The initial contraction is attributed to compressive lattice distortion caused by substitutional N atoms, which reduce interatomic distances. The subsequent expansion is likely due to phase transformations or the incorporation of excess N into interstitial sites, leading to lattice relaxation or swelling effects [28].

This evolution of lattice spacing is further supported by the progressive shift of the ZrO₂ (111) diffraction peak toward lower angles as the N:Ar ratio increases, indicating lattice expansion. This trend reflects increasing N incorporation, which generates compressive stress through both substitutional and interstitial mechanisms. At lower N flow rates, the residual compressive stress diminishes and approaches 0 at the 10:30 flow ratio. In this region, the lattice spacing remains relatively stable, suggesting the formation of a structurally relaxed, equilibrium microstructure. However, at higher N levels, the reappearance of compressive stress and increased lattice spacing imply the onset of stress-induced lattice distortion and possible microstructural instability.

Grain size, calculated via Equation (3), showed a clear refinement trend with N incorporation. At a N:Ar flow ratio of 0:30, the average grain size was 122 nm, while films grown under N₂-rich conditions (5:30 to 30:30) demonstrated significantly reduced grain sizes, ranging from 30 to 75 nm, as shown in Figure 5. This grain refinement is attributed to stress-induced grain boundary pinning and limited atomic mobility during growth, both of which inhibit grain coarsening [29]. The most pronounced refinement occurred at moderate N₂ levels, which also coincided with enhanced mechanical performance, indicating a favorable balance between microstructural densification and stress state. However, at the highest N:Ar ratio (30:30), a slight increase in grain size was observed, potentially resulting from stress accumulation, porosity formation, or microstructural degradation caused by target poisoning.

These results underscore the strong interdependence among nitrogen incorporation, residual stress, and grain structure and highlight the importance of process optimization in tailoring the microstructure and performance of reactive multilayer coatings.

3.3. Residual Stress

Residual stresses were quantified via substrate curvature measurements using Stoney’s equation. As shown in Figure 5, all films exhibit compressive stress, which initially decreases with the N:Ar ratio and approaches 0 at 10:30, then increases again at a higher N₂ flow. This trend implies that moderate N levels facilitate stress relaxation, possibly through improved interfacial accommodation or reduced atomic packing density.

The interplay among N content, residual stress, lattice spacing, and grain size plays a pivotal role in determining the microstructural evolution of reactive multilayer coatings. Increasing the N:Ar flow ratio alters the degree of N incorporation, which modulates internal stress through substitutional and interstitial mechanisms. At moderate N levels (e.g., 10:30), residual compressive stress is minimized, correlating with a contraction in lattice spacing due to substitutional N atoms. Beyond this point, further N enrichment leads to lattice expansion, likely caused by interstitial N incorporation or stress-induced phase changes.

Simultaneously, grain size shows a refinement trend with increasing N content, decreasing from 122 nm at 0:30 to 30–75 nm across N-rich conditions. This grain refinement is attributed to stress-enhanced grain boundary pinning and reduced atomic mobility. However, excessive N input can cause stress accumulation and microstructural degradation, leading to partial grain coarsening.

These observations suggest that an optimal N concentration balances lattice distortion and stress relaxation, resulting in a stable, fine-grained structure with enhanced mechanical properties. Collectively, this highlights the critical role of residual stress as a mediator, linking N content to both lattice and grain-scale structural responses.

3.4. Hardness and Modulus

The mechanical behavior of ZrO_xN_y/V₂O₃ nano-multilayers is closely associated with the residual stress state, which varies under different N:Ar flow ratios. As shown in Figure 6, hardness remains relatively stable (11.0, 10.1, 10.2, 10.1, and 8.6 GPa), while the elastic modulus decreases steadily (175.7, 152.3, 133.1, 137.3, and 124.3 GPa). Corresponding compressive stresses are measured as −0.097, −0.043, 0, −0.044, and −0.27 GPa, respectively. The lowest hardness and modulus are observed when the N:Ar ratio is 30:30, which also shows the highest magnitude of compressive stress.

Excessive N flow may induce target poisoning and structural degradation—e.g., grain enlargement and increased porosity—weakening stress retention and stiffness and thus degrading mechanical properties [30,31]. However, some findings suggest nanoindentation hardness and modulus can remain stable despite residual stress under certain conditions [32]. This inconsistency reveals a complex, material-sensitive stress–performance relationship, underscoring the need for precise stress control in film design.

3.5. H/E and H³/E²

The mechanical behavior of ZrO_xN_y/V₂O₃ nano-multilayers is strongly influenced by residual stress, which can be assessed through the hardness-to-modulus ratios H/E and H³/E² [33]. The H/E ratio reflects elastic strain capacity and correlates with wear resistance, while the H³/E² ratio is indicative of the film’s plastic deformation resistance and energy absorption ability prior to fracture [34,35].

As shown in Figure 7, both H/E and H³/E² ratios exhibit a strong dependence on the residual stress state, which is modulated by the N:Ar flow ratio. The H/E ratio, indicative of elastic strain tolerance, increases from approximately 0.064 to 0.077, corresponding to an improvement of around 20%. Similarly, the H³/E² ratio, which reflects resistance to plastic deformation, increases from ~0.046 GPa to 0.060 GPa, representing a 30% enhancement under optimized flow conditions.

These ratios initially increase with the reduction in compressive stress, reaching their respective maxima at approximately 0 residual stress. This indicates that films under near-0 or moderately compressive internal stress demonstrate enhanced mechanical performance, characterized by improved elastic strain to failure and energy dissipation capacity. The observed peak in both indicators at balanced stress states suggests an optimal trade-off between hardness and modulus, which contributes to better resistance against plastic deformation and cracking. Conversely, a notable decline in H/E and H³/E² at −0.27 GPa underscores the detrimental effects of excessive compressive stress, which likely induces microstructural instability, interfacial delamination, or defect formation, thereby weakening the film’s overall mechanical integrity.

These improvements coincide with the residual stress reaching a near-0 level at the 10:30 N:Ar ratio, where the combination of stress relief, microstructural refinement, and interface stability enables more efficient mechanical energy dissipation. The quantitative gains in these mechanical indicators highlight the effectiveness of reactive gas ratio tuning as a strategy for enhancing the toughness and durability of nano-multilayer coatings. These findings reinforce the importance of residual stress engineering in optimizing the reliability and functional performance of protective thin films.

4. Conclusions

This study systematically investigated the influence of residual stress on the structural and mechanical properties of ZrO_xN_y/V₂O₃ nano-multilayers fabricated via reactive magnetron sputtering under varying N:Ar flow ratios. The key findings are as follows:

(1)

Microstructural evolution: Increasing N flow induced a transition from smooth, equiaxed grains to columnar growth, along with improved crystallinity and a pronounced (111) texture in the ZrO₂ phase. Elemental analysis confirmed a gradual substitution of oxygen by N, forming Zr–O–N bonds and modifying the chemical environment.

(2)

Residual stress modulation: All multilayers exhibited compressive residual stress, which initially decreased and approached ~0 GPa at a 10:30 N:Ar ratio before increasing to −0.27 GPa at higher N₂ content. This trend was closely correlated with lattice parameter shifts and grain size refinement, indicating strong stress–structure coupling.

(3)

Mechanical performance: The nanoindentation results revealed that optimal mechanical properties were achieved under near-0 residual stress. Specifically, the highest H/E (~0.077) and H³/E² (~0.06 GPa) values were recorded at minimal internal stress, reflecting improved toughness, elastic strain tolerance, and resistance to plastic deformation.

(4)

Degradation at excessive stress: At high N₂ flow ratios, excessive compressive stress and target poisoning effects led to grain coarsening, porosity, and degraded film integrity, which in turn reduced hardness (down to 8.6 GPa) and modulus (to 124.3 GPa).

These findings highlight the critical role of stress engineering in controlling the microstructure and mechanical response of oxynitride/oxide multilayers. By tuning the N:Ar ratio, residual stress can be modulated to optimize hardness, toughness, and reliability. This work provides valuable guidance for the design of high-performance nano-multilayer coatings in applications requiring enhanced mechanical durability and structural stability.