# Nano-Scale Residual Stress Profiling in Thin Multilayer Films with Non-Equibiaxial Stress State

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## Abstract

**:**

_{3}N

_{4}/Ag/ZnO low-E coatings, by considering different fractions of area for DIC strain analysis and accordingly developing a unique influence function to maintain the sensitivity of the technique at is maximum during the calculation. Residual stress measurements performed using this novel FIB-DIC approach revealed that the individual Si

_{3}N

_{4}/ZnO layers in the multilayer stack are under different amounts of compressive stresses. The magnitude and orientation of these stresses changes significantly after heat treatment and provides a clear explanation for the observed differences in terms of scratch critical load. The results show that the proposed FIB-DIC combined-areas approach is a unique method for accurately probing non-equibiaxial residual stresses with nano-scale resolution in thin films, including multilayers.

## 1. Introduction

_{3}N

_{4}), which is commonly used because of its transparency over a wide spectral range from the near ultraviolet (UV) to the infrared (IR) region, tin oxide (SnO

_{2}), and zinc oxide (ZnO), the latter mainly enhancing reflective layer adhesion and promoting microstructural characteristics that reduce its resistivity. These dielectric layers not only act as an optical filler and function as anti-reflective barriers to improve the optical properties, but also protect the stack from both the substrate and the environment. Both reflective and dielectric layers are normally produced using the physical vapor deposition (PVD) technique and the overall thickness of the stack is normally $<300\text{}\mathrm{nm}$. Some typical configurations and properties for these layers are widely available in the literature [7,8,9].

**e(h)**at each milling depth

**h**, which can be converted into a residual stress depth profile by using suitable inverse calculation procedures and knowing the distribution of the elastic constants of the probed volume of material [19].

**ε*(z)**is the unknown distribution of the eigenstrain at the calculation depth

**z**; therefore,

**z/D**is the normalized depth at which eigenstrain is being determined, and

**F(z/D)**is the calibration influence (or sensitivity) function, which is usually calculated by Finite Element Analysis.

**F(z/D)**that are reported in Figure 2c,d, which show that a maximum exists for each of the sensitivity functions at the different values of the radius% selected for calculation. In order to avoid inaccuracies during stress calculation, a value of 80% was suggested to guarantee a sufficiently high strain sensitivity in the depth range of 0.015 <

**h/D**< 0.2 for both the hydrostatic and deviatoric stress components.

**h/D**values higher than 0.2 for all considered values of the radius%. Therefore, the range of 0.015 <

**h/D**< 0.2 for effective depth profiling has been suggested for optimal residual stress depth profiling. In this way, a depth resolution of 50 nm was demonstrated for pillar diameters in the range of 1–15 µm [20].

**h/D**= 0.25 in multilayer amorphous/crystalline films on a glass substrate. The main idea is to develop a unique influence function by considering different percentages of area (i.e. different radius% of the pillar) for the DIC analysis, in order to keep strain sensitivity always at its maximum during the calculation. In this way, we demonstrate nano-scale non-equibiaxial residual stress profiling in ultra-thin films (thickness < 300 nm) with an individual layer thickness of the order of 10–50 nm.

_{3}N

_{4}/Ag/ZnO multilayer stack on a glass substrate, where the influence of residual stress depth gradient on film adhesion (scratch critical load) is clearly identified (for the same average stress and hardness of the film). The results show that the nanoscale residual stress depth profile can be the main design parameter to be controlled for the optimization of adhesion in multilayer low-emissivity thin films on glass substrates.

## 2. Materials and Methods

#### 2.1. A New Approach for Improving the Sensitivity and Resolution of Residual Stress Depth Profiling in Very Thin Films

**h/D**. Higher values (>80%) of radius% should be used for

**h/D**< 0.05, while the adoption of lower values (<70%) should be recommended for $\mathit{h}/\mathit{D}>0.1$. This observation can be converted in the simple area selection scheme reported in Figure 3, where the optimal radius% to be used is plotted as a function of

**h/D**ratio (for both the deviatoric and hydrostatic calibration functions) precisely basing on the relative milling depth ranges for which the corresponding strain sensitivity functions values are higher than the others.

**h**/

**D**= 0.2. By doing so, a sufficiently high value of strain sensitivity can be achieved even at

**h/D**= 0.01 (by using radius% = 85% at the shallowest depths), and the maximum depth can be increased to

**h/D**= 0.25 (by using radius% = 60% at the deepest milling depths).

#### 2.2. Coating Deposition and Heat Treatment

#### 2.3. Nanoindentation and Nanoscratch Testing

#### 2.4. Residual Stress Depth Profiling

**h/D**= 0.18. Five high-resolution SEM micrographs were acquired prior to testing (reference surface images, namely step #0 in Figure 5) and after each of the material removal increments (step), maintaining the same contrast as the reference images, using an acceleration voltage of 5 kV and a beam current of 0.34 nA, integrating for each image 128 frames at 50 ns dwell time each.

#### 2.5. Validation by Residual Stress Curvature Measurement

## 3. Results

**L**(first adhesive failure) and

_{c2}**L**(full coating delamination) critical loads. In particular, a very significant difference in terms of

_{c3}**L**critical load is observed. The two failure events are visible in both cases from the SEM images reported in Figure 7c,d.

_{c2}**L**and

_{c2}**L**values. Specifically, a remarkable decay of

_{c3}**L**is observed that corresponds to surface delamination. This can be directly correlated to the measured tensile surface stress in sample A after heat treatment (Figure 8d).

_{c2}## 4. Discussion

_{3}N

_{4}/Ag/ZnO multilayer films, and a clear correlation with nanoscratch critical loads results was identified.

_{3}N

_{4}/Ag/ZnO nano-multilayer films. By considering all those aspects, resolution below 20 nm was achieved on an average, with improved surface sensitivity (down to

**h/D**= 0.01) and extended maximum allowable depth (up to

**h/D**= 0.25), in comparison with our previous paper [20].

^{3}), whilst curvature monitoring interrogates the response of entire sample and also includes stress relaxation effects because of microdefects and localized film delamination. Additionally, it is important to remind that the curvature method is based on the strong assumption that the residual stress state of the inner layers does not change after the deposition of additional layers. This is a limitation of this method and it can be a main explanation as to why the curvature method is not able to fully capture the non-biaxiality of the stress. Additionally, the non-biaxiality could also arise during the final cooling of the large area (thick) substrates.

## 5. Conclusions

_{3}N

_{4}/Ag/ZnO nano-multilayer films on glass substrate before and after heat treatment show that the method can capture the fine detail of the changes of the residual stress nano-scale gradients following thermal processing. The residual stress profiles evaluated by FIB-DIC agreed well with the results of nanoscratch testing, which confirmed that the reduction of scratch critical load can be correlated with the presence of tensile residual stresses at the film/substrate interface. The observations demonstrate that the adhesion of thin multi-layer films on glass can be significantly affected by the residual stress gradients, which should be used as a key design parameter for complex coated systems.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Typical silver-based low-emissivity (low-E) coating five-component stacking scheme. The thickness of the reflective layer has values of about 10 nm, while that of the dielectric layers could vary based on designed performances for the film. Coatings with multiple reflective layers are deposited following the five-component basic layer sequence.

**Figure 2.**(

**a**) Experimental example of ring-core focused ion beam (FIB) milling, (

**b**) the idea of multiple area% digital image correlation (DIC) analysis for improving depth resolution and surface sensitivity, (

**c**) FEM calculated hydrostatic part of the kernel function

**F(z/D)**for several values of the radius%, (

**d**) deviatoric components of the kernel functions for several values of the radius% (which defines the corresponding area% for DIC analysis, as reported in Figure 2a,b).

**Figure 3.**Optimal radius% (corresponding to area% for DIC) as a function of relative milling depth

**h/D**(dashed line: deviatoric part, full line: hydrostatic part).

**Figure 4.**Schematic representation of the adopted film architecture, which is also visible in Figure 2a.

**Figure 5.**Step-by-step FIB milling of a 1.5 µm pillar on the coating. Surface features are gold patterning to facilitate the DIC procedure. The different layers are visible in the micrographs.

**Figure 6.**Flowchart describing the entire workflow of the method, with main decision steps on how to select the core diameter, FIB/SEM parameters, DIC analysis, and final residual stress calculation.

**Figure 7.**Nanomechanical testing on the film before and after the heat treatment. (

**a**) Nanoindentation modulus profile, (

**b**) nano-hardness profile, (

**c**) SEM micrograph of a nanoscratch test BEFORE the heat treatment, (

**d**) SEM micrograph of a nanoscratch test AFTER the heat treatment.

**Figure 9.**Analysis of the surface residual stress gradient for the sample after heat treatment. (

**a**) Experimental relaxation strain (along one direction, as an example, where dashed lines represent the polynomial interpolation) for different values of radius%; (

**b**) Corresponding residual stress profiles (second principal stress, as an example).

**Figure 8.**Relaxation strain (with fitting of polynomial function, grade 4) along three directions before heat treatment (examples for radius% = 80%) (

**a**) and after heat treatment (

**b**). Principal residual stress profiles (σ1 and σ2) obtained by considering multiple radius%, (

**c**) before the heat treatment cycle and (

**d**) after the heat treatment cycle. (Dashed lines indicate the different layers of the films, according to the architecture described in Section 2.2).

Sample | Critical Load Lc2 (First Delamination, mN) | Critical Load Lc3 (Full Coating Delamination, mN) | Average Hardness (GPa) (Depth Range 25–35 nm) | Average Elastic Modulus (GPa) (Depth Range 25–35 nm) |
---|---|---|---|---|

BEFORE heat treatment | 4.39 ± 0.36 | 17.66 ± 0.76 | 9.2 ± 0.4 | 117 ± 3 |

AFTER heat treatment | 2.25 ± 0.13 | 15.80 ± 0.09 | 8.4 ± 0.4 | 118 ± 5 |

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## Share and Cite

**MDPI and ACS Style**

Sebastiani, M.; Rossi, E.; Zeeshan Mughal, M.; Benedetto, A.; Jacquet, P.; Salvati, E.; Korsunsky, A.M. Nano-Scale Residual Stress Profiling in Thin Multilayer Films with Non-Equibiaxial Stress State. *Nanomaterials* **2020**, *10*, 853.
https://doi.org/10.3390/nano10050853

**AMA Style**

Sebastiani M, Rossi E, Zeeshan Mughal M, Benedetto A, Jacquet P, Salvati E, Korsunsky AM. Nano-Scale Residual Stress Profiling in Thin Multilayer Films with Non-Equibiaxial Stress State. *Nanomaterials*. 2020; 10(5):853.
https://doi.org/10.3390/nano10050853

**Chicago/Turabian Style**

Sebastiani, Marco, Edoardo Rossi, Muhammad Zeeshan Mughal, Alessandro Benedetto, Paul Jacquet, Enrico Salvati, and Alexander M. Korsunsky. 2020. "Nano-Scale Residual Stress Profiling in Thin Multilayer Films with Non-Equibiaxial Stress State" *Nanomaterials* 10, no. 5: 853.
https://doi.org/10.3390/nano10050853