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Research Papers

# A Multilayer Strategy for Improving the Abrasion Resistance of Silica Nanoparticle-Based Motheye Antireflective Coatings on GlassOPEN ACCESS

[+] Author and Article Information
Barath Palanisamy

School of Mechanical, Industrial and
Manufacturing Engineering,
Oregon State University,
Corvallis, OR 97124
e-mail: barathp@gmail.com

Seung-Yeol Han

CSD Nano, Inc.,
Corvallis, OR 97124

Brian K. Paul

School of Mechanical, Industrial and
Manufacturing Engineering,
Oregon State University,
Corvallis, OR 97124

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the JOURNAL OF MICRO- AND NANO-MANUFACTURING. Manuscript received December 6, 2015; final manuscript received June 2, 2016; published online July 8, 2016. Assoc. Editor: Don A. Lucca.

J. Micro Nano-Manuf 4(3), 031005 (Jul 08, 2016) (10 pages) Paper No: JMNM-15-1083; doi: 10.1115/1.4033861 History: Received December 06, 2015; Revised June 02, 2016

## Abstract

Motheye antireflective coatings (ARCs) are based on periodic or stochastic features with dimensions below the wavelength of visible light which can be used to produce a gradient index of refraction between air and the substrate. In this work, two silica nanoparticle-based motheye ARCs of similar optical performance, but different physical structures, were deposited on glass and characterized for mechanical behavior to provide insights into the mechanisms for abrasion resistance in these films. Optical and mechanical performances were evaluated in light of the mechanical properties and physical structure of the films using models for describing the mechanical behavior of the films. The results show that the three-layer coating was found to have better abrasion resistance than a simple single layer coating largely due to better crack nucleation resistance and scratch resistance. The simple single-layer film showed better crack propagation resistance than the three-layer film due to the existence of nanoparticles (NPs) throughout the cross section of the film. The three-layer film appears to have higher work of adhesion based on exhibiting better delamination and spallation resistance.

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## Introduction

Antireflective coatings generally reduce reflective losses by reducing the refractive index (RI) mismatch between air and the solid media. The spectral reflection of most materials in air is due to the large mismatch in RI, which can be offset by having a surface with a gradually changing RI. Bernhard et al. [1,2] found that the antireflective nature of the cornea in night-flying moths was due to a field of interconnected domes about 200 nm high with about 300 nm center to center spacing. It was hypothesized that this structure, with dimensions below the wavelength of visible light, provided a gradient RI from the air into the cornea, eliminating spectral reflection [1]. These “motheye” gradient structures perform better across a wider spectrum of wavelengths than quarter-wavelength films [3]. RI gradients have been demonstrated using periodic surface structures [4,5] as well as with stochastic surface structures [6] with the use of etching [7] and stochastic subsurface structures such as with the use of porosity [8,9].

While the optical properties of gradient films are excellent at > 99.6% transmission in lab settings [10,11], often there are other demands from field application of the coatings, such as environmental degradation and mechanical damage. The mechanical robustness of optical coatings is important for resisting scratches and abrasion in many applications ranging from lenses to smart phones. Although gradient films are easier to manufacture because of the widely used sol–gel approach [1,12], the nature of gradient films based on porosity makes them vulnerable to poor mechanical performance. Porous air–glass gradient films are essentially a composite of air and glass making them susceptible to mechanical damage [13].

Several authors have reported on the scratch or abrasion resistance of nanoparticle-based ARCs produced using sol–gel processes [1416]. However, these reports provide little insight into the relationship between the structure, properties, and processing of the films and the impact of each on mechanical performance. In this paper, we formulate two different ARCs, both consisting of a Si-based inorganic polymer matrix and a distribution of pores and embedded NPs, to investigate the impact of film structure on the mechanical behavior of the ARCs. The objective of this paper is to evaluate the abrasion resistance of these two films produced under different processing conditions and investigate the mechanical behavior of films with both good and poor abrasion resistance as a means to better understand the factors affecting the abrasion resistance of gradient ARCs.

## Experimental Methods

The definition and metric for abrasion resistance are given in Table 1 along with definitions and metrics for several other mechanical behaviors underlying abrasion resistance in thin films [1720]. The primary metric used to assess abrasion resistance was the percent residual antireflection remaining after abrasion testing, a change in a measured property of the film, which is equal to the antireflection (Δ%R) after abrasion divided by the initial antireflection (Δ%R) before abrasion. An ultraviolet visual spectroscopy spectrophotometer (JASCO V-670) equipped with an integrating sphere was used to measure the mean spectral (between wavelengths of 400–900 nm) reflectance (%R) of the base uncoated glass samples and the coated glass samples both before and after abrasion. In all the cases, antireflection (Δ%R) was calculated by subtracting the %R of the coated substrate from the %R of the base uncoated substrate.

Abrasion testing was evaluated using the test apparatus shown in Fig. 1, which is a modified version of the EN1096-2 coated glass testing standard. A 400 g load with a high density felt (1.7 g/cm2) was used as the abrading medium with no circular motion on the boom. The stroke rate was set to 50 cycles per minute. Samples were measured for change in reflectance before and after abrasion testing. Three samples were tested per processing condition for this test, however, due to the nature of the test, each sample could be only tested once.

Two films were produced for evaluation. One film consisted of a single layer (1L) based on the recipe developed by Henning and Svensson [21] and Hæreid et al. [22] using tetramethylorthosilicate (TMOS) as a principal reactant to synthesize a very fine silica NP dispersion in suspension termed TMOS-b gel. The second film consisted of three layers (3L) in which the middle layer used the same procedure as above with the top and bottom layers consisting of a TMOS suspension synthesized in HCl, an acidic medium (TMOS-a). The rationale for using the TMOS-a gel as a bottom layer was to reduce the severity in structural transition from the nanoparticle-based TMOS-b coating to the substrate, thereby reducing interfacial stresses that could affect the mechanical performance of the coating. The top layer in the 3L film was also made of TMOS-a as it is known to provide a harder, more dense coating having less porosity. The TMOS-a layer also does not contain any NPs. The thickness of the top and bottom layers was estimated to be around 10–15 nm. A schematic of the film structures is shown in Fig. 2.

The as-synthesized NP suspensions were diluted to 50 vol. % and used to coat the smooth side of textured glass substrates containing 69–74% SiO2, 10–16%Na2O, 5–14% CaO, 0–6% MgO, and 0–3% Al2O3 (AGC Solite, Kingsport, TN) [23]. A spin coating technique followed by Han et al. [24] was used to deposit the wet films followed by heat treatment to synthesize a final NP microstructure similar to that observed elsewhere [25]. Through preliminary experimentation (stage 1 DOE), it was found that the coating spin speed and heat treatment time and temperature were all important affecting optical and mechanical performance of both films. Recipes were developed for two nearly equivalent optical films (one 1L and one 3L) to explore differences in mechanical performance. The mean and standard deviation for the optical performance of the two consequent films was 3.27 ± 0.24% (1L) and 3.11 ± 0.18% (3L). These conditions were achieved at a spin speed of 1500 rpm for 1L and 1800 rpm for 3L and an annealing time and temperature of 1 h at 580 °C for both films. Based on these results, a stage 2 factorial design was developed to understand the interdependence of annealing time (10, 30, and 60 min) and temperature (580, 595, and 610 °C) on the abrasion resistance of the films.

Upon finishing abrasion resistance studies, 1L and 3L films which possessed good, poor, and moderate abrasion resistance were selected for further analysis (Table 2) to help explain abrasion resistance results. Cross-sectional and surface morphologies of the films were characterized by scanning electron microscopy (SEM; FEI Quanta 600 FEG, Hillsboro, OR) operating at 20 kV and transmission electron microscopy (TEM) (FEI TITAN Chemi-STEM, Corvallis, OR) operating at 200 kV. Cross sections of size 15 μm × 6 μm × 0.2 μm were prepared using focused ion beam (FIB) milling cross-sectioning techniques (FEI Quanta 3D Dual Beam SEM/FIB, Raleigh, NC). A TA Q600 differential scanning calorimetry/thermogravimetric analysis (DSC/TGA) with a Hiden HPR-20 mass spectrometer was used to study the annealing mechanism of the films. The maximum ramp rate for the unit was ten times slower at 50 °C/min compared to the rapid thermal annealing unit typically used for annealing coated glass samples. For ease of sample preparation, silicon wafer was used as a substrate.

Finally, nanoindentation and scratch tests were used to measure important material and film properties needed for quantifying the fracture mechanics of the films using a well-developed set of energy-based and stress-based models from homogeneous thin film fracture mechanics. (A detailed description of these models has been provided in Appendix A.) Nanoindentation tests were performed using a CSM Instruments nanoindentation tester. A Berkovich diamond indenter with a max load of 300 μN at a loading rate of 600 μN/min was used. A CSM Instruments MicroScratch Tester (S/N 01-02526) with a 50 μm radius spheroconical indenter was used to perform scratch testing at a peak load of 700 mN over a track length of 1.4 mm at a loading rate of 500 mN/min.

## Results and Discussion

###### Abrasion Resistance.

After completing the experimental runs, the preliminary and residual antireflections of the two films were computed as a function of annealing time and temperature as shown in Fig. 3. These plots use standard error bars.

Based on Fig. 3, three conditions for each film structure were chosen for further structure–property analysis. As shown in Table 2, the three conditions consisted of: (1) the best optical and mechanical performance; (2) the worst optical and mechanical performance; and (3) poor optical and good mechanical performance. The rationale for selecting these particular conditions was primarily to narrow down from the processing condition based DOE 1 and for testing representative samples that allow for better understanding of underlying mechanisms. Overall, it was noted that the best 3L condition (580 °C at 30 min) had better residual antireflection (abrasion resistance) at ∼0.85 residual antireflection compared to ∼0.82 for the best 1L condition (580 °C at 60 min) although based on the standard error, this may not be significant when compared to 595 °C at 60 min although 580 °C at 60 min has significantly higher initial antireflection. Also, the initial antireflection for these same films for 3L was 3.48% (6% higher), while the corresponding 1L had 3.27% which appears to be significant according to the plots [26]. For all the conditions, the 3L film had better abrasion resistance. The abrasion resistance of the 1L film was found to improve with time.

An analysis of variance and a nonlinear regression were performed on this data showing that the mean antireflection of both films significantly decreases with time and an interaction between time and temperature. Temperature was found to reduce the mean antireflection of the 3L film. R-squared values for abrasion resistance were found to be 59.7% and 65.9% suggesting that additional factors exist (Appendix B) Table 3. Interestingly, temperature seems to have little impact on the abrasion resistance of the films and may actually decrease mechanical performance at higher temperature.

It is expected that the trend of improved abrasion resistance with time is consistent with higher cross-linking and denser structures. This is corroborated by the drop in optical performance with time suggesting the loss of nanostructure with densification. As shown in Table 2 and in all the analyses below, the high optical–high mechanical condition is represented in green, the moderate–low/low–low condition in red, and the low–high condition in yellow (see online figure for color).

###### Film Structure.

To better explain abrasion results, the structure of the six films was examined by SEM and TEM. SEM images were taken of the top surface of the films. TEM images were taken of film cross sections prepared using the dual beam FIB. Figures 4 and 5 depict the high-magnification images collected.

In 1L films made at 595 °C for 10 min, large tripod-shaped cracks can be seen, which appear to follow a bimodal distribution. This is likely due to residual stress which builds up within the film due to densification of the film. To further study the annealing mechanism, a typical annealing cycle was carried out at 580 °C for 1 h using the DSC/TGA unit. Based on the differential scanning calorimetry and mass spectrometry data shown in Fig. 6, annealing of the 1L film leads to the release of volatile constituents like organics and water vapor which could have contributed to cracking during volatilization. From the DSC curve, it can be seen that there is an endothermic dip associated with removal of water around 150 °C. This also corresponds to the mass spec curve wherein the evolution of water over time was tracked during the entire annealing cycle of the sample. Absorbed water on the sample is removed by simple dehydration and peaks around the same temperature. A chemical transition appears to be happening as temperature is increased from 250 °C to the annealing temperature of 580 °C shown by the exothermic spike. It is hypothesized that this is a reaction step before the Si–O–H bonds are terminated. Subsequent hold at 580 °C shows that water is still coming out until 30 min during annealing, and water evolution is near constant beyond 30 min. Since this occurs at temperatures well above dehydration, it is hypothesized that these water molecules are derived from the condensation reaction resulting from termination of Si–O–H bonds to form Si–O bonds. The corresponding plateau in the DSC curve suggests constant heat intake to maintain 580 °C temperature in the sample. There is continuous weight reduction in the TGA curve suggesting constant out gassing from the sample.

Going forward, the absence of cracks at 610 °C for the 1L films suggests that longer annealing times in combination with higher temperatures may result in stress relief or, alternatively, the “healing” of cracks via sintering. The high-magnification image at 610 °C for 60 min shows signs of nanocracks that may have healed. Softening of the film at higher temperatures could cause the film to flow under viscous creep bringing the film back together which would have sintered more rapidly at the higher temperature. Clustering from particle coarsening is seen at longer annealing times which may account for poorer optical performance but better residual antireflection (better mechanical properties) with annealing time.

For 3L films produced at 595 °C for 10 min, cracks have been replaced by pores averaging less than 100 nm, which are uniformly distributed across the surface. This suggests that the top layer is playing a role in mitigating cracking behavior within the film. It is apparent that the presence of observable cracks (1L) and widely distributed pores (3L) can reduce the hardness of the films and lower mechanical properties at shorter annealing times. At the same time, these features may enhance the optical performance and gradiency of the films with cracks and pores being subwavelength.

The TEM cross-sectional images reveal other structural details as shown in Fig. 5. In the TEM cross section, several layers are observed. The darkest layer is the top surface of the sample consisting of a PVD chromium layer deposited for the purpose of protecting the sample during FIB milling. The carbon layer is added as a contrast differentiation between the actual sample surface and the chromium layer.

In Fig. 5 (top), the black dots seen within the high-magnification image of the TMOS-b layer cross section produced at 580 °C for 60 min are NPs. This figure appears to show a NP size gradient which is larger near the film–substrate interface. This suggests that the particles nearer the substrate surface have reacted more than those further away from the surface possibly due to either concentration or temperature gradients during processing. This 1L film performed the best mechanically and comparable to the other 1L films optically.

As annealing temperature increases, the NPs appear to cluster. The NP clusters seen at 595 °C for 10 min appear to be nearly uniform in size and distribution. The sintering effect is apparent at the highest annealing temperature and time (610 °C for 60 min) showing lack of distinct features. At this annealing condition, the coating behavior approaches that of bulk glass which explains the better mechanical performance but lower optical performance at longer annealing times. It is interesting to note that the 580 °C film with the gradiency of NPs had better antireflection than the 610 °C film at an annealing time of 60 min.

In Fig. 5 (bottom), the three layers of TMOS-based coating are identifiable at higher magnification. The white patches that are visible are Si-based polymer matrix. The 3L films appear to have a denser distribution of subwavelength features than found at the 595 °C condition in the 1L film primarily arising from higher NP clustering.

###### Thin Film Fracture Mechanics.

The six sample conditions identified in Table 2 above were subjected to nano-indentation and single point microscratch tests to study the fracture mechanics of these films in an effort to better explain abrasion resistance results.

###### Nanoindentation Test.

The nanoindentation tests provided the indentation hardness and elastic modulus of the films as shown in Fig. 7. These data were used in fracture mechanics models, described in Appendix A, to drive the discussion surrounding Figs. 810 in Secs. 3.3.1 and 3.3.2.

For both 1L and 3L, the high optical–high mechanical films (solid green) were found to have better hardness to the moderate–low/low–low films (hatched red). The low optical–high mechanical films (dotted yellow) had hardnesses comparable to the green films (see online figure for color). While the hardness does not explain the mechanical behavior of the films alone, the 3L films tended to be harder and perform better mechanically than the 1L films (exception is at 610 °C, where the residual antireflection performance of 1L and 3L films was comparable). This may suggest that 3L had better suppression of crack nucleation which is consistent with the micrographs (Fig. 5) of the 3L film at 595 °C. The uniformly distributed NPs as observed in the cross section create a tortuous path for cracks and due to the hardness of the individual NPs themselves, there is a higher inhibition to crack nucleation. The coating thickness measured from the cross-sectional TEM images was overlaid as a line plot onto the hardness values. Within the limited data set, the 1L film shows a negative correlation between thickness and hardness. This is not apparent in the 3L film possibly arising from the complexity of the film structure.

In Fig. 8 (left), crack nucleation results appear to follow abrasion resistance results. The best 3L film (green) has 30% higher critical load for cracking (P) defined as a measure of crack nucleation resistance compared to the best 1L film (green). It is expected that 3L has a higher critical load for cracking largely due to higher hardness. This is consistent with the larger nanostructure found in the TMOS-b layer for the 3L film. It is interesting that, in general, the fracture toughness of 3L is less than 1L suggesting that the critical load for cracking as an indicator of crack nucleation may be a more important factor in determining the abrasion resistance of the films. The fracture toughness of the best 1L film (580 °C–60 min) is about 16% higher than that of the best 3L film (580 °C–30 min) on average which appears to be significant. The reduced fracture toughness in 3L may be due to the observed porosity in 3L compared with the NPs being the major phase observed in 1L. It is also possible that 3L has a lower fracture toughness compared to 1L due to the amorphous TMOS-a layer on top which provides lower resistance to crack propagation than the continuous layer filled with crystalline NPs. The amorphous TMOS-a layer appears to be detrimental to crack propagation resistance due to lack of ordered structure.

###### Scratch Test.

Scratch tests can provide insight into crack propagation as well as delamination resistance at the film–substrate interface. Figure 9 (top) shows the critical load for cracking which was measured during the scratch test, while Fig. 9 (bottom) shows the work of adhesion derived from the models using data from the nanoindentation and scratch tests. The critical load for cracking provides insight into crack nucleation and follows similar trends as shown for the critical load for cracking in nanoindentation with the 3 L films having generally higher crack nucleation resistance.

Work of adhesion is basically the work done in separating two materials from each other and hence in this case is a function depicting the film–substrate interaction. The work of adhesion is a function of the friction coefficient which was determined by the scratch test. From Fig. 9 (bottom), it is again apparent that the films with the worst abrasion resistance also have lower work of adhesion suggesting poor delamination resistance. It is to be highlighted that the high mechanical performance coating made at 610 °C for 30 min did not fail under the testing conditions maintained for the other samples. The friction coefficient for this coating condition was also the lowest at 0.03, while the rest had above 0.08. The values calculated for Wa were found to be comparable to that reported by others for similar coatings [27,28].

In Fig. 10, insight into the spallation resistance of the various coatings is provided based on Eq. (A8) for the strain energy release rate during crack growth, G. This graph shows that for 580 °C across both films, the energy release rate is very similar, while at 595 °C the 3L film shows more than 2 × higher G than 1L film. The fact that 610 °C 3L film did not show failure under the same testing condition shows that it has a much higher energy release rate than other films. It would require higher testing loads to determine the true G value for this film. It is expected that the acid gel allows for better structural transition from the substrate to the film, thus improving the adhesion in contrast to the sharp change in material composition and structure in the 1L film.

The results show that the best optical and mechanical properties of 3L were obtained at the lowest temperature and a moderate annealing time. The best 3L film had better optical performance than the best 1L film (0.2% increase) with comparable residual antireflection. We believe this is largely due to the ability to improve mechanical properties at lower annealing times which avoided excessive sintering of the nanostructure. The ability to achieve this with 3L is primarily attributed to the elimination of cracking during annealing due to the existence of a harder top coat that was better able to suppress crack nucleation. In general, 3L provided better crack nucleation resistance and scratch resistance and, to a lesser degree, better delamination resistance and spallation resistance. The use of a top film to increase the crack nucleation resistance of the film provides one means to decouple the general trend of reducing optical performance and increasing residual antireflection with increasing annealing time. Further, observations from the electron micrographs suggest that the bottom film in 3L provided a smoother structural and density gradient at the interface with the glass substrate, improving the delamination and spallation resistance of the film.

## Conclusions

Overall, the results show that while the two films studied in this paper had similar optical performance, the three-layer coating was found to have better abrasion resistance than the single-layer coating. Analyses of the film structure, calorimetric, and gravimetric behavior during annealing and thin film fracture mechanics have provided insights for interpreting these results. The presence of defects such as pores and cracks in the coatings caused during annealing reduced the mechanical performance of the coatings. Moderate annealing temperatures led to cracks and pores caused by residual stresses due to densification as well as the evolution of gases. With higher annealing temperatures, cracks appear to heal themselves in the single-layer film. The results show that improved abrasion resistance in the three-layer coating was due, in part, to the superior crack nucleation resistance provided by the use of a harder top layer, despite the better crack propagation resistance of the single-layer film provided by the NPs spread throughout the microstructure of the film. Further, some evidence exists that improved abrasion resistance in the three-layer structure was associated with interfacial properties like work of adhesion and energy release rate.

## Acknowledgements

This research was supported by the National Science Foundation under Grant No. IIP 1230456. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. The research in this paper was conducted at the Oregon State University and relates to products or technology licensed to CSD Nano, Inc. In accordance with the Oregon State University policy, Dr. Paul discloses that he holds a significant financial interest in CSD Nano, Inc.

## Appendices

###### Crack Resistance

The first line of defense for mechanical failure is to avoid crack nucleation [16,2933]. The critical load (in millinewton) for cracking under indentation (P) can be described as a function of both the elastic modulus and hardness of the film (H) given by the Malzbender's model [16] Display Formula

(A1)$P=Erh2[0.2ErH+0.75π4HEr]2$

where h is the penetration depth, and Er is the reduced elastic modulus of the film accounting for indenter deformation and the actual contact area of the indenter. Since P describes the load at which cracking initiates, this term is used to describe the crack nucleation resistance of the films.

A more normalized evaluator for crack propagation resistance is fracture toughness. This is because fracture toughness indicates the resistance of the material for crack growth. In nanoindentation, the fracture toughness (in MPa√m) is related to the indentation load using the following equation [31]: Display Formula

(A2)$KIC=0.016(EH)0.5Pc1.5$

where c is the length of radial cracks. Since it is difficult to measure the length of the radial cracks, the crack size was estimated using the model proposed by Bull [33] using the relation Display Formula

(A3)$c=hmcotφ+(QErH−1)hexcotφ$

where hm is the maximum depth of penetration, φ is the face-to-center angle of the indenter, Q is a constant, H is the hardness, and hex is the extra penetration caused when the indenter tip enters a crack. This “pop-in” phenomenon can be observed in the load versus displacement curve obtained during nanoindentation. In the results obtained in our nanoindentation tests, no such pop-in phenomenon was observed and hence hex was taken as zero reducing Eq. (A3) to Display Formula

(A4)$c=hmcotφ$

The computed value of c can be plugged into Eq. (A2) above to compute the fracture toughness of the coating. Thus, P and KIC together describe the crack resistance of the films considering both crack nucleation and crack propagation.

###### Scratch and Delamination Resistance

Scratch tests involve applying a normal load and a tangential load across a sample surface using a stylus [3436]. The load is applied progressively until the point of gross failure of the coated sample [35]. Appearance of cracks is marked by a lower critical load (LC1), and delamination occurs at LC2. The lower critical load (LC1; in Newton) is a measure of resistance to scratching or crack propagation, while LC2 (in Newton) can be used to compute the work of adhesion between the film and the substrate. The work of adhesion is a metric for delamination resistance and preferred over experimentally measured Lc2 as Wa considers other parameters like elastic modulus, friction coefficient, and film thickness and is hence a comprehensive function. The critical load for delamination, LC2, is calculated in general using the model derived by Bull et al. [34] Display Formula

(A5)$Lc2=Aυμ(2EWat)0.5$

where A is the cross-sectional area of the scratch, E is the elastic modulus of the film, υ is the Poisson's ratio of the film, t is the thickness of the film, μc is the coefficient friction, and Wa is the work of adhesion between the film and the substrate. The above equation suggests that delamination resistance increases with a decrease in μc and t and an increase in E and Wa.

The above expression was modified by Attar and Johannesson [36] since the tangential force causing coating removal does not act on the total scratch track cross-sectional area but only on the cross section of the coating. The modified expression is given by Display Formula

(A6)$Lc2=dυμ(2tEWa)0.5$

where d is the scratch width. Attar et al. also observed that concentrated load causes interface failure and flaking simultaneously. This expression can be rewritten to compute the work of adhesion (in Joules/meter2) based on the experimentally measured LC2 from the scratch test as follows: Display Formula

(A7)$Wa=Lc22υ2μ22d2tE$

###### Spallation Resistance

Spallation is the severest failure mechanism and signifies termination of the cracks as they reach the film–substrate interface causing material removal [37]. During buckling failure of the film, delamination may occur resulting in an energy release rate (in Joules/meter2) during crack growth given by Display Formula

(A8)$G=12πa(dΔUda)=(1−υ)(1−α)t(σ02−σc2)/E$

where a is the crack radius, ΔU is the energy difference, υ is the Poisson's ratio, α is a constant, t is the film thickness, σc is the critical stress, σ0 is the compressive yield stress, and E is the elastic modulus. The energy release rate during crack growth is the energy rate input into the coating needed for the cracks to reach the interface leading to spallation of the coating off the substrate. The higher this rate, the better the resistance of the film to spallation. In the above expression, the critical stress (in Pascal) is given by Hutchinson's equation [38] Display Formula

(A9)$σc=[π2E12(1−υ2)](ta)2$

Based on the work of adhesion given by Rickerby [39] and Laugier [40], the stress for delamination (in Pascal) is calculated using Display Formula

(A10)$σ=2EWat$
Assuming that spallation occurs when the compressive yield stress in the film equals the stress for delamination, the above two parameters can be inserted into Eq. (A8) to compute the spallation resistance of the film (Table 3).

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Li, X. , and Shen, J. , 2011, “ A Scratch-Resistant and Hydrophobic Broadband Antireflective Coating by Sol–Gel Method,” Thin Solid Films, 519(19), pp. 6236–6240.
Floch, H. G. , and Belleville, P. F. , 1994, “ A Scratch-Resistant Single-Layer Antireflective Coating by a Low Temperature Sol-Gel Route,” J. Sol-Gel Sci. Technol., 1(3), pp. 293–304.
Cook, R. F. , and Pharr, G. M. , 1990, “ Direct Observation and Analysis of Indentation Cracking in Glasses and Ceramics,” J. Am. Ceram. Soc., 73(4), pp. 787–817.
Mittal, K. , and Kern, W. , 1987, “ Selected Bibliography on Adhesion Measurement of Films and Coatings,” J. Adhes. Sci. Technol., 1(1), pp. 247–262.
Vossen, J. , 1978, Adhesion Measurement of Thin Films, Thick Films and Bulk Coatings, Vol. 640, ASTM Specification Technical Publications, West Conshohocken, PA, pp. 122–131.
Davies, P. , Blackman, B. R. K. , and Brunner, A. J. , 1998, “ Standard Test Methods for Delamination Resistance of Composite Materials: Current Status,” Appl. Compos. Mater., 5(6), pp. 345–364.
Henning, S. , and Svensson, L. , 1981, “ Production of Silica Aerogel,” Phys. Scr., 23(4B), p. 697.
Hæreid, S. , Anderson, J. , Einarsrud, M. , Hua, D. , and Smith, D. , 1995, “ Thermal and Temporal Aging of TMOS-Based Aerogel Precursors in Water,” J. Non-Cryst. Solids, 185(3), pp. 221–226.
AGC-Solar, 2012, “AGC Solite™ Glass Technical Sheet,” AGC Glass Company North America, Alpharetta, GA.
Han, S.-Y. , Paul, B. K. , and Chang, C.-H. , 2012, “ Nanostructured ZnO as Biomimetic Anti-Reflective Coatings on Textured Silicon Using a Continuous Solution Process,” J. Mater. Chem., 22(43), pp. 22906–22912.
Masalov, V. , Sukhinina, N. , Kudrenko, E. , and Emelchenko, G. , 2011, “ Mechanism of Formation and Nanostructure of Stöber Silica Particles,” Nanotechnology, 22(27), p. 275718. [PubMed]
Cumming, G. , 2007, “ Inference by Eye: Pictures of Confidence Intervals and Thinking About Levels of Confidence,” Teach. Stat., 29(3), pp. 89–93.
Fabbri, P. , Singh, B. , Leterrier, Y. , Månson, J.-A. , Messori, M. , and Pilati, F. , 2006, “ Cohesive and Adhesive Properties of Polycaprolactone/Silica Hybrid Coatings on Poly (Methyl Methacrylate) Substrates,” Surf. Coat. Technol., 200(24), pp. 6706–6712.
Volinsky, A. , Moody, N. , and Gerberich, W. , 2002, “ Interfacial Toughness Measurements for Thin Films on Substrates,” Acta Mater., 50(3), pp. 441–466.
Malzbender, J. , de With, G. , and den Toonder, J. M. J. , 2000, “ Determination of the Elastic Modulus and Hardness of Sol–Gel Coatings on Glass: Influence of Indenter Geometry,” Thin Solid Films, 372(1–2), pp. 134–143.
Malzbender, J. , de With, G. , and den Toonder, J. M. J. , 2000, “ Elastic Modulus, Indentation Pressure and Fracture Toughness of Hybrid Coatings on Glass,” Thin Solid Films, 366(1–2), pp. 139–149.
Anstis, G. , Chantikul, P. , Lawn, B. R. , and Marshall, D. , 1981, “ A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness—I: Direct Crack Measurements,” J. Am. Ceram. Soc., 64(9), pp. 533–538.
Nastasi, M. A. , Parkin, D. M. , and Gleiter, H. , 1993, Mechanical Properties and Deformation Behavior of Materials Having Ultra-Fine Microstructures, Springer, Heidelberg, Germany.
Bull, S. J. , 2011, “ Analysis Methods and Size Effects in the Indentation Fracture Toughness Assessment of Very Thin Oxide Coatings on Glass,” C. R. Mec., 339(7–8), pp. 518–531.
Bull, S. J. , Rickerby, D. S. , Matthews, A. , Leyland, A. , Pace, A. R. , and Valli, J. , 1988, “ The Use of Scratch Adhesion Testing for the Determination of Interfacial Adhesion: The Importance of Frictional Drag,” Surf. Coat. Technol., 36(1–2), pp. 503–517.
Blees, M. H. , Winkelman, G. B. , Balkenende, A. R. , and den Toonder, J. M. J. , 2000, “ The Effect of Friction on Scratch Adhesion Testing: Application to a Sol–Gel Coating on Polypropylene,” Thin Solid Films, 359(1), pp. 1–13.
Attar, F. , and Johannesson, T. , 1996, “ Adhesion Evaluation of Thin Ceramic Coatings on Tool Steel Using the Scratch Testing Technique,” Surf. Coat. Technol., 78(1), pp. 87–102.
Evans, A. , and Hutchinson, J. , 1984, “ On the Mechanics of Delamination and Spalling in Compressed Films,” Int. J. Solids Struct., 20(5), pp. 455–466.
Hutchinson, J. , and Suo, Z. , 1992, “ Mixed Mode Cracking in Layered Materials,” Adv. Appl. Mech., 29(63), p. 191.
Rickerby, D. , 1988, “ A Review of the Methods for the Measurement of Coating-Substrate Adhesion,” Surf. Coat. Technol., 36(1), pp. 541–557.
Laugier, M. T. , 1984, “ An Energy Approach to the Adhesion of Coatings Using the Scratch Test,” Thin Solid Films, 117(4), pp. 243–249.
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## References

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Chaoui, R. , Mahmoudi, B. , and Si Ahmed, Y. , 2008, “ Porous Silicon Antireflection Layer for Solar Cells Using Metal-Assisted Chemical Etching,” Phys. Status Solidi (a), 205(7), pp. 1724–1728.
Yanagishita, T. , Nishio, K. , and Masuda, H. , 2009, “ Anti-Reflection Structures on Lenses by Nanoimprinting Using Ordered Anodic Porous Alumina,” Appl. Phys. Express, 2(2), p. 2001.
Prado, R. , Beobide, G. , Marcaide, A. , Goikoetxea, J. , and Aranzabe, A. , 2010, “ Development of Multifunctional Sol–Gel Coatings: Anti-Reflection Coatings With Enhanced Self-Cleaning Capacity,” Sol. Energy Mater. Sol. Cells, 94(6), pp. 1081–1088.
Nagel, H. , Metz, A. , and Hezel, R. , 2001, “ Porous SiO2 Films Prepared by Remote Plasma-Enhanced Chemical Vapour Deposition—A Novel Antireflection Coating Technology for Photovoltaic Modules,” Sol. Energy Mater. Sol. Cells, 65(1–4), pp. 71–77.
Haereid, S. , Dahle, M. , Lima, S. , and Einarsrud, M. A. , 1995, “ Preparation and Properties of Monolithic Silica Xerogels From TEOS-Based Alcogels Aged in Silane Solutions,” J. Non-Cryst. Solids, 186, pp. 96–103.
Chen, D. , 2001, “ Anti-Reflection (AR) Coatings Made by Sol–Gel Processes: A Review,” Sol. Energy Mater. Sol. Cells, 68(3), pp. 313–336.
Katayama, Y. , Ando, E. , and Kawaguchi, T. , 1992, “ Characterization of SiO2 Films on Glass Substrate by Sol-Gel and Vacuum Deposition Methods,” J. Non-Cryst. Solids, 147–148, pp. 437–441.
Li, X. , and Shen, J. , 2011, “ A Scratch-Resistant and Hydrophobic Broadband Antireflective Coating by Sol–Gel Method,” Thin Solid Films, 519(19), pp. 6236–6240.
Floch, H. G. , and Belleville, P. F. , 1994, “ A Scratch-Resistant Single-Layer Antireflective Coating by a Low Temperature Sol-Gel Route,” J. Sol-Gel Sci. Technol., 1(3), pp. 293–304.
Cook, R. F. , and Pharr, G. M. , 1990, “ Direct Observation and Analysis of Indentation Cracking in Glasses and Ceramics,” J. Am. Ceram. Soc., 73(4), pp. 787–817.
Mittal, K. , and Kern, W. , 1987, “ Selected Bibliography on Adhesion Measurement of Films and Coatings,” J. Adhes. Sci. Technol., 1(1), pp. 247–262.
Vossen, J. , 1978, Adhesion Measurement of Thin Films, Thick Films and Bulk Coatings, Vol. 640, ASTM Specification Technical Publications, West Conshohocken, PA, pp. 122–131.
Davies, P. , Blackman, B. R. K. , and Brunner, A. J. , 1998, “ Standard Test Methods for Delamination Resistance of Composite Materials: Current Status,” Appl. Compos. Mater., 5(6), pp. 345–364.
Henning, S. , and Svensson, L. , 1981, “ Production of Silica Aerogel,” Phys. Scr., 23(4B), p. 697.
Hæreid, S. , Anderson, J. , Einarsrud, M. , Hua, D. , and Smith, D. , 1995, “ Thermal and Temporal Aging of TMOS-Based Aerogel Precursors in Water,” J. Non-Cryst. Solids, 185(3), pp. 221–226.
AGC-Solar, 2012, “AGC Solite™ Glass Technical Sheet,” AGC Glass Company North America, Alpharetta, GA.
Han, S.-Y. , Paul, B. K. , and Chang, C.-H. , 2012, “ Nanostructured ZnO as Biomimetic Anti-Reflective Coatings on Textured Silicon Using a Continuous Solution Process,” J. Mater. Chem., 22(43), pp. 22906–22912.
Masalov, V. , Sukhinina, N. , Kudrenko, E. , and Emelchenko, G. , 2011, “ Mechanism of Formation and Nanostructure of Stöber Silica Particles,” Nanotechnology, 22(27), p. 275718. [PubMed]
Cumming, G. , 2007, “ Inference by Eye: Pictures of Confidence Intervals and Thinking About Levels of Confidence,” Teach. Stat., 29(3), pp. 89–93.
Fabbri, P. , Singh, B. , Leterrier, Y. , Månson, J.-A. , Messori, M. , and Pilati, F. , 2006, “ Cohesive and Adhesive Properties of Polycaprolactone/Silica Hybrid Coatings on Poly (Methyl Methacrylate) Substrates,” Surf. Coat. Technol., 200(24), pp. 6706–6712.
Volinsky, A. , Moody, N. , and Gerberich, W. , 2002, “ Interfacial Toughness Measurements for Thin Films on Substrates,” Acta Mater., 50(3), pp. 441–466.
Malzbender, J. , de With, G. , and den Toonder, J. M. J. , 2000, “ Determination of the Elastic Modulus and Hardness of Sol–Gel Coatings on Glass: Influence of Indenter Geometry,” Thin Solid Films, 372(1–2), pp. 134–143.
Malzbender, J. , de With, G. , and den Toonder, J. M. J. , 2000, “ Elastic Modulus, Indentation Pressure and Fracture Toughness of Hybrid Coatings on Glass,” Thin Solid Films, 366(1–2), pp. 139–149.
Anstis, G. , Chantikul, P. , Lawn, B. R. , and Marshall, D. , 1981, “ A Critical Evaluation of Indentation Techniques for Measuring Fracture Toughness—I: Direct Crack Measurements,” J. Am. Ceram. Soc., 64(9), pp. 533–538.
Nastasi, M. A. , Parkin, D. M. , and Gleiter, H. , 1993, Mechanical Properties and Deformation Behavior of Materials Having Ultra-Fine Microstructures, Springer, Heidelberg, Germany.
Bull, S. J. , 2011, “ Analysis Methods and Size Effects in the Indentation Fracture Toughness Assessment of Very Thin Oxide Coatings on Glass,” C. R. Mec., 339(7–8), pp. 518–531.
Bull, S. J. , Rickerby, D. S. , Matthews, A. , Leyland, A. , Pace, A. R. , and Valli, J. , 1988, “ The Use of Scratch Adhesion Testing for the Determination of Interfacial Adhesion: The Importance of Frictional Drag,” Surf. Coat. Technol., 36(1–2), pp. 503–517.
Blees, M. H. , Winkelman, G. B. , Balkenende, A. R. , and den Toonder, J. M. J. , 2000, “ The Effect of Friction on Scratch Adhesion Testing: Application to a Sol–Gel Coating on Polypropylene,” Thin Solid Films, 359(1), pp. 1–13.
Attar, F. , and Johannesson, T. , 1996, “ Adhesion Evaluation of Thin Ceramic Coatings on Tool Steel Using the Scratch Testing Technique,” Surf. Coat. Technol., 78(1), pp. 87–102.
Evans, A. , and Hutchinson, J. , 1984, “ On the Mechanics of Delamination and Spalling in Compressed Films,” Int. J. Solids Struct., 20(5), pp. 455–466.
Hutchinson, J. , and Suo, Z. , 1992, “ Mixed Mode Cracking in Layered Materials,” Adv. Appl. Mech., 29(63), p. 191.
Rickerby, D. , 1988, “ A Review of the Methods for the Measurement of Coating-Substrate Adhesion,” Surf. Coat. Technol., 36(1), pp. 541–557.
Laugier, M. T. , 1984, “ An Energy Approach to the Adhesion of Coatings Using the Scratch Test,” Thin Solid Films, 117(4), pp. 243–249.

## Figures

Fig. 1

Schematic of abrasion test rig for felt abrasion test

Fig. 2

Schematic of the silica-based ARC for (a) 1L and (b) 3L

Fig. 3

Performance indicators as a function of annealing time and temperature for (top) the 1L and (bottom) the 3L films

Fig. 4

Top surface scanning electron micrographs of the films: (a) 1L and (b) 3L. Green, red, and yellow conditions are shown from top to bottom (see online figure for color).

Fig. 5

Cross-sectional transmission electron micrographs of the films (top) 1L and (bottom) 3L. Green, red, and yellow conditions are shown from left to right (see online figure for color).

Fig. 6

Simultaneous DSC/TGA and mass spec analysis during annealing of single-layer TMOS-NP-base gel film

Fig. 7

Mechanical properties of 1L and 3L. Line plot against right y-axis on hardness chart shows the coating thickness.

Fig. 8

Crack resistance depicted as critical load for cracking under indentation and fracture toughness

Fig. 9

Scratch resistance depicted using (top) critical loads (LC1) and delamination resistance depicted using (bottom) work of adhesion

Fig. 10

Spallation resistance depicted using strain energy release rate

## Tables

Table 1 Descriptive terms for mechanical behavior of thin films
Table 2 Film conditions selected for the structural analysis showing color coding used for subsequent analyses
Table 3 Regression models describing performance indicators as a function of time and temperature

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