Foam-core meniscus coating is being used to retrofit 100 nm-scale sol–gel anti-reflective coatings (ARCs) onto in-field solar panels through the deposition, evaporation, and curing of wet films. Advantages of this technique include the means to control fluid flow relative to substrate motion and the ability to conform to large, warped substrates. While simple in practice, no models exist for predicting critical outcomes such as film thickness. In this paper, preliminary experiments are used to identify important process parameters, and an analytical model is developed and validated for predicting the thickness of silica sol–gel films deposited on solar glass.

## Introduction

Sol–gel anti-reflective coatings (ARCs) increase the power output of solar cells by reducing the reflection at the air-glass interface of the up-facing surface of the cover glass, thereby increasing the incident flux on the solar cell [1]. The thickness of ARCs is critical to their performance with the thickness of most ARCs being on the order of 100 nm [2]. Today, most sol–gel ARCs are deposited on solar cell cover glass within the factory. However, based on industry data, over 300 GW of solar cell capacity was installed between the years of 2008 and 2017 without an ARC [35]. This suggests that more than 1 × 109 solar cell panels exist without an ARC, leaving approximately 12 GW of power uncaptured by installed solar assets.

Industrial sol–gel chemistries exist for the thermal curing of ARCs on solar cell panels. However, the deposition of 100 nm thick sol–gel films onto warped, one meter wide cover glass in the field is challenging. Sol–gel ARCs are typically deposited using dip coating and meniscus coating methods involving the deposition of a wet film followed by solvent evaporation and thermal curing [5]. The uniformity of the dry film thickness is governed by wet film formation during wetting of the substrate.

In dip coating [69], the substrate is pulled at a finite velocity from a fluid reservoir forming a meniscus between the fluid and substrate. Consequently, dip coating cannot be used for the retrofitting of ARCs onto installed solar panels. Meniscus coating is capable of depositing sol–gel films onto down-facing surfaces of stationary substrates by pumping excess amount of precursor through a rigid porous applicator with relative motion to the substrate [7]. The unused precursor is collected and is recirculated during the coating process. Challenges with this approach for in-field deposition include: (1) no compliance between the applicator and the substrate making large area coating difficult due to substrate warpage; (2) difficulties of coordinating applicator motion and fluid flow due to them being independent processes; and (3) need to recycle fluid, which can be difficult for in-field conditions.

In this paper, a meniscus coating process is introduced based on the use of an inexpensive foam-core applicator. The applicator is capable of regulating fluid flow in relation to the relative motion between the applicator and substrate. Foam-core applicators have been used to deposit low viscous sol–gel solutions onto one-meter-scale solar cell cover glass forming suitable 100 nm thick sol–gel ARCs. The foam core provides (1) a reservoir of precursor fluid and (2) compliance between the applicator and substrate during deposition, adapting to slight variations in surface topology. Below, initial screening studies are used to identify critical foam-core meniscus coating parameters that affect coating thickness. Subsequently, an analytical model is developed and experimentally validated by depositing sol–gel ARCs while varying applicator head velocity and mass loading of the foam.

## Preliminary Experiments

In both dip coating and meniscus coating, relative movement between the applicator and substrate induces sufficient shear stress within the fluid meniscus to shear off a wet film [69]. The faster the relative movement, the thicker the wet film. In both cases, the final film thickness is controlled by a combination of gravity, viscous forces, and surface tension within the process. The meniscus model extends the dip coating model by accounting for instabilities in the meniscus caused by a falling film [7]. However, neither model anticipates new process parameters in the foam-core meniscus coating process as described below.

### Experimental Setup.

A foam-core applicator was used to coat a tetramethyl orthosilicate (TMOS)-isopropanol solution (98% isopropanol) onto soda-lime glass. An illustration of the felt-covered foam-core applicator setup used in this work is shown in Fig. 1. The applicator head, consisting of a piece of foam wrapped in felt under tension (Fig. 2, top and middle), is loaded with precursor solution. The high surface energy density within the felt constrains the fluid within the foam. Next, the head is set on a glass substrate (Sa < 0.2 μm) and pulled across the surface of the glass at a controlled rate using a nylon thread connected to a direct current (DC) motor. In order to stabilize the head during deposition, the head was connected to guide wheels by a rigid aluminum guide plate (Fig. 2, bottom). As the head is drawn across the substrate, the felt-wrapped foam-core applicator forms a meniscus with the substrate, which is sheared off forming a wet film (Fig. 3). Evaporation of all solvents from the wet film leads to the formation of an uncured dry film on the surface of the glass. Finally, the uncured dry film is cured in an oven forming a final cured dry film.

In these experiments, the 50.8 mm wide by 292.1 mm long head was designed to coat a 200 mm × 200 mm glass substrate. The foam core head was produced by placing a 25 mm × 50.8 mm × 228.6 mm foam core (HSM solutions, Conover, NC, HR15VN flexible polyurethane) onto a 127 mm × 280 mm piece of felt (100% white polyester anti-pill fleece) and pressing both into a 50.8 mm wide channel as the central part of a fixture as shown in (Fig. 2, top and middle). To ensure a smooth, uniform felt surface, the felt was placed in tension by placing an aluminum head tensioning plate, containing two slots 12.5 mm deep on both sides, over the foam and clamping the felt by pressing the remaining felt into the slots using two aluminum bars. To evaluate the repeatability of this process, seven heads were produced and the height from the bottom of the head plate to the substrate was found to be 23.6 ± 0.70 mm (all ± terms express the experimental standard deviation unless otherwise stated).

### Experimental Objective and Experimental Design.

Prior to performing the experiment, efforts were made to determine the effect of dry head mass and fluid mass loading on the linear velocity of the foam-core head. The rotational speed of the DC motor was calibrated to linear velocity at two dry head masses (385 and 560 g) and three mass loadings (77, 97, and 157 g) by measuring the time to traverse a 508 mm wide glass. Figure 4 shows the calibration of the linear speed as a function of applied voltage to the motor for a dry head mass of 385 g. Each data point is an average of five measurements and error bars show the experimental standard deviation. The maximum relative standard deviation across all samples was found to be 0.72%, which was considered acceptable.

In all experiments, the effect of the coating process was investigated using uncured dry films to eliminate biases caused by the curing process. Uncured dry film thickness was evaluated by the optical thickness (film thickness × refractive index (RI)) of the uncured film. Optical thickness is a good estimate of the physical film thickness assuming that the refractive index of the film remains constant. To investigate the use of the optical thickness of the uncured film as a suitable performance measure, the TMOS-based recipe used in this paper was used to produce three sets of uncured (after deposition) and cured (after curing) films of different thicknesses on 1 in. × 1 in. glass test articles. The films were spin-coated and cured at 580 °C for 1 h (35 °C/min) [2]. During the experiment, the transmissive spectra of the bare glass, the uncured film, and the cured film were measured using a JASCO V-670 UV-Vis spectrophotometer. Afterward, the transmissive response of the bare glass was subtracted from that of the uncured and cured films (Fig. 5).

Based on the well-known quarter-wavelength anti-reflective phenomenon, the optical thickness of the film (film thickness × refractive index) is known to be one quarter the wavelength for the peak increase in transmission [10,11]. In the case of Fig. 5 (top), the first curve has a wavelength for peak increase in transmission of 1016 nm. Therefore, the optical thickness of the uncured film was determined to be 254 nm. Table 1 shows the optical thicknesses for all cured and uncured films.

The spin-coated test articles with cured films were sputter coated with gold and then efforts were made to cross section in an FEI Helios 650 DualBeam focused ion beam-scanning electron microscope (uncured films could not survive cross-sectioning). Film cross section was imaged in an FEI Titan 80-200 transmission electron microscope (Fig. 6) and film thickness was measured (Table 1). The average relative standard deviation of the cured film thickness across the three cured films was found to be 2.6% based on ten measurements in three different regions of each film. Further, the RI of the three cured films was calculated by dividing the mean optical thickness by the measured mean thickness of the cured films (Table 1). The mean RI was found to be 1.42±0.04, which is close to the RI of 1.47 of sputter-coated SiO2 films obtained in roll-to-roll processes [12]. This demonstrates that optical thickness is an excellent indicator of dry film thickness for the TMOS-based recipe used in experiments below.

Further, the average optical thickness ratio of the two sets of films was found to be 1.4±0.15 (Table 1). The large standard deviation was skewed by the third uncured film thickness, which had a maximum outside the measurement range of the spectrophotometer. Consequently, these findings were considered to be worse case and the uncured film optical thickness was considered an acceptable performance measure for the coating process.

### Experimental Protocol.

In all experiments, the head was primed with solution by compressing the foam five times while immersing it in a bath of solution to ensure full wetting throughout the foam and felt. The desired mass of solution was attained by compressing the head to a fixed height on a mesh suspended above the bath to remove extraneous fluid. To determine mass loading, the head mass was weighed using a digital scale (Pelouze FP5 ± 2 g accuracy) after loading and subtracted from the dry head mass.

Prior to coating, the glass substrate was degreased with soapy water, tap water, acetone, methyl alcohol, and de-ionized water. The glass was then dried using nitrogen and scored with a grid pattern defining test articles roughly 37.5 mm × 25 mm that could be broken off after deposition and used for dry film evaluation. After cleaning and scoring the substrate, the voltage on the DC motor was set to control the head velocity during coating. Next, the loaded applicator was connected to the guide and set on the substrate with scoring patterns facing down. Coating was performed by drawing the head across the substrate producing a wet film. All films were produced using a head velocity of 127 mm/s. After 3 min, coated glass test articles were broken out of the substrate for dry film evaluation. The ambient temperature was recorded at the start and end of all the experiments. The temperature range was found to be 20.7±1.6 °C. No postcoating heat treatment was performed on the films.

To evaluate coating uniformity and repeatability of the foam-core meniscus coating setup, three 200 × 200 mm substrates were coated in three different batches (a new foam core head was prepared for each batch and the coatings were applied) under constant ambient conditions at a head velocity of 127 mm/s, a mass loading of 100 g, and a head mass of 385 g. One spectrophotometry measurement was taken from each of 12 test articles taken randomly from across the middle 80 mm × 100 mm region from each of the three substrates. The overall batch-to-batch film optical thickness was found to be 129±8.6 nm. The relative standard deviation of the film optical thickness was found to be 3.6% and 6.7% within a batch and batch-to-batch, respectively.

### Preliminary Results.

The red peak shift in Fig. 7 (top) suggests that the optical thickness of the coatings increased from about 145 nm to 200 nm with an increase of mass loading from 80 to 120 g. Each spectrum is an average of 12 (3 batches × 4 test articles from each batch) test articles. It is expected that this is due to a larger hydrostatic pressure in the foam increasing fluid flow across the felt as well as the size of the meniscus and the final film thickness. Figure 7 (bottom) shows no peak shift when the head plate mass was increased from 352 to 527 g. Consequently, it was concluded that for the foam and felt used, head plate mass, in the ranges of investigation, does not have a significant effect on meniscus formation.

## Model Development

For purposes of modeling, the process is divided into two independent steps: (1) formation of a static meniscus between the applicator and the substrate and (2) formation of a dynamic meniscus and entrained wet film as the applicator is drawn at constant velocity. It is assumed that when the head is loaded, any solution within the foam settles down, saturating the felt and building a hydrostatic pressure head of height, hf, within the foam and felt system. Once loaded, the applicator head is set onto the substrate where solid surface interactions draw solution from the felt-foam reservoir forming a static meniscus of finite size. The amount of solution coated onto a 200 mm × 200 mm glass substrate is well below 1% of the mass loading. It is therefore assumed that during processing, the hydrostatic pressure head in the felt-foam remains constant.

In prior work, gravitational and surface tension forces within the meniscus have been identified as important for static meniscus formation [79]. Here, the hydrostatic pressure head in the meniscus (100 μm scale) was replaced with the hydrostatic pressure within the felt-foam (1–10 mm scale) enabling consideration for the effect of mass loading. The surface pressure caused by the curvature in the meniscus, $κ$, is added signifying concavity by the use of a negative sign. These two pressures generate an internal pressure in the static meniscus that is counterbalanced with solid surface interactions as follows:
$γLV−κ+ρghf=γLVcosθa$
(1)
where $γLV$ is the liquid–vapor surface tension, $ρ$ is the density, $g$ is the gravity, $θ$ is the contact angle, and a is the capillary length given by $γ/ρg$. Solving for the curvature of the static meniscus
$κ=ρghfγLV−cosθa$
(2)

A dynamic meniscus is formed upon moving the head relative to the substrate at a constant velocity, U. During coating, fluid from the foam head moves across the felt and into the dynamic meniscus. Pressure drop through the felt was found to be negligible due to low volumetric fluid flux.

The curvature of the dynamic meniscus formed during coating has been used to calculate the thickness of the entrained wet film, ho [6,8,9]. Building on this work, Maleki et al. [13] defined λ as the characteristic length of the dynamic meniscus connecting the static meniscus to the entrained film, determined as
$λ=βaCa13$
(3)

where Ca is the capillary number given by $μU/γ$. In prior work, the term β was numerically determined, experimentally validated and shown to be robust across a wide range of parameters for a given process.

When λ < a, capillarity dominates gravity in the dynamic meniscus. In such cases, capillary forces are offset by viscous forces and the curvature of the static meniscus is matched to the dynamic meniscus given by [13]
$κ=hoλ2$
(4)

$ho=λ2ρghfγLV−cosθa$
(5)
Substituting Eq. (3) into Eq. (5) and recognizing that θ is ∼0 for alcohol yields a final equation for the wet film thickness
$ho=β2μUγLV23hf−γLVρg$
(6)
$M=mha−mhb+mr$
(7)

where mhb and mha are the mass of the head before loading and after loading, respectively, and mr is the residual mass remaining in the felt/foam after fully squeezing the head, which was determined to be the weight of the felt after squeezing (62 g). In our case, mhb was found to be 80 g larger than the dry weight because of the inability to force out all of the fluid from the felt/foam. The remaining 18 g was expected to be distributed within the foam structure and was not considered connected to the pressure head.

Assuming that the loaded foam core is flat on the bottom and that all of the solution settles to the bottom, the hydrostatic head as a function of mass loading was determined by
$hf=Mρs Efw⋅l$
(8)

where $w$ is the foam width, $l$ is the foam length, $Ef$ is the porosity of the foam (89.5%), and $ρs$ is the density of the solution.

The final uncured dried film thickness, $d$, was predicted by knowing the concentration of TMOS, $C$, porosity of the dried film, $Efilm$, and wet film thickness predicted above
$d=hoC1−Efilm$
(9)

## Experimental Methods

For this work, calibration curves were collected to determine β and a follow-up experiment was used to validate the model. The sol–gel recipe used to calibrate the foam-core model was based on an aerogel refined from Palanisamy et al. [2] involving the use of TMOS (Sigma Aldrich, 98%) as a primary reagent in a solution of anhydrous >99.99% isopropyl alcohol (Macro), ammonium hydroxide (5 N), and distilled water. In prior work, spin coating of the original methanol sol–gel recipe was found to produce a sol–gel ARC consisting of an amorphous silica matrix containing pores and fine silica nanocrystals. The final molar ratio of the TMOS:isopropanol:ammonium hydroxide:distilled water solution used here was 1:83.5:0.33:6.67. An estimate for the porosity of the cured dry films (13%) was determined based on the effective index of refraction of the film determined previously [14]. The porosity of the uncured film (18%) was estimated by multiplying the porosity of the cured dry film with the optical thickness ratio (uncured to cured films) in Table 1.

The same felt and foam combination reported earlier was used for both calibration and validation experiments. During experimentation, the ambient temperature was between 16.2 and 16.6 °C. An AMW-2000 precision scale (0.1 g graduation and ± 0.2 g accuracy) was used for all mass measurements. For calibration, a full factorial experiment was conducted across five head velocities (95/111/128/144/160 mm/s) and three mass loadings (77/92/107 g). One replicate was conducted providing 30 total coatings with four spectrophotometric test articles each for a total of 120 dry film measurements. The order for producing the 30 coatings was randomized to remove any bias.

## Results and Discussion

On average, the uncured dry film coatings performed as ARCs, improving transmission through the glass substrate by an average of 3.23% at peak wavelengths between 480 and 1410 nm. Further, as expected, Fig. 8 shows an increase in film thickness with an increase in head velocity. The average model percent errors at a β of 0.21 for the 77, 92, and 107 g mass loading curves were 4.64%, 2.49%, and 2.28% reflecting good agreement.

Figure 8 clearly demonstrates that the model is able to adapt to changes in mass loading with the model accurately predicting a nearly linear increase in dry film thickness at higher mass loadings. Increases in mass loading are expected to increase the size of the meniscus due to the larger hydrostatic pressures provided by the foam. While calibration curves are expected to provide a good fit, it is encouraging that the model estimates the appropriate curvature and spacing between all three mass loading curves.

In order to validate the robustness of the model, a second set of coatings were produced using a different ARC recipe under a variety of head velocities (250, 275, 300, 325, and 349 mm/s) at 95 g mass loading. A methanol-based recipe was chosen for these validation experiments. The molar ratio of the TMOS:methanol:ammonium hydroxide:distilled water sol–gel solution was 1:157.8:0.33:6.67. After deposition, the film was air dried and annealed at 580 °C for 1 h in an atmospheric furnace [2]. The porosity of the cured dry film was taken from the literature. The viscosity, density, and surface tension of the methanol were also changed in the model.

Figure 9 shows that the model is robust providing values that are in good agreement with experimental results. The average modeling error for this plot is 8.1%. The larger amount of variation shown in the experimental data is due to the much faster evaporation rate of methanol which can influence dry film formation.

## Conclusions

A model was developed for predicting the dry film thickness produced from a felt-covered foam-core meniscus coating process for economically coating 100 nm thick films over large substrates. The model was calibrated and validated across multiple anti-reflective coating recipes. The model was found to accurately predict changes in optical film thickness due to both mass loading and velocity showing that both cured and uncured film thickness are affected by mass loading in the foam-core meniscus coating process. This was attributed to a larger meniscus caused by higher hydrostatic pressures. The mass of the applicator head was not found to affect the optical thickness of uncured films.

## Acknowledgment

This research was supported by the National Science Foundation Grant No. IIP 1230456 and via the Major Research Instrumentation program under Grant No. 1040588. The research described was conducted at Oregon State University (OSU) and relates to technology licensed to an external company. In accordance with OSU policy, Dr. Paul and Dr. Chang disclose that they hold a financial interest in this company.

## Funding Data

• National Science Foundation (Grant No. IIP 1230456, Funder ID: 10.13039/100000001).

• The National Science Foundation via the Major Research Instrumentation (MRI) Program (Grant No. 1040588, Funder ID: 10.13039/100000001).

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