Precise Intergranular Voids Control of MgF2 via Solidifying Micelle‐Carried Precursor for Tunable Refractive Index

Porosification of fluoride can be effectively utilized in various applications, based on its abundance of exposed active sites. However, previous approaches have drawbacks in terms of application in fields that require meticulous control over porosity. Herein, an innovative strategy is suggested for achieving precise porosity tuning using a micelle‐carried MgF2 precursor intermediate. As the size of the MgF2 precursor clusters increases through micellization, the sizes of the resulting solidified MgF2 grains and the intergranular voids between the grains increase. Controlled MgF2 with intergranular voids can achieve very low‐refractive indices (≈1.04) with extremely fine refractive index control intervals (0.01–0.04). By employing extreme controllability of refractive index, graded refractive index antireflective coating is applied to the quartz window, and an average transmittance of ≈97.96% (250–1100 nm) is obtained. Finally, the coating is applied to a perovskite half‐cell enabling a ≈22.46% increase in the light‐absorption efficiency.


Introduction
3] For this sense of view, broadband and omnidirectional antireflection coating (ARC) is a crucial key technology to enhance the use of incident light.ARC is highly desirable for achieving a high photoelectric efficiency as well as offering their cost-effectiveness and scalability.The primary challenge of existing ARCs lies in achieving a refractive index as close as that to the air (n = %1) by employing effective medium approximation (EMA), [4,5] which is attributed to the relatively high-refractive indices of existing solid materials in nature.Thus, precise refractive index control is another essential technique for the effective implementation of ARC to the variable refractive index substrate materials.To make low-refractive index materials, two main strategies are considered.First, the moth-eye structures are attractive to make an optimal ARC, [6,7] while it is challenging to implement the precisely designed structure to the optical materials such as curved lenses.Additionally, the discontinuity at the interface of moth-eye structure and the substrate materials make the light propagating through complexity of refractive index profiles that causes light loss.Furthermore, the structural and optical uniformity throughout the substrate decreases as the substrate area increases.10] To embed pores, most studies insert bead templates into the matrix of the material and subsequently remove them through an elimination process.This method is easy to control the density of pores through quantify of additives.However, controlling the pore size is inherently challenging, since the pore size is fully dependent on the templates.Meanwhile, light scattering is significantly influenced by the pore sizes.To minimize pore-induced scattering, the pore sizes should be less than %1/15 of the incident light's wavelength. [11]Consequently, to cover a wide range of wavelengths (ultraviolet [UV] to infrared [IR]), extremely small pores are required.However, templates with a narrow size distribution (low-polydispersity index, PDI) generally have larger sizes than the incident light.Conversely, sufficiently small templates that ignore scattering tend to have a comparatively high PDI, [12] leading to inevitable light loss due to nonuniform scattering.
Poloxamers have been adopted to produce porous materials for various fields, including drug delivery, [13] catalysis, [14] batteries, [15] and etc. [16] Due to their amphiphilic property, they form micelles in various solutions, allowing the formation of nano-to micropores in the matrix.Poloxamers are nonionic triblock copolymers composed of two hydrophilic poly(ethylene oxide) (PEO) blocks at the chain ends and a hydrophobic poly(propylene oxide) (PPO) block at the center.When a poloxamer is used as a self-template (micelle) to form a scaffold, it can solve the issue of scattering due to the small size of the micelles. [17]For poloxamers to form micelle structures in a solution, factors such as the critical micelle concentration (CMC), critical micelle temperature, and cloud point must be considered.Additionally, the size and shape of the resulting micelles are dominantly determined by the lengths of the PEO and PPO chains.When the concentration of the poloxamers is in the CMC range, they become thermodynamically stable and self-assemble into nanoscale (10-200 nm) micelles.During the solidification process, the poloxamer micelles are vaporized as byproducts through calcination, occupying pores within the medium.Below the CMC, the micelles disintegrate due to the interactions between the amphiphilic structure and the chains. [18]In contrast, at concentrations significantly higher than the CMC, the micelles begin to densely pack and assemble through mutual interactions, leading to comparatively large agglomerates. [19]This can result in scattering issues and light loss as the pore size increases.In addition, when removing the poloxamers through heat treatment, the micelle structure contracts, resulting in a decrease in the size of the formed pores.As the pore size decreases, the density of the air within the pores decreases, which impedes refractive index control.Therefore, a delicate balance between light scattering due to large pores (originating from micelle aggregation) and refractive index control based on pore density is essential for realizing of broadband-working ARC.
Herein, we trigger the growth of MgF 2 grains started from micellized precursor intermediate (MPI) encapsulated by poloxamers (F127 = [MPI] F127 and L35 = [MPI] L35 ).During the solidification of the MPIs to yield MgF 2 , intergranular voids are simultaneously introduced into the MgF 2 films.Before the solidification step (MPI status), the PPO chains are noncovalently binding with the precursor intermediates (Mg(CF 3 COO) 2 ), and the PEOs encapsulate the surface of the micelles, stabilizing the precursor intermediate clusters.The concentration of the poloxamer determines the size of the formed micelle (and MgF 2 grains); however, since an excessive amount of poloxamers can disrupt the chemical equilibrium, adding short length poloxamers could address the issue.By employing the strategy of controlling the size of the MPIs, we were able to precisely manipulate the density of the intergranular voids.The average-refractive index of the solidified MgF 2 films with voids was precisely adjusted from 1.40 to 1.04, and the refractive index gap between the substrate and air was continuously filled.Based on the strategy for achieving precise refractive indices control, a graded refractive index (GRIN) coating was produced to ensure the broadband and omnidirectional antireflection (AR) performance.The GRIN MgF 2 ARC was applied to a quartz substrate, and it delivered excellent average transmittance enhancements across the broadband spectrum (%96.33,%99.24, and %97.62% for UV, visible, and near-infrared [NIR], respectively).Additionally, it exhibited superior performance under high-angle (65°) incident condition, achieving low average reflectance values of %17.97%, %22.91%, and %18.42% in the UV, visible, and NIR regions, respectively.This broadband and omnidirectional GRIN MgF 2 ARC that was demonstrated to exhibit leading-edge performance was applied to perovskite half-cell (PHC), and it significantly improved the light-absorption efficiency of the PHC, achieving a maximum efficiency of %22.46%.

Preparation of the Micellized Mg(CF 3 COO) 2 Intermediate and MgF 2 Characterization
Although the method of embedding and subsequently removing templates to create pores in materials is suitable for achieving high porosity, it is challenging to precisely control the porosity in the nanoscale range.We propose a synthetic approach involving the formation of intergranular voids through MgF 2 growth using MPIs.Notably, this approach is well developed in drug delivery research, as shown in Figure 1a.The Mg(CF 3 COO) 2 are encapsulated by poloxamers, forming the micelle structures.During the solidification process, the encapsulated MPIs are transformed into MgF 2 .When the grain size of MgF 2 is small, the packing-density increases, resulting in compact film formation.As the grain size increases, the packing density of the film decreases and spaces are created between the grains.To increase the MgF 2 grain size, two different types of poloxamers with different chain lengths are employed to control the size and density of the MPIs.For large MgF 2 grains, intergranular voids are formed between the grains in the film.
As shown in the solution process schematics, Mg(OC 2 H 5 ) 2 undergoes fluorination with CF 3 COOH, followed by dissolution in isopropyl alcohol (IPA) to form the Mg(CF 3 COO) 2 intermediates.Porous materials have been widely studied through the control of cohesion using particle-and polymer-based approaches with the sol-gel method.[22] Fouriertransform infrared (FT-IR) spectroscopy was implemented to qualitatively analyze Mg(OC 2 H 5 ) 2 and Mg(CF 3 COO) 2 , as shown Figure S1a, Supporting Information.The absorption peaks of C-C bending, C-F stretching, and C-O stretching for Mg(CF 3 COO) 2 can be clearly observed at the wavenumbers of %1199, %1141, %1088 cm À1 , respectively.The %474 cm À1 peak indicative of the Mg-O bond of Mg(CF 3 COO) 2 shifted to a lower wavenumber compared to that of Mg(OC 2 H 5 ) 2 , attributed to the increased molecular mass and bond length. [23,24]Since the sizes of the MPIs vary depending on the molecular weight of the poloxamer, we employed F127 and L35, which have relatively high and low molecular weights, respectively.The zeta potential of Mg(CF 3 COO) 2 in IPA has a positive charge (%þ12.76mV).When a poloxamer is added to the precursor solution, the PEO segments bind with IPA, whereas the PPO segments encapsulate the Mg(CF 3 COO) 2 through noncovalent bonding in IPA, forming micelles and obtained clear solution as shown Figure S1c, Supporting Information.The zeta potential of the encapsulated MPIs in the solution changes from positive to negative ([MPI] F127 : %À7.33 mV, [MPI] L35 : %À7.73 mV) (Figure S1b, Supporting Information).Next, Mg(CF 3 COO) 2 and the MPIs are solidified by calcination, and the organics (poloxamers or solvent molecules) are decomposed and vaporized as byproducts (Figure S1d, Supporting Information).X-ray photoelectron spectroscopy (XPS) and grazing incidence X-ray diffraction (GIXRD) were implemented to determine the chemical state and crystallinity of the MgF 2 films solidified from the encapsulated MPIs.The XPS spectra in Figure 1b show the chemical states of Mg 2p and F 1s in MgF 2 .The peak indicative of the Mg─F and Mg─O bonds in the Mg 2p spectra of all the samples were observed at %50.9 and %49.5 eV, respectively, and the F 1s peak appeared at %685.71 eV, corresponding to the Mg─F bond.The peaks associated with Mg─F and Mg─O for all samples appeared in the same position, and the stoichiometry of Mg and F was 1:2. [25]ince the solvent molecules and poloxamers are fully eliminated during the calcination process (%300 °C), they do not affect the chemical states of MgF 2 .Thus, to evaluate the lattice structures of the MgF 2 film based on the chain length of the poloxamers, GIXRD analysis was performed as shown in Figure 1c.The diffraction patterns of MgF 2 revealed the presence of a tetragonal phase (JCPDS: 00-006-0290, space group: P42/mm), and the diffraction patterns of the MPIs-originated MgF 2 films appeared at very similar angles, indicating that the poloxamer does not alter the crystalline phase.Conversely, the diffraction peak intensities of MgF 2 increase with the addition of the poloxamers, and the MgF 2 film prepared using the [MPI] L35 ([MgF 2 ] L35 ) sample exhibits the highest intensity.Notably, the diffraction intensity of a materials is related to its grain sizes. [26]Here, the poloxamer acts as a surfactant for the precursors and promotes the growth of MgF 2 grains by soft-confinement during the solidification step.Furthermore, the size of the micelle and its distribution vary depending on the quantity and the length of the poloxamers employed, which, in turn, affects the amount of intermediate species captured within the micelles.This also affects the MgF 2 grain shape in the resulting solid film.
Scanning electron microscopy (SEM) analysis was conducted to measure the change in the grain sizes of MgF 2 under heterogenous poloxamers-loading conditions.Figure 2a shows crosssectional SEM images of MgF 2 , [MgF 2 ] F127 , and [MgF 2 ] L35 .The grains in the intact MgF 2 film derived from the as synthesized precursor solution are very small.When F127 introduced into the precursor solution, the sizes of the solidified MgF 2 grains increase compared with the previous sizes.When L35 is introduced instead of F127, the largest MgF 2 grains are observed.Additionally, as the grain size increases, the size of the intergranular voids also gradually increases.In the top-view SEM images, the sizes of the MgF 2 grains and intergranular voids are more clearly visible and distinguishable from the information in the cross-sectional SEM images (Figure 2b).To quantify the morphologies, the sizes of 100 grains per sample were measured using image analysis software (ImageJ, Figure 2c).The average grain size of the MgF 2 sample was %210.77(AE139.72)nm 2 , which increased to %539.34 (AE270.96)nm 2 and %1262.94(AE623.80)nm 2 when micellization was performed with F127 and L35 poloxamers, respectively.Small MgF 2 grains densely pack together; however, as the grain size increases, gaps form between the grains, serving as voids, the sizes of which are proportional to the grain sizes.From the observations, we expect that there are certain relationship among the existence, quantity, and type of poloxamers in the intermediate solution and the obtained grains and intergranular voids (porosity), which is clearly noticeable after the solidification step.
The MPI conditions, measured refractive indices of the solidified MgF 2 films, and variation in the series of the solidified MgF 2 films derived from various concentrations of poloxamers are summarized in Table S1, Supporting Information.Figure 2d plots the changes in the refractive indices in the UV (250 nm), visible (500 nm), and NIR (750 nm) regions, and the full-range refractive index profiles for different MPI conditions are depicted in Figure S2a, Supporting Information.As shown, the refractive index of MgF 2 decreases from 1.43 to 1.02 at λ = 250 nm (UV region), from 1.38 to 1.05 at λ = 500 nm (visible region), and from 1.38 to 1.07 at λ = 750 nm (NIR region).Since the decrease in the refractive index applies not only to the NIR and visible regions, but also to the UV region, the size of the intergranular voids formed in the MgF 2 films is expected to be 30 nm or less.Using our proposed method to control porosity, the resulting intergranular voids were relatively smaller than those obtained using bead templates.This eliminates additional concerns regarding the correlation among the wavelength of the incident light, the pore size, and scattering.Figure 2e shows the tunable refractive indices of MgF 2 for each poloxamer type, calculated from the average refractive indices of the representative wavelengths (250, 500, and 750 nm).The average-refractive index of [MgF 2 ] F127 was modulated in the 1.40-1.22range by adding various concentrations of F127.Although very low-refractive indices can be obtained using only one type of F127 (Figure S3a, Supporting Information), it cannot be fine-tuned, and as the concentration of F127 increases, the [MPI] F127 molecules become more densely packed, and the possibility of different types of blocks coming into contact with each other increases.This can lead to the gelation of the micellized [MPI] F127 , [27] which can be stabilized by various interactions such as van der Waals forces, hydrogen bonding, or electrostatic interactions, resulting in a hemisphere-shaped pattern with thicknesses of dozens of nanometers (Figure S3b, Supporting Information) and diameters of tens to hundreds of nanometers (Figure S3c, Supporting Information).In addition, these patterns cannot be used as thin films because they can scatter light.Contrarily, if a single type of L35 is used, the refractive index of [MgF 2 ] L35 cannot be adjusted from 1.39 to 1.17 because of the inherent size of the poloxamer's micelle and its CMC.Therefore, it is possible to finely adjust the refractive index using poloxamer blends ([MgF 2 ] F127þL35 n = 1.21-1.17)and L35 ([MgF 2 ] L35 n = 1.16-1.04).
Generally, the refractive index of a material is influenced by its elemental composition and porosity according to EMA.Here, the compositions of the materials are not highly altered, except the small amount (0.1-0.3 wt%) of poloxamers vaporized in the form of CO 2 during the calcination process, and the refractive index change mainly depends on the density of the intergranular voids.When estimating the porosity of thin films with small volumes, Brunauer-Emmett-Teller analysis using krypton gas [28] or refractive index is employed.To estimate the porosity of the films, Bragman's EMA theory [29] (Figure S2b, Supporting Information) was utilized, and the Equation ( 1) is shown as follows.
where n exp , n MgF 2 , and n air are the average-refractive indices of the experimental value, MgF 2 , and air, respectively.f pore is the volume fraction of the pores in the film.From the calculation, the intergranular void porosity of [MgF 2 ] F127x (0.

Proposed Mechanism of the Intergranular Void Porosity Control
The mechanism illustrated in Figure 3a is employed to explain the grain growth of MgF 2 and intergranular void formation from the MPI solution.First, the Mg(CF 3 COO) 2 solution becomes thermodynamically unstable because of the repulsive force between the hydrophobic PPO block and the polar solvent (IPA) in which the poloxamer is dissolved.Due to this repulsive force, PPO starts to bond with Mg(CF 3 COO) 2 by noncovalent interaction, and the hydrophilic PEO micellizes in the polar solvent environment.Consequently, the interfacial tension between the Mg(CF 3 COO) 2 precursor intermediate and the solvent molecules is reduced, and the free energy of the solution is lowered, which stabilizes the micelles (MPIs). [30]The loading capacity of the adsorbed Mg(CF 3 COO) 2 is determined by the strength of the hydrophobic interactions, aggregation number, CMC, and poloxamer concentration. [31]The size distributions of the MPIs that are encapsulated by F127 and L35 were measured by dynamic light scattering (DLS), as summarized in Figure 3b.The MPI size distributions are similar despite the significant difference in molecular weight between the two poloxamers because the variation in the repeat unit length of the PPO blocks does not significantly affect the size of the micelle core; consequently, a consistent size is maintained.Conversely, the overall size of the micelle is influenced by the repeat unit of PEO blocks, which forms the tail of the core.Thus, the difference in the chain length of PEO leads to variations in the overall size of the micelle, whereas the micelle core size, determined by the PPO block, remains relatively constant. [32]The reason for [MgF 2 ] L35 having a larger grain size than [MgF 2 ] F127 is elucidated using the concept of the MPI density.The molecular weight of F127 is %12 600 g mol À1 , whereas that of L35 (1900 g mol À1 ) is %6.63 times lower.
The CMC plays a crucial role in the formation of micelles in a solution, and F127 has a significantly lower CMC than L35 at 25 °C.As the temperature of the solution increases by 5 °C, the required CMC decreases significantly to one-tenth of the previous level.Since the MPI process is conducted at 60 °C, the required CMC is extremely low to the point where it cannot be measured. [33]Furthermore, when the same mass of poloxamer is added, L35 is expected to form approximately six times more micelles than F127 because of its lower molecular weight.
During the solidification process, the micelles that are formed coalesce to form large grains of MgF [MPI] L35 forms relatively more micelles than [MPI] F127 , occupying more space within the same volume.Although the tail (PEO) of L35 is shorter than that of F127 and the core sizes (PPO) of both poloxamers are similar, the overall micelle size of [MPI] L35 is slightly larger than that of [MgF 2 ] F127 .Thus, it is expected that the [MPI] L35 may be densely packed in a close arrangement, resulting in comparatively large overall grains.Based on the proposed solidification mechanism, the resulting size of the MgF 2 grains determines the size of the intergranular voids.As the grain size decreases, the energy at the grain boundaries decreases, [34] resulting in a decrease in the repulsion between at the interface.
This leads to a tighter adhesion between particles without creating large voids or pores, resulting in the formation of a dense film. [35]onversely, as the grain size increases, the energy at the grain boundaries increases, which represents excess free energy.This excess energy creates repulsive forces, [36] causing the space between the particles to increase and leading to the formation of voids or pores in the film.Transmission electron microscope (TEM) measurements were implemented to confirm the pore size (Figure 3c).The bright region corresponds to the permeable pore, showing the carbon grid, and the dark region corresponds to the solid MgF 2 .The pore diameters of MgF  intergranular void as well as the enlarged MgF 2 grains are also distinguishable.

Preparation and Performance of the GRIN MgF 2 ARC
The MgF 2 film with intergranular voids, prepared by solidifying the MPIs, can be used as an ARC material due to its low-refractive index and inherent transparency.Specifically, exploiting the fine adjustment of the refractive index by precise porosity control enables its application as a GRIN MgF 2 ARC.GRIN ARC aims to achieve broadband and omnidirectional antireflection by gradually descending the refractive index of the materials.Consequently, the design is less restrictive compared to ARCs following the quarter wavelength rule. [37]A three-layer-stacked GRIN MgF 2 film was prepared using the tuned refractive index layers as shown in Figure 4a.We designed a layered structure in which the grain size of MgF 2 gradually increases from the bottom layer to the top layer to create a refractive index gradient between the substrate and the air.Considering the refractive index of the outmost surroundings (quartz substrate and air), the first layer was set with n = 1.39, the second layer was selected having n = 1.23, and the final layer was set with n = 1.16.The approximate thickness of each stacked layer to construct the GRIN MgF 2 is around 120 nm, and the total thickness of the GRIN MgF 2 is %360 nm.
To confirm the AR performance of the GRIN MgF 2 film, we measured the transmittance of both side of the GRIN MgF 2coated quartz as shown in Figure 4b.The average transmittance of the bare quartz was approximately %92.99% in the range of 250-1100 nm.When a sequential GRIN MgF 2 coating was applied, starting from the high-refractive index layer to the low-refractive index layer, the average transmittance increased to the range of %95.34-%97.96%,achieving a maximum value of %99.68% at 457 nm.These results confirmed that the average transmittance of the GRIN MgF 2 -coated quartz increases by increasing the number of laminated porous MgF 2 layers.By filling the refractive index gap between the substrate and the air using the layers, the broadband ARC with excellent performance was realized.The thickness optimization of GRIN MgF 2 each stacked layer was simulated using Essential Macleod as shown in Figure S4, Supporting Information, and %99.43% of average transmittance could be achieved with appropriate optimization, which exhibited %1.47% higher transmittance than our obtained GRIN ARC.However, it becomes challenging for solution process to precisely control the nanometer-scale thickness.Additionally, the unwanted changes of former layer due to accumulated heat exposure make it difficult to implement the design accurately.
The incident light is applied from all directions, and as the angle of the incident light increases, the reflectivity also increases.Therefore, to evaluate the omnidirectional AR effect of the GRIN MgF 2 films, angle-dependent reflectance measurements were conducted with varying the angle of incidence from 30°to 65°in the range of 250-1100 nm (Figure 4c).The average reflectance values of GRIN MgF 2 at different angles (30°-65°) were determined to be %4.61%,%5.99%, and %3.79% in the UV, visible, and NIR ranges at 30°, respectively.These values are approximately 2.88%-4.96%lower than those of the bare quartz for the whole region.As the angle of incidence increases, the difference in the average reflectance between the two samples becomes increased.In particular, at 65°, the average reflectance of GRIN MgF 2 is %17.97,%22.91, and %18.42% in the UV, visible, and NIR ranges, respectively.These values are 5.67%-7.55%lower than those for quartz.Thus, the GRIN MgF 2 films show significant potential for achieving broadband and omnidirectional AR effect.
Figure 4d shows a photograph of the quartz substrates (upper panel) and GRIN MgF 2 (lower panel).On the bare quartz, the reflection of the camera lens is observed; however, when the GRIN MgF 2 coating is applied, the reflected image is eliminated.When the quartz substrate is tilted, the reflected image is projected onto the substrate, which is located at facing the quartz.However, when using the GRIN MgF 2 ARC, the omnidirectional AR effect allows all light to transmit through, and no image reflection was observed (Figure 4e).As shown in Figure 4f, the outstanding broadband and omnidirectional AR effect of the GRIN MgF 2 ARC enables the display of clean images without light reflections.
Attractive application of ARC in solar energy harvesting systems requires the absorption of a considerable amount of light from various angles of incidence a broadband spectrum.GRIN ARCs have been widely adopted in devices for controlling the optical path length of incident light.Perovskite solar cells (PSCs) are considered the next-generation replacements of silicon solar cells and are currently receiving significant research interest. [38]To further explore the broadband and omnidirectional AR capabilities of GRIN MgF 2 , PHCs were fabricated with the configuration shown in Figure 5a.GRIN MgF 2 was applied to indium tin oxide (ITO) glass, a representative glass electrode employed in the fabrication of PSCs, and optical evaluation was conducted as shown in Figure 5b.Due to the various reflection origins induced in the high-refractive index ITO (n = 1.85) and the glass (n = 1.51) interface, as well as the glass/air interface, the average transmittance of the substrate was only %81.02%.When a glass surface was coated with the GRIN MgF 2 , the average transmittance improved by %7.06%, with a more significant improvement of %9.41% achieved in the NIR region (700-1100 nm).This result is attributed to the reduction of the refractive index difference between the glass and air.The performance of all kinds of photoelectric devices, including PSCs, relies on the amount of charge carriers generated by the absorbed light.Since light incident from all angles needs to be absorbed and converted into electron-hole pairs, the transmittance of the transparent electrode depending on the angle of incidence is a crucial factor.Therefore, we measured the angledependent average transmittance to evaluate the effects of employing GRIN MgF 2 ARC on ITO glass shown in Figure 5c.The transmittance of the GRIN MgF 2 /ITO glass and ITO glass was measured from 30°to 65°in the range of 350-1100 nm, and the average transmittance was obtained.The average transmittance of ITO glass at an incidence of 30°w as %81%, and as the angle of incidence increased, the transmittance decreased to %70% at 65°.Conversely, the average transmittance of the GRIN MgF 2 /ITO glass was %84% at an incident angle of 30°, %3% above that of bare ITO glass, and %77% at an incident angle of 65°.This indicates that the effectiveness of the GRIN geometry increases with the angle of incidence.ITO glass was coated with CH 3 NH 3 PbI 3 (MAPbI 3 ) to investigate the change in absorption based on the increased transmittance (Figure 5d).Theoretically, the absorbance of MAPbI 3 is crucially dependent on how effectively the incident light is transmitted.In this regard, the transparency of the substrate and carrier transport layers and refractive index matching from MAPbI 3 to air are of significant importance.The qualitative analysis of the MAPbI 3 used to produce the PHCs is summarized in Figure S5, Supporting Information.The increase in the optical absorption efficiency of MAPbI 3 due to the GRIN MgF 2 AR effect was evaluated by integrating the absorbance values in the range of 400-900 nm.Under normal incidence on the PHC, the absorbance of MAPbI 3 increased by %22.46% using the GRIN MgF 2 ARC.The refractive index matching is well gradient from the MAPbI 3 with a refractive index of %2.68 to the top layer of GRIN MgF 2 with a refractive index of %1.16.Additionally, due to the fact that the material of MgF 2 has an extinction coefficient close to 0, it can be observed that the optical absorption is increased by the broadband GRIN MgF 2 effect.This indicates that the carrier-generation probability in MAPbI 3 is increased by %22.46%, which will increase the PSCs efficiency.These results demonstrate the excellent optical performance improvement of the PHC based on the glass electrode across a broadband and wide range of incident angles.

Conclusion
Overall, we controlled the size of the intermediate phase of Mg(CF 3 COO) 2 by encapsulation using heterogeneous poloxamers (F127 and L35).This process promoted the growth of MgF 2 grains with pores generated simultaneously between the grains during the solidification.Although the exact interaction between Mg(CF 3 COO) 2 and the poloxamers was not clearly elucidated, it is presumed that the encapsulation of the precursor intermediate occurs via noncovalent binding based on multiple experimental observations.By forming nanopores inside the thin film through our approach, the average-refractive index of MgF 2 was finely adjusted from 1.40 to 1.04.Additionally, when the refractive index controlled MgF 2 films were applied to quartz with a graded index configuration, the average transmittance reached %97.96% (250-1100 nm) and the maximum transmittance reached %99.68% at 457 nm.Furthermore, the superior omnidirectional AR effect resulted in a 15% decrease in the reflectance compared with that for the bare quartz at a high incident angles (65°).This GRIN ARC was also applied to the PHC, and the absorbance of MAPbI 3 increased by %22.46% compared to the %7.06% increase in the average transmittance for the ITO glass case.Our findings will provide valuable insights for applications in fields that require high and finely tuned porosity.
Preparation of the MgF 2 Film Formation: Mg(OC 2 H 5 ) 2 (0.57 g, 0.005 mol), F127(0.0-0.3 wt%), and L35(0.0-0.4 wt%) were dispersed in IPA (15 mL).Thereafter, slightly more than the stoichiometric amount of CF 3 COOH (1 mL, 0.013 mol) was added to the precursor solution.A clear solution was obtained within 2 h.Then, MgF 2 films were fabricated on Si wafer and quartz substrates.The substrates were cleaned sequentially in acetone, IPA, and deionized (DI) water to remove any contaminants.Then, UV/O 3 treatment was performed for 10 min before coating to create a uniform thin film.The MPI solutions were spin-casted onto the appropriate substrates, followed by calcination at 300 °C for 1 h.The reactions that led to the formation of MgF 2 are shown in Equation ( 2): Preparation of the PHC with the GRIN MgF 2 ARC: A 2 Â 2 cm ITO glass (OMNISCIENCE, 10 Ω sq À1 ) was cleaned by ultrasonic cleaning in acetone, IPA, and DI water, sequentially for 30 min.The glass side of the ITO glass was treated with UV/O 3 for 10 min to make it hydrophilic, and then GRIN MgF 2 ARC coating was performed using MPIs solution.Subsequently, MAPbI 3 was prepared by coating the ITO glass with a precursor solution of PbI 2 , CH 3 NH 3 I, and DMSO (1:1:1 molar ratio) dissolved in DMF in air 10 min UV/O 3 treatment at the ITO plane.(CH 3 CH 2 ) 2 O was used as an antisolvent to promote the vaporization of the solvent remaining on MAPbI 3 . [39]The transparent MAPbI 3 precursor film was heattreated on a hotplate at 65 °C for 2 min and 100 °C for 4 min.
Characterization: The FT-IR spectra (4000-500 cm À1 ) of Mg(OC 2 H 5 ) 2 and Mg(CF 3 COO) 2 were measured using a Bruker Alpha-P FT-IR spectrometer with attenuated total reflectance mode.The refractive indices of the porous MgF 2 film were measured using the UVISEL Plus Spectroscopic Ellipsometer (Horiba) at 5 nm intervals with a 70°incident angle from 190 to 810 nm.To determine the refractive index of MgF 2 , the classical exponential model suitable for transparent materials was used as shown in Equation (3): The ε ∞ and ε s indicate high-frequency dielectric constant and static dielectric function at a zero frequency.ω t , ω p , and ω oj are resonant frequency, plasma frequency, and resonant energy of an oscillator, respectively.Γ 0 and Γ d are broadening of each oscillator and collision frequency.f i and Υ j indicate oscillator strength and broadening parameter corresponding to the peak energy of each oscillator.The refractive indices of MgF 2 were determined using the high-frequency single oscillator based on the classical exponential model.The GIXRD and XRD patterns of the MgF 2 and MAPbI 3 films were recorded using a Rigaku SmartLab X-ray diffractometer with Cu Kα irradiation with a wavelength of 1.5406 Å (irradiated conditions: 45 kV, 100 mA, and 0.5°).To determine the chemical states of the MgF 2 and MAPbI 3 films, they were analyzed by highresolution XPS (Thermo Scientific) with a Kα spectrometer, and all the results obtained were measured using conventional monochromatic Al-Kα radiation (1486.6 eV) with the standard-emission geometry.The surface morphology and cross-sectional images of the MgF 2 film were measured by field-emission SEM using the Hitachi S-4800 system with a cold field-emission gun.Optical transmittance and absorbance were measured using a LAMBDA 365þ double-beam UV-vis-NIR spectrometer (PerkinElmer) at 1.0 nm intervals across the wavelength range of 250-1100 nm.The theoretical transmittance of GRIN MgF 2 was calculated through thickness optimization using Essential Macleod trial version (Thin Film Center Inc., USA).The angle-dependent transmittance was also measured at 5°intervals in the range of 30°-65°over the same interval step and wavelength range.The angle-dependent reflectance measurements were conducted at 5°intervals in the range of 30°-65°and at 1 nm intervals across the wavelength range of 250-1100 nm using a LAMBDA 1050 UV-vis-NIR spectrometer (PerkinElmer) equipped with tungsten-halogen and deuterium lamps.TEM images of MgF 2 were recorded using a JEOL (JEM-ARM200F) instrument operating at an accelerating voltage of 200 kV.The grain sizes and the diameters of the pores in the MgF 2 film were measured using the ImageJ software.The zeta potential analysis and DLS experiments of the core-shell micelle architecture of Mg(CF 3 COO) 2 were conducted using a Litesizer 500 particle size analyzer (Anton Paar).The zeta potential and hydrodynamic diameters were measured in the liquid phase at 25 °C in electrophoretic light-scattering detection and DLS-detection modes.

Figure 1 .
Figure 1.Preparation of MgF 2 grains using micellized precursor intermediates (MPIs) and their characterization.a) Schematic illustration of the micellized Mg(CF 3 COO) 2 encapsulated by poloxamers.b) X-ray photoelectron spectroscopy and c) grazing incidence X-ray diffraction analyses of the MgF 2 films after the solidification of Mg(CF 3 COO) 2 and the MPIs.

Figure 2 .
Figure 2. Analysis of the MgF 2 grain size and intergranular voids.a) Cross-sectional and b) top-view scanning electron microscopy (SEM) images.c) Measured grain size distribution of the representative MgF 2 , [MgF 2 ] F127 , and [MgF 2 ] L35 .d) Refractive index variation based on the quantity and type of poloxamers at the specific wavelength region (UV, visible, and near-infrared [NIR]).e) Average-refractive index of the MgF 2 films controlled using various MPIs.
At an [MPI] F127 (high molecular weight) concentration of 0.1 wt%, the MPI size are distributed in the range of 140-1550 nm.At 0.3 wt%, the [MPI] F127 size distribution shifts to the higher range of 580-1430 nm.Additionally, as the concentration increases up to 0.5 wt%, the micelle size distribution further increases to the range of 1680-6660 nm.In contrast, on applying [MPI] L35 (low molecular weight), the [MPI] L35 sizes are distributed in the range of 240-640 nm at 0.1 wt%.As the concentration increases to 0.3 wt%, the [MPI] L35 size distribution shifts to a range of 690-2320 nm, similar to the trend observed for [MPI] F127 .

2 .
When the precursor solution (Mg(CF 3 COO) 2 , [MPI] F127 , and [MPI] L35 ) is spin coated onto the desired substrate, it remains in an fluid state prior to calcination.When the remaining solute shrinks under heat treatment, MgF 2 grains and intergranular voids are formed simultaneously.The following speculations can account for the larger grain size of [MgF 2 ] L35 compared with that of [MgF 2 ] F127 .

Figure 3 .
Figure 3. Proposed intergranular void-generation mechanism of MgF 2 according to grain size.a) Intergranular void-generation mechanism of MgF 2 film through the MPIs.b) Dynamic light scattering of the micellized Mg(CF 3 COO) 2 intermediate with different heterogeneous poloxamer concentrations.c) Transmission electron microscope images of the solidified MgF 2 derived from the MPIs.

Figure 4 .
Figure 4. Preparation and performance of graded refractive index (GRIN) MgF 2 broadband and omnidirectional antireflection coating (ARC).a) Representative GRIN MgF 2 SEM image.Optical properties of the GRIN MgF 2 : b) transmittance and c) average angle-dependent reflectance by wavelength.Graphic images of GRIN MgF 2 : d) flat, e) tilted, and f ) zoomed out.

Figure 5 .
Figure 5. Preparation and performance of perovskite half-cells (PHCs) incorporating the GRIN MgF 2 ARC.a) Schematic of the GRIN MgF 2 -coated PHC.Optical properties of GRIN MgF 2 /ITO glass with b) normal transmittance and c) angle-dependent transmittance.d) Absorbance of GRIN MgF 2 /ITO glass/MAPbI 3 .