In this study, we report the fabrication, characterization, and modeling of a zigzag nanorod-structured graded-index antireflection coating fabricated by the oblique angle deposition (OAD) method. The optical properties of the reported coating were engineered by sculpting its composition and morphology using OAD, and the coating was designed to work with high-index, YAG:Ce ceramic phosphor plates. The coating enhances the normal-direction transmission of the phosphor plate over the broad visible-light spectrum. At 764 nm, the transmission is enhanced by 7.82%, compared to a potential maximum enhancement of 8.53%. For 633-nm light incident at 5°, the reported coating was measured to induce scattering loss of no greater than 1.27%. We developed a mathematical model that can use the OAD morphology information, developed from the film growth mechanism, as input parameters to simulate the optical properties of the nanostructured coatings. A finite-difference time-domain (FDTD) simulation was able to capture the polarization-dependent, antireflective performance of the coating, and the simulated transmission spectrum was in good agreement with both the measured spectrum and the spectrum calculated using the measured effective refractive indices in a transfer matrix formulation. In addition, the FDTD model was applied to predict the scattering losses. The simulation supports the experimental results and shows that the coating induces very weak scattering loss.

In phosphor-converted white light-emitting diodes (LEDs), a YAG:Ce phosphor works as a wavelength conversion element by absorbing part of the blue light incidence on the chip and converting it into yellow light via photoluminescence. YAG:Ce ceramic phosphor plates (CPPs), as a relatively new type of commercial phosphor, have been gaining active interest by LED manufacturers due to their advantages in high-luminance and high-power applications. With minimized interior index contrast and high thermal conductivity,1 YAG:Ce CPPs address some of the key problems encountered in using conventional powder-based phosphors, such as scattering losses2 and heat accumulation.3 However, new challenges also arise as YAG:Ce CPPs have a high refractive index (1.82) and introduce an interface between themselves and the ambient medium. Due to the index mismatch at the YAG:Ce/air interface, part of the emission arriving at the interface will be reflected into the LED package by Fresnel reflection. The reflection loss degrades the extraction efficiency of the LED and hinders the application of YAG:Ce CPPs. Therefore, the introduction of optical structures that are capable of eliminating the Fresnel reflection and enhancing the forward transmission of YAG:Ce would be highly beneficial for the application of YAG:Ce CPPs.

Graded-index, antireflection (AR) coatings have proven to be very effective in reducing Fresnel reflection over a broad range of the visible spectrum and over a wide range of incident angles compared to the conventional single-index AR coatings.4–9 Graded-index AR coatings comprise a refractive index profile that varies in a near continuous way from the substrate index to the ambient medium index. They reduce the Fresnel reflection by gradually reducing the index mismatch and inducing destructive and constructive interference in the reflected and transmitted beams, respectively. Usually, the ambient medium is air with a refractive index close to 1, but no naturally existing solid is available with a refractive index in the region of 1–1.38 (MgF2, Ref. 10) to match the refractive index of air. This index mismatch used to greatly restrict the performance of graded-index AR coatings, but recently the barrier has been overcome by nanostructure fabrication technologies. Various fabrication techniques have been reported to successfully produce ultralow index materials with a refractive index close to 1, such as solgel methods,11 oblique angle deposition (OAD),12–14 and etching.15–17 These ultralow index materials are generally porous, in which the pores are used to lower the overall refractive index. Compared to other fabrication techniques, OAD has two advantages that make it more suitable for engineering graded-index AR coatings: (1) OAD films are composed of nanocolumnar structures so scattering loss should be low and (2) the refractive index of OAD films can be predicted as a function of deposition conditions. OAD is also a relatively simple and low-cost process that allows for the large-area fabrication of a wide range of materials. Excellent antireflective performance of OAD-grown graded-index AR coatings has been reported previously,4,18–22 including bio-inspired coatings, but there are few reports trying to span such a wide index variation and looking at the polarization dependence of those coatings.

OAD of graded-index AR coatings is most commonly conducted in electron beam (e-beam) evaporation systems. OAD films fabricated in e-beam systems are composed of spatially distributed, tilted, nanocolumnar structures that are collectively oriented toward the vapor flux direction, so it is reasonable to deduce that the OAD film’s internal morphology can affect the electric-field screening of the film and make its antireflective performance sensitive to the polarization state of the incident light. To improve the performance of OAD films in antireflection applications, the relationship between the film morphology and the engineered optical properties needs to be understood such that both isotropic and anisotropic optical behaviors could be flexibly engineered into the films. Since the OAD-grown AR coatings are highly porous, in principle, scattering will adversely affect the antireflective performance of the interference-based AR coatings: scattering induced by imperfections in AR coatings will cause additional optical loss and should, therefore, be minimized. Limited research has been done to demonstrate these phenomena, so one aim of this study is to investigate the morphology dependence of the OAD-grown AR coating’s optical properties, particularly the polarization-dependent antireflective performance and scattering loss.

Commonly, graded-index AR coatings are studied by the transfer matrix method (TMM),23 treating multilayered AR coatings as a multilayered stack of 1D homogeneous films, The matrix method provides a good start for designing and fitting the index profiles of AR coatings, but the geometrical simplifications required make it necessary to conduct experiments on real films to provide the matrix approach with the required refractive index and dispersion relations for all the constituent layers. Neglecting the morphological information, like the interior index contrast and interface roughness, also limits TMM to spatially averaged transmittance and reflectance calculations. In comparison, the finite-difference time-domain (FDTD) method can, in principle, directly generate nearly complete results based on the film’s morphological information without having to conduct characterization experiments. In this sense, FDTD will serve as a powerful tool to study the morphology-dependent properties of the AR coating, which is not possible by TMM.24–26 

In this study, a graded-index AR coating composed of six layers of TiO2 and SiO2 zigzag nanorods was fabricated on the top surface of a YAG:Ce CPP by OAD using an e-beam system in the effort of enhancing its transmission in the normal direction. The refractive index dispersion relation of the constituent layers was investigated using ellipsometry. 3D FDTD simulations were carried out to investigate the morphology dependence of the optical properties of the obtained coating. To reduce computational expense and to better understand the morphology-property relation, a simplified simulation model was developed that conforms to the film growth mechanism and that model structure was used for FDTD modeling.

In oblique angle deposition (OAD), the substrate is mounted at an oblique angle with respect to the evaporation source. During the initial stages of film growth, incoming particles nucleate on the substrate discretely and form islands with different heights. As the deposition proceeds, taller islands receive more of particle flux and actively shield neighboring regions. Therefore, the film grows by gradually developing into columns with obstructed areas forming essentially empty space between the columns. The finished OAD film is a porous structure with spatially distributed slanted nanorods oriented toward the vapor flux direction. In this work, the AR coating was structured as zigzag nanorods by changing the growth direction of slanted nanorods via dynamic control of the substrate orientation during the deposition. The deposition angle was altered symmetrically about the substrate normal over a set period of time and this made the nanorods change their growth direction periodically to produce the zigzag, nanorod structure. Compared to a single-direction slanted nanorod structure, a zigzag-nanorod structure is more damage-resistant,27 and it offsets the undesired “wedging” effect in film thickness that is commonly encountered in nanorod-structured OAD films.28 Film porosity was controlled by tuning the overall deposition angle.

Several geometrical models have been proposed to relate the deposition angle with OAD film porosity.29,30 Generally, OAD film porosity increases with increasing deposition angle, so the refractive index of OAD films decreases with increasingly large deposition angles. With the appropriate choice of base materials and deposition angles, one could engineer a series of films with refractive indices between YAG:Ce (nYAG:Ce ≈ 1.82) and air (nair ≈ 1). SiO2 and TiO2 (at 550 nm, nSiO2 ≈ 1.46, nTiO2 ≈ 2.54 for amorphous phases, respectively) show little absorption and relatively low chromatic dispersion in the visible-light region and are compatible with e-beam systems where the OAD technique is practiced. These properties make them ideal base materials in the OAD process to engineer optical coatings with an arbitrary refractive index between YAG:Ce and air as long as the processing temperatures stay below 600 °C to avoid the rutile to anatase phase transition that reduces the refractive index of the titania. The coating was designed to approximately follow a Gaussian index profile and give enhanced normal transmission over the visible-light spectrum.31 The details of deposition are given in Table I, and the deposition conditions and film properties were based on the 2-step design procedure reported by Chen et al.32 

TABLE I.

Materials and deposition angles used for engineering the AR coating.

Constituent layerMaterialDeposition angle (deg)Targeted thickness (nm)
 YAG:Ce  2.60 × 105 
TiO2 75 34 
TiO2 −75 34 
TiO2 80 24 
TiO2 −80 24 
TiO2 85 44 
TiO2 −85 44 
SiO2 70 64 
SiO2 −70 64 
SiO2 80 64 
10 SiO2 −80 64 
11 SiO2 89 128 
 Air   
Constituent layerMaterialDeposition angle (deg)Targeted thickness (nm)
 YAG:Ce  2.60 × 105 
TiO2 75 34 
TiO2 −75 34 
TiO2 80 24 
TiO2 −80 24 
TiO2 85 44 
TiO2 −85 44 
SiO2 70 64 
SiO2 −70 64 
SiO2 80 64 
10 SiO2 −80 64 
11 SiO2 89 128 
 Air   

A YAG:Ce ceramic phosphor plate (CPP) (1 cm × 1 cm × 260 μm, OSRAM SYLVANIA) was used as the substrate for enhancing the normal transmission of LEDs. An e-beam evaporation system (Temescal) was used to fabricate the AR coating on the YAG:Ce CPP. The schematic of the deposition system is shown in Fig. 1. A stepper motor was built into the system to dynamically control the substrate mount’s horizontal tilt angle during the deposition. The motor was designed to shut down at a processing temperature higher than 155 °C. 99.9% pure TiO2 (CERAC) and 99.999% pure SiO2 (International Advanced Materials) were used as deposition sources. Prior to deposition, the substrates were cleaned in ultrasonic baths of acetone, ethanol, and deionized water for ten minutes each, followed by a deionized water rinse and drying in dry nitrogen. A piece of a silicon wafer was used to prepare “witness” samples for scanning electron microscopy. The substrate was first fixed onto the silicon wafer piece and then mounted to the system. The system pressure reached 10−7 Torr before deposition and was kept stable around 2×10−5 Torr and 10−6 Torr during the deposition of TiO2 and SiO2, respectively. The chamber temperature was kept approximately at room temperature during deposition by a cooling water jacket, but the substrate temperature could not be actively monitored. During the deposition, no motor malfunction was observed so that the substrate temperature was ensured to be far below the titania phase transition temperature, and likely below the motor cutoff of 155 °C. The deposition rate was controlled at constant values of 1 Å/s and 2 Å/s for the deposition of TiO2 and SiO2 respectively. The deposition rate and the deposited thickness were monitored by an in situ quartz crystal microbalance. The source material, deposition angle, and thickness of each layer were controlled according to the recipe listed in Table I.

FIG. 1.

Experimental setup of the E-beam evaporation system used for OAD fabrication. The substrate is mounted at an oblique angle α with respect to the evaporation source. The angle α is defined as the deposition angle.

FIG. 1.

Experimental setup of the E-beam evaporation system used for OAD fabrication. The substrate is mounted at an oblique angle α with respect to the evaporation source. The angle α is defined as the deposition angle.

Close modal

The refractive index and dispersion relations for each constituent layer were established using calibration samples: constituent layers were separately fabricated beforehand on silicon substrates under the same deposition conditions as used for the full coating, and then their optical properties were measured by ellipsometry using a variable-angle spectroscopic ellipsometer (VASE, J. A. Woollam Co, Inc.). The morphology of the obtained AR coating was characterized by field-emission SEM (SUPRA, Carl Zeiss AG) on the coated silicon wafer piece after platinum sputtering. The total transmission spectra of both coated and uncoated YAG:Ce CPPs were measured using a Perkin Elmer Lambda 900 spectrometer equipped with a Labsphere PELA-1000 integrating sphere at normal-incident angle with an unpolarized source in the wavelength range of 400–800 nm. To determine the scattering loss, bidirectional scattering distribution (BSDF) measurements were performed on the coated and uncoated YAG:Ce CPPs with a customized setup at OSRAM Sylvania. Horizontally polarized laser light at a wavelength of 633 nm was incident on the uncoated side of the CPP, and the light signal was collected by rotating the detector arm about the sample over a range of ±175°. The measurement was repeated by holding the sample so that the light was incident at angles of 5°, 15°, and 25° off normal.

As will be shown later, the finished AR coating is a two-material zigzag-nanorod structure assembled from slanted nanorods. The structural model of the AR coating was built by first defining individual nanorod components. We modeled TiO2 and SiO2 zigzag nanorods as two-arm assemblies of slanted nanorods, represented by parallelepipeds with a square undersurface as shown in Fig. 2. Though the actual zigzag nanorods possess more rounded profiles, angular structures are easier to draw, easier to mesh, and the addition of minute features like edges and corners in the modeled structure does not greatly alter the interaction with the incident light or cause substantial discrepancies in the modeling results. Several key parameters were defined to describe the dimension of zigzag-nanorod components: (1) a, the side length of the bottom surface; (2) h, the height of the nanorod of each layer; and (3) β, the oblique angle. The magnitudes of these parameters were obtained by analyzing the SEM images with image processing software (ImageJ) and taking an average over multiple measurements.

FIG. 2.

Structural model for a single nanorod (left) and a zigzag nanorod (right). The zigzag nanorod is modeled as a two-arm assembly of two nanorods.

FIG. 2.

Structural model for a single nanorod (left) and a zigzag nanorod (right). The zigzag nanorod is modeled as a two-arm assembly of two nanorods.

Close modal

Next, we proceeded to define the in-plane distribution of nanorods within each layer. Ideally, one would want to restore the actual in-plane distribution data with image tracing tools so that the modeled structure would be most consistent with the actual structure, but such an approach lacks generality and is too computationally expensive for this study. Therefore, we wanted to seek a setup that could balance fidelity to the actual structure with computational expense. As will be shown by characterization results, the in-plane distribution of zigzag nanorods appears random. However, earlier work has reported that OAD films are actually quasi-periodic:33 the distribution of inter-nanostructure spacing converges to a limit once the film thickness reaches a critical value. The nature of this quasi-periodicity is explained by the development of the “shadowing length” during film growth. The shadowing length is referred to as the lateral length of the region shadowed by taller surface objects along the direction of the incoming vapor flux (Fig. 3). It fluctuates during the initial stage of film growth as the material nucleates on the surface, but then approaches a constant as the film growth proceeds, giving the resultant film a uniform, inter-nanostructure spacing along the direction of vapor flux. The concept of a shadowing length was validated in models where it was used to predict the film porosity.30 It was demonstrated that the magnitude of the shadowing length is determined by the deposition angle and the material of deposition. Along the direction perpendicular to the vapor flux, however, the shadowing length is not applicable. Any shadowing is negligible, based on the nanorod diameter and not its length. Instead, a “bundling” phenomenon was discovered for the arrangement of nanostructures in many studies for various OAD films:34–36 nanostructures grow in a connected and misaligned manner, forming a chainlike association.

FIG. 3.

A schematic view showing the definition of shadowing length s: a taller surface object with height h casts a shadow on the substrate along the direction of the vapor flux, terminating the growth of shorter surface objects falling in the shadow region.

FIG. 3.

A schematic view showing the definition of shadowing length s: a taller surface object with height h casts a shadow on the substrate along the direction of the vapor flux, terminating the growth of shorter surface objects falling in the shadow region.

Close modal

In this work, we adapted the shadowing length concept to define the in-plane arrangement of zigzag nanorods. As shown in Fig. 4, the vapor flux is incident obliquely in the x-z plane, giving rise to shadowing growth in this plane that dominates the nanostructure growth, while leaving the nanostructure growth subject to a bundling association in the y-z plane. Following the spatially anisotropic shadowing growth mechanism, we defined that zigzag nanorods were spaced by an equal distance, d, along the x-axis, corresponding to a well-defined shadowing length. Here, the shadowing length was adapted from Ref. 30 by replacing the island height h with the nanorod height, namely, the thickness of the corresponding nanorod layer as defined in Table I. d was defined as a function of deposition angle and deposited material and was extracted from the measured film porosity and zigzag-nanorod width. To form the clusters, we first stacked zigzag nanorods along the y-axis spacing them one diameter apart. We then used a random number generator to shift the nanorods along the x-axis forming a simplified set of pseudoclusters. In the last step, all the individual nanorod layers were stacked along the z-direction to finish the 3D structural model for the multilayered, graded-index AR coating. In summary, the geometrical parameters input for building the structural model for the obtained AR coating are listed in Table II.

FIG. 4.

Definition of in-plane arrangement of nanostructures within each constituent layer. x- and y-axis lie in the film plane while the z-axis is normal to the film plane.

FIG. 4.

Definition of in-plane arrangement of nanostructures within each constituent layer. x- and y-axis lie in the film plane while the z-axis is normal to the film plane.

Close modal
TABLE II.

Geometrical parameters used for building the structural model for the reported AR coating.

Deposition conditionNanostructure height h (nm)Nanostructure width a (nm)Nanostructure tilt angle β (deg)Nanostructure spacing d (nm)
YAG: Ce      
75° TiO2 52 16.0 35 13 
−75° TiO2 48 16.0 −37 13 
80° TiO2 33 16.0 34 18 
−80° TiO2 32 16.0 −37 18 
85° TiO2 57 16.0 37 25 
−85° TiO2 42 16.0 −38 25 
70° SiO2 66 14.4 33 
−70° SiO2 67 14.4 −34 
80° SiO2 59 14.4 36 10 
10 −80° SiO2 62 14.4 −35 10 
11 89° SiO2 129 14.4 41 34 
Air      
Deposition conditionNanostructure height h (nm)Nanostructure width a (nm)Nanostructure tilt angle β (deg)Nanostructure spacing d (nm)
YAG: Ce      
75° TiO2 52 16.0 35 13 
−75° TiO2 48 16.0 −37 13 
80° TiO2 33 16.0 34 18 
−80° TiO2 32 16.0 −37 18 
85° TiO2 57 16.0 37 25 
−85° TiO2 42 16.0 −38 25 
70° SiO2 66 14.4 33 
−70° SiO2 67 14.4 −34 
80° SiO2 59 14.4 36 10 
10 −80° SiO2 62 14.4 −35 10 
11 89° SiO2 129 14.4 41 34 
Air      

3D, FDTD simulations were carried out in FDTD Solutions (Lumerical Solutions, Inc.) software. The simulation setup is shown in Fig. 5. A polarized plane-wave source in the wavelength range of 400–800 nm was incident on the coated side of YAG:Ce CPP at normal-incident angle and propagated toward the −z-direction. Both x-polarized and y-polarized sources were employed in the simulation. Transmission and reflection were monitored by field monitors placed inside the YAG:Ce CPP and above the AR coating, respectively. Periodic boundary conditions were imposed along x- and y-directions and perfectly matched-layer (PML) boundary conditions were applied along the z-direction. It is worth mentioning that by treating the YAG:Ce CPP as semi-infinite in the simulation, reflection at its bottom surface is neglected. This was corrected by subtracting the bottom-surface reflectance from the as-obtained transmittance.

FIG. 5.

FDTD simulation setup.

FIG. 5.

FDTD simulation setup.

Close modal

TMM was used to model the standard transmission spectrum of the reported coating. The structural model adopted in TMM modeling is a multilayered stack of homogeneous 1D slabs representing the individual nanorod layers. The thickness of each constituent slab is the only required geometric parameter, whose value is taken from Table II. Refractive indices and extinction coefficients for each slab were based on data from ellipsometry measurements. TMM modeling was carried out using Scout (W. Theiss) software.

SEM images in Fig. 6 demonstrate that a well-defined, two-material, nanospiral-structured coating was successfully developed. No delamination was observed between the TiO2 and SiO2 layers in the multimaterial AR coating. It has been reported that the lateral width of the nanostructures composing OAD films will broaden as the films become thicker.37 Column broadening will increase the scattering loss and change the areal density of nanostructures, so it is unwanted for optical applications. However, minimal column broadening along the growth direction can be observed from the SEM images. It is believed that the fine division of layer thickness helps to suppress the broadening effect. Also, the cross-sectional SEM image shows that the zigzag nanorods were grown in a connected manner from the bottom layer to the top layer. Studies have revealed that the surface of OAD films has a rough morphology.38 The extruding tips of existing zigzag-nanorod clusters may have served as templates that seeded the growth of subsequent zigzag-nanorod layers. This mechanism may have been important in the switch between TiO2 and SiO2, allowing the more dense SiO2 layer to grow atop a nominally less dense TiO2 layer.

FIG. 6.

Cross-sectional (left) and top-down (right) SEM images of the obtained coating. The arrow indicates the zigzag-nanorod tilt direction.

FIG. 6.

Cross-sectional (left) and top-down (right) SEM images of the obtained coating. The arrow indicates the zigzag-nanorod tilt direction.

Close modal

The standard transmission spectrum of coated and uncoated YAG:Ce CPP is shown in Fig. 7. The strong absorption of blue excitation source due to the 4f-5d band transition of Ce3+ ions is clearly seen around 460 nm. At longer wavelengths, the bare YAG:Ce is transparent, showing high transmittance around 80.5%. Based on the refractive index of undoped YAG,39,40 the maximum value of theoretical transmission for YAG in air is predicted to around 82.94%, and, therefore, an ideal AR coating could enhance the transmission by 8.53% at each interface. Some scattering induced by the interior structure of the YAG:Ce is likely to have contributed to the rest of the 2.44% optical loss. By fabricating zigzag nanorod-structured AR coatings on the top surface of YAG:Ce CPP to reduce index contrast and induce constructive interference in transmitted beams, the transmission of YAG:Ce CPP is seen to be enhanced over broad visible-light spectrum and reaches 88.32% at 764 nm.

FIG. 7.

Transmission spectrum of uncoated and coated YAG:Ce CPPs.

FIG. 7.

Transmission spectrum of uncoated and coated YAG:Ce CPPs.

Close modal

The results of the scattering measurement are shown in Fig. 8. The detector collected reflections from both surfaces of the sample. The solid lines are for the beam hitting a coated portion of the sample; the dashed lines are for the beam hitting the uncoated portion of the sample. One can see that when the light hits the coated portion, the reflected peaks are considerably lower in magnitude than for the uncoated regions. Unfortunately, the measurement of the standard forward transmission is limited by the low resolution of the setup which is only 1°. Therefore, the enhancement in the standard transmission is not quite discernible in the graph. Table III summarizes the reflection results in Fig. 8 and gives the predicted Fresnel reflection value for parallelly polarized, 633-nm light source incident on uncoated YAG:Ce CPP. Results here indicate that the AR coating can essentially reduce all the theoretical reflection caused by Fresnel reflection, which demonstrates that the antireflection properties are of high quality. One may notice that the scattering signal appears to deviate a bit from the theoretical direction. This deviation from the theoretical Fresnel prediction may result from the fact that scattering from the AR coating and scattering from the YAG:Ce CPP were collected simultaneously.

FIG. 8.

Scattering data from 633-nm red laser showing the antireflection effect of coating on YAG:Ce CPP (note the y-axis is in logarithmic scale).

FIG. 8.

Scattering data from 633-nm red laser showing the antireflection effect of coating on YAG:Ce CPP (note the y-axis is in logarithmic scale).

Close modal
TABLE III.

Reflectance as a function of incidence angle.

Angle of incidence (deg)Measured reflectivity—no coatingReflection—coated regionTheoretical one-surface reflectivity
0.153 0.073 0.085 
15 0.140 0.058 0.080 
25 0.099 0.055 0.068 
Angle of incidence (deg)Measured reflectivity—no coatingReflection—coated regionTheoretical one-surface reflectivity
0.153 0.073 0.085 
15 0.140 0.058 0.080 
25 0.099 0.055 0.068 

Ellipsometry was used on individual constituent layers of the OAD films for calibration. The films were treated as biaxial materials, and their porosity and refractive index dispersion relations were modeled using biaxial Bruggeman effective medium approximations (EMAs). Biaxial Bruggeman EMA is a more general form of the isotropic Bruggeman EMA with the directional dependence of the effective refractive index included. The biaxial Bruggeman EMA addresses biaxial anisotropy by including a set of screening factors, which describe the directional-dependent ability of an optical medium to screen the applied field. For a porous film with porosity f, the biaxial Bruggeman EMA calculates the film’s effective refractive index along direction i, neff,i, by

fna2neff,i2na2+κineff,i2+(1f)nb2neff,i2nb2+κineff,i2=0,i=x,y,z,
(1)

where na and nb are the refractive indices of air and base material (TiO2 or SiO2), respectively; κi is the screening factor of the film along direction i; and x, y, and z are orthogonal coordinate axes along which the electric-field vector of the incident light is aligned. To make the index definition consistent with the electric-field vectors of normal-incident light, the coordinate axes were defined in the same way as the coordinate directions shown in Fig. 5. Refractive indices of the constituent layers were measured by ellipsometry, and the results are plotted in Fig. 9 as a function of deposition angle, α, and the material.

FIG. 9.

Effective refractive indices neff,x, neff,y, and neff,z as a function of deposition angle and material.

FIG. 9.

Effective refractive indices neff,x, neff,y, and neff,z as a function of deposition angle and material.

Close modal

Figure 9 shows both TiO2 and SiO2 OAD films exhibiting biaxial anisotropy, as evidenced by unequal neff,i’s along three directions. Since neff,z is only pertinent to 90° incident light, we will limit our discussion hereafter to neff,x and neff,y. Figure 9 shows that neff,y and neff,x both decrease with increasing deposition angle, but neff,y is larger than neff,x for all deposition angles. The decrease of effective refractive index with increasing deposition angle occurs because shadowing growth is stronger at higher deposition angles, resulting in a higher film porosity. The inequality relation between neff,y and neff,x is directly related to the morphology of the AR coating. Individual slanted nanorods show directionally dependent ability of screening the electric field because the dimension of nanorods is directional dependent; and the anisotropy of slanted nanorods components enters the AR coating due to the collective alignment of components.

To quantify the degree of biaxial anisotropy, we defined the in-plane birefringence, Δn, for the film as Δn = neff,yneff,x, and plotted Δn as a function of deposition angle, α, in Fig. 10. The results show that the birefringence of TiO2 OAD films is much stronger than SiO2 ones, and the degree of birefringence decreases with increasing deposition angle. The higher birefringence of TiO2 OAD films is related to the high dielectric constant of TiO2. A higher dielectric constant indicates a stronger matter-field interaction, so TiO2 films are more sensitive to the polarization state of the applied field. The decrease in birefringence with increasing deposition angle is a result of the increase in film porosity. In OAD films deposited at high angles, a reduced amount of matter is present in the film to interact with electric field effectively so that the polarization-dependent optical response becomes less discernible in those highly porous films.

FIG. 10.

Birefringence Δn as a function of deposition angle at 642 nm for TiO2 OAD films and SiO2 OAD films.

FIG. 10.

Birefringence Δn as a function of deposition angle at 642 nm for TiO2 OAD films and SiO2 OAD films.

Close modal

The extinction coefficients were also studied in the ellipsometry measurement. The dispersion relation of extinction coefficients keff,x and keff,y is plotted in Fig. 11 for TiO2 films deposited at different deposition angles. keff,x and keff,y represent the extinction coefficient experienced by the normal-incident light polarized along the x- and y-directions, respectively. The bandgap of SiO2 is around 9.3 eV (133 nm), sufficiently far from the visible-light region to cause discernible absorption. It is shown in Fig. 11 that TiO2 films absorb weakly in the visible-light region, and the absorption is stronger at shorter wavelengths. In previous studies, an indirect bandgap of 3.5 eV (354 nm) has been determined for TiO2 films deposited under the same condition.41,42 As an indirect-bandgap material, TiO2 absorbs photons with energies below the bandgap in a continuous manner until the photons’ energy becomes sufficiently low. Therefore, it can be seen in the figure that absorption remains discernible at shorter visible wavelengths and becomes increasingly negligible at longer wavelengths. Films deposited at higher deposition angles absorb less than films deposited at lower angles due to the presence of less absorbing matter. In summary, the reported AR coating will exhibit slightly different index profiles under different polarization states of the operation light as well as slight optical absorption, both of which are mainly contributed by TiO2 layers.

FIG. 11.

Dispersion relation of extinction coefficients keff,x and keff,y for TiO2 OAD films deposited at different deposition angles.

FIG. 11.

Dispersion relation of extinction coefficients keff,x and keff,y for TiO2 OAD films deposited at different deposition angles.

Close modal

Figure 12 shows the transmission spectrum simulated by FDTD and TMM. The strong absorption by Ce3+ band transition in the wavelength range of 400–550 nm was excluded in the simulations to better render the properties of the AR coating. Transmittance under x-polarized and y-polarized incident light was calculated. Taking the anisotropic index profile as input, TMM shows the AR coating exhibits polarization-dependent antireflective performance, which could be mostly attributed to the highly birefringent TiO2 layers as we discussed in Sec. IV B. The deviation between the polarized transmittance is higher at wavelengths shorter than approximately 600 nm due to stronger field-matter interaction and gradually reduces as wavelength increases. On the other hand, the results of FDTD modeling show, taking the morphology information of the model as input, that using our simplified morphology model, FDTD is also able to capture the polarization-dependent antireflective performance without explicitly introducing a difference in refractive index of the material. It can be seen that FDTD-simulated spectra match TMM-simulated spectra well across the visible-light region showing a stronger dependence on wavelength for y-polarized light and a weaker dependence for x-polarized light below about 550 nm. The discrepancies below 550 nm are likely to have been caused by the assumptions made in the FDTD model for features along the x-axis, as the effects of assumptions will be amplified when field-matter interaction is relatively strong at shorter wavelengths. Assumptions made in the structural model, including a uniform inter-nanostructure spacing along x-axis, a uniform nanostructure width as well as alignment of nanostructures along the x-axis, and that the rods themselves contained no porosity could all lead to the modeling discrepancy. Nanorods are porous structures with relatively high internal surface area.39 

FIG. 12.

Transmission spectra simulated by TMM and FDTD for the reported coating under x-polarized and y-polarized electric field. Absorption due to Ce3+ has been omitted (see text).

FIG. 12.

Transmission spectra simulated by TMM and FDTD for the reported coating under x-polarized and y-polarized electric field. Absorption due to Ce3+ has been omitted (see text).

Close modal

In Fig. 13, polarized transmission spectra simulated by FDTD are averaged and compared with the measured transmission spectrum in the wavelength range of 550–800 nm. Transmittance below 550 nm is omitted due to the strong absorption. It can be seen that the spectrum simulated by FDTD agrees reasonably well with the measured spectrum. The discrepancy between simulated and measured transmittance may be attributed to the geometrical simplifications in the structural model and the assumption that the individual rods were dense. In the experiment, the assembly of constituent layers was done by a continuous bottom-up approach without any postprocess treatment of the surface of the deposited layers. It is expected that the morphology and thereby the refractive index of successive layers will be affected by the underlying layers to some degree, but the effect due to surface topology is neglected in the FDTD model as it is difficult to collect this information during experiment without interrupting the deposition process and possibly affecting the sample by repeatedly removing, measuring, and then replacing it in the chamber.

FIG. 13.

Comparison between measured regular transmission spectrum and simulated regular transmission spectrum under unpolarized incident light.

FIG. 13.

Comparison between measured regular transmission spectrum and simulated regular transmission spectrum under unpolarized incident light.

Close modal

To investigate the scattering loss induced by the AR coating itself, we simulated the scattering spectrum using the structural model in FDTD and the results are plotted in Fig. 14. To separate the relative contribution of the two different base materials, the scattering spectra of the TiO2 layers were separately calculated and plotted for comparison. It is found that the scattering loss induced by the AR coating itself is negligible: scattering loss is less than 0.4% above 550 nm. Low scattering loss will help maintain good collimation for the incident light propagating inside the AR coating, and thus constructive interference between transmitted beams can be achieved efficiently. The simulated scattering intensity is lower than 1%, and it decreases as the wavelength increases, indicating a Rayleigh-type scattering.43 By comparing the scattering intensity induced by the entire coating with just the TiO2 layers, we find that the major source of the scattering loss is the TiO2 layers. The high-index TiO2 zigzag nanorods possess a higher dielectric constant to interact with incident electric field, and thus most of the incident light will be scattered by the TiO2 layers, the layers close to the YAG phosphor.

FIG. 14.

FDTD-simulated scattering spectra for the entire coating and for TiO2 layers alone.

FIG. 14.

FDTD-simulated scattering spectra for the entire coating and for TiO2 layers alone.

Close modal

A zigzag nanorod-structured graded-index AR coating was fabricated by OAD on the YAG:Ce CPP by e-beam evaporation. The AR coating enhances the normal-direction transmission of YAG:Ce CPP across a broad spectral range, and the maximum improvement reaches 7.82% at 764 nm, which closely approximates the potential maximum predicted by the Fresnel equation of 8.53%. Scattering measurements over multiple angles also confirm that the AR coating is close to ideal. We developed a simplified geometrical model for the obtained AR coating and applied the model in an FDTD simulation to study the morphology and material dependence of the coating’s optical properties including the polarization-dependent antireflective performance and scattering loss. The simulated polarized transmission spectrum demonstrated that the model, though a crude representation of the actual structure, captures the polarization-dependent antireflective performance of the coating, according to the results obtained from ellipsometry. The simulated scattering spectrum also shows the coating induces weak scattering loss, which agrees with the experimental measurement at 633 nm. The TiO2 layers in the coating contribute most to the polarization-dependent optical response and to the scattering. The low scattering loss renders the reported coating is of high quality. We believe the introduction of OAD-grown nanostructured AR coatings could be useful in mitigating reflection losses in devices that rely on YAG:Ce or similar CPPs. Study on the underlying effect of the coating also allows for designing light converters with enhanced extraction in broad spectral and angular propagation ranges.

This work was supported by the National Science Foundation (NSF) (Grant No. ECCS-1127731). The authors would like to thank Lighting Enabled Systems & Applications (LESA) center at Rensselaer Polytechnic Institute for providing the FDTD software. The authors also gratefully acknowledge OSRAM SYLVANIA for providing the YAG:Ce CPP substrates, setting up the Perkin Elmer Lambda 900 spectrometer and customized laser system, and performing the optical and scattering experiments.

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