A low refractive index substrate for reducing specular reflectivity comprising a textured region of high refractive index material disposed on a higher elevation surface and a lower elevation surface

Abstract

A substrate for a display article, the substrate comprising: (a) a major surface; and (b) a textured region located on at least a portion of the major surface, the textured region comprising: (i) one or more upper surfaces located at a higher average elevation, the higher average elevation being parallel to a base plane, the base plane being disposed below the textured region and extending through the substrate; (ii) one or more lower surfaces located at a lower average elevation, the lower average elevation being parallel to the base plane, the lower average elevation being lower than the higher average elevation; and (iii) a high refractive index material disposed on each of the one or more lower surfaces located at the lower average elevation, the high refractive index material forming one or more intermediate surfaces located at an intermediate average elevation, the intermediate average elevation being parallel to the base plane, the intermediate average elevation being greater than the lower average elevation but less than the upper average elevation, the high refractive index material comprising a refractive index that is greater than the refractive index of the substrate.

Description

[0001] Priority claim

[0002] This application claims the benefit of priority to U.S. Provisional Application No. 63 / 049,843, filed on July 9, 2020, which is incorporated herein by reference in its entirety.

[0003] CROSS-REFERENCE TO RELATED APPLICATIONS

[0004] This application is related to, but does not claim priority from, the following commonly owned and assigned patent applications: U.S. Patent Applications Entitled “ANTI-GLARE SUBSTRATE FOR A DISPLAY ARTICLE INCLUDING A TEXTUREDREGION WITH PRIMARY SURFACE FEATURES AND SECONDARY SURFACE FEATURES IMPARTING A SURFACE ROUGHNESS THAT INCREASES SURFACE SCATTERING”; U.S. Patent Applications Entitled “TEXTURED REGION OF A SUBSTRATE TO REDUCE SPECULAR REFLECTANCE INCORPORATING SURFACE FEATURES WITH AN ELLIPTICAL PERIMETER OR SEGMENTS THEREOF, AND METHODOF MAKING THE SAME”; U.S. Patent Applications Entitled “DISPLAY ARTICLES WITH DIFFRACTIVE, ANTIGLARE SURFACES AND THIN, DURABLE ANTIREFLECTION The entire disclosure of each of the foregoing U.S. patent applications, publications, and patent documents is incorporated herein by reference. Technical Field

[0005] The present disclosure relates to substrates for display articles, wherein the substrate includes a textured region for reducing specular reflectivity, the textured region comprising a low refractive index substrate having a higher elevation surface and a lower elevation surface, and a high refractive index material disposed on the lower elevation surface. Background Art

[0006] Substrates that are transparent to visible light are used to cover displays in display products. Such display products include smartphones, tablets, televisions, computer monitors, and the like. These displays are typically liquid crystal displays (LCDs), organic light-emitting diodes (OLEDs), and other displays. The substrate protects the display, while its transparency allows the user of the device to view the display.

[0007] Reflecting ambient light, especially substrates with specular reflection, reduces a user's ability to view the display through the substrate. Specular reflection, in this case, is the reflection of ambient light that leaves the substrate like a mirror. For example, the substrate can reflect visible light reflected from or emitted by an object into the environment surrounding the device. Visible light reflected from the substrate reduces the contrast of light transmitted from the display through the substrate to the user's eyes. At certain viewing angles, the user sees the specularly reflected image rather than the visible light emitted by the display. Therefore, attempts have been made to reduce specular reflection of visible ambient light from the substrate.

[0008] Attempts have been made to reduce specular reflection from substrates by texturizing the reflective surface of the substrate. The resulting surface is sometimes referred to as an "anti-glare surface." For example, sandblasting and liquid etching the surface of the substrate can texturize the surface, which typically causes the surface to diffusely reflect ambient light rather than specularly. Diffuse reflection generally means that the surface still reflects ambient light at the same intensity, but the texture of the reflective surface scatters the light upon reflection. The more diffuse reflection, the less it interferes with the user's ability to see the visible light emitted by the display.

[0009] Such texturing methods (i.e., sandblasting and liquid etching) produce features on the surface that have imprecise and non-repeatable geometries (which provide the texture). The geometry of a textured surface of one substrate formed by sandblasting or liquid etching can never be exactly the same as the geometry of a textured surface of another substrate formed by sandblasting or liquid etching. Typically, only the surface roughness (i.e., R a ) is a repeatable goal of texturing.

[0010] There are several metrics used to judge the quality of an "anti-glare" surface. These metrics include: (1) image clarity, (2) pixel power deviation, (3) noticeable Moiré interference fringes, (4) transmission haze, (5) reduction of specular reflections, and (6) reflected color artifacts. Image clarity, more properly referred to as reflected image clarity, is a measure of how sharp an image appears when reflected from a surface. The lower the image clarity, the more diffuse rather than specular reflections appear from the textured surface. Surface features can magnify the various pixels of a display, which distorts the image viewed by the user. Pixel power deviation, also known as "sparkle," quantifies this effect. The lower the pixel power deviation, the better. Moiré interference fringes are large-scale interference patterns that, if visible, distort the image viewed by the user. Preferably, a textured surface does not produce noticeable Moiré interference fringes. Transmission haze is a measure of how much visible light emitted by a display is diffused by the textured surface as it is transmitted through the substrate. The greater the transmission haze, the less sharp the display appears (i.e., reduced apparent resolution). Specular reflection reduction is a measure of how effectively an anti-glare surface reduces specular reflections of ambient light compared to a baseline, non-anti-glare glass substrate. The greater the specular reflection reduction compared to the baseline, the better. Reflection color artifacts are a type of chromatic aberration in which a textured surface diffracts light as a function of wavelength upon reflection, meaning that the reflected light, while relatively diffuse, appears to be segmented by color. Textured surfaces produce as few reflection color artifacts as possible. Some of these properties are discussed in more detail below.

[0011] Targeting only a specific surface roughness cannot optimize all of these metrics simultaneously. A relatively high surface roughness, such as sandblasting or liquid etching, may be sufficient to convert specular reflections to diffuse reflections. However, high surface roughness can also produce high transmission haze and pixel power deviations. A relatively low surface roughness, while reducing transmission haze, may not fully convert specular reflections to diffuse reflections—failure to achieve the "anti-glare" purpose of texturing.

[0012] Therefore, there is a need for a new method of providing textured areas of a substrate - a method that is reproducible between substrates and causes the textured surface to sufficiently diffusely reflect, rather than specularly reflect, ambient light so as to achieve "anti-glare" (e.g., low image clarity, low specular reflection) but also a method that gives low pixel power deviation, low transmission haze, and low reflective color artifacts. Summary of the Invention

[0013] The present disclosure provides a new method for simultaneously giving many desired anti-glare performance metrics. A textured area is formed at the major surface of a substrate, which includes a substrate providing a surface at two different average elevations, such as when surface features are etched or otherwise formed into the substrate. A high refractive index material is then deposited onto the surface of the substrate at the lower of the two different average elevations, but not so high that the high refractive index material reaches the higher of the two different average elevations of the substrate. The surface features can be placed randomly but specifically to allow reproducibility between substrates. The surface features can have adjustable feature sizes to provide the desired optical results. The presence of the high refractive index material generally reduces pixel power deviation, and the presence of the surface features effectively scatters light upon reflection, resulting in low specular reflection.

[0014] According to a first aspect of the present disclosure, a substrate for a display article comprises: (a) a major surface; and (b) a textured region located on at least a portion of the major surface, the textured region comprising: (i) one or more upper surfaces located at a higher average elevation, the higher average elevation being parallel to a base plane, the base plane being disposed below the textured region and extending through the substrate; (ii) one or more lower surfaces located at a lower average elevation, the lower average elevation being parallel to the base plane, the lower average elevation being lower than the higher average elevation; and (iii) a high refractive index material disposed on each of the one or more lower surfaces located at the lower average elevation, the high refractive index material forming one or more intermediate surfaces located at an intermediate average elevation, the intermediate average elevation being parallel to the base plane, the intermediate average elevation being greater than the lower average elevation but less than the higher average elevation, the high refractive index material comprising a refractive index greater than the refractive index of the substrate or the low refractive index material providing the one or more upper surfaces.

[0015] According to a second aspect of the present disclosure, the substrate as described in the first aspect, wherein (i) the middle average elevation of the high refractive index material is smaller than the higher average elevation of the one or more higher surfaces by a distance of 100 nm to 190 nm; (ii) the lower average elevation of the one or more lower surfaces is smaller than the higher average elevation of the one or more higher surfaces by a distance of 220 nm to 370 nm; and (iii) the middle average elevation of the high refractive index material is greater than the lower average elevation of the one or more lower surfaces by a distance of 100 nm to 200 nm.

[0016] According to a third aspect of the present disclosure, the substrate as described in any one of the first to second aspects, wherein (i) the refractive index of the substrate or the low refractive index material is in the range of 1.4 to 1.6; and (ii) the refractive index of the high refractive index material is in the range of 1.6 to 2.3.

[0017] According to a fourth aspect of the present disclosure, the substrate as described in any one of the first to third aspects, wherein the high refractive index material occupies 22% to 49% of the area of a plane, which is (i) parallel to the base plane and (ii) extends through the high refractive index material, and the area is defined by the textured area.

[0018] According to a fifth aspect of the present disclosure, the substrate as described in any one of the first to fourth aspects comprises a glass substrate or a glass ceramic substrate.

[0019] According to a sixth aspect of the present disclosure, a substrate for a display article comprises: (I) a major surface; and (II) a textured region located on at least a portion of the major surface, the textured region comprising: (a) one or more higher surfaces located at a higher average elevation, the higher average elevation being parallel to a base plane, the base plane being disposed below the textured region and extending through the substrate; (b) one or more lower surfaces located at a lower average elevation, the lower average elevation being parallel to the base plane, the lower average elevation being lower than the higher average elevation; and (c) surface features protruding from or disposed within a surrounding portion located at the major surface, wherein (i) the surface features are The surface feature provides any of the following: the one or more higher surfaces or the one or more lower surfaces, (ii) the surrounding portion provides the other of the one or more higher surfaces or the one or more lower surfaces, whichever is not provided by the surface feature; and (d) a high refractive index material disposed on the one or more lower surfaces located at a lower average elevation, the high refractive index material comprising (i) a refractive index greater than the refractive index of the substrate or low refractive index material providing the one or more higher surfaces, and (ii) one or more intermediate surfaces located at an intermediate average elevation, the intermediate average elevation being parallel to the base plane, the intermediate average elevation being between the higher average elevation and the lower average elevation.

[0020] According to a seventh aspect of the present disclosure, the substrate of the sixth aspect, wherein (i) the surface features are disposed within the surrounding portion; and (ii) the high refractive index material is disposed within each surface feature, located on the one or more lower surfaces provided by the surface features at the lower average elevation.

[0021] According to an eighth aspect of the present disclosure, the substrate as described in any one of aspects 6 to 7, wherein the middle average elevation of the high refractive index material is smaller than the higher average elevation of the one or more higher surfaces by a distance of 120 nm to 190 nm.

[0022] According to a ninth aspect of the present disclosure, the substrate as described in any one of the sixth to eighth aspects, wherein the lower average elevation is smaller than the higher average elevation by a distance of 220 nm to 370 nm.

[0023] According to a tenth aspect of the present disclosure, the substrate as described in any one of aspects 6 to 9, wherein the middle average elevation of the high refractive index material is greater than the lower average elevation of the one or more lower surfaces by a distance of 100 nm to 200 nm.

[0024] According to an eleventh aspect of the present disclosure, in the substrate as described in any one of the sixth to tenth aspects, the refractive index of the substrate or the low-refractive-index material is in the range of 1.4 to 1.6.

[0025] According to a twelfth aspect of the present disclosure, in the substrate as described in any one of the sixth to eleventh aspects, the refractive index of the high refractive index material is in the range of 1.6 to 2.3.

[0026] According to a thirteenth aspect of the present disclosure, the substrate of any one of aspects six to twelfth, wherein (i) each surface feature has a perimeter parallel to the base plane; and (ii) the perimeter of each surface feature is circular or elliptical.

[0027] According to a fourteenth aspect of the present disclosure, the substrate of any one of aspects six to twelfth, wherein (i) each surface feature has a perimeter parallel to the base plane; and (ii) the perimeter of each surface feature has a longest dimension in the range of 5 μm to 200 μm.

[0028] According to a fifteenth aspect of the present disclosure, the substrate as described in any one of aspects six to fourteen, wherein the configuration of the surface features is not repeated but reflects a random distribution.

[0029] According to a sixteenth aspect of the present disclosure, the substrate as described in any one of aspects six to fourteen, wherein the surface features are arranged in a random distribution, and a minimum center-to-center distance separates each of the surface features.

[0030] According to the seventeenth aspect of the present disclosure, the substrate as described in any one of the sixth to sixteenth aspects, wherein the high refractive index material comprises AlN x 、SiO x N y or SiN x .

[0031] According to an eighteenth aspect of the present disclosure, the substrate as described in any one of aspects six to seventeen, wherein the high refractive index material occupies 22% to 49% of the area of a plane, which is (i) parallel to the base plane and (ii) extends through the high refractive index material, and the area is defined by the textured area.

[0032] According to a nineteenth aspect of the present disclosure, the substrate as described in any one of the sixth to eighteenth aspects, wherein the substrate comprises a glass substrate or a glass ceramic substrate.

[0033] According to the twentieth aspect of the present disclosure, the substrate as described in any one of aspects 6 to 19, wherein (i) the textured area exhibits a pixel power deviation in the range of 1.2% to 2.1%; (ii) the textured area exhibits a transmission haze in the range of 1.5% to 2.5%; (iii) the textured area exhibits a specular reflectance of 0.5% to 1.75%; and (iv) the textured area exhibits an image clarity of 25% to 85%.

[0034] According to a twenty-first aspect of the present disclosure, a method for forming a textured region of a substrate for a display article comprises: (a) forming surface features protruding from or disposed within a surrounding portion located at a major surface of a substrate according to predetermined positions of each surface feature, thereby forming a textured region, wherein (i) one or more higher surfaces of the textured region are located at a higher average elevation, the higher average elevation being parallel to a base plane disposed below the textured region and extending through the substrate, (ii) one or more lower surfaces of the textured region are located at a lower average elevation, the lower average elevation being parallel to the base plane and being lower than the higher average elevation, and (iii) The surface feature provides any of the following: the one or more higher surfaces or the one or more lower surfaces, and (iv) the surrounding portion provides the other of the one or more higher surfaces or the one or more lower surfaces, whichever the surface feature does not provide; and (b) depositing a high refractive index material on either the surface feature or the surrounding portion that provides the one or more lower surfaces located at the lower average elevation, the high refractive index material comprising (i) a refractive index that is greater than the refractive index of the substrate, and (ii) one or more intermediate surfaces located at an intermediate average elevation that is parallel to the base plane and is between the higher average elevation and the lower average elevation.

[0035] According to the twenty-second aspect of the present disclosure, the method as described in the twenty-first aspect further includes: using a spacing distribution algorithm to determine the position of each surface feature, thereby establishing a predetermined position of each surface feature.

[0036] According to the twenty-third aspect of the present disclosure, the method as described in the twenty-second aspect further includes: placing an etching mask on the main surface, and the etching mask either (i) prevents etching of the place where the surface feature is to be formed according to the predetermined position of the surface feature or (ii) only allows etching of the place where the surface feature is to be formed according to the predetermined position of the surface feature; wherein, forming the surface feature includes causing the etchant to contact at least the main surface of the substrate when the etching mask is placed on the main surface of the substrate.

[0037] According to a twenty-fourth aspect of the present disclosure, the method of aspect twenty-third, wherein the high refractive index material is deposited when the etch mask is disposed on the major surface and after the surface features have been formed.

[0038] According to a twenty-fifth aspect of the present disclosure, the method as described in the twenty-fourth aspect further comprises: removing the etching mask after the high refractive index material has been deposited. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In the attached figure:

[0040] Figure 1 is a perspective view of a display article of the present disclosure illustrating a substrate having a textured area for reducing specular reflectivity of light emitted from an external environment;

[0041] Figure 2 is an optical profilometer scan, which relates to Examples 2A-2G and also generally illustrates an embodiment of a textured region comprising one or more surfaces located at a high average elevation from a base plane and a high refractive index material disposed within the surface features, the high refractive index material forming a surface located at an intermediate average elevation from the base plane;

[0042] Figure 3A It passes through Figure 2 An elevational view of a section taken along line III-III of FIG. 1 , the elevational view illustrating a substrate providing a surface at a higher average elevation, a surface at a lower average elevation from a base plane, and a high refractive index material disposed on the surface at the lower average elevation, the high refractive index material providing a surface at an intermediate average elevation between the higher average elevation and the lower higher average elevation;

[0043] Figure 3B is with Figure 3A Same view, but illustrating that the surface features are not disposed within the surrounding portion of the substrate (e.g. Figure 3A (such as that) but rather a scenario where the material protrudes from the surrounding portion and the high refractive index material is disposed on the surrounding portion;

[0044] Figure 4 This is an illustration of the calculation of hexagon percentage;

[0045] Figure 5 is formed Figure 1 A schematic diagram of an embodiment of a method for textured regions of a substrate illustrating the steps of determining locations of surface features, placing an etch mask on a substrate to enable formation of the surface features at the determined locations, forming the surface features by etching while the etch mask is on the substrate, depositing a high refractive index material onto the substrate while the etch mask is still on the substrate, and then removing the etch mask.

[0046] Figure 6A is a graph relating to Comparative Example 1A, illustrating how the diffraction efficiency of transmitted light through a textured region of a substrate varies as a function of groove depth (i.e., the distance between the higher average elevation and the lower average elevation);

[0047] Figure 6B is a graph related to Comparative Example 1A, illustrating how the diffraction efficiency of light reflected from a textured region of a substrate varies depending on the groove depth;

[0048] Figure 7A is a graph related to Example 1B, illustrating how the diffraction efficiency of light transmitted through a textured region of a substrate varies depending on the depth of the grooves;

[0049] Figure 7B is a graph related to Example 1B, illustrating how the diffraction efficiency of light reflected from a textured region of a substrate varies depending on the groove depth;

[0050] Figure 7C is a graph relating to Example 1B, illustrating how the diffraction efficiency of light transmitted through a textured region of a substrate varies as a function of the filling fraction of the substrate (i.e., the percentage of the plane of high refractive index material passing through the textured region occupied by the substrate);

[0051] Figure 7D is a graph relating to Example 1B illustrating how the diffraction efficiency of light reflected from a textured region of a substrate varies as a function of the fill fraction of the substrate (i.e., the percentage of the plane of high refractive index material passing through the textured region occupied by the substrate);

[0052] Figure 7E is a graph related to Example 1B, illustrating how the diffraction efficiency of light transmitted through a textured region of a substrate varies depending on the angle of incident light;

[0053] Figure 7F is a graph related to Example 1B, illustrating how the diffraction efficiency of light reflected from a textured region of a substrate varies depending on the angle of incident light;

[0054] Figure 8 is a histogram relating to Examples 2A-2G illustrating center-to-center distances of objects randomly placed into a region via a spacing distribution algorithm (in order to distribute the placement of surface features of a subsequently formed textured region); and

[0055] Figure 93A-3D are histograms illustrating the center-to-center distances of objects randomly placed into a region (to distribute the placement of surface features of a subsequently formed textured region) via another spacing distribution algorithm. DETAILED DESCRIPTION

[0056] Now refer to Figure 1 , display article 10 includes substrate 12. In an embodiment, display article 10 further includes a housing 14 to which substrate 12 is attached, and a display 16 positioned within housing 14. In such embodiments, substrate 12 at least partially covers display 16 such that light emitted by display 16 is transmitted through substrate 12.

[0057] Substrate 12 includes a major surface 18, a textured region 20 defined on major surface 18, and a thickness 22 partially defined by major surface 18. Major surface 18 generally faces toward an external environment 24 surrounding display article 10 and away from display 16. Display 16 emits visible light that is transmitted through thickness 22 of substrate 12, exits major surface 18, and enters external environment 24.

[0058] Now refer to Figure 2-3B In an embodiment, textured region 20 includes one or more elevated surfaces 26 facing the external environment 24 and located at an elevated average elevation 28. A base plane 30 extends through substrate 12 below textured region 20. The elevated average elevation 28 is parallel to base plane 28. Base plane 30 provides a conceptual reference point and is not a structural feature. Within manufacturing capabilities, each of the one or more elevated surfaces 26 is located at approximately the elevated average elevation 28.

[0059] The textured area further includes one or more lower surfaces 32 facing the exterior environment 24 and located at a lower average elevation 34. The lower average elevation 34 is parallel to the base plane 28 and is less than the upper average elevation 28. Thus, "upper" and "lower" refer to relative elevations relative to each other from the base plane 28. Within manufacturing capabilities, each of the one or more lower surfaces 32 is located at approximately the lower average elevation 34.

[0060] Substrate 12 or a low-refractive-index material disposed on substrate 12 provides one or more higher surfaces 26 of textured region 20. In such embodiments, either substrate 12 or the low-refractive-index material providing one or more higher surfaces 26 has a refractive index of 1.4, 1.5, 1.6, or within a range of 1.4 to 1.6. In embodiments, substrate 12, regardless of whether substrate 12 provides one or more higher surfaces 26, has a refractive index of 1.4, 1.5, 1.6, or within a range of 1.4 to 1.6. For the purposes of this disclosure, any specific value of refractive index is for a wavelength of 589 nm and a temperature of 25° C.

[0061] The textured region 20 further includes a high refractive index material 36. In embodiments, the high refractive index material 36 has a composition that is different from the composition of the substrate 12. The high refractive index material 36 is disposed on each of the one or more lower surfaces 32 of the textured region 20 located at a lower average elevation 34. The high refractive index material 36 forms one or more intermediate surfaces 38 that face the external environment 24 and are located at an intermediate average elevation 40 that is parallel to the base plane 30. Each of the one or more intermediate surfaces 38 is located at approximately the intermediate average elevation 40 within manufacturing capabilities.

[0062] The high refractive index material 36 has a refractive index. The refractive index of the high refractive index material 36 is greater than the refractive index of the substrate 12. In embodiments, the refractive index of the high refractive index material 36 is 1.6, 1.7, 1.8, 1.9, 2.0, 2.01, 2.02, 2.03, 2.04, 2.05, 2.06, 2.07, 2.08, 2.09, 2.1, 2.2, 2.3, or within any range defined by any two of these values (e.g., 1.6 to 2.3, 1.8 to 2.2, 1.9 to 2.1, etc.). In embodiments, the high refractive index material is or includes Si. u Al v O x N y 、Ta2O5、Nb2O5、AlN x 、Si3N4、AlO x N y 、SiO x N y 、SiN x 、SiN x :H y , HfO2, TiO2, ZrO2, Y2O3, Al2O3, MoO3 and diamond-like carbon. In an embodiment, the high refractive index material is or includes AlN x 、SiO x N y or SiN x In an embodiment, the high refractive index material is or includes AlN x Regarding the “AlN x ”, “AlO x N y ", "SiO x N y ” and “SiN x" materials, the subscript allows one of ordinary skill in the art to refer to these materials as a class of materials without assigning a particular subscript value. The oxygen-nitrogen ratio can be adjusted through routine experimentation for adjusting the refractive index of high refractive index materials. For embodiments requiring a high film refractive index (e.g., greater than 1.8 or 1.9), SiN with a composition close to Si3N4 x For films with similar high refractive index, AlN with a composition close to AlN may be preferred. x Small fractions of oxygen or hydrogen (eg, 0-20 atomic %) may also be incorporated into these materials while achieving a similar high refractive index range.

[0063] The intermediate average elevation 40 of the one or more intermediate surfaces 38 of the high refractive index material 36 is greater than the lower average elevation 34 of the one or more lower surfaces 32 of the textured region 20, but is less than the upper average elevation 28 of the one or more upper surfaces 26 of the textured region 20. In short, the intermediate average elevation 40 is located between the upper average elevation 28 and the lower average elevation 34.

[0064] The upper average elevation 28 of one or more upper surfaces 26 of the textured region 20 is greater than the lower average elevation 34 of one or more lower surfaces 32 of the textured region 20 by a distance 42. This disclosure may refer to distance 42 as "groove depth" (not to be confused with "air groove depth" discussed later). In embodiments, distance 42 is 220 nm, 230 nm, 240 nm, 250 nm, 260 nm, 270 nm, 280 nm, 290 nm, 300 nm, 310 nm, 320 nm, 330 nm, 340 nm, 350 nm, 360 nm, or 370 nm, or any range bounded by any two of these values (e.g., 250 nm to 350 nm, 270 nm to 330 nm, 220 nm to 370 nm, etc.).

[0065] The middle average elevation 40 of the high refractive index material 36 is greater than the lower average elevation 34 of the one or more lower surfaces 32 of the textured region 20 by a distance 44. The distance 44 may be referred to as the "height" or "thickness" of the high refractive index material 36 deposited on the one or more lower surfaces 32. In embodiments, the distance 44 is 100 nm, 110 nm, 120 nm, 130 nm, 140 nm, 150 nm, 160 nm, 170 nm, 180 nm, 190 nm, or 200 nm, or within any range bounded by any two of these values (e.g., 100 nm to 200 nm, 120 nm to 180 nm, etc.).

[0066] The middle average elevation 40 of the high refractive index material 36 is less than the upper average elevation 28 of the one or more upper surfaces 26 of the textured region 20 by a distance 46. This distance 46 may be referred to herein as the "air trench depth." In embodiments, the distance 46 is 100 nm, 110 nm, 120 nm, 125 nm, 130 nm, 140 nm, 150 nm, 160 nm, 170 nm, 180 nm, or 190 nm, or within any range bounded by any two of these values (e.g., 120 nm to 190 nm, 125 nm to 190 nm, 130 nm to 180 nm, 100 nm to 190 nm, etc.). Note that Figure 3A and Figure 3B Not drawn to scale.

[0067] 36 occupies a percentage of area 48 of a plane 50 that is (i) parallel to base plane 30 and (ii) extends through high index material 36. Area 48 is bounded by textured region 20. In other words, area 48 does not extend laterally beyond textured region 20. The percentage of area 48 of plane 50 occupied by high index material 36 may be referred to herein as the "fill fraction" of high index material 36. In embodiments, the fill fraction of high index material 36 is 22%, 23%, 24%, 25%, 26%, 27%, 28%, 29%, 30%, 31%, 32%, 33%, 34%, 35%, 36%, 37%, 38%, 39%, 40%, 41%, 42%, 43%, 44%, 45%, 46%, 47%, 48%, or 49%, or within any range bounded by any two of these values (e.g., 44% to 45%, 22% to 49%, etc.). One hundred percent (100%) minus the filling fraction of high refractive index material 36 is the filling fraction of substrate 12 or a low refractive index material deposited on substrate 12 having a lower refractive index than high refractive index material 36 .

[0068] It is believed that when the filling fraction of the high refractive index material is between 22% and 49%, the specular reflectivity and the intensity of the first-order diffraction peak are minimized. The high refractive index material 36, which has a higher refractive index than the substrate 12 or the low refractive index material, is more reflective. Therefore, in order to maximize destructive interference during reflection, the high refractive index material 36 should occupy less than half of the textured area 20 at the main surface 18 that reflects ambient light. More than half of the textured area 20 at the main surface 18 that reflects ambient light should be the substrate 12 or the low refractive index material having a lower refractive index to balance the more reflective high refractive index material 36.

[0069] In an embodiment, textured region 20 includes surface features 52. In an embodiment, surface features 52 protrude from a surrounding portion 54 of textured region 20 at main surface 18. Such surface features 52 take the form of posts, ridges, and the like. In an embodiment, surface features 52 are disposed within (i.e., provided in) surrounding portion 54. Such surface features 52 take the form of blind holes, channels, or mesas extending from surrounding portion 54 into thickness 22 of substrate 12 or low refractive index material. In an embodiment, some of surface features 52 are disposed within surrounding portion 54, while some of surface features 52 protrude from surrounding portion 54. In an embodiment, surrounding portion 54 contiguously surrounds surface features 52.

[0070] Either the surface feature 52 or the surrounding portion 54 provides one or more higher surfaces 26 at a higher average elevation 28, while the other of the surface feature 52 and the surrounding portion 54 provides one or more lower surfaces 32 at a lower average elevation 34. Figure 3A ), the surface features 52 provide one or more higher surfaces 26 located at a higher average elevation 28. In such cases, the surrounding portion 54 provides one or more lower surfaces 32 located at a lower average elevation 34. When the surface features 52 are disposed within the surrounding portion 54 (see Figure 3B ), the surrounding portion 54 provides one or more higher surfaces 26 located at a higher average elevation 28. In such cases, the surface features 52 provide one or more lower surfaces 32 located at a lower average elevation 34.

[0071] The high refractive index material 36 is disposed on either the surface features 52 or the surrounding portion 64 that provide the one or more lower surfaces 32 at the lower average elevation 34. In embodiments where the surface features 52 are disposed within the surrounding portion 54, the high refractive index material 36 is disposed within the surface features 52 on the one or more lower surfaces 32 at the lower average elevation 34 provided by the surface features 52. In embodiments where the surface features 52 protrude from the surrounding portion 54, the high refractive index material 36 is disposed between the surface features 52 on the one or more lower surfaces 32 at the lower average elevation 34 provided by the surrounding portion 54. In embodiments where the high refractive index material 36 is disposed on the surrounding portion 54 and the surrounding portions 54 are contiguous, the high refractive index material 36 may form a surface intermediate body 38 that surrounds and abuts the surface features 52 that protrude through the high refractive index material 36 toward the external environment 24.

[0072] In an embodiment, the one or more upper surfaces 26 at the upper average elevation 28 are planar. In an embodiment, the one or more lower surfaces 32 at the lower average elevation 34 are planar. In other embodiments, the one or more lower surfaces 32 are convex or concave. In an embodiment, some of the one or more lower surfaces 32 are concave, while other of the one or more lower surfaces 32 are convex.

[0073] The textured region 20, which provides one or more higher surfaces 26 at a higher average elevation 28 and one or more lower surfaces 32 at a lower average elevation 34, is a diffractive structure that causes controlled scattering of reflected ambient light. The scattering of reflected ambient light reduces specular reflectivity and image clarity. As will be further demonstrated, a high-refractive-index material 36 having a refractive index greater than that of the substrate 12 or a low-refractive-index material on the substrate 12 improves light transmission through the textured region 20 (such as from the display 16), which reduces transmission haze and pixel power deviation compared to the case where only the textured region 20 is utilized without the high-refractive-index material 36.

[0074] In some embodiments, surface features 52 are arranged in a random distribution. In other words, in these embodiments, surface features 52 are not arranged in a pattern. However, in other embodiments, surface features 52 are arranged in a pattern, such as a hexagonal arrangement. When surface features 52 are arranged in a pattern, textured region 20 can produce a moiré interference pattern when reflecting ambient light. Additionally, not arranging surface features 52 in a pattern can reduce the wavelength dependence of scattered ambient light. Therefore, for some applications, it may be beneficial to avoid arranging surface features 52 in a pattern.

[0075] refer to Figure 4 One measure of randomness is the hexagonal percentage of the surface features 52. The hexagonal percentage is a metric used to locally quantify how closely the arrangement of objects in a region forms a hexagonal lattice. Each object in a region has a center point. For each center point in a region, the hexagonal percentage H at that center point is calculated using the angles of the six nearest center points to that center point relative to any axis according to the following equation:

[0076]

[0077] variable α k represents the angles of the six nearest neighbor center points. With respect to the hexagonal lattice, these six angles all differ by 60 degrees (π / 3 radians), so the exponents of the six summands differ by 2π radians, and the six complex numbers in the sum are all the same. In this case, H= 1. Perfect hexagonal lattice. Each center point in the area has its unique HAll values in this area H The mean of the values represents the deviation of the configuration from the hexagonal lattice. H The further the mean of the values is from 1, the more random the configuration.

[0078] Each surface feature 52 has a perimeter 56 that is parallel to the base plane 30. In an embodiment, the perimeter 56 of each surface 52 has the same shape. For example, in an embodiment, Figure 2 In the illustrated embodiments, the perimeter 56 of each surface feature 52 is circular. In embodiments, the perimeter 56 of each surface feature 52 is elliptical. In embodiments, the perimeter 56 of each surface feature 52 is hexagonal or polygonal. In embodiments, the perimeter 56 of the surface features 52 is one of two or more shapes (e.g., some are elliptical and some are circular).

[0079] The perimeter 56 of each surface feature 52 has a longest dimension 58. If the perimeter 52 is circular, the longest dimension 58 is the diameter of the perimeter 56. If the perimeter 56 is hexagonal, the longest dimension 58 is the major axis (the long diagonal). And so on. In embodiments, the longest dimension 58 of the perimeter 56 of each surface feature 52 is 5 μm, 10 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60 μm, 70 μm, 80 μm, 90 μm, 100 μm, 110 μm, 120 μm, 130 μm, 140 μm, 150 μm, 160 μm, 170 μm, 180 μm, 190 μm, or 200 μm, or within any range bounded by any two of these values (e.g., 5 μm to 200 μm, 20 μm to 100 μm, 80 μm to 120 μm, 30 μm to 70 μm, 25 μm to 75 μm, etc.).

[0080] In embodiments, a minimum center-to-center distance 60 separates surface features 52. For example, if the minimum center-to-center distance 60 is 100 μm, the center of one surface feature 52 may be separated by 100 μm or more, but not less than 100 μm, from the center of another adjacent surface feature 52. In embodiments, the minimum center-to-center distance 60 is 5 μm, 10 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60 μm, 70 μm, 80 μm, 90 μm, 100 μm, 110 μm, 120 μm, or 130 μm, or within any range bounded by any two of these values (e.g., 30 μm to 70 μm, 40 μm to 80 μm, 5 μm to 100 μm, 20 μm to 90 μm, 30 μm to 80 μm, etc.).

[0081] The high refractive index material 36, having a refractive index greater than that of the substrate 12 or a low refractive index material on the substrate 12, reduces the pixel power deviation produced by the textured region 20, which allows the minimum center-to-center spacing 60 to be greater than would otherwise be possible without the incorporation of the high refractive index material 36. Additionally, the incorporation of the high refractive index material 36 allows the surface features 52 to have a longer longest dimension 58 than would otherwise be possible without the high refractive index material 36. This is beneficial for several reasons. First, the longer the longest dimension 58 of the surface features 52, the easier it is to manufacture the surface features 52, and therefore the textured region 20. With the incorporation of the high refractive index material 36, the textured region 20 can be manufactured using low-cost methods such as inkjet printing, screen printing, or gravure offset printing. Second, the longer the longest dimension 58 of the perimeter 56 of the surface feature 52, the less transmission haze produced by the textured region 20. However, there is a practical limit to the longest dimension 58 of the surface feature 52 because if the longest dimension 58 is long enough, the surface feature 52 becomes visible to the human eye, which may be undesirable.

[0082] Third, when the longest dimension 58 of the perimeter 56 of the surface feature 52 is sufficiently long, the surface feature 52 scatters reflected light with higher intensity within a narrow range of angles from the specular angle, including approximately 0.3 degrees. This results in a higher pixel power deviation in the textured region 20. Additionally, this results in fewer reflected color artifacts because the reflected light is not scattered over a sufficiently wide range of angles to allow the human eye to distinguish between colors. For example, the angular separation between the peak scattering angles of the 450 nm wavelength portion of light and the 650 nm wavelength portion of light can be less than 0.4 degrees, less than 0.3 degrees, or even less than 0.2 degrees. Smaller angular separations between different wavelengths are preferred because the human eye has difficulty distinguishing very small angular separations. Therefore, with small scattering angle separations between wavelengths, fewer colors of the scattered light are visible to the observer.

[0083] In embodiments, substrate 12 comprises glass or a glass-ceramic. In embodiments, substrate 12 is a multi-component glass composition having approximately 40 mol% to 80 mol% silicon dioxide, with the balance being one or more other components, such as aluminum oxide, calcium oxide, sodium oxide, boron oxide, and the like. In some embodiments, the bulk composition of substrate 12 is selected from the group consisting of aluminosilicate glass, borosilicate glass, and phosphosilicate glass. In other embodiments, the bulk composition of substrate 12 is selected from the group consisting of aluminosilicate glass, borosilicate glass, phosphosilicate glass, soda-lime glass, alkali aluminosilicate glass, and alkali aluminoborosilicate glass. In further embodiments, substrate 12 is a glass-based substrate, including but not limited to glass-ceramic materials comprising approximately 90% by weight or greater of a glass component and a ceramic component. In other embodiments of display article 10, substrate 12 may be a polymeric material having durability and mechanical properties suitable for developing and maintaining textured region 20. In other embodiments, substrate 12 is or comprises a single crystal structure, such as sapphire.

[0084] In an embodiment, substrate 12 has a bulk composition comprising an alkali aluminosilicate glass comprising aluminum oxide, at least one alkali metal, and in some embodiments, greater than 50 mol % SiO , in other embodiments, at least 58 mol % SiO , and in yet other embodiments, at least 60 mol % SiO , wherein the ratio (Al 2 O 3 (mol %) + B 2 O 3 (mol %)) / ∑ alkali metal modifier (mol %) > 1, wherein the modifier is an alkali metal oxide. In a specific embodiment, the glass comprises, consists essentially of, or consists of: about 58 mol % to about 72 mol % SiO2; about 9 mol % to about 17 mol % Al2O3; about 2 mol % to about 12 mol % B2O3; about 8 mol % to about 16 mol % Na2O; and 0 mol % to about 4 mol % KO, wherein the ratio (Al2O3 (mol %) + B2O3 (mol %)) / ∑ alkali metal modifier (mol %) > 1, wherein the modifier is an alkali metal oxide.

[0085] In an embodiment, substrate 12 has a bulk composition comprising an alkali aluminosilicate glass comprising, consisting essentially of, or consisting of: from about 61 mol % to about 75 mol % SiO; from about 7 mol % to about 15 mol % AlO; from 0 mol % to about 12 mol % BO; from about 9 mol % to about 21 mol % NaO; from 0 mol % to about 4 mol % KO; from 0 mol % to about 7 mol % MgO; and from 0 mol % to about 3 mol % CaO.

[0086] In an embodiment, substrate 12 has a bulk composition comprising an alkali aluminosilicate glass comprising, consisting essentially of, or consisting of: about 60 mol % to about 70 mol % SiO; about 6 mol % to about 14 mol % AlO; 0 mol % to about 15 mol % BO; 0 mol % to about 15 mol % LiO; 0 mol % to about 20 mol % NaO; 0 mol % to about 10 mol % KO; 0 mol % to about 8 mol % MgO; 0 mol % to about 10 mol % CaO; 0 mol % to about 5 mol % ZrO; 0 mol % to about 1 mol % SnO; 0 mol % to about 1 mol % CeO; less than about 50 ppm AsO; and less than about 50 ppm Sb2O3; wherein 12 mol%≦Li2O+Na2O+K2O≦20 mol% and 0 mol%≦MgO+Ca≦10 mol%.

[0087] In an embodiment, the substrate 12 has a bulk composition comprising an alkali aluminosilicate glass comprising, consisting essentially of, or consisting of: about 64 mol % to about 68 mol % SiO2; about 12 mol % to about 16 mol % Na2O; about 8 mol % to about 12 mol % Al2O3; 0 mol % to about 3 mol % B2O3; 2 mol % to about 5 mol % K2O; 4 mol % to about 6 mol % MgO; and 0 mol % to about 5 mol % CaO, wherein: 66 mol % ≤ SiO2 + B2O3 + CaO ≤ 69 mol %; Na2O + K2O + B2O3 + MgO + CaO + SrO > 10 mol %; 5 mol % ≤ MgO + CaO + SrO ≤ 8 mol %. %; (Na2O+B2O3)—Al2O3≦2 mol %; 2 mol %≦Na2O—Al2O3≦6 mol %; and 4 mol %≦(Na2O+K2O)—Al2O3≦10 mol %.

[0088] In one embodiment, substrate 12 has a bulk composition comprising SiO2, Al2O3, P2O5, and at least one alkali metal oxide (RO), wherein 0.75>[(P2O5 (mol %) + RO (mol %)) / M2O3 (mol %)] ≤ 1.2, where M2O3 = Al2O3 + B2O3. In one embodiment, [(P2O5 (mol %) + RO (mol %)) / M2O3 (mol %)] = 1. In one embodiment, the glass does not contain B2O3, and M2O3 = Al2O3. In an embodiment, substrate 12 comprises: about 40 mol % to about 70 mol % SiO2; 0 mol % to about 28 mol % B2O3; about 0 mol % to about 28 mol % Al2O3; about 1 mol % to about 14 mol % PO5; and about 12 mol % to about 16 mol % RO. In some embodiments, the glass substrate comprises: about 40 mol % to about 64 mol % SiO2; 0 mol % to about 8 mol % B2O3; about 16 mol % to about 28 mol % Al2O3; about 2 mol % to about 12 mol % PO5; and about 12 mol % to about 16 mol % RO. Substrate 12 may further comprise at least one alkaline earth metal oxide, such as, but not limited to, MgO or CaO.

[0089] In some embodiments, substrate 12 has a bulk composition that is substantially free of lithium; that is, the glass comprises less than 1 mol % Li O, in other embodiments less than 0.1 mol % Li O, in other embodiments 0.01 mol % Li O, and in other embodiments 0 mol % Li O. In some embodiments, such glass is free of at least one of arsenic, antimony, and barium; that is, the glass comprises less than 1 mol % As O , Sb O , and / or BaO, in other embodiments less than 0.1 mol % As O , Sb O , and / or BaO, and in other embodiments 0 mol % As O , Sb O , and / or BaO.

[0090] In an embodiment, substrate 12 has a bulk composition comprising, consisting essentially of, or consisting of a glass composition, such as Corning ® Eagle XG ® Glass, Corning ® Gorilla ® Glass, Corning ® Gorilla ® Glass 2, Corning ® Gorilla ® Glass 3, Corning ® Gorilla ® Glass 4 or Corning ® Gorilla ® Glass 5.

[0091] In an embodiment, the substrate 12 has an ion-exchangeable glass composition that is strengthened by chemical means or thermal means known in the art. In an embodiment, the substrate 12 is chemically strengthened by ion exchange. In this process, metal ions at or near the major surface 18 of the substrate 12 are exchanged for larger metal ions having the same valence as the metal ions in the substrate 12. The exchange is typically performed by contacting the substrate 12 with an ion exchange medium, such as, for example, a molten salt bath containing the larger metal ions. The metal ions are typically monovalent metal ions, such as, for example, alkali metal ions. In one non-limiting example, chemical strengthening of the substrate 12 containing sodium ions by ion exchange is accomplished by immersing the substrate 12 in an ion exchange bath containing a molten potassium salt, such as potassium nitrate (KNO3), etc. In a specific embodiment, the ions in the surface layer of the substrate 12 adjacent to the major surface 18 and the larger ions are monovalent alkali metal cations, such as Li + (when present in glass), Na + , K +, Rb + and Cs + Alternatively, the monovalent cations in the surface layer of the substrate 12 may be monovalent cations other than alkali metal cations, such as Ag. + or similar replacement.

[0092] In such embodiments, the replacement of small metal ions with larger metal ions during the ion exchange process creates a compressive stress region in substrate 12 that extends from main surface 18 to a depth (referred to as the "depth of layer") under compressive stress. This compressive stress of substrate 12 is balanced by a tensile stress (also referred to as the "central tension") in the interior of substrate 12. In some embodiments, major surface 18 of substrates 12 described herein, when strengthened by ion exchange, has a compressive stress of at least 350 MPa, and the region under compressive stress extends to a depth below major surface 18 into thickness 22, i.e., the depth of layer, of at least 15 μm.

[0093] The ion exchange process is typically performed by immersing the substrate 12 in a molten salt bath containing larger ions to be exchanged for smaller ions in the glass. Those skilled in the art will appreciate that the parameters of the ion exchange process are typically determined by the composition of the glass and the desired depth of layer and compressive stress of the glass as a result of the strengthening operation, including but not limited to bath composition and temperature, immersion time, the number of immersions of the glass in the salt bath (or baths), the use of multiple salt baths, additional steps such as annealing, washing, and the like. For example, ion exchange of alkali-containing glass can be achieved by immersing the glass in at least one molten salt bath containing salts such as, but not limited to, nitrates, sulfates, and chlorides of larger alkali metal ions. The temperature of the molten salt bath typically ranges from about 380° C. to about 450° C., and the immersion time ranges from about 15 minutes to about 16 hours. However, temperatures and immersion times other than those described above may also be used. Such ion exchange treatment, when employed with a substrate 12 having an alkali aluminosilicate glass composition, produces a compressive stress region having a depth (depth of layer) ranging from about 10 μm up to at least 50 μm and a compressive stress ranging from about 200 MPa up to about 800 MPa and a central tension less than about 100 MPa.

[0094] An etching process may be used to create the textured region 20 of the substrate 12. Because the etching process removes alkali metal ions from the substrate 12 that would otherwise be replaced by larger alkali metal ions during the ion exchange process, a compressive stress region is preferably formed in the display article 10 after the textured region 20 is formed and developed.

[0095] In an embodiment, the textured region 20 exhibits a pixel power deviation ("PPD"). Details of the measurement system and image processing calculations for obtaining PPD values are described in U.S. Patent No. 9,411,180, entitled "Apparatus and Method for Determining Sparkle," and the prominent portions of that patent related to PPD measurement are incorporated herein by reference in their entirety. In addition, unless otherwise noted, an SMS-1000 system (Display-Messtechnik & Systeme) was used to generate and evaluate the PPD measurements of the present disclosure. The PPD measurement system includes: a pixelated source (e.g., a Lenovo Z50 140 ppi laptop) comprising a plurality of pixels, each of which has a reference index i and j and an imaging system optically positioned along an optical path originating from a pixelated source. The imaging system comprises: an imaging device positioned along the optical path and having a pixelated sensitive region, the pixelated sensitive region comprising a second plurality of pixels, wherein each of the second plurality of pixels is indexed m and n Reference; and a diaphragm positioned in an optical path between a pixelated source and an imaging device, wherein the diaphragm has an adjustable collection angle for an image originating from the pixelated source. Image processing calculations include: acquiring a pixelated image of a transparent sample, the pixelated image comprising a plurality of pixels; determining boundaries between adjacent pixels in the pixelated image; integrating within the boundaries to obtain an integrated energy for each source pixel in the pixelated image; and calculating the standard deviation of the integrated energy for each source pixel, wherein the standard deviation is the power dispersed per pixel. As used herein, all PPD values, properties, and limits are calculated and evaluated using a test setup employing a display device having a pixel density of 140 pixels per inch (PPI). In embodiments, the display article 10 exhibits a PPD of 1.2%, 1.3%, 1.4%, 1.5%, 1.6%, 1.7%, 1.8%, 1.9%, 2.0%, 2.1%, or within any range bounded by any two of these values (e.g., 1.2% to 2.1%, etc.). In embodiments, textured region 20 exhibits a PPD of less than 4%, less than 3%, less than 2.5%, less than 2.1%, less than 2.0%, less than 1.75%, or even less than 1.5%.

[0096] The textured regions 20 of the present disclosure produce such low pixel power deviation, which means that the display 16 of the display article 10 can have a higher-than-normal resolution. As mentioned in the preceding paragraph, the pixel power deviation value was determined using an industry-standard display having a resolution of 140 pixels per inch ("ppi"). The textured regions 20 of the present disclosure can deliver this resolution with low pixel power deviation. As a result, the resolution of the display 16 can be increased. In embodiments, the display 16 of the display article 10 has a resolution greater than 140 ppi, such as a resolution in the range of 140 ppi to 300 ppi.

[0097] In an embodiment, the textured region 20 exhibits a distinctness of image ("DOI"). As used herein, "DOI" is equal to 100*(R S - R 0.3° ) / R S , where R S is the specular reflectance flux measured from incident light directed onto the textured region 20 (at 20° from the normal), and R 0.3 is the flux R of the same incident light at 0.3° according to the specular reflectivity SMeasured reflectivity flux. Unless otherwise noted, the DOI values and measurements reported in this disclosure are obtained according to ASTM D5767-18, entitled "Standard Test Method for Instrumental Measurement of Distinctness-of-Image (DOI) Gloss of Coated Surfaces using a Rhopoint IQ Gloss Haze & DOI Meter" [Rhopoint Instruments Ltd.]. Additionally, DOI measurements are made when the back surface of substrate 12 (the side opposite major surface 18) is coupled to an absorber to remove reflections from the back surface. Therefore, the DOI values herein are "coupled" or "first surface" values. In embodiments, the textured region 20 exhibits a distinctness of image ("DOI") of 25%, 30%, 35%, 40%, 45%, 50%, 55%, 60%, 65%, 70%, 75%, 80%, or 85%, or within any range defined by any two of these values (e.g., 25% to 85%, etc.). In embodiments, the textured region 20 exhibits a distinctness of image of less than 90%, less than 80%, less than 70%, less than 60%, less than 50%, less than 40%, less than 35%, or even less than 30%.

[0098] In an embodiment, the textured area 20 exhibits a transmission haze. As used herein, the term "transmission haze" refers to the percentage of transmitted light scattered outside an angular cone of approximately ± 2.5° according to ASTM D1003, entitled "Sandard Test Method for Haze and Luminous Transmittance of Transparent Plastics," the entire contents of which are incorporated herein by reference. In an example, transmission haze is measured using a BYK Gardner HAZE-GARD Plus instrument with incident light at normal incidence (zero degrees) and an integrating sphere detector system. Note that although the title of ASTM D1003 refers to plastics, the standard also applies to substrates comprising glass materials. For optically smooth surfaces, the transmission haze is typically close to zero. In embodiments, the textured region 20 exhibits a transmitted haze of 1.5%, 1.6%, 1.7%, 1.8%, 1.9%, 2.0%, 2.1%, 2.2%, 2.3%, 2.4%, or 2.5%, or within any range defined by any two of these values (e.g., 1.5% to 2.5%, etc.). In embodiments, the textured region 20 exhibits a transmitted haze of less than 20%, less than 10%, less than 5%, less than 3%, less than 2.5%, or even less than 2.0%.

[0099] In embodiments, the textured region 20 exhibits a specular reflectance of 0.5%, 0.6%, 0.7%, 0.8%, 0.9%, 1.0%, 1.1%, 1.2%, 1.3%, 1.4%, 1.5%, 1.6%, 1.7%, 1.75%, or within any range bounded by any two of these values (e.g., 0.5% to 1.75%, etc.). Specular reflectance is determined herein using a "Rhopoint IQ Gloss Haze & DOI Meter" (Rhopoint Instruments, Inc.) at a 20-degree reflective incident angle and with the back surface of the substrate 12 coupled to an absorber to remove back surface reflections. The values reported by this instrument are in gloss units (GU), normalized to a value of 100 GU for a black glass control sample having a known primary surface reflectance value of 4.91% and a refractive index of 1.567 at a 20-degree incident angle. Therefore, the specular reflectance values mentioned herein represent the conversion of the instrument-generated values into absolute first surface specular reflectance (percentage) by multiplying the instrument-generated values by 0.0491 according to the equation.

[0100] In embodiments, the textured region 20 exhibits a transmittance of 85%, 86%, 87%, 88%, 89%, 90%, 91%, 92%, 93%, 94%, or 95% over a wavelength range of light from about 400 nm to about 800 nm, or within any range bounded by any two of these values (e.g., 85% to 95%, 90% to 92%, etc.). As used herein, the term "transmittance" is defined as the percentage of incident light power that is transmitted through the substrate 12 and out of the textured region 20 over a given wavelength range. In an example, transmittance is measured using a BYK Gardner HAZE-GARD Plus instrument using incident light at normal incidence (0 degrees) and an integrating sphere detector system. The reported transmittance is the total transmittance for all output angles.

[0101] In an embodiment, the textured region 20 simultaneously exhibits: (i) a pixel power deviation in the range of 1.2% to 2.1%, (ii) a transmission haze in the range of 1.5% to 2.5%, (iii) a specular reflectance of 0.5% to 1.75%, and (iv) an image clarity of 25% to 85%.

[0102] Now refer to Figure 5 , a method 100 for forming a textured region 20 is described herein. At step 102, method 100 includes forming surface features 52 on major surface 18 of substrate 12 that protrude from or are disposed within surrounding portions according to a predetermined location of each surface feature 52. At step 104, method 100 further includes depositing a high refractive index material 36 on surface features 52 or surrounding portions 54 that provide one or more lower surfaces 32 located at a lower average elevation 34. Steps 102 and 104 will be discussed further below.

[0103] In an embodiment, at step 106, method 100 further includes utilizing a spacing distribution algorithm to determine the location of each surface feature 52. The result is the predetermined location of each surface feature 52 as mentioned above. This step 106 is performed prior to step 102 of forming the surface features 52 into substrate 12. Exemplary spacing distribution algorithms include Poisson disk sampling, maximum-minimum spacing, and hard sphere distribution. The spacing distribution algorithm places objects 108 (representing surface features 52, or from which the placement of surface features 52 can be derived) on an area 110 that matches the desired minimum center-to-center distance 60 of the surface features 52, based on the minimum center-to-center distance 112 separating each object 108.

[0104] Poisson disk sampling inserts a first object 108 (circular, with a diameter that matches the desired longest dimension 58 of the surface feature 52) into the region 48. The algorithm then inserts a second object 108 into the region 48, placing the center at a random point within the region 48. If the placement of the second object 108 satisfies the minimum center-to-center distance 112 from the first object 108, the second object 108 remains in the region 48. The algorithm then repeats this process until no more such objects 180 can be placed within the region 110 that satisfy the minimum center-to-center distance 112. The result is a randomly distributed, yet specific, placement of objects 108.

[0105] The maximum-minimum distance algorithm is so named because it attempts to maximize the minimum nearest-neighbor center-to-center distance 112 of a point distribution (i.e., where the objects in the region are points). Because the maximum-minimum distance algorithm iteratively moves each object 108 farther from any neighbor, it generally does not achieve a perfect hexagonal lattice. The algorithm produces a random distribution with a relatively high average hexagonal percentage, typically exceeding 90%.

[0106] The hard-sphere distribution algorithm is a molecular dynamics simulation performed at finite temperature. Specifically, it is the LAMMPS molecular dynamics simulator (https: / / www.lammps.org / , last accessed on June 26, 2021). The result is a random but specific placement of objects 108 in region 110, unlike a hexagonal lattice. However, the hexagonal percentage is also higher than that produced by the Poisson disk algorithm.

[0107] In any case, the position of object 108 in region 110 thus becomes the predetermined position of each surface feature 52 subsequently formed into substrate 12 , or the predetermined position of each surface feature 52 derived from the position of object 108 in region 110 .

[0108] In an embodiment, at step 114, method 100 further includes disposing an etch mask 116 on major surface 18 of substrate 12. Subsequent step 102 of forming surface features 52 includes contacting substrate 12 with an etchant 118 while etch mask 116 is disposed on major surface 18 of substrate 12.

[0109] In an embodiment, etch mask 116 is formed on substrate 12 as a superimposed positive or superimposed negative of region 110 where object 108 is placed by the spacing distribution algorithm. In other words, in an embodiment, etch mask 116 is formed to match the placement of object 108 on major surface 18 of substrate 12, in which case etch mask 116 prevents subsequent etching from forming locations where surface features 52 are to be formed according to the predetermined locations of surface features 52. In such cases, surface features 52 produced by etching step 102 protrude from surrounding portions 54. In other embodiments, such as Figure 4 1 , etch mask 116 is formed as a negative of object 108 placed over region 110, thereby preventing etching where surrounding portion 54 is to exist and only allowing etching where surface features 52 are to exist (i.e., where the object is to be placed in the region).

[0110] In an embodiment, the etchant 118 comprises one or more of hydrofluoric acid and nitric acid. In an embodiment, the etchant 118 comprises both hydrofluoric acid and nitric acid. The etchant 118 may be sprayed onto the substrate 12 while the etch mask 116 is positioned on the substrate 12. The substrate 12 with the etch mask 116 may be immersed in a container 120 containing the etchant 118. In an embodiment, the etchant 118 contacts the substrate 12 for a period of 10 seconds, 20 seconds, 30 seconds, 40 seconds, 50 seconds, or 60 seconds, or within any range defined by any two of these values (e.g., 10 seconds to 60 seconds, etc.). After the period of time has expired, the substrate 12 is rinsed in deionized water and dried. The longer the etchant 118 contacts the substrate 12, the deeper the etchant 118 etches into the substrate 12, and thus the greater the distance 42 between the one or more higher surfaces 26 of the substrate 12 located at the higher average elevation 28 and the one or more lower surfaces 32 of the substrate 12 located at the lower average elevation 34.

[0111] As mentioned, at step 104, method 100 includes depositing a high refractive index material 36 on the surface features 52 or surrounding portions 54. In an embodiment, after the surface features 52 are formed during step 102, the high refractive index material 36 is deposited while the etch mask 116 is still disposed on the substrate 12. Maintaining the etch mask 116 on the substrate 12 while depositing the high refractive index material 36 helps ensure that the high refractive index material 36 is deposited only where desired, such as only on one or more lower surfaces 32 of the substrate 12 located at lower average elevations 34, whether such lower surfaces 32 are provided by the surface features 52 or the surrounding portions 54, and not on one or more higher surfaces 26 located at higher average elevations 28. The high refractive index material 36 may be deposited using various deposition methods such as vacuum deposition techniques, chemical vapor deposition (e.g., plasma-enhanced chemical vapor deposition, low-pressure chemical vapor deposition, atmospheric pressure chemical vapor deposition, plasma-enhanced atmospheric pressure chemical vapor deposition), physical vapor deposition (e.g., reactive sputtering or non-reactive sputtering, or laser ablation), thermal evaporation or electron beam evaporation, and / or atomic layer deposition. In an embodiment, reactive sputtering is used to deposit the high refractive index material 36.

[0112] In one embodiment, at step 122, method 100 further includes removing etch mask 116 after high refractive index material 36 has been deposited at step 104. Depending on the composition of etch mask 116, an organic solvent such as acetone or isopropyl alcohol may remove etch mask 116 from substrate 12.

[0113] In a variation, a film of low refractive index material is deposited on major surface 18 of substrate 12 prior to step 114. Etch mask 116 is then disposed on substrate 12 over the low refractive index material. Surface features 52 are then formed at step 102 by contacting the low refractive index material with etchant 118 while etch mask 116 is disposed over the low refractive index material. The remainder of method 100 then proceeds as explained above. Example

[0114] Comparative Example 1A—For Example 1, an embodiment of the textured region of the present disclosure was modeled as a diffraction grating using the commercial software package Gsolver (Grating Solver Development, Inc., Saratoga Springs, UT). The substrate was modeled as having a surrounding portion that provided a surface at a higher average elevation, and linear channels (as surface features) were placed within the surrounding portion that provided a surface at a lower average elevation below the higher average elevation. The linear channels had a center-to-center spacing (grating period) of 20 μm. The model assumed that the ambient light had a single wavelength of 550 nm. The substrate was assumed to be glass with a refractive index of 1.518. A high refractive index material, specifically SiO, having a higher refractive index of 1.892 was placed. x N y Added to the surface of the linear channel at the lower average elevation to obtain a fill fraction of 50%. Therefore, the high refractive index material provides a surface that is entirely located at an intermediate average elevation, which is between the higher average elevation and the lower average elevation of the substrate. The air groove depth (the distance between the higher average elevation of the substrate and the intermediate average elevation of the high refractive index material deposited in the linear channel) is set to 220 nm. The groove depth (the distance between the higher average elevation and the lower average elevation of the substrate) is then varied from about 220 nm to over 700 nm, and the height of the high refractive index material deposited in the channel is adjusted accordingly to maintain a 220 nm air groove depth. The model then calculates the diffraction efficiency ( ) of light transmitted through the modeled textured area for the 0th to 5th diffraction orders based on the variation in groove depth (and therefore also based on the height of the high refractive index material added to maintain a 220 nm air groove depth). Figure 6A ) and the diffraction efficiency of light reflected from the modeled textured area ( Figure 6B ) Both. Figure 6A and Figure 6B The modeling results of transmitted light and reflected light are reproduced respectively.

[0115] Figure 6A Modeling results reproduced at indicate that to maximize transmission through the substrate away from the textured region, the substrate trench depth should be 520 nm (0.52 µm). Therefore, the SiO added to the linear channel x N y The height of the high refractive index material should be 300 nm to maintain a 220 nm air trench depth. Unfortunately, Figure 6B As shown by the modeling results reproduced at , a 520 nm trench depth in the substrate cannot completely reduce the specular reflectivity (order 0 is specular reflectivity).

[0116] Example 1B—Example 1B is a modeling example similar to Comparative Example 1A. However, Example 1B does not fix the air trench depth and vary the trench depth of the substrate as in Comparative Example 1A. Instead, Example 1B varies the air trench depth of the substrate with the SiO x N y The ratio of the height of the high refractive index material to the depth of the air trench is fixed at 3 / 1.6 / 1.4. The model determines the transmitted light ( Figure 7A ) and reflected light ( Figure 7B ) according to the change of the groove depth of the substrate. The model parameters of Example 1B are the same as those of Comparative Example 1A in other respects, including SiO x N y 50% fill fraction of high refractive index material.

[0117] Figure 7A The graph at shows that the 0th-order (specular, not diffractive) transmission through the substrate out of the textured area remains high regardless of the substrate's groove depth. Diffractive transmission (1st order and higher) is very close to zero. This is because the aforementioned ratio of 3 / 1.6 / 1.4 is close to the ideal ratio for a transparent diffuser. Figure 7B The graph at shows that the specular reflectivity (0th order) and the diffuse reflectivity (1st order and higher) vary significantly with the groove depth of the substrate. When the groove depth of the substrate is about 0.10 µm and 0.50 µm, the specular reflectivity reaches a peak, making these groove depths of the substrate not preferred. However, when the groove depth of the substrate is between 0.22 µm and 0.37 µm, the specular reflectivity is minimized. The 1st order diffraction reflectivity is also minimized at about 0.30 µm. Using the ratios mentioned above, when the groove depth of the substrate is between 0.22 µm and 0.37 µm, then SiO x N y The height of the high index material is 0.12 µm to 0.20 µm and the air trench depth is 0.10 µm to 0.20 µm. An exemplary target using this model is a trench depth of 0.32 µm for the substrate, 0.17 µm for the SiO disposed within the surface features, x N y The model further demonstrates that, with proper design, the textured regions disclosed herein can suppress specular reflectivity by a factor of 5 or even 10 or more compared to non-textured flat glass.

[0118] Now refer to Figure 7C and Figure 7D , the model then determines the SiO x N yThe diffraction efficiency of transmission varies with the filling fraction of high refractive index material (100% minus the filling fraction of low refractive index substrate). Figure 7C ) and the diffraction efficiency of reflection ( Figure 7D ) both. The model assumes that the trench depth of the substrate is 0.32 µm and the SiO x N y The height of the high-index material is 0.17 µm and the depth of the air trench is 0.15 µm. For this model, a center-to-center distance of 20 µm and a wavelength of 550 nm are still assumed. Figure 7C The graph shows that according to the model, for all considered filling fractions, the specular transmittance is high and the transmissive scattering is low. This is because the trench depth of the substrate, the SiO2 placed in the surface features x N y The height of the high refractive index material and the depth of the air trench have been optimized according to transparent diffuser standards. Figure 7D The graph shows that, according to the model, a filling fraction range of 52% to 62% base material (low refractive index) minimizes specular reflection (0th order). This corresponds to a SiO x N y Filling fraction range of high refractive index material. In some applications, the optimization design may not only target the suppression of specular reflection (0th order), but may seek to minimize the intensity of specular reflectivity while also minimizing the intensity of one or more higher reflective diffraction orders (1st order, 2nd order, etc.). In applications where it is necessary to minimize the intensity of all reflective diffraction orders, the filling fraction of the low refractive index substrate or low refractive index material may be as high as 75% or may be from about 55% to about 78%. This corresponds to 25% or from about 22% to about 45% of high refractive index material (e.g., SiO x N y )’s fill fraction.

[0119] Now refer to Figure 7E and Figure 7F , the model determines the reflectivity ( Figure 7E ) and transmittance ( Figure 7F ) varies according to the incident light angle to obtain the following optimal modeling parameters: SiO x N y 45% filling fraction of high refractive index material, 0.32 µm substrate trench depth, 0.17 µm SiO x N y High refractive index material height and 0.15 µm air trench depth. Figure 7E As shown in the graph of , such a textured area is modeled to produce a specular reflectivity (first surface) of less than 1% for all light incident angles from 0 degrees to about 40 degrees. Figure 7FAs shown in the graph of , such a textured area is modeled to transmit greater than 90% of the incident light for all light incident angles from 0 degrees to about 40 degrees.

[0120] Examples 2A to 2G - For Examples 2A to 2G, a hard sphere spacing distribution algorithm (LAMMPS) was used to determine the location of each surface feature to be placed on the major surface 18 of the substrate. The hard sphere spacing distribution algorithm targets filling a specified area so that the placed objects (circular objects) occupy 50% of the area. This translates into a high refractive index material deposited on the substrate having a target fill fraction of 50%. The circular objects have a diameter of 50 μm and a minimum center-to-center spacing of 60 μm. More specifically, using software, a gas of "molecules" representing the objects (and therefore the desired surface features) is initially placed on a two-dimensional hexagonal lattice to fix the fill fraction at 50%. The gas is then heated and randomized in two dimensions. The molecules are given a repulsive hard sphere potential to maintain a minimum center-to-center spacing of 60 μm. As Figure 2 The resulting objects within the region were placed as illustrated in the graph of The resulting objects had an average hexagonal percentage of 0.49, indicating a large deviation from a hexagonal lattice and thus a highly randomized yet specific placement. Figure 8 The reproduced graph is a histogram showing how the fill fraction of all objects placed in the region varies according to the actual center-to-center distance to the nearest neighbor.

[0121] An etch mask was then formed on seven samples of the glass substrate, with the placement of the object superimposed according to the hard sphere spacing distribution algorithm. The etch mask for each sample was configured to allow etching into the substrate at locations within the region where the hard sphere spacing distribution algorithm positioned the object, but to deny etching into the substrate outside of the location where the object was located. The substrates of all seven samples with the etch mask were then contacted with an etchant. Each sample was contacted with the etchant for a different period of time, thereby allowing the generation of surface features that provided different groove depths. The etchant formed surface features positioned within the surrounding portion, wherein the surface features were positioned throughout the textured region where the algorithm placed the object within the region. Two samples were then set aside as Examples 2F and 2G as comparative examples.

[0122] After etching, the etching mask remained on the substrate of the remaining samples of Examples 2A-2E. A high refractive index material, specifically AlN, having a higher refractive index (~2.1) than the substrate (~1.51) was deposited onto the surface of each of the surface features. The deposition time varied for some samples, resulting in different heights of the deposited high refractive index material. The etching mask was then removed from the substrate of each sample. Due to the manufacturing process steps and a small amount of shadowing during deposition, the fill fraction of the high refractive index material AlN ranged from 40% to 49%.

[0123] Various optical measurements were then performed on all samples representing Examples 2A to 2G. Specifically, pixel power deviation ("PPD"), transmittance ("Trans."), transmittance haze ("haze"), distinctness of image ("DOI"), and specular reflectance ("Spec. Ref.") were measured. The results for each sample, along with the height of the AlN high-refractive index material deposited within each surface feature and the air trench depth, are set forth in Table 1 below. The "air trench depth" figures for Examples 2F and 2G refer to the elevation difference between the substrate at the surface feature and the surrounding substrate, since Examples 2F and 2G are comparative examples and did not deposit the AlN high-refractive index material into the surface features. Figure 2 The optical profilometer scan reproduced at is Example 2C after depositing the AlN high refractive index material within the surface features.

[0124]

[0125] Analysis of the data presented in Table 1 shows that the incorporation of high refractive index materials into the surface features of Examples 2A to 2E results in a significant reduction in pixel power deviation compared to both Examples 2F and 2G, without adversely affecting other measured optical properties to a significant degree. Examples 2B and 2C particularly demonstrate a beneficial combination of measured optical properties—specifically, a pixel power deviation of less than 1.5, a transmittance greater than 92%, a transmission haze less than 2%, an image clarity less than 50%, and a specular reflectance less than 0.85%. These combinations of values are difficult or impossible to achieve using other methods, particularly in the case of surface features having a longest dimension of approximately 50 μm, which are easier to manufacture than surface features having a smaller longest dimension.

[0126] Examples 3A to 3D - For Examples 3A to 3D, the location of each surface feature to be placed on the major surface of the substrate was determined using a Poisson disk sampling interval distribution algorithm. The algorithm targets filling the specified area so that the placed objects (circles) occupy 36% of the area. This translates into a target fill fraction of 36% for the high refractive index material deposited within the surface features. The circles have a diameter of 50 μm and a minimum center-to-center spacing of 60 μm. The circles placed within the area by the algorithm have a hexagonal percentage of 0.41 H , this hexagonal percentage is low and is considered highly randomized. Figure 9 The graph reproduced at is a histogram showing how the fill fraction of all objects placed in the region varies according to the actual center-to-center distance to the nearest neighbor.

[0127] An etching mask was then formed on four samples of glass substrates, overlaying the placement of objects according to the hard sphere spacing distribution algorithm. The etching mask for each sample was configured to allow etching into the substrate at locations within the region where the hard sphere spacing distribution algorithm positioned the object, but to deny etching into the substrate outside of the region where the object was located. An etchant was then applied to the substrates of all four samples with the etching mask. The etchant formed surface features positioned within the surrounding portion, wherein the surface features were positioned throughout the textured region where the algorithm positioned the object. Two samples were then set aside as Examples 3C and 3D for comparative purposes.

[0128] After etching, the etch mask remained on the substrate for the remaining samples of Examples 3A and 3B. A high-refractive-index material, specifically AlN, with a higher refractive index (~2.1) than the substrate (~1.51) was deposited within each of the surface features by reactive sputtering. The etch mask was then removed from the substrate for each sample. Due to the manufacturing process steps and minor shadowing during deposition, the fill fraction of the AlN high-refractive-index material ranged from 30% to 35%.

[0129] Various optical measurements were then performed on all samples representing Examples 3A to 3D. Specifically, pixel power deviation ("PPD"), transmittance ("Trans."), transmittance haze ("haze"), distinctness of image ("DOI"), and specular reflectance ("Spec. Ref.") were measured. The results for each sample, along with the height of the AlN high-refractive index material deposited within each surface feature and the air trench depth, are set forth in Table 2 below. The "air trench depth" numbers for Examples 3C and 3D refer to the depth of the surface feature relative to the surrounding area (since no AlN was added).

[0130]

[0131] Analysis of the data set forth in Table 2 shows that the incorporation of high refractive index materials into the surface features of Examples 3A-3B resulted in a significant reduction in pixel power deviation compared to both Examples 3C and 3D, without significantly adversely affecting other measured optical properties. The image clarity values of less than 85% for Examples 3A and 3B indicate that specular reflections are suppressed.

Claims

1. A substrate for a display article, comprising: main surface; and a textured region on at least a portion of the major surface, the textured region comprising: one or more elevated surfaces at a higher average elevation parallel to a base plane disposed below the textured region and extending through the substrate; one or more lower surfaces located at a lower average elevation, the lower average elevation being parallel to the base plane, the lower average elevation being less than the upper average elevation; and a high refractive index material disposed on each of the one or more lower surfaces located at the lower average elevation, the high refractive index material forming one or more intermediate surfaces located at an intermediate average elevation, the intermediate average elevation being parallel to the base plane, the intermediate average elevation being greater than the lower average elevation and less than the upper average elevation, the high refractive index material comprising a refractive index greater than that of the substrate or low refractive index material providing the one or more upper surfaces, wherein the high refractive index material occupies 22% to 49% of an area of a plane that is (i) parallel to the base plane and (ii) extends through the high refractive index material, the area being defined by the textured region.

2. The substrate according to claim 1, wherein The refractive index of the substrate or low-refractive-index material is in the range of 1.4 to 1.6; The high refractive index material has a higher refractive index than the base material or the low refractive index material.

3. The substrate according to claim 1 or claim 2, wherein The refractive index of the substrate or low-refractive-index material is in the range of 1.4 to 1.6; and The refractive index of the high refractive index material is in the range of 1.6 to 2.

3.

4. The substrate according to claim 1 or claim 2, wherein The median average elevation of the high index material is less than the higher average elevation of the one or more higher surfaces by a distance of 100 nm to 190 nm.

5. The substrate according to claim 1 or claim 2, wherein The median average elevation of the high index material is less than the higher average elevation of the one or more higher surfaces by a distance of 130 nm to 180 nm.

6. The substrate according to claim 1 or claim 2, wherein the substrate comprises a glass substrate or a glass ceramic substrate.

7. The substrate according to claim 1 or claim 2, wherein The textured areas exhibited pixel power deviations in the range of 1.2%-2.1%.

8. The substrate according to claim 1 or claim 2, wherein The textured region exhibits a pixel power deviation of less than 1.5%.

9. The substrate according to claim 1 or claim 2, wherein The textured region exhibits a specular reflectivity in the range of 0.5%-1.75%.

10. The substrate according to claim 1 or claim 2, wherein The textured region exhibits a specular reflectance of less than 0.85%.

11. The substrate according to claim 1 or claim 2, wherein The textured area exhibits an image clarity of 25% to 85%.

12. The substrate according to claim 1 or claim 2, wherein The textured area exhibits an image clarity of less than 50%.

13. The substrate according to claim 1 or claim 2, wherein The textured region exhibits a transmission haze of less than 2.5%.

14. The substrate according to claim 1 or claim 2, wherein The textured region exhibits a transmittance greater than 92%.

15. The substrate according to claim 1 or claim 2, wherein The high refractive index material includes AlN x 、SiO x N y or SiN x .

16. The substrate according to claim 1 or claim 2, further comprising one or more lower surfaces located at a lower average elevation, the lower average elevation being parallel to the base plane, the lower average elevation being lower than the upper average elevation, wherein The middle average elevation is greater than the lower average elevation but less than the upper average elevation, and the middle average elevation of the high refractive index material is greater than the lower average elevation of the one or more lower surfaces by a distance of 100 nm to 200 nm.

17. The substrate according to claim 16, wherein The median average elevation of the high index material is greater than the lower average elevation of the one or more lower surfaces by a distance of 120 nm to 180 nm.

18. The substrate according to claim 16, wherein The lower average elevation of the one or more lower surfaces is less than the higher average elevation of the one or more higher surfaces by a distance of 220 nm to 370 nm.

19. A method of forming a textured region of a substrate for use in a display article, the method comprising: a surface feature protruding from or disposed within a surrounding portion located at a major surface of a substrate according to predetermined locations of each surface feature, thereby forming a textured region, wherein (i) one or more upper surfaces of the textured region are located at an upper average elevation, the upper average elevation being parallel to a base plane, the base plane being disposed below the textured region and extending through the substrate, (ii) one or more lower surfaces of the textured region are located at a lower average elevation, the lower average elevation being parallel to the base plane, the lower average elevation being less than the upper average elevation, (iii) the surface features provide either the one or more upper surfaces or the one or more lower surfaces, and (iv) the surrounding portion provides the other of the one or more upper surfaces or the one or more lower surfaces, whichever the surface features do not provide; and depositing a high refractive index material on any of the surface features or the surrounding portion providing the one or more lower surfaces at the lower average elevation to form one or more intermediate surfaces at an intermediate average elevation, the intermediate average elevation being parallel to the base plane, the intermediate average elevation being less than the upper average elevation and greater than the lower average elevation, the high refractive index material comprising a refractive index greater than a refractive index of a substrate or low refractive index material providing the one or more upper surfaces, in, The high refractive index material occupies 22% to 49% of an area of a plane that is (i) parallel to the base plane and (ii) extends through the high refractive index material, the area being defined by the textured region.

20. A substrate for a display article, the substrate comprising: main surface; and a textured region on at least a portion of the major surface, the textured region comprising: one or more elevated surfaces at a higher average elevation, the higher average elevation being parallel to a base plane disposed below the textured region and extending through the substrate; one or more lower surfaces located at a lower average elevation, the lower average elevation being parallel to the base plane, the lower average elevation being less than the upper average elevation; a surface feature that projects from or is disposed within a surrounding portion located at the major surface, wherein (i) the surface feature provides either: the one or more upper surfaces or the one or more lower surfaces, and (ii) the surrounding portion provides the other of the one or more upper surfaces or the one or more lower surfaces, whichever the surface feature does not provide; and a high refractive index material disposed on one or more lower surfaces located at a lower average elevation, the high refractive index material comprising a refractive index greater than the refractive index of a substrate or low refractive index material providing the one or more higher surfaces, and the high refractive index material forming one or more intermediate surfaces located at an intermediate average elevation, the intermediate average elevation being parallel to the base plane and being between the higher average elevation and the lower average elevation, The high refractive index material occupies 22% to 49% of an area of a plane that is (i) parallel to the base plane and (ii) extends through the high refractive index material, the area being defined by the textured region.

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