Articles having anti-glare surfaces with sloped transition surfaces and related methods

Abstract

Articles having scattering regions designed to exhibit anti-glare performance attributes are described herein. The scattering region includes a plurality of structures extending outwardly from a base surface of the first major surface. Each of the plurality of structures includes an inclined portion extending from the base plane and a peak portion disposed at a peak height of the structure. The inclined portions of the plurality of structures constitute 5% or more of the total surface area of the scattering region. An Abbott-Firestone curve characterizing the 1 * 1 mm2 portion of the scattering region includes an intermediate portion between the portions representing the base plane and the peak portion, wherein the intermediate portion has an average slope with an amplitude of less than 420% / [mu] m and greater than 5% / [mu] m.

Description

Cross - Reference to Related Applications

[0001] This application claims the benefit of priority to U.S. Provisional Application Serial No. 63 / 420,222, filed on October 28, 2022, and U.S. Provisional Application Serial No. 63 / 542,398, filed on October 4, 2023, under 35 U.S.C.§119. This application is based on the content of the provisional applications and the content of the provisional applications is incorporated herein by reference in its entirety. Technical Field

[0002] The present disclosure relates to articles having an anti - glare surface with an inclined transition surface and methods of manufacturing such articles. Background Art

[0003] Substrates that are transparent to visible light are used to cover the displays of display articles. Such display articles include smart phones, tablets, televisions, computer monitors, vehicle interior displays, etc. Displays are typically liquid crystal displays and organic light - emitting diodes, etc. The substrate protects the display, while the transparency of the substrate allows the user of the device to view the display. Glare is a phenomenon associated with a reduced viewing experience in the presence of bright light sources. In addition, reflected images from the environment rather than from bright light sources can also cause degraded viewing in the display. For example, the visually distinct reflection image of the user himself or light from the surrounding environment can cause distraction, reduced readability, and visual fatigue.

[0004] There are several techniques for reducing glare, including anti - reflection coatings and anti - glare techniques. Anti - reflection coatings can reduce glare by directly reducing the total amount of reflection. However, some existing anti - reflection coatings may not reduce reflection to a large enough extent across the entire visible spectrum such that the user does not notice such reflections. Anti - glare techniques attempt to spread the reflection of light over a wide range of angles to reduce the peak intensity of the reflection and make the distracting reflection image less noticeable to the user. However, reflections at too large an angle can result in a relatively high haze, which reduces the contrast of the displayed image.

[0005] Therefore, an alternative to existing anti - glare and anti - reflection coating techniques that allows for the advantageous control of the angular distribution of scattered light would be beneficial. Summary of the Invention

[0006] Aspects (1) of the present disclosure relate to an article including a substrate, the substrate including: a first major surface; a second major surface opposite the first major surface; and a scattering region formed in the first major surface, wherein within the scattering region, the first major surface includes: a plurality of structures extending outward from the base surface of the first major surface, each of the plurality of structures extending from the base surface to a peak height, wherein: each structure of the plurality of structures includes an inclined portion extending from the base surface and a peak portion provided at the peak height of the structure, and the inclined portions of the plurality of structures constitute more than 5% of the total surface area of the scattering region, and the Abbott-Firestone curve of the 1x1 mm 2 portion of the scattering region includes: (a) a first portion representing the region of the scattering region closest to the base surface, (b) a second portion representing the peak portions of the plurality of structures, and (c) an intermediate portion extending between the first portion and the second portion, and the intermediate portion includes an average slope with an amplitude less than 420% / μm and greater than 5% / μm.

[0007] Aspects (2) of the present disclosure relate to the article as described in aspect (1), wherein the inclined portion constitutes more than 50% of the total surface area of the scattering region.

[0008] Aspects (3) of the present disclosure relate to the article as described in aspect (1), wherein: at least some of the plurality of peak portions are etched depth portions disposed within 20 nm of the maximum peak height relative to the base surface, and the etched depth portions constitute 60% or less of the total surface area of the scattering region.

[0009] Aspects (4) of the present disclosure relate to the article as described in aspect (3), wherein the etched depth portions constitute 40% or less of the total surface area of the scattering region.

[0010] Aspects (5) of the present disclosure relate to the article as described in any one of aspects (1) to (4), wherein the plurality of structures include a maximum feature size greater than or equal to 1 μm and less than 200 μm.

[0011] Aspects (6) of the present disclosure relate to the article as described in any one of aspects (1) to (5), wherein at least some of the inclined portions extend a lateral distance greater than or equal to 1.0 μm and less than or equal to 10 μm between the base surface and the peak portion, and the lateral distance extended by the inclined portion is measured in a direction parallel to the surface normal of the inclined portion and parallel to the base surface.

[0012] Aspect (7) of the present disclosure relates to an article as described in aspect (6), wherein the lateral distance is greater than or equal to 3.0 μm.

[0013] Aspect (8) of the present disclosure relates to an article as described in any one of aspects (6) to (7), wherein: each of the inclined portions includes a first edge disposed near the base surface and a second edge disposed near the peak region, and the slope of the first main surface changes in the direction along a 1-μm lateral distance at both the first edge and the second edge.

[0014] Aspect (9) of the present disclosure relates to an article as described in any one of aspects (1) to (8), wherein the first portion and the second portion of the Abbott-Firestone curve are vertical portions having a slope with an amplitude greater than 350% / m.

[0015] Aspect (10) of the present disclosure relates to an article as described in aspect (9), wherein: some of the peak portions are disposed within 20 nm of the maximum peak height relative to the base surface, and those peak portions are represented in the second portion of the Abbott-Firestone curve, and the Abbott-Firestone curve includes a third vertical portion that represents peak portions at peak heights disposed between the base surface and the maximum peak height.

[0016] Aspect (11) of the present disclosure relates to an article as described in aspect (10), wherein the Abbott-Firestone curve further includes: a fourth vertical portion that represents additional peak portions at peak heights disposed between the base surface and the maximum peak height other than the height associated with the third vertical portion, wherein the intermediate portion is a first intermediate portion disposed between the first portion and the third vertical portion; a second intermediate portion disposed between the third vertical portion and the fourth vertical portion; and a third intermediate portion disposed between the fourth vertical portion and the second portion.

[0017] Aspect (12) of the present disclosure relates to an article as described in aspect (11), wherein each of the first intermediate portion, the second intermediate portion, and the third intermediate portion is: (a) a section of the Abbott-Firestone curve that represents a height of at least 50 nm having an average slope that is at least 50% / μm less than that of an adjacent vertical portion; or (b) an inflection point of the Abbott-Firestone curve.

[0018] Aspects (13) of the present disclosure relate to an article as described in any one of aspects (1) to (12), wherein the article exhibits: a transmission haze of less than or equal to 3.5%, and a sparkle of less than or equal to 2.5% when measured at 140 ppi.

[0019] Aspects (14) of the present disclosure relate to an article as described in any one of aspects (1) to (13), wherein the bidirectional reflectance distribution function (“BRDF”) of the article measured from white light incident on the first major surface at an incident angle of 10° exhibits an intensity of less than 1.2x10 -4 sr -1 at a scattering angle of 30° relative to the specular surface.

[0020] Aspects (15) of the present disclosure relate to an article as described in any one of aspects (1) to (14), wherein when the article is viewed at a 0° viewing angle and light having a brightness of 45000 lux is incident on the first major surface at an incident angle of 20°, a first average modulation transfer function of the article averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm is at least 0.7.

[0021] Aspects (16) of the present disclosure relate to an article as described in any one of aspects (1) to (15), wherein after a pad applies a 270 g force along a trajectory for 100 cycles to CS8 material acting on the scattering region, the scattering region exhibits a trajectory visibility of less than or equal to 40%.

[0022] Aspects (17) of the present disclosure relate to an article comprising: a substrate comprising: a first major surface; a second major surface opposite the first major surface; and a scattering region formed in the first major surface, wherein within the scattering region, the first major surface comprises: a plurality of structures extending outward from the base surface of the first major surface, each of the plurality of structures extending from the base surface to a peak height, wherein: (a) each of the plurality of structures comprises an inclined portion extending from the base surface and a peak portion disposed at the peak height of the structure such that the scattering region comprises a plurality of inclined portions and a plurality of peak portions, (b) at least some of the inclined portions extend a lateral distance greater than or equal to 1.0 μm and less than or equal to 10 μm between the base surface and the peak portion, (c) the lateral distance extended by the inclined portion is measured in a direction parallel to the surface normal of the inclined portion and parallel to the base surface, (d) the inclined portions of the plurality of structures constitute more than 5% of the total surface area of the scattering region, and (e) a 1x1 mm 2The Abbott-Firestone curve of the portion does not include any horizontal portion representing a height of at least 0.05 μm having a slope with an amplitude less than 40% / μm between the height of the base surface and the peak height of the scattering region.

[0023] An aspect (18) of the present disclosure relates to an article as described in aspect (17), wherein the inclined portion constitutes more than 5% of the total surface area of the scattering region.

[0024] An aspect (19) of the present disclosure relates to an article as described in any one of aspects (17) to (18), wherein: at least some of the plurality of peak portions are etching depth portions disposed within 20 nm of the maximum peak height with respect to the base surface, and the etching depth portions constitute 60% or less of the total surface area of the scattering region.

[0025] An aspect (20) of the present disclosure relates to an article as described in aspect (19), wherein the etching depth portion constitutes 40% or less of the total surface area of the scattering region.

[0026] An aspect (21) of the present disclosure relates to an article as described in any one of aspects (17) to (20), wherein the plurality of structures include a maximum feature size greater than or equal to 1 μm and less than 200 μm.

[0027] An aspect (22) of the present disclosure relates to an article as described in any one of aspects (17) to (21), wherein: the inclined portion of each structure includes a first edge disposed near the base surface and a second edge disposed near the peak region, wherein the slope of the first main surface changes in the direction along a 1-μm lateral distance at both the first edge and the second edge.

[0028] An aspect (23) of the present disclosure relates to an article as described in any one of aspects (17) to (22), wherein: the Abbot-Firestone curve includes: a first portion representing the region of the scattering region closest to the base surface, a second portion representing the peak portions of the plurality of structures, and an intermediate portion extending between the first portion and the second portion, the intermediate portion having an average slope less than 420% / μm and greater than 5% / μm, the first portion and the second portion of the Abbot-Firestone curve being vertical portions having a slope with an amplitude greater than 350% / μm, and some of the peak portions are disposed within 20 nm of the maximum peak height, and those peak portions are represented in the second portion of the Abbot-Firestone curve.

[0029] Aspects (24) of the present disclosure relate to an article as described in aspect (23), wherein the Abbott-Firestone curve includes a third vertical portion representing a peak portion at a height disposed between the base surface and the maximum peak height.

[0030] Aspects (25) of the present disclosure relate to an article as described in aspect (24), wherein the Abbott-Firestone curve further includes: a fourth vertical portion representing an additional peak portion at a peak height disposed between the base surface and the maximum peak height, other than the height associated with the third vertical portion, wherein the intermediate portion is a first intermediate portion disposed between the first portion and the third vertical portion; a second intermediate portion disposed between the third vertical portion and the fourth vertical portion; and a third intermediate portion disposed between the fourth vertical portion and the second portion.

[0031] Aspects (26) of the present disclosure relate to an article as described in aspect (25), wherein each of the first intermediate portion, the second intermediate portion, and the third intermediate portion is: (a) a section of the Abbott-Firestone curve representing a height of at least 50 nm having an average slope of at least 50% / μm less than an adjacent vertical portion; or (b) an inflection point of the Abbott-Firestone curve.

[0032] Aspects (27) of the present disclosure relate to an article as described in any one of aspects (17) to (26), wherein the article exhibits: a haze of less than or equal to 3.5%, and a gloss of less than or equal to 2.5% when measured at 140 ppi.

[0033] Aspects (28) of the present disclosure relate to an article as described in any one of aspects (17) to (27), wherein the bidirectional reflectance distribution function (“BRDF”) of the article measured from white light incident on the first major surface at an incident angle of 10° exhibits less than 1.2x10 -4 sr -1 intensity at a scattering angle of 30° with respect to the specular surface.

[0034] Aspects (29) of the present disclosure relate to an article as described in any one of aspects (17) to (28), wherein when the article is observed at a 0° viewing angle and light having a luminance of 45000 lux is incident on the first major surface at an incident angle of 20°, the first average modulation transfer function of the article averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm is at least 0.7.

[0035] Aspects (30) of the present disclosure relate to an article as described in any one of aspects (17) to (29), wherein after the pad applies a 270 g force along a track for 100 cycles to the CS8 material acting on the scattering region, the scattering region exhibits a track visibility of less than or equal to 40%.

[0036] Aspects (31) of the present disclosure relate to a method of forming a scattering region of a substrate for a display article, the method comprising: determining a pattern of a plurality of structures on a first major surface of the substrate, wherein each of the plurality of structures includes a surface region disposed at a height measured relative to a reference plane extending through the display article; disposing one or more etch masks on the first major surface, the one or more etch masks allowing etching only on selected regions of the first major surface to form at least some of the plurality of structures; and after each of the one or more etch masks is disposed on the first major surface, contacting the display article with an etchant for a period of time to form the plurality of structures in a main etching step, removing the one or more etch masks from the first major surface, and exposing the entirety of the scattering region to a secondary etchant such that the plurality of structures include inclined portions and the corners of the plurality of structures are rounded.

[0037] Aspects (32) of the present disclosure relate to the method as described in aspect (31), wherein exposing the entirety of the scattering region to the secondary etchant includes immersing the article in a second etch solution comprising a concentration ratio of HF and HCl of 0.5M HF / 0.5M HCl to 3M HF / 3M HCl such that the etching rate of the article is greater than 0.5 m / min.

[0038] Aspects (33) of the present disclosure relate to the method as described in aspect (31), wherein exposing the entirety of the scattering region to the secondary etchant includes spraying the article with a second etch solution comprising a concentration ratio of HF and HCl of 16 mM HF / 20 mM HCl to 160 mM HF / 200 mM HCl to achieve an etching rate of 0.1 m / min to 1 μm / min.

[0039] Aspects (33) of the present disclosure relate to the method according to any one of aspects (31) to (33), wherein the overall exposure of the scattering region to the secondary etchant performs a secondary etching cycle of less than or equal to 20 minutes, such that less than or equal to 20 μm of material is removed from the scattering region.

[0040] Aspects (35) of the present disclosure relate to the method according to any one of aspects (31) to (34), wherein after the main etching step, the plurality of structures include a plurality of regions of the first main surface disposed at different heights relative to the base surface, wherein the heights differ from each other by 20 nm to 200 nm in a direction perpendicular to the base surface.

[0041] Aspects (36) of the present disclosure relate to the method according to any one of aspects (31) to (35), wherein the overall exposure of the scattering region to the secondary etchant reduces the filling rate of the scattering region composed of the unetched portion of the article in the main etching step by at least 5%.

[0042] It should be understood that both the foregoing general description and the following detailed description are merely exemplary and are intended to provide an overview or framework for understanding the nature and characteristics of the claims. The accompanying drawings are included to provide further understanding and are incorporated into and constitute a part of this specification. The drawings illustrate one or more embodiments and, together with the description, are used to explain the principles and operations of the embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] The accompanying drawings, which are incorporated into and constitute a part of this specification, illustrate several aspects of the present invention and, together with the description, explain the principles of the present invention. In the drawings:

[0044] Figure 1 A perspective view of a display article according to one or more embodiments of the present disclosure is depicted.

[0045] Figure 2 Schematically depicts according to one or more embodiments of the present disclosure Figure 1 a portion of the scattering region of the display article;

[0046] Figure 3A Schematically depicts according to one or more embodiments of the present disclosure Figure 2 the height profile of the depicted scattering region;

[0047] Figure 3B Schematically depicts according to one or more embodiments of the present disclosure Figure 2 a cross-sectional view of the transition surface between two regions at different heights of the depicted scattering region;

[0048] Figure 4 is a flowchart of a method of manufacturing a display article including a scattering region having a structure with a sloped transition region, according to one or more embodiments of the present disclosure;

[0049] Figure 5A 、 Figure 5B and Figure 5C are 2D cross-sectional height profiles of structures of articles formed, according to one or more embodiments of the present disclosure, to not have feature rounding, to have feature rounding via mask undercut, and to have feature rounding via secondary etch;

[0050] Figure 6A are surface height profiles and surface height histograms associated with Example 5, according to one or more embodiments of the present disclosure;

[0051] Figure 6B are surface height profiles and surface height histograms associated with Example 1, according to one or more embodiments of the present disclosure;

[0052] Figure 7 is a graph showing Abbott-Firestone (“AF”) curves generated from 1x1 mm 2 portions of scattering regions from Example 1 to Example 5, according to one or more embodiments of the present disclosure;

[0053] Figure 8 schematically depicts an apparatus for measuring the washout performance of an article, according to one or more embodiments of the present disclosure;

[0054] Figure 9 schematically depicts an interior of a vehicle including a display and an ambient light source that emits light, the light being incident on and scattered from the display, according to one or more embodiments of the present disclosure;

[0055] Figure 10 is a graph of washout performance metrics as a function of the water contact angle of the substrate in Examples 1 to 5, according to one or more embodiments of the present disclosure;

[0056] Figure 11A 、 Figure 11B and Figure 11C are graphs showing a comparison of the AF curves of Examples 6 to 11 with a control formed to have the same pattern without feature rounding, according to one or more embodiments of the present disclosure;

[0057] Figure 12A 、 Figure 12B and Figure 12Cis a scanning electron microscope image of a surface structure associated with Examples 9, 10, and 11 according to one or more embodiments of the present disclosure;;

[0058] Figure 13A , Figure 13B , Figure 13C and Figure 13D are surface height profiles and histograms representing portions of samples associated with Examples 12 - 14 and a comparable control sample without feature rounding according to one or more embodiments of the present disclosure;

[0059] Figure 14 is a graph showing the AF curves for Examples 12 - 14 and the AF curve for the control sample in Figure 13A according to one or more embodiments of the present disclosure;

[0060] Figure 15 is a graph of the bidirectional reflectance distribution function ("BRDF") amplitude as a function of scattering angle in Examples 12 - 14 and the control sample according to one or more embodiments of the present disclosure;

[0061] Figure 16A , Figure 16B , Figure 16C and Figure 16D are surface height profiles and histograms representing portions of samples associated with Examples 15 - 17 and a comparable control sample without feature rounding according to one or more embodiments of the present disclosure;

[0062] Figure 17 is a graph showing the AF curves for Examples 15 - 17 and the AF curve for the control sample in Figure 16A according to one or more embodiments of the present disclosure;

[0063] Figure 18 is a graph of the bidirectional reflectance distribution function ("BRDF") amplitude as a function of scattering angle in Examples 15 - 17 and the control sample according to one or more embodiments of the present disclosure;

[0064] Figure 19 is a surface height profile and histogram associated with another control sample without feature rounding for testing wear performance according to one or more embodiments of the present disclosure;

[0065] Figure 20 is a surface height profile and histogram associated with Example 23 according to one or more embodiments of the present disclosure;

[0066] Figure 21A and Figure 21B is after undergoing a wear test according to one or more embodiments of the present disclosureFigure 19 and Figure 20 an image of the sample represented in; and

[0067] Figure 22 is a histogram of the track visibility values calculated from the images of the samples depicted in Figure 21A and Figure 21B after a wear test according to one or more embodiments of the present disclosure. DETAILED DESCRIPTION

[0068] With general reference to the drawings, articles are described herein that include a surface having a scattering region that includes a plurality of structures. The structures extend outward from the base surface in a direction perpendicular to the base surface to a peak height. As a result of performing the manufacturing methods herein, each of the plurality of structures includes an inclined portion extending from the base surface and a peak portion disposed at the peak height relative to the base surface. The scattering region is manufactured according to the methods described herein such that the inclined portions of the plurality of structures combine to constitute at least 5% (projected into a plane extending parallel to the base surface) of the total surface area of the scattering region. The applicant has found that, relative to a scattering region in which the inclined portion is a smaller portion of the total surface area, such a large portion of the inclined portion constituting the total surface area of the scattering region advantageously provides a lower scattering amplitude at relatively high scattering angles (e.g., greater than or equal to 20° or greater than or equal to 30° relative to the specular surface). The methods described herein also enable the plurality of structures to be designed to provide a favorable combination of anti-glare ("AG") performance attributes. For example, the scattering regions described herein can be designed in the spatial frequency domain based on a target radial power spectral density ("PSD") of the article and converting the target radial PSD into a phase profile (or "phase map") for forming the plurality of structures via the etching methods described herein. The target radial PSD can be selected to achieve low washout (due to the inclined portions described herein) without compromising other favorable AG performance attributes. For example, the articles described herein can achieve a transmission haze of less than 3.5% (or even less than or equal to 3.0%, less than or equal to 2.5%, less than or equal to 2.0%, less than 1.5% or less than 1.25%), a coupled specular reflectance (Rs) of less than 15, and a flash (as measured at 140 ppi) of less than 2.5%, while exhibiting low washout (as described in more detail herein).

[0069] The multiple structures of the scattering regions described herein can be formed via a multi-step etching process. An initial etching step (the “primary etching step” described herein) is performed using one or more patterned masks (e.g., formed using photolithography or any other suitable process described herein). For example, the patterned mask can cover an area of the first major surface of the article in an arrangement based on a phase mask generated using a target radial PSD. The masked article can then be exposed to a first etchant solution such that the uncovered regions of the first major surface are etched to a target etch depth, and after the initial etching step, the first major surface includes a plurality of first regions disposed at a first average height relative to a base plane disposed at the etch depth and a plurality of second regions disposed at the base plane, wherein a transition surface extends between the first and second regions. The first regions can represent the unetched portions of the first major surface, and the second regions can represent the etched portions of the first major surface. After completion of the initial etching step, the multiple structures can be formed via a finishing secondary etching step. The secondary etching step can be performed using an immersion or spray etching process and involves exposing the entire scattering region to a second etchant solution that etches the material of the article at an etch rate of at least 0.1 μm / min for a period of at least 1 minute. It has been found that the secondary etching step rounds the sharp corners that exist after the initial etching step and converts the transition surface into the sloped portions of the multiple structures. The secondary etching step generally reduces the fill factor associated with portions of the first major surface disposed at the initial etch depth relative to the base plane and increases the percentage of the surface area occupied by the sloped portions to provide the reduced scour benefits described herein.

[0070] While alternative techniques exist for producing the sloped portions described herein, such as reducing the adhesion between the mask and the article during the initial etching step, as described herein, it has been determined that the multiple etching fabrication techniques described herein beneficially provide sloped portions with a more uniform shape. The multiple etching fabrication techniques are more predictable and repeatable than existing methods. This results in more consistent optical properties that can be more specifically tailored for various applications. A further benefit of the multi-step etching process described herein is that after the initial etching step, the secondary etching step tends to round the corners at both the top and bottom of the transition surface of the article. Adhesion control techniques are not thought to round the bottom corners, and thus articles formed using such techniques tend to have sharper bottom corners, which are thought to be associated with poorer scour performance.

[0071] As will be further understood upon consideration of the remainder of the description, the multiple structures described herein can have a variety of different forms and shapes. While the multiple structures described herein can generally be characterized as protrusions extending outwardly from the body of the article away from the base plane, the exact shape of the structures can vary. For example, in an embodiment, at least some peak portions of the structures disposed at the peak height can include a dimension greater than or equal to 1 μm2 The surface area such that the peak portions are planar-shaped regions of the first major surface. Alternatively or additionally, at least some of the peak portions include a smaller surface area (e.g., less than 0.25 μm 2 ), such that at least some of the plurality of structures do not include any planar portion disposed at a constant height relative to the base surface. Regardless of the exact shape of the structures described herein, the presence of the inclined portions has been determined to be associated with improved flushing performance. In an embodiment, the inclined portion can include a slope (in terms of the height change relative to the base surface) that is less than or equal to 1.0 (e.g., greater than or equal to 0.01 and less than or equal to 0.3) to provide the optical performance benefits described herein.

[0072] The surface profile of the scattering regions described herein can be characterized by generating an Abbott-Firestone (“AF”) curve for a randomly selected 1x1 mm 2 area of the scattering region. The AF curve can be generated by measuring the surface height profile of the scattering region using white light interferometry providing a lateral measurement resolution of less than or equal to 500 nm (e.g., 360 nm). Unless otherwise specified herein, the AF curves included herein are generated using a per-pixel detector with a lateral resolution of 360 nm and a 50x objective with a numerical aperture of 500 nm. Then, the surface height profile can be used to generate a histogram of the surface height at each pixel in the dataset. The histogram can then be integrated to generate the AF curve. The AF curve of the scattering region according to the present disclosure includes a first portion representing a region of the scattering region disposed closest to the base surface, a second portion representing the peak portions of the plurality of structures, and an intermediate portion extending between the first portion and the second portion. The first and second portions of the AF curve can vary. In an embodiment, the AF curve can be characterized as including first and second vertical portions having a relatively high slope (e.g., greater than or equal to 350% / μm, including an undefined slope). The intermediate portion can include a slope that is less than the first and second portions and greater than or equal to 5% / μm. The lengths of the vertical and intermediate portions can vary depending on the etch depth in the primary etch step and the material removal extent in the secondary etch step described herein. Additionally, the number of vertical and intermediate portions can vary depending on the number of sub-etch steps performed in the primary etch step (e.g., two sub-etch steps can be performed such that the first major surface includes features disposed primarily at four heights based on the etch depth used in each sub-etch step, such that the AF curve includes four vertical portions and three intermediate portions). Characterizing the inclined portion via the AF curve provides a representation of the percentage of the surface area occupied by various surface heights. The intermediate portion having a slope within the range described herein indicates the level of feature rounding to provide the improved flushing performance described herein.

[0073] Advantageous aspects of the beveled portion described herein are that the article can exhibit improved wear performance. It is believed that when the scattering region is worn by particulate debris, sharp features such as corners may break off, which can result in visible damage. The scattering regions of the present disclosure lack such sharp features, and the beveled portion allows for the dispersion of forces when abrasive particles (e.g., dirt, dust, other debris) are pressed against the first major surface, thereby reducing the likelihood of visible damage. This improved wear performance is particularly beneficial when the article is subjected to repeated contact from a user (e.g., when the article is used as a protective cover for a touch screen). Indeed, as described herein, when articles according to the present disclosure are subjected to the CS8 wear test, they exhibit less visible track damage than comparable articles without the rounded features. This demonstrates that the articles described herein exhibit improved durability for touch applications.

[0074] The context of the articles described herein may be particularly useful in the context of in-vehicle displays. The vehicle interior may include one or more displays (e.g., a central counsel display, an instrument panel display, a pillar display, a seatback display, and other displays). Such displays may be fixed in an orientation relative to the driver. When in operation, the vehicle is subjected to ambient light conditions that can cause relatively severe glare. For example, sunlight can enter the vehicle interior through side windows or the windshield and reflect or scatter from the display, resulting in bright glare that can distract the driver and degrade the performance of the display due to washout. The articles described herein can reduce such washout from the ambient light conditions typically encountered. This advantageous washout performance can be achieved while also providing advantageous specular and haze performance.

[0075] As used herein, the term "target radial PSD" refers to the target radial PSD of the scattering region mathematically calculated from the desired far-field scattering pattern of the surface.

[0076] As used herein, "specular reflectance (Rs)" or "Rs" is defined as the peak intensity of light reflected from the first surface of the substrate within a cone at an angle of + / - 0.1°. Unless otherwise specified herein, the specular reflectance uses a RhopointIQ glossmeter that reports Rs values in gloss units.

[0077] The articles described herein can be characterized by a distinctness-of-image value. The term "reflected image distinctness", "image distinctness", "DOI", or similar terms are defined by Method A of ASTM procedure D5767 (ASTM 5767), entitled "Standard Test Methods for Instrumental Measurements of Distinctness-of-Image Gloss of Coating Surfaces". According to Method A of ASTM 5767, glass reflectance factor measurements are made on at least one roughened surface of a glass article at the specular viewing angle and at angles slightly off the specular viewing angle (0.2° to 0.4° away from the specular viewing angle). Such measurements can be made using a goniophotometer (Rhopoint IQ (goniophotometer) 20° / 60° / 85°, Rhopoint Instruments) calibrated to a certified black glass standard as specified in ASTM procedures D523 and D5767.

[0078] As used herein, the term "haze" or "transmission haze" refers to the percentage of transmitted light scattered outside a cone of approximately ±2.5° according to ASTM D1003, entitled "Standard Test Method for Haze and Luminous Transmittance of Transparent Plastics", the contents of which are incorporated herein by reference in their entirety. Note that although the title of ASTM D1003 refers to plastics, the standard is equally applicable to substrates including glass materials. For optically smooth surfaces, the transmission haze is typically close to zero.

[0079] As used herein, the terms "sparkle", "sparkle contrast", "display sparkle", "pixel power deviation", "PPD", or similar terms refer to a visual phenomenon that occurs when a textured transparent surface is combined with a pixelated display. Generally, the quantification of sparkle involves imaging a luminous or analog display with a textured surface in the field of view. The sparkle calculation for region P is equal to σ(P) / μ(P), where σ(P) is the standard deviation of the integrated intensity distribution of each display pixel contained within region P divided by the average intensity μ(P). The following guidelines are followed: (1) J. Gollier et al., "Apparatus and method for determining sparkle", US9411180B2, July 20, 2016; (2) A. Stillwell et al., "Perception of Sparkle in Anti-Glare Display Screens", JSID 22(2), 129-136 (2014); and (3) C. Cecala et al., "Fourier Optics Modeling of Display Sparkle from Anti-Glare Cover Glass: Comparison to Experimental Data", The Optical Society of America Imaging and Applied Optics Congress, JW5B.8 (2020); those skilled in the art can construct an imaging system to quantify sparkle. Alternatively, commercially available systems (e.g., SMS-1000, Display Messtechnik & Systeme GmbH & Co. KG, Germany) can also be used. Unless otherwise stated, the following procedure is used to measure sparkle with a 140PPI display. Image a 140PPI display (e.g., Z50, Lenovo Group Limited, Hong Kong, China) that has only the green sub-pixels lit (R = 0, B = 0, G = 255) at full display brightness using an f = 50mm lens / machine vision camera combination (e.g., C220503 1:2.8 50mm Φ30.5, Tamron, Japan and Stingray F-125B, Allied Vision Technologies GmbH, Germany). The lens is set to aperture = 5.6, depth of field = 0.3, working distance = approximately 290 mm; with these settings, the ratio of display pixels to camera pixels is approximately 1 to 9. The field of view for analysis includes approximately 7500 display pixels. The camera settings have gain and gamma correction turned off.During the analysis prior to calculating the flash, periodic intensity variations such as from a display and aperiodic intensity variations such as dead pixels are removed.

[0080] The antiglare performance can be measured without any surface coupled to the glass (described herein as "uncoupled") or a black absorber coupled to the back surface of the glass (described herein as "coupled").

[0081] Now referring to Figure 1 , an article 10 according to an example embodiment is depicted. The article 10 includes a substrate 12. In the depicted embodiment, the article 10 is a display article (e.g., a display cover article) and further includes a housing 14 coupled to the substrate 12 and a display 16 within the housing 14. In such embodiments, the substrate 12 at least partially covers the display 16 such that light emitted by the display 16 can transmit through the substrate 12.

[0082] Depending on the implementation, the substrate 12 can be a variety of materials. For example, in an embodiment, such as in the embodiment depicted in Figure 1 , the substrate 12 is a glass or glass-ceramic substrate. Various characteristics and examples of such glass or glass-ceramic substrates are described in more detail herein. In an embodiment, the substrate 12 can be composed of a material other than glass (such as paper, plastic, or other suitable polymeric materials). In an embodiment, the substrate 12 can include a combination of glass and polymeric materials. In an example, the scattering region 20 described herein is formed in a polymeric material layer formed on a glass substrate. In an embodiment, the substrate 12 is transparent or exhibits an average transmittance of greater than or equal to 70% (e.g., greater than or equal to 80%, greater than or equal to 85%, greater than or equal to 90%, greater than or equal to 92%, greater than or equal to 92.5%, greater than or equal to 93%) for light normally incident on the substrate 12 in the wavelength range of 400 nm to 700 nm. In an embodiment, the substrate 12 is opaque or exhibits an average transmittance of less than or equal to 30% for light normally incident on the substrate in the wavelength range of 400 nm to 700 nm. In an embodiment, the substrate 12 is colored to exhibit a colored appearance under ambient lighting (e.g., from sunlight).

[0083] The substrate 12 includes a first major surface 18, a second major surface 19, a scattering region 20 defined on the first major surface 18, and a thickness 21 partially defined by the first major surface 18 (e.g., representing the minimum distance between the first major surface 18 and the second major surface 19 at a particular point on the first major surface 18). In the depicted embodiment, the substrate 12 is substantially planar in shape such that the first major surface 18 and the second major surface 19 are generally flat (except for the plurality of surface features formed in the first major surface 18 in the scattering region 20, as described herein). Embodiments in which the substrate 12 includes a curved shape (e.g., via suitable thermoforming and cold forming techniques) are also contemplated and within the scope of the present disclosure. In such embodiments, the reference herein to a "surface normal" (depicted as surface normal 33 in Figure 1 ), refers to the local surface normal at the point where light from the external environment 24 is incident on the first major surface 18. In the depicted embodiment, the first major surface 18 generally faces the external environment 24 surrounding the article 10 and is remote from the display 16. In an embodiment, the display 16 emits visible light that transmits through the thickness 21 of the substrate 12, exits the first major surface 18, and enters the external environment 24.

[0084] As Figure 1 depicted, light from the external environment 24 represented by the incident light ray 22 can be incident on the first major surface 18 at an incident angle θ i (representing the zenith angle at which the incident light ray 22 extends relative to the surface normal 33 of the first major surface 18, depicted as the z - direction in Figure 1 ). The incident light ray 22 can represent light from a plurality of different sources external to the article 10. For example, the incident light ray 22 can represent sunlight incident on the first major surface 18 or light from another external light source (e.g., light reflected or scattered from an external object, light generated by another source). The scattering region 20 scatters the light represented by the incident light ray 22 in a scattering direction represented by the scattered light ray 25. The light is scattered in a particular direction, the scattering amplitude of which depends on the incident angle θi and the scattering angle θi relative to the surface normal 33. As shown, the scattered light ray 25 is scattered in a scattering direction that extends at an azimuthal angle Φ relative to a first direction ( Figure 1 depicted as the x - direction) when projected onto a plane perpendicular to the first major surface 18 extending along the surface normal 33.

[0085] In an embodiment, the scattering region 20 is designed based on a target radial PSD. The target radial PSD can be azimuthally averaged with respect to the azimuthal angle Φ such that the PSD is statistically isotropic with respect to the azimuthal angle. Irrespective of the azimuthal angle Φ, the target radial PSD varies with the zenith angle θ according to the same functional relationship sand vary. Such a target radial PSD advantageously minimizes the effect of the rotational orientation of the article 10 in the external environment 24 on the AG performance.

[0086] Figure 2 A plan view of region II of the scattering region 20 of the article 10 depicted schematically in accordance with an example embodiment of the present disclosure is shown. As shown, the scattering region 20 includes a plurality of structures 26. The plurality of structures 26 generally vary in size and peripheral shape and include longitudinal axes extending in a plurality of different directions in a plane parallel to the base plane 30 (see Figure 3A ). However, the randomness in the structure of the plurality of structures 26 is different from the randomness in some existing AG surfaces (e.g., produced by sandblasting) because the arrangement of the plurality of structures 26 is reproducible (within manufacturing tolerances) via the methods described herein.

[0087] Figure 3A Figure 2 In an embodiment, the plurality of structures 26 are designed based on a target radial PSD in the Fourier domain, as described herein. In an embodiment, the plurality of structures 26 include features that project outwardly from a base plane defined by a portion of the first major surface 18. For example, is depicted

[0088] A cross-sectional view of the scattering region 20 depicted in is shown. As shown, the article 10 includes a base plane 30, which represents the portion of the first major surface 18 that is closest to the second major surface 19. The base plane 30 generally represents the portion of the first major surface 18 that contacts one or more of the first etchant solutions in the main etching steps described herein. That is, the base plane 30 represents the region where most of the material of the substrate 20 is removed during the main etching step. For example, the main etching step may include only one sub-etching step, and in such embodiments, the base plane 30 may represent the region of the first major surface 18 that is not covered by an etch mask during the main etching step.In an embodiment, the main etch step can be controlled such that a plurality of first portions 32 of the first major surface 18 are substantially planar and disposed within the base plane 30 (or within a tolerance of less than 1% of the etch depth from the base plane 30 described herein). For example, in an embodiment, in terms of root mean square (RMS) variation, within a particular first portion of the plurality of first portions 32, the surface height variation (or roughness) can be less than 50 nm (or less than 20 nm RMS, or less than 10 nm RMS). For example, in these embodiments, each of the plurality of first portions 32 of the first major surface 18 can be characterized by a surface height variation ranging from 0.1 nm RMS to 50 nm RMS, from 0.1 nm RMS to 20 nm RMS, from 0.1 nm RMS to 10 nm RMS, or from 0.1 nm RMS to 1 nm RMS. In some embodiments, the peak portions 42 can exhibit similar surface roughness characteristics (e.g., when not fully rounded).

[0089] As Figure 3A shown, the plurality of structures 26 generally include protrusions, wherein the first major surface 18 extends outwardly from the base plane 30 away from the second major surface 19. Each of the plurality of structures 26 can be of a different shape (e.g., including different peripheral shapes) and / or include a different number of sub-structures. In Figure 3A the example shown, the first structure 26a includes a strut protruding from the base plane 30 and does not include an intermediate sub-structure. In contrast to the first structure 26a, the second structure 26b includes a sub-structure, wherein the curvature or surface shape of the first major surface 18 suddenly changes in a region other than at the outer boundary of the structure or at the peak portions, as described herein. In the depicted example, the second structure 26b includes a first sub-structure 36 and a second sub-structure 38, the first sub-structure 36 and the second sub-structure 38 being portions of the first major surface 18 that are substantially flat and disposed at different heights h 2 and h 3 from the base plane 30. Such sub-structures can be produced by a plurality of sub-etch steps in the main etch step described herein.

[0090] In an embodiment, the first major surface 18 includes a plurality of different regions disposed at different heights relative to the base surface 30. The surface height profile of the scattering region 20 can form a multi-modal height distribution relative to the base surface 30, where, in some cases, the number of modes is determined based on the number of sub-etching steps performed during the primary etching step described herein or the degree of material removal during the secondary etching step. Each mode of the multi-modal height distribution can be characterized by a different peak in a histogram of surface height frequencies generated from the surface height profile obtained by white light interferometry. In an example where the primary etching step includes only a single sub-etching step, the surface height profile of the scattering region 20 can form a bimodal height distribution, where the histogram includes two different peaks: one associated with a plurality of first portions 32 disposed in the base surface 30, and one associated with a plurality of second portions 34 disposed at a first height h 1 above the base surface 30. The plurality of second portions 34 can represent portions of the first major surface 18 that are not etched during the primary etching step described herein. As a result, h 1 can correspond to the etching depth selected for the primary etching step. In an example where the primary etching step includes a plurality of sub-etching steps, the surface height profile of the scattering region 20 can form a multi-modal height distribution having at least 3 modes or at least 3 different peaks in the histogram (the secondary etching step described herein can render the plurality of intermediate peaks indistinguishable from one another). In such embodiments having a plurality of sub-etching steps, h 1 can represent the sum of the etching depths associated with each individual sub-etching step of the primary etching step described herein. 1

[0091] Each of the plurality of structures 26 (or sub-structures thereof) includes an inclined portion 40 and a peak portion 42 disposed at the peak height associated with the structure (or sub-structure). In the inclined portion 40, the surface height of the first major surface 18 increases as the lateral distance from the nearest one of the plurality of first portions 32 increases. The average slope of the first major surface 18 within the inclined portion 40 can be greater than the average slope within the plurality of first portions 32. Within the inclined portion 40, the first major surface can have a slope ranging from 0.01 to less than or equal to 0.1 as a function of the lateral position in a direction perpendicular to the surface normal of the inclined portion 40. In an embodiment, for example, the inclined portion 40 includes a region of the first major surface 18 where the surface height is greater than or equal to 10 nm and less than 100 nm per 1 μm linear distance measured in a direction extending perpendicular to the inclined portion 40, where the linear distance is measured in a plane parallel to the base surface 30. Due to the inclined portion 40 having such a slope, sharp features (e.g., corners) of the first major surface 18 are eliminated, which helps to reduce the scattering amplitude at relatively high scattering angles. ​

[0092] The peak portions associated with each of the plurality of structures 26 (and associated sub-structures) can vary in shape. In the depicted embodiment, for example, the peak portion 42 is a substantially flat portion disposed at a height h relative to the base surface 30 1 . In alternative embodiments, at least some (if not all) of the plurality of structures 26 do not include any planar portions (due to the secondary etching process described herein, the tops of the structures can be fully rounded), and thus, the peak portion 42 can include a single point on a sub-structure disposed at the peak height. Additionally, the peak heights of adjacent structures in the plurality of structures 26 need not be the same as each other. For example, as Figure 3A shown, the second structure 26b includes a first peak region 42a disposed at a height h relative to the base surface 30 3 , a second peak region 42b disposed at a height h relative to the base surface 30 1 , and a third peak region 42c disposed at a height h relative to the base surface 30 3 . The arrangement of the surface heights of the peak portion 42 is generally determined by a pattern associated with one or more etching masks used in the main etching step described herein.

[0093] It has been found that when the inclined portions 40 of the plurality of structures 26 account for at least 5% (or even at least 10%, or even at least 15%, or even at least 20%, or even at least 30%, or even at least 40%, or even at least 50%) of the total surface area of the scattering region 20 (projected into the base surface 30), the excellent flushing and mechanical wear properties described herein can be provided. That is, when observing the scattering region 20 facing the first main surface 18 in a direction perpendicular to the base surface 30, the inclined portions 40 account for at least 5% of the total surface area of the scattering region 20. The uniformity of the inclined portions described herein provided by the multi-step etching process described herein (e.g., in terms of slope and transition width) can contribute to achieving this area ratio and can ensure a uniform flushing reduction, regardless of the specific location within the scattering region 20.

[0094] The inclined portions 40 can also be characterized by a lateral transition width w, over which the first main surface 18 transitions between modes in the multi-peak height distribution associated with the surface height profile of the scattering region 20. Referring to Figure 3B , in an embodiment, each of the inclined portions 40 includes a first edge 43 disposed near the peak portion 42 and a second edge 44 disposed adjacent to a feature (e.g., one of the plurality of first portions 32) at the lower surface height. As Figure 3B shown, the inclined portion 40 can include a width w. The width w is measured as the distance between the first edge 43 and the second edge 44 in a direction parallel to the base surface 30( Figures 1 to 2The lateral distance in the plane (the x-y plane depicted). The lateral distance is also measured in a direction extending parallel to the projection of the surface normal 46 of the inclined portion 40 into the x-y plane. In an embodiment, the width w is greater than or equal to 1.0 μm and less than or equal to 10.0 μm (e.g., e.g., greater than or equal to 1.0 μm and less than or equal to 9.0 μm, greater than or equal to 1.0 μm and less than or equal to 8.0 μm, greater than or equal to 1.0 μm and less than or equal to 7.0 μm, greater than or equal to 1.0 μm and less than or equal to 6.0 μm, greater than or equal to 1.5 μm and less than or equal to 6.0 μm, greater than or equal to 2.0 μm and less than or equal to 6.0 μm, greater than or equal to 3.0 μm and less than or equal to 10 μm). A width within such ranges indicates a lack of sharpness in the transition of the slope of the first major surface 18. The first major surface 18 transitions gradually between the slopes (e.g., as in a fillet), rather than in a relatively sharp corner at the first edge 43 and the second edge 44. As described in more detail herein, such feature rounding helps reduce the high spatial frequency content in the radial PSD of the scattering region 20, thereby providing favorable flushing performance. Unless otherwise stated, the width w is the maximum measured value of the lateral distance on a particular transition surface.

[0095] The width w can be measured using a variety of different techniques. For example, the width w can be physically measured by generating a line profile of the first major surface 18. The line profile can be generated by surface height measurements of the first major surface 18 via white light interferometry. The line profile can also be obtained by other known methods (e.g., using a scanning electron microscope, an atomic force microscope, or a stylus profilometer). The image is sampled in a direction perpendicular to the extension of the inclined portion 40 (in a direction extending parallel to the projection of the surface normal 46 into the x-y plane, where the surface normal is located at the first edge 43) at the point where the width w is measured. The width w at a particular point on the inclined portion 40 is calculated as the minimum lateral distance between points set at heights that differ from each other by within 10% of the difference between adjacent heights in a multimodal height distribution. The particular modality used to image the first major surface 18 when measuring the width w can vary depending on the size of the width w. When the width is less than 2.0 μm, an atomic force microscope can be used to image the first major surface 18. When the width w is greater than or equal to 2.0 μm, the line profile can be extracted from white light interferometer data, as described herein. The resulting width w can be measured as the minimum lateral distance between points set at heights that differ from each other by within 10% of the difference between adjacent heights in a multimodal height distribution.

[0096] Referring again to Figure 3A , Fourier analysis of diffraction can be used to determine the physical structure of the plurality of structures 26. As Figure 3AAs shown, the incident radiation from the external environment 24 can be approximated as a uniform plane wave, which is expressed as where I 0 represents the uniform intensity of the incident radiation, and K x0 and K y0 represent the wave vector components associated with the wavelength and the angle of incidence of the incident radiation on the first major surface 18 (e.g., the angle of incidence can be decomposed into Figure 1 the components in the x - z and y - z planes depicted in). In this case, the scalar near - field of the outgoing radiation (after interacting with the first major surface 18) can be approximated as u near (x,y) = ρu 0 (x,y)·e iφ(x,y) (2) where ρ is the Fresnel coefficient of the interface, and is the local phase accumulated through the two - channel by the distance to the first major surface 18, and H(x,y) represents the pattern formed by the plurality of structures 26. In this example, the incident radiation is approximated to have a uniform intensity distribution, and the interface between the substrate 12 and the external environment 24 is approximated to impose only a spatially varying phase, such that the outgoing radiation in the near - field also has a uniform intensity distribution.

[0097] In Figure 3A this example depicted in, the far - field scattering pattern associated with the outgoing radiation can be represented in the spatial frequency (k) space and is related to the near - field u near (x,y) calculated by Fourier transform using Equation 3, and is expressed as where k x and k x represent the scattering vector components (k x = |k|*cos(Φ), k y = |k|*sin(Φ)), where k is expressed as Φ is the azimuth angle depicted in Figure 3, and λ is the wavelength of the scattered radiation. As used herein, the "PSD" of the scattering region 20 is expressed as where A is the area of the scattering region 20. As used herein, the term "target radial PSD" refers to Equation 5 when averaged over the full range of the azimuth angle Φ. The target radial PSD is expressed as the azimuth - angle averaged PSD using the following equation( <psd>_Φ): Thus, the target radial PSD depends only on the magnitude of the spatial frequency and the wavelength of the scattered radiation. Unless otherwise stated, the wavelength is assumed to be 550 nm for expressing the radial PSD. The term "target radial PSD" refers to the result calculated according to Equation 6. In an embodiment, the plurality of structures 26 are configured such that when input into Equation 2, H(x, y) substantially matches the target radial PSD. An example family of target radial PSDs that can be used to design the scattering region 20 can be expressed as where α is an exponential decay parameter, k max is the spatial frequency associated with a non-zero scattering angle θ max at which the target radial PSD is zero, and k peak is the spatial frequency associated with a peak angle θ peak at which the target radial PSD has a peak. Assuming a wavelength of 550 nm, different values of the parameters α, θ max and θ peak can be used to generate target radial PSDs that provide different performance attributes. Guidance on the selection of parameters for a particular combination of performance attributes can be found in U.S. Provisional Patent Application No. 63 / 420,222, filed Oct. 28, 2022, which is incorporated herein by reference in its entirety.

[0098] Once a suitable target radial PSD is identified, the target radial PSD can be used to determine the phase distribution of the first major surface 18 using the methods described herein For example, an inverse Fourier transform of a target radial PSD can be used to generate a phase map. Such methods typically produce non-binary complex-valued phase maps (and thus are inconsistent with surfaces having a bimodal height distribution such as the surface shown in FIG. 3). Non-binary phases are problematic because some existing manufacturing processes (such as the etching methods described herein) are not capable of producing such structures. Thus, a threshold can be applied to the phase map such that discrete regions ("pixels") of the phase map form a discrete distribution of phases. The imaginary part terms of the generated phase can be discarded, and a threshold can be applied to the real values such that pixels having an average value below the threshold are assigned a first phase (e.g., π / 2), and pixels having an average value above the threshold are assigned a second phase (e.g., -π / 2). In an embodiment, the value of the threshold is selected such that an equal number of pixels are calculated to have the first phase and the second phase (e.g., each phase occupies 50% of the surface area of the scattering region). The pixel size can be selected based on the estimated minimum feature size achievable via the etching process described herein. In an embodiment, the pixel size is greater than or equal to 200 nm (e.g., greater than or equal to 300 nm, greater than or equal to 400 nm, greater than or equal to 500 nm, greater than or equal to 600 nm, greater than or equal to 700 nm, greater than or equal to 800 nm, greater than or equal to 900 nm, greater than or equal to 1000 nm).

[0099] Figure 4 FIG. 400 is a flow chart depicting an example method 400 of manufacturing an article 10 in accordance with an example embodiment of the present disclosure. Reference will be made to Figures 1 to 3B the various components and processes depicted therein to assist in the description of method 400. The method for forming article 10 is not particularly limited and any suitable method can be used. At block 402, a pattern of a plurality of structures 26 is determined. In an embodiment, the pattern is determined via the techniques described herein with respect to Figures 3A to 3B FIGS., i.e., by selecting a target radial PSD, generating a phase map based on the target radial PSD, and thresholding the generated phase map.

[0100] At block 404, one or more etch masks are disposed on substrate 12, and a main etch step is performed using one or more etchants to form sharp features in the scattering region based on the pattern determined at block 402. For example, to form the first etch mask of one or more etch masks, a resist may be disposed on the first major surface 18 and patterned. The nature of the deposition and patterning of the resist may vary depending on the manufacturing techniques used. In embodiments, various nanoimprint or lithography techniques may be used to deposit and pattern the resist layer. In such embodiments, the minimum feature size (e.g., minimum linear dimension) associated with the plurality of structures 26 may be set to at least 400 nm (e.g., greater than or equal to 500 nm, greater than or equal to 600 nm, greater than or equal to 700 nm, greater than or equal to 800 nm, greater than or equal to 900 nm, greater than or equal to 1.0 μm, greater than or equal to 1.5 μm, greater than or equal to 2.0 μm, greater than or equal to 2.5 μm, greater than or equal to 5.0 μm) to facilitate the use of existing resist application and patterning techniques. In embodiments, for example, the resist may be formed using thermoplastic nanoimprint lithography, and the resist may be formed of a thermoplastic polymer that is spin-coated onto substrate 12 and subsequently imprinted via a mold to form a first pattern that at least partially corresponds to the pattern of the plurality of structures 26 on the first major surface 18. The resist may then be thermally cured to form the etch mask. Other methods of forming the resist (e.g., gravure offset printing, other printing techniques) are also contemplated and within the scope of the present disclosure.

[0101] Lithography techniques (e.g., photoimprint nano-lithography, optical lithography) may also be used, and the resist may be deposited onto the first major surface 18 via a suitable coating method (e.g., spin coating). In such embodiments, a mask including a first pattern that at least partially corresponds to the pattern determined for the plurality of structures 26 is aligned with the first major surface 18, and the resist may be exposed to radiation from a suitable light source (e.g., UV radiation) to cure the resist and form the etch mask. The resist may then be processed such that portions of the first major surface 18 are exposed through the cured resist. Any suitable lithography technique may be used to pattern the resist.

[0102] After patterning the resist, the exposed regions of the first major surface 18 (through the cured and patterned resist) are exposed to a suitable etchant for a suitable etch period, which is determined based on the target etch depth in the main etch step. Each region of the first major surface 18 exposed by the patterned resist may be in direct contact with the etchant, which may degrade substrate 12 and remove material therefrom. In embodiments, the etchant contacting the first major surface 18 is HF / HNO 3 Etchant. In an embodiment, the etchant consists of hydrofluoric acid (HF, 49 w / w%) and nitric acid (HNO 3 , 69 w / w%), where HF is 0.1 - 5 v / v% and HNO 3 is 0.1 - 5 v / v% HNO 3 . Typical concentrations for achieving the etch depths discussed herein are 0.1 v / v% HF / 1 v / v% HNO3 to 0.5 v / v% HF / 1 v / v% HNO 3 solution. In an embodiment, the etching can be performed using an immersion or spray etching process from room temperature to about 45°C.

[0103] The main etching step can include any suitable number of sub-etching steps, where each sub-etching step includes exposing different regions of the first main surface 18 to the etchant through different masks. For example, the main etching step can include two sub-etching steps, where a first etching mask is deposited and patterned on the first main surface 18, and a first set of regions is exposed to the etchant to etch the first region to a first etch depth. After removing the first etching mask, a second etching mask can be deposited and patterned on the first main surface 18 to facilitate exposing a second region of the first main surface 18 to the etchant to etch the second region to a second etch depth relative to the height obtained after the first sub-etching step. The pattern of the second etching mask can be determined in a manner similar to the first etching mask. For example, in an embodiment, the same target radial PSD used in the first etching step can be used to generate the pattern for the second etching. However, when the resist is disposed on the first main surface 18, the substrate 12 can be rotated by an angle (e.g., 90°, 180°, or any other angle) such that the pattern is applied to the first main surface 18 in a different orientation compared to the first etching. Alternatively, a different target radial PSD than that used in the first etching can be used to generate the pattern for the second etching.

[0104] The first region and the second region exposed to the etchant in the first sub-etching step and the second sub-etching step can be arranged such that the first sub-etching step and the second sub-etching step result in a surface height profile having a four-mode distribution (in terms of the distribution in the histogram generated from the white light interferometry data, having four different surface height peaks). Embodiments are envisioned in which even more than two sub-etching steps are performed to provide an even higher number of modes. It has been found that providing at least four modes in the surface height profile can provide certain performance improvements over a single sub-etching step design, such as improved specular reflectance reduction and reduced DOI. The multiple levels enable interference suppression of specular reflection over a wider range of optical wavelengths. The performance attributes for the multi-level design will be described in more detail herein with respect to examples.

[0105] The main etching step at the normal execution block 404 is typically performed such that sharp features are formed in the scattering region. "Sharp" means that the regions exposed to the etchant during the etchant step are uniformly removed to produce a multi-level surface structure that includes a plurality of base-surface-shaped regions disposed at different heights relative to the base surface 30 (adjacent heights can differ from each other by 20 nm to 200 nm in a direction perpendicular to the base surface 30), wherein the transition surfaces extending between each of the levels extend substantially perpendicular to the base surface 30 (i.e., such that the first main surface 18 lacks the inclined portion 40). Such sharpness is typically achieved by promoting adhesion between the resist and the substrate 12 to prevent undercutting of the resist during the main etching step. In an embodiment, an adhesion promoter (e.g., hexamethyldisilazane (HDMS) or N,N-dimethyl-N-(3-(trimethoxysilyl)propyl)octadecane-1-ammonium chloride, YSAM C18) is coated onto the first main surface 18 before coating the resist. In an embodiment, any adhesion promoter described in U.S. Patent No. 9,884,782, filed on April 1, 2015, which is incorporated herein by reference in its entirety, can be coated onto the glass before depositing the resist in the main etching step. Such adhesion promoters typically exhibit a dual adhesion or attraction function, wherein a portion of the reagent is attracted to the substrate 12 and another portion of the reagent is attracted to the photoresist material. For certain articles described herein, it has been found that providing an adhesion promoter on the first main surface 18 that exhibits a water contact angle (after deposition) of greater than or equal to 65° (before the deposition of the risk or other masking material) should provide features of sufficient sharpness. The water contact angle exhibiting sharp features can vary depending on the adhesion promoter used. For example, when HDMS is used as the adhesion promoter, a water contact angle of at least 75° (e.g., at least 80°) has been found to be sufficient, while when using YSAM C18, a water contact angle of at least 90° has been found to be sufficient. Any other method capable of providing sharp features without significant feature rounding can also be used. Such sharpness indicates a high adhesion between the resist and the substrate 12, which allows precise control of the shape of the features formed in the first main surface 18 during the main etching step and thus the optical properties on the scattering region 20.

[0106] Still referring to Figure 4 , after the main etching step is completed, a secondary etching step is performed at block 406 by applying a secondary etchant to the scattering region 20 to round sharp features and form a plurality of structures. During the secondary etching step, after removing the mask used for the main etching step, the entire scattering region 20 can be in direct contact with the secondary etchant. It has been found that such a secondary etching step rounds the sharp features (e.g., corners) in the article 10 to provide the improved flushing performance described herein. The secondary etching step can be accomplished using any suitable etching process, such as an immersion process or a spraying process. For example, in an immersion process, the article can be immersed in a second etching solution comprising HF and HCl having a concentration ratio of 0.5M HF / 0.5M HCl to 3M HF / 3M HCl such that the etching rate of the article is greater than 0.1 μm / min or greater than 0.5 μm / min. In such embodiments, the article can be exposed to the second etching solution for a period of at least 1 minute (e.g., greater than or equal to 1 minute and less than or equal to 30 minutes, greater than or equal to 1 minute and less than or equal to 20 minutes, greater than or equal to 5 minutes and less than or equal to 20 minutes). In a spraying process, the article 10 can be sprayed with a second etching solution having an HF and HCl concentration ratio of 16 mM HF / 20 mM HCl to 160 mM HF / 200 mM HCl to achieve an etching rate of 0.1 μm / min to 1 μm / min for a period of at least 1 minute (e.g., greater than or equal to 1 minute and less than or equal to 30 minutes, greater than or equal to 1 minute and less than or equal to 20 minutes, greater than or equal to 5 minutes and less than or equal to 20 minutes). It has been found that such periods and concentrations provide a suitable amount of feature rounding for improved flushing performance.

[0107] Without wishing to be bound by theory, it is believed that due to the variable etching rates at the various regions of the sharp features formed at block 404, the secondary etching process results in feature rounding. Based on computational fluid dynamics modeling, it is believed that convex corners (e.g., at the first edge 43 depicted in Figure 3B experience a greater etching rate than the flat regions of the first main surface 18 (e.g., the plurality of first portions 32) because convex corners exhibit the largest area per unit volume exposed to the secondary etchant, providing a greater area for the etching reaction to occur. Additionally, the exposed structure of the convex corners facilitates better supply of reactants, resulting in a high acid concentration being maintained in this region. In contrast, concave corners (e.g., at the second edge 44 depicted in Figure 3B ) have a relatively low surface area per unit volume and limited reactant supply, resulting in a lower etching rate. Although flat surfaces have a relatively low surface area to volume ratio, they are considered to exhibit a moderate etching rate (between convex and concave corners) due to the improved supply of reactants in the open space (relative to concave corners).

[0108] An alternative method for providing a rounded feature is to forego the secondary etch step at block 406 and instead reduce the adhesion between the resist and the substrate 12 during the primary etch step performed at block 404. For example, changing the surface chemistry of the adhesion promoter described herein (in terms of hydrophobic groups) can provide a degree of control over undercut during etching and feature rounding. Alternatively or additionally, the amount of adhesion promoter coated on the surface can also affect the amount of adhesion. The adhesion promoter can also be removed from the first major surface 18 before coating the resist on the first major surface 18 to change the adhesion of the resist. The applicant has found that changing the water contact angle of the first major surface 18 prior to the mask can change the adhesion to the resist and thus affect the amount of feature rounding. For example, it has been found that depositing the adhesion promoter (after deposition) on the first major surface 18 exhibiting a water contact angle greater than or equal to 40° and less than or equal to 65° (e.g., greater than or equal to 45° and less than or equal to 60°, greater than or equal to 48° and less than or equal to 52°) provides an appropriate amount of feature rounding (e.g., in terms of the transition width of the feature and the AF curve of the appropriately sloped intermediate portion).

[0109] It is believed that the surface structure provided by the secondary etch step described herein has a different shape than the surface structure provided by alternative methods of adhesion control during the primary etch step. Figure 5A , Figure 5B , Figure 5C Depicted are 2D surface height profiles of various samples (i.e., line profiles generated from white light interferometry data representing a cross-section through the substrate 12 taken in a direction perpendicular to the base plane 30). Figure 5A is a sample after undergoing the primary etch step described herein, having strong adhesion between the substrate and the resist (the substrate exhibits a water contact angle greater than 70° prior to the mask). Figure 5B is a sample after undergoing the primary etch step, where the adhesion promoter chemistry is changed to reduce the adhesion between the substrate and the resist to promote undercut (after depositing the adhesion promoter, the substrate exhibits a water contact angle less than 65°). Figure 5C is a sample after undergoing the primary etch step and the secondary etch step described herein with respect to Figure 4 . In the Figure 5A example shown, the represented surface includes a first region 502 defining the base plane, a second region 504 disposed at a peak height just less than 200 nm relative to the base plane. The transition surface 506 separates the first region 502 and the second region 504. As shown, the transition surface 506 defines a transition width w of less than 1 μm (see Figure 3B ). Additionally, the defined feature has relatively sharp corners. In Figure 5B In the example shown, the represented surface includes a first region 508 that defines a base surface, and a plurality of second regions 510 that are disposed at a peak height that is just less than 150 nm relative to the base surface. A transition surface 512 separates the first region 508 and the second regions 510. However, contrary to the Figure 5A sample shown in

[0110] the transition surface 512 defines a transition width w that is greater than 1 μm. Additionally, the convex corner 514 is rounded, indicating the degree of undercut. However, the concave corner 516 is relatively unaffected by undercut, and thus the slope of the surface still changes abruptly at the concave corner 516. Figure 5C In the example shown, the represented surface includes a first region 518 that defines a base surface, and a plurality of second regions 520 that are disposed at a peak height that is between 150 nm and 200 nm relative to the base surface. A transition surface 522 separates the first region 518 and the second regions 520. The transition surface 522 defines a transition width w that is greater than 1 μm. However, contrary to the Figure 5B example shown in Figure 5C both the convex corner 524 and the concave corner 526 are rounded, such that the abrupt transition in the surface slope in the Figure 5B example shown in Substrate characteristics

[0111] is less abrupt than the abrupt transition in the surface slope in the

[0112] Figure 5B example shown in Substrate characteristics

[0111] It is believed that the removal of such high spatial frequency features is associated with a reduction in the scattering amplitude at high scattering angles (i.e., excellent flushing performance). Additionally, as described in more detail, such gradual surface transitions are believed to be associated with excellent wear performance.

[0112] Now, various characteristics of the substrate 12 will be described in accordance with embodiments of the present disclosure.

[0113] In an embodiment, the substrate 12 has a body composition including an alkali aluminosilicate glass, the alkali aluminosilicate glass including alumina, at least one alkali metal, and in some embodiments greater than 50 mol% SiO 2 , and in other embodiments at least 58 mol% SiO 2 , and in still other embodiments at least 60 mol% SiO 2 , where the ratio (Al 2 O 3 (mol%) + B 2 O 3 (mol%)) / ∑ alkali metal modifiers (mol%) > 1, where the modifier is an alkali metal oxide. In a particular embodiment, the glass comprises, consists essentially of, or consists of: about 58 mol% to about 72 mol% SiO 2 ; about 9 mol% to about 17 mol% Al 2 O 3 ; about 2 mol% to about 12 mol% B 2 O 3 ; about 8 mol% to about 16 mol% Na 2 O; and 0 mol% to about 4 mol% K 2 O, where the ratio (Al 2 O 3 (mol%) + B 2 O 3 (mol%)) / ∑ alkali metal modifiers (mol%) > 1, where the modifier is an alkali metal oxide.

[0114] In an embodiment, the substrate 12 has a body composition including an alkali aluminosilicate glass, the alkali aluminosilicate glass comprising, consisting essentially of, or consisting of: about 61 mol% to about 75 mol% SiO 2 , about 7 mol% to about 15 mol% Al 2 O 3 ; 0 mol% to about 12 mol% B 2 O 3 ; about 9 mol% to about 21 mol% Na 2 O; 0 mol% to about 4 mol% K 2 O; 0 mol% to about 7 mol% MgO; and 0 mol% to about 3 mol% CaO.

[0115] In an embodiment, the substrate 12 has a body composition including an alkali aluminosilicate glass, the alkali aluminosilicate glass comprising, consisting essentially of, or consisting of: about 60 mol% to about 70 mol% SiO 2 , about 6 mol% to about 14 mol% Al 2 O 3 ; 0 mol% to about 15 mol% of B 2 O 3 ; 0 mol% to about 15 mol% of Li 2 O; 0 mol% to about 20 mol% of Na 2 O; 0 mol% to about 10 mol% of K 2 O; 0 mol% to about 8 mol% of MgO; 0 mol% to about 10 mol% of CaO; 0 mol% to about 5 mol% of ZrO 2 ; 0 mol% to about 1 mol% of SnO 2 ; 0 mol% to about 1 mol% of CeO 2 ; less than about 50 ppm of As 2 O 3 ; and less than about 50 ppm of Sb 2 O 3 ; wherein 12 mol% ≤ Li 2 O + Na 2 O + K 2 O ≤ 20 mol% and 0 mol% ≤ MgO + Ca ≤ 10 mol%.

[0116] In an embodiment, substrate 12 has a bulk composition comprising an alkali aluminosilicate glass, the alkali aluminosilicate glass comprising, consisting essentially of, or consisting of: about 64 mol% to about 68 mol% of SiO 2 , about 12 mol% to about 16 mol% of Na 2 O; about 8 mol% to about 12 mol% of Al 2 O 3 ; 0 mol% to about 3 mol% of B 2 O 3 ; about 2 mol% to about 5 mol% of K 2 O; about 4 mol% to about 6 mol% of MgO; and 0 mol% to about 5 mol% of CaO, wherein: 66 mol% ≤ SiO 2 + B 2 O 3 + CaO ≤ 69 mol%; Na 2 O + K 2 O + B 2 O 3 + MgO + CaO + SrO > 10 mol%; 5 mol% ≤ MgO + CaO + SrO ≤ 8 mol%; (Na 2 O + B 2 O 3 ) — Al 2 O 3 ≤ 2 mol%; 2 mol% ≤ Na 2 O — Al 2 O 3 ≤ 6 mol%; and 4 mol% ≤ (Na 2 O + K 2 O) — Al 2 O 3 ≤ 10 mol%.

[0117] In an embodiment, the substrate 12 has a bulk composition comprising SiO 2 , Al 2 O 3 , P 2 O 5 and at least one alkali metal oxide (R 2 O), where 0.75 > [(P 2 O 5 (mol%) + R 2 O (mol%)) / M 2 O 3 (mol%)] ≤ 1.2, where M 2 O 3 ═ Al 2 O 3 + B 2 O 3 。In an embodiment, [(P 2 O 5 (mol%) + R 2 O (mol%)) / M 2 O 3 (mol%)] = 1, and in an embodiment, the glass does not include B 2 O 3 and M 2 O 3 ═ Al 2 O 3 。In an embodiment, the substrate 12 comprises: about 40 to about 70 mol% of SiO 2 ; 0 to about 28 mol% of B 2 O 3 ; about 0 to about 28 mol% of Al 2 O 3 ; about 1 to about 14 mol% P 2 O 5 ; and about 12 to about 16 mol% of R 2 O. In some embodiments, the glass substrate comprises: about 40 to about 64 mol% of SiO 2 ; 0 to about 8 mol% of B 2 O 3 ; about 16 to about 28 mol% of Al 2 O 3 ; about 2 to about 12 mol% of P 2 O 5 ; and about 12 to about 16 mole % of R 2 O. The substrate 12 may further comprise at least one alkaline earth metal oxide, such as but not limited to MgO or CaO.

[0118] In some embodiments, the substrate 12 has a bulk composition that is substantially free of lithium; that is, the glass contains less than 1 mole % of Li 2 O, and in other embodiments, less than 0.1 mole % of Li 2 O, and in other embodiments, 0.01 mole % of Li 2 O, and in other embodiments, 0 mole % of Li 2 O. In some embodiments, such glass is free of at least one of arsenic, antimony, and barium; that is, the glass contains less than 1 mole %, and in other embodiments less than 0.1 mole %, and in still other embodiments 0 mole % of As 2 O 3 、Sb 2 O 3 and / or BaO.

[0119] In an embodiment, the substrate 12 has a bulk composition comprising, consisting essentially of, or consisting of a glass composition, such as Eagle ( Eagle ) glass, glass, glass 2, glass 3, glass 4 or glass 5.

[0120] In an embodiment, the substrate 12 has an ion-exchangeable glass composition that is strengthened by chemical 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 first major surface 18 of the substrate 12 are exchanged for larger metal ions having the same valence as the metal ions in the glass substrate. The exchange is typically performed by contacting the substrate 12 with an ion-exchange medium, such as, for example, a molten salt 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, the chemical strengthening of the substrate 12 containing sodium ions by ion exchange is accomplished by immersing the substrate 12 in an ion-exchange bath comprising a molten potassium salt (such as potassium nitrate (KNO 3 ), etc.). In a particular embodiment, the ions in the surface layer of the substrate 12 adjacent to the first major surface 18 and the larger ions are monovalent alkali metal cations, such as Li + (when present in the glass), Na + , K + , Rb + and Cs + . Alternatively, a monovalent cation other than an alkali metal cation (such as, Ag + etc.) may be used to replace the monovalent cation in the surface layer of the substrate 12.

[0121] In such embodiments, a compressive stress region is created in the substrate 12 by replacing smaller metal ions with larger metal ions in an ion exchange process, and the compressive stress region extends from the first major surface 18 to a depth under compressive stress (referred to as "depth of the layer"). This compressive stress of the substrate 12 is balanced by a tensile stress (also referred to as "central tension") within the substrate 12. In some embodiments, when enhanced by ion exchange, the first major surface 18 of the substrate 12 described herein has a compressive stress of at least 350 MPa, and the region under compressive stress extends at least 1 μm into the thickness 21 below the first major surface 18, i.e., the layer depth.

[0122] The ion exchange process is typically performed by immersing the substrate 12 in a molten salt bath that contains larger ions to be exchanged with the smaller ions in the glass. Those skilled in the art will understand that the parameters of the ion exchange process, including but not limited to the bath composition and temperature, immersion time, number of immersions of the glass in the salt bath (or salt baths), use of multiple salt baths, additional steps (such as annealing, washing, etc.), are typically determined by the composition of the glass and the desired layer depth and compressive stress of the glass as a result of the strengthening operation. For example, ion exchange of an alkali metal-containing glass can be achieved by immersion in at least one molten bath containing a salt with a larger alkali metal ion (such as but not limited to nitrates, sulfates, and chlorides). The temperature of the molten salt bath is typically in the range of about 380 °C to about 450 °C, while the immersion time is in the range of about 15 minutes to about 16 hours. However, different temperatures and immersion times may also be used. When used with a substrate 12 having an alkaline aluminosilicate glass composition, such ion exchange treatment results in a compressive stress region with a depth (layer depth) in the range of about 10 μm to at least 50 μm, a compressive stress in the range of about 200 MPa to about 800 MPa, and a central tension of less than about 100 MPa.

[0123] Since the etching process available for creating the scattering region 20 of the substrate 12 can remove alkali metal ions that would otherwise be replaced by larger alkali metal ions during the ion exchange process, it is preferred to process the compressive stress region in the article 10 after forming and processing the scattering region 20. Example

[0124] Embodiments of the present disclosure can be further understood by considering the following examples.

[0125] Examples 1 to 5

[0126] Examples 1 to 5 are fabricated by forming a plurality of structures 26 by varying the adhesion between the resist and the substrate 12 during the main etching step. In particular, an adhesion promoter (HMDS) is deposited on the substrate 12. However, the water contact angle of the first main surface 18 changes after disposing the adhesion promoter to vary the adhesion strength with the photoresist (Megaposit TM SPR220, MicroChemicals AZ1500). The water contact angle is varied by exposing the HMDS layer to tetramethylammonium hydroxide for different exposure times to vary the silane concentration of the promoter. The water contact angle of the first main surface 18 varies from 76° (strong adhesion and minimal undercut) to 50° (relatively weak adhesion and substantial undercut). After determining the pattern of the plurality of structures 26 via the methods described herein, the photoresist is exposed to light based on the pattern to facilitate the formation of openings in the resist and etch the substrate 12 to form the base surface 30. Similar results can be achieved using a positive resist or a negative resist. In Example 1, the substrate 12 exhibits a water contact angle of approximately 76° before applying the adhesion promoter. In Example 2, the substrate 12 exhibits a water contact angle of approximately 71°. In Example 3, the substrate 12 exhibits a water contact angle of approximately 68°. In Example 4, the substrate 12 exhibits a water contact angle of approximately 61°. In Example 5, the substrate 12 exhibits a water contact angle of approximately 50°. The photoresist is cured into the same pattern as in each of Examples 1 to 5.

[0127] Figure 6A is the 2D surface height profile 600 measured from the scattering region 20 of Example 1. The 2D surface height profile represents a 1x1 mm 2 portion of the region, which is measured using a white light interferometer with a lateral resolution of 360 nm per pixel. Each pixel in the measurement represents the surface height. Based on the 2D surface height profile 600, a histogram 602 of height frequencies is generated. The histogram 602 includes a first peak 604 representing the unetched portion of the scattering region 20 during the main etching step and a second peak 606 representing the fully etched region (establishing the base surface 30). The count of surface heights outside the first peak 604 and the second peak 606 is very low, indicating a minimal slope of the transition surface between the platforms at the heights associated with the first peak 604 and the second peak 606. Figure 6B Depicts a 2D surface height profile 608 (with a large amount of feature rounding) measured from the scattering region 20 of Example 5. As shown, the histogram 610 includes only a single peak 612, representing a fully etched region (establishing the base plane 30). The height rounding of the features in this example eliminates the upper peak associated with the single peak height. However, as shown in the histogram 610, the frequency of heights above the height associated with the single peak 612 is higher than the region outside the first peak 604 and the second peak 606 associated with Example 1. This indicates a gentle slope of the scattering region 20 and a lack of a vertical transition surface.

[0128] AF curves are used to characterize each of Examples 1 through 5. By integrating surface height histograms (illustrated by the histogram 602 and the histogram 610 depicted in Figure 6A and Figure 6B respectively), the percentage of the surface area occupied by each height is generated to produce the AF curves. Figure 7 is a graph including the AF curves of each example. As shown, the AF curve 614 of Example 1 includes a first portion 616, which represents the region of the scattering region 20 that is closer to the base plane 30 (the region of the first main surface 18 where most of the material is removed during the main etching step), a second portion 618, which represents the peak portion (e.g., the unetched or minimally etched portion where the least amount of material of the substrate 12 is removed during the main etching step), and an intermediate portion 620 that extends between the first portion 616 and the second portion 618. For Example 1, the first portion 616 and the second portion 618 represent the percentage of the first main surface 18 that is set at the heights associated with the first peak 604 and the second peak 606 depicted in FIG. 6. The first portion 616 and the second portion 618 are the vertical portions of the AF curve of Example 1, having a relatively high or undefined slope. In the depicted embodiment, the first portion 616 and the second portion 618 have a slope greater than 420% / μm.

[0129] As described herein, the boundaries of the various "portions" (e.g., the first portion, the second portion, and the intermediate portion) of the AF curves described herein can be identified by locating the sections of the AF curve where the slope suddenly changes. The portion boundaries can be characterized as AF curve sections where the slope transitions at least 5% / μm over a section representing a 100 nm surface height or can be characterized as inflection points of the AF curve. The inflection point itself can represent the intermediate portion described herein.

[0130] As Figure 7 As shown, the degree of feature rounding imparted by reducing the adhesion of the photoresist during the main etch step in Examples 1 through 5 changes the shape of the AF curve. For Examples 1 through 5, the length of the second portion of the AF curve (representing the peak portion 42 of the plurality of structures 26) is shorter, indicating that a smaller percentage of the first major surface 18 is disposed at a height corresponding to the etch depth in the main etch step relative to the base plane 30. Additionally, the middle portion of the AF curve (representing the sloped portion 40 of the plurality of structures 26) obtains a greater slope with a greater degree of feature rounding. By way of illustration, in the AF curve 614 associated with Example 1, the slope of the middle portion 620 is approximately 0.6% / μm. In contrast, the AF curve 622 associated with Example 4 includes a middle portion 624 having a slope of approximately 238.9% / μm. The greater slope of the middle portion generally indicates that the sloped portion 40 of the plurality of structures 26 occupies a greater area fraction of the first major surface 18 in the scattering region 20 (projected into the base plane 30). The AF curve 622 representing Example 4 has a middle portion 624 representing approximately 35% of the scattering region 20. This can be determined based on the projection of the middle portion onto the vertical axis of the AF curve. The applicant has found that when the sloped portion 40 of the plurality of structures 26 occupies more than 5% of the total surface area of the scattering region 20 and the middle portion of the AF curve has a slope greater than or equal to 5% / μm and less than 420% / μm (e.g., greater than or equal to 10% / μm and less than or equal to 200% / μm, greater than or equal to 20% and less than or equal to 150% / μm), the degree of feature rounding is sufficient to provide the excellent flushing performance described herein.

[0131] As Figure 7 shown, the AF curve 626 associated with Example 5 includes a first portion 628, a second portion 632, and a middle portion 634, where the first portion 628 is a substantially vertical portion representing the maximum etched portion of the first major surface 18, and the second portion 632 represents the peak portion 42 of the plurality of structures 26. Due to the high degree of feature rounding, the second portion 632 is different in shape from the second portions of Examples 1 through 4. Since there is no plateau at the peak height and the feature is fully rounded, the second portion 632 is a relatively small section at the highest height where the AF curve 626 transitions from zero to a finite slope. Due to the high degree of feature rounding, the middle portion 634 has a relatively high slope (approximately 375% / μm).

[0132] "Washout" metrics have been developed to quantify the impact of glare events (e.g., exposure to sunlight) on the contrast and resolution of a combined display. Such metrics are useful for examining the performance of cover materials for applications that may be exposed to light from external light sources (e.g., automotive interior displays, outdoor displays). To quantify "washout", the modulation transfer function (MTF) of an anti-glare surface is measured under various lighting conditions, and the average value of the MTF over multiple spatial frequencies is used to evaluate the impact of the lighting conditions on the display performance. The MTF at a specific spatial frequency f can be expressed as where and, I(f) max and I(f) min are the maximum and minimum intensities of the input or output modulated image at spatial frequency f. In this expression, MF in represents the MF value associated with the input pattern emitted through the sample cover material. The MF out value represents the MF value when the cover material is placed above the input pattern (e.g., from a display) and under the tested lighting conditions. A higher MTF value generally means a smaller impact of the lighting conditions on the display performance (and thus better performance of the scattering region of the cover material). In an embodiment, an MTF value greater than or equal to 0.60 (e.g., greater than or equal to 0.65, greater than or equal to 0.70, greater than or equal to 0.75, greater than or equal to 0.76, greater than or equal to 0.77, greater than or equal to 0.78, greater than or equal to 0.79, greater than or equal to 0.80, greater than or equal to 0.81, greater than or equal to 0.82, greater than or equal to 0.83, greater than or equal to 0.84, greater than or equal to 0.85, greater than or equal to 0.86, greater than or equal to 0.87, greater than or equal to 0.88, greater than or equal to 0.89, greater than or equal to 0.90, greater than or equal to 0.91, greater than or equal to 0.92, greater than or equal to 0.93, greater than or equal to 0.94, and greater than or equal to 0.95) is preferred for a given lighting condition, indicating a minimum degradation of the display performance caused by exposure to external light.

[0133] Figure 8 FIG. schematically depicts an apparatus 800 for measuring the washout effect. As shown, a sample 802 (e.g., corresponding to substrate 12 described herein) is placed above a display 804. The sample 802 is positioned such that the scattering region faces outward (instead of facing the display 804). As shown in block 805, which depicts a front view of the sample 802 and the display 804, the display 804 generates a plurality of target patterns 806, where the intensity of the light emitted by the display 804 varies with a specific spatial frequency f i and vary. A plurality of first light sources 808 are distributed around the sample 802. The plurality of first light sources 808 (e.g., indoor light) are configured to emit relatively low-intensity light to simulate the sample 802 encountering normal lighting conditions (e.g., indoor light). As reported herein, the plurality of first light sources 808 are configured to emit white light having 130 lux and a color temperature of 2100K. The projection light source 810 is configured to emit a relatively high-intensity light source to simulate sunlight illumination. The projection light source 810 is positioned such that the light emitted therefrom impinges on the sample at an incident angle θ i . on the sample. In an embodiment, the projection light source 810 is movable or otherwise adjustable to change the incident angle θ i . In an embodiment, the projection light source 810 emits light over an emission area such that the light emitted by the projection light source 810 impinges on the sample 802 at an incident angle θ i within a range.

[0134] The camera 812 is positioned to receive light scattered from the sample 802. The camera is positioned such that the light scattered from the sample 802 will enter the camera 812 at a viewing angle θ v (or a viewing angle range). In an embodiment, the camera 812 is movable or otherwise adjustable to change the viewing angle θ v . The computing system 814 receives the image generated by the camera 812 and analyzes the image to calculate a plurality of MTF values for each of the plurality of target patterns 806 emitted by the display 804. For each target pattern in the target pattern 806, the computing system 814 can use Equation 8 and Equation 9 to calculate the MTF value and generate an output measuring the dependence of the measured MTF value on spatial frequency. The plurality of first light sources 808 and the projection light source 810 allow the measurement of MTF values under a plurality of different lighting conditions to determine the efficacy of the pattern on the sample 802 in reducing washout. When only the first light sources 808 emit light, the "indoor light washout" effect can be measured. When both the first light sources 808 and the projection light source 810 emit light, the "sunlight washout" effect can be measured.

[0135] Such washout measurements can be particularly useful in evaluating the performance of cover materials for automotive interior displays. Figure 9 Shows a vehicle interior 1000 including three different vehicle interior systems 100, 200, and 300 according to an exemplary embodiment. The vehicle interior system 1000 includes a center console base 110 having a surface 120 including a display 130. The vehicle interior system 200 includes an instrument panel base 210 having a surface 220 including a display 230. The instrument panel base 210 generally includes an instrument panel 215, and the instrument panel 215 may further include a display 216. The vehicle interior system 300 includes a steering wheel base 310 having a surface 320 and a display 330. In one or more embodiments, the vehicle interior system may include a base that is an armrest, a pillar, a seatback, a floor, a headrest, a door panel, or any part of the vehicle interior that includes a surface. In an embodiment, the displays 130, 230, 330 are flat and include cover glass having a flat main surface. In an embodiment, one or more of the displays 130, 230, 330 are curved, and the curved display may include curved cover glass that can be thermoformed or cold formed to have such a curvature. For example, such embodiments may include an opaque layer formed of the photocurable ink described herein disposed on a cold formed glass substrate.Such cold forming may involve any of the techniques described in U.S. Pre - authorized Publication No. 2019 / 0329531A1, titled "Laminating thin strengthened glass to curved molded plastic surface for decorative and display cover application", U.S. Pre - authorized Publication No. 2019 / 0315648A1, titled "Cold - formed glass article and assembly process thereof", U.S. Pre - authorized Publication No. 2019 / 0012033A1, titled "Vehicle interior systems having a curved cover glass and a display or touch panel and methods for forming the same", and U.S. Patent Application No. 17 / 214,124, titled "Curved glass constructions and methods for forming same", which patents are hereby incorporated by reference in their entirety.

[0136] Various components of the vehicle interior 1000 may be subjected to illumination from various light sources. As Figure 9 depicted, for example, a first ambient light source 900 may emit light that transmits through a first side window of the vehicle and impinges on the display 216 at an incident angle θ i1 The display 216 may be oriented such that the light scattered at a specific scattering angle θ v1 will enter the driver's field of view and distract the driver. A second ambient light source 902 may emit light that transmits through a second side window of the vehicle and impinges on the display 130 at an incident angle θ i2 The display 130 may be oriented such that the light scattered at a specific scattering angle θ v2 will enter the driver's field of view and distract the driver. The first ambient light source 900 and the second ambient light source 902 may represent sunlight at different points in time. In fact, the ISO 15002 / SA 1757 standard specifies a first condition where 45 k lux of light (direct sunlight) impinges on the display 216 at an angle of 20° and is scattered into the driver at a scattering angle of 0° (i.e., where θ i1 = 20° and θ v1 = 0°, associated with the "washout" 1 " metric in this article), and a second condition, where 45 kLux of light (direct sunlight) is incident on the display 130 at an angle of 45° and scattered into the driver at a scattering angle of 20° (i.e., where θ i2 = 45° and θ v2 = 20°, associated with the "washout" 2 " metric in this article). Figure 8 The apparatus 800 depicted in can test such conditions for washout by changing the orientation of the sample 802 and adjusting the projection light source 810.

[0137] Using Figure 8 the apparatus 800 depicted in , the two conditions of ISO 15002 / SA 1757 described in this article are used to test Examples 1 to 5. Using Mini 4 as the display 804. Using Pixelink 3.1MP PL-B776 as the camera 812. Using a collimated LED light source (emitting 45000 Lux of white light) at the projection light source 810 (manufactured by Mightex Systems, model LCS-6500-65-22). Using and positioning multiple projection light sources so as to emit light incident on the sample 802 at incident angles of 20° and 45°. The sample 802 and the camera 812 are also mounted on a rotating stage so as to make the viewing angle θ v and the incident angle θ i adjustable for the two conditions. The laboratory room light is used as the first light source 808 and is measured to have a brightness of 132 lux.

[0138] To quantitatively evaluate the effect of the sample 802, the MTF values at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm are averaged for each series. The "washout" metric described in this article is the average of the MTF values at these spatial frequencies for each condition.

[0139] Figure 10 is a graph of the Figure 8 and Figure 9 described washout 2 metric in this article, the washout 2 metric is a function of the water contact angle of the substrate after the disposal (and modification) of the adhesion promoter. As shown, for water contact angles above 65°, the washout 2 metric is generally below 0.5. However, when the photoresist exhibits a water contact angle below 65°C. Washout 2 An index higher than 0.6 and above indicates more favorable erosion performance. These results show that a higher degree of feature rounding, and thus the surface characterized by the AF curve with the features described herein, is associated with better erosion performance.

[0140] Examples 6 - 11

[0141] In Examples 6 to 11, Corning Glass 5 was used as the substrate. To perform the main etch, an adhesion layer (HMDS) was applied to the first major surface. Then a photoresist (<2 μm thick, Megaposit TM SPR220, MicroChemicals AZ1500) was applied over the adhesion layer and subsequently exposed to UV light. Positive toning was used such that the areas exposed to UV were removed by an alkaline developer (<1% TMAH tetramethylammonium hydroxide or 0.24 wt% potassium hydroxide or 1 wt% sodium carbonate Na 2 CO 3 ), while the unexposed areas were unaffected by the developer. Finally, the patterned features were transferred to the glass using wet etching (dipping / spraying). At room temperature, the main etchant was hydrofluoric acid (e.g., HF / HNO 3 or HF / HCl). Typically, the unmasked side was laminated with an acid-resistant etch mask to prevent etching. In Examples 6 to 11, the same pattern was formed using the main etch step.

[0142] For Examples 6 to 11, a secondary etch step was performed where the glass was loaded in a vertical orientation and the secondary etchant was sprayed onto the top of the glass such that the etchant flowed from the top of the sample over the surface to the bottom of the sample under the influence of gravity. The concentration of the second etch solution was varied from 16 mM HF / 20 mM HCl to 160 mM HF / 200 mM HCl to achieve an etch rate of 0.1 to 1 μm / min. The etch time varied between 5 minutes and 20 minutes. Examples 6 and 7 used an etch rate of 1 μm / min. Examples 8 and 9 used an etch rate of 0.02 μm / min. Examples 10 and 11 used an etch rate of 0.1 μm / min. The optical properties of the samples were measured both before and after the secondary etch. The results are provided in Table 1 below. Three samples were measured for each etch configuration. Table 1

[0143] As shown, the systematic difference between the samples before and after the secondary spray etching step is that the samples exhibit lower transmission haze after the secondary etching step. Thus, transmission haze can be used to monitor the secondary etching step described herein. Additionally, the samples subjected to secondary etching exhibit specular reflectance, DOI, and gloss values comparable to those of the unpolished samples. These results indicate that the feature rounding provided via the method described herein can help improve the erosion performance without degrading other important AR performance attributes.

[0144] Figure 11A , Figure 11B and Figure 11C are AF curves representing the surfaces of Examples 6 to 11. These curves generally show how the secondary etching step changes the profile of the first major surface 18. Figure 11A , 11B and each of 11C includes a control AF curve representing the sample before secondary etching. Figure 11A represents Examples 6 and 7, which were formed using an etching rate of 1 μm / min in the secondary etching step. As shown by the AF curve associated with Example 6, a 5-minute etching cycle results in an approximately 8% decrease in the fill rate of the scattering region 20, where the fill rate is occupied by the portion of the first major surface 18 set at the etching depth of the primary etching step relative to the base surface. The slope of the middle portion 1100 (between the vertical portions associated with the platform height) also increases relative to the control. As shown by the AF curve associated with Example 7, increasing the etching time of the secondary etching step to 20 minutes results in a 20% decrease in the fill rate associated with the portion of the first major surface 18 set at the etching depth of the first etching step relative to the base surface. Additionally, the slope of the middle portion 1102 further increases relative to the middle portion 1100 associated with Example 6. Figure 11B and 11C indicate that lower etching rates of 0.1 μm / min and 0.2 μm / min can also be used to effectively provide feature rounding, where the same etching cycle results in a smaller decrease in the fill rate of the portion set at the etching depth of the primary etching step relative to the base surface.

[0145] Figures 12A to 12C is for measuring Figure 11A , Figure 11B and Figure 11C the SEM images of the cross-sections of the samples for the AF curves depicted in. Figure 12A is an SEM image of one of the samples of Example 9. Figure 12B is an SEM image of one of the samples of Example 10. Figure 12C SEM image of one of the samples in Example 11. The trend revealed by these images is that the total amount of substrate etched during the secondary etching step is proportional to the degree of feature rounding. In Figure 12C no discernible sharp corners were observed, while relatively sharp top corners were still exhibited in Figure 12A associated with a total etch of 44 μm in the secondary etching step. Based on these results, it is believed that the degree of rounding is insensitive to the selected etch rate and sensitive to the total amount of etching that occurs during the secondary etching step. It is believed that a slower etch rate (e.g., 0.1 μm / min) can be used for a longer period of time (e.g., 200 minutes) to provide the same degree of feature rounding as a faster etch rate (e.g., 1.0 μm / min) in a shorter period of time (e.g., 20 minutes). However, for manufacturing efficiency, a faster etch rate may be preferred.

[0146] Examples 12 to 14

[0147] Examples 12 to 14 are formed by patterning in the first major surface 18 of substrate 12 (made of the same material as Examples 6 to 11) via the method described herein. Slightly different etch depths are used in the primary etching step to form each of these examples. Figure 13A The surface height profile 1300 of a control sample without any secondary etching is depicted. As shown, the corresponding histogram 1302 includes a first peak 1304 representing the base plane 30 and a second peak 1306 representing the peak portion 42 of the plurality of structures 26. The first peak 1304 and the second peak 1306 are separated by an etch depth 1307 of approximately 132 nm. To fabricate Examples 12 to 14, the samples were subjected to an immersion etching step in a 1M HF / 1M HCl solution to affect the rounding of the features (the etch depth of each sample is slightly different). Figure 13B is the surface height profile 1310 of Example 12, which was exposed to a 2-minute secondary etching. Figure 13C is the surface height profile 1320 of Example 13, which was exposed to a 3-minute secondary etching. Figure 13D is the surface height profile 1330 of Example 14, which was exposed to an 8-minute secondary etching. As shown in histograms 1312, 1322, and 1332, a longer secondary etching period generally results in a broadening of the histogram peaks. For example, the histogram 1332 associated with Example 14 includes a first peak 1334 and a second peak 1336 that are wider than the first peak 1302 and the second peak 1306 associated with the control sample without secondary etching.

[0148] Examples 12 to 14 are further characterized by the Figure 14 AF curves shown. The first AF curve 1400 is associated with the Figure 13A associated with a control sample of the surface height profile representation therein. As shown, the first AF curve 1400 includes a first portion 1402 representing a region of a first major surface etched in the main etching step and a second portion 1404 representing a portion of the first major surface that was not etched during the main etching step. The first AF curve 1400 further includes an intermediate portion 1406 extending between the first portion 1402 and the second portion 1404. Due to the lack of feature rounding, when the etch depth is about 0.18 μm, the intermediate portion 1406 has a relatively small slope of about 25% / μm. The second AF curve 1408 represents Example 12. The second AF curve 1408 includes a first portion 1410, a second portion 1412, and an intermediate portion 1414. As shown, the intermediate portion 1414 has an average slope of about 83% / μm, and due to a small amount of secondary etching imparting feature rounding, the average slope of the intermediate portion is larger compared to the control sample. The third AF curve 1416 associated with Example 13 includes an intermediate portion 1418 having an average slope of about 100% / μm, and due to a longer secondary etching step, the average slope of the intermediate portion is still greater than that of Example 12. The fourth AF curve 1420 associated with Example 14 includes an intermediate portion 1422 having an average slope of about 154% / μm, and due to a longer secondary etching step, the average slope of the intermediate portion is still greater than that of Example 13. These examples demonstrate that the slope of the intermediate portion of the AF curve is generally proportional to the amount of material removed during the secondary etching step described herein and can be controlled by selecting appropriate etch rates and etch durations.

[0149] Bidirectional reflectance distribution function (BRDF) measurements were performed on Examples 12 to 14 and comparative examples fabricated using an existing non-mask-based HF etching process (producing a randomized pattern). The measurements were performed in reflection mode using a REFLET 180S system from Synopsys, Inc. The measurement wavelength range (i.e., the spectral range of the light source for the scattered light) was from 400 nm to 1700 nm, and the angle of incidence of the light was 10°. Figure 15 is a graph of the scattering amplitude in (sr -1 ) as a function of the viewing angle. As shown, relative to the specular surface, the sample with feature rounding exhibits lower scattering intensity at scattering angles greater than or equal to 30°. In fact, at a 30° scattering angle, in terms of the actual (non-normalized) BRDF amplitude, Example 14 exhibits a BRDF amplitude of less than 1.2x10 -4 sr -1 while the control exhibits a BRDF amplitude of 4x10 -4 sr -1 BRDF amplitude. At higher scattering angles, the difference is even greater. At a scattering angle of 40°, in terms of the actual (non-normalized) BRDF amplitude, Example 14 exhibits 5x10 -5 sr -1 BRDF amplitude, while the control exhibits 1.7x10 -4 sr -1 BRDF amplitude. Such relatively low BRDF amplitudes at high scattering angles achieved by samples with characteristic rounding demonstrate the excellent flushing performance of such samples.

[0150] Examples 15 to 17

[0151] Examples 15 to 17 differ from the previous examples in that the main etching step includes a plurality of sub-etching steps to produce a surface height profile with more than 2 modes. Figure 16A Depicts the surface height profile 1600 of a control sample without any secondary etching. As shown in the histogram 1602, the surface height profile includes a first peak 1604 associated with an area where the first main surface 18 was not etched during the main etching step and a second peak 1606 associated with an area where the first main surface 18 was etched during two sub-etching steps of the main etching step. The intermediate peaks 1607 and 1608 are associated with areas where the first main surface 18 was etched during only one of the sub-etching steps of the main etching step. To fabricate Examples 15 to 17, samples with a Figure 16A represented surface height profile were subjected to an immersion etching step in a 1M HF / 1M HCl solution to affect the rounding of the features. Figure 16B Is the surface height profile 1610 of Example 15, which was exposed to a secondary etching for 0.5 minutes. Figure 16C Is the surface height profile 1620 of Example 16, which was exposed to a secondary etching for 3 minutes. Figure 16D Is the surface height profile 1630 of Example 17, which was exposed to a secondary etching for 5 minutes. As shown in the histograms 1612, 1622, and 1632, longer secondary etching time periods generally result in broader histogram peaks. In fact, the histograms 1622 and 1632 associated with Example 16 and Example 17 exhibit only three distinct peaks because feature rounding causes the intermediate peaks to merge. As Figure 16D shown, for example, the histogram 1632 includes a first peak 1634 associated with an area where the first main surface 18 was not etched during the main etching step and a second peak 1636 associated with an area where the first main surface 18 was etched during two sub-etching steps of the main etching step. However, compared to the histogram 1612 associated with Example 15, the histogram 1632 includes only a single distinct intermediate peak 1638.

[0152] The AF curve is used to further characterize Examples 15 through 17 and is shown in Figure 17 . As shown, a longer secondary etch step typically results in a vertical portion of the AF curve having a smaller slope from feature rounding. A vertical portion having a slope less than 400% / μm typically indicates a relatively high degree of feature rounding and a minimum planar area of the scatter region 20. Each AF curve associated with Examples 14 through 17 can be characterized as having four distinct vertical portions, each having an average slope greater than 350% / μm. The vertical portions represent peak portions 42 of a plurality of structures 26 at different peak heights in the corresponding histogram. The vertical portions are separated from each other by intermediate portions that are: (a) a section of the AF curve representing at least 50 nm in height and having an average slope at least 50% / μm less than an adjacent vertical portion; or (b) an inflection point of the AF curve. For illustration, Figure 17 includes the AF curve 1700 associated with Example 17. In this example, the features are significantly rounded. The AF curve 1700 includes a first portion 1702, a second peak portion 1704, a third portion 1706, and a fourth portion 1708. The first portion 1702 represents a location in the first major surface 18 where the most material is removed during the primary etch step and the secondary etch step. The second peak portion 1704 represents a location where the least material is removed during the primary etch step and the secondary etch step. The third portion 1706 and the fourth portion 1708 are associated with the intermediate peak 1638 described herein with respect to Figure 16D . The first portion 1702, the second portion 1704, the third portion 1706, and the fourth portion 1708 are vertical portions of the AF curve 1700, each having an average slope greater than 350% / μm.

[0153] The AF curve 1700 further includes a first intermediate portion 1710, a second intermediate portion 1712, and a third intermediate portion 1714. The first intermediate portion 1710 separates the second portion 1704 from the third portion 1706 and includes a section of the AF curve 1700 representing a surface height of about 0.1 μm. The first intermediate portion 1710 includes an average slope of about 150% / μm. The second intermediate portion 1712 is an inflection point of the AF curve 1700 that separates the third portion 1706 from the fourth portion 1708. The third intermediate portion 1714 extends between the fourth portion 1708 and the first portion 1702, and the third intermediate portion 1714 includes a section of the AF curve 1700 representing a surface height of about 0.06 μm. The third intermediate portion 1714 includes an average slope of about 133% / μm. Thus, the AF curve includes four vertical portions having an average slope greater than or equal to 350% / μm, where adjacent vertical portions are separated by intermediate portions that are: (a) a section of the AF curve representing a height of at least 50 nm with an average slope that is at least 50% / μm less than the adjacent vertical portion; or (b) an inflection point of the AF curve. The AF curves associated with Examples 15 and 16 exhibit similar characteristics, where a reduced amount of secondary etching results in vertical portions with a larger slope and intermediate portions with a smaller slope.

[0154] Bidirectional reflectance distribution function (BRDF) measurements were performed on Examples 15 through 17. The measurements were performed in reflection mode using a REFLET 180S system from Synopsys, Inc. The measurement wavelength range was from 400 nm to 1700 nm, and the light incident angle was 10°. Figure 18 is a plot of the scattering amplitude in (sr -1 ) as a function of the viewing angle. As shown, the sample with the characteristic rounding exhibits lower scattering intensity at scattering angles greater than or equal to 30°. For the actual (non-normalized) BRDF amplitude, each of Examples 16 and 17 exhibits a BRDF amplitude of less than 3 x 10 -5 sr -1 at a 30° scattering angle, while Example 15 exhibits a BRDF amplitude of 9 x 10 -4 sr -1 and the control exhibits a BRDF amplitude of 1.5 x 10 -3 sr -1 at a 30° scattering angle.

[0155] It is generally believed that, relative to samples fabricated using a single sub-etch step, samples fabricated with multiple sub-etch steps in the main etch step tend to have increased specularity and haze. However, in a multiple sub-etch step design, the specular reflection and coupled clarity of the image can be significantly reduced. The presence of multiple layers enables interference suppression of specular reflection over a wide optical bandwidth. Typically, the design used will be determined by the performance attributes desired for a particular application. A single sub-etch design may be desired in applications where low haze, specularity, and excellent wash performance are desired (such as in automotive interior displays), while applications requiring excellent specular reflectance reduction and / or DOI may be suitable for a multiple sub-etch design.

[0156] Examples 18 to 22

[0157] Examples 18 to 22 were fabricated in a manner similar to Examples 6 to 11 herein (using a single sub-etch step main etch step followed by a secondary etch step with varying time lengths). The main etch step of Examples 18 to 22 was designed such that the unetched portion of the first main surface 18 during the main etch step occupied approximately 75% of the total surface area of the scattering region 70. Doing so results in a fill rate of close to 50% with such a height difference after the secondary etch step. It is believed that such a 50% fill rate is associated with excellent specular reflection performance. The secondary etch step varied between 9 minutes and 13 minutes. After the secondary etch step, the amount of the scattering region 20 disposed at the etch depth of the main etch step relative to the base surface 30 decreased proportionally with the length of the secondary etch step. A longer secondary etch step resulted in a greater percentage decrease in the fill rate associated with the portion of the scattering region disposed at the etch depth of the main etch step relative to the base surface 30 after the secondary etch step. The optical properties of the examples and comparative examples generated using a random, maskless-based HF etch process were measured. The results are shown in Table 2 below. Table 2

[0158] As shown, relative to the comparative examples, each of Examples 18 to 22 exhibited significantly lower specular reflectance (each exhibiting an Rs value of less than 6.2), DOI (each exhibiting a coupled DOI of less than 70%), and transmittance haze (each exhibiting a transmittance haze of less than 3%) than the comparative examples. In addition, each exhibited a wash as described herein greater than 0.7 1 The measured value (for light incident on the scattering region at an incident angle of 20° and a viewing angle of 0°) is a significant improvement over the comparative example. These results demonstrate the ability of the scattering regions described herein to achieve excellent scrub performance while minimizing or even having no negative impact on other optical properties, including haze, DOI, R-spec, PPD, and color breakup.

[0159] Example 23

[0160] Two samples were subjected to the CS8 abrasion test to determine whether the feature rounding provided by the method described herein provided any performance benefits from the perspective of abrasion resistance. Figure 19 are the surface height profile 1900 and histogram 1902 associated with the baseline surface design without secondary etching. As shown, the etch depth associated with the primary etch step is approximately 172 nm, and the surface is designed to have a 50% fill rate associated with the unetched portion of the first primary surface 18. Figure 20 shows the surface height profile 2000 and histogram 2002 associated with Example 23 after undergoing secondary etching (1M HF / 1M HCl for 2400 seconds (dip etch)), where Example 23 is based on Figure 19 the design modification shown in. As shown in histogram 2002, the secondary etching results in feature rounding, indicated by the broadening of the peaks and the increase in the count at the height between the peaks. This feature rounding is also associated with the inclined portions 40 of the plurality of structures 26 having a greater slope, such that the transition width is greater than Figure 19 that represented by the control.

[0161] Figures 19 - 20 The sample represented in was subjected to the CS8 abrasion test. In this test, a vertical load of 270 g was applied to a commercially available CS8 material (a rubber matrix containing particles embedded therein). The CS8 material was moved at a stroke length of 25 mm at a rate of 60 cycles per minute. The scattering region underwent 100 pad movement cycles. The results are shown in Figure 21A and Figure 21B in. Figure 21A shows the results for the control sample without secondary etching. Figure 21B Shows the results of Example 23. As shown, the feature rounding provided by the secondary etch results in a significant reduction in the visibility of wear tracks caused by particles. This visibility is quantified using a dark field light scattering imaging system. The system includes an annular light source (24 cm in diameter) that emits white light with an intensity of approximately 10,000 lux into the scattering region. A digital camera (placed at a linear distance of 25 cm from the sample) images the illuminated sample through the annular light source. The worn damage area has different light reflection characteristics compared to the unworn portion. The track visibility is defined by quantifying the contrast between the worn area and the unworn area. To this end, the image is digitized, and the intensity of each pixel is represented using grayscale, where 0 is black and 255 is white. A threshold is established for the unworn portion, and each pixel with a grayscale value above the threshold is classified as being associated with the worn portion. For each pixel classified as being associated with the worn portion, the visibility value of the track is calculated as follows: where I abraded is the measured pixel intensity associated with the pixel classified as being associated with the worn section, and I non-abraded is the measured pixel intensity associated with the nearest pixel classified as not being worn. Figure 22 Shows a histogram of the track visibility values of the pixels classified as being associated with the Figure 21A and 21B worn area of the sample depicted in. As shown, Example 23 exhibits an average track visibility of less than 20%, where the maximum track visibility value is less than 40%. The control sample without secondary etch exhibits an average track visibility of more than 40%, where the maximum value exceeds 85%. These results confirm the visual observations from Figure 21A and Figure 21B . The feature rounding provided by the secondary etch described herein results in less visible damage from abrasive particles, which is beneficial for touch applications that may encounter particulate debris.

[0162] Unless otherwise expressly stated, any method described herein should not be construed as requiring that its steps be performed in a particular order. Thus, when a method claim does not actually recite its steps as following a certain order or when it is not otherwise specifically indicated in the claims or the specification that the steps are limited to a particular order, no particular order is intended to be implied. Additionally, as used herein, "a" is intended to include one or more than one component or element and is not intended to be construed as meaning only one.

[0163] It will be apparent to those skilled in the art that various modifications and variations can be made without departing from the spirit or scope of the disclosed embodiments. Since those skilled in the art can combine the spirit and essence of the embodiments to make various improvements, combinations, sub-combinations and variations to the disclosed embodiments, the disclosed embodiments should be considered to include all the content within the scope of the appended claims and their equivalents.< / psd>

Claims

1. An article, comprising: a substrate, the substrate comprising: a first major surface; a second major surface, the second major surface being opposite to the first major surface; and a scattering region formed in the first major surface, wherein, within the scattering region, the first major surface comprises: a plurality of structures extending outward from the base plane of the first major surface, each of the plurality of structures extending from the base plane to a peak height, wherein: each of the plurality of structures comprises an inclined portion extending from the base plane and a peak portion provided at the peak height of the structure, the inclined portions of the plurality of structures constitute more than 5% of the total surface area of the scattering region, The 1x1mm part characterizing the scattering region 2 The Abbott-Firestone curve of the part includes: a first portion, the first portion representing the region of the scattering region closest to the base plane, a second portion, the second portion representing the peak portions of the plurality of structures, and an intermediate portion extending between the first portion and the second portion, and the intermediate portion comprises an average slope with an amplitude less than 420% / μm and greater than 5% / μm.

2. The article according to claim 1, wherein the inclined portion constitutes more than 50% of the total surface area of the scattering region.

3. The system according to claim 1, wherein at least some of the plurality of peak portions are etching depth portions disposed within 20 nm of the maximum peak height relative to the base plane, and the etching depth portions constitute 60% or less of the total surface area of the scattering region.

4. The article according to claim 3, wherein the etching depth portions constitute 40% or less of the total surface area of the scattering region.

5. The article according to any one of claims 1 to 4, wherein, the plurality of structures include a maximum feature size greater than or equal to 1 μm and less than 200 μm.

6. The article according to any one of claims 1 to 5, wherein at least some of the inclined portions extend a lateral distance greater than or equal to 1.0 μm and less than or equal to 10 μm between the base plane and the peak portions, wherein the lateral distance extended by the inclined portion is measured in a direction parallel to the surface normal of the inclined portion and parallel to the base plane.

7. The article according to claim 6, wherein the lateral distance is greater than or equal to 3.0 μm.

8. The article according to any one of claims 6 to 7, wherein each of the inclined portions includes a first edge disposed close to the base plane and a second edge disposed close to the peak region, and the slope of the first major surface varies in the direction along a 1 μm lateral distance at both the first edge and the second edge.

9. The article according to any one of claims 1 to 8, wherein the first portion and the second portion of the Abbott-Firestone curve are vertical portions having a slope with an amplitude greater than 350% / m.

10. The article according to claim 9, wherein Some of the peak portions are set within 20 nm of the maximum peak height relative to the base surface, and those peak portions are represented in the second portion of the Abbott-Firestone curve, and the Abbott-Firestone curve includes a third vertical portion that represents peak portions at peak heights set between the base surface and the maximum peak height.

11. The article of claim 10, wherein the Abbott-Firestone curve further comprises: a fourth vertical portion that represents additional peak portions at peak heights set between the base surface and the maximum peak height other than the height associated with the third vertical portion, wherein the intermediate portion is a first intermediate portion set between the first portion and the third vertical portion; a second intermediate portion that is set between the third vertical portion and the fourth vertical portion; and a third intermediate portion that is set between the fourth vertical portion and the second portion.

12. The article of claim 11, wherein each of the first intermediate portion, the second intermediate portion, and the third intermediate portion is: (a) a section of the Abbott-Firestone curve that represents a height of at least 50 nm with an average slope that is at least 50% / μm less than an adjacent vertical portion; or (b) an inflection point of the Abbott-Firestone curve.

13. The article of any one of claims 1 to 12, wherein the article exhibits: a haze of less than or equal to 3.5%, and a gloss of less than or equal to 2.5% when measured at 140 ppi.

14. The article according to any one of claims 1 to 13, wherein the bidirectional reflectance distribution function ("BRDF") of the article measured from white light incident on the first major surface at an incident angle of 10° exhibits an intensity of less than 1.2x10 -4 sr -1 at a scattering angle of 30° with respect to the specular surface.

15. The article of any one of claims 1 to 14, wherein when the article is viewed at a 0° angle of view and light having a luminance of 45000 lux is incident on the first major surface at an incident angle of 20°, the first average modulation transfer function of the article averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm is at least 0.

7.

16. The article of any one of claims 1 to 15, wherein, after the pad applies a 270 g force along a track for 100 cycles to the CS8 material acting on the scattering region, the scattering region exhibits a track visibility of less than or equal to 40%.

17. An article, comprising: a substrate that includes: a first major surface; a second major surface that is opposite the first major surface; and a scattering region that is formed in the first major surface, wherein within the scattering region, the first major surface includes: a plurality of structures that extend outward from the base surface of the first major surface, each of the plurality of structures extending from the base surface to a peak height, wherein: Each of the plurality of structures includes an inclined portion extending from the base surface and a peak portion disposed at the peak height of the structure, such that the scattering region includes a plurality of inclined portions and a plurality of peak portions. At least some of the inclined portions have a lateral distance between the base surface and the peak portion that is greater than or equal to 1.0 μm and less than or equal to 10 μm. The lateral distance extended by the inclined portion is measured in a direction parallel to the surface normal of the inclined portion and parallel to the base surface. The inclined portions of the plurality of structures constitute more than 5% of the total surface area of the scattering region, and The 1x1 mm part characterizing the scattering region 2 The Abbott-Firestone curve of the part does not include any horizontal part representing a height of at least 0.05 μm with a slope having an amplitude of less than 40% / μm between the height of the base surface and the peak height of the scattering region.

18. The article according to claim 17, wherein the inclined portions constitute more than 5% of the total surface area of the scattering region.

19. The article according to any one of claims 17 to 18, wherein at least some of the plurality of peak portions are etched depth portions disposed within 20 nm of the maximum peak height relative to the base surface, and the etched depth portions constitute 60% or less of the total surface area of the scattering region.

20. The article according to claim 19, wherein the etched depth portions constitute 40% or less of the total surface area of the scattering region.

21. The article according to any one of claims 17 to 20, wherein, the plurality of structures include a maximum feature size that is greater than or equal to 1 μm and less than 200 μm.

22. The article according to any one of claims 17 to 21, wherein the inclined portion of each structure includes a first edge disposed near the base surface and a second edge disposed near the peak region, wherein, the slope of the first main surface varies in the direction along a 1-μm lateral distance at both the first edge and the second edge.

23. The article according to any one of claims 17 to 22, wherein the Abbot-Firestone curve includes: a first portion that represents the region of the scattering region closest to the base surface, a second portion that represents the peak portions of the plurality of structures, and an intermediate portion that extends between the first portion and the second portion, the intermediate portion includes an average slope that is less than 420% / μm and greater than 5% / μm, the first portion and the second portion of the Abbot-Firestone curve are vertical portions having a slope with an amplitude greater than 350% / μm, and some of the peak portions are disposed within 20 nm of the maximum peak height, and those peak portions are represented in the second portion of the Abbot-Firestone curve.

24. The article according to claim 23, wherein the Abbot-Firestone curve includes a third vertical portion that represents peak portions disposed at a height between the base surface and the maximum peak height.

25. The article according to claim 24, wherein the Abbot-Firestone curve further includes: A fourth vertical portion, the fourth vertical portion representing an additional peak portion at a peak height between the base surface and the maximum peak height, other than the height associated with the third vertical portion, where the intermediate portion is a first intermediate portion disposed between the first portion and the third vertical portion; A second intermediate portion, the second intermediate portion being disposed between the third vertical portion and the fourth vertical portion; and A third intermediate portion, the third intermediate portion being disposed between the fourth vertical portion and the second portion.

26. The article according to claim 25, wherein each of the first intermediate portion, the second intermediate portion, and the third intermediate portion is: (a) a section of the Abbott-Firestone curve representing a height of at least 50 nm with an average slope of at least 50% / μm less than that of an adjacent vertical portion; or (b) an inflection point of the Abbott-Firestone curve.

27. The article according to any one of claims 17 to 26, wherein the article exhibits: a haze transmission of less than or equal to 3.5%, and a flare of less than or equal to 2.5% when measured at 140 ppi.

28. The article according to any one of claims 17 to 27, wherein the bidirectional reflectance distribution function ("BRDF") of the article measured from white light incident on the first major surface at an incident angle of 10° exhibits an intensity of less than 1.2x10 -4 sr -1 at a scattering angle of 30° relative to the specular surface.

29. The article according to any one of claims 17 to 28, wherein when the article is viewed at a 0° angle of view and light with a brightness of 45000 lux is incident on the first major surface at an incident angle of 20°, the first average modulation transfer function of the article averaged at spatial frequencies of 1.67 cycles / mm, 4.11 cycles / mm, 7.33 cycles / mm, 10.38 cycles / mm, and 13.08 cycles / mm is at least 0.

7.

30. The article according to any one of claims 17 to 29, wherein, after the pad applies a 270 g force along a trajectory for 100 cycles to the CS8 material acting on the scattering region, the scattering region exhibits a trajectory visibility of less than or equal to 40%.

31. A method of forming a scattering region of a substrate for a display article, the method comprising: determining a pattern of a plurality of structures on a first major surface of the substrate, wherein each of the plurality of structures includes a surface region disposed at a height measured relative to a base surface extending through the display article; disposing one or more etching masks on the first major surface, the one or more etching masks allowing etching only on selected regions of the first major surface to form at least some of the plurality of structures; and after each of the one or more etching masks is disposed on the first major surface, bringing the display article into contact with an etchant for a period of time to form the plurality of structures in a main etching step, removing the one or more etching masks from the first major surface, and exposing the entire scattering region to a secondary etchant such that the plurality of structures include inclined portions and the corners of the plurality of structures are rounded.

32. The method according to claim 31, wherein the overall exposure of the scattering region to the secondary etchant comprises immersing the article in a second etchant solution comprising a concentration ratio of HF to HCl of from 0.5 M HF / 0.5 M HCl to 3 M HF / 3 M HCl, such that the etching rate of the article is greater than 0.5 m / min.

33. The method according to claim 31, wherein the overall exposure of the scattering region to the secondary etchant comprises spraying the article with a second etchant solution comprising a concentration ratio of HF to HCl of from 16 mM HF / 20 mM HCl to 160 mM HF / 200 mM HCl to achieve an etching rate of from 0.1 m / min to 1 μm / min.

34. The method according to any one of claims 31 to 33, wherein, the overall exposure of the scattering region to the secondary etchant is carried out for a secondary etching cycle of less than or equal to 20 minutes, such that less than or equal to 20 μm of material is removed from the scattering region.

35. The method according to any one of claims 31 to 34, wherein after the main etching step, the plurality of structures comprise a plurality of regions of the first main surface disposed at different heights relative to the base surface, wherein the heights differ from each other by 20 nm to 200 nm in a direction perpendicular to the base surface.

36. The method according to any one of claims 31 to 35, wherein the overall exposure of the scattering region to the secondary etchant reduces the filling rate of the scattering region composed of the unetched portion of the article in the main etching step by at least 5%.

Images