Ultrasonic nanogeometric shape control process and method

Abstract

To provide a suitable ultrasonic nanogeometric shape control process and method. [Solution] A system and method for manufacturing nanostructures on a substrate that can be used for display eyepieces, for example, in head-wearable devices is disclosed. Manufacturing and / or etching the substrate may include immersing the substrate in a bath and applying ultrasonic treatment to the bath over a first period of time. The ultrasonic treatment applied to the first bath may agitate the fluid to provide a substantially uniform first reactive environment across the surface of the substrate. The substrate may be immersed in a second bath, and ultrasonic treatment may be applied to the second bath over a second period of time. The ultrasonic treatment applied to the second bath may agitate the fluid to provide a substantially uniform second reactive environment across the surface of the substrate. A predetermined amount of material may be removed from the surface of the substrate during the second period to produce an etched substrate.

Description

Technical Field

[0004] , ,

[0001] Cross - reference to Related Applications This application claims priority to U.S. Provisional Patent Application No. 63 / 177,294, filed on April 20, 2021, the content of which is hereby incorporated by reference in its entirety.

[0002] Field The present disclosure generally relates to systems and methods for displaying visual information, and more particularly, to an eyewear for displaying visual information in an augmented reality or mixed reality environment. More specifically, the present disclosure relates to systems and methods for manufacturing a lattice used in eyewear for displaying visual information in an augmented reality or mixed reality environment.

Background Art

[0003] Background Virtual environments are ubiquitous in computing environments and are used in video games (where the virtual environment can represent a game world); maps (where the virtual environment can represent the terrain to be navigated); simulations (where the virtual environment can simulate a real - world environment); digital storytelling (where virtual characters can interact with each other in the virtual environment); and many other applications. Modern computer users generally perceive and interact with virtual environments comfortably. However, the user experience with virtual environments can be limited by the technology used to present the virtual environment. For example, conventional displays (e.g., 2D display screens) and audio systems (e.g., fixed speakers) may not be able to realize a virtual environment in a way that creates an engaging, realistic, and immersive experience.

[0004] Virtual reality ("VR"), augmented reality ("AR"), mixed reality ("MR"), and related technologies (collectively "XR") share the ability to present users of XR systems with sensory information corresponding to a virtual environment represented by data within a computer system. This disclosure assumes distinctions between VR systems, AR systems, and MR systems (however, some systems may be classified as VR in one aspect (e.g., a visual aspect) and simultaneously as AR or MR in another aspect (e.g., an auditory aspect)). As used herein, a VR system presents a virtual environment that replaces the user's real environment in at least one aspect. For example, a VR system may present a user with a view of the virtual environment while simultaneously obscuring the view of the real environment, such as by using a light-shielding head-mounted display. Similarly, a VR system may present a user with audio corresponding to the virtual environment while simultaneously blocking (attenuating) audio from the real environment.

[0005] VR systems can experience various drawbacks stemming from replacing the user's real-world environment with a virtual one. One drawback is the sensation of motion sickness that can occur when the user's field of view in the virtual environment no longer corresponds to the state of their inner ear that detects their balance and orientation in the real (non-virtual) environment. Similarly, users may experience disorientation in a VR environment where they cannot directly see their own body and limbs (the view on which the user feels "grounded" in the real world). Another drawback is the computational load (e.g., storage, processing power) imposed on VR systems, especially in real-time applications that aim to immerse the user in the virtual environment, as they must present a complete 3D virtual environment. Likewise, users tend to be sensitive to even slight imperfections in the virtual environment, any of which can detract from the sense of immersion; therefore, such environments may need to reach a very high standard of presence to be considered immersive. Furthermore, another drawback of VR systems is that such applications of the system cannot utilize the wide range of sensory data from the real world, such as the various sights and sounds experienced in the real world. A related drawback is that VR systems can sometimes struggle to create shared environments where multiple users can interact, because users sharing a physical space in the real world may not be able to see or interact with each other directly in the virtual environment.

[0006] As used herein, an AR system presents a virtual environment that overlaps with or overlays the real environment in at least one aspect. For example, an AR system can present a user with a view of the virtual environment overlaid on the user's view of the real environment, such as a transparent head-mounted display that presents a display image while allowing light to pass through the display and enter the user's eyes. Similarly, an AR system can present a user with audio corresponding to the virtual environment while simultaneously mixing audio from the real environment. Likewise, as used herein, an MR system, like an AR system, can present a virtual environment that overlaps with or overlays the real environment in at least one aspect, and further, the virtual environment within the MR system may enable interaction with the real environment in at least one aspect. For example, a virtual character in the virtual environment may toggle a light switch in the real environment, turning a corresponding light bulb in the real environment on or off. As another example, a virtual character may react (e.g., with facial expressions) to audio signals in the real environment. By maintaining the presentation of the real environment, AR and MR systems can avoid some of the aforementioned shortcomings of VR systems. For example, visual cues from the real environment (including the user's own body) can remain visible, and such systems do not need to present the user with a fully realized 3D environment for immersion, thus reducing user motion sickness. Furthermore, AR and MR systems can utilize sensory input from the real world (e.g., scenery, objects, and the views and sounds of other users) to create new applications that enhance that input.

[0007] Presenting a virtual environment in a realistic way and creating a robust and cost-effective user immersion experience can be challenging. For example, a head-mounted display may include an optical system with one or more multilayer eyepieces, which can be expensive and fragile components. Each layer, for instance, may be manufactured through a complex process involving multiple steps to achieve a diffraction grating and associated film for effectively projecting a digital image to the user. The diffraction grating may include, for example, a multilayer structure formed on the nanoscale. While these multilayer structures can be manufactured using lithography processes, such processes can be expensive, and achieving the desired geometric shape at the nanoscale can be difficult. For example, manufacturing a sub-50 nm nanostructure with high fidelity (no breaks, smooth line edges) may require the use of expensive lithography techniques such as E-beam lithography to achieve the desired nanostructure resolution. Even with such lithography techniques, aligning components to manufacture the lithography master and / or final product at the nanometer scale can be difficult, and the resulting nanostructure may be prone to uneven line edge roughness (LER). Therefore, there is a need for an inexpensive process for manufacturing multilayer nanoscale structures.

[0008] To address the problems associated with expensive lithography techniques used to fabricate nanostructures, the systems and methods according to embodiments of the present disclosure rely on an ultrasonic process for etching and forming desired nanostructures on a substrate. For example, embodiments of the present disclosure may use an ultrasonic sequencing process to achieve desired etching selectivity of different material layers deposited on a substrate. The ultrasonic sequencing process may include immersing the substrate in a bath of a base solution, an acid solution, and / or water and applying ultrasonic treatment to the bath. Systems and methods according to embodiments of the present disclosure can etch, for example, silicon-based structures, such as Si, SiO2, Si3N4, etc., and have multilayer nanostructures with high fidelity, smooth LER, and consistent alignment between batches. [Overview of the project] [Means for solving the problem]

[0009] overview This specification discloses systems and methods for manufacturing nanostructures on a substrate. A substrate containing multiple nanostructures can be used for eyepieces for displays such as headwearable devices. An exemplary method for manufacturing and / or etching a substrate containing multiple nanostructures for eyepieces may include immersing the substrate in a bath and applying sonication to the bath over a first period. The sonication applied to the first bath can agitate the fluid to provide a substantially uniform first reactive environment across the surface of the substrate. The substrate may be immersed in a second bath, and sonication may be applied to the second bath over a second period. The sonication applied to the second bath can agitate the fluid to provide a substantially uniform second reactive environment across the surface of the substrate. In some examples, a predetermined amount of material may be removed from the surface of the substrate during the second period to produce an etched substrate. In some examples, the predetermined amount of material to be removed may depend on the length of the first period and further on the length of the second period. Embodiments of this specification provide systems and methods for inexpensively manufacturing nanostructures of less than 50 nm with high fidelity (no breaks, smooth line edges) to achieve a desired nanostructure resolution. Furthermore, embodiments of this specification provide systems and methods for achieving interlayer alignment of nanostructures having smooth line edge roughness (LER). This specification also provides, for example, the following: (Item 1) A method for etching a substrate containing multiple nanostructures, wherein the method is The method involves immersing the substrate in a first bath, wherein the first bath contains a first fluid. The method involves applying ultrasonic treatment to the first bath over a first period of time, wherein the application of ultrasonic treatment stirs the first fluid to provide a substantially uniform first reactive environment across the surface of the substrate. The method involves immersing the substrate in a second bath, wherein the second bath contains a second fluid. The method involves applying ultrasonic treatment to the second bath over a second period, wherein the application of ultrasonic treatment agitates the second fluid to provide a substantially uniform second reactive environment over the surface of the substrate, and a predetermined amount of material is removed from the surface of the substrate during the second period to produce an etched substrate. Includes, A method in which the amount of the material is predetermined based on the length of the first period and further based on the length of the second period. (Item 2) The method according to item 1, wherein the thickness of the predetermined amount of material removed from the surface is in the range of 5 to 50 nm. (Item 3) The method according to item 1, wherein the predetermined amount of material is uniformly removed from the surface of the substrate such that the cross-sections of the plurality of nanostructures of the etched substrate are symmetrical. (Item 4) The substrate comprises a base containing a first material, The nanostructures of the plurality of nanostructures are arranged on the base, and the nanostructures include a first layer, the first layer includes a second material different from the first material, The nanostructures of the plurality of nanostructures have substantially uniform widths. The base is associated with a first etching rate of a first set of ultrasonic treatment conditions, and the first layer is associated with a second etching rate of the first set of ultrasonic treatment conditions. The method described in item 1. (Item 5) The method according to item 4, wherein each of the plurality of nanostructures has a geometric shape corresponding to one of a stepped shape, a concave shape, and a blazed shape. (Item 6) The ultrasonic treatment conditions of the first set are: The temperature associated with one or more of the first bath and the second bath, The time length associated with the first period, The time length associated with the second period, The concentration of the acid solution, and Concentration of base solution The method described in item 4, which includes one or more of the following. (Item 7) The method according to item 1, wherein the substrate is formed from at least one of silicon, silicon dioxide, and silicon nitride. (Item 8) The acid solution is the method described in item 1, wherein the acid solution contains sulfuric acid at a concentration of approximately 2% in water. (Item 9) The aforementioned base solution is the method according to item 1, wherein the base solution contains water at a concentration of approximately 2% hydrogen peroxide or potassium hydroxide. (Item 10) Depositing a mask on one or more surfaces of the substrate, Removing one or more portions of the mask from the substrate It further includes, The method according to item 1, wherein at least a portion of the surface of the substrate is masked during the second period. (Item 11) It is a compound, A base material, A base having a first surface, Multiple nanostructures arranged on the first surface and A base material comprising Equipped with, The substrate is configured to be etched by applying an ultrasonic processing sequence to the substrate to form an etched substrate, and the etched substrate includes a plurality of etched nanostructures. The etched nanostructure is a compound produced by removing a first predetermined amount of material from the first surface and further removing a second predetermined amount of material from one or more surfaces of the plurality of nanostructures. (Item 12) The compound according to item 11, wherein the thickness of the predetermined amount of material removed from the first surface is in the range of 5 to 50 nm. (Item 13) The compound according to item 11, wherein the predetermined amount of material is uniformly removed from the first surface and further uniformly removed from one or more surfaces of the plurality of nanostructures such that the cross-sections of the plurality of etched nanostructures of the etched substrate are symmetrical. (Item 14) The ultrasonic processing sequence is The method involves immersing the substrate in a first bath, wherein the first bath contains a first fluid. The method involves applying ultrasonic treatment to the first bath over a first period of time, wherein the application of ultrasonic treatment stirs the first fluid to provide a substantially uniform first reactive environment over the first surface of the substrate. The method involves immersing the substrate in a second bath, wherein the second bath contains a second fluid. The method involves applying ultrasonic treatment to the second bath over a second period, wherein the application of ultrasonic treatment agitates the second fluid to provide a substantially uniform second reactive environment over the first surface of the substrate, and the predetermined amount of material is removed during the second period to produce an etched substrate. Includes, The amount of the material is predetermined based on the length of the first period and further based on the length of the second period, according to item 11. (Item 15) The base comprises a first material, The nanostructure of the plurality of nanostructures includes a first layer, and the first layer includes a second material different from the first material. The base is associated with a first etching rate for a first set of ultrasonic treatment conditions, The first layer is associated with a second etching rate for the first set of ultrasonic treatment conditions. The compound listed in item 14. (Item 16) Each of the aforementioned nanostructures has a substantially uniform width. The compound according to item 15, wherein each etched nanostructure of the plurality of nanostructures has a geometric shape corresponding to one of a step shape, a concave shape, and a blazed shape. (Item 17) The ultrasonic treatment conditions of the first set are: The temperature associated with one or more of the first bath and the second bath, The time length associated with the first period, The time length associated with the second period, The concentration of the acid solution, and Concentration of the base solution A compound listed in item 15, containing one or more of the following. (Item 18) The acid solution is the compound described in item 14, containing approximately 2% sulfuric acid in water. (Item 19) The aforementioned base solution is the compound described in item 14, containing approximately 2% hydrogen peroxide or potassium hydroxide in water. (Item 20) The substrate is the compound according to item 11, formed from at least one of silicon, silicon dioxide, and silicon nitride. [Brief explanation of the drawing]

[0010] [Figure 1A] Figures 1A to 1C illustrate exemplary mixed reality environments relating to one or more embodiments of the present disclosure. [Figure 1B]Figures 1A to 1C illustrate exemplary mixed reality environments relating to one or more embodiments of the present disclosure. [Figure 1C] Figures 1A to 1C illustrate exemplary mixed reality environments relating to one or more embodiments of the present disclosure.

[0011] [Figure 2A] Figures 2A to 2D illustrate components of an exemplary mixed reality system that can be used to generate and interact with a mixed reality environment, according to one or more embodiments of the present disclosure. [Figure 2B] Figures 2A to 2D illustrate components of an exemplary mixed reality system that can be used to generate and interact with a mixed reality environment, according to one or more embodiments of the present disclosure. [Figure 2C] Figures 2A to 2D illustrate components of an exemplary mixed reality system that can be used to generate and interact with a mixed reality environment, according to one or more embodiments of the present disclosure. [Figure 2D] Figures 2A to 2D illustrate components of an exemplary mixed reality system that can be used to generate and interact with a mixed reality environment, according to one or more embodiments of the present disclosure.

[0012] [Figure 3A] Figure 3A shows an exemplary mixed reality handheld controller that can be used to provide input to a mixed reality environment, according to one or more embodiments of the present disclosure.

[0013] [Figure 3B] Figure 3B shows an exemplary auxiliary unit that can be used with an exemplary mixed reality system according to one or more embodiments of the present disclosure.

[0014] [Figure 4] Figure 4 shows an exemplary functional block diagram of an exemplary mixed reality system according to one or more embodiments of the present disclosure.

[0015] [Figure 5] Figure 5 shows an exemplary ultrasonic processing configuration according to one or more embodiments of the present disclosure.

[0016] [Figure 6] Figures 6A and 6B show exemplary nanostructures for exemplary mixed reality systems, fabricated according to one or more embodiments of the present disclosure.

[0017] [Figure 7] Figures 7A–7C show exemplary nanostructures for exemplary mixed reality systems, fabricated according to one or more embodiments of the present disclosure.

[0018] [Figure 8] Figures 8A and 8B show exemplary nanostructures for exemplary mixed reality systems, fabricated according to one or more embodiments of the present disclosure.

[0019] [Figure 9] Figures 9A and 9B show exemplary nanostructures for exemplary mixed reality systems, fabricated according to one or more embodiments of the present disclosure.

[0020] [Figure 10] Figures 10A and 10B show exemplary nanostructures for exemplary mixed reality systems, fabricated according to one or more embodiments of the present disclosure.

[0021] [Figure 11] Figures 11A–11C show exemplary nanostructures for exemplary mixed reality systems according to one or more embodiments of the present disclosure.

[0022] [Figure 12] Figures 12A–12C show exemplary nanostructures for exemplary mixed reality systems according to one or more embodiments of the present disclosure.

[0023] [Figure 13] Figures 13A–13E show exemplary nanostructures for exemplary mixed reality systems according to one or more embodiments of the present disclosure.

[0024] [Figure 14] Figure 14 shows an exemplary block diagram of a process for fabricating nanostructures for exemplary mixed reality systems according to one or more embodiments of the present disclosure.

[0025] [Figure 15] Figure 15 shows an exemplary block diagram of a process for fabricating nanostructures for exemplary mixed reality systems according to one or more embodiments of the present disclosure.

[0026] [Figure 16] Figure 16 shows an exemplary block diagram of a process for fabricating nanostructures for exemplary mixed reality systems according to one or more embodiments of the present disclosure. [Modes for carrying out the invention]

[0027] Detailed explanation The following examples refer to the accompanying drawings illustrating specific examples that form part of this specification and can be implemented. It should be understood that other examples may be used and structural modifications may be made without departing from the scope of the disclosed examples.

[0028] Mixed reality environment Like all people, users of a mixed reality system are present in the real environment, that is, in all three-dimensional parts and contents of the "real world" that are perceptible to the user. For example, the user perceives the real environment using their normal human senses (sight, sound, touch, taste, smell) and interacts with the real environment by moving their body within it. A position in the real environment can be described as coordinates in coordinate space. For example, coordinates can include latitude, longitude, and altitude relative to sea level; distance in three orthogonal dimensions from a reference point; or other appropriate values. Similarly, vectors can describe quantities that have direction and magnitude in coordinate space.

[0029] A computing device can maintain a representation of a virtual environment in, for example, the memory associated with the device. As used herein, a virtual environment is a computational representation of a three-dimensional space. A virtual environment can include representations of any object, action, signal, parameter, coordinate, vector, or other properties associated with that space. In some examples, the circuitry of a computing device (e.g., a processor) can maintain and update the state of a virtual environment. That is, the processor can determine the state of the virtual environment at a second time t1 based on data associated with the virtual environment and / or inputs provided by the user at a first time t0. For example, if an object in the virtual environment is located at a first coordinate at time t0 and has certain programmed physical parameters (e.g., mass, coefficient of friction), the input received from the user instructs that a force should be applied to the object in a direction vector. The processor can apply the laws of kinematics to determine the object's position at time t1 using basic mechanics. The processor can determine the state of the virtual environment at time t1 using any appropriate information known about the virtual environment and / or any appropriate inputs. When maintaining and updating the state of a virtual environment, the processor may run any appropriate software, including: software related to the creation and deletion of virtual objects in the virtual environment; software for defining the behavior of virtual objects or characters in the virtual environment (e.g., scripts); software for defining the behavior of signals in the virtual environment (e.g., audio signals); software for creating and updating parameters associated with the virtual environment; software for generating audio signals in the virtual environment; software for handling input and output; software for implementing network operations; software for applying asset data (e.g., animation data for moving virtual objects over time); or many other possibilities.

[0030] Output devices such as displays or speakers can present any or all aspects of a virtual environment to the user. For example, a virtual environment may include virtual objects that can be presented to the user (this may include representations of inanimate objects; people; animals; lights, etc.). A processor can determine the view of the virtual environment (e.g., corresponding to a “camera” with origin coordinates, view axes, and a frustum) and render a viewable scene of the virtual environment corresponding to that view on the display. Any suitable rendering technique may be used for this purpose. In some examples, the viewable scene may include only some virtual objects in the virtual environment and exclude certain other virtual objects. Similarly, a virtual environment may include audio aspects that can be presented to the user as one or more audio signals. For example, virtual objects in a virtual environment may generate sounds resulting from the object’s position coordinates (e.g., a virtual character may speak or produce sound effects). Alternatively, a virtual environment may be associated with musical cues or ambient sounds that may or may not be associated with a specific location. The processor can handle audio signals corresponding to "listener" coordinates, such as the synthesis of sounds within a virtual environment, determine a mixed and processed audio signal to simulate the audio signal heard by the listener at listener coordinates, and present the audio signal to the user through one or more speakers.

[0031] Because virtual environments exist only as computational structures, users cannot directly perceive them using their normal senses. Instead, users can only perceive virtual environments indirectly, such as through displays, speakers, or haptic output devices. Similarly, while users cannot directly touch, manipulate, or interact with virtual environments, they can provide input data via input devices or sensors to a processor that can use the device or sensor data to update the virtual environment. For example, a camera sensor can provide optical data indicating that the user is attempting to move an object within the virtual environment, and the processor can use that data to cause the object to respond accordingly within the virtual environment.

[0032] A mixed reality system can present a user with a mixed reality environment ("MRE") that combines aspects of the real and virtual environments, for example, using a transparent display and / or one or more speakers (which may be incorporated, for example, into a wearable head device). In some embodiments, one or more speakers may be located outside the head-mounted wearable unit. As used herein, an MRE is a simultaneous representation of the real environment and its corresponding virtual environment. In some examples, the corresponding real and virtual environments share a single coordinate space. In some examples, the real coordinate space and the corresponding virtual coordinate space are related to each other by a transformation matrix (or other suitable representation). Thus, a single coordinate (in some examples, together with the transformation matrix) can define a first location in the real environment and a second corresponding location in the virtual environment, and vice versa.

[0033] In MRE, virtual objects (e.g., in a virtual environment associated with the MRE) can correspond to real-world objects (e.g., in a real-world environment associated with the MRE). For example, if the real-world environment of the MRE includes a real-world ramp post (real-world object) at its position coordinates, the virtual environment of the MRE may include a virtual ramp post (virtual object) at its corresponding position coordinates. As used herein, a real-world object, combined with its corresponding virtual object, constitutes a "mixed-reality object." A virtual object does not need to perfectly match or align with its corresponding real-world object. In some examples, a virtual object can be a simplified version of its corresponding real-world object. For example, if the real-world environment includes a real-world ramp post, the corresponding virtual object may include a cylinder with approximately the same height and radius as the real-world ramp post (reflecting that the ramp post can have a nearly cylindrical shape). Simplifying virtual objects in this way can improve computational efficiency and simplify the calculations performed on such virtual objects. Furthermore, in some examples of MRE, not all real-world objects in the real-world environment are necessarily associated with corresponding virtual objects. Similarly, in some MRE examples, not all virtual objects within the virtual environment are necessarily associated with corresponding real-world objects. That is, some virtual objects may exist only within the MRE's virtual environment without any real-world counterparts.

[0034] In some examples, virtual objects may have properties that sometimes differ significantly from those of their corresponding real-world objects. For instance, a real-world environment within an MRE might contain a green, two-armed cactus (a thorny, inanimate object), while a corresponding virtual object within the MRE might possess the characteristics of a green, two-armed virtual character with human facial features and an expressionless face. In this example, the virtual object resembles its corresponding real-world object in certain properties (color, number of arms), but differs in other properties (facial features, personality). In this way, virtual objects can represent real-world objects in creative, abstract, exaggerated, or imaginative ways, or otherwise give behavior (e.g., human personality) to inanimate real-world objects. In some examples, virtual objects may be purely imaginative creations with no real-world counterparts (e.g., a virtual monster in a virtual environment that, in some cases, occupies a position corresponding to an empty space in the real-world environment).

[0035] Compared to VR systems, which present a virtual environment to the user while obscuring the real environment, mixed reality systems presenting MRE offer the advantage that the real environment remains perceptible while the virtual environment is being presented. Therefore, users of mixed reality systems can experience and interact with the corresponding virtual environment using visual and auditory cues associated with the real environment. For example, as mentioned above, users of VR systems may struggle to perceive or interact with virtual objects displayed in the virtual environment because they cannot directly perceive or interact with the virtual environment. However, users of MR systems may find it intuitive and natural to interact with virtual objects by seeing, hearing, and touching the corresponding real objects within their own real environment. This level of interactivity can enhance the user's sense of immersion, connection, and engagement with the virtual environment. Similarly, by presenting the real and virtual environments simultaneously, mixed reality systems can reduce the negative psychological (e.g., cognitive dissonance) and negative physical (e.g., motion sickness) associated with VR systems. Mixed reality systems further offer many possibilities for applications that can enhance or modify the experience of the real world.

[0036] Figure 1A shows an exemplary reality environment 100 in which a user 110 uses a mixed reality system 112. The mixed reality system 112 may include a display (e.g., a transparent display) and one or more speakers, as well as one or more sensors (e.g., a camera), as described below, for example. The illustrated reality environment 100 includes a rectangular room 104A in which the user 110 is standing, and reality objects 122A (a lamp), 124A (a table), 126A (a sofa), and 128A (a painting). Room 104A further includes position coordinates 106, which can be considered the origin of the reality environment 100. As shown in Figure 1A, an environment / world coordinate system 108 (including x-axis 108X, y-axis 108Y, and z-axis 108Z) having its origin 106 (world coordinates) can define the coordinate space of the reality environment 100. In some embodiments, the origin 106 of the environment / world coordinate system 108 may correspond to the location where the mixed reality system 112 is powered on. In some embodiments, the origin 106 of the environment / world coordinate system 108 may be reset during operation. In some examples, the user 110 may be considered a real object in the real environment 100. Similarly, parts of the user 110's body (e.g., hands, feet) may be considered real objects in the real environment 100. In some examples, a user / listener / head coordinate system 114 (including x-axis 114X, y-axis 114Y, and z-axis 114Z) with point 115 (e.g., user / listener / head coordinate) as its origin can define a coordinate space for the user / listener / head on which the mixed reality system 112 is positioned. The origin 115 of the user / listener / head coordinate system 114 may be defined for one or more components of the mixed reality system 112. For example, the origin 115 of the user / listener / head coordinate system 114 may be defined relative to the display of the mixed reality system 112, such as during the initial calibration of the mixed reality system 112. Matrices (which may include translation matrices and quaternion matrices or other rotation matrices), or other suitable representations, can characterize the transformation between the user / listener / head coordinate system 114 space and the environment / world coordinate system 108 space.In some embodiments, the left ear coordinates 116 and the right ear coordinates 117 may be defined relative to the origin 115 of the user / listener / head coordinate system 114. Matrices (which may include translation matrices and quaternion matrices or other rotation matrices), or other suitable representations, can characterize the transformation between the left ear coordinates 116 and the right ear coordinates 117 and the user / listener / head coordinate system 114 space. The user / listener / head coordinate system 114 can simplify the representation of the user's head, or the position of a head-mounted device relative to, for example, the environment / world coordinate system 108. The transformation between the user coordinate system 114 and the environment coordinate system 108 can be determined and updated in real time using simultaneous localization and mapping (SLAM), visual odometry, or other techniques.

[0037] Figure 1B shows an exemplary virtual environment 130 corresponding to a real environment 100. The illustrated virtual environment 130 includes a virtual rectangular room 104B corresponding to a real rectangular room 104A, and virtual objects 122B corresponding to a real object 122A; virtual object 124B corresponding to a real object 124A; and virtual object 126B corresponding to a real object 126A. The metadata associated with virtual objects 122B, 124B, and 126B may include information derived from the corresponding real objects 122A, 124A, and 126A. The virtual environment 130 further includes a virtual monster 132 that does not correspond to any real object in the real environment 100. Real object 128A in the real environment 100 does not correspond to any virtual object in the virtual environment 130. A persistent coordinate system 133 (including x-axis 133X, y-axis 133Y, and z-axis 133Z) with point 134 as its origin (persistent coordinates) can define the coordinate space of the virtual content. The origin 134 of the persistent coordinate system 133 may be defined with respect to / relative to one or more real objects, such as real object 126A. Matrices (which may include translation matrices and quaternion matrices or other rotation matrices), or other suitable representations, can characterize transformations between the persistent coordinate system 133 space and the environment / world coordinate system 108 space. In some embodiments, each of the virtual objects 122B, 124B, 126B, and 132 may have its own persistent coordinate point with respect to the origin 134 of the persistent coordinate system 133. In some embodiments, there may be multiple persistent coordinate systems, and each of the virtual objects 122B, 124B, 126B, and 132 may have its own persistent coordinate point with respect to one or more persistent coordinate systems.

[0038] Persistent coordinate data can be coordinate data that persists with respect to the physical environment. Persistent coordinate data may be used by an MR system (e.g., MR systems 112, 200) to position persistent virtual content, and the persistent virtual content does not have to be tied to the movement of the display on which the virtual object is displayed. For example, a two-dimensional screen may only display a virtual object relative to its position on the screen. As the two-dimensional screen moves, the virtual content may move with the screen. In some embodiments, persistent virtual content may be displayed in the corner of a room. The MR user may look at the corner, see the virtual content, look out from the corner (the virtual content may no longer be visible because, due to the user's head movement, it may have moved from within the user's field of view to outside of it), or look behind them and see the virtual content in the corner (similar to how a real object may behave).

[0039] In some embodiments, persistent coordinate data (e.g., a persistent coordinate system and / or persistent coordinate frame) may include an origin and three axes. For example, a persistent coordinate system may be assigned by the MR system to the center of a room. In some embodiments, the user may move around in the room, leave the room, and re-enter the room, and the persistent coordinate system may remain at the center of the room (e.g., persisting relative to the physical environment). In some embodiments, virtual objects may be displayed using a transformation to persistent coordinate data that enables the display of persistent virtual content. In some embodiments, the MR system may use simultaneous localization and mapping to generate persistent coordinate data (e.g., the MR system may assign persistent coordinate systems to points in space). In some embodiments, the MR system may map the environment by generating persistent coordinate data at regular intervals (e.g., the MR system may assign persistent coordinate systems within a grid, where each persistent coordinate system may be at least 5 feet from another persistent coordinate system).

[0040] In some embodiments, persistent coordinate data may be generated by the MR system and transmitted to a remote server. In some embodiments, the remote server may be configured to receive persistent coordinate data. In some embodiments, the remote server may be configured to synchronize persistent coordinate data from multiple observation instances. For example, multiple MR systems may map the same room with persistent coordinate data and transmit that data to the remote server. In some embodiments, the remote server may use this observation data to generate standard persistent coordinate data that can be obtained based on one or more observations. In some embodiments, the standard persistent coordinate data may be more accurate and / or reliable than a single observation of persistent coordinate data. In some embodiments, the standard persistent coordinate data may be transmitted to one or more MR systems. For example, an MR system may use image recognition and / or location data to recognize that it is located in a room with corresponding standard persistent coordinate data (e.g., from the fact that another MR system has previously mapped the room). In some embodiments, an MR system may receive standard persistent coordinate data corresponding to its location from the remote server.

[0041] In relation to Figures 1A and 1B, the environment / world coordinate system 108 defines a shared coordinate space for both the real environment 100 and the virtual environment 130. In the illustrated example, the coordinate space has its origin at point 106. Furthermore, the coordinate space is defined by the same three orthogonal axes (108X, 108Y, 108Z). Thus, a first location in the real environment 100 and a second corresponding location in the virtual environment 130 can be described with respect to the same coordinate space. This simplifies the identification and representation of corresponding locations in the real and virtual environments, as the same coordinates can be used to identify both locations. However, in some examples, the corresponding real and virtual environments do not need to use a shared coordinate space. For example, in some examples (not shown), matrices (which may include translational matrices and quaternion matrices or other rotation matrices), or other suitable representations, can characterize transformations between the real environment coordinate space and the virtual environment coordinate space.

[0042] Figure 1C shows an exemplary MRE 150 that simultaneously presents aspects of the real environment 100 and the virtual environment 130 to the user 110 via the mixed reality system 112. In the illustrated example, the MRE 150 simultaneously presents to the user 110 real objects 122A, 124A, 126A, and 128A from the real environment 100 (e.g., via the transparent portion of the display of the mixed reality system 112) and virtual objects 122B, 124B, 126B, and 132 from the virtual environment 130 (e.g., via the active display portion of the display of the mixed reality system 112). As described above, the origin 106 functions as the origin of the coordinate space corresponding to the MRE 150, and the coordinate system 108 defines the x, y, and z axes of the coordinate space.

[0043] In the illustrated example, the mixed reality object includes corresponding pairs of real and virtual objects (i.e., 122A / 122B, 124A / 124B, 126A / 126B) that occupy corresponding positions in coordinate space 108. In some examples, both the real and virtual objects may be visible to the user 110 simultaneously. This may be desirable, for example, when the virtual object presents information designed to extend the view of the corresponding real object (such as in a museum application where the virtual object presents a missing piece of an old, damaged sculpture). In some examples, the virtual object (122B, 124B, and / or 126B) may be displayed in a way that obscures the corresponding real object (122A, 124A, and / or 126A) (e.g., via active pixelated occlusion using a pixelated occlusion shutter). This may be desirable, for example, when the virtual object acts as a visual replacement for the corresponding real object (such as in an interactive storytelling application where an inanimate real object becomes a “living” character).

[0044] In some examples, real-world objects (e.g., 122A, 124A, 126A) may be associated with virtual content or helper data that does not necessarily constitute a virtual object. Virtual content or helper data can facilitate the processing or handling of virtual objects in a mixed reality environment. For example, such virtual content may include a two-dimensional representation of the corresponding real-world object; a custom asset type associated with the corresponding real-world object; or statistical data associated with the corresponding real-world object. This information can enable or facilitate calculations involving real-world objects without incurring unnecessary computational overhead.

[0045] In some examples, the presentation described above may also incorporate audio modes. For example, in MRE150, the virtual monster 132 may be associated with one or more audio signals, such as footsteps generated when the monster walks around MRE150. As will be further described below, the processor of the mixed reality system 112 may compute an audio signal corresponding to the mixture and processed synthesis of all such sounds within MRE150 and present the audio signal to the user 110 via one or more speakers included in the mixed reality system 112 and / or one or more external speakers.

[0046] Exemplary Mixed Reality System An exemplary mixed reality system 112 may include a wearable head device (e.g., a wearable augmented reality or mixed reality head device) comprising: displays (which may comprise left and right transmissive displays, which may be near-eye displays, and associated components for coupling light from the displays to the user's eyes); left and right speakers (e.g., positioned adjacent to the user's left and right ears, respectively); an inertial measuring unit (IMU) (e.g., mounted on the temple arms of the head device); an orthogonal coil electromagnetic receiver (e.g., mounted on the left temple piece); left and right cameras (e.g., depth (time-of-flight) cameras) oriented away from the user; and left and right eye cameras oriented towards the user (e.g., for detecting the user's eye movements). However, the mixed reality system 112 may incorporate any suitable display technology and any suitable sensors (e.g., optical, infrared, acoustic, LiDAR, EOG, GPS, magnetic). Furthermore, the mixed reality system 112 may incorporate networking capabilities (e.g., Wi-Fi capabilities) for communicating with other devices and systems, including other mixed reality systems. The mixed reality system 112 may further include a battery (which may be mounted in an auxiliary unit such as a belt pack designed to be worn around the user's waist), a processor, and memory. The wearable head device of the mixed reality system 112 may include a tracking component, such as an IMU or other suitable sensor, configured to output a set of coordinates of the wearable head device relative to the user's environment. In some examples, the tracking component may provide input to a processor that performs simultaneous localization and mapping (SLAM) and / or visual odometry algorithms. In some examples, the mixed reality system 112 may also include a handheld controller 300 and / or auxiliary unit 320, which may be a wearable belt pack, as further described below.

[0047] Figures 2A to 2D show components of an exemplary mixed reality system 200 (which may correspond to mixed reality system 112) that may be used to present an MRE (which may correspond to MRE150) or other virtual environment to a user. Figure 2A shows a perspective view of a wearable head device 2102 included in the exemplary mixed reality system 200. Figure 2B shows a plan view of the wearable head device 2102 mounted on the user's head 2202. Figure 2C shows a front view of the wearable head device 2102. Figure 2D shows an end view of an exemplary eyepiece 2110 of the wearable head device 2102. As shown in Figures 2A to 2C, the exemplary wearable head device 2102 includes an exemplary left eyepiece (e.g., a left transparent waveguide set eyepiece) 2108 and an exemplary right eyepiece (e.g., a right transparent waveguide set eyepiece) 2110. Each eyepiece 2108 and 2110 may include a transmissive element from which the real environment can be viewed, as well as a display element for presenting a display that overlaps with the real environment (e.g., via imagewise modulated light). In some examples, such a display element may include a surface diffractive optical element for controlling the flow of imagewise modulated light. For example, the left eyepiece 2108 may include a left internally coupled grating set 2112, a left orthogonal pupillary dilation (OPE) grating set 2120, and a left exit (output) pupillary dilation (EPE) grating set 2122. As used herein, pupil may refer to the emission of light from an optical element such as a grating set or reflector. Similarly, the right eyepiece 2110 may include a right internally coupled grating set 2118, a right OPE grating set 2114, and a right EPE grating set 2116. Imagewise modulated light can be transmitted to the user's eye via the internally coupled gratings 2112 and 2118, OPE 2114 and 2120, and EPE 2116 and 2122. Each internally coupled grating set 2112, 2118 can be configured to deflect light toward its corresponding OPE grating set 2120, 2114.Each OPE grating set 2120, 2114 can be designed to gradually deflect light downward toward its associated EPE 2122, 2116, thereby extending the formed exit pupil horizontally. Each EPE 2122, 2116 can be configured to gradually redirect at least a portion of the light received from its corresponding OPE grating set 2120, 2114 toward the user's eyebox position (not shown) defined behind the eyepieces 2108, 2110, thereby extending the formed exit pupil vertically toward the eyebox. Alternatively, instead of the internal coupling grating sets 2112 and 2118, OPE grating sets 2114 and 2120, and EPE grating sets 2116 and 2122, the eyepieces 2108 and 2110 may include other arrangements of gratings and / or refractive and reflective mechanisms to control the coupling of imagewise-modulated light to the user's eye.

[0048] In some examples, the wearable head device 2102 may include a left temple arm 2130 and a right temple arm 2132, the left temple arm 2130 including a left speaker 2134, and the right temple arm 2132 including a right speaker 2136. The orthogonal coil electromagnetic receiver 2138 may be located within the left temple piece or in another suitable location within the wearable head unit 2102. The inertial measurement unit (IMU) 2140 may be located within the right temple arm 2132 or in another suitable location within the wearable head device 2102. The wearable head device 2102 may also include a left depth (e.g., time-of-flight) camera 2142 and a right depth camera 2144. The depth cameras 2142 and 2144 may be appropriately oriented in different directions to cover a wider field of view together.

[0049] In the examples shown in Figures 2A to 2D, the left source 2124 of imagewise modulated light can be optically coupled to the left eyepiece 2108 via the left internal coupling grating set 2112, and the right source 2126 of imagewise modulated light can be optically coupled to the right eyepiece 2110 via the right internal coupling grating set 2118. The imagewise modulated light sources 2124 and 2126 can include, for example, fiber optic scanners; projectors including electronic optical modulators such as digital light processing (DLP) chips or liquid crystal on silicon (LCoS) modulators; or light-emitting displays such as micro light-emitting diodes (μLEDs) or micro organic light-emitting diode (μOLED) panels coupled to the internal coupling grating sets 2112 and 2118 using one or more lenses on each side. The input coupling grating sets 2112 and 2118 can deflect the light from the imagewise modulated light sources 2124 and 2126 to an angle exceeding the critical angle of total internal reflection (TIR) ​​of the eyepieces 2108 and 2110. The OPE grid sets 2114 and 2120 gradually deflect the light propagating by TIR downwards toward the EPE grid sets 2116 and 2122. The EPE grid sets 2116 and 2122 gradually fuse the light toward the user's face, including the pupil of the user's eye.

[0050] In some examples, as shown in Figure 2D, each of the left eyepiece 2108 and the right eyepiece 2110 includes multiple waveguides 2402. For example, each eyepiece 2108, 2110 may include multiple individual waveguides, each dedicated to its respective color channel (e.g., red, blue, and green). In some examples, each eyepiece 2108, 2110 may include multiple sets of such waveguides, each set configured to impart a different wavefront curvature to the emitted light. The wavefront curvature may be convex to the user's eye, for example, to present a virtual object positioned at a distance in front of the user (e.g., only a distance corresponding to the reciprocal of the wavefront curvature). In some examples, the EPE grid sets 2116, 2122 may include curved grid grooves that achieve convex wavefront curvature by changing the Poynting vector of the emitted light crossing each EPE.

[0051] In some examples, stereoscopically adjusted left and right eye images can be presented to the user through imagewise optical modulators 2124, 2126 and eyepieces 2108, 2110 to create the perception that the displayed content is three-dimensional. The perceived presence of the three-dimensional virtual object can be enhanced by selecting waveguides (and thus corresponding to wavefront curvature) so that the virtual object is displayed at a distance close to the distance indicated by the stereoscopic left and right images. This technique can also reduce motion sickness experienced by some users, which may be caused by the difference between the depth perception cue provided by the stereoscopic left and right eye images and the autonomic nervous system regulation of the human eye (e.g., focus depending on object distance).

[0052] Figure 2D shows a top-down end view of the right eyepiece 2110 of an exemplary wearable head device 2102. As shown in Figure 2D, the multiple waveguides 2402 can include a first subset 2404 of three waveguides and a second subset 2406 of three waveguides. The two subsets of waveguides 2404, 2406 can be distinguished by different EPE gratings featuring different grating line curvatures to impart different wavefront curvatures to the emitted light. Within each subset of waveguides 2404, 2406, each waveguide can be used to couple different spectral channels (e.g., one of the red, green, and blue spectral channels) to the user's right eye 2206. (Although not shown in Figure 2D, the structure of the left eyepiece 2108 is similar to that of the right eyepiece 2110.)

[0053] Figure 3A shows an exemplary handheld controller component 300 of the mixed reality system 200. In some examples, the handheld controller 300 includes a grip portion 346 and one or more buttons 350 arranged along the top surface 348. In some examples, the buttons 350 may be configured to be used as optical tracking targets for tracking, for example, six-degree-of-freedom (6DOF) motion of the handheld controller 300, together with a camera or other optical sensor (which may be mounted on the head unit of the mixed reality system 200 (e.g., a wearable head device 2102)). In some examples, the handheld controller 300 includes a tracking component (e.g., an IMU or other suitable sensor) for detecting position or orientation, such as position or orientation relative to the wearable head device 2102. In some examples, such a tracking component may be located within the handle of the handheld controller 300 and / or mechanically coupled to the handheld controller. The handheld controller 300 can be configured to provide one or more output signals corresponding to one or more of the following: the state of a button being pressed; or the position, orientation, and / or movement of the handheld controller 300 (e.g., via the IMU). Such output signals can be used as inputs to the processor of the mixed reality system 200. Such inputs may correspond to the position, orientation, and / or movement of the handheld controller (and, by extension, the position, orientation, and / or movement of the user's hand holding the controller). Such inputs may also correspond to the user pressing button 350.

[0054] Figure 3B shows an exemplary auxiliary unit 320 of the mixed reality system 200. The auxiliary unit 320 may include a battery to supply energy to operate the system 200 and may include a processor to run programs to operate the system 200. As shown, the exemplary auxiliary unit 320 includes a clip 2128 for attaching the auxiliary unit 320 to a user's belt, for example. Other form factors, including form factors that do not involve attaching the unit to a user's belt, may be suitable for the auxiliary unit 320 and will become apparent. In some examples, the auxiliary unit 320 is coupled to a wearable head device 2102 via a multi-conduit cable that may include, for example, electric wires and optical fibers. Wireless connectivity between the auxiliary unit 320 and the wearable head device 2102 may also be used.

[0055] In some examples, the mixed reality system 200 may include one or more microphones for detecting sound and providing corresponding signals to the mixed reality system. In some examples, the microphones may be attached to or integrated with the wearable head device 2102 and may be configured to detect the user's voice. In some examples, the microphones may be attached to or integrated with the handheld controller 300 and / or auxiliary unit 320. Such microphones may be configured to detect ambient sounds, surrounding noise, the voice of the user or a third party, or other sounds.

[0056] Figure 4 shows an exemplary functional block diagram that may correspond to exemplary mixed reality systems, such as the mixed reality system 200 described above (which may correspond to mixed reality system 112 relating to Figure 1). As shown in Figure 4, the exemplary handheld controller 400B (which may correspond to the handheld controller 300 ("Totem")) includes a totem-to-wearable head device 6-degree-of-freedom (6DOF) totem subsystem 404A, and the exemplary wearable head device 400A (which may correspond to wearable head device 2102) includes a totem-to-wearable head device 6DOF subsystem 404B. In this example, the 6DOF totem subsystem 404A and the 6DOF subsystem 404B work together to determine the six coordinates of the handheld controller 400B relative to the wearable head device 400A (e.g., three translational offsets and three rotations along axes). The six degrees of freedom may be expressed relative to the coordinate system of the wearable head device 400A. The three translational offsets can be represented as X, Y, and Z offsets in such a coordinate system, as a translational matrix, or as any other representation. The rotational degrees of freedom can be represented as a sequence of yaw, pitch, and roll rotations, as a rotation matrix, as a quaternion, or as any other representation. In some examples, a wearable head device 400A; one or more depth cameras 444 (and / or one or more non-depth cameras) included in the wearable head device 400A; and / or one or more optical targets (e.g., button 350 on the handheld controller 400B described above, or a dedicated optical target included in the handheld controller 400B) can be used for 6DOF tracking. In some examples, the handheld controller 400B may include a camera as described above, and the wearable head device 400A may include an optical target for optical tracking in conjunction with the camera. In some examples, the wearable head device 400A and the handheld controller 400B each include a set of three orthogonally oriented solenoids used to wirelessly transmit and receive three identifiable signals.The 6DOF of the wearable head device 400A relative to the handheld controller 400B can be determined by measuring the relative magnitudes of three identifiable signals received in each of the coils used for receiving. Furthermore, the 6DOF totem subsystem 404A may include an inertial measurement unit (IMU) that is useful for providing improved accuracy and / or more timely information regarding the rapid movement of the handheld controller 400B.

[0057] In some embodiments, the wearable system 400 may include a microphone array 407 that includes one or more microphones positioned on a headgear device 400A. In some embodiments, the microphone array 407 may include four microphones. Two microphones may be positioned on the front of the headgear 400A, and two microphones may be positioned on the back of the headgear 400A (e.g., one on the left rear and one on the right rear). In some embodiments, the signals received by the microphone array 407 may be transmitted to a DSP 408. The DSP 408 may be configured to perform signal processing on the signals received from the microphone array 407. For example, the DSP 408 may be configured to perform noise reduction, acoustic echo rejection, and / or beamforming on the signals received from the microphone array 407. The DSP 408 may be configured to transmit the signals to a processor 416.

[0058] In some cases, for example, to compensate for the movement of the wearable head device 400A relative to coordinate system 108, it may be necessary to transform the coordinates from local coordinate space (e.g., a coordinate space fixed relative to the wearable head device 400A) to inertial coordinate space (e.g., a coordinate space fixed relative to the real environment). For example, such a transformation may be necessary to maintain the illusion that a virtual object exists in the real environment (e.g., a virtual person sitting in a real chair and facing forward, regardless of the position and orientation of the wearable head device), so that the display of the wearable head device 400A presents the virtual object in a position and orientation that would be expected relative to the real environment (e.g., the same position in the lower right corner of the display) and orientation, rather than a fixed position and orientation on the display (and, for example, so that it does not appear unnaturally positioned in the real environment when the wearable head device 400A moves and rotates). In some cases, the compensatory transformation between coordinate spaces can be determined by processing images from the depth camera 444 using SLAM and / or visual odometry procedures to determine the transformation of the wearable head device 400A relative to coordinate system 108. In the example shown in Figure 4, the depth camera 444 can be coupled to the SLAM / visual odometry block 406 and provide images to the block 406. The implementation of the SLAM / visual odometry block 406 may include a processor configured to process these images and determine the position and orientation of the user's head, which can be used to identify transformations between the head coordinate space and another coordinate space (e.g., inertial coordinate space). Similarly, in some examples, additional information about the user's head pose and position is obtained from the IMU 409. The information from the IMU 409 can be integrated with the information from the SLAM / visual odometry block 406 to provide improved accuracy and / or more timely information regarding the rapid adjustment of the user's head pose and position.

[0059] In some examples, the depth camera 444 can supply 3D images to a hand gesture tracker 411, which may be implemented in the processor of a wearable head device 400A. The hand gesture tracker 411 can identify the user's hand gestures, for example, by matching the 3D images received from the depth camera 444 with stored patterns representing hand gestures. Other suitable techniques for identifying the user's hand gestures will become apparent.

[0060] In some examples, one or more processors 416 may be configured to receive data from the wearable head device's 6DOF headgear subsystem 404B, IMU 409, SLAM / visual odometry block 406, depth camera 444, and / or hand gesture tracker 411. The processor 416 may also send and receive control signals from the 6DOF totem system 404A. The processor 416 may be wirelessly coupled to the 6DOF totem system 404A, as in an example where the handheld controller 400B is not connected. The processor 416 may further communicate with additional components such as an audiovisual content memory 418, a graphical processing unit (GPU) 420, and / or a digital signal processor (DSP) voice spatializer 422. The DSP voice spatializer 422 may be coupled to a head-related transfer function (HRTF) memory 425. The GPU 420 may include a left channel output coupled to the left source of imagewise modulated light 424 and a right channel output coupled to the right source of imagewise modulated light 426. The GPU 420 can output stereoscopic image data to the sources of imagewise modulated light 424, 426, for example, as described above with reference to Figures 2A to 2D. The DSP audio spatializer 422 can output audio to the left speaker 412 and / or the right speaker 414. The DSP audio spatializer 422 can receive an input from the processor 419 indicating a direction vector from the user to a virtual sound source (which may be moved by the user, for example, via the handheld controller 320). Based on the direction vector, the DSP audio spatializer 422 can determine the corresponding HRTF (for example, by accessing an HRTF or by interpolating multiple HRTFs). Next, the DSP audio spatializer 422 can apply the determined HRTF to an audio signal, such as an audio signal corresponding to a virtual sound generated by a virtual object.This can enhance the realism and presence of virtual sounds by incorporating the user's relative position and orientation to virtual sounds in a mixed reality environment; that is, by presenting virtual sounds that match the user's expectations of how those virtual sounds would sound if they were real sounds in a real environment.

[0061] In some examples, as shown in Figure 4, one or more of the processor 416, GPU 420, DSP voice spatializer 422, HRTF memory 425, and audiovisual content memory 418 may be included in an auxiliary unit 400C (which may correspond to the auxiliary unit 320 described above). The auxiliary unit 400C may include a battery 427 for powering its components and / or for powering the wearable head device 400A or the handheld controller 400B. Including such components in an auxiliary unit that can be worn on the user's waist can limit the size and weight of the wearable head device 400A, and thus reduce fatigue in the user's head and neck.

[0062] Figure 4 shows elements corresponding to various components of an exemplary mixed reality system, but various other suitable arrangements of these components will become apparent to those skilled in the art. For example, the elements shown in Figure 4 as associated with the auxiliary unit 400C could instead be associated with the wearable head device 400A or the handheld controller 400B. Furthermore, some mixed reality systems may completely omit the handheld controller 400B or the auxiliary unit 400C. Such variations and modifications should be understood to fall within the scope of the disclosed examples.

[0063] Ultrasonic treatment for nanostructure fabrication An exemplary mixed reality system (e.g., mixed reality system 200) wearable head device or head-mounted display may include an optical system having an eyepiece for presenting images to the user via the display. The eyepiece may include one or more optical gratings (e.g., an internally coupled grating set 2112, a left orthogonal pupillary dilation (OPE) grating set 2120, and a left exit pupillary dilation (EPE) grating set 2122; the right eyepiece 2110 may include a right internally coupled grating set 2118, a right OPE grating set 2114, and a right EPE grating set 2116). One or more optical gratings may be used to transmit imagewise light to the user's eye.

[0064] As mentioned above, nanostructures forming optical lattices can be fabricated by lithography processes. These nanostructures can be multilayer symmetric and / or asymmetric. However, fabricating nanostructures using lithography can be expensive and complex. For example, fabricating nanostructures smaller than 50 nm with high fidelity (no breaks, smooth line edges) may require expensive lithography techniques such as E-beam lithography to achieve the desired nanostructure resolution. Even with such lithography techniques, aligning components to fabricate lithography masters and / or final products at the nanometer scale can be challenging, and the resulting nanostructures may be prone to uneven line edge roughness (LER).

[0065] To address the problems associated with expensive lithography techniques used to fabricate nanostructures, the systems and methods according to embodiments of the present disclosure rely on an ultrasonic process for etching and forming desired nanostructures on a substrate. For example, embodiments of the present disclosure may use an ultrasonic sequencing process to achieve desired etching selectivity of different material layers deposited on a substrate. The ultrasonic sequencing process may include immersing the substrate in a bath of a base solution, an acid solution, and / or water and applying ultrasonic treatment to the bath. Systems and methods according to embodiments of the present disclosure can etch, for example, silicon-based structures, such as Si, SiO2, Si3N4, etc., and have multilayer nanostructures with high fidelity, smooth LER, and consistent alignment between batches.

[0066] As used herein, sonication may refer to the process of applying acoustic energy and agitation using a transducer to a container containing a fluid as a medium in order to provide reactive etching species and / or remove the reacted species, residues, particles, debris, etc. Figure 5 shows an example of an exemplary sonication configuration 500 according to embodiments of the present disclosure. The exemplary configuration 500 may include at least a transducer 502, a container 504, and a liquid bath 506. The transducer 502 may be provided for applying sound waves to the container 504. For example, the transducer may provide waves in the range of 20 to 200 kHz. The liquid bath, for example, the fluid, may be a base solution, an acid solution, and / or water. In some embodiments, the acid solution may include sulfuric acid, citric acid, etc. In some embodiments, the base solution may include potassium hydroxide and / or hydrogen peroxide. In some examples, the acid solution and base solution may have a chemical concentration of about 1 to 20% with a pH in the range of about 3 to 11. In some embodiments, the energy from the transducer may be pulsed at specific intervals rather than being pulsed continuously.

[0067] As shown in the figure, the substrate 508 to be etched may be placed inside the container 504. In one or more examples, the substrate may be made of silicon, silicon dioxide, silicon nitride, and / or other silicon-based substrate materials. In some embodiments, the liquid bath of the ultrasonic treatment configuration 500 may be at room temperature during the ultrasonic treatment process. In some embodiments, the liquid bath of the ultrasonic treatment configuration may be at a high temperature, for example, above room temperature, about 40-80°C. For example, a heater (not shown) may be coupled to the container 504 to achieve a desired temperature for the liquid bath 506.

[0068] In one or more examples, the substrate 508 can be sequentially placed in baths of a base solution, an acid solution, and / or water. Once the substrate 508 is immersed in the liquid bath 506, the transducer 502 can apply sound waves to the container 504. The waves can agitate the fluid in the container 504. In this way, the ultrasonic treatment assists the reaction between the fluid and the substrate, as well as the rate of removal of reactants, such as etched material and the reacted solution, from the substrate surface, and can replenish the substrate surface with a fresh reaction environment, such as unreacted solution, to continue the reaction. In some examples, the acid and / or base solution may be selected based on its reactivity with the substrate material. For example, the acid and / or base solution may be selected based on its ability to react with the surface of the substrate material and remove material from the surface of the substrate 508, such as by etching.

[0069] In some cases, multiple hydrolysis reactions occurring on the surface of substrate 508 can gradually remove the silicon material. For example, hydrolysis of silicon dioxide bonds can occur on the surface of substrate 508 due to proton transfer from hydronium ions (H3O+), hydroxides (OH-), and / or hydrogen-bonded complex molecules present in acidic and / or basic solutions. For example, silanol (SI-OH) bonds can be formed at the solid-liquid interface (e.g., silicon dioxide to solution), thereby reducing the energy barrier between silicon dioxide and silanol bonds. This can lead to an increase in reactions due to protonation, as less energy is required to break the intermolecular bonds. The reduction in the energy barrier can also be due to the presence of h-bonded complexes in aqueous solutions, which can contribute to proton transfer. Equations governing the acidic and basic protonation reactions of silicon at the silanol-solution interface present on the substrate surface are provided below in Equations 1 and 2. [ka]

[0070] Table 1 shows exemplary etching rates of silicon and silicon dioxide nanostructures using the sonication process according to embodiments of the present disclosure. As used herein, etching rate can be used to refer to the rate at which material is removed from the surface of a substrate. In some embodiments, immersing the substrate in a liquid bath and applying sonication to the bath can provide a substantially uniform reaction environment across the entire surface of the substrate, thereby providing substantially uniform etching and material removal across the entire surface of the substrate. The examples shown in Table 1 may correspond to treating the substrate with a base solution (2% base solution at pH 11 in water) for about 8 minutes at about 60C and an acid solution (2% acid solution at pH 3 in water) for about 20 minutes at about 60C. The concentrations of the base and acid solutions are exemplary and are not intended to limit the scope of the present disclosure. Furthermore, the etching rates shown in Table 1 are exemplary and can vary with different sonication conditions, e.g., temperature, acid and / or base solution concentrations, and duration of the sonication process. In some embodiments, the sonication conditions can be adjusted to provide a stable and / or consistent etching rate. [Table 1]

[0071] As shown in the table, treating silicon substrates and / or silicon dioxide substrates by a base-water process sequence (e.g., immersing the substrate in a base solution bath, applying ultrasonic treatment, then immersing the substrate in a water bath and applying ultrasonic treatment) may not result in the identifiable removal of the material from the surface of the substrate. Similarly, treating silicon substrates and silicon dioxide substrates by an acid-water process sequence (e.g., immersing the substrate in a basic acid solution, applying ultrasonic treatment, then immersing the substrate in a water bath and applying ultrasonic treatment) may not result in the identifiable removal of the material from the surface of the substrate.

[0072] However, the base-acid-water and base-water-acid-water process sequences can yield distinct etching rates. As seen in Table 1, silicon and silicon dioxide are associated with different etching rates for different process sequences, respectively. This difference in etching rates may be due to the weaker energy barrier associated with silicon bonds compared to silicon oxide bonds. For example, O-Si-O bonds can lead to stronger and slower hydrolysis reactions in silicon dioxide, see, e.g., equations 1 and 2, as well as material removal. For instance, treating a silicon substrate with a base-acid-water process sequence can provide an etching rate of about 1–4 nm / min, while treating a silicon dioxide substrate with the same base-acid-water process (e.g., same solution strength, time, and temperature) yielded an etching rate of about 0.2–0.7 nm / min. Similarly, treating silicon substrates with a base-water-acid-water process sequence provided an etching rate of approximately 1–4 nm / min, while treating silicon dioxide substrates with the same base-water-acid-water process (e.g., same solution strength, time, and temperature) resulted in an etching rate of approximately ±5 nm / min.

[0073] Applying the sonication process sequence described above can provide a predictable etching rate for the substrate material. Therefore, sonication can be used to reduce the dimensions of nanostructures in a controlled and intentional manner. Due to a substantially uniform reaction environment, line edge roughness (LER) can be smoother compared to conventional lithography techniques, and precise dimensions can be achieved by adjusting one or more sonication conditions. For example, the amount of material removed can be adjusted by adjusting the duration, temperature, and / or solution strength of the sonication bath. Furthermore, since silicon and silicon dioxide are associated with consistent and / or predictable etching rates, the difference in etching rates between these two materials can be utilized to fabricate multilayer structures in a selective and controllable manner.

[0074] Figures 6A-6B, 7A-7B, 8A-8B, 9A-9B, and 10A-10B show examples of substrates having multiple nanostructures that can be manufactured according to embodiments of the present disclosure. Nanostructures manufactured according to embodiments of the present disclosure can be used, for example, for one or more gratings for an eyepiece that can be used in a wearable head device (e.g., wearable head device 2102).

[0075] Figure 6A shows an exemplary substrate 600A according to an embodiment of the present disclosure. As shown in the figure, the substrate 600A may include a base 602A and a plurality of nanostructures 604A. The exemplary substrate 600A may be a silicon substrate. The plurality of nanostructures 604A may form a pattern on the surface of the base 602A. As shown in the figure, the plurality of nanostructures 604A may take the form of a line-and-space pattern so that the nanostructures can protrude from the surface of the base 602A. The pattern shape is not intended to limit the scope of the present disclosure, and any suitable nanopattern, including but not limited to pillar patterns, discontinuous lines, curves, holes, cylinders, etc., may be used without departing from the scope of the present disclosure. The plurality of nanostructures 604A may be associated with a first height (600h1) and a first width (600d1). In one or more examples, the nanostructure 604A may have a width (600d1) in the range of approximately 100–250 nm and a height (600h1) in the range of approximately 70–150 nm. For example, 604A may have a width (600d1) of 196 nm and a height (600h1) of 79 nm. These exemplary dimensions are provided for illustrative purposes only and are not intended to limit the scope of this disclosure.

[0076] Figure 6B shows an exemplary etched substrate 600B etched according to one or more embodiments of the present disclosure. For example, substrate 600B may be produced by etching a silicon substrate 600A using a base-acid-water sonication process sequence according to one or more examples of the present disclosure. As described above, the silicon substrate may have an etching rate of about 1 to 4 nm / min using the base-acid-water sequence. As shown in the figure, the etched nanostructure 604B may have a line width 600d2 reduced compared to the line width 600d1. For example, the nanostructure 604B may have a width 600d2 of 145 nm and a height 600h2 of 77 nm. These exemplary dimensions are provided for illustrative purposes only and are not intended to limit the scope of the present disclosure. Furthermore, as shown in the figure, the line edge roughness (LER) of the nanostructure 604B can be smoother, particularly compared to the LER associated with conventional lithography processes at the nanoscale. Comparing the dimensions of nanostructure 604A and nanostructure 604B, the change in width between 600d1 and 600d2 (600Δd) can be -51 nm, while the change in height between 600h1 and 600h2 (600Δh) can be approximately -2 nm. In this way, the line width dimension d can be reduced to achieve the desired geometric shape of the nanostructure, while the height of the nanostructure can be kept relatively constant.

[0077] Figure 7A shows an exemplary substrate 700A according to an embodiment of the present disclosure. As shown in the figure, the substrate 700A may include a base 702A and a plurality of nanostructures 704A. The exemplary substrate 700A may be a silicon dioxide substrate. The plurality of nanostructures 704A may form a pattern on the surface of the base 702A. As shown in the figure, the plurality of nanostructures 704A may be a line-and-space pattern so that the nanostructures 704A may protrude from the surface of the base 702A. The pattern shape is not intended to limit the scope of the present disclosure, and any suitable nanopattern may be used as described above without departing from the scope of the present disclosure. The plurality of nanostructures 704A may be associated with a first height (700h1) and a first width (700d1). In one or more examples, the nanostructures 704A may have a width (600d1) in the range of about 100 to 250 nm and a height (600h1) in the range of about 70 to 150 nm. For example, 704A may have a width of 157 nm, 700d1, and a height of 122 nm, 700h1. These exemplary dimensions are provided for illustrative purposes only and are not intended to limit the scope of this disclosure.

[0078] Figure 7B shows an exemplary etched substrate 700B that can be etched according to one or more embodiments of the present disclosure. For example, substrate 700B may be produced by etching a silicon dioxide substrate 700A using a base-acid-water sonication process sequence according to one or more examples of the present disclosure. As described above, the silicon dioxide substrate may have an etching rate of about 0.2 to 0.8 nm / min using the base-acid-water sequence. As shown in the figure, the etched nanostructure 704B may have a line width 700d2 reduced compared to line width 700d1, and a height 700h2 increased compared to height 700h1. For example, nanostructure 704B may have a width 700d2 of 141 nm and a height 700h2 of 125 nm. Comparing the dimensions of nanostructure 704A and nanostructure 704B, the width change between 700d1 and 700d2 (700Δd1) can be approximately -16 nm, while the height change between 700h1 and 700h2 (700Δh1) can be approximately +3 nm. These exemplary dimensions are provided for illustrative purposes only and are not intended to limit the scope of this disclosure. As in the example described above, the line width dimension d can be reduced to achieve the desired nanostructure geometric shape, while the height of nanostructure 704B can remain relatively constant. Furthermore, the LER of nanostructure 704B can be smoother compared to LER associated with conventional lithography processes, particularly at the nanoscale.

[0079] Figure 7C shows an exemplary etched substrate 700C that can be etched according to one or more embodiments of the present disclosure. For example, substrate 700C can be produced by etching a silicon dioxide substrate 700B using a base-acid-water sonication process sequence according to one or more examples of the present disclosure. Thus, multiple sequential sonication processes can be performed to achieve a desired nanostructure geometry. As shown in the figure, the etched substrate 700C may have a line width 700d3 that is reduced compared to the line width 700d2, and a height 700h3 that is increased compared to the height 700h2. For example, 704C may have a width 700d3 of 125 nm and a height 700h3 of 124 nm. Comparing the dimensions of nanostructure 704C to nanostructure 704C, the change in width between 700d2 and 700d3 (700Δd2) may be about -16 nm, while the change in height between 700h1 and 700h2 (700Δh2) may be about -1 nm. These exemplary dimensions are provided for illustrative purposes only and are not intended to limit the scope of this disclosure. As in the examples described above, the line width dimension d can be reduced to achieve the desired nanostructure geometric shape, while the height of the nanostructure can remain relatively constant. Furthermore, the LER of the nanostructure 704C may be smoother compared to LER associated with conventional lithography processes, particularly at the nanoscale.

[0080] Figure 8A shows an exemplary substrate 800A according to an embodiment of the present disclosure. As shown in the figure, the substrate 800A may include a base 802A and a plurality of nanostructures 804A. The exemplary substrate 800A may be a silicon substrate. The plurality of nanostructures 804A may form a pattern on the surface of the base 802A. As shown in the figure, the plurality of nanostructures 804A may be a line-and-space pattern that can protrude from the surface of the base 802A. The pattern shape is not intended to limit the scope of the present disclosure, and any suitable nanopattern may be used as described above without departing from the scope of the present disclosure. The plurality of nanostructures 804A may be associated with a first height (800h1) and a first width (800d1). In one or more examples, the nanostructures 804A may have a width 800d1 in the range of about 100 to 250 nm and a height 800h1 in the range of about 70 to 150 nm. For example, 804A may have a width of approximately 219 nm (800d1) and a height of approximately 115 nm (800h1). These exemplary dimensions are provided for illustrative purposes only and are not intended to limit the scope of this disclosure.

[0081] Figure 8B shows an exemplary etched substrate 800B that can be etched according to one or more embodiments of the present disclosure. For example, substrate 800B may be produced by etching a silicon substrate 800A using a base-water-acid-water sonication process sequence according to one or more examples of the present disclosure. As described above, the silicon substrate may have an etching rate of about 1 to 4 nm / min using the base-water-acid-water sequence. As shown in the figure, the etched nanostructure 804B may have a line width 800d2 that is reduced compared to the line width 800d1, and a height 800h2 that is increased compared to the height 800h1. For example, nanostructure 804B may have a width 800d2 of about 114 nm and a height 800h2 of about 114 nm. Comparing the dimensions of nanostructure 804A and nanostructure 804B, the change in width between 800d1 and 800d2 (800Δd) can be approximately -105 nm, while the change in height between 800h1 and 800h2 (800Δh) can be approximately -1 nm. These exemplary dimensions are provided for illustrative purposes only and are not intended to limit the scope of this disclosure. As in the example described above, the line width dimension d can be reduced to achieve a desired nanostructure geometric shape, while the height of the nanostructure can remain relatively constant. Furthermore, as shown in the figure, the LER of nanostructure 804B can be smoother compared to LER associated with conventional lithography processes, particularly at the nanoscale.

[0082] Figure 9A shows an exemplary substrate 900A according to embodiments of the present disclosure. As shown in the figure, the substrate 900A may include a base 902A and a plurality of nanostructures 904A. The exemplary substrate 900A may be a silicon dioxide substrate. The plurality of nanostructures 904A may form a pattern on the surface of the base 902A. As shown in the figure, the plurality of nanostructures 904A may be a line-and-space pattern that can protrude from the surface of the base 902A. The pattern shape is not intended to limit the scope of the present disclosure, and any suitable nanopattern may be used as described above without departing from the scope of the present disclosure. The plurality of nanostructures 904A may be associated with a first height (900h1) and a first width (900d1). In one or more examples, the nanostructures 904A may have a width (900d1) in the range of about 100 to 250 nm and a height (900h1) in the range of about 70 to 150 nm. For example, 904A may have a width of approximately 125 nm (900d1) and a height of approximately 123 nm (900h1). These exemplary dimensions are provided for illustrative purposes only and are not intended to limit the scope of this disclosure.

[0083] Figure 9B shows an exemplary etched substrate 900B that can be etched according to one or more embodiments of the present disclosure. For example, substrate 900B may be produced by etching a silicon dioxide substrate 900A using a base-acid-water sonication process sequence according to one or more examples of the present disclosure. As described above, the silicon dioxide substrate may have an etching rate of about 0 nm / min using the base-water-acid-water sequence. As shown in the figure, the etched nanostructure 904B may have substantially the same dimensions as nanostructure 904A. For example, nanostructure 904B may have a width 900d2 of about 125 nm and a height 900h2 of about 123 nm. Comparing the dimensions of nanostructure 604A and nanostructure 604B, the change in width between 900d1 and 900d2 (900Δd) can be about 0 nm, while the change in height between 900h1 and 900h2 (900Δh) can be about 0 nm. These exemplary dimensions are provided for illustrative purposes only and are not intended to limit the scope of this disclosure. In some examples, the LER of nanostructure 904B can be smoother than the LER of nanostructure 904A.

[0084] Figure 10A shows an exemplary substrate 1000A according to an embodiment of the present disclosure. As shown in the figure, the substrate 1000A may include a base 1002A and a plurality of nanostructures 1004A. The exemplary substrate 1000A may be a silicon substrate. The plurality of nanostructures 1004A may form a pattern on the surface of the base 1002A. As shown in the figure, the plurality of nanostructures 1004A may be a line-and-space pattern that can protrude from the surface of the base 1002A. The pattern shape is not intended to limit the scope of the present disclosure, and any suitable nanopattern may be used as described above without departing from the scope of the present disclosure. The plurality of nanostructures 1004A may be associated with a first height 1000h1 and a first width 1000d1. In one or more examples, the nanostructures 1004A may have a width 1000d1 in the range of about 100 to 250 nm and a height 1000h1 in the range of about 70 to 150 nm. For example, 1004A may have a width of approximately 126 nm (1000d1) and a height of approximately 130 nm (1000h1). These exemplary dimensions are provided for illustrative purposes only and are not intended to limit the scope of this disclosure.

[0085] Figure 10B shows an exemplary etched substrate 1000B that can be etched according to one or more embodiments of the present disclosure. For example, substrate 1000B may be produced by etching a silicon substrate 1000A using a base-water-acid-water sonication process sequence according to one or more examples of the present disclosure. As described above, the silicon substrate may have an etching rate of about 1 to 4 nm / min using the base-acid-water sequence. As shown in the figure, the etched substrate 1000B may have a line width 1000d2 that is reduced compared to line width 1000d1, but the height may remain approximately the same (e.g., ±5 nm). For example, 1004B may have a width 1000d2 of about 47 nm and a height 1000h2 of about 125 nm. Comparing the dimensions of nanostructure 1004A and nanostructure 1004B, the width change between 1000d1 and 1000d2 can be approximately -79 nm, while the height change between 1000h1 and 1000h2 can be approximately -5 nm. These exemplary dimensions are provided for illustrative purposes only and are not intended to limit the scope of this disclosure. As in the example described above, the line width dimension d can be reduced to achieve a desired nanostructure geometric shape, while the height of the nanostructure can remain relatively constant. Furthermore, the LER of nanostructure 1004B can be smoother compared to the LER associated with conventional lithography processes, particularly at the nanoscale. Substrate 1000B was manufactured using a process sequence similar to that of substrate 800B, but in some examples, the finer line width of substrate 1000B may be due to variations in one or more sonication conditions, such as the length of exposure to sonication, the temperature of the liquid bath, and the concentration of the acid and / or base solution.

[0086] Exemplary multilayer nanopatterns As described above, different substrate materials (e.g., silicon and silicon dioxide) can be associated with consistent and / or predictable etching rates. Furthermore, varying the sonication process sequence (e.g., base-acid-water (BAW), base-water-acid-water (BWAW)) can provide different relative etching rates between substrate materials. Thus, the difference in etching rates between these two materials can be utilized to fabricate multilayer structures in a selective and controllable manner. For example, by adjusting the sonication conditions, e.g., the duration of the sonication bath, temperature, solution strength, and / or process sequence, the amount of material removed can be predetermined and / or controlled. Thus, multilayer nanostructures with various cross-sectional shapes can be achieved by exposing the substrate to a single set of sonication conditions. In some embodiments, but not limited to these, various geometric shapes, including stepped, concave, and blazed, can be achieved using the fabrication processes according to embodiments of this disclosure.

[0087] Figures 11A–11C, 12A–12C, and 13A–13E illustrate exemplary multilayer substrates at various stages of an ultrasonic manufacturing process according to embodiments of the present disclosure. For example, Figures 11B and 11C show an exemplary substrate having a stepped shape, manufactured according to embodiments of the present disclosure. Figures 12B and 12C show an exemplary substrate having a concave shape, manufactured according to embodiments of the present disclosure. Figure 13E shows an exemplary substrate having a blazed shape, manufactured according to embodiments of the present disclosure. The exemplary multilayer structures can be formed from one or more layers of silicon-based materials, including but not limited to silicon, silicon dioxide, silicon nitride, and / or other silicon-based materials. As shown in the figures and described in more detail below, lattice shapes, such as stepped shapes, concave shapes, and blazed shapes, can be achieved by taking advantage of different etching rates of different materials.

[0088] Figures 11A to 11C illustrate exemplary multilayer substrates at various stages of an ultrasonic manufacturing process according to embodiments of the present disclosure. For example, Figure 11A shows a multilayer substrate 1100A before the ultrasonic process. As shown in the figure, the multilayer substrate 1100A may include a base 1102A and a plurality of nanostructures 1104A. Each of the plurality of nanostructures 1104A may include a first layer 1106A placed on the base 1102A and a second layer 1108A placed on the first layer 1106A. As shown in the figure, both the first layer 1106A and the second layer 1108A may have the same width. In some embodiments, the base 1102A and the first layer 1106A may be formed from silicon dioxide, and the second layer 1108A may be formed from silicon. In some embodiments, the first and second layers may be deposited using lithography techniques.

[0089] As mentioned above, silicon and silicon dioxide can be associated with different etching rates. For example, silicon can be associated with a higher etching rate than silicon dioxide. For instance, as mentioned above, the base-water-acid-water process sequence can provide an etching rate of about 1-4 nm for silicon and about 0 nm for silicon dioxide. Therefore, referring to substrate 1100A, using silicon dioxide for base 1102A and the first layer 1106A and silicon for the second layer 1108A can result in a stepped shape because silicon has a relatively higher etching rate compared to silicon dioxide.

[0090] Figure 11B shows a stepped substrate 1100B manufactured according to an embodiment of the present disclosure, for example, by applying a base-water-acid-water process sequence to a substrate 1100A. As shown in the figure, the stepped substrate 1100B may include a base 1102B and a plurality of nanostructures 1104B. Each nanostructure 1104B may include a first layer 1106B of silicon dioxide and a second layer 1108B of silicon. As shown in the figure, the substrate 1100B may have a stepped shape in which the width or diameter of the second layer 1108B may differ from the width or diameter of the first layer 1106B. This difference in width between the first layer 1106B and the second layer 1108B may be due to the relative difference in etching rates of silicon and silicon dioxide during the sonication process sequence. For example, as described above, the base-water-acid-water process sequence may provide an etching rate of about 1 to 4 nm for silicon and about 0 nm for silicon dioxide. These exemplary etching rates are consistent with the shape of substrate 1100B, compared to substrate 1100A where the second layer 1108B has a narrower width than the second layer 110A. Base 1102B and the first layer 1106B have approximately the same dimensions as base 1102A and the first layer 1106A.

[0091] Figure 11C shows a stepped substrate 1100C manufactured according to an embodiment of the present disclosure, for example, by applying a base-acid-water process sequence to a substrate 1100A. As shown in Figure 11C, the substrate 1100C may include a silicon dioxide base 1102C and one or more nanostructures 1104C. Each nanostructure 1104C may include a first layer of silicon dioxide 1106C and a second layer of silicon 1108B. As shown in the figure, the substrate 1100C may have a stepped shape in which the width or diameter of the second layer 1108C may differ from the width of the first layer 1106C. This difference in width between the first layer 1106B and the second layer 1108C may be due to the relative difference in etching rates of silicon and silicon dioxide during the sonication process sequence. For example, as described above, the base-acid-water process sequence may provide an etching rate of about 1 to 4 nm for silicon and about 0.2 to 0.7 nm for silicon dioxide. These exemplary etching rates are consistent with the shape of substrate 1100C, compared to substrate 1100A where the second layer 1108C has a smaller width than the second layer 1108A. Base 1102C has a lower height than base 1102A. The first layer 1106C has a smaller width than the first layer 1106A.

[0092] Furthermore, referring to both substrates 1100B and 1100C, sonication provides a substantially uniform reaction environment across the surface of the substrate, allowing the stepped nanostructure 1104C to be centered, for example, so that each nanostructure 1104C can have a symmetrical cross-section. In comparison, such alignment of nanostructures using conventional lithography techniques can be difficult and expensive to achieve due to the nanoscale of the structure.

[0093] As described above, substrates 1100B and 1100C illustrate the effect of applying different process sequences to template substrates. A comparison of the exemplary substrates 1100B and 1100C demonstrates this difference. For example, silicon dioxide is associated with a higher etching rate when the base-acid-water process sequence is applied to substrate 1100C than when the base-acid-water process sequence is applied to substrate 1100B. Therefore, as shown in the figure, the first layer 1106C can have a smaller width than the first layer 1106B. Similarly, the height associated with base 1102C can be shorter than the height associated with base 1102B. Thus, different process sequences can be used to achieve different etched substrate shapes and dimensions.

[0094] Figures 12A to 12C illustrate exemplary multilayer substrates at various stages of an ultrasonic manufacturing process according to embodiments of the present disclosure. Figure 12A shows the multilayer substrate 1100A before the ultrasonic process. As shown in the figure, the multilayer substrate 1200A may include a base 1202A and a plurality of nanostructures 1204A. Each of the plurality of nanostructures 1104A may include a first layer 1206A placed on the base 1202A and a second layer 1208A placed on the first layer 1206A. As shown in the figure, both the first layer 1206A and the second layer 1208A may have the same width. In some embodiments, the base 1202A and the second layer 1208A may be formed from silicon, and the first layer 1106A may be formed from silicon dioxide.

[0095] As mentioned above, silicon and silicon dioxide can be associated with different etching rates. For example, silicon can be associated with a higher etching rate than silicon dioxide. Therefore, referring to substrate 1200A, if silicon is used for base 1202A and the second layer 1208A, and silicon dioxide is used for the first layer 1206A, a concave shape can be obtained because silicon has a relatively higher etching rate compared to silicon dioxide. Nanostructures with a concave shape can be used in light trapping applications such as color-selective waveguides and / or solar cells.

[0096] Figure 12B shows a concave-angle substrate 1200B manufactured according to an embodiment of the present disclosure, for example, by applying a base-water-acid-water process sequence to a substrate 1200A. As shown in the figure, the stepped substrate 1200B may include a base 1202B and a plurality of nanostructures 1204B. Each nanostructure 1204B may include a first layer of silicon 1206B, a second layer of silicon dioxide 1208B, and a third layer of silicon 1210B. As shown in the figure, the third layer 1210B may be placed on the base 1202B, the first layer 1206B may be placed on the third layer 1210B, and the second layer 1208B may be placed on the first layer. As shown in the figure, the substrate 1200B may have a concave-angle shape in which the width of each layer, for example, the first layer 1206B, the second layer 1208B, and the third layer 1210B may differ. For example, the first layer 1206B can be wider than the second and third layers 1208B and 1210B. In some examples, the third layer 1210B can be wider than the second layer 1208B.

[0097] The differences in width between the first layer 1206B, the second layer 1208B, and the third layer 1210B can be attributed to the relative differences in etching rates between silicon and silicon dioxide during the sonication process sequence. For example, as described above, the base-water-acid-water process sequence may provide an etching rate of approximately 1–4 nm for silicon and approximately 0 nm for silicon dioxide. These exemplary etching rates are consistent with the shape of substrate 1200B compared to substrate 1200A. For example, the first layer 1206B of silicon dioxide may have approximately the same dimensions as the first layer 1206A. In contrast, the second layer 1208A of silicon may have a smaller width than the second layer 1208A. Furthermore, the third layer 1210B of silicon may be etched from base 1202A. For example, during the etching process, a series of materials can be removed from the silicon base 1202A, forming a third layer 1210B below the first layer 1206A. Thus, the base 1202B can be shorter than the base 1202A.

[0098] Figure 12C shows a concave-angle substrate 1200C manufactured according to an embodiment of the present disclosure, for example, by applying a base-acid-water process sequence to a substrate 1200A. As shown in Figure 12C, the substrate 1200C may include a silicon base 1202C and one or more nanostructures 1204C. Each nanostructure 1204C may include a first layer of silicon 1206C, a second layer of silicon dioxide 1208C, and a third layer of silicon 1210C. As shown in the figure, the third layer 1210C may be placed on the base 1202C, the first layer 1206C may be placed on the third layer 1210C, and the second layer 1208C may be placed on the first layer. As shown in the figure, the substrate 1200C may have a concave-angle shape in which the widths of each layer, for example, the first layer 1206C, the second layer 1208C, and the third layer 1210C, may differ. For example, the first layer 1206C can be wider than the second and third layers 1208C and 1210C. In some examples, the third layer 1210C can be wider than the second layer 1208C.

[0099] The differences in width between the first layer 1206C, the second layer 1208C, and the third layer 1210C can be attributed to the relative differences in etching rates between silicon and silicon dioxide during the ultrasonic processing sequence. For example, as described above, the base-acid-water process sequence may provide etching rates of approximately 1–4 nm for silicon and approximately 0.2–0.7 nm for silicon dioxide. These exemplary etching rates are consistent with the shape of substrate 1200C compared to substrates 1200A and 1200C. For example, each of the first and second layers 1206C and 1208C may have a smaller width than the first and second layers 1206A and 1208A. Furthermore, the first layer 1206C of silicon dioxide may have smaller dimensions, such as width and height, than the first layer 1206B. As described above with respect to the third layer 1210B, the third silicon layer 1210C can be etched from the base 1202A. For example, during the etching process, a series of materials can be removed from the silicon base 1202A, forming the third layer 1210C below the first layer 1206A. Thus, the base 1202C can be shorter than the base 1202A.

[0100] Furthermore, referring to both substrates 1200B and 1200C, sonication provides a substantially uniform reaction environment across the surface of the substrate, allowing the stepped nanostructure 1204C to be centered, for example, so that each nanostructure 1204C can have a symmetrical cross-section. Centering such nanostructures using conventional lithography techniques can be difficult and expensive to achieve due to the scale of the structure. Moreover, sonication provides a smooth LER and can reduce the occurrence of line breaks compared to conventional lithography techniques.

[0101] As described above, substrates 1200B and 1200C illustrate the effect of applying different process sequences to template substrates. For example, silicon dioxide is associated with a higher etching rate when the base-acid-water process sequence is applied to substrate 1200C than when the base-acid-water process sequence is applied to substrate 1200B. Therefore, as shown in the figure, the first layer 1206C can have a smaller width than the first layer 1206B. Similarly, the height associated with base 1202C can be shorter than the height associated with base 1202B. Thus, different process sequences can be used to achieve different etched substrate shapes and dimensions.

[0102] Figures 13A to 13E illustrate exemplary multilayer substrates at various stages in an ultrasonic manufacturing process according to embodiments of the present disclosure. Figure 13A shows the multilayer substrate 1300A before the ultrasonic process. As shown in the figure, the multilayer substrate 1300A may include a base 1302A and a plurality of nanostructures 1304A. Each of the plurality of nanostructures 1304A may include a first layer 1306A placed on the base 1302A and a second layer 1308A placed on the first layer 1306A. As shown in the figure, both the first layer 1306A and the second layer 1308A may have the same width. In some embodiments, the base 1302A and the first layer 1306A may be formed from silicon dioxide, and the second layer 1308A may be formed from silicon. As described above, silicon and silicon dioxide may be associated with different etching rates. For example, silicon may be associated with a higher etching rate than silicon dioxide. Therefore, referring to the substrate 1300A, if silicon dioxide is used for the base 1302A and the first layer 1306A, and silicon is used for the second layer 1308A, the first layer may have a lower etching rate than the second layer.

[0103] Figure 13E shows an exemplary substrate 1300E having a blazed shape, manufactured according to embodiments of the present disclosure. In one or more embodiments, the substrate 1300E can be manufactured by an ultrasonic sequencing process according to an example of the present disclosure, e.g., a base-water-acid-water sequencing process and / or a base-acid-water sequencing process. As shown in the figure, the blazed shape may include a first layer 1306E placed on the base 1302E and a second layer 1308E placed on the first layer 1306E. For example, the first layer may be formed from silicon dioxide and the second layer may be formed from silicon. As shown in the figure, the first layer 1306E may be wider than the second layer 1308E, but at least one side of the first layer 1306E and the second layer 1308E may be aligned to form an asymmetric blazed structure.

[0104] Figures 13B–13D show exemplary substrates 1300B–1300D and illustrate intermediate steps in the manufacturing of substrate 1300E. As shown in these figures, masks 1312B–1312D can be placed on one or more surfaces of the substrate. Masks 1312B–1312D can be formed from materials that do not react with the acid and base solutions used during the sonication sequence process. In some embodiments, the mask may be a chromium mask, but other materials can be used without departing from the scope of this disclosure. Thus, during sonication, the masked substrate surface may not be etched, or it may be etched to produce an asymmetrical blazed shape.

[0105] Exemplary ultrasonic treatment process sequence Figure 14 shows an exemplary block diagram relating to a process 1400 for manufacturing a multilayer structure according to embodiments of the present disclosure. For example, process 1400 may involve steps for manufacturing multilayer substrates, such as substrates 1100B, 1200B, and 1300D, using a base-water-acid-water process sequence. The following steps relating to process 1400 may be described in reference to Figures 11A and 11B, and this is not intended to limit the process to other substrates, such as 600B, 700B, and 700C.

[0106] In one or more embodiments, a substrate, for example, substrate 1100A, can be deposited and immersed in a bath of a base solution, for example, a liquid bath 506, and ultrasonic treatment can be performed by applying sound waves to the bath (step 1402). For example, to perform ultrasonic treatment, a transducer, for example 502, can be applied to the solution, for example 506. As described above, the base solution can react with the surface of the substrate. Furthermore, the applied sound waves can agitate the base solution so that reacted molecules can be continuously removed and unreacted base solution can be continuously replenished on the surface of the substrate. In one or more examples, immersion of the substrate in a base solution can prime the substrate surface for reaction with a subsequent solution, for example, an acid solution, but does not result in the removal of material, for example, a reduction in the size of one or more nanostructures. For example, the base solution can lower the energy barrier and weaken the bonds between molecules located on or near the substrate surface. In some embodiments, after a predetermined time, the substrate can be removed from the bath of base solution (step 1404). The time can be based, for example, on the desired shape of the manufactured structure and the etching rate of the substrate material with respect to given ultrasonic treatment conditions, such as temperature and base solution concentration.

[0107] In some embodiments, the substrate can be immersed in a water bath, and ultrasonic treatment can be applied to the bath (step 1406). As described above, the water can react with the silicon and silicon dioxide present on the surface of the substrate. As described above, ultrasonic treatment of the water bath can continuously provide a reactive environment to the surface of the substrate. In some embodiments, after a predetermined time, the substrate can be removed from the water bath (step 1408). In some embodiments, the amount of time can be based, for example, on the desired shape of the manufactured structure and the etching rate of the substrate material with respect to given ultrasonic treatment conditions, such as temperature, acid and base solution concentrations, etc.

[0108] In some embodiments, the substrate can be immersed in a bath of acid solution, and sonication can be applied to the bath (step 1410). In some embodiments, the acid solution can react with silicon and silicon dioxide present on the surface of the substrate, and a predetermined volume of material can be removed based on the length of time the sonication is applied to the substrate. As described above, sonication of a water bath can continuously provide a reactive environment to the surface of the substrate. In some embodiments, after a predetermined time, the substrate can be removed from the bath of acid solution (step 1412). In some embodiments, the volume of material removed can be based on one or more sonication conditions, including but not limited to temperature, acid and base solution concentrations, and the time of exposure to the solution. In some embodiments, the amount of time can be based, for example, on the desired shape of the manufactured structure and the etching rate of the substrate material against given sonication conditions, such as temperature, acid solution concentration, etc.

[0109] In some embodiments, the substrate can be immersed in a water bath, and ultrasonic treatment can be applied to the bath (step 1414). In some examples, the water can remove reactants, residues, and / or debris from the surface of the substrate. In some examples, the water can provide a clean surface free of reactants. As described above, ultrasonic treatment of the water bath can continuously provide a reactive environment to the surface of the substrate. In some embodiments, after a predetermined time, the substrate can be removed from the water bath (step 1416). In some embodiments, the substrate removed from the bath in step 1416 may correspond to substrates 600B, 700B, 700C, 1100B, 1200B, and / or substrate 1300D.

[0110] Figure 15 shows an exemplary block diagram relating to a process 1500 for manufacturing a multilayer structure according to embodiments of the present disclosure. For example, process 1500 may relate to steps for manufacturing multilayer substrates, such as substrates 1100C, 1200C, and 1300D, using a base-acid-water process sequence. The following steps relating to process 1500 may be described in reference to Figures 11A and 11C, and this is not intended to limit the process to other substrates, such as 800B, 900B, 1000B, 1200C, and 1300D.

[0111] In one or more embodiments, a substrate, for example, substrate 1100A, can be immersed in a bath of a base solution, for example, a liquid bath 506, and sound waves can be applied to the bath to perform ultrasonic treatment (step 1502). Step 1502 may be the same as step 1402 described above. In some embodiments, after a predetermined time, the substrate can be removed from the bath of the base solution (step 1504). The amount of time can be based, for example, on the desired shape of the manufactured structure and the etching rate of the substrate material with respect to given ultrasonic treatment conditions, such as temperature, base solution concentration, etc.

[0112] In some embodiments, the substrate can be immersed in a bath of acid solution, and sonication can be applied to the bath (step 1506). Step 1506 may be the same as step 1410 described above. In some embodiments, after a predetermined time, the substrate can be removed from the bath of acid solution (step 1508). In some embodiments, the amount of time can be based, for example, on the desired shape of the manufactured structure and the etching rate of the substrate material with respect to given sonication conditions, such as temperature, acid solution concentration, etc.

[0113] In some embodiments, the substrate can be immersed in a water bath, and ultrasonic treatment can be applied to the bath (step 1510). Step 1510 may be the same as step 1414 described above. In some embodiments, after a predetermined time, the substrate can be removed from the water bath (step 1512). In some embodiments, the substrate removed from the bath in step 1412 may correspond to substrate 1100C, substrate 1200C, and / or substrate 1300D.

[0114] Therefore, an ultrasonic processing sequence can be used to etch a substrate to form nanostructures suitable for the optical grating according to embodiments of the present disclosure. Such ultrasonic processing techniques can reduce one or more dimensions of an initial substrate in a controlled manner, for example, based on known etching rates of different materials, to achieve the desired geometric shape and / or dimensions of one or more nanostructures. Furthermore, since ultrasonic processing can provide a substantially uniform reaction environment across the surface of the substrate, the stepped nanostructures 1104C can be centered, for example, so that each nanostructure 1104C can have a symmetrical cross-section. In comparison, such alignment of nanostructures using conventional lithography techniques can be difficult and expensive to achieve due to the scale of the structures. Finally, the ultrasonic processing sequence according to embodiments of the present disclosure can provide a smooth LER without line breaks.

[0115] Embodiments of the present disclosure can also provide a method for manufacturing a substrate having an asymmetric cross-sectional shape. For example, Figure 16 shows an exemplary block diagram relating to a process 1600 for manufacturing a multilayer structure, such as a multilayer blazed structure, according to embodiments of the present disclosure. For example, process 1600 may relate to steps for manufacturing a blazed multilayer substrate, such as 1300E.

[0116] In one or more embodiments, a mask can be applied to one or more surfaces of the substrate (step 1602). For example, Figure 13B shows an exemplary substrate 1300B with a mask 1312B applied to its surface. As shown in the figure, the mask can be applied at an angle such that one or more surfaces of the substrate 1300B are positioned on, but not on, the entire surface. In some examples, the mask can include a GLAD (Glare-Oriented Deposition) mask and / or protective material using physical deposition such as an E-beam. The E-beam process can evaporate one or more metallic or inorganic materials, such as chromium (Cr), titanium (Ti), nickel (Ni), silicon dioxide (SiO2), titanium dioxide (TiO2), aluminum oxide (Al2O3), etc., to ensure stable adhesion of the deposited material to the coated surface. During the GLAD process, the substrate can be angled with respect to the source of the mask material, thereby creating shadows on the deposition pathways on the nanopattern on the surface of the substrate. In one or more embodiments, the mask can be a chromium mask. In one or more embodiments, the mask may be formed from a material resistant to the selected acid and base solutions used during the sonication process sequence described above.

[0117] In one or more embodiments, one or more portions of the mask can be removed (step 1604). For example, Figure 13C shows an exemplary substrate 1300C in which one or more portions of the mask have been removed so that mask 1312C remains on the surface of the substrate. One or more portions of the mask, e.g., mask 1312B, can be removed via a dry etching process. For example, plasma and / or reactive gases such as fluorocarbons, oxygen, chlorine, and / or boron trichloride can be used to remove portions of the mask. In some examples, dry etching can be antistrope so that portions of the mask located on a horizontal substrate surface are removed, but portions of the mask on a vertical substrate surface remain. In some examples, other antistrope mask removal processes can be used. As shown in the figure, following step 1604, the remaining mask 1312C can be positioned along the right vertical side of the nanostructure 1304C.

[0118] In one or more embodiments, the sonication processes described above, for example, sonication process 1400 and / or sonication process 1500, can be applied to a substrate (step 1606). For example, the base-water-acid-water sonication process and / or the base-acid-water sonication process can be applied to a substrate, for example, substrate 1300C. Figure 13D shows an exemplary substrate 1300D after the sonication process has been applied. As shown in the figure, the sonication process can remove material from one or more layers of the nanostructure 1304D. For example, material can be removed from the second layer 1308D of silicon. As shown in the figure, a mask 1312D positioned along the right edge of the nanostructure 1304D can prevent material from being removed from the right edge of the nanostructure 1304D during sonication. Thus, the use of mask 1312D can prevent material from being removed from the masked surface of the substrate during sonication, thereby creating an asymmetric blazed structure.

[0119] In one or more embodiments, the remaining mask, e.g., mask 1312D, can be removed from the substrate, e.g., 1300D (step 1608). In some embodiments, the mask can be removed using a wet etching process. For example, the substrate, e.g., substrate 1300D, can be immersed in a solution configured to etch the mask, e.g., 1312D, without reacting with and / or removing the substrate material, e.g., silicon and silicon dioxide. Figure 13E shows an exemplary blazed substrate 1300E that can be produced by process 1600.

[0120] This specification discloses systems and methods for manufacturing nanostructures on a substrate. A substrate containing multiple nanostructures can be used for eyepieces for displays such as headwearable devices. An exemplary method for manufacturing and / or etching a substrate containing multiple nanostructures for eyepieces may include immersing the substrate in a bath and applying sonication to the bath over a first period. The sonication applied to the first bath can agitate the fluid to provide a substantially uniform first reactive environment across the surface of the substrate. Embodiments disclosed herein may provide a robust and easily manufactured display system that can provide consistent digital image quality during use. The substrate may be immersed in a second bath, and sonication may be applied to the second bath over a second period. The sonication applied to the second bath can agitate the fluid to provide a substantially uniform second reactive environment across the surface of the substrate. In some examples, a predetermined amount of material may be removed from the surface of the substrate during the second period to produce an etched substrate. In some examples, the predetermined amount of material to be removed may depend on the length of the first period and further on the length of the second period.

[0121] In one or more examples, a process for fabricating nanostructures on a substrate may include depositing a mask on one or more surfaces of the substrate and removing one or more portions of the mask from the substrate. In some examples, at least a portion of the substrate surface is masked during etching.

[0122] In one or more examples, a predetermined amount of material can be uniformly removed from the surface of a substrate so that the cross-sections of multiple nanostructures of the etched substrate can be symmetrical. In one or more examples, the thickness of the predetermined amount of material removed from the surface can be in the range of approximately 5 to 50 nm.

[0123] In one or more examples, the substrate may include a base containing a first material. Multiple nanostructures may be arranged on the base, and the nanostructures may include a first layer. In some examples, the first layer may include a second material different from the first material. In some examples, the nanostructures may have a substantially uniform width. In some examples, the base may be associated with a first etching rate of a first set of sonication conditions. The first layer may be associated with a second etching rate of a first set of sonication conditions. In one or more examples, the substrate may be formed from at least one selected from silicon, silicon dioxide, and silicon nitride. In one or more examples, the acid solution may include sulfuric acid at a concentration of about 2% in water. In one or more examples, the base solution may include hydrogen peroxide or potassium hydroxide at a concentration of about 2% in water.

[0124] In one or more examples, each nanostructure of the multiple nanostructures may have a geometric shape corresponding to one selected from stepped, concave, and blazed shapes. In one or more examples, the sonication conditions may include one or more of the temperature associated with one or more of the first and second baths, the duration associated with the first period, the duration associated with the second period, the concentration of the acid solution, and the concentration of the base solution.

[0125] The compounds according to embodiments of the present disclosure may include a substrate comprising a base having a first surface and a plurality of nanostructures disposed on the first surface. In some examples, the substrate may be configured to be etched by applying a sonication process sequence to the substrate to form an etched substrate. In some examples, the etched substrate may comprise a plurality of etched nanostructures, which may be produced by removing a first predetermined amount of material from the first surface and a second predetermined amount of material from one or more surfaces of the plurality of nanostructures.

[0126] In one or more examples, the thickness of a predetermined amount of material removed from the surface of the substrate can be in the range of approximately 5 to 50 nm. In one or more examples, a predetermined amount of material can be uniformly removed from the first surface and one or more surfaces of multiple nanostructures so that the cross-sections of multiple etched nanostructures of the etched substrate can be symmetrical.

[0127] In one or more examples, the sonication process sequence may include immersing a substrate in a first bath, the first bath containing a first fluid, and applying sonication to the first bath over a first period, wherein the application of sonication agitates the first fluid to provide a substantially uniform first reactive environment across the surface of the substrate. In some examples, the sonication process sequence may include immersing a substrate in a second bath, the second bath containing a second fluid, and applying sonication to the second bath over a second period, wherein the application of sonication agitates the second fluid to provide a substantially uniform second reactive environment across the surface of the substrate. In one or more examples, a predetermined amount of material may be removed during the second period to produce an etched substrate. In one or more examples, the amount of the predetermined amount of material may be based on the length of the first period and further on the length of the second period. In one or more examples, the sonication conditions may include one or more of the following: temperature associated with one or more of the first and second baths, duration associated with the first period, duration associated with the second period, concentration of the acid solution, and concentration of the base solution.

[0128] In one or more examples, the base of the substrate may contain a first material, and the nanostructures of a plurality of nanostructures may form a first layer, the first layer containing a second material different from the first material. In one or more examples, the base may be associated with a first etching rate of a first set of sonication conditions, and the first layer may be associated with a second etching rate of a first set of sonication conditions. In one or more examples, the substrate may be formed from at least one selected from silicon, silicon dioxide, and silicon nitride. In one or more examples, the acid solution may contain sulfuric acid at a concentration of about 2% in water. In one or more examples, the base solution may contain hydrogen peroxide or potassium hydroxide at a concentration of about 2% in water.

[0129] In one or more examples, each nanostructure of the multiple nanostructures has a substantially uniform width. In one or more examples, each etched nanostructure of the multiple nanostructures may have a geometric shape corresponding to one selected from stepped, concave, and blazed shapes.

[0130] While the disclosed examples are adequately illustrated with reference to the accompanying drawings, it should be noted that various variations and modifications will be apparent to those skilled in the art. For example, elements and / or components shown in the drawings may not be to scale and / or may be exaggerated for illustrative purposes. As another example, elements of one or more implementations may be combined, deleted, modified, or supplemented to form further implementations. Other combinations and modifications should be understood to fall within the scope of the disclosed examples as defined by the accompanying claims.

Claims

[Claim 1] The invention described herein.

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