Patent Publication Number: US-2023160820-A1

Title: Tunable shrinkage and trim process for fabricating gratings

Description:
CROSS REFERENCE TO RELATED APPLICATION 
     This application claims the benefit of priority to U.S. Provisional Application No. 63/282,160, filed on Nov. 22, 2021. The content of the above-mentioned application is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The present disclosure generally relates to fabrication methods of gratings and, more specifically, to tunable shrinkage and trim process for fabricating gratings. 
     BACKGROUND 
     An artificial reality system, such as a head-mounted display (“HMD”) or heads-up display (“HUD”) system, generally includes a near-eye display (“NED”) system in the form of a headset or a pair of glasses, and configured to present content to a user via an electronic or optic display within, for example, about 10-20 mm in front of the eyes of a user. The NED system may display virtual objects or combine images of real objects with virtual objects, as in virtual reality (“VR”), augmented reality (“AR”), or mixed reality (“MR”) applications. For example, in an AR system, a user may view both images of virtual objects (e.g., computer-generated images (“CGIs”)) and the surrounding environment by, for example, seeing through transparent display glasses or lenses (also referred to as an optical see-through AR system). 
     One example of an optical see-through AR system may include a pupil-expansion light guide display system, in which an image light representing a CGI may be coupled into a light guide (e.g., a transparent substrate), propagate within the light guide, and be coupled out of the light guide at different locations to expand an effective pupil. Diffractive optical elements may be coupled with the light guide to couple the image light into or out of the light guide via diffraction, such as surface relief gratings, holographic gratings, metasurface gratings, etc. 
     SUMMARY OF THE DISCLOSURE 
     Consistent with an aspect of the present disclosure, a method is provided. The method includes forming a shrink material layer over a patterned substrate including a photoresist pattern. The method also includes exposing the patterned substrate with the shrink material layer to an activating radiation via a grey-tone mask that provides a predetermined light transmittance profile for the activating radiation. The method also includes removing at least a portion of the shrink material layer. 
     Consistent with another aspect of the present disclosure, a method is provided. The method includes configuring a grey-tone mask to provide a non-uniform light transmittance profile for a radiation for creating a varying duty cycle profile in a grating to be fabricated. The method also includes applying a shrink material over a photoresist pattern. The method also includes exposing the photoresist pattern with the shrink material to the radiation transmitting through the grey-tone mask to cause a reaction between the shrink material and the photoresist pattern at selective portions of the photoresist pattern covered by the shrink material. The method further includes removing at least a portion of the shrink material to form the grating. 
     Consistent with another aspect of the present disclosure, a method is provided. The method includes forming a photoresist pattern through a lithography mask via a lithography process, the photoresist pattern including a first duty cycle profile. The method also includes applying a shrink material over the photoresist pattern. The method also includes exposing the photoresist pattern with the shrink material to a radiation through a grey-tone mask having a non-uniform light transmittance profile for the radiation, the non-uniform light transmittance profile corresponding to a second duty cycle profile that is different from the first duty cycle profile. The method further includes removing at least a portion of the shrink material to form a grating having the second duty cycle profile. 
     Other aspects of the present disclosure can be understood by those skilled in the art in light of the description, the claims, and the drawings of the present disclosure. The foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The following drawings are provided for illustrative purposes according to various disclosed embodiments and are not intended to limit the scope of the present disclosure. In the drawings: 
         FIGS.  1 A- 1 C  illustrate schematic diagrams showing processes for selectively reducing critical dimensions of lithography-defined features, according to an embodiment of the present disclosure; 
         FIGS.  2 A- 2 C  illustrate schematic diagrams showing processes for selectively reducing critical dimensions of lithography-defined features, according to an embodiment of the present disclosure; 
         FIGS.  3 A- 3 C  illustrate schematic diagrams showing processes for selectively reducing critical dimensions of lithography-defined features, according to an embodiment of the present disclosure; 
         FIGS.  4 A- 4 C  illustrate schematic diagrams showing processes for selectively reducing critical dimensions of lithography-defined features, according to an embodiment of the present disclosure; 
         FIG.  5 A  illustrates a schematic diagram of a grey-tone mask configured with a one-dimensional (“1D”) light transmittance variation, according to an embodiment of the present disclosure; 
         FIG.  5 B  illustrates a schematic diagram of a grey-tone mask configured with a two-dimensional (“2D”) light transmittance variation, according to an embodiment of the present disclosure; 
         FIG.  6 A  illustrates a flow chart showing a method for selectively reducing critical dimensions of lithography-defined features, according to an embodiment of the present disclosure; 
         FIG.  6 B  illustrates a flow chart showing a method for selectively reducing critical dimensions of lithography-defined features, according to an embodiment of the present disclosure; 
         FIG.  6 C  illustrates a flow chart showing a method for selectively reducing critical dimensions of lithography-defined features, according to an embodiment of the present disclosure; 
         FIG.  6 D  illustrates a flow chart showing a method for selectively reducing critical dimensions of lithography-defined features, according to an embodiment of the present disclosure; 
         FIGS.  7 A and  7 B  schematically illustrate diagrams of light guide display systems, according to various embodiments of the present disclosure; 
         FIG.  8 A  schematically illustrates a diagram of a near-eye display (“NED”), according to an embodiment of the present disclosure; and 
         FIG.  8 B  schematically illustrates a cross-sectional view of half of the NED shown in  FIG.  8 A , according to an embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Embodiments consistent with the present disclosure will be described with reference to the accompanying drawings, which are merely examples for illustrative purposes and are not intended to limit the scope of the present disclosure. Wherever possible, the same reference numbers are used throughout the drawings to refer to the same or similar parts, and a detailed description thereof may be omitted. 
     Further, in the present disclosure, the disclosed embodiments and the features of the disclosed embodiments may be combined. The described embodiments are some but not all of the embodiments of the present disclosure. Based on the disclosed embodiments, persons of ordinary skill in the art may derive other embodiments consistent with the present disclosure. For example, modifications, adaptations, substitutions, additions, or other variations may be made based on the disclosed embodiments. Such variations of the disclosed embodiments are still within the scope of the present disclosure. Accordingly, the present disclosure is not limited to the disclosed embodiments. Instead, the scope of the present disclosure is defined by the appended claims. 
     As used herein, the terms “couple,” “coupled,” “coupling,” or the like may encompass an optical coupling, a mechanical coupling, an electrical coupling, an electromagnetic coupling, or any combination thereof. An “optical coupling” between two optical elements refers to a configuration in which the two optical elements are arranged in an optical series, and a light output from one optical element may be directly or indirectly received by the other optical element. An optical series refers to optical positioning of a plurality of optical elements in a light path, such that a light output from one optical element may be transmitted, reflected, diffracted, converted, modified, or otherwise processed or manipulated by one or more of other optical elements. In some embodiments, the sequence in which the plurality of optical elements are arranged may or may not affect an overall output of the plurality of optical elements. A coupling may be a direct coupling or an indirect coupling (e.g., coupling through an intermediate element). 
     The phrase “at least one of A or B” may encompass all combinations of A and B, such as A only, B only, or A and B. Likewise, the phrase “at least one of A, B, or C” may encompass all combinations of A, B, and C, such as A only, B only, C only, A and B, A and C, B and C, or A and B and C. The phrase “A and/or B” may be interpreted in a manner similar to that of the phrase “at least one of A or B.” For example, the phrase “A and/or B” may encompass all combinations of A and B, such as A only, B only, or A and B. Likewise, the phrase “A, B, and/or C” has a meaning similar to that of the phrase “at least one of A, B, or C.” For example, the phrase “A, B, and/or C” may encompass all combinations of A, B, and C, such as A only, B only, C only, A and B, A and C, B and C, or A and B and C. 
     When a first element is described as “attached,” “provided,” “formed,” “affixed,” “mounted,” “secured,” “connected,” “bonded,” “recorded,” or “disposed,” to, on, at, or at least partially in a second element, the first element may be “attached,” “provided,” “formed,” “affixed,” “mounted,” “secured,” “connected,” “bonded,” “recorded,” or “disposed,” to, on, at, or at least partially in the second element using any suitable mechanical or non-mechanical manner, such as depositing, coating, etching, bonding, gluing, screwing, press-fitting, snap-fitting, clamping, etc. In addition, the first element may be in direct contact with the second element, or there may be an intermediate element between the first element and the second element. The first element may be disposed at any suitable side of the second element, such as left, right, front, back, top, or bottom. 
     When the first element is shown or described as being disposed or arranged “on” the second element, term “on” is merely used to indicate an example relative orientation between the first element and the second element. The description may be based on a reference coordinate system shown in a figure, or may be based on a current view or example configuration shown in a figure. For example, when a view shown in a figure is described, the first element may be described as being disposed “on” the second element. It is understood that the term “on” may not necessarily imply that the first element is over the second element in the vertical, gravitational direction. For example, when the assembly of the first element and the second element is turned 180 degrees, the first element may be “under” the second element (or the second element may be “on” the first element). Thus, it is understood that when a figure shows that the first element is “on” the second element, the configuration is merely an illustrative example. The first element may be disposed or arranged at any suitable orientation relative to the second element (e.g., over or above the second element, below or under the second element, left to the second element, right to the second element, behind the second element, in front of the second element, etc.). 
     When the first element is described as being disposed “on” the second element, the first element may be directly or indirectly disposed on the second element. The first element being directly disposed on the second element indicates that no additional element is disposed between the first element and the second element. The first element being indirectly disposed on the second element indicates that one or more additional elements are disposed between the first element and the second element. 
     The term “processor” used herein may encompass any suitable processor, such as a central processing unit (“CPU”), a graphics processing unit (“GPU”), an application-specific integrated circuit (“ASIC”), a programmable logic device (“PLD”), or any combination thereof. Other processors not listed above may also be used. A processor may be implemented as software, hardware, firmware, or any combination thereof. 
     The term “controller” may encompass any suitable electrical circuit, software, or processor configured to generate a control signal for controlling a device, a circuit, an optical element, etc. A “controller” may be implemented as software, hardware, firmware, or any combination thereof. For example, a controller may include a processor, or may be included as a part of a processor. 
     The term “non-transitory computer-readable medium” may encompass any suitable medium for storing, transferring, communicating, broadcasting, or transmitting data, signal, or information. For example, the non-transitory computer-readable medium may include a memory, a hard disk, a magnetic disk, an optical disk, a tape, etc. The memory may include a read-only memory (“ROM”), a random-access memory (“RAM”), a flash memory, etc. 
     The term “film,” “layer,” “coating,” or “plate” may include rigid or flexible, self-supporting or free-standing film, layer, coating, or plate, which may be disposed on a supporting substrate or between substrates. The terms “film,” “layer,” “coating,” and “plate” may be interchangeable. The term “diffraction efficiency” as used herein is a quantitative measurement of the extent to which energy of an incident light is diffracted by a diffractive element. The diffraction efficiency may be defined as a ratio between an intensity (or optical power) of a diffracted light output from the diffractive element and an intensity (or optical power) of the incident light. The diffraction efficiency of the diffractive element may be calculated for a specific incident light, or a specific polarized component in the incident light. 
     In a pupil-replication or pupil-expansion light display system, a light source assembly may generate an image light representing a virtual image. An in-coupling grating may couple the image light into a light guide as an in-coupled light. The in-coupled light may propagate within the light guide toward an out-coupling grating through total internal reflection (“TIR”). Hence, the in-coupled light is also referred to as a TIR propagating light. When propagating inside the light guide, the TIR propagating light may be incident onto different portions of the out-coupling grating. The out-coupling grating may couple the TIR propagating light out of the light guide at the different portions as a plurality of out-coupled or output lights. In this manner, the out-coupling grating may replicate the image light received from the light source assembly to expand an effective pupil of the light guide display assembly. As the TIR propagating light are gradually coupled out of the light guide at different portions of the out-coupling grating, the intensity of the TIR propagating light inside the light guide may gradually decrease. When the out-coupling grating provides a uniform or constant diffraction efficiencies for the TIR propagating light (or a predetermined polarized component of the TIR propagating light) incident onto different portions of the out-coupling grating, the intensities or illuminances of the out-coupled lights may gradually decrease. Thus, the light guide display system may provide a non-uniform illuminance at the output side of the light guide, and the images perceived by eyes of a user may have a low uniformity. 
     To compensate for the decrease in the light intensity of the TIR propagating light as it is gradually coupled out of the light guide, the diffraction efficiency of the out-coupling grating may be configured to gradually increase. When a surface relief grating (“SRG”) is implemented as the out-coupling grating, the SRG may be configured to have a broad spatial variation of duty cycle ranging from, e.g., 0.1 to 0.9. The diffraction efficiency of the SRG is determined, in part, by the duty cycle. For example, as the duty cycle of the SRG increases, the diffraction efficiency may increase accordingly. Thus, the spatial variation of the duty cycle may provide a spatial variation of the diffraction efficiency at different regions of the SRG. Accordingly, the intensities or illuminances of the out-coupled lights from different portions of the light guide may be adjustable for improving the illuminance uniformity within the eye-box region. 
     In conventional lithography technologies, it may be challenging to fabricate SRGs with a substantially high duty cycle (e.g., 0.8, 0.9, etc.), due to the critical dimension being as small as 20-60 nm without using double patterning techniques and 193-nm immersion technology. State-of-the-art 193-nm lithography may use a bright field mask with negative tone development (“NTD”) and an organic developer for printing iso-hole and iso-trench. A trench shrink material may be used as a negative photoresist. However, it may be challenging to achieve varying shrinkage amounts at selective areas using traditional shrink materials and processes. In addition, it may be also challenging to fabricate SRGs with a substantially low duty cycle, e.g., 0.4, 0.3, 0.2, 0.1, etc., due to the critical dimension being as small as 20-60 nm without using double patterning techniques and the 193-nm immersion technology. State-of-the-art 193-nm lithography may use positive tone development (“PTD”) and an aqueous developer for printing features with a low duty cycle. Trim etch process is often used to further reduce the duty cycle. However, it may be challenging to achieve variable trim amounts at selective areas using traditional trim materials and processes. It may be also expensive and time consuming to change the mask for different design iterations of variable duty cycle maps, or accommodate the duty cycle correction from etch bias changes. 
     In view of the limitations in conventional technologies, the present disclosure provides various methods for selectively adjusting (e.g., reducing) critical dimensions of predefined features using a grey-tone mask. The predefined features may include a plurality of lithography-defined features of a photoresist pattern, such as photoresist lines, trenches, holes, or contact openings, etc. Through configuring a light transmittance variation of the grey-tone mask, the critical dimensions of the lithography-defined features may be selectively reduced. For example, the critical dimensions of the lithography-defined features at selective portions of the photoresist pattern may be reduced. In addition, through configuring a light transmittance variation of the grey-tone mask, the reduction amounts of the critical dimensions of the respective lithography-defined features of the photoresist pattern may be configurable, thereby providing final features of desirable critical dimensions. 
     The disclosed methods may allow much smaller critical dimensions to be defined as part of the manufacturing process for various devices, e.g., microelectronic devices (e.g., integrated circuits) and optical devices (e.g., gratings) including nano-sized features, without using a new lithography mask or changing the lithography conditions. For example, the disclosed methods and processes may be used to fabricate an SRG with nano-sized features and a broad variation of the duty cycle. The broad variation of the duty cycle of the SRG may include at least one of a substantially low duty cycle (e.g., 0.4, 0.3, 0.2, or 0.1, etc.) and/or a substantially high duty cycle (e.g., 0.8, or 0.9, etc.). For illustrative purposes, one-dimensional (“1D”) SRGs are used as examples to explain the fabrication processes and methods. The disclosed fabrication processes and methods may also be applied to fabricate two-dimensional (“2D”) SRGs and three-dimensional (“3D”) SRGs. The SRGs fabricated based on the disclosed methods and processes may be implemented as an out-coupling grating in a light guide display system to further improve the illuminance uniformity within the eye-box region. 
       FIGS.  1 A- 1 C  illustrate schematic diagrams showing processes for selectively reducing a critical dimension of predefined features (e.g., lithography-defined features), according to an embodiment of the present disclosure. For illustrative purposes, trenches in a photoresist pattern are used as examples of the predefined features (e.g., lithography-defined features) to explain the processes. The disclosed processes may also be applied to selectively reducing other predefined features (e.g., other lithography-defined features), such as holes and contact openings in a photoresist pattern. 
     As shown in  FIG.  1 A , a substrate  101  with a first photoresist pattern  104  may be provided. In some embodiments, the substrate  101  provided with the first photoresist pattern  104  may also be referred to as a patterned substrate  105 . In some embodiments, the patterned substrate  105  may include at least one of a photoresist layer, an ion implant layer, a dielectric layer, a microelectronic wafer, a microelectromechanical systems structures, or a functional surface of a microelectromechanical system. The substrate  101  may provide support and protection to various layers, films, and/or structures formed thereon. In some embodiments, the substrate  101  may be a wafer, a glass, a plastic, a sapphire, or a combination thereof, etc. In some embodiments, the substrate  101  may include silicon, a silicon substrate coated with a metal surface, a silicon wafer coated with copper, copper, aluminum, a polymeric resin, silicon dioxide, a metal, doped silicon dioxide, silicon nitride, silicon carbide, tantalum, polysilicon, ceramics, an aluminum-copper mixture, glass, coated glass, gallium arsenide, other Group III/V compounds, etc. In some embodiments, the substrate  101  may be rigid, semi-rigid, flexible, or semi-flexible. In some embodiments, the substrate  101  may include a flat surface or a curved surface, on which the various layers, films, and/or structures may be formed. In some embodiments, the substrate  101  may be a part of another element or device (e.g., another opto-electrical element or device, another electrical element or device). For example, the substrate  101  may be a solid optical lens, a part of a solid optical lens, or a light guide, etc. 
     The first photoresist pattern  104  may include a plurality of photoresist structures  103  with sizes at the nano level or micron level. The photoresist structures  103  may include a plurality of predefined features. In the embodiment shown in  FIG.  1 A , the photoresist structures  103  may be rectangular pillars (also referred to as photoresist lines  103  for discussion purposes). The cross-sections of the photoresist structures  103  may be rectangular shapes. In some embodiments, the cross-sections of the photoresist structures  103  may be triangular shapes, trapezoidal structures, more complex shapes, or a combination thereof. The photoresist structures  103  may define a plurality of openings for forming a plurality of trenches  107 . For illustrative purposes, the photoresist structures  103  are schematically illustrated as rectangular structures filled with dots, and the trenches  107  are shown as spaces between the rectangular structures filled with dots. 
     The photoresist structures  103  may be arranged in a 1D array or a 2D array on the substrate  101 . The photoresist structures  103  may be slanted or may be perpendicular with respect to the substrate  101 . In some embodiments, the photoresist structures  103  may be integrally formed as a part of the substrate  101  at a surface (e.g., an upper surface shown in  FIG.  1 A ) of the substrate  101 , based on the same material or different materials. In some embodiments, the photoresist structures  103  may be formed or disposed at (e.g., affixed to) a surface (e.g., an upper surface shown in  FIG.  1 A ) of the substrate  101 , and the photoresist structures  103  and the substrate  101  may fabricated based on the same material or different materials. 
     In some embodiments, a period or pitchp of the first photoresist pattern  104  may be defined as a distance between two neighboring photoresist structures  103 . In some embodiments, the periodp may be uniform or constant for the entire photoresist pattern  104 . In some embodiments, at least one periodp between two neighboring photoresist structures  103  may be different from another period p between another two neighboring photoresist structures  103 . That is, in some embodiments, the period p of the first photoresist pattern  104  may vary along one or two directions within a plane of the first photoresist pattern  104 . A line width w 1  of the first photoresist pattern  104  may be defined as a width of a single photoresist structure  103  of the first photoresist pattern  104 . In some embodiments, the line width w 1  may be uniform or constant for the entire photoresist pattern  104 . In some embodiments, the line width w 1  may vary along one or two directions within a plane of the first photoresist pattern  104 . That is, at least two photoresist structures  103  may have different widths. A width w 2  of the trench  107  may be a difference between the periodp and the line width w 1 . A duty cycle (“DC” in  FIG.  1 A ) of the first photoresist pattern  104  may be defined as a ratio between the line width w 1  and the period p. In some embodiments, the duty cycle of the first photoresist pattern  104  may be uniform or constant for the entire photoresist pattern  104 . In some embodiments, the duty cycle of the first photoresist pattern  104  may vary along one or two directions within a plane of the first photoresist pattern  104 , e.g., a duty cycle at a first portion of the first photoresist pattern  104  may be different from a duty cycle at a second portion of the first photoresist pattern  104 . A duty cycle variation of the first photoresist pattern  104  may be referred to as a first duty cycle variation. 
     A depth d of the first photoresist pattern  104  may be defined as a depth of the trench  107  or a height of the photoresist structure  103 . An aspect ratio of the first photoresist pattern  104  may be defined as a ratio between the depth d and the width w 2  of the trench  107 . The respective trench  107  may have two sidewalls and a bottom wall between the two sidewalls. The height of the sidewall may be equal to the depth d of the first photoresist pattern  104 , and the width of the bottom wall may be equal to the width w 2  of the trench  107 . The width w 2  of the trench  107  may be referred to as a critical dimension of the trench  107  (or of the first photoresist pattern  104 ). The respective photoresist structure  103  may include two sidewalls and a top wall between the two sidewalls. The height of the sidewall may be equal to the depth d of the first photoresist pattern  104 , and the width of the top wall may be equal to the line width w 1 . In some embodiments, a surface of the first photoresist pattern  104  may include the sidewalls of the respective photoresist structures  103  (or the sidewalls of the respective trenches  107 ), the top walls of the respective photoresist structures  103 , and the bottom walls of the respective trenches  107 . 
     In some embodiments, the patterned substrate  105  may function as a patterned grating (e.g., an SRG)  105 , and the photoresist structures  103  may function as the grating lines or grating elements. For discussion purposes, such a patterned grating (e.g., an SRG)  105  may be referred to as a base grating (e.g., a base SRG)  105 . For example, the base SRG  105  may be a 1D grating or a 2D grating. The base SRG  105  may be a slanted grating or a non-slanted grating. The base SRG  105  may function as an optically isotropic grating or an optically anisotropic grating. The base SRG  105  may be a reflective grating or a transmission grating. For illustrative purposes,  FIG.  1 A  shows the patterned substrate  105  as a 1D, binary non-slanted grating with a rectangular profile. In some embodiments ,the patterned grating  105  may be a slant grating with a complex profile, e.g., a step profile, a triangular profile, a trapezoidal profile, or a combination thereof, or a blazed grating. 
     For illustrative purposes,  FIG.  1 A  shows that the periodp of the first photoresist pattern  104  may be uniform or constant for the entire photoresist pattern  104 , e.g., about 200 nm. The width w 2  of the trenches  107  may not be uniform or constant for the entire photoresist pattern  104 . For example, the width w 2  of the trench  107  may decrease in +x-axis direction, and the widths w 2  of the trenches  107  located at a left portion, a central portion, and a right portion of the first photoresist pattern  104  may be 100 nm, 60 nm, and 60 nm, respectively. Accordingly, the duty cycle at the left portion, the central portion, and the right portion of the first photoresist pattern  104  may be calculated as 0.5, 0.7, and 0.7, respectively. Although not shown, in some embodiments, the plurality of trenches  107  may be configured with a predetermined 1D or 2D width variation in one or two dimensions within a plane (e.g., an x-y plane shown in  FIG.  1 A ) perpendicular to a thickness direction (e.g., a z-axis direction shown in  FIG.  1 A ) of the first photoresist pattern  104 . Accordingly, the first photoresist pattern  104  may be configured with a predetermined 1D or 2D duty cycle variation in one or two dimensions within the plane (e.g., the x-y plane shown in  FIG.  1 A ) perpendicular to the thickness direction (e.g., the z-axis direction shown in  FIG.  1 A ) of the first photoresist pattern  104 . In some embodiments, the period p, the linewidth w 1 , and the duty cycle of the first photoresist pattern  104  may be uniform for the entire photoresist pattern  104 , respectively, such as a first photoresist pattern  204  used in the processes shown in  FIGS.  2 A- 2 C . 
     The patterned substrate  105  may be fabricated using any suitable methods, such as etching, lithography (e.g., photolithography, holographic lithography, or nano-imprint lithography, etc.), ink-jet printing, or micro-molding, etc. In some embodiments, the fabrication processes of the patterned substrate  105  may include forming a layer of a photoresist composition (also referred to as  103  for discussion purposes) over the substrate  101 ; exposing the layer of the photoresist composition  103  to an activating radiation (referred to as a first activating radiation) through a patterned photomask; and developing the exposed layer of the photoresist composition  103  in a developer base to form the first photoresist pattern  104 . 
     In some embodiments, the photoresist composition  103  may include a mixture of a photoresist (e.g., a polymer or monomers) and one or more photosensitive compound (e.g., one or more photoacid generators (“PAGs”)). In some embodiments, the photoresist composition  103  may include a first PAG configured to generate acid groups (referred to as first acid groups) when subject to the first activating radiation. The first acid groups may react with the photoresist in the layer of the photoresist composition  103 , resulting in a solubility difference between the exposed regions and the unexposed regions of the layer of the photoresist composition  103  in the developer base. That is, the first PAG may be configured for the formation of the first photoresist pattern  104 , and may be referred to as a PAG for primary exposure. In some embodiments, the photoresist composition  103  may include additional ingredients, e.g., a second PAG different from the first PAG, an initiator for polymerization, etc. 
     In some embodiments, the photoresist composition  103  may be dissolved in one or more solvents to form a solution, and the solution may be applied over (e.g., coated on) the substrate  101  to form the layer of the photoresist composition  103 . In some embodiments, after forming the layer of the photoresist composition  103  over the substrate  101 , and before exposing the layer of the photoresist composition  103  to the first activating radiation through the patterned photomask, the fabrication processes of the patterned substrate  105  may further include heat treating the layer of the photoresist composition  103  in a softbake process (e.g., post apply baking) to remove the one or more solvents. 
     In some embodiments, the patterned photomask may be a binary half-tone photomask that uses two levels of grey tones (e.g., including optically opaque regions with about 0% light transmittance and optically transparent regions with about 100% light transmittance). The first activating radiation through the patterned photomask may activate the first PAG to generate first acid groups that react with the photoresist in the layer of the photoresist composition  103 , resulting in a solubility difference between the exposed regions and the unexposed regions of the layer of the photoresist composition  103  in the developer base. In some embodiments, the photoresist composition  103  may include a positive photoresist, and the exposed regions of the layer of the photoresist composition  103  corresponding to the optically transparent regions of the patterned photomask may be soluble and removed in the subsequent development step (e.g., via an aqueous developer base). In some embodiments, the photoresist composition  103  may include a negative photoresist, and the unexposed regions of the layer of the photoresist composition  103  corresponding to the optically opaque regions of the patterned photomask may be soluble and removed in the subsequent development step (e.g., via an organic developer base). In some embodiments, after exposing the layer of the photoresist composition  103  to the activating radiation through the patterned photomask, and before developing the exposed layer of the photoresist composition  103  to form the first photoresist pattern  104 , the fabrication processes of the patterned substrate  105  may further include heat treating the layer of the photoresist composition  103  in a hardbake process (e.g., post exposure baking). 
     Referring to  FIG.  1 A , after the patterned substrate  105  is provided, a layer of a shrink material  110  (also referred to as a shrink material layer  110 ) may be formed over the patterned substrate  105 . The shrink material layer  110  may be formed at the patterned substrate  105  using any suitable methods, e.g., coating, dipping, deposition, etc. In some embodiments, the shrink material  110  may be dissolved in a mixture of one or more solvents (e.g., one or more organic solvents) to form a solution. A suitable amount of the solution may be dispensed on the patterned substrate  105  using any suitable solution dispensing process, e.g., spin coating, slot coating, blade coating, roll-coating, spray coating, or jet (ink-jet) coating or printing, etc. In some embodiments, the formed shrink material layer  110  may be heat treated in a softbake process (e.g., post apply baking) to remove the one or more solvents from the dispensed solution. 
     The shrink material layer  110  may be applied to at least a portion of the surface of the first photoresist pattern  104  to flatten or planarize the first photoresist pattern  104 . At least one (e.g., each) of the trenches  107  may be filled with the shrink material  110 . For example, the entire trench  107  between the neighboring photoresist structures  103  may be filled with the shrink material  110 . The first photoresist pattern  104  provided with the shrink material layer  110  may have a substantially uniform thickness D across the entire first photoresist pattern  104 . In some embodiments, as shown in  FIG.  1 A , the shrink material  110  may be disposed at the entire surface of the first photoresist pattern  104 , e.g., covering the sidewalls of the respective photoresist structures  103  or respective trenches  107 , the top walls of the respective photoresist structures  103 , and the bottom walls of the respective trenches  107 . In such a configuration, the thickness D may be greater than the depth d of the trench  107 . In some embodiments, the shrink material  110  may not be disposed at the top walls of the respective photoresist structures  103 . In such a configuration, the thickness D may be substantially equal to the depth d of the trench  107 . 
     In some embodiments, the shrink material  110  may include a polymer or small molecules (e.g., molecule weight less than 1000) with protected amine functionalities (e.g., including one or more amine functional groups and one or more amine protecting groups). Examples of the polymer or small molecules with protected amine functionalities may include tert-butyl carbamate methacrylate- polymethyl methacrylate (“PMMA”) copolymer, methacrylate copolymer with photobase generator group, etc. The polymer or small molecules with protected amine functionalities may be soluble in a mixture of one or more organic solvents to form a solution. At least one of the organic solvents may have a boiling point greater than 150° C. Examples of the organic solvent may include propylene glycol methyl ether acetate (“PGMEA”), propylene glycol methyl ether, anisole, cyclohexanone, propylene carbonate, di(propylene glycol) butyl ether, di(propylene glycol) methyl ether, di(propylene glycol) methyl ether acetate, butyl lactate, 2-ethylhexyl-lactate, benzyl benzoate, n-methyl-2-pyrrolidinone, gamma-butyrolactone, tripropylene glycolmethylether, 1,6-diacetoxyhexane, 3-phenoxy toluene, benzyl alcohol, tolyl ether, terpineol, etc. In some embodiments, the total solid content in the formulation may be within a range of about 0.5-10 wt%. For example, the concentration of the polymer or small molecules with protected amine functionalities in the solution may be within a range of about 0.5-10 wt%. In some embodiments, the solution may include PGMEA, dissolved with tert-butyl carbamate methacrylate-PMMA copolymer of 5 wt% and a photoacid generator of 1 wt%. In some embodiments, the solution may include PGMEA, dissolved with methacrylate copolymer with a photobase generator group of 5 wt%. 
     In some embodiments, the shrink material  110  may include monomers that are photopolymerizable. The photo-polymerization of the shrink material  110  may result in a shrink of the trench  107 . Such a photo-polymerization of the shrink material  110  may also be referred to as a shrink polymerization for discussion purposes. Examples of the monomers capable of shrink polymerization may include cross-linkable acrylate-methacrylate mixtures (e.g., Bisphenol A (“BPA”) diacrylate), thiol-ene compositions including aromatic thiols (e.g., benzene dithiol isomers) and aromatic ene (or yne) monomers (e.g., BPA diallyl ether), epoxy or glycidyl ether or oxetane monomers including fluorene bisglycidyl ether or other aromatic cyclic ethers, etc. The monomers may be soluble in a mixture of one or more organic solvents to form a solution. At least one of the organic solvents may have a boiling point greater than 150° C. In some embodiments, the total solid content in the formulation may be within a range of about 0.5-10 wt%. For example, the concentration of the monomers in the solution may be within a range of about 0.5-10 wt%. Examples of the organic solvent may include PGMEA, propylene glycol methyl ether, anisole, cyclohexanone, propylene carbonate, di(propylene glycol) butyl ether, di(propylene glycol) methyl ether, di(propylene glycol) methyl ether acetate, butyl lactate, 2-ethylhexyl-lactate, benzyl benzoate, n-methyl-2-pyrrolidinone, gamma-butyrolactone, tripropylene glycolmethylether, 1,6-diacetoxyhexane, 3-phenoxy toluene, benzyl alcohol, tolyl ether, terpineol, etc. 
     The patterned substrate  105  may include a photosensitive material that may be activated when the patterned substrate  105  with the shrink material layer  110  is exposed to an activating radiation, e.g., a second activating radiation different from the first activating radiation. The activated photosensitive material may react with the shrink material  110 . Such a photosensitive material may be referred to as a photosensitive material for secondary exposure. In some embodiments, the photosensitive material for secondary exposure may be included in the first photoresist pattern  104 . For example, the photoresist structures  103  may be configured to include the photosensitive material for secondary exposure before forming the solution for dispensing. Thus, the photosensitive material for secondary exposure may be distributed in the first photoresist pattern  104 . 
     In some embodiments, the photosensitive material for secondary exposure may be disposed at (e.g., on) the surface of the first photoresist pattern  104 , after the first photoresist pattern  104  is fabricated and before the shrink material layer  110  is formed over the first photoresist pattern  104 . For example, before forming the shrink material layer  110  over the patterned substrate  105 , a solution dissolved with the photosensitive material for secondary exposure may be applied to the surface of the first photoresist pattern  104 . In some embodiments, the photosensitive material for secondary exposure may be at least disposed at (e.g., on) the sidewalls of the respective photoresist structures  103  (or the sidewalls of the respective trenches  107 ). In some embodiments, the photosensitive material for secondary exposure may also be disposed at the top walls of the respective photoresist structures  103 . 
     In some embodiments, the photosensitive material for secondary exposure may include a residual first PAG from the first photoresist pattern  104 . The residual first PAG may be the first PAG that has not been activated by the first activating radiation and, thus, remains in the first photoresist pattern  104  after the first photoresist pattern  104  is fabricated. In some embodiments, the photosensitive material for secondary exposure and the first PAG may be the same PAG. That is, the first PAG for fabricating the first photoresist pattern  104  (or for primary exposure) may also function as the photosensitive material for secondary exposure, and the photosensitive material for secondary exposure may be included in the first photoresist pattern  104  (or the photoresist composition  103 ). 
     In some embodiments, the photosensitive material for secondary exposure may be different from the residual first PAG in the first photoresist pattern  104 . In such an embodiment, the photosensitive material for secondary exposure may be included in the first photoresist pattern  104 , or disposed at (e.g., on) the surface of the first photoresist pattern  104  before the shrink material layer  110  is formed over the patterned substrate  105 . In some embodiments, the photosensitive material for secondary exposure and the first PAG for primary exposure may be activated by activating radiations of the same wavelength. In some embodiments, the photosensitive material for secondary exposure and the first PAG for primary exposure may be activated by activating radiations of different wavelengths. For example, the first PAG may be activated by an activating radiation with a wavelength of equal to or less than 350 nm, and the photosensitive material for secondary exposure may be activated by an activating radiation with a wavelength of greater than 350 nm. 
     In some embodiments, the shrink material  110  may be configured to include a polymer or small molecules with protected amine functionalities. The photosensitive material for secondary exposure configured to include a PAG (e.g., a second PAG) configured to generate acid groups (e.g., second acid groups), under the second activating radiation. The second acid groups may react with the amine functional groups of the molecular units (e.g., small molecules or fragments of polymeric molecules) in the shrink material  110 , de-protecting the amine functional groups. The second PAG may be included in the first photoresist pattern  104  or disposed at (e.g., on) the first photoresist pattern  104  before the shrink material layer  110  is formed over the first photoresist pattern  104 . 
     In some embodiments, the second PAG may be included in the first photoresist pattern  104 , and may include the residual first PAG from the first photoresist pattern  104 . In some embodiments, the second PAG and the first PAG may be the same PAG. That is, the PAG for primary exposure may also function as the PAG for secondary exposure. In some embodiments, the second PAG may be different from the first PAG, and the second PAG may be included in the first photoresist pattern  104 , or disposed at (e.g., on) the surface of the first photoresist pattern  104  before the shrink material layer  110  is formed over the patterned substrate  105 . In some embodiments, the second PAG and the first PAG may be activated by activating radiations of different wavelengths. For example, the first PAG may be activated by an activating radiation with a wavelength of equal to or less than 350 nm, and the second PAG may be activated by an activating radiation with a wavelength of greater than 350 nm. In some embodiments, the second PAG and the first PAG may be activated by activating radiations of the same wavelength. 
     In some embodiments, the shrink material  110  may be configured to include monomers capable of shrink polymerization, and the photosensitive material for secondary exposure may be configured to include an initiator for the photo-polymerization of the monomers. Such an initiator may be referred to as a shrink polymerization initiator for discussion purposes. The shrink polymerization initiator may be included in the first photoresist pattern  104 , or disposed at (e.g., on) the surface of the first photoresist pattern  104  before the shrink material layer  110  is formed over the patterned substrate  105 . The shrink material  110  itself may not include the shrink polymerization initiator. The shrink polymerization initiator may be configured to generate, under the second activating radiation, initiating species that may react with the monomer double bonds in the shrink material  110 , resulting in a polymerization of the monomers. The shrink polymerization initiator may be included in the first photoresist pattern  104  or disposed at (e.g., on) the first photoresist pattern  104 . In some embodiments, the photoresist composition  103  may be configured to include the shrink polymerization initiator, before the first photoresist pattern  104  is fabricated. For example, the shrink polymerization initiator and the photoresist may be mixed to form the photoresist composition  103 , and the photoresist composition  103  may be dissolved in the solvent to form the solution for dispensing. In some embodiments, the shrink polymerization initiator may be disposed at (e.g., on) the surface of the first photoresist pattern  104 , before the shrink material layer  110  is formed over the first photoresist pattern  104 . 
     In some embodiments, the shrink polymerization initiator may include a third PAG that generates initiating species for photoinduced radical polymerization of monomers under the second activating radiation. In some embodiments, the third PAG may be included in the first photoresist pattern  104 , and may include the residual first PAG from the first photoresist pattern  104  (or the photoresist composition  103 ). That is, the PAG for primary exposure may also function as the PAG for secondary exposure. In some embodiments, the third PAG may be different from the first PAG in the photoresist composition  103 , and the third PAG may be included in the first photoresist pattern  104 , or disposed at (e.g., on) the surface of the first photoresist pattern  104  before the shrink material layer  110  is formed over the patterned substrate  105 . In some embodiments, the third PAG and the first PAG may be activated by activating radiations of different wavelengths. For example, the first PAG may be activated by an activating radiation with a wavelength of equal to or less than 350 nm, and the third PAG may be activated by an activating radiation with a wavelength of greater than 350 nm. In some embodiments, the third PAG and the first PAG may be activated by activating radiations of the same wavelength. 
     In some embodiments, the shrink polymerization initiator may include a photoradical generator or photoradical initiator that generates initiating species for photoinduced cationic polymerization of monomers under an activating radiation. The photoradical initiator may be included in the first photoresist pattern  104 , or disposed at (e.g., on) the surface of the first photoresist pattern  104  before the shrink material layer  110  is formed over the patterned substrate  105 . The photoradical initiator may be classified as one-component (type I system), two-component (type II system), and multicomponent photo-initiating system. In some embodiments, the photoradical initiator may include one-component (type I system), such as phosphine oxides (e.g., phenylbis(acyl) phosphine oxide (“BAPO”), diphenyl(acyl) phosphine oxide (“TPO”)), a Norrish Type 1 initiator, etc. In some embodiments, the photoradical initiator may include two-component (type II system), such as a camphoroquinone-tertiary amine system. 
     As shown in  FIG.  1 B , after the shrink material layer  110  is formed over the patterned substrate  105 , the patterned substrate  105  provided with the shrink material layer  110  may be exposed to an activating radiation (referred to as the second activating radiation) via a grey-tone (or grey-scale) mask  115 . The grey-tone mask  115  may be configured to provide a predetermined 1D or 2D light transmittance profile of the second activating radiation. That is, at different portions of the grey-tone mask  115 , the light transmittance may be different. Any desirable light transmittance profile may be configured for the grey-tone mask  115 , depending on the duty cycle profile to be achieved for the grating. In some embodiments, the light transmittance profile may be uniform, continuously gradient, or arbitrary with desired discrete values. For example, the grey-tone mask  115  may include at least three levels of grey tones to provide at least three different levels of transmission of the second activating radiation. In some embodiments, the different levels of transmission may be 0%, 25%, 50%, 75%, and 100%, etc. Thus, when a light  117  having a spatially uniform light intensity is incident onto the grey-tone mask  115 , a transmitted light  119  of the grey-tone mask  115  may have a spatially varying light intensity. 
     In some embodiments, the grey-tone mask  115  may be configured with a predetermined 1D or 2D light transmittance variation in one or two dimensions within a plane (e.g., the x-y plane shown in  FIG.  1 B ) perpendicular to a thickness direction (e.g., the z-axis direction shown in  FIG.  1 B ) of the grey-tone mask  115 . Thus, a light transmitted through the grey-tone mask  115  may have a predetermined 1D or 2D light intensity variation in one or two dimensions within the plane perpendicular to the thickness direction of the grey-tone mask  115 . In some embodiments, in the one or two dimensions within the plane perpendicular to the thickness direction of the grey-tone mask  115 , the light transmittance of the grey-tone mask  115  may decrease or increase in a gradient manner. The gradient manner may be a linearly gradient manner, a non-linearly gradient manner, a stepped gradient manner, or a suitable combination thereof. 
     For example,  FIG.  5 A  illustrates an x-y section of a grey-tone mask  500  configured with a 1D light transmittance variation according to an embodiment of the present disclosure, and  FIG.  5 B  illustrates an x-y section of a grey-tone mask  550  configured with a 2D light transmittance variation according to an embodiment of the present disclosure. The light transmittance of the grey-tone mask  500  or  550  is represented by grey scales, in which the darker grey indicates a lower light transmittance, and the lighter grey indicates a higher light transmittance. For discussion purpose, the grey-tone mask  500  shown in  FIG.  5 A  may include six levels of grey tones arranged in the x-axis direction. The light transmittance of the grey-tone mask  550  may increase in the +x-axis direction. For discussion purpose, the grey-tone mask  500  shown in  FIG.  5 B  includes six levels of grey tones arranged in both of the x-axis direction and y-axis direction. The light transmittance of the grey-tone mask  550  may increase in both of the +x-axis direction and the +y-axis direction. 
     Referring back to  FIG.  1 B ,  FIG.  1 B  shows that the grey-tone mask  115  is configured with a 1D light transmittance variation in an x-axis direction. The light transmittance of the grey-tone mask  115  is represented by grey scales, in which the darker grey indicates a lower light transmittance, and the lighter grey indicates a higher light transmittance. For illustrative purposes,  FIG.  1 B  shows that the light transmittance of the grey-tone mask  115  increases in the +x-axis direction. Thus, the intensity of the light  119  transmitted through the grey-tone mask  115  increases in the +x-axis direction, and the patterned substrate  105  may be subject to the second activating radiation with the exposure intensity gradually increasing in the +x-axis direction. 
     In some embodiments, when exposed to the second activating radiation via the grey-tone photomask (also referred to as a secondary exposure), the patterned substrate  105  with the shrink material layer  110  may be subject to a secondary photoreaction, in which the second activating radiation may activate the photosensitive material for secondary exposure included in or disposed over the first photoresist pattern  104 , and the activated photosensitive material for secondary exposure may react with the shrink material layer  110 . For example, the second activating radiation may activate the second PAG to generate the second acid groups that may react with the amine functional groups of the molecular units (e.g., small molecules or fragments of polymeric molecules) in the shrink material  110 , or activate the shrink polymerization initiator to generate the initiating species that may react with the monomer double bonds in the shrink material  110 . 
     The amount of the second acid groups or initiating species generated in the first photoresist pattern  104  may be determined, in part, by the intensity of the second activating radiation. In some embodiments, the second activating radiation with a higher intensity may generate more second acid groups or initiating species in the first photoresist pattern  104 . Here “the first photoresist pattern” may encompass a photoresist pattern including the photosensitive material for secondary exposure and/or a photoresist pattern disposed with the photosensitive material for secondary exposure. 
     In some embodiments, the wavelength of the second activating radiation may be substantially the same as, or different from (e.g., longer than) the wavelength of the first activating radiation, depending on the activating wavelengths of the photosensitive material for secondary exposure and the first PAG for primary exposure. In some embodiments, the wavelength of the first activating radiation to activate the first PAG may be equal to or less than 350 nm, and the wavelength of the second activating radiation to activate the photosensitive material for secondary exposure may be greater than 350 nm. 
     In some embodiments, after the secondary exposure of the patterned substrate  105  with the shrink material layer  110 , the patterned substrate  105  with the shrink material layer  110  may be heat treated in a hardbake process (e.g., post exposure bake, not shown). In some embodiments, the temperature of the post exposure bake may be within a range from about 90° C. to about 200° C., or within a range from about 90° C. to about 150° C. In some embodiments, the time duration of the post exposure bake may be within a range from about 1 minute to about 5 mins. For example, for the shrink material layer  110  including the polymer or small molecules with protected amine functionalities, the temperature of the post exposure bake may be within a range from about 90° C. to about 200° C. (e.g., 110° C.), and the time duration of the post exposure bake may be within a range from about 1 minute to about 5 minutes (e.g., 1 minute). In some embodiments, for the shrink material layer  110  including the monomers, the temperature of the post exposure bake may be within a range from about 90° C. to about 150° C. (e.g., 90° C.), and the time duration of the post exposure bake may be within a range from about 1 minute to about 5 minutes. 
     In some embodiments, during the post exposure bake of the patterned substrate  105  with the shrink material layer  110 , the second acid groups or initiating species generated in the first photoresist pattern  104  may diffuse into the shrink material layer  110 , thereby reacting with the shrink material layer  110 . The second acid groups or initiating species generated in the first photoresist pattern  104  may diffuse into the shrink material layer  110  at least through the sidewalls of the respective photoresist structures  103 . In some embodiments, the second acid groups or initiating species generated in the first photoresist pattern  104  may also diffuse into the shrink material layer  110  through the top walls of the respective photoresist structures  103 . 
     For example, in some embodiments, the shrink material layer  110  may be configured to include molecular units (e.g., small molecules or fragments of polymeric molecules) with protected amine functional groups, and the patterned substrate  105  may be configured to include the second PAG in the first photoresist pattern  104  or disposed over the first photoresist pattern  104 . When exposed to the second activating radiation via the grey-tone photomask, the second PAG may generate the second acid groups (or secondary-photoreaction-generated acid groups), which may diffuse to the shrink material layer  110  and react with the molecular units (e.g., small molecules or fragments of polymeric molecules) with protected amine functional groups. 
     In some embodiments, the shrink material layer  110  may be configured to include the monomers capable of shrink polymerization, and the patterned substrate  105  may be configured to include the shrink polymerization initiator in the first photoresist pattern  104  or disposed over the first photoresist pattern  104 . When exposed to the second activating radiation via the grey-tone photomask, the shrink polymerization initiator may generate the initiating species, which may diffuse to the shrink material layer  110  and react with the monomer double bonds in the monomers. 
     The shrink material layer  110  may include a first portion in which the concentration of the diffused second acid groups or initiating species is greater than or equal to a threshold value, and a second portion in which the concentration of the diffused second acid groups or initiating species is less than the threshold value. The reaction between the diffused second acid groups or initiating species and the shrink material layer  110  may substantially occur in the first portion of the shrink material layer  110 , and may not occur in the second portion of the shrink material layer  110 . For illustrative and discussion purposes,  FIG.  1 B  shows the shrink material  110  filled into the trench  107  (e.g.,  107 - 1 ) may include a first portion  107   a  and a second portion  107   b . The first portion  107   a  may be located closer to the sidewalls of the trench  107 - 1  (that is also the interface of the trench  107 - 1  and the shrink material layer  110 ) than the second portion  107   b . In some embodiments, the first portion  107   a  may include the diffused second acid groups or initiating species with a concentration greater than or equal to a predetermined value, and the second portion  107   b  may include the diffused second acid groups or initiating species with a concentration less than the predetermined value. In some embodiments, the second acid groups or initiating species may diffuse into the first portion  107   a , and may not diffuse into the second portion  107   b . The reaction between the diffused second acid groups or initiating species and the shrink material  110  filled into the trench  107  may substantially occur in the first portion  107   a , rather than in the second portion  107   b . 
     As shown in  FIG.  1 C , after the secondary exposure and the post exposure bake, the patterned substrate  105  with the shrink material layer  110  may be rinsed using a rinsing solution (not shown). In some embodiments, the rinsing solution may include one or more organic solvents. Examples of the organic solvent may include propylene PGMEA, propylene glycol methyl ether, anisole, cyclohexanone, propylene carbonate, di(propylene glycol) butyl ether, di(propylene glycol) methyl ether, di(propylene glycol) methyl ether acetate, butyl lactate, 2-ethylhexyl-lactate, benzyl benzoate, n-methyl-2-pyrrolidinone, gamma-butyrolactone, tripropylene glycolmethylether, 1,6-diacetoxyhexane, 3-phenoxy toluene, benzyl alcohol, tolyl ether, terpineol, etc. 
     The secondary exposure of the patterned substrate  105  with the shrink material layer  110  may result in a solubility difference between the first portion of the shrink material layer  110  that has reacted with the diffused second acid groups or initiating species and the second portion of the shrink material layer  110  that has not reacted with the diffused second acid groups or initiating species. The first portion of the shrink material layer  110  may be substantially insoluble in the rinsing solution, and therefore may remain on the substrate  101 . The second portion of the shrink material layer  110  may be substantially soluble in the rinsing solution, and thereby may be removed from the substate  101 . For example, for the shrink material  110  filled into the trench  107 - 1 , the secondary exposure of the patterned substrate  105  with the shrink material layer  110  may result in a solubility difference between the first portion  107   a  and the second portion  107   b . The first portion  107   a  may be substantially insoluble in the rinsing solution, and therefore may remain on the substrate  101 . The second portion  107   b  may be substantially soluble in the rinsing solution, and therefore may be removed from the substate  101 . In some embodiments, the first photoresist pattern  104  may be substantially insoluble in the rinsing solution, without being affected by the rinsing solution. 
     After the rinse using the rising solution, the remaining portion (e.g., the first portion) of the shrink material  110  may be attached or bonded to at least one sidewall of at least one photoresist structure  103  of the first photoresist pattern  104 , or may be provided at (e.g., coated at) at least one sidewall of at least one trench  107  of the first photoresist pattern  104 , forming an interface layer  120  on the first photoresist pattern  104 . The photoresist structure  103  with the reacted shrink material attached to the sidewall thereof may form a photoresist structure  123  having an increased width w 3 , compared to the width w 1  of the corresponding photoresist structure  103  shown in  FIG.  1 B . Accordingly, the trench  127  with the reacted shrink material provided at the sidewall thereof may have a reduced width w 4 , compared to the width w 2  of the corresponding trench  107  shown in  FIG.  1 B . That is, at least one trench  107  of the first photoresist pattern  104  may be shrunken with a reduced width. 
     For example, for the shrink material  110  filled into the trench  107 - 1 , the remaining first portion  107   a  may be attached to the sidewalls of the photoresist structures  103 - 1  and  103 - 2 , forming two photoresist structures  123 - 1  and  123 - 2  with increased width w 3 , compared to the width w 1  of the corresponding photoresist structures  103 - 1  and  103 - 2  shown in  FIG.  1 B . The sidewalls of the trench  107 - 1  may be provided with the reacted shrink material  110 , forming a trench  127 - 1  with a reduced width w 4 , compared to the width w 2  of the corresponding trench  107 - 1  shown in  FIG.  3 B . That is, the trench  107 - 1  of the first photoresist pattern  104  may be shrunken. In some embodiments, when the shrink material layer  110  is also formed at the top surfaces of the respective photoresist structures  103  of the first photoresist pattern  104 , the reacted shrink material may also be attached to the top wall of at least one photoresist structure  103 . Thus, the height of the photoresist structure  123  with the reacted shrink material at the top wall may be increased, as compared to the height of the corresponding photoresist structure  103  shown in  FIG.  1 B . For example, the heights of the photoresist structure  123 - 1  and  123 - 3  with the reacted shrink material at the top wall may be greater than the height of the corresponding photoresist structures  103 - 1  and  103 - 2  shown in  FIG.  1 B . 
     Referring to  FIGS.  1 A- 1 C , after the rinse, the first photoresist pattern  104  with the first duty cycle variation may be transformed to a second photoresist pattern  124  with a second duty cycle variation. The second photoresist pattern  124  may include a plurality of photoresist structures (e.g., lines)  123  and a plurality of trenches  127 . The trenches  107  of the first photoresist pattern  104  may be selectively shrunken to form the trenches  127  of the second photoresist pattern  124 . Compared to the widths w 2  of the respective trenches  107  of the first photoresist pattern  104 , the widths w 4  of the respective trenches  127  of the second photoresist pattern  124  may be selectively reduced. In some embodiments, the width reductions of the respective trenches  127  may be non-uniform across the second photoresist pattern  124 . Accordingly, compared to the duty cycles at the respective portions of the first photoresist pattern  104 , the duty cycles at the respective portions of the second photoresist pattern  124  may be selectively increased, in a non-uniform manner across the second photoresist pattern  124 . 
     In some embodiments, the width reductions of the respective trenches  127  of the second photoresist pattern  124  may be determined, in part, by an exposure intensity variation of the secondary exposure via the grey-tone mask  115 . The exposure intensity variation of the secondary exposure via the grey-tone mask  115  may include information of local exposure intensities to which the respective portions of the first photoresist pattern  104  are exposed. In some embodiments, a greater local exposure intensity of the secondary exposure may result in a greater width reduction of a corresponding trench  127  of the second photoresist pattern  124 . 
     In some embodiments, the exposure intensity variation of the secondary exposure via the grey-tone mask  115  may be determined, in part, by the light transmittance variation of the grey-tone mask  115 . Thus, the width reductions (or shrink) of the respective trenches  127  of the second photoresist pattern  124  may be determined, in part, by the light transmittance variation of the grey-tone mask  115 . The light transmittance variation of the grey-tone mask  115  may include information of local light transmittances across the grey-tone mask  115 . In some embodiments, a greater local light transmittance of the grey-tone mask  115  may result in a greater width reduction of a corresponding trench  127  of the second photoresist pattern  124 . 
     Thus, through adjusting a local light transmittance of the grey-tone mask  115 , the width reduction of a corresponding trench  127  of the second photoresist pattern  124  may be adjustable. In addition, through configuring the light transmittance variation of the grey-tone mask  115 , a width reduction variation of the respective trenches  127  of the second photoresist pattern  124  may be configurable. The width reduction variation of the respective trenches  127  of the second photoresist pattern  124  may include information of the width reductions of the respective trenches  127  across the second photoresist pattern  124 . 
     Accordingly, through adjusting a local light transmittance of the grey-tone mask  115 , the duty cycle increase at a corresponding portion of the second photoresist pattern  124  may be adjustable. In addition, through configuring the light transmittance variation of the grey-tone mask  115 , a duty cycle increase variation of the second photoresist pattern  124  may be configurable. The duty cycle increase variation of the second photoresist pattern  124  may include information of the duty cycle increases at the respective portions of the second photoresist pattern  124 . 
     For discussion purposes,  FIG.  1 B  and  FIG.  1 C  show that as the light transmittance of the grey-tone mask  115  gradually increases in the +x-axis direction, the width reductions of the respective trenches  127  of the second photoresist pattern  124  may increase in the +x-axis direction. Referring to  FIG.  1 B , as the light transmittance of the grey-tone mask  115  gradually increases in the +x-axis direction, the intensity of the light  119  may gradually increase in the +x-axis direction, the amount of the second acid groups or initiating species generated in the shrink material layer  110  may gradually increase in the +x-axis direction, and the amount of the second acid groups or initiating species that diffuse into the shrink material layer  110  may gradually increase in the +x-axis direction. Thus, the amount of the shrink material  110  that react with the diffused second acid groups or initiating species may gradually increase in the +x-axis direction. After the rinse, referring to  FIG.  1 C , the amount of the shrink material  110  that has not reacted and, thus, is removed by the rinsing solution may gradually decrease in the +x-axis direction. Thus, the width reductions (or shrinks) of the respective trenches  127  of the second photoresist pattern  124  may increase in the +x-axis direction. Accordingly, the duty cycle increases at the respective portions of the second photoresist pattern  124  (as compared with the duty cycles of the first photoresist pattern  104 ) may increase in the +x-axis direction. 
     For example, referring to  FIGS.  1 A- 1 C , the width w 4  of the trenches  127  located at the left portion of the second photoresist pattern  124  may be substantially the same as the width w 2  of the corresponding trenches  107  of the first photoresist pattern  104 , e.g., about 100 nm. The width w 4  of the trenches  127  located at the central portion of the second photoresist pattern  124  may be reduced to 40 nm, and the width w 4  of the trenches  127  located at the right portion of the second photoresist pattern  124  may be reduced to 20 nm. Compared to the width w 2  of the trenches  127  located at corresponding portions of the first photoresist pattern  104  (e.g., 100 nm, 60 nm, and 60 nm), the width w 4  of the trenches  127  located at the left portion, the central portion, and the right portion of second photoresist pattern  124  may be reduced by about 0 nm, 20 nm, and 40 nm, respectively. In other words, the trenches  127  located at the left portion, the central portion, and the right portion of second photoresist pattern  124  may be shrunken by about 0 nm, 20 nm, and 40 nm in width, respectively. The width reductions (or shrink) of the respective trenches  127  of the second photoresist pattern  124  may increase in the +x-axis direction. 
     Further, the duty cycles of the left portion, the central portion, and the right portion of the second photoresist pattern  124  may be calculated as 0.5, 0.8, and 0.9, respectively. Compared to the duty cycles at corresponding portions of the first photoresist pattern  104  (e.g., 0.5, 0.7, 0.7), the duty cycles at the left portion, the central portion, and the right portion of second photoresist pattern  124  may be increased by 0, 0.1, and 0.2, respectively. The duty cycle increases of the respective portions of the second photoresist pattern  124  may increase in the +x-axis direction. The second photoresist pattern  124  may have be configured to have a broader duty cycle variation (e.g., from 0.5 to 0.9, with a range of 0.4) compared to the first photoresist pattern  104  (e.g., from 0.5 to 0.7, with a range of 0.2). In some embodiments, through configuring the light transmittance variation of the grey-tone mask  115 , the duty cycles at the respective portions of the second photoresist pattern  124  may be configured to include at least one substantially high duty cycle, e.g., 0.8, 0.9, etc. In some embodiments, the substrate  101  with the second photoresist pattern  124  may function as patterned grating (e.g., an SRG)  100 . The SRG  100  may have a broader duty cycle variation than the base SRG  105 . 
     The light transmittance variation of the grey-tone mask  115  shown in  FIG.  1 B , and the width reductions of the respective trenches  127  shown in  FIG.  1 C  are for illustrative purposes. In some embodiments, the grey-tone mask  115  may be configured with a predetermined 1D or 2D light transmittance variation in one or two dimensions within the plane (e.g., the x-y plane shown in  FIG.  1 B ) of the grey-tone mask  115 . Thus, the light  119  transmitted through the grey-tone mask  115  may be configured to have a predetermined 1D or 2D light intensity variation in the one or two dimensions within the plane of the grey-tone mask  115 . Accordingly, the trenches  127  of the second photoresist pattern  124  may be configured to have a predetermined 1D or 2D width reduction variation in the one or two dimensions within the plane of the second photoresist pattern  124 . The second photoresist pattern  124  may be configured to have a predetermined 1D or 2D duty cycle variation in the one or two dimensions within the plane of the second photoresist pattern  124 . 
       FIGS.  2 A- 2 C  illustrate schematic diagrams showing processes for selectively reducing a critical dimension of predefined features (e.g., lithography-defined features), according to an embodiment of the present disclosure. For illustrative purposes, trenches in a photoresist pattern (e.g., trenches  207  in a first photoresist pattern  204  shown in  FIG.  2 A ) are used as examples of the lithography-defined features to explain the processes. The disclosed processes may also be applied to selectively reducing other predefined features (e.g., lithography-defined features), such as holes and contact openings. The processes shown in  FIGS.  2 A- 2 C  may include steps or processes similar to those shown in  FIGS.  1 A- 1 C . An SRG  200  fabricated based on the processes shown in  FIGS.  2 A- 2 C  may include elements, which are similar to those included in the SRG  100  fabricated based on the processes shown in  FIGS.  1 A- 1 C . Descriptions of the similar steps and similar elements can refer to the descriptions rendered above in connection with  FIGS.  1 A- 1 C . Although the substrate  101  and films or layers are shown as having flat surfaces, in some embodiments, the substrate and films or layers formed thereon may include curved surfaces. 
     For example, as shown in  FIGS.  2 A- 2 C , a substrate  201  with the first photoresist pattern  204  may be provided (also be referred to as a patterned substrate  205 ), and a layer of the shrink material  110  (or the shrink material layer  110 ) may be formed over the patterned substrate  205  to flatten or planarize the first photoresist pattern  204 . In some embodiments, the patterned substrate  205  may function as the base SRG  205 . The material and fabrication process of the patterned substrate  205  may be similar to the material and fabrication process of the patterned substrate  105  shown in  FIG.  1 A , respectively. In the embodiment shown in  FIG.  2 A , the first photoresist pattern  204  may have a uniform periodp (e.g., about 200 nm), a uniform width w 2  of the trench  207  (e.g., about 60 nm), and a uniform duty cycle (e.g., about 0.7) for the entire photoresist pattern  204 . 
     After the shrink material layer  110  is formed over the patterned substrate  205 , the patterned substrate  205  provided with the shrink material layer  110  may be exposed to a second activating radiation via the grey-tone mask  115 . When a light  217  having a spatially uniform light intensity is incident onto the grey-tone mask  115 , a transmitted light  219  of the grey-tone mask  115  may have a spatially varying light intensity. Thus, an exposure intensity of the secondary exposure may spatially vary. After the secondary exposure, the patterned substrate  205  with the shrink material layer  110  may be subject to the post exposure bake. After the post exposure bake, the patterned substrate  205  with the shrink material layer  110  may be rinsed with the rinsing solution (not shown). After the processes shown in  FIGS.  2 A- 2 C , the first photoresist pattern  204  may be transformed to a second photoresist pattern  224  having at least one shrunken trench. 
     For discussion purposes,  FIG.  2 B  and  FIG.  2 C  show that as the light transmittance of the grey-tone mask  115  gradually increases in the +x-axis direction, the width reductions of respective trenches  227  of the second photoresist pattern  224  may increase in the +x-axis direction. Accordingly, the duty cycle increases at the respective portions of the second photoresist pattern  224  may increase in the +x-axis direction. For example, referring to  FIGS.  2 A- 2 C , the width w 4  of the trenches  227  located at the left portion of the second photoresist pattern  224  may be substantially the same as the width w 2  of the corresponding trenches  207  of the first photoresist pattern  204 , e.g., about 60 nm. The width w 4  of the trenches  227  located at the central portion of the second photoresist pattern  224  may be reduced to 40 nm, and the width w 4  of the trenches  227  located at the right portion of the second photoresist pattern  224  may be reduced to 20 nm. Thus, compared to the width w 2  of the trenches  207  located at corresponding portions of the first photoresist pattern  204  (e.g., 60 nm, 60 nm, and 60 nm), the width w 4  of the trenches  227  located at the left portion, the central portion, and the right portion of second photoresist pattern  224  may be reduced by about 0 nm, 20 nm, and 40 nm, respectively. In other words, the trenches  227  located at the left portion, the central portion, and the right portion of second photoresist pattern  224  may be shrunken by about 0 nm, 20 nm, and 40 nm, respectively. The width reductions (or shrink) of the respective trenches  227  of the second photoresist pattern  224  may increase in the +x-axis direction. 
     Further, the duty cycles of the left portion, the central portion, and the right portion of the second photoresist pattern  224  may be calculated as 0.7, 0.8, and 0.9, respectively. Compared to the duty cycles at corresponding portions of the first photoresist pattern  204  (e.g., 0.7, 0.7, 0.7), the duty cycles at the left portion, the central portion, and the right portion of second photoresist pattern  224  may be increased by 0, 0.1, and 0.2, respectively. The duty cycle increases of the respective portions of the second photoresist pattern  224  may increase in the +x-axis direction. The second photoresist pattern  224  may be configured with a broader duty cycle variation (e.g., from 0.7 to 0.9, with a range of 0.2) compared to the first photoresist pattern  204  (e.g., with the constant duty cycle). In some embodiments, through configuring the light transmittance variation of the grey-tone mask  115 , the duty cycles at the respective portions of the second photoresist pattern  224  may be configured to include at least one substantially high duty cycle, e.g., 0.8, 0.9, etc. In some embodiments, the substrate  201  with the second photoresist pattern  224  may function as a patterned grating (e.g., an SRG)  200 . The SRG  200  may have a broader duty cycle variation than the base SRG  205 . 
       FIGS.  3 A- 3 C  illustrate schematic diagrams showing processes for selectively reducing a critical dimension of predefined features (e.g., lithography-defined features), according to an embodiment of the present disclosure. For illustrative purposes, photoresist structures (e.g., photoresist lines  303  having rectangular cross-sections) in a first photoresist pattern  304  are used as examples of the predefined features (e.g., lithography-defined features) to explain the processes. The disclosed processes may also be applied to selectively reducing other predefined features, such as photoresist structures having other cross-sectional shape. The processes shown in  FIGS.  3 A- 3 C  may include steps or processes similar to those shown in  FIGS.  1 A- 1 C  or  FIGS.  2 A- 2 C . A second photoresist pattern  324  (or an SRG  300 ) fabricated based on the processes shown in  FIGS.  3 A- 3 C  may include elements, which are similar to those included in the second photoresist pattern  124  (or the SRG  100 ) fabricated based on the processes shown in  FIGS.  1 A- 1 C , or the second photoresist pattern  224  (or the SRG  200 ) fabricated based on the processes shown in  FIGS.  2 A- 2 C . Descriptions of the similar steps and similar elements can refer to the descriptions rendered above in connection with  FIGS.  1 A- 1 C  or  FIGS.  2 A- 2 C . Although the substrate and films or layers are shown as having flat surfaces, in some embodiments, the substrate and films or layers formed thereon may include curved surfaces. 
     As shown in  FIG.  3 A , a substrate  101  with the first photoresist pattern  304  may be provided. In some embodiments, the substrate  101  provided with the first photoresist pattern  304  may also be referred to as a patterned substrate  305 . In some embodiments, the patterned substrate  305  may function as a base SRG  305 . The patterned substrate  305  may be similar to the patterned substrate  105  shown in  FIG.  1 A  or the patterned substrate  205  shown in  FIG.  2 A . The configuration of the first photoresist pattern  304  may be similar to the configuration of the first photoresist pattern  104  shown in  FIG.  1 A  or the configuration of the first photoresist pattern  204  shown in  FIG.  2 A . For example, the first photoresist pattern  304  may include a plurality of photoresist structures  303  with sizes at the nano level or micron level that define or form a plurality of predefined features. In the embodiment shown in  FIG.  3 A , the predefined features may include photoresist lines  303 . For illustrative purposes, the photoresist lines  303  are schematically illustrated as rectangular structures filled with dots, and two neighboring photoresist lines  303  may be spaced apart by a trench  307 . The plurality of photoresist line  303  may be arranged in a 1D or 2D array. A periodp of the first photoresist pattern  304  may be uniform or may not be uniform for the entire photoresist pattern  304 . A width w 1  of the first photoresist pattern  304  may be uniform or may not be uniform for the entire photoresist pattern  304 . A duty cycle of the first photoresist pattern  304  may be uniform or may not be uniform for the entire photoresist pattern  304 . 
     For discussion purposes,  FIG.  3 A  show that the period p of the first photoresist pattern  304  may be uniform for the entire photoresist pattern  304 , e.g., about 200 nm. The width w 1  of the photoresist line  303  may be not uniform for the entire photoresist pattern  304 , and a width w 2  of the trench  307  between two neighboring photoresist lines  303  may be not uniform for the entire photoresist pattern  304 . For example, in the embodiment shown in  FIG.  3 A , the width w 1  of the photoresist line  303  decreases in +x-axis direction. For example, the width w 1  of the photoresist line  303  located at a left portion, a central portion, and a right portion of the first photoresist pattern  304  may be 140 nm, 100 nm, and 100 nm, respectively. Accordingly, the duty cycle at the left portion, the central portion, and the right portion of the first photoresist pattern  304  may be calculated as 0.7, 0.5, and 0.5, respectively. Although not shown, in some embodiments, the plurality of photoresist line  303  may be configured with a predetermined 1D or 2D width variation in one or two dimensions within a plane (e.g., an x-y plane shown in  FIG.  3 A ) perpendicular to a thickness direction (e.g., a z-axis direction shown in  FIG.  3 A ) of the first photoresist pattern  304 . Accordingly, the first photoresist pattern  304  may be configured with a predetermined 1D or 2D duty cycle variation in one or two dimensions within the plane (e.g., the x-y plane shown in  FIG.  3 A ) of the first photoresist pattern  304 . 
     The fabrication process of the first photoresist pattern  304  may be similar to the fabrication process of the first photoresist pattern  104  shown in  FIG.  1 A  or the fabrication process of the first photoresist pattern  204  shown in  FIG.  2 A . For example, the fabrication processes of the patterned substrate  305  may include forming a layer of a photoresist composition (also referred to as  303  for discussion purposes) over the substrate  101 ; exposing the layer of the photoresist composition  303  to an activating radiation (referred to as a first activating radiation) through a patterned photomask (e.g., a binary half-tone photomask); and developing the exposed layer of the photoresist composition  303  in a developer base to form the first photoresist pattern  304 . In some embodiments, the fabrication processes of the patterned substrate  305  may also include a post apply bake and a post exposure bake. 
     The photoresist composition  303  may include a photoresist that includes a mixture of a photoresist and a first PAG (or PAG for primary exposure). The first PAG may be configured to generate first acid groups when subject to the first activating radiation. The first acid groups may react with the photoresist in the layer of the photoresist composition  303 , resulting in a solubility difference between the exposed regions and the unexposed regions of the layer of the photoresist composition  303  in the developer base. In some embodiments, the photoresist composition  303  may include a positive photoresist, and the exposed regions of the layer of the photoresist composition  303  corresponding to the optically transparent regions of the patterned photomask may be soluble and removed in the subsequent development step (e.g., via an aqueous developer base). 
     Referring to  FIG.  3 A , after the patterned substrate  305  is provided, a layer of a shrink material  310  (also referred to as a shrink material layer  310 ) may be formed over the patterned substrate  305 . The process of forming the shrink material layer  310  over the patterned substrate  305  may be similar to the process of forming the shrink material layer  110  over the patterned substrate  105  shown in  FIG.  1 A  or over the patterned substrate  205  shown in  FIG.  2 A . The shrink material layer  310  may be applied to at least a portion of the surface of the first photoresist pattern  304  to flatten or planarize the first photoresist pattern  304 . At least one (e.g., each) of the trenches  307  may be filled with the shrink material  310 . For example, the shrink material  310  may fill the entire trench  307  between the neighboring photoresist lines  303 . The first photoresist pattern  304  provided with the shrink material layer  310  may have a substantially uniform thickness D across the entire photoresist pattern  304 . In some embodiments, as shown in  FIG.  3 A , the shrink material layer  310  may be disposed at the entire surface of the first photoresist pattern  304 , including the sidewalls of the respective photoresist lines  303  or respective trenches  307 , the top walls of the respective photoresist lines  303 , and the bottom walls of the respective trenches  307 . In such a configuration, the thickness D may be greater than the depth d of the photoresist line  303 . In some embodiments, the shrink material  310  may not be disposed at the top walls of the respective photoresist lines  303 . In such a configuration, the thickness D may be substantially equal to the depth d of the trench  307 . 
     The shrink material layer  310  may include a polymer or small molecules that are aqueous-soluble or organic solvent soluble (e.g., fluoro-soluble). The shrink material layer  310  may also include a photosensitive material that may react with the first photoresist pattern  304 , when the patterned substrate  305  with the shrink material layer  310  is exposed to an activating radiation, e.g., a second activating radiation different from the first activating radiation. Such a photosensitive material may be referred to as a photosensitive material for secondary exposure. In some embodiments, the photosensitive material for secondary exposure may include a fourth PAG. The fourth PAG may be configured to generate fourth photo acid groups when exposed to the second activating radiation. Such a fourth PAG may also be referred to as a PAG for secondary exposure. In some embodiments, the fourth PAG for secondary exposure and the first PAG for primary exposure may be activated by activating radiations of different wavelengths. For example, the activating wavelength of the fourth PAG may be longer than the activating wavelength of the first PAG. In some embodiments, the activating wavelength of the first PAG may be equal to or less than 350 nm, and the activating wavelength of the fourth PAG may be greater than 350 nm. 
     In some embodiments, a mixture of the aqueous-soluble or organic solvent soluble (e.g., fluoro-soluble) polymer or small molecules and the fourth PAG may be dissolved in a mixture of one or more of solvents to form a solution. Example of the solvents may include an aqueous solvent, a fluorinated solvent, etc. In some embodiments, the total solid content in the formulation may be within a range of about 0.5-10 wt%. For example, the solution may include propylene glycol methyl ether (“PGME”), dissolved with poly(acrylic acid) of 5 wt% and the second PGA of 1 wt%. In some embodiments, the solution may include PGME, dissolved with poly(hydroxystyrene) of 5 wt% and the second PGA of 1 wt%. 
     As shown in  FIG.  3 B , after the shrink material layer  310  is formed over the patterned substrate  305 , the patterned substrate  305  with the shrink material layer  310  may be exposed to an activating radiation (referred to as the second activating radiation) via the grey-tone (or grey-scale) mask  115 . When a light  317  having a spatially uniform light intensity is incident onto the grey-tone mask  115 , a transmitted light  319  of the grey-tone mask  115  may have a spatially varying light intensity. Thus, an exposure intensity of the patterned substrate  305  with the shrink material layer  310  may spatially vary. When exposed to the second activating radiation via the grey-tone photomask  115  (also referred to as a secondary exposure), the patterned substrate  305  with the shrink material layer  110  may be subject to a secondary photoreaction, such that the photosensitive material for secondary exposure in the shrink material layer  310  may be activated. For example, the fourth PAG included in the shrink material layer  310  may be activated to generate the fourth acid groups. The amount of the fourth acid groups generated in the shrink material layer  310  may be determined, in part, by the intensity of the second activating radiation (or the secondary exposure intensity). In some embodiments, the second activating radiation with a higher light intensity (or a higher secondary exposure intensity) may generate more fourth acid groups in the shrink material layer  310 . 
     The wavelength of the second activating radiation to activate the fourth PAG included in the shrink material layer  310  may be different from (e.g., longer than) the wavelength of the first activating radiation to activate the first PAG included in the first photoresist pattern  304  (or the photoresist composition  303  forming the first photoresist pattern  304 ). For example, the wavelength of the first activating radiation to activate the first PAG may be equal to or less than 350 nm, and the wavelength of the second activating radiation to activate the fourth PAG included in the shrink material  310  may be greater than 350 nm. Thus, when the first photoresist pattern  304  includes a residual first PGA, the residual first PGA may not be activated by the second activating radiation. 
     In some embodiments, after the secondary exposure, the patterned substrate  305  with the shrink material layer  310  may be heat treated in a hardbake process (e.g., post exposure bake). In some embodiments, the temperature of the post exposure bake may be within a range from about 90° C. to about 200° C., and the time duration of the post exposure bake may be within a range from about 1 minute to about 5 minutes. In some embodiments, the temperature of the post exposure bake may be about 110° C., and the time duration of the post exposure bake may be about 1 minute. During the post exposure bake of the patterned substrate  305  with the shrink material layer  310 , the fourth acid groups generated in the shrink material layer  310  may diffuse into the first photoresist pattern  304 , thereby reacting with the first photoresist pattern  304 . The fourth acid groups generated in the shrink material layer  310  may diffuse into the first photoresist pattern  304  at least through the sidewalls of the respective photoresist lines  303 . In some embodiments, the fourth acid groups generated in the shrink material layer  310  may also diffuse into the first photoresist pattern  304  through the top walls of the respective photoresist lines  303 . 
     The first photoresist pattern  304  may include a first portion, in which the concentration of the diffused fourth acid groups is greater than or equal to a threshold value, and a second portion, in which the concentration of the diffused fourth acid groups is less than the threshold value. The reaction between the diffused fourth acid groups and the first photoresist pattern  304  may substantially occur in the first portion of the first photoresist pattern  304 , and may not occur in the second portion of the first photoresist pattern  304 . For illustrative and discussion purposes,  FIG.  3 B  shows that the photoresist line  303  (e.g.,  303 - 1 ) may include a first portion  303   a  and a second portion  303   b . The first portion  303   a  may be a portion between the solid rectangle and the dashed rectangle as shown in  FIG.  3 B . The second portion  303   b  may be a portion encompassed by the dashed rectangle as shown in  FIG.  3 B . The first portion  303   a  may be located closer to the sidewalls of the photoresist line  303 - 1  than the second portion  303   b . The sidewalls are also where the interfaces between the photoresist line  303 - 1  and the shrink material layer  310  are located. In some embodiments, the first portion  303   a  of the photoresist line  303 - 1  may include the diffused fourth acid groups with a concentration greater than or equal to the predetermined value, and the second portion  303   b  of the photoresist line  303 - 1  may include the diffused fourth acid groups with a concentration less than the predetermined value. In some embodiments, the fourth acid groups may diffuse into the first portion  303   a  of the photoresist line  303 - 1 , and may not diffuse into the second portion  303   b  of the photoresist line  303 - 1 . The reaction between the diffused fourth acid groups and the photoresist line  303 - 1  may occur substantially in the first portion  303   a , rather than in the second portion  303   b . 
     As shown in  FIG.  3 C , after the secondary exposure and the post exposure bake, the patterned substrate  305  with the shrink material layer  310  may be developed using a developer base (not shown). In some embodiments, the developer base may include an aqueous solvent, a fluorinated solvent, etc. The shrink material layer  310  may be substantially soluble in the developer base, and therefore may be removed by the developer base. In addition, the secondary exposure of the patterned substrate  305  with the shrink material layer  310  may result in a solubility difference between the first portion of the first photoresist pattern  304  that has reacted with the diffused fourth acid groups and the second portion of the first photoresist pattern  304  that has not reacted with the diffused fourth acid groups in the developer base. The first portion of the first photoresist pattern  304  may be substantially soluble in the developer base, and therefore may be removed from the substate  101 . The second portion of the first photoresist pattern  304  may be substantially insoluble in the developer base, and therefore may remain on the substrate  101 . For example, the first portion  303   a  of the photoresist line  303 - 1  may be substantially soluble in the developer base, and may be removed from the substate  101 . The second portion  303   b  of the photoresist line  303 - 1  may be substantially insoluble in the developer base, and may remain on the substrate  101 . The remaining portion (e.g., the second portion  303   b ) may form a photoresist line  323  (e.g.,  323 - 1 ) with a reduced width w 3 , compared to the width w 1  of the corresponding photoresist line  303 - 1  shown in  FIG.  3 B . That is, the photoresist line  303 - 1  of the first photoresist pattern  304  may be trimmed. Accordingly, a trench  327  (e.g.,  327 - 1 ) adjacent to the photoresist line  323  (e.g.,  323 - 1 ) may have an increased width w 4 , compared to the width w 2  of the corresponding trench  307  (e.g.,  307 - 1 ) of the first photoresist pattern  304 . 
     In some embodiments, when the shrink material layer  310  is also formed at the top surfaces of the respective photoresist lines  303  of the first photoresist pattern  304 , the top of at least one photoresist line  303  may also be trimmed. Thus, the height of the photoresist line  323  may be reduced, as compared to the height of the corresponding photoresist line  303  shown in  FIG.  3 B . For example, the height of the photoresist line  323 - 1  may be less than the height of the corresponding photoresist line  303 - 1  shown in  FIG.  3 B . 
     Referring to  FIGS.  3 A- 3 C , the first photoresist pattern  304  with the first duty cycle variation may be transformed to a second photoresist pattern  324  with a second duty cycle variation. The second photoresist pattern  324  may include a plurality of photoresist lines  323  and a plurality of trenches  327 . The respective photoresist lines  303  of the first photoresist pattern  304  may be selectively trimmed to form the respective photoresist lines  323  of the second photoresist pattern  324 . Compared to the widths w 1  of the respective photoresist lines  303  of the first photoresist pattern  304 , the widths w 3  of the respective photoresist lines  323  of the second photoresist pattern  324  may be selectively reduced. In some embodiments, the width reductions of the respective photoresist lines  323  may be non-uniform across the second photoresist pattern  324 . Accordingly, compared to the duty cycles at the respective portions of the first photoresist pattern  304 , the duty cycles at the respective portions of the second photoresist pattern  324  may be selectively reduced, in a non-uniform manner across the second photoresist pattern  324 . 
     In some embodiments, the width reductions of the respective photoresist lines  323  of the second photoresist pattern  324  may be determined, in part, by an exposure intensity variation of the secondary exposure via the grey-tone mask  115 . The exposure intensity variation of the secondary exposure via the grey-tone mask  115  may include information of local exposure intensities to which the respective portions of the first photoresist pattern  304  are exposed. In some embodiments, a greater local exposure intensity of the secondary exposure may result in a greater width reduction of a corresponding photoresist line  323  of the second photoresist pattern  324 . 
     In some embodiments, the exposure intensity variation of the secondary exposure via the grey-tone mask  115  may be determined, in part, by the light transmittance variation of the grey-tone mask  115 . Thus, the width reductions of the respective photoresist lines  323  of the second photoresist pattern  324  may be determined, in part, by the light transmittance variation of the grey-tone mask  115 . The light transmittance variation of the grey-tone mask  115  may include information of local light transmittances at respective portions of the grey-tone mask  115 . In some embodiments, a greater local light transmittance of the grey-tone mask  115  may result in a greater width reduction of a corresponding photoresist line  323  of the second photoresist pattern  324 . 
     Thus, through adjusting a local light transmittance of the grey-tone mask  115 , the width reduction of a corresponding photoresist line  323  of the second photoresist pattern  324  may be adjustable. In addition, through configuring the light transmittance variation of the grey-tone mask  115 , a width reduction variation of the respective photoresist lines  323  of the second photoresist pattern  324  may be configurable. The width reduction variation of the respective photoresist lines  323  of the second photoresist pattern  324  may include information of the width reductions of the respective photoresist lines  323  across the second photoresist pattern  324 . 
     Accordingly, through adjusting a local light transmittance of the grey-tone mask  115 , the duty cycle reduction of a corresponding portion of the second photoresist pattern  324  may be adjustable. In addition, through configuring the light transmittance variation of the grey-tone mask  115 , a duty cycle reduction variation of the second photoresist pattern  324  may be configurable. The duty cycle reduction variation of the second photoresist pattern  324  may include information of the duty cycle reductions at respective portions of the second photoresist pattern  324 . 
     For discussion purposes,  FIG.  3 B  and  FIG.  3 C  show that as the light transmittance of the grey-tone mask  115  gradually increases in the +x-axis direction, the width reductions of the respective photoresist lines  323  of the second photoresist pattern  324  may increase in the +x-axis direction. Referring to  FIG.  3 B , as the light transmittance of the grey-tone mask  115  gradually increases in the +x-axis direction (as shown in  FIG.  3 B ), the intensity of the light  319  may gradually increase in the +x-axis direction, the amount of the fourth acid groups generated in the shrink material layer  310  may gradually increase in the +x-axis direction, and the amount of the fourth acid groups that diffuse into the respective photoresist lines  303  may gradually increase in the +x-axis direction, e.g., increasing from the leftmost photoresist line  303  to the rightmost photoresist line  303 . The reaction between the first photoresist pattern  304  and the diffused fourth acid groups may gradually increase in the +x-axis direction. For example, the sizes of the first portions of the respective photoresist lines  303  that react with the diffused fourth acid groups may gradually increase in the +x-axis direction. 
     After the development, referring to  FIG.  3 C , the sizes of the first portions of the respective photoresist lines  303  that are removed by the developer base may gradually increase in the +x-axis direction. Thus, compared to the widths w 1  of the respective photoresist lines  303  of the first photoresist pattern  304 , the width reductions of the respective photoresist lines  323  of the second photoresist pattern  324  may increase in the +x-axis direction. Accordingly, compared to the duty cycles at the respective portions of the first photoresist pattern  304 , the duty cycle reductions of the respective portions of the second photoresist pattern  324  may increase in the +x-axis direction. 
     For example, referring to  FIGS.  3 A- 3 C , the width w 3  of the photoresist line  323  located at the left portion of the second photoresist pattern  324  may be substantially the same as the width w 1  of the corresponding photoresist line  303  of the first photoresist pattern  304 , e.g., about 140 nm. The width w 3  of the photoresist line  323  located at the central portion of the second photoresist pattern  324  may be reduced to 40 nm, and the width w 3  of the photoresist line  323  located at the right portion of the second photoresist pattern  324  may be reduced to 20 nm. Compared to the widths w 2  of the photoresist lines  303  located at corresponding portions of the first photoresist pattern  304  (e.g., 140 nm, 100 nm, and 100 nm), the widths w 3  of the photoresist lines  323  located at the left portion, the central portion, and the right portion of second photoresist pattern  324  may be reduced by about 0 nm, 60 nm, and 80 nm, respectively. In other words, the photoresist lines  323  located at the left portion, the central portion, and the right portion of the second photoresist pattern  324  may be trimmed by about 0 nm, 60 nm, and 80 nm in width, respectively. The width reductions of the respective photoresist lines  323  of the second photoresist pattern  324  may increase in the +x-axis direction. 
     Further, the duty cycles of the left portion, the central portion, and the right portion of the second photoresist pattern  324  may be calculated as 0.7, 0.2, and 0.1, respectively. Compared to the duty cycles at corresponding portions of the first photoresist pattern  304  (e.g., 0.7, 0.5, 0.5), the duty cycles at the left portion, the central portion, and the right portion of second photoresist pattern  324  may be reduced by 0, 0.3, and 0.4, respectively. The duty cycle reductions of the respective portions of the second photoresist pattern  324  may increase in the +x-axis direction. In some embodiments, the second photoresist pattern  324  may have be configured to have a broader duty cycle variation (e.g., from 0.7 to 0.1, with a range of 0.6) compared to the first photoresist pattern  304  (e.g., from 0.7 to 0.5, with a range of 0.2). In some embodiments, through configuring the light transmittance variation of the grey-tone mask  115 , the duty cycles at the respective portions of the second photoresist pattern  324  may be configured to include at least one substantially low duty cycle, e.g., 0.4, 0.3, 0.2, 0.1, etc. In some embodiments, the substrate  101  with the second photoresist pattern  324  may function as patterned grating (e.g., an SRG)  300 . The SRG  300  may have a broader duty cycle variation than the base SRG  305 . 
     The light transmittance variation of the grey-tone mask  115  shown in  FIG.  3 B  and the width reductions of the respective photoresist lines  323  shown in  FIG.  3 C  are for illustrative purposes. In some embodiments, the grey-tone mask  115  may be configured with a predetermined 1D or 2D light transmittance variation in one or two dimensions within the plane (e.g., the x-y plane shown in  FIG.  3 B ) of the grey-tone mask  115 . Thus, the light  319  transmitted through the grey-tone mask  115  may be configured to have a predetermined 1D or 2D light intensity variation in the one or two dimensions within the plane of the grey-tone mask  115 . Accordingly, the photoresist lines  323  of the second photoresist pattern  324  may be configured to have a predetermined 1D or 2D width reduction variation in the one or two dimensions within the plane of the second photoresist pattern  324 . The second photoresist pattern  324  may be configured to have a predetermined 1D or 2D duty cycle variation in the one or two dimensions within the plane of the second photoresist pattern  324 . 
       FIGS.  4 A- 4 C  illustrate schematic diagrams showing processes for selectively reducing a critical dimension of predefined features (e.g., lithography-defined features), according to an embodiment of the present disclosure. For illustrative purposes, photoresist structures in a photoresist pattern (e.g., photoresist lines  403  in a first photoresist pattern  404  shown in  FIG.  4 A ) are used as examples of the lithography-defined features to explain the processes. The disclosed processes may also be applied to selectively reducing other lithography-defined features. The processes shown in  FIGS.  4 A- 4 C  may include steps or processes similar to those shown in  FIGS.  1 A- 1 C ,  FIGS.  2 A- 2 C , or  FIGS.  3 A- 3 C . An SRG  400  fabricated based on the processes shown in  FIGS.  4 A- 4 C  may include elements, which are similar to those included in the SRG  100  fabricated based on the processes shown in  FIGS.  1 A- 1 C , those included in the SRG  200  fabricated based on the processes shown in  FIGS.  2 A- 2 C , or those included in the SRG  300  fabricated based on the processes shown in  FIGS.  3 A- 3 C . Descriptions of the similar steps and similar elements can refer to the descriptions rendered above in connection with  FIGS.  1 A- 1 C ,  FIGS.  2 A- 2 C , or  FIGS.  3 A- 3 C . Although the substrate  101  and films or layers are shown as having flat surfaces, in some embodiments, the substrate and films or layers formed thereon may include curved surfaces. 
     For example, as shown in  FIGS.  4 A- 4 C , the substrate  101  with the first photoresist pattern  404  may be provided (also be referred to as a patterned substrate  405 ), and a layer of the shrink material  310  (or the shrink material layer  310 ) may be formed over the patterned substrate  405  to flatten or planarize the first photoresist pattern  404 . In some embodiments, the patterned substrate  405  may function as the base SRG  405 . The material and fabrication process of the patterned substrate  405  may be similar to the material and fabrication process of the patterned substrate  305  shown in  FIG.  3 A , respectively. In the embodiment shown in  FIG.  4 A , the first photoresist pattern  404  may have a uniform periodp (e.g., about 100 nm), a uniform width w 2  of the trench  407  (e.g., about 100 nm), and a uniform duty cycle (e.g., about 0.5) for the entire first photoresist pattern  404 . 
     After the shrink material layer  310  is formed over the patterned substrate  405 , the patterned substrate  405  provided with the shrink material layer  310  may be exposed to a second activating radiation via the grey-tone mask  115 . When a light  417  having a spatially uniform light intensity is incident onto the grey-tone mask  115 , a transmitted light  419  output from the grey-tone mask  115  may have a spatially varying light intensity. Thus, an exposure intensity of the secondary exposure may spatially vary. After the secondary exposure, the patterned substrate  405  with the shrink material layer  310  may be subject to the post exposure bake. After the post exposure bake, the patterned substrate  405  with the shrink material layer  310  may be developed using a developer base (not shown). After the processes shown in  FIGS.  4 A- 4 C , the first photoresist pattern  404  may be transformed to a second photoresist pattern  424  having at least one trimmed photoresist line. 
     For discussion purposes,  FIG.  4 B  and  FIG.  4 C  show that as the light transmittance of the grey-tone mask  115  gradually increases in the +x-axis direction, the width reductions of respective photoresist lines  423  of the second photoresist pattern  424  may increase in the +x-axis direction. Accordingly, the duty cycle reductions at the respective portions of the second photoresist pattern  424  may increase in the +x-axis direction. For example, referring to  FIGS.  4 A- 4 C , the width w 4  of the photoresist lines  423  located at the left portion of the second photoresist pattern  424  may be substantially the same as the width w 2  of the corresponding trenches  407  of the first photoresist pattern  404 , e.g., about 100 nm. The width w 4  of the photoresist lines  423  located at the central portion of the second photoresist pattern  424  may be reduced to 40 nm, and the width w 4  of the photoresist lines  423  located at the right portion of the second photoresist pattern  424  may be reduced to 20 nm. Thus, compared to the width w 2  of photoresist lines  403  located at corresponding portions of the first photoresist pattern  404  (e.g., 100 nm, 100 nm, and 100 nm), the widths w 4  of the photoresist lines  423  located at the left portion, the central portion, and the right portion of second photoresist pattern  424  may be reduced by about 0 nm, 60 nm, and 80 nm, respectively. In other words, the photoresist lines  423  located at the left portion, the central portion, and the right portion of second photoresist pattern  424  may be shrunken by about 0 nm, 60 nm, and 80 nm in width, respectively. The width reductions (or shrink) of the respective photoresist lines  423  of the second photoresist pattern  424  may increase in the +x-axis direction. 
     Further, the duty cycles of the left portion, the central portion, and the right portion of the second photoresist pattern  424  may be calculated as 0.5, 0.2, and 0.1, respectively. Compared to the duty cycles at corresponding portions of the first photoresist pattern  404  (e.g., 0.5, 0.5, 0.5), the duty cycles at the left portion, the central portion, and the right portion of second photoresist pattern  424  may be reduced by 0, 0.3, and 0.4, respectively. The duty cycle increases of the respective portions of the second photoresist pattern  424  may increase in the +x-axis direction. The second photoresist pattern  424  may be configured to have a broader duty cycle variation (e.g., from 0.5 to 0.1, with a range of 0.4) compared to the first photoresist pattern  404  (e.g., with the constant duty cycle of 0.5). In some embodiments, through configuring the light transmittance variation of the grey-tone mask  115 , the duty cycles at the respective portions of the second photoresist pattern  424  may be configured to include at least one substantially low duty cycle, e.g., 0.4, 0.3, 0.2, or 0.1, etc. In some embodiments, the substrate  101  with the second photoresist pattern  424  may function as patterned grating (e.g., an SRG)  400 . The SRG  400  may have a broader duty cycle variation than the base SRG  405 . 
     The present disclosure also provides a method for selectively reducing critical dimensions of lithography-defined features.  FIG.  6 A  illustrates a flow chart showing a method  600  for selectively reducing critical dimensions of lithography-defined features, according to an embodiment of the present disclosure. As shown in  FIG.  6 A , the method  600  may include forming a shrink material layer over a patterned substate including a photoresist pattern (step  601 ). The method  600  may also include exposing the patterned substate with the shrink material layer to an activating radiation via a grey-tone mask (step  602 ). The grey-tone mask may provide a predetermined light transmittance profile for the activating radiation. The predetermined light transmittance profile may be a non-uniform light transmittance profile. In some embodiments, the non-uniform light transmittance profile may be a gradient profile or an arbitrary profile with arbitrarily selected light transmittances. The light transmittance profile may be configured to be any suitable profile based on the duty cycle profile in a final grating to be fabricated. The method  600  may further include removing at least a portion of the shrink material layer that has not reacted with the photoresist pattern (step  603 ). For example, removing the portion of the shrink material layer may include rinsing the patterned substrate with the shrink material layer using a rinsing solution to remove the unreacted shrink material. The variation of the light transmittance of the grey-tone mask may result in any desirable varying duty cycles in the photoresist pattern of a final grating. In some embodiments, by configuring the light transmittance profile of the grey-tone mask, the duty cycles of the final grating may be controlled to vary between 0.1 and 0.9, in the range of 0.8. In some embodiments, the method  600  may include additional steps that are not shown in  FIG.  6 A , but have been described above in connection with other figures. 
     In some embodiments, the predetermined light transmittance profile of the grey-tone mask may be a non-uniform light transmittance profile. In some embodiments, the patterned substrate may include a photosensitive material that is activated under the activating radiation to react with the shrink material layer. In some embodiments, the photosensitive material may be disposed in the photoresist pattern or disposed between the photoresist pattern and the shrink material layer. In some embodiments, the shrink material layer may include a material including one or more amine functional groups and one or more amine protecting groups, and the photosensitive material may include a photoacid generator. In some embodiments, the shrink material layer may include monomers, and the photosensitive material may include an initiator for a photo-polymerization of the monomers. In some embodiments, removing at least a portion of the shrink material layer may include: rinsing the patterned substrate with the shrink material layer using a rinsing solution to remove a portion of the shrink material that has not reacted with the photoresist pattern. In some embodiments, a portion of the shrink material layer remains on the photoresist pattern after the rinsing to increase a width of at least one photoresist line included in the photoresist pattern. 
     In some embodiments, when at least a portion of the shrink material that has not reacted with the photoresist pattern is removed and the remaining portions of the shrink material that have reacted with the photoresist pattern remain on the surface of the photoresist pattern, the width of at least one photoresist line included in the photoresist pattern may be increased. As a result, a width of the trench between to neighboring photoresist lines may be reduced. Accordingly, the duty cycle at the corresponding portion of the photoresist pattern may be increased. By adjusting the light transmittance profile provided by the grey-tone mask, the photoresist lines of the photoresist pattern may be selectively increased in the width due to the attachment of the shrink material on the surfaces of the selective photoresist lines. In addition, the increases in the widths of the selective photoresist lines may be tunable. Thus, the duty cycles corresponding to the selective portions of the photoresist pattern may be adjusted or tuned to any suitable, desirable values. 
     In some embodiments, after exposing the patterned substrate with the shrink material layer to the activating radiation via the grey-tone mask and before removing at least a portion of the shrink material layer, the method may also include heat treating the patterned substrate with the shrink material layer. In some embodiments, the patterned substrate with the shrink material layer has a uniform thickness. 
       FIG.  6 B  illustrates a flow chart showing a method  610  for selectively reducing critical dimensions of lithography-defined features, according to an embodiment of the present disclosure. As shown in  FIG.  6 B , the method  610  may include forming a shrink material layer over a patterned substate including a photoresist pattern (step  611 ). The method  610  may also include exposing the patterned substate with the shrink material layer to an activating radiation via a grey-tone mask (step  612 ). The method  610  may also include heat treating the patterned substrate with the shrink material layer (step  613 ). The method  610  may also include developing the patterned substrate with the shrink material layer using a developer base to remove the shrink material layer and a portion of the photoresist pattern that has reacted with the shrink material layer (step  614 ). In some embodiments, substantially all of the shrink material layer may be removed in the developing process. When the portion of the photoresist pattern that has reacted with the shrink material layer is removed, a width of at least one photoresist line included in the photoresist pattern may be reduced. The method  610  may include other steps not shown in  FIG.  6 B , but have been described above in connection with other figures. 
     In some embodiments, the shrink material layer may include a photosensitive material that is activated under the activating radiation to react with the photoresist pattern. In some embodiments, the shrink material layer may include a material that is aqueous-soluble or organic solvent soluble (e.g., fluoro-soluble), and the photosensitive material may include a photoacid generator. In some embodiments, the photoacid generator included in the photosensitive material may be a first photoacid generator with a first activating wavelength, the photoresist pattern may include a second photoacid generator with a second activating wavelength, and the first activating wavelength may be greater than the second activating wavelength. 
     In some embodiments, removing at least a portion of the shrink material layer may include developing the patterned substrate with the shrink material layer using a developer base to remove the shrink material layer and a portion of the photoresist pattern that has reacted with the shrink material layer. In some embodiments, substantially all of the shrink material layer may be removed from the photoresist pattern. In some embodiments, removing the portion of the photoresist pattern that has reacted with the shrink material layer may reduce a width of at least one photoresist line included in the photoresist pattern. When the portion of the photoresist pattern that has reacted with the shrink material layer is removed, a width of at least one photoresist line included in the photoresist pattern may be reduced (i.e., the photoresist line is trimmed). Accordingly, the duty cycle at the corresponding portion of the photoresist pattern may be reduced. By adjusting the light transmittance profile provided by the grey-tone mask, the photoresist lines of the photoresist pattern may be selectively reduced (or trimmed) in the width. In addition, the reductions in the widths of the selective photoresist lines may be tunable. Thus, the duty cycles corresponding to the selective portions of the photoresist pattern may be adjusted to any suitable, desirable values. 
     In some embodiments, after exposing the patterned substrate with the shrink material layer to the activating radiation via the grey-tone mask and before removing at least a portion of the shrink material layer, the method may also include heat treating the patterned substrate with the shrink material layer. In some embodiments, the patterned substrate with the shrink material layer has a uniform thickness. 
       FIG.  6 C  illustrates a flow chart showing a method  620  for selectively reducing critical dimensions of lithography-defined features, according to an embodiment of the present disclosure. The method  620  may include configuring a grey-tone mask to provide a non-uniform light transmittance profile for a radiation for creating a varying duty cycle profile in a grating to be fabricated (step  621 ). The method  620  may also include applying a shrink material over a photoresist pattern (step  622 ). The method  620  may also include exposing the photoresist pattern with the shrink material to the radiation transmitting through the grey-tone mask to cause a reaction between the shrink material and the photoresist pattern at selective portions of the photoresist pattern covered by the shrink material (step  623 ). Amounts of the shrink material that reacts with the photoresist pattern at selective portions of the photoresist pattern may be different. The method  620  may also include removing at least a portion of the shrink material to form the grating (step  624 ). In some embodiments, the method  620  may include other steps not shown in  FIG.  6 C , such as those described above in connection with method  600  and method  610 . 
       FIG.  6 D  illustrates a flow chart showing a method  630  for selectively reducing critical dimensions of lithography-defined features, according to an embodiment of the present disclosure. The method  630  may include forming a photoresist pattern through a lithography mask via a lithography process, the photoresist pattern including a first duty cycle profile (step  631 ). The method  630  may also include applying a shrink material over the photoresist pattern (step  632 ). The method  630  may also include exposing the photoresist pattern with the shrink material to a radiation through a grey-tone mask having a non-uniform light transmittance profile for the radiation, the non-uniform light transmittance profile corresponding to a second duty cycle profile that is different from the first duty cycle profile (step  633 ). The method  630  may also include removing at least a portion of the shrink material to form a grating having the second duty cycle profile (step  634 ). The method  630  may include other steps not shown in  FIG.  6 D , such as those described above in connection with method  600  and method  610 . 
     Gratings fabricated based on the fabrication processes and methods disclosed herein have various applications in a number of technical fields. For example, the gratings fabricated based on the fabrication processes and methods disclosed herein may be implemented in various systems for augmented reality (“AR”), virtual reality (“VR”), and/or mixed reality (“MR”) applications, e.g., near-eye displays (“NEDs”), head-up displays (“HUDs”), head-mounted displays (“HMDs”), smart phones, laptops, televisions, vehicles, etc. Some exemplary applications in AR, VR, and MR fields or some combinations thereof will be explained below. NEDs have been widely used in a wide variety of applications, such as aviation, engineering, scientific research, medical devices, computer games, videos, sports, training, and simulations. NEDs can function as a VR device, an AR device, and/or an MR device. When functioning as AR and/or MR devices, NEDs are at least partially transparent from the perspective of a user, enabling the user to view a surrounding real world environment. Such NEDs are also referred to as optically see-through NEDs. When functioning as VR devices, NEDs are opaque such that the user is substantially immersed in the VR imagery provided via the NEDs. An NED may be switchable between functioning as an optically see-through device and functioning as a VR device. 
       FIG.  7 A  illustrates an x-z sectional view of a light guide display system or assembly  700 , according to an embodiment of the present disclosure. The light guide display system  700  may be a part of a system (e.g., an NED, an HUD, an HMD, a smart phone, a laptop, or a television, etc.) for VR, AR, and/or MR applications. As shown in  FIG.  7 A , the light guide display system  700  may include a light source assembly  705 , a light guide  710 , and a controller  717 . The controller  717  may be configured to perform various controls, adjustments, or other functions or processes described herein. The light source assembly  705  may include a light source  720  and an light conditioning system  725 . In some embodiments, the light source  720  may be a light source configured to generate a coherent or partially coherent light. The light source  720  may include, e.g., a laser diode, a vertical cavity surface emitting laser, a light emitting diode, or a combination thereof. In some embodiments, the light source  720  may be a display panel, such as a liquid crystal display (“LCD”) panel, a liquid-crystal-on-silicon (“LCoS”) display panel, an organic light-emitting diode (“OLED”) display panel, a micro light-emitting diode (“micro-LED”) display panel, a digital light processing (“DLP”) display panel, a laser scanning display panel, or a combination thereof. In some embodiments, the light source  720  may be a self-emissive panel, such as an OLED display panel or a micro-LED display panel. In some embodiments, the light source  720  may be a display panel that is illuminated by an external source, such as an LCD panel, an LCoS display panel, or a DLP display panel. Examples of an external source may include a laser, an LED, an OLED, or a combination thereof. The light conditioning system  725  may include one or more optical components configured to condition the light from the light source  720 . For example, the controller  717  may control the light conditioning system  725  to condition the light from the light source  720 , which may include, e.g., transmitting, attenuating, expanding, collimating, and/or adjusting orientation of the light. 
     The light source assembly  705  may generate an image light  730  and output the image light  730  to an in-coupling element  735  disposed at a first portion of the light guide  710 . The light guide  710  may receive the image light  730  at the in-coupling element  735  located at the first portion of the light guide  710 . In some embodiments, the in-coupling element  735  may couple the image light  730  into a total internal reflection (“TIR”) path inside the light guide  710 . The image light  730  may propagate inside the light guide  710  through TIR along the TIR path, toward an out-coupling element  745  located at a second portion of the light guide  710 . The first portion and the second portion may be located at different portions of the light guide  710 . The out-coupling element  745  may be configured to couple the image light  730  out of the light guide  710 . For example, the out-coupling element  745  may be configured to couple the image light  730  out of the light guide  710  as a plurality of output lights  732  propagating toward the eye-box region  759 . Each of the plurality of the output lights  732  may present substantially the same image content as the image light  730 . Thus, the out-coupling element  745  may be configured to replicate the image light  730  received from the light source assembly  705  at an output side of the light guide  710  to expand an effective pupil of the light guide display system  700 , e.g. in an x-axis direction shown in  FIG.  7 A . In some embodiments, the light guide display system  700  may expand and direct the image light  730  to an exit pupil  757  positioned in the eye-box region  759  of the light guide display system  700 . The exit pupil  757  may be a location where an eye  760  is positioned in the eye-box region  759 . The relative positions of the eye  760  and the light source assembly  705  shown in  FIG.  7 A  are for illustrative purposes. In some embodiments, the eye  760  and the light source assembly  705  may be disposed at different sides of the light guide  710 . 
     The light guide  710  may include a first surface or side  710 - 1  facing the real-world environment and an opposing second surface or side  710 - 2  facing the eye-box region  759 . Each of the in-coupling element  735  and the out-coupling element  745  may be disposed at the first surface  710 - 1  or the second surface  710 - 2  of the light guide  710 . In some embodiments, as shown in  FIG.  7 A , the in-coupling element  735  may be disposed at the second surface  710 - 2  of the light guide  710 , and the out-coupling element  745  may be disposed at the first surface  710 - 1  of the light guide  710 . In some embodiments, the in-coupling element  735  may be disposed at the first surface  710 - 1  of the light guide  710 . In some embodiments, the out-coupling element  745  may be disposed at the second surface  710 - 2  of the light guide  710 . In some embodiments, both of the in-coupling element  735  and the out-coupling element  745  may be disposed at the first surface  710 - 1  or the second surface  710 - 2  of the light guide  710 . In some embodiments, the in-coupling element  735  or the out-coupling element  745  may be integrally formed as a part of the light guide  710  at the corresponding surface. In some embodiments, the in-coupling element  735  or the out-coupling element  745  may be separately formed, and may be disposed at (e.g., affixed to) the corresponding surface. 
     In some embodiments, each of the in-coupling element  735  and the out-coupling element  745  may have a designed operating wavelength band that includes at least a portion of the visible wavelength band. In some embodiments, the designed operating wavelength band of each of the in-coupling element  735  and the out-coupling element  745  may not include the IR wavelength band. For example, each of the in-coupling element  735  and the out-coupling element  745  may be configured to deflect a visible light, and transmit an IR light without a deflection or with negligible deflection. 
     In some embodiments, each of the in-coupling element  735  and the out-coupling element  745  may include one or more diffraction gratings, one or more cascaded reflectors, one or more prismatic surface elements, and/or an array of holographic reflectors, or any combination thereof. In some embodiments, each of the in-coupling element  735  and the out-coupling element  745  may include one or more diffractive structures, e.g., diffraction gratings. The diffraction grating may include a surface relief grating, a volume hologram grating, a polarization hologram grating (e.g., a liquid crystal polarization hologram grating), a metasurface grating, or any combination thereof. For discussion purposes, the in-coupling element  735  and the out-coupling element  745  may also be referred to as the in-coupling grating  735  and the out-coupling grating  745 , respectively. In some embodiments, a pitch of the in-coupling grating  735  may be configured to enable TIR of the image light  730  within the light guide  710 . In some embodiments, a pitch of the out-coupling grating  745  may be configured to couple the image light  730  propagating inside the light guide  710  through TIR out of the light guide  710  via diffraction. 
     The light guide  710  may include one or more materials configured to facilitate the total internal reflection of the image light  730 . For example, the light guide  710  may be the substrate  101  shown in  FIGS.  1 A- 4 C . The light guide  710  may have a relatively small form factor. The light guide  710  coupled with the in-coupling element  735  and the out-coupling element  745  may also function as an image combiner (e.g., AR or MR combiner). The light guide  710  may combine the image light  732  representing a virtual image and a light  734  from the real world environment (or a real world light  734 ), such that the virtual image may be superimposed with real-world images. With the light guide display system  700 , the physical display and electronics may be moved to a side of a front body of an NED. A substantially fully unobstructed view of the real world environment may be achieved, which enhances the AR or MR user experience. 
     In some embodiments, the light guide  710  may include additional elements configured to redirect, fold, and/or expand the pupil of the light source assembly  705 . For example, in some embodiments, the light guide display system  700  may include a redirecting element  740  coupled to the light guide  710 , and configured to redirect the image light  730  to the out-coupling element  745 , such that the image light  730  is coupled out of the light guide  710  via the out-coupling element  745 . In some embodiments, the redirecting element  740  may be arranged at a location of the light guide  710  opposing the location of the out-coupling element  745 . For example, in some embodiments, the redirecting element  740  may be integrally formed as a part of the light guide  710  at the corresponding surface. In some embodiments, the redirecting element  740  may be separately formed and disposed at (e.g., affixed to) the corresponding surface of the light guide  710 . 
     In some embodiments, the redirecting element  740  and the out-coupling element  745  may have a similar structure. In some embodiments, the redirecting element  740  may include one or more diffraction gratings, one or more cascaded reflectors, one or more prismatic surface elements, and/or an array of holographic reflectors, or any combination thereof. In some embodiments, the redirecting element  740  may include one or more diffractive structures, e.g., diffraction gratings. The diffraction grating may include a surface relief grating, a volume hologram grating, a polarization hologram grating (e.g., a liquid crystal polarization hologram grating), a metasurface grating, or any combination thereof. For discussion purposes, the redirecting element  740  may also be referred to as the redirecting grating  740 . 
     In some embodiments, the redirecting element  740  and the out-coupling element  745  may be configured to replicate the image light  730  received from the light source assembly  705  at the output side of the light guide  710  in two different directions, thereby providing a two-dimensional (“2D”) expansion of the effective pupil of the light guide display system  700 . For example, the out-coupling element  745  may be configured to replicate the image light  730  received from the light source assembly  705  at the output side of the light guide  710  to expand the effective pupil of the light guide display system  700 , e.g. in the x-axis direction shown in  FIG.  7 A . The redirecting element  740  may be configured to replicate the image light  730  received from the light source assembly  705  at the output side of the light guide  710  to expand the effective pupil of the light guide display system  700 , e.g., in the y-axis direction shown in  FIG.  7 A . 
     In some embodiments, one of the redirecting grating  740  and the out-coupling grating  745  may be disposed at the first surface  710 - 1  of the light guide  710 , and the other one of the redirecting grating  740  and the out-coupling grating  745  may be disposed at the second surface  710 - 2  of the light guide  710 . In some embodiments, the redirecting grating  740  and the out-coupling grating  745  may have different orientations of grating fringes (or grating vectors), thereby expanding the input image light  730  in two different directions. For example, the out-coupling grating  745  may expand the image light  730  along the x-axis direction, and the redirecting grating  740  may expand the image light  730  along the y-axis direction. The out-coupling grating  745  may further couple the expanded input image light out of the light guide  710 . Accordingly, the light guide display system  700  may provide pupil replication (or pupil expansion) at a light output side of the light guide display system  700 . In some embodiments, the redirecting grating  740  and the out-coupling grating  745  may be disposed at the same surface of the light guide  710 . In addition, to expand the exit pupil (or effective pupil) of the light guide display system  700  in more than two directions, more than two gratings (or layers of diffractive structures) may be disposed at the light output region of the light guide  710 . 
     In some embodiments, multiple functions, e.g., redirecting, folding, and/or expanding the pupil of the light generated by the light source assembly  705  may be combined into a single element, e.g. the out-coupling element  745 . For example, the out-coupling element  745  itself may be configured to provide a 2D expansion of the effective pupil of the light guide display system  700 . For example, the out-coupling grating  745  may be a 2D grating including a single grating layer or a single layer of diffractive structures. 
     In some embodiments, the light guide display system  700  may include a plurality of light guides  710  disposed in a stacked configuration (not shown in  FIG.  7 A ). At least one (e.g., each) of the plurality of light guides  710  may be coupled with or include one or more diffractive elements (e.g., in-coupling element, out-coupling element, and/or redirecting element), which may be configured to direct the image light  730  toward the eye  760 . In some embodiments, the plurality of light guides  710  disposed in the stacked configuration may be configured to output an expanded polychromatic image light (e.g., a full-color image light). In some embodiments, the light guide display system  700  may include one or more light source assemblies  705  and/or one or more light guides  710 . In some embodiments, at least one (e.g., each) of the light source assemblies  705  may be configured to emit a monochromatic image light of a specific wavelength band corresponding to a primary color (e.g., red, green, or blue) and a predetermined FOV (or a predetermined portion of an FOV). 
     In some embodiments, the light guide display system  700  may include three different light guides  710  configured to deliver component color images (e.g., primary color images) by in-coupling and subsequently out-coupling, e.g., red, green, and blue lights, respectively, in any suitable order. In some embodiments, the light guide display system  700  may include two different light guides configured to deliver component color images (e.g., primary color images) by in-coupling and subsequently out-coupling, e.g., a combination of red and green lights, and a combination of green and blue lights, respectively, in any suitable order. In some embodiments, at least one (e.g., each) of the light source assemblies  705  may be configured to emit a polychromatic image light (e.g., a full-color image light). 
     In the embodiment shown in  FIG.  7 A , the out-coupling grating  745  (and/or the redirecting grating  740  if included) may be a grating fabricated based on the disclosed processes and methods, such as the SRG  100  shown in  FIG.  1 C , the SRG  200  shown in  FIG.  2 C , the SRG  300  shown in  FIG.  3 C , or the SRG  400  shown in  FIG.  4 C . For example, the out-coupling grating  745  may be fabricated to have a predetermined duty cycle variation in one or more dimensions, e.g., within a plane (e.g., an x-y plane shown in  FIG.  7 A ) perpendicular to a thickness direction of the out-coupling grating  745  (e.g., a z-axis direction shown in  FIG.  7 A ). The out-coupling grating  745  may have a broad duty cycle variation. Thus, the out-coupling grating  745  may be configured to provide a broad diffraction efficiency variation in the one or more dimensions. 
     For example, the out-coupling grating  745  may be configured to provide a predetermined (e.g., a non-uniform) diffraction efficiency profile, e.g., a predetermined 1D or 2D diffraction efficiency profile, to image lights incident onto different portions of the out-coupling grating  745 , when the Bragg condition is substantially satisfied. The predetermined non-uniform diffraction efficiency profile may allow the light guide display system  700  to have a predetermined illuminance distribution (or profile) along the one or more dimensions of the expanded exit pupil. The predetermined illuminance distribution may be any suitable illuminance distribution profile in the one or more dimensions, such as a Gaussian distribution or any other desirable distribution. In some embodiments, the predetermined illuminance distribution may be substantially uniform over an expanded exit pupil. In some embodiments, the predetermined illuminance distribution may be non-uniform depending on the application needs. 
       FIG.  7 B  illustrates an x-z sectional view of a light guide display assembly or system  750 , according to an embodiment of the present disclosure. The light guide display system  750  may include elements, structures, and/or functions that are the same as or similar to those included in the light guide display system  700  shown in  FIG.  7 A . Descriptions of the same or similar elements, structures, and/or functions can refer to the descriptions rendered above in connection with  FIG.  7 A . As shown in  FIG.  7 B , the light guide  710  may be coupled with an out-coupling grating  755  that couples the image light  730  out of the light guide  710 , via diffraction, as a plurality of output lights, e.g.,  767   a ,  767   b , and  767   c . The out-coupling grating  755  may be fabricated based on the disclosed processes and methods, and may have a broad duty cycle variation along one or two dimensions in a plane (e.g., the x-y plane) of the out-coupling grating  755  perpendicular to the thickness direction of the out-coupling grating  755 . Thus, the out-coupling grating  755  may provide a broad diffraction efficiency variation along one or two dimensions in the plane of the out-coupling grating  755 . 
     For illustrative and discussion purposes,  FIG.  7 B  shows that the duty cycle of the out-coupling grating  755  is configured to gradually increase along the +x-axis direction, e.g., from about 0.1 to about 0.9. The image light  730  propagating inside the light guide  710  via TIR may be incident onto different portions (e.g., A1, A2, A3, etc.) of the out-coupling grating  755  along the +x-axis direction. When the Bragg condition is substantially satisfied, the out-coupling grating  755  may diffract the image light  730  incident onto different portions (e.g., A1, A2, A3, etc.) of the out-coupling grating  755  along the +x-axis direction, with the diffraction efficiency gradually increasing along the +x-axis direction. For example, the diffraction efficiency of the out-coupling grating  755  provided to the image light  730  incident onto the position A2 may be larger than the position A1, and the diffraction efficiency of the out-coupling grating  755  provided to the image light  730  incident onto the position A3 may be larger than the position A2. Thus, the increase in the diffraction efficiency of the out-coupling grating  755  provided to the image light  730  may compensate for the decrease in the light intensity of the image light  730  due to portion of the image light  730  being coupled out when propagating along the light guide  710 . 
     Accordingly, the difference between the light intensities of the output lights  767   a ,  767   b , and  767   c  out-coupled from different portions (e.g., A1, A2, A3, etc.) of the light guide  710  may be reduced, and the uniformity of the illuminance within the eye-box region  759  may be improved at least along the +x-axis direction (or the exit pupil expansion direction). In some embodiments, through configuring the duty cycle variation of the out-coupling grating  755  along one or two dimensions of the out-coupling grating  755  (e.g., the x-axis direction and/or the y-axis direction), the light intensities of the output lights  767   a ,  767   b , and  767   c  out-coupled from different portions (e.g., A1, A2, A3, etc.) of the light guide  710  may be configured to be substantially the same. Thus, the light guide display system  750  may be configured to provide a substantially uniform illuminance at the output side of the light guide  710  or over the effective pupil within the eye-box region  759 . Compared to a conventional light guide display system including an out-coupling grating with a narrow duty cycle variation (e.g., from 0.5 to 0.7), the light guide display system  750  with the disclosed out-coupling grating  755  with a broad duty cycle variation (from 0.1 to 0.9) may further improve the illuminance at the output side of the light guide  710  or over the effective pupil within the eye-box region  759 . 
     The uniform illuminance distribution at the output side is an example of the illuminance profile that may be provided by the disclosed light guide display system  750 . The present disclosure is not limited to providing a uniform illuminance distribution at the output side of the light guide  710 . Any suitable, predetermined illuminance distribution (or profile), including controlled or preconfigured non-uniform illuminance distribution patterns may be provided by the disclosed light guide display system  750 , following the same or similar principles described below using the uniform illuminance distribution as an example. 
     Although not shown, in some embodiments, the light guide display system  750  may include two or more out-coupling gratings  755 . In some embodiments, the two or more out-coupling gratings  755  may have a substantially same duty cycle variation. In some embodiments, the two or more out-coupling gratings  755  may have different duty cycle variations. In some embodiments, the light guide display system  750  may also include a redirecting grating (not shown). In some embodiments, the out-coupling grating  755  and the redirecting grating may have a substantially same duty cycle variation. In some embodiments, the out-coupling grating  755  and the redirecting grating may have different duty cycle variations. 
     Although not shown in  FIG.  7 B , in some embodiments, the duty cycle variation of the out-coupling grating  755  may be configured, such that the out-coupling grating  755  may be configured to diffract the image light  730  toward regions outside of the eye-box region  759  with a relatively small (e.g., negligible) diffraction efficiency, and diffract the image light  730  toward regions inside the eye-box region  759  with a relatively large diffraction efficiency. Thus, the loss of the image light  730  directed to regions outside of the eye-box region  759  may be reduced. As a result, the power consumption of the light source assembly  705  may be significantly reduced, while the power efficiency of the light guide display system  750  may be significantly improved. 
     The configurations of the light guide display system  700  shown in  FIG.  7 A  and the light guide display system  750  shown in  FIG.  7 B  are used as example display systems configured to provide a predetermined illuminance distribution at the eye-box region  759  by including one or more gratings fabricated based on the disclosed processes and methods. The gratings fabricated based on the disclosed processes and methods may be implemented into any suitable systems (e.g., display systems, illumination systems, etc.) other than the disclosed light guide display systems, for providing a predetermined illuminance distribution within a predetermined region. 
       FIG.  8 A  illustrates a schematic diagram of a near-eye display (“NED”)  800  according to an embodiment of the disclosure.  FIG.  8 B  is a cross-sectional view of half of the NED  800  shown in  FIG.  8 A  according to an embodiment of the disclosure. For purposes of illustration,  FIG.  8 B  shows the cross-sectional view associated with a left-eye display system  810 L. The NED  800  may include a controller (not shown), which may be similar to other controllers shown in other figures. The NED  800  may include a frame  805  configured to mount to a user’s head. The frame  805  is merely an example structure to which various components of the NED  800  may be mounted. Other suitable type of fixtures may be used in place of or in combination with the frame  805 . The NED  800  may include right-eye and left-eye display systems  810 R and  810 L mounted to the frame  805 . The NED  800  may function as a VR device, an AR device, an MR device, or any combination thereof. In some embodiments, when the NED  800  functions as an AR or an MR device, the right-eye and left-eye display systems  810 R and  810 L may be entirely or partially transparent from the perspective of the user, which may provide the user with a view of a surrounding real-world environment. In some embodiments, when the NED  800  functions as a VR device, the right-eye and left-eye display systems  810 R and  810 L may be opaque to block the light from the real-world environment, such that the user may be immersed in the VR imagery based on computer-generated images. 
     The left-eye and right-eye display systems  810 L and  810 R may include image display components configured to project computer-generated virtual images into left and right display windows  815 L and  815 R in a field of view (“FOV”). The right-eye and left-eye display systems  810 R and  810 L may be any suitable display systems. In some embodiments, the right-eye and left-eye display systems  810 R and  810 L may include one or more gratings fabricated based on the disclosed processes and methods. In some embodiments, the right-eye and left-eye display systems  810 R and  810 L may include one or more display systems disclosed herein, such as the light guide display system  700  shown in  FIG.  7 A  or the light guide display system  750  shown in  FIG.  7 B . For illustrative purposes,  FIG.  8 A  shows that the left-eye display systems  810 L may include a light source assembly (e.g., a projector)  835  coupled to the frame  805  and configured to generate an image light representing a virtual image. 
     As shown in  FIG.  8 B , the left-eye display systems  810 L may also include a viewing optical system  880  and an object tracking system  890  (e.g., eye tracking system and/or face tracking system). The viewing optical system  880  may be configured to guide the image light output from the left-eye display system  810 L to the exit pupil  757 . The exit pupil  757  may be a location where an eye pupil  855  of the eye  760  of the user is positioned in the eye-box region  759  of the left-eye display system  810 L. For example, the viewing optical system  880  may include one or more optical elements configured to, e.g., correct aberrations in an image light output from the left-eye display systems  810 L, magnify an image light output from the left-eye display systems  810 L, or perform another type of optical adjustment of an image light output from the left-eye display systems  810 L. Examples of the one or more optical elements may include an aperture, a Fresnel lens, a convex lens, a concave lens, a filter, any other suitable optical element that affects an image light, or a combination thereof. 
     The object tracking system  890  may include an IR light source  891  configured to illuminate the eye  760  and/or the face, and an optical sensor  893  (e.g., a camera) configured to receive the IR light reflected by the eye  760  and generate a tracking signal relating to the eye  760  (e.g., an image of the eye  760 ). In some embodiments, the NED  800  may include an adaptive dimming element that may dynamically adjust the transmittance of lights reflected by real-world objects, thereby switching the NED  800  between a VR device and an AR device or between a VR device and an MR device. In some embodiments, along with switching between the AR/MR device and the VR device, the adaptive dimming element may be used in the AR and/MR device to mitigate differences in brightness of lights reflected by real-world objects and virtual image lights. 
     In some embodiments, the present disclosure provides a method including forming a shrink material layer over a patterned substrate including a photoresist pattern. The method may also include exposing the patterned substrate with the shrink material layer to an activating radiation via a grey-tone mask that provides a predetermined light transmittance profile for the activating radiation. The method may also include removing at least a portion of the shrink material layer. 
     In some embodiments, the predetermined light transmittance profile is a non-uniform light transmittance profile. In some embodiments, the patterned substrate includes a photosensitive material that is activated under the activating radiation to react with the shrink material layer. In some embodiments, the photosensitive material is disposed in the photoresist pattern or disposed between the photoresist pattern and the shrink material layer. In some embodiments, the shrink material layer includes a material including one or more amine functional groups and one or more amine protecting groups, and the photosensitive material includes a photoacid generator. In some embodiments, the shrink material layer includes monomers, and the photosensitive material includes an initiator for a photo-polymerization of the monomers. In some embodiments, removing at least a portion of the shrink material layer may include: rinsing the patterned substrate with the shrink material layer using a rinsing solution to remove a portion of the shrink material that has not reacted with the photoresist pattern. In some embodiments, a portion of the shrink material layer remains on the photoresist pattern after the rinsing to increase a width of at least one photoresist line included in the photoresist pattern. In some embodiments, the shrink material layer includes a photosensitive material that is activated under the activating radiation to react with the photoresist pattern. In some embodiments, the shrink material layer includes a material that is aqueous-soluble or organic solvent soluble (e.g., fluoro-soluble), and the photosensitive material includes a photoacid generator. In some embodiments, the photoacid generator included in the photosensitive material is a first photoacid generator with a first activating wavelength, the photoresist pattern includes a second photoacid generator with a second activating wavelength, and the first activating wavelength is greater than the second activating wavelength. In some embodiments, removing at least a portion of the shrink material layer may include: developing the patterned substrate with the shrink material layer using a developer base to remove the shrink material layer and a portion of the photoresist pattern that has reacted with the shrink material layer. In some embodiments, removing the portion of the photoresist pattern that has reacted with the shrink material layer reduces a width of at least one photoresist line included in the photoresist pattern. In some embodiments, the method may also include, after exposing the patterned substrate with the shrink material layer to the activating radiation via the grey-tone mask and before removing at least a portion of the shrink material layer, heat treating the patterned substrate with the shrink material layer. In some embodiments, the patterned substrate with the shrink material layer has a uniform thickness. 
     In some embodiments, the present disclosure also provides a method including configuring a grey-tone mask to provide a non-uniform light transmittance profile for a radiation for creating a varying duty cycle profile in a grating to be fabricated. The method may also include applying a shrink material over a photoresist pattern. The method may also include exposing the photoresist pattern with the shrink material to the radiation transmitting through the grey-tone mask to cause a reaction between the shrink material and the photoresist pattern at selective portions of the photoresist pattern covered by the shrink material. The method may further include removing at least a portion of the shrink material to form the grating. 
     In some embodiments, removing at least a portion of the shrink material comprises at least one of: rinsing the photoresist pattern with the shrink material using a rinsing solution to remove a portion of the shrink material that has not reacted with the photoresist pattern; or developing the photoresist pattern with the shrink material using a developer base to remove the shrink material and a portion of the photoresist pattern that has reacted with the shrink material to reduce a width of at least one photoresist line included in the photoresist pattern. In some embodiments, amounts of the shrink material that reacts with the photoresist pattern at different selective portions of the photoresist pattern are different. 
     In some embodiments, the present disclosure provides a method including forming a photoresist pattern through a lithography mask in a lithography process, the photoresist pattern including a first duty cycle profile. The lithography mask may be different from the grey-tone mask. The lithography process may be any suitable process for making the photoresist pattern. The gray-tone mask may be used to adjust the duty cycle in the photoresist pattern after the photoresist pattern is fabricated using the lithography process, without the need of changing the lithography mask, as typically performed in a conventional technology. With the disclosed method, the process of adjusting the duty cycles of the photoresist pattern may be significantly simplified, and the flexibility in adjusting the duty cycles may be significantly increased. In some embodiments, the method may also include applying a shrink material to the photoresist pattern over the photoresist pattern. The method may also include exposing the photoresist pattern with the shrink material to a radiation through a grey-tone mask having a non-uniform light transmittance profile for the radiation, the non-uniform light transmittance profile corresponding to a second duty cycle profile that is different from the first duty cycle profile. The method may further include removing at least a portion of the shrink material to form a grating having the second duty cycle profile. In some embodiments, removing at least a portion of the shrink material layer may include at least one of: rinsing the photoresist pattern with the shrink material using a rinsing solution to remove a portion of the shrink material that has not reacted with the photoresist pattern; or developing the photoresist pattern with the shrink material using a developer base to remove the shrink material and a portion of the photoresist pattern that has reacted with the shrink material to reduce a width of at least one photoresist line included in the photoresist pattern. 
     Further, when an embodiment illustrated in a drawing shows a single element, it is understood that the embodiment or another embodiment not shown in the figures but within the scope of the present disclosure may include a plurality of such elements. Likewise, when an embodiment illustrated in a drawing shows a plurality of such elements, it is understood that the embodiment or another embodiment not shown in the figures but within the scope of the present disclosure may include only one such element. The number of elements illustrated in the drawing is for illustration purposes only, and should not be construed as limiting the scope of the embodiment. Moreover, unless otherwise noted, the embodiments shown in the drawings are not mutually exclusive, and they may be combined in any suitable manner. For example, elements shown in one figure/embodiment but not shown in another figure/embodiment may nevertheless be included in the other figure/embodiment. In any optical device disclosed herein including one or more optical layers, films, plates, or elements, the numbers of the layers, films, plates, or elements shown in the figures are for illustrative purposes only. In other embodiments not shown in the figures, which are still within the scope of the present disclosure, the same or different layers, films, plates, or elements shown in the same or different figures/embodiments may be combined or repeated in various manners to form a stack. 
     Various embodiments have been described to illustrate the exemplary implementations. Based on the disclosed embodiments, a person having ordinary skills in the art may make various other changes, modifications, rearrangements, and substitutions without departing from the scope of the present disclosure. Thus, while the present disclosure has been described in detail with reference to the above embodiments, the present disclosure is not limited to the above described embodiments. The present disclosure may be embodied in other equivalent forms without departing from the scope of the present disclosure. The scope of the present disclosure is defined in the appended claims.