PRIORITY CLAIMS 
       [0001]    This application is a continuation of and claims the priority benefit of commonly-assigned co-pending International Application Number PCT/US2013/038675, filed Apr. 29, 2013, the entire contents of which are incorporated herein by reference. This application claims the benefit of priority of commonly-assigned, co-pending U.S. Provisional application Ser. No. 61/798,629 (Attorney Docket No. RO-020-PR), to Boris Kobrin et al., entitled “CYLINDRICAL POLYMER MASK AND METHOD OF FABRICATION”, filed Mar. 15, 2013, the entire disclosure of which is herein incorporated by reference. 
         [0002]    International Application Number PCT/US2013/038675 claims the benefit of priority of commonly-assigned, co-pending U.S. Provisional application Ser. No. 61/641,711 (Attorney Docket No. RO-013-PR), to Boris Kobrin et al., entitled “SEAMLESS MASK AND METHOD OF MANUFACTURING”, filed May 2, 2012, the entire disclosure of which is herein incorporated by reference. 
         [0003]    International Application Number PCT/US2013/038675 claims the benefit of priority of commonly-assigned, co-pending U.S. Provisional application Ser. No. 61/641,650 (Attorney Docket No. RO-014-PR), to Boris Kobrin et al., entitled “LARGE AREA MASKS AND METHODS OF MANUFACTURING”, filed May 2, 2012, the entire disclosure of which is herein incorporated by reference. 
         [0004]    International Application Number PCT/US2013/038675 claims the benefit of priority of commonly-assigned, co-pending U.S. Non-Provisional application Ser. No. 13/756,348 (Attorney Docket No. RO-018-US), to Boris Kobrin et al., entitled “CYLINDRICAL MASTER MOLD AND METHOD OF FABRICATION”, filed Jan. 31, 2013, the entire disclosure of which is herein incorporated by reference. 
         [0005]    International Application Number PCT/US2013/038675 claims the benefit of priority of commonly-assigned, co-pending U.S. Non-Provisional application Ser. No. 13/756,370 (Attorney Docket No. RO-019-US), to Boris Kobrin et al., entitled “CYLINDRICAL PATTERNED COMPONENT FOR CASTING CYLINDRICAL MASKS”, filed Jan. 31, 2013, the entire disclosure of which is herein incorporated by reference. 
       CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0006]    This application is also related to commonly-assigned International Patent Application Publication Number WO2009094009, the entire disclosure of which is herein incorporated by reference, and U.S. Pat. No. 8,182,982, the entire disclosure of which are incorporated herein by reference. 
     
    
     FIELD OF THE DISCLOSURE 
       [0007]    The present disclosure is related to lithography methods. More specifically, aspects of the present disclosure are related to rotatable masks, including cylindrical polymer masks and methods of fabrication thereof. 
       BACKGROUND 
       [0008]    Photolithography fabrication methods have use in a wide variety of technological applications, including micro-scale and nano-scale fabrication of solar cells, LEDs, integrated circuits, MEMs devices, architectural glass, information displays, and more. 
         [0009]    Roll-to-roll and roll-to-plate lithography methods typically use cylindrically shaped masks (e.g. molds, stamps, photomasks, etc.) to transfer desired patterns onto rigid or flexible substrates. A desired pattern can be transferred onto a substrate using, for example, imprinting methods (e.g. nanoimprint lithography), the selective transfer of materials (e.g. micro- or nano-contact printing, decal transfer lithography, etc.), or exposure methods (e.g. optical contact lithography, near field lithography, etc.). Some advanced types of such cylindrical masks use soft polymers as patterned layers laminated on a cylinder&#39;s outer surface. Unfortunately, lamination of a layer on a cylindrical surface creates a seam line where the edges of the lamination layer meet. This can create an undesirable image feature at the seam when the pattern is repeatably transferred to a substrate by using the cylindrical mask. 
         [0010]    In addition to fabricating a mask having a seamless polymer layer, it would be desirable to fabricate polymer layers with smooth surfaces that are thick and uniform for use in subsequent rolling lithography fabrication methods. 
         [0011]    Patterned substrates and structured coatings have attractive properties for a variety of applications, including architectural glass, information displays, solar panels, and more. For example, nanostructured coatings can provide desirable antireflection characteristics for architectural glass. Current methods of patterning substrates, including methods such as electron beam lithography, photolithography, interference lithography, and other methods, are often too costly for practical use in the manufacture of patterned substrates or structured coatings in applications requiring larger areas, especially those having areas of 200 cm 2  or more. 
         [0012]    As such, there is a need in the art for large area patterned layers and low cost methods of manufacturing the same. It is within this context that a need for the present invention arises. 
         [0013]    Nanostructuring is necessary for many present applications and industries and for new technologies and future advanced products. Improvements in efficiency can be achieved for current applications in areas such as solar cells and LEDs, and in next generation data storage devices, for example and not by way of limitation. 
         [0014]    Nanostructured substrates may be fabricated using techniques such as e-beam direct writing, Deep UV lithography, nanosphere lithography, nanoimprint lithography, near-field phase shift lithography, and plasmonic lithography, for example. 
         [0015]    Earlier authors have suggested a method of nanopatterning large areas of rigid and flexible substrate materials based on near-field optical lithography described in International Patent Application Publication No. WO2009094009 and U.S. Pat. No. 8,182,982, which are both incorporated herein in their entirety. According to such methods, a rotatable mask is used to image a radiation-sensitive material. Typically the rotatable mask comprises a cylinder or cone with a mask pattern formed on its surface. The mask rolls with respect to the radiation sensitive material (e.g., photoresist) as radiation passes through the mask pattern to the radiation sensitive material. For this reason, the technique is sometimes referred to as “rolling mask” lithography. This nanopatterning technique may make use of Near-Field photolithography, where the mask used to pattern the substrate is in contact with the substrate. Near-Field photolithography implementations of this method may make use of an elastomeric phase-shifting mask, or may employ surface plasmon technology, where the rotating mask surface includes metal nano holes or nanoparticles. In one implementation such a mask may be a near-field phase-shift mask. Near-field phase shift lithography involves exposure of a radiation-sensitive material layer to ultraviolet (UV) light that passes through an elastomeric phase mask while the mask is in conformal contact with a radiation-sensitive material. Bringing an elastomeric phase mask into contact with a thin layer of radiation-sensitive material causes the radiation-sensitive material to “wet” the surface of the contact surface of the mask. Passing UV light through the mask while it is in contact with the radiation-sensitive material exposes the radiation-sensitive material to the distribution of light intensity that develops at the surface of the mask. 
         [0016]    In some implementations, a phase mask may be formed with a depth of relief that is designed to modulate the phase of the transmitted light by it radians. As a result of the phase modulation, a local null in the intensity appears at step edges in the relief pattern formed on the mask. When a positive radiation-sensitive material is used, exposure through such a mask, followed by development, yields a line of radiation-sensitive material with a width equal to the characteristic width of the null in intensity. For 365 nm (Near UV) light in combination with a conventional radiation-sensitive material, the width of the null in intensity is approximately 100 nm. A polydimethylsiloxane (PDMS) mask can be used to form a conformal, atomic scale contact with a layer of radiation-sensitive material. This contact is established spontaneously upon contact, without applied pressure. Generalized adhesion forces guide this process and provide a simple and convenient method of aligning the mask in angle and position in the direction normal to the radiation-sensitive material surface, to establish perfect contact. There is no physical gap with respect to the radiation-sensitive material. PDMS is transparent to UV light with wavelengths greater than 300 nm. Passing light from a mercury lamp (where the main spectral lines are at 355-365 nm) through the PDMS while it is in conformal contact with a layer of radiation-sensitive material exposes the radiation-sensitive material to the intensity distribution that forms at the mask. 
         [0017]    Another implementation of the rotating mask may include surface plasmon technology in which a metal layer or film is laminated or deposited onto the outer surface of the rotatable mask. The metal layer or film has a specific series of through nanoholes. In another embodiment of surface plasmon technology, a layer of metal nanoparticles is deposited on the transparent rotatable mask&#39;s outer surface, to achieve the surface plasmons by enhanced nanopatterning. 
         [0018]    The abovementioned applications may each utilize a rotatable mask. The rotatable masks may be manufactured with the aid of a master mold (fabricated using one of known nanolithography techniques, like e-beam, Deep UV, Interference and Nanoimprint lithographies). The rotatable masks may be made by molding a polymer material, curing the polymer to form a replica film, and finally laminating the replica film onto the surface of a cylinder. Unfortunately, this method unavoidably would create some “macro” stitching lines between pieces of polymer film (even if the master is very big and only one piece of polymer film is required to cover entire cylinder&#39;s surface one stitching line is still unavoidable). It is within this context that the present invention arises. 
       SUMMARY 
       [0019]    According to aspects of the present disclosure, a cylindrical mask may be fabricated by patterning a master mold, forming a patterned polymer mask by casting liquid polymer on the master mold, and curing the liquid polymer. A portion of one end of the patterned polymer mask may be cutoff or the liquid polymer is not cast on a strip at an end of the master mold. The master mold and the patterned polymer mask may be rolled to form a laminate cylinder to form a gap on the patterned polymer mask. The laminate cylinder may be inserted into a casting cylinder with the substrate to the master mold in contact with the casting cylinder and the gap filled with additional liquid polymer, which can be cured to form a free standing polymer by removing the casting cylinder and separating the master mold from the laminate. 
         [0020]    According to other aspects of the present disclosure a cylindrical mask may be fabricated using a hollow casting cylinder and a mask cylinder. The casting cylinder may have an inner diameter that is larger than the outer diameter of the mask cylinder. The casting and mask cylinders may be coaxially assembled and a liquid polymer inserted in a space surrounding the mask cylinder between the inner surface of the casting cylinder and the outer surface of the mask cylinder. After curing the liquid polymer, the casting cylinder may be removed. 
         [0021]    According to other aspects, a substrate may be patterned by successively repeating imprinting the substrate with a master mask having a pattern, the pattern having a smaller area than the substrate until a desired area of the substrate is patterned. Each successive imprinting may overlap part of a previously imprinted portion of the substrate. Imprinting the substrate with the master mask may include (i) depositing a polymer precursor liquid; (ii) pressing the polymer precursor liquid between the master mask and the substrate; and (iii) curing the polymer precursor liquid. The resulting substrate may have a patterned layer with a plurality of imprints, and each boundary between the imprints includes an imprint overlapping a portion of another imprint. 
         [0022]    Additional aspects of the present disclosure describe cylindrical molds that may be used to produce cylindrical masks for use in lithography. A structured porous layer may be deposited on an interior surface of a cylinder. A radiation-sensitive material may be deposited over the porous layer in order to fill pores formed in the layer. The radiation-sensitive material in the pores may be cured by exposing the cylinder with a light source. The uncured resist and porous layer may be removed, leaving behind posts on the cylinder&#39;s interior surface. 
         [0023]    Further aspects of the present disclosure include a cylindrical master mold assembly having a cylindrical patterned component with a first diameter and a sacrificial casting component with a second diameter. The component with the smaller radius may be co-axially inserted into the interior of the component with the larger radius. Patterned features may be formed on the interior surface of the cylindrical patterned component that faces the sacrificial casting component. The sacrificial casting component may be removed once a cast polymer has been cured to allow the polymer to be released. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0024]      FIGS. 1A-1C  depict generic cylinders that are labeled to help clarify descriptive language used in the description and claims of the present invention. 
           [0025]      FIG. 2  depicts a mask cylinder assembled inside of a cylindrical cast according to embodiments of the present invention. 
           [0026]      FIG. 3  is a flowchart of a method of fabricating a cylindrical mask according to embodiments of the present invention. 
           [0027]      FIGS. 4A-4D  illustrate an assembly apparatus according to embodiments of the present invention. 
           [0028]      FIGS. 5A-5D  are a process flow diagram depicting a method of fabricating a cylindrical mask according to embodiments of the present invention. 
           [0029]      FIGS. 6A-6H  are a process flow diagram depicting a method of fabricating a cylindrical mask having multiple layers of polymer as a compliant outer layer according to embodiments of the present invention. 
           [0030]      FIG. 7  is a schematic diagram illustrating an example of printing a pattern using rolling mask nanolithography with a cylindrical mask fabricated in accordance with an embodiment of the present invention. 
           [0031]      FIG. 8A  is an overhead view of a cylindrical master mold assembly comprising a cylindrical patterned component with a sacrificial casting component co-axially inserted inside according to an aspect of the present disclosure. 
           [0032]      FIG. 8B  is a perspective view of a cylindrical master mold assembly shown in  FIG. 2A . 
           [0033]      FIG. 9  is a block diagram of instructions that describe a method for forming a cylindrical mask with cylindrical master mold assembly according to aspects of the present disclosure. 
           [0034]      FIG. 10A  is an overhead view of a cylindrical master mold assembly comprising a sacrificial casting component with a cylindrical patterned component co-axially inserted inside according to an aspect of the present disclosure. 
           [0035]      FIG. 10B  is a perspective view of the cylindrical master mold assembly shown in  FIG. 4A . 
           [0036]      FIGS. 10C-10E  depict how the cylindrical mask may be removed from the cylindrical patterned component according to aspects of the present disclosure. 
           [0037]      FIG. 11  is a block diagram of instructions that describe a method for forming a cylindrical mask with cylindrical master mold assembly according to aspects of the present disclosure. 
           [0038]      FIGS. 12A-12C  depict cylindrical masks where a gas retainer is formed between the elastomeric cylinder and the rigid transparent cylinder according to aspects of the present disclosure. 
           [0039]      FIG. 13A  depicts a master mask according to an embodiment of the present invention. 
           [0040]      FIG. 13B  depicts a master mask being used to pattern a larger area substrate according to an embodiment of the present invention. 
           [0041]      FIG. 13C  depicts an individual imprint of larger area substrate using a master mask according to an embodiment of the present invention. 
           [0042]      FIGS. 13D-13E  depict micrographs of the resulting patterned substrate according to an embodiment of the present invention. 
           [0043]      FIGS. 14A-14G  depict a process flow of imprinting a large area substrate according to an embodiment of the present invention. 
           [0044]      FIGS. 15A-15C  depict examples of patterned large area substrates according to embodiments of the present invention. 
           [0045]      FIG. 16  is an overhead view of a cylinder master mold with protrusions extending out from the interior surface according to an aspect of the present disclosure. 
           [0046]      FIGS. 17A-17G  are schematic diagrams that show the process of forming the master mold according to aspects of the present disclosure. 
           [0047]      FIGS. 18A-18D  are schematic diagrams that show the process of forming the master mold according to additional aspects of the present disclosure that utilize an epitaxial seed layer. 
           [0048]      FIGS. 19A ,  19 B,  19 B′, and  19 C are schematic diagrams that show the process of forming the master mold according to additional aspects of the present disclosure that utilize self-assembled monomers formed on the interior of the master mold. 
           [0049]      FIGS. 20A ,  20 B,  20 B′, and  20 C are schematic diagrams that show the process of forming the master mold according to additional aspects of the present disclosure that utilize self-assembled monomers formed on the exterior surface of the master mold. 
           [0050]      FIGS. 21A-21G  are schematic diagrams that depict a process flow of producing a free-standing mask using a rolled laminate according to various aspects of the present disclosure. 
           [0051]      FIG. 22A  is an overhead view of a cylindrical master mold assembly having a rolled laminate used in making a cylindrical mask according to various aspects of the present disclosure. 
           [0052]      FIG. 22B  is a perspective view of the cylindrical master mold assembly shown in  FIG. 22A . 
           [0053]      FIG. 23  is a process flow diagram depicting a method of fabricating a cylindrical polymer mask using a rolled laminate according to various aspects of the present disclosure. 
           [0054]      FIG. 24A  is an overhead view of a cylindrical master mold assembly used in making a multilayered cylindrical mask according to various aspects of the present disclosure. 
           [0055]      FIG. 24B  is an overhead view of the cylindrical master mold assembly shown in  FIG. 24A . 
           [0056]      FIG. 25  is a process flow diagram depicting a method of fabricating a multilayered cylindrical polymer mask according to various aspects of the present disclosure. 
       
    
    
     DETAILED DESCRIPTION 
       [0057]    The following definitions of terms help to clarify and aid in the understanding of the descriptive terminology used in the description and claims of the present disclosure. 
         [0058]    As used herein, 
         [0059]    “opposing ends” of a component refers the opposite faces of a cylinder or other axially symmetric shape as shown in  FIG. 1A . 
         [0060]    “outer surface” of a component refers to the exterior surface on the sides of a cylinder or other axially symmetric shape as depicted in  FIGS. 1A and 1B . 
         [0061]    “inner surface” of a component refers to the interior surface on the inner sides of a hollow cylinder or other axially symmetric shape as depicted in  FIG. 1B . 
         [0062]    “outer radius/diameter” of a component refers to a radius/diameter of an outer surface of a cylinder or other axially symmetric shape as depicted in  FIGS. 1A and 1B . Where a component&#39;s outer surface is of a shape that has radius/diameter that is not constant, such as with a cone or other axially symmetric shape, the outer radius/diameter may refer to any such radii/diameters, so long as they correspond to the outer surface. 
         [0063]    “inner radius/diameter” of a component refers to a radius/diameter of an inner surface of a cylinder or other axially symmetric shape as depicted in  FIG. 1B . Where a component&#39;s inner surface is of a shape that has radius/diameter that is not constant, such as with a cone or other axially symmetric shape, the inner radius/diameter may refer to any such radii/diameters, so long as they correspond to the inner surface. 
         [0064]    “coaxially assembling” components means assembling the components so that they have the same axis of symmetry as depicted in  FIG. 1C . 
         [0065]    “mask cylinder” or “masking cylinder” refers to a cylindrical substrate for a cylindrical mask, onto the outer surface of which a compliant layer is formed. 
         [0066]    “cast cylinder” or “casting cylinder” refers to a cylindrically shaped cast. 
       I. Casting Using Coaxial Components  
       [0067]    Aspects of the disclosure of this SECTION I include methods and apparatus for making rotatable masks. Various other methods and apparatus are also included in this section. Casting/molding processes and coaxial casting components may be used to cast a compliant layer of a rotatable mask, which can provide benefits that may include minimizing or eliminating the presence of a seam in the rotatable mask. There may be various other advantages to implementations of this section. 
         [0068]    It is further noted that this SECTION I has applicability to and can readily be implemented in various aspects of the remaining SECTIONS II-VI of this description, including but not limited to any such sections that may involve the use of coaxial casting components and assemblies for making rotatable masks. By way of example and not by way of limitation, various aspects of the disclosure of this SECTION I can readily be applied to implementations of SECTION II of this description, which involves the use of sacrificial casting components and coaxially assembling components for fabrication of rotatable masks. 
         [0069]    In order to fabricate a cylindrical mask, polymer material can be used as a compliant outer layer of a cylindrical mask. In embodiments of the present invention, a casting process can be used to form a compliant outer layer by casting polymer on the outer surface of a mask cylinder to create a seamless outer layer. A casting process in embodiments of the present invention can involve coaxially assembling a casting cylinder and a mask cylinder and inserting a liquid polymer in the space in the cast surrounding the mask cylinder. The polymer is then cured and the casting cylinder is removed to create a seamless cylindrical mask that can be used to fabricate a variety of devices. The polymer layer of the cylindrical mask can be patterned to create a mask pattern that can be repeatably transferred to a substrate, e.g. by roll-to-roll lithography, roll-to-plate lithography, etc. 
         [0070]    In embodiments of the present invention, a method of fabricating a cylindrical mask can include coaxially assembling a casting cylinder and a mask cylinder, inserting liquid polymer in the space between the casting and mask cylinders, curing the polymer, and removing the casting cylinder. The method can further include patterning the polymer, which can be an additional step after removing the casting cylinder, or which can be incorporated into the fabrication process by using a cylinder having a pattern on its surface so that the pattern is transferred to the polymer when it comes into contact with the cylinder&#39;s surface. 
         [0071]    In embodiments of the present invention, assembling a casting cylinder around the mask cylinder can involve the use of an assembly apparatus that holds the mask and casting cylinders in place during the fabrication of the cylindrical mask. The assembly apparatus can be designed to preserve the coaxial alignment of the cylinders during the casting process, creating cylindrical space of uniform thickness around the mask cylinder that corresponds to the outer compliant layer of the cylindrical mask. The fixture can be designed to permit a liquid polymer material to be inserted into this space while the cylinders are assembled with the fixture. 
         [0072]    In embodiments of the present invention, an assembly apparatus used to preserve the coaxial alignment of cylinders in the fabrication process can include a set of plates, with the plates held together at opposing ends of the cylinders by a pin. The plates can include grooves aligned with the sides of the cylinders, or other means, to hold the alignment of the cylinders in place. One of the plates can have holes, or other means, that permit a liquid polymer to be poured through it and into the space corresponding to the outer compliant layer of the cylindrical mask. 
         [0073]    The casting fixtures may be removed by disassembly. For example, after the polymer between the cylinders has cured, the casting cylinder may be separated into two or more sections by cutting it lengthwise from its exterior surface down to the tube cured polymer without significant damage to the polymer or leaving a small amount of the casting cylinder material. The cut can be made by saw, chemical etching, or laser. The sections of casting cylinder may then be the separated from the cured polymer and from each other. 
         [0074]    Embodiments of the present invention are capable of creating patterned cylindrical masks having uniform and seamless outer layers with ideal thickness and smoothness for the repeatable transfer of the mask&#39;s pattern onto substrates for the fabrication of various devices. 
         [0075]    Turning now to  FIG. 2 , an assembly  200  of a mask cylinder  202  surrounded by a casting cylinder  204  is depicted according to an embodiment of the present invention. The cylinders  202  and  204  are coaxially assembled to so that their axes  206  are aligned, thereby creating a cylindrical region  208  of uniform thickness around the mask cylinder which can define the shape of the outer polymer layer of the cylindrical mask. Cylinders  202  and  204  can be held in place using an assembly apparatus (not pictured) that aligns their axes and permits a liquid polymer to be inserted into cylindrical region  208  of the assembly, such as by pouring it through openings or holes in the apparatus. Polymer precursor can be inserted in the space  208  between the cylinders  202  and  204 . The polymer precursor may be in the form of a monomer, a polymer, a partially cross-linked polymer, or any mixture of thereof in a liquid or semi-liquid form. The polymer precursor can be cured to form the outer polymer layer of the cylindrical mask. The polymer may be patterned with a mask pattern in a variety of ways. For example, the inner surface of casting cylinder  204  may contain a mask pattern so that the outer surface of the polymer material matches the pattern on the inner surface of the casting cylinder  204 . As another example, the outer surface of the mask cylinder  202  may contain a mask pattern so that this pattern is transferred to the inner surface of the polymer after it is formed on the mask cylinder. As another example, the polymer material may be patterned after subsequent fabrication steps and removal of the casting cylinder  204  by patterning the outer surface of the polymer using various lithography methods. As another example, the pattern may also be patterned by some combination of the above. 
         [0076]    Turning to  FIG. 3 , a flowchart of fabricating a seamless cylindrical mask is depicted according to embodiments of the present invention. Fabricating a cylindrical mask  300  can include coaxially assembling the cylinders as indicated at  302 , which can involve assembling a casting cylinder and a mask cylinder so that the axis of both the casting cylinder and the mask cylinder are the same. The casting cylinder may be a hollow cylinder with an inner diameter that is larger than the outer diameter of the mask cylinder, such that a space is left between the cylinders. This difference in diameters can define the thickness of the outer compliant layer of the mask so that, where D cast  is the inner diameter of the casting cylinder and D mask  is the outer diameter of the mask cylinder, the thickness T of the compliant layer of the cylindrical mask will be 
         [0000]    
       
         
           
             
               T 
               = 
               
                 
                   
                     D 
                     cast 
                   
                   - 
                   
                     D 
                     mask 
                   
                 
                 2 
               
             
             , 
           
         
       
     
         [0000]    or half the difference in diameters. The thickness T can be selected as desired for various application specific requirements by using cylinders having the required diameters corresponding to the equation above. Fabrication  300  can also include inserting polymer precursor as indicated at  304  into the space in the casting cylinder that surrounds the outer surface of the mask cylinder. Inserting the polymer precursor can be done, for example, by pouring a liquid or semi-liquid polymer precursor material in through the top of the assembled cylinders into the space between them. Inserting the polymer precursor may be done in other ways, so long as the polymer precursor material is introduced into the space between the cylinders. Preferably, the polymer should substantially fill this space. The method for fabricating a cylindrical mask  300  can also include curing the polymer precursor as indicated at  306  to form a polymer layer. Curing the polymer precursor may involve applying UV radiation, heat, or other curing treatment to the assembly to harden the polymer. Once the polymer is cured, the method  300  may further include removing the casting cylinder, as indicated at  308 , leaving behind a cylindrical mask having a compliant outer layer corresponding to the cured polymer. The method  300  may also include patterning the polymer, and this can be accomplished, for example, by patterning the outer surface of the compliant layer after the removing the cast or by using patterned cylinders in the fabrication process so that patterning the polymer is integrated into the other fabrication steps. 
         [0077]    It is noted that although the casting cylinder is shown as being assembled outside and around the mask cylinder, the reverse configuration is also possible. In such an implementation, the outer surface of the casting cylinder could be patterned and a negative of the pattern on the outer surface of the casting cylinder would be transferred to a polymer material on the inside surface of the mask cylinder when the casting cylinder is removed. 
         [0078]    It is noted that removing the casting cylinder can be performed in a variety of ways. By way of example and not by way of limitation, the casting cylinder can be cut using a saw, a laser, wet or dry etching, or other means. When cutting the casting cylinder, care should be taken not to damage the polymer layer underneath. If a laser is used to cut the casting cylinder, a special layer could be deposited on the inside surface of the casting cylinder to act as an etch stop layer, and this layer should be reflective to the light that is used to cut the casting cylinder material. Cutting can be performed using one or more cut lines to make it easier to subsequently peel off the casting cylinder from the polymer surface. Once the casting cylinder is cut, it can be peeled off of the polymer surface mechanically. By way of example and not by way of limitation, the casting cylinder may be etched away chemically using etching chemicals that do not also etch away the polymer or mask cylinder within. By way of example and not by way of limitation, the casting cylinder may be treated with a low friction coating or other release coating prior to assembly so that, after the curing the casting cylinder can be slid off the polymer surface. By way of example and not by way of limitation, if the casting cylinder&#39;s coefficient of thermal expansion is larger than the polymer&#39;s, the casting cylinder could be heated to expand the casting cylinder and slide it off (if the polymer can withstand such temperatures). By way of example and not by way of limitation, the casting cylinder may be treated with a uniform coating, which can be dissolved after curing the polymer, and the casting cylinder can be slid off the polymer surface. The casting cylinder may also be removed by other means, and such other means of removal are within the scope of the present invention. Accordingly, the scope of the present invention is not to be limited to any specific method of removal unless explicitly recited in the claims. 
         [0079]    Turning to  FIG. 4 , details of an example of an assembly apparatus according to embodiments of the present invention is depicted. In  FIG. 4A , an entire assembly apparatus  400  is depicted that can be used to fabricate a seamless cylindrical mask according to embodiments of the present invention. Apparatus  400  can include plates  402  held together by a pin  406 . The plates  402  can be held together at opposing ends of the cylinders (not pictured), and pin  406  preferably lines up with the axes of the cylinders. By way of example, the first plate  402   a  can be oriented as a top plate during assembly and the second plate  402   b  can be oriented as a bottom plate. The first plate  402   a  can further include holes to permit a polymer to be poured through it and into a space between the cylinders. The plates can also include grooves  410  that align with the placement of the sidewalls of the mask cylinder and casting cylinder to facilitate holding them in place. 
         [0080]      FIG. 4C  depicts a top view of a first plate  402   a  according to an embodiment of the present invention. The placement of holes  408  can correspond to the space inside of the casting cylinder surrounding the mask cylinder. First grooves  410   a  can be aligned with a mask cylinder  412  and second grooves  410   b  can be aligned with a casting cylinder  414  during fabrication of a cylindrical mask in embodiments of the present invention, as shown in  FIG. 4C . In the embodiment shown in  FIGS. 4B-4C  it can be seen that holes  408  are positioned between the grooves  410   a  and  410   b  where the surfaces of the mask cylinder  412  and casting cylinder  414  would line up, in order to better facilitate pouring the polymer precursor  416  into the space between the two cylinders. It is noted that holes  408  can be designed in any of a variety of shapes, patterns, numbers of holes, etc., that permit the polymer precursor  416  to be inserted through the assembly apparatus, and the holes shown in  FIG. 4C  are provided for illustration purposes only. It is further noted that although circular plates are generally depicted, other shapes may be used, and the plates shown in the figures are for illustration purposes only. 
         [0081]      FIG. 4D  depicts a plan view of plate  402  according to an embodiment of the present invention. Plate  402  can include grooves  410  to enable the apparatus  400  to hold the cylinders in place during fabrication of a cylindrical mask. Plate  402  can include first grooves  410   a  aligned with a mask cylinder and second grooves  410   b  aligned with a casting cylinder during fabrication of a cylindrical mask in embodiments of the present invention. It is noted that grooves  410  can be designed in any of a variety of shapes and patterns depending on the cylinders used to fabricate the cylindrical mask, and the grooves shown in the figures are provided for descriptive purposes only. It is also noted that both a first plate  402   a  and a second plate  402   b  can have grooves for holding the alignment of the cylinders in place such as are shown in  FIGS. 4A-4D . 
         [0082]    Turning to  FIGS. 5A-5D , a process flow of fabricating a cylindrical mask is depicted according to embodiments of the present invention. In  FIG. 5A , a casting cylinder  504  is coaxially assembled around a mask cylinder  502  to create assembly  506  using an assembly apparatus that holds the cylinders in place and aligns their center axes. In  FIG. 5A , the fixture includes a first plate  508   a , a second plate  508   b , and a pin  510  that can attach to the plates  508  to hold them together at opposing ends of cylinders  502  and  504 . The cylinders  502  and  504  can be made from a variety of materials, including, for example, glass, metal, polymer, or other materials. 
         [0083]    The mask cylinder,  502 , is preferably made of a material that is transparent to UV or other radiation used in the photolithography process employing the Cylinder Mask. Examples of materials for the mask cylinder  502  include fused silica. The casting cylinder  504  is preferably made from a material that is dimensionally stable for successful casting and is also amenable to the removal process, e.g., as described above. The casting cylinder may be transparent to UV or other radiation, but does not have to be so configured in all embodiments. 
         [0084]    The inner surface of the casting cylinder  504  may include a mask pattern that corresponds to a desired pattern for the outer surface of the cylindrical mask&#39;s compliant layer so that the polymer is patterned during the casting process depicted in  FIG. 5 . Likewise, the outer surface of the mask cylinder  502  may include a mask pattern for the inner surface of the cylindrical mask&#39;s compliant layer. Alternatively, the surfaces of the cylinders  502  and  504  may have no patterns, and the outer surface of the polymer may be patterned by various lithography methods after the compliant layer is formed. In  FIG. 5B , a liquid polymer  512  is inserted into the space between the cylinders, between the inner surface of the casting cylinder  504  and the outer surface of the mask cylinder  502 . By way of example, inserting polymer precursor  512  can be accomplished by pouring it on the top of the assembly  506  through the fixture, through openings  514  left in top plate  508   a  and into a space inside of the casting cylinder that surrounds the mask cylinder. In  FIG. 5C , the polymer is cured, e.g., by applying UV radiation, temperature treatment, or other curing means  516  to the assembly  506 . In  FIG. 5D , the casting cylinder  504  is removed from the cured polymer  518 , leaving behind cylindrical mask  520  with the cured polymer  518  as a compliant outer layer. If patterned cylinders were not used in the fabrication process, the process of  FIG. 5  can further include patterning the outer surface of the compliant outer layer  518  with a desired mask pattern after removing the casting cylinder  504 . 
         [0085]    It is noted that a pattern should be formed on a surface of the polymer, preferably the outer surface for contact lithography, so that the cylindrical mask may be used to transfer a pattern onto a substrate. In embodiments of the present invention, the outer surface of the polymer may be patterned by a variety of means. In embodiments of the present invention, a mask pattern may applied to the inner surface of the casting cylinder prior to filling the cast with a liquid polymer, such that the mask pattern is transferred to the outer surface of the polymer during casting on the mask cylinder. In other embodiments, the outer surface of the polymer may be patterned after removal of the casting cylinder. Regardless of the method of patterning chosen, care should be taken to avoid stitching errors when forming the mask pattern so that this pattern is also seamless. Accordingly, it is preferable that cylindrical masks of embodiments of the present invention include not only a seamless compliant layer, but also a seamless pattern on a surface of the compliant layer. 
         [0086]    It is noted that patterning the inner surface of the casting cylinder or the outer surface of the mask cylinder can be done using a variety of techniques according to embodiments of the present invention. For example, the inner or outer surface of a cylinder may be patterned by successively imprinting it with a smaller master mask, as described in SECTION III of this description and in commonly-assigned, co-pending application No. 61/641,650, (attorney docket no. RO-014-PR), filed May 2, 2012, the entire disclosure of which is herein incorporated by reference. As another example, a cylinder surface may be patterned using any of a variety of known techniques, including nanoimprint lithography, nanocontact printing, photolithography, etc. As another example, the cylinder surface can be patterned using an anodization process. This can be accomplished, for example, by using a casting cylinder made of aluminum. An aluminum surface for anodization may alternatively be provided, for example, by depositing an aluminum layer on a surface of a cylinder. A nanoporous surface can then be created on the aluminum surface using an anodization process. As another example, patterning the inner surface can be performed by self-assembly of nanoparticles or nanospheres. Nanoparticles or nanospheres can be deposited from suspension using dipping methods, spraying methods, or other methods. Upon drying, cylinder material can be etched using these nanoparticles or nanospheres as an etch mask, then removing or etching away such etch mask. 
         [0087]    Patterning the polymer on the outer surface of the cylindrical mask, after removal of the casting cylinder, can be done using a variety of techniques according to embodiments of the present invention. For example, the outer surface of the polymer may be patterned by successively imprinting it with a smaller master mask, as described in SECTION III of this description and in commonly-assigned, co-pending application No. 61/641,650 (attorney docket no. RO-014-PR), mentioned above. As another example, the outer surface of the polymer may be patterned using any of a variety of known techniques, including nanoimprint lithography, nanocontact printing, photolithography, nanosphere lithography, self-assembly, interference lithography, anodic aluminum oxidation, and the like. 
         [0088]    It is also noted that the compliant layer of the cylindrical mask is not limited to a single polymer layer, but can include multiple layers of polymer having different properties. Embodiments of the present invention can include forming a two layer polymer for the compliant outer layer of a cylindrical mask. The outermost layer of the two layer polymer can be a harder layer having a higher durability than a softer, innermost polymer layer, thereby allowing patterning of higher resolution or higher aspect ratio nanostructures than can be done with just a soft polymer layer. The inner surface of the casting cylinder can be pretreated with a release coating to facilitate its removal from the outermost polymer layer at the end of fabrication. Forming a two layer polymer can involve depositing liquid polymer of the outermost layer on an inner patterned surface of a casting cylinder. For a two-layer polymer, the outer surface may be patterned after removal of the casting cylinder (instead of patterning the inside of the casting cylinder), in the same manner as a single layer cushioning material. The hard polymer layer can then be cured, for example, by temperature treatment, UV radiation, or other means. After curing, the inner surface of this hard polymer layer can be surface treated to promote adhesion to the other, softer, innermost polymer layer. Surface treatment can be done, for example, by plasma treatment, corona discharge, deposition of adhesion coating, or other means. A softer, innermost polymer layer can then be formed in the same manner as described above for a single layer polymer. It is also noted that a multilayered cylindrical mask can be formed by successively repeating the casting process described herein by casting a new polymer layer on the outer surface of a previously manufactured polymer layer. In this case, a larger casting cylinder should be used each time, after the previous casting cylinder is removed, in order to leave space for the new polymer layer between the outer surface of the previously manufactured polymer layer and the inner surface of the new casting cylinder. 
         [0089]    In embodiments that use two or more polymer layers it is desirable that the optical index of both the material covering the prior pattern and the prior pattern are index matched. Also, it is desirable that the photolithography tool that uses the resulting mask be configured to accommodate masks with increasing diameters. 
         [0090]    Turning to  FIG. 6 , a more detailed process flow for forming a cylindrical mask having a two-layer polymer as its outer compliant layer is depicted according to an embodiment of the present invention. By way of example, fabricating a cylindrical mask having a compliant outer layer that is a two layer polymer can include patterning the inner surface of a casting cylinder  602 , as depicted in  FIG. 6A . The patterned inner surface can then be treated with a release coating  604  to facilitate subsequent release of the casting cylinder from the outer surface of the outermost polymer layer, as shown in  FIG. 6B . In  FIG. 6C , a liquid polymer material  606  is deposited on the inner surface of the casting cylinder to form the outermost layer of the multilayered compliant outer laminate. 
         [0091]    The polymer may be deposited in accordance with any of a number of known methods. By way of example, and not by way of limitation, the polymer may be deposited by dipping, ultrasonic spraying, microjet or inkjet type dispensing, and possibly dipping combined with spinning. Polymer material  606  can preferably be a harder polymer, such as h-PDMS as described in Truong, T. T., et al, Soft Lithography Using Acryloxy Perfluoropolyether Composite Stamps.  Langmuir  2007, 23, (5), 2898-2905, the disclosure of which is herein incorporated by reference. Using a more durable outer layer can permit the patterning of higher resolution or higher aspect ratio nanostructures than can be done with a single layer of polymer as the outer laminate of a cylindrical mask. In  FIG. 6D , the outermost polymer layer  606  is cured by UV radiation, temperature treatment, or other curing means  608   a . In  FIG. 6E , curing can be followed by surface treatment of the inner surface of the outer polymer layer  606  to promote adhesion between the polymer layers, for example by plasma treatment, corona discharge, deposition of adhesion coating, or other means. In  FIG. 6F , the casting cylinder  602  having the outer polymer layer  606  on its inner surface is assembled around a mask cylinder  610  using an assembly apparatus having plates  612  held together on opposing ends of the cylinders  602  and  610  by pin  614 . In  FIG. 6G , liquid polymer  618  is inserted into the casting cylinder by pouring it through holes or openings  620  in the top plate  612   a  of the apparatus. Liquid polymer  618  can correspond to an inner polymer layer, which can be softer than the outer polymer layer, and liquid polymer  618  is inserted in the space between the inner surface of the casting cylinder  602  and the outer surface of the mask cylinder, and more specifically between the inner surface of the outer polymer layer and the outer surface of the mask cylinder. In  FIG. 6H , inner polymer layer  618  is cured by applying curing means  608   b , which can be UV radiation, heat, or other means, to the assembly  616 . In  FIG. 6I , casting cylinder  602  is removed leaving behind cylindrical mask  622  having a compliant outer layer that includes inner polymer layer  618  and outer polymer layer  606  on the outer surface of a mask cylinder  610 . Cylindrical mask  622  has a patterned outer surface that corresponds to the mask pattern applied to the inner surface of the casting cylinder  602  in the step of  FIG. 6A . 
         [0092]    It is further noted that the thickness of the polymer layer(s) may vary according to various application specific requirements. The thickness of the polymer layer(s) may preferably be, but is not required to be, in the range of about 0.5 mm-5 mm. Where a two-layer polymer is used, a softer innermost layer may be relatively thick, for example in the range of about 0.5-5 mm, and the harder, outermost, patterned layer may be relatively thin, for example in the range of about 0.5-10 μm. 
         [0093]    It is further noted that the polymer used to fabricate the cylindrical mask can be, for example, Polydimethylsiloxane (PDMS) materials, such as Sylgard® 184 of Dow Corning®, h-PDMS (“hard” PDMS), soft-PDMS gel, etc. Where two layers of polymer are used, the soft inner polymer may be a soft-PDMS gel and the outer layer can be Sylgard® 184, for example. As another example, the inner layer may be Sylgard® 184 and the outer layer may be h-PDMS. It is noted that a variety of other elastomeric and polymer materials can be used to fabricate a cylindrical mask and are within the scope of the present invention. Other possible polymers that may be used include optical adhesives, e.g., mercapto-ester based adhesives, a number of which are available from Norland products of Cranbury, N.J., perfluoropolyethers, or other UV curable or heat curable polymers. 
         [0094]    It is also noted that the means used for curing polymer in embodiments of the present invention can depend on the type of polymer being cured, the cylinder material used, and other factors. For example, curing can be done thermally, with UV radiation, or other means. 
         [0095]    It is further noted that those having ordinary skill in the art can conceive of various modifications to the design of an assembly apparatus or the method of preserving the alignment of cylinders in place without departing from the teachings of the present invention. 
         [0096]    It is also noted that the present invention can be used to form various different patterns for various substrates and devices. Patterns can include features of having dimensions of different sizes and can preferably include micro or nanoscaled features, and more preferably have nanoscaled features. 
         [0097]    Embodiments of the present invention may be used in conjunction with a type of lithography known as “rolling mask” nanolithography. An example of a “rolling mask” near-field nanolithography system is described, e.g., in commonly-assigned International Patent Application Publication Number WO2009094009, which is incorporated by reference herein. An example of such a system is shown in  FIG. 7 . The “rolling mask” may be in the form of a glass (e.g. quartz) frame in the shape of hollow cylinder  711 , which contains a light source  712 . An elastomeric film  713  formed on the outer surface of the cylinder  711  as described above may have a nanopattern  714  fabricated in accordance with the desired pattern to be formed on a substrate  715 . The nanopattern  714  can be designed to implement phase-shift exposure, and in such case is fabricated as an array of nanogrooves, posts or columns, or may contain features of arbitrary shape. 
         [0098]    By way of example, and not by way of limitation, the nanopattern  714  on the cylinder  711  may have features in the form of parallel lines having a linewidth of about 50 nanometers and a pitch of about 200 nanometers or greater. In general, the linewidth may be in a rage from about 1 nanometer to about 500 nanometers and pitch may range from about 10 nanometers to about 10 microns. Although examples are described herein in which the nanopattern  714  is in the form of regularly parallel lines, the nanopattern may alternatively be a regularly repeating two-dimensional pattern, having regularly-spaced and arbitrarily-shaped spots. Furthermore, the pattern features (lines or arbitrary shapes) may be irregularly spaced. 
         [0099]    The nanopattern  714  on the cylinder  711  is brought into a contact with a photosensitive material  716 , such as a photoresist that is coated on a substrate  715 . The photosensitive material  716  is exposed to radiation from the light source  712  and the pattern  714  on the cylinder  711  is transferred to the photosensitive material  716  at the place where the nanopattern contacts the photosensitive material. The substrate  715  is translated as the cylinder rotates such that the nanopattern  714  remains in contact with the photosensitive material. Depending on the nature of the photosensitive material, portions of the pattern that are exposed to radiation may react with the radiation so that they become removable or non-removable. 
         [0100]    By way of example, if the photosensitive material is a type of photoresist known as a positive resist, the portion of the material that is exposed to light becomes soluble to a developer and the portion of the material that is unexposed remains insoluble to the developer. By way of counterexample, if the photosensitive material is a type of photoresist known as a negative resist, the portion of the material that is exposed to light becomes insoluble to a developer and the unexposed portion of the material is dissolved by the photoresist. 
         [0101]    In certain embodiments of the present invention, the photosensitive material  716  may be exposed by passing the substrate past the cylinder  711  two or more times. For sufficiently small values of the pitch and linewidth, the linear pattern of exposure resulting from one pass is unlikely to line up with each other. As a result, lines from one pass are likely to end up between lines of a previous pass. By careful choice of the pitch, linewidth, and number of passes it is possible to end up with a pattern of lines in the photosensitive material  716  that has a pitch smaller than the pitch of the lines in the pattern  714  on the cylinder  711 . 
         [0102]    When patterning the polymer, care should be taken to avoid stitching errors in the pattern. Preferably, fabrication of a cylindrical mask in embodiments of the present invention also involves patterning a seamless pattern on a seamless polymer layer. This prevents a seam from being transmitted to a substrate when the cylindrical mask is used to repeatably pattern a substrate, both because the compliant outer layer itself is seamless, and because the pattern contained on a surface of the compliant layer is also seamless. 
         [0103]    It is further noted that embodiments of the invention may be applied to fabrication of rolling masks that are axi-symmetric but not cylindrical, e.g., masks that are frusto-conical in shape. In such cases, a mask element and cast element may be co-axially aligned with plates held together by one or more pins. When co-axially assembled, the facing surfaces of the mask element and the cast element may have similar shapes and the same aspect ratio so that a space of substantially uniform thickness is defined between them. 
       II. Casting Using Sacrificial Components 
       [0104]    Aspects of the disclosure of this SECTION II include methods and apparatus for making rotatable masks using sacrificial casting components. Various other methods and apparatus are also included in this section. Sacrificial casting components in accordance with aspects of this section may be used in conjunction with patterned casting components in order to cast a compliant layer for a rotatable mask, which can provide benefits that may include preserving a patterned casting component for future use without damage to a pattern on its surface. There may be various other advantages to implementations of this section. 
         [0105]    It is further noted that this SECTION II has applicability to and can readily be implemented in various aspects of the remaining SECTIONS I and III-VI of this description, including but not limited to any such sections that may involve the use of coaxial casting components and assemblies for making rotatable masks. By way of example and not by way of limitation, various aspects of the disclosure of this SECTION II can readily be implemented in SECTION VI of this description, which involves the use of coaxially assembling components for fabrication of multilayered rotatable masks. 
         [0106]    Aspects of the present disclosure describe various patterned component assemblies and methods for fabricating near-field optical lithography masks for “Rolling mask” lithography with the patterned component assemblies. In rolling mask lithography, a cylindrical mask is coated with a polymer, which is patterned with desired features in order to obtain a mask for phase-shift lithography or plasmonic printing. The features that are patterned into the polymer may be patterned through the use of the patterned component assemblies described in the present application. The pattern component may include patterned features that range in size from about 1 nanometer to about 100 microns, preferably from about 10 nanometers to about 1 micron, more preferably from about 50 nanometers to about 500 nanometers. The cylindrical mask may be used to print features ranging in size from about 1 nanometer to about 1000 nanometers, preferably about 10 nanometers to about 500 nanometers, more preferably about 50 nanometers to about 200 nanometer 
         [0107]    A first aspect of the present disclosure describes a cylindrical master mold assembly comprised of a cylindrical patterned component that has a first diameter and a sacrificial casting component that has a second diameter. The second diameter may be smaller than the first diameter. Patterned features may be formed on the interior surface of the cylindrical patterned component and the sacrificial casting component may be inserted co-axially into the interior of the cylindrical patterned component. A polymer material may then fill the gap between the patterned component and the sacrificial casting component in order to form the cylindrical mask. The sacrificial casting component may be removed once the polymer has been cured. According to certain aspects of the present disclosure, the sacrificial casting component may be fractured in order to allow the cylindrical mask to be removed. Additionally, certain aspects of the present disclosure also provide for the sacrificial casting component to be deformed in order to allow the cylindrical mask to be removed. 
         [0108]    According to an additional aspect of the present disclosure a cylindrical master mold assembly may have a cylindrical patterned component that has a first diameter, and a sacrificial casting component that has a second diameter. The second diameter may be larger than the first diameter. The patterned component may have patterned features formed on its exterior surface. The patterned component may be inserted co-axially into the sacrificial casting component. A polymer may then fill the gap between the patterned component and the sacrificial casting component. Once the polymer has cured, the sacrificial casting component may be broken away, leaving the cylindrical mask on the patterned component. The cylindrical mask may then be peeled off of the patterned component. 
         [0109]    According to a further aspect, a cylindrical mask may comprise a cylindrical elastomer component with an inner radius and a rigid transparent cylindrical component having an outer radius. A gas retainer is configured to retain a volume of gas between an inner surface of the elastomer component and an outer surface of the rigid transparent cylindrical component. The elastomer component has a major surface with a nanopattern formed in the major surface. The outer radius of the rigid transparent component is sized to fit within the cylindrical elastomer component. 
         [0110]    In some implementations, the gas retainer may include two seals. Each seal seals a corresponding end of the volume of gas. Such seals may be in the form of O-rings or gaskets. In some implementations, the volume of gas may be retained by a bladder disposed between the major surface of the elastomer component and the major surface of the rigid transparent cylindrical component. 
         [0111]    In some implementations, the major surface of the cylindrical elastomeric component on which the nanopattern is formed is an outer cylindrical surface. 
         [0112]    The authors have described a “Rolling mask” near-field nanolithography system earlier in International Patent Application Publication Number WO2009094009, which is incorporated herein by reference. One of the embodiments is show in  FIG. 7 . The “rolling mask” consists of a glass (e.g., fused silica) frame in the shape of hollow cylinder  711 , which contains a light source  712 . An elastomeric cylindrical rolling mask  713  laminated on the outer surface of the cylinder  711  has a nanopattern  714  fabricated in accordance with the desired pattern. The rolling mask  713  is brought into a contact with a substrate  715  coated with radiation-sensitive material  716 . 
         [0113]    A nanopattern  714  can be designed to implement phase-shift exposure, and in such case is fabricated as an array of nanogrooves, posts or columns, or may contain features of arbitrary shape. Alternatively, nanopattern can be fabricated as an array or pattern of nanometallic islands for plasmonic printing. The nanopattern on the rolling mask can have features ranging in size from about 1 nanometer to about 100 microns, preferably from about 10 nanometers to about 1 micron, more preferably from about 50 nanometers to about 500 nanometers. The rolling mask can be used to print features ranging in size from about 1 nanometer to about 1000 nanometers, preferably about 10 nanometers to about 500 nanometers, more preferably about 50 nanometers to about 200 nanometers. 
         [0114]    The nanopattern  714  on the rolling mask  713  may be manufactured with the use of a cylindrical master mold assembly. Aspects of the present disclosure describe the cylindrical master mold assembly and methods for forming the nanopattern on the rolling mask  713 . 
         [0115]      FIG. 8A  is an overhead view of a master mold assembly  800 . The master mold assembly  800  comprises a cylindrical patterned component  820  and sacrificial casting component  830 . The cylindrical patterned component  820  may have a first radius R 1  and the sacrificial casting component  830  may have a second radius R 2 . According to a first aspect of the present disclosure, R 1  may be greater than R 2  in order to allow for the sacrificial casting component  830  to be co-axially inserted into the interior of the cylindrical patterned component  820  with a space  840  between them. 
         [0116]    The patterned component  820  may be made from a material that is transparent to optical radiation, such as infrared, visible, and/or ultraviolet wavelengths. By way of example, and not by way of limitation, the cylinder may be a glass such as fused silica. It is noted that fused silica is commonly referred to as “quartz” by those in the semiconductor fabrication industry. Although quartz is common parlance, “fused silica” is a better term. Technically, quartz is crystalline and fused silica is amorphous. As may be seen in  FIG. 8B , the interior surface of the patterned component  820  may be patterned with the desired pattern  825  that will be used to form the nanopattern  714  on the cylindrical mask  713 . By way of example, and not by way of limitation, the pattern  825  may be formed with the use of structured porous mask or a self-assembled monolayer (SAM) mask in conjunction with photolithography techniques described in SECTION IV of this description and in commonly owned U.S. patent application Ser. No. 13/756,348, entitled “CYLINDRICAL MASTER MOLD AND METHOD OF FABRICATION” (Attorney Docket No. RO-018-US) filed Jan. 31, 2013, and incorporated by reference herein in its entirety. 
         [0117]    The sacrificial casting component  830  should be able to be removed after the cylindrical rolling mask  713  has been cured without damaging the nanopattern  714 . According to aspects of the present disclosure, the sacrificial casting component  830  may be a thin walled cylinder that is formed from a material that is easily fractured. By way of example, and not by way of limitation, the material may be glass, sugar, or an aromatic hydrocarbon resin, such as Piccotex™ or an aromatic styrene hydrocarbon resin, such as Piccolastic™. Piccotex™ and Piccolastic™ are trademarks of Eastman Chemical Company of Kingsport, Tenn. By way of example, and not by way of limitation, the sacrificial casting component  830  may be approximately 1 to 10 mm thick, or in any thickness range encompassed therein, e.g., 2 to 4 mm thick. The nanopattern  714  of the cylindrical mask  713  is not located on the surface of the sacrificial casting component  830 , and therefore the nanopattern  714  is not susceptible to damage during the removal. According to additional aspects of the present disclosure, the sacrificial casting component  830  may be made from a material that is dissolved by a solvent that does not harm the patterend component  820  or the cylindrical mask  713 . By way of example, a suitable dissolvable material may be a sugar based material and the solvent may be water. Dissolving the sacrificial casting component  830  instead of fracturing may provide additional protection to the nanopattern  714 . 
         [0118]    According to yet additional aspects of the present disclosure, the casting component  830  may be a thin walled sealed cylinder made from malleable material such as plastic or aluminum. Instead of fracturing the sacrificial casting component  830 , the sealed component may be removed by collapsing the component by evacuating the air from inside the cylinder. According to yet another aspect of the present disclosure, the sacrificial casting component  830  may be a pneumatic cylinder made of an elastic material. Examples of elastic materials that may be suitable for a pneumatic cylinder include, but are not limited to plastic, polyethylene, polytetrafluoroethylene (PTFE), which is sold under the name Teflon®, which is a registered trademark of E. I. du Pont de Nemours and Company of Wilmington, Del. During the molding process, the sacrificial casting component  830  may be inflated to form a cylinder and once the cylindrical mask  713  has cured, the casting component  830  may be deflated in order to be removed without damaging the cylindrical mask. In some implementations, such a pneumatic cylinder may be reusable or disposable depending, e.g., on whether it is relatively inexpensive to make and easy to clean. 
         [0119]    As in  FIG. 9 , aspects of the present disclosure describe a process  900  that may use cylindrical master mold assemblies  800  to form cylindrical masks  713 . First, at  960  a sacrificial casting component  830  may be co-axially inserted into a cylindrical patterned component  820 . Then, the space  840  between the sacrificial casting component  830  and the cylindrical patterned component  820  is filled with a liquid precursor that, when cured, forms an elastomeric material at  961 . By way of example, and not by way of limitation, the material may be polydimethylsiloxane (PDMS). 
         [0120]    Next, at  962  the liquid precursor is cured to form the elastomeric material that will serve as the cylindrical mask  713 . By way of example, the curing process may require exposure to optical radiation. The radiation source may be located co-axially within the master mold assembly  800  when the sacrificial casting component  830  is transparent to the wavelengths of radiation required to cure the liquid precursor. Alternatively, the radiation source may be located outside of the master mold assembly  800  and the exposure may be made through the cylindrical patterned component  820 . Once the cylindrical mask  713  has cured, the sacrificial casting component  830  may be removed at  962 . By way of example, and not by way of limitation, the casting component  830  may be removed by fracturing, dissolving, deflating, or collapsing. 
         [0121]      FIG. 10A  is an overhead view of a cylindrical master mold assembly  1000  according to an additional aspect of the present disclosure. As shown, the cylindrical patterned component  1020  may have a first radius R 1  and the sacrificial casting component  1030  may have a second radius R 2  that is larger than R 1 . The cylindrical master mold assembly  1000  is formed by co-axially inserting the cylindrical patterned component  1020  inside of the sacrificial casting component  1030  leaving an empty space  1040  between the two components. 
         [0122]    The patterned component  1020  may be made from a material that is transparent to optical radiation, such as infrared, visible and/or ultraviolet wavelengths. By way of example, and not by way of limitation, the cylinder may be a glass, such as quartz. As shown in the perspective view in  FIG. 10B , a pattern  1025  is formed on the exterior surface of the cylindrical patterned component  1020 . By way of example, and not by way of limitation, the pattern  1025  may be formed through the use of nano lithography techniques such as, but not limited to e-beam direct writing, Deep UV lithography, nanosphere lithography, nanoimprint lithography, near-field phase shift lithography, and plasmonic lithography. 
         [0123]    The sacrificial casting component  1030  may be removed after the cylindrical rolling mask  713  has been cured without damaging the nanopattern  714 . According to aspects of the present disclosure, the sacrificial casting component  1030  may be a thin walled cylinder that is formed from a material that is easily fractured. By way of example, and not by way of limitation, the material may be glass. The nanopattern  714  of the cylindrical mask  713  is not located on the surface of the sacrificial casting component  1030 , and therefore the nanopattern  714  is not susceptible to damage during the removal. According to additional aspects of the present disclosure, the sacrificial casting component  1030  may be made from a material that is dissolved by a solvent that does not harm the patterend component  1020  or the cylindrical mask  713 . By way of example, a suitable dissolvable material may be a sugar based material and the solvent may be water. Dissolving the sacrificial casting component  1030  instead of fracturing may provide additional protection to the nanopattern  714 . 
         [0124]    After the sacrificial casting component  1030  has been removed, the cylindrical mask  713  remains on the patterned component  1020  as shown in  FIG. 10C . In order to remove the cylindrical mask  713  from the patterned component  1020  the cylindrical mask  713  may be peeled back against itself. Starting from one end of the patterned component  1020 , the cylindrical mask is pulled back over itself in a direction parallel to the axis of the patterned component  1020 , such that the interior surface where the nanopattern  714  was formed is revealed.  FIG. 10D  depicts the removal process at a point where the cylindrical mask  713  has been partially removed. In order to fold back on itself during the removal process, the cylindrical mask  713  should be relatively thin, e.g., 4 millimeters thick or thinner. As such, the difference between the first and second radii should preferably be 4 millimeters or less. Once the entire cylindrical mask  713  has been removed from the patterned component  1020 , it will have been turned completely inside out, revealing the nanopattern  714  on the exterior surface as shown in  FIG. 10E . 
         [0125]    As in  FIG. 11 , aspects of the present disclosure describe a process  1100  that may use cylindrical master mold assemblies  1000  to form cylindrical masks  713 . First, at  1160  a cylindrical patterned component  1020  is co-axially inserted into a sacrificial casting component  1030 . Then, the space  1040  between the sacrificial casting component  1030  and the cylindrical patterned component  1020  is filled with a liquid precursor that, when cured, forms an elastomeric material at  1161 . By way of example, and not by way of limitation, the material may be polydimethylsiloxane (PDMS). 
         [0126]    Next, at  1162  the liquid precursor is cured to form the elastomeric material that will serve as the cylindrical mask  713 . By way of example, the curing process may require exposure to optical radiation. The radiation source may be located co-axially within the master mold assembly  1000 . Alternatively, the radiation source may be located outside of the master mold assembly  1000  and the exposure may be made through the sacrificial casting component  1030  if the casting component  1030  is transparent to the wavelengths of radiation required to cure the liquid precursor. Once the cylindrical mask  713  has cured, the sacrificial casting component  1030  may be removed at  1163 . By way of example, and not by way of limitation, the sacrificial casting component  1030  may be removed by fracturing and/or dissolving. Finally, at  1164  the cylindrical mask is pulled back over itself in a direction parallel to the axis of the patterned component  1020 , such that the interior surface where the nanopattern  714  was formed is revealed. 
         [0127]      FIG. 12A  depicts a cylindrical mask  1200  according to an additional aspect of the present disclosure. Cylindrical mask  1200  is substantially similar to the cylindrical mask depicted in  FIG. 7 , with the addition of a gas retainer  1218  located between the elastomeric rolling mask  1213  and the rigid hollow cylinder  1211 . By way of example, and not by way of limitation, the elastomeric rolling mask  1213  may have a patterned surface  1214  and may be a made in substantially the same manner as described in processes  900  or  1100 . The rigid hollow cylinder may also be transparent to optical radiation. By way of example, and not by way of limitation, the hollow cylinder may be a glass such as fused silica. A light source  1212  may be placed inside hollow cylinder  1211 . The gas retainer  1218  retains a volume of gas  1217  between the outer surface of the cylinder  1211  and the inner surface of the elastomeric mask  1213 . The gas retainer  1218  may be pressurized in order to provide an additional tunable source of compliance for the elastomeric rolling mask  1213 . By way of example, and not by way of limitation, the gas retainer  1218  may be formed by a pair of seals or by an inflatable bladder. 
         [0128]      FIG. 12B  is a cross sectional view along the line  6 - 6  shown in  FIG. 12A  of a cylindrical rolling mask  1201  that depicts an aspect of the present disclosure where the gas retainer  1218  is formed by pair of seals  1218   s . Each seal  1218   s  may be a hollow cylinder, ring, or torus-like shape, such as, but not limited to an O-ring or gasket. The seals  1218   s  may be made of a suitable elastomer material. The elastomeric mask  1213  may then be spaced apart from the rigid hollow cylinder  1211  at each end by a seal  1218   s . The inner radius of the elastomeric mask  1213  can be chosen such that the volume of gas  1217  bounded by the interior surface of the elastomeric mask  1213 , the seals  1218   s  and the rigid outer surface of the rigid hollow cylinder  1211  may be pressurized. When the volume of gas  1217  is pressurized, the elastomeric mask  1213  may be spaced away from the outer surface of the rigid hollow cylinder  1211  by the pressure of the volume of gas  1217  retained between the inner surface of the elastomeric mask  1213  and the outer surface of the cylinder  1211 . The cylinder  1211  may optionally include grooves sized and shaped to receive the seals  1218   s  and facilitate retaining the seals when the gas in the volume is pressurized. 
         [0129]      FIG. 12C  is a cross sectional view along the line  6 - 6  shown in  FIG. 12A  of a cylindrical rolling mask  1202  that depicts an aspect of the present disclosure where the gas retainer  1218  is formed by a bladder  1218   B . The bladder  1218   B  may be cylindrical in shape and positioned between the rigid hollow cylinder  1211  and the elastomeric mask  1213 . When volume of gas  1217  within the bladder  1218   B  is pressurized, the bladder  1218   B  supports the elastomeric mask  1213  above the outer surface of the rigid hollow cylinder  1211 . 
       III. Patterning a Larger Area Substrate Using Successive Imprints 
       [0130]    Aspects of the disclosure of this SECTION III include methods and apparatus for patterning a larger area master mask using a successive imprinting scheme with a smaller area master mask. Various other methods and apparatus are also included in this section. Successive imprints can be used to pattern a relatively large area substrate for a variety purposes, which can provide benefits that may include minimizing or eliminating the visibility or effect of seams between imprints. Various other advantages of this section will be apparent upon reading this section. 
         [0131]    It is further noted that this SECTION III has applicability to and can readily be implemented in various aspects of the remaining SECTIONS I, II, and IV-VI of this description, including but not limited to any such sections that may involve the use of patterned components. By way of example and not by way of limitation, various aspects of the disclosure of this SECTION III can readily be applied to implementations of SECTION V of this description, which involves the use of a rolled laminate having a pattern for making a rotatable mask. 
         [0132]    In embodiments of the present invention, a small master mask having a desired pattern can be used to inexpensively pattern a large area substrate. A small master can be successively imprinted onto a large area substrate using a polymer precursor liquid that is polymerized or cured. An array of imprints is formed by the successive imprinting scheme, where each successive imprint overlaps part of a previous imprint so that there is no un-patterned interstitial space. In this manner, the desired pattern of the master is replicated generating a macroscopically continuous pattern whose dimension is limited only by the size of the substrate. The successive imprinting scheme results in a large area substrate having a patterned layer or structured coating with a nearly invisible boundary between the individual imprints, or replicas, of the master. 
         [0133]    In embodiments of the present invention, a method of patterning a large area substrate can include imprinting the substrate with a master mask having a pattern, wherein the pattern has a smaller area than the substrate area to be patterned. The method can further include successively repeating the imprinting process until a desired area of the substrate is patterned. Each successive imprint can include depositing a polymer precursor liquid, pressing the polymer precursor liquid between the master mask and the substrate, and polymerizing or curing the polymer precursor liquid such that it becomes a solid material. 
         [0134]    It is noted that in embodiments of the present invention, substrates to be patterned can be a variety of shapes, sizes, materials, etc., but should generally be larger than the master mask used to successively imprint the substrate. Master masks can also be a variety of shapes, sizes, materials, etc., and can have patterns of a variety of shapes and sizes, but should generally be smaller than the substrate area to be patterned. In embodiments of the present invention, substrates to be patterned can have a variety of characteristics and, for example, can be flexible, rigid, flat or curved. Likewise, master masks can have a variety of characteristics and, for example, can be flexible or rigid. 
         [0135]    In embodiments of the present invention, desired patterns can include features of a variety of different sizes, shapes, and arrangements. A variety of physical or other properties can be imparted to a substrate by using patterns having various features depending on application specific requirements. 
         [0136]    Turning to  FIGS. 13A-13C , a master mask and a method of fabricating a larger area substrate with a master mask are depicted according to embodiments of the present invention. 
         [0137]    In  FIG. 13A , master mask  1302  having pattern  1304  is depicted, which can be used to imprint a larger area substrate by repeatedly imprinting the larger area substrate with the master mask  1302 . While the master mask  1302  depicted in  FIG. 13A  is has a circular shape, and its pattern  1304  covers a rectangular area of the mask, it is noted that both the master mask  1302  and the master pattern  1304  can be a variety of different shapes and sizes in embodiments of the present invention, and the master pattern  1304  can cover all or part of the area of the master mask  1302 . Master pattern  1304  should correspond to the desired pattern for a large area substrate, and can vary depending on various application specific requirements. For example, the master pattern  1304  can include a uniform array of posts or uniform array of holes as used in many structured coating applications. It is noted that in structured coating embodiments of the present invention, an array of posts is preferred over an array of holes as experiments have shown that a post array master pattern leads to a lower visibility of seams at the boundaries of successive imprints. By way of example  FIGS. 13D and 13E  provide a micrograph of an array of posts formed in a photoresist by exposure to UV light through a pattern in a cylindrical mask and developing the exposed resist. 
         [0138]      FIG. 13B  depicts a master mask  1302  used to imprint a larger area substrate  1306 . Master mask  1302  can be used to repeatedly imprint a portion of the substrate  1306  until a desired area of the substrate is patterned. Each successive imprint with the master mask  1302  can overlap part of the previously imprinted portion  1308  of the substrate  1306 , and the pattern of the imprint  1308  that is left on the substrate  1306  corresponds to the mask pattern  1304 . 
         [0139]      FIG. 13C  depicts an individual imprint during a successively repeating imprint scheme according to embodiments of the present invention. In  FIG. 13C , it can be seen that a polymer precursor liquid  1310  spreads as the liquid is pressed between a master mask  1302  and a substrate  1306 . By way of example and not by way of limitation, the polymer precursor liquid  1310  may be a monomer, a polymer, a partially cross-linked polymer, or any mixture of thereof. An imprinting scheme as depicted in  FIGS. 13A-13C  according to embodiments of the present invention should preferably include a method of controlling the spread of the polymer precursor liquid in order to minimize the presence of air bubbles, fill the features of the master pattern, and prevent the liquid from flowing outside of the border of the mask pattern contained on the master mask and onto an open area of a previously cured imprint. There are a variety of methods that can be used to control the spread of the polymer precursor liquid during each imprint. In the example shown in  FIG. 13C , controlling the spread of polymer precursor liquid  1310  includes maintaining a continuous line of pressure along a line of contact  1312  between the master mask  1302  and the substrate  1306 . Mechanical pressure can be applied along the contact line  1312  to force the spread of polymer precursor liquid  1310  towards an open area of the substrate  1306  in the direction of pressure  1314  and maintain the liquid  1310  within the boundary of the master pattern  1304 . In some embodiments, maintaining a continuous line of pressure can be better facilitated by using a flexible substrate for substrate  1306 , thereby creating a more clearly defined line of contact  1312  between the master mask  1302  and the substrate  1306 . In other embodiments, maintaining a continuous line of pressure of can be facilitated by using a flexible mask for master mask  1302 . In still other embodiments, maintaining a continuous line of pressure can be facilitated by using a curved mask or curved substrate for mask  1302  or substrate  1306 , respectively. In still other embodiments, the spread of polymer precursor liquid  1310  can be controlled by other means. 
         [0140]    Turning to  FIGS. 14A-14G , a process flow of a method of patterning a substrate is depicted according to an embodiment of the present invention. In  FIGS. 14A-14G , master mask  1402  is used to pattern the substrate  1404 , and master mask  1402  should be smaller than substrate  1404 . More specifically, the area of the master pattern  1406  of the mask  1402  should be smaller than the area to be patterned on the substrate  1404 , and the master pattern  1406  should correspond to the desired pattern of the larger area substrate  1404 . Master mask  1402  is used to pattern the substrate  1404  by successively imprinting the substrate  1404  until it is fully patterned, or at least until a desired area of the substrate  1404  is patterned. 
         [0141]    In  FIG. 14A , a polymer precursor liquid  1408  is deposited onto a substrate  1404 , and the polymer precursor liquid  1408  corresponds to the patterned layer or structured coating of the large area substrate  1404 . It is noted that polymer precursor liquid  1408  can be deposited in a variety of ways. For example, in the embodiment shown in  FIGS. 14A-14G , polymer precursor liquid  1408  is deposited onto the substrate  1404  as discrete drops for each successive imprint. In other embodiments, polymer precursor liquid  1408  can be deposited onto the master mask  1402 . In still other embodiments, polymer precursor liquid  1408  can be deposited continuously through the patterning process as opposed to discrete drops before each imprint. It is noted that the material used for polymer precursor liquid  1408  can vary depending on various application specific requirements. The amount of polymer precursor liquid  1408  that is deposited can vary depending of various application specific requirements, including, for example, the desired thickness of the layer, the size of the desired imprint area, and the feature depth and pitch of the desired pattern to be formed. 
         [0142]    In  FIG. 14B , polymer precursor liquid  1408  is pressed between the master mask  1402  and the substrate  1404  in order to transfer the master pattern  1406  to polymer precursor liquid  1408 . Pressing the polymer precursor liquid as shown in  FIG. 14B  preferably should be done with care and using a method of controlling the spread of the polymer precursor liquid in order to minimize air bubbles, fill the features of the master pattern  1406 , and maintain the polymer precursor liquid  1408  within the area of the master pattern  1406  during the imprint process. Controlling the spread of the polymer precursor liquid can include, for example, maintaining a continuous line of pressure as depicted in  FIG. 13C  and described above. In  FIG. 14A-14G , pressing the polymer precursor liquid  1408  between the master mask  1402  and the substrate  1404  is depicted as pressing the master mask  1402  against the substrate  1404 , but it is noted that the present invention is not limited to such embodiments. In embodiments of the present invention, pressing the polymer precursor liquid between the master mask  1402  and the substrate  1404  can involve pressing the substrate  1404  against the master mask  1402 . In other embodiments, pressing the polymer precursor liquid  1408  between the master mask  1402  and the substrate  1404  can be done by still other means, such as by pressing both the master mask  1402  and the substrate  1404  against each other simultaneously. 
         [0143]    In  FIG. 14C , the patterned polymer precursor liquid is cured or polymerized using curing means  1410 , which can be a source of UV radiation, heat, or other equivalent means depending on the nature of the polymer precursor liquid, specifically, the mechanism by which the polymer precursor liquid can be cured or polymerized. After the polymer precursor liquid is cured or polymerized, master mask  1402  can be removed and a successive imprint can be formed. 
         [0144]    In  FIG. 14D , a successive imprint is formed that overlaps part of the previously imprinted and cured portion  1412  by again depositing liquid polymer precursor liquid  1408 . To minimize the visibility of the border between successive imprints, part of the polymer precursor liquid should be deposited onto part of the previously imprinted portion  1412  of the substrate  1404 , within the area of where the master pattern  1406  will overlap the previously imprinted portion, as depicted in  FIG. 14D . 
         [0145]    In  FIG. 14E , the polymer precursor liquid  1408  is again pressed between the master mask  1402  and the substrate  1404  to transfer the master pattern  1406  onto the polymer precursor liquid and imprint another portion of the substrate  1404 . Care should be taken to control the flow of the polymer precursor liquid  1408  and prevent it from flowing onto a portion of the previously cured portion  1412  of the substrate that is beyond the boundary of the master pattern  1406 . 
         [0146]    In  FIG. 14F , the polymer precursor liquid is again cured using curing means  1410 , after curing the master mask  1402  can be removed, leaving behind a larger patterned portion  1412  on the substrate  1404 , as shown in  FIG. 14G . This process can be successively repeated until the substrate  1404  is fully patterned, or until a desired area of the substrate  1404  is patterned. 
         [0147]    After each portion of the substrate is imprinted, the un-patterned area of the substrate  1404  may be cleaned as desired by wet cleaning or dry cleaning processes. By way of example, wet cleaning processes may include use of chemicals e.g., common organic solvents such as acetone, physical removal of the particles and/or plasma cleaning. The selective cleaning process of the un-patterned area may require the use of shadow mask (not shown) to prevent any damage of patterned area. To prevent any contaminations or damages of the patterned area, the patterned area may optionally be selectively treated with hydrophobic silane. In other words, the patterned area may be made hydrophobic and the un-patterend area may be made hydrophilic. By way of example, the cleaning process may include hydrophobic surface treatment (of both the patterned and un-patterned area) followed by plasma treatment of the un-patterned area and the region of the patterned area that will be overlapped during the next imprint. 
         [0148]    In an additional embodiment a checkered board type pattern of patterned and unpatented areas are generated on a substrate and treated with hydrophobic silane. Then the substrate is plasma treated using shadow mask so that only the unpattern surface of the substrate and the surface where the new imprint is to be overlapped are exposed to plasma. In the second step all the un-patterned area of the substrate is then imprinted. 
         [0149]    In  FIGS. 15A-15C , a variety of patterned substrates imprinted according to the methods described herein are depicted. It is noted that embodiments of the present invention include master mask and master patterns having a variety of different shapes and sizes, and successive imprints can be arranged in a variety of different arrays and arrangements. Likewise the larger substrate that is patterned with the master mask can be a variety of shapes, sizes, etc. 
         [0150]    The embodiments shown in  FIG. 15A-15C  depict two dimensional arrays and arrangements, although it is noted that the present invention is not limited to such embodiments. Embodiments of the present invention can include imprint schemes that involve two dimensional arrays of successive imprints, one-dimensional arrays of successive imprints, or other arrangements of successive imprints in the imprinting scheme. However, it is noted that two dimensional arrays and arrangements are preferred in some embodiments of the present invention as it can minimize the visibility of seams between successive imprints. 
         [0151]    In  FIG. 15A , a substrate  1502   a  patterned with a two-dimensional rectangular array of successive imprints  1504   a  is depicted. The pattern on the substrate  1502   a  can be virtually continuous and uniform at the macro-level as the visibility of seam lines  1506   a  at the borders between successive imprints is minimal. In various applications of the present invention, the presence of seam lines can have little to no effect on the desired functional properties of the patterned or structured substrate. 
         [0152]    In  FIG. 15B , substrate  1502   b  is depicted having a two-dimensional hexagonal array of successive imprints  1504   b  according to embodiments of the present invention. 
         [0153]    In  FIG. 15C , substrate  1502   c  is depicted having a randomized two-dimensional arrangement of successive imprints  1504   c  creating randomized seam lines  1506   c  between successive imprints. Randomizing the imprints can provide certain benefits in some applications of the present invention, and the visibility of the seams  1506   b  can be minimized on the macro level by providing a randomized pattern instead of a regular array. In  FIG. 15C , substrate  1502   c  depicted is fully patterned edge to edge, according to some embodiments of the present invention, and amount of surface area that can be pattern is limited only by the size of the substrate chosen. 
         [0154]    It is noted that increasing the amount of seam lines, up to a certain limit, can minimize the visibility of such seam lines while providing minimal or no detraction from desired properties created by the pattern or structure imprinted onto the substrate. For example, in an architectural glass implementation of an embodiment of the present invention, a nanostructured coating can be applied to provide antireflection properties on the glass using an imprinting scheme as described herein. Increasing the number of seam lines can minimize their visibility at the macro level while still providing the required anti-reflection properties provided by the nanostructure. This can be contrasted with known methods that attempt to minimize seam lines by patterning the entire large area with a single uniform layer at a very high cost. 
         [0155]    In embodiments of the present invention, substrates to be patterned can be a variety of shapes and sizes, but should generally be larger than the master mask used to successively imprint the substrate. In some embodiments, substrates to be patterned can have square shapes, rectangular shapes, or other shapes. In some embodiments, substrates can be flat, curved, or have other three-dimensional surfaces. In some embodiments, substrates can have dimensions of 150 mm×150 mm or greater. In some embodiments, substrates to be patterned can have dimensions of 400 mm×1000 min and larger. Embodiments of the present invention can also include substrates having smaller areas than those mentioned, although it is believed that embodiments of the present invention have particular applicability to embodiments involving larger area substrates, such as those having areas of 200 cm 2  or more. 
         [0156]    In embodiments of the present invention, master masks can be a variety of shapes and sizes, and can have patterns of a variety of shapes and sizes, but should generally be smaller than the substrate area to be patterned. In some embodiments, master masks can have dimensions of 10 mm to 50 mm and areas of 100 mm 2  to 2500 mm 2 . In other embodiments, the master masks can have dimensions and areas outside of those mentioned above, although it is noted that preferred embodiments include square masks having dimensions of 10 mm×10 mm to 50 mm×50 mm. In some embodiments, master masks can have circular shapes, rectangular shapes, or other shapes. In some embodiments, a master pattern can cover an entire surface of a master mask or part of a surface of a master mask. 
         [0157]    In embodiments of the present invention, desired patterns can include features of a variety of different sizes, shapes, and arrangements. In some embodiments, desired patterns can include micro-scale features, nano-scale features, or other scale features. In some embodiments, features can include features having dimensions in the range of 100 nm to 400 nm. In some embodiments, features can be shaped as holes, posts, or other shapes. In some embodiments, features can be arranged in a regular array or a randomized pattern. 
         [0158]    It is noted that the figures are primarily depicted with respect to flat substrates and patterning flat surfaces, but the present invention is not so limited. Embodiments of the present invention can be used to pattern curved surfaces or substrates having a variety of other shapes but successively imprinting such surfaces with a smaller area master mask as described herein. 
         [0159]    It is noted that embodiments of the present invention can be used to pattern very large area substrates with patterns having small feature dimensions on the micro-scale or nano-scale. More specifically, embodiments of the present invention can be used to provide nanostructured coatings on large surface areas having nano-scaled feature dimensions. More specifically, embodiments of the present invention can be used to provide nanostructured coatings have arrays of features, e.g., posts or holes, having a characteristic dimension (CD) of 1 nanometers (nm) to 1000 nm, a pitch of 1.1 times the CD to 10 times the CD, and a depth of 10 nm to 10000 nm. A preferred embodiment of the present invention includes a CD between 50 nm and 400 nm, a pitch of 2 times the CD, and a depth ranging from 100 nm to 1000 nm. The CD is generally a dimension of the features along a direction perpendicular to the depth. Examples of CD include a width or diameter for circular or nearly circular shaped features. 
         [0160]    In embodiments of the present invention, the master mask pattern can be created by a variety of methods. For example, the master mask can be patterned by electron beam lithography, photolithography, interference lithography, nanosphere lithography, nanoimprint lithography, self-assembly, anodic alumina oxidation, or other means. 
         [0161]    It is noted that substrates in embodiments of the present invention can be a variety of types of materials and types of substrates. For example, substrates can be made of plastic films, glass, semiconductors, metals, other smooth substrates, or other materials. 
         [0162]    It is noted that substrates patterned according to embodiments of the present invention can include a surfaces for a variety of different applications. For example, embodiments of the present invention can be used for solar panels, information displays, architectural glass, and a variety of other applications. For example, embodiments of the present invention can be used for nanostructured solar cells, light absorption enhancement layers, anti-reflective coatings, self-cleaning coatings, TCO for solar cells and displays, nanostructured thermoelectric cells, low-E glass, anti-icing coatings, anti-glare coatings, efficient display color filters, FPD wire grid polarizers, LED light extraction layers, nanopatterned magnetic media, nanopatterned water filtration media, nanoparticles for drug deliver, ultrasensitive sensors, nanoelectrodes for batteries, and other applications. It is also noted that patterned substrates according to embodiments of the present invention can be used as large masks that are themselves used to pattern other large surfaces such as those mentioned above. 
         [0163]    It is noted that uniform patterns are typically used in various structured coating applications. While using successive imprints as described herein may create non-uniformities at the borders between imprints, the entire area patterned can appear macroscopically continuous and desired properties imparted by the pattern will be unaffected or very minimally affected by the borders. 
         [0164]    It is also noted that while embodiments of the present invention have primarily been described with respect to two-dimensional arrays of imprints, the present invention is not limited to such embodiments. For example, embodiments of the present invention can include one dimensional arrays of imprints and other imprinting schemes that involve imprints that repeats in only one dimension. However, it is noted that two dimensional arrays and imprinting schemes that repeat in two dimensions are preferred as this minimizes this visibility of the borders between imprints. 
       IV. Patterning a Surface of a Casting Component  
       [0165]    Aspects of the disclosure of this SECTION IV include methods and apparatus for patterning a surface of a casting component, including various exposure and epitaxial techniques. Various other methods and apparatus are also included in this section. Patterning a casting surface in accordance with aspects of this section can be used conjunction with a casting process of a compliant layer for a rotatable mask, which can provide benefits that may include minimizing or eliminating any seams in the pattern of the rotatable mask. Various other advantages of this section will be apparent upon reading this section. 
         [0166]    It is further noted that this SECTION IV has applicability to and can readily be implemented in various aspects of the remaining SECTIONS I-III, V, and VI of this description, including but not limited to any such sections that may involve the use of patterned casting components. By way of example and not by way of limitation, various aspects of the disclosure of this SECTION IV can readily be applied to implementations of SECTION VI of this description, which involves the use of a patterned casting component for forming a multilayered rotatable mask. 
         [0167]    Aspects of the present disclosure describe a mold and methods for manufacturing molds that may be useful in the fabrication of lithography masks, for example, near-field optical lithography masks for “Rolling mask” lithography, or masks for nanoimprint lithography. In rolling mask lithography, a cylindrical mask is coated with a polymer, which is patterned with desired features in order to obtain a mask for phase-shift lithography or plasmonic printing. The features that are patterned into the polymer may be patterned through the use of the molds described in the present application. The molds may include patterned features that protrude from an interior surface of an optically transparent cylinder. The protruding features may range in size from about 1 nanometer to about 100 microns, preferably from about 10 nanometers to about 1 micron, more preferably from about 50 nanometers to about 500 nanometers. The mask can be used to print features ranging in size from about 1 nanometer to about 1000 nanometers, preferably about 10 nanometers to about 500 nanometers, more preferably about 50 nanometers to about 200 nanometer 
         [0168]    An aspect of the present disclosure describes a mold that may be made with a porous mask. A layer of structured porous material may be deposited or grown on an interior surface of an optically transparent cylinder. One example of grown porous material is a porous alumina fabricated using anodization of aluminum layer (Anodized Aluminum Oxide—AAO). The interior of the cylinder may then be coated with a radiation-sensitive material. The radiation-sensitive material will fill in the pores that are formed in the structured porous material. The radiation-sensitive material may then be developed by exposing the exterior of the cylinder with a light source. Exposure from the exterior allows the radiation-sensitive material that has filled the pores to be cured without curing the remaining resist. The uncured resist and the porous mask material may be removed, thereby forming a mold that has posts extruding from its interior surface. 
         [0169]    According to an additional aspect of the present disclosure, an epitaxial layer may be grown on the interior surface of the cylinder. Structured porous material may then be deposited or otherwise formed on the epitaxial layer. The epitaxial layer may then be grown using the pores in the porous layer as a guide. The epitaxial layer may be grown to a thickness greater than the structured porous layer, or the structured porous layer may be etched back to leave the epitaxial post behind. According to certain aspects of the present disclosure, the epitaxial material may be a semiconductor material. Each of the epitaxial posts may be configured to be a light emitting diode (LED). The LED posts may further be configured to be individually addressable such that radiation may be selectively produced by individual posts. 
         [0170]    According to an additional aspect of the present disclosure, the mold may be formed with a self-assembled monolayer of nanospheres. The monolayer may be formed over a layer of radiation-sensitive material that has been formed on the interior surface of a cylinder. The radiation-sensitive material may then be exposed by a light source located in the interior of the cylinder. The self-assembled monolayer masks portions of the radiation-sensitive material during exposure. The exposed regions may then be removed by a developer. The radiation-sensitive material that was shielded by the self-assembled monolayer may then be cured and in order to form posts that are made from a glass-like substance. 
         [0171]    According to an additional aspect of the present disclosure, a self-assembled monolayer of nanospheres formed may comprise quantum dots. The quantum dots may be formed over a layer of radiation-sensitive material that has been formed on the interior surface of a cylinder. The quantum dots may be used to expose the radiation-sensitive material directly below each dot. As such, there may be no need for an external light source. The developer may then remove the unexposed portions of the radiation-sensitive material. The exposed portions of the radiation-sensitive material may then be cured to form a glass-like substance. 
         [0172]    According to an additional aspect of the present disclosure, a self-assembled monolayer of nanospheres may be formed on the exterior surface of the cylinder and a radiation-sensitive material may be formed on the interior surface of the cylinder. A light source positioned outside of the cylinder may be used to produce the radiation that exposes the radiation-sensitive material. The nanospheres may mask portions of the radiation-sensitive material from the radiation. The exposed portions may be removed with a developer, thereby leaving behind posts. The posts may be cured to produce a glass-like material. 
         [0173]    According to an additional embodiment of the present invention the self-assembled monolayer may comprise quantum dots. The quantum dots may be formed on an exterior surface of a cylinder. The quantum dots may be used to expose portions of a radiation-sensitive material that has be formed on an interior surface of the cylinder. As such, there may be no need for an external light source. The developer may then remove the unexposed portions of the radiation-sensitive material. The exposed portions of the radiation-sensitive material may then be cured to form a glass-like substance. The radiation-sensitive material that has been formed on the interior surface of a cylinder. 
         [0174]    A “Rolling mask” near-field nanolithography system has been described in International Patent Application Publication Number WO2009094009, which has been incorporated herein by reference. One of the embodiments is shown in  FIG. 7 . The “rolling mask” consists of glass (e.g., fused silica) frame in the shape of hollow cylinder  711 , which contains a light source  712 . An elastomeric film  713  laminated on the outer surface of the cylinder  711  has a nanopattern  714  fabricated in accordance with the desired pattern. The rolling mask is brought into a contact with a substrate  715  coated with radiation-sensitive material  716 . 
         [0175]    A nanopattern  714  can be designed to implement phase-shift exposure, and in such case is fabricated as an array of nanogrooves, posts or columns, or may contain features of arbitrary shape. Alternatively, nanopattern can be fabricated as an array or pattern of nanometallic islands for plasmonic printing. The nanopattern on the rolling mask can have features ranging in size from about 1 nanometer to about 100 microns, preferably from about 10 nanometers to about 1 micron, more preferably from about 50 nanometers to about 500 nanometers. The rolling mask can be used to print features ranging in size from about 1 nanometer to about 1000 nanometers, preferably about 10 nanometers to about 500 nanometers, more preferably about 50 nanometers to about 200 nanometers. 
         [0176]    The nanopattern  714  on the cylinder  711  may be manufactured with the use of a master mold. Aspects of the present disclosure describe the master methods and methods for forming a mold that has features that will form a nanopattern  714  that has holes or depressions. In order to form holes or depressions in the rolling mask, the master mold may have protrusions, such as posts. 
         [0177]      FIG. 16  is an overhead view of a master mold  1600  according to an aspect of the present disclosure. The master mold  1600  is a hollow cylinder  1620  that has an exterior surface  1621  and an interior surface  1622 . The cylinder  1620  may be made from a material that is transparent to radiation that is in the visible and/or ultraviolet wavelengths. By way of example, and not by way of limitation, the cylinder may be a glass such as fused silica. The master mold  1600  has protrusions  1633  that extend outwards from the interior surface  1622 . 
         [0178]      FIGS. 17A-17G  are cross sectional views of the master mold  1600  as seen along the line  3 - 3  shown in  FIG. 16 . Each figure depicts a processing step used in the fabrication of the master mold  1600  according to aspects of the present disclosure. 
         [0179]      FIG. 17A  is a depiction of the master mold after a structured porous layer  1730  on an interior surface of the cylinder  1720 . By way of example, and not by way of limitation, the, cylinder  1720  may be made of a transparent material, such as fused silica. It is noted that fused silica is commonly referred to as “quartz” by those in the semiconductor fabrication industry. Although quartz is common parlance, “fused silica” is a better term. Technically, quartz is crystalline and fused silica is amorphous. The structured porous layer  1730  contains a high density of cylindrical pores  1729  that are aligned perpendicular to the surface on which the structured porous layer is disposed. The size and density of the pores  1729  may be in any range suitable for the desired features of the mask pattern, e.g., as discussed above with respect to  FIG. 16 . By way of Example and not by way of limitation, the nanostructured porous layer  1730  may be a layer of anodic aluminum oxide (AAO) that has been formed on an interior surface  1722  of the cylinder  1720 . AAO is a self-organized nanostructured material containing a high density of cylindrical pores that are aligned perpendicular to the surface on which the AAO layer is disposed. The AAO may be formed by depositing a layer of aluminum on the interior surface  1722  of a cylinder  1720  made of fused silica and then anodizing the aluminum layer. Alternatively, the cylinder  1720  may be made completely from aluminum, and then internal or external surfaces of such a cylinder could be anodized to form a porous surface. Anodizing the aluminum layer may be done by passing an electric current through an electrolyte (often an acid) with the aluminum layer acting as a positive electrode (anode). 
         [0180]    In alternative implementations, the nanostructured porous layer may be fabricated using a self-assembled monolayer or by direct writing techniques, such as laser ablation or ion beam lithography. 
         [0181]    As shown in  FIG. 17A , the pores  1729  may not penetrate through the entire depth of the layer  1730 . If the pores  1729  do not extend through the structured porous layer  1730  down to the interior surface  1722  of the cylinder, the material of the structured porous layer may be etched back with an etch process. If the etch process is isotropic, the original size of the pores  1729  must be made small enough to account for growth during the etching process. For example, if the final diameter of the pores is desired to be 300 nm, and the original diameter of the pores  1729  is 50 nm, then the isotropic etch must remove 125 nm of porous material in order to enlarge the diameter of the pores  1729  to 300 nm. Additionally, if the etch process is isotropic, only 125 nm of material may be removed from the bottom of the pore in order to extend the pore to the interior surface  1722  of the cylinder. If more material needs to be removed in order to reach the interior surface  1722 , then the diameter of the pores  1729  may become larger than desired.  FIG. 17B  depicts the enlarged pores  1729  that completely extend through the nanostructured porous layer  1730 . 
         [0182]    After the pores  1729  have been etched to the proper dimensions and depths, a radiation-sensitive material  1731  may be deposited over the nanostructured porous layer  1730  and the exposed portions of the interior surface  1722 , as shown in  FIG. 17C . By way of example, and not by way of limitation, the radiation-sensitive material  1731  may be deposited by dipping, spraying, rolling, or any combination thereof. By way of example, and not by way of limitation, the radiation-sensitive material  1731  may be a photoresist or a UV curable polymer. Examples of suitable photoresists include commercially available formulations such as TOK iP4300 or Shipley 1800 series from Dow Chemical Co. Examples of suitable UV-curable materials include UV polymerizable adhesives for polymers and glass. Additionally, the radiation-sensitive material  1731  contains silicon and other constituents that enable the material to be annealed after it has cured in order to produce a glass-like material. Other constituents that may be used to help form the glass-like material include Oxygen and Silicon. The radiation-sensitive material  1731  may be a solid film, or it may be a liquid layer as long as it does not flow excessively during exposure. 
         [0183]    Next,  FIG. 17D  shows the cured material  1732  in the pores  1729 . The radiation-sensitive material  1731  is cured by exposure to a radiation  1723  from a radiation source (not shown). By way of example, and not by way of limitation, the radiation  1723  may be produced by a radiation source that produces ultraviolet light or the radiation  1723  may be produced by a radiation source that produces light in the visible spectrum. The radiation source may be located outside of the cylinder and may emit radiation  1723  that passes through the wall of the cylinder  1720 . The illumination through the cylinder  1720  limits the exposure to the material  1731  deposited in the AAO pores  1729 . Additionally, the exposure cures the material  1731  to a depth of roughly twice the exposure wavelength. By way of example, when an ultraviolet wavelength is used for curing, then the cured material  1732  may have a thickness of approximately 600 nm. The curing sensitivity of the radiation-sensitive material  1731  must be sufficiently high to allow the radiation-sensitive material inside the pores  1729  to be cured before the material  1731  above the pores  1729  is cured. Also, the depth of the pores  1729  may be greater than the projected thickness of the cured material  1732  in order to prevent exposure of the radiation-sensitive material  1731  directly above the pores  1729 . 
         [0184]      FIG. 17E  shows the master mold  1700  after the excess radiation-sensitive material has been removed after the cured material  1732  has been formed. The remaining unexposed radiation-sensitive material  1721  may be removed with a developer or other solvent. Thereafter, as shown in  FIG. 17F , the cured material  1732  is annealed in order to form a glass-like material  1733 . Finally, once the annealing is completed, the AAO layer  1730  may be selectively etched away with a wet etching process.  FIG. 17G  depicts the final structure of the master mold  1700 . The glass-like material  1733  protrudes from the interior surface  1722  of the cylinder  1720 . 
         [0185]    According to an additional aspect of the present disclosure, the protrusions may be formed through an epitaxial growth process.  FIG. 18A  is an overhead view of a master mold  1800 . The master mold  1800  is a hollow cylinder  1820  that has an exterior surface  1821  and an interior surface  1822 . The cylinder  1820  may be made from a material that is transparent to radiation that is in the visible and/or ultraviolet wavelengths. By way of example, and not by way of limitation, the cylinder may be a glass such as fused silica. An epitaxial seed layer  1824  may be formed on the interior surface  1822 . By way of example, and not by way of limitation, the epitaxial seed layer  1824  may be a semiconductor material such as silicon or gallium arsenide (GaAs). The master mold  1800  has protrusions  1833  that extend outwards from the epitaxial seed layer  1824 . The protrusions may be the same material as the epitaxial seed layer  1824 .  FIGS. 18B-18D  are cross-sectional views of the master mold  1800  along the line  4 - 4 . 
         [0186]      FIG. 18B  is a depiction of a structured porous layer  1830  that is deposited over the epitaxial seed layer  1824 . As shown in  FIG. 18B , the pores  1829  might not penetrate through the entire depth of the structured porous layer  1830 . 
         [0187]    When the pores  1829  do not extend through the structured porous layer  1830  down to the epitaxial seed layer  1824 , then the structured porous layer material may be etched back with an etch process. If the etch process is isotropic, the original size of the pores  1829  must be made small enough to account for growth during the etching process. For example, if the final diameter of the pores is desired to be 300 nm, and the original diameter of the pores  1829  is 50 nm, then the isotropic etch must remove 125 nm of aluminum in order to enlarge the diameter of the pores  1829  to 300 nm. Additionally, if the etchant is an isotropic etchant, only 125 nm of material may be removed from the bottom of the pore in order to extend the pore to the epitaxial seed layer  1824 . If more material needs to be removed in order to reach the epitaxial seed layer  1824 , then the diameter of the pores  1829  may become larger than desired.  FIG. 18C  depicts the enlarged pores  1829  that completely extend through the structured porous layer  1830 . 
         [0188]    Once the pores  1829  have been completed, the protrusions  1833  may be formed with an epitaxial growth process, such as, but not limited to vapor-phase epitaxy (VPE). The growth of the protrusions  1833  is guided by the pores  1829  in the structured porous layer  1830 . The protrusions  1833  may be grown to a height that allows them to protrude beyond the structured porous layer  1830 . However, the protrusions  1833  may be shorter than the structured porous layer  1830 , if the structured porous layer will be subsequently etched back in order to expose the protrusions  1833 . 
         [0189]    According to aspects of the present disclosure, protrusion  1833  formed through epitaxial growth of a semiconductor material may further be configured to be LEDs. Each of the protrusions  1833  may be individually addressable such that each may be controlled to emit light as desired. This is beneficial for use as a master mold, because the molding process no longer requires an external light source. The protrusions  1833  may function as a physical mold, and may be used to cure the photomask that is being molded at the same time. Further, the ability to control individual protrusions allows for a single master mold to be utilized in order to form multiple different patterns by selecting which protrusions will also cure the material in the photomask. 
         [0190]    According to yet another additional aspect of the present disclosure, a self-assembled monolayer may be used as a mask to pattern the protrusions  1933  in a master mold  1900 .  FIGS. 19A-19C  are cross-sectional views of a master mold  1900  at different processing steps during the mold&#39;s fabrication.  FIG. 19A  depicts the formation of a self-assembled monolayer (SAM)  1940  formed over a radiation-sensitive material  1931  on the interior surface  1922  of the cylinder  1920 . By way of example, and not by way of limitation, the SAM  1940  may be formed from metal nanospheres, or quantum dots. By way of example, and not by way of limitation, the radiation-sensitive material  1931  may be photoresist or a UV curable polymer. Additionally, the radiation-sensitive material  1931  contains silicon and other constituents that enable the material to be annealed in order to produce a glass-like material. 
         [0191]    Next, at  FIG. 19B , the radiation-sensitive material  1931  is exposed with radiation  1923  from a radiation source (not shown). Plasmonic lithography may be utilized, e.g., if the SAM  1940  comprises metal nanospheres. The metal nanospheres may be used as plasmonic mask antennae. The portions of the radiation-sensitive material  1931  that are exposed to radiation may become soluble to a developer solvent used to develop the radiation-sensitive material. The portion of the radiation-sensitive material that is unexposed  1932  may remain insoluble to the developer solvent. It is noted that alternative aspects of the present disclosure include use of a reverse tone process in which portions of the radiation-sensitive material  1931  that are exposed to radiation become insoluble to a developer and portions of the radiation-sensitive material that are not so exposed remain soluble to the developer. Alternative aspects of the present disclosure where the SAM  1940  comprises quantum dots may not need an additional light source to expose the radiation-sensitive material  1931 . As shown in FIG.  19 B′ the quantum dots in the SAM  1940  may be activated in order to expose the radiation-sensitive material  1931 . When the exposure is made by the quantum dots, the radiation-sensitive material may be cured by the exposure. The non-exposed portions of the radiation-sensitive material  1931  may therefore be removed by the developer. Finally, in  FIG. 19C  the protrusions  1933  are annealed in order to convert the cured radiation-sensitive material  1932  into glass-like material. 
         [0192]    Alternative aspects of the present disclosure include implementations in which the mask itself is made with light emitting diodes (LEDs). Such a mask may be implemented, e.g., using a polymer mask with an array of holes smaller than features that are desired to be printed, with a corresponding layer of LEDs above it. A specific subset of the LEDs may be turned on to define the pattern to be printed. 
         [0193]    According to an additional aspect of the present disclosure, a SAM  2040  may be formed on the exterior surface  2021  of the cylinder  2020  as show in  FIG. 20A . The SAM  2040  may be substantially similar to the SAM  1940 . The formation of a SAM  2040  on the exterior surface allows for the light used for the exposure to originate from outside of the cylinder  2020  as shown in  FIG. 20B . In  FIG. 20B , the radiation-sensitive material  2031  may be exposed with radiation  2023  that is emitted by a radiation source (not shown) that is located outside of the cylinder  2020 . Alternatively, if the SAM  2040  comprises quantum dots, then the radiation source that produces the radiation  2023  may be omitted, and the quantum dots may be used to expose the radiation-sensitive material  2031  instead, as shown in FIG.  20 B′. Finally,  FIG. 20C  shows the removal of the non-exposed radiation-sensitive material, and the annealing of the protrusions  2033  to form the glass-like material. 
       V. Forming a Rotatable Mask Using a Rolled Laminate 
       [0194]    Aspects of the disclosure of this SECTION V include methods and apparatus for forming a rotatable mask using a rolled laminate. Various other methods and apparatus are also included in this section. Forming a rotatable mask in accordance with aspects of this section can be used to form a compliant layer for a rotatable mask, which can provide benefits that may include minimizing or eliminating any seams layer where the edges of the laminate meet. There may be various other advantages to implementations of this section. 
         [0195]    It is further noted that this SECTION V has applicability to and can readily be implemented in various aspects of the remaining SECTIONS I-IV and VI of this description, including but not limited to any such sections that may involve a compliant layer rolled onto the outer surface of a rotatable substrate. By way of example and not by way of limitation, various aspects of the disclosure of this SECTION V can readily be applied to implementations of SECTION I of this description, which involves the use of coaxial assemblies to form a cast a compliant layer. 
         [0196]    A process flow diagram depicting a method  2100  for fabricating a free standing polymer mask according to various aspects of the present disclosure is depicted in  FIGS. 21A-21G . Various steps in the process flow  FIGS. 21A-21G  may be performed in accordance with various aspects of the above description for forming a free standing polymer mask. 
         [0197]    The method  2100  may include first making a patterned master mold/mask  2112  (alternatively referred to herein as a first master mask or “submaster” mask because it may be a mask used to pattern to a main rotatable mask for a subsequent fabrication process), as depicted in  FIGS. 21A and 21B . The patterned submaster may be created by patterning a substrate  2105  to create the pattern  2110  on the submaster  2112 . Patterning the submaster mask may be accomplished in a variety of ways. In some implementations, patterning the substrate to create a submaster mask utilizes involves successively overlapping cured imprints on a substrate  2105  with a smaller mask to create a quasi-seamless pattern  2110  for the submaster mask, according to various aspects of the disclosure of SECTION III of this description. In yet further implementations, the submaster may be patterned using any of a variety of known techniques, such as, e.g., nanoimprint lithography, nanocontact printing, photolithography, etc. 
         [0198]    The method  2100  may further include casting an elastomeric material  2115  (alternatively referred to herein as a polymer precursor liquid or liquid polymer precursor), such as polydimethylsiloxane (PDMS), on a patterned area of the submaster mold  2112 , as depicted in  FIG. 21C . Casting the elastomeric material  2115  may include depositing a polymer precursor liquid on the submaster and curing the polymer precursor liquid to create a cured polymer. Accordingly, aspects of the pattern of the submaster  2112  may be transferred to the elastomeric material  2115  to form a patterned polymer mask upon curing. The elastomeric material  2115  may be cast in such a manner that a strip  2120  of the patterned submaster  2112  does not have elastomeric material  2115  cast thereon. In some implementations, this may be accomplished by removing or cutting off a strip of the cast material  2115  after it is cured. In yet further implementations, this may be accomplished by simply not casting the elastomeric material or not depositing the polymer precursor liquid on a portion of the patterned submaster. In yet further implementations, this may be accomplished by some combination of the above. The uncast strip portion  2120  of the patterned submaster  2112  may be at an end of the submaster to enable it to overlap an opposing end of the laminate upon being rolled inside of a casting component. 
         [0199]    Next, a strip  2125  may be removed from the submaster of the laminate created by the previous steps, as depicted in  FIG. 21D , in such a manner that the missing strip portion  2120  of the cured polymer  2115  and the missing strip portion  2125  of the patterned submaster  2112  are in staggered locations with respect to one another. The strip  2125  that is removed from the patterned submaster may be at an opposing end of the laminate with respect to the missing strip  2120  of the cured polymer, thereby enabling the laminate to be rolled with these strip portions overlapping one another. In some implementations, a strip  2125  of the patterned submaster  2112  may be removed before a strip  2120  of the cast elastomeric material is removed. 
         [0200]    As in  FIG. 21E , the laminate of the submaster  2112  and the cast polymer  2115  may then be rolled and placed in a casting cylinder  2130 , with the unpatterned surface of the substrate  2105  of the submaster  2112  in contact with the inner surface of the casting cylinder  2130 . Accordingly, the outer surface of the laminate may be adjacent to the inner surface of the casting cylinder  2130  when it is rolled. In some implementations, the casting cylinder  2130  into which the laminate is rolled is a sacrificial casting component and utilizes various aspects of the disclosure of SECTION II of this description. 
         [0201]    Rather than rolling the laminate inside of a sacrificial casting cylinder  2130  with the unpatterned surface of the substrate  2105  in contact with the inner surface of the casting cylinder  2130 , in some implementations the laminate is rolled around a sacrificial casting cylinder, with the unpatterned surface of the substrate of the submaster in contact with the outer surface of the sacrificial casting cylinder, according to various aspects of the disclosure of SECTION II of this description. 
         [0202]    A gap  2120  may be formed in the polymer mask  2115  along the length of the cylinder, which may correspond to the strip  2120  of removed/uncast elastomeric material  2115 . A patterned portion of the submaster mold  2112  under the polymer mask  2115  may be exposed from the gap  2120  and extend across the gap  2120 . The staggered locations of the removed/missing strip portions of the laminate enable it to be rolled in such a manner that the gap  2120  is exposed to a patterned portion of the submaster  2112 , but without another seam being formed at the boundary between opposing ends of the rolled laminate due to the overlapped portions. 
         [0203]    As in  FIG. 21F , the gap  2120  may then be filled with more liquid elastomeric material (i.e. more polymer precursor liquid) to fill in the gap  2120  in the cured polymer  2115 . As such, the pattern on the submaster mold  2112  may transferred to the added elastometric material upon curing to thereby fill in the seam and form a substantially seamless polymer mask pattern. In some implementations, the filling in the gap may utilize various aspects of the disclosure of SECTION I. For example, in some implementations coaxial cylinders may be assembled using an assembly apparatus that enables liquid polymer precursor to be poured into the gap. 
         [0204]    After curing, the casting cylinder  2130  can be removed from the laminate of the submaster mold  2112  and the polymer mask  2115  having the gap  2120  filled in. The polymer mask  2115  may also be separated from the submaster mold  2112 , yielding a free standing polymer mask having a substantially seamless pattern  2140  on its outer surface, such as depicted in  FIG. 21F . 
         [0205]    In some implementations, the cast elastomeric material is PDMS with a thickness in a range from about 1 mm to about 3 mm, to thereby produce a cylindrical mask having a compliant layer 1-3 mm thick. 
         [0206]    In some implementations, the submaster may have a PET film substrate, and the pattern may be formed thereon using a UV-cured polymer. 
         [0207]    Some implementations of the present disclosure can include a free standing polymer mask and a method for fabricating the same. 
         [0208]    In some implementations, the method includes first making a patterned master mold (a patterned master mold may alternatively be referred to herein as a master mask). Next, an elastomeric material, such as polydimethylsiloxane (PDMS), is cast on the patterned area of the master mold to form a patterned polymer mask upon curing (elastomeric material may be alternatively referred to herein as polymer, pre-polymer, polymer precursor, or polymer precursor liquid). The polymer mask is configured to have a missing portion at an end of the master mask mold, wherein a portion of the end of the polymer mask may be cutoff or the elastomeric material may not be cast on a strip at the end of the master mold. The laminate of the mask mold and the polymer mask is then rolled and placed in a casting cylinder in a way that the substrate to the master mold is in contact with the casting cylinder. A gap is formed in the polymer mask along the length of the cylinder, wherein the gap corresponds to the missing portion of the cured polymer mask, and the master mold under the polymer mask is exposed from the gap and extends across the gap. The gap is then filled with additional liquid elastomeric material. As such, the pattern on the master mold is transferred to the added elastometric material upon curing, thereby filling in a seam in the polymer mask pattern. After curing, the laminate of the master mold and the polymer mask can be removed from the casting cylinder and the polymer mask may be in turn separated from the master mold, yielding a free standing polymer mask. 
         [0209]      FIG. 22A  is an overhead view of a cylindrical master mold assembly  2230  that can be used to form a polymer mask according to various aspects of the present disclosure. The cylindrical master mold assembly  2230  includes a casting cylinder  2232 , a master mold  2234  and a patterned polymer mask  2236  with a gap  2237  along the length of the cylinder.  FIG. 22B  is a perspective view of a cylindrical master mold assembly shown in  FIG. 22A . 
         [0210]    The patterned mask  2236  may be patterned with a mask pattern in a variety of ways. In one example, the inner surface of the master mold may contain a mask pattern so that this pattern is transferred to the outer surface of the polymer mask. As another example, the polymer mask may be patterned after subsequent fabrication steps and removal of the casting cylinder by patterning the outer surface of the polymer using various lithography methods. As another example, the pattern may also be patterned by some combination above. 
         [0211]    Once the substrate of the master mold  2234  is patterned, an elastomeric material may be cast on the patterned area of the mold  2234 . In some implementations, the elastomeric material may be Polydimethylsiloxane (PDMS), such as Sylgard 184 of Dow Corning™, h-PDMS, soft-PDMS gel, etc. The elastomeric material may be deposited in accordance with any of a number of known methods. By way of example, and not by way of limitation, the elastomeric material may be deposited by dipping, ultrasonic spraying, microjet or inkjet type dispensing, and possibly dipping combined with spinning After the curing process, the polymer, such as PDMS, is cured to form a patterned polymer mask  2236  on the master mold  2234 . Curing the polymer may depend on the type of polymer being cured and other factors. For example, curing can be done thermally, with UV radiation, or other means. 
         [0212]    The laminate of the master mold  2234  and the polymer mask  2236  is rolled and coaxially inserted into a casting cylinder  2232  in a way that the substrate to the master mold  2234  is in contact with the casting cylinder  2232  (i.e. the outer surface of the laminate is adjacent to the inner surface of the casting cylinder). Since a portion of one end of the polymer mask  2236  is missing, a gap  2237  is formed in the polymer mask along the length of cylinder  2232 , and the underneath master mold is exposed from the gap and extends across the gap. A strip  2239  of the master mold  2234  (i.e. the patterned substrate) can also be removed from the laminate at a staggered location relative to the gap  2237  so that the laminate can be rolled inside of the cylinder  2232  without a seam. The missing strips  2237 ,  2239  of the laminate may be at opposite ends of the laminate to allow the laminate to be rolled with the ends of the laminate overlapping each other as depicted in  FIGS. 22A-22B . 
         [0213]    The casting cylinder  2232  should be able to be removed after the cylindrical master mold assembly of the present disclosure is formed. According to aspects of the present disclosure, the casting cylinder  2232  may be a thin walled cylinder that is formed from a material that is easily fractured. By way of example, and not by way of limitation, the material may be glass, sugar, or an aromatic hydrocarbon resin, such as Piccotex™ or an aromatic styrene hydrocarbon resin, such as Piccolastic™. Piccotex™ and Piccolastic™ are trademarks of Eastman Chemical Company of Kingsport, Tenn. By way of example, and not by way of limitation, the casting cylinder  2232  may be approximately 1 to 10 mm thick, or in any thickness range encompassed therein, e.g., 2 to 4 mm thick. As shown in  FIG. 22A , the polymer mask  2236  is not in contact with the casting cylinder  2232 , and therefore the nanopattern on the polymer mask is protected from damage during the removal. According to additional aspects of the present disclosure, the casting cylinder  2232  may be made from a material that is dissolved by a solvent that does not harm the polymer mask  2236 . By way of example, a suitable dissolvable material may be a sugar based material and the solvent may be water. Dissolving the casting cylinder  2232  instead of fracturing may provide additional protection to the nanopattern. 
         [0214]    According to yet additional aspects of the present disclosure, the casting cylinder  2232  may be a thin walled sealed cylinder made from malleable material such as plastic or aluminum. Instead of fracturing the casting cylinder  2232 , the sealed component may be removed by collapsing the component by evacuating the air from inside the cylinder. According to yet another aspect of the present disclosure, the casting component  2232  may be a pneumatic cylinder made of an elastic material. Examples of elastic materials that may be suitable for a pneumatic cylinder include, but are not limited to plastic, polyethylene, polytetrafluoroethylene (PTFE), which is sold under the name Teflon®, which is a registered trademark of E. I. du Pont de Nemours and Company of Wilmington, Del. During the molding process, the casting cylinder  2232  may be inflated to form a cylinder and once the polymer mask  2236  has cured, the casting cylinder  2232  may be deflated in order to be removed without damaging the polymer mask. In some implementations, such a pneumatic cylinder may be reusable or disposable depending, e.g., on whether it is relatively inexpensive to make and easy to clean. 
         [0215]    Next, the gap  2237  in the polymer mask  2236  along the length of the cylinder is filled with polymer, such as liquid PDMS. During the curing process, the pattern on the master mold  2234  is transferred to the added polymer. As such, a cylindrical master mold assembly  2230  of  FIGS. 22A-22B  may be formed. 
         [0216]    Curing the liquid polymer may involve applying UV radiation, heat or other means. As an example of applying radiation, the radiation source may be located co-axially within the master mold assembly  2230 . Alternatively, the radiation source may be located outside of the master mold assembly  2230  and the exposure may be made through the casting cylinder  2232  and the master mold  2234  when the casting cylinder  2232  and the master mold  2234  are transparent to the wavelengths of radiation required to cure the liquid polymer. 
         [0217]    The laminate of the master mold  2234  and the patterned polymer mask  2236  may be thereafter removed from the casting cylinder  2232 . Removing the casting cylinder may be performed in a variety of ways. By way of example, and not by way of limitation, the casting component  2232  may be removed by fracturing, dissolving, deflating, or collapsing. By way of example, and not by way of limitation, the casting cylinder can be cut using a saw, a laser, wet or drying etching, or other means. When cutting the casting cylinder, care should be taken not to damage the layer/mask underneath. If a laser is used to cut the casting cylinder, a special layer could be deposited on the inside surface of the casting cylinder to act as an etch stop layer, and this layer should reflective to the light that is used to cut the casting cylinder material. Cutting can be performed using one or more cut lines to make it easier to subsequently peel off the casting cylinder from the laminate. Once the casting cylinder is cut, it can be peeled off of the laminate mechanically. By way of example, and not by way of limitation the casting cylinder may be etched way chemically using etching chemicals that do not also etch away the master mold and the polymer mask within. The casting cylinder may also be removed by other means, and such other means of removal are within the scope of the present disclosure. In some implementations, the casting cylinder  2232  is a sacrificial casting component according to various aspects of SECTION II of this description. 
         [0218]    Next, the polymer mask  2236  may be separated from the master mold  2234 , such as, e.g., by peeling it off, resulting in a free standing PDMS mask having a thickness of 1-3 mm. 
         [0219]    Aspects of the present disclosure include a process  2300  that may use cylindrical master mold assemblies  2230  to form a free standing polymer mask. A flowchart depicting process  2300  that includes various aspects of the above disclosure is depicted in  FIG. 23 . Various aspects of process  2300  are also described with reference to mold assemblies  2230  of  FIGS. 22A-22B . First, at  2310 , pattern a master mold  2234 . The master mold may be patterned by successively imprinting it with a smaller master mask. At  2320 , form a patterned polymer mask by casting elastomeric materials or polymer on the master mold  2234  and curing the material/polymer. At  2330 , the laminate of the master mold  2234  and the patterned polymer mask  2236  is rolled and inserted coaxially into a casting cylinder  2232 . At  2340 , the gap in the patterned polymer mask  2236  is filled with a liquid polymer. At  2342 , the liquid polymer is cured during the curing process, and thereby transferring the patterns on the master mold along the gap to the cured polymer. At  2350 , the casting cylinder  2232  and the master mold  2234  are removed to form a free standing polymer mask. 
       VI. Forming a Multilayer Mask Using Casting Components 
       [0220]    Aspects of the disclosure of this SECTION VI include methods and apparatus for forming a multilayered mask using coaxial casting components in multiple stages. Various other methods and apparatus are also included in this section. Forming a multilayered mask in accordance with aspects of this section can be used to form a compliant layer for a rotatable mask, which can provide benefits that may include extra cushioning or compliance in the rotatable mask. There may be various other advantages to implementations of this section. 
         [0221]    It is further noted that this SECTION VI has applicability to and can readily be implemented in various aspects of the remaining SECTIONS I-V of this description, including but not limited to any such sections that may involve forming a patterned compliant layer of rotatable mask. By way of example and not by way of limitation, various aspects of the disclosure of this SECTION VI can readily be applied to implementations of SECTION IV of this description, which involves the patterning of a surface of a casting component. 
         [0222]    Aspects of the present disclosure include a multilayer polymer mask and a method of fabricating the same. The method of making the multilayer polymer mask may involve two stages. 
         [0223]      FIG. 24A  depicts an overhead view of a cylindrical master mold assembly in a first stage to form a multilayer polymer mask according to some implementations of the present disclosure. A cylindrical master mold  2410  is formed with features/patterns on the inner surface of the cylinder. A first casting cylinder  2420  is next inserted coaxially into the master mold  2410  to create a cylindrical region between the casting cylinder  2420  and the master mold  2410 . Next, the cylindrical region between the casting cylinder  2420  and the master mold  2410  is filled with a liquid polymer to form a patterned polymer mask  2430  upon curing. Thereafter, the first casting cylinder  2420  is removed and the polymer mask  2430  is peeled off from the interior of the cylindrical master mold  2410 . As such, a free standing polymer mask may be formed. In some implementations, a free standing polymer mask  2430  is alternatively formed using aspects of the SECTION V of this description, wherein a laminate is rolled into a cylinder and a gap in the laminate is filled in to produce a substantially seamless pattern on a cylindrical mask. In some implementations, a free standing polymer mask  2430  is formed using various aspects of SECTION II of this description, including implementations wherein the first casting cylinder  2420  is a sacrificial component and removing the first casting cylinder is performed in accordance with aspects of that section. In some implementations, the cylindrical master mask is formed by patterning the inner surface of the cylinder in accordance with various aspects of SECTION IV of this description. 
         [0224]      FIG. 24B  depicts an overhead view of a cylindrical master mold assembly in a second stage to form a multilayer polymer mask according to some implementations of the present disclosure. The polymer mask  2430  is covered with a protective film  2432  and inserted into a second casting cylinder  2440 , with the protective film against the interior surface of the casting cylinder  2440 . A fused silica mask cylinder  2450  is in turn inserted coaxially into the second casting cylinder  2440  and the film-covered polymer mask  2430 , and thereby creating a cylindrical region between the fused silica mask cylinder and the inner diameter of the polymer mask  2430 . This gap is then filled with liquid polymer to form cushion layer  2460  upon curing. Then the second casting cylinder  2440  and the protection film  2432  are removed. As a result, a multilayer polymer mask is formed. In some implementations, the second casting cylinder  2440  is also a sacrificial casting component in accordance with various aspects of SECTION II of this description, thereby allowing yet additional layers to be formed by repeating a process similar to the second stage accordingly. 
         [0225]      FIG. 2  depicts an assembly  200  that may be used to form a patterned polymer mask according to various aspects of the present disclosure. In some implementations, aspects of this disclosure may be used in the first stage mentioned above for forming a multilayer polymer mask. The assembly  200  includes a master mold  204  and a first casting cylinder  202  surrounded by the master mold  204 . The first casting cylinder  202  may correspond to the first casting cylinder  2420  of  FIG. 24A . The first casting cylinder  202  may also correspond to a sacrificial casting cylinder, such as sacrificial casting component  830  of  FIG. 8A . The master mold  204  and the casting cylinder  202  are coaxially assembled in a way that their axes  206  are aligned, thereby creating a cylindrical region  208  with uniform thickness around the master mold  204  which can define the shape of a polymer layer of the cylindrical mask. The outer diameter of the casting cylinder  202  is larger than the outer diameter of the final fused silica mask cylinder  2450  of the multilayer mask. Polymer precursor can be inserted in the space  208  between the master mold  204  and the casting cylinders  202 . The master mold  204  and the casting cylinder  202  can be held in place using an assembly apparatus (not pictured) that aligns their axes and permits a liquid polymer to be inserted into cylindrical region  208  of the assembly, such as by pouring it through openings or holes in the apparatus. Inserting the polymer precursor may be done, for example, by pouring a liquid or semi-liquid polymer precursor material in through the top of the assembly apparatus into the space between the mold  204  and the cylinder  202 . The polymer precursor may be in the form of a monomer, a polymer, a partially cross-linked polymer, or any mixture of thereof in a liquid or semi-liquid form. The polymer precursor can be cured to form the inner polymer layer of the cylindrical mask. Curing the polymer precursor may involve applying UV radiation or heat. During the curing process, the patterns on the inner surface of the master mold  204  may be transferred to the outer surface of the polymer. 
         [0226]    In the above mentioned first stage, patterning the inner surface of the master mold  2410  may be done using a variety of techniques. For example, the inner surface of the master mold may be patterned by successively imprinting it with a smaller master mask as described above in SECTION III of this description. As another example, a cylinder surface may be patterned using any of a variety of known techniques, including nanoimprint lithography, nanocontact printing, photolithography, etc. 
         [0227]    In the above mentioned first stage, the cast cylinder  2420  may be removed. The patterned polymer mask may be in turn peeled off from the master mold  2410  to form a free standing polymer mask in a thickness of about 1 to 3 mm. It is noted that removing the casting cylinder  2420  and the polymer mask  2430  can be performed in a variety of ways, including various ways as mentioned above in the present disclosure. 
         [0228]    In the above mentioned first stage, the polymer mask  2430  may be covered with a protective layer  2432 . In one example, the protective layer may be a film of polyethylene terephthalate (PET). The protective layer  2432  may be deposited on the polymer mask  2430 , and the film-covered polymer mask  2430  is then inserted coaxially into a second casting cylinder  2440  with the protective film  2432  against the inner surface of the second casting cylinder  2440 . The inner diameter of the second casting cylinder  2440  is equivalent to the inner diameter of the master mold  2410  utilized in the first stage mentioned above. The second casting cylinder  2440  may be a thin walled cylinder that is formed from a material that is easily fractured, such as discussed in associated with the casting cylinder  2232  of  FIG. 22A  and  FIG. 22B  or as described with reference to a sacrificial casting component in SECTION II. In some implementations, the protective film enables the second casting cylinder  2440  to be made of separate parts. 
         [0229]    In the above mentioned second stage, a substrate for the rotatable mask, such as a fused silica mask cylinder  2450  is inserted coaxially into the second casting cylinder  2440  and the film-covered polymer mask  2430 . The fused silica mask cylinder  2450  may be a hollow cylinder with an outer diameter that is smaller than the inner diameter of the polymer mask  2430 , thereby creating a cylindrical region of uniform thickness around the mask cylinder  2450  between the outer surface of the mask cylinder and the inner surface of the polymer mask  2430 . 
         [0230]    In the above mentioned second stage, the cylindrical region created between the polymer mask  2430  and the fused silica mask cylinder  2450  may be filled with a liquid polymer and thereby forming a cushion layer  2460  at the inner surface of the polymer mask upon curing. The liquid polymer may be inserted into the cylindrical region in a variety of ways, including various ways mentioned above in the present disclosure. 
         [0231]    In the above mentioned second stage, the second casting cylinder  2440  may be removed. Also, the protective film  2432  may be separated from the polymer mask  2430  having cured cushion layer  2460 . As a result, a multilayer polymer mask including the polymer mask  2430  and the cushion layer  2460  may be formed. Removing the cast cylinder and protective film may be performed in a variety of ways, such as various ways mentioned elsewhere in this disclosure. 
         [0232]    Aspects of the present disclosure include a process  2500  that may use cylindrical master mold assemblies  2400  and  2401  to form a multilayer polymer mask. A flowchart depicting process  2500  is depicted in  FIG. 25  that may include various aspects of the above disclosure. Various aspects of process  2500  are also described with reference to  FIGS. 24A-24B . At  2510 , the method  2500  may include patterning a master mold/mask  2410  so that the inner surface of the master mold includes a pattern. At  2520 , coaxially assemble the patterned master mold  2410  and the first casting cylinder  2420  so that the axis of both the mold and the cylinder are the same. The casting cylinder  2420  may be a hollow cylinder with an outer diameter that is smaller than an inner diameter of the master mold  2410 , such that a space is left between the mold and the cylinder. At  2530 , space between the mold  2410  and the casting cylinder  2420  is filled with a liquid polymer precursor, resulting in a patterned polymer mask upon curing. At  2540 , the first casting cylinder  2420  is removed and the patterned polymer mask  2430  is peeled off from the master mold  2410 , thereby forming a free standing polymer mask. In some implementations, the casting cylinder  2420  may be a sacrificial casting component in accordance with various aspects of SECTION II of this description, so that the master mask  2410  can be preserved for future use, whereby the casting cylinder  2420  is removed by fracturing, dissolving, collapsing, or otherwise removing it in a manner that enables the cured polymer to be subsequently removed at  2540  from the master mask  2410  after removal of the casting cylinder  2420 . At  2550 , the polymer mask  2430  is covered with a protective layer or film  2432 . At  2560 , the film-covered polymer mask  2430  is coaxially inserted into a second casting cylinder  2440 . At  2570 , a fused silica mask cylinder  2450  is coaxially inserted into the second casting cylinder  2440  and the film-covered mask  2430 . The fused silica mask cylinder  2450  may be a hollow cylinder with an outer diameter that is smaller than an inner diameter of the polymer mask  2430 , thereby leaving a space left between the cylinder and the mask. At  2580 , the space between the fused silica mask cylinder  2450  and the polymer mask  2430  is filled with additional liquid polymer precursor, thereby forming a cushion layer  2460  upon curing. At  2590 , the casting cylinder  2440  and the protective film may be removed to form a multilayer polymer mask. In some implementations, the casting cylinder  2440  may also be a sacrificial casting component. 
         [0233]    Forming a multilayer mask in accordance with various aspects of the present disclosure may provide several advantages. For example, a casting cylinder, e.g. first casting cylinder  2420  mentioned above used to form an outer layer, may be made with separable components having seams, thereby potentially simplifying the process and reducing costs. Polymer used to form a layer in contact with an unpatterned surface, e.g. polymer  2460  used to form inner layer adjacent to the inner surface of outer layer  2430  mentioned above, may also fill in seams caused by using such separate components. Likewise, in some implementations of the present disclosure, a protective film provided over a patterned surface enables a casting tube, e.g. second casting cylinder  2440  mentioned above, to be made of separable components, whereby the protective film may prevent a seam of separable components from transferring to patterned features covered by the film. Furthermore, in some implementations, a mold or mask used in the casting process, such as, e.g., the cylindrical master mold  2410 , does not have to be broken to remove the molded material, thereby preserving it for future use and preventing damage to the molded material by the breaking process. 
         [0234]    Those of ordinary skill in the art will readily appreciate that various aspects of the present disclosure may be combined with various other aspects without departing from the scope of the present disclosure. By way of example and not by way of limitation, it will readily be appreciated by those of ordinary skill in the art that various aspects of the disclosures of SECTIONS I-VI above can be combined into numerous different permutations in fabrication methods and rotatable masks involved in implementing the present disclosure. 
         [0235]    It is noted that various aspects of the present disclosure have been described with reference to multilayered masks generally having two compliant layers. It is noted that aspects of the present disclosure can readily be implemented to form multilayered masks having more than two compliant layers. 
         [0236]    It is further noted that various aspects of the present disclosure have been described with reference to rotatable masks having cylindrical shapes. It is noted that aspects of the present disclosure can readily be implemented in rotatable masks having other shapes, such as, e.g., shapes containing frusto-conical elements or other axially symmetric shapes. 
         [0237]    It is further noted that various aspects of the present disclosure may inverted, switched around, reordered, etc., in order to produce seamless or quasi seamless feature patterns different desired surfaces, such as, e.g., inner or outer surfaces of casting cylinders, final masking cylinders, layers, or other elements used in fabrication processes. 
         [0238]    More generally it is important to note that while the above is a complete description of the preferred embodiments of the present invention, it is possible to use various alternatives, modifications and equivalents. Therefore, the scope of the present invention should be determined not with reference to the above description but should, instead, be determined with reference to the appended claims, along with their full scope of equivalents. Any feature described herein, whether preferred or not, may be combined with any other feature described herein, whether preferred or not. 
         [0239]    In the claims that follow, the indefinite article “a”, or “an” when used in claims containing an open-ended transitional phrase, such as “comprising,” refers to a quantity of one or more of the item following the article, except where expressly stated otherwise. Furthermore, the later use of the word “said” or “the” to refer back to the same claim term does not change this meaning, but simply re-invokes that non-singular meaning. The appended claims are not to be interpreted as including means-plus-function limitations or step-plus-function limitations, unless such a limitation is explicitly recited in a given claim using the phrase “means for” or “step for.”
A cylindrical mask may be fabricated using a hollow casting cylinder and a mask cylinder. The casting cylinder has an inner diameter that is larger than the outer diameter of the mask cylinder. The casting and mask cylinders are coaxially assembled and a liquid polymer inserted in a space surrounding the mask cylinder between the inner surface of the casting cylinder and the outer surface of the mask cylinder. After curing the liquid polymer, the casting cylinder is removed. A surface of the cured polymer can be patterned. It is emphasized that this abstract is provided to comply with the rules requiring an abstract that will allow a searcher or other reader to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims.