Abstract:
The present invention provides a method of forming a desired pattern in a layer positioned on a substrate with a mold, the method including, inter alia, contacting the layer with the mold forming a shape therein having a plurality of features extending in a first direction; and altering dimensions of the shape of the layer in a second direction, orthogonal to the first direction, to eliminate a subset of the plurality of features having a dimension less that a predetermined magnitude while obtaining the desired pattern in the layer.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     The present application claims priority to U.S. Provisional Application No. 60/632,104, filed on Dec. 1, 2004, entitled “Eliminating Printabilty of Sub-Resolution Defects in Imprint Lithography,” listing Sidlgata V. Sreenivasan as an inventor, the entirety of which is incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     The field of the invention relates generally to nano-fabrication of structures. More particularly, the present invention is directed to a technique to reduce defect replication in patterns formed during nano-scale fabrication. 
     Nano-fabrication involves the fabrication of very small structures, e.g., having features on the order of nano-meters or smaller. One area in which nano-fabrication has had a sizeable impact is in the processing of integrated circuits. As the semiconductor processing industry continues to strive for larger production yields while increasing the circuits per unit area formed on a substrate, nano-fabrication becomes increasingly important. Nano-fabrication provides greater process control while allowing increased reduction of the minimum feature dimension of the structures formed. Other areas of development in which nano-fabrication has been employed include biotechnology, optical technology, mechanical systems and the like. 
     An exemplary nano-fabrication technique is commonly referred to as imprint lithography. Exemplary imprint lithography processes are described in detail in numerous publications, such as United States patent application publication 2004/0065976 filed as U.S. patent application Ser. No. 10/264,960, entitled, “Method and a Mold to Arrange Features on a Substrate to Replicate Features having Minimal Dimensional Variability”; United States patent application publication 2004/0065252 filed as U.S. patent application Ser. No. 10/264,926, entitled “Method of Forming a Layer on a Substrate to Facilitate Fabrication of Metrology Standards”; and U.S. Pat. No. 6,936,194, entitled “Functional Patterning Material for Imprint Lithography Processes,” all of which are assigned to the assignee of the present invention. 
     The fundamental imprint lithography technique disclosed in each of the aforementioned United States patent application publications and United States patent includes formation of a relief pattern in a polymerizable layer and transferring a pattern corresponding to the relief pattern into an underlying substrate. The substrate may be positioned upon a motion stage to obtain a desired position to facilitate patterning thereof. To that end, a template is employed spaced-apart from the substrate with a formable liquid present between the template and the substrate. The liquid is solidified to form a solidified layer that has a pattern recorded therein that is conforming to a shape of the surface of the template in contact with the liquid. The template is then separated from the solidified layer such that the template and the substrate are spaced-apart. The substrate and the solidified layer are then subjected to processes to transfer, into the substrate, a relief image that corresponds to the pattern in the solidified layer. 
     To that end, imprint lithography may have unlimited resolution in pattern replication. However, this may result in difficulties related to defect sensitive applications such as microelectronic devices. The primary advantage of all “imaging” lithography solutions such as photolithography, EUV lithography, e-beam, etc. is that the machine system can be “de-tuned” to set a desired resolution limit. For example, in optical/EUV lithography, the resolution of the process is defined by R=(k 1 ×λ)/NA, where k 1  is a scaling factor that is less than 1 and is a function of mask complexity and resist dose settings; λ is the wavelength of light; and NA is the numerical aperture of the optical system. For EUV lithography, λ=˜13.2 nm. To that end, to print devices using EUV lithography with a desired resolution (d R ) of 40 nm (with k 1 =0.8 based on acceptable mask and process complexity), NA needs to equal ˜0.264. As a result, any features that were placed on the mask that may result in features less than the desired resolution (40 nm) on the wafer may be inherently “filtered out”. This sets the threshold on what should be detectable as defects on the mask using a mask inspection tool to avoid the printing of defects that are less than d R =40 nm. 
     To that end, it may be desired to provide an improved method of patterning substrates substantially absent of defects employing imprint lithography. 
     SUMMARY OF THE INVENTION 
     The present invention provides a method of forming a desired pattern in a layer positioned on a substrate with a mold, the method including, inter alia, contacting the layer with the mold forming a shape therein having a plurality of features extending in a first direction; and altering dimensions of the shape of the layer in a second direction, orthogonal to the first direction, to eliminate a subset of the plurality of features having a dimension less that a predetermined magnitude while obtaining the desired pattern in the layer. These embodiments and others are described more fully below. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a simplified plan view of an imprint lithography system having a mold spaced-apart from a multi-layered structure; 
         FIG. 2  is a simplified side view of the multi-layered structure shown in  FIG. 1 , having a pattern thereon comprising recessed and raised defects; 
         FIG. 3  is a simplified side view of the mold, having protruding and indention defects therein, after contact with the multi-layered structure shown in  FIG. 1 , forming a plurality of features therein; 
         FIG. 4  is a simplified side view of the multi-layered structure shown in  FIG. 3 , after exposure to a trim etch to eliminate features associated with the indention defect of the mold; 
         FIG. 5  is a simplified side view of the multi-layered structure shown in  FIG. 4 , having a conformal layer positioned thereon; 
         FIG. 6  is simplified side view of the multi-layered structure shown in  FIG. 5 , having a crown surface formed thereon; 
         FIG. 7  is a simplified side view of the multi-layered structure shown in  FIG. 6 , after subjecting the crown surface to an etch process to expose regions of the substrate; 
         FIG. 8  is a simplified side view of the multi-layered structure shown in  FIG. 7 , after exposure to a blanket etch, with features associated with the indention defect of the mold removed from the multi-layered structure; 
         FIG. 9  is a simplified side view of the multi-layered structure shown in  FIG. 3 , having a conformal layer positioned thereon; 
         FIG. 10  is simplified side view of the multi-layered structure shown in  FIG. 9 , having a crown surface formed thereon; 
         FIG. 11  is a simplified side view of the multi-layered structure shown in  FIG. 10  after subjecting the crown surface to an etch process to expose regions of the substrate; 
         FIG. 12  is a simplified side view of the multi-layered structure shown in  FIG. 11 , after exposure to a trim etch to eliminate features associated with the protruding defect of the mold; 
         FIG. 13  is a simplified side view of the multi-layered structure shown in  FIG. 12 , after exposure to a blanket etch; 
         FIG. 14  is a simplified side view of the mold having protruding and indention defects therein, after contact with the multi-layered structure shown in  FIG. 1 , forming a plurality of features therein; 
         FIG. 15  is a simplified side view of the multi-layered structure shown in  FIG. 14 , after exposure to a trim etch to eliminate features associated with the indentation defect of the mold; 
         FIG. 16  is a simplified side view of the multi-layered structure shown in  FIG. 15 , having a conformal layer positioned thereon; 
         FIG. 17  is a simplified side view of the multi-layered structure shown in  FIG. 16 , having a crown surface formed thereon; 
         FIG. 18  is a simplified side view of the multi-layered structure shown in  FIG. 17 , after subjecting the crown surface to an etch process to expose regions of the substrate; 
         FIG. 19  is a simplified side view of the multi-layered structure shown in  FIG. 18 , after exposure to a trim etch to eliminate features associated with the protruding defect of the mold; and 
         FIG. 20  is a simplified side view of the multi-layered structure shown in  FIG. 19 , after exposure to a blanket etch. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Referring to  FIG. 1 , a system  10  to form a relief pattern on a multi-layered structure  12  includes a stage  14  upon which multi-layered structure  12  is supported and a template  16 , having a mold  18  with a patterning surface  20  thereon. In a further embodiment, multi-layered structure  12  may be coupled to a chuck (not shown), the chuck (not shown) being any chuck including, but not limited to, vacuum and electromagnetic. 
     Multi-layered structure  12  may comprise a substrate  22 , a transfer layer  24 , and a polymeric material  26 , with transfer layer  24  being positioned between polymeric material  26  and substrate  22 . Transfer layer  24  may comprise a low-k silicon containing dielectric and may be formed using any known techniques, dependent upon the materials and the application desired, including but not limited to drop dispense, spin-coating, dip coating, chemical vapor deposition (CVD), physical vapor deposition (PVD), and the like. In a further embodiment, multi-layered structure  12  may comprise an underlying organic layer (not shown) positioned between transfer layer  24  and substrate  22 . 
     Polymeric material  26  may be an anti-reflective coating (BARC) layer, such as DUV30J-6 available from Brewer Science, Inc. of Rolla, Mo. Additionally, polymeric material  26  may be a silicon-containing low-k layer, or a BCB layer, for example. In an alternative embodiment, a composition for polymeric material  26  may be silicon-free and consists of the following: 
     COMPOSITION 1 
     isobornyl acrylate 
     n-hexyl acrylate 
     ethylene glycol diacrylate 
     2-hydroxy-2-methyl-1-phenyl-propan-1-one 
     In COMPOSITION 1, isobornyl acrylate comprises approximately 55% of the composition, n-hexyl acrylate comprises approximately 27%, ethylene glycol diacrylate comprises approximately 15% and the initiator 2-hydroxy-2-methyl-1-phenyl-propan-1-one comprises approximately 3%. The initiator is sold under the trade name DAROCUR® 1173 by CIBA® of Tarrytown, N.Y. The above-identified composition also includes stabilizers that are well known in the chemical art to increase the operational life of the composition. 
     Template  16  and/or mold  18  may be formed from such materials including but not limited to, fused-silica, quartz, silicon, organic polymers, siloxane polymers, borosilicate glass, fluorocarbon polymers, metal, and hardened sapphire. As shown, patterning surface  20  comprises features defined by a plurality of spaced-apart recesses  28  and protrusions  30 . Further, patterning surface  20  is shown comprising a protruding defect  31   a  and an indention defect  31   b , with protruding defect  31   a  and indention defect  31   b  having a dimension less than a desired resolution, described further below. In a further embodiment, patterning surface  20  may be substantially smooth and/or planar. Patterning surface  20  may define an original pattern that forms the basis of a pattern to be formed on multi-layered structure  12 . 
     Template  16  may be coupled to an imprint head  32  to facilitate movement of template  16 , and therefore, mold  18 . In a further embodiment, template  16  may be coupled to a template chuck (not shown), the template chuck (not shown) being any chuck including, but not limited to, vacuum and electromagnetic. A fluid dispense system  34  is coupled to be selectively placed in fluid communication with multi-layered structure  12  so as to deposit polymeric material  26  thereon. It should be understood that polymeric material  26  may be deposited using any known technique, e.g., drop dispense, spin-coating, dip coating, chemical vapor deposition (CVD), physical vapor deposition (PVD), and the like. 
     A source  36  of energy  38  is coupled to direct energy  38  along a path  40 . Imprint head  32  and stage  14  are configured to arrange mold  18  and multi-layered structure  12 , respectively, to be in superimposition and disposed in path  40 . Either imprint head  32 , stage  14 , or both vary a distance between mold  18  and multi-layered structure  12  to define a desired volume therebetween that is filled by polymeric material  26 . 
     Typically, polymeric material  26  is disposed upon multi-layered structure  12  before the desired volume is defined between mold  18  and multi-layered structure  12 . However, polymeric material  26  may fill the volume after the desired volume has been obtained. After the desired volume is filled with polymeric material  26 , source  36  produces energy  38 , e.g., broadband ultraviolet radiation that causes polymeric material  26  to solidify and/or cross-link conforming to the shape of a surface  42  of multi-layered structure  12  and patterning surface  20 . Control of this process is regulated by a processor  44  that is in data communication with stage  14 , imprint head  32 , fluid dispense system  34 , source  36 , operating on a computer readable program stored in a memory  46 . 
     To that end, as mentioned above, either imprint head  32 , stage  14 , or both vary a distance between mold  18  and multi-layered structure  12  to define a desired volume therebetween that is filled by polymeric material  26 . As a result, a pattern may be recorded in polymeric material  26  that conforms to a shape of patterning surface  20 . However, it may be desired to pattern polymeric material  26  substantially absent of any features having a dimension less than a desired resolution (d R ). Features having a dimension less than a desired resolution may result in, inter alia, undesirable patterning of subsequent layers positioned on multi-layered structure  12 , undesired functionality in devices formed from multi-layered structure  12 , and misalignment between multi-layered structure  12  and mold  18 . 
     Referring to  FIG. 2 , multi-layered structure  12  is shown after being subjected to processing conditions to form a pattern therein, and more specifically, after contact with mold  18 , shown in  FIG. 1 , defining a multi-layered structure  112  comprising a plurality of protrusions  48  and recessions  50 . As mentioned above, mold  18 , shown in  FIG. 1 , may comprise a protruding defect  31   a  and an indention defect  31   b . As a result, upon contact between multi-layered structure  12  and mold  18 , both shown in  FIG. 1 , polymeric material  26  may conform to protruding defect  31   a  and indention defect  31   b  to form a recessed defect  52  and a raised defect  54 , respectively, in polymeric material  26 , with recessed defect  52  and raised defect  54  having a dimension less than the desired resolution, which is undesirable. To that end, it may be desired to form multi-layered structure  112  substantially absent of recessed defect  52  and raised defect  54 . To that end, a method of minimize, if not prevent, patterning of features having a dimension less than a desired resolution in multi-layered structure  12  is described below. 
     Referring to  FIG. 3 , in a first embodiment, to minimize, if not prevent, patterning of recessed defect  52 , shown in  FIG. 2 , within multi-layered structure  12  patterning surface  20  of mold  18  may be modified prior to contact with multi-layered structure  12 . More specifically, a dimension of recessions  28  and indention defect  31   b  of patterning surface  20  may be increased along a first direction by a factor of (k×d R ), with k generally being less than 1 and the first direction being orthogonal to patterning surface  20 . Contact between multi-layered structure  12  and mold  18  may then occur, with polymeric fluid  26  conforming to a shape of patterning surface  20 , defining a polymerizable layer  126  having a first shape. Recessions  28  and protrusions  30  of mold  18  may define protrusions  56  and recessions  58 , respectively, in polymerizable layer  126 , and protruding defect  31   a  and indention defect  31   b  may define a recessed defect  60   a  and raised defect  60   b , respectively, in polymerizable layer  126 , which are undesirable. Further, protrusions  56 , recessions  58 , recessed defect  60   a , and raised defect  60   b  may extend from multi-layered structure  12  in a second direction, orthogonal to the first direction and orthogonal to surface  42  of multi-layered structure  12 , shown in  FIG. 1 . 
     Referring to  FIG. 4 , multi-layered structure  12  is shown after subjecting polymerizable layer  126  to a trim etch process. To that end, a dimension of protrusions  56  and raised defect  60   b , shown in  FIG. 3 , of polymerizable layer  126  may be decreased in a third direction, orthogonal to the second direction, by the aforementioned factor of (k×d R ). As a result of subjecting polymerizable layer  126  to the aforementioned trim etch process, any features positioned upon polymerizable layer  126  having a dimension less than the factor (k×d R ) may be removed from multi-layered structure  12 . As a result, raised defect  60   b , shown in  FIG. 3 , may be removed from multi-layered structure  12 , as desired. However, a dimension of recessed defect  60   a  may be increased along the third direction. 
     Referring to  FIG. 5 , after removal of raised defect  60   b  from multi-layered structure  12 , both shown in  FIG. 3 , a reverse tone of protrusions  56  are transferred into transfer layer  24 . To that end, a conformal layer  62  may be positioned over protrusions  56 , defining a multi-layered structure  212 . This may be achieved by methods including, but not limited to, spin-on techniques, contact planarization, and the like. To that end, conformal layer  62  may be formed from exemplary compositions such as: 
     COMPOSITION 2 
     hydroxyl-functional polysiloxane 
     hexamethoxymethylmelamine 
     toluenesulfonic acid 
     methyl amyl ketone 
     COMPOSITION 2 
     hydroxyl-functional polysiloxane 
     hexamethoxymethylmelamine 
     gamma-glycidoxypropyltrimethoxysilane 
     toluenesulfonic acid 
     methyl amyl ketone 
     In COMPOSITION 2, hydroxyl-functional polysiloxane comprises approximately 4% of the composition, hexamethoxymethylmelamine comprisies approximately 0.95%, toluenesulfonic acid comprises approximately 0.05% and methyl amyl ketone comprises approximately 95%. In COMPOSITION 3, hydroxyl-functional polysiloxane comprises approximately 4% of the composition, hexamethoxymethylmelamine comprisies approximately 0.7%, gamma-glycidoxypropyltrimethoxysilane comprises approximately 0.25%, toluenesulfonic acid comprises approximately 0.05%, and methyl amyl ketone comprises approximately 95%. 
     Conformal layer  62  includes first and second opposed sides. First side  64  faces polymerizable layer  126 . The second side faces away from polymerizable layer  126 , forming normalization surface  66 . Normalization surface  66  is provided with a substantially normalized profile by ensuring that the distances k 1 , k 3 , k 5 , k 7 , k 9 , k 11 , k 13 , and k 15  between protrusions  56  and normalization surface  66  are substantially the same and that the distance k 2 , k 4 , k 6 , k 8 , k 10 , k 12 , and k 14  between recessions  58  and normalization surface  66  are substantially the same. 
     One manner in which to provide normalization surface  66  with a normalized profile is to contact conformal layer  62  with a planarizing mold (not shown) having a planar surface. Thereafter, the planarizing mold (not shown) is separated from conformal layer  62  and radiation impinges upon conformal layer  62  to polymerize and, therefore, to solidify the same. The radiation impinged upon conformal layer  46  may be ultraviolet, thermal, electromagnetic, visible light, heat, and the like. In a further embodiment, the radiation impinged upon conformal layer  62  may be impinged before the planarizing mold (not shown) is separated from conformal layer  62 . To ensure that conformal layer  62  does not adhere to the planarizing mold (not shown), a low surface energy coating may be deposited upon the planarizing mold (not shown). 
     Alternatively, release properties of conformal layer  62  may be improved by including in the material from which the same is fabricated a surfactant. The surfactant provides the desired release properties to reduce adherence of conformal layer  62  to the planarizing mold (not shown). For purposes of this invention, a surfactant is defined as any molecule, one tail of which is hydrophobic. Surfactants may be either fluorine containing, e.g., include a fluorine chain, or may not include any fluorine in the surfactant molecule structure. An exemplary surfactant is available under the trade name ZONYL® FSO-100 from DUPONT™ that has a general structure of R 1 R 2 , where R 1 ═F(CF 2 CF 2 ) Y , with y being in a range of 1 to 7, inclusive and R 2 ═CH 2 CH 2 O(CH 2 CH 2 O) x H, where X being in a range of 0 to 15, inclusive. It should be understood that the surfactant may be used in conjunction with, or in lieu of, the low surface energy coating that may be applied to the planarizing mold (not shown). 
     Referring to  FIGS. 5 and 6 , a blanket etch is employed to remove portions of conformal layer  62  to provide multi-layered structure  212  with a crown surface  68 . Crown surface  68  is defined by an exposed surface  70  of each of protrusions  56  and upper surfaces of portions  72  that remain on conformal layer  62  after the blanket etch. The blanket etch may be a wet etch or dry etch. In a further embodiment, a chemical mechanical polishing/planarization may be employed to remove portions of conformal layer  62  to provide multi-layered structure  212  with crown surface  68 . 
     Referring to  FIGS. 5 ,  6 , and  7 , crown surface  68  is subjected to an anisotropic plasma etch. The etch chemistry of the anisotropic etch is selected to maximize etching of protrusions  56 , while minimizing etching of portions  72 . In the present example, advantage was taken of the distinction of the silicon content between protrusions  56  and conformal layer  62 . Specifically, employing a plasma etch with an oxygen-based chemistry, it was determined that an in-situ hardened mask  74  would be created in the regions of portions  72  proximate to crown surface  68 , forming a multi-layered structure  312 . This results from the interaction of the silicon-containing polymerizable material with the oxygen plasma. As a result of hardened mask  74  and the anisotropy of the etch process, regions  76  of substrate  22  in superimposition with protrusions  56  are exposed. 
     Referring to  FIGS. 7 and 8 , hardened mask  74 , conformal layer  62 , and polymerizable layer  126  may be removed by exposing multi-layered structure  312  to a blanket fluorine etch, defining a multi-layered structure  412  having protrusions  78  and recessions  80 . To that end, recessed defect  52 , shown in  FIG. 2 , is removed from multi-layered structure  412 , as desired. However, a dimension of raised defect  54  may be increased along the third direction. Furthermore, raised defect  54  may not have a dimension greater than (2k×d R ), and thus, the raised defect  54  may have no undesirable effects on devices formed from multi-layered structure  12 . 
     Referring to  FIG. 9 , in a second embodiment, to minimize, if not prevent, patterning of raised defect  54  within multi-layered structure  12 , both as shown in  FIG. 2 , patterning surface  20  of mold  18  may be modified prior to contact with multi-layered structure  12 , analogous to that mentioned above with respect to  FIG. 3 . To that end, after contact between mold  18  and polymeric material  26  to define polymerizable layer  126 , conformal layer  162  may be positioned upon polymerizable layer  126 , defining a multi-layered structure  512 . Conformal layer  162  may be analogous to that as mentioned above with respect to  FIG. 5 . 
     Referring to  FIGS. 9 and 10 , analogous to that as mentioned above with respect to  FIGS. 5 and 6 , a blanket etch is employed to remove portions of conformal layer  162  to provide multi-layered structure  512  with a crown surface  168 . Crown surface  168  is defined by an exposed surface  170  of each of protrusions  56  and an exposed surface  171  of raised defect  60   b  and upper surfaces of portions  172  that remain on conformal layer  162  after the blanket etch. The blanket etch may be a wet etch or dry etch. In a further embodiment, a chemical mechanical polishing/planarization may be employed to remove portions of conformal layer  162  to provide multi-layered structure  512  with crown surface  168 . 
     Referring to  FIGS. 9 ,  10 , and  11 , analogous to that as mentioned above with respect to  FIGS. 5 ,  6 , and  7 , crown surface  168  is subjected to an anisotropic plasma etch. The etch chemistry of the anisotropic etch is selected to maximize etching of protrusions  56  and raised defect  60   b , while minimizing etching of portions  172 . In the present example, advantage was taken of the distinction of the silicon content between protrusions  56 /raised defect  60   b  and conformal layer  162 . Specifically, employing a plasma etch with an oxygen-based chemistry, it was determined that an in-situ hardened mask  174  would be created in the regions of portions  172  proximate to crown surface  168 , forming a multi-layered structure  612 . This results from the interaction of the silicon-containing polymerizable material with the oxygen plasma. As a result of hardened mask  174  and the anisotropy of the etch process, regions  176  in superimposition with protrusions  56  and region  79  in superimposition with raised defect  60   b  are exposed, defining protrusions  82  in superimposition with recesses  58  and defect  84  in superimposition with recessed defect  60   a.    
     Referring to  FIG. 12 , multi-layered structure  612  is shown after being subjected to a trim etch process. To that end, a dimension of protrusions  82  and defect  84 , shown in  FIG. 11 , may be decreased in the third direction by the aforementioned factor of (k×d R ). As a result, any features positioned upon multi-layered structure  612  having a dimension less than the factor (k×d R ) may be removed from multi-layered structure  612 , and more specifically, defect  84 , shown in  FIG. 11 , may be removed from multi-layered structure  612 , as desired. However, a dimension of region  79  may be increased along the third direction. 
     Referring to  FIGS. 12 and 13 , analogous to that as mentioned above with respect to  FIGS. 7 and 8 , hardened mask  174 , conformal layer  162 , and polymerizable layer  126  may be removed by exposing multi-layered structure  612  to a blanket fluorine etch, defining a multi-layered structure  712  having protrusions  82  and recessions  86 . To that end, raised defect  54 , shown in  FIG. 2 , may be removed from multi-layered structure  712 , as desired. However, a dimension of recessed defect  52  may be increased along the third direction. 
     Referring to  FIG. 14 , in a third embodiment, to minimize, if not prevent, patterning of recessed defect  52  and raised defect  54  within multi-layered structure  12 , as shown in  FIG. 2 , patterning surface  20  of mold  18  may be modified prior to contact with multi-layered structure  12 . More specifically, a dimension of recessions  28  and indention defect  31   b  of patterning surface  20  may be decreased along the first direction by a factor of (k×d r ) and the first direction being orthogonal to patterning surface  20 . Contact between multi-layered structure  12  and mold  18  may then occur, with polymeric fluid  26  conforming to a shape of patterning surface  20 , defining a polymerizable layer  126 . Recessions  28  and protrusions  30  of mold  18  may define protrusions  156  and recessions  158 , respectively, in polymerizable layer  126 , and protruding defect  31   a  and indention defect  31   b  may define a recessed defect  160   a  and raised defect  160   b , respectively, in polymerizable layer  126 , which are undesirable. Further, protrusions  156 , recessions  158 , recessed defect  160   a , and raised defect  160   b  may extend from multi-layered structure  12  in the second direction, orthogonal to the first direction and orthogonal to surface  42  of multi-layered structure  12 , shown in  FIG. 1 . 
     Referring to  FIG. 15 , multi-layered structure  12  is shown after subjecting polymerizable layer  126  to a trim etch process. To that end, a dimension of protrusions  158  and raised defect  160   b , shown in  FIG. 14 , of polymerizable layer  126  may be decreased in the second direction by the factor of (k×d r ). As a result of subjecting polymerizable layer  126  to the aforementioned trim etch process, any features positioned upon polymerizable layer  126  having a dimension less than the factor (k×d r ) may be removed from multi-layered structure  12 . As a result, raised defect  160   b , shown in  FIG. 14 , may be removed from multi-layered structure  12 , as desired. However, a dimension of recessed defect  160   a  may be increased along the third direction. 
     Referring to  FIG. 16 , after removal of raised defect  160   b  from multi-layered structure  12 , both shown in  FIG. 14 , a reverse tone of protrusions  156  are transferred into transfer layer  24 . To that end, a conformal layer  262  may be positioned over protrusions  156 , defining a multi-layered structure  812 . Conformal layer  262  may be analogous to that as mentioned above with respect to  FIG. 5 . 
     Referring to  FIGS. 16 and 17 , analogous to that as mentioned above with respect to  FIGS. 5 and 6 , a blanket etch is employed to remove portions of conformal layer  262  to provide multi-layered structure  812  with a crown surface  268 . Crown surface  268  is defined by an exposed surface  270  of each of protrusions  156  and upper surfaces of portions  272  that remain on conformal layer  262  after the blanket etch. The blanket etch may be a wet etch or dry etch. In a further embodiment, a chemical mechanical polishing/planarization may be employed to remove portions of conformal layer  262  to provide multi-layered structure  812  with crown surface  268 . 
     Referring to  FIGS. 16 ,  17 , and  18 , analogous to that as mentioned above with respect to  FIGS. 5 ,  6 , and  7 , crown surface  268  is subjected to an anisotropic plasma etch. The etch chemistry of the anisotropic etch is selected to maximize etching of protrusions  156 , while minimizing etching of portions  272 . In the present example, advantage was taken of the distinction of the silicon content between protrusions  156  and conformal layer  262 . Specifically, employing a plasma etch with an oxygen-based chemistry, it was determined that an in-situ hardened mask  274  would be created in the regions of portions  272  proximate to crown surface  268 , forming a multi-layered structure  912 . This results from the interaction of the silicon-containing polymerizable material with the oxygen plasma. As a result of hardened mask  274  and the anisotropy of the etch process, regions  276  in superimposition with protrusions  56  are exposed, defining protrusions  90  in superimposition with recesses  158  and defect  92  in superimposition with recessed defect  160   a , shown in  FIG. 14 . 
     Referring to  FIG. 19 , multi-layered structure  912  is shown after being subjected to a trim etch process. To that end, a dimension of protrusions  90  and defect  92 , shown in  FIG. 18 , may be decreased in the third direction by the factor (2×k×d r ). As a result, any features positioned upon multi-layered structure  912  having a dimension less than the factor (2×k×d r ) may be removed from multi-layered structure  912 , and more specifically, defect  92 , both shown in  FIG. 18 , may be removed from multi-layered structure  912 , as desired. 
     Referring to  FIGS. 19 and 20 , analogous to that as mentioned above with respect to  FIGS. 7 and 8 , hardened mask  274 , conformal layer  262 , and polymerizable layer  126  may be removed by exposing multi-layered structure  912  to a blanket fluorine etch, defining a multi-layered structure  1012  having protrusions  90  and recessions  94 . To that end, recessed defect and raised defect  54 , shown in  FIG. 2 , may be removed from multi-layered structure  1012 , as desired. 
     Referring to  FIG. 11 , in still a further embodiment, to minimize, if not prevent, patterning of recessed defect  52 , a conformal coating (not shown) may be positioned upon multi-layered structure  612  such that region  79  in superimposition with raised defect  60   b  may be filled with the conformal coating (not shown) and a desired dimension of protrusions  82  may be obtained. The conformal coating (not shown) may be that similar to one used in RELACS® by Clariant, Inc. Further, multi-layered structure  612  may be subjected the blanket etch, as mentioned above with respect to  FIGS. 7 and 8 , to obtain the desired structure. In still a further embodiment, in place of the conformal coating (not shown), a reflow process may be employed wherein the polymerizable layer  126  may be heated over a glass transition temperature associated therewith. 
     In still a further embodiment, referring to  FIG. 2 , multi-layered structure  112  may be formed employing electron beam lithography, ion beam lithography, etc. As a result, the above-mentioned methods of removing of defects formed upon multi-layered structure  112  may be applied. More specifically, a desired pattern to be formed upon multi-layered structure  112  may be stored in a computer-readable memory (not shown). To that end, prior to formation of protrusions  48  and recessions  50  upon multi-layered structure  112 , the desired pattern located in the computer-readable memory (not shown) may be altered such that a dimension of protrusions  50  may be increased in the third direction by a factor a 1 . To that end, upon formation of protrusions  48  and recession  50  upon multi-layered structure  112 , protrusions  48  may be subjected to a trim etch process, analogous to that as mentioned above with respect to  FIG. 3 , to remove raised defect  60   b  while obtaining the desired pattern in multi-layered structure  112 . 
     The embodiments of the present invention described above are exemplary. Many changes and modification may be made to the disclosure recited above, while remaining within the scope of the invention. The scope of the invention should, therefore, be determined with reference to the appended claims along with their full scope of equivalents.