Patent Publication Number: US-10774246-B2

Title: Dry adhesives and methods for making dry adhesives

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     The present invention is a Divisional application of U.S. Non-provisional application Ser. No. 12/448,243 entitled “DRY ADHESIVES AND METHODS FOR MAKING DRY ADHESIVES” filed on Jun. 12, 2009, which is a national stage entry of Patent Cooperation Treaty international application serial number PCT/US2007/025684, entitled “DRY ADHESIVES AND METHODS FOR MAKING DRY ADHESIVES” filed on Dec. 14, 2007, which claims the benefit of U.S. Provisional Application Ser. No. 60/874,787, filed on Dec. 14, 2006, all are incorporated herein by reference. 
    
    
     FIELD OF THE INVENTION 
     This invention relates to dry adhesives, and methods for making dry adhesives including, for example, microfibers and nanofibers. 
     BACKGROUND OF THE INVENTION 
     There have been recent findings on the mechanisms by which geckos adhere to and climb smooth vertical surfaces. Geckos are exceptional in their ability to climb up smooth vertical surfaces because their hierarchical micro/nanoscale foot-hairs with their spatulate tips can attach to almost any smooth or micro/nanoscale rough surface repeatedly with a controllable adhesion pressure up to around 10 N/cm 2  (100 kPa) [K. Autumn, Y. A. Liang, S. T. Hsieh, W. Zesch, W. P. Chan, T. W. Kenny, R. Fearing, and R. J. Full, Nature, 405, 681 (2000)]. Recent findings have shown that van der Waals and possibly capillary forces play a dominant role in their fibrillar adhesion [K. Autumn, Y. A. Liang, S. T. Hsieh, W. Zesch, W. P. Chan, T. W. Kenny, R. Fearing, and R. J. Full, Nature, 405, 681 (2000)] [K. Autumn, M. Sitti, Y. A. Liang, A. M. Peattie, W. R. Hansen, S. Sponberg, T. W. Kenny, R. Fearing, J. N. Israelachvili, and R. J. Full, PNAS, 99, 12252 (2002)] [G. Huber, H. Mantz, R. Spolenak, K. Mecke, K. Jacobs, S, N. Grob, and E. Artz, PNAS, 102(45), 16293 (2005)] [G. Huber, S, N. Grob, R. Spolenak, and E Artz, Biology Letters, 1, 2 (2005)]. 
     Many adhesion and contact mechanics models for the microfibrillar interfaces have been developed [H. Gao and H. Yao, PNAS, 101, 7851 (2004)] [T. Tang, C. Hui, and N. J. Glassmaker, J. Roy. Soc. Interface, 2, 505 (2005)] [N. J. Glassmaker, A. Jagota, C. Hui, and J. Kim, J. Roy. Soc. Interface, 1, 1 (2004)] [C. Hui, N. J. Glassmaker, T. Tang, and A. Jagota, J. Roy. Soc. Interface, 1, 35 (2004)] [B. N. J. Persson, J. Chemical Physics, 118, 7614 (2003)] [A. J. Crosby, M. Hageman, and A. Duncan, Langmuir, 21, 11738 (2005)] and synthetic fibrillar adhesives have been attempted to be fabricated. Fabrication methods for recent micro/nanoscale synthetic dry adhesives consist of electron-beam lithography [A. K. Geim, S. V. Dubnos, I. V. Grigorieva, K. S. Novoselov, A. A. Zhukov, and S. Y. Shapoval, Nature Materials, 2, 461 (2003)], replication of templates using molding or casting [D. Campolo, S. Jones, and R. S. Fearing, Proc. of the IEEE Nanotechnology Conf., 12 (2003)], drawing [H. E. Jeong, S. H. Lee, P. Kim, and K. Y. Suh, Nano Letters, 6, 1508 (2004)], printing [M. Sitti and R. S. Fearing, J. Adhesion Science and Technology, 17(5), 1055 (2003)], growing [Y. Zhao, T. Tong, L. Delzeit, A. Kashani, M. Meyyappan, and A. Majumdar, J. Vac. Sci. Techno. B, 24(1), 331 (2006)], and more complex microfabrication combined with self-assembly [M. T. Northen and K. L. Turner, Nanotechnology, 16, 1159 (2005)]. These works focused on fabricating micro/nanoscale high aspect ratio and high density polymer or carbon nanotube fibers on a flat substrate. 
     Some researchers have attempted to recreate the spatulate tips that occur naturally on gecko hairs as such broadened tips on fibers provide additional surface area, promoting adherence, while acting to prevent clumping of the fibers. 
     U.S. Pat. No. 6,722,026 discloses a method of removably adhering a semiconductor substrate with microfibers which possess spatulate tips, but does not disclose a method for fabrication of such spatulate tips. U.S. patent application Ser. No. 11/281,768 (published as US 2006-0202355 A1) discloses a variety of formulae for enhancing friction of fibers and mentions fibers with T-shaped ends, but does not describe a method of fabrication for such T-shaped ends. 
     U.S. Pat. No. 6,737,160 and U.S. patent application Ser. No. 10/039,574 (published as US 2003 0124312 A1), Ser. No. 10/655,271 (published as US 2005 0072509 A1), Ser. No. 10/747,923 (published as US 2005 0148984 A1) and Ser. No. 11/030,752 (published as US 2005 0151385 A1) describe the use of microfibers as dry adhesives, and describe several methods for the fabrication of spatulate tips on such microfibers. One method uses an oxide/nitride semiconductor process to fabricate the shafts, the ends of which are then roughened to produce spatula. This method cannot make spatulate tips. Another described method uses a pipette, through which a liquid polymer is extruded until a hemispherical drop forms at the end of the pipette, which could then be flattened against a smooth surface to create a flat spatulate tip. This method can allow only micrometer scale fibers due to the diameter limitation of micro-pipettes. Another described method to fabricate spatulate tips is lithographically induced self-construction. This technique uses electrostatic attraction to pull liquid through a mask, to thereby ‘sprout’ spatulae. This could enable micro/nano-meter scale low aspect ratio fibers with no tips. A third method described to fabricate spatulate tips involves the use of a nano-imprinting roller. This could also enable micro/nano-meter scale low aspect ratio fibers with no tips. A final method uses a two-layer photoresist process to make fibers with tips. This method can only make fibers with tips from photoresist polymers, which are very brittle. 
     U.S. patent application Ser. No. 10/863,129 (published as US 2005-0271869-A1) and Ser. No. 10/982,324 (published as US-2005-0271870-A1) disclose a method for forming hierarchical structures of microfibers with smaller microfibrils attached to the end. In one embodiment, these applications describe a method to fabricate microstructures with broader tips on narrow shafts that could be considered to be spatulate tips. This method uses a time multiplexed deep etching process, such as the Bosch process to etch wells in a substrate. Through alternation of etching and passivation, the process can produce an array of microfibers with large heads on top of narrow shafts. This process can make microfibers with flat tips from only silicon type of stiff and brittle materials that can be etched in the Bosch process. 
     The microfiber fabrication methods described above are very expensive for producing commercial quantities of adhesive materials. Therefore there is a need for better methods for economically producing microfiber-based dry adhesives. Moreover, fibers with flat tips and diameters of hundreds of nanometer cannot be reliably fabricated from wide range of polymer materials in the above processes. 
     Accordingly, there is a need for improved dry adhesives and improved methods for making dry adhesives. In particular, there is a need for dry adhesives having greater adhesive forces and improved durability. In addition, there is a need for methods of making dry adhesives with lower costs of production. Those and other advantages of the present invention will be described in more detail hereinbelow. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to dry adhesives and methods for making dry adhesives. Prior art efforts to produce microfiber-based dry adhesives have not produced adhesive forces of magnitudes equal to those produced by gecko adhesion, have not shown acceptable durability, and have suffered from very high costs of production, making them commercially infeasible. The present invention provides dry adhesives and methods for fabrication of dry adhesives which provide superior adhesive qualities, and does so in a manner which is reproducible, scalable and cost effective. The invention also includes: apparatus (e.g., Kraus vibratory doser) to add alkaline material (such as, pulverized calcite limestone) directly to the tank assembly when additional alkalinity is needed to complete the ferrous iron oxidation and precipitation reactions; and a separate container assembly to thicken iron oxides produced by the treatment process. The invention has the capacity to discharge substantially iron free water with circumneutral pH. 
     The present invention provides improved dry adhesive materials and methods for fabrication of dry adhesive materials. These dry adhesive materials may be, for example, micro- and nanofiber-based materials. In particular, the present invention provides methods for the fabrication of such fibers which will produce flat tips on the fibers. These tips are sometimes described herein as being “spatulate” tips, although the present invention may be used to form flattened tips of many shapes and is not limited to only forming spatulate tips. 
     According to one embodiment, the present invention includes a method of forming a dry adhesive fiber in a structure including an etch layer and a barrier layer, wherein the etch layer and the barrier layer are adjacent to each other and are made from different materials. The method includes forming an opening through the etch layer and to the barrier layer, expanding the opening in the etch layer at the barrier layer, filling the opening with a material, removing the barrier layer from the material in the opening, and removing the etch layer from the material in the opening. 
     According to another embodiment, the method includes forming a plurality of dry adhesive fibers including forming a plurality of openings through the etch layer and to the barrier layer, expanding the openings in the etch layer at the barrier layer, filling the openings with a material, forming a backing layer over the openings and on a surface of the etch layer opposite the barrier layer wherein the material in a plurality of the openings is connected via the backing layer, removing the barrier layer from the material in the openings, and removing the etch layer from the material in the opening and from the backing layer. 
     According to another embodiment, the present invention includes a dry adhesive fiber. The fiber includes a tip having a flat surface, a layer of fluorocarbon on the flat surface of the tip, a base, a stem connecting the tip and the base wherein the stem has a surface, and a hydrophobic and low surface energy layer on the surface of the stem. 
     According to another embodiment, the present invention includes a dry adhesive including a plurality of fibers, with each of the fibers including a tip having a flat surface, a layer of fluorocarbon on the flat surface of the tip, a base, a stem connecting the tip and the base wherein the stem has a surface, and a hydrophobic and low surface energy layer on the surface of the stem. In addition, the dry adhesive includes a backing layer connected to the bases of the plurality of fibers. 
     According to another embodiment, the present includes a dry adhesive fiber array including two or more layers of dry adhesive fibers. 
     Many variations are possible with the method and fiber according to the present invention. For example, fibers may be formed by molding a master template fabricated using deep reactive ion etching and the notching effect in the following steps: (a) A silicon-on-insulator wafer top surface is patterned using optical lithography; (b) A negative fiber array template is formed using a two-step deep reactive ion etching process: At first, isotropic etching is conducted for forming circular supporting base of each fiber; then, DRIE is followed for the vertical walls, and the notching effect on the oxide layer forms a template for molding fibers with spatulate flat tips; (c) The template is filled with a liquid polymer under vacuum and the polymer is cured, or it is filled by gas phase deposition of a polymer; and (d) Polymer fiber arrays with spatulate tips and a backing layer are released from the template: The bottom silicon layer is etched away by XeF 2  dry etching; thin oxide layer is removed by buffered oxide etching; top silicon layer is etched away by XeF 2  etching. 
     Many other variations are possible with the present invention. For example, different materials may be used to make the fibers and the dry adhesive, and the geometry and structure of the fibers and the dry adhesive may vary. In addition, different types of etching and other material removal processes, as well as different deposition and other fabrication processes may also be used. These and other teachings, variations, and advantages of the present invention will become apparent from the following detailed description of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings for the purpose of illustrating the embodiments, and not for purposes of limiting the invention, wherein: 
         FIG. 1  illustrates one embodiment of a dry adhesive fiber according to the present invention; 
         FIG. 2  illustrates one embodiment of a dry adhesive including a plurality of fibers attached to a backing layer; 
         FIGS. 3A-D  is a Schematic illustration of process flow steps for the fabrication of microfiber arrays according to one embodiment of the present invention; 
         FIGS. 4 a -4 h    illustrate one embodiment of a method of forming a two layer fiber array  30  according to the present invention; 
         FIG. 5 . is a scanning electron microscope image of the isometric view of a polyurethane elastomer microfiber array illustrated in  FIG. 3  with 4.5 μm fiber diameter, nine μm tip diameter, 20 μm length, and 44% fiber density (Scale bar: 50 μm); 
         FIG. 6  is a graph of macroscale adhesion (upper plot) and overall work of adhesion (lower plot) of polyurethane microfibers and flat polyurethane flat control surface on a six mm diameter glass hemisphere for varying preloads; 
         FIG. 7( a )  illustrates a scanning electron microscope image of the profile view of a polyurethane elastomer microfiber array with spatulate tips with around 5 μm fiber stem diameter, 9 μm tip diameter, 20 μm length, and 44% fiber density; 
         FIG. 7( b )  illustrates experimental pull-off force (adhesion) (F ad ) data for elastomer microfiber arrays on a silicon disk with 0.43 mm radius with four different normalized backing layer thicknesses (h/a) for a 10 mN preload (four data points were plotted for each backing thickness on different fiber array locations); 
         FIGS. 8 a  and 8 b    illustrates schematics of the force analysis in two different backing layer thickness cases under constant displacement: (a) fibers on an infinitesimal thick backing layer; (b) fibers on a very thick backing layer; 
         FIG. 9  illustrates the stem-fiber angle and the tip wedge angle; 
         FIG. 10  illustrates the stem being angled obligue to the backing layer and tip; 
         FIGS. 11A and 11B  illustrate where the cross sectional area of the stem of the plurality of fibers includes a plurality of cross sectional areas along the longitudinal length; 
         FIG. 12  illustrates the stem being angled oblique to the backing layer and tip; and 
         FIG. 13  illustrates the second plurality of fibers having oblique angles relative to the tip of the first and second plurality of fibers. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention is directed to dry adhesives and methods for making dry adhesives. The term “dry adhesive”, as used herein, refers generally to individual dry adhesive fibers and also to materials including a plurality of dry adhesive fibers connected together. The present invention will also be described in terms of micro- and nanofibers, although the present invention is applicable to a wide variety of sizes and is not necessarily limited to a particular size range. 
       FIG. 1  illustrates one embodiment of a dry adhesive fiber  10  according to the present invention. In that embodiment, the fiber  10  includes a tip  12 , a base  14 , and a stem  16 . The shape of the fiber  10  and the relative size of the various parts of the fiber  10  can vary from that shown in the figure. Different applications and materials, for example, can make different shapes and sizes desirable, and such variations are within the scope of the present invention. 
     The tip  12  includes a flat surface  20 . A layer of fluorocarbon  22  may be on the flat surface  20 , as described hereinbelow. The layer of fluorocarbon  22  may be of varying thickness, and is not necessarily shown to scale in  FIG. 1 . In this particular illustration, the layer of fluorocarbon  22  is shown as being relatively thick for the purpose of illustration. 
     The base  14  is opposite the tip  12  and is often attached to a backing layer, as is described in more detail with respect to  FIG. 2 . The base  14  is illustrated as being thicker than the stem  16  and is also illustrated as including a curved surface  24  extending outward from the stem  16  to the edge of the base  14 . The relatively large, curved shape of the base  14  allows the base  14  to better withstand strain causes by the bending of the fiber  10 , thereby providing for greater durability of the fiber  10 . However, in other embodiments the base  14  may have different shapes and sizes. For example, the base  14  may be thinner than the stem or of the same thickness as the stem  16 . For example, the base  14  may be indistinguishable from the stem  16  in size and shape, although it is still the base  14  because it represents the end of the fiber  10  that is typically attached to another structure, such as a backing layer. 
     The stem  16  connects the tip  12  and the base  14 . The stem  16  may also include a hydrophobic layer  26  as will be described in more detail hereinbelow. The stem  16  is shown as being at right angles to both the tip  12  and the base  14  in  FIG. 2 . However, in other embodiments the stem  16  may be oriented differently, such as at an oblique angle (acute or obtuse) with respect to one or both of the tip  12  and the base  14  (see  FIGS. 10, 12, and 13 ). In addition, the stem  16  is illustrated as being straight, although the stem  16  may be made to be curved or to have other non-straight characteristics. The angular orientation of the end  16   a  of the fiber  16  with tip  12  is tangent with a point along the curvature of tip  12 .  FIG. 13  also illustrates the second layer of fibers  110  at an oblique angle (acute or obtuse) with respect to one or both of the tip  112  and the base  114  (not shown) or tip  12  (when there is no base  114 ).  FIGS. 10, 12, and 13  are illustrations and are not meant to limit the invention with regards to uniform and non-uniform cross-sectional areas, and orientation of fibers  16 ,  110  relative to base  14  or tip  12  or tip  112 . 
       FIG. 2  illustrates one embodiment of a dry adhesive structure  30  including a plurality of fibers  10  attached to a backing layer  32 . The combination of a plurality of fibers  10  connected to a backing layer  32  will sometimes also be referred to herein as an array  30  or a fiber array  30 . The backing layer  32  is connected to the bases  14  of the fibers  10 . The dry adhesive structure  30  is not limited to the specifics illustrated in  FIG. 2 . On the contrary, a dry adhesive  30  according to the present invention may be made in different sizes, with different numbers of fibers  10  having different spacings and different shapes and dimensions. The number of fibers  10 , their spacing, dimensions, and other characteristics of the dry adhesive  30  may be uniform or may vary (non-uniform). For example, the dry adhesive  30  may have alternating patterns of fiber sizes and spacings, or the shape of the fibers  10  may be different in different parts of the dry adhesive  30 . Many other variations are also possible. 
     The backing layer  32  may be the same as the material used to make the fibers  10 , or the backing layer  32  may be made from a different material. The thickness of the backing layer  32  can have a significant effect on the performance of the fiber array  30 , and this is discussed in more detail hereinbelow. 
       FIGS. 3 a -3 d    illustrate a method of making a dry adhesive according to one embodiment of the present invention. 
       FIG. 3 a    illustrates the basic structure in which a dry adhesive is formed. The structure includes an etch layer  40  and a barrier layer  42 , as well as a substrate  44  on which the etch  40  and barrier  42  layers are formed. The etch layer  40  and the barrier layer  42  are adjacent to each other and are made from different materials.  FIG. 3 a    is not necessarily to scale, and the dimensions and shapes of the various parts of the structure may vary depending on the particular application. 
     The etch layer  42  may be a single, homogenous layer, or it may be formed from and include more than one layer of the same or different materials. As used herein, etch layer  40  means one or more layers which are etched or from which material is otherwise removed so as to form the structure described herein. In the illustrated embodiment, the etch layer  40  is changed so as to form a mold for use in manufacturing the dry adhesive fibers  10  and the dry adhesive fiber array  30 . 
     The barrier layer  42  may also be made from one or several layers of the same or different materials. The barrier layer  42  is made from a different material having different properties than the etch layer  40 . Unlike the etch layer  40 , the barrier layer  42  acts as a stop and does not dramatically change its shape during the manufacturing process. The barrier layer  42  maintains a relatively constant-flat shape that is used to form the flat surfaces  20  on the tips  12  of the fibers  10 . 
     In practice, the barrier layer  42  will lose some material during the formation of the openings, which are described below. However, this loss of material is very small compared to that of the etch layer  40 , and the concept of barrier materials is well understood in the art. As used herein, barrier layer  42  generally means the one or more layers which form a border of the openings  50  (described below) but which are not significantly etched or from which significant material is not otherwise removed during the formation of the openings  50 , which are described below. 
     The barrier layer  42  is generally described as having a flat shape, although in other embodiments the barrier layer  42  may be formed otherwise so as to form different shapes for the tips  12  of the fibers  10 . For example, the barrier layer  42  may be formed with a curved shape, or with a surface having other features such as recesses or protrusions. 
     The substrate  44  may be used in connection with the etch  40  and barrier  42  layers. However, in methods where the substrate  44  is not required to form and/or to support the etch  40  and barrier  42  layers, the substrate layer  44  may be omitted. 
     With reference to  FIG. 3 b   , openings  50  are formed in the etch layer  40 . The openings  50  are formed through the etch layer  40  and to the barrier layer  42 . The openings  50  may be created, for example, by forming a patterned layer  52  on the surface of the etch layer  40  and then exposing the structure to an etching process or to other processes for removing the exposed material from the etch layer  40 . The patterned layer  52  may be photoresist, a contact mask, or some other material used to selectively expose portions of the etch layer  40 . In other embodiments, the patterned layer  52  may be omitted and the openings may be formed directly, such as through e-beam processes. 
     After the openings  50  are formed, the openings  50  are expanded in the etch layer  40  at the barrier layer  42  to form expanded openings  54  which will shape the tip  12  of the fibers  10 . The process of forming the expanded openings  54  will be described in more detail hereinbelow. 
     The openings  50  may also be expanded  56  near the top surface  58  of the etch layer  40 , on the surface  58  opposite the barrier layer  42 . This expanded opening  56  will shape the base  14  of the fibers  10 . By expanding  56  the opening  50 , the base  14  will be thicker than the stem  16 . Furthermore, if the expanded opening  56  is given a rounded shape, it will cause the base  14  to be formed with a rounded shape, as described herein. The formation of this expanded opening  56  may, for example, be performed with an isotropic etch prior to the formation of the opening  50  and may be performed in the portions of the etch layer  40  not covered by the patterning layer  52 . 
     The process of forming the openings  50  may, under some processes, form a layer of hydrophobic material  60  on the side walls of the openings. Similarly, under some processes, a fluorocarbon layer  62  may be formed on the barrier layer  42  where the flat surface  20  of the tip  12  will be formed. This fluorocarbon layer  62  has been found to cause increased adhesion at the flat surface  20  of the tip  12 . The hydrophobic layer  60  is a smooth, non-stick surface which is also advantageous. The formation of these layers  60  and  62  will be described in more detail hereinbelow. 
     After the openings  50 ,  54 ,  56  are formed, the photoresist or other patterned layer  52  may be removed. 
     With reference to  FIG. 3 c   , after the openings  50  are formed, they are filled with a material  70 . The material  70  may be a polymer, a metal, or any other material from which the fibers  10  can be made. After the openings  50  are filled with the material  70 , the backing layer  32  may be formed over the openings  50  and on the surface  58  of the etch layer  40  opposite the barrier layer  42 . The material  70  in the openings  50  is connected together via the backing layer  32 , forming a single structure including a plurality of fibers  10  and the backing layer  32 . 
     The backing layer  32  may be formed in several ways. The backing layer  32  may be formed separately from the material  70  filling the openings  50  and applied over the openings  50  and on the surface  58  of the etch layer  40 . Alternatively, the backing layer  32  may be formed from the same material  70  as that used in the openings  50 , in which case, for example, the process of filling the openings  50  may be allowed to continue after the openings  50  are filled, so that the material  70  fills the surface  58  over the openings  50  to form the backing layer  32 . A mold (not shown) may be formed on top  58  of the etching layer  40  to contain the extra material  70  used to form the backing layer  32 . In addition, a step of compressing or squeezing the material forming the backing layer  32  may also be performed so that the backing layer  32  is formed to a desired thickness. Other methods of controlling the thickness of the backing layer  32  are also possible, such as by trimming or cutting excessive backing layer  32  material. The thickness of the backing layer  32  can have a significant effect on the performance of the fiber array  30 , and will be discussed in more detail hereinbelow 
     With reference to  FIG. 3 d   , after the material  70  in the openings  50  has cured or otherwise achieves a desired state, the etch layer  40  and barrier layer  42  may be removed from the material  70 , leaving the molded dry adhesive fibers  10  and backing later  32 . In addition, the substrate layer  44  may also be removed if it was used. 
     The use of wet etch processes for the removal of the etch layer  40  tend to cause “clumping” of, or an attraction between, adjacent fibers  10 . This is caused by hydrostatic pressure from the liquid remaining from the wet etching. It has been found that dry etch processes are particularly advantageous for removing the etch layer  40  and reducing or eliminating the clumping or lateral or vertical collapsing of fibers. However, the use of a dry etch process is not required with the present invention, and other processes may be used. For example, supercritical carbon dioxide (CO 2 ) drying can be used to release the fibers without clumping or collapsing issues where after wet etching of the etch layer, released fibers can be soaked in liquid CO 2 , heated and applied pressure over the supercritical point to remove CO 2 . 
     Although this embodiment of the method has been described in terms of making several fibers  10  attached to a backing layer  32 , the present invention may also be used to make a single fiber  10 , or to make a plurality of fibers  10  that are not connected to a backing layer  32 . Furthermore, the present invention may also include two or more layers of fibers  10  or fiber arrays  30  having two or more layers of fibers  10 . 
       FIGS. 4 a -4 h    illustrate one embodiment of a method of forming a two layer fiber array  30  according to the present invention. In this embodiment, the two layers of fibers are different sizes. The smaller fibers  110  (shown in  FIGS. 4 g  and 4 h   ) may be smaller in volume, or smaller in their dimensions. Alternatively, it is also possible to form a multi-layer fiber array  30  in which the different layers of fibers are the same size. 
       FIGS. 4 a  and 4 b    are analogous to  FIGS. 3 a  and 3 b    and they illustrate the first structure in which the openings  50  are created and in which the first layer of fibers  10  will be formed. 
       FIGS. 4 c  and 4 d    illustrate the second structure in which the second layer of fibers  110  is formed. In the illustrated embodiment, the second structure includes an etch layer  140  and a barrier layer  142 , as well as a substrate  144  on which the etch  140  and barrier  142  layers are formed. The etch layer  140  and the barrier layer  142  are adjacent to each other and are made from different materials. The second structure may include the same or different elements as those described hereinabove with respect to  FIGS. 3 a  and 3 b   . In other words, the openings  150  in the second structure may have the same features as the openings  50  in the first structure, although they differ in their size.  FIG. 4 a    is not necessarily to scale, and the particular dimensions of the various parts of the structure may vary depending on the particular application. 
       FIGS. 4 c  and 4 d    are similar to  FIGS. 4 a  and 4 b   , except that the fibers  110  to be formed in the process of  FIGS. 4 c  and 4 d    are smaller than those formed in the process of  FIGS. 4 a  and 4 b   . For example,  FIG. 4 a    may represent a process with a twenty μm thick etch layer  40 , three μm diameter openings  50 , and twelve μm spacing between opening  50  centers. In contrast,  FIG. 4 c    may represent a process with a two μm thick etch layer  140 , a 300 nm diameter openings  150 , and 800 nm spacing between opening  150  centers. 
     Similarly, the etching process of both  FIGS. 4 b  and 4 d    may be, for example, a dry etching process. That process may include isotropic etching, followed by deep reactive ion etching, and then expanding the opening  50 ,  150  near the barrier layer  42 ,  142  to form a desired shape for the base  14 ,  114  of the fibers  10 ,  110 . 
     However, variations are also possible with this aspects of the present invention and, for example, the second fibers  110  may be larger than the first fibers  10 . 
       FIG. 4 e    illustrates the structures of  FIGS. 4 b  and 4 d    being connected together. The dashed line illustrates where the two structures are joined together. When connected, the structures are oriented so that the openings  50 ,  150  correspond to or engage with each other. In other words, the exposed openings  50  in the first structure corresponding to or engage with exposed openings  150  in  FIG. 4 d   . This orientation is accomplished in  FIG. 4 e    by rotating the top structure 180 degrees before connecting the two together. 
     This connection may be formed, for example, by silicon fusion bonding or by other processes. In one embodiment, the bonding is accomplished with ten minutes of piranha cleaning to remove photoresist and anti-reflective coating. Followed by ten minutes of oxygen plasma etching to remove the film that is natively generated in the openings  50 ,  150  during deep reactive ion etching. Followed by ten minutes of piranha cleaning for final surface cleaning. After the final cleaning, the two structures are pressed to each other and annealed at 1,000 degrees Celsius in a quartz furnace to bond them. 
       FIG. 4 f    illustrates the bonded structure after the top layers (the barrier layer  42  and substrate  44 ) are removed. This may be done, for example, with a buffered oxide etching process. The resulting structure is a two layer mold open at the top where the barrier layer  42  and substrate  44  used to be. 
       FIG. 4 g    illustrates the two layer structure after being filled with a material  70 . As described above, the material  70  may by any of many different materials, and this process may be, but is not required to be, performed in a vacuum chamber. 
       FIG. 4 g    also illustrates that not all of the second openings  150  are necessarily utilized. In this embodiment, one of the second openings  180  is not connected to the first openings  50  and, therefore, that opening  180  is not filled with material  70 . 
       FIG. 4 h    illustrates the resulting two layer fiber array  30  after the surrounding structure or mold (the remaining etch layers  40 ,  140 , the second barrier layer  142 , and the second substrate  144 ) has been removed. The removal may be performed, for example, with a XeF 2  etch to remove the bottom silicon layer and a buffered oxide etch to remove the oxide layer, as described above with respect to  FIGS. 3 a -3 d   . A further XeF 2  etch may be used to remove the upper silicon layer. 
     Although the present invention has been described in terms of a two layer fiber array  30 , the present invention may also be used to produce a fiber array  30  having more than two layers. Furthermore, the present invention is not limited to multilayer fiber arrays  30 , and it may also be used, for example, to make multilayer individual fibers and to make other structures. 
     The theory related to the present invention will now be presented. Flat and larger diameter (also referred to as cross-sectional area) spatulate tips  12  are postulated to enhance the adhesion and work of adhesion significantly due to the increased tip contact area at the fiber-surface interface [H. Gao and H. Yao, PNAS, 101, 7851 (2004)]. In order to model the work of adhesion enhancement approximately, a single polymer fiber  10  is assumed to be stretched while its volume is conserved. In addition, if pull-off of each fiber tip  12  is assumed to happen simultaneously where overall pull-off force per unit area is a constant value (c 1 ) and the elastic deformation is assumed to happen at the fiber stem  16  only where the polymer Young&#39;s modulus (E) is assumed to be constant. Then, the maximum stretched length (x c ) and work of adhesion (W) of a single fiber  10  during separation can be computed as 
     
       
         
           
             
               
                 
                   
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     where x 0  is the initial stem  16  length, D is the fiber spatulate tip  12  diameter, and d 0  is the fiber stem  16  diameter. From (1) and (2), elastomer fibers  10  with larger diameter tips  12  elongate and dissipate energy significantly, and thus the work of adhesion per fiber  10  is increased. Moreover, adhesion is also increased by a fiber array  30  with larger flat spatulate tips  12  since: (1) The fracture mechanics of the microfibers is flaw insensitive [M. Murphy, B. Aksak, and M. Sitti, Langmuir, under review (2006)] (the stress at the interface is uniform and equal to the intrinsic adhesion strength at the instant of pull-off) and thus enables the maximum possible adhesion pressure; (2) Flat and compliant spatulate tips  12  enable easier contact to a smooth surface with almost no alignment problem; (3) Fiber stretching enables larger number of fibers  10  staying in contact with a smooth surface during pull-off. Therefore, this invention is focused on fabrication of polymer microfibers  10  with flat and larger spatulate tips  12  for fibrillar adhesives with improved adhesion capability. 
     One embodiment of the fabrication process according to the present invention will now be provided. The present invention is not limited to the specifics details of this embodiment, and these details are illustrative of the present invention, and not limiting.  FIG. 3 a - d    illustrates one embodiment of the fabrication process of polymer microfibers with flat and larger diameter spatulate tips  12 .  FIG. 3 a    illustrates a silicon-on-insulator (SOI) wafer (purchased from Addison Engineering) which is used as a substrate  44  which has 20 μM thick top silicon layer as the etch layer  40  and 0.5 μm thick SiO 2  layer as the barrier layer  42 . After an optical lithography step forms a desired pattern  52  on the top  58  of the etch layer  40 , the negative fiber array template is formed in  FIG. 3( b ) . The required fiber profile shape is obtained in two steps. At first, isotropic etching is used for forming the circular supporting shape  56  of the base  14  of each fiber  10  to reduce the stress concentration for preventing the fracture of fibers  10  at their bases  14 . Next, deep reactive ion etching (DRIE) is followed for forming vertical high aspect ratio microchannels  50 . Isotropic etching and DRIE were carried out consecutively in STS Multiplex ICP RIE with 20 mT pressure, 130 sccm SF 6 , 20 sccm O 2 , 600 W coil power, and 120 W platen power. When the vertical etching reaches to the silicon oxide layer  42 , it cannot proceed vertically anymore and then starts to expand laterally  54  on the oxide interface between the etch layer  40  and the barrier layer  42 . This effect is called the notching effect [M. E. McNie, D. O. King, V. Nayar, M. C. L. Ward, J. S. Burdess, C. Quinn, and S. Blackstone, Proc. of IEEE International SOI Conference, 60 (1997)]. By controlling the lateral etching  54  time, the spatulate tip  12  diameter is determined. Then, in  FIG. 3( c ) , the template is filled with a liquid polymer  70  under vacuum to remove not only the trapped air but also the native gas in the liquid polymer  70 , and then the polymer  70  is cured. Here, any polymer  70  (e.g. Parylene® C) or any other fiber material  70  can be also gas phase deposited inside to the template  50 . In  FIG. 3( d ) , the polymer fiber array  30  with a backing layer  32  is released by three step etching: At first, the bottom silicon layer  44  is etched away by XeF 2  dry etching; The thin oxide layer  42  is removed by buffered oxide etching (BOE); Finally, the 20 μm thick top silicon layer  40  is etched away by XeF 2  etching in around 30 minutes to release the fibers  10  with a backing layer  32 . Here, the final etching step is particularly important. Since using a wet etching technique such as KOH etching would result in clumped fibers  10  due to capillary forces during drying, XeF 2  dry etching is used to prevent any clumping issues. Moreover, since the DRIE process natively creates a hydrophobic thin submicron film  60  on the template microchannel  50  side walls during the process [A. A. Ayon, R. Braff, C. C. Lin, H. H. Sawin, and M. A. Schmidt, J. of Electrochemical Society, 146(1), 339 (1999)], each released polymer fiber  10  is expected to be coated with this hydrophobic and low surface energy thin film  26  on their side walls  16  (not at the spatulate tip  12  surface  20 ). The film  60  on the side walls of the openings  50  and the fibers  10  can be characterized as a passivation film or a fluorocarbon thin film. This very low surface energy coating  26  could reduce the cohesion of microfibers  10  significantly, and thus it could minimize any clumping during the mechanical contact of neighboring fibers  10 . 
     Besides forming the flat spatulate tips  12 , the above fabrication process has other advantages with respect to previous fibrillar adhesive fabrication methods: (1) Fiber material can be fabricated from any polymer  70  which can be in a liquid solution form or can be gas phase deposited; (2) Array  30  of fibers  10  can be fabricated in large areas up to 8 inch wafer size cost effectively using a single mask; (3) The yield is almost 100%; (4) This method can be extended to the fabrication of hundreds of nanometer diameter fibers  10  easily by using a higher resolution lithography step in  FIG. 3 a    by using phase masks or interference lithography. 
     High tensile strength elastomer polyurethane (ST-1060, BJB Enterprise) with Young&#39;s modulus of around 3 MPa was selected as the fiber adhesive material.  FIG. 5  illustrates a scanning electron microscope (SEM) (Hitachi 2460N) image of the resulting microfiber array  30  with 4.5 μm fiber diameter, 9 μm tip diameter, 4.5 μm base supporter diameter, 20 μm length, and 12 μm spacing between each fiber center (44% fiber tip area density). These geometries are held by 80 sec isotropic etching for the fiber base supporter structures and by 21 min 20 sec vertical etching for the fiber and spatulate tips  12 . 
     Performance of a fibrillar adhesive is characterized by its macroscale adhesion (P) and overall work of adhesion (W). To characterize these parameters for the fabricated fiber arrays  30  during adhering to a glass hemisphere, a custom tensile macroscale adhesion measurement setup was built. A glass hemisphere instead of a flat glass surface was selected as the test surface in order to have no alignment errors during the measurements. A 6 mm diameter very smooth glass hemisphere (ISP Optics, QU-HS-6) attached to a load cell (Transducer Techniques, GSO-25) was moved vertically by a motorized stage (Newport, MFA-CC) with 100 nm resolution. The hemisphere was contacted to and retracted from the fiber array sample with a pre-specified preload force and a very slow speed (1 μm/s) to minimize any viscoelastic effects. The maximum tensile force during the glass hemisphere and fiber array separation (pull-off force) gave the adhesion, and the hysteresis area between the loading and unloading curves gave the dissipated energy between the loading and unloading of the fiber array. Dividing this dissipated energy by the maximum circular contact area during loading gave W 10 . During the force measurements, an inverted microscope (Nikon Eclipse TE200) is used to measure the real circular maximum contact area between the hemisphere and the fiber array  30 . 
     Adhesion and overall work of adhesion of 15×15 mm 2  area and one mm thick ST-1060 polyurethane fiber array  30  samples and a 1 mm thick flat and smooth ST-1060 surface were measured on the glass hemisphere using the above setup. The flat polyurethane surface was used as a control substrate to show the relative enhancement of P and W by structuring the same material as a cylindrical microfiber with flat spatulate tips. Since ST-1060 is also etched slightly during the final XeF 2  dry etching step in  FIG. 1( d ) , flat sample was also exposed to XeF 2  for about 30 minutes to have the same surface roughness with the flat spatulate tip surface. 
     Using the above setup, the fiber array  30  and the glass hemisphere interface adhesion and overall work of adhesion are measured as shown in  FIG. 6 . Plots show the error bars measured from the force-distance data at two different locations on the fiber array  30  for preloads up to 25 mN. Adhesion values saturate as preload increases, and the array of fibers has around 4 times higher adhesion than the flat surface. Dividing the adhesion to the optically measured maximum circular contact area during loading, maximum adhesion pressure for the fiber array  30  can be computed as 18 N/cm 2  at a preload pressure of 12 N/cm 2 . Overall work of adhesion of the fibers  10  is five times higher than the one from the flat elastomer surface. This energy dissipation enhancement is due to the lost energy during separating the elastic and highly stretched fibers  10  from the adhered glass surface as given in (2). ST-1060 fibers stretched up to 500% strain in the experiments (observed by profile view optical imaging) which would show the reason of the enhancement of the elastic energy loss during unloading of the fibers  10 . 
     Macroscale adhesion data from the fiber array  30  in this work are compared with the previous works as given in Table 1. Table 1 is a comparison of adhesive strength among various natural and synthetic gecko inspired micro/nanofibers [Y. Zhao, T. Tong, L. Delzeit, A. Kashani, M. Meyyappan, and A. Majumdar, J. Vac. Sci. Techno. B, 24(1), 331 (2006)]. The polymer fibers  10  with spatulate tips  12  show better adhesion pressure than other synthetic gecko inspired fibrillar adhesives with no spatulate tips  12  although the single fiber  10  in this work is over 20 times thicker than the single fibers  10  which were fabricated in other works. In order to even increase the adhesion performance in this work, microfibers with tips  12  can be scaled down to hundreds of nanometers in diameter using phase mask type of sub-micron lithography techniques. In addition, N times self-similar scaling down in fiber diameter will generate {square root over (N)} times higher adhesion [E. Arzt, S. Gorb, and R. Spolenak, PNAS, 100, 10603 (2003)], and smaller fibers will need less preload than larger fibers to obtain the same adhesion. 
     
       
         
           
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 Materials &amp; Structures 
                 Macroscale Adhesion (N/cm 2 ) 
               
               
                   
               
             
            
               
                 Gecko (Tokay) foot-hairs with 
                 10 [Autumn, Nature, 405, 681 
               
               
                 spatulate tips 
                 (2000)] 
               
               
                 Silicone rubber fibers with 60 μm 
                 0.003 [Sitti, J. Adhesion Science 
               
               
                 length and 200 nm diameter 
                 and Technology, 17(5), 1055 (2003) 
               
               
                 Polyurethane fibers 20-60 μm 
                 0.5 [D. Campolo, S. Jones, and R. S. 
               
               
                 length and 200 nm diameter 
                 Fearing, Proc. of the IEEE 
               
               
                   
                 Nanotechnology Conf., 12 (2003)] 
               
               
                 Polyimide fibers with 2 μm 
                 3 [A. K. Geim, S. V. Dubnos, I. V. 
               
               
                 length and 500 nm diameter 
                 Grigorieva, K. S. Novoselov, A. A. 
               
               
                   
                 Zhukov, and S. Y. Shapoval, Nature 
               
               
                   
                 Materials, 2, 461 (2003)] 
               
               
                 Polyurethane fibers with 100 μm 
                 3.8 [M. Murphy, B. Aksak, and M. 
               
               
                 length and 25 μm diameter 
                 Sitti, Langmuir, under review (2006)] 
               
               
                 Multi-walled carbon nanotubes 
                 11.7 [Y. Zhao, T. Tong, L. Delzeit, 
               
               
                 with 40 μm length and 20-30 
                 A. Kashani, M. Meyyappan, and A. 
               
               
                 nm diameter 
                 Majumdar, J. Vac. Sci. Techno. B, 
               
               
                   
                 24(1), 331 (2006)] 
               
               
                 Polyurethane fibers with 20 μm 
                 18 
               
               
                 length, 4.5 μm diameter, and 
               
               
                 9 μm spatulate tips 
               
               
                   
               
            
           
         
       
     
     The Effect of the Backing Layer Thickness. 
     It has also be found that the thickness of the backing layer  32  has a greater effect on the performance of dry adhesives than was previously known. The effect of the backing layer  32  thickness on adhesion was investigated for single-level elastomer fibrillar adhesives  30 . Polyurethane microfiber arrays  30  with spatulated tips  12  on a 160 μm thick backing layer  32  show nine times greater adhesion strength (around 22 N/cm 2 ) than those with a 1120 μm thick backing  32 . A theoretical model is proposed to explain this difference in which very thin backing layers  32  promote equal load sharing, maximizing adhesion, while very thick backings can lead to reduced adhesion due to edge stress concentration. Therefore, backing layer  32  thickness should be considered as a significant parameter for design of high performance fibrillar adhesives. 
     As discussed above, the adhesion of biologically inspired fibrillar dry adhesive has been studied extensively in combination with developments of various fabrication methods. Based on dominant forces of van der Waals [K. Autumn, M. Sitti, Y. A. Liang, A. M. Peattie, W. R. Hansen, S. Sponberg, T. W. Kenny, R. Fearing, J. N. Israelachvili, and R. J. Full, PNAS, 99, 12252 (2002)] and possibly capillary [G. Huber, H. Mantz, R. Spolenak, K. Mecke, K. Jacobs, S. N. Grob, and E. Artz, PNAS, 102(45), 16293 (2005)] forces, vertical cylindrical micro/nanofiber arrays [A. K. Geim, S. V. Dubnos, I. V. Grigorieva, K. S. Novoselov, A. A. Zhukov, and S. Y. Shapoval, Nature Materials, 2, 461 (2003)] were proposed as fibrillar adhesives at first. Design parameters for these fibers were proposed as the fiber radius, aspect ratio [C. Greiner, A. del Compo, and E. Arzt, Langmuir, 23, 3495 (2007)], tip shape [H. Gao and H. Yao, PNAS, 101, 7851 (2004)], and material properties [K. Autumn, C. Majidi, R. E. Groff, A. Dittmore, and R. Fearing, J. Exp. Biol., 209, 3558 (2006)]. Inspired by footpads of various animals in nature such as insects and geckos, spatulated tips on single-level cylindrical [S. Kim and M. Sitti, Applied Physics Letters, 89, 261922 (2006)][N. J. Glassmaker, A. Jagota, C-Y. Hui, &amp; J. Kim, J. R. Soc. Interface, 1, 22 (2004)], angled [B. Aksak, M. P. Murphy, and M. Sitti, Langmuir, 23, 3322 (2007)] and hierarchical [N. J. Glassmaker, A. Jagota, C-Y. Hui, W. L. Noderer, M. K. Chaudhury, PNAS, 104, 10786 (2007)][A. del Campo and E. Arzt, Molecular Bioscience, 7(2), 118 (2007)] fibers were introduced for developing high performance fibrillar adhesives. In addition, one of the recent findings demonstrates that the real contact perimeter is a more important geometrical factor governing adhesion than the real contact area [M. Varenberg, A. Peressadko, S. Gorb, and E. Arzt, Applied Physics Letters, 89, 121905 (2006)]. However, the role of backing layer  32  thickness on adhesion has not been investigated in detail so far. 
     The backing layer  32  thickness effect on adhesion of elastomeric single-level microfiber structures  30  will now be described. Although a thick backing layer  32  improves the roughness adaptation and fiber  10  contact abilities due to increased effective compliance, this study shows that a thick backing layer  32  could reduce the macroscale adhesion of the fibers  10  on smooth surfaces significantly. 
     We measured the pull-off force of single-level elastomer fiber array  30  samples with different backing layer  32  thicknesses and developed a theoretical model to explain the observed results. Polyurethane (ST-1060, BJB Enterprise) fiber array  30  samples with spatulated tips  12  are fabricated using the procedure reported in S. Kim and M. Sitti, Applied Physics Letters, 89, 261922 (2006). Briefly, we first fabricate negative silicon fiber array templates using deep reactive ion etching as described hereinabove. Liquid polyurethane  70  is filled into these silicon negative templates  50  and cured. The silicon templates  50  are then etched using XeF 2 , and the fibers  10  are released. The final backing layer  32  thickness of each sample is determined by regulating the gap between the negative template and a glass slide on it. 
     All fiber arrays  30  in the samples have a stem  16  diameter of around five μm and a tip  12  and base  14  support diameter of nine μm. The total length of a fiber  10  is 20 μm and the minimum spacing between fiber centers is 12 μm as displayed in  FIG. 7( a ) . A custom tensile setup was built to measure the adhesion of the samples. The measure of adhesion in this work is the pull-off load. A silicon disk with 0.43 mm radius and nanometer scale surface roughness was fabricated by patterning a polished silicon (100) wafer using optical lithography and deep reactive ion etching. The silicon disk was attached to a load cell (Transducer Techniques, GSO-25), and moved vertically by a motorized stage (Newport, MFA-CC) with 100 nm resolution. The disk was contacted to and retracted from the fiber array sample with specified preload forces and a slow speed (1 μm/s) to minimize viscoelastic effects. The maximum pull-off force was recorded. In addition, the contact area and the deformation of fiber array  32  during loading and unloading was recorded using a camera (Dage-MT1, DC330) attached to an inverted optical microscope (Nikon, Eclipse TE200). 
     Adhesion of four samples with 160, 280, 630, and 1120 μm backing layer  32  thicknesses was measured and is shown in  FIG. 7( b ) . Pull-off forces were measured at five different locations on each fiber array  30  for a preload of ten mN. The sample with the thinnest backing layer  32  (160 μm) showed the highest adhesion, with average pull-off force about nine times greater than that of the 1120 μm layer  32 . 
     Our interpretation of this surprising finding, that reduced compliance enhances adhesion, lies in the idea that a thinner backing layer  32  promotes equal sharing of the load by the fibers  10 . As shown schematically in  FIG. 8( a ) , if a displacement  8  were applied to three fibers  10  on an infinitesimally thin backing layer  32 , each one would experience the same vertical tension, F y1 . If the fiber pulled-off at a characteristic force F f =k f δ f  where k f  is the stiffness of the fiber  10  and δ f  is the fiber  10  elongation at pull-off, then the pull-off force of the system would be 3F f . If the thin layer  32  were replaced by a very thick backing  32  ( FIG. 8( b ) ), the y-direction forces would be F y1 =k f δ and F y2 =k f δ+F B  where F B  is the additional force required to keep the tip  12  attached to the disk due to non-uniform deformation of the backing layer  32 . Because the backing layer  32  is elastic, F B =αk f δ for some positive α. The two fibers  10  on the side will pull-off when k f δ+F B =F f  and the total force at pull-off would be (3−α)F f . 
     To quantify this idea for a large number of fibers  10  in contact, we note that the spacing of the fibers  10  are typically very small in comparison with the contact radius a and the thickness of the elastic layer h. Hence, we can treat these fibers  10  as a foundation consisting of elastic springs between the rigid indenter and the backing layer  32 . The foundation can support a normal stress σ, which is related to the displacement of foundation, d by σ=kd where k is the stiffness of the foundation. Note that d is the difference in normal displacement between the surface of the indenter and the backing layer  32 . The stiffness can be determined by assuming that the fibers  10  are bars with height L and effective cross-sectional area A eff , k=ρEA eff /L where ρ is the number of fibrils per unit area. From the known geometry and stiffness of the fibers, k=2.37×10 −10  N/m 3    
     where ρ=1/(12×10 −6 ) 2  fibers/m 2 , E=3 MPa, A eff =πr 2 , r=2.5 μm, and L=14 μm. 
     The maximum pull-off force occurs in the equal load sharing (ELS) regime, where all the fibers in adhesive contact with the indenter bear the same load. To see how ELS depends on the backing layer thickness and the contact area, assume that all the fibers in contact are in this regime, so at pull-off, we have
 
σ f   kδ   f   (3)
 
     In the ELS limit, the maximum pull-off force F max  is directly proportional to the contact area,
 
 F   max =πα 2 σ f   (4)
 
     where a is the radius of the disk. The ELS limit is strictly valid if the backing layer thickness h is very small compared to a. Another limit is a very thick backing layer with very stiff fibers, that is, when h/aΘ∞ and α≡ka/2G is very large where G is the shear modulus. In this limit, the interfacial displacement is dominated by the deformation of the elastic layer and the stress distribution is given by the classical solution of a rigid punch in contact with a half space [K. L. Johnson, Contact Mechanics, Cambridge University Press (1985)]. The normal stress at the punch edge has a square root singularity characteristic of an opening crack. For α&gt;&gt;1 and h/a&gt;&gt;1, the pull-off force F ad  in this limit can be derived as
 
 F   ad =4 F   max /(2πα) 1/2   (5)
 
     This equation shows that, given F max , the maximum extent of strength reduction can be predicted. The data in  FIG. 7( b )  show a decrease in pull-off force with increasing thickness. Theoretically, in the limit of very small thickness, pull-off force should asymptotically approach the ELS limit, which depends on the unknown fiber pull off stress, σ f . In this limit, the pull-off load is significantly affected by variability in σ f . This is reflected in the scatter of the pull-off force data associated with the sample with the smallest h/a. 
     The theoretical problem of determining pull-off forces as a function of α and h/a is more involved and will be addressed in a future work. 
     In summary, polyurethane microfiber arrays  30  with spatulated tips  12  on 160 μm thick backing layer  32  show adhesion strength (around 22 N/cm 2 ), nine times greater than fiber arrays  30  with thickness of 1120 μm. A theoretical model is proposed to explain this difference in which very thin backing layers  32  promote equal load sharing, maximizing adhesion. In the other extreme, very thick backings  32  can lead to reduced adhesion, because of edge stress concentration similar to a rigid punch in adhesive contact with a half space. This work shows the significance of backing layer  32  thickness on equal load sharing of single-level microfiber arrays  30  on smooth surfaces. 
     The present invention describes a method for fabrication of polyurethane elastomer microfiber arrays with flat spatulate tips. For a preload pressure of around 12 N/cm 2 , adhesion pressures up to 18 N/cm 2  and overall work of adhesion up to 11 J/m 2  are demonstrated for polyurethane fibers with 4.5 μm fiber diameter, 9 μm tip diameter, 20 μm length, and 44% fiber tip area density on a 6 mm diameter glass hemisphere. These repeatable fibrillar adhesives would have wide range of applications as space, biomedical, sports, etc. adhesives. 
     Although the present invention has generally been described in general terms and in terms of specific embodiments and implementations, the present invention is applicable to other methods, apparatuses, systems, and technologies. For example, the present invention can be used with a variety of materials, such as metals, ceramics, other polymers, Paralyne, carbon, crystals, liquid crystals, Teflon, semiconductors, piezoelectric materials, conductive polymers, shape memory alloy materials, and organic materials, and these and other materials could be deposited or molded inside the etch layer  40  as described hereinabove. Furthermore, the base  14  of the fibers  10  may not be necessary in some cases, in which case the base may be omitted or it may be considered to be the part of the fiber  10  attached to another structure. The spatulate tip fibers  10  with or without a hydrophobic surface coating can be used as a superhydrophobic surface where the water contact angle could be increased more due to spatulate tip geometry and fiber spacing. During the fiber tip formation (etching), if the etching time is long enough the tip endings could combine and fibers with a continuous flat thin-film can be formed as another type of fiber based adhesives or materials. Different fiber cross-section geometry (square, ellipsoid, triangle, etc.), base geometry (pyramid, etc.), tip diameter, fiber packing geometry (hexagonal or square), high or low aspect ratio, and constant or variable fiber density is possible with the present invention. Although the etch layer removal has generally been described in terms of a dry etch process, it is still possible to use a wet etching method according to the present invention. The spatulate fibers  10  can be used as static friction enhancing materials in addition to enhanced adhesion materials. Micro or nanoscale patterning methods such as interference lithography, electron-beam lithography, nanoimprinting, directed self-assembly, dip pen lithography, laser micro- or nano-machining, micro/nano-milling, and extreme UV lithography can be used to pattern the etch layer for fabricating micro- or nanoscale fibers with spatulate tips. 
       FIG. 9  illustrates the stem-fiber angle δ and the tip wedge angle α. The stem-fiber angle δ and the tip wedge angle α are controlled angles during the silicon removal process. The range of these angles is 1-180 degrees and 1-179 degrees, respectively. Stem-fiber angle δ is the angle between the stem outer surface  16   b  and the tip outer surface  12   b , which varies depending on the location of the point along the tip outer surface  12   b . Tip wedge angle α is the angle between the tip outer surface  12   b  and the tip flat surface  20 , which varies depending on the location of the point along the tip outer surface  12   b . The three illustrations of the fiber  10  show tips  12  with different tip heights (h 1 , h 2 , h 3 ) and tip diameters or cross sections (d 2 , d 3 , d 4 ) relative to stems  16  with the same stem diameter or cross section (d 1 ). Any ratio of diameters to height are acceptable. The tips  12  can have a curvature (as shown in the figures) or a straight line (not shown) between the tip flat surface edge (or outer perimeter of the tip diameter)  20   a  and the junction  16   a  of tip  12  and stem  16 . The angles are controlled during the silicon removal process. After the vertical removal process reaches to the silicon oxide (barrier) layer, these angles could be controlled by specifically tuning and controlling the silicon removal step duration, removal ion type, and removal ion energy level parameters. 
       FIGS. 11A and 11B  illustrate where the cross sectional area of the stem of the plurality of fibers includes a plurality of cross sectional areas along the longitudinal length, where the plurality of cross sectional areas comprise a first cross sectional area smaller than a second cross sectional area to form a non-uniform stem diameter along the longitudinal length.  FIG. 11B  illustrates the first cross sectional area is adjacent to the backing layer  14  and the second cross sectional area is adjacent to the tip  12  of the each fiber  16  of the plurality of fibers.  FIG. 11A  illustrates the first cross sectional area is adjacent to the tip  12  of the each fiber  16  of the plurality of fibers and the second cross sectional area is adjacent to the backing layer  14 .  FIGS. 11A and 11B  provide examples and are not meant to limit the present invention. The non-uniform cross-sectional areas can also be applied to single-level fiber embodiments (shown in  FIGS. 1, 2, 8, and 10 ), and to second layer smaller fibers  110 . 
       FIG. 13  illustrates the second plurality of fibers having oblique angles relative to the tip including an angle between the tip of the each fiber of the secondary plurality of fibers and the stem of the each fiber of the secondary plurality of fibers not being equal to 90 degrees. 
     The examples provided herein are illustrative and not limiting, and other variations and modifications of the present invention are contemplated. Those and other variations and modifications of the present invention are possible and contemplated, and it is intended that the foregoing specification and the following claims cover such modifications and variations.