AND NANOFEATURES USING GAS EXPANSION AND DEFORMABLE,

HARDENABLE MEDIA, AND ARTICLES MADE BY SUCH METHODS

by

Mary Bee Eng Chan, Xun Guo, Soon Fatt Yoon and Jung-Hoon Chun

Related Document

[0001] Priority is hereby claimed to provisional U.S. Patent application No. 60/664,258, filed on March 21, 2005, entitled METHOD TO FABRICATE MICROFEATURES WITH CONTINUOUS RELIEF which is incorporated herein fully by reference.

Background

[0002] A convenient and inexpensive fabrication method of 3-D curved structures at the micrometer (microstructures) and nanometer (nanostructure) scale, with controllable curvature and cross-sectional geometry, would be important to many applications, including: telecommunication, miniaturized total analytical systems, TV display and projection systems, biological devices and microelectromechanical systems (MEMS) based sensors. Other methods to produce very small, variable curvature and cross-section, such as: resist reflow of patterns; gray mask photolithography; ion beam milling or laser writing; ink jet printing; self-assembly of polymer beads; and electrowetting, suffer from some disadvantages. Some techniques (e.g. ink jet printing or electrowetting) can produce lens-like structures with circular cross-sections only. Ink jet printing and resist reflow suffer from limitations of fixed curvature or small variations in curvatures. Gray mask photolithography and beam milling require using expensive facilities.

[0003] Nano-scale or nano-structures as used herein means features that have a characteristic size of between about 10

and microscale as used herein means features that are larger than nanoscale but smaller than millimeter scale. Characteristic size, as used herein means a size that reasonably represents the item being described such as a diameter of a circle, a long side of a rectangle, a depth of a hole, etc.

[0004] Grey scale lithography has been used for the production of convex structures. It is able to fabricate controllable and relatively large curvatures, but with relatively rough surface. Curved microstructures with smooth convex surfaces have also been fabricated using material melting and reflowing processes in which self-assembly, ink- jet, or photolithography has been employed to pattern the structural materials. A smooth surface is obtained because the curvature is formed naturally due to surface tension when the materials are heated over their glass transition temperature (T _g ) or even over their melting temperature and there is no hard contact to the convex surface. Besides the disadvantages resulting from the methods to pattern the materials (e.g. high cost in photolithography, large dimension deviation in ink-jet process, etc.), the curved structures fabricated by reflowing have relatively small curvatures. Further, the elevated temperature (normally at the range of 150°C-200°C) limits the usable materials . Smooth curved microstructures have also been fabricated using a hot intrusion process. In the process, plastic materials are intruded into a nickel mold which is made using LIGA processes and a curved surface is obtained when the intruded material does not fully filled the cavity in the nickel mold. In intrusion process, a pre-fabricated nickel mold is essential and the LIGA process for fabrication of the nickel mold is very costly. Further, the intruded material has to be heated over its T ₃ and high pressure is also required.

[0005] Thus, there is a need for methods to fabricate three-dimensionally curved microstructures and nanostructures that do not require extremely expensive facilities, tooling or materials. There is further a need for such a process that produces very smooth surfaces having a wide range of

controlraBlY prδaucibϊe ¹ curvature, including very small radii of curvature. There is also a need for a process to produce such articles at relatively low temperatures, under relatively low pressures. With all of these needs it would be beneficial for the method to be able to produce curvatures of differing radii, by varying readily accessible and variable parameters.

[0006] Disclosed herein are novel methods for fabricating three-dimensional (3-D) curved microstructures and nanostructures with controllable sizes of features. The disclosed methods are elegant and can be used for fabricating an array of 3-D curved microstructures and nanostructures with tunable curvature and cross-sectional geometry.

Summary

[0007] A method of fabricating three-dimensionally (3-D) curved microstructures and nanostructures uses trapped gas . For example, a microstructured tooling element such as a stamp having blind microholes (micrometer scale diameters) is placed on top of a photopolymerizable liquid resin that is non- wetting with respect to the material of the stamp. When heat is applied, the gas in the blind microholes expands due to heat transfer. The expanded gas displaces the resin at the mouth of the microholes to form 3-D curved indentations in the resin which is subsequently solidified, such as by rapid photopolymerization. By changing factors, such as the duration of the pre-heating, different depths, or curvatures can be produced. Several arrays of homogeneous 3-D curved microstructures and nanostructures having different cross- sectional geometries were fabricated using various shapes of the blind holes. A model describes the preheating heat transfer process and the produced curvature of indentations. It shows that the theoretical predictions of the produced curvature of microstructures agree well with experimental data. An alternate to a photopolymer is a thermosetting polymer such as an epoxy-, an isocyanate, or moisture-curing polymer, which hardens with appropriate duration and temperature .

P[0 ¹ C00l8L]^"S"ISAOEpIta./rtJijDalOs ¹ Mu!".m3m1ary i,s provi,ded. b _η el.ow, preceding the claims .

[0009] The inventions disclosed herein will be understood with regard to the following description, appended claims and accompanying drawings , where :

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figs. 1A-1F show schematically, six stages of a procedure for fabricating extremely small structures, using a stamp placed onto a prepolymer, where, due to heat transferred into entrapped gas, expansion generates depressions, which can be used, among other uses, as a mold to replicate convex features ;

[0011] Figs. 2A and 2B are digital representations of SEM images of fabricated elements having extremely small structures, with Fig. 2A(I) showing a fabricated concave polyurethane mold with a plurality of circular depressions; Fig. 2A(II) showing a replicated convex profile made by soft lithography; Fig. 2B(I) showing a fabricated mold made using epoxy prepolymer with a pattern of a plurality of square depressions; and Fig. 2B(II) showing a replicated convex PDMS profile made with the mold shown in Fig. 2(1);

[0012] Fig. 3 shows, schematically, growth of a spherical cap due to gas expansion, with the initial radius being r ₀ , and the final equilibrium radius being r _c ;

[0013] Fig. 4 shows, graphically, heights of convex microstructures on a molded PDMS replica made from molds subjected to different preheating times, with sample population at each temperature being eight; and error bars representing one standard deviation of height of samples measured, with a small digital image of a representative sample shown adjacent each data point;

[0014] Fig. 5 is a digital representation of a microscope image of a PDMS microlens array and images, with Fig. 5A showing a lens array of convex elements; and Figs. 5B and 5C

showing images recorded with a transmission optical microscope by projection of an object ^W T" and object ^W C", as shown in insets repectively, through the array of convex lenses; and

[0015] Fig. 6 is a schematic representation of a stamp and a corresponding mold with elongated channels, made from the stamp according to a method of an invention hereof.

Detailed Discussion

[0016] Fig. 1 shows six stages, A, B, C, D, E and F, which outline schematically fabrication steps of an embodiment of a method invention hereof, which embodiment is based on heated gas expansion and photopolymerization. At stage A, a prepolymer holder was made by cutting a piece of Teflon film (of about 2mm thick) with a 30mm x 30mm opening and gluing it at the bottom of a petri dish 102, using double sided tape. A photopolymerizable prepolymer target material 104 (described in detail, below) was filled flush into the petri dish 102, forming a planar surface 106. The prepolymer 104 was degassed in a vacuum oven (not shown) (0 atmospheric pressure at 25°C) for 30 minutes to remove trapped air.

[0017] As shown at stage B, in a glove box 108 filled with argon of gauge pressure about 0-lmbar, a piece of transparent PolyDiMethylSiloxane (PDMS) forms a stamp 110 with an array of ~200μm deep blind-holes 112a, 112b, 112c, bounded by lands 114a, 114b, etc., which are all in a plane 116. A blind hole, as used herein, is a hole that forms a shaft or well, having an open end and a closed end. The stamp was gently brought into contact with the prepolymer 104. It was found to be advantageous to contact the petri dish with one side, e.g. 114a touching the mouth 118 of the petri dish 102 first and tilting the stamp 110 gradually, to minimize gas trapped at the interface between the stamp surface 116 and the prepolymer surface 106. The two surfaces 106 and 116 were mated. Inert gas, such as argon gas was thus entrapped in the capped blind- holes 112a, 112b, 112c formed between the stamp 110 and the prepolymer 104 surface 106.

_U fo'&ϊϊϊ ^{'" !Ll} Hlt' ^r Pl3yy ^t! star|) 110 was prepared by soft lithography from either a deep reactive ion etched silicon master mold or a SU-8 photolithographically formed master mold. Any other suitable method for forming an appropriately shaped stamp would be possible.

[0019] Subsequently, as shown at stage C, the assembly with the stamp 110 and the prepolymer 104 in the dish 102 was moved into a small photopolymerization chamber 120 below a ultraviolet (UV) lamp 126 (a 400 W PK 102 UV lamp with 365nm wavelength, I & J Fishnar) . This chamber had an internal hotplate to maintain the temperature of the chamber at 65 ⁰ C. A glass plate 122 (5mm in thickness) heated to 65 ⁰ C was placed on top of the PDMS stamp 110 to pre-heat it for about 15 seconds before UV irradiation started, as shown in stage D.

[0020] Pre-heating of the PDMS stamp 110 heats the argon gas trapped within the stamp holes 112a, 112b, 112c, increasing its pressure, which in turn produces indentations (also referred to herein as depressions) 130a, 130b, 130c into the deformable prepolymer 104. Below, a model of the dependence of the indentation depth on the stamp pre-heating process parameters is shown for a circular stamp hole case. As shown in stage E, after UV polymerization, the PDMS stamp 110 was peeled off and the photopolymerized polymer mold 105 (no longer a prepolymer) was ultrasonically cleaned in acetone, ethanol and deionized water each for three minutes. Finally, as shown in stage F, the photopolymerized polymer mold 105, with 3-D curved microstructures 131a, 131b, 131c, was used as a mold for soft lithography as described in Y. Xia, G. M. Whitesides, Annu. Rev. Mater. Sci. 1998, 28, 153 and J. L. Wilbur, R. J>. Jackman, G. M. Whitesides, Chem. Mater. 1996, 8, 1380, order to replicate complementary convex features 171a, 171b, 171c in a molded article 172.

[0021] As used herein, a stamp means a tooling element having a substantially planar surface, configured to mate with a free, substantially planar surface of a volume of a hardenable material. The planar surface of the stamp has open

riPeCgi.Ton,/sU.iSTrliJeGo,/pe,ln,iQrQegNiro..5ns are arranged, x.n .locations where it is desired to create one or more depressions in the product made using the stamp. The shape of the open regions and the relative arrangement thereof define the shapes and relative arrangement of depressions in the product 172 made using the stamp.

[0022] Figs. 2A and 2B show digital representations of SEM images of a fabricated sheet 228 of 3-D curved concave microstructures, such as at 131a, 131b, 131c and their convex replications, such as at 171a, 171b, 171c, using stamps with circular and square cross-section blind-holes. The mold 228 shown in Fig. 2A was fabricated by a stamp with circular cross-section blind-holes with a characteristic size of 80μm in diameter spaced 80μm apart using a polyurethane (PUR) based prepolymer. In one experiment, the blind holes ranged from 5 to 56 μm deep. Fig. 2A(I) illustrates the generated concave polyurethane microstructure mold depressions 231a, 231b, the diameter of which are 84μm, slightly larger than that of the 80μm blind-hole in the stamp (not shown) . Fig. 2A(II) shows the lens-like convex profiles 271a, 271b, of the PDMS body 272, molded from the polyurethane microstructures 231a, 231b in the mold 228 shown in Fig. 2A (I) .

[0023] Fig. 2B (I) shows a sheet 248 of epoxy photopolymerized concave microstructures, formed from a stamp (not shown) with square cross-section blind-holes having a characteristic size side length of about 60μm (60μm by 60μm) . The molded convex epoxy relief cross-section 241a, 241b, is about 65μm by 65μm. Fig. 2B (II) shows a PDMS replica 258, with convex features 281a, 281b molded from the mold 248 shown in Fig. 2B (I) . The polyurethane and epoxy microstructured depressions, 231a, 241a, respectively, have high homogeneity with less than 10% replication error.

[0024] In general, each depression has a bottom surface having a contour having a shape of a portion of a surface of a gas bubble formed in the formerly deformable hardened material .

P[0C02T5/] USTOhGe /ab1o.0ve0e ¹ Mxi-3amples were carried out in an inert atmosphere, such as an argon gas to prevent any undesireable reactions that might prevent obtaining a very clean, smooth surface. However, there may be reactions that are desireable, because, for example, they may produce a surface texture having an extremely small grain. In such a case, an appropriately reactive atmosphere can be used.

Materials

[0026] The PDMS silicon rubber was RTV 651 which has two parts - the base and the curing agent manufactured by GE Silicones. The process used was as recommended by the manufacturer. If not specified, the chemicals used as components of UV curable prepolymer were purchased from UCB Chemicals. The PolyUrethane pre-polymer formulation consists of four components: EB 270 - an aliphatic urethane acrylate aliphatic, trimethylolpropane triacrylate (TMPTA) from Sartomer Chemicals, EB 350 - a silicone diacrylate release additive, and Irgacure 651 (i.e., 2, 2-dimethoxy-2- phenylacetophenone) supplied by Ciba Chemicals as photoinitiator. The ratio of these components is 68/30/2/0.2 by weight. The preparation followed the published procedure, in H. P. Herzig, Micro-optics: Elements, Systems and Applications, Taylor & Francis, London 1997. The epoxy prepolymer consists of EB 600, TMPTA and Irgacure 651 blended with a ratio of 68/32/0.2 by weight. EB 600 is a bisphenol-A epoxy diacrylate.

[0027] Turning now to a model relating the depression depth of the deformable material, and the stamp preheating parameters, the following simplifying assumptions were made: (1) there is no mass transfer between the gas and the stamp or the prepolymer: (2) work involved in compression and displacement of the prepolymer is inconsequential to the final equilibrium state; (3) the depression 130a is spherical, forming a "cap" at the aperture of the stamp opening 112a; and (4) the prepolymer behaves as a Newtonian liquid.

[002S1 As shown schematically m Fig. 3, the dynamics of the gas/prepolymer spherical interface is described by the modified Rayleigh equation:

where r is the radius r of the spherical cap 130 as shown in Fig. 3, t is the time, and AP is the pressure drop across the gas/prepolymer interface, "approximately given by the difference between the pressure of gas (argon) , P ₃ and the ambient pressure, P _a . (See W. V. Pinczewski, Chem. Eng. Sci . , 1981, 36, 405, K. Terasaka, H. Tsuge, Chem. Eng. Sci., 1991, 46, 85, H. Z. Li, Chem. Eng. Sci., 1999, 54, 2247, R. J. Albalak, Fundamental of Bubble Growth, Polymer Devolatilization, M. Dekker, New York, 1996) . The viscosity, density, and surface tension of prepolymer 104 are μ _L , p _L , and σ _L , respectively. The three terms in the right hand side of equation (1) represent the effects of inertial force, surface tension and viscous force, respectively. The modified Rayleigh equation is not strictly applicable to this problem, because the speed of motion of the moving "bubble" center represented by the dark circle at the head of the arrows r ₀ , r, and r _c , is comparable to the rate of change (rate of decline in this case) of the bubble radius. It is not, however, of interest to model the precise dynamics of the indentation; rather, the Rayleigh equation is used to: (1) define the equilibrium condition of the fully-indented prepolymer and (2) define the indentation timescale for comparison with other timescales of the problem (namely the heat transfer timescale) . For these purposes, the modified Rayleigh equation is adequate.

-t0029] It is convenient to re-express equation (1) in a dimensionless form. The equilibrium radius r _e , of the

2σ. spherical cap 130, defined by r = —-, provides a natural ^e AP

4μ _r length scale. The quantity t _o ≡-—^- provides a natural timescale t ₀ for the approach to the equilibrium radius; it is also called the time scale for viscous relaxation effect.

_ T

Introducing the dimensionless coordinate r ≡— and the

_ t dimensionless time coordinate t ≡— , and dividing by AP yields

a dimensionless form of the modified Rayleigh equation,

where E ₁ ≡ —ψ^~ parameterizes the relative importance of the ¹ 4μ _L ² AP inertia and viscosity terms. The parameters used in the calculation are summarized in Table 1.

Table 1. Parameters used in calculation

[0030] In the present problem, the ratio of the inertia parameter over viscosity, ξ _∑l is small (about 5.11 x 10 ^"5 ) so that the dynamics is dominated by viscosity. The timescale, t ₀ for the approach of the radius to equilibrium is short, of about 5.3 milliseconds. This timescale is much shorter than the heat conduction timescale (to be discussed below) . Thus, it is reasonable to treat the pre-polymer indentations 130a, 130b, as being instantaneously in equilibrium with the temperature-dependent pressure in the stamp holes 112a, 112b.

[0031] It is reasonable to model heating of the stamp 110 with a standard semi-infinite plane approximation (thus treating the prepolymer as an extension of the stamp 110 for this purpose) . A standard analysis of heat conduction theory gives the instantaneous temperature penetration T ₃ at depth x and time t in PDMS under such a situation

where T _c is the temperature of oven for heating the prepolymer 104, T ₀ is the room temperature, erf(x) is an error function, and α is the thermal diffusivity of PDMS. Then the temperature of the trapped gas in the indentation 130, T _b can be approximately estimated by setting the depth x as d ₀ (the thickness of the PDMS stamp 114 as shown in Fig. ID), which yields

[0032] The heat conduction timescale is of order,

2a which is about 9s, much longer than the viscous relaxation time of the bubble/polymer interface. Thus the bubble radius is approximately stationary during photopolymerization.

[0033] The indentation of the bubble into the prepolymer 104 also increases the volume of the trapped gas, with a consequent reduction in the ideal gas law pressure. Putting all this together gives a model relation for the bubble radius, r(t) as a function of the heating time:

where R and Η are the radius of mouth and the depth of blind- holes in PDMS stamp, respectively as shown in Fig. 3 and r is the same as r(t), which varies with time.

[0034] Basic geometric inspection of Fig. 3 yields that, for the indentation radius, r

R ² + h ² r=——— . (6)

2h

PΓ T / u s o s ./ ^•■ ' ,1 o o H-3

[0035] Equations (4), (5) and (6) together provide a model relating the indentation depth (h) to the duration t of the pre-heating temperature prior to photopolymerization.

[0036] To test this model, a series of experiments with epoxy prepolymer were performed, with fixed experimental parameters other than the pre-heating time. The heights of the convex features on molded PDMS replicas were measured by stylus profile meter (Z560, Silicon Instrument) to be from 8 to 20 μm and are shown graphically and by digital images of SEM pictures in Fig. 4. The SEM pictures demonstrate the profile of the lens-like structures for different preheating times .

[0037] The model predictions are also plotted. The model captures the trend of curvature produced as exemplified by depression depth and replica height. This suggests that the developed model, though basic and approximate, does a remarkably good job of predicting the process behavior.

[0038] Argon gas was used instead of air to avoid an inhibition effect of oxygen on free radical photopolymerization. Initially experiments in air were attempted, but, after UV irradiation, there was always a tacky uncured polymer layer on the surface of produced polymeric microstructures . Acetone cleaning of this layer caused non- uniformity of the concave features. The argon gas environment improves the uniformity of the features.

[0039] One issue associated with fabrication is the capillary effect at the mouths of the blind holes when the PDMS stamp is in contact with the prepolymer. The capillary effect induces flow of prepolymer up into the blind holes (which is the opposite of the desired ultimate identation effect) . Such capillary effect relates to the cross-sectional diameter of the capillary, surface tension of the liquid and contact angle between liquid and solid. For fixed dimensions of holes, possible ways to reduce the capillary effect include: using materials with low surface energy for the stamp; or low surface tension for the prepolymer; or both.

IPCT"/ ^v USOB/,10ONI-3

Here, PDMS was used in the experiments as the stamp material, due to its relatively low surface free energy. The ring-like structures 452, 454 (Fig. 4) surrounding the lens-like structures 471a, 471b were due to the capillary effect. The prepolymer used was an epoxy. The prepolymer contains EB 350, which is a silicone diacrylate, widely used as a release agent, to decrease the surface tension of prepolymers . As shown by the SEM images in Fig. 4, the ring-like edge structures 452, 454 occurred in the short preheating time of 17 seconds or less (corresponding to relatively low heated temperature/pressure) . For longer preheating times greater than 21 seconds, the relatively high temperature/pressure not only lowers the surface tension of the prepolymer but also hinders the filling of prepolymer into the stamp hole. Nonetheless, the experimental results indicate that the capillary effect causes some prepolymer to fill into the stamp hole, but such effect is insignificant, especially for long preheating times.

[0040] One useful application of an article having a plurality of convex very small features is as a microlens or nanolens array. The soft lithographically replicated transparent PDMS convex features in Fig. 5(A) were molded from a concave mold made according to the method of an invention hereof, discussed above, and used as a microlens array to form images of a pattern in a transmission microscope (AXiovert 200, Carl Zeiss), with an object (~3cm by 3cm characters of "C" and "T" cut on a piece of black paper). Fig. 5(A) shows the lens array with nothing projected through. Shown in Fig. 5 (B) and (C) are images of ^W T" and "C" patterns projected through the fabricated microlens array. The microlens array is able to project sharp and well-focused images with approximately the same high quality. This implies that the curvatures in the convex features have the identical focal length (i.e. the radius of curvature) in a single array.

[0041] Variations on the methods described above may be applied. The target medium used above has been most frequently described as a photopolymerizable polymer. Other media may be

, ~T/UGOS./.1OpMKB used. What is required, in general, is that the medium be deformable enough to be deformed by the elevated pressure within the closed off blind ended cavity, and hardenable over a time scale short enough to become hard during a time that makes economic sense for a commercial production process.

[0042] Another example is an epoxy-based medium, such as an Epon brand epoxies with amine hardeners available from Resolution Performance Products L.L.C. of Houston, Texas. Additional alternatives include but are not limited to: heat hardenable media, media that harden under other forms of light, or radiation, moisture hardenable or reaction hardenable, whether known today, or discovered or developed in the future .

[0043] The size and shape- of the depression in the article formed with a stamp can be varied in many ways . The cross- section of its opening is substantially congruent with the shape of the opening in the stamp, with some slight change in dimensions, for instance a slightly smaller perimeter in the stamp than in the formed article. The depressions can be isolated from each other, such as shown in Fig. 2A, or, the shape can be an extended figure, such as a long channel, as shown schematically in Fig. 6. Fig. 6 shows schematically, in a perspective view, a stamp 610 having elongated openings 612a, 612b, etc., separated by elongated land 614a, 614b, etc. The lands form a planar surface 616.

[0044] A formed article 605, has elongated depressions 631a, 631b, formed from expansion of gas within the space formed by elongated stamp channels 612a, and the surface of a deformable prepolymer, as discussed above. The article 605 may be used as a mold.

[0045] The extended figure can also be a spiral, or even letters of the alphabet, or a line of script. The cross- section of the depression 631b will have a generally semicircular cap shape at its bottom, as shown in Fig. 3 and Fig. 6. The shape may be somewhat distorted at spots, for instance near the corners of a depression formed with square or

rectangular open regions m the stamp. The spacing between depressions is limited primarily only by the consideration to prevent leaking of gas from the blind hole. For instance, a land that is a knife-edge would probably not provide an adequate seal .

[0046] The depth of the depression can be varied. The depth depends, as discussed, in part on the depth H of the blind hole in the stamp.

1 [0047] The depth of the depression that forms in the formed article also depends on the heating parameters, such as the duration and temperature of heating, which relates to the amount of heat transferred to the expanding gas.

[0048] The orientation of the feature of the formed product can be either concave (cup like) or convex (mound-like) . Depressions are always formed in the first instance with the opening facing the stamp (except for the small ring-like features 452 (Fig. 4) formed due to capillarity) . Typically, the formed polymeric item 105 that is made according to an invention hereof, is used as a mold for another material, which molding material is applied to the surface in which the depressions have been formed. That secondary molding material 172 may be applied so that the shape made has a protruding convex region, which is its region of importance. Or, it may be relatively thin, essentially coating the mold 105 in only a thin layer, so that a surface of the molded secondary molding material that faces away from the polymeric mold 105 forms a concavity, which is the region of importance. However, the deformable medium may be thin enough so that the mound-like side of the deformable medium may be used as the important part of such a product. Alternatively, the item formed from contact with the stamp can be the end product, with the concave depressions being the important aspect of the formed item. Or, a series of items having concave and convex curvatures can be formed as mold and molded article, in turn.

[0049] This discussion presents new methods for fabricating 3-D curved microstructures, including arrays thereof, with the

p ip x . ^■■■ it it *Q in Fu /" t ιπππi Mi« ^"::: S advantage oFlow cost and high throughput. The experimental results show that the concave profiles generated in the photopolymerized polymer are homogeneous and can produce different cross-sectional geometries (depending on the shape of the blind holes) . The depressions in the photopolymerized polymer were generated by heating gas trapped in cavities before photopolymerization. By changing the duration of the pre-heating, different curvatures and depths were produced. Theoretical analysis was conducted to analyze the indentation of a gas bubble into the prepolymer during the preheating process. Through the scaling analysis, it was determined that the contribution to the bubble indentation process due to the inertial force effect is negligible, compared to that due to the viscous force effect. Furthermore, the obtained short time scale for the viscous relaxation effect suggests the polymer indentation can be considered instantaneously in equilibrium with the temperature-dependent pressure in the stamp holes. As a result, a useful model was developed to describe the preheating heat transfer process and the produced curvature of indentations. The theoretical predictions agree well with experimental data. In addition, ring-like edge structures resulting from filling of some prepolymer into the stamp holes were observed during the short preheating time. This is largely attributed to the capillary effect. However, it was found such capillary effect is insignificant, specifically for long preheating times. Finally, the disclosed methods were implemented to fabricate microlens arrays in transparent polymers. A PDMS microlens array produced by a method of an invention hereof was found to be able to form images of high quality and uniformity across the array. Due to simplicity of the fabrication and ability to generate microscale and nanoscale curved features from a variety of patterns, other possible applications include biological sensors, and microphotonic devices, just to name two. Structures having concave or convex features at a nanometer scale may also be produced, using a stamp having blind holes on a nanometer scale.

Wo ^' sϋl and described herein include methods of making articles having very small (nano-scale and microscale) features, such as depressions, and methods for using the formed item as a mold of additional molded products. Inventions hereof also include the formed articles, which may be molds and items molded from such molds, either as first generation molded elements or subseuquent generations.

[0051] Thus, this document discloses many related inventions .

[0052] One invention disclosed herein is a method for fabricating an article having a plurality of very small geometric features, comprising the steps of: providing a quantity of a deformable, hardenable target material, having a substantially planar surface; providing a stamp comprising a substantially planar solid surface having a plurality of very small scale open regions; contacting the planar surface of the stamp to the planar surface of the target material; maintaining conditions such that at substantially each open region, a depression forms in the planar surface of the deformable material which is concave facing the stamp; maintaining conditions such that the target material hardens with the depression formed therein, thereby forming the article; and removing the stamp from contact with the target material . The depressions may have a nanometerscale characteristic dimension or larger, such as up to micrometer scale, such as from 10 nanometers to up to about 300 micrometers .

[0053] According to one embodiment, the open regions are substantially circular openings. Or, they may have a rectangular cross-section, or a cross-section of virtually any shape. They may be elongated channels, such as parallel rows, or a spiral .

[0054] According to preferred embodiments, the plurality of open regions comprise closed end wells, also known as blind holes, of substantially equal depths. The wells may have substantially equal radii.

[0055] According to a related embodiment, the depressions can have substantially equal depths.

[0056] According to yet another preferred embodiment, the step of maintaining conditions such that a depression forms comprises increasing pressure adjacent substantially each open region, thereby deforming the deformable medium to form the depression. The step of increasing pressure may comprise preventing escape of gas from a volume that forms between the stamp and the deformable medium, at the open region. The step of increasing pressure may comprise maintaining the stamp and deformable medium in contact as gas evolves from the deformable medium. Alternatively, or in addition, the step of increasing pressure may comprise providing heat to the deformable medium.

[0057] According to still another embodiment the plurality of open regions can comprise closed end wells of unequal depths. The depressions may then have unequal radii. And, the depressions may have unequal depths.

[0058] With a basic embodiment, the target material comprises an ultraviolet light hardening prepolymer, and the step of maintaining conditions such that the target material hardens comprises applying light to the target material.

[0059] For a related embodiment, the target may comprise an epoxy hardening material, or a radiation hardening material, or a heat hardening material. ,

[0060] Various preferred embodiments include the target material comprising a liquid, a liquid and solid mixture, a liquid and gas mixture, or a viscous material.

[0061] A related embodiment to any of the above embodiments further comprises the step of providing molding material into the depressions of the formed article, thereby forming a molded article having features that correspond to the depressions. The molded article may comprise a lens array, comprising a plurality of convex lens elements, which

. Alternatively, the molded article may comprise a plurality of concave lens elements, which correspond to the depressions.

[0062] Yet another preferred embodiment comprises conducting the steps in an inert gas environment. Or, the steps may be conducted in a reactive gas environment, which may create a surface having a very fine texture.

[0063] A related embodiment further comprises the step of controlling the amount of heating provided to the deformable media by providing more heat to generate relatively deeper depressions in the deformable medium. More heat can be provided by heating for a longer period of time, or, by providing more heat flow per unit of time.

[0064] By a similar embodiment, the step providing a stamp may comprise providing a stamp with relatively deeper holes to generate relatively deeper depressions in the deformable median.

[0065] According to another preferred embodiment, an invention disclosed herein is a method for fabricating an article having at least one very small geometric feature, comprising the steps of: providing a quantity of a deformable, hardenable target material, having a substantially planar surface; providing a stamp comprising a substantially planar solid surface having at least one very small scale open region; contacting the planar surface of the stamp to the planar surface of the target material; maintaining conditions such that at substantially each at least one open region, a depression forms in the planar surface of the deformable material which is concave facing the stamp; maintaining conditions such that the target material hardens with the depression formed therein, thereby forming the article; and removing the stamp from contact with the target material. The depression may have a nanometerscale characteristic dimension or larger, such as up to micrometer scale, such as from 10 nanometers to up to about 300 micrometers.

_ _

[0U66J ^'"' " Tne""at ^" least one depression may be an elongated straight channel or channels, or a spiral channel.

[0067] With a similar embodiment, the step of maintaining conditions such that a depression forms may comprise increasing pressure adjacent the open region, thereby deforming the deformable medium to form the depression. The step of increasing pressure may comprise preventing escape of gas from a volume that forms between the stamp and the deformable medium, at the open region. More specifically, the step of increasing pressure may comprise maintaining the stamp and deformable medium in contact as gas evolves from the deformable medium. Or the step of increasing pressure may comprise providing heat to the deformable medium. The target material may comprise an ultraviolet light hardening prepolymer. In that case, the step of maintaining conditions such that the target material hardens may comprise applying light to the target material. An especially helpful way to do this is with the stamp comprising a light transparent material, the step of applying light to the target material comprising applying light through the stamp toward the target material.

[0068] As with the other embodiments discussed above, the target material may comprise a material that hardens from exposure to heat, radiation, moisture, reactive chemicals, time, or may be an epoxy hardening material.

[0069] Further, with various embodiments, the target material may be a liquid, a liquid and solid mixture, a liquid and gas mixture, or viscous.

[0070] With any embodiment discussed, a further embodiment further includes the step of providing molding material into the depression of the formed article, thereby forming a molded article having features that correspond to the depression.

[0071] The steps may be conducted in an inert atmosphere or a reactive gas atmosphere, which may thereby create a surface having a very fine texture .

ffeI]' ^' " ^S EMIa ^C yS ^lll tlse erαbcdiments further, the step of controlling the amount of heating provided to the deformable media is conducted by providing more heat to generate a relatively deeper depression in the deformable medium.

[0073] In connection with another embodiment, the step of providing a stamp comprises providing a stamp with a relatively deeper hole to generate a relatively deeper depression in the deformable median.

[0074] A slightly different, yet related embodiment is an article having a plurality of very small geometric features formed by a process comprising the steps of: providing a quantity of a deformable, hardenable target material, having a substantially planar surface; providing a stamp comprising a substantially planar solid surface having a plurality of very small scale open regions; contacting the planar surface of the stamp to the planar surface of the target material; maintaining conditions such that at substantially each open region, a depression forms in the planar surface of the deformable material which is concave facing the stamp; maintaining conditions such that the target material hardens with the depression formed therein, thereby forming the article; and removing the stamp from contact with the target material .

[0075] With this embodiment, as with those discussed above, the depression may have a characteristic dimension on the scale of from 10 nanometers to 300 μm, in either range of between 10 and 100 nanometers or 100 nanometers and 300 μm.

[0076] The depressions may have any cross-sectional shape, including circular, rectangular, square, or any, just to name a few. Or, they may comprise elongated channels, or a single elongated channel either straight or spiral, or any other elongated shape .

[0077] The stamp by which this embodiment of an article was made may comprise one or a plurality of open regions comprising closed end wells of substantially equal depths.

EJ.rT /1 FBO6/1.0OH-3 . , _{η n} . tOU78] For several related important embodiments, the depressions may have substantially equal radii cross-section, or radii of curvature at their bottoms. Their depths may be substantially equal, or unequal.

[0079] With some embodiments, the article comprises hardened ultraviolet light hardening prepolymer, or hardened epoxy hardening material, or a hardened radiation hardening material .

[0080] Regarding the phase of the materials, the article may comprise a material hardened from a liquid, or a liquid and solid mixture, or a liquid and a gas mixture, or a viscous material .

[0081] An article of an invention hereof comprises a lens array, comprising a plurality of convex or concave lens elements, which correspond to the depressions.

[0082] Moreover, the article may have a surface having a very fine texture, formed by conducting the step of maintaining conditions such that at substantially each open region, a depression forms in the planar surface of the deformable material which is concave facing the stamp, in a reactive gas atmosphere.

[0083] A related preferred embodiment further entails an article having a plurality of very small geometric features, comprising: a body of a hardened, formerly deformable material, having a substantially planar surface; and spaced apart on the planar surface, a plurality of very small depressions, each depression having a bottom surface having a contour having a shape of a portion of a surface of a gas bubble formed in the formerly deformable hardened material. In some circumstances, the bottom surface may have a contour that is a portion of a sphere and in some circumstances a contour that is a portion of a half-sphere.

[0084] For related embodiments, the depressions may have a perimeter that is circular, semi-circular or rectangular. The

perimeters ^" or some or all of the depressions may be congruent. The depressions may comprise depressions of substantially equal depths or of unequal depths. The hardened material may comprise a photopolymerised polymer, or an epoxy. The depressions may have a characteristic dimension of between nanometer scale and micrometer scale, from approximately 10 nanometers to 300 micrometers. They may be spaced in a regular array. The surface of the depressions may be smooth, relative to the characteristic dimension of the depression, or finely textured.

[0085] Many techniques and aspects of the inventions have been described herein. The person skilled in the art will understand that many of these techniques can be used with other disclosed techniques, even if they have not been specifically described in use together. For instance, any material that can be hardened under controlled circumstances can be used. Stamps with any pattern of openings, and any shape can be used with any type of hardenable material. More heat can be applied, either by increasing the rate heat flow, or increasing the duration of heating.

[0086] This disclosure describes and discloses more than one invention. The inventions are set forth in the claims of this and related documents, not only as filed, but also as developed during prosecution of any patent application based on this disclosure. The inventors intend to claim all of the various inventions to the limits permitted by the prior art, as it is subsequently determined to be. No feature described herein is essential to each invention disclosed herein. Thus, the inventors intend that no features described herein, but not claimed in any particular claim of any patent based on this disclosure, should be incorporated into any such claim.

[0087] Some assemblies of hardware, or groups of steps, are referred to herein as an invention. However, this is not an admission that any such assemblies or groups are necessarily patentably distinct inventions, particularly as contemplated by laws and regulations regarding the number of inventions

43 invention. It is intended to be a short way of saying an embodiment of an invention.

[0088] An abstract is submitted herewith. It is emphasized that this abstract is being provided to comply with the rule requiring an abstract that will allow examiners and other searchers to quickly ascertain the subject matter of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims, as promised by the Patent Office's rule .

[0089] The foregoing discussion should be understood as illustrative and should not be considered to be limiting in any sense. While the inventions have been particularly shown and described with references to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the inventions as defined by the claims.

[0090] The corresponding structures, materials, acts and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or acts for performing the functions in combination with other claimed elements as specifically claimed.

[0091] What is claimed is: