Abstract:
A method is disclosed of implementing lens elements or lens arrays having dimensions ranging from a few centimeters down to the micro-scale or nano-scale using the surface tension of the lens material in a molten state to allow the curved shape of the lens to be precisely defined. The method has useful application in the fabrication of lens elements and lens arrays out of a large variety of material types, including elemental materials, as well as compound materials and alloys. The method also allows the implementation of lenses having far superior surface smoothness compared to other approaches, as well as very accurate lens shapes. The method allows the making of high quality lenses and lens arrays, wherein the diameter of the lenses are on the order of a few microns or less. Convex, concave, plano-convex, plano-concave, compound lenses, and many other types of lens shapes can be implemented using the method of the present invention.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application claims the benefit of Provisional Application No. 61/071,777, filed May 16, 2008, the entire contents of which are hereby incorporated by reference in this application. 
     
    
     FIELD OF INVENTION 
       [0002]    The present invention relates to lenses, and, more particularly, to a method of implementing lens elements or lens arrays having dimensions ranging from a few centimeters down to the micro- or nano-scale using the surface tension of the lens material in a molten state to allow the curved shape of the lens to be precisely defined. 
       BACKGROUND OF THE INVENTION 
       [0003]    The making of lenses and lens arrays is an extremely important part of modern technology, particularly in optics and photonics. Lenses at the macro-scale (i.e., a few centimeters in diameter or larger) can be made using a variety of methods, including various machining methods (e.g., diamond turning, etc.), molding, embossing, etc., to obtain adequately high levels of precision for most applications. The fabrication of lenses and lens arrays at the micro-scale is a more recent development and has become a very important part of modern semiconductor manufacturing. These micro-lenses and micro-lens arrays are typically made using specialized semiconductor processes to allow the implementation of lens profiles with performance far inferior to that of similar types of lenses made at the macro-scale. These methods include: photolithography of a resist pattern followed by a re-flow of the resist and a subsequent Reactive Ion Etching (RIE) of the underlying substrate to form a curved and smooth lens shape; gray-scale lithography followed by a RIE; micromachining fabrication of a tool mold having the lens pattern on it followed by hot embossing or molding of a material into the lens shape; the direct micromachining of a substrate surface using a focused ion beam (FIB); etc. 
         [0004]    While these methods have allowed the implementation of lenses and lens arrays at the small dimensional size, including the micro-scale, they have several shortcomings. First, these methods involve fabrication processes that are extremely difficult to control or to obtain reproducible results from batch to batch. As a result, the yield of these methods can be quite low with the resultant consequence of higher cost components. Second, most of these processes result in some significant distortions of the lens shapes with negative consequences for the performance of the lenses or lens arrays. Third, the surface smoothness of RIE etched or FIB machined surfaces are typically very rough (e.g., more than a few nanometers) which degrade the performance of the lens elements due to photon scattering as well as other effects. Fourth, the use of a FIB tool to make lenses is an extremely slow process, is performed on a very expensive tool, and is, therefore, an extremely expensive method to make lenses and lens arrays. Fifth, the use of molding and embossing allows the high cost of the tool mold to be amortized over many parts, so as to obtain a relatively low cost method for making lenses and lens arrays; however, molding and embossing is an elevated temperature process, and the materials used in these processes tend to have large thermal expansion coefficients, thereby resulting in lens shapes that distort as the lens material cools back to room temperature. Sixth, none of the methods discovered to date allow the fabrication of extremely small-dimensioned lenses and lens arrays. The existing methods are limited to lenses having a diameter of at least tens to hundreds of microns, or more. Seventh, as the lower limit of the dimensions that lenses and lens arrays can be fabricated using existing methods are approached, the distortions on the shape of the lenses, surface roughness of the lens, as well as other quality aspects of the lens increasingly and quickly degrade. Consequently, there is an enormous opportunity for a new technique, whereby lenses and lens arrays can be fabricated that have excellent optical properties. 
       SUMMARY OF THE INVENTION 
       [0005]    It is, therefore, an object of the present invention to provide a method for the fabrication of singular lens elements or lens arrays. 
         [0006]    It is another object of the present invention to provide a method for the fabrication of singular lens elements or lens arrays having small dimensions, specifically from a few millimeters in diameter down to a few tens of nanometers in diameter. 
         [0007]    It is another object of the present invention to provide a method for the fabrication of singular lens elements or lens arrays using the surface tension of the lens material to form the correct lens shape. 
         [0008]    It is another object of the present invention to provide a method for the fabrication of singular lens elements or lens arrays out of a large variety of different elemental or compound materials. 
         [0009]    It is another object of the present invention to provide a method for the fabrication of singular lens elements or lens arrays that are either of the concave or convex lens type. 
         [0010]    It is another object of the present invention to provide a method for the fabrication of singular lens elements or lens arrays that are either of the plano-concave or plano-convex lens type. 
         [0011]    It is another object of the present invention to provide a method for the fabrication of singular lens elements or lens arrays that are of the compound lens type. 
         [0012]    It is another object of the present invention to provide a method for the fabrication of singular lens elements or lens arrays that are of the positive meniscus or negative meniscus lens type. 
         [0013]    It is another object of the present invention to provide a method for the fabrication of singular lens elements or lens arrays that allows extremely smooth surface finishes. 
         [0014]    It is another object of the present invention to provide a method for the fabrication of singular lens elements or lens arrays having excellent optical properties and also low manufacturing costs. 
         [0015]    It is another object of the present invention to provide a method for the design and fabrication of singular lens elements or lens arrays with predictable, but arbitrary shaped curved surfaces. 
         [0016]    It is another object of the present invention to provide a method for the fabrication of singular lens elements or lens arrays for applications at the extreme short wavelengths, such as the near ultra-violet, extreme ultra-violet, or x-ray wavelengths. 
         [0017]    These and other objectives are realized in the present invention by using a novel and very flexible fabrication methodology combined with innovative design improvements. The present invention results from surface tension effects that are common when two different materials come into contact and one of the materials is heated to above its melting point. 
         [0018]    The present invention relates to lenses, and, more particularly, to a method of making lens elements or lens arrays having dimensions ranging from a few centimeters down to the micro-scale or nano-scale using the surface tension of the lens material in a molten state to allow the curved shape of the lens to be precisely defined. The method of the present invention has useful application in the fabrication of lens elements and lens arrays out of a large variety of material types, including elemental materials, as well as compound materials and alloys. Furthermore, the method of the present invention allows the implementation of lenses having far superior surface smoothness compared to other approaches, as well as very accurate lens shapes. There are many benefits provided by the method of the present invention, including low cost, high level of accuracy and surface smoothness, etc. But importantly, the method of the present invention is the only method available for making high quality lenses and lens arrays in which the diameters of the lenses are on the order of a few microns or less. Convex, concave, plano-convex, plano-concave, compound lenses, and many other types of lens shapes can be made using the method of the present invention 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0019]      FIGS. 1   a  and  1   b  are cross sectional illustrations of a convex (converging) lens element and a concave (diverging) lens element, respectively. 
           [0020]      FIG. 2  is a cross sectional illustration of several types of simple lenses. 
           [0021]      FIG. 3  is a scanning electron micrograph of a microlens array. 
           [0022]      FIG. 4  is an illustration of surface tension effect of a liquid placed onto the surface of another material with the contact angle being shown. 
           [0023]      FIGS. 5   a  and  5   b  are an illustration of a fabrication process according to the present invention for making a concave lens. 
           [0024]      FIG. 6   a  and  6   b  are an illustration of a fabrication process according to the present invention for making a convex lens. 
           [0025]      FIGS. 7   a - 7   d  are an illustration of a fabrication process according to the present invention for making a concave lens array. 
           [0026]      FIGS. 8   a - 8   d  are an illustration of a fabrication process according to the present invention for making a convex lens array. 
           [0027]      FIGS. 9   a - 9   d  are an illustration of a fabrication process according to the present invention for making a refractive plano-concave lens array type. 
           [0028]      FIGS. 10   a - 10   d  are an illustration of a fabrication process for making a refractive lens from ruthenium for an Extreme Ultraviolet system. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0029]    The present invention is directed to a method of fabricating lens elements and lens arrays using the surface tension of the lens material(s) to develop a desired lens surface contour or shape and thereby make a high performance refractive lens. A variety of different types of lenses can be fabricated using the method of the present invention, including concave or convex lenses, as well as many others types of lenses. Additionally, lens arrays composed of a multiplicity of lens elements can also be made using the method of the present invention. Furthermore, the method of the present invention allows the fabrication of lens elements and lens arrays having an unprecedented small lateral lens diameter, as well as extremely smooth surface finishes, which is not possible with existing methods of lens and lens array fabrication. The present invention also provides an extremely low cost and relatively simple production method for lens elements and lens arrays, as compared to existing methods. 
         [0030]      FIGS. 1   a  and  1   b  illustrate two common types of lens elements that are used to transmit and refract radiation so as to concentrate or diverge an electromagnetic radiation beam. Specifically,  FIGS. 1   a  and  1   b  are cross sectional illustrations of a convex (converging) lens element  10  and a concave (diverging) lens element  12 , respectively. These lens elements are composed of materials that have a differing index of refraction, as compared to the surrounding medium (usually air or free space, but possibly a liquid in some special circumstances). Electromagnetic radiation  14  propagates through the surrounding medium and impinges onto either converging lens element  10  or diverging lens element  12 , each of which has perfect or approximate axial symmetry and transmits and refracts the radiation  14 . The radiation  14  continues through the lens element  10  or  12  and exits the other side. The differing index of refraction between the lens material and the surrounding medium combined with the curvature of the lens results in the bending of the radiation either toward the center axis of converging lens element  10  or away from the center axis of diverging lens element  12 . The shapes of lenses shown in  FIGS. 1   b  and  1   a  are concave and convex, respectively, which results in the radiation passing through the lens to become diverging  16  or converging  18 , respectively. 
         [0031]    As shown in  FIGS. 11 and 1   b,  the focal length of a lens in free space can be calculated using lens equation 1 below: 
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         [0000]    where: f is the focal length of the lens; n is the index of refraction of the lens material; R 1  is the radius of curvature of the lens surface closest to the light source; R 2  is the radius of curvature of the lens surface farthest from the light source; and d is the thickness of the lens (the distance along the lens axis between the two surface vertices). 
         [0032]    If the lens thickness is small compared to the radii of curvature, R 1  and R 2 , then lens equation 1 can be simplified by the so-called thin lens equation 2, given by: 
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         [0033]    The focal length is positive for converging lenses and negative for diverging lenses and the optical power of a lens is given by 1/f. 
         [0034]      FIG. 2  illustrates the common types of simple lenses, which are classified according to the curvature of the two optical surfaces. A lens is termed bi-convex if both surfaces are convex, as shown. A lens  22  is termed “bi-concave” if both of its surfaces are concave, as shown. If one of the two surfaces is flat and the other surface is curved, the lens is termed plano-convex (lens  24 ) or plano-concave (lens  26 ), depending on the curvature of the non-flat surface. If the two surfaces are curved, with one surface being convex and the other surface being concave, if the concave surface has a greater radius than that of the convex surface, the lens  28  is termed “positive meniscus”. Conversely, if the convex surface has a radius greater than that of the concave surface, the lens  30  is termed “negative meniscus”. 
         [0035]      FIG. 3  is a Scanning Electron Micrograph (SEM) of an array  40  of microlenses  42  made using standard microfabrication techniques. This lens array  40  was made by photolithography on the surface of a substrate, followed by a plasma reaction ion etching of the surface to form the curved surface of each of the microlenses  42 . 
         [0036]      FIG. 4  is an illustration of a liquid droplet on a solid surface  52  displaying the effect of contact angle and wetting. When the liquid droplet  50 , solid surface  52  and ambient gas (e.g., air) are brought into contact with one another, intermolecular interactions between and within these materials result. The amount of wetting depends on the energies (or surface tensions) of the interfaces involved, such that the potential energy is minimized. The degree of wetting is described by the contact angle  54 , which is the angle at which the liquid-vapor interface meets the solid-liquid interface. If the wetting is very favorable, the contact angle  54  will be low (e.g., approximately 0 degrees), and the fluid will spread to cover a larger area of the surface  52 . If the wetting is unfavorable, the contact angle  54  will be large (e.g., approximately 150 to 180 degrees), and the fluid will form a compact droplet  50  on the surface. Regardless of the amount of wetting, the shape of a drop wetted to a rigid surface is approximately a truncated sphere. 
         [0037]    A contact angle of 90° or greater generally characterizes a surface as not-wettable, and one less than 90° as wettable. When the liquid is water, a wettable surface is termed hydrophilic and a non-wettable surface as hydrophobic. Superhydrophobic surfaces have contact angles greater than 150°, showing almost no contact between the liquid drop and the surface. 
         [0038]    The effects of surface tension, contact angle and wetting are used in the method of the present invention to fabricate lenses and lens arrays, as described below. 
         [0039]    In general, the surface tension, contact angle and wetting all depend on the liquids and solids and surrounding medium (usually air), as well as temperature, pressure, and external forces (i.e., gravity, electrical field, etc.). A set of thermodynamic equations can be used to predict the contact angle of the liquid/solid interface. 
         [0040]    The shape of the lens can be predicted using these equations of thermodynamics as follows. The Young equation 3 is given by: 
         [0000]      0=γ SV −γ SL −γ LG  cos Θ c ,   Eq. 3 
         [0000]    where γ SV  is the solid-vapor interfacial energy, γ SL  is the solid-liquid interfacial energy, γ LG  is the liquid-gas interfacial energy, and Θ c  is the equilibrium contact angle. This equation 3 assumes a perfectly flat surface  52 . Knowing the respective interfacial energies allows the contact angle  54  to be calculated, and thereby, the shape and type of the lens to be designed and fabricated, as desired. 
         [0041]      FIGS. 5   a  and  5   b  are an illustration of one method or process of the present invention to fabricate a single lens element. The process begins with the making of a hole  60  in a layer of material  62 . The method for making the hole  60  varies, depending on the size of the hole, as well as the materials from which the substrate  62  is made. One method is to perform photolithography on a thin device layer, resulting in a pattern transfer from a photo mask to a resist layer mask on the surface of the device layer. 
         [0042]    Subsequently, the device layer is etched using Reactive Ion Etching (RIE) or a similar technique that allows the hole  60  to be precisely etched, even if the hole dimensions are relatively small. After the etching is completed, the material  64  from which the lens  66  is to be made is deposited on to the substrate  62  so as to leave the material  64  in the hole  60  as shown in  FIG. 5   a.  For example, this may be accomplished using a lift-off procedure. Subsequently, the substrate  62  is then heated to a temperature at which the lens material  64  becomes molten and changes its shape based on the surface tension and contact angle between it and the substrate material it is in contact with, as shown in  FIG. 5   b.  The substrate  62  is then cooled to room temperature to solidify the lens material  64  and retain the lens shape  66 . 
         [0043]    The lens  66  made by the fabrication process shown in  FIGS. 5   a  and  5   b  is a concave lens type, and is a result of the lens material  64  in the molten liquid state wetting the surface  68  of the substrate  62 . A convex lens  72  shape can also be fabricated using a similar method by employing a lens material  70  that, in the molten state, has a large contact angle with respect to the substrate material  62 , as shown in  FIGS. 6   a  and  6   b.    
         [0044]    The shape of the lens  66  or  72  is controlled by several parameters, including: the contact angle of the lens material  64  or  70  in the molten state on the substrate material  62 ; the amount of lens material deposited into the hole  60  prior to the melting process; the diameter of the hole  60  made in the substrate; the temperature of the process; and the pressure of the process. Gravity forces may also be a consideration if the lens is of sufficient size, but for small-dimensioned lenses, gravity will have a negligible effect. Also, external forces, such as an applied electrical field, may be used to control the shape of the lens element made using this technique. The shape of the lens can be designed as desired using the Young equation 3 set forth above. 
         [0045]    Importantly, this technique does not require the etching, machining, or other similar types of processes on a lens material to form the lens shape, and therefore, avoids the problems of surface defects and roughness that significantly degrade the quality and performance of lenses made with other methods. Using the method of the present invention allows the lens surface to be exceptionally smooth, and, therefore, to have unprecedented optical performance. This is a result of the surface energy minimization that is inherent in this technique, wherein the surface will assume the smoothest shape possible in order to reduce its potential energy. Any roughness of the surface would necessarily have a higher energy state than a smooth surface. 
         [0046]      FIGS. 7   a - 7   d  illustrate one method of fabricating a microlens array  80  using the method of the present invention. A substrate  86  with a material layer  84  is provided, as in  FIG. 7   a.  An array of holes  82  is made in material layer  84  on substrate  86 , as shown in  FIG. 7   b.  The holes  82  are then filled with a lens material  88 , as shown in  FIG. 7   c.  Subsequently, a portion of the substrate  86  is released from underneath the array of holes  82  filled with the lens material  88 , as shown in  FIG. 7   d.  The substrate  86  is then heated to a selected temperature that causes the lens material  88  to become molten and change its shape based on the surface tension and contact angle between it and the material layer  84  it is in contact with, as shown in  FIG. 7   d  in order to form the shape of the plurality of lens elements  89  forming the lens array  80  shown in  FIG. 7   d.  In this example, the material layer  84  and the lens material  88  are selected so that the lenses  89  are all concave. 
         [0047]      FIGS. 8   a - 8   d  illustrate one method of fabricating another microlens array  90  using the method of the present invention. Here again, a substrate  96  with a material layer  94  is provided, as in  FIG. 8   a.  An array of holes  92  is made in material layer  94  on substrate  96 , as shown in  FIG. 8   b.  The holes  92  are then filled with a lens material  98 , as shown in  FIG. 8   c.  Subsequently, a portion of the substrate  96  is released from underneath the array of holes  92  filled with the lens material  98 , as shown in  FIG. 8   d.  The substrate  96  is then heated to a selected temperature that causes the lens material  98  to become molten and change its shape based on the surface tension and contact angle between it and the material layer  94  it is in contact with, as shown in  FIG. 8   d  in order to form the shape of the plurality of lens elements  99  forming the lens array  90  shown in  FIG. 8   d.  In this example, the material layer  94  and the lens material  98  are selected so that the lenses  99  are all convex. 
         [0048]      FIGS. 9   a - 9   d  illustrate one method of fabricating a plano-concave lens array  100  using the method of the present invention. A substrate  106  with a material layer  104  is provided, as in  FIG. 9   a.  An array of holes  102  is made in material layer  104  on substrate  106 , as shown in  FIG. 9   b.  After the holes  102  are made in the material layer  104 , a spacer layer  103  is deposited in the holes  102 , followed by the deposition of the lens material layer  104 . Subsequently, a portion of the substrate  106  is released from underneath the array of holes  102  filled with the lens material  108 , as shown in  FIG. 9   d.  The substrate  106  is then heated above the melting temperature of the lens material  108 , whereupon the lens material  108  through surface tension and contact angle between it and the material layer  104  it is in contact with forms the desired smooth contour of a plano-concave lens  109 . The substrate  106  and spacer layers  103  are removed, thereby leaving a plano-concave lens type  109 , as shown. Obviously, a plano-convex lens, a plano-concave lens array, or a plano-convex lens array can be made using similar methods. 
         [0049]    Importantly, the present invention provides a method for making lenses and lens arrays having low cost, as well as excellent performance. Furthermore, the present invention is not as constrained on dimensional size as the existing methods of fabricating lenses and lens arrays. Specifically, the fabrication of microlenses and microlens arrays is presently restricted to lenses wherein the diameter is on the order of several tens of microns or larger, with hundreds of microns being more common. One reason for this is that the existing techniques for fabricating lenses result in surface roughness, as well as shape distortions that become greater as the size of the lens is decreased. Therefore, lenses made with the existing techniques having dimensions below a few hundred microns have sub-standard performance. The present method can be used to make lower cost and higher performance lenses and lens arrays having dimensions comparable to other techniques (i.e., a few centimeters to tens of microns), but also can be used to fabricate lenses and lens arrays having dimensions that have unprecedented small dimensions (e.g., tens of microns and below). 
         [0050]    The ability to make extremely small refractive lenses fulfills the needed application for manipulating short wavelength radiation, particularly in the Near Ultraviolet, (NUV), the Extreme Ultraviolet (EUV), and the X-Ray wavelengths, which have wavelengths that range from a few microns to a few nanometers. In these applications, refractive lenses are very difficult and costly to make, and the lens diameters may be very small (e.g., a lens diameter not much larger than the wavelength). However, conventional techniques to fabricate lens elements at these wavelengths result in rough surfaces and non-optimal shapes, which severely degrade the performance of these lenses. 
         [0051]    An example of such a refractive lens is shown in  FIGS. 10   a - 10   d,  which illustrate the fabrication of a refractive lens, wherein the lens material is ruthenium (Ru) and is designed to be used in an Extreme Ultraviolet (EUV) application, such as a EUV photolithographic system for next generation semiconductor integrated circuit fabrication. The method illustrated in  FIGS. 10   a - 10   d  is similar to that described for  FIGS. 7   a - 7   d,  in that a substrate  116  is provided with a material layer  114  and array of holes  112  in material layer  114 . After the holes  112  are made in the material layer, a portion of the substrate  116  is released from underneath the holes, whereupon the substrate  116  is heated above the melting temperature of the lens material  118  so that the lens material through surface tension and the contact angle between it and the material layer forms the desired convex lenses. It should be noted that other shaped lenses can be made using the method of the present invention. 
         [0052]    It is understood that the present disclosure conveys the most significant attribute of the present invention, that is, the use of surface tension effects of a material in a molten state on a solid surface that has been specifically machined to form a smooth and desired lens shape. Moreover, the present disclosure describes a few of the specific methods to implement different lens structures and types. However, it is also understood that the present invention is not limited only to the specific methods described herein and is equally applicable to any method using surface tension to form a lens or lens array. 
         [0053]    While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiments, it is to be understood that the invention is not to be limited to the disclosed embodiments, but on the contrary, is intended to cover various modifications and equivalent arrangements of the disclosed embodiments.