Abstract:
A carrier with ultraphobic surfaces for promoting more effective cleaning and drying of the carrier. In the invention, entire surfaces or portions of surfaces of a carrier are made ultraphobic. The ultraphobic surfaces of the carrier cause liquids that may come in contact with the surface, such as may be used in cleaning, to quickly and easily “roll off” without leaving a liquid film or substantial number of liquid droplets. As a result, less time and energy is expended in drying the surfaces, and redeposited residue is minimized, thereby improving overall process quality. In addition, the ultraphobic surfaces may be resistant to initial deposition of contaminants, where the contaminants may be in liquid or vapor form.

Description:
RELATED APPLICATIONS  
       [0001]    This application claims the benefit of U.S. Provisional Patent Application Serial No. 60/462,963, entitled “Ultraphobic Surface for High Pressure Liquids”, filed Apr. 15, 2003, hereby fully incorporated herein by reference. 
     
    
     
       FIELD OF THE INVENTION  
         [0002]    The present invention relates generally to carriers for delicate electronic components, and more particularly to a carrier having ultrahydrophobic or ultralyophobic surfaces formed thereon.  
         BACKGROUND OF THE INVENTION  
         [0003]    The process of forming semi-conductor wafers or other delicate electronic components into useful articles requires high levels of precision and cleanliness. As these articles become increasingly complex and miniaturized, contamination concerns grow. Contamination problems are reduced by providing controlled fabrication environments known as “clean rooms”. Such clean rooms are protected from chemical and particulate contamination to the extent technically and economically feasible.  
           [0004]    While clean rooms substantially remove most contaminants found in ambient air, it is often not possible or advisable to completely process components in the same clean room environment. Moreover, not all contamination and contaminants are eliminated. For that and other reasons, delicate electronic components are transported, stored, and fabricated in bulk using protective carriers. Examples of specialized carriers are disclosed in U.S. Pat. Nos. 6,439,984; 6,428,729; 6,039,186; 6,010,008; 5,485,094; 5,944,194; 4,815,601; 5,482,161; 6,070,730; 5,711,427; 5,642,813; and 3,926,305, all assigned to the owner of the present invention, and all of which are hereby fully incorporated herein by reference. For the purposes of the present application, the term “carrier” includes, but is not limited to: semiconductor wafer carriers such as H-bar wafer carriers, Front Opening Unified Pods (FOUPs), and Standard Mechanical Interface Pods (SMIFs); reticle carriers; and other carriers used in the micro-electronic industry for storing, transporting, fabricating, and generally holding small electronic components such as hard drive disks and other miscellaneous mechanical devices.  
           [0005]    Contamination and contaminants can be generated in many different ways. For example, particulates can be generated mechanically by wafers as they are inserted into and removed from wafer carriers, and as doors are attached and removed from the carriers, or they can be generated chemically in reaction to different processing fluids. Contamination can also be the result of out-gassing on the carrier itself, biological in nature due to human activity, or even the result of improper or incomplete washing of the carrier. Contamination can also occur on the exterior of a carrier as it is transported from station to station during processing.  
           [0006]    Process contaminants and contamination may be reduced by periodically washing and/or cleaning carriers. Typically, a carrier is cleaned of contaminants and contamination by placing it in a cleaning apparatus, which subjects the exterior and interior surfaces to a flood or spray of cleaning fluids. After the washing step, a considerable amount of fluid may remain on the carrier. This residual fluid is typically dried with a stream of dry gas or by centrifugal spinning.  
           [0007]    Carriers often have intricate arrangements of surfaces that are difficult to dry. In addition, a residual amount of the cleaning fluid may adhere to the surfaces of a carrier as a film or in a multiplicity of small droplets after the washing step. Any contaminants suspended in the residual cleaning fluid may be redeposited on the surface as the fluid dries, leading to contaminant carryover when the carrier is reused. Consequently, process efficiency and effectiveness is diminished overall.  
           [0008]    What is still needed in the industry is a carrier with features that promote more effective cleaning and drying of the carrier with reduced levels of residual process contamination.  
         SUMMARY OF THE INVENTION  
         [0009]    The present invention includes a carrier with ultraphobic surfaces for promoting more effective cleaning and drying of the carrier. In the invention, entire surfaces or portions of surfaces of a carrier are made ultraphobic. The ultraphobic surfaces of the carrier cause liquids that may come in contact with the surface, such as may be used in cleaning, to quickly and easily “roll off” without leaving a liquid film or substantial number of liquid droplets. As a result, less time and energy is expended in drying the surfaces, and redeposited residue is minimized, thereby improving overall process quality. In addition, the ultraphobic surfaces may be resistant to initial deposition of contaminants, where the contaminants may be in liquid or vapor form.  
           [0010]    In a particularly preferred embodiment of the invention, the ultraphobic surface includes a multiplicity of closely spaced microscale to nanoscale asperities formed on a substrate. For the purpose of the present application, “microscale” generally refers to dimensions of less than 100 micrometers, and “nanoscale” generally refers to dimensions of less than 100 nanometers. The surface is designed to maintain ultraphobic properties up to a certain predetermined pressure value. The asperities are disposed so that the surface has a predetermined contact line density measured in meters of contact line per square meter of surface area equal to or greater than a contact line density value “Λ L ” determined according to the formula:  
         Λ   L     =       -   P       γ                   cos        (       θ     a   ,   0       +   ω   -     90   ∘       )                                 
 
           [0011]    where P is the predetermined pressure value, γ is the surface tension of the liquid, and θ a,0  is the experimentally measured true advancing contact angle of the liquid on the asperity material in degrees, and ω is the asperity rise angle. The predetermined pressure value may be selected so as to be greater than the anticipated liquid pressures expected to be encountered during cleaning or use of the carrier.  
           [0012]    The asperities may be formed in or on the substrate material itself or in one or more layers of material disposed on the surface of the substrate. The asperities may be any regularly or irregularly shaped three dimensional solid or cavity and may be disposed in any regular geometric pattern or randomly. The asperities may be formed using photolithography, or using nanomachining, microstamping, microcontact printing, self-assembling metal colloid monolayers, atomic force microscopy nanomachining, sol-gel molding, self-assembled monolayer directed patterning, chemical etching, sol-gel stamping, printing with colloidal inks, or by disposing a layer of carbon nanotubes on the substrate.  
           [0013]    Alternatively, randomly patterned surfaces may be produced by any of a variety of known processes, including chemical vapor deposition (CVD) or chemical modification processes such as cold gas plasma or corona discharge treatments.  
           [0014]    The invention may also include a process for producing a carrier with surfaces having ultraphobic properties at liquid pressures up to a predetermined pressure value. The process includes steps of selecting an asperity rise angle; determining a critical contact line density “Λ L ” value according to the formula:  
         Λ   L     =       -   P       γ                   cos        (       θ     a   ,   0       +   ω   -     90   ∘       )                                 
 
           [0015]    where P is the predetermined pressure value, γ is the surface tension of the liquid, and θ a,0  is the experimentally measured true advancing contact angle of the liquid on the asperity material in degrees, and ω is the asperity rise angle; providing a carrier with a surface portion; and forming a multiplicity of projecting asperities on the surface portion so that the surface has an actual contact line density equal to or greater than the critical contact line density.  
           [0016]    The process may further include the step of determining a critical asperity height value “Z c ” in meters according to the formula:  
         Z   c     =       d        (     1   -     cos        (       θ     a   ,   0       +   ω   -     180   ∘       )         )         2                 sin                   (       θ     a   ,   0       +   ω   -     180   ∘       )                               
 
           [0017]    where d is the distance in meters between adjacent asperities, θ a,0  is the true advancing contact angle of the liquid on the surface in degrees, and ω is the asperity rise angle in degrees. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0018]    [0018]FIG. 1 a  is a perspective view of one embodiment of a carrier with ultraphobic surfaces thereon according to the present invention;  
         [0019]    [0019]FIG. 1 b  is a perspective view of an alternative embodiment of a carrier with ultraphobic surfaces thereon according to the present invention;  
         [0020]    [0020]FIG. 1 c  is a perspective view of another alternative embodiment of a carrier with ultraphobic surfaces thereon according to the present invention;  
         [0021]    [0021]FIG. 1 d  is a perspective view of yet another alternative embodiment of a carrier with ultraphobic surfaces thereon according to the present invention;  
         [0022]    [0022]FIG. 1 e  is a perspective, enlarged view of an ultraphobic surface according to the present invention, wherein a multiplicity of nano/micro scale asperities are arranged in a rectangular array;  
         [0023]    [0023]FIG. 2 is a top plan view of a portion of the surface of FIG. 1;  
         [0024]    [0024]FIG. 3 is a side elevation view of the surface portion depicted in FIG. 2;  
         [0025]    [0025]FIG. 4 is a partial top plan view of an alternative embodiment of the present invention wherein the asperities are arranged in a hexagonal array;  
         [0026]    [0026]FIG. 5 is a side elevation view of the alternative embodiment of FIG. 4;  
         [0027]    [0027]FIG. 6 is a side elevation view depicting the deflection of liquid suspended between asperities;  
         [0028]    [0028]FIG. 7 is a side elevation view depicting a quantity of liquid suspended atop asperities;  
         [0029]    [0029]FIG. 8 is a side elevation view depicting the liquid contacting the bottom of the space between asperities;  
         [0030]    [0030]FIG. 9 is a side elevation view of a single asperity in an alternative embodiment of the invention wherein the asperity rise angle is an acute angle;  
         [0031]    [0031]FIG. 10 is a side elevation view of a single asperity in an alternative embodiment of the invention wherein the asperity rise angle is an obtuse angle;  
         [0032]    [0032]FIG. 11 a partial top plan view of an alternative embodiment of the present invention wherein the asperities are cylindrical and are arranged in a rectangular array;  
         [0033]    [0033]FIG. 12 is a side elevation view of the alternative embodiment of FIG. 11;  
         [0034]    [0034]FIG. 13 is a table listing formulas for contact line density for a variety of asperity shapes and arrangements;  
         [0035]    [0035]FIG. 14 is a side elevation view of an alternative embodiment of the present invention;  
         [0036]    [0036]FIG. 15 is a top plan view of the alternative embodiment of FIG. 14; and  
         [0037]    [0037]FIG. 16 is a top plan view of a single asperity in an alternative embodiment of the present invention. 
     
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0038]    [0038]FIG. 1 a  depicts, in exemplary fashion, an embodiment of a carrier  12  according to the present invention. Carrier  12  generally includes a body portion  13  in the form of an enclosure  14 , with a top  14   a , a bottom  14   b , a pair of opposing sides  14   c ,  14   d , a back  14   e , and an open front  14   f . Open front  14   f  may be selectively closable by means of a door  15 . Within enclosure  14 , one or more device support portions  16 , in the form of wafer supports  17 , are provided to support wafers in a parallel, spaced apart, relationship to each other. Carrier  12  may have other components or portions for facilitating its use in a process, such as for example, a kinematic coupling portion  18 , and a robotic handling flange  19 .  
         [0039]    Ultraphobic surface  20  may be formed on the entire surface of carrier  12  or on any desired portion thereof. Thus, ultraphobic surfaces may be placed in critical locations of the carrier  12  while other portions have conventional surfaces. Ultraphobic surfaces  20  may be formed in any of a variety of configurations and using a variety of processes as described hereinbelow.  
         [0040]    Various other embodiments of carriers are depicted in FIGS. 1 b - d . In each of these embodiments, ultraphobic surfaces  20  may be formed where desired on the carrier  12 .  
         [0041]    Surfaces resistant to wetting by liquids may be referred to as hydrophobic where the liquid is water, and lyophobic relative to other liquids. The surface may be generally referred to as an ultrahydrophobic or ultralyophobic surface if the surface resists wetting to an extent characterized by any or all of the following: very high advancing contact angles of liquid droplets with the surface (greater than about 120 degrees) coupled with low contact angle hysteresis values (less than about 20 degrees); a markedly reduced propensity of the surface to retain liquid droplets; or the presence of a liquid-gas-solid interface at the surface when the surface is completely submerged in liquid. For the purposes of this application, the term ultraphobic is used to refer generally to both ultrahydrophobic and ultralyophobic surfaces.  
         [0042]    An enlarged view of one preferred embodiment of an ultraphobic surface  20  according to the present invention is depicted in FIG. 1 e . The surface  20  generally includes a substrate  22  with a multiplicity of projecting asperities  24 . Each asperity  24  has a plurality of sides  26  and a top  28 . Each asperity  24  has a width dimension, annotated “x” in the figures, and a height dimension, annotated “z” in the figures.  
         [0043]    As depicted in FIGS. 1 e - 3 , asperities  24  are disposed in a regular rectangular array, each asperity spaced apart from the adjacent asperities by a spacing dimension, annotated “y” in the figures. The angle subtended by the top edge  30  of the asperities  24  is annotated ψ, and the rise angle of the side  26  of the asperities  24  relative to the substrate  22  is annotated ω. The sum of the angles ψ and ω is 180 degrees.  
         [0044]    Generally, surface  20  will exhibit ultraphobic properties when a liquid-solid-gas interface is maintained at the surface. As depicted in FIG. 7, if liquid  32  contacts only the tops  28  and a portion of the sides  26  proximate top edge  30  of asperities  24 , leaving a space  34  between the asperities filled with air or other gas, the requisite liquid-solid-gas interface is present. The liquid may be said to be “suspended” atop and between the top edges  30  of the asperities  24 .  
         [0045]    As will be disclosed hereinbelow, the formation of the liquid-solid-gas interface depends on certain interrelated geometrical parameters of the asperities  24 , the properties of the liquid, and the interaction of the liquid with the solid surface. According to the present invention, the geometrical properties of asperities  24  may be selected so that the surface  20  exhibits ultraphobic properties at any desired liquid pressure.  
         [0046]    Referring to the rectangular array of FIGS. 1 e - 3 , surface  20  may be divided into uniform areas  36 , depicted bounded by dashed lines, surrounding each asperity  24 . The area density of asperities (δ) in each uniform area  36  may be described by the equation:  
               δ   =     1     y   2         ,           (   1   )                               
 
         [0047]    where y is the spacing between asperities measured in meters.  
         [0048]    For asperities  24  with a square cross-section as depicted in FIGS. 1 e - 3 , the length of perimeter (p) of top  28  at top edge  30 :  
           p= 4 x,   (2)  
         [0049]    where x is the asperity width in meters.  
         [0050]    Perimeter p may be referred to as a “contact line” defining the location of the liquid-solid-gas interface. The contact line density (Λ) of the surface, which is the length of contact line per unit area of the surface, is the product of the perimeter (p) and the area density of asperities (δ) so that:  
         Λ= pδ.   (3)  
         [0051]    For the rectangular array of square asperities depicted in FIGS. 1 e - 3 :  
         Λ=4 x/y   2 .  (4)  
         [0052]    A quantity of liquid will be suspended atop asperities  24  if the body forces (F) due to gravity acting on the liquid are less than surface forces (f) acting at the contact line with the asperities. Body forces (F) associated with gravity may be determined according to the following formula:  
           F=ρgh,   (5)  
         [0053]    where (ρ) is the density of the liquid, (g) is the acceleration due to gravity, and (h) is the depth of the liquid. Thus, for example, for a 10 meter column of water having an approximate density of 1000 kg/m 3 , the body forces (F) would be:  
           F =(1000 kg/m 3 )(9.8 m/s 2 )(10 m)=9.8×10 4  kg/m 2 -s.  
         [0054]    On the other hand, the surface forces (f) depend on the surface tension of the liquid (γ), its apparent contact angle with the side  26  of the asperities  24  with respect to the vertical θ s , the contact line density of the asperities (Λ) and the apparent contact area of the liquid (A):  
           f=−ΛA γcosθ s .  (6)  
         [0055]    The true advancing contact angle (θ a,0 ) of a liquid on a given solid material is defined as the largest experimentally measured stationary contact angle of the liquid on a surface of the material having essentially no asperities. The true advancing contact angle is readily measurable by techniques well known in the art.  
         [0056]    Suspended drops on a surface with asperities exhibit their true advancing contact angle value (θ a,0 ) at the sides of the asperities. The contact angle with respect to the vertical at the side of the asperities (θ s ) is related to the true advancing contact angle (θ a,0 ) by ψ or ω as follows:  
         θ s =θ a,0 +90°−ψ=θ a,0 +ω−90°.  (7)  
         [0057]    By equating F and f and solving for contact line density Λ, a critical contact line density parameter Λ L  may be determined for predicting ultraphobic properties in a surface:  
                 Λ   L     =         -   ρ                   g                 h       γ                   cos        (       θ     a   ,   0       +   ω   -     90   ∘       )             ,           (   8   )                               
 
         [0058]    where g is the density ρ of the liquid, (g) is the acceleration due to gravity, (h) is the depth of the liquid, the surface tension of the liquid (γ), ω is the rise angle of the side of the asperities relative to the substrate in degrees, and (θ a,0 ) is the experimentally measured true advancing contact angle of the liquid on the asperity material in degrees.  
         [0059]    If Λ&gt;Λ L , the liquid will be suspended atop the asperities  24 , producing an ultraphobic surface. Otherwise, if Λ&lt;Λ L , the liquid will collapse over the asperities and the contact interface at the surface will be solely liquid/solid, without ultraphobic properties.  
         [0060]    It will be appreciated that by substituting an appropriate value in the numerator of the equation given above, a value of critical contact line density may be determined to design a surface that will retain ultraphobic properties at any desired amount of pressure. The equation may be generalized as:  
                 Λ   L     =       -   P       γ                   cos        (       θ     a   ,   0       +   ω   -     90   ∘       )             ,           (   9   )                               
 
         [0061]    where P is the maximum pressure under which the surface must exhibit ultraphobic properties in kilograms per square meter, γ is the surface tension of the liquid in Newtons per meter, θ a,0  is the experimentally measured true advancing contact angle of the liquid on the asperity material in degrees, and co is the asperity rise angle in degrees.  
         [0062]    It is generally anticipated that a surface  20  formed according to the above relations will exhibit ultraphobic properties under any liquid pressure values up to and including the value of P used in equation (9) above. The ultraphobic properties will be exhibited whether the surface is submerged, subjected to a jet or spray of liquid, or impacted with individual droplets. It will be readily appreciated that the pressure value P may be selected so as to be greater than the largest anticipated liquid or vapor pressure to which the carrier will be subjected during use or cleaning.  
         [0063]    It will be generally appreciated that the value of P should be selected so as to provide an appropriate safety factor to account for pressures that may be momentarily or locally higher than anticipated, discontinuities in the surface due to tolerance variations, and other such factors.  
         [0064]    If the surface  20  is intended for very low values of P where the liquid contact may be in the form of droplets on the surface, the value of P must be selected to account for the smaller apparent contact area of a droplet as opposed to a uniform layer of liquid. In general, the apparent contact area (A) in square meters of a small droplet on the surface is given by the relation:  
               A   =           π     1   3            (     6      V     )         2   3              (       (       (     1   -     cos                   θ   a         )       sin                   θ   a         )          (     3   +       (       (     1   -     cos                   θ   a         )       sin                   θ   a         )     2       )       )       -     2   3             ,           (   10   )                               
 
         [0065]    where V is the volume of the droplet in cubic meters, and θ a  is the apparent advancing contact angle of the droplet on the surface. The critical contact line density Λ L  parameter for suspending a droplet on the surface becomes:  
                 Λ   L     =         -   ρ                       g        (   V   )         1   3              (       (       (     1   -     cos                   θ   a         )       sin                   θ   a         )          (     3   +       (       (     1   -     cos                   θ   a         )       sin                   θ   a         )     2       )       )       -     2   3                 (     36                 π     )       1   3          γ                   cos        (       θ     a   ,   0       +   ω   -     90   ∘       )             ,           (   11   )                               
 
         [0066]    where V is the volume of the droplet in cubic meters, (ρ) is the density of the liquid, (g) is the acceleration due to gravity, (γ) is the surface tension of the liquid, ω is the rise angle of the side of the asperities relative to the substrate in degrees, θ a  is the apparent advancing contact angle of the droplet on the surface, and (θ a,0 ) is the experimentally measured true advancing contact angle of the liquid on the asperity material in degrees. Equation 11 may be useful to check the value of P selected for low pressure ultraphobic surfaces to ensure that the surface will suspend droplets.  
         [0067]    Once the value of critical contact line density is determined, the remaining details of the geometry of the asperities may be determined according to the relationship of x and y given in the equation for contact line density. In other words, the geometry of the surface may be determined by choosing the value of either x or y in the contact line equation and solving for the other variable.  
         [0068]    The liquid interface deflects downwardly between adjacent asperities by an amount D 1  as depicted in FIG. 6. If the amount D 1  is greater than the height (z) of the asperities  24 , the liquid will contact the substrate  22  at a point between the asperities  24 . If this occurs, the liquid will be drawn into space  34 , and collapse over the asperities, destroying the ultraphobic character of the surface. The value of D 1  represents a critical asperity height (Z c ), and is determinable according to the following formula:  
                 D   1     =       Z   c     =       d        (     1   -     cos        (       θ     a   ,   0       +   ω   -     180   ∘       )         )         2                 sin                   (       θ     a   ,   0       +   ω   -     180   ∘       )             ,           (   12   )                               
 
         [0069]    where (d) is the distance between adjacent asperities, ω is the asperity rise angle, and θ a,0  is the experimentally measured true advancing contact angle of the liquid on the asperity material. The height (z) of asperities  24  must be at least equal to, and is preferably greater than, critical asperity height (Z c ).  
         [0070]    Although in FIGS. 1 e - 3  the asperity rise angle co is 90 degrees, other asperity geometries are possible. For example, Co may be an acute angle as depicted in FIG. 9 or an obtuse angle as depicted in FIG. 10. Generally, it is preferred that co be between 80 and 130 degrees.  
         [0071]    It will also be appreciated that a wide variety of asperity shapes and arrangements are possible within the scope of the present invention. For example, asperities may be polyhedral, cylindrical as depicted in FIGS. 11-12, cylindroid, or any other suitable three dimensional shape. In addition, various strategies may be utilized to maximize contact line density of the asperities. As depicted in FIGS. 14 and 15, the asperities  24  may be formed with a base portion  38  and a head portion  40 . The larger perimeter of head portion  40  at top edge  30  increases the contact line density of the surface. Also, features such as recesses  42  may be formed in the asperities  24  as depicted in FIG. 16 to increase the perimeter at top edge  30 , thereby increasing contact line density. The asperities may also be cavities formed in the substrate.  
         [0072]    The asperities may be arranged in a rectangular array as discussed above, in a polygonal array such as the hexagonal array depicted in FIGS. 4-5, or a circular or ovoid arrangement. The asperities may also be randomly distributed so long as the critical contact line density is maintained, although such a random arrangement may have less predictable ultraphobic properties, and is therefore less preferred. In such a random arrangement of asperities, the critical contact line density and other relevant parameters may be conceptualized as averages for the surface. In the table of FIG. 13, formulas for calculating contact line densities for various other asperity shapes and arrangements are listed.  
         [0073]    Generally, the substrate material may be any material upon which micro or nano scale asperities may be suitably formed and which is suitable for use in the processing environment in which the carrier is used. The asperities may be formed directly in the substrate material itself, or in one or more layers of other material deposited on the substrate material, by photolithography or any of a variety of suitable methods. A photolithography method that may be suitable for forming micro/nanoscale asperities is disclosed in PCT Patent Application Publication WO 02/084340, hereby fully incorporated herein by reference.  
         [0074]    Other methods that may be suitable for forming asperities of the desired shape and spacing include nanomachining as disclosed in U.S. Patent Application Publication No. 2002/00334879, microstamping as disclosed in U.S. Pat. No. 5,725,788, microcontact printing as disclosed in U.S. Pat. No. 5,900,160, self-assembled metal colloid monolayers, as disclosed in U.S. Pat. No. 5,609,907, microstamping as disclosed in U.S. Pat. No. 6,444,254, atomic force microscopy nanomachining as disclosed in U.S. Pat. No. 5,252,835, nanomachining as disclosed in U.S. Pat. No. 6,403,388, sol-gel molding as disclosed in U.S. Pat. No. 6,530,554, self-assembled monolayer directed patterning of surfaces, as disclosed in U.S. Pat. No. 6,518,168, chemical etching as disclosed in U.S. Pat. No. 6,541,389, or sol-gel stamping as disclosed in U.S. Patent Application Publication No. 2003/0047822, all of which are hereby fully incorporated herein by reference. Carbon nanotube structures may also be usable to form the desired asperity geometries. Examples of carbon nanotube structures are disclosed in U.S. Patent Application Publication Nos. 2002/0098135 and 2002/0136683, also hereby fully incorporated herein by reference. Also, suitable asperity structures may be formed using known methods of printing with colloidal inks. Of course, it will be appreciated that any other method by which micro/nanoscale asperities may be formed with the requisite degree of precision may also be used.  
         [0075]    In some applications, particularly where the carrier will not be subjected to high fluid pressures or where the surface is intended to repel droplets of liquid that may precipitate or condense on the surface, ultraphobic surface  20  may be formed with a coating of polymer material applied using known chemical vapor deposition or chemical surface modification techniques. For example, a thin layer of a low surface energy material may be applied to the surfaces of a carrier using gas phase polymerization. For the purposes of the present application, a low surface energy material is generally any material having a surface energy value lower than about 35 mN/m. The resulting ultraphobic surface  20  will be generally characterized by randomly shaped and arranged asperities formed in the low surface energy material. Alternatively, the carrier surfaces may be subjected to a chemical surface modification process, such as cold oxygen plasma, or corona discharge treatment. In sum, any process capable of producing randomly shaped and arranged asperities having the desired contact line density may be used and is contemplated within the scope of the invention.  
         [0076]    In another embodiment for low fluid pressure applications, a fractal ultraphobic surface may be formed as a layer of material on the substrate. In one such embodiment, a layer of alkylketene dimer (AKD) or similar material may be melted or poured on the polymer substrate and allowed to harden in a nitrogen gas atmosphere. One suitable method for forming an AKD surface is more fully described by T. Onda, et. al., in an article entitled “Super Water Repellant Fractal Surfaces”, Langmuir, Volume 12, Number 9, May 1, 1996, at page 2125, which article is fully incorporated herein by reference.  
         [0077]    In another embodiment suitable for low fluid pressure applications, polymer material, such as polypropylene, may be dissolved in a solvent, such as p-xylene. A quantity of non-solvent such as methyl ethyl ketone may be added to the solution, and the solution deposited on the carrier substrate. When the solvent is evaporated, a porous, gel-like ultraphobic surface structure will result.  
         [0078]    In each of the above polymer layers, the resulting surface will be generally characterized by randomly shaped and arranged micrometer scale asperities. Although the actual contact line density and critical contact line density values for such surfaces are difficult to determine due to the variations in individual asperities, these surfaces will exhibit ultraphobic properties if the contact line density value for the surface equals or exceeds the critical contact line density for the surface. For such surfaces, the actual contact line density will necessarily be an average value for the surface due to the variability of dimensions and geometry of individual asperities. In addition, asperity rise angle ω in equations 9 and 11 should be an average value for the surface.  
         [0079]    The present invention may be embodied in other specific forms without departing from the spirit or essential attributes thereof, and it is, therefore, desired that the present embodiment be considered in all respects as illustrative and not restrictive.