Patent Publication Number: US-6986284-B2

Title: System and method for characterizing a textured surface

Description:
BACKGROUND 
   The present invention relates to a system and method for characterizing a textured surface useful for assessing and/or characterizing textured surfaces of various items, e.g., polishing pads, in particular polishing pads used in chemical-mechanical planarization (CMP), for purposes such as production quality control and development of such items. 
   CMP polishing is a process currently practiced in the semiconductor and other industries for creating flat surfaces on integrated circuit wafers and magnetic storage disks, among other things. Generally, CMP involves flowing or otherwise placing a polishing slurry or fluid between the wafer, memory disk or other workpiece to be planarized and a CMP polishing pad, and moving the pad and workpiece relative to one another while biasing the pad and workpiece together. CMP polishing pads generally have a textured surface that allows slurry to move throughout the network of voids formed when the peaks and valleys of the textured surface are brought into contact with the surface of the workpiece. The textured surfaces of CMP polishing pads having various topographies adapted to different polishing scenarios are known in the art. 
   Surface flow resistance is a critical characteristic of CMP polishing pads that impacts flow patterns of the polishing slurry in the voids between the pad and workpiece during polishing. Liquid flow patterns affect the delivery of fresh slurry to the workpiece surface, the removal of polishing debris from the surface and the conveyance of heat from both chemical reaction and mechanical abrasion. More accurate optimization of CMP performance and more effective design of CMP polishing pads and slurries would be possible if the exact flow patterns in the voids could be predicted. However, the surface flow resistance of a CMP polishing pad is impossible to measure dynamically on a CMP machine because the spaces between the pad and workpiece are inaccessible to conventional measuring devices. In addition, CMP generally involves variously overlapping and concurrent physics due to the orbital action of CMP that make it virtually impossible to isolate from CMP data typically collected the effects of fluid flow pattern. 
   Research and modeling of CMP to date have applied fluid flow treatments adapted from bearing theory, which describes CMP pads in terms of roughness parameters or a distribution of surface peaks, aka “asperities.” These conventional approaches generally suffer from three shortcomings: (1) the pad surface descriptors are not easily related to measurable physical quantities; (2) it is unclear how the pad surface descriptors change under conditions of compression, shear and wetting that prevail in the pad-wafer gap during CMP; and (3) the fluid motion description is oversimplified such that practical features of interest, such as grooves or perforations, are difficult to model. 
   STATEMENT OF THE INVENTION 
   The present invention differs from conventional CMP characterization approaches in at least three ways. First, the present invention provides an insightful method of isolating fluid flow from the other physics of a typical CMP process. Second, the present invention permits the determination of the behavior of a CMP polishing pad&#39;s textured surface under various conditions of compression, shear and wetting. Third, the present invention applies the fluid mechanics concept of “porous media flow” to the flow region formed in the space between the textured surface of a pad and a wafer when the pad is pressed against the wafer. With these differences, the present invention provides, among other things, new and versatile descriptors of the working surfaces of CMP pads and a method of determining these descriptors using fast and cost-effective testing. 
   In a first aspect, the present invention is directed to a method of characterizing a textured surface having a plurality of asperities, comprising the steps of: a) moving a confining surface and the textured surface into confronting relationship with one another so that at least some of the asperities of the textured surface contact the confining surface so as to define a flow region; b) causing a fluid to flow within the flow region so as to create pressure in fluid within the flow region; and c) measuring the pressure of the fluid at a plurality of locations in the flow region so as to obtain pressure data. In a second aspect, the present invention is directed to an apparatus for characterizing a textured surface having a plurality of asperities, comprising: a) a confining surface having an area and including a plurality of pressure measuring structures distributed over the area, the confining surface adapted for confronting the textured surface so as to define a flow region among the plurality of asperities; b) a fluid delivery system fluidly communicating with the flow region when the confining surface is confronting the textured surface so as to provide a fluid to the flow region such that the fluid is under pressure within the flow region; and c) a pressure measuring system operatively connected to each one of the plurality of pressure measuring structures and adapted to measure the pressure within the flow region proximate each one of the plurality of pressure measuring structures. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a partial high level schematic diagram/partial elevational view of a textured surface characterization system and apparatus according to the present invention; 
       FIG. 2  is an enlarged cross-sectional view showing the confined spaced formed between the confining surface of the confinement apparatus of  FIG. 1  and the textured surface of an item when the item is placed into contact with the confining surface; 
       FIG. 3  is a schematic diagram illustrating the radial flow of fluid and the radial arrangement of pressure measurement structures during testing of a textured specimen in the apparatus of  FIG. 1 ; 
       FIG. 4  is a plot of measured and computed pressures of the fluid in the flow region versus radius; 
       FIG. 5  is a cross-sectional view of the textured surface characterization apparatus as taken along line  5 — 5  of  FIG. 1  showing the confining surface; 
       FIG. 6  is a cross-sectional view of the top of the textured surface characterization apparatus as taken along line  6 — 6  of  FIG. 5 ; 
       FIG. 7A  is a perspective view of an “ideal” textured sample used to generate the plots of  FIGS. 7B and 7C ;  FIG. 7B  is a plot of radial pressure profiles of the fluid in the fluid flow region along radial lines L 1  through L 12  for the ideal textured sample of  FIG. 7A ;  FIG. 7C  is a plot of angular pressure drop profiles at radii r 0  through r 9  for the ideal textured sample of  FIG. 7A ; and 
       FIG. 8A  is a plot of radial pressure profiles of the fluid in the fluid flow region along radial lines L 1  through L 12  for a textured sample having a variation in thickness;  FIG. 8B  is a plot of angular pressure drop profiles at radii r 0  through r 9  for the same sample. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   Referring now to the drawings,  FIG. 1  shows in accordance with the present invention a textured surface characterization system, which is generally denoted by the numeral  100 . Characterization system  100  may be used for characterizing a textured surface  104  of an item  108 , e.g., in order to assess various aspects of the textured surface. 
   Characterization system  100  may be particularly useful for characterizing textured surface  104  when this surface is designed to confront a confining surface (not shown) during normal use of item  108 . As discussed above, an item  108  having such a textured surface that is critical to the proper functioning of the item is a polishing pad, in particular a polishing pad used for CMP. The quality and characteristics of the textured surface, i.e., working surface, of a CMP polishing pad are important because they relate to, among other things, the quality of a surface (not shown) planarized using the polishing pad, the polishing efficiency of the pad, the life of the pad and the operating parameters of the pad. Thus, a CMP polishing pad is a prime example of item  108  suitable for characterization using characterization system  100 . Characterization system  100  may be used, e.g., as a quality control tool for assessing the quality of textured surface  104  when item  108  is a part of a production run or, alternatively, as a development tool for designing the textured surface, designing a process for making the textured surface and/or designing equipment for making the textured surface. 
   Referring to  FIGS. 1 and 2 , characterization of textured surface  104  generally includes engaging item  108  with a characterization apparatus  110  of characterization system  100  and moving the item so that textured surface  104  contacts a confining surface  112  so as to create a substantially confined space  116  between the confining surface and the textured surface. Confined space  116  results from the asperities  120  (generally, the relatively high peaks of textured surface  104 ) contacting confining surface  112  and spacing the lower peaks and valleys away from the confining surface. Confined space  116  includes one or more flow regions  124  wherein fluid  128  can flow substantially parallel to confining surface  112  and out of confined space  116  at periphery  132  of item  108  (i.e., global flow) and one or more non-flow regions  136 , typically the relatively deep valleys, wherein the fluid flow, if any, essentially remains local to the non-flow regions (i.e., local flow). 
   The flow of fluid  128  in flow region(s)  124  occurs in many interconnecting channels defined by confining surface  112  and textured surface  104 . Thus, this flow may be characterized as porous media flow and analyzed using well-established theoretical fluid mechanics for porous media flow. Referring to  FIG. 3 , and occasionally to  FIG. 2 ,  FIG. 3  illustrates the testing of a circular item  108  wherein fluid  128  is introduced into confined space  116  at an inlet  140  located at the center of the item so that the flow of the fluid in flow region(s)  124  is substantially radial relative to the item  108 . An advantage of this radial flow configuration is that the radial flow of fluid  128  requires consideration of flow conditions at only the parallel top and bottom boundaries used to confine the fluid, and not at any additional boundaries connecting the top and bottom. For example, if flow region  124  were rectangular and confined on opposing sides so as to induce a substantially linear flow from one end of the flow region to the other, the flow equations would be complicated by the boundary conditions at the confined sides. That said, however, it is noted that this linear flow scheme and other non-radial flow schemes are within the scope of the present invention, regardless of whether or not the resulting flow equations are more complex than the radial flow equations described herein. 
   In the radial flow model of  FIG. 3 , fluid  128  is introduced into confined space  116  at inlet  140  at a pressure p i . As fluid  128  flows through flow region(s)  124  within confined space  116  from inlet  140  to periphery  132  of item  108 , the pressure p in the fluid drops as a result of, among other things, frictional and momentum losses as the fluid flows across confining surface  112  ( FIG. 2 ) and textured surface  104  and around asperities  120  globally in a substantially radial direction relative to item  108 . As mentioned, these losses can be characterized using porous media flow theory. Accordingly, the pressure drop Δp from an initial pressure p 0  at a radius r 0  to the pressure p(r) at any successively larger radius r may be approximated as: 
           p   0     -     p   ⁡     (   r   )         =           w   ⁢           ⁢   µ         (     2   ⁢   π   ⁢           ⁢   H     )     ⁢   ρ   ⁢           ⁢   g       ⁢         α   ⁡     (     1   -   ɛ     )       2         D   E   2     ⁢     ɛ   3         ⁢   ln   ⁢     r     r   0         +         w   2           (     2   ⁢   π   ⁢           ⁢   H     )     2     ⁢   ρ   ⁢           ⁢   g       ⁢         β   ⁡     (     1   -   ɛ     )           D   E     ⁢     ɛ   3         ⁡     [       1     r   0       -     1   r       ]               
 
where: w is the mass flow rate;
 
   α is a known constant; 
   β is a known constant; 
   ε is the flowing void fraction of flow region  124 ; 
   μ is the viscosity of fluid  128 ; 
   ρ is the density of the fluid; 
   g is the gravitational constant; 
   H is the effective channel height between confining surface  112  and textured surface  104 ; and 
   D E  is the characteristic length within the flow region, which is of the same order of magnitude as the mean asperity spacing. 
   As can be seen, the unknowns in the foregoing equation are the pressure drop Δp, the flowing void fraction ε and the characteristic length D E  of flow region  124 . The two latter unknowns are properties of textured surface  104  that have heretofore not been utilized in describing textured surfaces, but nonetheless may be helpful in characterizing these surfaces, e.g., in terms of attributes of the surfaces desirable for accomplishing the function(s) for which the surfaces are designed. Referring to  FIG. 2 , generally, the flowing void fraction ε characterizes the accessible flow volume within flow region(s)  124 , and characteristic length D E  characterizes the average spacing between asperities  120  of textured surface  104  and relates to the effective width of the passageways for fluid  128  within the flow region(s). In the context of polishing pads, including those used in CMP, these attributes include the ability of textured surface  104  to evenly distribute a slurry in the region between the pad and a semiconductor wafer or memory disk, conduct the slurry to the peripheral edge of the pad and to create a substantially uniform fluid pressure across all portions of the pad immediately confronting the wafer/disk. Some polishing pads include grooves or other structures that prevent portions of these pads from immediately confronting the wafer/disk; for these pads the flowing void fraction and characteristic length also control the relative amount of slurry conveyed in the grooved and ungrooved regions of the pad. 
   Referring again to  FIG. 3 , pressure drops Δp at various radii r spaced from r 0  can be determined experimentally by measuring the pressure of fluid  128  at various locations along the flow path of the fluid from inlet  140  to periphery  132  of item  108 .  FIG. 4  illustrates a plot  142  of fluid pressures p(r) measured at the discrete radial locations (r) identified in  FIG. 3 . The measurement of these and other pressures are described in more detail below. Using these measured pressures, flowing void fraction ε and characteristic length D E  can be determined using computational fluid dynamics matching of the radial profile of measured pressures at various mass flow rates w, fluid properties ρ and μ, and gap heights H. 
   The various pressures p(r) needed to determine pressure drops Δp may be measured using characterization system  100  ( FIG. 1 ) of the present invention. In this connection, characterization apparatus  110  may be configured for testing circular items  108  using the radial flow discussed above. For example, referring to  FIGS. 1 and 5 , and occasionally to  FIG. 2 , confining surface  112  of characterization apparatus  110  may include an array of pressure measurement structures  144 , e.g., pressure sensors (not shown) or pressure taps fluidly communicating with pressure sensors, for measuring the pressure of fluid  128  in confined space  116  at various locations throughout the confined space. The pressure sensors may be any suitable type, such as mechanical or piezoelectric devices.  FIG. 6  illustrates an embodiment wherein each pressure measurement structure  144  is a pressure tap comprising a cylindrical passageway  148  having a constriction  152  at the end proximate confining surface  112 . In an embodiment suitable for characterizing polishing pads or samples thereof, the diameter of constriction  152  is about 0.031 inch (0.8 mm). Of course, the pressure tap may be configured and sized otherwise to suit a particular design. 
   Referring again to  FIGS. 1 and 5 , and occasionally to  FIG. 2 , in order to induce a radial flow of fluid  128  within flow region(s)  124 , confining surface  112  may include an inlet  156  centrally located relative to the confining surface to provide fluid  128  to confined space  116  at its geometric center. Since the flow of fluid  128  is substantially radial when the fluid is in confined space  116  it is generally most convenient to arrange at least a portion of the pressure measurement structures  144  radially relative to inlet  156 . In the embodiment shown in  FIG. 5 , pressure measurement structures  144  are primarily located along radial lines L 1 –L 12  spaced 15° apart from immediately adjacent such radial lines. The pressure measurement structures  144  located along each of these radial lines L 1 –L 12  are located at radii r 0 –r 9 . In the embodiment shown, the diameter of confining surface  112  is about 8 inches (200 mm) and radii r 0 –r 9  have a regular spacing of about 0.4 inch (10 mm). 
   Additional pressure measurement structures  160  are located at radii r 4  and r 9  midway between adjacent the pressure measurement structures  144  located at these radii. Additional pressure measurement structures  160  are provided to allow additional data to be collected for more complete characterization of the behavior of the flow of fluid  128  in confined space  116  along circles of fixed radius. Again, the arrangement of pressure measurement structures  144 ,  160  shown in  FIG. 5  is illustrative. Many other arrangements of structures  144 ,  160 , including rectangular arrangements, are possible, though theoretical flow computations may be complicated by alternative arrangements. 
   Optionally, confining surface  112  may include an array of temperature measurement structures  164 , e.g., thermocouples, for measuring the temperature of fluid  128  at various locations across the confining surface. Temperature data obtained using temperature measurement structures  164  may be used, e.g., to adjust fluid properties ρ and μ to enhance the precision of the results of the computational fluid dynamics analysis, particularly where it is expected that relatively large temperature variations will occur as fluid  128  flows from inlet  156  to periphery  132  of item  108 . During characterization of polishing pads, in particular those used for CMP, it is normally the case that any variation in temperature that occurs along the entire flow path of fluid  128  in flow region(s)  124  has a negligible impact on fluid properties and, therefore, need not be considered in the computation, although it can be. If the temperature variation along the flow path of fluid  128  is significant, it will improve the accuracy of the porous media flow equations if the fluid density and fluid viscosity are corrected for temperature changes. Similar to pressure measurement structures  144 ,  160 , temperature measurement structures  164  may, but need not, be arranged in a substantially radial pattern relative to inlet  156 .  FIG. 6  shows one of temperature measurement structures  164  as comprising a thermocouple  168  surrounded by thermal insulation  172 . Both thermocouple  168  and insulation  172  may be flush with confining surface  112  so as to not influence the flow of fluid  128  within confined space  116 . Of course, other types and arrangements of temperature measurement structures  164  may be used. 
   Referring to  FIGS. 1 and 2 , as mentioned above, characterization of item  108  is typically performed with textured surface  104  in contact with confining surface  112  with a certain pressure applied between the item and the confining surface. During characterization, item  108  should be held substantially fixed relative to confining surface  112 . To facilitate the proper positioning of item  108  relative to confining surface  112  and/or for precisely controlling the pressure applied between the item and confining surface, characterization apparatus  110  may include a positioning device  176 , such as an elevator, having a movable platen  180  for supporting the item, moving the item into and out of contact with the confining surface and/or creating various contact pressures between the item and the confining surface. Device  176  may include any type of actuator, e.g., hydraulic, geared, screw type or pneumatic, among others, that provides the force and/or position control appropriate for the type of item  108  being characterized. Platen  180  should provide a rigid support for item  108 . Accordingly, platen  180  may be made of any suitably stiff material, such as stainless steel. Of course, platen  180  may be made of another material, if desired. It is within the scope of the present invention that platen  180  may be freely rotating while remaining parallel to confining surface  112  and include a source of motive power and required mechanical linkages to provide such rotation. The latter may take the form of an internal drive system within the confines of positioning device  176  or a rim-driven system mounted externally to platen  180 . 
   Confining surface  112  should likewise be substantially unyielding when subject to the pressures applied by item  108  and fluid  128 . Accordingly, confining surface  112  may be defined by a confining region  184  of a relatively rigid stop  188 . In the embodiment shown, stop  188  is machined from a relatively thick slab of stainless steel to provide confining surface  112  with its unyieldingness. In addition, confining surface  112  should be substantially smooth so as to not influence the characterization process in any unintended or negative way. In general, it is preferred that confining surface  112  have no surface variations having a height exceeding 1% of the height of the variations (i.e. texture) of the item being characterized. Thus, stop  188  is generally highly polished at confining surface  112 . Like platen  180 , other materials may be substituted for the stainless steel just mentioned, if desired. Moreover, those skilled in the art will recognize that stop  188  need not be a relatively thick monolith, but may be constructed otherwise, such as out of a thin plate and suitable reinforcing. Characterization apparatus  110  may include a relatively rigid base  192  supporting positioning device  176  and one or more ties  196  rigidly connecting stop  188  to the base. Base  192  may rest upon a work bench  200  or other suitable structure, or may be part of such structure. 
   Referring to  FIG. 1 , and also to  FIGS. 2 and 3 , several systems may be provided to support the functionality of characterization apparatus  110 . These items may include a fluid delivery system  204 , a pressure sensing system  208 , a temperature sensing system  212 , a positioning device control system  216  and one or more systems (not shown) for controlling, monitoring and collecting data from the other systems, among others. The systems for controlling, monitoring and collecting data from systems  204 ,  208 ,  212 ,  216  may be implemented on a computer  220 , such as a general purpose computer, e.g., personal computer, or a computer configured especially for characterization system  100 . 
   Characterization of textured surface  104  may be performed using any suitable fluid  128 , e.g., liquid or gas. Accordingly, fluid delivery system  204  may be any type of system for delivering fluid  128  to confined space  116  under a pressure and at a flow rate desired for the particular type of item  108  under characterization and the configuration of characterization apparatus  110 . Some exemplary pressures for characterization wherein fluid  128  is air are discussed below in connection with characterization performed on various samples, including samples of CMP polishing pads. Flow rates for these samples were generally on the order of 0.1–100 standard liters per minute. Those skilled in the art will readily understand how to design and implement a suitable fluid delivery system  204  such that a detailed explanation is not necessary herein. Fluid delivery system  204  may be in electrical communication with computer  220  via one or more appropriate communication links  224 , e.g., one two-way link or two one-way links, which may include A/D (analog to digital), D/A (digital to analog) and other signal converters or other interfaces, depending upon the type actuators and transducers (not shown) the fluid control system utilizes. 
   Pressure sensing system  208  may include a plurality of pressure sensors/transducers (the plurality represented by box  228 ) each in fluid communication with a corresponding one of the pressure taps, i.e., pressure measurement structures  144 ,  160 , for measuring the pressure in fluid  128  at that tap. Alternatively, as mentioned above, each pressure sensor/transducer may be one of pressure measurement structure  144 ,  160  itself. Each pressure sensor/transducer may be in electrical communication with computer  220  via an appropriate communication link  232 , which may include an A/D converter, other signal converter or other interface (not shown), depending upon the type of pressure sensors/transducers utilized. 
   If temperature measurement structures  164  are provided, temperature sensing system  212  may similarly include the plurality of temperature measurement structures, e.g., thermocouples, each for measuring the temperature of fluid  128  at that temperature measurement structure. Each thermocouple may be in electrical communication with computer  220  via an appropriate communication link  236 , which may include an A/D converter, other signal converter or other interface (not shown), depending upon the type of thermocouple utilized. 
   Positioning device control system  216  controls the operation of positioning device  176 . Control system  216  and positioning device  176  may be operatively configured to control the movement of platen  180  based on the position of textured surface  104  relative to confining surface  112  and the pressure applied between the textured surface and confining surface. Thus, like fluid delivery system  204 , positioning device control system  216  may be in electrical communication with computer  220  via one or more appropriate communication links  240 , e.g., one two-way link or two one-way links, which may include A/D, D/A and other signal converters or other interfaces (not shown), depending upon the type actuator and transducers (not shown) positioning device  176  utilized. 
   Although characterization system  100  has been described as having a centralized control scheme, those skilled in the art will appreciate that the various systems needed to make characterization apparatus  110  operational may be controlled using a distributed control scheme. In addition, although characterization apparatus  110  has been described as having a particular configuration, those skilled in the art will appreciate that it may be configured differently. For example, confining surface  112  is shown as being configured for item  108  having a globally flat textured surface  104 . However, confining surface  112  may be configured for a textured surface  104  having another contour, such as for example a domed or conical shape, or an entirely asymmetric form. Similarly, platen  180  may be contoured as needed to suit a particular configuration of item  108 . Numerous other changes are possible, including, switching the locations of stop  188  and platen  180  and such that the platen is fixed and the stop is movable, among others. 
   EXAMPLES 
   Example 1 
   Referring to  FIG. 7A , and also to  FIGS. 1 and 2 ,  FIG. 7A  illustrates a textured surface  104  of an item  108  having a highly regular texture that provides the item with highly-regular flow regions  124  when the textured surface is in contact with confining surface  112  of characterization apparatus  110  of  FIG. 1 . Textured surface  104  is an example of an “ideal” (i.e. homogeneous) surface that, when characterized using characterization system  100 , should display substantially radially uniform and axi-symmetric fluid pressure drop profiles due to the highly regular texture. Textured surface  104  includes a mounting surface  244  and a plurality of structures  248  (asperities) integrally formed atop the mounting surface. Each structure  248  is generally a cylindrical mesa having a radius of about 75 microns and a height above mounting surface  244  of about 50 microns. The plurality of structures  248  are arranged in a regular array. (Such material is marketed by 3M Inc., St. Paul, Minn., under the trade name SlurryFree™ Fixed Abrasive). When structures  248  are placed into contact with circular confining surface  112 , flow region  124  spans the height between confining surface  112  and mounting surface  244  originating at inlet  156 , e.g., radial lines L 1 –L 12  ( FIG. 5 ) and at radii r 0 –r 9  that are concentric with the fluid inlet. 
   Referring to  FIG. 7B , and also to  FIGS. 2 and 5 ,  FIG. 7B  shows radial pressure profiles pL n  (n=1–12) of fluid  128 , in this case air, present within confined space  116  between item  108  of  FIG. 7A  and confining surface  112  along radial lines L 1 –L 12  ( FIG. 5 ) when the fluid is injected into the confined space at a pressure of 4 psig. As can be readily seen, radial pressure profiles pL n  are nearly identical to one another. Similarly, as shown in  FIG. 7C , angular pressure drop profiles Δpr n  (n=0–9) at radii r 0 –r 9 , respectively, are relatively uniform, except for several irregularities, particularly at r 0  where fluid  128  is locally disturbed due to the change in direction the fluid experiences proximate inlet  156  and, perhaps, due to several of structures  248  proximate the fluid inlet not being located symmetrically relative to the inlet. All in all, however, the pressure and pressure drop profiles pL n , Δpr n  of  FIGS. 7B and 7C , respectively, are highly uniform, as expected for item  108  having an “ideal” textured surface. 
   Example 2 
     FIGS. 8A and 8B  show, respectively, radial pressure profiles pL n ′ (n=1–12) and angular pressure drop profiles Δpr n ′ (n=0–9) wherein item  108  ( FIG. 1 ) is a sample of a microporous-polyurethane polishing pad. Generally, the polishing pad is made of polyurethane and includes a textured surface  104  consisting of asperities of random size and spacing. Although this sample has a uniform texture along radial lines L 1 –L 12  ( FIG. 5 ) and relative to radii r 0  –r 9 , the sample has a non-uniform thickness over the area of confining surface  112  ( FIG. 5 ). Since the upper surface of platen  180  ( FIG. 1 ) is held parallel to confining surface  112  by the stiffness of the platen and positioning device  176  relative to stop  188 , the non-uniform thickness causes asperities  120  ( FIG. 2 ) in the thicker region(s) to be compressed and thereby distorted more than the asperities in the thinner region(s). Thus, although the spaces between asperities  120  ( FIG. 2 ) when the sample is not compressed are generally uniform across the sample, when some of the asperities are compressed more than others, these spaces become non-uniform, resulting in flow region  124  in the region(s) of greater compression being more flow-constrictive than the flow regions in the region(s) of less compression. greater compression being more flow-constrictive than the flow regions in the region(s) of less compression. 
   As can be expected, the constricted flow in the region(s) of greater compression cause a larger pressure drop in fluid  128 . This is readily seen in  FIG. 8B  in the central region of the sample, particularly at radii r 0 , r 1  and r 2  ( FIG. 5 ), where the pressure drop is relatively large. The magnitudes of pressure drops at corresponding angular pressure drop profiles Δpr 0 ′, Δpr 1 ′ and Δpr 2 ′ can be especially appreciated when compared to the angular pressure profiles Δpr n  of  FIG. 7C  of the “ideal” item  108  of  FIG. 7A , resulting from the same fluid and inlet pressure used in Example 2.Generally, pressure drop profile Δpr n ′ of  FIG. 8A  indicates that the tested sample is thicker in its central region than in its peripheral region. In addition, due to the relatively high concentricity of pressure drops Δpr 0 ′–Δpr 9 ′, it can be seen that the thicker region of the sample is generally concentric with confining surface  112  ( FIG. 5 ), with some skew in quadrants Q 3  and Q 4 . 
   Radial pressure profiles as shown in Examples 1 and 2 may be used along with the equations for flow in porous media to determine the void fraction and characteristic length that best describe the textured surface under consideration. The method of the present invention may be conducted at various degrees of compression to establish how the physical properties of void fraction and characteristic length vary under applied load, which can in turn be used to assess fluid flow distribution in a polishing process, in particular a CMP process, wherein the downward force on the workpiece varies from point to point. Further, the method of the present invention may be conducted at various degrees of rotation of the platen relative to the confining surface, while maintaining the platen parallel to the confining surface, to establish how the physical properties of void fraction and characteristic length vary under shear conditions, which can in turn be used to assess fluid flow distribution in a polishing process, in particular a CMP process, wherein the relative velocity between the polishing pad and the workpiece varies from point to point. 
   The method of the present invention may be applied to textured surfaces consisting of multiple layers, in particular polishing pads mounted on sub-pads that provide increased conformability to a workpiece. The method of the present invention may also be applied to textured surfaces containing large grooves, perforations, or voids in the surface, in particular polishing pads having one or more grooves to permit flow of a liquid across the surface. 
   The void fraction and characteristic length obtained by the method of the present invention may be compared between pads having subpads and/or grooves and pads without subpads and/or grooves to establish the impact of the subpad and/or grooves on the conformability of the pad surface to a workpiece, which can in turn be used to assess fluid flow distribution in a polishing process, in particular a CMP process, wherein the topography of a workpiece varies from point to point. 
   The method of the present invention may be applied to textured surfaces that have been subjected to various degrees of conditioning or roughening, in particular polishing pads conditioned with diamond conditioners to create a uniformly roughened surface. The void fraction and characteristic length obtained by the method of the present invention may be compared among polishing pads subjected to mild conditioning (short conditioning times and/or low conditioning force) and polishing pads subjected to harsh conditioning (long conditioning times and/or high conditioning force) to establish the impact of conditioning on the fluid flow distribution in a polishing process, in particular a CMP process.