Patent Publication Number: US-6990870-B2

Title: System for determining characteristics of substrates employing fluid geometries

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   The present application is a divisional application of U.S patent application Ser. No. 10/318,365 entitled METHOD FOR DETERMINING CHARACTERISTICS OF SUBSTRATES EMPLOYING FLUID GEOMETRIES, filed Dec. 12, 2002 now U.S. Pat. No. 6,871,558, and is a divisional of U.S patent application Ser. number 10/863,800 entitled SYSTEM FOR DETERMINING CHARACTERISTICS OF SUBSTRATES EMPLOYING FLUID GEOMETRIES, filed Jun. 8, 2004, both of which are incorporated by reference herein. 

   BACKGROUND OF THE INVENTION 
   The present invention relates generally to lithography systems. More particularly, the present invention is directed to determining spatial relationships between an imprinting mold and a substrate upon which a pattern will be formed using the imprinting mold. 
   Imprint lithography has shown promising results in fabrication of patterns having feature sizes smaller than 50 nm. As a result, many prior art imprint lithography techniques have been advocated. U.S. Pat. No. 6,334,960 to Willson et al. discloses an exemplary lithography imprint technique that includes providing a substrate having a transfer layer. The transfer layer is covered with a polymerizable fluid composition. A mold makes mechanical contact with the polymerizable fluid. The mold includes a relief structure, and the polymerizable fluid composition fills the relief structure. The polymerizable fluid composition is then subjected to conditions to solidify and polymerize the same, forming a solidified polymeric material on the transfer layer that contains a relief structure complimentary to that of the mold. The mold is then separated from the solid polymeric material such that a replica of the relief structure in the mold is formed in the solidified polymeric material. The transfer layer and the solidified polymeric material are subjected to an environment to selectively etch the transfer layer relative to the solidified polymeric material to form a relief image in the transfer layer. 
   U.S. Pat. No. 5,772,905 to Chou discloses a lithographic method and apparatus for creating patterns in a thin film coated on a substrate in which a mold, having at least one protruding feature, is pressed into a thin film carried on a substrate. The protruding feature in the mold creates a recess in the thin film. The mold is removed from the thin film. The thin film then is processed such that the thin film in the recess is removed exposing the underlying substrate. Thus, patterns in the mold are replaced in the thin film, completing the lithography process. The patterns in the thin film will be, in subsequent processes, reproduced in the substrate or in another material which is added onto the substrate. 
   Yet another imprint lithography technique is disclosed by Chou et al. in  Ultrafast and Direct Imprint of Nanostructures in Silicon , Nature, Col. 417, pp. 835–837, June 2002, which is referred to as a laser assisted direct imprinting (LADI) process. In this process a region of a substrate is made flowable, e.g., liquefied, by heating the region with the laser. After the region has reached a desired viscosity, a mold, having a pattern thereon, is placed in contact with the region. The flowable region conforms to the profile of the pattern and is then cooled, solidifying the pattern into the substrate. 
   An important consideration when forming patterns in this manner is to maintain control of the distance and orientation between the substrate and the mold that contains the pattern to be recorded on the substrate. Otherwise, undesired film and pattern anomalies may occur. 
   There is a need, therefore, for accurately determining spatial relationships between a mold and a substrate upon which the mold will form a pattern using imprinting lithographic processes. 
   SUMMARY OF THE INVENTION 
   The present invention provides a system for determining characteristics of a first substrate, lying in a first plane, and a second substrate, lying in a second plane with a volume of fluid disposed therebetween. The system includes a displacement mechanism to cause relative movement between the volume and one of the first and second substrates to effectuate a change in properties of an area of the fluid, defining changed properties. A detector system senses the changed properties and produces data in response thereto. A processing system receives the data and produces information corresponding to the characteristics. These and other embodiments are discussed more fully below. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a simplified plan view of a lithographic system incorporating a detection system in accordance with one embodiment of the present invention; 
       FIG. 2  is a partial simplified elevation view of a lithographic system shown in  FIG. 1 ; 
       FIG. 3  is a simplified representation of material from which an imprinting layer, shown in  FIG. 2 , is comprised before being polymerized and cross-linked; 
       FIG. 4  is a simplified representation of cross-linked polymer material into which the material, shown in  FIG. 3 , is transformed after being subjected to radiation; 
       FIG. 5  is a simplified elevation view of a mold spaced-apart from an imprinting layer, shown in  FIG. 1 , after patterning of the imprinting layer; 
       FIG. 6  is a simplified elevation view of an additional imprinting layer positioned atop of the substrate, shown in  FIG. 5 , after the pattern in the first imprinting layer is transferred therein; 
       FIG. 7  is a top-down view of a region of a wafer, shown in  FIG. 1 , that is sensed by a detection system shown therein in accordance with one embodiment of the present invention; 
       FIG. 8  is a cross-section of the resulting shape of an imprinting layer shown in  FIG. 1 , being formed with the mold and the wafer not being in parallel orientation with respect to one another; 
       FIG. 9  is a top-down view of a region of a wafer, shown in  FIG. 1 , that is sensed by a detection system shown therein in accordance with an alternate embodiment of the present invention; 
       FIG. 10  is a top-down view of a region of a wafer, shown in  FIG. 1 , that is sensed by a detection system shown therein in accordance with another alternate embodiment of the present invention; 
       FIG. 11  is a simplified plan view of a lithographic system incorporating a detection system in accordance with a second embodiment of the present invention; and 
       FIG. 12  is a simplified plan view of a lithographic system incorporating a detection system in accordance with a third embodiment of the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 1  depicts a lithographic system  10  in which a detection system in accordance with one embodiment of the present invention is included. System  10  includes an imprint head  12  and a stage  14 , disposed opposite to imprint head  12 . A radiation source  16  is coupled to system  10  to impinge actinic radiation upon motion stage  14 . To that end, imprint head  12  includes a throughway  18  and a mirror  20  couples actinic radiation from radiation source  16 , into throughway  18 , to impinge upon a region  22  of stage  14 . Disposed opposite to region  22  is a detection system that includes a CCD sensor  23  and wave shaping optics  24 . CCD sensor  23  is positioned to sense images from region  22 . Detection system is configured with wave shaping optics  24  positioned between CCD sensor  23  and mirror  20 . A processor  25  is in data communication with CCD sensor  23 , imprint head  12 , stage  14  and radiation source  16 . 
   Referring to both  FIGS. 1 and 2 , connected to imprint head  12  is a first substrate  26  having a mold  28  thereon. First substrate  26  may be held to imprint head  12  using any known technique. In the present example first substrate  26  is retained by imprint head  12  by use of a vacuum chuck (not shown) that is connected to imprint head  12  and applies a vacuum to first substrate  26 . An exemplary chucking system that may be included is disclosed in U.S. patent application Ser. No. 10/293,224 entitled “A Chucking System for Modulating Shapes of Substrates”, which is incorporated by reference herein. Mold  28  may be planar or include a feature thereon. In the present example, mold  28  includes a plurality of features defined by a plurality of spaced-apart recessions  28   a  and protrusions  28   b . The plurality of features defines an original pattern that is to be transferred into a second substrate, such as wafer  30 , coupled to stage  14 . To that end, imprint head  12  is adapted to move along the Z axis and vary a distance “d” between mold  28  and wafer  30 . Stage  14  is adapted to move wafer  30  along the X and Y axes, with the understanding that the Y axis is into the sheet upon which  FIG. 1  is shown. With this configuration, the features on mold  28  may be imprinted into a flowable region of wafer  30 , discussed more fully below. Radiation source  16  is located so that mold  28  is positioned between radiation source  16  and wafer  30 . As a result, mold  28  is fabricated from material that allows it to be substantially transparent to the radiation produced by radiation source  16 , such as fused silica or quartz glass. 
   Referring to both  FIGS. 2 and 3 , a flowable region, such as an imprinting layer  34 , is disposed on a portion of surface  32  that presents a substantially planar profile. Flowable region may be formed using any known technique such as a hot embossing process disclosed in U.S. Pat. No. 5,772,905, which is incorporated by reference in its entirety herein, or a laser assisted direct imprinting (LADI) process of the type described by Chou et al. in  Ultrafast and Direct Imprint of Nanostructures in Silicon , Nature, Col. 417, pp. 835–837, June 2002. In the present embodiment, however, flowable region consists of imprinting layer  34  being deposited as a plurality of spaced-apart discrete beads  36  of material  36   a  on wafer  30 , discussed more fully below. Imprinting layer  34  is formed from a material  36   a  that may be selectively polymerized and cross-linked to record the original pattern therein, defining a recorded pattern. Material  36   a  is shown in  FIG. 4  as being cross-linked at points  36   b , forming cross-linked polymer material  36   c.    
   Referring to  FIGS. 2 ,  3  and  5 , the pattern recorded in imprinting layer  34  is produced, in part, by mechanical contact with mold  28 . To that end, imprint head  12  reduces the distance “d” to allow imprinting layer  34  to come into mechanical contact with mold  28 , spreading beads  36  so as to form imprinting layer  34  with a contiguous formation of material  36   a  over surface  32 . Were mold  28  provided with a planar surface, distance “d” would be reduced to provide imprinting layer  34  with a substantially planar surface. In the present example, distance “d” is reduced to allow sub-portions  34   a  of imprinting layer  34  to ingress into and fill recessions  28   a.    
   To facilitate filling of recessions  28   a , material  36   a  is provided with the requisite properties to completely fill recessions  28   a  while covering surface  32  with a contiguous formation of material  36   a . In the present example, sub-portions  34   b  of imprinting layer  34  in superimposition with protrusions  28   b  remain after the desired, usually minimum distance “d”, has been reached, leaving sub-portions  34   a  with a thickness t 1 , and sub-portions  34   b  with a thickness, t 2 . Thicknesses “t 1 ” and “t 2 ” may be any thickness desired, dependent upon the application. Typically, t 1  is selected so as to be no greater than twice the width u of sub-portions  34   a , i.e., t 1 &lt;2u, shown more clearly in  FIG. 5 . 
   Referring to  FIGS. 2 ,  3  and  4 , after a desired distance “d” has been reached, radiation source  16 , shown in  FIG. 1 , produces actinic radiation that polymerizes and cross-links material  36   a , forming cross-linked polymer material  36   c . As a result, the composition of imprinting layer  34 , transforms from material  36   a  to material  36   c , which is a solid. Specifically, material  36   c  is solidified to provide side  34   c  of imprinting layer  34  with a shape conforming to a shape of a surface  28   c  of mold  28 , shown more clearly in  FIG. 5 . After imprinting layer  34  is transformed to consist of material  36   c , shown in  FIG. 4 , imprint head  12 , shown in  FIG. 2 , is moved to increase distance “d” so that mold  28  and imprinting layer  34  are spaced-apart. 
   Referring to  FIG. 5 , additional processing may be employed to complete the patterning of wafer  30 . For example, wafer  30  and imprinting layer  34  may be etched to transfer the pattern of imprinting layer  34  into wafer  30 , providing a patterned surface  32   a , shown in  FIG. 6 . To facilitate etching, the material from which imprinting layer  34  is formed may be varied to define a relative etch rate with respect to wafer  30 , as desired. The relative etch rate of imprinting layer  34  to wafer  30  may be in a range of about 1.5:1 to about 100:1. 
   Alternatively, or in addition to, imprinting layer  34  may be provided with an etch differential with respect to photo-resist material (not shown) selectively disposed thereon. The photo-resist material (not shown) may be provided to further pattern imprinting layer  34 , using known techniques. Any etch process may be employed, dependent upon the etch rate desired and the underlying constituents that form wafer  30  and imprinting layer  34 . Exemplary etch processes may include plasma etching, reactive ion etching, chemical wet etching and the like. 
   Referring to both  FIGS. 1 and 2 , an exemplary radiation source  16  may produce ultraviolet radiation. Other radiation sources may be employed, such as thermal, electromagnetic and the like. The selection of radiation employed to initiate the polymerization of the material in imprinting layer  34  is known to one skilled in the art and typically depends on the specific application which is desired. Furthermore, the plurality of features on mold  28  are shown as recessions  28   a  extending along a direction parallel to protrusions  28   b  that provide a cross-section of mold  28  with a shape of a battlement. However, recessions  28   a  and protrusions  28   b  may correspond to virtually any feature required to create an integrated circuit and may be as small as a few tenths of nanometers. As a result, it may be desired to manufacture components of system  10  from materials that are thermally stable, e.g., have a thermal expansion coefficient of less than about 10 ppm/degree Centigrade at about room temperature (e.g. 25 degrees Centigrade). In some embodiments, the material of construction may have a thermal expansion coefficient of less than about 10 ppm/degree Centigrade, or less than 1 ppm/degree Centigrade. 
   Referring to  FIGS. 1 ,  2  and  7 , an important consideration to successfully practice imprint lithography techniques is accurately determining distance “d”. To that end, the detection system of the present invention is configured to take advantage of the change in the geometry of beads  36  as the distance “d” is reduced. Assuming beads  36  behave as a non-compressible fluid with a volume “v”, distance “d” may be defined as follows:
 
 d=V/A   (1)
 
where A is a liquid filled area measured by CCD sensor  23 . To that end, the combination of CCD sensor  23  and wave shaping optics  24  allows the detection system to sense one or more beads  36  in region  22 . With first substrate  26  spaced-apart from wafer  30 , the volume of one or more beads  36  provides each bead  36  with an area  40  associated therewith. As distance “d” is reduced and substrate  26  comes into mechanical contact with beads  36 , compression occurs. This compression effectuates a change in properties of the area  40  of beads  36 , referred to as changed properties. These changes relate to the geometries of one or more beads  36 , such as the shape, size or symmetry of the area  40 . In the present example the changed properties are shown as  42  and concern the size of the area  40 . Specifically, the compression results in the area  40  of beads  36  increasing.
 
   The change in area  40  is sensed by CCD sensor  23 , which produces data corresponding to the same. Processor  25  receives the data corresponding to the change in the area  40  and calculates, using equation 1, the distance “d”. Assuming CCD sensor  23  consists of a N×M array of pixels, distance “d” is ascertained by processor  25  through the following equation:
 
 d=V/t   p ( P   a )  (2)
 
where t p  is the total number of pixels in the N×M array and P a  is the area of each pixel.
 
   With volume of beads  36  being fixed, the resolution of CCD sensor  23  that is desired to accurately measure the area A may be defined as follows:
 
Δ A= (A/ d )Δ d   (3)
 
Assuming that the total volume, v, of one of beads  36  sensed by CCD sensor  23  is 200 nl, i.e., 0.1 mm 3  and d=200 nm, then liquid filled area “A” is 1000 mm 2 . From equation (2) it may be determined that the desired resolution of CCD sensor  23  is 5 mm 2 .
 
   It should be noted that processor  25  may be employed in a feedback loop operation. In this manner, distance “d” may be calculated multiple times until it is determined that the desired distance “d” has been reached. Such calculations may be performed dynamically in real time, or sequentially, with the distance “d” being determined as incremental movements of imprint head  12  along the Z axis occur. Alternatively, or in addition thereto, processor  25  may be in data communication with a memory  27  that includes computer-readable information in the form of a look-up table  29 . The information in look-up table  29  may include geometries, shown as  31   a ,  31   b  and  31   c  as related to differing distances, shown as d a , d b  and d c . In this manner, information concerning the geometry of one or more beads  36  may be obtained by CCD sensor  23  and received by processor  25 . The information is then processed to relate the same to the geometry in look-up table  29  that most closely matches the geometry of the one or more beads  36  sensed by CCD sensor  23 . Once a match is made, processor  25  determines a magnitude of distance “d” present in look-up table  29  that is associated with the matching geometry. 
   Additional information concerning characteristics of first substrate  26  and wafer  30  other than the distance “d” therebetween may be obtained by analyzing the fluid geometry of one or more beads  36 . For example, by analyzing the symmetry of beads  36  an angular orientation between first substrate  26  and wafer  30  may be determined. Assume first substrate  26  lies in a first plane P 1  and wafer  30  lies in a second plane P 2 . Assuming area  40  is radially symmetric, any loss of radial symmetry in area  40  may be employed to determine that first plane P 1  and second plane P 2  do not extend parallel to one another. Additionally, data concerning the shape of area  40 , in this case the lack of radial symmetry, may be employed to determine the angle Θ formed between first and second planes P 1  and P 2  and, therefore, between first substrate  26  and wafer  30 , shown in  FIG. 8 . As a result, undesired thicknesses in imprinting layer  34  may be ascertained and, therefore, avoided. Other information may be obtained, as well, such as the contamination of first substrate  26  or wafer  30  or both by particulate matter. 
   Specifically, the presence of particulate matter on substrate  26  may manifest as many different shapes. For purposes of the present discussion, one or more beads  36 , shown in  FIG. 2 , having an asymmetrical area associated therewith may indicate the presences of particulate contaminants on either first substrate  26  or wafer  30 . Further, with a priori knowledge of contaminants, specific shapes of one ore more beads  36  may be associated with a particular defect, such as particulate contamination, as well as the presence of the defect, e.g., on first substrate  26 , wafer  30  and/or stage  14 . This information may be included in a look-up table as discussed above so that processor may classify the defect and characterize first substrate  26  and/or wafer  30 , accordingly. 
   Referring to  FIGS. 1 ,  2  and  9 , by analyzing information from two or more beads, shown as  36   d  and  36   e  in region  22 , the magnitude of the distance “d” between first substrate  26  and wafer  30  may be concurrently determined at differing sites. The distance information for each of beads  36   d  and  36   e  is determined as discussed above. Assuming beads  36   d  and  36   e  have substantially identical areas, changes in the areas due to first substrate  26  coming into mechanical contact therewith should be substantially the same, were first substrate  26  and wafer  30  substantially parallel and the distance, “d”, would be uniform over region  22 . Any difference between the areas of beads  36   d  and  36   e  after mechanical contact with first substrate  26  may be attributable to first substrate  26  and wafer  30  not being parallel, which could result in a non-uniform distance “d” between first substrate  26  and wafer  30  over region  22 . Further, the angle θ formed between first substrate  26  and wafer  30  may be determined from this information, as discussed above. Assuming that areas of beads  36   d  and  36   e  differed initially, similar information may be obtained by comparing the relative changes in the areas of beads  36   d  and  36   e  that result from mechanical contact with first substrate  26 . 
   Specifically, it may be determined by analyzing the relative changes between areas of beads  36   d  and  36   e  it may be determined whether first substrate  26  and wafer  30  at regions located proximate to beads  36   d  and  36   e  are spaced apart an equal distance “d”. If this is the case, then it may be concluded that first substrate  26  and wafer  30  extend parallel to one another. Otherwise, were first substrate  26  and wafer  30  found not to extend parallel to one another, the magnitude of the angle θ formed therebetween may be determined. 
   Referring to  FIGS. 1 ,  2  and  10 , another advantage of examining multiple beads in a regions, such as beads  36   f ,  36   g ,  36   h ,  36   i  and  36   j , is that a shape of either first substrate  26  or wafer  30  may be obtained. This is shown by examining the changes in beads  36 . For example, after compression of beads  36   f ,  36   g ,  36   h ,  36   i  and  36   j  by first substrate  26  each is provided with area  136   f ,  136   g ,  136   h ,  136   i  and  136   j , respectively that defines a compression pattern  137 . As shown, beads  36   f  and  36   j  have the greatest area, beads  36   g  and  36   i  have the second greatest area and bead  36   h  has the smallest area. This may be an indication that first substrate  26  has a concave surface, i.e., is bowed, or that wafer  30  is bowed. From experimental analysis additional information concerning differing types of compression patterns may be obtained to classify and characterize differing shapes or defects in system  10 . These may also be employed in look-up table  29  so that processor  25  may match a compression pattern sensed by CCD sensor  23  with a compression pattern in look-up table  29  and automatically ascertain the nature of processing performed by system  10 , i.e., whether system  10  is functioning properly and/or acceptable imprints are being generated. 
   CCD sensor  23  may also be implemented for endpoint detection of the spreading of imprinting layer  34  over wafer  30 . To that end, one or more pixel of CCD sensor  23  may be arranged to sense a portion of wafer  30 . The portion, shown as  87   a ,  87   b ,  88   a  and  88   b , in  FIG. 7 , is located in region  22  and is proximate to a periphery of imprinting layer  34  after “d” has reached a desired magnitude. In this fashion, pixels of CCD sensor  23  may be employed as an endpoint detection system that indicates when a desired distance “d” has been achieved, thereby resulting in spreading of beads  36  to form imprinting layer  34  of desired thicknesses. This facilitates determining the magnitude of movement imprint head  12  should undertake in order to facilitate an imprint of imprinting layer  34 . To that end, once CCD sensor  23  detects the presence of imprinting layer  34  proximate to portions  87   a ,  87   b ,  88   a  and  88   b , data concerning the same is communicated to processor  25 . In response, processor  25  operates to halt movement of imprint head  12 , fixing the distance “d” between first substrate  26  and wafer  30 . 
   Referring to  FIGS. 2 ,  7  and  11  in accordance with another embodiment of the present invention, detection system may include one or more photodiodes, four of which are shown as  90   a ,  90   b ,  90   c  and  90   d  may be included to facilitate endpoint detection. Photodiodes  90   a ,  90   b ,  90   c  and  90   d  include wave shaping optics  91  and are arranged to sense a predetermined portion of first substrate  26 , such as  88   a . However, it is advantageous to have photodiodes  90   a ,  90   b ,  90   c  and  90   d  sense portions  88   b ,  87   a  and  87   b , as well. For ease of discussion however, photodiodes  90   a ,  90   b ,  90   c  and  90   d  are discussed with respect to region  88   a , with the understanding that the present discussion applies equally to use of additional photodiodes to sense regions  87   a ,  87   b  and  88   b.    
   To facilitate endpoint detections, photodiodes  90   a ,  90   b ,  90   c  and  90   d  are positioned to sense a portion of first substrate  26  that is located proximate to a periphery of imprinting layer  34  after “d” has reached a desired magnitude. As a result, photodiodes  90   a ,  90   b ,  90   c  and  90   d  may be employed as an endpoint detection system as discussed above with respect to CCD sensor  23  shown in  FIG. 1 . Referring again to  FIGS. 2 ,  7  and  11 , photodiodes  90   a ,  90   b ,  90   c  and  90   d  are in data communication with processor  25  to transmit information concerning portions  88   a  and  88   b , such as intensity of light reflected from portions  88   a  and  88   b . Specifically, portions  88   a  and  88   b  may be reflective, i.e., a mirror reflects ambient onto photodiodes  90   a ,  90   b ,  90   c  and  90   d . Upon being covered by imprinting layer  34 , the energy of light reflecting from portions  88   a  and  88   b  is substantially reduced, if not completely attenuated, thereby reducing the power of optical energy impinging upon photodiodes  90   a ,  90   b ,  90   c  and  90   d . Photodiodes  90   a ,  90   b ,  90   c  and  90   d  produce a signal in response thereto that is interpreted by processor  25 . In response, processor  25  operates to halt movement of imprint head  12 , fixing the distance “d” between first substrate  26  and wafer  30 . It should be understood that the detection system discussed with respect to photodiodes  90   a ,  90   b ,  90   c  and  90   d  may be used in conjunction with CCD sensor  23  and wave shaping optics  24 , discussed with respect to  FIG. 1 . The advantage of employing photodiodes  90   a ,  90   b ,  90   c  and  90   d  is that data acquisition is faster than that provided by pixels of CCD sensor  23 . 
   Referring to  FIGS. 2 ,  11  and  12 , another embodiment of the present invention is shown that facilitates determining characteristics of first substrate  26  and wafer  30  without knowing the volume associated with beads  36 . To that end, the present embodiment of system  110  includes an interferometer  98  that may be used with the CCD sensor  23  the photodiodes  90   a ,  90   b ,  90   c  and  90   d  or a combination of both. As discussed above, system  110  includes wave shaping optics  24 , radiation source  16 , mirror  20  and imprint head  12 . Imprint head  12  retains first substrate  26  disposed opposite wafer  30 , with wafer  30  being supported by stage  14 . Processor  25  is in data communication with imprint head  12 , stage  14 , radiation source  16 , CCD sensor  23  and interferometer  98 . Also disposed in an optical path of interferometer  98  is a 50—50 mirror  120  that enables a beam produced by interferometer  98  to be reflected onto region  22 , while allowing CCD sensor  23  to sense region  22 . 
   Use of interferometry facilitates determining distance “d” without having accurate information concerning the initial volume of beads  36 . An exemplary interferometry system employed to measure distance “d” is described in U.S. patent application Ser. No. 10/210,894, entitled “Alignment Systems for Imprint Lithography”, which in incorporated herein by reference. 
   Employing interferometer  98  facilitates concurrently determining the initial distance “d” and the change in distance Δd. From this information the volume associated with one or more beads  36  may be obtained. For example, interferometer  98  may be employed to obtain two measurements of first substrate  26  at two differing times t 1  and t 2  to obtain first substrate  26  displacement measurement L T . During the same time, wafer  30  displacement measurement, L S , may be obtained, in a similar manner. The change in distance, Δd, between first substrate  26  and wafer  30  is obtained as follows:
 
Δ d=|L   T   −L   S |  (4)
 
During times t 1  and t 2 , measurements are taken with CCD sensor  23  to determine the change in area of one or more of beads  36  as a function of the total number of pixels in which one or more of beads  36  are sensed. At time t 1 , the total number of pixels in which one or more beads  36  are sensed is n p1 . At time t 2 , the total number of pixels in which one or more beads  36  are sensed is n p2 . From these two values the change in pixels, Δn p , is defined as follows:
 
Δ n   p   =|n   p2   −n   p1 |  (5)
 
From equations 4 and 5 the value of distance “d” may be obtained from either of the following equations:
 
 d   1 =(Δ d/Δn   p ) n   p1   (6)
 
 d   2 =(Δ d/Δn   p ) n   p2   (7)
 
where d=d 1 =d 2 . Knowing d 1  and d 2 , by substitution we can obtain the volume V of the one or more beads  36  being sensed by CCD sensor  23  by either of the following equations:
 
 V   1   =d   1 ( n   p1 ×pixelsize)  (8)
 
 V   2   =d   2 (n p2 ×pixelsize)  (9)
 
where V=V 1 =V 2 , and (n p1 ×pixelsize)=(n p2 ×pixelsize)=A. When first substrate  26  and wafer  30  may be maintained to be parallel, interferometer  98  may be measured outside of region  22 , shown in  FIG. 1 . Otherwise, interferometer  98  measurements should be made proximate to a center of region  22 , or expanding beads  36 . In this manner, the substrate  26  characteristic information obtained using system  10 , shown in  FIG. 1 , may be obtained employing system  110 , shown in  FIG. 12 .
 
   The embodiments of the present invention described above are exemplary. Many changes and modifications may be made to the disclosure recited above, while remaining within the scope of the invention. Therefore, the scope of the invention should be determined not with reference to the above description, but instead should be determined with reference to the appended claims along with their full scope of equivalents.