Abstract:
A subject having a test surface is held by a holder so that an axis line of the test surface intersects the direction of gravity and applied with a load, from above and beneath, that is optimized for accurate measurement of surface profile of the test surface. For optimization of the load, the test surface is applied with variable exploratory load strong enough to cause bending deformation in the test surface and a linear-functional relationship existing between more than two different exploratory loads and sizes of surface deformation caused with the different exploratory loads is derived. With the aid of linear-functional relationship, a load that induces the subject to cause surface deformation less than a predetermined size of surface deformation admissible, for example, as a manufacturing en-or is used as an optimized load.

Description:
BACKGROUND OF THE INVENTION 
   Standing position/upright standing position 
   1. Field of the Invention 
   The present invention relates to a subject holding method and a subject holding device for holding a subject having a test surface such as an optical element in a stationary standing position with respect to a measuring system and a measuring instrument, such as an optical interference device, equipped with the subject holding device. 
   2. Description of Related Art 
   In semiconductors manufacturing techniques, it is typically to use photomasks for exposing semiconductor wafers in order to transfer a desired circuit pattern thereon. For the exposure of such a semiconductor wafer to a circuit pattern, it is quite usual to put a photomask so as to keep a mask surface in a substantially horizontal position during exposure, in other words, so as to hold the photomask in such a manner that an axis line (an ordinary line) of the mask surface is oriented in a direction of gravity. In order to transfer the circuit pattern precisely, the photomask should be carefully held for prevention of an occurrence of flexure of the mask surface due to external influence, for example, gravitational influence. Consequentially, there have been proposed a variety of techniques of maintaining surface flatness of photomasks during exposure of semiconductor wafer to a circuit pattern as known from, for example, Unexamined Japanese Patent Publication Nos. 9-306832 and 2000-223414. 
   On the other hand, there is a strong demand on the part of photomask manufacturer to measure optical properties, such as surface accuracy and a distribution of refractive index, of photomasks preferably without being affected by gravity. 
   For the purpose of preventing the photomask from being distorted by gravitational influence during the measurement of optical properties of the photomask, it is conceivably preferable that the photomask is held in an upright standing position, i.e. in a position in which a normal line of the mask surface is perpendicular to a direction of gravity. In this context, the photomask standing simply by itself is wonky and inept at measurement. It is essential for the measurement of mask surface that the photomask must be held in a stationary state under load during measurement. 
   It is, however, quite difficult to find an optimized load to be applied to the photomask Although it is obvious that the load must be large enough to maintain the photomask in a stationary standing position, if it is too large, the photomask encounters flexure large enough to lead to imprecise measurement of the mask surface. Heretofore, techniques for finding an optimized load for maintaining the photomask in a standing position without flexure have not yet put on a firm footing, and besides, operators have no alternative but to rely on their experience and skill in finding an optimized load It is hardly capable of meeting product diversification to determine an optimized load by such a rule of thumb acquired by skilled operators. Further, if the determination of an optimize load is improper, photomasks possibly cause surface deformation beyond the bounds of admissible production error, it can not be denied that photomask are possibly disqualified as acceptable products even while they are at acceptable surface quality levels. 
   SUMMARY OF THE INVENTION 
   It is therefore an object of the present invention to provide a subject holding method and a subject holding device for holding a subject having a test surface as a measuring object under an optimized load that has no adverse effect on measurements. 
   It is another object of the present invention to provide a subject holding method and a subject holding device for holding a subject having a test surface as a measuring object under an optimized load so as thereby to maintain the subject in a stationary standing position with sect to a measurement system. It is a further object of the present invention to provide a me g instrument equipped with a subject holding device for measurement of a surface profile of a subject. 
   The foregoing objects are achieved by a subject holding method comprises the steps of supporting a subject so as to put an axis line of a test surface of the subject approximately perpendicularly to a direction of gravity, applying different exploratory loads to the subject in the direction of gravity at least more than two times so that the subject causes different sizes of surface deformation in the test surface, deriving a linear-functional relationship existing between the exploratory loads and the surface deformation, determining an optimized load under which the subject causes surface deformation less than a predetermined size, and holding the subject under the optimized load. 
   The exploratory load may be applied to the subject in rotational asymmetric directions with respect to the axis line of the test surface. In this instance, the subject is fired from the optimized load once after measurement of a size of surface deformation and restored to the same after having been repositioned by a predetermined angle of turn around the axis line of the test surface. After performing these steps, a judgment as to whether the optimized load is suitably acceptable or not can be made by comparing the sizes of surface deformation before and after the repositioning of the subject 
   The subject holding method is implemented by a subject holding device comprising supporting means for supporting the subject from opposite sides of an axis line of a test surface of the subject so as to put the axis line approximately perpendicularly to a direction of gravity, load generating means for generating different loads which are applied to the subject in the direction of gravity through the supporting means so that the subject cause different sizes of surface deformation in the test surface, optimized load deriving means for deriving a linear-functional relationship existing between the exploratory loads and the sizes of surface deformation for at least two different exploratory loads and determining an optimized load that makes the subject to cause surface deformation less than a predetermined size from the linear-functional relationship, and control means for controlling the load generating means to generate the optimized load derived from the linear-functional relationship. 
   The load generating means generates a load having a line of action that is perpendicular to an axis line of a measuring plane in which the test surface is positioned at a predetermined distance from the measuring plane in a direction of the axis line. 
   A surface profile measuring instrument equipped with the subject holding device for measuring a surface profile of a subject comprises the subject holding device and a surface profile measurement system that measures a surface profile of a test surface of a subject held by the subject holding device. The surface profile measurement system may comprise an interference optical system having a reference surface for forming an interference fringe pattern between surface wavefronts from the test surface and the reference surface and measuring a surface profile of the test surface on the basis of an optical image of the interference fringe pattern. 
   According to the subject holding method and device of the present invention, a subject is supported under an optimized load in a position wherein an axis line of a test surface of the subject is put perpendicularly to a direction of gravity, so as to be held in a stationary state. The optimized load is found from a linear-functional relationship existing between exploratory loads and surface deformation caused by the exploratory loads and, in particular, determined so that it acts on the subject to cause surface deformation less than a predetermined size of surface deformation admissible, for example, as a manufacturing error. Consequentially, the optimized load does not in any way have an adverse effect on measurements. Besides, it is prevented to invite a situation in which subjects at acceptable surface quality levels are disqualified resulting from inaccurate assessment of test surface due to an improper load acting on the subjects. 
   According to the According to the measuring instrument of the present invention, it is realized to perform measurement of surface profile of subjects with a high degree of accuracy. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The foregoing and other objects and features of the present invention will be clearly understood from the following detailed description when reading with reference to the accompanying drawings, wherein the same reference signs have been used to denote same or similar parts throughout the drawings, and in which: 
       FIG. 1  is a schematic view illustrating a measuring instrument according to an embodiment of the present invention; 
       FIG. 2  is a schematic view of a holding device for holding a subject being measured according to an embodiment of the present invention; 
       FIG. 3  is a chart illustrating a sequential procedure of holding a subject under an optimized load by the subject holding device; 
       FIG. 4  is a graphic chart showing a process of determining an optimized load to be applied to the subject being measured; 
       FIG. 5  is a schematic diagram showing a fundamental principle of determination of optimized load; and 
       FIG. 6  is a schematic view of an alternative holding device for holding a subject being measured. 
   

   DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   In the following description, the term “an axis line of a test surface” as used hereinafter shall mean and refer to a normal line of a test surface when the test surface is flat or a normal line passing through a center of a test surface when the test surface is curved In particular, when the subject is an optical element, the term “axis line shall means and refer to an optical axis of the optical element. 
   Referring to the accompanying drawings in detail, and in particular, to  FIG. 1  showing a measuring instrument according to an embodiment of the present invention for use in measuring, for example, a surface profile, a distribution of internal refraction indices, or the like of a subject such as a photomask in a clean room. The measuring instrument comprises an interferometric optical system  10  equipped with a computerized analytic unit  30 , a subject holding device  20   a  (shown in detail in  FIGS. 2A and 2B ) for holding a subject and the computer unit  30 . The interferometric optical system  10  is known in various types and may take any well known type such as one of Fizeau type laser interferometers. Specifically, the interferometric optical system  10  comprises a laser source  11 , an interference optical system  10  and an image sensor device  17  such as a CCD (Charge Coupled Device) or a CMOS (Complementary Metal-Oxide Semiconductor) device. The optical system comprises a magnifying lens  12 , a beam splitter  13  for reflecting a laser beam from the laser source  11  at a right angle, a collimator lens  14  and a transparent reference plate  15 , for example a glass plate, having a reference plane  15   a  arranged in order from the laser source  11  along an optical axis L. The optical system further comprises a focusing lens  16  arranged behind the beam splitter  13  on a side remote from the collimator lens  14  with respect to the beam splitter  13  so as to focus a laser beam passing through the beam splitter  13  onto the image sensor device  17 . Although not shown in  FIG. 1 , the reference plate  15  is provided with a fringe scan adapter operative to cause axial micromotion of the reference plate  15  in a direction of the optical axis L during a fringe scan measurement. 
   The computer unit  30 , that is made up of microprocessor, various memories, operation programs stored in the memories and other elements, includes functional blocks, namely at least an image analysis block  31  for analyzing a interference patter, an optimized load deriving block  32  for deriving a linear-functional relationship between a load and surface deformation and determining an optimized load to be applied to a subject based on the linear-functional relationship in a programmed analytic process, a load detection block  33  for detecting a load applied to a subject and a control block  34  for controlling the subject holding device  20   a , in particular an actuator  28  of the subject holding device  20   a . The computer unit  30  is connected to an external monitor (not shown) on which an image of interference pattern is displayed and a terminal device (not shown) through which various information are input into the computer unit  30 . 
   Referring to  FIGS. 2A and 2B  showing a subject holding device  20   a  in detail and a subject holding device according to an embodiment of the present invention, the subject holding device  20   a  comprises a backboard  21  having a square-shaped aperture  21   a  through which a surface wavefront of transmitted beam is monitored and a stationary table  27  secured thereto, stationary upper and movable lower jaws  22   a  and  23   a  having flat support faces, respectively, for nipping a subject  40   a  therebetween from above and beneath, a pair of load cells  24  for detecting loads acting on the subject  40   a  nipped between the upper and lower jaws  22   a  and  23   a , and a load applying mechanism for applying a load to the subject  40   a  in rotational asymmetric directions with respect to an axis line C of a test surface (a center normal line of a test surface of a subject). The stationary upper jaw  22   a  is secured to the backboard  21  and, on the other hand, the movable lower jaw  23   a  is mounted on a movable table  25  (which will be described below) through the load cells  24 . The load applying mechanism comprising the movable table  25  that is supported by a pair of guide blocks  26  mounted on the stationary table  27  so as to move up and down through guidance by linear guidepaths formed in the guide blocks  26 , load generating means such as, for example, a linear actuator  28  mounted in the stationary table  27  that is connected to the movable table  25  through a plunger  28   a  thereof so as to generate a load, in particular a compressive load in this embodiment, to be applied to the subject  40   a , and a regulator  29  for regulating a distance of protrusion of the plunger  28   a  which is connected between the control block  34  of the computer unit  30  and the linear actuator  28 . 
   The stationary upper jaw  22   a  and the movable lower jaw  23   a  are formed so as to nip the subject  40   a  in such a manner that the axis line C is put perpendicularly to a direction of gravity (a direction from the top to the bottom of the drawing). Although not shown in  FIGS. 2A and 2B , the upper and lower jaws  22   a  and  23   a  are provided with bracings for steadying front, rear and side surfaces of the subject  40   a  so as thereby to prevent the subject from inclining. Further, the upper and lower jaws  22   a  and  23   a  and their associated bracings are preferably made of a dust-free material such as polyether ether ketone (PEEK) or the like. The movable table  25  at an under side is provided with a pair of guide rods  25   a . The guide blocks  26  snugly receive the guide rods  25   a  for sliding movement so as thereby to allow the movable table  25  to move up and down. 
   The linear actuator  28  causes up and down linear movement of the plunger  28   a  in a direction D that is collinear with the line of action of the plunger  28   a  as shown in  FIG. 2B  so as to push up and pull down the movable table  25 . A apparent in  FIG. 2B , the linear actuator  28  is positioned so that the line of action of the plunger  28  is separated by a specified distance from a plane in which the subject  40   a  is held between the upper and lower jaws  22   a  and  23   a  and intersects the axis line C at a substantially right angle. According to the load applying mechanism, when the actuator  28  is activated, the plunger  28   a  is forced upward to push the movable table  25  upward in the direction D, so as thereby to hold down the subject  40   a  against the upper jaw  22 A through the load cells  24  and the lower jaw  23   a . Consequently, the subject  40   a  receives a vertical compression stress and a bending moment to the subject  40   a , thereby causing surface deformation due to bending in a test surface  41   a  thereof. At this time, the load cells  24  detect a vertical compression stress acting on the subject  40   a  and output a signal representing the load to the load detection block  33  of the computer unit  30 . As perceivable in  FIGS. 2A and 2B , the arrangement wherein the linear actuator  28  and the load cells  24  are located beneath the lower jaw  24  eliminates a possibility that the subject  40   a  is covered with dust flung due to motion of the linear actuator  28  and its associated parts at, in particular, the test surface  41   a . Although not shown in  FIGS. 2A and 2B , the subject holding device  20   a  is equipped with an inclination adjusting mechanism for adjusting an angle of inclination of a square-shaped subject  40   a  held thereby relative to the reference plate  15 , in particular the reference surface  15   a.    
   The following description will be directed to a practical sequential procedure of holding a subject  40   a  in the subject holding device  20   a  for use in combination with the interferometric  10  shown in  FIG. 1 . 
     FIG. 3  is a chart illustrating a sequential procedure of holding a subject  40   a  in the subject holding device  20   a  for use in combination with the interferometric measuring instrument shown in  FIG. 1 . 
   First of all, in a first step  1 , a subject  40   a  such as a parallel plate having an axis line C (a center normal line) is put between the upper and lower jaws  22   a  and  23   a  with a test surface  41   a  facing the interferometric  10  so as to locate the axis line C intersects the direction of gravity at a substantially right angle. At this time, the inclination adjusting mechanism associated with the reference plate  15  is operated to adjust a position of the reference plate  15  so that the reference surface  15   a  is parallelized to the test surface  41   a  of the subject  40   a . Subsequently, in step  2 , the linear actuator  28  is activated to apply a given compressive load to the subject  40  though the upper and lower jaws  23   a  and  25  in rotational asymmetric directions with respect to the axis line C in such a way that the test surface  40   a  causes bending deformation asymmetrical with respect to the axis line C in the test surface  41   a  under the load and a moment In step S 3 , a size of surface deformation of the test surface  41   a  occurring resulting from the action of load on the subject  40   a  is found by analyzing an image of a fringe pattern with the use of the interferometer  10  provided with the computer unit  30 . Specifically, a laser beam emanating from the laser source  11  and passing through the magnifying lens  12  is totally reflected at a right angel by the beam splitter  13  and then collimated by the collimator lens  14 . The collimated rays enter the reference plate  15  and then partly reflect on the reference surface  15   a  of the reference plate  15  internally and partly pass through the reference plate  15 . The reflected rays travel back passing through the collimator lens  14  as a reference beam. On the other hand, the collimated rays coming out of reference plate  15  impinge and reflect on the test surface  41   a  of the subject  40   a . The reflected rays travel back passing through the collimator lens  14  as an object beam. These reference beam and object beam passing through the collimator lens  14  are integrated with and interfere with each other, thereby forming an interfered surface wavefront The integrated beam further travels back and totally passes through the beam splitter  13 , and is then focused to for an optical image of fringe pattern representing a surface profile of the test surface  41   a  of the subject  40   a  on the image sensor device  17  by the focusing lens  16 . The image sensor device  17  converts the image of fringe pattern into image data signals and sends them to the image analysis block  31  of the computer unit  30 . The image analysis block  31  analyzes the image of fringe patter and finds a size of surface deformation of the test surface  41   a  of the subject  40   a  for the given load in programmed sequence. In this instance, a size of surface deformation is represented by an indicator such as a P-V value that is a measurement of an axial dance between an apex of a maximum concave deformation and a bottom of a convex deformation occurring in the test surface  41   a . The measurement is performed varying a plunger protrusion distance, and hence the given load, linearly increasingly so as to find a predetermined number of P-V values as indictors of surface deformation for various loads. The load varying with a change in plunger protrusion distance is monitored by the load cells  24 . In step  4 , an optimized load is derived by the aid of linear-functional relationship, for example a linear function, in the optimized load deriving block  32 . Specifically, first of all, a graphic representation of the measured P-V values (q) relative to the measured loads (p) is provided such as, for example, shown in FIG.  3 ( 4 ) and formula size by drawing a straight lineation (shown by a broken line) approximated as congruous to a sequential line (shown by a solid line) of a graphic representation as possible as representing a linear function. In this instance, the linear function is derived from the straight lineation and expressed in the formula of q(nm)=0.444p+137.38. 
   Subsequently, load-free surface deformation is figured out by substituting 0 (zero) for p in the linear function. A solution is found as 137.38. Further, a difference of the load-free surface deformation from maximum surface deformation admissible, for example, as a manufacturing error is figured out For instance, in the case where the maximum allowable surface deformation is 142.38 nm in P-V value, the difference is 5 nm. An optimized load is then set to a load, for example 11.2 g, with which the test surface  41   a  causes a change in surface deformation from the load-free surface deformation less than 5 nm in P-V value. 
   Approximation of the linear function to the sequential line of the graphic representation between P-V values (q) and loads (p) is based on the following logic. 
   Referring to  FIG. 4 , when applying a load to a subject  40   a  in the direction D that is collinear with the line of action of the plunger  28   a  of the linear actuator  28  as shown in  FIG. 2 , a size of surface deformation of a test surface  41   a  of the subject  40   a  due to bending can be modeled after a pendent straight beam with a free end to which a bending moment Mo is applied. In a fixed x-y coordinate system on the deformation model, a size of deformation (y) is given by the following formula.
 
 y =−Mo x   2 /(2 EI )
 
where E and I are the Young&#39;s modulus and the geometric second moment of area of the subject As apparent from the formula, the size of bending deformation (y) is given by a linear function of moment (Mo). This indicates the fact that the subject  40   a  causes surface deformation (y) varies linear-functionally with respect to a load applied thereto.
 
   In step  5 , when the optimized load is derived as described above, the control block  34  provides a command signal representative of the optimized load to activate the linear actuator  28  to protrude the plunger  28   a  so as to apply the optimized load to the subject  40   a  through the upper and lower jaws  22   a  and  23   a . A surface profile of the test surface  41   a  of the subject  40   a  is measured on the basis of an image of a fringe pattern with the use of the interferometer  10  provided with the computer unit  30  while it is held between the upper and lower jaws  22   a  and  23   a  under the optimized load. 
   Thereafter, in step  6 , the linear actuator  28  is deactivated to retract the plunger so as thereby to free the subject  40   a  from constriction with the upper and lower jaws  22   a  and  23   a  and then reactivated to protrude the plunger  28   a  so as thereby to apply the optimized load to the subject  40   a  through the upper and lower jaws  22   a  and  23   a  after turning the subject  40   a  substantially 90 degrees in position around the axis line C. Then, the same measurement of surface profile of the test surface  41   a  of the subject  40   a  is executed while the subject  40   a  is held under the optimized load. In step  7 , a verification test as to whether the optimized load is credible is conducted by comparative analysis of the surface profiles of the test surface  41   a  of the subject  40   a  held in the two different positions, for example, in the following way. 
   Coordinate transformation is performed for data of the surface profile of the test surface  41   a  after the repositioning of the subject  40   a  by turning the coordinate axes of the system of measurement 90 degrees. The data of the surface profiles of the surface  41   a  before and after the coordinate transformation are compared in order to find a finite difference between them. The optimized load is verified to be credible and effectually acceptable when the difference is less than a predetermined maximum difference, i.e. a predetermined verification tolerance, or to be incredible and unacceptable when the difference is beyond the predetermined verification tolerance. 
   Finally, in step  8 , when the optimized load is effectually acceptable, the control block  34  provides a command signal representative of the verified optimized load to activate the linear actuator  28  to apply the optimized load to the subject  40   a  through the protrude-the plunger  28   a , so as thereby to hold the subject  40  in a stationary standing position between the upper and lower jaws  22   a  and  23   a . The subject  40   a  held by the subject holding device  20   a  under the optimized load is put in condition for accurate measurement of optical properties of the test surface  41   a  of the subject  40   a  by the use of the interferometric measuring instrument equipped with the computer unit  30 . 
   In the sequence of holding a subject  40   a  in the subject holding device  20   a  described above, the credibility verification test in step  7  nay be left out of the sequential procedures. 
     FIG. 6  shows a subject holding device  20   b  according to an alternative embodiment in which the same parts or mechanisms of the subject holding device as those of the previous embodiment are denoted by the same reference numerals and not described for simplicity. As shown in  FIG. 6 , the subject holding device  20   b  is structured suitably for a round subject such as an optical lens element  40   b  having a test surface  41   b . Specifically, the subject holding device  20   b  has upper and lower stationary upper and movable lower jaws  22   b  and  23   b . The upper jaw  22   b  has an inverted V-shaped support face, and the lower jaws  23   a  has a V-shaped support face for nipping the subject  40   b  therebetween from above and beneath According to the subject holding device  20   b , the subject  40   b  is tightly and snugly held between the upper and lower jaws  22   b  and  23   b . These upper and lower jaws  22 B and  23 B may be prepared as replaceable parts for the upper and lower jaws  22   a  and  23   a  of the subject holding device  20   a  shown in  FIGS. 2A and 2B . 
   In any embodiments described above, the load applied to the subject may be a load causing tensile deformation in a test surface. 
   Although the above description is directed to the Fizeau type laser interferometer, the subject holding method and device are implemented in combination with various types of interferometric including a Michelson type interferometers, an inclined axis type interferometers and the like or with various types of surface profile measuring instruments including moire topographic measuring instruments, light-section type surface profile measuring instruments, etc. 
   It is to be understood that although the present invention has been described with regard to preferred embodiments thereof various other embodiments and variants may occur to those skilled in the art, which are within the scope and spirit of the invention, and such other embodiments and variants are intended to be covered by the following claims.