Patent Publication Number: US-8542345-B2

Title: Measurement apparatus, exposure apparatus, and device manufacturing method to measure numerical aperture of the optical system using interference fringe

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to a measurement apparatus which measures the numerical aperture of an optical system to be measured, an exposure apparatus including the measurement apparatus, and a method of manufacturing a device using the exposure apparatus. 
     2. Description of the Related Art 
     An exposure apparatus for manufacturing devices such as semiconductor devices illuminates an original, on which a pattern is formed, with light to project the pattern of the original onto a substrate by a projection optical system. With this operation, the pattern of the original is transferred onto the photosensitive agent on the substrate. The resolution of the projection optical system depends on the numerical aperture (NA) of the projection optical system; the resolution improves as the numerical aperture increases. In view of this, the numerical aperture of the projection optical system is an important index indicating the performance of the projection optical system. 
     To calculate the numerical aperture of the projection optical system, one known method calculates a resolution RP of the projection optical system and computes the numerical aperture based on a relation RP=λ/NA (Japanese Patent Laid-Open No. 2002-5787). This method calculates the resolution RP by transferring various patterns having different line widths onto a substrate via the projection optical system, and measuring, by a measurement apparatus such as an SEM, the pattern thus formed on the substrate. Unfortunately, it is difficult to precisely calculate the numerical aperture because the resolution RP also depends on the properties of the photosensitive agent (photoresist) and the aberration of the projection optical system. 
     SUMMARY OF THE INVENTION 
     The present invention provides a technique advantageous to more precisely calculate the numerical aperture of an optical system to be measured. 
     One of the aspect of the present invention provides a measurement apparatus which measures a numerical aperture of an optical system to be measured, the measurement apparatus comprising a mirror configured to reflect test light which passes through the optical system, an interferometer unit which includes an image sensor and is configured to form an interference fringe on an image sensing plane of the image sensor by reference light and the test light reflected by the mirror, and a controller configured to control the interferometer unit, and to compute a numerical aperture of the optical system based on the interference fringe captured by the image sensor, wherein the controller is configured to compute a numerical aperture NA of the optical system by multiplying a quotient ΔNA/ΔR, describing a change ΔNA in numerical aperture NA of the optical system with respect to a change ΔR in pupil radius R of the optical system in the image sensing plane, by the pupil radius R of the optical system in the image sensing plane. 
     Further features of the present invention are made apparent from the following description of exemplary embodiments with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a view showing the schematic arrangement of a measurement apparatus according to a first embodiment of the present invention; 
         FIG. 2  is a flowchart showing the sequence of an operation for measuring the numerical aperture (NA) of an optical system to be measured; 
         FIG. 3  is a graph illustrating the change width of the output (pixel value) from each pixel of an image sensor upon fringe scanning; and 
         FIG. 4  is a view showing the schematic arrangement of an exposure apparatus according to a second embodiment of the present invention. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Various embodiments of the present invention will be described below with reference to the accompanying drawings. 
       FIG. 1  is a view showing the schematic arrangement of a measurement apparatus according to a first embodiment of the present invention. Although the measurement apparatus according to the first embodiment includes a Fizeau interferometer as an interferometer for measuring the wavefront aberration of an optical system to be measured (e.g., a projection optical system of an exposure apparatus), it may include an interferometer of another scheme. The arrangement and operation of the measurement apparatus according to the first embodiment of the present invention will now be explained with reference to  FIG. 1 . 
     Light from a light source (e.g., a laser light source)  101  which emits light, having high coherence and an oscillation wavelength close to the wavelength of light for use in an optical system  116  to be measured, is guided to an interferometer unit  102 . Inside the interferometer unit  102 , a condenser lens  103  converges the light on a spatial filter  104 . The diameter of the spatial filter  104  can be set to about ½ that of an Airy disk, which is determined depending on the numerical aperture (NA) of a collimator lens  106 . With this setting, the light emerging from the spatial filter  104  turns into an ideal spherical wave. The resultant light is transmitted through a half mirror  105 , converted into collimated light by the collimator lens  106 , and output from the interferometer unit  102 . 
     The light emerging from the interferometer unit  102  strikes a TS (transmissive sphere)  114  via mirrors  111 ,  112 , and  113  of a light extension optical system  110 . At this time, a TS driving mechanism TSD controls the position of the TS  114  in the X, Y, and Z directions. The TS driving mechanism TSD includes a Z stage  124 , X stage  123 , and Y stage  122  for driving the TS  114  in the Z, X, and Y directions, respectively, and a stage base plate  121 . The mirror  111  is fixed on the stage base plate  121 . The mirror  112  is fixed on the Y stage  122  and moves in the Y direction. The mirror  113  is fixed on the X stage  123  and moves in the X direction. 
     The light which strikes the TS  114  and is reflected by a Fizeau surface as the final surface of the TS  114  serves as reference light. The reference light travels back to the interferometer unit  102  via the TS  114 , the mirrors  113 ,  112 , and  111 , and the light extension optical system  110 . 
     The light transmitted through the TS  114  serves as test light. The test light forms an image on the object plane of the optical system  116 , enters and passes through the optical system  116 , and forms an image again on the image plane of the optical system  116 . The test light is reflected by an RS (reflective sphere)  117 , and travels back to the interferometer unit  102  via the optical system  116 , the TS (transmissive sphere)  114 , the mirrors  113 ,  112 , and  111 , and the light extension optical system  110 . The RS (reflective sphere)  117  exemplifies a mirror which reflects the test light having passed through the optical system  116 . 
     An RS driving mechanism RSD controls the position of the RS  117  in the X, Y, and Z directions. The RS driving mechanism RSD includes a Z stage  127 , X stage  126 , and Y stage  125  for driving the RS  117  in the Z, X, and Y directions, respectively. The RS driving mechanism RSD can position the RS  117  at an arbitrary image height position in the optical system  116 . 
     The light beams having traveled back to the interferometer unit  102  in the form of reference light and test light are transmitted through the collimator lens  106 , reflected by the half mirror  105 , and converged on a spatial filter  107 . The spatial filter  107  serves to shield any stray light and steep wavefronts. The reference light and test light having passed through the spatial filter  107  are guided to the image sensing plane of an image sensor  109  by an imaging lens  108  as nearly collimated light beams. An interference fringe is formed on the image sensing plane of the image sensor  109  by superposition of the reference light and the test light. 
     A high-precision position measurement device such as a laser length measurement device measures the positions of the X stage  123 , Y stage  122 , and Z stage  124  which constitute the TS driving mechanism TSD (these positions indirectly indicate the X, Y, and Z positions of the TS  114 ), and the positions of the X stage  126 , Y stage  125 , and Z stage  127  which constitute the RS driving mechanism RSD (these positions indirectly indicate the X, Y, and Z positions of the RS  117 ). Based on the measurement results obtained by the position measurement device, a TS driving controller  128  which controls the TS driving mechanism TSD, and an RS driving controller  129  which controls the RS driving mechanism RSD control the positions of the TS  114  and RS  117 , respectively, with high accuracy under the control of a position controller  130 . 
     The position controller  130  can move the TS  114  and the RS  117  to an arbitrary image height position in the optical system  116  by controlling the TS driving controller  128  and the RS driving controller  129  based on a command from a main controller  131 . This makes it possible to measure the wavefront aberration of the optical system  116  at an arbitrary image height position in the optical system  116 . 
     The interference fringe captured by the image sensor  109  is transferred to the main controller  131 . The wavefront of the optical system  116  is computed based on a plurality of interference fringes captured in accordance with the fringe scanning method. 
     The principle of a method of measuring the numerical aperture (NA) of the optical system  116  will now be explained. First, the image sensor  109  captures a first interference fringe formed on the image sensing plane of the image sensor  109  in a first state that is the position of the RS  117 , serving as a mirror which reflects the test light having passed through the optical system  116 , relative to the optical system  116 . Next, the position of the RS  117  relative to the optical system  116  is changed from the first state to a second state, and the image sensor  109  captures a second interference fringe formed on the image sensing plane of the image sensor  109  in the second state. 
     More specifically, the first state can be, for example, a state in which an interference fringe in a null state (a state in which there is no interference fringe accounted for by alignment of the RS  117  with respect to the optical system  116 ) is formed as a first interference fringe. The second state can be, for example, a state in which a tilt fringe is formed as a second interference fringe. The change from the first state to the second state can be performed by, for example, moving the RS  117  by ΔX in the X direction along the image plane of the optical system  116 . Alternatively, the change from the first state to the second state can be performed by, for example, moving the RS  117  by ΔY in the Y direction along the image plane of the optical system  116 . A case in which the change from the first state to the second state is performed by moving the RS  117  by ΔX in the X direction along the image plane of the optical system  116  will be exemplified hereinafter. Note that ΔX can be interpreted as a variable representing the amount of movement of the RS  117  between the first state and the second state. 
     A first radius R 1  is set to an arbitrary value as the pupil radius of the optical system  116  in the image sensing plane of the image sensor  109 . A wavefront difference W 1  is then computed. The wavefront difference W 1  is the difference between the wavefront of the optical system  116  computed based on a first interference fringe formed in the first state using the first radius R 1 , and the wavefront of the optical system  116  computed based on a second interference fringe formed in the second state using the first radius R 1 . Also, a second radius R 2  (R 1 ≠R 2 ) is set to an arbitrary value as the pupil radius of the optical system  116  in the image sensing plane of the image sensor  109 . A wavefront difference W 2  is then computed. The wavefront difference W 2  is the difference between the wavefront of the optical system  116  computed based on a first interference fringe formed in the first state using the second radius R 2 , and the wavefront of the optical system  116  computed based on a second interference fringe formed in the second state using the second radius R 2 . Note that the first radius R 1  and the second radius R 2  can be arbitrarily set for wavefront computation, as described above. 
     Assume that a change in pupil radius R of the optical system  116  in the image sensing plane of the image sensor  109  is ΔR (=R 1 −R 2 ), and a change in wavefront difference is ΔW (=W 1 −W 2 ) herein. The change ΔW in wavefront difference with respect to the change ΔR in pupil radius R of the optical system  116  in the image sensing plane, for use in wavefront computation, is given by:
 
Δ W/ΔR =( W 1 −W 2)/( R 1 −R 2)  (1)
 
     A wavefront difference W generated upon moving the RS  117  by ΔX is given by:
 
 W =NA·Δ X   (2)
 
where NA is the numerical aperture of the optical system  116 .
 
     Equation (2) can be rewritten to describe the NA as:
 
NA= W/ΔX   (3)
 
     From equation (3), a quotient ΔNA/ΔR describing a change ΔNA in numerical aperture NA with respect to a change ΔR in pupil radius R of the optical system  116  in the image sensing plane of the image sensor  109  is given by:
 
ΔNA/Δ R =(Δ W/ΔR )/Δ X =( W 1 −W 2)/{( R 1 −R 2)·Δ X}   (4)
 
     Hence, based on the quotient ΔW/ΔR calculated in accordance with equation (1) and the amount of movement ΔX of the RS  117 , the quotient ΔNA/ΔR describing the change ΔNA in numerical aperture NA with respect to the change ΔR in pupil radius R of the optical system  116  in the image sensing plane of the image sensor  109  can be calculated in accordance with equation (4). 
       FIG. 3  is a graph illustrating the change width of the output (pixel value) from each pixel of the image sensor  109  upon fringe scanning. The abscissa indicates the position (pixel coordinate) in the image sensing plane of the image sensor  109 . A light incidence region in the image sensing plane of the image sensor  109  (i.e., a region where an interference fringe is formed) is the pupil region of the optical system  116  in the image sensing plane of the image sensor  109 . Using the radius R of this region, the numerical aperture NA of the optical system  116  can be calculated in accordance with:
 
NA=(ΔNA/Δ R )× R   (5)
 
     An operation for measuring the numerical aperture (NA) of the optical system  116  will now be explained with reference to the flowchart shown in  FIG. 2 . The main controller (controller)  131  controls this operation. 
     In step S 210 , the main controller  131  controls the RS driving mechanism RSD so that the position of the RS  117  relative to the optical system  116  becomes the first state, and acquires data on a first interference fringe formed on the image sensing plane of the image sensor  109 . The main controller  131  also controls the RS driving mechanism RSD so that the position of the RS  117  relative to the optical system  116  becomes the second state, and acquires data on a second interference fringe formed on the image sensing plane of the image sensor  109 . 
     In step S 220 , based on radii R 1  and R 2 , wavefront differences W 1  and W 2 , and an amount of movement ΔX, a quotient ΔNA/ΔR is computed in accordance with equation (4). The wavefront difference W 1  is the difference between the wavefront of the optical system  116  computed based on a first interference fringe using the first radius R 1 , and the wavefront of the optical system  116  computed based on a second interference fringe using the first radius R 1 . The wavefront difference W 2  is the difference between the wavefront of the optical system  116  computed based on a first interference fringe using the second radius R 2 , and the wavefront of the optical system  116  computed based on a second interference fringe using the second radius R 2 . 
     In step S 230 , the main controller  131  computes a pupil radius R of the optical system  116  in the image sensing plane of the image sensor  109  using at least one of the first interference fringe or the second interference fringe, or using another interference fringe captured by the image sensor  109 . 
     In step S 240 , the main controller  131  computes a numerical aperture NA of the optical system  116  by multiplying the quotient ΔNA/ΔR by the pupil radius R of the optical system  116  in the image sensing plane of the image sensor  109 , as shown in equation (5). 
     A method of calculating the numerical aperture of the optical system  116  based on a null fringe and a tilt fringe has been exemplified in the above-mentioned embodiment. However, according to the principle of the present invention, it is possible to calculate the numerical aperture of the optical system  116  based on interference fringes obtained in at least two states different in the alignment state (positional relationship) of the RS  117  with respect to the optical system  116 . Since the quotient ΔNA/ΔR is determined depending on the arrangement of an interferometer, it does not need to be calculated for each measurement of the numerical aperture of the optical system. 
       FIG. 4  is a view showing the schematic arrangement of an exposure apparatus according to a second embodiment of the present invention. This exposure apparatus includes a projection optical system which projects the pattern of an original onto a substrate, and a measurement apparatus which measures the numerical aperture of the projection optical system as an optical system to be measured. The principle, operation, and arrangement of this measurement apparatus can be the same as in the first embodiment. 
     Referring to  FIG. 4 , a light beam emitted by a light source  1  such as an excimer laser (an ArF excimer laser or a KrF excimer laser) is converted into one having a beam shape symmetrical about the optical axis by a beam shaping optical system  2 , and is guided to a light path switching mirror  3  in measuring a projection optical system  16 . The light path switching mirror  3  is retracted outside the light path during substrate exposure. The light beam emerging from the beam shaping optical system  2  enters an incoherence unit  4  in substrate exposure and is reduced in coherence. After that, the light beam passes through an illumination optical system and illuminates an original  15 . The projection optical system  16  serves as both an optical system which projects the pattern of the original  15  onto a substrate  18 , and a measurement target (an optical system to be measured) for the measurement apparatus. 
     The arrangement of the measurement apparatus will now be explained. In measuring the projection optical system  16 , the light beam from the beam shaping optical system  2  is reflected by the light path switching mirror  3 , and guided, by a light extension optical system  6 , to the vicinity of an interferometer unit  29  located near the location plane of the original  15 . The light beam emerging from the light extension optical system  6  is converged on one point by a condenser lens  7 . A pinhole  8  has been formed near the focal plane of the condenser lens  7 . The light beam having passed through the pinhole  8  is converted into collimated light by a collimator lens  9 . The diameter of the pinhole  8  has been set nearly equal to that of an Airy disk, which is determined depending on the numerical aperture of the collimator lens  9 . As a consequence, the light beam emerging from the pinhole  8  is a nearly ideal spherical wave. 
     The collimated light from the collimator lens  9  is reflected by a half mirror  10  and guided to a TS (transmissive sphere)  12  via a plane mirror  11  located on an X-Y-Z stage mechanism  13 . The TS  12  corresponds to the foregoing TS  114 . 
     At this time, the TS  12  can be inserted into and retracted from the light path by moving the X-Y-Z stage mechanism  13 . The X-Y-Z stage mechanism  13  can function as the foregoing TS driving mechanism TSD. 
     An RS  20  is located on an X-Y-Z stage mechanism  19  serving as a substrate stage mechanism which holds the substrate  18 . The RS  20  corresponds to the foregoing RS  117 . The center of curvature of the RS  20  lies in a plane flush with the surface of the substrate  18 . The light beam from the projection optical system  16  is reflected by the RS  20 , passes through the projection optical system  16  and the TS  12  while tracing back along roughly the same light path it has traversed, is transmitted through the half mirror  10  of the interferometer via the plane mirror  11 , and enters the interferometer unit  29 . The interferometer unit  29  corresponds to the foregoing interferometer unit  102 . The interferometer unit  29  includes a lens  27  and an image sensor  28  as same as the interferometer unit  102 . 
     A driving controller  30  which controls the X-Y-Z stage mechanism  13 , and a driving controller  31  which controls the X-Y-Z stage mechanism  19  control the positions of the TS  12  and the RS  20 , respectively, with high accuracy under the control of a position controller  32 . A main controller (controller)  33  controls the X-Y-Z stage mechanism  13  and the X-Y-Z stage mechanism  19  through the position controller  32 , and controls the interferometer unit  29 . The main controller (controller)  33  not only controls a substrate exposure operation but also performs a process for measuring the numerical aperture of the projection optical system  16  as an optical system to be measured. Details of the measurement controlled by the main controller  33  are the same as in the main controller  131  of the first embodiment. 
     A device manufacturing method according to another embodiment of the present invention is suitable for manufacturing, for example, a semiconductor device and a liquid crystal device. This method includes, for example, a step of transferring the pattern of an original onto a photosensitive agent applied on a substrate using the above-mentioned exposure apparatus, and a step of developing the photosensitive agent. The devices are further processed by, for example, known subsequent steps (e.g., etching, resist removal, dicing, bonding, and packaging). 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and functions. 
     This application claims the benefit of Japanese Patent Application No. 2008-238388, filed Sep. 17, 2008, which is hereby incorporated by reference herein in its entirety.