Patent Publication Number: US-2006017933-A1

Title: Heterodyne laser interferometer with porro prisms for measuring stage displacement

Description:
DESCRIPTION OF RELATED ART  
      A standard plane mirror interferometer configuration can be used for a multi-axis measurement of stage displacement and rotation. However, this configuration has a disadvantage for rotation measurements. As the stage rotates, the measurement beam translates, or walks off, relative to the reference beam location on the detector. The magnitude of the overlap of the reference and measurement beams decreases with this walk-off. Any solution that reduces this walk-off has superior dynamic range.  
      Rotations of the stage about an arbitrary axis can create an angle between reference and measurement beams (also called “beam pointing”) in addition to creating walk-off. Both effects limit the dynamic range of the measurements. Corner and roof reflectors have been implemented in a number of forms to minimize beam pointing and extend the dynamic range.  
      Double pass “roof” mirror interferometer designs have been implemented in the past. U.S. Pat. No. 6,208,424 (“de Groot”) discloses an exemplary double pass roof mirror design. The de Groot design requires a large space on the stage for measuring one axis because the measurement beam is separated both vertically (Z-direction) and horizontally (Y-direction) to strike the roof mirror at four different locations. This is an undesirable feature for wafer lithography. As the stage size requirement is large, stages limited by the measurement requirement are larger and heavier. Heavier stages can in turn limit the wafer throughput. In general, minimizing the space on the stage required for a displacement measurement can help wafer throughput.  
      Thus, what is needed is an interferometer design that minimizes the walk-off and the angle between reference and measurement beams while reducing the stage size requirement.  
     SUMMARY  
      In one embodiment of the invention, an interferometer system for measuring a displacement along a first direction includes (1) a measurement roof optic (e.g., a porro prism) mounted to a stage translatable along the first direction, (2) a polarizing beam splitter having (a) a first face opposite the measurement roof optic and (b) a second face opposite the first face, (3) a first wave plate located between the measurement porro prism and the first face of the polarizing beam splitter, and (4) a redirecting optic located opposite the first face of the polarizing beam splitter. A measurement path through the system includes only segments located substantially in a plane defined by the first direction and a second direction orthogonal to the first direction. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIGS. 1, 2 , and  3  illustrate an interferometer system that minimizes beam pointing and walk-off in one embodiment of the invention.  
       FIGS. 4, 5 , and  6  illustrate an interferometer system that minimizes beam pointing and walk-off in another embodiment of the invention.  
       FIG. 7  illustrates a variation of the interferometer system in  FIGS. 1, 2 , and  3  in one embodiment of the invention. 
    
    
      Use of the same reference numbers in different figures indicates similar or identical elements. Figures are not drawn to scale and are for illustrative purposes only.  
     DETAILED DESCRIPTION  
       FIG. 1  illustrates an interferometer system  100  in one embodiment of the invention. Although oriented to measure displacement along the Z-direction, system  100  can be oriented to measure along any axis.  
      A laser source  101  directs a coherent, collimated light beam to a left face  102  of a polarizing beam-splitter (PBS)  103 . The light beam consists of two orthogonally polarized frequency components. One frequency component f A  (e.g., a measurement beam initially S-polarized with respect to the PBS hypotenuse face) enters the system&#39;s measurement path while the other frequency component f B  (e.g., a reference beam initially P-polarized with respect to the PBS hypotenuse face) enters the system&#39;s reference path.  
       FIG. 2  illustrates the measurement path alone. The measurement path includes two passes to a measurement roof optic  104  (e.g., a porro prism). A porro prism is a 45-90-45° reflecting prism having two reflecting faces that form the 90° angle for reflecting the light beam through a total angle of 180°. Measurement porro prism  104  is mounted to a stage  108  whose translation along the Z-direction is to be measured. In a first measurement pass, a polarizing beam-splitter (PBS)  103  reflects the measurement beam through a lower face  105  to a half-wave plate  106 . Half-wave plate  106  rotates the polarization state of the measurement beam from the S-polarization to the P-polarization. The measurement beam then propagates to one reflecting surface of measurement porro prism  104 . Measurement porro prism  104  has its apex, which extends into or out of the page, substantially along the Y-direction. Measurement porro prism  104  reflects the measurement beam from two reflecting surfaces and the measurement beam exits in an offset path and without tilt relative to the input beam about the Y-direction back to PBS  103 . As the measurement beam is substantially P-polarized when it impinges measurement porro prism  104 , there is little phase shift caused by the reflection from measurement porro prism  104 . Nonetheless, an appropriate coating may be provided on the input face of measurement porro prism  104  to reduce any undesired phase shift.  
      PBS  103  now transmits the measurement beam through an upper face  109  to a redirecting optic  110  (e.g., a cube corner retroreflector). Cube corner  110  reflects the measurement beam from three reflecting surfaces and the measurement beam exits cube corner  110  in an offset but parallel path back to PBS  103 . Thus, cube corner  110  offsets the measurement beam in the X-direction and retroreflects beam tilts due to stage rotation about the X-direction. An appropriate coating may be provided on the reflecting faces of cube corner  110  to reduce any undesired phase shift. PBS  103  again transmits the measurement beam through lower face  105  toward half-wave plate  106 , which starts a second measurement pass through system  100 .  
      In the second measurement pass, half-wave plate  106  rotates the polarization state of the measurement beam back from the P-polarization to the S-polarization. The measurement beam then propagates to measurement porro prism  104 . Measurement porro prism  104  again reflects the measurement beam in an offset path and without tilt relative to the input beam about the Y-direction back to PBS  103 . PBS  103  now reflects the measurement beam through a left face  102  to detector  112 .  
       FIG. 3  illustrates the reference path alone. The reference path includes two passes to a reference roof optic  114  (e.g., a porro prism). In a first reference pass, PBS  103  transmits the reference beam through a right face  115  to a half-wave plate  116 . Half-wave plate  116  rotates the polarization state of the reference beam from the P-polarization to the S-polarization. The reference beam then propagates to one reflecting surface of reference porro prism  114 .  
      Reference porro prism  114  has its apex, which extends into or out of the page, substantially along the Y-direction. Reference porro prism  114  reflects the reference beam from two reflecting surfaces and the reference beam exits in an offset path and without tilt relative to the input beam about the Y-direction back to PBS  103 . Reference porro prism  114  also helps to match the optical path through glass in the reference path of the interferometer with the optical path through glass in the measurement path, which minimizes thermal effects. As the reference beam is substantially S-polarized when it impinges reference porro prism  114 , there is little phase shift caused by the reflection from reference porro prism  114 . Nonetheless, an appropriate coating may be provided on the reflecting faces of reference porro prism  114  to reduce any undesired phase shift. In one embodiment, porro prism  114  is replaced with a retroreflector. In this embodiment, the measurement and reference paths would be the same as those illustrated in  FIG. 1 .  
      PBS  103  now reflects the reference beam through upper face  109  to cube corner  110 . Cube corner  110  reflects the reference beam from three reflecting surfaces and the reference beam exits in an offset but parallel path back to PBS  103 . PBS  103  reflects the reference beam toward half-wave plate  116 , which starts a second reference pass through system  100 .  
      In the second reference pass, half-wave plate  116  rotates the polarization state of the reference beam from the S-polarization back to the P-polarization. The reference beam then propagates to reference porro prism  114 . Reference porro prism  114  again reflects the reference beam in an offset path and without tilt relative to the input beam about the Y-direction back to PBS  103 . Referring to  FIG. 1 , PBS  103  now recombines the reference beam with the measurement beam and transmits them to detector  112 . Detector  112  then measures the change in the phase of the recombined beam to determine the relative displacement of stage  108  along the Z-direction.  
       FIG. 7  illustrates an interferometer system  100 A, which is a variation of interferometer system  100  in one embodiment of the invention. In system  100 A, reference porro prism  114  is replaced with a reference plane mirror  114 A and half-wave plate  116  is replaced with a quarter-wave plate  116 A that extends across right face  115  of PBS  103 . To ensure the optical path through glass in the measurement and reference paths are balanced, a glass slug  122  is placed between quarter-wave plate  116 A and reference plane mirror  114 A. Alternatively, glass slug  122  can be placed between quarter wave plate  116 A and PBS  103 . Also, quarter wave plate  116 A, or glass slug  122 , can be coated with a reflective coating that replaces reference plane mirror  114 A.  
      The measurement path in system  100 A is the same as the measurement path in system  100  and will not be repeated.  
      In the reference path, PBS  103  transmits the reference beam through quarter-wave plate  116 A and glass slug  122  onto reference plane mirror  114 A. Reference plane mirror  114 A reflects the reference beam back onto itself and back through quarter-wave plate  116 A. As the reference beam passes through quarter-wave plate  116 A twice, the newly S-polarized reference beam is reflected by PBS  103  into cube corner  110 . Cube corner  110  returns the reference beam in an offset but parallel path into PBS  103 .  
      PBS  103  reflects the reference beam through quarter-wave plate  116 A and glass slug  122  onto reference plane mirror  114 A. Reference plane mirror  114 A reflects the reference beam back onto itself and back through quarter-wave plate  116 A. The newly P-polarized reference beam is recombined with the measurement beam and transmitted by PBS  103  onto detector  112 .  
       FIG. 4  illustrates an interferometer system  400  in one embodiment of the invention. Although oriented to measure displacement along the Z-axis, system  400  can be oriented to measure along any axis.  
      As described above, laser source  101  directs a light beam consisting of two orthogonally polarized frequency components to left face  102  of PBS  103 . Again one frequency component f A  (e.g., a measurement beam initially S-polarized with respect to the PBS hypotenuse face) enters the system&#39;s measurement path while the other frequency component f B  (e.g., a reference beam initially P-polarized with respect to the PBS hypotenuse face) enters the system&#39;s reference path.  
       FIG. 5  illustrates that the measurement path alone. The measurement path includes two passes to a measurement roof optic  404  (e.g., a porro prism) mounted to stage  108  whose translation along the Z-direction is to be measured. In a first measurement pass, PBS  103  reflects the measurement beam through lower face  105  to a quarter-wave plate  406 . Quarter-wave plate  406  transforms the linearly polarized light to circularly polarized light. The measurement beam then impinges the apex of measurement porro prism  404 . Measurement porro prism  404  has its apex, which extends horizontally on the page, substantially along the Y-direction. Measurement porro prism  404  reflects the measurement beam without tilt relative to the input beam about the Y-direction back through quarter-wave plate  406 .  
      As the measurement beam is circularly polarized when it impinges measurement porro prism  404 , the reflection from prism  404  may cause an undesired phase shift and change the polarization of the measurement beam from circular to elliptical. Thus, for a measurement porro prism  404  made of a single piece of glass, an appropriate coating  420  ( FIG. 4B ) may be provided on the two reflecting faces of prism  404  to compensate the undesired phase shift and shift handedness from left to right or from right to left. Producing 180 (modulo  360 ) degrees phase shift between S and P polarization will achieve this goal.  
      In one embodiment for a BK7 measurement porro prism  404 , coating  420  includes a first layer of silicon dioxide (SiO 2 ) having a quarter wave optical thickness (QWOT) of 1.7504 and formed on the uncoated glass faces  415 A and  415 B of prism  404 , a second layer of titanium dioxide (TiO 2 ) layer having a QWOT of 1.2771 and formed on the first layer, a third layer of SiO 2  having a QWOT of 1.6731 and formed on the second layer, and a fourth layer of TiO 2  having a QWOT of 1.9918 and formed on the third layer. QWOT is equal to 4*n*t divided by λ, where n is the refractive index, t is the physical thickness, and λ is the design wavelength. The indices of refraction of TiO2 and SiO2 are 2.432 and 1.477, respectively at 633 nm design wavelength. Coating  420  can be formed by physical vapor deposition (PVD) with ion assist. Coating  420  on each reflecting surface achieves a 90 degree phase shift between S and P polarizations at an angle of incidence of 45 degrees. Thus, after exiting measurement porro prism  404 , coating  420  has produced a total phase shift on the return beam of 180 degrees and the circular polarization will shift handedness from left to right or from right to left.  
      In other embodiments, a first coating that produces 0 degree phase shift is formed on one reflecting surface of measurement porro prism  404  and a second coating that produces 180 degree phase shift is formed on the other reflecting surface of the measurement porro prism  404 . Thus, the coatings produce a total phase shift on the return beam of 180 degrees and the circular polarization will shift handedness from left to right or from right to left.  
      Referring back to  FIG. 5 , quarter-wave plate  406  transforms the circularly polarized light to linearly polarized light. The measurement beam then propagates to PBS  103 . PBS  103  now transmits the measurement beam through upper face  109  to cube corner  110 . Thus, cube corner  110  offsets the measurement beams in the Y-direction and retroreflects beam tilts due to stage rotation about the X-direction. In another embodiment, cube corner  110  is replaced with a porro prism. Cube corner  110  reflects the measurement beam from three reflecting surfaces and the measurement beam exits in an offset but parallel path back to PBS  103 . An appropriate coating may be provided on the reflecting faces of cube corner  110  to reduce any undesired phase shift. PBS  103  again transmits the measurement beam through lower face  105  toward quarter-wave plate  406 , which starts a second measurement pass through system  400 .  
      In the second measurement pass, half-wave plate  406  transforms the linearly polarized light to circularly polarized light. The measurement beam then impinges the apex of measurement porro prism  404 . Measurement porro prism  404  then reflects the measurement beam without tilt relative to the input beam about the Y-direction back through quarter-wave plate  406 . Quarter-wave plate  406  transforms the circularly polarized light to linearly polarized light. The measurement beam then propagates to PBS  103 . PBS  103  now reflects the measurement beam through left face  102  to detector  112 .  
       FIG. 6  illustrates that the reference path alone. The reference path includes two passes to a reference roof optic  414  (e.g., a porro prism). In a first reference pass, PBS  103  transmits the reference beam through right face  115  to a half-wave plate  416 . Half-wave plate  416  transforms the linearly polarized light into circularly polarized light. The reference beam then impinges the apex of reference porro prism  414 . Reference porro prism  414  has its apex, which extends horizontally on the page, substantially along the Z-direction. Reference porro prism  414  reflects the reference beam without tilt relative to the input beam about the Z-direction back through quarter-wave plate  416 .  
      As the reference beam is circularly polarized when it impinges measurement porro prism  414 , the reflection from prism  414  may cause an undesired phase shift and change the polarization of the measurement beam from circular to elliptical. Thus, for a measurement porro prism  414  made of a solid piece of glass, a coating  422  ( FIG. 4B ) similar to coating  420  described above may be provided on the reflecting faces of mirror  416  to compensate the undesired phase shift and preserve the circular polarization.  
      In another embodiment, reference porro prism  414  is replaced with a reference plane mirror. However, if measurement porro prism  404  is made of solid glass, a glass slug may be placed in the reference path to balance the optical path through glass in the measurement and reference paths similar to the configuration shown in  FIG. 7 .  
      Referring back to  FIG. 6 , quarter-wave plate  416  transforms the circularly polarized light to linearly polarized light. The reference beam propagates to PBS  103 . PBS  103  now reflects the reference beam through upper face  109  to cube corner  110 . Cube corner  110  reflects the reference beam from three reflecting surfaces and the reference beam exits in an offset but parallel path back to PBS  103 . PBS  103  again reflects the reference beam through right face  115  toward quarter-wave plate  416 , which starts a second reference pass through system  400 .  
      In the second measurement pass, quarter-wave plate  406  transforms the linearly polarized light to circularly polarized light. The measurement beam then impinges the apex of reference porro prism  414 . Reference porro prism  404  then reflects the reference beam without tilt relative to the input beam about the Z-direction back through quarter-wave plate  416 . Quarter-wave plate  416  transforms the circularly polarized light to linearly polarized light. The reference beam then propagates to PBS  103 . PBS  103  now recombines the reference beam with the measurement beam and transmits them to detector  112 . Detector  112  then measures the change in the beat frequency of the recombined beam to determine the relative displacement of stage  108  along the Z-direction.  
      In the operation of systems  100  and  400 , porro prisms  104  and  404  accommodate the rotation of stage  108  along the Y-direction by ensuring that the measurement beam enters and exits without tilt relative to the input beam about the Y-direction (i.e., minimizes beam pointing). However, depending on the location of the rotational axes  118  ( FIG. 1 ) and  418  ( FIG. 4 ) of stage  108 , the separation between the input and output paths of the measurement beam may change and thereby cause walk-off at detector  112 . In this embodiment, rotational axes  118  and  418  are located inside measurement porro prisms  104  and  404  to minimize walk-off at detector  112 . The optimum rotational axis occurs parallel to the roof axis of the porro prism. If the height from the input face to of the apex of the porro prism is “h” and the index of the porro prism material is “n,” then this optimum rotational axis is located inside the porro prism at a distance h/n from the input face of the porro prism. The stage can rotate about any axis in general, but rotations of the stage about these other axes cause beam walk-off. Rotations parallel to but offset from the optimum axis are not expected to be a significant limitation of the dynamic range of the system.  
      In one embodiment, measurement porro prisms  104  and  404  are each replaced with a hollow mirror with two reflective surfaces oriented orthogonal to each other. In this embodiment, rotational axes  118  and  418  can be located at the apex of mirrors  104  and  404  to minimize walk-off at detector  112 . Note that other porro prisms in the embodiments described above can also be replaced with this type of mirror.  
      Systems  100 ,  100 A, and  400  offers space-savings over the prior art. The measurement beam now only strikes measurement porro prism  104  and  404  at two locations, thereby decreasing the overall size of systems  100 ,  100 A, and  400 . Specifically, in systems  100  and  100 A, the measurement and reference beams only travel in a plane along the X and Z-directions so there is not beam separation along the Y-direction at nominal alignment. In system  400 , the measurement and reference beams only travel in a plane along the Y and Z-directions so there is no beam separation along the X-direction at nominal alignment.  
      Various other adaptations and combinations of features of the embodiments disclosed are within the scope of the invention. “Turned” configurations are shown in the figures, i.e. a configuration where the interferometer input beam is aligned with a direction substantially orthogonal to the measurement axis. However, “unturned” configurations are trivial rearrangements of the components such that the interferometer input beam is inline with the measurement direction. Note that any wave plate described in the embodiments above may be a discrete wave plate or a wave plate coating formed on an optical component. Numerous embodiments are encompassed by the following claims.