Abstract:
A reflective optical system, in which radiation from a radiation source is directed to an image focus or intermediate focus, including one or more mirrors (symmetric about the optical axis). Each mirror has at least first and second reflective surfaces, whereby radiation from the source undergoes successive grazing incidence reflections in an optical path at first and second reflective surfaces. The first and second reflective surfaces are formed such that the angles of incidence of the successive grazing incidence reflections at the first and second reflective surfaces are substantially equal. Each mirror may be formed as an electroformed monolithic component, wherein the first and second reflective surfaces are each provided on a respective one of two contiguous sections of the mirror. The reflective optical system may be embodied in a collector optical system for EUV lithography, or in an EUV or X-ray telescope or imaging optical system.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims priority to and the benefit of the filing date of PCT Application No. PCT/EP2007/006736, filed Jul. 30, 2007 and European Patent Application No. EP 06 425 539.1, filed Jul. 28, 2006, which are each hereby incorporated by reference in their entirety. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    The present invention relates to reflective (mirror based) optics, and more particularly to multi-reflection optical systems and their fabrication. 
         [0003]    A well known optical design for X-ray applications is the type I Wolter telescope. The optical configuration of type I Wolter telescopes consists of nested double-reflection mirrors operating at grazing incidence angles low enough to assure high reflectivity from the coating material, normally gold. In type I Wolter mirrors, the X-ray radiation from distant sources is first reflected by a parabolic surface and then by a hyperboloid, both with cylindrical symmetry around the optical axis. 
         [0004]    More recently, a variation of the type I Wolter design already proposed for other applications, in which the parabolic surface is replaced by an ellipsoid, has found application for collecting the radiation at 13.5 nm emitted from a small hot plasma used as a source in Extreme Ultra-Violet (EUV) microlithography, currently considered a promising technology in the semiconductor industry for the next generation lithographic tools. Here, there is a performance requirement to provide a near constant radiation energy density or flux across an illuminated silicon wafer target at which an image is formed. The hot plasma in EUV lithography source is generated by an electric discharge (Discharge Produced Plasma or DPP source) or by a laser beam (Laser Produced Plasma or LPP source) on a target consisting of Lithium, Xenon, or Tin, the latter apparently being the most promising. The emission from the source is roughly isotropic and, in current DPP sources, is limited by the discharge electrodes to an angle of about 60° or more from the optical axis. EUV lithography systems are disclosed, for example, in US2004/0265712A1 entitled “Detecting Erosion In Collector Optics With Plasma Sources In Extreme Ultraviolet (EUV) Lithography Systems”, US2005/0016679A1 entitled “Plasma-based debris mitigation for extreme ultraviolet (EUV) light source” and US2005/0155624A1 entitled “Erosion mitigation for collector optics using electric and magnetic fields”. 
         [0005]    The purpose of the collector in EUV sources is to transfer the largest possible amount of in-band power emitted from the plasma to the next optical stage, the illuminator, of the lithographic tool. The collector efficiency is defined as the ratio between the in-band power at the intermediate focus and the total in-band power radiated by the source in 2π sr. For a given maximum collection angle on the source side, the collector efficiency is mainly determined by the reflectivity of the coating on the optical surface of the mirrors. 
         [0006]    A problem with known systems is that that collector efficiency is significantly lower than it might be since the reflectivity of the coating is not exploited in the most efficient way; any improvement in the collector efficiency is highly desirable. 
         [0007]    A further problem is that, with the collector efficiencies available, there is imposed the need to develop extremely powerful sources, and to have high optical quality and stability in the collector. 
         [0008]    A further problem is that, with the collector efficiencies available, the overall efficiency of the lithographic equipment may not be high enough to sustain high volume manufacturing and high wafer throughput. 
         [0009]    A further problem is that the collector lifetime may be relatively short due to exposure to extremely powerful sources. 
       BRIEF DESCRIPTION OF THE INVENTION 
       [0010]    The present invention seeks to address the aforementioned and other issues. 
         [0011]    Various embodiments of the present invention find application in diverse optical systems, examples being collector optics for lithography, and telescope or imaging (e.g., X-ray) systems. 
         [0012]    According to one aspect of various embodiments of the present invention there is provided a collector reflective optical system, in which radiation from a radiation source is directed to an image focus, comprising: one or more mirrors, the or each mirror being symmetric about an optical axis extending through the radiation source and the or each mirror having at least first and second reflective surfaces whereby, in use, radiation from the source undergoes successive grazing incidence reflections in an optical path at the first and second reflective surfaces; and wherein the at least first and second reflective surfaces are formed such that the angles of incidence of the successive grazing incidence reflections at the first and second reflective surfaces are substantially equal. 
         [0013]    The angles of incidence of said successive grazing incidence reflections may be substantially equal for all rays incident on said reflective surfaces. 
         [0014]    Each mirror may be formed as an electroformed monolithic component, and wherein the first and second reflective surfaces are each provided on a respective one of two contiguous sections of the mirror. 
         [0015]    For each mirror, said at least first and second reflective surfaces may have figures, and positions and/or orientations relative to the optical axis whereby said angles of incidence are equal. 
         [0016]    Moreover, in some embodiments for each mirror, the first reflective surface is nearest to the radiation source, and radiation from the second reflective surface is directed to the image focus on the optical axis; and wherein said first and second reflective surfaces are defined, for a given point of reflection at said reflective surfaces, by 
         [0000]    
       
         
           
               
             
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         [0017]    where ρ 1  is the length from the source to the first reflective surface, 
         [0018]    ρ 2  is the length from the image focus to the second reflective surface, 
         [0019]    θ 1  is the angle between the optical axis and a line joining the source and a first point of reflection at the first reflective surface, 
         [0020]    θ 2  is the angle between the optical axis and a line joining the image focus and a second point of reflection at the second reflective surface, 
         [0021]    2c is the length along the optical axis from the source to the image focus, 
         [0022]    2a is the constant length of the optical path, and 
         [0023]    k is a constant. 
         [0024]    The values of a and k may be determined by 
         [0000]    
       
         
           
             
               a 
               = 
               
                 
                   
                     ρ 
                     
                       1 
                       , 
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                 2 
               
             
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             = 
             
               
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         [0000]    where subscript  “R”  denotes values for the point of intersection R of the first and second reflective surfaces. 
         [0025]    According to another aspect of various embodiments of the invention there is provided a collector optical system for EUV lithography, comprising the reflective optical system wherein radiation is collected from the radiation source. 
         [0026]    According to another aspect of various embodiments of the invention there is provided an EUV lithography system comprising: a radiation source, for example a LPP source, the collector optical system; an optical condenser; and a reflective mask. 
         [0027]    According to another aspect of various embodiments of the invention there is provided an imaging optical system for EUV or X-ray imaging, comprising the reflective optical system. 
         [0028]    According to another aspect of various embodiments of the invention there is provided an EUV or X-ray imaging system, comprising: the imaging optical system; and an imaging device, for example a CCD array, disposed at the image focus. 
         [0029]    According to another aspect of various embodiments of the invention there is provided an EUV or X-ray telescope system, comprising: the reflective optical system; wherein radiation from a source at infinity is reflected to the image focus. 
         [0030]    In the EUV or X-ray telescope system, in some embodiments for each mirror, the first reflective surface is nearest to the radiation source, and radiation from the second reflective surface is directed to the image focus, and wherein the first and second reflective surfaces are defined, for a given point of reflection at said reflective surfaces, by 
         [0000]    
       
         
           
               
             
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         [0031]    where ρ 1  is the length from a reference plane to the first reflective surface, 
         [0032]    ρ 2  is the length from the image focus to the second reflective surface, 
         [0033]    ρ 3  is the length between the points of incidence at said first and second reflective surfaces, 
         [0034]    θ 2  is the angle between the optical axis and a line joining the image focus and a second point of reflection at the second reflective surface, 
         [0035]    2c is the length along the optical axis from the source to the image focus, 
         [0036]    2a is the constant length of the optical path, and 
         [0037]    k is a constant. 
         [0038]    The values of a and k are more preferably determined by 
         [0000]    
       
         
           
             
               a 
               = 
               
                 
                   
                     ρ 
                     
                       1 
                       , 
                       R 
                     
                   
                   + 
                   
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                       2 
                       , 
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                 2 
               
             
             , 
             
               
 
             
              
             and 
           
         
       
       
         
           
             
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             , 
           
         
       
     
         [0039]    where subscript  “R”  denotes values for the point of intersection R of the first and second reflective surfaces. 
         [0040]    According to another aspect of various embodiments of the invention there is provided an EUV or X-ray imaging system, comprising the EUV or X-ray telescope system, and an imaging device, for example a CCD array, disposed at the image focus. 
         [0041]    In each of the aforementioned aspects of various embodiments of the invention, a plurality of minors may be provided in nested configuration. 
         [0042]    Also, the two of more of the mirrors may each have a different geometry. 
         [0043]    In addition, the mirrors may have mounted thereon, for example on the rear side thereof, one or more devices for the thermal management of the mirror, for example cooling lines, Peltier cells and temperature sensors. 
         [0044]    The mirrors may have mounted thereon, for example on the rear side thereof, one or more devices for the mitigation of debris from the source, for example erosion detectors, solenoids and RF sources. 
         [0045]    In accordance with various embodiments of the invention a two-reflection mirror for nested grazing incidence optics is provided, in which significantly improved overall reflectivity is achieved by making the two grazing incidence angles equal for each ray. The various embodiments of invention are applicable to non-imaging collector optics for Extreme Ultra-Violet microlithography where the radiation emitted from a hot plasma source needs to be collected and focused on the illuminator optics. The various embodiments of the invention are also described herein, embodied in a double-reflection mirror with equal reflection angles, for the case of an object at infinity, for use in X-ray applications. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0046]    Embodiments of the invention will now be described in detail, by way of example, with reference to the accompanying drawings, in which: 
           [0047]      FIG. 1  shows an example of a known EUV lithography system; 
           [0048]      FIG. 2  shows the grazing incidence reflection in the collector optics of EUV lithography systems; 
           [0049]      FIG. 3  depicts the conceptual optical layout of a known type I Wolter collector for EUV plasma sources; 
           [0050]      FIG. 4  illustrates theoretical reflectivity of selected materials at 13.5 nm. 
           [0051]      FIG. 5  shows geometry and conventions of the two-reflection mirror for EUV lithography applications, in accordance with one embodiment of the invention; 
           [0052]      FIG. 6  shows the optical layout of a nested collector according to another embodiment of the invention; 
           [0053]      FIG. 7  illustrates total reflectivity experienced by each ray as a function of the emission angle for the nested collector of  FIG. 4  and for a type I Wolter design; and 
           [0054]      FIG. 8  shows the geometry and conventions of the two-reflection mirror according to another embodiment of the invention, when the source focus is at infinity, for example in X-ray imaging applications. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0055]    In the description and drawings, like numerals are used to designate like elements. Unless indicated otherwise, any individual design features and components may be used in combination with any other design features and components disclosed herein. 
         [0056]    In the illustrations of optical elements or systems herein, unless indicated otherwise, cylindrical symmetry around the optical axis is assumed; and references to an “image focus” are references to an image focus or an intermediate focus. 
         [0057]    In relation to the “substantially equal” grazing incidence angles in the fabricated mirrors, as used herein, this is to be interpreted as angles sufficiently similar as to result in enhanced collector efficiency, and more preferably significantly enhanced or maximized collector efficiency. While in no way limiting, it is to be interpreted as angles that differ by 10% or less, or by 5% or less, and even by 1% or less. The angles may be identical, but is not required. 
         [0058]    Various embodiments of the invention may provide the collection efficiency that is improved and/or maximized. Various embodiments of the invention also may relax the effort in developing extremely powerful sources, improving the optical quality and stability of the collector output and increasing the collector lifetime. Various embodiments of the invention additionally may increase overall efficiency of the lithographic equipment, allowing higher wafer throughput. 
         [0059]      FIG. 1  shows an example of a known EUV lithography system. The system  100  includes a laser  110 , a laser-produced plasma  120 , an optical condenser  130 , an optical collector  131 , an erosion detector  135 , a reflective mask  140 , a reduction optics  150 , and a wafer  160 . Alternatively, the laser  100  and the laser produced plasma  120  can be replaced with an electric discharge source  150 . 
         [0060]    The laser  110  generates a laser beam to bombard a target material like liquid filament Xe or Sn. This produces the plasma  120  with a significant broadband extreme ultra-violet (EUV) radiation. The optical collector  131  collects the EUV radiation from the plasma. After the collector optics, the EUV light is delivered to the mask through a number of mirrors coated with EUV interference films or multilayer (ML) coating. The laser-produced plasma can be replaced with the electric discharge source  150  to generate the EUV light. The Xe or Sn is used in the electric discharge source  150 . The optical condenser  130  illuminates the reflective mask  140  with EUV radiation at 13-14 nm wavelengths. The collector optics  131  and condenser optics  130  may include a ML coating. The optical collectors  131  may be eroded over time for being exposed to the plasma  120 . The optical collectors  131  include circuitry or interface circuits to the erosion detector  135 . The erosion detector  135  detects if there is an erosion in the single-layer or ML coating of the collectors  131 . By monitoring the erosion in the ML coating continuously, severe erosion may be detected and replacement of eroded collectors may be performed in a timely fashion. 
         [0061]    The reflective mask  140  has an absorber pattern across its surface. The pattern is imaged at 4:1 demagnification by the reduction optics  150 . The reduction optics  150  includes a number of mirrors such as mirrors  152  and  154 . These mirrors are aspherical with tight surface figures and roughness (e.g., less than 3 Angstroms). The wafer  160  is resist-coated and is imaged by the pattern on the reflective mask  140 . Typically, a step-and-scan exposure is performed, i.e., the reflective mask  140  and the wafer  160  are synchronously scanned. Using this technique, a resolution less than 50 nm is possible. 
         [0062]      FIG. 2  shows the grazing incidence reflection in the collector optics of EUV lithography systems, i.e. in a sectional view within an exemplary EUV chamber. The light source, in this case a discharge produced plasma (DPP) source  205 , and collector mirrors  210  for collecting and directing the EUV light  215  for use in the lithography chamber  105  are inside the EUV chamber. The collector mirrors  210  may have a nominally conical/cylindrical or elliptical structure. 
         [0063]    Tungsten (W) or other refractory metals or alloys that are resistant to plasma erosion may be used for components in the EUV source. However, plasma-erosion may still occur, and the debris produced by the erosion may be deposited on the collector mirrors  210 . Debris may be produced from other sources, e.g., the walls of the chamber. Debris particles may coat the collector mirrors, resulting in a loss of reflectivity. Fast atoms produced by the electric discharge (e.g., Xe, Li, Sn, or In) may sputter away part of the collector mirror surfaces, further reducing reflectivity. 
         [0064]    In certain circumstances, a magnetic field is created around the collector mirrors to deflect charged particles and/or highly energetic ions  220  and thereby reduce erosion. A magnetic field may be generated using a solenoid structure. This magnetic field may be used to generate Lorentz force when there is a charged particle traveling perpendicular or at certain other angles with respect to the magnetic field direction. By applying high current (I) and many loops around the ferromagnetic tube, a high magnetic field can be generated. 
         [0065]      FIG. 3  depicts the conceptual optical layout of a known type I Wolter collector for EUV plasma sources. The purpose of the collector in EUV sources is to transfer the largest possible amount of in-band power emitted from the plasma to the next optical stage, the illuminator ( 130 ;  FIG. 1 ), of the lithographic tool. 
         [0066]    With reference to  FIG. 3 , although many more nested mirrors in the collector optical system  300  may be illustrated, only two ( 302 ,  304 ) are shown. The radiation from the source  306  is first reflected by the hyperbolic surfaces  308 ,  310 , then reflected by the elliptical surfaces  312 ,  314 , and finally focused to an image or intermediate focus  316  on the optical axis  320 . As in the type I Wolter telescope mentioned above, the elliptical ( 312 ,  314 ) and the hyperbolic ( 308 ,  310 ) surfaces share a common focus  318 . For each of the mirrors  302 ,  304 , etc. the different sections on which the surfaces  308 ,  312  are disposed may be integral, or may be fixed or mounted together. 
         [0067]    The output optical specification of the collector  300 , in terms of numerical aperture and etendue, must match the input optical requirements for the illuminator ( 130 ;  FIG. 1 ). The collector  300  is designed to have maximum possible efficiency, while matching the optical specification of the illuminator ( 130 ;  FIG. 1 ) on one side and withstanding the thermal load and the debris from the plasma source  306  on the other side. Indeed, the power requirement for in-band radiation at the intermediate focus  316  has been seen to increase from the original 115 W towards 180 W and more, due to the expected increase in exposure dose required to achieve the desired resolution and line-width roughness of the pattern transferred onto the wafer ( 160 ;  FIG. 1 ). Since the maximum conversion efficiency of both DPP and LPP sources is limited to a few percent, and since the reflectivity of normal incidence mirrors in the illuminator  130  and the projection optics box can not exceed about 70%, for each of the 6-8 mirrors or more along the optical path to the plane of the wafer  160 , the collector  300  must withstand thermal loads in the range of several kilowatts. Deformations induced by such high thermal loads on the thin metal shell of which the mirrors  302 ,  304  are made may jeopardize the stability and the quality of the output beam of the collector  300  even in presence of integrated cooling systems on the back surface of the mirrors. 
         [0068]    It is apparent from the foregoing that any improvement in the collector efficiency has benefits for relaxing the need for developing extremely powerful sources, for increasing the wafer throughput of the lithographic equipment, and for improving the optical quality and stability of the collector output, as well as the benefit of increasing the collector lifetime. 
         [0069]      FIG. 4  illustrates theoretical reflectivity of selected materials at 13.5 nm, i.e. some example of the dependence of the reflectivity on the grazing incidence angle for some selected materials at a wavelength of 13.5 nm. For a given maximum collection angle on the source side, the collector efficiency is mainly determined by the reflectivity of the coating on the optical surfaces  308 - 314  of the mirrors  302 ,  304 . Since each ray experiences two reflections, the overall reflectivity is given by the product of the reflectivity of each of the two reflections. 
         [0070]      FIG. 5  shows geometry and conventions of the two-reflection mirror  302  for EUV lithography applications, in accordance with one embodiment of the invention. Although many more nested mirrors in the collector optical system may be illustrated, only one ( 302 ) is shown. The design according to various embodiments of the invention is based on the discovery that the overall reflectivity is maximized when, for all rays, the two grazing incidence angles, and thus the reflectivity of the two reflections, are equal, at least for the kind of dependence on the grazing incidence angle shown in  FIG. 4 . This condition cannot be satisfied for all rays in a type I Wolter design. Indeed, in the latter, for each mirror, the two grazing incidence angles can be made equal for one ray at most. 
         [0071]    In accordance with various embodiments of the invention, double-reflection collector mirrors  302 ,  304  are provided, in which the above condition (equal grazing incidence angle) is satisfied for all rays collected by each mirror  302 ,  304 . A very brief theoretical treatment and the description of the design is given hereinafter, as is a comparison of the expected efficiency of a nested collector  300  according to embodiments of the invention to the efficiency of type I Wolter collector. Although Abbe&#39;s condition is not satisfied in the collector according to an embodiment of the invention, coma aberration is of concern only to the extent it affects the collector efficiency. Due the finite size of the plasma source and possibly the shape errors of the collector mirrors, the relative contribution of coma aberration is considered negligible. 
       Mirror Surface Shapes 
       [0072]    Various embodiments of the present invention employ, in the reflective surfaces of the mirrors, certain shapes/geometries in order to enhance performance; and in order that the mathematical definitions of these geometries may be better understood, the parameters and notation used in those representations will be briefly addressed below. 
         [0073]    In the geometry shown in  FIG. 5 , a ray emitted from the object or source focus S (i.e. plasma source  306 ) is reflected at point P on the first surface  308 , reflected at point Q on the second surface  312  and finally focused to the image or intermediate focus IF ( 316 ). Symmetry around the optical axis  320  is assumed. The positions of the source  306  and the image focus  316  define the vector 2c=IF−S of length 2c. The ray path is described by the three adjacent vectors ρ 1 u 1 =P−S, p 2  u 2 =IF−Q, and ρ 3 u 3 =Q−P of length ρ 1 , ρ 2 , and ρ 3 , respectively. The direction of each vector is defined by the unit vectors u 1 , u 2 , and u 3  forming angles θ 1 , θ 2 , and θ 3  measured counterclockwise with respect to the optical axis  320 . If three vectors ρ 1 u 1 , ρ 2 u 2 , and ρ 3 u 3  are assigned as functions of a parameter t, the geometry of the cross sections of the two surfaces  308 ,  312  is defined with respect to S by the tips of the vectors ρ 1 u 1  and ρ 1 u 1 +ρ 3 u 3 . 
         [0074]    In accordance with embodiments of the invention, the three vectors p 1 u 1 , p 2 u 2 , and p 3 u 3  satisfy the following relation 
         [0000]      ρ 1   u   1 +ρ 2   u   2 +ρ 3   u   3 =2 c.   (1) 
         [0075]    In addition, in order for a spherical wave emitted from the source S ( 306 ) and reflected by the two surfaces  308 ,  312  to be focused to the image focus IF ( 316 ), the optical path is the same for all the rays. In accordance with embodiments of the invention, if 2a is the constant length of the optical path, then 
         [0000]      ρ 1 +ρ 2 +ρ 3 =2 a.   (2) 
         [0076]    Finally, using the reflection conditions at point P and Q (the points of reflection at the surfaces  308  and  312 , respectively) and the fact that, in accordance with embodiments of the invention, the two grazing incidence angles ψ 13 =(θ 1 −θ 3 )/2ψ 23 =(θ 3 −θ 2 )/2 are equal, i.e. 
         [0000]      θ 1 −θ 3 =θ 3 −θ 2    
         [0000]    enables the geometry of the mirrors (reflective surfaces) in accordance with embodiments of the invention, to be defined. More specifically, the following system is employed in accordance with embodiments of the invention. 
         [0000]    
       
         
           
             
               
                 
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                                   cos 
                                    
                                   
                                     ( 
                                     
                                       
                                         θ 
                                         1 
                                       
                                       - 
                                       
                                         θ 
                                         2 
                                       
                                     
                                     ) 
                                   
                                 
                                 - 
                                 1 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           
                             
                               
                                 ρ 
                                 1 
                               
                                
                               cos 
                                
                               
                                   
                               
                                
                               
                                 θ 
                                 1 
                               
                             
                             + 
                             
                               
                                 ρ 
                                 2 
                               
                                
                               cos 
                                
                               
                                   
                               
                                
                               
                                 θ 
                                 2 
                               
                             
                             + 
                             
                               
                                 ( 
                                 
                                   
                                     2 
                                      
                                     
                                         
                                     
                                      
                                     a 
                                   
                                   - 
                                   
                                     ρ 
                                     1 
                                   
                                   - 
                                   
                                     ρ 
                                     2 
                                   
                                 
                                 ) 
                               
                                
                               
                                 cos 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         1 
                                       
                                       + 
                                       
                                         θ 
                                         2 
                                       
                                     
                                     2 
                                   
                                   ) 
                                 
                               
                             
                           
                           = 
                           
                             2 
                              
                             
                                 
                             
                              
                             c 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0077]    If θ 1 , a, c, k are given, these are 3 equations in 3 unknowns ρ 1 , ρ 2  and θ 2  that can be solved numerically. The resulting profile (mirror figure or geometry) is then rotated around the optical axis  320  to obtain the axial symmetric two-surfaces mirror  302 . The surfaces  308 ,  312  defined by (4) cannot be described by second order algebraic equations. In particular, these surfaces  308 ,  312  are not generated by conic sections and do not have a common focus, as happens in two-reflection systems consisting of ellipsoids and/or hyperboloids. 
         [0078]    The values θ 1,R  and |θ 2,R | of the angles θ 1  and ∥θ 2 | at the intersection point R are the minimum angles at both the source  306  and the image focus  316 . Since ρ 3 =0 at R, assuming that c is assigned, the length ρ 1,R  and ρ 2,R  are known and the constants a and k are determined by relation (2) and (4a) 
         [0000]    
       
         
           
             
               
                 
                   
                     a 
                     = 
                     
                       
                         
                           ρ 
                           
                             1 
                             , 
                             R 
                           
                         
                         + 
                         
                           ρ 
                           
                             2 
                             , 
                             R 
                           
                         
                       
                       2 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
             
               
                 
                   k 
                   = 
                   
                     
                       ρ 
                       
                         1 
                         , 
                         R 
                       
                     
                      
                     
                       ρ 
                       
                         2 
                         , 
                         R 
                       
                     
                      
                     
                       
                         
                           sin 
                           4 
                         
                          
                         
                           ( 
                           
                             
                               
                                 θ 
                                 
                                   2 
                                   , 
                                   R 
                                 
                               
                               - 
                               
                                 θ 
                                 
                                   1 
                                   , 
                                   R 
                                 
                               
                             
                             4 
                           
                           ) 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0079]    When θ 1  is allowed increase from its minimum value θ 1,R , relations (4) give the shape of both surfaces  308 ,  312  of the mirror  302 . The maximum value of θ 1  is arbitrary to a certain extent. A convenient choice is such that the minimum distance of the mirror  302  from the source  306  is some prescribed value  ρ 1    so that a spherical region of radius  ρ 1    around the source  306  is left free for the hardware required to mitigate the debris from the plasma source  306 . Alternatively, in order to ease the mounting of the mirror on a common supporting structure, the maximum value for θ 1  can be is chosen such that all the mirrors end at the same horizontal coordinate on side of the image focus  316 . 
         [0080]    The figures/geometries of the outer mirrors  304 , etc. (see  FIG. 6 ), are calculated iteratively as follows. The vertex R′ of the second mirror  304  ( FIG. 6 ) is defined by the intersection of the rays through points A and B. These rays also define the minimum values θ 1,R′  and θ 2,R′  of the angles θ 1  and |θ 2 | and the corresponding length of ρ 1,R′  and ρ 2,R′ . The above procedure can then be applied to calculate the new constant values a′ and k′ from (5) and (6) and the mirror shape from (4). The process can then be iterated to cover the desired numerical aperture with a proper number of nested mirrors. 
         [0081]      FIG. 6  shows the optical layout of a nested collector  300  according to another embodiment of the invention. This is the same as the above-described embodiment, except as described hereinafter. The nested collector  300  consists of 15 double-reflection mirrors ( 302 ,  304 , etc.) with a thickness of 2 mm. In this case, there is a focal length 2c of 1500 mm, a minimum distance ρ 1  between the optics  300  and the source focus  306  of 110 mm and a minimum and maximum angles of the radiation at the intermediate focus  316  of 1.5° and 8°, respectively. The corresponding minimum and maximum collected angles are 9.2° and 86.8°, equivalent to 5.3 sr (taking into account the obscurations from the mirror thickness). As mentioned hereinbefore, the collection efficiency of the collector is defined as the ratio between the power at the image or intermediate focus and the power emitted from the source in 2π sr. For an isotropic point source, the collection efficiency of each mirror  302 ,  304 , etc. is given by 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         η 
                         = 
                         
                           
                             ∫ 
                             
                               θ 
                               
                                 1 
                                 , 
                                 R 
                               
                             
                             
                               θ 
                               
                                 1 
                                 , 
                                 A 
                               
                             
                           
                            
                           
                             
                               R 
                                
                               
                                 ( 
                                 
                                   ψ 
                                   13 
                                 
                                 ) 
                               
                             
                              
                             
                               R 
                                
                               
                                 ( 
                                 
                                   ψ 
                                   23 
                                 
                                 ) 
                               
                             
                              
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               1 
                             
                              
                             
                                 
                             
                              
                             
                                
                               
                                 θ 
                                 1 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           = 
                           
                             
                               ∫ 
                               
                                 θ 
                                 
                                   1 
                                   , 
                                   R 
                                 
                               
                               
                                 θ 
                                 
                                   1 
                                   , 
                                   A 
                                 
                               
                             
                              
                             
                               
                                 
                                   R 
                                   2 
                                 
                                  
                                 
                                   ( 
                                   
                                     
                                       
                                         θ 
                                         1 
                                       
                                       - 
                                       
                                         
                                           θ 
                                           2 
                                         
                                          
                                         
                                           ( 
                                           
                                             θ 
                                             1 
                                           
                                           ) 
                                         
                                       
                                     
                                     4 
                                   
                                   ) 
                                 
                               
                                
                               sin 
                                
                               
                                   
                               
                                
                               
                                 θ 
                                 1 
                               
                                
                               
                                  
                                 
                                   θ 
                                   1 
                                 
                               
                             
                           
                         
                         , 
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0000]    where R(ψ) is the mirror reflectivity at the grazing incidence angle ψ. Assuming a reflective coating of Ruthenium with theoretical reflectivity, the total collection efficiency for the collector in  FIG. 6  is 50.9%. This value should be compared with the calculated efficiency of 40.1% for a reference collector design based on a type I Wolter configuration matching the same boundary conditions in terms of focal length, angles at the intermediate focus and maximum collected angle. 
         [0082]    In accordance with embodiments of the invention, the manufacturing process for fabrication of each of the nested grazing incidence mirrors  302  (as well as the outer mirrors  304 , etc.; see  FIG. 6 ), of the assembly of nested mirrors as a whole, is based on electroforming, whereby the mirror  302 ,  304 , etc. is obtained by galvanic replication from a negative master (not shown). In this case, it is appropriate to extend the two sections of the mirror providing the two reflecting surfaces  308 ,  312  until they join at a given point (R). In this way, the two sections of the mirror are manufactured in a monolithic structure, thus avoiding the need for further relative alignment. Techniques for the manufacture of mirrors by electroforming are disclosed in, for example, EP-A-1329040, entitled “Telescope Mirror For High Bandwidth Free Space Optical Data Transmission” and WO2005/054547, entitled “Fabrication Of Cooling And Heat Transfer Systems By Electroforming”. 
         [0083]      FIG. 7  illustrates total reflectivity experienced by each ray as a function of the emission angle for the nested collector  300  of  FIG. 6  and for a type I Wolter design. The nested collector  300  according to embodiments of the invention is more effective than the type I Wolter design, at least at large emission angles. As the inner mirrors collect a small angular range, the gain in reflectivity at lower emission angles is more limited. 
         [0084]      FIG. 8  shows the geometry and conventions of the two-reflection mirror according to another embodiment of the invention, when the source focus is at infinity, for example in EUV or X-ray imaging applications. The design is similar to the above-described embodiment, and so will be briefly discussed. In this case u 1  is parallel to the optical axis  320  and θ 1 =0, as shown in  FIG. 8 . Only the projection of equation (1) on the optical axis  320  is applicable, 
         [0000]      ρ 1 +ρ 2   u   1   ·u   2 +ρ 3   u   1   ·u   3 =2 c.   (8) 
         [0085]    Instead, equation (2) is still valid. 
         [0086]    In accordance with embodiments of the invention, with the two grazing incidence angles ψ 13 =θ 3 /2 and ψ 23 =(θ 3 −θ 2 )/2 being equal, gives θ 3 =θ 2 /2. Using the reflection conditions at point P and Q in  FIG. 8 , with θ 2  is chosen as the independent variable, in accordance with embodiments of the invention, the geometries of the reflective surfaces are defined by 
         [0000]    
       
         
           
             
               
                 
                     
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 ρ 
                                 1 
                               
                               + 
                               
                                 
                                   ρ 
                                   3 
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       
                                         θ 
                                         2 
                                       
                                       / 
                                       2 
                                     
                                     ) 
                                   
                                 
                               
                             
                             = 
                             
                               
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 c 
                               
                               - 
                               
                                 
                                   ρ 
                                   2 
                                 
                                  
                                 
                                   cos 
                                    
                                   
                                     ( 
                                     
                                       θ 
                                       2 
                                     
                                     ) 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               
                                 ρ 
                                 1 
                               
                               + 
                               
                                 ρ 
                                 3 
                               
                             
                             = 
                             
                               
                                 2 
                                  
                                 
                                     
                                 
                                  
                                 a 
                               
                               - 
                               
                                 ρ 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
         [0087]    As before, with c assigned, the constants a and k are determined in accordance with embodiments of the invention, once the minimum value |θ 2,R | of the angle of |θ 2 | at point R is given, by 
         [0000]    
       
         
           
             
               
                 
                   
                     a 
                     = 
                     
                       
                         
                           ρ 
                           
                             1 
                             , 
                             R 
                           
                         
                         + 
                         
                           ρ 
                           
                             2 
                             , 
                             R 
                           
                         
                       
                       2 
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   10 
                   ) 
                 
               
             
             
               
                 
                   k 
                   = 
                   
                     
                       ρ 
                       
                         2 
                         , 
                         R 
                       
                     
                      
                     
                       
                         
                           sin 
                           4 
                         
                          
                         
                           ( 
                           
                             
                               θ 
                               
                                 2 
                                 , 
                                 R 
                               
                             
                             4 
                           
                           ) 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
         [0088]    The process for the determination of the first  302  and subsequent (not shown) mirrors is then identical to that described for the collector  300  in the embodiment of  FIG. 5 . 
         [0089]    In contrast with embodiments of the present invention, in double-reflection conical mirrors for X-ray telescopes, axial rays do not come to a point geometric focus and the optics is not corrected for on-axis spherical aberration. 
         [0090]    The design of double-reflection mirrors  302 ,  304 , etc. according to embodiments of the invention, with equal grazing incidence angles, is effective in increasing the efficiency of collectors for EUV microlithography, at least at large emission angles. The increasing demand for high power level needed for high volume manufacturing tools requires enhancing the performance of the subsystems to the physical limits. For collectors, this implies, among others, increasing the collected solid angle and improving the overall reflectivity. To this end, the collector optical systems according to the present invention have a collection efficiency 27% greater than a type I Wolter configuration for the selected reference specifications set out herein. 
         [0091]    While the invention has been described in terms of various specific embodiments, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the claims.