Abstract:
A design method of extreme ultraviolet lithography projection objective comprises: determining the optical design parameters of the lithography projection objective, setting the projection objective to include six lenses and an aperture diaphragm, and dividing the six lenses into the three groups according to the beam propagation direction; determining the radii and the intervals of the first and third groups, respectively; and determining the radii and the intervals of the second group of lenses according to the parameters of the foregoing two groups of lenses. The design method has the advantage of avoiding the blindness in revising and error testing of the existing structure of the conventional optical design method by calculating lens structures that meet the parameter conditions, so that light rays can be selected conveniently according to the special requirements of optical processing detection, and a mass of searches and judgments can be avoided.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a U.S. National Phase Application of PCT International Application No. PCT/CN2012/000254 filed on Feb. 28, 2012, which claims priority to Chinese Patent Application No. 201110404929.7, filed on Dec. 7, 2011, the contents of each of which are incorporated herein by reference in their entirety for all purposes. 
     FIELD OF THE INVENTION 
     The present invention relates to a method for extreme ultraviolet lithography (EUVL) projection objective design. 
     BACKGROUND OF THE INVENTION 
     For the IC manufacturing process, the highly précised projection objective is used to project the pattern on the mask to the wafer with resist. The existing deep ultraviolet (DUV) lithography takes the laser source of 193 nm wavelength. With the assistance of resolution enhancement technology like off-axial illumination, phase shift mask, and optical proximity correction, the DUV lithography can achieve the 45 nm node of the industrial IC manufacturing. But for the 32 nm node and below, extreme ultraviolet (EUV) lithography is the most promising next generation tech. The wavelength of EUV lithography is about 11˜15 nm. Like the DUV lithography, deep ultraviolet lithography (DUVL) also takes the step-scan model. 
     EUVL system includes plasma source, reflective illumination system, reflective mask, reflective projection objective, and the wafer covered with EUV resist, and the scanner. The ray beams emerged from the source get reshaped and uniformed by the illumination system, and then illuminate on the reflective mask. The reflected ray beams from the mask incident into the projection objective, and finally generate a pattern on the wafer with resist. 
     Typical EUVL projection objectives are co-axial optical systems. The object, image, and all the reflective elements are rotational symmetry. This feature is good for the correction of aberration and the manufacturing of the objective. Because of the folding and obstruction of the light path, the projection objective takes an off-axial field on object and image plane. Generally, there are several constraints for objective design except for known ones: 1. Achievable setting of a aperture diaphragm, which may set on one of the lenses  2 ˜ 5 ; 2. Enough working distance on both object and image side to ensure the space for mask and wafer setting; 3 non-obstruction design in the light path, all the used area on each element has enough space from the light path passed near it. 4. Suitable light path for the reflective mask, the incidental and emergent angle of ray beams on mask should be large enough to avoid obstruction with each other. 5. High resolution. 6. Extremly small distortions. 7. Teleconcentricity on the image plane. 
     Published document (M. F. Bal, Next-Generation Extreme Ultraviolet Lithographic Projection Systems[D], Delft: Technique University Delft, 2003) disclosed a method for EUVL projection objective design. The method makes exhaustive search on the first order parameters of the lenses of the objective with constraints of the magnification, conjugation relationship of the object and image, and then sifts the results of the exhaustive search by obstruction situation judgment, finally gets available structures of the objective, as “initial structures” for further optimization and design. The disadvantage of this method is that the calculation needed is too large for a common PC. It will take about a week to find an available structure. 
     SUMMARY OF THE INVENTION 
     As a solution to these and other objects, the method for EUVL projection objective design has the following steps: 
     STEP  101  Setting the optical parameters of the projection objective: object side numerical aperture NAO, the magnification of the objective M, the image side numerical aperture NAI, the object field height YOB, the image field height YIM; and the incidental angle of chief ray on object side CA; 
     STEP  102  The projection objective is set besides the mask and wafer plane. The objective includes six lenses and one aperture diaphragm. From the mask side along the beam propagation direction, the position relationship of them is: the first lens M 1 , aperture diaphragm, the second lens M 2 , the third lens M 3 , the fourth lens M 4 , the fifth lens M 5 , and the sixth lens M 6 . And the aperture diaphragm is set on the second lens M 2 ; 
     STEP  103  Setting the ratio of the object field height to the separation between the mask and the first lens M 1  ratio; setting the ratio of the separation between the first lens M 1  and the second lens M 2  to the separation between the mask and the first lens M 1  ratio 2 ; the clear space between the first lens M 1  and the ray beam emerged from M 2  CLEAPE1; the working distance between wafer and the sixth lens M 6  WDI; the ratio of WDI to the separation between the fifth lens M 5  and the sixth lens M 6  ratio 3 ; the clear space between the sixth lens M 6  and the incidental ray beam onto the fifth lens M 5  CLEAPE6; the clear space between the fifth lens M 5  and the emerged ray beam from M 6  CLEAPE5; 
     STEP  104  Setting the separation between the mask and the first lens M 1  as −l 1 , then there is |−l 1 |=YOB/ratio 1 ; setting the separation between the first lens M 1  and the second lens M 2  as −d 1 , then there is |−d 1 |=YOB/ratio 1 ·ratio 2 ; 
     STEP  105  Denoting the radius of the first lens M 1  as r 1 , then there is: 
     
       
         
           
             
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     Wherein the h z1  denotes the height of chief ray RAY1 on the first lens M 1 , and the z z1  denotes the axial distance of the incidental point of chief ray RAY1 on the first lens M 1  to the vertex of the first lens M 1 ; 
     STEP  106  Denoting the radius of the second lens M 2  as r 2 , then there is: 
     
       
         
           
             
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     Wherein the U a2  denotes the slope angle of the upper marginal ray RAY2 on the first lens M 1 , the h a2  denotes the height of the upper marginal ray RAY2 on the second lens M 2 , and the h b1  denotes the height of the lower marginal ray RAY3 on the first lens M 1 ; 
     STEP  107  Denoting the interval between the fifth lens M 5  and the sixth lens M 6  as d 5 , then there is |d 5 |=WDI·ratio 3 ; 
     STEP  108  Setting a dummy surface D 1  in the light path of the objective. The position of the dummy surface D 1  is exactly the same position as the fifth lens M 5 . Make sure that the incidental chief ray RAY1 on the sixth lens M 6  is parallel to the optical axial OA. Denote the radius of the sixth lens M 6  as r 6 , then there is: 
     
       
         
           
             
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     Wherein the h b6  denotes the height of the lower marginal ray RAY3 on the sixth lens M 6 , the h bD1  denotes the height of the lower marginal ray RAY3 on the dummy surface D 1 , the z b6  denotes the axial distance between incidental point of the lower marginal ray on the sixth lens M 6  and the vertex of the sixth lens M 6 , and the U′ b6  denotes the slope angle of the lower marginal ray RAY3 on the sixth lens M 6 ; 
     STEP  109  Denoting the radius of the fifth lens M 5  as r 5 , then there is: 
     
       
         
           
             
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     Wherein the h b5  denotes the height of lower marginal ray RAY3 on the fifth lens M 5 , the h a6  denotes the height of lower marginal ray RAY3 on the sixth lens M 6 , the U′ b5  denotes the slope angle of the lower marginal ray RAY3 on the fifth lens M 5 , the z a6  denotes the axial distance between the incidental point of the upper marginal ray RAY2 on the sixth lens M 6  and the vertex of the sixth lens M 6 , and the U′ b5  denotes the slope angle of the lower marginal ray RAY3 on the fifth lens M 5 ; 
     STEP  110  Setting the radius of the third lens M 3  as r 3 , according to the object-image conjugation relationship, the magnification relationship, the pezval sum condition and the conjugation relationship of the entrance and exit pupil and the radii of the first lens M 1 , the second lens M 2 , the fifth lens M 5 , the sixth lens M 6 , and the separations between them, the radius of the fourth lens M 4  denoted as r 4 , the separation between the third lens M 3  and the fourth lens M 4  denoted as d 3 , the separation between the second lens M 2  and the third lens M 3  denoted as l 3 , and the separation between the fourth lens M 4  and the fifth lens M 5  denoted as d 5 , exactly the image distance of the fourth lens M 4  denoted as l′ 4 , can be calculated; 
     STEP  111  Gathering the radii of the six lenses and its position relationships from the steps mentioned above, people can get the whole design of the EUVL projection objective. 
     Furthermore, the invention separate the projection objective into three lens groups, the first lens group G 1  includes the first lens M 1  and the second lens M 2 ; the second lens group G 2  includes the third lens M 3  and the fourth lens M 4 ; the third lens group G 3  includes the fifth lens M 5  and the sixth lens M 6 ; wherein the process of choosing the radius of the third lens M 3  denoted as r 3  is: the second lens group G 2  is taken as an independent optical system, and the magnification of G 2  is β=M. The entrance pupil distance of G 2  enp 2  equals to the exit pupil distance ENP1, i.e. enp 2 =ENP1, and the exit pupil distance of G 2  equals to the entrance pupil distance of G 3 , i.e. exp 2 =EXP3. 1500 mm&gt;(−l 3 −enp 2 )&gt;0 and 0&gt;d 3 &gt;1500 mm are taken as constraint conditions, and the available range of the radius of the third lens r 3  is decided by the object-image conjugation relationship, the magnification condition, the pezval sum condition, and the conjugation relationship of the entrance and exit pupil. The radius of the third lens M 3  denoted as r 3  is picked up from the available range. 
     Furthermore, the details of the STEP  108  are: 
     STEP  201  Choose the radius of the third lens M 3  as r 3 , set the error factor ξ B  and ξ exp     2   , then take β(1)=M and exp 2 (1)=EXP1, set the loop time k=1; 
     STEP  202  Take the parameters β(k), exp 2 (k), and the chosen r 3 , with the conjugation relationship of the object and the image, the magnification, the pezval sum condition, and the conjugation relationship of the entrance and exit pupil, then get the structural parameters d 3 (k), l 3 (k), l′ 4 (k), and r 4 (k) of the second lens group G 2 ; 
     STEP  203  Put the r 3 , d 3 (k), l 3 (k), l′ 4 (k), and r 4 (k) into the optical design software CODEV to obtain the magnification M(k) and the real exit pupil distance EXP2(k) of the second lens group G 2 ; 
     STEP  204  If |EXP2(k)−EXP1|≦ξ exp2  and |M(k)−M|≦ξ B , end the optimization process, and take the current r 3 , d 3 (k), l 3 (k), l′ 4 (k), and r 4 (k) as the structural parameters of the second lens group G 2 . If not, go to the STEP  205 ; 
     STEP  205  Take β(k+1)=β(k)=β(k)·[M/M(k)] σ , and exp 2 (k+1)=exp 2 (k)·[EXP1/EXP2(k)] σ , where σ≦1, making k=k+1, and go back to the STEP  202 . 
     The present invention has the following advantages: it is one object of the invention is to provide a complete method for the design of the initial structures of EUVL projection objective that allows to generate EUVL projection objective designs according to different parameter constraints avoiding the aimlessness in the traditional modification and trial process with the existing structures. 
     It is another object of the invention to further avoid the massive searching and judging by choosing specific series of structures which suit the demands of optical testing and manufacturing. 
     It is another object of the invention to further narrow down the searching range of the parameters, lower down the load of calculation and substantially shrink the step length of searching by making group by group search for the whole objective candidates. 
     It is another object of the invention to provide a method to obtain complete initial structures for the EUVL reflective objectives with six lenses, while asking for no existing reflective optical structures as a starting point. 
     It is another object of the invention to avoid misjudgment of the obstruction situation caused by the differences between the real light path and the axial light path by turning to real ray trace model. 
     The invention is explained in more detail below on the basis of exemplary embodiments illustrated in the accompanying figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present disclosure and its advantages, reference is now made to the following description, taken in conjunction with the accompanying drawings, in which: 
         FIG. 1  is a schematic diagram of the EUVL projection objective with six lenses and its grouping strategy. 
         FIG. 2  is a schematic diagram of the light path of G 1 ; 
         FIG. 3  is a diagram illustrating the calculation for the parameters of M 1 ; 
         FIG. 4  is a diagram illustrating the ratio 2 -dependent profile of the curvature of M 1  1/r 1  under different ratio 1 ; 
         FIG. 5  is a diagram illustrating the ratio 2 -dependent profile of the CLEAPE2 under different ratio 1 . 
         FIG. 6  is a diagram illustrating the calculation for the parameters of M 2 ; 
         FIG. 7  is a diagram illustrating the ratio 2 -dependent profile of the curvature of M 2  1/r 2  under different CLEAPE2; 
         FIG. 8  is a diagram illustrating the ratio 2 -dependent profile of the curvature of M 2  1/r 2  under different ratio 1 ; 
         FIG. 9  is a schematic diagram of the reversal light path of G 3 ; 
         FIG. 10  is a diagram illustrating the calculation for the parameters of M 6 ; 
         FIG. 11  is a diagram illustrating the ratio 3 -dependent profile of the curvature of M 6  1/r 6  under different CLEAPE6; 
         FIG. 12  is a diagram illustrating the calculation for the parameters of M 5 ; 
         FIG. 13  is a diagram illustrating the ratio 3 -dependent profile of the curvature of M 5  1/r 5  under different CLEAPE5; 
         FIG. 14  is a schematic diagram of the light path of G 2 ; 
         FIG. 15( a )  is a diagram illustrating the r 3 -dependent profile of the parameter d 3  in G 2 ; 
         FIG. 15( b )  is a diagram illustrating the r 3 -dependent profile of the parameter −l 3 -ENP 2  in G 2 ; 
         FIG. 15( c )  is a diagram illustrating the r 3 -dependent profile of the parameter l′ 4  in G 2 ; 
         FIG. 15( d )  is a diagram illustrating the r 3 -dependent profile of the parameter r 4  in G 2 ; 
         FIG. 16( a )  is a diagram illustrating the sifting situation of the parameter d 3  in G 2 ; 
         FIG. 16( b )  is a diagram illustrating the sifting situation of the parameter −l 3 −ENP 2  in G 2 ; 
         FIG. 17  is a diagram illustrating the convergence situation of the magnification of G 2  when iteration time goes up; 
         FIG. 18( a )  is a schematic diagram of the light path of G 1  lens group in an embodiment; 
         FIG. 18( b )  is a schematic diagram of the light path of G 3  lens group in an embodiment; 
         FIG. 18( c )  is a schematic diagram of three layouts of G 2  which are used to connect the layout of G 1  in  FIG. 18( a )  and the layout of G 3  in  FIG. 18( b ) ; 
         FIG. 18( d )  is a schematic diagram of three embodiments of the EUVL projection objective; 
         FIG. 19( a )  is a schematic diagram of the fourth embodiment of the EUVL projection objective; 
         FIG. 19( b )  is a schematic diagram of the fifth embodiment of the EUVL projection objective; 
         FIG. 19( c )  is a schematic diagram of the sixth embodiment of the EUVL projection objective; 
         FIG. 20  is a schematic diagram of a typical EUVL projection exposure system; 
     
    
    
     Wherein:  101 —mask  102 —wafer,  103 —optical axial  104 —chief ray  105 —upper marginal ray  106 —lower marginal ray  107 —aperture diaphragm. 
     DETAILED DESCRIPTION OF THE EMBODIMENTS 
     First of all, the definition of the parameters should be clarified as following. 
     Real object point/image point are defined as the intersection of two marginal ray of the ray beam, real object height/image height are defined as the height of the non-axial real object point/image point; Real image plane/object plane are defined as the normal plane of the optical axial. Real entrance pupil distance is defined as distance between the real object plane and the real entrance pupil plane. Real exit pupil distance is defined as distance between the real image plane and the real exit pupil plane, where the real entrance/exit pupil planes are defined as the normal plane of the optical axial, meanwhile through the intersection of the chief ray and optical axial  103 . For convenience, we take object/image point, object/image height, object/image plane, entrance/exit pupil plane as those non-axial parameters mentioned above for short. For axial parameters, there will be special notifications. 
     STEP  101  Setting the optical parameters of the projection objective: numerical aperture on object side NAO, the magnification of the objective M, the numerical aperture on image side NAI, the object field height YOB, the image field height YIM, the chief ray angle CA on the mask. 
     The relationship of the parameters mentioned above is:
 
NAO=NAI·| M |, YOB=YIM/| M| 
 
     Determine the chief ray angle on the object side with the object side numerical aperture NAO. Because the mask for EUVL is reflective, the incident and emerged ray beam should not be blocked by each other, the chief ray  104  of the ray beam, the upper marginal ray  105  of the ray beam, and the lower marginal ray  106  of the ray beam must all be lower or upper than the height of the object field YOB (as shown in  FIG. 1 ). To make sure that the light paths meet no obstruction, the range of the chief ray angle on the object side is |CA|&gt;arcsin (NAO). 
     STEP  102  The projection objective is setting between the mask  101  and the wafer  102 . It includes six lenses and one aperture diaphragm  107 , the position relationships of the six lenses and the aperture diaphragm are: from the mask  101  along the beam propagation direction are successively the mask  101 , and the first lens M 1 , the aperture diaphragm, the second lens M 2 , the third lens M 3 , the fourth lens M 4 , the fifth lens M 5  and the sixth lens M 6 . The aperture diaphragm is set on the second lens M 2  to make sure that the aperture diaphragm is achievable when the objective is manufactured. 
     STEP  103  Denote the ratio of the object field height to the separation between the mask  101  and the first lens M 1  as ratio 1 . Denote the ratio of the separation between the second lens M 2  and the first lens M 1  to the separation between the mask  101  and the first lens M 1  as ratio 2 . Denote the clear space between the first lens M 1  and the ray beam emerged from the second lens M 2  as CLEAPE1. Denote the distance between the wafer and the sixth lens M 6  as WDI, and denote the ratio of the WDI to the interval between the fifth lens M 5  and the sixth lens M 6  as ratio 3 . Denote the clear space between the sixth lens M 6  and the incidental ray beam onto the fifth lens M 5  as CLEAPE6, and denote the clear space between the fifth lens M 5  and the ray beam emerged from the sixth lens M 6  as CLEAPE5. 
     The EUVL projection objective is separated into three lens groups, the first lens group G 1  includes the first lens M 1  and the second lens M 2 ; the second lens groups G 2  includes the third lens M 3  and the fourth lens M 4 ; the third lens group G 3  includes the fifth lens M 5  and the sixth lens M 6 , as shown in  FIG. 1 . 
     STEP  104  Set the distance between the mask  101  and the first lens M 1  as −l 1 , then there is
 
ratio 1 =YOB/|− l   1 |
 
|− l   1 |=YOB/ratio 1  
 
     Set the separation between the second lens M 2  and the first lens M 1  as −d 1 , then there is
 
ratio 2   =|−d   1   |/|−l   1   |=|−d   1 |·ratio 1 /YOB
 
|− d   1 |=YOB/ratio 1 ·ratio 2  
 
     STEP  105  Denote the radius of the first lens M 1  as r 1 . 
     With the chief ray angle CA on the object plane and the condition of aperture diaphragm on the second lens M 2 , the radius of the first lens M 1  r 1  for different ratio 1  and ratio 2  can be calculated. When the radius r 1  is decided, the clear space CLEAPE2 near the second lens M 2  can be calculated by CODEV which is the software for optical design. 
     As shown in  FIG. 2 , the chief rays  104  emerges from the mask  101  and incidents into the first lens M 1 , and then incidents into the second lens M 2 . To make sure that the aperture diaphragm is physically achievable, the aperture diaphragm  107  of EUVL objective is put on the second lens M 2 , i.e. the chief ray  104  pass through the center of the third lens M 2 . With this condition, the radius of the first lens M 1  r 1  under certain ratio 1  and ratio 2  can be calculated. 
     Refer to  FIG. 3 , with the real ray trace model, there is 
     
       
         
           
             
               
                 
                   
                     
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                                     z 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       2 
                     
                     - 
                     
                       CA 
                       2 
                     
                   
                   ) 
                 
               
             
           
         
       
     
     Wherein the θ z1  denotes the slope angle of the normal at the intersection of chief ray RAY1 and the first lens M 1 ; the h z1  denotes the height of the chief ray RAY1 on the first lens M 1 ; the I z1  denotes the incidental angle of the chief ray RAY1 on the first lens M 1 ; the I′ z1  denotes the reflective angle of the chief ray RAY1 on the first lens M 1 ; the I z2  denotes the slope angle of the chief ray RAY1 on the first lens M 1 ; the z z1  denotes the axial distance between incidental point of the upper marginal ray on the first lens M 1  to the vertex of the first lens M 1 . 
       FIG. 4  is the diagram of 1/r 1  versus ratio 2  under different ratio 1 . 
       FIG. 5  is the diagram of CLEAPE2 versus ratio 2  under different ratio 1    
     STEP  106  Denote the radius of the second lens M 2  as r 2 . 
     With the parameters of the first lens M 1  gotten through the calculations above, the radius the second lens M 2  r 2  can be calculated. With the non-obstruction requirement of the off-axial light path of the EUVL objective, and the clear space between the lens and the light path nearby, the radius of the second lens r 2  can be calculated. 
     With the real ray trace model of the geometrical optic, there is 
     
       
         
           
             
               
                 
                   
                     
                       h 
                       
                         a 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     
                       r 
                       2 
                     
                   
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       θ 
                       
                         a 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁡ 
                     
                       ( 
                       
                         
                           U 
                           
                             a 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         - 
                         
                           I 
                           
                             a 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁡ 
                     
                       ( 
                       
                         
                           U 
                           
                             a 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         - 
                         
                           
                             ( 
                             
                               
                                 I 
                                 
                                   a 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                               
                               + 
                               
                                 I 
                                 
                                   a 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   2 
                                 
                                 ′ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             U 
                             
                               a 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           2 
                         
                         - 
                         
                           
                             U 
                             
                               a 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                             ′ 
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ( 
                     
                       
                         
                           U 
                           
                             a 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                         
                         2 
                       
                       - 
                       
                         
                           arctan 
                           ⁡ 
                           
                             ( 
                             
                               
                                 
                                   h 
                                   
                                     b 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     1 
                                   
                                 
                                 - 
                                 
                                   CLEAPE 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   1 
                                 
                                 - 
                                 
                                   h 
                                   
                                     a 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     2 
                                   
                                 
                               
                               
                                 - 
                                 
                                   d 
                                   1 
                                 
                               
                             
                             ) 
                           
                         
                         2 
                       
                     
                     ) 
                   
                 
               
             
           
         
       
     
     So, there is 
     
       
         
           
             
               r 
               2 
             
             = 
             
               
                 h 
                 
                   a 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
               
               / 
               
                 sin 
                 ( 
                 
                   
                     
                       U 
                       
                         a 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         2 
                       
                     
                     2 
                   
                   - 
                   
                     
                       arctan 
                       ⁡ 
                       
                         ( 
                         
                           
                             
                               h 
                               
                                 b 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 1 
                               
                             
                             - 
                             
                               CLEAPE 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             - 
                             
                               h 
                               
                                 a 
                                 ⁢ 
                                 
                                     
                                 
                                 ⁢ 
                                 2 
                               
                             
                           
                           
                             - 
                             
                               d 
                               1 
                             
                           
                         
                         ) 
                       
                     
                     2 
                   
                 
                 ) 
               
             
           
         
       
     
     Wherein the θ a2  denotes the slope angle of the normal of the intersection of the upper marginal ray RAY2 and the second lens M 2 ; the h a2  denotes the height of the upper marginal ray RAY2 on the second lens M 2 ; the h b1  denotes the height of the lower marginal ray RAY3 on the first lens M 1 ; the I a2  denotes the incidental angle of the upper marginal ray on the second surface M 2 ; the I′ a2  denotes the reflective angle of the upper marginal ray on the second surface M 2 ; the U a2  denotes the slope angle of the upper marginal ray RAY2 on the first lens M 1 ; and the U′ a2  denotes the slope angle of the upper marginal ray RAY2 emerged from the first lens M 1 . 
       FIG. 7  is the diagram of 1/r 2  versus ratio 2  under different CLEAPE1 
       FIG. 8  is the diagram of 1/r 2  versus ratio 2  under different ratio 1 . 
     When the −l 1 , −d 1 , r 1  and r 2  are gotten, the real image height YIM1, the real entrance pupil ENP1, and the real entrance pupil diameter EXD1 of the first lens group can be calculated. The calculation process is an existing technology and will not be shown here in detail. 
     STEP  107  Set the separation between the fifth lens M 5  and the sixth lens M 6  as d 5 , then there is |d 5 |=WDI·ratio 3 . 
     The third lens group G 3  is near the image side (wafer side) of the objective. In actual design process, it takes a reversal light path layout for design of G 3 . As shown in  FIG. 10 , the light path in G 3  is a reverse path referred to the direction of the EUVL objective light path. To avoid confusion, the parameters in G 3  will still take the rule of definition in forward direction light path. 
     Get the image numerical aperture NAI, since it&#39;s already known that
 
NAO=NAI·| M| 
 
     Get the image field height YIM, since it&#39;s already known that
 
YOB=YIM/| M| 
 
     Get the separation between the fifth lens M 5  and the sixth lens M 6  d 5  
 
| d   5 |=WDI·ratio 3  
 
     STEP  108  Setting a dummy surface D 1  in the light path, the dummy surface D 1  is at the exactly same position as the position of fifth lens M 5 . Make the chief ray on the sixth lens M 6  parallel to the optical axial OA and denote the radius of the sixth lens M 6  as r 6 . 
     In the reversal light path, the dummy surface is set between the wafer  102  and the sixth lens M 6 , in front of the sixth lens M 6 . Then the radius of the sixth lens M 6  r 6  under different positions can be calculated, with the non-obstruction condition of the fifth lens M 5  and the incidental ray beam on the wafer  102 , the condition of teleconcentricity on the image plane, and the r 6  determined by ratio 3 . As shown in  FIG. 10 . 
     
       
         
           
             
               
                 
                   
                     
                       h 
                       
                         b 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         6 
                       
                     
                     / 
                     
                       r 
                       6 
                     
                   
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       θ 
                       
                         b 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         6 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁡ 
                     
                       ( 
                       
                         
                           U 
                           
                             b 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             6 
                           
                         
                         - 
                         
                           I 
                           
                             b 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             6 
                           
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁡ 
                     
                       ( 
                       
                         
                           U 
                           
                             b 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             6 
                           
                         
                         - 
                         
                           
                             ( 
                             
                               
                                 I 
                                 
                                   b 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   6 
                                 
                               
                               + 
                               
                                 I 
                                 
                                   b 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   6 
                                 
                                 ′ 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             U 
                             
                               b 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               6 
                             
                           
                           2 
                         
                         + 
                         
                           
                             U 
                             
                               b 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               6 
                             
                             ′ 
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             arctan 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   ( 
                                   
                                     
                                       h 
                                       
                                         b 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         6 
                                       
                                     
                                     - 
                                     
                                       ( 
                                       
                                         
                                           h 
                                           
                                             b 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             D 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             1 
                                           
                                         
                                         - 
                                         
                                           CLEAPE 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           5 
                                         
                                       
                                       ) 
                                     
                                   
                                   ) 
                                 
                                 / 
                                 
                                   ( 
                                   
                                     
                                       - 
                                       
                                         d 
                                         5 
                                       
                                     
                                     - 
                                     
                                       z 
                                       
                                         b 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         6 
                                       
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                           
                           3 
                         
                         + 
                         
                           
                             U 
                             
                               b 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               6 
                             
                             ′ 
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     So, there is 
     
       
         
           
             
               r 
               6 
             
             = 
             
               
                 h 
                 
                   b 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   6 
                 
               
               / 
               
                 sin 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         arctan 
                         ⁡ 
                         
                           ( 
                           
                             
                               ( 
                               
                                 
                                   h 
                                   
                                     b 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     6 
                                   
                                 
                                 - 
                                 
                                   ( 
                                   
                                     
                                       h 
                                       
                                         b 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         D 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         1 
                                       
                                     
                                     - 
                                     
                                       CLEAPE 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       5 
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                             / 
                             
                               ( 
                               
                                 
                                   - 
                                   
                                     d 
                                     5 
                                   
                                 
                                 - 
                                 
                                   z 
                                   
                                     b 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     6 
                                   
                                 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       2 
                     
                     + 
                     
                       
                         U 
                         
                           b 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           6 
                         
                         ′ 
                       
                       2 
                     
                   
                   ) 
                 
               
             
           
         
       
     
     herein the θ b6  denotes the slope angle of the lower marginal ray RAY3 on the sixth lens M 6 , the h b6  denotes the height of the lower marginally RAY3 on the sixth lens M 6 , the h 6D1  denotes the height of the lower marginal ray RAY3 on the dummy surface D 1 , the I b6  denotes the incidental angle of the lower marginal ray RAY3 on the sixth lens M 6 , the I′ b6  denotes the reflective angle of the lower marginal ray RAY3 on the sixth lens M 6 , and the z b6  denotes the axial distance between intersection of the upper marginal ray to the vertex of the sixth lens M 6 . 
       FIG. 11  is the diagram of 1/r 6  versus ratio 3  under different CLEAPE5 
     STEP  109  Denote the radius of the fifth lens M 5  as r 5 , 
     As shown in  FIG. 12 , setting a dummy surface D 2  in the light path, the dummy surface D 2  is at the exactly same position as the position of sixth lens M 6 . But in the reversal light path, the dummy surface is set between the fifth lens M 5  and the second lens group G 2 , right behind the fifth lens M 5 . The radius of the fifth lens M 5  r 5  under different M 6  positions can be calculated, with the clear space CLEAPE6 between the incidental ray beam on the fifth lens M 5  and the sixth lens M 6 , and the calculated radius of the sixth lens M 6  r 6 . 
     
       
         
           
             
               
                 
                   
                     
                       h 
                       
                         b 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         5 
                       
                     
                     / 
                     
                       r 
                       5 
                     
                   
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       θ 
                       
                         b 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         5 
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁡ 
                     
                       ( 
                       
                         
                           U 
                           
                             b 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                         - 
                         
                           I 
                           5 
                           ′ 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁡ 
                     
                       ( 
                       
                         
                           U 
                           
                             b 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             5 
                           
                         
                         - 
                         
                           
                             ( 
                             
                               
                                 I 
                                 
                                   b 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   5 
                                 
                                 ′ 
                               
                               + 
                               
                                 I 
                                 
                                   b 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   5 
                                 
                               
                             
                             ) 
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             U 
                             
                               b 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               5 
                             
                           
                           2 
                         
                         + 
                         
                           
                             U 
                             
                               b 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               5 
                             
                             ′ 
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                   ⁢ 
                   
                     sin 
                     ⁡ 
                     
                       ( 
                       
                         
                           
                             arctan 
                             ⁡ 
                             
                               ( 
                               
                                 
                                   ( 
                                   
                                     
                                       h 
                                       
                                         b 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         5 
                                       
                                     
                                     - 
                                     
                                       ( 
                                       
                                         
                                           h 
                                           
                                             a 
                                             ⁢ 
                                             
                                                 
                                             
                                             ⁢ 
                                             6 
                                           
                                         
                                         - 
                                         
                                           CLEAPE 
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           6 
                                         
                                       
                                       ) 
                                     
                                   
                                   ) 
                                 
                                 / 
                                 
                                   ( 
                                   
                                     
                                       - 
                                       
                                         d 
                                         5 
                                       
                                     
                                     - 
                                     
                                       z 
                                       
                                         a 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         6 
                                       
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                           
                           2 
                         
                         + 
                         
                           
                             U 
                             
                               b 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               5 
                             
                             ′ 
                           
                           2 
                         
                       
                       ) 
                     
                   
                 
               
             
           
         
       
     
     Then, there is 
     
       
         
           
             
               r 
               5 
             
             = 
             
               
                 h 
                 
                   b 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   5 
                 
               
               / 
               
                 sin 
                 ⁡ 
                 
                   ( 
                   
                     
                       
                         arctan 
                         ⁡ 
                         
                           ( 
                           
                             
                               ( 
                               
                                 
                                   h 
                                   
                                     b 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     5 
                                   
                                 
                                 - 
                                 
                                   ( 
                                   
                                     
                                       h 
                                       
                                         a 
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         6 
                                       
                                     
                                     - 
                                     
                                       CLEAPE 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       6 
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                             / 
                             
                               ( 
                               
                                 
                                   - 
                                   
                                     d 
                                     5 
                                   
                                 
                                 - 
                                 
                                   z 
                                   
                                     a 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     6 
                                   
                                 
                               
                               ) 
                             
                           
                           ) 
                         
                       
                       2 
                     
                     + 
                     
                       
                         U 
                         
                           b 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           5 
                         
                         ′ 
                       
                       2 
                     
                   
                   ) 
                 
               
             
           
         
       
     
     Wherein the h b5  denotes the height of lower marginal ray RAY3 on the fifth lens M 5 , the h a6  denotes the height of lower marginal ray RAY3 on the sixth lens M 6 , the U′ b5  denotes the slope angle of the lower marginal ray RAY3 on the fifth lens M 5 , the z a6  denotes the axial distance between the incidental point of the upper marginal ray RAY2 on the sixth lens M 6  and the vertex of the sixth lens M 6 , and the I′ b5  denotes the slope angle of the lower marginal ray RAY3 on the fifth lens M 5 . 
       FIG. 13  is the diagram of 1/r 5  versus ratio 3  under different CLEAPE6. 
     When the d 5 , r 6 , r 5 , and WDI are gotten, the real object height YOB3, and the real entrance pupil ENP3 can be calculated. The calculation process is an existing technology and will not be shown here in detail. 
     STEP  110  Setting the radius of the third lens M 3  as r 3 , according to the object-image conjugation relationship, the magnification relationship, the pezval sum condition, the conjugation relationship of the entrance and exit pupil and the radii of the first lens M 1 , the second lens M 2 , the fifth lens M 5 , the sixth lens M 6 , and the separations between them, the radius of the fourth lens M 4  denoted as r 4 , the separation between the third lens M 3  and the fourth lens M 4  denoted as d 3 , the separation between the second lens M 2  and the third lens M 3  denoted as l 3 , and the separation between the fourth lens M 4  and the fifth lens M 5  denoted as d 5  (exactly the image distance of the fourth lens M 4  denoted as l′ 4 ) can be calculated through the paraxial iterative algorithm. 
     The detailed description of this step is as follow: 
     Referring to  FIG. 14 , by taking the second lens group G 2  as an individual optical system, the unknown parameters of G 2  include optical characteristics and the optical structure parameters. The optical characteristics include the entrance pupil diameter of the second lens group END2, the entrance pupil distance of the second lens groups ENP2 (i.e. the distance between the real object plane  1401  of the second lens group G 2  and the entrance pupil  1402  of the second lens group G 2 ), and the object field height YOB2 of the second lens group G 2 . The optical structure parameters include the distance between the real object plane  1401  and the third lens M 3  (l 3 ), the separation between the third lens M 3  and the fourth lens M 4  (d 3 ), the distance between the fourth lens M 4  and the image plane IM2 (l′ 4 ), the radius of the third lens M 3  (r 3 ), and the radius of the fourth lens M 4  (r 4 ). 
     Since the parameters of the first lens group G 1  have been chosen, the exit pupil diameter EXD1 should be equal to the entrance pupil diameter END2, i.e. making END2=EXD1; 
     The real image height of the first lens group YIM1 should be equal to the real object height of the second lens group YOB2, i.e. making YOB2=YIM1; 
     The exit pupil distance of the first lens group EXP1 should be equal to the entrance pupil distance of the second lens group ENP2, i.e. making ENP2=EXP1; 
     Since the parameters of the second lens group G 2  have been chosen, the entrance pupil diameter ENP3 should be equal to the entrance pupil diameter EXP2, i.e. making EXP2=ENP3; 
     The real object height of the third lens group YOB3 should be equal to the real image height of the second lens group YIM2, i.e. making YIM2=YOB3; 
     With the combination of paraxial calculation and iterative calculation, the parameters of the second lens group G 2  can be calculated with the parameters mentioned above. 
     Referring to the calculation process of the parameters of G 2 , four equations including object-image conjugation relationship, pupil-stop conjugation relationship, the pezval sum condition, and the magnification condition are needed for the five unknown parameters of the second group G 2 . With one parameter like the radius of the third lens r 3 , the equation could give us a paraxial solution for the second lens group G 2 . 
     With the object-image conjugation relationship, there is 
     
       
         
           
             
               
                 1 
                 
                   l 
                   3 
                 
               
               + 
               
                 1 
                 
                   l 
                   3 
                   ′ 
                 
               
             
             = 
             
               2 
               
                 r 
                 3 
               
             
           
         
       
       
         
           
             
               
                 l 
                 4 
               
               - 
               
                 l 
                 3 
                 ′ 
               
             
             = 
             
               - 
               
                 d 
                 3 
               
             
           
         
       
       
         
           
             
               
                 1 
                 
                   l 
                   4 
                 
               
               + 
               
                 1 
                 
                   l 
                   4 
                   ′ 
                 
               
             
             = 
             
               2 
               
                 r 
                 4 
               
             
           
         
       
     
     Wherein, the l 3  denotes the object distance of the third lens M 3 ; the l′ 3  denotes the image distance of the third lens M 3 ; the d 3  denotes the separation between the third lens M 3  and the fourth lens M 4 ; the l 4  denotes the object distance of the fourth lens M 4 , the l′ 4  denotes the image distance of the fourth lens M 4 . 
     With the magnification relationship, there is 
     
       
         
           
             
               
                 
                   l 
                   4 
                   ′ 
                 
                 
                   l 
                   4 
                 
               
               · 
               
                 
                   l 
                   3 
                   ′ 
                 
                 
                   l 
                   3 
                 
               
             
             = 
             β 
           
         
       
     
     Wherein the β denotes the paraxial magnification of the second lens group G 2 , making β=M 
     With the pezval sum condition, there is 
     
       
         
           
             
               pizsum 
               2 
             
             = 
             
               - 
               
                 ( 
                 
                   
                     1 
                     
                       r 
                       1 
                     
                   
                   - 
                   
                     1 
                     
                       r 
                       2 
                     
                   
                   + 
                   
                     1 
                     
                       r 
                       5 
                     
                   
                   - 
                   
                     1 
                     
                       r 
                       6 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Then 
     
       
         
           
             
               
                 1 
                 
                   r 
                   3 
                 
               
               - 
               
                 1 
                 
                   r 
                   4 
                 
               
             
             = 
             
               pizsum 
               2 
             
           
         
       
     
     With the pupil-stop conjugation relationship, there is 
     
       
         
           
             
               
                 1 
                 
                   ( 
                   
                     
                       l 
                       3 
                     
                     - 
                     
                       enp 
                       2 
                     
                   
                   ) 
                 
               
               + 
               
                 1 
                 
                   l 
                   
                     p 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     3 
                   
                   ′ 
                 
               
             
             = 
             
               2 
               
                 r 
                 3 
               
             
           
         
       
       
         
           
             
               
                 l 
                 
                   p 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
               
               - 
               
                 l 
                 
                   p 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
                 ′ 
               
             
             = 
             
               - 
               d 
             
           
         
       
       
         
           
             
               
                 1 
                 
                   l 
                   
                     p 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     4 
                   
                 
               
               + 
               
                 1 
                 
                   
                     l 
                     4 
                     ′ 
                   
                   + 
                   
                     exp 
                     2 
                   
                 
               
             
             = 
             
               2 
               
                 r 
                 4 
               
             
           
         
       
     
     Wherein, the enp 2  denotes the paraxial entrance pupil distance of the second lens group G 2 ; the enp 2  denotes the exit pupil distance of the first lens groups G 1 ; the l′ p3  denotes the paraxial image distance of the entrance pupil of the second lens group G 2  with the third lens M 3 ; the l p4  denotes the paraxial object distance of the entrance pupil of the second lens group G 2  with the fourth lens M 4 ; the exp 2  denotes the exit pupil distance of the second lens group G 2 , i.e. the entrance pupil distance of the third lens G 3 . 
     The solutions are as follow: 
     
       
         
           
             
               d 
               3 
             
             = 
             
               
                 1 
                 4 
               
               · 
               
                 
                   
                     r 
                     3 
                     2 
                   
                   · 
                   
                     ( 
                     
                       
                         2 
                         · 
                         
                           enp 
                           2 
                         
                         · 
                         β 
                         · 
                         
                           exp 
                           2 
                         
                         · 
                         
                           pizsum 
                           2 
                         
                       
                       - 
                       
                         exp 
                         2 
                       
                       + 
                       
                         
                           enp 
                           2 
                         
                         · 
                         
                           β 
                           2 
                         
                       
                     
                     ) 
                   
                 
                 
                   β 
                   · 
                   
                     enp 
                     2 
                   
                   · 
                   
                     exp 
                     2 
                   
                   · 
                   
                     ( 
                     
                       1 
                       + 
                       
                         
                           pizsum 
                           2 
                         
                         · 
                         
                           r 
                           3 
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
               l 
               3 
             
             = 
             
               
                 1 
                 2 
               
               · 
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 2 
                                 · 
                                 
                                   enp 
                                   2 
                                 
                                 · 
                                 β 
                                 · 
                                 
                                   exp 
                                   2 
                                 
                                 · 
                                 
                                   pizsum 
                                   2 
                                 
                                 · 
                                 
                                   r 
                                   3 
                                 
                               
                               - 
                               
                                 
                                   r 
                                   3 
                                 
                                 · 
                               
                             
                           
                         
                         
                           
                             
                               
                                 exp 
                                 2 
                               
                               + 
                               
                                 
                                   r 
                                   3 
                                 
                                 · 
                                 
                                   enp 
                                   2 
                                 
                                 · 
                                 
                                   β 
                                   2 
                                 
                               
                               + 
                               
                                 2 
                                 · 
                                 
                                   enp 
                                   2 
                                 
                                 · 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           β 
                           · 
                           exp 
                         
                         + 
                         
                           2 
                           · 
                           
                             enp 
                             2 
                           
                           · 
                           β 
                           · 
                           
                             exp 
                             2 
                           
                         
                       
                     
                   
                 
                 
                   
                     - 
                     
                       exp 
                       2 
                     
                   
                   + 
                   
                     
                       enp 
                       2 
                     
                     · 
                     
                       β 
                       2 
                     
                   
                 
               
             
           
         
       
       
         
           
             
               l 
               3 
               ′ 
             
             = 
             
               
                 1 
                 4 
               
               · 
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               
                                 
                                   
                                     2 
                                     · 
                                     
                                       enp 
                                       2 
                                     
                                     · 
                                     β 
                                     · 
                                     
                                       exp 
                                       2 
                                     
                                     · 
                                     
                                       pizsum 
                                       2 
                                     
                                     · 
                                     
                                       r 
                                       3 
                                     
                                   
                                   - 
                                   
                                     
                                       r 
                                       3 
                                     
                                     · 
                                   
                                 
                               
                             
                             
                               
                                 
                                   
                                     exp 
                                     2 
                                   
                                   + 
                                   
                                     
                                       r 
                                       3 
                                     
                                     · 
                                     
                                       enp 
                                       2 
                                     
                                     · 
                                     
                                       β 
                                       2 
                                     
                                   
                                   + 
                                   
                                     2 
                                     · 
                                     
                                       enp 
                                       2 
                                     
                                     · 
                                   
                                 
                               
                             
                           
                         
                       
                       
                         
                           
                             
                               exp 
                               2 
                             
                             + 
                             
                               2 
                               · 
                               
                                 enp 
                                 2 
                               
                               · 
                               β 
                               · 
                               
                                 exp 
                                 2 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   · 
                   
                     r 
                     3 
                   
                 
                 
                   
                     ( 
                     
                       
                         β 
                         · 
                         
                           r 
                           3 
                         
                         · 
                         
                           pizsum 
                           2 
                         
                       
                       + 
                       1 
                       + 
                       β 
                     
                     ) 
                   
                   · 
                   
                     enp 
                     2 
                   
                   · 
                   
                     exp 
                     2 
                   
                 
               
             
           
         
       
       
         
           
             
               l 
               4 
             
             = 
             
               
                 1 
                 4 
               
               · 
               
                 
                   
                     ( 
                     
                       
                         
                           
                             
                               
                                 r 
                                 3 
                               
                               · 
                               
                                 exp 
                                 2 
                               
                             
                             + 
                             
                               2 
                               · 
                               
                                 enp 
                                 2 
                               
                               · 
                               β 
                               · 
                               
                                 exp 
                                 2 
                               
                             
                             - 
                             
                               
                                 r 
                                 4 
                               
                               · 
                               
                                 enp 
                                 2 
                               
                               · 
                               
                                 β 
                                 2 
                               
                             
                             + 
                           
                         
                       
                       
                         
                           
                             
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   β 
                                   2 
                                 
                                 · 
                                 
                                   exp 
                                   2 
                                 
                                 · 
                                 
                                   enp 
                                   2 
                                 
                               
                             
                             + 
                             
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 
                                   β 
                                   2 
                                 
                                 · 
                                 
                                   exp 
                                   2 
                                 
                                 · 
                                 
                                   enp 
                                   2 
                                 
                                 · 
                                 
                                   pizsum 
                                   2 
                                 
                               
                             
                           
                         
                       
                     
                     ) 
                   
                   · 
                   
                     r 
                     3 
                   
                 
                 
                   
                     enp 
                     2 
                   
                   · 
                   β 
                   · 
                   
                     exp 
                     2 
                   
                   · 
                   
                     ( 
                     
                       
                         
                           
                             1 
                             + 
                             β 
                             + 
                             
                               2 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 β 
                                 · 
                                 
                                   r 
                                   3 
                                 
                                 · 
                                 
                                   pizsum 
                                   2 
                                 
                               
                             
                             + 
                           
                         
                       
                       
                         
                           
                             
                               
                                 pizsum 
                                 2 
                               
                               · 
                               
                                 r 
                                 3 
                               
                             
                             + 
                             
                               
                                 pizsum 
                                 2 
                                 2 
                               
                               · 
                               
                                 r 
                                 3 
                                 2 
                               
                               · 
                               β 
                             
                           
                         
                       
                     
                     ) 
                   
                 
               
             
           
         
       
       
         
           
             
               l 
               4 
               ′ 
             
             = 
             
               
                 - 
                 
                   1 
                   2 
                 
               
               · 
               
                 
                   
                     
                       
                         
                           
                             r 
                             3 
                           
                           · 
                           
                             exp 
                             2 
                           
                         
                         + 
                         
                           2 
                           · 
                           
                             enp 
                             2 
                           
                           · 
                           
                             β 
                             2 
                           
                         
                         - 
                         
                           
                             r 
                             3 
                           
                           · 
                           
                             enp 
                             2 
                           
                           · 
                           
                             β 
                             2 
                           
                         
                         + 
                       
                     
                   
                   
                     
                       
                         
                           2 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           
                             
                               β 
                               2 
                             
                             · 
                             
                               enp 
                               2 
                             
                             · 
                             
                               exp 
                               2 
                             
                           
                         
                         + 
                         
                           2 
                           · 
                           
                             β 
                             2 
                           
                           · 
                           
                             r 
                             3 
                           
                           · 
                           
                             enp 
                             2 
                           
                           · 
                           
                             exp 
                             2 
                           
                           · 
                           
                             pizsum 
                             2 
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             enp 
                             2 
                           
                           · 
                           
                             β 
                             2 
                           
                         
                         - 
                         
                           exp 
                           2 
                         
                         - 
                         
                           
                             exp 
                             2 
                           
                           · 
                           
                             pizsum 
                             2 
                           
                           · 
                         
                       
                     
                   
                   
                     
                       
                         
                           r 
                           3 
                         
                         + 
                         
                           
                             r 
                             3 
                           
                           · 
                           
                             β 
                             2 
                           
                           · 
                           
                             pizsum 
                             2 
                           
                           · 
                           
                             enp 
                             2 
                           
                         
                       
                     
                   
                 
               
             
           
         
       
       
         
           
             
               l 
               
                 p 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 3 
               
               ′ 
             
             = 
             
               
                 1 
                 4 
               
               · 
               
                 
                   ( 
                   
                     
                       
                         
                           
                             2 
                             · 
                             
                               enp 
                               2 
                             
                             · 
                             β 
                             · 
                             
                               exp 
                               2 
                             
                             · 
                             
                               pizsum 
                               2 
                             
                             · 
                             
                               r 
                               3 
                             
                           
                           - 
                           
                             
                               r 
                               3 
                             
                             · 
                             
                               exp 
                               2 
                             
                           
                           + 
                           
                             
                               r 
                               3 
                             
                             · 
                             
                               exp 
                               2 
                             
                             · 
                           
                         
                       
                     
                     
                       
                         
                           
                             β 
                             2 
                           
                           + 
                           
                             2 
                             · 
                             
                               enp 
                               2 
                             
                             · 
                             β 
                             · 
                             
                               exp 
                               2 
                             
                           
                           + 
                           
                             2 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               
                                 enp 
                                 2 
                                 2 
                               
                               · 
                               
                                 β 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                   ) 
                 
                 
                   
                     ( 
                     
                       
                         
                           exp 
                           2 
                         
                         · 
                         
                           pizsum 
                           2 
                         
                         · 
                         
                           r 
                           3 
                         
                       
                       + 
                       
                         exp 
                         2 
                       
                       + 
                       
                         
                           enp 
                           2 
                         
                         · 
                         β 
                       
                     
                     ) 
                   
                   · 
                   
                     enp 
                     2 
                   
                   · 
                   β 
                 
               
             
           
         
       
       
         
           
             
               l 
               
                 p 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 4 
               
             
             = 
             
               
                 - 
                 
                   1 
                   4 
                 
               
               · 
               
                 
                   ( 
                   
                     
                       
                         
                           
                             
                               - 
                               2 
                             
                             · 
                             
                               exp 
                               2 
                               2 
                             
                             · 
                             
                               pizsum 
                               2 
                             
                             · 
                             
                               r 
                               3 
                             
                           
                           - 
                           
                             
                               r 
                               3 
                             
                             · 
                             
                               exp 
                               2 
                             
                           
                           - 
                           
                             2 
                             · 
                             
                               enp 
                               2 
                             
                             · 
                             β 
                             · 
                           
                         
                       
                     
                     
                       
                         
                           
                             exp 
                             2 
                           
                           - 
                           
                             2 
                             · 
                             
                               exp 
                               2 
                               2 
                             
                           
                           + 
                           
                             
                               r 
                               3 
                             
                             · 
                             
                               enp 
                               2 
                             
                             · 
                             
                               β 
                               2 
                             
                           
                         
                       
                     
                   
                   ) 
                 
                 
                   ( 
                   
                     
                       
                         
                           
                             2 
                             · 
                             
                               exp 
                               2 
                             
                             · 
                             
                               pizsum 
                               2 
                             
                             · 
                             
                               enp 
                               2 
                             
                           
                           + 
                           
                             
                               pizsum 
                               2 
                               2 
                             
                             · 
                             
                               r 
                               3 
                               2 
                             
                             · 
                             
                               exp 
                               2 
                             
                           
                           + 
                         
                       
                     
                     
                       
                         
                           
                             
                               enp 
                               2 
                             
                             · 
                             β 
                           
                           + 
                           
                             
                               enp 
                               2 
                             
                             · 
                             β 
                             · 
                             
                               pizsum 
                               2 
                             
                             · 
                             
                               r 
                               3 
                             
                           
                           + 
                           
                             exp 
                             2 
                           
                         
                       
                     
                   
                   ) 
                 
               
             
           
         
       
       
         
           
             
               r 
               4 
             
             = 
             
               
                 r 
                 3 
               
               / 
               
                 ( 
                 
                   1 
                   + 
                   
                     
                       pizsum 
                       2 
                     
                     · 
                     
                       r 
                       3 
                     
                   
                 
                 ) 
               
             
           
         
       
     
     Then the radius of the fourth lens r 4 , the separation between the third lens and the fourth lens d 3 , the object distance of the third lens l 3 , and the image distance of the fourth lens l′ 4  can be obtained. 
     STEP  111  From the radii and their position relationships of the six lenses calculated from the steps mentioned above, the whole design of the EUVL projection objective can be obtained. 
     The above mentioned r 3  is an artificially chosen value. Because the input parameters are all paraxial values, the values got from the equations do not fit the demands of the non-paraxial parameters. However, with the trend of the variation of the paraxial parameters, we can judge whether a reasonable G 2  is exist or not under the combination of the current G 1  and G 3 , and then get an available range of r 3 . 
     The invention takes the second lens group G 2  as an individual optical system, by taking the paraxial magnification of G 2  as β=M, making the paraxial entrance pupil distance of the second lens enp 2  equal to the exit pupil distance of the first lens group, i.e. enp 2 =ENP1; making the paraxial exit pupil distance of the second lens group exp 2  equal to the entrance pupil distance of the G 3 , i.e. exp 2 =EXP3; 1500 mm&gt;(−l 3 −enp 2 )&gt;0 and 0&gt;d 3 &gt;1500 mm as constraint conditions, the available range of radius of the third lens r 3  can be decided with the conjugation relationship of object and image, the magnification condition, the pezval sum condition, and the conjugation relationship of the entrance and exit pupil. Then, the radius of the third lens r 3  can be picked up from that available range. 
     Here is the description of the chosen range of the r 3  with examples. 
     The input parameters are shown in table 1. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
             
             
               
                   
                 1/r 3   
                 −0.002~0.002 
               
               
                   
                 Entrance pupil distance ENP2 
                 −1883.508480 
               
               
                   
                 Exit pupil distance EXP2 
                 352.613104 
               
               
                   
                 Pezval sum pizsum 2   
                 −0.000811 
               
               
                   
                 Magnification M 
                 −0.496181 
               
               
                   
                 Entrance pupil diameter END2 
                 143.574801 
               
               
                   
                 Object file height YOB2 
                 −174.424131 
               
               
                   
                   
               
               
                   
                 make 
               
               
                   
                 enp 2  = ENP1 
               
               
                   
                 exp 2  = EXP3 
               
               
                   
                 β = M 
               
             
          
         
       
     
     Different parameters versus 1/r 3  are shown in  FIG. 15( a ) ˜( d ). For an available EUVL projection objective, the total track should be controlled in a reasonable range. In this embodiment, the total track is constrained below 2000 mm; the third lens M 3  should be set behind the second lens M 2 ; the fourth lens M 4  should be set in front of the third lens M 3 ; and all the intervals should be shorter than the total track, leading to 1500 mm&gt;(−l 3 −enp 2 )&gt;0 and 0&gt;d 3 &gt;1500 mm. 
     For convenience, we set the object distance and the interval in  FIG. 15( a )  and  FIG. 15( b )  out of the available range to zero. Then the  FIG. 15( a )  and  FIG. 15( b )  are converted to  FIG. 16( a )  and  FIG. 16( b ) , making the available range of r 3  clear. By comparing and analyzing  FIG. 16( a )  and  FIG. 16( b ) , we can know whether there is available solution for the second lens group G 2  or not. 
     For the paraxial magnification β and the real magnification M of the second lens group G 2  are different, the paraxial exit pupil distance exp 2  and the real exit pupil distance EXP 2  of the second lens group G 2  are different either, the solved parameters from the steps above cannot be taken as the result of G 2  immediately. 
     Actually, for any off-axial optical system with two lenses, the real and paraxial parameters cannot be exactly the same. 
     For an off-axial optical system with two spherical lenses, there must be a set of paraxial parameters for it when its real characteristics match the needs. We can get it by the iteration and approach method. The detailed steps are as follow: 
     The following steps are for further optimization for the parameters of the second lens group: 
     STEP  201  Choose a radius of the third lens r 3 , set the error factor ξ B  and ξ exp     2   , and take β(1)=M and exp 2 (1)=EXP1, set the loop time k=1. 
     STEP  202  Through the parameters β(k), exp 2 (k), and the chosen r 3 , with the conjugation relationship of the object and the image, the magnification, the pezval sum condition, and the conjugation relationship of the entrance and exit pupil, get the parameters d 3 (k), l 3 (k), l′ 4 (k), and r 4 (k) of the second lens group G 2 . 
     STEP  203  Put the r 3 , d 3 (k), l 3 (k), l′ 4 (k), and r 4 (k) into the optical design software CODEV, and obtain the magnification M(k) and the real exit pupil distance EXP2(k) of the second lens group G 2 . 
     STEP  204  If |EXP2(k)−EXP1|≦ξ exp     2    and |M(k)−M|≦ξ B , end the optimization process, and take the current r 3 , d 3 (k), l′ 3 (k), l′ 4 (k), and r 4 (k) as the parameters of the second lens group G 2 , if not, go to the step  205 . 
     STEP  205  Take β(k+1)=β(k)·[M/M(k)] σ , exp 2 (k+1)=exp 2 (k)·[EXP1/EXP2(k)] σ , wherein the σ≦1, making k=k+1, and go back to STEP  202 . 
     In this invention, there is 
               σ   ∈     {       1   4     ,     1   2     ,   1     }       ,         
wherein the [M/M(k)] σ and [EXP 1/EXP2(k)] σ  are called approach factors. When the solution space of the second lens group is small, and the [M/M(k)] 1  and [EXP1/EXP2(k)] 1  (σ=1) deal the paraxial magnification and the exit pupil distance with the above approach factors, the solution may get out of the reasonable range and make the results far from convergent. So we can take
 
               σ   =     1   2       ,         
i.e. with the approach factors of [M/M(k)] 1/2  and [EXP1/EXP2(k)] 1/2 , or
 
               σ   =     1   4       ,         
i.e. with the approach factors of [M/M(k)] 1/4  and [EXP1/EXP2(k)] 1/4  to make the searching process stable, although the later one may get too many iteration times. So
 
             σ   =     1   2           
is the most suitable and well applied factor.
 
       FIG. 17  is the convergence situation of the G 2 &#39;s magnification M versus the iteration times. 
     EMBODIMENT 1 
     The layout of a randomly chosen structure of the first lens group G 1  is shown in  FIG. 18( a ) , the aperture diaphragm is set on the second lens M 2 , and the incidental angle of the chief ray on the mask is 5°. This structure is reasonably arranged with considerations of practical machining. Its optical characteristics and structural parameters are shown in table 2, wherein the 
     
       
         
           
             
               pizsum 
               1 
             
             = 
             
               
                 1 
                 
                   r 
                   1 
                 
               
               - 
               
                 
                   1 
                   
                     r 
                     2 
                   
                 
                 . 
               
             
           
         
       
     
     
       
         
               
               
               
             
           
               
                   
                 TABLE 2 
               
               
                   
                   
               
             
             
               
                   
                 NAO 
                 0.05 
               
               
                   
                 CA 
                 5.00000 
               
               
                   
                 ratio 1   
                 0.153 
               
               
                   
                 ratio 2   
                 0.352 
               
               
                   
                 YOB 
                 132.5000 
               
               
                   
                 −l 1   
                 304.7500 
               
               
                   
                 −d 1   
                 −304.749986 
               
               
                   
                 r 1   
                 −1160.173602 
               
               
                   
                 r 2   
                 −9301.878824 
               
               
                   
                 l′ 2   
                 1970.7450 
               
               
                   
                 YIM1 
                 −368.998492 
               
               
                   
                 EXP1 
                 1970.744988 
               
               
                   
                 pizsum 1   
                 −0.000754435 
               
               
                   
                   
               
             
          
         
       
     
     The layout of a randomly chosen structure of the third lens group G 3  is shown in  FIG. 18( b ) . Its optical characteristics and structural parameters are shown in table 3, wherein the 
     
       
         
           
             
               pizsum 
               3 
             
             = 
             
               
                 1 
                 
                   r 
                   5 
                 
               
               - 
               
                 
                   1 
                   
                     r 
                     6 
                   
                 
                 . 
               
             
           
         
       
     
     
       
         
               
               
               
             
           
               
                   
                 TABLE 3 
               
               
                   
                   
               
             
             
               
                   
                 NAI 
                 0.25 
               
               
                   
                 CA 
                 telecentricity 
               
               
                   
                 ratio 3   
                 9.000000 
               
               
                   
                 YIM 
                 26.5000 
               
               
                   
                 l′ 6   
                 320.0000 
               
               
                   
                 d 5   
                 −288.0000 
               
               
                   
                 r 6   
                 −358.854572 
               
               
                   
                 r 5   
                 −411.048060 
               
               
                   
                 −l 5   
                 273.972300 
               
               
                   
                 YOB3 
                 −76.985423 
               
               
                   
                 ENP3 
                 354.566741 
               
               
                   
                 pizsum 3   
                 −0.000354 
               
               
                   
                   
               
             
          
         
       
     
     With the parameters of G 1  and G 3  obtained from the processes mentioned above, the essential parameters for the calculation of G 2  can be obtained, which is shown in table 4. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 4 
               
               
                   
                   
               
             
             
               
                   
                 1/r 3   
                 −0.002~0.002 
               
               
                   
                 Entrance pupil distance ENP2 
                 −1970.744988 
               
               
                   
                 Exit pupil distance EXP2 
                 354.566741 
               
               
                   
                 Pezval sum pizsum 2   
                 −0.001108 
               
               
                   
                 Magnification M 
                 −0.208633 
               
               
                   
                 Entrance pupil diameter END2 
                 72.144399 
               
               
                   
                 Object file height YOB2 
                 −368.998492 
               
               
                   
                   
               
             
          
         
       
     
     Three layouts of the structures of G 2  are shown in  FIG. 18( c ) , of which the corresponding radii of the lenses of G 3  are 500 mm, 450 mm, and −500 mm. 
     The parameters of the three embodiments are shown in table 5, table 6 and table 7. Table 8 shows the comparison of the total track with the maximum diameter of the three embodiments, wherein there are c 1 =1/r 1 , c 2 =1/r 2 , c 3 =1/r 3 , c 4 =1/r 4 , c 5 =1/r 5 , c 6 =1/r 6 . The d 1  denotes the distance between the mask and the first lens M 1 ; the d 2 □d 6  denote the separation between the corresponding lens to the next lens; and the d 7  denotes the separation between the sixth lens M 6  to the wafer. 
     For the first embodiment, the third lens M 3  is set behind the image plane, which is not convenient for the moving of the scanner. The total track of the second embodiment is relatively small, but the maximum diameter of which is relatively large. The maximum diameter of the third embodiment is relatively small, but the total track of which relatively is large. The proper radius of the third lens M 3  can be chosen according to the engineering practice. 
     
       
         
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                 curvature 
                 Thickness 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 d 1   
                 865.6667 
               
               
                   
                 c 1   
                 −0.000862 
                 d 2   
                 −304.7500 
               
               
                   
                 c 2   
                 −0.000108 
                 d 3   
                 294.8853 
               
               
                   
                 c 3   
                 0.002000 
                 d 4   
                 −712.911491 
               
               
                   
                 c 4   
                 0.000892 
                 d 5   
                 1562.2970 
               
               
                   
                 c 5   
                 0.002433 
                 d 6   
                 −288.000 
               
               
                   
                 c 6   
                 0.002787 
                 d 7   
                 320.0000 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 6 
               
               
                   
                   
               
               
                   
                 curvature 
                 Thickness 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 d 1   
                 865.6667 
               
               
                   
                 c 1   
                 −0.000862 
                 d 2   
                 −304.7500 
               
               
                   
                 c 2   
                 −0.000108 
                 d 3   
                 336.3676 
               
               
                   
                 c 3   
                 0.002222 
                 d 4   
                 −512.9432 
               
               
                   
                 c 4   
                 0.001114 
                 d 5   
                 1363.527 
               
               
                   
                 c 5   
                 0.002433 
                 d 6   
                 −288.000 
               
               
                   
                 c 6   
                 0.002787 
                 d 7   
                 320.0000 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 7 
               
               
                   
                   
               
               
                   
                 curvature 
                 Thickness 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 d 1   
                 865.6667 
               
               
                   
                 c 1   
                 −0.000862 
                 d 2   
                 −304.7500 
               
               
                   
                 c 2   
                 −0.000108 
                 d 3   
                 1049.8990 
               
               
                   
                 c 3   
                 −0.002500 
                 d 4   
                 −142.7610 
               
               
                   
                 c 4   
                 −0.003608 
                 d 5   
                 269.1092 
               
               
                   
                 c 5   
                 0.002433 
                 d 6   
                 −288.000 
               
               
                   
                 c 6   
                 0.002787 
                 d 7   
                 320.0000 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
               
             
           
               
                   
                 TABLE 8 
               
               
                   
                   
               
               
                   
                 System # 
                 Total length 
                 Maximum diameter 
               
               
                   
                   
               
             
             
               
                   
                 System1 
                 1737.1874 
                 888.3862 
               
               
                   
                 System2 
                 1779.8679 
                 771.7360 
               
               
                   
                 System3 
                 1769.1643 
                 407.6502 
               
               
                   
                   
               
             
          
         
       
     
     Referring to the  FIG. 19( a ) ,  FIG. 19( b ) ,  FIG. 19( c ) , the other three embodiments obtained through grouping design method are shown, of which the detail parameters are shown in table 9, table 10 and table 11. Some of the embodiments may be unsuitable for manufacturing, and they will only be shown here as examples of the design method. 
     
       
         
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 9 
               
               
                   
                   
               
               
                   
                 curvature 
                 Thickness 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 d 1   
                 749.5141 
               
               
                   
                 c 1   
                 −0.001541 
                 d 2   
                 −224.8542 
               
               
                   
                 c 2   
                 −0.002866 
                 d 3   
                 1344.351 
               
               
                   
                 c 3   
                 −0.001000 
                 d 4   
                 −570.4919 
               
               
                   
                 c 4   
                 −0.001149 
                 d 5   
                 418.7801 
               
               
                   
                 c 5   
                 0.001968 
                 d 6   
                 −222.1395 
               
               
                   
                 c 6   
                 0.003442 
                 d 7   
                 251.7581 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 10 
               
               
                   
                   
               
               
                   
                 curvature 
                 Thickness 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 d 1   
                 749.5141 
               
               
                   
                 c 1   
                 −0.0015411 
                 d 2   
                 −224.8542 
               
               
                   
                 c 2   
                 −0.0038309 
                 d 3   
                 1119.093 
               
               
                   
                 c 3   
                 −0.0004762 
                 d 4   
                 −781.3919 
               
               
                   
                 c 4   
                 0.00033972 
                 d 5   
                 −222.1395 
               
               
                   
                 c 5   
                 0.00196793 
                 d 6   
                 1259.953 
               
               
                   
                 c 6   
                 0.00344177 
                 d 7   
                 251.7581 
               
               
                   
                   
               
             
          
         
       
     
     
       
         
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 11 
               
               
                   
                   
               
               
                   
                 curvature 
                 Thickness 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                   
                   
                 d 1   
                 407.9396 
               
               
                   
                 c 1   
                 −0.000581 
                 d 2   
                 −274.6366 
               
               
                   
                 c 2   
                 0.000798 
                 d 3   
                 1072.295 
               
               
                   
                 c 3   
                 −0.002000 
                 d 4   
                 −233.6414 
               
               
                   
                 c 4   
                 −0.004080 
                 d 5   
                 202.4978 
               
               
                   
                 c 5   
                 0.002501 
                 d 6   
                 −244.6155 
               
               
                   
                 c 6   
                 0.003203 
                 d 7   
                 274.6155 
               
               
                   
                   
               
             
          
         
       
     
       FIG. 20  is a schematic diagram of a typical EUVL projection exposure system. The ray beam emerges from the source  2001 , gets reshaped and uniformed by the illumination system  2002 , and then incidents into the reflective mask  101 . Reflected by the mask, the ray beam incidents into the projection system  2003 , and then generates an image on the wafer  102  with exposure. The EUVL projection objective obtained by the design of this invention can be applied to that EUVL system. The ray beam with 13.5 nm wavelength emerged from the EUV source, passed through the illumination system, incidents into the mask, gets reflected, and then incidents into the first lens M 1 , the second lens M 2 , the third lens M 3 , the fourth lens M 4 , the fifth lens M 5 , and the sixth lens M 6 , then finally generates an image on the wafer. 
     Although the embodiments have been described associated with specific projection-optical systems as used in the exposure apparatus, it should be clear that this invention can also be applied to many other projection optical systems in general. And even though the invention has been described on the basis of specific embodiments, numerous variations and alternative embodiments can be deduced by the person skilled in the art, e.g. by combination and/or exchange of features of individual embodiments. Accordingly, it goes without saying for the person skilled in the art that such variations and alternative embodiments are also encompassed by the present invention, and the scope of the invention is only restricted within the meaning of the accompanying patent claims and the equivalents thereof.