Abstract:
An optical system compatible with short wavelength (extreme ultraviolet) radiation comprising four optical elements providing five reflective surfaces for projecting a mask image onto a substrate. The five optical surfaces are characterized in order from object to image as concave, convex, concave, convex and concave mirrors. The second and fourth reflective surfaces are part of the same optical element. The optical system is particularly suited for ring field step and scan lithography methods. The invention uses aspheric mirrors to minimize static distortion and balance the static distortion across the ring field width, which effectively minimizes dynamic distortion.

Description:
The United States Government has rights in this invention pursuant to Contract No. W-7405-ENG-48 between the U.S. Department of Energy and the University of California, for the operation of Lawrence Livermore National Laboratory. 
    
    
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention is related to an optical system for use with short wavelength radiation in photolithography equipment. 
     2. Background of the Invention 
     Photolithography is a well-known manufacturing process used to create devices upon substrates. The process typically involves exposing a patterned mask to collimated radiation thereby producing patterned radiation, which is passed through an optical reduction system. The reduced patterned radiation or mask image is projected onto a substrate coated with photoresist. Radiation exposure changes the properties of the photoresist, allowing subsequent processing. 
     Exposure tools used in photolithography have two common methods of projecting a patterned mask onto a substrate: “step and repeat” and “step and scan.” The step and repeat method sequentially exposes portions of a substrate to a mask image. The step and repeat optical system has a projection field that is large enough to project at least one die image onto the substrate. After each image exposure, the substrate is repositioned and the process is repeated. 
     In contrast, the step and scan method scans the mask or reticle onto a wafer substrate over an annular field or a slit field that is the full height of one or more of the dies. Referring to FIG. 1, a ring field lithography system  100  for use in the step and scan method is shown. A moving mask  101  is illuminated by a radiation beam  103 , which reflects off the mask  101  and is directed through a reduction ring field optical system  107 . Within the optical system  107 , the image is inverted and the arcuate shaped ring field  109  is projected onto a moving substrate  111 . The arcuate shaped reduced image ring field  109  can only project a portion of the mask  101 , thus the reduced image ring field  109  must scan the complete mask  101  onto the substrate  111 . Because the mask  101  and substrate  111  move synchronously, a sharp image is scanned onto the substrate  111 . The dimensions of the arcuate slit are typically described by a ring field radius and a ring field width. 
     These step and scan ring field systems have less distortion than step and repeat systems because it is easier to correct distortion over the narrow slit width. Referring to FIG. 2, an image is projected by the optical system onto to wafer through an arcuate ring field slit  201 , which is geometrically described by a ring field radius  203 , a ring field width  205 , and a length  207 . Ring field coverage is up to 180° in azimuth  209 . 
     As manufacturing methods improve, the minimum resolution dimension or critical dimension (CD) that can be achieved decreases, thereby allowing more electronic components or devices to be fabricated within a given area of a substrate. The number of devices that can be fabricated within an area of substrate is known as device density. With existing technology, 0.18 μm resolution is possible using projection systems designed to operate at either 248 or 193 nanometers. One well-known means of improving the resolution dimension and increasing device density is to use shorter exposure wavelength radiation during photolithography processes. The relationship between resolution (R) and radiation wavelength is described by the formula: R=(K 1 λ)/(NA), wherein R is the resolution dimension, K 1  is a process dependent constant (typically 0.7), λ is the wavelength of the radiation, and NA is the numerical aperture of the optical system at the wafer plane. Either reducing the operating wavelength or an increasing in the numerical aperture will improve the resolution of the system. 
     Improving the resolution by increasing the numerical aperture (NA) has several drawbacks. The most prevalent drawback is the concomitant loss of depth of focus. The depth of focus determines, in part, the process latitude or the available “process window”. A reduced depth of focus limits the available process window. The relationship between NA and depth of focus (DOF) is described by the formula: DOF=(K 2 λ)/NA 2 , wherein DOF is depth of focus, and K 2  is a process dependent constant (typically close to unity). This simple relationship shows the inverse relationship between DOF and NA. For several reasons, including practical wafer flatness and scanning stage errors, a large depth of focus is on the order of 1.0 micrometers is desirable. 
     There is a rapid loss in DOF as the NA is increased. It is preferable to use shorter wavelengths combined with a low NA to maximize resolution and available DOF simultaneously. A state-of-the-art extreme ultraviolet (EUV) projection system operating at 13.4 nm achieves a 100 nm resolution (assuming K 1 =0.7) with a depth of focus of 1.0 μm at a NA of 0.10. This large depth of focus improves process latitude, thus enhancing the “process window”. In contrast, a deep ultraviolet (DUV) wavelength projection lithography optical system operating at a wavelength (λ) of 193 nm can only achieve a minimum critical dimension of 180 nm at a numerical aperture of 0.75, assuming the same value for the process dependent constant K 1 . Further, the depth of focus of the DUV optical system is reduced to 0.34 μm, resulting in a loss of process latitude that adversely impacts device yield. As the process window shrinks, it becomes more difficult to maintain the CD control required for high-density integrated circuits in commercial production. 
     To produce integrated circuits with ever smaller critical dimensions and higher device density with sufficient process latitude for volume manufacture, it is necessary to develop projection systems operating at extreme ultraviolet (EUV) wavelengths (from 4 to 20 nm). Radiation at these wavelengths must be focused using mirrors coated with multilayer coatings that have high reflectivity at near normal incidence angles. The reflection of radiation off of a mirror is known as “bounce”. 
     State of the art EUV imaging systems have relatively low numerical apertures in the range of 0.08 to 0.10 and can resolve features on the order of 100 nm. To extend the resolution of EUV lithography below 100 nm, optical systems having higher numerical apertures are needed. Increasing the numerical aperture of current EUV designs results in a substantial degradation in the residual wavefront error, making these designs unsuitable for projection lithography. 
     Prior art contains few examples of high (&gt;0.10) numerical aperture designs suitable for EUV lithography. An optical system that is usable in the extreme ultraviolet portion of the spectrum is disclosed in U.S. Pat. No. 5,315,629 to Jewell et al., which is herein incorporated by reference. The &#39;629 patent discloses a four mirror design with a numerical aperture of 0.10 and a ring field width of 0.5 mm. The design has diffraction-limited performance with approximately 10 nanometers of static distortion at the edge of its 0.5 mm ring field. The disclosure states that the numerical aperture of the optical system can be increased to approximately 0.14 without loss in image quality, if the image distortion tolerance is relaxed. The increase in numerical aperture would enable the design to resolve features less than 100 nanometers. However, as this design is re-optimized to minimize the residual wavefront error, the ability to correct distortion over any meaningful ring field width is lost. For example, the residual distortion at a numerical aperture of 0.14 is on the order of 30-40 nm at the edge of the 0.5 mm ring field. This is too much distortion for a practical lithographic projection, even when the effects of scan-averaging are included. 
     An optical system that is usable in the extreme ultraviolet portion of the spectrum is disclosed in U.S. Pat. No. 5,212,588 to Viswanathan et al., which is herein incorporated by reference. The &#39;588 patent demonstrate a multi-bounce projection system that incorporates two coaxial aspheric mirrors in a 4-bounce arrangement, where mirror M 1  is convex and mirror M 2  is concave. To obtain high resolution imagery, the field curvature needs to be corrected to substantially zero so that the imaging surface is perfectly flat. The &#39;588 projection system is designed so that the two mirrors have substantially the same radius of curvature. Since M 1  is convex and M 2  is concave, the flat field condition is automatically satisfied (the Petzval sum is made almost identically zero). While the &#39;588 patent describes a number of embodiments with excellent performance, all the designs suffer one disadvantage in that the exit pupil is centrally obscured. This central obscuration is undesirable since it will degrade resolution and reduce the process latitude for the variety of complex geometries that must be patterned. 
     In view of the foregoing, there is a need for an optimized optical system that is compatible with short wavelength radiation and has a high numerical aperture for improved resolution, and which addresses the above and other problems. 
     SUMMARY OF THE INVENTION 
     The present invention is directed to a catoptric optical system that is used to project a reduced mask image onto a wafer with short wavelength radiation. The preferred embodiment comprises an optical system having four mirrored surfaces in a novel five bounce configuration. The imaging bundle is reflected off of one of the mirrored surfaces, mirror M 2 , twice. The present invention allows for higher device density because the optical system has improved resolution that results from the relatively high numerical aperture. The optical system is designed to have a numerical aperture of approximately 0.15 and operate at a wavelength of approximately 13.1 nm. Under these conditions, resolution on the order of 50 nm can be achieved. 
     An embodiment of the present invention also includes a well-defined accessible aperture stop that helps to ensure that the imagery is stationary. Illuminated properly, this projection system should have no variation in critical dimension across the field due to vignetting or clipping of the imaging bundles. 
     Further, an embodiment of the present invention has a balanced static centroid distortion curve across the ring field width. More specifically, the centroid distortion levels at the edges of the ring field width are substantially equal and quantitatively higher than the centroid distortion at the center of the ring field width. By balancing the static centroid distortion curve across the ring field width, the dynamic scan-averaged distortion is minimized. 
     The mirrors are arranged so that the negative contribution to the Petzval sum from the two reflections off mirror M 2  is corrected by the single bounce from mirror M 3  and the single bounce from mirror M 4 . The remaining net negative sum is corrected using mirror M 1 , which has comparatively little optical power. To minimize the Petzval sum, the radii of mirrors M 2 , M 3 , and M 4  are approximately equal. The spacing between the mirrors is set so that the imaging bundles are unobscured at the chosen reduction ratio. To minimize the residual wavefront error, all four reflective surfaces of the inventive optical system are aspheric. 
     Other advantages and features of the present invention will become apparent from a reading of the following description when considered in conjunction with the accompanying drawings of which the following is a brief description. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIG. 1 is a view of a ring field lithography system. 
     FIG. 2 is a view of a ring field slit. 
     FIG. 3 is a schematic depiction of the main elements of the exemplary EUV lithography apparatus according to the present invention. 
     FIG. 4 is a view of the optical system according to the present invention. 
     FIG. 5 is a graph showing distortion v. position across the ring field width. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     The following is a detailed description of the presently preferred embodiments of the present invention. However, the present invention is in no way intended to be limited to the embodiments discussed below or shown in the drawings. Rather, the description and the drawings are merely illustrative of the presently preferred embodiments of the invention. 
     The present invention is a photolithography optical system designed for use with extreme ultraviolet (EUV) radiation. FIG. 3 schematically depicts the exemplary inventive apparatus for semiconductor EUV lithography. The apparatus comprises a radiation source  301  that emits EUV radiation  303 . The EUV radiation  303  may be processed by a condenser  305  to produce an EUV beam  307  to uniformly illuminate a portion of a mask  309 . The radiation reflected from the mask  309  produces a patterned EUV beam  311 , which is introduced into an optical system  313 . The optical system  313  projects a reduced image  315  of the mask  309  onto a wafer  317 . 
     EUV radiation has a wavelength (λ) between about 4 to 20 nm and may be produced by any suitable means including a laser produced plasma, synchrotron radiation, electric discharge sources, high-harmonic generation with femto-second laser pulses, discharge-pumped x-ray lasers, and electron-beam driven radiation devices. The sources may be continuous or pulsed. Laser-produced plasma (LPP) sources focus an intense pulsed laser beam onto a target. Suitable targets are metals and noble gases. Targets of noble gas molecule clusters in a supersonicjet produce a bright “spark” with a broad emission spectrum ranging from visible light to EUV radiation. High-repetition-rate (3,000-6,000 Hz) pulsed laser drivers deliver 1,500 W of focused power to the target regions. A LPP gas source converts the incident laser power into EUV light in the required spectral bandwidth. 
     Condenser optics typically collect EUV radiation from the LPP source and condition the radiation to uniformly illuminate the mask. The condenser illuminates a narrow ring field at the mask with the EUV radiation, where the illumination must have a spatial nonuniformity of less than 1% in the cross scan dimension. The condenser further directs the EUV beam into the entrance pupil of the optical system with a partial coherence of approximately 0.7. Separate collection channels each act in concert to direct radiation across the entire ring field and the optical system entrance pupil. 
     Since EUV radiation is absorbed by all materials, reflective optical elements rather than refractive elements are best suited for EUV optical systems. The inventive optical system comprises four reflective optical elements (mirrors) listed in order from mask to wafer: M 1 , M 2 , M 3 , and M 4 . The optical system is placed in a vacuum or other suitable atmosphere. 
     In the lithographic process, the EUV radiation is collected and illuminates a mask, producing an image that can be projected to the wafer. The object end of the inventive optical system departs enough from the telecentric condition so that the light rays incident upon the reflective mask have sufficient clearance to prevent vignetting or clipping by mirror edges. 
     Referring to FIG. 4, there is shown an exemplary optical system for EUV semiconductor lithography. The optical elements are all arranged in a coaxial configuration such that the vertex of each surface of revolution lies on a common centerline  414 . Only off-axis sections of each mirror are used. Because this is a ring field optical configuration, only off-axis sections of the parent mirrors are utilized as shown in FIG.  4 . Thus, the off-axis section of the first optical element (M 1 )  405 , the off-axis section of the second optical element (M 2 )  409 , the off-axis section of the third optical element (M 3 )  413 , and the off-axis section of the four optical element (M 4 )  421  are exposed to EUV radiation. The use of off-axis sections, which are smaller in area than the full aspheric parent mirrors, facilitates the deposition uniform reflective multilayer coatings. The ability to achieve the required uniform layer thickness is enhanced as the reflective area of the mirror is decreased. 
     EUV Beam  1   403  diverges from a reflective mask  401  onto concave aspheric mirror M 1   405 . Beam  2   407  is reflected from mirror M 1   405  in a divergent cone to a convex aspheric mirror M 2   409 . Beam  3   411  is reflected from mirror M 2   409  in a divergent cone to a concave aspheric mirror M 3   413 . Beam  4   415  is reflected from mirror M 3   413  in a convergent cone back to convex aspheric mirror M 2   409 . At this location, the aperture stop  412  is place on the mechanical centerline  414  of the optical system. Beam  5   419  is reflected from mirror M 2   409  in a divergent cone to a concave aspheric mirror M 4   421 . Beam  6   423  is reflected from mirror M 4   421  in a convergent cone forming a reduced image of the mask  401  pattern onto a wafer  425 . The projected EUV aerial image enables a chemical reaction in a photoresist layer on the wafer  425  forming the latent image in the photoresist. This latent image is then subsequently processed by well-known means to form the patterned wafer. 
     Concave mirrors have positive optical power and convex mirrors have negative optical power. Using this convention, the optical power configuration of the inventive system from object to image (including the double bounce from mirror M 2   409  ) can be described as: positive, negative, positive, negative and positive, corresponding to mirrors M 1   405 , M 2   409  (first bounce), M 3   413 , M 4   409  (second bounce), and M 4   421 , respectively. This configuration of alternating positive and negative optical powers allows the optical system to achieve a Petzval sum that is approximately zero, while enabling correction of both astigmatism and distortion. 
     Since the focal length of the inventive optical system can be scaled to accommodate a variety of packaging concepts, it is useful to describe the inventive optical system relative to this quantity. In the preferred embodiment, the absolute radii of the mirrors M 1   405 , M 2   409 , M 3   413 , and M 4   417 , relative to the system focal length, are listed in Table 2. 
     
       
         
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                   
                 Reflective surface radii from object plane to image 
               
               
                 Reflective Surface 
                 plane as a fraction of the system focal length ± 10% 
               
               
                   
               
             
             
               
                 M1 
                 5.1613 
               
               
                 M2 
                 1.0819 
               
               
                 M3 
                 1.2735 
               
               
                 M4 
                 1.1411 
               
               
                   
               
             
          
         
       
     
     Referring to Table 3, the relative positions of the mirrors M 1   405 , M 2   409  (first bounce), M 3   413 , M 2   409  (second bounce), and M 5   421  for the preferred embodiment are listed. For a 4-to-1 reduction, the distance of the mask  401  to M 1   405  is 388.845 mm. 
     
       
         
               
               
             
           
               
                 TABLE 3 
               
               
                   
               
               
                   
                 Axial separations of the mirrors as a fraction of the 
               
               
                 Surface 
                 system focal length ± 10% 
               
               
                   
               
             
             
               
                 M1 to M2 
                 0.8671 
               
               
                 M2 to M3 
                 0.6006 
               
               
                 (first bounce) 
               
               
                 M3 to M2 
                 0.6006 
               
               
                 M2 to S4 
                 0.5655 
               
               
                 (second bounce) 
               
               
                 M4 to image 
                 0.8559 
               
               
                   
               
             
          
         
       
     
     EUV multilayers are constructed using alternating layers of two materials with different optical properties. These materials need to have low intrinsic absorption at EUV wavelengths and provide an optical impedance mismatch at the layer interfaces so that reflected waves can be generated. Common material pairs with desirable reflectance characteristics include molybdenum/silicon (Mo/Si) for wavelengths near 13.4 nm and molybdenum/beryllium (Mo/Be) for wavelengths near 11.3 nm. 
     Since the optical impedance between these material pairs is low, many layer pairs are required to achieve a useful reflectance. The multilayer mirror may be designed for specific radiation wavelengths and incidence angles. As the reflectance of the multilayer stack is maximized with the addition of multilayer pairs, the reflectance of the multilayer mirrors may be affected by variations in the radiation wavelength and angle of incidence. 
     The multilayer mirror may only have a narrow wavelength bandwidth that produces maximum reflectance. This narrow spectral bandwidth means that the multilayer reflectance is, for a fixed angle of incidence, sensitive to shifts in the incident radiation wavelength. The multilayer mirror reflectance may decrease if the incident radiation wavelength deviates outside the mirror&#39;s maximum reflectance bandwidth. 
     In an EUV optical system, the multilayer mirror reflectance may also be affected by the radiation incidence angle. Although multilayer mirrors may be designed to maximize reflectance for a specific incidence angle, this maximum reflectance may only exist over a narrow range proximate to the design incidence angle. A multilayer mirror optimized for perpendicular radiation may produce maximum reflectance over a wider range of incidence angles than a mirror specifically designed for more acute incidence angles. The reflectance can decrease significantly when the incidence angle deviates outside the multilayer&#39;s angular bandwidth. 
     The ability of mirrors to equally reflect radiation over a range of incidence angles can be important because rays passing through an optical system may not impinge upon mirrors at the same angle across the beam width. The projected beam of an EUV optical system converges and expands, the individual rays of the beam do not travel in parallel paths. Maximum reflectivity over a wider range of ray angles can be maintained by configuring all mirrors so that the mean incidence angles are close to perpendicular. An embodiment of the present invention utilizes a mirror system configuration having near perpendicular or low mean incidence angles. Low mean incidence angles at each mirror ensures that the optical system transmission, which is described by the formula T sys =R 1 ×R 2 × . . . ×R i , where R i  represents the reflectivity of the i th  mirror, will be maximized. Low mean incidence angles also help to ensure that multilayer amplitude and phase effects as measured in the exit pupil of the projection system have little or no impact on imaging performance. These amplitude and phase effects can substantially alter the partially coherent imaging characteristics of the system, thus limiting the ability to control the CD across the field format. 
     Table 4 shows the mean incidence angles of each mirror surface for a preferred embodiment of the present invention. Multilayer coatings that have either a uniform or graded thickness can be designed and applied to each of the mirror surfaces to maximize the EUV transmission of the inventive five bounce system. The maximum EUV transmission of the inventive optical system may be greater than 17% if the reflectance of the mirrors is greater than 70%, which is close to the maximum theoretical reflectance of a Mo/Si multilayer mirror. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 4 
               
               
                   
                   
               
               
                   
                 Mirror 
                 Mean Incidence Angle 
               
               
                   
                   
               
             
             
               
                   
                 M1 
                 12.4° 
               
               
                   
                 M2 
                  9.0° 
               
               
                   
                 M3 
                  7.3° 
               
               
                   
                 M4 
                 14.0° 
               
               
                   
                 M5 
                  7.0° 
               
               
                   
                   
               
             
          
         
       
     
     Table 5 shows the maximum aspheric departure from a best-fit spherical surface centered on the off-axis section of each mirror of the preferred embodiment. The table has two entries for mirror M 2 , one corresponding to each reflection surface of M 2 , since there are two instantaneous clear apertures on this surface. The inventive optical system is designed using low aspheric departures across the off-axis section of the parent to facilitate mirror metrology using visible wavelengths. The off-axis sections of the present projection system can be designed so that the aspheric departures are small relative to a visible wavelength. Mirrors having small aspheric departures can be tested at their centers of curvature without the need for null optics that adversely impact the absolute accuracy of metrology testing. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 5 
               
               
                   
                   
               
               
                   
                 Mirror 
                 Maximum aspheric departure 
               
               
                   
                   
               
             
             
               
                   
                 M1 
                 &lt;6.5 μm 
               
               
                   
                 M2 (first bounce) 
                 &lt;12.6 μm  
               
               
                   
                 M3 
                 &lt;1.5 μm 
               
               
                   
                 M2 (second bounce) 
                 &lt;0.5 μm 
               
               
                   
                 M5 
                 &lt;7.8 μm 
               
               
                   
                   
               
             
          
         
       
     
     In another embodiment, the inventive optical system has a physically accessible, real aperture stop on mirror M 4 . The physical aperture stop ensures that imaging bundles from each field point within the ring field are not clipped or vignetted and are formed in the small manner. The physical aperture stop also makes the projected imagery, setting aside the effects of the field dependent aberrations and variations in illumination from the condenser across the ring field, independent of position within the ring field. The aerial images from different field points in the ring field will look the same and variations in projected feature size will be minimized. This type of projected imagery is known as “stationary imagery”. 
     Tables 7, 8, and 9 contain constructional data and other relevant information for the currently preferred configuration of mirrors M 1 , M 2 , M 3 , and M 4 . The inventive as a 4:1 reduction ratio, a numerical aperture of 0.15, and a 0.5 mm ring is capable of 50 nm resolution and depth of focus of approximately 0.6 μm. 
     Referring to Table 7, parameters describing the mirror surfaces of the preferred embodiment are listed. Note that surface  2  and surface  4  describe the first and second bounces from mirror M 2 , respectively. The radius of curvature refers to the radius of curvature of each optical element, and the thickness refers to the vertex-to-vertex thickness between the optical surfaces. For example, the thickness of the object is 388,8452 mm and represents distance from the mask to the vertex of mirror M 1 . 
     
       
         
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                 TABLE 7 
               
               
                   
                   
               
               
                   
                 Surface 
                 Radius of 
                   
                   
               
               
                   
                 Number 
                 Curvature 
                 Thickness 
                 Element Definition 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 Object 
                 Infinite 
                 388.8452 
                 Mask 
               
               
                   
                 1 
                 A(1) 
                 −329.6116 
                 M1 
               
               
                   
                 2 
                 A(2) 
                 228.2796 
                 M2 (first bounce) 
               
               
                   
                 3 
                 A(3) 
                 −228.2796 
                 M3 
               
               
                   
                 4 
                 A(2) 
                 214.9420 
                 M2 (second bounce) 
               
               
                   
                 5 
                 A(5) 
                 −325.3325 
                 M4 
               
               
                   
                 Image 
                 Infinite 
                   
                 Wafer 
               
               
                   
                   
               
             
          
         
       
     
     Referring to Table 8, the aspheric parameters A( 1 )-A( 4 ) for the optical elements M 1 , M 2 , M 3 , and M 4  are set forth for a preferred embodiment. The aspheric profile of each mirror is uniquely determined by its K, A, B, C, and D values. 
     
       
         
               
               
               
               
               
               
               
             
           
               
                 TABLE 8 
               
               
                   
               
               
                 Asphere 
                 CURV 
                 K 
                 A 
                 B 
                 C 
                 D 
               
               
                   
               
             
             
               
                 A(1) 
                 −0.00050972 
                 8.124574 
                 0.0 
                 −3.7218E−15 
                 7.1103E−20 
                 −5.6845E−25 
               
               
                 A(2) 
                 −0.00243176 
                 1.036632 
                 0.0 
                  4.0876E−15 
                 2.1809E−19 
                  0.0000E+00 
               
               
                 A(3) 
                 −0.00206582 
                 0.051920 
                 0.0 
                  3.0920E−16 
                 1.4981E−20 
                 −1.4479E−25 
               
               
                 A(4) 
                 −0.00230546 
                 0.191661 
                 0.0 
                 −4.3963E−16 
                 1.1452E−20 
                 −4.3459E−25 
               
               
                   
               
             
          
         
       
     
     The sag of the aspheric surface (through 10th order) parallel to the z-axis (z) is a function of radial coordinate (h) given by Equation (1) wherein h is the radial coordinate, is the curvature of the surface (1/R), and A, B, C, and D are the 4th, 6th, 8th, and 10th order deformation coefficients, respectively. Mirrors M 1 , M 3 , and M 4  are all oblate spheroids with 6 th , 8 th , and 10 th  order polynomial deformations. The reflective surfaces of M 2  are oblate spheroids with 6 th  and 8 th  horder polynomial deformations.        z   =         ch   2       1   +       1   -       (     1   +   k     )          c   2          h   2               +     Ah   4     +     Bh   6     +     Ch   8     +     Dh   10                              
     Table 9 gives first order data for the preferred embodiment of the inventive optical system. 
     
       
         
               
               
               
             
           
               
                   
                 TABLE 9 
               
               
                   
                   
               
             
             
               
                   
                 Center of ring field (mask, mm) 
                 −211.0  
               
               
                   
                 Effective focal length (mm) 
                 380.10 
               
               
                   
                 Paraxial reduction ratio 
                  0.25 
               
               
                   
                 Finite F/N o   
                 ƒ/3.34 
               
               
                   
                 Total track (mm) 
                 −51.16 
               
               
                   
                   
               
             
          
         
       
     
     Another advantage of the present invention is that the centroid distortion is balanced across the ring field width. As shown in FIG. 5, “balanced” means that the variation in static distortion across the width of the ring field is quadratic. In scanning lithography, the entire wafer field is covered by synchronously scanning both the mask and wafer across the projected ring field. Excessive or unbalanced static distortion can cause the time-averaged printed image to be blurred or smeared along a field-dependent trajectory. This leads to image properties that are field invariant in the scan direction, but which vary in the perpendicular or cross-scan dimension. By creating a static distortion field that varies quadratically across the ring field (i.e., “balancing” the static distortion), both the blurring (smearing) and placement (dynamic distortion) are minimized. 
     Table 10 shows the performance of the system as described by the root mean square (RMS) wavefront error and corresponding Strehl ratio. 
     
       
         
               
               
               
             
           
               
                 TABLE 10 
               
               
                   
               
               
                 Ring field Radius 
                 rms wavefront error 
                   
               
               
                 (mm) 
                 (λ = 13.1 nm) 
                 Strehl Ratio 
               
               
                   
               
             
             
               
                 52.500 
                 0.022 λ 
                 0.981 
               
               
                 52.625 
                 0.017 λ 
                 0.988 
               
               
                 52.750 
                 0.014 λ 
                 0.993 
               
               
                 52.875 
                 0.012 λ 
                 0.994 
               
               
                 53.000 
                 0.012 λ 
                 0.994 
               
               
                   
               
             
          
         
       
     
     Table 11 shows the deviation (distortion) of the image centroid at the wafer from its ideal location. 
     
       
         
               
               
               
             
               
               
               
             
           
               
                 TABLE 11 
               
               
                   
               
               
                 Ideal image point 
                 Chief ray 
                 Centroid 
               
               
                 (mm) 
                 distortion (nm) 
                 distortion (nm) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 52.500 
                 9.95 
                 11.90 
               
               
                 52.550 
                 6.50 
                 7.80 
               
               
                 52.600 
                 3.78 
                 4.46 
               
               
                 52.650 
                 1.78 
                 1.87 
               
               
                 52.700 
                 0.53 
                 0.06 
               
               
                 52.750 
                 0.01 
                 −0.98 
               
               
                 52.800 
                 0.24 
                 −1.24 
               
               
                 52.850 
                 1.22 
                 −0.72 
               
               
                 52.900 
                 2.96 
                 0.60 
               
               
                 52.950 
                 5.46 
                 2.71 
               
               
                 53.000 
                 8.73 
                 5.62 
               
               
                   
               
             
          
         
       
     
     Since the inventive optical projection system has an odd number of reflections, the mask and wafer are located of the same side of the imaging system. This introduces a limitation on the wafer travel. In the preferred configuration, the separation of the mask and wafer in the scan plane is 263.75 mm. The skilled artisan will readily appreciate that the entire optical system can be scaled by a constant greater than 1.0 to increase the separation between the mask and wafer. For example, if the inventive optical system were scaled by a factor of 1.5×, the mask to wafer separation would be almost 400 mm. When the optical system is scaled, the incidence angles remain the same and the compatibility of the design with multilayer coatings is unaffected. However, the distortion, wavefront error measured in waves, and the mirror asphericity increases proportionally to the scale factor. The limits imposed by mirror fabrication technology and the associated mirror metrology may limit the scale factor that can be used to increase the mask to wafer separation. 
     While the present invention has been described in terms of a preferred embodiment, those skilled in the art will readily appreciate that numerous modifications, substitutions and additions may be made to the disclosed embodiment without departing from the spirit and scope of the present invention. For example, although an optical system has been described above for use with a semiconductor photolithography system, those skilled in the art will readily appreciate that the inventive optical system may be utilized in any similar lithography device and that the present invention is in no way limited to the mechanisms described above. 
     Similarly, the skilled artisan will readily appreciate that the optical system shown in FIG. 4 is in no way limited to use with a particular type of lithography system or a particular lithography machine. Those skilled in the art will also readily appreciate that the optical system may be used with any similar lithography mechanism. It is intended that all such modifications, substitutions and additions fall within the scope of the present invention, which is best defined by the claims below.