Patent Publication Number: US-2006018045-A1

Title: Mirror arrangement and method of manufacturing thereof, optical system and lithographic method of manufacturing a miniaturized device

Description:
BACKGROUND OF THE INVENTION  
      1. Field of the Invention  
      The present disclosure relates to a mirror arrangement for reflecting electromagnetic radiation, and to a method for manufacturing such a mirror arrangement. The present disclosure further relates to an optical system having a mirror arrangement and to a lithographic method of manufacturing a miniaturized device using a projection exposure system.  
      2. Brief Description of Related Art  
      A mirror arrangement has a mirror surface the geometry of which determines the optical properties of the mirror. The mirror arrangement can be integrated within an optical system and determine a path of rays therein. In particular, the optical system may comprise a projection optical system as it is used in lithographical methods for imaging a reticle onto a photosensitive layer for manufacturing of miniaturized components.  
      A success of such optical systems depends among other things on the precision in which the shape of the mirror surface of the mirror arrangement matches a predefined shape of the mirror surface.  
      From U.S. Pat. No. 5,986,795 a mirror arrangement is known the mirror surface of which is deformable to form the optical properties of the mirror variably and to particularly be able to adapt these to desired optical properties. According to this the mirror arrangement of the art comprises a substrate having a mirror side facing towards the radiation to be reflected, where a mirror surface is provided and a back side facing away from the mirror side. Further, a reaction plate is arranged in a distance apart from the back side and between the substrate and the reaction plate a plurality of actuators arranged with a distance from each other is provided, which actuators are hold with one end to the substrate and with the other end to the reaction plate. By operation of the actuators it is possible to deform the substrate and by this the mirror surface in a predefined manner. Concerning the arrangement of the art it is further provided to keep the layer thickness of the substrate and the thickness of the reaction plate over the cross section of the mirror surface not constant but to design the thicknesses variably in order to manipulate the bending characteristics of the substrate.  
      The arrangement of the related art is complicated with respect to its assembly having a plurality of actuators and with respect to the control of the actuators during operation.  
      It is further known to provide deformable mirror arrangements by applying a piezoelectric layer onto a back side of a substrate providing a mirror surface. By triggering of a piezoeffect in such a layer consequently the mirror surface is deformable. Nevertheless a bending characteristics of the mirror surface cannot be adapted to a desired characteristic.  
     SUMMARY OF THE INVENTION  
      The present invention has been accomplished taking the above problems into consideration.  
      It is an object of the present invention to provide a mirror arrangement having a deformable mirror surface and which is adaptable to a desired characteristic with respect to a bending characteristic of the mirror surface on operation of an actuator.  
      Further it is an object of the present invention to provide an optical system having the aforementioned mirror arrangement.  
      Still further it is an object of the present invention to provide a lithographic method of manufacturing a miniaturized device using a projection exposure system.  
      In order to achieve such object, the present invention provides a mirror arrangement for reflecting electromagnetic radiation, the mirror arrangement comprising a substrate having a mirror side facing towards the radiation to be reflected and a back side opposite to the mirror side, wherein a mirror surface is provided on the mirror side and wherein an actuator arrangement for generating a deformation of the substrate is mounted on the back side of the substrate, wherein the actuator arrangement comprises at least one active layer having an areal adhering contact with a portion of the back side of the substrate.  
      The at least one active layer has a first layer thickness at a first location within the portion and a second layer thickness at a second location disposed at a distance from the first location within the portion, wherein the first layer thickness differs from the second layer thickness by more than 1%. Because of the locally different layer thicknesses of the active layer the actuator provides locally different operational forces for deformation of the substrate. By an appropriate selection of the layer thickness distribution of the active layer on the substrate it is thereby possible to set a distribution of deformation force of the actuator on the substrate.  
      Between the two locations being disposed within a distance from each other the layer thickness changes preferably continuously and continually. In particular the active layer can be made from a material which comprises a ferroelectric material, a piezoelectric material, a magnetostrictive material, an electrostrictive material and a memory metal alloy.  
      According to one embodiment of the invention the layer thicknesses at the both locations differ by more than 1%. Further the layer thicknesses can have bigger differences at the both locations. As for example 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9% ore more.  
      According to a further embodiment of the invention the at least one active layer has a rotational symmetric distribution of layer thickness with respect to an axis of symmetry. According to an alternative embodiment the distribution of layer thickness of the active layer is rotationally unsymmetric; which is, at all locations within the portion, rotationally non-symmetric with respect to all lines extending through each respective location.  
      According to a further embodiment of the invention the distribution of the layer thickness is substantially representable by one single Zernike polynomial. With such a distribution of layer thickness it is possible to set wavefront variations using the mirror surface which also correspond to the corresponding Zernike polynomial, when the mirror stands in the pupil, respectively, correspond to polynomials, which are determined by the position of the mirror and by the transfer behaviour of the optical system. Such wavefront variations are desired in optical systems for further compensation of aberrations. In alternative for the description of the distribution of the layer thickness based on Zernike polynomials also other appropriate functional systems are possible as for example splines, Tschebyscheff polynomials, modular descriptions, free surface forms.  
      According to a further embodiment of the invention the substrate has a first substrate thickness at the first location within the portion and a second substrate thickness at the second location within the portion, and wherein the first substrate thickness differs from the second substrate thickness by more than 1%. Also bigger differences as for example 2%, 3%, 4%, 5%, 6%, 7%, 8%, 9%, 10%, 11%, 12%, 13%, 14% or more are provided.  
      According to an embodiment the actuator arrangement comprises one single active layer, wherein the areal adhering contact of the active layer with the portion of the back side of the substrate is mediated by an intermediate adhesion layer firmly joining the active layer to the back side of the substrate. The intermediate adhesion layer can comprise an adhesive, a solder, an eutecticum, a paste and other layers. According to an embodiment the adhesion mediation layer also provides an electrode layer for exciting the active layer. According to an alternative embodiment an electrode layer is a supplement to the adhesion mediation layer as a further layer arranged between the active layer and the substrate. According to an embodiment of the invention the electrode layer continuously extends over the portion of the back side of the substrate.  
      According to an embodiment of the invention the actuator arrangement comprises a plurality of active layers which are stacked one above the other, wherein each pair of active layers are joined to each other by an areal adhering contact.  
      According to an embodiment of the invention the mirror arrangement comprises a bottom layer of the plurality of active layers and arranged closest to the substrate, wherein the areal adhering contact of the bottom active layer with the portion of the back side of the substrate is mediated by an intermediate adhesion layer firmly joining the active layer to the back side of the substrate. According to an embodiment of the invention an electrode layer for exciting the active layer is disposed between the bottom active layer and the substrate. According to an embodiment of the invention the electrode layer comprises the adhesion mediating layer.  
      According to an embodiment of the invention at least one electrode layer for exciting at least one active layer of a pair of adjacent layers is disposed between said pair of adjacent active layers. According to an embodiment of the invention the electrode layer continuously extends over the portion of the back side of the substrate.  
      According to an alternative embodiment of the invention the electrode layer comprises a plurality of non-overlapping partial electrodes, distributed over the portion of the back side of the substrate. According to a further embodiment of the invention first and second partial electrodes of each pair of partial electrodes are electrically insulated from each other. Still further according to an embodiment of the invention an electrical resistance between first and second partial electrodes of each pair of partial electrodes is greater than 1 M Ω. According to an exemplary embodiment the plurality of partial electrodes are arranged in a hexagonal pattern. The plurality of partial electrodes is groupable into electrode groups, wherein the electrode groups are arranged in a hexagonal pattern.  
      The invention further provides a method of manufacturing a mirror arrangement for reflecting electromagnetic radiation, wherein the method comprises: 
          applying a paste of a precursor material to a back side of a substrate and distributing the precursor material on the back side to form a layer such that the layer has a first layer thickness at a first location and a second layer thickness at a second location disposed at a distance from the first location, wherein the first layer thickness differs from the second layer thickness by more than 1%;     sintering the layer of the precursor material to form an active layer; and     providing a mirror surface on a front side opposite to the back side of the substrate.        

      According to an exemplary embodiment the distributing of the precursor material comprises rotating of the substrate about an axis of rotation. The rotating proceeds such that the precursor material distributes according to an equilibrium between the centripetal force and the gravitational force at the different locations of the precursor material. Also a viscosity of the precurser material can provide a force affecting the shape of the surface, the layer thicknesses respectively.  
      According to another embodiment the distributing of the precursor material comprises pressing a shaped stamp into the layer to shape the layer according to a surface shape of the stamp. By this also the desired layer thicknesses distribute according to the shape of the surface shape of the stamp. According to an exemplary embodiment the surface shape of the stamp comprises at least one of a concave portion and a convex portion. According to another exemplary embodiment the surface shape of the stamp comprises at least one of plural concave portions and plural convex portions.  
      The invention further provides an optical system having a plurality of optical elements, wherein at least one of the optical element comprises a mirror arrangement as described above.  
      According to another embodiment of the invention an optical system is provided, the optical system having a plurality of optical elements, wherein at least one of the optical elements comprises a mirror arrangement for reflecting electromagnetic radiation, wherein the mirror arrangement comprises a substrate having a mirror side facing towards the radiation to be reflected and a back side opposite to the mirror side, wherein a mirror surface is provided on the mirror side and wherein an actuator arrangement for generating a deformation of the substrate is mounted on the back side of the substrate, wherein the actuator arrangement comprises at least one active layer having an areal adhering contact with a portion of the back side of the substrate; wherein the at least one active layer has a first layer thickness at a first location within the portion and a second layer thickness at a second location disposed at a distance from the first location within the portion, wherein the first layer thickness differs from the second layer thickness by more than 1%; and wherein the at least one active layer comprises at least one of a ferroelectric material, a piezoelectric material, a magnetostrictive material, an electrostrictive material and a memory metal alloy.  
      According to another embodiment of the invention the optical system can also be a catadioptrical system wherein at least one of the optical elements comprises a refractive lens. In an alternative embodiment the optical system comprises only mirrors as the optical elements.  
      According to another embodiment of the invention the optical system further comprises a mount for mounting a patterning structure to be imaged in a region of an object plane of the optical system, and a mount for mounting a substrate having a radiation sensitive layer in an image plane of the optical system.  
      According to an embodiment the optical system comprises an objective of a lithographic system for imaging a pattern forming structure (reticle) onto a photosensitive layer (resist), which is provided on a substrate (wafer).  
      According to another embodiment of the invention lithographic method of manufacturing a miniaturized device using a projection exposure system optical system is provided, wherein the method comprises: disposing a patterning structure to be imaged in a region of an object plane of an imaging optics of the projection exposure system; disposing a substrate carrying a resist in a region of an image plane of the imaging optics and exposing portions of the substrate with images of the patterning structure using the projection exposure system; wherein the projection exposure system comprises a plurality of optical elements, and wherein at least one of the optical elements comprises a mirror arrangement as described above. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
      The forgoing as well as other advantageous features of the invention will be more apparent from the following detailed description of exemplary embodiments of the invention with reference to the accompanying drawings, wherein  
       FIG. 1 ,  
       FIG. 2 ,  
       FIG. 3 ,  
       FIG. 4 , and  
       FIG. 5  respectively show an embodiment of a mirror arrangement according to the invention;  
       FIGS. 6   a - 6   d,    
       FIG. 7 , and  
       FIG. 8  show steps of manufacturing of mirror arrangements;  
       FIG. 9   a  and  
       FIG. 9   b  show lines of height of a thickness distribution of an active layer according to further embodiments of mirror arrangements according to the present invention;  
       FIG. 10  shows a further embodiment of a mirror arrangement according to the present invention with a plurality of active layers;  
       FIG. 11  shows an example for a pattern of partial electrodes for the exciting the active layer according to a mirror arrangement according to the present invention;  
       FIG. 12  shows an optical system according to an embodiment of the present invention; and  
       FIG. 13  shows a further projection exposure system optical system for manufacturing a miniaturized device according to an embodiment of the present invention. 
    
    
      It is noted that not all possible embodiments of the present invention necessarily exhibit each and every, or any, of the advantages described herein.  
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS  
      In the exemplary embodiments described below, components that are alike in function and structure are designated as far as possible by alike reference numerals. Therefore, to understand the features of the individual components of a specific embodiment, the descriptions of other embodiments and of the summary of the invention should be referred to.  
      In  FIG. 1  an embodiment of a mirror arrangement  1  is illustrated schematically in a section. The mirror arrangement  1  comprises a substrate  3  made of a glass material, as for example Zerodur, which has a small coefficient of thermal expansion. Also any other appropriate substrate can be used as for example a substrate made of silicon. The glass substrate  3  has a front side  5  and a back side  7 . The front side  5  and the back side  7  are in their form rotational symmetric with respect to an axis  9 . The front side  5  bears a mirror surface  11 , i.e. the surface which determines the optical properties of the mirror arrangement  1 . For this the front side  5  of the substrate  3  can be metallized in order to provide a metallically reflecting mirror surface  11 . It is also possible to provide the front side  5  with several layers of a dielectric medium, in order to provide the mirror surface  11  by a layered structure.  
      The back side  7  of the substrate  3  is firmly joint to the active layer  13  made of a piezomaterial as for example lead-circonate-titanate (PZT). Also the layer  13  made of piezomaterial is rotationally symmetric with respect to axis  9 , wherein the back side  0 . 15  facing away from the substrate is a flat surface.  
      The front side  5  of the substrate  3 , respectively, the mirror surface  11  has a concave parabolic shape. The back side  7  of the substrate  3  exhibits a similar form so that the substrate exhibits a same thickness (a 1 , a 2 ) at each location on the substrate.  
      Nevertheless a layer thickness of layer  13  made of piezomaterial is dependent on location. It thus exhibits at a location I, a thickness b 1  which is greater than a thickness b 2  at a location II.  
      For the operation of the layer  13  as actuator an electrical potential generated by a controlled voltage supply  16  is applied to an electrode  12  provided between the substrate  3  and the layer  13  and to a further electrode  14  provided at a back side  15  of the layer  13 , so that based on the piezoelectrical effect in layer  13  this layer generates a mechanical force which leads to deformation of the substrate as well as the mirror surface  11 . In the illustrated exemplary embodiment the electrodes  12  and  14  are area electrodes extending continuously over the whole surface of the active layer  13 . The electrode  12  by this forms also a intermediate adhesion layer between the substrate  3  and the active layer  13 . For this the electrode  12 , the intermediate adhesion layer, respectively, can be formed by a gold paste.  
      This deformation is determined by the thickness and rigidity of the substrate  3 , the thickness and rigidity of the layer  13  made of piezomaterial and the location dependency of the layer thickness of the layer  13 . Depending on the location dependent layer thickness of layer  13  the location dependency of the piezo force is determined.  
      In the following further variants of the embodiment illustrated in  FIG. 1  will be described. Concerning this, components which correspond with respect to their function or their structure with components of  FIG. 1  are provided with the same reference numerals as in  FIG. 1 , but are supplemented for the reason of differentiation with a letter.  
      The mirror arrangement  1   a  shown in  FIG. 2  differs from the mirror arrangement in  FIG. 1  in that the substrate  3   a  also exhibits a location dependent layer thickness. So, thicknesses of the substrate a 1 , a 2 , respectively at two locations I and II are different.  
      The geometrical relations of the mirror arrangement in  FIG. 2  and also in the other figures are shown schematically only and do not provide conclusions on real existing geometries. Particularly curvatures of the individual surfaces of the mirror arrangement, as for example  11   a ,  7   a  and  15   a  are illustrated exaggerated. Realistic values for dimensions of the mirror arrangement are given exemplarily for the mirror arrangement  1   a , shown in  FIG. 2 : 50 mm&lt;r&lt;500 mm; a 1 &gt;a 2 /2, a 2 &gt;r/10, in particular a 2 &gt;r/5 and further preferred a 2 &gt;r/2.5; b 1 &lt;0.5 mm; b 1 &gt;b 2 &gt;0.05 mm, wherein the location I has a distance 0.75 r from the axis  9   a  and the location II has a distance r/4 from the axis  9   a , wherein r is a radius with respect to the axis  9   a.    
      The mirror arrangement  1   b  shown in  FIG. 3  differs from the mirror arrangement  1   a  shown in  FIG. 2  substantially in that the back side  15   b  of the layer  13   b  made of piezomaterial is not a planar surface but a concave surface. By this the location dependency of the layer thickness of layer  13   b  is further enhanced. At location I the thickness b 1  of the layer  13   b  is considerably larger than at location II.  
      Concerning the mirror arrangement  1   c  shown in  FIG. 4  the layer thickness of the substrate  3   c  is location dependent and at a location I lying with respect to the axis  9   c  radially outside bigger than at a radially inner lying location II. The layer thickness of layer  13   c  made of piezomaterial however is substantially constant.  
      The mirror arrangement id shown in  FIG. 5  differs from the mirror arrangement  1   a  shown in  FIG. 2  substantially in that the back side  7   d  of the layer  3   d  is a planar surface and the back side  15   d  of the layer  13   d  made of piezomaterial is not a planar surface.  
       FIG. 6  explains a process for the manufacturing of a mirror arrangement wherein for example the mirror arrangements shown in  FIG. 1  to  5  are manufacturable by the process explained according to  FIG. 6 .  
      The process uses a mould  21  into which at the beginning of the process ( FIG. 6   a ) the substrate  3  will be inserted. The mould is rotatable round an axis  9  and has an annular wall  23 .  
      Onto the back side  7  of the substrate  3  a piece  25  of PZT-paste, the precursor material of the piezoelectric layer  13  to be produced, will be applied. Then the form  21  will be put into rotation around the axis  9 , so that the piece  25  of PZT-paste spreads on the back side  7  of the substrate  3  ( FIG. 6   b ). Then the PZT-paste  25  covers the whole back side  7  of the substrate  3  and impinges to the inner side of the wall  23  of the form  21  ( FIG. 6   c ). After some time the surface  15  of the PZT-paste  25  will acquire a stable concave surface, the geometry of which is determined by an equilibrium between the centripetal force caused by the rotation acting on the PZT-paste  25  which centripetal force tries to drive the PZT-paste radially to an outer side thus enlarging the layer thickness of the paste on the substrate  3  radially outside, and the gravitational force which acts opposite to the enlargement of the layer thickness of the PZT-paste  25  radially outside. The form of the surface  15  will after some time acquire a parabolic form.  
      Then the PZT-paste  25  is heated (arrows ˜ 27  in  FIG. 6   d  represent heat radiation) so that the PZT-paste  25  solidifies within the following sintering process and finally forms the layer  13  made of piezomaterial of the mirror arrangement to be manufactured. The piezoelectric layer  13  by this has a location dependent distribution of layer thickness which in the present example is determined by the planar form of the back side  7  of the substrate  3  and by the co-working of centripetal force and gravitational force at rotation. The form of the back side  7  however can also be concave or convex.  
       FIG. 7  shows a further embodiment of the method of manufacturing a piezoelectric layer with location dependent layer thickness. For this the substrate  3  again is arranged in a form  21  with an annular wall  23 . On the back side  7  of the substrate  3  the pasty precursor material is distributed for forming the piezoelectric layer. A stamp  30  having a predetermined geometrically shaped surface  33  fits into the form and is pressed into it in order to form the shape of the PZT-paste. This will be sintered afterwards.  
      According to a further embodiment of the method of manufacturing a piezoelectric layer a so-called Mandrel technique is employed. A polished and with gold (Au) vapor-deposited stamp  30  having a predetermined geometric shape of a stamp surface  33  fits into the form and is pressed into the latter such forming the shape of the PZT-paste  25 . Thereafter the PZT-paste  25  is sintered at temperatures in a range of 400° C. to 900° C. In the subsequent process of cooling the vapor-deposited gold peels from stamp  30  and remains at the PZT-layer  25  because a coefficient of thermal expansion of the stamp  30  is considerably larger than a coefficient of thermal expansion of the PZT-layer  25 . A temperature at which such peeling takes place can be determined empirically. In the vicinity of the peeling temperature a temperature cooling speed, with which the stamp and the sintered layer are being cooled during a process of cooling, is reduced essentially so that internal tensions in the arrangement distribute as even as possible.  
       FIG. 8  shows a further variation for the manufacturing of a mirror arrangement which works in a similar way as the variation explained using  FIG. 5 . Here, the back side  7  of the substrate  3 , is not formed as a planar surface but as a concave annular surface, so that the substrate  3  exhibits a location dependent thickness. By rotation around an axis of symmetry  9  of the substrate  3  again a pasty precursor material for the piezoelectric layer is distributed on the back side of the substrate  3 .  
       FIG. 9   a  shows a top view onto an active layer  15   e  of a mirror arrangement  1   e . Here, the lines  31  and  32  represent lines of height of a distribution of layer thickness of the active layer. Differently from the embodiments explained above the distribution of layer thickness of the active layer  13   e  of the mirror arrangement  1   e  is not rotational symmetric to an axis. Rather the lines of height  31  represent a reduced layer thickness of the active layer and the lines of height  32  represent a enlarged layer thickness of the active layer. By this a symmetry of the distribution of thickness is a two-fold symmetry around an axis  9   e , wherein main axis of this symmetry in  FIG. 9   a  are provided with the reference numerals  35  and  34 . The distribution in thickness represented by the lines of height  31 ,  32  correspond to a Zernike-polynomial U nm  with n=4 and m=1. Another distribution of layer thickness of an active layer  15   g  is shown in  FIG. 9   b . Here, similar as described above, the lines  31   b  and  32   b  represent lines of height of a distribution of layer thickness of the active layer  13   g . The lines of height  31   b  represent a reduced layer thickness of the active layer and the lines of height  32   b  represent an enlarged layer thickness of the active layer. By this a symmetry of the distribution of thickness is a two-fold symmetry around an axis  9   g , wherein main axes of this symmetry are provided with the reference numerals  35   b  and  34   b  in  FIG. 9   b . The distribution in thickness represented by the lines of height  31   b ,  32   b  corresponds to a Zernike polynomial U nm  with n=2 and m=0. Background information concerning Zernike polynomials can be taken, e.g., from the book “Optical Shop Testing” from Daniel Malacara, 2 nd  Edition, John Wiley &amp; Sons, Inc. 1992. The above selected notation U nm  corresponds to the notation of the book of Malacara.  
      Such a distribution of layer thickness generates, with a corresponding excitation of the active layer, a deformation of the mirror surface which again is representable by a Zernike polynomial, so that also wavefronts of the light being reflected from the mirror surface suffer an according deformation in the wavefront. The deformation generated by the mirror surface of the mirror arrangement  1   e  can thus serve for the specific generation or compensation of an astigmatism in an optical system.  
      The distribution in layer thickness of the active layer as explained according to  FIG. 9   a  can for example be generated using the process explained according to  FIG. 7 , if the stamp surface  33  is manufactured in advance having a surface shape which corresponds to the desired distribution in layer thickness of the active layer.  
      The distribution in layer thickness as explained according to  FIG. 9  is only exemplary. Also other distributions in thickness can be chosen, which correspond to other Zernike polynomials. Further, also distributions in layer thickness of complete other form and nature can be used.  
       FIG. 10  shows a section corresponding to  FIG. 1  to  5  through a mirror arrangement  1   f  having two active layers  13   f   1  and  13   f   2  which are applied one above the other on a substrate  3   f  which provides a mirror surface  11   f . Between the substrate  3   f  and the active layer  13   f  a passing through electrode  12   f  is provided, between the active layers  13   f   1  and  13   f   2  a structured electrode  14   f   1  is provided in order to excite the active layer  13   f   1  by potential differences between the electrode  12   f  and the partial electrodes of the electrode layer  14   f   1 . On the active layer  13   f   2  an electrode layer  14   f   2  structured into partial electrodes is applied in order to excite the active layer  13   f   2  by potential differences between the partial electrodes of the electrode layer  14   f   2  and the partial electrodes of the electrode layer  14   f   1 .  
      A structure of the electrode layer  14   f   1  is schematically illustrated in  FIG. 11 . The electrode layer  14   f   1  comprises a plurality of partial electrodes  41  which are electrically isolated from each other and which can, independently from each other, be provided with an electrical potential by a control not shown in  FIGS. 10 and 11 . The pattern the partial electrodes  41  are arranged in is structured as follows: eighteen partial electrodes can be grouped to one hexagon  43 . The hexagons  43  are arranged as a regular hexagonal pattern in the area. Each hexagon  43  is separable into six uniform triangles  44 , wherein each of the triangles contains three partial electrodes  41  which exhibit the form of a kite quadrangle. It has been found that the design of the electrode layer forming the described pattern of partial electrodes is particularly advantageous for the control of the deformation of the mirror surface. By the possibility to control the partial electrodes independent from each other an additional agree of freedom is given for adjusting desired deformations of the mirror surface.  
       FIG. 12  shows an optical system  100  which images a reticle being arranged within an object plane  101  onto one wafer being arranged within an image plane  103  of the optical system  100 . The optical system is a pure reflective optical system with plural mirrors M 1 , M 2 , M 3 , M 4 , M 5 , and M 6 , thus providing a path of rays of the system. Here, the mirror M 6  is a mirror with a deformable surface, wherein an actuator of the mirror M 6  comprises an active layer made of piezomaterial which exhibits a non-constant distribution of layer thickness.  
      Background information for the optical system shown in  FIG. 12  can be obtained by the EP 0 779 528 A2.  
      Besides the employment of the deformable mirror in a pure reflective optical system also an employment of the deformable mirror is provided in a katadioptrical system. Background information concerning katadioptrical imaging systems can for example be obtained from U.S. Pat. No. 6,229,647 B1 and EP 1069448 B1. By this it is possible to provide the deformation of the mirror surface such that the wavefront deviations are generated by the deformation are representable by Zernike polynomials. In this case the deformable mirror is particularly well suited for the compensation of aberrations of the optical system. But it is also possible to provide deformations of the mirror surface deviating from the latter. Examples for this are compensations of non-homogeneous heat transfers into the mirror caused by radiation. Then the distribution of layer thickness of the active layer is preferably adjusted such that it is adjusted to the location dependent heat transfer caused by radiation that provided an according control of the actuators a deformation caused by the heat absorption is compensable. Also other effects induced by radiation as for example Compaction, Lens Heating or similar is thus compensable.  
      An example for an exemplary embodiment of the mirror arrangement of the present invention is explained in  FIG. 13 , illustrating a projection exposure system as being used for manufacturing a miniaturized device in lithographic processes. A projection exposure system  200  comprises an illumination means  201 , a projection optic  209 , a control means  16   g , a sensor  217 , and an image forming reticle  203  a substrate with a photosensitive layer or wafer  221 . The illumination means  201  illuminates the reticle  203  so that a beam  205  passing through the reticle according to the pattern of the reticle is formed in the projection optic  209  by at least one lens  207  such that it impinges onto a mirror  211  will be reflected from this mirror into a ray  205 ′ and eventually impinges onto the mirror arrangement  1   g  according to the present invention. The mirror arrangement according to the present invention forms the beam  205 ′ at an adjusted deformation of the mirror surface as described above and reflects it such that it impinges as beam  219  onto the mirror  211 . This will be reflected from the mirror  211  onto at least one lens  215  which forms the beam  219 ′ and lets it leave the projection optic  209  in order to image the reticle  203  onto the surface of the wafer  221 . For the control of the mirror arrangement according to the present invention a schematically sketched sensor  217  is provided which senses deviations of wavefronts of a beam emerging from the projection optic with respect to a set-shape of these wave fronts. According to the sensed wavefront deviations a control  16   g  controls the mirror arrangement  1   g  having the active layer by setting appropriate voltages in order to reduce the wavefront deviations.  
      In order to adjust the form of the piezoelectric layer of the above explained embodiment according to  FIG. 6  or  8  as precise as possible an angular speed minor ω should be maintained as exactly as possible when rotating the form so that deviations Δω of the rotational velocity are small, for example Δω/ω≦10 −8 . For this a varnish centrifuge can be used as is employed for the coating of semiconductor wafers with photoresists.  
      Besides the application of the piezomaterial as precursor material onto the substrate it is also possible to apply piezoceramics directly onto the substrate (direct application). It is also possible to provide adhesion mediation between the substrate and the piezolayer as for example pastes particularly a gold paste, and adhesive or a solder. The piezolayer can also be formed by grinding. The grinding can be conducted on the accomplished ceramics or a green mood of the same. The piezoceramics can be formed by any production process for ceramics as for example a sol-gel-process.  
      In the above described embodiments the active layer consist of a piezoelectric material. Nevertheless it is also possible to use other active materials for the manufacturing of the active layer as for example a ferroelectric material, a piezoelectric material, a magnetostrictive material, an electrostrictive material or a memory metal alloy. Magnetostrictive materials for example can be formed on the basis of Lanthanit-ferrum-alloys as for example Terfenol or Terfenol-D, and electrostrictive materials can for example be formed on the basis of Lead-magnesium-niobate as for example PMN or Lanthanum-circonate-titanate as for example PLZT. These materials can be employed in the same manner as in the above described embodiments thus forming the active layer formed according to the present invention. Further information concerning appropriate active materials can be obtained from the PhD-thesis “Ein Beitrag zur Untersuchung von Bimorphspiegeln für die Präzisionsoptik”, by Timo Richard Möller, published in Shaker Verlag 2002, ISBN 3-8322-0555-1.  
      While the invention has been described also with respect to certain specific embodiments thereof, it is evident that many alternatives, modifications and variations will be apparent to those skilled in the art. Accordingly, the exemplary embodiments of the invention set forth herein are intended to be illustrative and not limiting in any way. Various changes may be made without departing from the spirit and scope of the present invention as defined in the following claims.  
      Summarized, described herein is a mirror arrangement for reflecting electromagnetic radiation, the mirror arrangement comprising: a substrate having a mirror side facing towards the radiation to be reflected and a back side opposite to the mirror side, wherein a mirror surface is provided on the mirror side and wherein an actuator arrangement for generating a deformation of the substrate is mounted on the back side of the substrate, wherein the actuator arrangement comprises at least one active layer having an areal adhering contact with a portion of the back side of the substrate; wherein the at least one active layer has a first layer thickness at a first location within the portion and a second layer thickness at a second location disposed at a distance from the first location within the portion, wherein the first layer thickness differs from the second layer thickness by more than 1%; and wherein the at least one active layer comprises at least one of a ferroelectric material, a piezoelectric material, a magnetostrictive material, an electrostrictive material and a memory metal alloy.