METHOD OF PRODUCING AN OPTICAL ELEMENT FOR A LITHOGRAPHY APPARATUS

Abstract

A method of producing an optical element for a lithography apparatus, comprising the steps of: a) detecting a height profile of a surface of a crystal substrate of the optical element, and b) ascertaining, using the height profile detected, an installed orientation (2, 4, 6) of the optical element in an optical system of the lithography apparatus in relation to a stress-induced birefringence on incidence of polarized radiation, where the installed orientation (2, 4, 6) is an orientation in relation to a rotation of the optical element about a center axis of the optical element that runs through the surface.

Claims

1. A method of producing an optical element for a lithography apparatus, comprising the steps of: a) detecting a height profile of a surface of a crystal substrate of the optical element, and b) ascertaining, using the height profile detected, an installed orientation of the optical element in an optical system of the lithography apparatus in relation to a stress-induced birefringence on incidence of polarized radiation, where the installed orientation has an orientation in relation to a rotation of the optical element about a center axis of the optical element that runs through the surface.

2. The method of claim 1, comprising the following step that precedes step a): polishing the surface of the crystal substrate so as to create the height profile of the surface.

3. The method of claim 2, wherein the polishing comprises magneto-rheological polishing of the surface.

4. The method of claim 2, wherein the polishing of the surface is conducted by sweeping across the surface in a spiral, and the spiral sweeping proceeds from an outer region of the surface in a spiral about a center of the surface defined by the center axis toward the center.

5. The method of claim 2, wherein the surface is polished by rotating the optical element about the center axis and simultaneously moving a polishing tool radially toward a center of the surface defined by the center axis.

6. The method of claim 1, comprising the following step after step b): marking the installed orientation ascertained on the optical element.

7. The method of claim 6, wherein the method, after the marking of the installed orientation ascertained on the optical element, comprises a step of polishing the surface to remove the height profile of the surface such that a marking identifying the installed orientation ascertained on the optical element is preserved.

8. The method of claim 1, wherein the crystal substrate includes a crystal having cubic symmetry, a monocrystal, a fluoride crystal, calcium fluoride, magnesium fluoride, barium fluoride and/or lutetium aluminium garnet.

9. The method of claim 1, wherein the surface of the crystal substrate is formed by a crystal plane of the crystal substrate.

10. The method of claim 1, wherein the surface of the crystal substrate is formed by a crystal plane, a crystal plane or a crystal plane of the crystal substrate.

11. The method of claim 1, wherein the optical element comprises a transmitting optical element, a partly transmitting optical element, a beam splitter, a beam splitter of an optical pulse extender, a lens element and/or a chamber window of the lithography apparatus.

12. The method of claim 1, wherein the ascertaining of the installed orientation of the optical element ascertains an angle of rotation (a) of the optical element in relation to the rotation of the optical element about the center axis for which stress-induced birefringence on incidence of the polarized radiation is lower and/or minimal compared to other angles of rotation in relation to the rotation of the optical element about the center axis.

13. The method of claim 1, wherein the ascertaining of the installed orientation of the optical element ascertains an angle of rotation (a) of the optical element relative to a polarization plane of the incident polarized radiation.

14. The method of claim 1, wherein the ascertaining of the installed orientation of the optical element ascertains an angular distribution of height values (H) of the ascertained height profile of the surface, and wherein angles (6) of the angular distribution correspond to a respective angle of rotation (a) of the optical element in relation to the rotation of the optical element about the center axis.

15. The method of claim 2, comprising the following step after step b): marking the installed orientation ascertained on the optical element.

16. The method of claim 2, wherein the crystal substrate comprises at least one of a crystal having cubic symmetry, a monocrystal, a fluoride crystal, calcium fluoride, magnesium fluoride, barium fluoride, or lutetium aluminium garnet.

17. The method of claim 2, wherein the surface of the crystal substrate is formed by a [111] crystal plane of the crystal substrate.

18. The method of claim 2, wherein the surface of the crystal substrate is formed by a [100] crystal plane, a [010] crystal plane, or a [001] crystal plane of the crystal substrate.

19. The method of claim 2, wherein the optical element comprises at least one of a transmitting optical element, a partly transmitting optical element, a beam splitter, a beam splitter of an optical pulse extender, a lens element, or a chamber window of the lithography apparatus.

20. The method of claim 2, wherein the ascertaining of the installed orientation of the optical element ascertains an angle of rotation of the optical element in relation to the rotation of the optical element about the center axis for which stress-induced birefringence on incidence of the polarized radiation is lower and/or minimal compared to other angles of rotation in relation to the rotation of the optical element about the center axis.

Description

BRIEF DESCRIPTION OF DRAWINGS

[0061] FIG. 1 shows a schematic view of one embodiment of a DUV lithography apparatus;

[0062] FIG. 2 shows an optical element of the lithography apparatus from FIG. 1;

[0063] FIG. 3 shows the optical element from FIG. 2 in a top view;

[0064] FIG. 4 shows the optical element from FIG. 2 in a front view;

[0065] FIG. 5 illustrates a plane of a crystal lattice;

[0066] FIG. 6 illustrates a plane of a crystal lattice;

[0067] FIG. 7 illustrates a plane of a crystal lattice;

[0068] FIG. 8 illustrates a plane of a crystal lattice;

[0069] FIG. 9 shows a crystal substrate of the optical element from FIG. 2 during a polishing operation on a surface of the optical element;

[0070] FIG. 10 shows a view similar to FIG. 9, with illustration of a polishing pattern;

[0071] FIG. 11 shows a greyscale image of a height profile of the surface from FIG. 9 after polishing;

[0072] FIG. 12 shows an angular distribution of height values of the image in the height profile from FIG. 11; and

[0073] FIG. 13 shows a flow diagram for illustration of a method of producing an optical element for a lithography apparatus.

DETAILED DESCRIPTION

[0074] Unless indicated to the contrary, elements that are the same or functionally the same have been given the same reference signs in the figures. It should also be noted that the illustrations in the figures are not necessarily true to scale.

[0075] FIG. 1 shows a schematic view of a DUV lithography apparatus 100, which comprises a beam-shaping and illumination system 102 and a projection system 104 (also referred to hereinafter as projection lens). In this case, DUV stands for deep ultraviolet and denotes a wavelength of the working light of between 30 and 250 nm. The beam-shaping and illumination system 102 and the projection system 104 are preferably each arranged in a vacuum housing (not shown). Each vacuum housing is evacuated with the aid of an evacuation device (not illustrated). The vacuum housings are surrounded by a machine room (not illustrated), in which driving apparatuses for mechanically moving or adjusting optical elements can be provided. Furthermore, electrical controllers and the like may also be arranged in the machine room.

[0076] The DUV lithography apparatus 100 has a light source 106. For example, an ArF excimer laser that emits radiation 108 in the DUV range, at for example 193 nm, may be provided as the light source 106. In the beam-shaping and illumination system 102, the radiation 108 is focused and filtered such that only the desired operating wavelength (working light) is passing through. For example, the beam-shaping and illumination system 102 may include a narrow band optical filter that allows light components of the radiation 108 having the desired operating wavelength (working light) within a narrow band of wavelengths to pass through, and filters out or removes other components of the radiation 108 having wavelengths outside of the narrow band of wavelengths. The beam-shaping and illumination system 102 may have optical elements (not illustrated), for example mirrors or lens elements.

[0077] After passing through the beam-shaping and illumination system 102, the radiation 108 is guided onto a photomask (reticle) 110. The photomask 110 takes the form of a transmissive optical element and may be disposed outside the systems 102, 104. The photomask 110 has a structure which is imaged on a wafer 112 in reduced form by use of the projection system 104.

[0078] The projection system 104 has a plurality of lens elements 114, 116, 118 and/or mirrors 120, 122 for projecting an image of the photomask 110 onto the wafer 112. In this case, individual lens elements 114, 116, 118 and/or mirrors 120, 122 of the projection system 104 may be arranged symmetrically relative to an optical axis 124 of the projection system 104. It should be noted that the number of lens elements and mirrors shown here is purely illustrative and is not restricted to the number shown. A greater or lesser number of lens elements 114, 116, 118 and/or mirrors 120, 122 may also be provided.

[0079] An air gap between the last lens element (not shown) and the wafer 112 can be replaced by a liquid medium 126 which has a refractive index greater than 1. The liquid medium 126 can be high-purity water, for example. Such a set-up is also referred to as immersion lithography and has an increased photolithographic resolution. The medium 126 can also be referred to as an immersion liquid.

[0080] The ArF excimer laser used by way of example in a DUV lithography apparatus 100, as light source 106, emits radiation in the form of short light pulses of duration about ns. In the case of typical pulse energies of 10 mJ or more, the high power peaks of the laser constitute a considerable degradation risk for downstream optical elements of the beam-shaping and illumination system 102 and of the projection system 104. In order to avoid degradation of downstream optics, it is possible to use an optical pulse extender (optical pulse stretcher, OPuS) 128. The optical pulse stretcher 128 comprises one or more beam dividers 130 (e.g. 45 beam dividers) that outcouple a portion of the radiation 108. The outcoupled portion of the radiation 108 then experiences, with the aid of multiple reflection at highly reflective mirrors (not shown), a time delay with respect to the portion of the radiation 108 transmitted by the beam splitter 130, before following the latter after being reflected again at the beam splitter 130. The highly reflective mirrors are mounted adjustably, for example, on holders 132.

[0081] The beam dividers 130 used in the optical pulse stretcher 128 are produced here in particular from a crystal material with cubic symmetry, for example calcium fluoride (CaF.sub.2).

[0082] Lens elements for the DUV lithography apparatus 100, for example the lens elements 114, 116, 118, or a chamber window 134 of a gas chamber of the light source 106, may also be produced from a crystal material with cubic symmetry, for example CaF.sub.2.

[0083] It is known that optically isotropic crystals, for example as a result of stresses or mechanical stress, can cause stress-induced birefringence of an incident light beam. Birefringence means that the refractive index depends on the polarization direction. It is also possible for cubic crystals such as CaF.sub.2, which are intrinsically optically isotropic, to become birefringent, for example, under mechanical stress (stress-induced birefringence). The causes of such disorder and stress may originate from the process of crystal growth, from the material processing, from mechanical stress, from mechanical contact with a mount, from temperature gradients resulting from inhomogeneous heating in operation and/or as a result of material degradation (possibly in conjunction with the occurrence of sliding planes).

[0084] Stress-induced birefringence of the beam splitter 130, of one of the lens elements 114, 116, 118, of the chamber window 134 or of other optical elements of the DUV lithography apparatus 100 can disrupt the polarization properties of the transmitted radiation 108. In particular, different refraction of the two polarization components of the radiation 108 can occur at a surface of the optical element 114, 116, 118, 130, 134 in question, so as to result in different deflections and hence splitting of the polarization components. In addition, on passage through the respective optical element 130, 114, 116, 118, 134, a phase difference may occur between the polarization components of the transmitted radiation. The result is a blurred image, which limits the achievable resolution of the DUV lithography apparatus 100.

[0085] FIG. 2 shows, by way of example, an optical element 200 of the DUV lithography apparatus 100. The optical element 200 is, for example, a beam splitter 130 of the optical pulse stretcher 128. In other examples, however, it may be another optical element (e.g. 114, 116, 118, 134) of the DUV lithography apparatus 100. The optical element 200 has a crystal substrate 202. The crystal substrate 202 comprises, for example, a CaF.sub.2 crystal. In the ready-produced state, the optical element 200 also has coatings and the like, which are not shown in the figures and are not described further hereinafter, since this concerns a process for producing the crystal substrate 202, especially for processing the crystal substrate 202.

[0086] The crystal substrate 202 has an end face 206 which has a surface 208 and faces the incident radiation 204. It should be noted that, in the state in which a coating (not shown) has been applied to the end face 206, the surface 208 of the crystal substrate 202contrary to the representation in the figures (e.g. FIG. 2) is not visible.

[0087] The surface 208 of the crystal substrate 202 may be formed, for example, by a [111] crystal plane 302 (FIG. 5) of the crystal lattice 300 of the crystal substrate 202. Alternatively, the surface 208 of the crystal substrate 202 may also be formed, for example, by a [100] crystal plane 304, [010] crystal plane 306 or [001] crystal plane 308 of the crystal lattice 300 of the crystal substrate 202. In other examples, the surface 208 of the crystal substrate 202 may also be formed by any other plane of the crystal lattice 300 of the crystal substrate 202.

[0088] In FIGS. 5 to 8, these crystal planes 302, 304, 306, 308 of a cubic crystal 300, for example a CaF.sub.2 monocrystal, are identified. The nomenclature of the crystal planes 302, 304, 306, 308 corresponds to the nomenclature of crystal planes in the crystal lattice based on Miller indices a, b, c, which is customary in crystallography. In FIGS. 5 to 8, the crystal plane 302 is shown by [abc]=[111], the crystal plane 304 by [abc]=[100], crystal plane 306 by [abc]=[010] and the crystal plane 308 by [abc]=[001].

[0089] The radiation 204 incident on the optical element 200 as shown in FIG. 2 is, for example, linear-polarized DUV radiation (similarly to the radiation 108 in FIG. 1) with a propagation direction 210. A vector of the electrical field of the radiation 204 is labelled by the reference sign E. The radiation 204 shown in FIG. 2 is vertically polarized in particular. A polarization plane 212 of the radiation 204 is formed by the electrical field vector E and the propagation direction 210. In other examples, the radiation 204 may, for example, also be horizontally polarized. For example, as shown in the figure, a Cartesian coordinate system having x, y, and z axis can be used as a reference. The vertical direction can refer to a direction parallel to the y-z plane, and the horizontal direction can refer to a direction parallel to the x-y plane. As described in more detail hereinafter, it is possible by suitable rotation of the optical element 200 about a center axis 214, i.e. by suitable adjustment of an angle of rotation (azimuthal angle ) of the optical element 200, to minimize disruption of the polarization properties of the radiation 204 on passage through the optical element 200.

[0090] FIG. 3 shows the optical element 200 from FIG. 2 in a top view. As can be seen in FIG. 3, the propagation direction 210 of the incident radiation 204 is inclined relative to the surface 208 by an angle . The angle is, for example, 45. The radiation transmitted by the optical element 200 is identified by the reference numeral 204. If the optical element 200 is a beam splitter, there is also a reflected component of the radiation 204, but this is not shown in the figures for reasons of clarity.

[0091] FIG. 4 shows the optical element from FIG. 2 in a front view looking at the surface 208 of the crystal substrate 202 (it is also pointed out here that, in the state in which one or more coatings have been applied to the surface 208 of the crystal substrate 202, the surface 208contrary to the representation in the figuresis no longer visible). FIG. 4 once again illustrates the rotation of the optical element 200 about its center axis 214 for adjustment of the angle . This adjustment of the angle is also referred to as clocking. Additionally shown in FIG. 4 are values of the angle of 0, 90, 180, 270 and 360.

[0092] There follows a description of a method of producing an optical element for a lithography apparatus with reference to FIGS. 9 to 13. For example, the optical element 200 shown in FIGS. 2 to 4 is produced for the DUV lithography apparatus 100 shown in FIG. 1. In particular, the method ascertains an installed orientation of the optical element 200 in an optical system (for example the beam-shaping and illumination system 102 or the projection system 104 in FIG. 1) which is favorable in relation to stress-induced birefringence.

[0093] In a first step S1 of the process, the surface 208 of the crystal substrate 202 of the optical element 200 is polished. The polishing in step S1 is especially effected in such a way that a height profile 216 (see enlarged detail in FIG. 3) of the surface 208 is created, by means of which a structure which is present in the crystal substrate 202 and is indicative of and/or causes stress-induced birefringence becomes visible at the surface 208 as a surface structure with the height profile 216.

[0094] For this purpose, the surface 208 is processed, for example, by a magneto-rheological polishing method using what is called a round method (R-phi method) in which the surface 208 is processed in a spiral pattern 218 (FIG. 10). It can also be stated that the surface 208 is swept in a similar manner to a phonographic record, where a pickup runs in a spiral pattern across the record.

[0095] An apparatus 220 (FIG. 9) for magneto-rheological polishing has, for example, a rotating wheel 222 as a tool head with a magnet 224 in its interior. By use of a nozzle (not shown), a magneto-rheological fluid 226 is applied continuously to the rotating wheel 222. The magneto-rheological fluid 226 especially comprises magnetic particles, polishing media and water. The magnetic field generated by the magnet 224 alters the viscosity of the fluid 226. For example, iron particles in the fluid 226 become aligned and form a rigid structure that adheres to the wheel 222, and water and abrasive particles become concentrated as a solidified, thin polish layer on the surface of the wheel 222. The apparatus 220 for magneto-rheological polishing also comprises a holder (not shown) for holding and rotating (arrow 228) of the crystal substrate 202 about its center axis 214. In addition, the apparatus 220 for magneto-rheological polishing also has a device (not shown) for moving the wheel 222 in a radial direction 230 of the optical element 200.

[0096] By rotating the optical element 200 about the center axis 214 in the direction of movement 228 (FIG. 9) and simultaneously moving the polishing tool 222 radially toward a center 232 of the surface 208 which is defined by the center axis 214, the surface 208 is polished. This brings about spiral sweeping (spiral pattern 218 in FIG. 10) of the surface 208 by the polishing head 222. In particular, the surface 208 is processed in a polishing manner from an outer region 234 (FIG. 10) of the surface 208 in a spiral manner toward the center 232.

[0097] The applicant has established in experiments that the described polishing by the round method removes material at the surface 208 such that a surface structure with a height profile 216 (FIG. 3) indicative of stress-induced birefringence is created. In other words, the polishing described elaborates a structure present in the crystal substrate 202 which is associated with stress-induced birefringence as a characteristic height profile 216 of the surface 208. This means consequently that the height profile 216 created by the polishing according to the invention corresponds to a stress-induced birefringence when the optical element 200 is used in an optical system. Accordingly, by evaluating the height profile 216, it is possible to ascertain a favorable and/or optimal installed orientation (especially an optimal azimuthal angle ) of the optical element 200.

[0098] In a second step S2 of the method, the height profile 216 of the surface 208 of the crystal substrate 202 that has been created in step S1 is detected.

[0099] FIG. 11 shows, by way of example, a detected surface fit image 400 of the surface 208 after polishing in step S1. The surface fit image 400 is detected, for example, by interferometry measurement. In the surface fit image 400 in FIG. 11, the height profile 216 (FIG. 3) of the surface 208 is shown in greyscale after polishing in step S1. Thus, the grey shades in the surface fit image 400 in FIG. 11 correspond to different height values. Since the surface fit image 400 has been ascertained, for example, by an interferometry measurement, the grey shades shown in FIG. 11 can also constitute intensities detected in the interferometry measurement, which in turn correspond to height values of the height profile 216.

[0100] The height profile 216 detected by the surface fit image 400 has, for example (e.g. for a CaF.sub.2 crystal substrate), as a function of the azimuthal angle , six local minima 402, 404, 406, 408, 410 and 412 (i.e. minima of the height H or intensity I) at average angle values of 1, 2, 3, 4, 5 and 6. In FIG. 11, for reasons of clarity, only the three main minima 404, 408 and 412 at average angles of 2, 4 and 6 are identified. FIG. 12 shows all six minima 402, 404, 406, 408, 410 and 412. It is pointed out that, for a crystal substrate 202 made of a material other than CaF.sub.2for example BaF.sub.2 or LuAGa height profile 216 detected by a surface fit image 400 may also have different material-characteristic properties.

[0101] It is noted that three recesses 414 that can be seen in the surface fit image 400 in FIG. 11 were caused by a holder (not shown). In order to record the surface fit image 400, however, the holder is removed and hence the recesses 414 are of no importance for the evaluation.

[0102] In a third step S3 of the process, using the height profile 216 ascertained, i.e., for example, using the surface fit image 400 shown in FIG. 11, a favorable installed orientation of the optical element 200 in an optical system 102, 104 is ascertained. In particular, an installed orientation of the optical element 200 for which stress-induced birefringence on incidence of polarized radiation 204 (FIG. 2) is at a minimum is ascertained. The installed orientation is an orientation in relation to the rotation (azimuthal rotation) of the optical element 200 about its center axis 214.

[0103] In particular, an angle of rotation (FIG. 2) of the optical element 200 in relation to the rotation about the center axis 214 for which stress-induced birefringence on incidence of the polarized radiation 204 is at a minimum is ascertained. It is possible here, for example, also to ascertain multiple values for the angle of rotation for which stress-induced birefringence on incidence of the polarized radiation 204 has a minimum (e.g. a local minimum). In addition, the angle of rotation a may also additionally be ascertained relative to the plane of polarization 212 (FIG. 2) of the incident polarized radiation 204.

[0104] As shown in FIG. 12, the installed orientation of the optical element 200 is ascertained by ascertaining an angle distribution 416 of height values H or corresponding intensity values of the detected height profile 216 of the surface 208, i.e., for example, of the surface fit image 400. For this purpose, the height values H or intensity values I are integrated or averaged in predetermined angle ranges 46 (e.g. circle segments 418, FIG. 11) of the detected surface fit image 400. It should be noted that the angle range and the corresponding circle segment 418 in FIG. 11, for reasons of illustration, are shown in excessively large size. In addition, the integrated and/or averaged values (e.g. height values H or intensity values I) are plotted as angle distribution 416 over the entire angle range of the full-circle of 360. FIG. 12 thus shows the six minima at 1, 2, 3, 4, 5 and 6 in the angle distribution 416.

[0105] In addition, FIG. 12 shows a graph 420 adapted from the literature that shows the intrinsic birefringence of a [111]-oriented CaF.sub.2 crystal. As the applicant is thus able to demonstrate, a high degree of accordance, especially with regard to the position of the six minima 402, 404, 406, 408, 410 and 412, is apparent between the graph 420 that describes the birefringence and the angle distribution 416 ascertained with the aid of the detected height profile 216, i.e. from the surface fit image 400. The applicant is thus able to present an alternative method of ascertaining the installed orientation of an optical element which is favorable with regard to stress-induced birefringence. In particular, the installed orientation which is favorable with regard to stress-induced birefringence, i.e. the angle of rotation a which is favorable with respect to stress-induced birefringence, can be ascertained directly from the surface fit image 400 of the height profile 216 as one or more of the angles 1 to 6 of the minima 402 to 412 (especially 2, 4, 6 of the main minima 404, 408, 412), without an additional test setup and an additional test method. In particular, it is possible to modify a process step of polishing the surface 208 (step S1) and of detecting the height profile 216 (surface fit image 400) which is required in any case such that the information as to the optimal installation angle is also obtained without any great extra difficulty. An angle 2, 4, 6 of each of the main minima 404, 408, 412 in FIG. 12 can be regarded as a favorable installation angle (FIG. 2) for the purposes of clocking of the optical element 200.

[0106] In a fourth step S4 of the method, the favorable installation orientation ascertained, for example one of the angles 2, 4, 6, is marked on the optical element 200. This allows the favorable installed orientation ascertained to be read off on the optical element 200 itself, for example by a customer, and/or ascertained by use of a measuring device, for example a commercially available interferometer.

[0107] In step S4, in particular, a marking 424 (FIGS. 2 and 3) is made on the optical element 200 at one or more of the favorable angles of rotation 2, 4, 6 ascertained in step S3. In the example shown, the marking 424 is painted onto an outer face 422 of the optical element 200 (for example with a marker pen). In other examples, a marking 424 may also be engraved into the optical element 200 and/or made in an edge region of the surface 208.

[0108] In an optional fifth step S5 of the method, the surface 208 is polished again. This further polishing step serves to remove the height profile 216 of the surface 208 which is created in step S1. This does not remove the marking 424 applied (FIG. 2) that indicates the installed orientation ascertained. Employing step S5 makes it possible to achieve a lower roughness of the surface 208. At the same time, the marking 424 that shows the user the angle of orientation with which the optical element 200 should be installed into an optical system (e.g. 102, 104, FIG. 1) in order to minimize stress-induced birefringence is preserved.

[0109] In some implementations, the processing of data described above can be performed by one or more computers that include one or more data processors configured to execute one or more computer programs that include a plurality of instructions according to the principles described above. For example, the processing of data can include processing (e.g., analyzing) the surface fit image 400. The processing of data can include ascertaining, using the height profile detected, an installed orientation of the optical element in an optical system of the lithography apparatus in relation to a stress-induced birefringence on incidence of polarized radiation. The processing of data can include ascertaining an angle of rotation of the optical element in relation to the rotation of the optical element about the center axis for which stress-induced birefringence on incidence of the polarized radiation is lower and/or minimal compared to other angles of rotation in relation to the rotation of the optical element about the center axis. The processing of data can include ascertaining an angle of rotation of the optical element relative to a polarization plane of the incident polarized radiation. The processing of data can include ascertaining an angular distribution of height values H of the ascertained height profile of the surface. The one or more computers can include one or more data processors for processing data, such as the surface fit image 400, one or more storage devices for storing data, and/or one or more computer programs including instructions that when executed by the one or more computers cause the one or more computers to carry out the processes. The one or more computers can include one or more input devices, such as a keyboard, a mouse, a touchpad, and/or a voice command input module, and one or more output devices, such as a display, and/or an audio speaker. In some implementations, the one or more computers can include digital electronic circuitry, computer hardware, firmware, software, or any combination of the above. The features related to processing of data can be implemented in a computer program product tangibly embodied in an information carrier, e.g., in a machine-readable storage device, for execution by a programmable processor; and method steps can be performed by a programmable processor executing a program of instructions to perform functions of the described implementations. Alternatively or in addition, the program instructions can be encoded on a propagated signal that is an artificially generated signal, e.g., a machine-generated electrical, optical, or electromagnetic signal, that is generated to encode information for transmission to suitable receiver apparatus for execution by a programmable processor.

[0110] A computer program can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment.

[0111] For example, the one or more computers can be configured to be suitable for the execution of a computer program and can include, by way of example, both general and special purpose microprocessors, and any one or more processors of any kind of digital computer. Generally, a processor will receive instructions and data from a read-only storage area or a random access storage area or both. Elements of a computer system include one or more processors for executing instructions and one or more storage area devices for storing instructions and data. Generally, a computer system will also include, or be operatively coupled to receive data from, or transfer data to, or both, one or more machine-readable storage media, such as hard drives, magnetic disks, solid state drives, magneto-optical disks, or optical disks. Machine-readable storage media suitable for embodying computer program instructions and data include various forms of non-volatile storage area, including by way of example, semiconductor storage devices, e.g., EPROM, EEPROM, flash storage devices, and solid state drives; magnetic disks, e.g., internal hard disks or removable disks; magneto-optical disks; and CD-ROM, DVD-ROM, and/or Blu-ray discs.

[0112] In some implementations, the processes described above can be implemented using software for execution on one or more mobile computing devices, one or more local computing devices, and/or one or more remote computing devices (which can be, e.g., cloud computing devices). For instance, the software forms procedures in one or more computer programs that execute on one or more programmed or programmable computer systems, either in the mobile computing devices, local computing devices, or remote computing systems (which may be of various architectures such as distributed, client/server, grid, or cloud), each including at least one processor, at least one data storage system (including volatile and non-volatile memory and/or storage elements), at least one wired or wireless input device or port, and at least one wired or wireless output device or port.

[0113] In some implementations, the software may be provided on a medium, such as CD-ROM, DVD-ROM, Blu-ray disc, a solid state drive, or a hard drive, readable by a general or special purpose programmable computer or delivered (encoded in a propagated signal) over a network to the computer where it is executed. The functions can be performed on a special purpose computer, or using special-purpose hardware, such as coprocessors. The software can be implemented in a distributed manner in which different parts of the computation specified by the software are performed by different computers. Each such computer program is preferably stored on or downloaded to a storage media or device (e.g., solid state memory or media, or magnetic or optical media) readable by a general or special purpose programmable computer, for configuring and operating the computer when the storage media or device is read by the computer system to perform the procedures described herein. The inventive system can also be considered to be implemented as a computer-readable storage medium, configured with a computer program, where the storage medium so configured causes a computer system to operate in a specific and predefined manner to perform the functions described herein.

[0114] Although the present invention has been described with reference to exemplary embodiments, it is modifiable in various ways.

LIST OF REFERENCE SIGNS

[0115] 100 DUV lithography apparatus [0116] 102 Beam-shaping and illumination system [0117] 104 Projection system [0118] 106 Light source [0119] 108 Radiation [0120] 110 Photomask [0121] 112 Wafer [0122] 114 Lens element [0123] 116 Lens element [0124] 118 Lens element [0125] 120 Mirror [0126] 122 Mirror [0127] 124 Optical axis [0128] 126 Medium [0129] 128 Optical pulse extender [0130] 130 Beam splitter [0131] 132 Holder [0132] 134 Chamber window [0133] 200 Optical element [0134] 202 Crystal substrate [0135] 204, 204 Radiation [0136] 206 End face [0137] 208 Surface [0138] 210 Direction of propagation [0139] 212 Polarization plane [0140] 214 Center axis [0141] 216 Height profile [0142] 218 Spiral pattern [0143] 220 Apparatus [0144] 222 Wheel [0145] 224 Magnet [0146] 226 Fluid [0147] 228 Direction of rotation [0148] 230 Direction [0149] 232 Center [0150] 234 Region [0151] 300 Crystal [0152] 302 Crystal plane [0153] 304 Crystal plane [0154] 306 Crystal plane [0155] 308 Crystal plane [0156] 310 Crystal axis [0157] 312 Crystal axis [0158] 314 Crystal axis [0159] 316 Crystal axis [0160] 400 Surface fit image [0161] 402 Minimum [0162] 404 Minimum [0163] 406 Minimum [0164] 408 Minimum [0165] 410 Minimum [0166] 412 Minimum [0167] 414 Cutout [0168] 416 Angle distribution [0169] 418 Circle segment [0170] 420 Graph [0171] 422 Lateral surface [0172] 424 Marking [0173] Angle [0174] Angle [0175] Angle [0176] 1 Angle [0177] 2 Angle [0178] 3 Angle [0179] 4 Angle [0180] 5 Angle [0181] 6 Angle [0182] a Miller index [0183] b Miller index [0184] c Miller index [0185] E Vector of the electrical field [0186] H Height value [0187] I Intensity value [0188] S1-S5 Method steps [0189] X Direction [0190] Y Direction [0191] Z Direction