JP2019505829A - Method for polishing optical surface and optical element - Google Patents

Abstract

The invention comprises a substrate (1) having an optical surface (2) embodied as a free-form surface and an area (3) adjacent to the side of the optical surface (2), the side of the optical surface (2). The area (3) adjacent to the threshold does not exceed the polishing reference threshold Δz _S in the form of local astigmatism (Δz) at each location (P), which is Δz _S = (k _max −k _min ) / 8D. given by ^2, _{wherein, k min} denotes the minimum local curvature at each location (P) of the zone _{(3), k max} represents the maximum local curvature at each location (P) of the zone (3), It relates to an optical element (10) in which D ² = 2500 mm ² , preferably D ² = 900 mm ² , in particular D ² = 100 mm ² applies. The present invention is a method for polishing an optical surface (2) with a polishing tool (6), the optical surface (2) embodied as a free-form surface and an area (3) adjacent to the side of the optical surface (2). And polishing the optical surface (2) by moving the polishing surface (7) of the polishing tool (6), and a threshold (Δz) of the polishing reference (Δz) at each location (P) of the zone (3) The shape of the zone (3) is adapted to the polishing tool (6), in particular to the shape of the polishing surface (7) of the polishing tool (6) so that Δz _S ) is not exceeded, and the polishing reference (Δz) is optical It also relates to a method comprising the step of representing a measure of the polishing error in the optical surface (2) produced by moving the polishing tool (6) over the area (3) adjacent to the surface (2).
[Selection] Figure 2

Description

  The present invention relates to a method for polishing an optical surface with a polishing tool and an optical element.

[Reference to related applications]
This application claims the priority of German Patent Application No. 10 2015 223 983.7 dated December 2, 2015, the entire disclosure of which is incorporated by reference into the context of the present application.

  Patent Document 1 discloses a method of manufacturing an optical element having an optical surface extending to the vicinity of the edge of a substrate. In order to manufacture an optical element, a substrate having a major surface extending outside the edge of the optical surface is first prepared. The substrate is also polished in a region where the major surface extends out of the optical surface. After polishing, the substrate material including a portion of the surface extending out of the optical surface is removed.

  In general, it is usually not only the optical surface itself, i.e. the area of use, but also the so-called overrun area, i.e. the optical surface, that is at least partially polished when polishing the optical surface for the purpose of producing a highly accurate optical surface. There is also an area adjacent to. The reason for this procedure is that for the purpose of polishing the edge area of the optical surface, due to the size of the polishing tool used, at least the polishing tool is usually used to allow the edge area of the optical surface to be polished with the desired accuracy. This is because it is necessary to partially move to the excess area.

  Even if the center of the polishing tool used is already located significantly outside the optical surface, a part of the polishing tool usually extends into the optical surface and consequently also contributes to ablation on the optical surface. Thus, the shape of the excess region affects the polishing quality of the optical surface. If the excess region is geometrically unsuitable for polishing, a polishing error or surface error occurs when polishing the optical surface. Such polishing or surface errors are also referred to below as polishing signatures and generally lead to a significant increase in correction effort at the optical surface. If the polishing error is not correctable within the subsequent correction process range, the optical surface cannot be made according to the specification, i.e. the optical surface cannot be used for the desired application.

US Pat. No. 7,118,449

  It is an object of the present invention to provide a method for polishing an optical surface and an optical element with less polishing error.

  The purpose of this is a method of polishing an optical surface with a polishing tool, which polishes over an optical surface embodied as a free-form surface and an area adjacent to the side of the optical surface, usually also embodied as a free-form surface. Polishing the optical surface by moving the polishing surface of the tool, and shape the area of the polishing tool, in particular the polishing surface of the polishing tool, so as not to exceed the polishing criteria threshold at each location of the area. Adapting to shape (or diameter), the polishing criteria is achieved by a method that includes representing a measure of the polishing error in the optical surface created by moving the polishing tool across an area adjacent to the optical surface.

  The present invention provides an optical surface that meets the specifications for surface quality with respect to morphology and roughness, where the polishing error in the optical surface created by moving the polishing tool across the area adjacent to the optical surface is as small as possible or below a threshold. It is proposed to design the shape of the adjacent area so that it can be made or to adapt the area to the polishing tool used for polishing. This is ensured if the polishing criteria are met at each location in the area adjacent to the optical surface, i.e., the polishing criteria (which usually varies with location) does not exceed the threshold at each location. In this case, the polishing error can be corrected by a subsequent correction process so that an optical surface satisfying a desired specification can be produced.

  Both the optical surface and the area are usually free-form surfaces, i.e. surfaces that deviate from spherical and planar forms. As an example, the free-form surface may be a so-called aspheric surface that is radially symmetric with respect to the central axis, but may also be a free-form surface that has a shape that is not (radial) symmetric, that is, is not rotationally symmetric. The free-form surface can have a circular periphery. However, it is also possible for the free-form surface to have a peripheral edge deviating from the circular form.

  In general, a free-form surface has a minimum curvature in at least two locations, typically multiple locations, in any case, and the minimum curvature deviates from the maximum curvature at each location. Usually, the maximum curvature and the minimum curvature of a free-form surface are different from each other in at least two places.

  In a variant of the method, the polishing surface of the polishing tool performs a rotational movement with respect to the axis of rotation during movement over the optical surface and adjacent areas. The axis of rotation is usually aligned substantially perpendicular to the optical surface and / or the area at each location. During (reciprocating) movement, the polishing tool is pressed against the optical surface over the optical surface. This is also true if the abrasive tool is moved at least partially to the adjacent area. The speed of the rotational movement can vary depending on the location on the optical surface or adjacent area, or can be constant during the entire polishing process, if applicable.

  The shape of the polishing surface is critical when polishing with a polishing tool. The polishing surface is the surface of the polishing tool that contacts the optical surface and / or the adjacent area. The polishing surface must be adaptable to the surface shape of the object to be polished even during rotation of the polishing tool. When viewed from the polishing tool, the surface to be polished is deviated from the polishing surface, which is generally a flat surface, and is hereinafter referred to as (local) deformation or (local) deviation. This local deformation or deviation leads to locally different ablation behavior under the polishing tool. This not only leads to different ablation behavior within the polishing surface, but also leads to different ablation behavior across the entire surface to be polished.

  As a result of local deformation / deviation of the optical surface from the polished surface, the optical surface (as used in the typical case after grinding) is used to remove depth damage and polish the optical surface as a whole. It is impossible to perform constant material ablation in the region). As a result of attempting a constant material ablation on the surface to be polished, a polishing error, also referred to as a polishing signature, occurs, which substantially depends on the shape of the polishing symmetry surface. This polishing signature may have steep or high frequency components, which are problematic for subsequent correction processes that should be able to produce surfaces with strictly given specifications.

  Therefore, in order to evaluate the shape of the surface to be polished with respect to its polishing properties, the introduction of polishing criteria or geometric criteria is proposed. For this purpose, the above-described deformation or deviation of the surface to be polished from the polishing plane of the polishing tool is determined, for example, at an arbitrary location on the surface to be polished. Deviations or deformations between the polishing surface and the optical surface of the polishing tool are decomposed at each location into an orthogonal polynomial system, such as a Zernike polynomial, and usually only the lowest coefficient of decomposition is used as a measure of the abrasiveness. Zernike coefficients are respectively assigned to components with different deviations or to different wavefront aberrations. Thus, for example, the Zernike coefficient Z4 indicates the focal component of the deviation, and the Zernike coefficient Z5 / Z6 indicates the local astigmatism or astigmatism component of the deviation.

  In an advantageous variant of the method, local astigmatism at each location in the surface region is selected as the polishing criterion. It has proved advantageous to simply use the astigmatism component of the deviation as a measure of the surface polish. Similarly, the focal component Z4 specifies how strongly the polishing surface must bend, but the polishing surface or polishing tool need not fit during rotation. Therefore, deformation or deviation in the focal component Z4 should be considered as static deformation. In contrast, the deformation astigmatism component Z5 / 6 specifies how the polishing tool must be dynamically adapted during rotation. The astigmatism component Z5 / 6 is referred to as “local astigmatism”. If the polishing tool or polishing surface can no longer dynamically adapt during rotation, significant local polishing errors are expected.

  As further described above, higher order terms or Zernike coefficients could be used for the polishing criteria. However, it has been found that the astigmatism component is generally a sufficient reference for evaluating the surface polishability of typical surfaces used in optical elements, for example, free-form surfaces.

  As further described above, the shape of the area adjacent to the optical surface is selected such that the local astigmatism does not exceed a threshold value representing the maximum value of local astigmatism anywhere in the area. The threshold prescription that must not be exceeded depends on several parameters such as the rotational speed of the polishing tool, the area of the polishing tool's polishing surface, the polishing ablation obtained during polishing, and the correction capability of the correction process after polishing. change. A comprehensive understanding of the process is required to set thresholds based on these parameters. Usually this understanding is not directly available in practice. Therefore, the threshold of the polishing criterion in the form of local astigmatism is usually set by comparison with the polishing error of the fabricated or polished optical surface.

  In general, it is understood that the threshold for polishing criteria should not be exceeded not only in the area adjacent to the optical surface, but also in the optical surface itself. The optical surface itself is usually sufficiently flat, i.e., without sharp undulations (gradients) and therefore generally meets the polishing criteria.

In one development, the local astigmatism Δz at each location of the area is
Δz = (k _max −k _min ) / 8D ² (1)
Where D indicates the diameter of the polishing surface of the polishing tool, _kmin indicates the minimum local curvature at each location in the area, and _kmax indicates the maximum at each location in the area. Indicates the local curvature. As is known from differential geometry, two principal curvatures k _Min and k _Max can be assigned to each location or point of the surface, which represents the reciprocal of the minimum and maximum curvature radii at each location. That is, the following applies: k _Min = 1 / R _Max , k _Max = 1 / R _Min . This relationship is mathematically correct even when the two main curvatures k _Min and k _Max take negative values. Local astigmatism has a unit of length and, according to the above definition, varies with the diameter of the normally rotationally symmetric polishing surface of the polishing tool.

Furthermore, since the calculation of local astigmatism as described above, ie using the Zernike polynomial decomposition at each location of the area, is relatively complex, local astigmatism is approximated according to equation (1) of the present development. Calculated. The deformation or deviation of the surface from the polished surface further examined above is the average curvature of the surface at each location corresponding to the focal component Z4 (1/2 (k _Min + k _Max )) and local astigmatism Z5 / 6. Is substantially composed of a difference in curvature (k _Max −k _Min ) that roughly corresponds to. Since the curvatures k _Min and k _Max are calculated from the (known) parameterization derivative of the surface, the local astigmatism of the surface, in this case the area adjacent to the optical surface, is calculated directly from the surface geometry It is only necessary to take into account the diameter of the polishing surface.

  In one development, the polishing surface of the polishing tool forms a flat surface. Generally, a polishing tool whose polishing surface is a flat design is used for polishing. When rotating the polishing surface about an axis, the polishing surface usually has a circular shape so as not to create an imbalance during the rotational movement. If the polishing surface is a planar design, this further simplifies the calculation of the deformation or deviation of the surface to be polished from the polishing surface.

  There are various options for achieving an area that meets the polishing criteria.

  In one variation, the shape of the optical surface and the shape of the laterally adjacent area are determined based on an analytical representation of both the optical surface and the laterally adjacent area.

  Since the optical surface is used for reflection or transmission of radiation, its shape is usually represented by an analytical expression relating to the optical design, for example in the form of a polynomial equation or a polynomial line / polynomial surface. In the simplest case, an analytical representation of the surface of the optical surface can be used to determine the shape of the area, i.e. the analytical representation of the optical surface is extended to the coordinates of the adjacent area. When expanding a polynomial representation of the shape of an optical surface to an area adjacent to the optical surface, the polynomial expression of the shape of the optical surface is usually Cannot be extended to adjacent areas without violating the polishing standards in this area. If the polishing criteria are not met when extending the analytical representation of the surface of the optical surface to an adjacent area, a different solution must be selected for this area.

  In one development, the polishing criteria threshold for the laterally adjacent area is taken into account when determining the (target) shape of the optical surface. In this case, meeting the polishing criteria in the above area is employed as an additional boundary condition in the optical surface design or (target) shape layout. Since the additional boundary conditions limit the number of degrees of freedom when setting the target shape of the optical surface, it is usually necessary to provide additional degrees of freedom in this case in order not to degrade the optical performance of the optical surface. One option for the introduction of additional degrees of freedom is represented by using higher order polynomials in the analytical representation of the surface. In order to meet the polishing criteria without degradation of the properties of the optical surface, it may be possible to suppress steep slopes in areas adjacent to the optical surface by using such polynomials.

  In yet another variation, the shape of the area is determined without using an analytical representation of the surface of the area. In principle, the area adjacent to the optical surface can be designed freely. As an example, it is possible to pre-determine the outer edge of the area and fill the area using a filling algorithm. This allows for the suppression of adverse gradients and the ideal design of the area as desired with respect to the polishing criteria. Having to rely on a point cloud or similar representation of a surface by the absence of an analytical representation of the surface tends to be disadvantageous with this method.

  In yet another variation, the method further includes machining the substrate to create an optical surface to be polished and laterally adjacent areas in a step prior to polishing. Prior to polishing, the optical surface, i.e. the region of the substrate to be used optically, is processed or formed by mechanical pre-processing, e.g. by milling or grinding, possibly with free abrasive grains. This also applies to the area adjacent to the optical surface, which is likewise mechanically preprocessed. Machining creates a shape in the area adjacent to the optical surface that does not exceed the polishing criteria threshold for a given size or given diameter of the polishing surface of the polishing tool.

  In a development of the method, an optical surface having an ersatz shape is produced during the machining and polishing of the substrate, the surrogate shape deviating from the target shape of the optical surface and the target of the optical surface. The shape is made from the surrogate shape in a correction process following polishing. This development describes the case where no shape satisfying the polishing criteria is found in the case of the target shape of the optical surface given by the optical design, for example in the area adjacent to the optical surface represented by an analytical function or polynomial. . In this case, a substitute shape can be obtained. This surrogate shape should meet the polishing criteria in the area adjacent to the optical surface, but may deviate from the target shape set by the optical design on the optical surface according to yet other criteria. During the creation of the optical surface and the area by machining, ie during shaping, a surrogate shape deviating from the target shape given by the optical design at the optical surface is first created by grinding and polishing as described above. In one or more correction processes following polishing, the surrogate shape, ie the deviation between the machining of the optical surface and the shape created during subsequent polishing, is adapted to the target shape of the optical surface (especially) Finally, the target shape is generated on the optical surface.

  In yet another development, the polishing criteria threshold is selected such that at least one subsequent correction process can correct polishing errors at the optical surface. Further, as described above, the threshold definition varies depending not only on parameters relating to the polishing or polishing tool, but also on the correction capability of the correction process after polishing. The polishing criteria threshold should be selected so that the optical surface can be produced with the desired specifications by one or possibly multiple subsequent correction processes.

  In one development, the subsequent correction process is selected from the group comprising ion beam machining and magnetoviscous polishing. Ion beam processing represents a correction method that locally implants an ion or ion beam into the optical surface to cause material ablation at the optical surface. Alternatively or additionally, a correction process in the form of a so-called magneto-viscous polishing can be performed. In this correction process, the magnetorheological liquid serves as a tool. As an example, a liquid is applied to a rotating grindstone and solidified by a magnetic field so that material ablation can be obtained upon contact with the surface to be processed. Other correction processes that facilitate correction at small spatial wavelengths and usually result in little or no degradation of surface quality in the medium and high spatial wavelength ranges are also post-polishing in addition to the two above-described correction processes. It is also understood that it can be used. Surface quality in medium and high spatial wavelength ranges is usually obtained by polishing optical surfaces and mechanical pre-processing.

Still another embodiment of the present invention is an optical element, which is an optical element including a substrate having an optical surface embodied as a free-form surface and an area adjacent to a side of the optical surface, the optical surface The laterally adjacent area does not exceed the polishing reference threshold Δz _S in the form of local astigmatism at each location, the threshold being
Δz _S = (k _max −k _min ) / 8D ² (1 ′)
Where k _min denotes the minimum local curvature at each location of the area, k _max denotes the maximum local curvature at each location of the area, and D ² = 2500 mm ² , preferably D ² = It relates to an optical element in which 900 mm ² , in particular D ² = 100 mm ² applies.

Further, as described above, the local astigmatism approximated by the equation (1) changes according to only the diameter of the polishing surface of the used polishing tool in addition to the main curvature at each location in the above-mentioned area. However, since the polishing surface of the polishing tool cannot be selected arbitrarily large, the value D is limited to the maximum value, and as a result, the local astigmatism threshold Δz _S is also limited to the maximum value independent of the diameter of the polishing tool. Is done.

  In one embodiment, the optical surfaces continuously merge into an area adjacent to the optical surface. It is advantageous for polishing of the optical surface if the area is continuously adjacent to the edge of the optical surface, i.e. without kinking.

  In yet another embodiment, the optical surface has a roughness of less than 1 nm rms in the spatial wavelength range from 1 mm to the maximum range of the optical surface. Within the meaning of the present application, the maximum surface range is understood to mean the maximum length of a straight line connecting two points along the edge of the optical surface. For an optical surface with a circular edge, the maximum range represents the diameter of the optical surface. In the case of an optical surface having an edge or edge contour in the form of an ellipse, the maximum range represents the length of the major axis, ie the maximum diameter, such as an ellipse. As a result of mechanical pre-processing, polishing, and optionally subsequent correction processes, the desired quality or surface roughness can be provided at the optical surface for short, medium, and long spatial wavelengths.

  In one embodiment, the area extends outward from the optical surface by a distance of 50 mm or less. From the optical surface, the area of the substrate that must meet the polishing criteria usually does not extend outside the diameter of the polishing surface of the used polishing tool. If the distance from the optical surface is greater, the polishing tool will not protrude into the optical surface, so even the steepness of the shape of the outer area will usually not affect the polishing error.

  In yet another embodiment, the optical element has at least a reflective coating on the optical surface, in particular a coating that reflects EUV radiation. In this case, the optical element is usually a mirror, in particular an EUV mirror. In general, reflective coatings are provided only on optical surfaces, not adjacent areas. However, the substrate can optionally have a reflective coating, either in whole or in part, in adjacent areas. The optical surface is a portion of the surface of the substrate that is disposed in the beam path of the optical mechanism and inductively reflects the radiation used by the optical mechanism. The optical mechanism can be, for example, a lithographic apparatus, in particular an EUV lithographic apparatus, but the optical element can also be used advantageously with other optical mechanisms.

  Further features and advantages of the present invention will become apparent from the following description of exemplary embodiments of the invention, with reference to the drawing figures, which illustrate essential details of the invention, and from the claims. The individual features can be realized individually in the variant of the invention individually or as a plurality in any desired combination.

  Exemplary embodiments are shown in schematic form and are described in the following description.

Figure 2 shows a schematic diagram of a top view of an optical surface and an area adjacent to it. FIG. 2 shows a schematic view of an polishing tool moved across an optical surface being polished and an adjacent area. FIG. 2 shows a schematic view of an polishing tool moved across an optical surface being polished and an adjacent area. FIG. 2 shows a schematic diagram of a correction process of a form of ion beam machining of an optical surface after polishing. 1 shows a schematic view of an optical element in the form of an EUV mirror. FIG. 2 shows a schematic diagram of a local deviation of the substrate surface from a plane along the cross section of the substrate shown in FIGS. FIG. 2 shows a schematic diagram of local astigmatism along the cross section of the substrate shown in FIGS.

  In the following description of the drawings, the same reference numerals are used for identical or functionally identical components.

  FIGS. 1a to 1d schematically show a substrate 1 on which an optical surface 2, i.e. a use region, and an area 3 (excess region) adjacent to the side of the optical surface 2 are formed. The optical surface 2 has an elliptical edge 4 surrounded by an adjacent area 3 in a ring shape. The area 3 adjacent to the optical surface 2 extends to a similarly elliptical edge 5 outside the substrate 1. In the example shown, the substrate 1 is a so-called zero-expansion material, such as Zerodur® or ULE®, ie a substrate 1 that can be used for an EUV mirror. It is also possible to use a substrate 1 in the form of another material, for example in the form of quartz glass.

  The optical surface 2, i.e. both the optically used area of the substrate 1 and the adjacent area 3, are free-form surfaces, i.e. surfaces that do not extend radially symmetrically and do not extend mirror-symmetrically with respect to one of the axes of the xyz coordinate system in the illustrated example. Form each one. The shape of the optical surface 2 is, after polishing and after further correction processes, a predetermined tolerance range from the target shape given by the optical design of the optical mechanism in which the surface follows the optical specifications, i.e. the optical surface 2 is arranged in the beam path. Chosen to deviate only within. The area 3 adjacent to the optical surface 2 and continuously, i.e. without a transition in the form of a kink, leading to the edge 4 of the optical surface 2 is also embodied as a free-form surface. The shape of the area 3 is selected at each location P of the area so as to meet the polishing criteria described in more detail below.

  The polishing process of the optical surface 2 by the polishing tool 6 is shown in FIGS. 1b and 1c. The polishing tool 6 has a circular polishing plane 7 on which the polishing tool 6 is pressed against the surface of the substrate 1. During polishing, the polishing tool 6 is rotated with respect to the rotating shaft 8 in contact with the center of the polishing surface 7, and the polishing tool 6, and more precisely the polishing surface 7 is moved over the optical surface 2 (see FIG. 1b). Is a reciprocating motion.

  In order to be able to polish the edge of the optical surface 2 as well, it is necessary to move the polishing tool 6 at least partly to the adjacent area 3, as shown in FIG. Usually, it is necessary to move the polishing tool 6 to the area 3 until the polishing surface 7 remains pressed only on the area 3 but not on the optical surface 2. As can be seen in FIG. 1 c, when the polishing tool 6 is moved to the area 3 adjacent to the optical surface 2, a part of the polishing plane 7 is also pressed against the optical surface 2. Thus, the shape of the area 3 adjacent to the optical surface 2 affects how the material of the substrate 1 is ablated at the optical surface 2 being polished. As a result, the ablation capability of the polishing tool 6 may be adversely affected by the unfavorably selected shape of the area 3 adjacent to the optical surface 2, so that the polishing tool 6 is moved to the area 3 adjacent to the optical surface 2. In order to minimize surface or polishing errors in the optical surface 2 caused by movement, the shape of the area must be selected appropriately.

For this purpose, the shape of the area 3 is adapted to the shape of the polishing tool 6, more precisely to the diameter D of the polishing surface 7, so that the threshold Δz _S of the polishing reference Δz is not exceeded at each location P in the area 3. To do. The polishing criterion Δz is a measure of the polishing error that occurs at the optical surface 2 due to the movement of the polishing tool 6 over the area 3 at each location P. The polishing error on the optical surface 2 or on the entire surface is caused by the deviation of the surface from the shape of the polishing surface 7 which is flat in the illustrated example, and the deviation at each location P depends on the diameter D of the polishing surface 7. change.

  FIG. 3a shows a cross section of the substrate 1 extending in the y direction along the cut line indicated by the broken line in FIG. 1a. In FIG. 3a, the area of the optical surface 2 can be seen in the middle and the adjacent area 3 can be seen on the left and right. FIG. 3b is a plot of relevant values of local astigmatism as described below. When the deviation A of the polishing surface 7 from the optical surface 2 at each location P is decomposed into an orthogonal polynomial system in the form of Zernike polynomials, only the low order terms, i.e. the focus term Z4 and astigmatism Z5 / 6 are taken into account. In this case, it is possible to identify that the focal term Z4 indicates only a static component of the deviation A when the polishing surface 7 is rotated with respect to the rotation axis 8, and the static component generates a polishing error. It is not important or secondary to it. This is not the case in the case of (local) astigmatism Z5 / 6, because (local) astigmatism Z5 / 6 exhibits a dynamic component of deviation A, and in the case of rotation the polishing surface 7 or polishing Specify how strongly and dynamically the tool 6 must be adapted to the optical surface 2 or the adjacent area 3 to be polished at each location P.

As a result, the local astigmatism Z5 / 6 is a suitable polishing criterion, i.e. a measure of the polishing error that has occurred at the optical surface 2 when the polishing tool 6 is located at each location P in the area 3 adjacent to the optical surface 2. Represent. FIG. 3 b shows the local astigmatism Δz as a function of the location P in both the optical surface 2 and the adjacent area 3. FIG. 3b also shows a threshold value Δz _{S for} local astigmatism Δz that should not be exceeded to ensure that the optical surface 2 can be made with the desired specifications.

As can be seen in FIG. 3b, the portion of the zone 3 located in the left-hand side of the cross section in the Y direction of the optical surface 2 in the illustrated example exceeds the threshold Δz _S , but the optical surface itself has a threshold Δz at each location P. _It has a local astigmatism Δz below _S. As a result, in the example shown in FIG. 3b, the area 3 is not adapted to the polishing tool 6 and more precisely to the diameter D of the polishing surface 7 so that a sufficiently small polishing error is provided at the optical surface 2. Therefore, the shape of the area 3 needs to be appropriately changed so as to satisfy the polishing standard.

Instead of calculating the local astigmatism Δz using decomposition into an orthogonal polynomial system, as described above, the local astigmatism Δz at each location P can be approximately calculated by the following equation.
Δz = (k _max −k _min ) / 8D ²
In the equation, D indicates the diameter of the polishing surface 7 of the polishing tool 6, _kmin indicates the minimum local curvature at each location P in the area 3, and _kmax indicates the maximum local curvature at each location P in the area 3. . Here, the minimum and maximum curvatures k _Min and k _Max are the reciprocals of the maximum and minimum curvature radii at each location P, that is, the following applies. k _Min = 1 / R _Max , k _Max = 1 / R _Min .

  Unlike what is shown in FIG. 3b, there are a number of options for creating an area 3 that meets the polishing criteria. As an example, an analytical representation of the surface z (x, y) of the optical surface 2, for example in the form of a polynomial or polynomial equation, can be extended to the area 3 adjacent to the optical surface 2. In the simplest case, an analytical representation of the surface z (x, y) of the optical surface 2 can also be used for the adjacent area 3. However, this presupposes that the analytical representation of the surface z (x, y) of the shape of the optical surface 2 does not have too sharp undulations in the area 3 adjacent to the optical surface 2. By optimizing the representation of the surface z (x, y) of the optical surface 2, this generally tends to have some disadvantages for polishing outside the optical surface 2, so that polishing in the area 3 Different solutions must be selected under certain circumstances to meet the conditions.

As an example, the threshold value Δz _S of the polishing reference Δz of the laterally adjacent section 3 can be taken into account as an additional condition when determining the shape of the optical surface 2 executed according to the optical design. Since the additional condition represents a limit on the degree of freedom that can be used, firstly, in order to maintain the polishing standard in the adjacent area 3, and secondly, by introducing the additional condition, the optical performance of the optical surface 2 is not deteriorated. In addition, it may be necessary to use higher order polynomials for the analytical representation of the surface z (x, y) of the optical surface 2 and the area 3.

Alternatively, the shape of the area 3 can be determined without using an analytical representation of the surface, for example by filling the area 3 between the outer edge 4 of the optical surface 2 and the outer edge 5 of the substrate 1 with a filling algorithm. Ideal as desired to suppress undesired rises or gradients and to meet the polishing criteria so that the threshold Δz _S of the polishing criterion Δz in the form of local astigmatism is not exceeded at any point in zone 3 Let's design this area.

  Yet another option according to the polishing criteria in zone 3 consists in using a surrogate shape of the optical surface 2. This is particularly advantageous when the polishing criteria cannot be met in zone 3 by an analytical representation of the surface z (x, y). In this case, starting with an analytical representation of the surface z (x, y) of the area 3 where the polishing criteria are not met, the optical design meets the analysis criteria in the adjacent area 3 but follows a specific criterion, for example the maximum given gradient It is possible to search for a surrogate shape of the optical surface 2 and area 3 that deviates from the target shape of the optical surface 2 given by

In this case, the substrate 1 is processed by mechanical processing before polishing, for example, by grinding or during polishing, so that the optical surface 2 is produced with a substitute shape deviating from the target shape of the optical surface 2. During machining or shaping and polishing of the substrate 1, the area 3 adjacent to the optical surface 2 is also in the form of local astigmatism Δz where the area meets the polishing criteria, ie where the area 3 is at any location P. It is manufactured in a shape that does not exceed the polishing reference threshold value Δz _S.

  To produce an optical surface 2 having a given target shape, the optical surface 2 having a surrogate shape is post-processed in a correction process after polishing, as exemplarily shown in FIG. 1d. In the example shown, the correction process is an ion beam machining process, and material ablation locally, i.e. at each location P of the optical surface 2, to adapt the surrogate shape of the optical surface 2 to the target shape given by the optical design. To achieve this, a movable control ion beam gun 9 aligns the ion beam on the optical surface 2.

  If the optical surface 2 is not made in the form of a surrogate shape during grinding and polishing, but directly attempts to create the target shape of the optical surface 2 during polishing, the correction process shown in FIG. It is understood that so-called magnetoviscous polishing is also usually performed. In general, such a correction process is necessary because the optical surface 2 is close to the desired target shape only at medium and long spatial wavelengths for polishing, while short space is required during subsequent correction processes such as ion beam processing. This is because the optical surface 2 that satisfies the specifications in the entire spatial wavelength region can be produced by adapting to the target shape even at the wavelength.

The threshold value Δz _S of the polishing reference Δz is selected in a subsequent correction process so that the polishing error of the optical surface 2 can be corrected to at least an extent that the optical surface 2 approximates a target shape having the desired accuracy or tolerance. . An appropriate threshold value Δz _S can be set by comparison with a polishing error of a manufactured or polished optical surface.

  As an example, after the ion beam processing shown in FIG. 1d, the optical surface 2 can have a roughness R of less than 1 nm rms in the spatial wavelength region from 1 nm to the maximum range L of the optical surface 2, as shown in FIG. The maximum range L represents the length L of the maximum diameter of the edge 4 formed in an ellipse, that is, the major axis of the optical surface 2.

As shown in FIG. 2, for the purpose of manufacturing an EUV mirror 10, a reflective coating 11 can be applied to the optical surface 2 that satisfies the specifications of the target shape or form and roughness R. In the example shown, the coating 11 is designed to reflect EUV radiation 13 in the EUV wavelength range of about 5 nm to about 30 nm, and for this purpose the coating is 13.5 nm corresponding to the working wavelength of the EUV mirror 10. It has the maximum reflectivity at the wavelength. In the illustrated example, the reflective coating 11 has alternating layers 12a, 12b made of materials having different refractive indexes. In the illustrated example, the first layer 12a is made of silicon (having a high refractive index), and the second layer 12b is made of molybdenum (having a low refractive index). Other material combinations, such as molybdenum and beryllium, ruthenium and beryllium, or lanthanum and B ₄ C, are possible depending on the wavelength used in the EUV wavelength range.

In the optical element 10, the area 3 adjacent to the optical surface 2 provided with the reflective coating 11 does not exceed the threshold value Δz _S of the local astigmatism Δz at each location P. That is, the following applies at each location P: Δz ≦ Δz _s , where
Δz _S = (k _max −k _min ) / 8D ²
_Where k _Min and k _Max are further defined as described above, and the following applies to D ² : D ² = 2500 mm ² , preferably D ² = 900 mm ² , especially D ² = 100 mm ² . It can be seen that as the threshold Δz _S decreases, the polishability increases. However, the smaller the threshold value Δz _S is selected, the harder it is to find the shape of the area 3 that does not exceed the threshold value Δz _S at all locations P.

  It will be appreciated that the area 3 adjacent to the optical surface 2 and satisfying the polishing criteria does not extend outwardly from the optical surface 2 by a distance d which usually corresponds to the diameter D of the polishing surface 7 of the polishing tool 6. When the polishing tool 6 is moved further away from the optical surface 2, the polishing surface 7 is laterally separated from the optical surface 2, so that polishing in this region does not affect the polishing error on the optical surface 2. Unlike the one shown in FIGS. 1 a to 1 d, the outer edge of the area 3 does not necessarily correspond to the outer edge 5 of the substrate 1, and in some cases, the substrate 1 extends further outward than the outer edge of the area 3. There is no need to meet the polishing criteria in the outer region.

Claims (17)

A substrate (1) comprising an optical surface (2) embodied as a free-form surface and an area (3) adjacent to the side of the optical surface (2), the optical element (10)
The section (3) adjacent to the side of the optical surface (2) does not exceed a polishing reference threshold Δz _S in the form of local astigmatism (Δz) at each location (P), the threshold Is
Δz _S = (k _max −k _min ) / 8D ²
Where k _min denotes the minimum local curvature at each location (P) of the zone (3), and k _max denotes the maximum local curvature at each location (P) in the zone (3). , D ² = 2500 mm ² , preferably D ² = 900 mm ² , in particular D ² = 100 mm ² .   2. The optical element according to claim 1, wherein the optical surface (2) continuously joins the area (3) adjacent to the optical surface (2). 3.   The optical element according to claim 1 or 2, wherein the optical surface (2) has a roughness (R) of less than 1 nm rms in a spatial wavelength region of 1 mm to a maximum range (L) of the optical surface (2). An optical element.   The optical element according to any one of claims 1 to 3, wherein the section (3) extends outward from the optical surface (2) by a distance (d) of 50 mm or less.   5. Optical element (10) according to claim 1, wherein at least the optical surface (2) has a reflective coating, in particular a coating (11) that reflects EUV radiation (13). element. A method of polishing an optical surface (2) with a polishing tool (6),
By moving the polishing surface (7) of the polishing tool (6) across the optical surface (2) embodied as a free-form surface and the area (3) adjacent to the side of the optical surface (2), Polishing the optical surface (2), wherein the shape of the area (3) is such that the threshold (Δz _S ) of the polishing criterion (Δz) is not exceeded at each location (P) of the area (3). The polishing tool (6) is adapted in particular to the shape of the polishing surface (7) of the polishing tool (6), the polishing reference (Δz) being the zone (3) adjacent to the optical surface (2). Represents a measure of the polishing error in the optical surface (2) made by moving the polishing tool (6) over
Method.   7. The method according to claim 6, wherein the polishing surface (7) of the polishing tool (6) rotates in relation to a rotation axis (8) during movement over the optical surface (2) and the zone (3). How to do.   The method according to claim 6 or 7, wherein local astigmatism (Δz) at each location (P) of the zone (3) is selected as a polishing criterion. The method according to claim 8, wherein the local astigmatism Δz at each location (P) of the section (3) is
Δz = (k _max −k _min ) / 8D ²
Where D indicates the diameter of the polishing surface (7) of the polishing tool (6), _kmin indicates the minimum local curvature at each location (P) of the zone (3), and k _max Is a method of indicating the maximum local curvature at each location (P) of the zone (3).   The method according to any one of claims 6 to 9, wherein the polishing surface (7) of the polishing tool (6) forms a flat surface.   11. The method according to any one of claims 6 to 10, wherein the shape of the optical surface (2) and the shape of the side adjacent area (3) are the same as the optical surface (2) and the side adjacent. A method for obtaining based on an analytical expression of both faces (z (x, y)) of the zone (3). The method as claimed in claim 11, in determining the shape of the optical surface (2), taking into account the threshold (Delta] z _S) of said lateral said polishing criterion adjacent zone (3) (Delta] z) .   11. The method according to any one of claims 6 to 10, wherein the shape of the area (3) is determined without using an analytical expression of the surface of the area (3). 14. The method according to any one of claims 6 to 13, wherein in the step before the polishing step,
Method further comprising machining the substrate (1) to produce the optical surface (2) and the laterally adjacent area (3) to be polished.   15. A method according to claim 14, wherein an optical surface (2) having a surrogate shape is produced during machining and polishing of the substrate (1), the surrogate shape being a target shape of the optical surface (2). And the target shape of the optical surface (2) is made from the substitute shape in a correction process after the polishing. 16. The method according to any one of claims 6 to 15, wherein the threshold (Δz _S ) of the polishing reference (Δz) is set so that the polishing error at the optical surface (2) is at least one subsequent. How to choose to be correctable in the correction process.   The method of claim 16, wherein the subsequent correction process is selected from the group comprising ion beam machining and magnetoviscous polishing.

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