CN116075682A - Method for determining a wavefront generated by a diffractive optical element - Google Patents
Method for determining a wavefront generated by a diffractive optical element Download PDFInfo
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- CN116075682A CN116075682A CN202180058762.5A CN202180058762A CN116075682A CN 116075682 A CN116075682 A CN 116075682A CN 202180058762 A CN202180058762 A CN 202180058762A CN 116075682 A CN116075682 A CN 116075682A
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- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B9/00—Measuring instruments characterised by the use of optical techniques
- G01B9/02—Interferometers
- G01B9/02034—Interferometers characterised by particularly shaped beams or wavefronts
- G01B9/02038—Shaping the wavefront, e.g. generating a spherical wavefront
- G01B9/02039—Shaping the wavefront, e.g. generating a spherical wavefront by matching the wavefront with a particular object surface shape
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Abstract
A method for determining a wavefront (54) generated by a diffractive optical element (24) comprises the steps of: providing an n-dimensional non-periodic pattern (58) representing a diffractive structure (34) disposed on the diffractive optical element, wherein n has a value of 1 or 2; and determining by calculation the wavefront (54) produced by the diffractive optical element while taking into account the n-dimensional non-periodic pattern, wherein in the course of the calculation the n-dimensional non-periodic pattern (58) is embedded in a higher-dimensional representation, the diffractive structure being represented by the periodic pattern (64) in the higher-dimensional representation.
Description
The present application claims priority from german patent application 10 2020 209580.9, filed on 7/30/2020. The entire contents of this patent application are incorporated by reference into this application.
Technical Field
The present invention relates to a method for determining a wavefront generated by a diffractive optical element, and to a method and a measuring device for interferometry of the surface shape of a test object.
Background
Interferometry devices and methods in which a diffractive optical element generates test and reference waves from an input wave are known for high-precision interferometry of optical surfaces, which can range down to sub-nanometer levels. The diffractive optical element allows the wavefront of the test wave to be adapted to the target surface of the test object such that the wavefront is incident on each location of the target shape in a substantially perpendicular manner and reflected back from that location to itself. Next, with the aid of an interference pattern formed by superimposing the reflected test wave on the reference wave, a deviation from the target shape can be determined.
US2018/0106591A1 describes an embodiment of such an interferometry device in which a complex coded Computer Generated Hologram (CGH) is used as a diffractive optical element. In addition to the test wave directed at the surface to be measured and the reference wave passing through the reference arm, the CGH also generates a plurality of calibration waves from the input wave.
It is necessary to know the wavefront of the test wave generated by the diffractive optical element very accurately to determine the surface shape of the test object accurately. To this end, in the prior art, FEM ("finite element method") programs to solve Maxwell's equations in the real domain can be used. FEM allows a very accurate calculation of the local electromagnetic field.
However, for interferometry methods, the results must be available in the fourier domain, i.e. there is an interest in decomposing the electromagnetic field into plane waves describing the direction to the test surface or to the reference surface. Therefore, FEM calculations must be performed over a very large area in order to be able to calculate the fourier representation of the electromagnetic field with the required accuracy. The structures on the surface of the CGH must be scanned very accurately. The resulting grid and the resulting memory requirements are enormous. Therefore, such FEM calculation requires a supercomputer and takes several days. Therefore, FEM programs are not feasible in real domain (real domain).
Disclosure of Invention
Aims to solve
The object of the present invention is to provide a method and a measuring device of the initially mentioned type which solve the above-mentioned problems and in particular to determine the wavefront generated by the diffractive optical element with high accuracy and at the same time with a reasonable computational complexity and thus in a relatively short time.
Solution according to the invention
According to the invention, the above object is for example achieved with a method for determining a wavefront generated by a diffractive optical element, the method comprising the steps of: providing an n-dimensional non-periodic pattern representing a diffractive structure disposed on a diffractive optical element, wherein n has a value of 1 or 2; and determining the wavefront generated by the diffractive optical element by calculation while taking into account the n-dimensional non-periodic pattern, wherein in the calculation of the determined wavefront the n-dimensional non-periodic pattern is embedded in a higher-dimensional representation (higher-dimensional representation) from which the diffractive structure is represented by the periodic pattern.
For n=2, the non-periodic pattern is a two-dimensional non-periodic pattern, i.e. the pattern is non-periodic in both dimensions. The higher dimensional representation is understood to mean a representation of at least the (n+1) dimension. The once-encoded diffraction pattern is periodic and therefore cannot be assigned an aperiodic n-dimensional representation. In contrast, double-encoded diffraction patterns are also typically periodic.
However, in case the diffraction pattern diffracts in only one direction, i.e. the diffraction occurs only in a plane, the diffraction pattern may also be non-periodic and thus may be specified in the above-mentioned non-periodic one-dimensional representation. The three or more times encoded diffraction pattern is in principle non-periodic and thus may be specified in the above-mentioned non-periodic two-dimensional representation.
According to the present invention, embedding the n-dimensional non-periodic pattern into a higher-dimensional representation, wherein the diffractive structure is represented by the periodic pattern, facilitates calculating the wavefront generated by the diffractive optical element with high accuracy while the computational complexity is substantially reduced, so that the time frame for determining the wavefront can be kept relatively short.
According to an embodiment, during computational determination of the wavefront, the pattern emerging from the higher-dimensional periodic representation is represented by a fourier series, and the n-dimensional non-periodic pattern is converted to a fourier representation by the expansion coefficients contained in the fourier series of the periodic pattern. The expansion coefficients are also called fourier coefficients. The expansion coefficients of the fourier series may be determined by a one-dimensional FFT algorithm, in particular by the "rank-1 lattice" algorithm known to those skilled in the art.
According to another embodiment, the wavefront generated by the diffractive optical element is determined by an algorithm based on a fourier representation of the n-dimensional non-periodic pattern and a topography (topograph) of the diffractive structure arranged on the diffractive optical element. The algorithm may be based on fourier modal methods, in particular the RCWA (rigorous coupled wave analysis) method known to those skilled in the art.
According to a further embodiment, the non-periodic pattern is two-dimensional and represents a diffraction pattern of at least 3 encodings. A multiply encoded diffraction pattern or a multiply encoded CGH is understood to represent a complex encoded phase grating or CGH having a plurality of different phase functions. In other words, the multiply encoded diffraction pattern comprises a plurality of diffraction structure patterns arranged overlapping each other; in the case of a 3-order encoded diffraction pattern, there are three diffraction structure patterns arranged one above the other. When an input wave is radiated onto the diffractive optical element, each different phase function is used to generate a separate wave. Typically, the individually generated waves have different propagation directions and may be configured to have different wavefronts.
According to another embodiment, the diffractive optical element is configured for use in a measurement apparatus for interferometry of the surface shape of the test object. According to an embodiment, the test object is an optical element of a microlithographic projection exposure apparatus, in particular of a projection lens of a microlithographic projection exposure apparatus.
According to another embodiment, the wavefront correction is determined by comparing a wavefront simulated based on the layout of the diffraction structure with a wavefront determined taking into account the topography of the diffraction structure. The layout of the diffraction structure is understood to mean a plan view of the pattern produced by the diffraction structure, i.e. the topography of the diffraction structure is not considered here.
In this case, the pattern may have a binary design, i.e. certain elements of the pattern cause a specific phase step, while the regions between these elements cause a different phase step or no phase step. The layout itself may have a two-dimensional design or a one-dimensional design. The wavefront correction described above takes into account the three-dimensional or rigorous effects of the diffractive structure. According to an embodiment, the wavefront modeled under two-dimensional consideration of the diffraction structure is a target wavefront corresponding to a target shape of the test object surface.
Furthermore, the invention provides a method for interferometrically measuring the surface shape of a test object, comprising the steps of: the method comprises radiating a test wave generated by a diffractive optical element onto a surface of a test object, determining a wavefront of the test wave by calculation by a method according to any of the embodiments or embodiment variants described above, and evaluating an interference pattern generated by the test wave after interaction with the test object surface, wherein the wavefront of the test wave determined by calculation is taken into account.
According to an embodiment of the method for interferometry, the test wave and the reference wave are simultaneously generated by radiating an input wave onto the diffractive optical element, the reference wave being superimposed on the test wave when the interferogram is generated. In the generation of the interferogram, the reference wave is superimposed on the test wave after the test wave interacts with the surface of the test object. Alternatively, the reference wave can be generated at a fizeau element. In particular, the surface of the test object is an optical surface, such as a mirror surface or a surface of a microlithography lens.
According to another embodiment, at least one calibration wave is additionally generated when the input wave is radiated onto the diffractive optical element.
According to a further embodiment, the test object is an optical element of a microlithographic projection exposure apparatus, in particular of a projection lens of the microlithographic projection exposure apparatus.
According to a further embodiment, the test object is an optical element for EUV microlithography. EUV microlithography is understood as meaning microlithography having an operating wavelength of less than 100nm, in particular an operating wavelength of about 13.5nm or about 6.8 nm.
Further, the present invention provides a method of producing a diffractive optical element comprising the steps of: determining a structural pattern of the diffraction structure of the diffractive optical element for generating the specific target wavefront based on a simulation calculation considering only the layout of the diffraction structure; and determining the wavefront generated by the optical element by calculation according to an embodiment or embodiment variant of the method described above for determining the wavefront generated by the diffractive optical element, wherein the topography of the diffractive structure arranged on the diffractive optical element is taken into account in the calculation of the determined wavefront. Furthermore, the method according to the invention comprises determining a correction of the structural pattern based on the wavefront difference between the actual wavefront and the target wavefront, to minimize the wavefront difference, and generating the diffractive optical element based on the corrected structural pattern.
According to an embodiment of the aforementioned method of manufacturing, the target wavefront corresponds to a target shape of an optical surface of the test object, and the diffractive optical element is configured for interferometry of the test object.
Furthermore, the present invention provides a measurement apparatus for interferometrically measuring a surface shape of a test object, the measurement apparatus comprising: a diffraction optical element for generating a test wave radiated to a surface of the test object; and a wavefront determining means configured to determine a wavefront of the test wave by calculation taking into account an n-dimensional non-periodic pattern representing a diffraction structure arranged on the diffractive optical element, wherein n has a value of 1 or 2, and in the process embed the n-dimensional non-periodic pattern into a higher-dimensional representation, wherein the diffraction structure is represented by the periodic pattern. Furthermore, the measuring device according to the invention comprises detection means for acquiring an interference pattern generated by the test wave after interaction with the surface of the test object.
By evaluating the interferogram, it is possible to determine the surface shape of the test object taking into account the wavefront of the test wave determined by the calculation; in particular, the measuring device comprises a suitably configured evaluation device.
Features indicated above in relation to the above-described embodiments, exemplary embodiments or embodiment variants, etc. of the interferometry method according to the invention can be applied correspondingly to the measuring device according to the invention and vice versa. These and other features of embodiments according to the invention are explained in the description of the drawings and in the claims. Each feature may be implemented alone or in combination as an embodiment of the invention. Furthermore, they may describe advantageous embodiments which are individually protectable and are only properly claimed during or after application.
Drawings
The above and further advantageous features of the invention are explained in the following detailed description of exemplary embodiments according to the invention with reference to the figures. In the figure:
FIG. 1 shows an exemplary embodiment of a measurement device for interferometrically determining the shape of an optical surface, comprising a diffractive optical element for generating a test wave for irradiation onto the surface, and an evaluation device configured to determine the shape of the surface based on the wavefront of the test wave determined by the calculation by the wavefront determining device;
FIG. 2 shows a schematic diagram illustrating the function of the wavefront determining device of FIG. 1;
FIG. 3 shows a cross-section of a plan view of an embodiment of a diffraction structure of the diffractive optical element in FIG. 1, representing a two-dimensional non-periodic pattern;
FIG. 4 shows a pixelated version of the cross-section of FIG. 3;
FIG. 5 shows the distribution of two one-dimensional aperiodic functions;
FIG. 6 shows a unit cell of a two-dimensional periodic function generated by embedding the function of FIG. 5;
fig. 7 shows a two-dimensional periodic function, based on the unit cell shown in fig. 6,
FIG. 8 shows the spectrum of the two-dimensional periodic function of FIG. 7; and
fig. 9 shows the spectra of two one-dimensional non-periodic functions.
Detailed Description
In the exemplary embodiments or embodiment variants described below, elements that are functionally or structurally similar to one another have identical or similar reference numerals as possible. Thus, for an understanding of the nature of individual elements of certain exemplary embodiments, reference should be made to the description of other exemplary embodiments or to the general description of the invention.
For ease of illustration, the Cartesian xyz coordinate system is labeled in the drawings, from which the positional relationship of the various components in the drawing are apparent. In fig. 1, the y-direction extends into the plane of the drawing perpendicular to the plane of the drawing, the x-direction extends to the right, and the z-direction extends upward.
FIG. 1 illustrates an exemplary embodiment of a measurement device 10 to determine the shape of an optical surface 12 of a test object 14 by interferometry. The measurement device 10 is particularly useful for determining deviations of the actual shape of the surface 12 from a target shape.
The test object 14 provided may be, for example, a mirror of a projection lens of a projection exposure apparatus for EUV microlithography, which has an aspherical surface for reflecting EUV radiation having a wavelength of less than 100nm, in particular a wavelength of about 13.5nm or about 6.8 nm. The aspherical surface of the mirror may have a free-form surface which deviates from each rotationally symmetrical aspherical surface by more than 5 μm and deviates from each spherical surface by at least 1mm.
The measuring device 10 comprises a light source 16 for providing sufficiently coherent measuring radiation as an input wave 18. In this exemplary embodiment, light source 16 includes an optical waveguide 20 having an exit surface 22. The optical waveguide 20 is connected to a radiation source (not shown in fig. 1), for example in the form of a laser. For example, a helium-neon laser with a wavelength of about 633nm may be provided for this purpose.
However, the illumination radiation may also have different wavelengths in the visible or invisible wavelength range of the electromagnetic radiation. The light source 16 with the light guide 20 constitutes only one example of a light source that may be used in the measuring device 10. In alternative constructions, an optical configuration with lens elements, mirror elements, etc. may be provided in addition to the optical waveguide 20 for providing a suitable input wave 18.
Illumination radiation provided by the light source 16 exits the exit surface 22 of the optical waveguide 20 in the form of an input wave 18 having a spherical wavefront and divergently propagates along a propagation axis 42 directed toward the diffractive optical element 24. In the process, the input wave 18 first passes through a beam splitter and then through a diffractive optical element 24. In an alternative configuration, a collimator may be provided between the beam splitter 38 and the diffractive optical element 24 for generating the input wave 18 with a planar wavefront.
The diffractive optical element 24 is used to generate a test wave 26, a reference wave 28, and three calibration waves 50, 52, and 53 from the input wave 18. To this end, the diffractive optical element 24 is constructed in the form of a complex coded CGH and comprises a diffractive structure 34, which is typically formed by at least two diffractive individual patterns arranged one above the other in a plane. In the case of two superimposed diffraction individual patterns, they may for example be formed by a first diffraction individual pattern in the form of a basic grating and a second diffraction individual pattern in the form of a supergrating.
Depending on the number k of diffraction individual patterns arranged in a superimposed manner, the resulting diffraction pattern is referred to as a k-th order encoded diffraction pattern. In the exemplary embodiment shown in fig. 1, the diffractive structure 34 is formed by a 5-order encoded diffraction pattern, i.e. the diffraction pattern consists of five diffractive individual patterns superimposed on each other.
The first of the diffracted individual patterns produces a test wave 26 whose wavefront 54 is at least partially modified into the target shape of the optical surface 12 as it propagates from the input wave 18. In other words, the first diffractive individual pattern is configured such that the target wavefront of the test wave 26 generated by the diffractive optical element 24 corresponds to, or at least approximates, the target shape of the optical surface 12. Thus, the wavefront of test wave 26 is tailored such that test wave 26 is incident on surface 12 in a perpendicular or near-perpendicular manner, has a target shape at each location thereof, and reflects back onto itself. As will be explained in detail below, the wavefront of test wave 26 incident on surface 12 is determined by calculation, wherein the wavefront determined by calculation is denoted by reference numeral 54a.
The test wave 26 propagates in the direction of the test object 14 and is incident on the optical surface 12 of the test object 14. Test wave 26 is reflected back by surface 12 to diffractive optical element 24 and is again diffracted as it passes through diffractive structure 34. In the process, the reflected test wave 26 is converted back into an approximately spherical wave, the wavefront of which has a corresponding deviation from the spherical wavefront due to the deviation of the surface 12 of the test object 14 from the target shape.
The second diffractive individual pattern of the diffractive structure 34 generates a reference wave 28 having a planar wavefront in transmission from the input wave. Furthermore, the measuring device 10 comprises a reflective optical element 30, which is embodied as a planar mirror and serves to reflect back a reference wave 28 having a planar wavefront. In another configuration, the reference wave 28 may have a spherical wavefront, and the reflective optical element may be configured as a spherical mirror. The reflected reference wave 28 passes through the diffractive optical element 24 again and is diffracted again. In the process, the reflected reference wave 28 is converted back into a spherical wave.
The measurement apparatus 10 also includes a capture device 36 having a beam splitter 38 for directing the combination of the reflected test wave 26 and the reflected reference wave 28 away from the beam path of the input wave 18, and an interferometer camera 40 for acquiring an interferogram produced by superimposing the reference wave 28 with the test wave 26. In the process, the measuring device 10 is in a so-called test mode, in which the three calibration waves 50, 52 and 53 are blocked from striking the respective calibration mirrors 70, 71 and 72 by the respective shutters 74, 75 and 76. Alternatively, the calibration mirrors 70, 71 and 72 may also be removed from the beam paths of the calibration waves 50, 52 and 53 in the test mode so that the calibration waves 50, 52 and 53 are not reflected back to the diffractive optical element 24.
Thus, the diffractive optical element 24 also serves to superimpose the reflected reference wave 28 on the reflected test wave 26. The two waves are incident on the beam splitter 38 as converging beams and are reflected thereby in the direction of the interferometer camera 40. The two converging light beams 44 pass through an eyepiece 46 and are ultimately incident on an acquisition region 48 of the interferometer camera 40. The interferometer camera 40 may be configured, for example, in the form of a CCD sensor and acquires an interference pattern 41 generated by the interference wave. Disposed in the focal point of the converging beam 44 may be a diaphragm (not shown in fig. 1) as a spatial filter for reducing scattered radiation.
The evaluation means 78 of the measuring device 10 determine the actual shape of the optical surface 12 of the test object 14 from the acquired interferograms 41 or from a plurality of such interferograms 41. In the process, the evaluation device 78 additionally considers the wavefront 54a of the test wave 26 determined by calculation, which is provided to the evaluation device 78 by the wavefront determining device 56. This relates to the wavefront of the test wave 26 after the test wave 26 is generated at the diffractive structure 34 of the diffractive optical element 24, i.e. the wavefront before the test wave 26 is incident on the optical surface 12.
In determining the surface shape, the evaluation device 78 takes into account, inter alia, the results of the calibration measurements of the diffraction element 24. Due to the calibration measurements described in more detail below, it is possible to take into account variations in the optical properties of the diffractive optical element 24, which variations are caused, for example, by temperature variations. This change affects the wavefront of the test wave 26 generated by the diffractive optical element 24. According to an embodiment, the evaluation means 78 uses the result of the calibration measurement to correct the wavefront 54a provided by the wavefront determining means 56. According to an alternative embodiment, the result of the calibration measurement is already taken into account by the wavefront determining means 56 when calculating the wavefront 54.
Alternatively or in addition to the evaluation device 78, the measuring device 10 can have a data memory or an interface to a network, in order to be able to determine the surface shape using the interferogram 41, wherein the interferogram 41 is stored or transmitted by an external evaluation unit via the network.
For performing calibration measurements, the measurement device 10 is operated in a calibration mode, in which the test object 14 is not arranged in the beam path of the test wave 26 or the beam path of the test wave 26 is blocked by a shutter. Shutters 74, 75 and 76 in the beam paths of calibration waves 50, 52 and 53 are opened and closed again in sequence, one at a time.
When the shutter 74 is open, the collimated wave 50 with a planar wavefront is reflected back to itself by the planar collimating mirror 70. Superposition of the reflected calibration wave 50 and the reflected reference wave 28 at the acquisition region 48 of the interferometer camera 40 produces a first calibration interferogram. When the shutter 75 is opened, the converging calibration wave 52 with the spherical wavefront is reflected back to itself by the convex spherical calibration mirror 71. Superposition of the reflected calibration wave 52 and the reflected reference wave 28 produces a second calibration interferogram on the acquisition region 48 of the interferometer camera 40. When the shutter 76 is open, the extended calibration wave 53 with a spherical wavefront is reflected back to itself by the concave spherical calibration mirror 72. Superposition of the reflected calibration wave 53 and the reflected reference wave 28 produces a third calibration interferogram on the acquisition region 48 of the interferometer camera 40. By evaluating the three calibration interferograms, the above-described change in the optical characteristics of the diffractive optical element 24 is determined as a result of the calibration measurement.
The wavefront determining device 56 determines the wavefront 54 from a one-or two-dimensional non-periodic pattern 58 and a topography 60 of the diffractive structure 34. Pattern 58 corresponds to the outline seen in the plan view of diffraction structure 34, or the diffraction pattern described above resulting from the diffractive individual patterns being arranged in a superimposed manner. The two-dimensional pattern 58 is non-periodic in both dimensions due to the superposition of the five diffracted individual patterns. The topography 60 of the diffractive structure 34 is understood to mean, inter alia, a function of the height distribution of the diffractive structure 34 as a two-dimensional area in which the pattern 58 extends.
The wavefront determining means 56 for computationally determining the wavefront 54 may be part of the measuring device 10. Alternatively, the measuring device 10 may also be provided as an external computing unit. In this case, the measuring device 10 has an interface for transmitting the wavefront to the evaluation device 78.
As illustrated in fig. 2 and described in detail below, the wavefront determining device 56 is configured to initially embed an aperiodic two-dimensional pattern 58 into a higher-dimensional representation (step S1), where the diffractive structure 34 is represented by a periodic pattern 64. In other words, the periodic pattern may be used for three-dimensional or higher-dimensional representations of the two-dimensional pattern 58. In particular, the pattern 58 is embedded in a higher-dimensional representation by a dimension converter module 62.
Further, the wavefront determining device 56 is configured to represent the periodic pattern 64 by a fourier series 66 (step S2). In particular, this procedure is implemented by the FFT module 65. Further, the wavefront determining device 56 is configured to convert the non-periodic pattern 58 into a fourier representation 68 of the non-periodic pattern by the expansion coefficients contained in the fourier series 66 (step S3). In particular, this procedure is implemented by the conversion module 67.
Furthermore, using an algorithm 69 based on the fourier representation 68 of the non-periodic pattern 58 and the topography 60 of the diffractive structure 34, the wavefront determining device 56 is configured to determine the wavefront 54 generated by the diffractive optical element 24. In particular, this procedure is realized by means of the modules provided for this purpose. For example, algorithm 69 may be based on the RCWA (rigorous coupled wave analysis) method known to those skilled in the art.
In summary, the wavefront determining device 56 is configured to perform the following steps:
step S1-embedding an aperiodic pattern into a higher dimensional representation, wherein the former is represented by a periodic pattern;
step S2, representing the periodic pattern through a Fourier series;
step S3, converting the aperiodic pattern into a Fourier representation through expansion coefficients contained in the Fourier series; and
step S4-determining the wavefront generated by the diffractive optical element from the fourier representation of the non-periodic pattern and the topography of the diffractive structure.
Taking into account the topography 60 of the diffractive structure 34, the determination of the wavefront 54 generated by the diffractive optical element 24 by the wavefront determining device 56 can be used to generate the diffractive optical element 24 as follows: first, based on a simulation calculation considering only the layout of the diffractive structure 34, a structure pattern 58 is determined for the diffractive structure 34 of the diffractive optical element 24 to be produced, which should be configured to produce a specific target wavefront. Thus, the wavefront generated by the diffractive optical element 24 is determined by a calculation based on the sequence of steps S1 to S4 described above, wherein the topography 60 of the diffractive structure 34 arranged on the diffractive optical element 24 is taken into account. Further, a correction of the structural pattern is determined based on the wavefront difference between the actual wavefront and the target wavefront to minimize the wavefront difference. Finally, the diffractive optical element 24 is generated based on the corrected structural pattern.
To perform the various steps, the wavefront determining device 56 may include the modules described above; alternatively, multiple steps or all steps may be performed in one module.
As explained above, the diffraction structure 34 according to fig. 1 is a 5-order encoded diffraction pattern, which consists of five diffraction individual patterns superimposed on each other. The non-periodic pattern 58 provided to the wavefront determining device 56 corresponds to a segment of the 5 th order encoded diffraction pattern or the entire n th order encoded diffraction pattern.
Fig. 3 shows an example of an aperiodic pattern 58 in the form of 10 mu m x 10 mu m sections of a 5-degree encoded diffraction pattern. In fig. 3, the white areas represent the air-filled areas of the diffractive optical element 24 implemented as a phase CGH, while the black areas correspond to areas with glass. As can be seen from this representation, in this embodiment, the non-periodic pattern 58 is a two-dimensional non-periodic pattern. Fig. 4 shows a pixelated version of the non-periodic pattern 58 of fig. 3 having a 250nm pixel size. This version resembles the true structure of an exemplary embodiment of the diffraction pattern produced by a mask writer (mask writer) having a beam cross-section of 250 nm.
In a general form, the two-dimensional non-periodic pattern 58 formed by a 5-th order encoded diffraction grating may be defined by up to 5 grating vectors and is generated, for example, by the following binarization rule:
wherein->
And->
(1)
To make matters clearer, a method for determining the fourier representation 68 of the non-periodic pattern 58, which is initially performed by the wavefront determining device 56 in the process of computationally determining the wavefront 54 of the test wave 26, will be explained below primarily based on the one-dimensional non-periodic pattern 58e and then extended to the two-dimensional non-periodic pattern 58 in fig. 3 or 4. For example, the one-dimensional non-periodic pattern 58e may be formed by twice encoding a diffraction pattern, wherein diffraction occurs only in-plane.
To explain the determination of the fourier representation 68 of the non-periodic pattern 58, the one-dimensional non-periodic pattern 58e is defined by the following binarization rule:
f(x)＝Θ(cos(2πx)+αcos(2πβx)) (2)
wherein the step function
It is evident that f (x) is non-periodic with respect to irrational number β, e.g
However, it is possible to determine the Fourier spectrum of this function by embedding it in a two-dimensional function (step S1)
q(x,y)＝Θ(cos(2πx)+αcos(2πy)) (4)
The function f (x) is obtained from q (x, y) by projection onto a line.
f(x)＝q(x,βx) (5)
The function q (x, y) =q (x+1, y) =q (x, y+1) is periodic along both the x-and y-coordinates, thus representing a periodic pattern 64 (see fig. 7). Thus, the function q (x, y) may be represented as a fourier series 66 (step S2).
And expansion coefficient
From the identity of equation (5), it follows that f (x) also has a Fourier representation, where
Expression (8) corresponds to the fourier representation 68 of the aforementioned non-periodic pattern 58. Expression (8) passes the expansion coefficient c of expression (7) contained in fourier series 66 nm To determine, refer to step S3.
In contrast to the periodic function, the spectrum of f (x) is defined on a non-equidistant grid. This will be more clear if the following fourier representation is used:
where k corresponds to an irrational number index.
The above techniques demonstrate how to calculate the fourier representation of the binarization function without introducing a length factor.
The method described above to calculate the fourier representation 68 of the one-dimensional non-periodic pattern 58e in the general representation forms specified under (2) and (3) is explained below based on a specific example. Consider in this example two functions, each representing one-dimensional non-periodic pattern 58e:
f 2 (x) ＝Θ(cos(2πx)+0.8cos(2x)) (11)
these are obtained by selecting α=0.8 and
or->
And is derived from equation (2). Fig. 5 shows the procedure for these two functions. The spectra of these two functions can be determined by embedding the functions into a two-dimensional periodic function
q(x,y)＝Θ(cos(2πx)+0.8cos(2πy)) (12)
Fig. 6 shows q (x, y) unit cells. Two functions f 1 (x) And f 2 (x) Is obtained by projecting q (x, y) onto a line in each case:
the lines depicted in fig. 7 illustrate these cases. Spectra of q (x, y)
Can be effectively determined by a Fast Fourier Transform (FFT) and is illustrated in fig. 8. f (f) 1 (x) And f 2 (x) From the fourier coefficients c, a fourier representation 68 of the spectral form of (c) nm As described in equation (9).
Table 1 below lists f 1 (x) The 13 strongest fourier coefficients of (c) and their respective indices k.
Table 1
FIG. 9 shows two functions f 1 (x) And f 2 (x) Is a spectrum of (a). Although the spectra look very different, they can all be constructed from the q (x, y) spectra by simple ordering, as shown above.
The present example exhibits the characteristics described below. First, the fourier coefficients do not depend on the choice of the grating vector β, but only on other parameters of the binarization rule. Typically, the diffractive optical element in the form of a CGH is defined using a fixed binarization rule, only the grating vector varies over the surface. Thus, the calculation of the spectrum is simplified to a one-time determination and a fast distribution of the spectrum of the embedding function q (x, y).
The spectra are dense. In other words, any direction k can be approximated as closely as possible to the desired one by the sum k=n+βm (see equation (9)). For example, for
k=pi can pass m=1004248 and n= -1420218 approximate to five digits accuracy,/for example>
The method for determining the fourier representation 68 of the non-periodic pattern, which was described above based on the one-dimensional non-periodic pattern 58e, is extended to the two-dimensional non-periodic pattern 58 shown in fig. 3 in the form of the diffraction structure 34 of the quintic encoded diffractive optical element 24, and the spectrum of the following function is calculated according to an embodiment:
wherein the method comprises the steps of
To this end, according to one embodiment, a periodic function is defined
Having an expansion coefficient
The volume integral is calculated over a unit cube.
From the equation
This corresponds to a projection onto a two-dimensional plane, the Fourier representation 68 appearing immediately in the form of the spectrum sought
As already described above with respect to one-dimensional non-periodic patterns,
is independent of the grating vector +.>
But merely the properties of other parameters of the binarization rule. Thus, if the binarization rule does not change on the diffraction surface, the Fourier integral in equation (19) need only be calculated once for each diffractive optical element 24.
Pixelation of the non-periodic pattern 58 according to fig. 3 shown in fig. 4 may be considered in a higher dimensional space by two additional dimensions.
Those skilled in the art will recognize that the above equations can be readily extended to twice, three times, four times, six times or more encoded diffractive optical element CGHs.
In an embodiment, the algorithm 69 implemented in step S4 for determining the wavefront 54 generated by the diffractive optical element 24 based on the fourier representation 68 and the topography 60 of the diffractive structure 34 is based on fourier modal methods, such as the RCWA (rigorous coupled wave analysis) method known to a person skilled in the art.
The fourier mode method for solving Maxwell's system of equations uses a grating vector (reciprocal grating vectors) for periodic structures
And (5) formulating. For this reason, in all these methods, the electromagnetic field coefficient +.>
And->
The dielectric constant ε (x, y) is approximated by its finite Fourier seriesIs that
Wherein the method comprises the steps of
By using these approximations, the Maxwell's system of equations becomes algebraic or ordinary differential equations in the z-coordinate, which can be solved by known methods.
Fourier mode methods fail in the case of aperiodic diffractive structures. According to an embodiment of the invention, a variation of the formula is specified that allows calculation of the Maxwell equation. For this purpose, the integral used to calculate the fourier coefficients from equation 25 is replaced by the following integral:
for periodic structures, both integrals provide the same result
For aperiodic CGH structures, a new aperiodic approximation of the field and dielectric constant can be obtained:
wherein the vector is
Are no longer defined on equidistant grids. The preceding paragraphs demonstrate how fourier coefficients are efficiently calculated. Using these coefficients and the reconstructed RCWA equation, maxwell can be approximated and solved as a conventional differential equationEquation (d).
The above description of exemplary embodiments, embodiments or embodiment variants is to be understood as being made by way of example. The disclosure thus embodied primarily enables one skilled in the art to understand the invention and its related advantages and secondarily encompasses variations and modifications of the structure and method which will be apparent to those skilled in the art. Accordingly, all such changes and modifications as well as equivalents thereof, so long as they come within the scope of the invention as defined in the appended claims, are intended to be within the scope of the claims.
List of reference numerals
10. Measuring device
12. Optical surface
14. Test object
16. Light source
18. Input wave
20. Optical waveguide
22. Exit surface
24. Diffraction optical element
26. Test wave
28. Reference wave
30. Reflective optical element
34. Diffraction structure
36. Capturing device
38. Beam splitter
40. Interferometer camera
41. Interference pattern
42. Propagation axis
44. Converging light beam
46. Eyepiece lens
48. Acquisition region
50. Plane calibration wave
52. Spherical calibration wave
53. Spherical calibration wave
54. Wavefront of test wave
54a by calculating the determined wavefront of the test wave
56. Wavefront determination device
58. Aperiodic pattern of diffractive structures
58e one-dimensional non-periodic pattern
60. Morphology of diffraction structure
62. Dimension converter module
64. Periodic patterns in higher dimensional representations
65 FFT module
66. Fourier series of periodic pattern
67. Conversion module
68. Fourier representation of non-periodic patterns
69. Algorithm
70. Plane alignment mirror
71. Spherical surface calibration reflecting mirror
72. Spherical surface calibration reflecting mirror
74. Shutter device
75. Shutter device
76. Shutter device
78. Evaluation device
Claims (14)
1. A method for determining a wavefront generated by a diffractive optical element, comprising the steps of:
providing an n-dimensional non-periodic pattern representing a diffractive structure disposed on the diffractive optical element, wherein n has a value of 1 or 2; and
the wavefront generated by the diffractive optical element is determined by a calculation while taking into account the n-dimensional non-periodic pattern, wherein the n-dimensional non-periodic pattern is embedded in a higher-dimensional representation in the course of the calculation to determine the wavefront, the diffractive structure being represented by the periodic pattern in the higher-dimensional representation.
2. The method of claim 1, wherein in computationally determining the wavefront, a pattern emerging from the higher-dimensional periodic representation is represented by a fourier series, and the n-dimensional non-periodic pattern is converted to a fourier representation by a plurality of expansion coefficients contained in the fourier series of the periodic pattern.
3. The method of claim 2, wherein the wavefront generated by the diffractive optical element is determined by an algorithm based on the fourier representation of the n-dimensional non-periodic pattern and a topography of the diffractive structure disposed on the diffractive optical element.
4. The method of any one of the preceding claims, wherein the non-periodic pattern is two-dimensional and represents a diffraction pattern encoded at least 3 times.
5. The method of any one of the preceding claims, wherein the diffractive optical element is configured for use in a measurement apparatus for interferometrically measuring the shape of a surface of a test object.
6. The method of any of claims 3 to 5, wherein a wavefront correction is determined by comparing a wavefront simulated based on a layout of the diffraction structure with the wavefront determined taking into account the topography of the diffraction structure.
7. A method for interferometrically measuring the shape of a surface of a test object, comprising the steps of:
radiating a test wave generated by a diffractive optical element onto a surface of the test object;
determining the wavefront of the test wave by calculation by a method according to any of the preceding claims; and
an interferogram is evaluated, which is generated by the test wave after interaction with the surface of the test object, wherein the wavefront of the test wave determined by calculation is taken into account.
8. The method of claim 7, wherein the test wave and the reference wave are generated simultaneously by radiating an input wave on the diffractive optical element, the reference wave being superimposed on the test wave when the interferogram is generated.
9. The method of claim 8, wherein at least one calibration wave is additionally generated when the input wave is radiated onto the diffractive optical element.
10. The method of any of claims 7 to 9, wherein the test object is an optical element of a microlithographic projection exposure apparatus.
11. The method of any of claims 7 to 10, wherein the test object is an optical element for EUV microlithography.
12. A method for producing a diffractive optical element, comprising the steps of:
determining a structural pattern of a diffraction structure of a diffractive optical element for generating a specific target wavefront, based on a simulation calculation considering only a layout of the diffraction structure;
determining by calculation a wavefront generated by the optical element of any one of claims 1 to 6, wherein the topography of the diffractive structure arranged on the diffractive optical element is taken into account in the calculation of the wavefront;
determining a correction of the structural pattern based on a wavefront difference between the actual wavefront and the target wavefront to minimize the wavefront difference; and
the diffractive optical element is generated based on the corrected structural pattern.
13. The method of claim 12, wherein the target wavefront corresponds to a target shape of an optical surface of a test object, the diffractive optical element configured for interferometry of the test object.
14. A measurement device for interferometrically measuring a shape of a surface of a test object, comprising:
a diffractive optical element for generating a test wave radiated on the surface of the test object;
a wavefront determining means configured to determine a wavefront of the test wave by calculation taking into account an n-dimensional non-periodic pattern representing a diffraction structure arranged on the diffractive optical element, where n has a value of 1 or 2, and in the process embed the n-dimensional non-periodic pattern into a higher-dimensional representation, where the diffraction structure is represented by a periodic pattern; and
and the detection device is used for acquiring an interference pattern generated by the test wave after the test wave interacts with the surface of the test object.
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| DE102020209580.9 | 2020-07-30 | ||
| DE102020209580.9A DE102020209580B3 (en) | 2020-07-30 | 2020-07-30 | Method for determining a wavefront generated by means of a diffractive optical element, method for producing a diffractive optical element and measuring device for interferometric shape measurement of a surface of a test object |
| PCT/EP2021/070631 WO2022023188A1 (en) | 2020-07-30 | 2021-07-23 | Method for determining a wavefront generated by means of a diffractive optical element |
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| DE (1) | DE102020209580B3 (en) |
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| DE102006035022A1 (en) | 2006-07-28 | 2008-01-31 | Carl Zeiss Smt Ag | Method for producing an optical component, interferometer arrangement and diffraction grating |
| DE102012217800A1 (en) | 2012-09-28 | 2014-04-03 | Carl Zeiss Smt Gmbh | Diffractive optical element and measuring method |
| DE102015202695A1 (en) | 2015-02-13 | 2016-08-18 | Carl Zeiss Smt Gmbh | Test device and method for testing a mirror |
| DE102015209490A1 (en) | 2015-05-22 | 2016-11-24 | Carl Zeiss Smt Gmbh | Interferometric measuring arrangement |
| DE102017217369A1 (en) | 2017-09-29 | 2019-04-04 | Carl Zeiss Smt Gmbh | Compensation optics for an interferometric measuring system |
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