Interferometric measurement method
The method addresses interferometer errors in freeform surface characterization by calibrating interferometer errors through sequential positioning and tilt sensitivity determination, ensuring precise measurement of freeform optical surfaces.
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- CARL ZEISS SMT GMBH
- Filing Date
- 2025-11-24
- Publication Date
- 2026-06-04
Smart Images
Figure EP2025084021_04062026_PF_FP_ABST
Abstract
Description
[0001] P 60987 WO 24 November 2025
[0002] - 1 - Mu / EW
[0003] Interferometric measurement method
[0004] The following disclosure is based on the German patent application with file number 102024 135 315.5, which was filed on November 28, 2024. The disclosure content of this patent application is made clear by reference to the content of the present application.
[0005] SCOPE OF APPLICATION AND STATE OF THE ART
[0006] The invention relates to methods for the interferometric determination of the shape of an optical surface of a test specimen designed as a freeform surface.
[0007] A general application of interferometric measurement methods of the type considered here is the high-precision interferometric measurement of the shape of optical surfaces and optically transparent objects. A specific application is ultra-high-precision interferometric measurement, as used, for example, in the production of lithographic projection optics. This involves measurement uncertainties of less than 1 / 100 of the visible wavelength.
[0008] In interferometric surface measurement, a test wave reflected from the surface under investigation is generally superimposed on a reference wave, and the resulting interference pattern is recorded. This allows the actual surface shape, as measured, to be compared interferometrically with a desired target shape for inspection purposes. Deviations are quantified based on interferograms to determine whether manufacturing tolerances are met or exceeded. The interferograms are captured with a measuring camera and further processed for evaluation.
[0009] Historically, the deviation of an optical surface of a test specimen from its nominal shape is also referred to in this application as a fit defect or "fit." Therefore, such procedures are often also called fit measurement or fit testing. One goal of a fit measurement is to characterize the fit, i.e., a test specimen defect, as accurately as possible.
[0010] To obtain meaningful measurement results, interferometric measurements must be metrologically traceable. For this purpose, measuring devices are calibrated either on a case-by-case basis or at predetermined intervals. In metrology, calibration is a process for determining and documenting the deviation of a measuring instrument or standard from another instrument or standard, which in this case is referred to as a standard. Calibration typically includes a second step: taking the determined deviation into account when subsequently using the measuring instrument to correct the readings.
[0011] A fundamental problem is that the setup of an interferometer in practice is not ideal, but rather exhibits deviations from an ideal setup. This can occur, for example, because the optical components within it deviate from the perfect surface shape and / or are not perfectly aligned. This can lead, for instance, to errors in the reference wave because its wavefront does not correspond closely enough to the specified target wavefront. Such errors are introduced into the measurement results as interferometer errors and can lead to an inaccurate characterization of the surface shape of the measured optical surface. Therefore, one task on the path to sufficiently error-free test results is to reliably separate errors in the test specimen from errors in the test setup.
[0012] In some cases, a rotation averaging method is used to separate the errors of the device under test (DUT) from the errors of the interferometer. In this method, the optical element under test (hereinafter also referred to as the "DUT") is rotated around a rotational axis in equidistant steps between individual measurements, and interferograms are recorded and evaluated at a number of different rotational positions. The rotation averaging method is able to assign "rotating" signatures to the DUT, while "non-rotating" errors are attributed to the test setup. This leads to a very good estimation of the absolute errors.
[0013] Freeform surface mirrors or freeform lenses are increasingly used in lithographic projection optics. For the purposes of this application, a freeform surface is a surface that cannot be described by a rotationally symmetric function. The deviation from a spherical surface or a rotationally symmetric aspherical surface lies outside the manufacturing tolerances.
[0014] In the interferometric testing of freeform surfaces, the rotational mediation method, which can be applied to rotationally symmetric aspheres, is not applicable due to the asymmetry of the test specimen or the surface being tested. Documents WO 2017 / 081328 A1 and DE 10 2006 057 606 B4 refer to interferometers suitable for measuring the surface of aspheres and freeform surfaces. The interferometer ("tilted wave interferometer") uses an ensemble of wavefronts tilted relative to each other to locally compensate for the deviation of the test specimen from the best-fitting sphere.
[0015] Document US 8 269 981 B1 describes an indirect method for calibrating so-called nano-freeform surfaces, where the freeform surface is a rotationally symmetric asphere and a standard is located within the dynamic range.
[0016] Document US 8 687 203 B2 describes a method for measuring freeform surfaces by absolute calibration of the optical surface in an interferometer using variable illumination directions.
[0017] Document DE 10 2012 217 800 A1 describes an indirect calibration method for measuring freeform surfaces, which describes the calibration for the asymmetric test surface of rotation-averaging calibrations of numerous aspherical surfaces that are positioned in different positions relative to the test surface.
[0018] TASK AND SOLUTION
[0019] It is an object of the invention to provide a method for characterizing the surface shape of an optical surface of an optical element, which makes it possible to carry out a reliable test even when the surface to be tested is designed as a freeform surface and is therefore not rotationally symmetric.
[0020] To solve this problem, the invention provides a measuring method with the features of claim 1. Preferred embodiments are specified in the dependent claims. The wording of all claims is made clear by reference to the content of the description.
[0021] According to one formulation of the invention, a method for the interferometric determination of the shape of a freeform optical surface of a test specimen is provided using an interferometer. A freeform surface within the meaning of this application is a surface that cannot be described by a rotationally symmetric function. The deviation from a spherical surface or a rotationally symmetric aspherical surface lies outside the dynamic range of conventional interferometers. In particular, a freeform surface is understood to be a surface shape with a deviation from any rotationally symmetric asphere of at least 10 pm, in particular at least 100 pm or even at least 1000 pm. Preferably, the freeform surface further deviates from any sphere by at least 0.05 mm, in particular at least 0.1 mm, at least 1 mm or at least 5 mm.
[0022] In this method, the test specimen is arranged sequentially or successively in different measurement positions. These positions include a nominal position and a multitude of different, non-nominal measurement positions, each of which can be described by a change in position relative to the nominal position. In each measurement position, a test wave directed at the surface of the specimen, with a wavefront adapted to the desired surface shape, and a reference wave are generated. After reflection of the test wave from the surface of the specimen, the reference wave and the test wave are superimposed. An interferogram generated by this superposition is recorded, and phase information derived from the interferogram is then evaluated to determine the surface shape.
[0023] The "nominal position" serves as the reference position of the test specimen for all measurements. The nominal position can be chosen, for example, such that, in the case of a surface free of form defects, where the actual shape corresponds to the desired target shape, and with a fault-free interferometer, no interferogram fringes would be produced. In practice, the nominal position is set to a measurement position of the test specimen in which the deviation between the wavefront of the test wave and the shape of the surface is so small that an interferogram with a fringed pattern resolvable by the measuring camera is produced. Preferably, the nominal position of the test specimen is chosen in which the deviation between the wavefront of the test wave and the shape of the surface is minimized.In this case, well-evaluable stripe patterns are usually also available if the measurement position is changed to a practically useful extent starting from this nominal position, so that evaluable stripe patterns are also created at the non-nominal measurement positions.
[0024] The procedure includes a calibration operation to determine the interferometer's error. This calibration operation establishes the prerequisites for separating the test piece errors from the interferometer error. The interferometer error comprises a constant component, i.e., a component independent of the tilt angle, and a variable component, the return error, which depends on the tilt angle. The interferometer error can be understood as a two-dimensional function that describes the difference between the measured fit error and the ideal fit error. If the interferometer error were zero, the measurement would directly measure the ideal fit error or the ideal fit. In practical applications, however, the interferometer error also influences the measurement result. The better this component is known, the more precise the surface form measurement result.
[0025] Ideally, in interferometers of the type considered here, the light reflected from the reference surface and the light reflected from the surface under test take a common path back through the optics. This would ideally be the case if the surface under test were perfectly spherical and exactly concentric with the reference surface. Inaccuracies in the measurements resulting from failure to meet this condition are often referred to as retrace errors. When measuring freeform surfaces, there are systematically sometimes large deviations from this condition, so that the measurement results are influenced by retrace errors to a practically relevant degree. This is taken into account during the calibration process.
[0026] The procedure, or rather its calibration operation, comprises an initial set of measurements. In this initial set of measurements (in step A), the test specimen is successively positioned and measured in different non-nominal tilting positions. Each tilting position can be described by a change in position, specifically a tilt of the test specimen relative to its nominal position, about a tilting axis oriented transversely to the propagation direction of the test wave by a specific tilting angle. The tilting axis is essentially tangential to the surface, i.e., as close to or within the surface as possible. Therefore, to a first approximation, the change in position caused by tilting results in a tilting motion, but not, to any significant extent, in a lateral displacement of the measured surface relative to the incoming test wave.
[0027] The procedure, or rather its calibration operation, further includes (in step B)) the determination of an interferometer error tilt sensitivity based on the results of the first set of measurements. The interferometer error tilt sensitivity represents or describes the dependence of the interferometer error on a tilting of the test specimen, i.e., the functional relationship between these quantities. For this purpose, a corresponding return error caused by the tilting is determined for each position change, and the interferometer error tilt sensitivity is calculated based on these return errors. The interferometer tilt sensitivity can also be expressed based on an interferometer tilt model. This model describes the functional relationship between a change in the interferometer error as a function of a gradient or difference in slope between the test wave and the test specimen surface.The parameters of this model are optimized by minimizing the difference between error model predictions and return errors.
[0028] The procedure comprises (in step C) a second set of measurements, in which the test specimen is successively positioned and measured in different non-nominal shift measurement positions. Each shift measurement position can be described by a change in position in the form of a displacement of the test specimen relative to its nominal position in a direction perpendicular to the propagation direction of the test wave by a displacement distance. In contrast to a change in the measurement position by tilting, such a displacement results in the pass generally changing in measurements with the shifted measurement positions relative to each other.
[0029] In the following step D), the change in the interferometer error relative to the target position is subtracted from the shift measurements using the interferometer error-deviation model or the interferometer tilt sensitivity. The magnitude of the change relative to the target position is quantified as the lateral shear of the test surface deviation between the target and the shifted position, based on the results of the second set of measurements.
[0030] Step D) of the procedure further includes determining the surface form error based on shear (also referred to here as Passe shear). This can be done computationally by integrating the Passe shear or the Passe gradient. The term "integration" here encompasses both the mathematical operation of integration in the narrower sense and computational operations of numerical optimization that perform a calculation comparable to integration in its result—that is, a calculation that corresponds to the inverse of a derivative or differentiation.
[0031] Once the surface shape error is known, the previously unknown interferometer error can be calculated in step E) using the surface shape errors determined in step D).
[0032] Once this is determined, it is possible to separate the interferometer error from the test specimen error. The desired surface shape of the test specimen is then calculated by subtracting the target surface shape (according to the optical design) and the determined surface shape error (i.e., the pass), which indicates how the actual surface shape underlying the measurement deviates from the ideal target surface shape.
[0033] In practice, all measurements are usually carried out first, and then the measurement results are evaluated.
[0034] The following may be helpful for a further understanding of the claimed invention and its operation. In this method, phase information from interferometers is evaluated. From this, the fit of the measured surface is determined, i.e., the fit error compared to the target surface shape as defined by the optical design. The actual surface shape, i.e., the desired measurement result, then results from the target surface shape and the fit error or shape deviation.
[0035] The calibration process is based, among other things, on the assumption that the measured pass or form deviation of the test piece remains practically unchanged during the tilting movements between measurements of the first set of measurements. Therefore, changes in the phase information in the interferograms are attributable to changes in the interferometer error, i.e., to that part of the interferometer error that can change depending on the tilt angle.
[0036] A fundamental problem with interferometric measurements is how to eliminate the interferometer error from the measurement results, i.e., how to separate the test object error from the test system error (or interferometer error). This problem is essentially solved by determining, in a suitable manner, which fit (i.e., which fit error) is consistent with all measurements. Such a separation of test object error and test system error can be achieved for spherical surfaces, for example, using the classical rotary switching method, which, however, is not applicable here. In the claimed invention, this problem is addressed, among other things, by the measurements of the second set of measurements, in which the test object is measured in different shift measurement positions. When evaluating the results, it is then assumed that the same fit (i.e., which fit error) is obtained in a measurement before and a measurement after a shift.The same fit error exists, but shifted relative to each other by the corresponding positional change or displacement distance. After correcting the measurement with the interferometer tilt model, this information can then be used to separate the previously unknown shape of the surface to be measured from the also unknown interferometer error.
[0037] If the interferometer error is known after the calibration operation, further test specimens can be measured and the measurement results can be corrected by direct calibration on the initially measured freeform surface for the interferometer error; without incurring any further calibration effort.
[0038] According to a further development of the invention, the wavefront change caused by tilting or shifting the test specimen position is simulated by ray tracing, and the calculated contributions of at least one optical surface to the measured wavefronts are subtracted from the differences between the measurements in the nominal and non-nominal measurement positions.
[0039] According to a further embodiment of the invention, the displacement of rays on at least one optical surface due to the change in the test position between the target and non-target positions is calculated by ray tracing, and the contribution of these surfaces to the retrace error is determined. Furthermore, the determined contributions are used to ascertain the effect of displacement movements on the change in the interferometer error.
[0040] According to a further embodiment of the invention, the change in the interferometer error is determined from the difference between the local gradient of the target surface shape in the nominal and non-nominal test positions. The functional relationship is calculated separately for each camera pixel by fitting a low-order polynomial, in particular a linear or quadratic model, to describe the measured calibration data. Furthermore, the determined contributions are used to determine the effect of the shift movement on the change in the interferometer error.
[0041] According to a further embodiment of the invention, the change in the interferometer error is determined from the difference between the local gradient of the target surface shape in the nominal and non-nominal test positions. The functional relationship is calculated separately for each camera pixel by fitting a low-order polynomial, in particular a linear or quadratic model, to describe the measured calibration data. Furthermore, the determined contributions are used to determine the effect of the shift movement on the change in the interferometer error.
[0042] According to a further development, the desired shape of the test specimen is a freeform surface. In this context, a freeform surface is understood to be a surface that does not exhibit rotational symmetry. In particular, the freeform surface exhibits a deviation of at least 10 pm, in other embodiments of 100 µm, and in still other embodiments of 1000 pm from any rotationally symmetric surface at at least one point on the surface.
[0043] According to further training, in every measurement a gradient between the optical surface and the incident wavefront z fulfills the conditions
[0044] 3z / 3x<0.5N_x A / D_x and
[0045] 3z / 3y<0.5N_y A / D_y
[0046] Here, x and y denote the orthogonal axes tangential to the freeform surface, N_x and N_y the number of camera pixels, D_x and D_y the size of the measured area along each of these axes, and A the central wavelength of the electromagnetic radiation illumination. If these conditions are met, particularly well-suited interferograms can be generated.
[0047] According to a further embodiment of the invention, the inclination deviations between the inclination calibration measurements and the target position measurement are greater than 10 urad, in particular greater than 50 urad.
[0048] According to a further embodiment of the invention, the relative displacements between the passe-shear measurements and the target position measurement are less than 1% of the measured surface area D_x, D_y, in particular less than 0.1%.
[0049] According to a further embodiment of the invention, the longest calibrated spatial wavelength, i.e., the inverse of the spatial frequencies, is limited to less than 20 mm, and in other embodiments to less than 50 mm. In some embodiments, the longest calibrated spatial wavelength is more than 5 mm, and in others, more than 20 mm. According to a further embodiment, the deviation of the optical surface from the target freeform is measured within the calibrated spatial frequency range with an accuracy of better than 1 nm, and in other embodiments, with an absolute accuracy of better than 0.1 nm. This high level of accuracy is achieved by using the invention.
[0050] According to a further embodiment of the invention, the non-nominal measurement positions are tilted in two dimensions. The two-dimensional change in the inclination of the test specimen means that the normal of the non-nominally arranged optical test surface is altered by tilting it along two axes of inclination that do not coincide with the normal of the optical test surface in the nominal position. At least one measurement is performed along each tilting axis.
[0051] According to a further embodiment of the invention, the displacements of the non-nominal measurement positions are changed in two dimensions. The two-dimensional change of the test shaft displacement means a displacement of the test shaft in two axes perpendicular to the propagation direction of the test shaft. These displacement axes are not parallel to each other, and at least one measurement is performed along each displacement axis. In addition, in some embodiments, the inclination of the test shaft is adjusted so that the wavefront difference between the nominal and the non-nominal displacement position is minimized.
[0052] According to a further embodiment of the invention, the optical test surface is formed by an optical element for microlithography. In particular, this optical element functions as a component of a projection exposure tool for microlithography, for example as part of a projection lens or an illumination system within the optical system. According to a further embodiment of the invention, the optical element is designed as an EUV mirror.
[0053] According to a further embodiment of the invention, the matching optics forming the test wave comprise a diffractive optical element, in particular a CGH (computer-generated hologram). BRIEF DESCRIPTION OF THE DRAWINGS
[0054] Further advantages and aspects of the invention will become apparent from the claims and from the description of exemplary embodiments of the invention, which are explained below with reference to the figures.
[0055] Fig. 1 shows a schematic representation of an interferometric measuring arrangement that can be used in carrying out the procedure;
[0056] Fig. 2 shows the measuring arrangement of Fig. 1 with reflected rays that lead to a return error;
[0057] Fig. 3 schematically shows a tilting of the test specimen;
[0058] Fig. 4 schematically shows a displacement of the surface of the test specimen;
[0059] Fig. 5 shows a flowchart to illustrate the process steps of an exemplary embodiment.
[0060] DETAILED DESCRIPTION OF THE EXECUTION EXAMPLES
[0061] To facilitate understanding of various aspects of the procedure, Fig. 1 shows a schematic representation of an interferometric measurement setup (IF) that can be used in carrying out the procedure. Document US 8,269,981 B1 shows an example of an interferometer that can be used here.
[0062] A preferred application is the measurement of the surface shape of mirrors used in optical systems for EUV microlithography, i.e., microlithography that utilizes extreme ultraviolet (EUV) radiation. Such mirrors often exhibit freeform surfaces, meaning surface shapes that deviate significantly from rotationally symmetric spherical or aspherical surface shapes. In this example, the test specimen PR is a mirror from a projection lens for EUV microlithography with a freeform surface designed for reflecting EUV radiation.
[0063] The measuring arrangement IF in Fig. 1 is designed for the interferometric determination of the actual shape of an optical surface FFF of a test specimen PR. In particular, the measuring arrangement IF can be used to determine a deviation of the actual shape of the surface FFF from a nominal shape. Such a shape deviation of an optical surface of a test specimen from its nominal shape is, for historical reasons, also referred to in this application as a fit error or "fit." Therefore, such methods are often also called fit measurement or fit testing. One goal of a fit measurement is to characterize the fit, i.e., a test specimen defect, as accurately as possible. If the measured surface shape corresponds exactly to the surface shape specified by the optical design and the interferometer error is perfectly calibrated, the fit assumes a value of zero.
[0064] The measuring arrangement IF includes a light source LQ to provide a sufficiently coherent measurement radiation as an input wave EW. In the exemplary embodiment, the light source LQ comprises an optical waveguide with an exit surface. The optical waveguide is connected to a radiation source (not shown), e.g., a laser. For this purpose, a helium-neon laser with a wavelength of approximately 633 nm can be used, for example.
[0065] The measuring arrangement includes a wavefront-forming element, in this example a diffractive optical element CGH, for generating a test wave PW and a reference wave RW from the input wave EW, as well as a reflective optical element REF for reflecting the reference wave RW. The diffractive optical element is designed as a complexly coded computer-generated hologram (CGH) and contains diffractive structures that form several superimposed diffractive structural patterns arranged in a single plane. In other embodiments, for example, a different diffractive optical element or an optical freeform surface can be used as the wavefront-forming element.
[0066] One of the diffractive structural patterns is configured to generate the test wave PW with a wavefront at least partially adapted to the shape of the optical surface (freeform surface FFF). The other diffractive structural pattern generates the reference wave RW with a planar wavefront. The test wave PW can be generated, for example, in a first diffraction order of the first structural pattern, and the reference wave RW in a first diffraction order of the second structural pattern, at the diffractive structure.
[0067] Furthermore, the measuring arrangement IF includes a detection device with a beam splitter ST for extracting the combination of the reflected test wave PW and the reflected reference wave RW from the beam path of the input wave EW, and an interferometer camera K for capturing an interferogram generated by superimposing the (reflected) test wave PW with the (reflected) reference wave RW. The illumination radiation provided by the light source LQ emerges from the exit surface of the optical waveguide as an input wave EW with a spherical wavefront and propagates divergently along a propagation axis directed towards the diffractive optical element CGH. The input wave EW first passes through the beam splitter ST and then through the diffractive optical element CGH.
[0068] The diffractive optical element CGH generates, through transmission by diffraction at one of the superimposed diffractive structural patterns, the test wave PW directed at the surface FFF of the test specimen PR from the input wave EW. This test wave has a wavefront adapted to a target shape of the surface FFF. During this transformation, the wavefront is adjusted so that the test wave strikes the surface perpendicularly at every point in the target shape and is reflected back onto itself.
[0069] The test wave PW propagates towards the test specimen PR and, after being generated at the diffractive optical element CGH, next encounters the optical surface FFF of the test specimen PR. From the surface FFF, the test wave is reflected back to the diffractive optical element CGH and diffracted again upon passing through the diffractive structures. This results in a reverse transformation of the reflected test wave PR into an approximately spherical wave, whose wavefront exhibits deviations from a spherical wavefront due to deviations of the surface FFF of the test specimen from the target shape.
[0070] Furthermore, the diffractive optical element CGH generates the reference wave RW, directed towards the reflective optical element REF, from the input wave EW by diffraction at the other of the diffractive structural patterns. The reference wave RW has a propagation direction that differs from that of the test wave PW and a wavefront adapted to the surface shape of the reflective optical element REF.
[0071] After being generated at the diffractive optical element CGH, the reference wave RW next encounters the reflective optical element REF and is reflected back onto itself. No further optical elements are present in the beam path of either the reference wave RW or the test wave PW. The reflected reference wave RW then passes through the diffractive optical element CGH again and is diffracted once more. This diffraction process transforms the reflected reference wave RW back into a spherical wave.
[0072] The diffractive optical element CGH thus also serves to superimpose the reflected test wave PW with the reflected reference wave PW. Both waves converge as beams onto the beam splitter ST and are reflected by it towards the interferometer camera K. Both convergent beams pass through an eyepiece OK and finally strike a detection plane of the interferometer camera K. The interferometer camera K can, for example, be configured as a CCD sensor SENS and captures an interferogram generated by the interfering waves. An aperture BL can be positioned at the focus of the convergent beams as a spatial filter to reduce scattered radiation.
[0073] From the recorded interferogram or from the phase information contained therein, an evaluation unit of the measuring arrangement IF (not shown) determines the actual shape of the optical surface FFF of the test specimen PR.
[0074] Calibration operation
[0075] The following are examples of calibration operations used to determine an interferometer error (IF). err to determine the interferometer. The procedure steps are explained using various parameters and variables, which are defined below. The variables in bold are 2D functions; the rest are scalar quantities.
[0076] Definition of variables
[0077] M = measured phase (2D) a ± , a2, %i, %2 = Tilt angles and positions of the freeform surface (FFF) relative to the nominal position.
[0078] Passe(a) = unknown form deviation (surface form error) of the freeform surface
[0079] (FFF) relative to the nominal position measured at tilt angle a
[0080] IF err (a) = Unknown interferometer error when measuring the freeform surface (FFF) relative to the nominal position at tilt angle α
[0081] S a ,S x = Known wavefront sensitivity with respect to tilt angle α or displacement γ according to design, provided by ray tracing
[0082] A(%i) = Known function that describes a local tilt of the freeform surface, which is generated by a displacement by x-, provided by ray tracing.
[0083] During the calibration operation, the test specimen is successively positioned in different measuring positions. These measuring positions include a nominal position and several (in particular three or more) non-nominal measuring positions, which deviate from the nominal position in different ways and can each be described by a change in position relative to the nominal position.
[0084] The "nominal position" serves as the reference position of the test specimen for all measurements. In practice, the nominal position is preferably set to a measurement position of the test specimen in which the deviation between the wavefront of the test wave and the shape of the surface is so small that an interferogram with a fringe pattern that is easily resolvable by the measuring camera and has the largest possible fringe spacing is produced. This usually results in interferograms that are still readily evaluable even with small deviations from the nominal position.
[0085] In each of the measuring positions, an interferogram is generated by superimposing a test wave PW directed at the surface of the test object and a reference wave RW in the manner described above. This interferogram is then recorded and evaluated with regard to the phase information it contains.
[0086] The position changes are generated by tilting and displacement movements relative to the nominal position. The tilting movements can be described as rotations about a tilting axis TA (see Fig. 3), which runs essentially transversely to the propagation direction of the test wave and tangentially to the freeform surface, so that tilting does not result in any relevant parasitic displacement transverse to the surface. Thus, essentially the same surface area is always measured from slightly different directions. The shift movements can be described as rotations about a rotational axis RA (see Fig. 4), which passes through the center of a sphere BS that is best adapted to the freeform surface. Each rotation results in a displacement of the measured area transversely to the test wave. This means that slightly offset surface areas are measured in each case.
[0087] Exemplary implementation according to a simplified first scenario
[0088] The flowchart in Fig. 5 now describes a typical sequence of an exemplary calibration operation according to a first scenario. Compared to more realistic scenarios, this first scenario contains some simplifying assumptions, but it is well suited to illustrating the fundamental relationships.
[0089] One simplifying assumption is that the interferometer error IF is assumed to be err that changes in the test specimen position due to tilting do not affect the measured fit error, and that this also applies to the measured fit error. Thus, for all tilt angles a lt a2with a± A a2assuming that the following relationships hold: IFerr a- ) = IF err ( 2)
[0090] Passe^a ) = Passe(cr2) for any «1, «2
[0091] In a first set of measurements, the test specimen is successively moved into different non-nominal tilting measurement positions and measured to determine the interferometer's response to tilting of the freeform surface. This first set of measurements is labeled M1-TI in Fig. 5.
[0092] In step C-IFTS, an interferometer error tilt sensitivity is calculated. This represents the dependence of the interferometer error IF. errfrom a tilting of the test specimen or a functional relationship between tilting and interferometer error. For this purpose, a return error caused by the corresponding change in position is calculated for each tilting position. This results from the fact that the test wave is not completely reflected back into itself at the freeform surface, but that the reflected rays of the test wave (see dashed rays in Fig. 2, 3 or 4) take a different path through the interferometer system than the rays directed towards the test specimen. The measured phases M at the different tilting angles c, a2, etc. (where c indicates the angle in the target position) can be described as follows:
[0093] M al = Passe(c1) + IF err a) + a^S a
[0094] M al = Pass a2) + IF err (a2+ a2S a
[0095] This equation essentially states that the measured phase is affected by the fit error (passe) at the respective tilt angle, as well as by the interferometer error IF. err is influenced by the corresponding tilt angle. This approach further considers that the freeform surface, in principle, causes a wavefront deformation when tilted from its nominal position. This contribution of an ideal freeform surface can be determined by beam calculation models. The dependence of the wavefront change on a change in position is parameterized here by the parameter S, i.e., by a wavefront sensitivity S. a with respect to tilt angle α or with respect to a displacement γ according to the design. According to this simplified first scenario, the interferometer error should not depend on the tilt angle, so the interferometer error tilt sensitivity takes on the value zero according to:
[0096] The procedure further includes the measurement of a so-called Passe shear in this application. This quantitatively describes the dependence of the measured phase on a displacement perpendicular to the propagation direction of the test wave (see Fig. 4).
[0097] For this purpose, a second set of measurements is carried out according to step M2-SH in Fig. 5, in which the test specimen is successively positioned and measured in different non-nominal shift measurement positions. The shift measurement positions can each be described by a change in position in the form of a displacement of the test specimen relative to the nominal position in a direction perpendicular to the propagation direction of the test wave by a displacement distance x. The phases M measured for different displacements x x1 , M x2 can be described as follows:
[0098] M xl = Passe(x^ + IF err a(x ) + x S x
[0099] M X2= Passe(x2) + ^err( ff (^2)) + X 2 x
[0100] Based on the measurements of the second set, the Passe shear can be calculated according to step C-PSS in Fig. 5. This can be described as the gradient of the Passe in the corresponding displacement direction, as long as the displacements remain small. The Passe shear or Passe gradient can be described as follows:
[0101] It should be noted here that the interferometer error IF err is unknown. The value is also not needed here because, in the simplifying first scenario, it is assumed that it is the same for all measurements.
[0102] After step C-PSS, which determines the fit shear, information about the underlying fit is now indirectly available. In step C-PS according to Fig. 5, the fit responsible for the fit shear, or the fit error, is calculated by integrating the fit shear according to:
[0103] Now all the values needed to calculate the interferometer error (IF) are available. err before, which in step C-IFERR can be expressed in equation form as follows:
[0104] IFerr = M X1 — Passe(x ) — X^S x
[0105] After completing this sequence of steps, the previously unknown interferometer error IF is thus determined. err This is known. It is now possible to calculate the proportion of the interferometer error from a measurement result that is influenced by both the interferometer error and the test object error, so that a more reliable statement can be made about the test object error.
[0106] Using the now known interferometer error, the freeform surface of another test specimen can be measured with the now calibrated interferometer, and the interferometer error determined through calibration can be taken into account. The following then applies to the measured phase:
[0107] The new passe Passe_new (i.e., the passe of the test specimen measured in the new measurement) can then be determined by including the interferometer error IF, which is now known from the calibration operation. err as described below:
[0108] If this fit is known, the actual surface shape of the freeform surface results from the target shape specified according to the design and the fit error (fit).
[0109] Example implementation according to a more realistic second scenario
[0110] A second, significantly more realistic scenario differs from the first in that it now assumes the interferometer error is a function of the tilt angle of the measured surface. In other words, this takes into account that the return error changes depending on the tilt angle, which is also intuitively plausible. Just as in the first scenario, it is assumed that the measured pass does not depend on the tilt angle.
[0111] The second scenario differs from the first in that the interferometer error is a variable quantity dependent on the tilt angle and has a non-zero value. Therefore, the following relationship results for step C-IFTS, as shown in Fig. 5:
[0112] The measurement operations in the second scenario remain unchanged, including measurements with different displacement positions. However, the following equation now applies to the Passe shear calculated in step C-PSS:
[0113] It should be noted again that the absolute values of the interferometer error IF err These values are unknown. However, they are not needed, as it is only necessary to know how the interferometer error changes with positional changes. In this more realistic scenario, the function A(x-]) expresses the extent to which a local displacement of the freeform surface affects the local tilt position.
[0114] The subsequent steps of calculating the passe from the passe shear (steps C-PSS and C-IFERR in Fig. 5) then proceed analogously to the simplified first scenario, so that: and
[0115] IF err = M xl— Passe(x ) — XiS x Using the now known interferometer error, the freeform surface of another test object can now be measured with the now calibrated interferometer, analogous to the first scenario, and the interferometer error determined through calibration can be taken into account.
[0116] Iterative calibration operation according to the third scenario
[0117] A third scenario, even more realistic than the second, assumes that both the interferometer error and the measured pass change depending on the tilt angle. In practice, this often manifests itself in the fact that a single calibration run of the aforementioned measurement and evaluation steps does not yet yield sufficiently precise values for the interferometer error. In such cases, an iterative calibration operation is performed, with the first iteration corresponding to the sequence of steps in the second scenario.
[0118] In the subsequent iteration, the Passe distortion, which results from a tilt corresponding to the difference of two tilt angles, is subtracted from the previous result.
[0119] This effectively corrects certain errors in the model's assumptions. The distortion of pass P due to the tilt angle and displacement difference is addressed through ray tracing.
[0120] Further refinements towards even more realistic scenarios can be implemented by, for example, taking into account that the interferometer error can vary from measurement to measurement or from test object to test object, i.e., it is a time-dependent quantity. The interferometer error depends, among other things, on different settings in the interferometer, such as the level of incoherence of the light source, the adjustment settings of the interferometer's optical components, the brightness of the light source, and other factors. Such influences can be taken into account, for example, by measuring a test object with a known pass using the interferometer, so that the interferometer is calibrated against a previously created "normal" with a known pass.
Claims
Patent claims 1. Method for interferometric determination of the shape of an optical surface of a test object designed as a freeform surface by means of an interferometer, wherein: the test object is successively arranged in different measuring positions, the measuring positions comprising a nominal position and a plurality of non-nominal measuring positions deviating from it, each of which can be described by a change in position relative to the nominal position;In each of the measuring positions, a test wave directed at the surface of the test specimen with a wavefront adapted to the target shape of the surface and a reference wave are generated; the reference wave and the test wave are superimposed after reflection of the test wave at the surface of the test specimen; an interferogram generated by the superposition is recorded and phase information derived from the interferogram is evaluated to determine the shape of the surface; characterized by a calibration operation to determine an interferometer error of the interferometer, wherein the calibration operation comprises the following steps:; A) a first set of measurements, wherein the test specimen is successively arranged and measured in different non-nominal tilting measurement positions, the tilting measurement positions being describable by a change in position in the form of a tilting of the test specimen relative to the nominal position about a tilting axis perpendicular to a propagation direction of the test wave and tangential to the surface by a tilting angle; B) Determining an interferometer error tilt sensitivity based on the results of the first set of measurements, wherein the interferometer error tilt sensitivity represents a dependence of the interferometer error on a tilting of the test specimen, wherein for each of the position changes a return error caused by the position changes and using the return errors the interferometer error tilt sensitivity is determined, C) a second set of measurements, wherein the test specimen is successively arranged and measured in different non-nominal shift measurement positions, the shift measurement positions being describable by a change in position in the form of a displacement of the test specimen relative to the nominal position in a direction perpendicular to the propagation direction of the test wave by a displacement distance; D) Determining a Passe shear using the results of the second set of measurements, wherein measured values of the second set are corrected by subtracting the interferometer error tilt sensitivity for each of the shift measurement positions, wherein the Passe shear describes the change of a surface form error as a function of the displacement distance; E) Determining the Passe based on the Passe shear by integrating the Passe gradient; F) Determining the interferometer error using the passes determined in step D).
2. The method of claim 1, wherein the deviation of the interferometer error determined from the first series of measurements is used to correct the second series of measurements before the surface error is calculated.
3. Method according to one of the preceding claims, wherein all measurements are first carried out and then the measurement results are evaluated.
4. A method according to any of the preceding claims, wherein in step A) the position changes between different tilting measurement positions are brought about by rolling the test specimen and / or wherein in step A) the tilting movement is 2-dimensional and / or wherein in step C) the displacement is a 2-dimensional rolling movement.
5. Method according to one of the preceding claims, wherein the calibration of the interferometer error is carried out directly using a freeform surface with unknown surface shape error, wherein preferably the freeform surface used for calibration deviates from the target shape by less than 1 nm.
6. Method according to one of the preceding claims, wherein, in each measurement, a gradient between the optical surface and the incident wavefront z defines the conditions 3z / 3x<0.5N_x A / D_x and 3z / 3y<0.5N_y A / D_y is satisfied, where x and y denote the orthogonal axes tangential to the freeform surface, N_x and N_y the number of camera pixels, and D_x, D_y the size of the measured Area along each of these axes and A is the central wavelength of the illumination of the electromagnetic radiation.
7. Method according to any of the preceding claims, wherein ray tracing is used for: the calculation of the wavefront sensitivities for displacement and tilt of the measured freeform surface (S_x,S_a); the calculation of the pixel coordinate distortion for tilted or shifted measurement surfaces (P(a_0 )-> P(a_1 )); the calculation of the angle of incidence changes due to the tilt and displacement of the test surface (A(a)).
8. Method according to any of the preceding claims, wherein the tilt measurement positions are set by tilting in two dimensions and / or wherein the shift measurement positions are set by displacement in two dimensions.
9. Method according to one of the preceding claims, wherein the wavefront change caused by tilting or shifting the test specimen position is simulated by ray tracing, and the calculated contributions of at least one optical surface to the measured wavefronts are subtracted from the differences between the measurements in the nominal position and the non-nominal measurement position.
10. Method according to one of the preceding claims, wherein the optical surface of the test specimen, designed as a freeform surface, is a freeform surface which has a deviation of at least 100 pm, preferably at least 1000 pm, from any rotationally symmetric surface at at least one point of the surface.
11. Method according to one of the preceding claims, wherein the optical surface designed as a freeform surface is formed on a test specimen in the form of an optical element of an optical system, in particular a projection lens or an illumination system, of a projection exposure system for microlithography, in particular as a mirror surface of an EUV mirror.
12. Method according to one of the preceding claims, wherein a deviation of the optical surface from the nominal shape is achieved with an absolute accuracy of better than 1nm, in particular with an absolute accuracy of better than 0.1 nm, within the calibrated spatial frequency range.
13. Method for manufacturing an optical element using the method according to any one of claims 1 to 12 for measuring the deviation of a surface of the optical element from the nominal shape and for adjusting the shape of the optical surface to eliminate the measured deviation.
14. Method according to claim 13, wherein the method for measuring the deviation of the optical surface from the nominal shape is measured with an accuracy of better than 1 nm.
15. Method according to claim 13 or 14, wherein the measured optical surface is a lens surface or a reflecting surface of a mirror and / or wherein the calibration surface and the optical surface to be measured are each a freeform surface and / or wherein the optical element is designed for use in a microlithography projection exposure device and / or wherein the optical element is designed for an operating wavelength of less than 30 nm, in particular less than 15 nm.