Apparatus and method for determining angular reflectance profile - Patents.com

Abstract

The apparatus comprises a multi-layer structure configured to reflect electromagnetic radiation. The apparatus comprises a sensor configured to detect an angular distribution of the electromagnetic radiation after reflection from the multi-layer structure. The apparatus comprises a processor configured to generate a first function based at least in part on the angular distribution of the electromagnetic radiation detected by the sensor. The processor is configured to compare the first function to a plurality of known functions associated with the plurality of known angular reflectance profiles to identify a second function from the plurality of known functions that is closest to the first function. The processor is configured to determine an angular reflectance profile of the multi-layer structure based at least in part on the known angular reflectance profile associated with the second function.

Description

[Technical field]

[0001] [CROSS REFERENCE TO RELATED APPLICATIONS] This application claims priority to European Application 22167102.7, filed April 23, 2022, which is incorporated herein by reference in its entirety.

[0002] [Technical field] The present invention relates to characterizing the reflectance profile of multi-layer structures used to reflect electromagnetic radiation in optical devices. [Background technology]

[0003] A lithographic apparatus is a machine that is configured to apply a desired pattern onto a substrate. Lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). A lithographic apparatus may, for example, project a pattern in a patterning device (e.g. mask) onto a layer of radiation-sensitive material (resist) provided on the substrate.

[0004] To project a pattern onto a substrate, a lithographic apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features that can be formed on the substrate. Lithographic apparatus using extreme ultraviolet (EUV) radiation having a wavelength in the range of 4-20 nm (e.g., 6.7 nm or 13.5 nm) may be used to form smaller features on a substrate than lithographic apparatus using radiation having a wavelength of, for example, 193 nm. Summary of the Invention [Problem to be solved by the invention]

[0005] Multilayer structures are used to interact with electromagnetic radiation in various devices. For example, multilayer structures may be used as fiducial markers for sensing systems and / or to ensure that certain wavelengths or ranges of wavelengths of electromagnetic radiation are preferentially reflected in optical systems. Due to differences in materials and layer thicknesses, different multilayer structures have different reflectivity characteristics. The reflectivity of a multilayer structure may vary depending at least in part on the angle of incidence of electromagnetic radiation incident on the multilayer structure and then reflected by the multilayer structure. That is, a first angle of incidence may be associated with a greater reflectivity than a second angle of incidence. Thus, different multilayer structures may have different angular reflectivity profiles. When an angular distribution of electromagnetic radiation is reflected by a multilayer structure, the intensity profile of the reflected electromagnetic radiation may depend at least in part on the angular reflectivity profile of the multilayer structure. Thus, the angular reflectivity profile of the multilayer structure may affect the output of a system that uses the reflected electromagnetic radiation. For example, measurements performed by a sensing system to detect reflected electromagnetic radiation may be affected by the angular reflectivity profile of the multilayer structure. If the angular reflectance profile of the multi-layer structure is not taken into account, the accuracy of measurements performed by the sensing system may be adversely affected. It is therefore desirable to determine the angular reflectance profile of the multi-layer structure to facilitate understanding of the effect that the angular reflectance profile of the multi-layer structure has on reflected electromagnetic radiation.

[0006] In many known devices, the multi-layer structure is accompanied by other optical components that interact with the electromagnetic radiation. Such optical components may also affect the intensity profile of the electromagnetic radiation. It may be difficult to distinguish between the effect of the angular reflectivity profile of the multi-layer structure on the intensity profile of the electromagnetic radiation and the effect of other optical components on the intensity profile of the electromagnetic radiation. In many known devices, it is very difficult or practically impossible to accurately measure the angular reflectivity profile of the multi-layer structure separately. It would therefore be desirable to provide an apparatus and method for determining the angular reflectivity profile of a multi-layer structure to facilitate understanding of the effect of the angular reflectivity profile of the multi-layer structure on reflected electromagnetic radiation. [Means for solving the problem]

[0007] According to a first aspect of the present disclosure, there is provided an apparatus comprising a multi-layer structure configured to reflect electromagnetic radiation. The apparatus comprises a sensor configured to detect an angular distribution of the electromagnetic radiation after reflection from the multi-layer structure. The apparatus comprises a processor. The processor is configured to generate a first function based at least in part on the angular distribution of the electromagnetic radiation detected by the sensor. The processor is configured to compare the first function to a plurality of known functions associated with the plurality of known angular reflectance profiles to identify a second function from the plurality of known functions that is closest to the first function. The processor is configured to determine an angular reflectance profile of the multi-layer structure based at least in part on the known angular reflectance profile associated with the second function.

[0008] The apparatus of the first aspect advantageously allows a user to determine the angular reflectivity profile of the multi-layer structure through measurement of the angular distribution of electromagnetic radiation reflected by the multi-layer structure and comparison with known angular reflectivity profiles, and allows a user to understand the effect of the multi-layer structure on the intensity profile of the reflected electromagnetic radiation. This information may be used to improve processes performed using the reflected electromagnetic radiation (e.g., to correct measurements performed using the reflected electromagnetic radiation).

[0009] The sensor may output the intensity of the electromagnetic radiation as a function of the angle of incidence of the electromagnetic radiation, i.e. the sensor may output the intensity of the electromagnetic radiation as a function of position in a pupil plane of the device.

[0010] The pupil plane may be defined by the numerical aperture of the device. The pupil plane may be defined as the Fourier transform plane of a plane in which the sensor is located (which may be referred to as the image plane) and / or as the Fourier transform plane of a plane in which the multi-layer structure is located (which may be referred to as the object plane).

[0011] The apparatus may comprise an illumination system configured to condition the electromagnetic radiation to form an illumination field in which an angular distribution of the electromagnetic radiation rotates, and a sensor may be configured to detect the rotation of the angular distribution of the electromagnetic radiation through the illumination field after reflection from the multi-layer structure.

[0012] As the reflectance characteristics of the multilayer structure depend at least in part on the angle of incidence of the electromagnetic radiation and the angle of incidence of the electromagnetic radiation rotates through the illumination field, the detected angular reflectance profile of the multilayer structure also rotates through the illumination field. The inventors have found that different multilayer structures have angular reflectance profiles that behave differently when rotated through the illumination field. Thus, detecting the rotation of the angular distribution of the electromagnetic radiation through the illumination field provides useful information for determining the angular reflectance profile of the multilayer structure and distinguishing between different angular reflectance profiles of different multilayer structures.

[0013] The illumination system may comprise a curved reflective surface configured to condition the electromagnetic radiation to form an illumination field with a rotating angle of incidence of the electromagnetic radiation. The curved reflective surface may comprise a plurality of substantially flat reflective elements positioned at different angles to form the curved reflective surface.

[0014] The illumination field may be arc-shaped.

[0015] The apparatus may include a diffuser configured to interact with electromagnetic radiation such that the electromagnetic radiation substantially fills a numerical aperture of the apparatus.

[0016] The diffuser advantageously provides a substantially perfect measurement of the angular reflectance profile of the multilayer over the numerical aperture of the device. The diffuser advantageously avoids misleading results that can occur when other imperfect illumination modes are used.

[0017] The diffuser may form part of the multi-layer structure. The diffuser may comprise an optically rough surface formed adjacent (e.g., below) the multi-layer structure. The optically rough layer may comprise chrome.

[0018] The processor may be configured to generate the first function by mathematically decomposing an angular distribution of electromagnetic radiation detected by the sensor into a plurality of Zernike polynomial functions.

[0019] The inventors have found that Zernike polynomial functions are suitable for accurately describing the angular distribution of electromagnetic radiation detected by a sensor.

[0020] Mathematically decomposing generally involves expressing or representing a function as a combination of simpler component functions. In this example, the angular distribution of electromagnetic radiation detected by a sensor is represented as a combination of component Zernike polynomial functions.

[0021] Different angular distributions of electromagnetic radiation have different amounts or contributions to the Zernike polynomial functions.

[0022] Each of the plurality of known functions may comprise a plurality of Zernike polynomial functions.

[0023] The plurality of Zernike polynomial functions may not include rotationally symmetric Zernike polynomial functions.

[0024] Not including rotationally symmetric Zernike polynomial functions advantageously excludes rotationally static contributions (e.g. contributions from other optical components, such as an illumination system, present in the apparatus) that do not vary as the angular distribution of electromagnetic radiation rotates through the illumination field.

[0025] The processor may be configured to perform a fitting process to identify the second function from a plurality of known functions.

[0026] The processor may be configured to generate the plurality of known functions based at least in part on a plurality of known reflectance profiles associated with the plurality of known multi-layer structures.

[0027] The plurality of known functions may be formed from a plurality of Zernike polynomial functions.

[0028] The fitting process may comprise performing a least squares fit.

[0029] The fitting process may comprise fitting sine and / or cosine functions to determine the amplitudes of the Zernike polynomial functions.

[0030] According to a second aspect of the present disclosure, there is provided a lithographic apparatus comprising the apparatus of the first aspect. The lithographic apparatus comprises a support structure configured to support a patterning device capable of forming a pattern in a cross-section of the radiation beam to form a patterned radiation beam. The multi-layer structure forms part of a reference marker located on the patterning device or the support structure. The lithographic apparatus comprises a substrate table configured to hold a substrate. The sensor forms part of the substrate table. The lithographic apparatus comprises a projection system configured to project the patterned radiation beam onto the substrate. The lithographic apparatus comprises a measurement system comprising the reference marker and the sensor.

[0031] In known lithographic apparatus, the effect of the angular reflectance profile of the multi-layer structure on the measurement results performed by the measurement system is not taken into account, resulting in measurement errors (e.g., pupil measurement errors), i.e., the actual performance of the illumination system may be better than the known measurement system reports, which may lead to unnecessary actions such as replacing a fiducial marker (e.g., a support structure or a patterning device).

[0032] Determining the angular reflectivity profile of a multi-layer structure forming part of a lithographic apparatus advantageously provides greater insight into the performance of the lithographic apparatus and avoids unnecessary actions as previously described with respect to known lithographic apparatus.

[0033] The illumination system may be configured to condition the radiation beam. The processor may be configured to determine an angular reflectance profile of the illumination system at least in part dependent on the angular reflectance profile of the multi-layer structure.

[0034] Determining the angular reflectance profile of an illumination system of a lithographic apparatus advantageously provides useful information that can be used to improve the performance of the lithographic apparatus.

[0035] Determining the angular reflectance profile of the illumination system may involve a processing step that removes the effect of the angular reflectance profile of the multi-layer structure from the angular distribution of electromagnetic radiation detected by the sensor.

[0036] Non-telecentric imaging performed by the illumination system, in combination with other effects such as defocus errors, can lead to undesired shifts of patterned features on the substrate, leading to lithography errors such as overlay errors. Determining the angular reflectance profile of the illumination system advantageously reduces non-telecentric imaging and increases the accuracy of the lithographic apparatus.

[0037] The processor may be configured to perform a simulation of a proposed radiation beam propagating through the lithographic apparatus depending at least in part on the angular reflectance profile of the illumination system.

[0038] Taking into account the reflectance profile of the illumination system when performing a simulation of a proposed radiation beam propagating through a lithographic apparatus advantageously increases the accuracy of the simulation.

[0039] The illumination system may be configured to redistribute the electromagnetic radiation into an illumination mode, which may be a dipole illumination mode, a quadrupole illumination mode, etc. The proposed radiation beam may be adjusted to form the illumination mode.

[0040] The processor may be configured to determine an angular reflectance profile of the projection system depending at least in part on the angular reflectance profile of the multi-layer structure.

[0041] Determining the angular reflectance profile of the projection system of a lithographic apparatus advantageously provides useful information that can be used to improve the performance of the lithographic apparatus.

[0042] Determining the angular reflectance profile of the projection system may involve a processing step that removes the effect of the angular reflectance profile of the multi-layer structure from the angular distribution of electromagnetic radiation detected by the sensor.

[0043] According to a third aspect of the present disclosure, there is provided a method for determining an angular reflectance profile of a multi-layer structure. The method comprises reflecting electromagnetic radiation from the multi-layer structure. The method comprises detecting an angular distribution of the electromagnetic radiation after reflection from the multi-layer structure. The method comprises generating a first function based at least in part on the angular distribution of the electromagnetic radiation. The method comprises comparing the first function to a plurality of known functions associated with the plurality of known angular reflectance profiles to identify a second function from the plurality of known functions that is closest to the first function. The method comprises determining the angular reflectance profile of the multi-layer structure based at least in part on the known angular reflectance profile associated with the second function.

[0044] The method may comprise adjusting the electromagnetic radiation to form an illumination field in which an angular distribution of the electromagnetic radiation is rotated. Detecting the angular distribution of the electromagnetic radiation may comprise detecting a rotation of the angular distribution of the electromagnetic radiation through the illumination field after reflection from the multi-layer structure.

[0045] The method may comprise diffusing the electromagnetic radiation before reflection from the multi-layer structure such that the angular distribution of the electromagnetic radiation is substantially continuous.

[0046] Generating the first function may comprise mathematically decomposing the angular distribution of the electromagnetic radiation into a plurality of Zernike polynomial functions.

[0047] The plurality of Zernike polynomial functions may not include rotationally symmetric Zernike polynomial functions.

[0048] Comparing the first function to a plurality of known functions associated with a plurality of known angular reflectance profiles to identify a second function from the plurality of known functions that is closest to the first function may comprise performing a fitting process.

[0049] According to a fourth aspect of the present disclosure there is provided a method of projecting a patterned beam of radiation onto a substrate, the method comprising using the multi-layer structure of the third aspect to perform a measurement, the method comprising taking into account in said measurement an angular reflectance profile of the multi-layer structure determined using the method of the third aspect.

[0050] Adjusting the electromagnetic radiation may comprise using an illumination system. Considering the angular reflectance profile of the multi-layer structure may comprise determining an angular reflectance profile of the illumination system at least in part depending on the angular reflectance profile of the multi-layer structure.

[0051] The method may comprise performing a simulation of the proposed patterned beam of radiation depending at least in part on the angular reflectance profile of the illumination system.

[0052] Projecting the patterned beam of radiation onto the substrate may comprise using a projection system. Taking into account the angular reflectance profile of the multilayer structure may comprise determining an angular reflectance profile of the projection system in dependence at least in part on the angular reflectance profile of the multilayer structure.

[0053] According to a fifth aspect of the present disclosure there is provided a computer program comprising computer readable instructions arranged to cause a computer to carry out a method according to either the third or fourth aspect.

[0054] According to a fifth aspect of the present disclosure there is provided a computer readable medium storing a computer program according to the fifth aspect.

[0055] According to a sixth aspect of the present disclosure there is provided a computing device comprising a memory storing processor-readable instructions, the computing device comprising a processor arranged to read and execute instructions stored in said memory, the processor-readable instructions comprising instructions arranged to control a computer to perform a method according to either of the third or fourth aspects. [Brief description of the drawings]

[0056] Embodiments of the invention will now be described, by way of example only, with reference to the accompanying schematic drawings in which: FIG. 1 depicts a schematic diagram of a lithographic system comprising a radiation source and a lithographic apparatus comprising a multi-layer structure according to one aspect of the present disclosure. FIG. 2 shows a schematic of a portion of the lithographic apparatus of FIG. 1 including an apparatus for determining the angular reflectivity profile of a multi-layer structure according to one aspect of the present disclosure. FIG. 3 shows a schematic of the angular distribution of electromagnetic radiation reflected from a multilayer structure. FIG. 4 shows the angular distribution of the reflected electromagnetic radiation of FIG. 3 expressed in a pupil plane with angular coordinates. FIG. 5 shows the angular distribution of the electromagnetic radiation of FIG. 4 represented in the pupil plane on a unit circle. FIG. 6 illustrates a schematic of electromagnetic radiation formed within an illumination field according to one aspect of the present disclosure. 7A-E show five unit circle pupil plane representations of the angular distribution of electromagnetic radiation rotating through the illumination field of FIG. 6 according to one aspect of the present disclosure. FIG. 8 shows a graph of three known angular reflectance profiles belonging to three known multi-layer structures having different centroid wavelengths. FIG. 9 shows three sets of five unit circle pupil plane representations of the effect of the known angular reflectance profile of FIG. 8 on the angular distribution of electromagnetic radiation shown in FIG. 7 as it rotates through the illumination field of FIG. FIG. 10 illustrates multiple Zernike polynomial functions formed by mathematically decomposing three sets of five unit circle pupil plane representations of FIG. 9 according to one aspect of the present disclosure. FIG. 11 illustrates two sets of Zernike polynomial functions formed by mathematically decomposing the angular distribution of electromagnetic radiation of FIG. 7 according to one aspect of the present disclosure. FIG. 12 illustrates a method for determining the angular reflectance profile of a multi-layer structure according to one aspect of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0057] 1 shows a lithography system comprising a radiation source SO and a lithographic apparatus LA. The radiation source SO is configured to generate a beam of EUV radiation B and to provide the EUV radiation beam B to the lithographic apparatus LA. The lithographic apparatus LA comprises an illumination system IL, a support structure MT configured to support a patterning device MA (e.g. a mask), a projection system PS, and a substrate table WT configured to support a substrate W.

[0058] The illumination system IL is configured to condition the EUV radiation beam B before it is incident on the patterning device MA. In addition, the illumination system IL may include a facetted field mirror device 10 and a facetted pupil mirror device 11. Together the facetted field mirror device 10 and the facetted pupil mirror device 11 provide the EUV radiation beam B with a desired cross-sectional shape and a desired intensity distribution. The illumination system IL may include other mirrors or devices in addition to or instead of the facetted field mirror device 10 and the facetted pupil mirror device 11.

[0059] After being so conditioned, the EUV radiation beam B interacts with the patterning device MA. As a result of this interaction, a patterned EUV radiation beam B' is generated. The patterned EUV radiation beam B' may comprise a number of sub-beams generated through interaction with the patterning device MA. The projection system PS is configured to project the patterned EUV radiation beam B' onto a substrate W. To that end, the projection system PS may comprise a number of mirrors 13, 14 configured to project the patterned EUV radiation beam B' onto a substrate W held by a substrate table WT. The projection system PS may apply a reduction factor to the patterned EUV radiation beam B' to form an image having smaller features than corresponding features on the patterning device MA. For example, a reduction factor of 4 or 8 may be applied. Although the projection system PS is illustrated in FIG. 1 as having only two mirrors 13, 14, the projection system PS may include a different number of mirrors (for example six or eight mirrors as shown in FIG. 2).

[0060] Substrate W may include a previously formed pattern, in which case lithographic apparatus LA aligns the image formed by the patterned EUV radiation beam B' with the previously formed pattern on substrate W.

[0061] A relative vacuum, ie a small amount of gas (eg hydrogen) at a pressure well below atmospheric pressure, may be provided in the radiation source SO, the illumination system IL and / or the projection system PS.

[0062] The radiation source SO shown in Fig. 1 is of a type that may be designated, for example, as a laser-produced plasma (LPP) source. A laser system 1, which may include, for example, a CO2 laser, is arranged to inject energy via a laser beam 2 into a fuel, such as, for example, tin (Sn), provided from a fuel emitter 3. Although the following description refers to tin, any suitable fuel may be used. The fuel may be, for example, in liquid form or may be, for example, a metal or alloy. The fuel emitter 3 may comprise, for example, a nozzle configured to direct the tin, in the form of droplets, along a trajectory towards a plasma formation region 4. The laser beam 2 is incident on the tin in the plasma formation region 4. The injection of laser energy into the tin generates a tin plasma 7 in the plasma formation region 4. During de-excitation and recombination of the electrons and ions of the plasma, radiation including EUV radiation is emitted from the plasma 7.

[0063] EUV radiation from the plasma is collected and focused by a collector 5. Collector 5 may, for example, comprise a near normal incidence radiation collector 5 (often more commonly referred to as a normal incidence radiation collector). Collector 5 may have a multi-layer mirror structure arranged to reflect EUV radiation (e.g., EUV radiation having a desired wavelength, such as 13.5 nm). Collector 5 may have an elliptical configuration with two foci. The first focus may be at the plasma formation region 4 and the second focus may be at an intermediate focus 6, as described below.

[0064] The laser system 1 may be spatially separated from the radiation source SO. In this case, the laser beam 2 may be passed from the laser system 1 to the radiation source SO by a beam delivery system (not shown) including, for example, suitable directing mirrors and / or beam expanders and / or other optical elements. The laser system 1, the radiation source SO and the beam delivery system may be taken together as a radiation system.

[0065] The radiation reflected by the collector 5 forms an EUV radiation beam B. The EUV radiation beam B is focused to an intermediate focus 6 in order to form an image therein of the plasma present in the plasma formation region 4. The image at the intermediate focus 6 acts as a virtual radiation source for the illumination system IL. The radiation source SO is positioned such that the intermediate focus 6 is located at or near an aperture 8 in a closure structure 9 of the radiation source SO.

[0066] Although FIG. 1 illustrates the radiation source SO as a laser-produced plasma (LPP) source, any suitable source, such as a discharge-produced plasma (DPP) source or a free-electron laser (FEL), may be used to produce EUV radiation.

[0067] The lithographic apparatus LA comprises an apparatus comprising an illumination system IL configured to condition electromagnetic radiation B. The apparatus comprises a multi-layer structure 100 configured to reflect electromagnetic radiation B. The apparatus comprises a sensor 110 configured to detect an angular distribution of the electromagnetic radiation B after reflection from the multi-layer structure 100. The apparatus comprises a processor 120. The processor 120 is configured to generate a first function based at least in part on the angular distribution of the electromagnetic radiation detected by the sensor 110. The processor 120 is configured to compare the first function to a plurality of known functions associated with the plurality of known angular reflectance profiles to identify a second function from the plurality of known functions that is closest to the first function. The processor 120 is configured to determine an angular reflectance profile of the multi-layer structure 100 based at least in part on the known angular reflectance profile associated with the second function. Further details regarding this process are described below and illustrated throughout Figures 2-13.

[0068] In the example of FIG. 1, the parts of the apparatus form part of a measurement system. The measurement system comprises a multi-layer structure 100 and a sensor 110. In the example of FIG. 1, the multi-layer structure 100 forms part of a reference marker located on the patterning device MA. The multi-layer structure 100 may be located elsewhere. For example, the multi-layer structure 100 may be located on a support structure MT. The sensor 110 forms part of a substrate table WT. The measurement system comprises a reference marker and a sensor 110. For example, the multi-layer structure 100 may comprise a transmission image sensor ("TIS") reference marker or an "ILIAS" (Integrated Lens Interferometer At Scanner) reference marker at the reticle (e.g., patterning device MA) level, and the sensor 110 may comprise an ILIAS sensor at the wafer (e.g., substrate W) level. The TIS is a sensor used to measure the position at the substrate level of a projected aerial image of a mark pattern at the mask (reticle) level. The projected image at the substrate level may be a line pattern having a linewidth comparable to the wavelength of the exposure radiation. The TIS measures these mask patterns with a photocell underneath using a transmission pattern. The sensor data may be used to measure the position of the mask relative to the substrate table in six degrees of freedom (three translational and three rotational). In addition, the magnification and scaling of the projected mask may be measured. The ILIAS is an interferometric wavefront measurement system that may perform static measurements for lens aberrations up to high order. The ILIAS may be implemented as an integrated measurement system used for system initialization and calibration. Alternatively, the ILIAS may be used for "on-demand" monitoring and recalibration.

[0069] The measurement system is configured to measure the angular distribution of electromagnetic radiation B at the patterning device MA in the lithographic apparatus LA. This measurement may be referred to in the art as the EUV scanner pupil at reticle level. The measurement results performed by the measurement system may be used to determine the performance of the illumination system IL. The multi-layer structure 100 may be configured to maximize the reflectance over a range of incidence angles provided by the illumination system IL (which may be referred to in the art as the "pupil plane"). The relative change in reflectance of the multi-layer structure 100 across the pupil plane (i.e. across different incidence angles) may be referred to in the art as the "reference apodization". This reference apodization may contribute to a change in the intensity profile of the electromagnetic radiation B across the pupil plane (i.e. across different incidence angles).

[0070] The aperture stop of the lithographic apparatus LA may comprise a physical stop located anywhere in the lithographic apparatus LA that performs a truncation of the radiation beam B depending at least in part on the angle of incidence of the radiation beam B. The entrance and exit pupils of the lithographic apparatus LA may be defined as images of the aperture stop as observed at the entrance or exit of the projection system PS. The sub-beams forming the radiation beam B may propagate over a range of angles around the chief ray angle. The chief ray angle may for example be around 6° and the range of angles may vary from around 1° to around 11° around the chief ray angle (e.g. in the Y direction).

[0071] Imaging telecentricity may at least partially determine the performance of the illumination system IL. Imaging non-telecentricity may result, for example, from misalignment of the illumination system IL with respect to the optical axis. Imaging non-telecentricity, in combination with other errors such as defocus errors, may lead to undesired shifts of features patterned on the substrate W, leading to lithography errors such as overlay errors. Imaging telecentricity may at least partially depend on the angular reflectance profile of the multi-layer structure 100 (i.e., in the example of FIG. 1, the fiducial marker apodization of the TIS or ILIAS). Due to differences in materials and layer thicknesses, different multi-layer structures 100 have different reflectance characteristics that may be referred to in the art as "apodization fingerprints". In the example of Fig. 1, each multi-layer structure 100 is used in combination with a measurement system comprising the multi-layer structure 100, the sensor 110 having its own corresponding EUV reflectance characteristic over the applicable range of angles of incidence of electromagnetic radiation (i.e. the numerical aperture or so-called "pupil plane" of the lithography apparatus LA). One important characteristic of the multi-layer structure 100 is the centroid wavelength (i.e. the wavelength of electromagnetic radiation at which the multi-layer structure 100 is most reflective). The centroid wavelength of the multi-layer structure 100 is at least partially determined by the thicknesses of the layers of the multi-layer structure 100. The multi-layer structure 100 is therefore manufactured with tight manufacturing tolerances. Despite these tight manufacturing tolerances, differences in reflectance characteristics and, as a result, differences in imaging telecentricity effects exist between different multi-layer structures 100.

[0072] In known apparatuses, the influence of angle-dependent reflectance properties of the multilayer structure (e.g., in the example of known lithography apparatus, the reference apodization) is not corrected. Thus, when used as part of a measurement system, the unaccounted for influence of the angle-dependent reflectance properties of the multilayer structure may be erroneously attributed to other inaccuracies. For example, in known lithography apparatuses, the reference apodization may be interpreted as a pupil measurement error, so that the actual performance of the illumination system measured by the measurement system comprising the multilayer structure is better than the measurement system reports. Other lithography processes that may be affected by the reference apodization of the multilayer structure include imaging (e.g., when performing simulations using the measured pupil) and projection (e.g., when determining and / or calibrating the apodization of other parts, such as the projection system).

[0073] FIG. 2 illustrates a schematic of a portion of the lithographic apparatus LA of FIG. 1 including an apparatus for determining an angular reflectance profile of a multi-layer structure 100 according to an aspect of the present disclosure. The apparatus includes an illumination system (not shown in FIG. 2) configured to condition electromagnetic radiation B. The apparatus includes a multi-layer structure 100 configured to reflect electromagnetic radiation B. The multi-layer structure 100 may include alternating layers of two or more materials. For example, the multi-layer structure 100 may include about forty alternating layers of molybdenum and silicon. The multi-layer structure 100 may further include an absorbing layer and a capping layer. The absorbing layer may include, for example, a tantalum-based material. The capping layer may include, for example, ruthenium. Other materials and total number of layers may be used. The angular reflectance and wavelength response (e.g., centroid wavelength) of the multi-layer structure 100 are determined at least in part by the thicknesses of the individual molybdenum and silicon layers, the intermixed layers therebetween, and top layers such as a ruthenium cap layer. For example, the ruthenium cap layer may have a substantial impact on the reflectivity properties of the multi-layer structure 100. In general, the thicker the molybdenum and silicon layers, the larger the centroid wavelength and vice versa. Depending on the application, the layers of the multi-layer structure 100 may be selected to reflect a range of wavelengths of a given electromagnetic radiation. In the example of the EUV lithography apparatus of FIG. 1, the layers may be designed to provide the highest reflectivity for EUV light having a wavelength of 13.53 nm, for example. One or more layers of the multi-layer structure 100 may be affected by passive processes, such as, for example, temperature changes and / or oxidation. One or more layers of the multi-layer structure 100 may be affected by manufacturing processes, such as, for example, etching and / or cleaning steps during production, gas flood cleaning procedures in the lithography apparatus, etc. Thus, each multi-layer structure 100 tends to have its own angle- and wavelength-dependent reflectivity properties (e.g., reference apodization).

[0074] In the example of Fig. 2, the device comprises a diffuser 130 configured to interact with the electromagnetic radiation 105 before reflection from the multi-layer structure 100 such that the reflected electromagnetic radiation 140 substantially fills the numerical aperture of the device. In the example of Fig. 2, the diffuser 130 comprises an optically rough layer disposed near (e.g., below) the multi-layer structure 100 and configured to scatter the incident electromagnetic radiation B. The diffuser 130 may take other forms and / or be disposed elsewhere in the device (e.g., in another optical element upstream of the multi-layer structure 100). The diffuser 130 scatters the incident electromagnetic radiation 105 over a wide range of directions such that the electromagnetic radiation 105 is incident on the multi-layer structure 100 over a larger number of angles of incidence. Thus, the multi-layer structure 100 reflects the electromagnetic radiation 105 over a number of angles corresponding to the numerical aperture of the device. Thus, the diffuser 130 provides a substantially complete probing of the angle-dependent reflectivity profile of the multi-layer structure 100 over the entire numerical aperture of the device. For example, the illumination system may provide a beam of electromagnetic radiation 105 that comprises a discrete angular distribution of electromagnetic radiation, which after interaction with the diffuser 130 and the multi-layer structure 100 may be converted into a continuous angular distribution of electromagnetic radiation 140. In the example of Figure 2, it can be seen that the reflected electromagnetic radiation 140 substantially fills an entrance 150 of the projection system PS.

[0075] The electromagnetic radiation 140 reflected by the multi-layer structure 100 travels through a projection system PS. As mentioned above, the projection system PS typically comprises a number of mirrors 13-18 configured to project a patterned EUV radiation beam B' onto a substrate W, as shown in FIG. 1. However, in FIG. 2 the lithographic apparatus has been reconfigured to perform a pupil measurement (i.e. how the intensity of the electromagnetic radiation 140 varies across an angular distribution or pupil position of the electromagnetic radiation 140). The apparatus comprises a sensor 110 configured to detect the angular distribution of the electromagnetic radiation 140 after reflection from the multi-layer structure 100. In the example of FIG. 2 the sensor is an ILIAS sensor. The sensor 110 comprises a shearing grating structure 155 as an element for receiving radiation and a camera chip 160 as an element for detecting radiation. Different diffraction orders are detected at different areas of the camera chip 160. The sensor is configured to measure a substantially complete pupil (filled by electromagnetic radiation 140 after interaction with diffuser 130) at wafer level (e.g., near the substrate table WT in FIG. 1). An example of a series of pupil images detected by sensor 110 is described below with reference to FIG. 7. The following discussion with reference to FIGS. 3-6 will aid in understanding FIG. 7.

[0076] FIG. 3 shows a schematic of an angular distribution of electromagnetic radiation 140 reflected from the multi-layer structure 100. The incident electromagnetic radiation 105 has a chief ray incidence angle CRAO. The angular distribution of the incident electromagnetic radiation 105 lies between a maximum positive incidence angle CRAO+thmax and a maximum negative incidence angle CRAO-thmax, forming a cone-shaped volume through which the incident electromagnetic radiation 105 propagates. The incident electromagnetic radiation 105 may have a discrete angular distribution that does not satisfy the numerical aperture 170 of the device. That is, there are angles of incidence at which no electromagnetic radiation propagates within the cone-shaped volume. After interaction with the diffuser 130 and the multi-layer structure 100, the reflected electromagnetic radiation 140 has a substantially continuous angular distribution of electromagnetic radiation 140 that substantially satisfies the numerical aperture 170 of the device. That is, the reflected electromagnetic radiation 140 propagates at substantially all angles of incidence within the cone-shaped volume.

[0077] FIG. 4 shows the angular distribution of the reflected electromagnetic radiation 140 of FIG. 3, represented in a pupil plane with angular coordinates θx (theta x) and θy (theta y). θ (theta) represents the angle of incidence of the reflected electromagnetic radiation 140. θx extends along the x-axis shown in FIG. 3 and has a maximum value CRAO+thmax and a minimum value CRAO-thmax. θy extends along the y-axis shown in FIG. 3 and has a maximum value CRAO+thmax and a minimum value CRAO-thmax. The magnitude of the order of incidence angle thmax may have a value of, for example, about 4.8°. When viewed in the pupil plane, the reflected electromagnetic radiation 140 has a substantially continuous circular distribution of angles of incidence. The angle of incidence at a given position I in the pupil plane may be calculated by the following equation:

number

[0078] Figure 5 shows the angular distribution of the electromagnetic radiation of Figure 4 represented in the pupil plane on a unit circle. The unit circle has dimensionless coordinates ranging from -1 to +1 along the σx (sigma x) axis (corresponding to the θx axis of Figure 4) and from -1 to +1 along the σy (sigma y) axis (corresponding to the θy axis of Figure 4). The relationship between the numerical aperture of the device and the angle of incidence of the electromagnetic radiation may be defined by the following equation:

number

[0079] FIG. 6 shows a schematic representation of electromagnetic radiation formed in an illumination field 180 according to one aspect of the disclosure. The illumination field 140 may be formed, for example, by the illumination system IL of FIG. 1. In the example of FIG. 6, the illumination field 140 is shown as viewed at reticle level (i.e., near the reticle MA of FIG. 1). The illumination field 140 is reflected by a multi-layer structure (not shown) towards an entrance pupil 190 of the projection system PS. The chief ray 195 at the center 200 of the illumination field forms a chief ray incidence angle CRAO with respect to the optical axis z of the apparatus. In the example of FIG. 6, the illumination field 140 is arc-shaped (i.e., the illumination field 140 is a portion of a circle segment). From a reduced perspective at the substrate W level, the illumination field 140 may extend, for example, from about -13 mm to about 13 mm in the x-direction (the center 200 of the illumination field 140 is located at x=0). From the perspective at the patterning device MA level (i.e., before demagnification), the illumination field 140 may be about four times larger. The chief ray 195 of the illumination field 140 may have an incidence angle of, for example, about 6° at the center 200 of the illumination field 140. The inner and outer radii R of the illumination field 140 may be out may correspond to the scan length 210 along the y-axis of the lithographic apparatus LA.

[0080] The illumination system IL may comprise a curved reflective surface configured to condition the electromagnetic radiation to form an illumination field 140 in which the angle of incidence of the electromagnetic radiation rotates. The curved reflective surface may comprise a plurality of substantially flat reflective elements positioned at different angles to form the curved reflective surface. The rotation of the angular distribution of the electromagnetic radiation through the illumination field 140 is described below with reference to Figure 7. The sensor 110 of Figures 1 and 2 is configured to detect the rotation of the angular distribution of the electromagnetic radiation through the illumination field 140 after reflection from the multi-layer structure 100.

[0081] 7A-E show five unit circle pupil plane representations of the angular distribution of electromagnetic radiation rotating through the illumination field of FIG. 6 according to one aspect of the present disclosure. The first pupil plane distribution shown in FIG. 7A corresponds to the left edge of the illumination field (i.e., x=-12.72 mm). The second pupil plane distribution shown in FIG. 7B corresponds to a position between the left edge and the center 200 of the illumination field 140 (i.e., x=-8.48 mm). The third pupil plane distribution shown in FIG. 7C corresponds to the center 200 of the illumination field 140 (i.e., x=0). The fourth pupil plane distribution shown in FIG. 7D corresponds to a position between the center 200 and the right edge of the illumination field 140 (i.e., x=8.48 mm). The fifth pupil plane distribution shown in FIG. 7E corresponds to the right edge of the illumination field 140 (i.e., x=12.72 mm). Each angular distribution may have angles of incidence on the multi-layer structure ranging from about 1° to about 11° (ie, ±5° around a chief ray angle of 6°).

[0082] Radius R of the lighting field 140 out and the y-axis may be represented as the azimuth angle dphi. At the center 200 of the illumination field 140, the azimuth angle dphi is zero. Moving away from the center 200 of the illumination field 140 along the x-axis, the azimuth angle dphi increases. As can be seen from Figures 7A-7E, the angular distribution of electromagnetic radiation rotates when moving along the x-axis of the illumination field 140 (i.e., as the azimuth angle dphi changes). The azimuth angle dphi is determined by the x position in the illumination field 140 and the illumination field radius Rslit according to the following equation:

number

[0083] On average, the properties of the multi-layer structure 100 (e.g., layer thicknesses) that determine the angular reflectance characteristics are substantially constant along the x-axis across the illumination field 140. Thus, as the angular distribution of electromagnetic radiation rotates across the illumination field 140, the reference apodization imparted to the electromagnetic radiation by the multi-layer structure also rotates across the illumination field 140. Thus, the reference apodization imparted to the electromagnetic radiation by the multi-layer structure may be determined by the reflectance profile of the multi-layer structure at the center 200 of the illumination field 140, which rotates as a function of the azimuthal angle dphi.

[0084] FIG. 8 shows a graph of three known angular reflectance profiles 220-240. The three known angular reflectance profiles belong to three known multilayer structures with different centroid wavelengths. The first known reflectance profile 220 corresponds to a first known multilayer structure with a relatively low centroid wavelength "CWHM lower". The second known reflectance profile 230 corresponds to a second known multilayer structure with an average centroid wavelength "CWHM nominal". The third known reflectance profile 240 corresponds to a third known multilayer structure with a relatively high centroid wavelength "CWHM upper". A calibration measurement may be performed to determine the angular reflectance profiles 220-240 of the known multilayer structures. Alternatively, the reflectance profile information may be provided by a supplier of the known multilayer structure. Over the range of incidence angles shown in FIG. 8, the known reflectance profiles 220-240 follow generally the same pattern of gradually increasing with increasing incidence angle until it rapidly decreases at larger incidence angles. However, the associated slopes are different, and the reflectivities of the known multilayer structures at upper and lower values ​​of the angle of incidence are significantly different. Thus, each multilayer structure has its own characteristic angular reflectivity characteristics. Although only three known angular reflectivity profiles are shown in Figure 8, it is understood that the present invention may utilize a greater number of known reflectivity profiles, such as ten or more (e.g., forty) known reflectivity profiles.

[0085] FIG. 9 shows three sets 250-270 of five unit circle pupil plane representations of the effect of the known angular reflectance profile of FIG. 8 on the angular distribution of electromagnetic radiation shown in FIG. 7 rotating through the illumination field of FIG. 6. The first set 250 of the five unit circle pupil plane representations corresponds to the effect of the first known reflectance profile 220 having a relatively low centroid wavelength. The second set 260 of the five unit circle pupil plane representations corresponds to the effect of the second known reflectance profile 230 having an average centroid wavelength. The third set 270 of the five unit circle pupil plane representations corresponds to the effect of the third known reflectance profile 240 having a relatively high centroid wavelength. As in FIG. 7, the first pupil plane distribution shown in FIG. 9A corresponds to the left edge of the illumination field (i.e., x=-12.72 mm). The second pupil plane distribution shown in FIG. 9B corresponds to a position between the left edge and the center 200 of the illumination field 140 (i.e., x=-8.48 mm). The third pupil plane distribution shown in Figure 9C corresponds to the center 200 (i.e., x=0) of the illumination field 140. The fourth pupil plane distribution shown in Figure 9D corresponds to a position between the center 200 and the right edge (i.e., x=8.48 mm) of the illumination field 140. The fifth pupil plane distribution shown in Figure 9E corresponds to the right edge (i.e., x=12.72 mm) of the illumination field 140.

[0086] The effect of the multilayer structure on the angular distribution of electromagnetic radiation (i.e., reference apodization) varies with the centroid wavelength. For example, a known multilayer structure with relatively thin layers may result in a relatively low centroid wavelength reflectance profile 220, and a known multilayer with relatively thick layers may result in a relatively high centroid wavelength reflectance profile 240. A relatively low centroid wavelength reflectance profile 220 may shift the angular distribution of electromagnetic radiation toward lower angles of incidence, effectively moving the centroid of the angular distribution downward in the pupil plane (as shown in the first set 250). A relatively high centroid wavelength reflectance profile 240 may shift the angular distribution of electromagnetic radiation toward larger angles of incidence, effectively moving the centroid of the angular distribution upward in the pupil plane (as shown in the third set 270). Such a shift may result in large differences in the intensity of the electromagnetic radiation appearing at different angles of incidence. For example, a radiation beam having a dipole Y illumination mode (eg, as conditioned by the illumination system IL of FIG. 1) may experience dramatic changes in reflectivity between the poles of the dipole Y illumination mode due to the effect of the reflectivity profile of the multi-layer structure.

[0087] As shown in Figure 7, the angular distribution of electromagnetic radiation rotates in response to changes in the azimuthal angle dphi when moving along the x-axis of the illumination field 140. As a result, the effect of a known angular reflectance profile 220-240 on the angular distribution of electromagnetic radiation also rotates across the illumination field 140, as shown in Figure 9. Differences in multilayer properties (e.g., layer materials, thicknesses, etc.) between different multilayer structures with different reflectance profiles 220-240 are visualized as different apodization profiles, which behave differently when moving through the illumination field 140.

[0088] The apodization profile for a given multilayer structure may be described using Zernike polynomials, which are a well-known sequence of polynomials that are orthogonal on a unit circle. A given apodization profile expressed on a unit circle (such as that shown in FIG. 9 ) may be mathematically constructed using multiple Zernike polynomials. Similarly, a given apodization profile may be mathematically decomposed into multiple Zernike polynomials with different contributions. The contributions (or magnitudes) of a given Zernike polynomial may vary in different ways depending on the reflectance characteristics (e.g., centroid wavelength) of a given multilayer structure.

[0089] FIG. 10 illustrates a number of Zernike polynomial functions formed by mathematically decomposing the three sets 250-270 of the five unit circle pupil plane representations of FIG. 9 according to one aspect of the disclosure. The first nine Zernike polynomials Z1-Z9 are illustrated in FIG. 10. It is understood that a greater or lesser number of Zernike polynomials Z1-Z9 may be considered, for example up to the 25th Zernike polynomial Z25. The horizontal axis of each graph represents the x-position (corresponding to a change in azimuth angle dphi, as discussed above) in the illumination field 140 of FIG. 6. It is understood that FIG. 10 includes more illumination field x-positions than the five illustrated in FIGS. 9A-E. The vertical axis of each graph represents the relative intensity of radiation after reflection from a given multilayer structure. Dot 320 corresponds to the first reflectance profile 220 (i.e., the first set of pupil plane representations 250) having a relatively low centroid wavelength. The circle 330 corresponds to the second known reflectance profile 230 (i.e., the second set of pupil plane representations 260) having an average centroid wavelength, and the cross 340 corresponds to the third known reflectance profile 240 (i.e., the third set of pupil plane representations 270) having a relatively high centroid wavelength.

[0090] Zernike polynomials are expressed in polar coordinates (r, phi). The rightmost columns of Zernike polynomials (i.e. Z1, Z4 and Z9) have only radial dependence. That is, the rightmost columns of Zernike polynomials (i.e. Z1, Z4 and Z9) have no argument dependence and are therefore rotationally symmetric. For all other columns, the Zernike polynomials have an angle (phi) dependence (i.e. are rotationally asymmetric). Pairs of rotationally asymmetric Zernike polynomials with the same angular degree M and the same radial degree, e.g. Z2 and Z3, Z5 and Z6, can be distinguished. One can also distinguish between rotationally asymmetric Zernike polynomials that behave according to sin(M*dhi) (=symmetric in X direction) and those that behave according to cos(M*dphi) (=symmetric in Y direction). For the Zernike decomposition of the reference apodization profile across the slit, the angular Zernike coefficient pair (eg, Z2 and Z3) can be written as follows using a rotation matrix with dphi as the rotation angle:

number

[0091] where fp denotes the field point position in the illumination field (0=centre), and Z2(0) and Z3(0) are the Z2 and Z3 Zernike coefficient values ​​at the centre of the illumination field, respectively.

[0092] At each position in the lighting field, 2 (dphi)+Z3 2 Losses across the field in Z2 "leaks" into Z3 so that "(dphi)" is practically constant.

number

[0093] The (phi, r) polar coordinate system in which the Zernike polynomials are written can be rotated according to the azimuth angle dphi. In effect, the radial term r remains the same, and the angular term phi is given an additional offset dphi according to the x-position in the illumination field. The additional offset may be applied using a rotation matrix that describes the Zernike polynomials as a function of the azimuth angle dphi across the illumination field. With reference to FIG. 2, the processor 120 may be configured to generate a plurality of Zernike polynomial functions for each known reflectance profile associated with a plurality of known multi-layer structures.

[0094] As can be seen from Fig. 10, the contribution of each Zernike polynomial Z1-Z9 varies differently across the illumination field for each known reflectance profile 320-340. This variation provides a means by which the angular reflectance profiles of different multi-layer structures may be determined by comparison with the known reflectance profiles 320-340. Referring again to Fig. 2, the sensor 110 is configured to detect the angular distribution of electromagnetic radiation after reflection from the multi-layer structure 100. In performing this measurement, the effect of the reflectance profile of the multi-layer structure 100 (i.e., the reference apodization) is also measured.

[0095] 11 illustrates two sets 410, 420 of Zernike polynomial functions Z1-Z9 formed by mathematically decomposing the angular distribution of electromagnetic radiation of FIG. 7 according to one aspect of the present disclosure. The first set 410 of Zernike polynomial functions Z1-Z9 corresponds to the angular distribution of electromagnetic radiation measured by the sensor 110 at wafer level (i.e., near the substrate W in FIG. 1). The second set 420 of Zernike polynomial functions Z1-Z9 corresponds to the angular distribution of electromagnetic radiation at reticle level (i.e., near the reticle MA in FIG. 1 before interaction with the multi-layer structure 100). The second set 420 may be computed at least in part based on the first set 410 and knowledge of the projection system PS.

[0096] 2, the processor 120 is configured to generate a first function 410 based at least in part on the angular distribution of the electromagnetic radiation 140 detected by the sensor 110. An example of a set of functions corresponding to the angular distribution of the electromagnetic radiation of FIG. 7 generated by the processor 120 is shown in FIG. 11. The processor 120 is configured to compare the first function 410 to a plurality of known functions 320-340 associated with the plurality of known angular reflectance profiles 220-240 to identify a second function from the plurality of known functions 220-240 that is closest to the first function 410. An example of the plurality of known reflectance profiles 220-240 is shown in FIGS. 8 and 9. An example of a plurality of known functions associated with the plurality of known angular reflectance profiles 220-240 is shown in FIG. 10. The processor 120 is configured to determine an angular reflectance profile of the multi-layer structure 100 based at least in part on the known angular reflectance profiles 220-240 associated with the second function.

[0097] The processor 120 is configured to generate the first function by mathematically decomposing the angular distribution of electromagnetic radiation detected by the sensor 110 into a number of Zernike polynomial functions 410. Mathematically decomposing generally involves expressing or representing a function as a combination of simpler component functions. In this example, the angular distribution of electromagnetic radiation detected by the sensor is represented as a combination of component Zernike polynomial functions Z1-Z9. The processor 120 may perform the decomposition across the illumination field in a manner similar to that described above with respect to Equations 1-3.

[0098] In fact, when the sensor 110 measures the angular distribution of electromagnetic radiation across the illumination field, the resulting measurement comprises a reference apodization provided by the multilayer structure 100 (rotating according to the azimuthal angle dphi) together with other contributions from other optical components of the lithographic apparatus LA. A first additional contribution is provided by the projection system PS. The optical elements of the projection system PS have their own angular reflectivity profile that impart their own apodization influence to the electromagnetic radiation before it reaches the sensor 110. A second additional contribution is provided by the diffuser 130. The reflectivity profile of the diffuser 130 may be determined by the scattering properties of the rough layer that forms the diffuser 130. The scattering profile of the diffuser 130 may be determined by the local surface roughness. The diffuser 130 reflectivity profile typically has a shape similar to a Gaussian distribution.

[0099] For the lithography apparatus LA, one purpose of pupil measurements (e.g., those performed by ILIAS) is to characterize the pupil plane (i.e., the angular distribution of electromagnetic radiation) in front of the reticle level MA. If the ILIAS sensor is present at the wafer level W, the apodization contributions of both the projection system PS and the multilayer structure 100 must be corrected. It is therefore beneficial to separate the reference apodization brought about by the multilayer structure 100 from the other contributions. A practical way to do this is to subtract resolved Zernike polynomials determined in the center of the illumination field. This removes the substantially constant Gaussian diffuser contribution and, while removing the rotationally symmetric Zernike polynomials (e.g., radial Zernike Z1, Z9, Z16, etc.), leaves behind rotationally asymmetric polynomials that vary across the illumination field due to the rotation across the illumination field of the reference apodization contribution, as described above with reference to FIG. 9.

[0100] In general, the Zernike polynomials have a part Zfidapo associated with the multi-layer structure and a part Zresidual associated with the rotationally symmetric (i.e. "static" over the illumination field) contribution. For Z2 and Z3 the following relations can be defined:

number

[0101] When moving away from the center of the illumination field (ie, x=0), the portion Zfidapo associated with the multilayer structure rotates through an azimuthal angle dphi according to the following relationship:

number

[0102] Since the profile is symmetric across the Y axis, Z2fidapo(0) can be defined as equal to zero. Substituting Equations 4-7, we obtain the following relationship:

number

[0103] Assuming the residual is constant, the last part of the equation can be eliminated by subtracting the median value (i.e., x=0). Thus, by subtracting Zcentre and assuming Zresidual is constant across all positions along the illumination field, we obtain the following relationship:

number

[0104] This results in the following relationship:

number

[0105] By fitting the delta Zernike profiles for Z2 and Z3, the value of Z3fidapo (i.e., the part of the Zernike polynomial related to the multi-layer structure) at the center of the illumination field can be obtained. The same applies for all other rotationally asymmetric Zernike polynomial pairs (e.g., Z5 and Z6, etc.) with the same angular and radial orders. The processor 120 may be configured to perform a fitting process to identify the second function from a number of known functions. For example, the fitting algorithm may compare the Zernike profile of the angular distribution of the electromagnetic radiation detected by the sensor 110 with the Zernike profiles of the known reflectance profiles 220-240 and identify which known reflectance profile 220-240 best matches the measured behavior. The best-fitting known Zernike profile may be determined as the Zernike profile of the multi-layer structure 100. The fitting algorithm may be configured to separate the contributions of the Zernike polynomials (which can therefore be attributed to a reference apodization associated with the multilayer structure) that rotate through the illumination field from other contributions that are static with respect to rotation (e.g., contributions from the projection system PS or diffuser 130 that scatter the profile).

[0106] Fitting the delta Zernike profile may comprise performing a least squares fit. For example, if the delta Zernike profile (e.g., the profile given by Equations 12 and 13) is a sine and cosine function, the amplitude of said profile may be determined by directly fitting the sine and cosine functions to the measured Zernike profile. In the above example of dZ2 and dZ3 profiles, the amplitude is Z3fidapo(0). The same reasoning applies for other pairs of Zernike profiles that change with changes in azimuth angle, as described above. In this way, a set of measured Zernike amplitudes "Zmeas" may be determined. This process may be repeated for all known reflectance profiles "Zrefn" and a minimum norm, e.g., min(||Zmeas-Zrefn||), to be compared with the measured reflectance profile may be determined to find the best matching known reflectance profile. A known reflectance profile that shows poor correlation (e.g., a relatively low R 2 Measured Zernike amplitude values ​​Zmeas having a sine / cosine function (Zmeas value) may be ignored (i.e., these are profiles that do not look like the expected sine / cosine functions). Other fitting procedures may be used, such as least absolute deviation.

[0107] The result of the processing may be understood as a description of a reference apodization profile of the multi-layer structure 100 at the pupil plane. The reference apodization profile of the multi-layer structure 100 may be stored in memory and subsequently referenced when performing pupil measurements (e.g., when measuring illumination characteristics for certification of the illumination system IL or when measuring projection characteristics for characterization of the projection system PS).

[0108] The processor 120 may use the angular reflectance profile of the multi-layer structure 100 to improve understanding and operation of the illumination system IL. For example, the processor 120 may be configured to determine a reflectance profile of the angular multi-layer structure of the illumination system IL, at least in part depending on the angular reflectance profile determined by the processor 120. This may involve removing the effect of the angular reflectance profile of the multi-layer structure 100 from the angular distribution of the electromagnetic radiation detected by the sensor 110 (e.g., the angular distributions shown in Figures 7A-E). The processor 120 may be configured to perform a simulation of a proposed radiation beam B traveling through the lithographic apparatus LA, at least in part depending on the angular reflectance profile of the illumination system IL.

[0109] The processor 120 may use the angular reflectance profile of the multi-layer structure 100 to improve the understanding and operation of the projection system PS. For example, the processor 120 may be configured to determine an angular reflectance profile of the projection system PS depending at least in part on the angular reflectance profile of the multi-layer structure 100. This may involve removing the effect of the angular reflectance profile of the multi-layer structure 100 from the angular distribution of electromagnetic radiation detected by the sensor 110. For example, the sensor 110 may be configured to measure several shifted pupils (i.e., angular distribution of electromagnetic radiation) that are subsequently used by an algorithm (e.g., by the processor 120) to separate the contributions of the illumination system IL and the projection system PS. This process may involve measuring the same pupil at different angles of incidence. To achieve this, the reticle stage MT may be tilted to change the angle of the radiation beam B entering the projection system PS.

[0110] FIG. 12 illustrates a method of determining an angular reflectance profile of a multi-layer structure according to one aspect of the disclosure. A first step S1 comprises reflecting electromagnetic radiation from the multi-layer structure. A second step S2 comprises detecting an angular distribution of the electromagnetic radiation after reflection from the multi-layer structure. A third step S3 comprises generating a first function based at least in part on the angular distribution of the electromagnetic radiation. A fourth step S4 comprises comparing the first function to a plurality of known functions associated with the plurality of known angular reflectance profiles to identify a second function from the plurality of known functions that is closest to the first function. A fifth step S5 comprises determining an angular reflectance profile of the multi-layer structure based at least in part on the known angular reflectance profile associated with the second function.

[0111] The method may comprise an optional step of adjusting the electromagnetic radiation to form an illumination field in which the angular distribution of the electromagnetic radiation rotates. Detecting the angular distribution of the electromagnetic radiation may comprise detecting a rotation of the angular distribution of the electromagnetic radiation through the illumination field after reflection from the multi-layer structure. The method may comprise an optional step of diffusing the electromagnetic radiation before reflection from the multi-layer structure such that the angular distribution of the electromagnetic radiation is substantially continuous. Generating the first function comprises mathematically decomposing the angular distribution of the electromagnetic radiation into a plurality of Zernike polynomial functions. The plurality of Zernike polynomial functions may not include rotationally symmetric Zernike polynomial functions. Comparing the first function to a plurality of known functions associated with a plurality of known angular reflectance profiles to identify a second function from the plurality of known functions that is closest to the first function may comprise performing a fitting process.

[0112] The method of projecting a patterned beam of radiation onto a substrate may comprise using a multi-layer structure to perform a measurement and taking into account in said measurement an angular reflectivity profile of the multi-layer structure determined using the method of FIG. 12. Adjusting the electromagnetic radiation may comprise using an illumination system IL. Taking into account the angular reflectivity profile of the multi-layer structure may comprise determining an angular reflectivity profile of the illumination system IL at least in part depending on the angular reflectivity profile of the multi-layer structure. The method may comprise an optional step of performing a simulation of the proposed patterned beam of radiation at least in part depending on the angular reflectivity profile of the illumination system. Projecting the patterned beam of radiation onto a substrate may comprise using a projection system PS. Taking into account the angular reflectivity profile of the multi-layer structure may comprise determining an angular reflectivity profile of the projection system at least in part depending on the angular reflectivity profile of the multi-layer structure.

[0113] Although specific reference may be made in this text to the use of lithographic apparatus in the manufacture of ICs, it should be understood that the lithographic apparatus described herein may have other applications including the manufacture of integrated optical systems, guidance and detection patterns for magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, etc.

[0114] Although specific reference may be made in this text to embodiments of the invention in the context of a lithographic apparatus, embodiments of the invention may be used in other apparatus. Embodiments of the invention may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes objects such as wafers (or other substrates) or masks (or other patterning devices). These apparatus may be generally referred to as lithography tools. Such lithography tools may use vacuum or atmospheric (non-vacuum) conditions. Technical fields in which the invention may be utilized include EUV image sensing, EUV illumination, EUV imaging, and EUV projection.

[0115] Where the context permits, embodiments of the invention may be implemented in hardware, firmware, software, or any combination thereof. Embodiments of the invention may be implemented as instructions stored on a machine-readable medium, which may be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a manner readable by an apparatus (e.g., a computing device). For example, a machine-readable medium may include a read-only memory (ROM), a random access memory (RAM), a magnetic storage medium, an optical storage medium, a flash memory device, an electrical / optical / acoustic or other form of transmission signal (e.g., carrier wave, infrared signal, digital signal, etc.), and the like. Furthermore, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be understood that such description is merely for convenience and that such actions may in fact be caused by a computing device, processor, controller, or other device executing the firmware, software, routines, instructions, etc., causing actuators or other devices to interact with the physical world. For example, a computer program comprising computer readable instructions may be configured to cause a computer to perform the method of Figure 12 and any optional steps thereof. A computer readable medium may be configured to store the computer program. As another example, a computing device may comprise a memory storing processor readable instructions and a processor arranged to read and execute instructions stored in said memory. The processor readable instructions may comprise instructions arranged to control a computer to perform the method of Figure 12 and any optional steps thereof.

[0116] Although specific embodiments of the invention have been described above, it will be understood that the invention may be practiced otherwise than as described. The above description is intended to be illustrative and not limiting. Thus, it will be apparent to those skilled in the art that modifications may be made to the invention as described without departing from the scope of the claims set out below.

[0117] Item 1: reflecting electromagnetic radiation from the multi-layer structure; detecting an angular distribution of the electromagnetic radiation after reflection from the multi-layer structure; generating a first function based at least in part on the angular distribution of the electromagnetic radiation; comparing the first function to a plurality of known functions associated with a plurality of known angular reflectance profiles to identify a second function from the plurality of known functions that is closest to the first function; determining an angular reflectance profile of the multi-layer structure based at least in part on a known angular reflectance profile associated with the second function; and A method for determining an angular reflectance profile of a multi-layer structure comprising: Item 2: conditioning the electromagnetic radiation to form an illumination field having a rotating angular distribution of the electromagnetic radiation; detecting the angular distribution of the electromagnetic radiation comprises detecting the rotation of the angular distribution of the electromagnetic radiation through the illumination field after reflection from the multi-layer structure. The method according to item 1. Item 3: 3. The method of claim 1 or 2, comprising diffusing the electromagnetic radiation before reflection from the multilayer structure such that the angular distribution of the electromagnetic radiation is substantially continuous. Item 4: 4. The method of any of claims 1 to 3, wherein generating the first function comprises mathematically decomposing the angular distribution of the electromagnetic radiation into a plurality of Zernike polynomial functions. Item 5: 5. The method of any of items 2 to 4, wherein the plurality of Zernike polynomial functions does not include a rotationally symmetric Zernike polynomial function. Item 6: 6. The method of claim 1, wherein comparing the first function to a plurality of known functions associated with a plurality of known angular reflectance profiles to identify a second function from the plurality of known functions that is closest to the first function comprises performing a fitting process. Item 7: Using a multilayer structure according to any one of items 1 to 6 for carrying out the measurement, taking into account in the measurement an angular reflectance profile of the multilayer structure determined using the method according to any one of items 1 to 6; 1. A method for projecting a patterned beam of radiation onto a substrate comprising: Item 8: adjusting the electromagnetic radiation comprises using a lighting system; and considering the angular reflectance profile of the multi-layer structure comprises determining an angular reflectance profile of the illumination system at least in part dependent on the angular reflectance profile of the multi-layer structure. The method according to item 7. Item 9: 9. The method of claim 7 or 8, comprising performing a simulation of a proposed patterned beam of radiation at least in part dependent on an angular reflectance profile of the illumination system. Item 10: projecting the patterned beam of radiation onto the substrate comprises using a projection system; and considering the angular reflectance profile of the multi-layer structure comprises determining an angular reflectance profile of the projection system at least in part dependent on the angular reflectance profile of the multi-layer structure. 10. The method according to any one of items 7 to 9. Item 11: 11. A computer program comprising computer readable instructions configured to cause a computer to carry out the method according to any of items 1 to 10. Item 12: 12. A computer-readable medium storing the computer program according to item 11. Item 13: a memory storing processor readable instructions; a processor arranged to read and execute instructions stored in said memory; Equipped with The processor-readable instructions comprise instructions arranged to control a computer to perform a method according to any one of items 1 to 10. Computer equipment.

Claims

1. a multi-layer structure configured to reflect electromagnetic radiation; a sensor configured to detect an angular distribution of the electromagnetic radiation after reflection from the multi-layer structure; generating a first function based at least in part on the angular distribution of the electromagnetic radiation detected by the sensor; comparing the first function to a plurality of known functions associated with a plurality of known angular reflectance profiles to identify a second function from the plurality of known functions that is closest to the first function; determining an angular reflectance profile of the multi-layer structure based at least in part on a known angular reflectance profile associated with the second function; and A processor configured to execute An apparatus comprising:

2. an illumination system configured to condition the electromagnetic radiation to form an illumination field having a rotating angular distribution of the electromagnetic radiation; the sensor is configured to detect the rotation of the angular distribution of the electromagnetic radiation through the illumination field after reflection from the multi-layer structure.

2. The apparatus of claim 1.

3. 3. The apparatus of claim 1 or 2, comprising a diffuser configured to interact with the electromagnetic radiation such that the electromagnetic radiation substantially fills a numerical aperture of the apparatus.

4. 4. The apparatus of claim 1, wherein the processor is configured to generate the first function by mathematically decomposing an angular distribution of the electromagnetic radiation detected by the sensor into a plurality of Zernike polynomial functions.

5. The apparatus of claim 4 , wherein the plurality of Zernike polynomial functions does not include a rotationally symmetric Zernike polynomial function.

6. The apparatus of claim 1 , wherein the processor is configured to perform a fitting process to identify the second function from the plurality of known functions.

7. An apparatus according to any one of claims 1 to 6, a support structure configured to support a patterning device capable of forming a pattern in a cross-section of a radiation beam to form a patterned radiation beam, the multi-layer structure forming part of the patterning device or a fiducial marker located on the support structure; a substrate table configured to hold a substrate, of which the sensor forms part; a projection system configured to project the patterned beam of radiation onto the substrate; and a measurement system comprising the fiducial marker and the sensor; 1. A lithographic apparatus comprising:

8. the illumination system is configured to condition the radiation beam; the processor is configured to determine an angular reflectance profile of the illumination system at least in part dependent on an angular reflectance profile of the multi-layer structure. A lithographic apparatus according to claim 7 when dependent on claim 2.

9. The lithographic apparatus of claim 8 , wherein the processor is configured to perform a simulation of a proposed radiation beam propagating through the lithographic apparatus depending at least in part on an angular reflectance profile of the illumination system.

10. A lithographic apparatus according to any of claims 7 to 9, wherein the processor is configured to determine an angular reflectance profile of the projection system at least in part dependent on an angular reflectance profile of the multi-layer structure.

11. reflecting electromagnetic radiation from the multi-layer structure; detecting an angular distribution of the electromagnetic radiation after reflection from the multi-layer structure; generating a first function based at least in part on the angular distribution of the electromagnetic radiation; comparing the first function to a plurality of known functions associated with a plurality of known angular reflectance profiles to identify a second function from the plurality of known functions that is closest to the first function; determining an angular reflectance profile of the multi-layer structure based at least in part on a known angular reflectance profile associated with the second function; and A method for determining an angular reflectance profile of a multi-layer structure comprising:

12. conditioning the electromagnetic radiation to form an illumination field having a rotating angular distribution of the electromagnetic radiation; detecting the angular distribution of the electromagnetic radiation comprises detecting the rotation of the angular distribution of the electromagnetic radiation through the illumination field after reflection from the multi-layer structure. The method of claim 11.

13. 13. A method according to claim 11 or 12, comprising diffusing the electromagnetic radiation before reflection from the multi-layer structure such that the angular distribution of the electromagnetic radiation is substantially continuous.

14. 14. The method of claim 11, wherein generating the first function comprises mathematically decomposing the angular distribution of the electromagnetic radiation into a plurality of Zernike polynomial functions.

15. a memory storing processor readable instructions; a processor arranged to read and execute instructions stored in said memory; Equipped with The processor readable instructions comprise instructions arranged to control a computer to perform a method according to any of claims 11 to 14. Computer equipment.

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