Method for determining optical properties

Abstract

A method for determining an optical property of a projection system, the method comprising: obtaining measurement data representative of measurement radiation output from the projection system; obtaining an estimated illumination profile of the input radiation received by the projection system; generating estimated data representing estimated radiation output from the projection system based on the estimated illumination profile; fitting the estimated data to the measured data to generate a parameter fit; and calculating an optical property of the projection system based on the parameter fitting.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority from European application 23156496.4, filed on February 14, 2023, which is incorporated herein by reference in its entirety. Technical Field

[0003] The present invention relates to a method and an apparatus for determining optical properties of a projection system. The projection system may be a projection system of a lithographic apparatus. Background Art

[0004] A lithographic apparatus is a machine configured to apply a desired pattern to a substrate. A lithographic apparatus can be used, for example, in the manufacture of integrated circuits (ICs). For example, a lithographic apparatus can project a pattern (often also referred to as a "design layout" or "design") of a patterning device (e.g., a mask) onto a layer of radiation-sensitive material (resist) provided on a substrate (e.g., a wafer).

[0005] As semiconductor manufacturing processes continue to advance, the size of circuit elements has continued to decrease, while the number of functional elements (such as transistors) per device has steadily increased over the decades, following a trend commonly referred to as "Moore's Law". In order to keep up with Moore's Law, the semiconductor industry is pursuing technologies that can create smaller and smaller features. In order to project a pattern onto a substrate, a lithography apparatus can use electromagnetic radiation. The wavelength of this radiation determines the minimum size of the features patterned on the substrate. Typical wavelengths currently used are 365nm (i-line), 248nm, 193nm, and 13.5nm. A lithography apparatus using extreme ultraviolet (EUV) radiation with a wavelength in the range of 4nm to 20nm (e.g., 6.7nm or 13.5nm) can be used to form smaller features on a substrate than a lithography apparatus using, for example, radiation with a wavelength of 193nm.

[0006] Radiation patterned by a patterning device is focused onto a substrate using a projection system. The projection system can be arranged to condition the radiation beam so that it is delivered to the patterning device with a desired spatial and angular distribution. The projection system may introduce optical aberrations that cause the image formed on the substrate to deviate from the desired image (e.g., a diffraction-limited image of the patterning device).

[0007] It may be desirable to provide methods and apparatus for accurately determining aberrations introduced by a projection system so that these aberrations can be better controlled or eliminated. Furthermore, it may be desirable to provide methods and apparatus for accurately determining other properties of a projection system, such as polarization and apodization introduced by the projection system. These properties can also cause the image formed on a substrate to deviate from the desired image. Summary of the Invention

[0008] According to a first aspect, a method for determining optical properties of a projection system is provided. The method comprises: obtaining measurement data representing measurement radiation output from the projection system; obtaining an estimated illumination profile of input radiation received by the projection system; generating estimated data representing the estimated radiation output from the projection system based on the estimated illumination pupil and / or profile; fitting the estimated data to the measurement data to generate a parametric fit; and calculating the optical properties of the projection system based on the parametric fit.

[0009] Radiation output from the projection system has an illumination profile that differs from the input illumination profile. At least some of the differences may be attributable to optical properties of the projection system, which in turn cause variations in the radiation. These variations can include, for example, phase shifts (e.g., due to aberrations), intensity variations (e.g., due to apodization), and / or polarization variations. It would be advantageous to accurately determine the optical properties of the projection system so that these variations can be accounted for, for example, during any imaging process using the projection system. This method enables accurate determination of one or more optical properties of the projection system with reduced processing requirements. Consequently, the determination can be completed more quickly and thus performed regularly without significant device downtime. Furthermore, the method can be performed without specialized equipment (e.g., high-power on-board processing), which may be required by some other methods for determining optical properties. Therefore, the method can be performed user-side and / or over the typical lifespan of the device. This may be advantageous compared to other methods that may only be performed after initial manufacturing, testing, and / or calibration of the projection system. The method may be computer-implemented. The measurement data may represent measured radiation output from the projection system during a shearing interferometry process.

[0010] The measurement data may represent at least one component of the measured output radiation, wherein the component is selected from the group consisting of a phase component, an amplitude component, and an offset component. The estimated data may represent a corresponding at least one component of the estimated output radiation. That is, if the measurement data includes a phase component, the estimated data may also include a phase component. It has been found that accurate determination of optical properties can be performed using fewer than all components of the measurement data or simulation data, requiring relatively low processing power.

[0011] Components of the measured data and corresponding components of the estimated data can each include a phase component. The phase component at least partially represents aberrations in the lithographic apparatus, for example due to aberrations of optical components in the lithographic apparatus. The phase component can also represent other optical properties, such as apodization and polarization, whose variations may be caused by the optical components. Thus, optical properties such as these can be determined using the phase components of the estimated and measured data.

[0012] Obtaining an estimated illumination profile may include obtaining simulation data representing simulated radiation output from the projection system, fitting the measured data to the simulation data to generate a profile fit; and generating the estimated illumination profile based on the profile fit. The simulation data may include multiple sets of simulation data. Each of the multiple sets may be based on input of radiation to the projection system having a predetermined illumination profile from a set of predetermined illumination profiles. The estimated illumination profile may include a weighted combination of the set of predetermined illumination profiles. The simulation data may be pre-calculated. The use of pre-calculated simulation data enables rapid implementation of the simulation data, enabling determinations to be performed relatively quickly and with relatively low processing requirements. Alternatively, the simulation data may be directly simulated when needed. The simulation data may be generated based on ray tracing of the projection system for each of the predetermined illumination profiles. Alternative methods of generating the simulation data are possible, such as using an optical model of the projection system, for example representing optical (e.g., diffraction) physical phenomena occurring in the projection system.

[0013] Each predetermined illumination profile may be at least partially defined by the angular distribution, apodization and / or polarization of the input radiation.Beneficially, real physical effects caused by optical elements of the projection system, such as aberrations, apodization and polarization, can be determined in this way.

[0014] The measurement data may represent at least one component of the measured output radiation. The at least one component may be selected from the group consisting of a phase component, an amplitude component, and an offset component. The simulation data may represent at least one corresponding component of the estimated output radiation. That is, if the measurement data includes an offset component, the simulation data may also include an offset component. It has been found that accurate determination of optical properties can be performed using fewer than all components of the measurement data or simulation data, requiring relatively low processing power.

[0015] The components of the measured data and the corresponding components of the simulated data can each include an offset component. The offset components of the measured data and the offset components of the simulated data are independent of aberrations in the lithographic apparatus. Therefore, fitting using the amplitude or offset components enables relatively rapid determination of optical properties of the projection system with relatively low processing requirements.

[0016] The measured data, simulated data and / or estimated data may include images. These images may be visually represented. These images may include data points (e.g., pixels) having relative spatial dependencies.

[0017] Simulation data can be calculated by obtaining a theoretical model of the projection system and using the theoretical model to propagate each predetermined illumination profile in a set of predetermined illumination profiles. The theoretical model can define or approximate the optical properties of the projection system. The theoretical model can provide an approximation of the diffraction of radiation passing through the projection system. The calculations can be performed in advance, i.e., pre-calculated. Alternatively, simulation data can be calculated on demand.

[0018] Fitting can include fitting a basis function to the data. The basis function can be a Zernike polynomial. Alternatively, other basis functions can be used, such as Tatian Zernike polynomials.

[0019] The optical properties may include one or more aberrations caused by the projection system. The optical properties may additionally or alternatively include apodization of the projection system. The optical properties may additionally or alternatively include polarization caused by the projection system. Such optical properties may be affected by one or more of the plurality of optical elements in the projection system. Advantageously, actual physical effects caused by the projection system, such as aberrations, apodization, and polarization, can be determined using this method.

[0020] Each of the predetermined irradiation profiles can be represented using a polynomial. Polynomials of up to a finite order can be used, for example, to advantageously reduce processing requirements, thereby increasing the speed of the method. Any number of polynomial functions can be used, for example, two, three, or ten. A third order can provide a good compromise between speed and accuracy of the method.

[0021] The method may further include calculating adjustments based on the determined optical properties. The adjustments may include calibration of the projection system or a component external to the projection system. One or more components may be adjusted. The adjustments may include or further include real-time control operations, such as real-time control operations of the projection system or a component external to the projection system. One or more components may be controlled.

[0022] Advantageously, the methods herein can be used to adjust a projection system, thereby improving the performance of the projection system or an associated process. The process can be, for example, a future exposure to be performed by imaging using the projection system. As described above, the methods herein can be performed without the need for specialized equipment (e.g., ray tracing components, high power processing) that may be required for some other methods. These other methods can be performed once for one type of lithographic apparatus, and the data determined thereby used to calculate adjustments applicable to all apparatus of that type. On the other hand, the methods herein can be performed on the user side and / or during the typical service life of a lithographic apparatus, so that adjustments specific to a particular lithographic apparatus can be calculated. This is particularly beneficial for apodization, which can depend on each individual lens used in a particular lithographic apparatus and is therefore difficult to generalize for the same type of apparatus. Therefore, adjustments calculated according to the methods herein can provide more precise adjustments to optimize the apodization effect for a particular lithographic apparatus.

[0023] The method may also include providing instructions to a component for adjusting the projection system or an external component to apply the adjustment. The component for adjusting the projection system may be, for example, a controller. The controller may be configured to control the position, tilt, or other characteristics of an element associated with the projection system. For example, the element may be an optical element of the projection system, or a support structure that positions an object in the object plane or image plane of the projection system. Thus, the instructions may include instructions for changing the position, tilt, or other characteristics of the element.

[0024] The method may also include providing an indication that the projection system or an element thereof needs to be replaced. Replacing the projection system or an associated element may avoid imaging problems associated with a specific optical property. For example, it may be determined that an aberration greater than an acceptable range is generated by the projection system, and adjustments may not adequately correct the aberration. In this case, an indication may be provided that replacement of the optical element may contribute to the identified aberration, such that the aberration is reduced or eliminated. As an alternative to replacement, the indication may indicate that the projection system or an element thereof needs cleaning.

[0025] According to a second aspect of the present invention, a method for determining optical properties of a projection system is provided, the method comprising: obtaining a measured illumination profile of input radiation received by the projection system; fitting the measured illumination profile to a set of predetermined illumination profiles to generate a parametric fit; and calculating the optical properties of the projection system based on the parametric fit. Obtaining the measured illumination profile may comprise illuminating a pinhole in an object plane of the projection system and receiving radiation output from the projection system while scanning the illuminated pinhole within the object plane.

[0026] Each predetermined illumination profile may be at least partially defined by the intensity, apodization and / or polarization of the input radiation.Beneficially, real physical effects caused by optical elements of the projection system, such as aberrations, apodization and polarization, can be determined in this way.

[0027] According to a third aspect of the present invention, a method for determining an estimated illumination profile for a projection system is provided. The method comprises: obtaining measurement data representing measured radiation output from the projection system; obtaining simulation data representing simulated radiation output from the projection system; fitting the measurement data to the simulation data to generate a profile fit; and generating an estimated illumination profile based on the profile fit, wherein the estimated illumination profile comprises a weighted combination of a set of predetermined illumination profiles. The simulation data may comprise multiple sets of simulation data. Each of the multiple sets may be based on input of radiation to the projection system having a predetermined illumination profile from a set of predetermined illumination profiles. While a desired illumination pupil and / or profile may be selected, the actual illumination pupil and / or profile may differ from the desired illumination pupil and / or profile. Accurately determining the estimated illumination pupil and / or profile for a projection system advantageously enables optimization of imaging processes using the projection system. The method enables accurate determination of the estimated illumination pupil and / or profile with reduced processing requirements. Furthermore, the method can be performed without requiring specialized equipment (e.g., high-power onboard processing) that may be required for some other methods of determining the illumination profile. Thus, the method can be performed at the user's side and / or during the typical service life of the device. This may be advantageous compared to other methods that may only be performed after initial manufacture, testing and / or calibration of the projection system. The method may be computer-implemented. The measurement data may represent measurement radiation output from the projection system during the shearing interferometry process.

[0028] According to a fourth aspect of the present invention, there is provided a method for determining optical properties of a projection system, the method comprising: obtaining measurement data representing measured radiation output from the projection system; obtaining simulation data representing simulated radiation output from the projection system; fitting the measurement data to the simulation data to generate a parameter fit; and calculating the optical properties of the projection system based on the parameter fit.

[0029] Radiation output from the projection system has an illumination profile that differs from the input illumination pupil and / or profile. This difference may be due to the optical properties of the projection system, which in turn cause variations in the radiation. These variations can include, for example, phase shifts (e.g., due to aberrations), intensity variations (e.g., due to apodization), and / or polarization variations. It would be advantageous to accurately determine the optical properties of the projection system so that these variations can be accounted for, for example, in any imaging process using the projection system. This method enables accurate determination of one or more optical properties of the projection system with reduced processing requirements. Consequently, the determination can be completed more quickly and can therefore be performed regularly without significant device downtime. Furthermore, the method can be performed without the need for specialized equipment (e.g., high-power onboard processing) that may be required for some other methods of determining optical properties. Therefore, the method can be performed user-side and / or over the typical service life of the device. This can be advantageous compared to other methods that can only be performed after initial manufacture, testing, and / or calibration of the lithographic apparatus. The method can be computer-implemented. The measurement data can represent measured radiation output from the projection system during a shearing interferometry process.

[0030] According to a fifth aspect of the present invention, a computer-readable medium is provided, which includes instructions that, when executed by a computer, cause the computer to perform the method of any one of the first, second, third, fourth or fifth aspects.

[0031] According to a sixth aspect of the present invention, there is provided a measurement system comprising a projection system and a processor configured to perform the method of any one of the first, second, third, fourth or fifth aspects.

[0032] The measurement system may further include a first support configured to hold the first measurement patterning device in an object plane of the projection system. The measurement system may further include a second support configured to hold the second measurement patterning device in an image plane of the projection system. The measurement system may further include a positioning system configured to scan at least one of the first and second supports relative to one of the first and second supports. The measurement system may further include a sensor configured to generate measurement data.

[0033] The measurement system may further comprise a controller operable to apply adjustments to the projection system or a component external to the projection system. Additionally or alternatively, the controller may be operable to provide an indication that the projection system or an element thereof requires replacement or cleaning.

[0034] According to a seventh aspect of the present invention, a lithographic apparatus is provided that includes the measurement system of the sixth aspect. Currently, high precision requirements are placed on lithographic processes. Better definition or optimization of the optical properties of the projection system or the illumination profile received by the projection system can help achieve these high precision requirements.

[0035] The lithographic apparatus may further comprise a controller operable to apply adjustments to the lithographic apparatus. The adjustments may be to the projection system or a component thereof.

[0036] The lithographic apparatus may further comprise a display screen configured to display an indication, which may be an indication that the projection system or a component thereof requires replacement or cleaning. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0038] - Figure 1 A schematic overview of a photolithographic apparatus is depicted;

[0039] - Figure 2 depicts a schematic overview of a measurement system that may be used in combination with the methods described herein;

[0040] - Figure 3 A method for determining optical properties of a projection system is shown;

[0041] - Figure 4 A method for determining an estimated illumination profile for a projection system is shown;

[0042] - Figure 5 An alternative method for determining the optical properties of a projection system is shown. DETAILED DESCRIPTION

[0043] In this document, the terms "radiation" and "beam" are used to cover all types of electromagnetic radiation, including ultraviolet radiation (e.g., having a wavelength of 365 nm, 248 nm, 193 nm, 157 nm, or 126 nm) and EUV (extreme ultraviolet radiation, e.g., having a wavelength in the range of about 5 to 100 nm).

[0044] As used herein, the terms "reticle," "mask," or "patterning device" should be broadly interpreted as referring to a general patterning device that can be used to impart a patterned cross-section to an incident radiation beam that corresponds to the pattern to be created in a target portion of a substrate. The term "light valve" can also be used in this context. In addition to classical masks (transmissive or reflective, binary, phase-shift, hybrid, etc.), examples of other such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0045] Figure 1 A lithographic apparatus LA is schematically shown. The lithographic apparatus LA comprises an illumination system (also referred to as an illuminator) IL configured to condition a radiation beam B (e.g., UV radiation, DUV radiation, or EUV radiation), a mask support (e.g., a mask table) MT configured to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to accurately position the patterning device MA according to certain parameters, a substrate support (e.g., a wafer stage) WT configured to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW configured to accurately position the substrate support according to certain parameters, and a projection system (e.g., a refractive projection lens system) PS configured to project a pattern imparted to the radiation beam B by the patterning device MA onto a target portion C (e.g., comprising one or more dies) of the substrate W. The plane in which mask MA can be supported (i.e., the plane of mask table MT) can be referred to as mask level. The plane in which substrate W can be supported (i.e., the plane of substrate support WT) can be referred to as substrate level. Mask level and substrate level can be considered to be the object plane and image plane, respectively, of the projection system. Mask level and substrate level are defined with reference to the projection system and exist regardless of whether the support or structure is positioned at mask level or substrate level.

[0046] In operation, the illumination system IL receives a radiation beam from a radiation source SO, for example via a beam delivery system BD. The illumination system IL may include various types of optical components, such as refractive, reflective, magnetic, electromagnetic, electrostatic and / or other types of optical components, or any combination thereof, for guiding, shaping and / or controlling the radiation. The illuminator IL may be used to condition the radiation beam B so that it has a desired spatial and angular intensity distribution in its cross-section at the plane of the patterning device MA. The spatial and angular intensity distribution of the radiation beam B may be referred to as the illumination pupil. Other characteristics of the radiation beam B may also be controlled, such as the polarization of the radiation beam B. The specific characteristics of the radiation beam B may be referred to as the illumination profile of the radiation beam B. The illumination profile may be selected based on, for example, properties of the projection system PS, properties of the patterning device MA and / or properties of the substrate W. The lithographic exposure may be optimized for accuracy and / or duration. The illumination pupil and / or profile may be selected to optimize the lithographic exposure.

[0047] The term "projection system" PS as used herein should be broadly interpreted as covering various types of projection systems, including refractive, reflective, catadioptric, anamorphic, magnetic, electromagnetic and / or electrostatic optical systems, or any combination thereof, as applicable to the exposure radiation used, and / or other factors such as the use of an immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein may be considered synonymous with the more general term "projection system" PS.

[0048] The lithographic apparatus LA may also be of a type having two or more substrate supports WT (also referred to as "dual stage" or "multi-stage"). In such a "multi-stage" machine, the substrate supports WT may be used in parallel, and / or preparatory steps for subsequent exposure of the substrate W may be performed on a substrate W located on one of the substrate supports WT, while another substrate W on another substrate support WT is being used to expose a pattern on another substrate W.

[0049] In addition to the substrate holder WT, the lithographic apparatus LA may further include a measurement stage. The measurement stage is configured to hold sensors. The sensors may be configured to measure properties of the projection system PS or radiation beam B. The measurement stage may hold multiple sensors. When the substrate holder WT is removed from the projection system PS, the measurement stage may be moved below the projection system PS. The plane of the measurement stage, regardless of whether one or more sensors are located therein, may be referred to as a measurement level. The measurement level is located near the image plane of the projection system PS.

[0050] In operation, a radiation beam B is incident on a patterning device (e.g. a mask) MA which is held on a mask holder MT and is patterned by a pattern (design layout) present on the patterning device MA. After having passed through the mask MA, the radiation beam B passes through a projection system PS which focuses the beam onto a target portion C of the substrate W. With the aid of a second positioner PW and a position measurement system IF, the substrate holder WT can be accurately moved, for example, in order to position a different target portion C in the path of the radiation beam B at a focused and aligned position. Similarly, the first positioner PM and possibly a further position sensor (which is located in the Figure 1 The patterning device MA and the substrate W can be precisely positioned relative to the path of the radiation beam B using mask alignment marks M1, M2 and substrate alignment marks P1, P2. Although the substrate alignment marks P1, P2 are shown as occupying dedicated target portions, they can also be located in the space between target portions. When the substrate alignment marks P1, P2 are located between target portions C, they are referred to as scribe line alignment marks.

[0051] To illustrate the present invention, a Cartesian coordinate system is used. The Cartesian coordinate system has three axes, namely the x-axis, the y-axis, and the z-axis. Each of these three axes is orthogonal to the other two axes. Rotation about the x-axis is called an Rx rotation. Rotation about the y-axis is called an Ry rotation. Rotation about the z-axis is called an Rz rotation. The x-axis and the y-axis define a horizontal plane, while the z-axis is in a vertical direction. The Cartesian coordinate system does not limit the present invention and is only used for illustration. On the contrary, other coordinate systems (such as cylindrical coordinate systems) can also be used to illustrate the present invention. The orientation of the Cartesian coordinate system can be different, for example, so that the z-axis has a component along the horizontal plane.

[0052] The projection system PS may introduce optical aberrations and errors in the illumination pupil and / or profile. Thus, while a desired illumination pupil and / or profile may be selected, the actual illumination pupil and / or profile received at the substrate W may differ from the desired one. Consequently, the projection system PS may affect the quality and characteristics of the image projected by the projection system PS. Errors and aberrations can affect patterning accuracy, critical dimensions, and overlay in lithographic exposures.

[0053] Figure 2 is a schematic diagram of a measurement system 20 that can be used to determine optical properties of a projection system PS, such as aberrations caused by the projection system PS. The measurement system 20 may form part of a lithographic apparatus. For example, Figure 2 The projection system PS shown can be Figure 1 The measurement system 20 comprises a first measurement patterning device MA' which can be positioned at a mask level 22, for example by a mask holder such as a Figure 1 The mask level 22 is the object plane 22 of the projection system PS. The measurement system 20 further comprises a second measurement patterning device MA'' which can be positioned at the substrate level 24, for example by a substrate support such as Figure 1 The substrate is supported by a substrate holder WT (depicted in FIG). The substrate level 24 is the image plane 24 of the projection system PS. The measurement patterning device MA′, MA″ comprises a plurality of patterned areas, for example in the form of a reflective or transmissive diffraction grating. Consequently, radiation incident on the measurement patterning device MA′, MA″ is at least partially refracted and / or diffracted due to interaction with the measurement patterning device MA′, MA″.

[0054] The measurement system 20 further comprises a sensor 26 positioned to detect radiation that has been transmitted through (or refracted or diffracted by) the second measurement patterning device MA. The sensor 26 may be positioned in a plane conjugate to a pupil plane of the projection system PS. The sensor 26 is configured to detect a spatial intensity distribution of radiation incident on the sensor 26. The sensor 26 may, for example, comprise an array of individual detector elements or sensing elements. For example, the sensor 26 may comprise an active pixel sensor, such as, for example, a CMOS (Complementary Metal Oxide Semiconductor) sensor array. Alternatively, the sensor 26 may comprise a CCD (Charge Coupled Device) sensor array.

[0055] In use, a radiation beam B is provided to the measurement system 20. The radiation beam B may be provided by, for example, an illumination source such as Figure 1 The radiation beam B propagates through the measurement system 20. Figure 2 , shown with arrows. In the imaginary Cartesian coordinate system used for illustrative purposes, radiation beam B generally travels in the negative z-direction through measurement system 20. However, it should be understood that other arrangements of measurement systems are possible that perform similar functions to those described herein. In these other measurement systems, the radiation beam may travel in different directions, and its path may be altered, for example, by optical elements such as mirrors. The radiation beam B provided to the measurement system may be modified for use in a measurement process using measurement system 20. For example, radiation beam B may be diffused.

[0056] A radiation beam B is directed to a first measurement patterning device MA'. It interacts with the first measurement patterning device MA' before being received as input radiation by the projection system PS. The radiation beam B is projected by the projection system PS such that an image of the first measurement patterning device MA' on the object plane 22 is formed at the image plane 24. During the measurement process, a second measurement patterning device MA' is positioned approximately co-located with the image formed by the first measurement patterning device MA'. The radiation beam B interacts with the second measurement patterning device MA' before being received by the sensor 26. Due to the interaction of the radiation beam B with the measurement patterning devices MA', MA', the radiation received by the sensor 26 contains an interference pattern.

[0057] The measurement system 20 further comprises a positioning system PW. The positioning system moves the second measurement patterning device MA" within the image plane 24 (e.g. in an imaginary xy plane). The positioning system PW may move the second measurement patterning device MA" itself, or may move a support holding the second measurement patterning device MA", and movement or scanning of the second measurement patterning device MA" may be considered to comprise either arrangement. Due to the movement, the second measurement patterning device MA" is scanned relative to the first measurement patterning device MA', albeit in a conjugate plane. Thus, the second measurement patterning device MA" is scanned relative to the image of the first measurement patterning device MA' projected onto the image plane 24. The second patterning device MA" and / or the support holding the second measurement patterning device MA" are mechanically coupled to the sensor 26 such that the sensor is also scanned relative to the first measurement patterning device MA'. Mechanical coupling in Figure 2 It is not shown in the figure, but may comprise, for example, a physical connection between the sensor 26 and a support table holding the second measurement patterning device MA".

[0058] In other arrangements, the sensor 26 need not be mechanically coupled to the second measurement patterning device MA" and / or its support. In such an arrangement, the second measurement patterning device MA" (or its support) can be moved without movement of the sensor. Alternatively, the positioning system PW can move the first measurement patterning device MA' (or its support) such that the first measurement patterning device MA' is scanned relative to the second measurement patterning device MA". In any arrangement, the positioning system PW can be considered to provide relative scanning between the first patterning device MA' and the second measurement patterning device MA".

[0059] The movement (scanning) can be performed in steps. That is, instead of a continuous movement of the second measurement patterning device MA", the device MA" is moved in discrete steps. The size of the step can be selected based on the pitch of the diffraction grating of the measurement patterning device MA', MA". Scanning can also be performed in more than one direction. For example, the measurement patterning devices MA', MA" can be moved relative to each other in the x-direction and then moved relative to each other in the y-direction. Alternatively, the measurement patterning devices MA', MA" can be moved relative to each other in the y-direction and then moved relative to each other in the x-direction. Alternatively, the measurement patterning devices MA', MA" can be moved relative to each other in the x-direction and then moved relative to each other in the y-direction. Alternatively, the measurement patterning devices MA', MA" can be moved relative to each other in the x-direction and the y-direction at the same time. By scanning the first measurement patterning device MA' or the second measurement patterning device MA" relative to each other, a shearing interferometer is formed. The sensor 26 is positioned to measure the interference pattern formed by radiation traveling through the first patterning device MA' and the second patterning device MA" at specific relative positions to each other. The data generated in this way can be considered to be generated during the shearing interferometry process. The measurements taken at different scanning positions can be analyzed in order to derive information about the radiation at each relative scanning position.

[0060] The sensor 26 outputs data representing the radiation on the sensor 26 at a specific scanning position. The output data can be visually represented as an image. By using the sensor 26 to measure in multiple scanning positions, a collection of data (or a collection of images) can be obtained. Each image represents the spatial intensity distribution of the radiation incident on the sensor 26 at the corresponding scanning position. The intensity of the radiation at each position (e.g., each pixel) on the sensor 26 will change as the scanning occurs (i.e., it changes with each scanning position). This change is generally periodic in nature. Based on the variation signal measured by the sensor 26, various types of information can be extracted from the data obtained by the sensor 26, for example, by decomposing the variation signal. Specifically, offset, amplitude, and phase difference (also known as phase shift) can be extracted. In order to extract the above information, the variation signal can be decomposed using a sine function. Typically, the longest sine period that matches the variation signal is used. However, higher-order and / or non-sinusoidal variations can be used for decomposition.

[0061] The offset is a measure of the average intensity of the radiation, for example, averaged over an integer number of sinusoidal variation periods. The amplitude is a measure of the difference between the offset and the maximum (and / or minimum) intensity measured. The phase difference is a measure of the phase shift of a sinusoidal function fitted to a periodic signal. For a given incident beam direction, each diffraction order of the radiation that has been diffracted by the first measurement patterning device MA' undergoes a phase shift that corresponds to the light trajectory of that diffraction order through the projection system PS. The phase shift is therefore caused by the projection system PS. Each diffraction order is then diffracted by the second measurement patterning device MA" and may be diffracted along different directions onto different light trajectories. Due to the coherent and incoherent interference of the diffraction orders based on their trajectories, the signal output by the sensor 26 captures the phase shift information. The data representing the phase difference described herein is also referred to as phase data, or the phase component of the data. The offset may also be referred to as direct current (DC). The amplitude may also be referred to as alternating current (AC). The term "contrast" may also be used to refer to twice the amplitude (i.e. 2×amplitude or 2×AC).

[0062] The extracted offset data represents the offset at each location on sensor 26 and can be visually represented as an image (e.g., the "intensity" at each location quantifies the magnitude of the offset), referred to as an offset map. Similarly, the extracted amplitude data represents the amplitude at each location on sensor 26 and can be visually represented as an image (e.g., the "intensity" at each location quantifies the magnitude of the amplitude), referred to as an amplitude map. Similarly, the extracted phase data represents the phase at each location on sensor 26 and can be visually represented as an image (e.g., the "intensity" at each location quantifies the magnitude of the phase difference), referred to as a phase map.

[0063] Typically, the projection system PS has an optical transfer function that can be non-uniform, which can affect the image projected by the projection system PS. The projection system PS can cause phase shifts (e.g., due to aberrations), intensity variations (e.g., due to apodization (transmission) of radiation traveling through it), and polarization variations. The magnitude of these effects and their properties (e.g., the type of aberration) can also depend on the polarization of the radiation. Analysis of one or more of the offset, amplitude, and phase data can yield information about the aberrations, polarization, and apodization caused by the projection system PS. Other components of the measurement system 20, such as the sensor 26, can also cause aberrations (e.g., phase shifts), polarization variations, and intensity variations. Therefore, it can be beneficial to calibrate for such aberrations and variations to accurately identify the properties of the projection system PS. Most variations caused by the sensor 26 will typically have a different "fingerprint" from that of the projection system and, therefore, be distinguishable. Consequently, any effects caused by the sensor 26 can be removed from the data.

[0064] Aberrations, polarization, and apodization of (or caused by) the projection system PS can be referred to simply as the optical properties of the projection system PS. Generally, it is convenient to have accurate knowledge of the optical properties of the projection system PS. By accurately knowing the optical properties of the projection system PS, the intended image projected by the projection system PS can be predicted with greater accuracy. By accurately knowing the optical properties of the projection system PS, adjustments to the projection system PS can be made to optimize the resulting image. The projection system PS typically includes a plurality of optical elements. Adjustments can be made to one or more of these optical elements based on the optical properties of the projection system PS. Such adjustments can correct the optical properties of the projection system PS; for example, they can correct aberrations caused by the projection system PS. Alternatively, an indication can be provided that an optical element should be replaced, cleaned, or otherwise addressed. This indication can be directed to the user; for example, it can be displayed on a display associated with the projection system PS, the measurement system 20, or an external device.

[0065] Figure 2 A controller CN is further depicted. The controller CN is operable to apply adjustments to the projection system PS, for example, adjustments to one or more of the optical elements of the projection system PS. The controller CN, or an adjustment component to which the controller CN sends instructions, may be operable to perform any combination of: displacing one or more optical elements; tilting one or more optical elements; and / or deforming one or more optical elements. The displacement of the optical elements may be in any direction (x, y, z, or a combination thereof). The tilting of the optical element is typically performed by rotating the optical element out of a plane perpendicular to the optical axis about an axis in the x or y direction, although rotation about the z axis may be used for non-rotationally symmetric optical elements. Deformation of the optical element may be performed, for example, by applying a force to the side of the optical element using an actuator and / or heating a selected area of ​​the optical element using a heating element.

[0066] The controller CN may additionally or alternatively be arranged to apply adjustments to components external to the projection system PS. For example, the controller CN may be operable to adjust Figure 1 The support structure MT and / or substrate table WT of the lithographic apparatus LA are adjusted so as to correct aberrations caused by placement errors. Adjustments of both the projection system and external components of the projection system may be in the form of calibration or real-time adjustment. Calibration may be performed before the projection system is used for its intended purpose, such as a series of lithographic exposures. Calibration may be performed periodically, for example once a day or once a week. Real-time adjustment may be performed more regularly, for example once an hour or once a minute. Real-time adjustment may be referred to as a real-time control operation because it is possible to control the operation while it is in progress. As described in more detail below, the process described herein is less computationally intensive than other methods of determining adjustments and may therefore be very suitable for real-time adjustment.

[0067] The controller CN may also include or be in communication with a processor (not shown) configured to determine such adjustments, for example based on one or more optical properties of the projection system PS. Methods of determining optical properties of the projection system PS will be described in more detail below.

[0068] The controller CN may additionally or alternatively be configured to provide an indication that the optical element should be replaced, cleaned or otherwise processed.The controller CN may be in communication with a display screen for displaying said indication.

[0069] Figure 3 A method for determining a projection system (e.g., Figure 2 Method 300 for determining the optical properties of a projection system PS).

[0070] In a first step 310, measurement data representing radiation output from the projection system is obtained. The measurement data is associated with (e.g., obtained from) empirical measurements of radiation that has traveled through a real projection system. That is, the measurement data is associated with actual (measured) radiation output from the projection system when the projection system receives actual input radiation as input. The measurement data may be obtained using the method described above with reference to Figure 2 The measurement system 20 described is generated. For example, the input radiation is a radiation beam B, and the measurement data can include a signal output by the sensor 26, or data extracted from the signal output by the sensor 26 (e.g., offset, amplitude, and / or phase data). The measurement data can be measured as part of the method 300 for determining optical properties of the projection system, for example, in real time before or concurrently with the other steps of the method 300. Alternatively, the measurement data can be obtained from previously measured data. For example, the measurement data may have been previously generated from a historical measurement process and stored in a storage device. In this case, obtaining the measurement data can include receiving the measurement data from the storage device.

[0071] In a second step 320, an estimated illumination profile is obtained. The estimated illumination profile is an estimate of the characteristics (e.g., spatial and angular intensity distribution and / or polarization) of the radiation beam received by the projection system. It will be appreciated that although an illumination system providing radiation to the projection system may be controlled to provide radiation having a desired illumination profile, the actual illumination profile provided may differ from the desired illumination profile. Methods for obtaining the estimated illumination profile will be described below with reference to Figure 4 are described in more detail.

[0072] In a third step 330, estimate data is generated. The estimate data is calculated based on the estimated illumination profile obtained in the second step 320. The estimate data represents the estimated radiation that would be output from the projection system if the projection system received radiation having the estimated illumination profile as input. The estimate data can be generated using general optical principles governing the propagation of radiation based on currently known optical characteristics of the projection system (e.g., known dimensions, refractive indices, etc. of various optical elements therein). The estimate data can be in the form of an estimate signal to be output by the sensor, or can be data extracted therefrom (e.g., offset, amplitude, and / or phase data).

[0073] In a fourth step 340, the estimated data is fitted to the measured data. Fitting can include fitting a set of basis functions to the measured data. A particularly convenient set is the Zernike polynomials, which form a set of orthogonal polynomials confined on the unit circle. Determining each scalar map may involve determining coefficients in such an expansion. Since the Zernike polynomials are orthogonal on the unit circle, the Zernike coefficients can be obtained from the measured scalar map by sequentially calculating the inner product of the measured scalar map with each Zernike polynomial and dividing it by the square of the norm of the Zernike polynomial. It will be appreciated that other sets of basis functions may be used. For example, some embodiments may use Tatian Zernike polynomials, such as for occluded aperture systems.

[0074] The estimated data can be fitted directly to the measurement graph. Alternatively, the data can be compressed, for example, by representing each data set as a Zernike polynomial. In this compressed format, the fit can then be performed by comparing the Zernike coefficients of the estimated data with those of the measured data. Using a compressed format has the benefit of reduced storage space and increased processing speed.

[0075] The output of fitting the estimated data to the measured data is a parameter fit. The parameter fit can include, for example, a set of Zernike coefficients that quantize the fit. A finite number of coefficients can be determined, for example, Zernike coefficients with a Noll index up to 5. The Noll index of 5 is used for illustrative purposes only, and any number of coefficients can be used, for example, Noll indices up to 3, 10, or any other number.

[0076] In a fifth step 350, the optical properties of the projection system are determined based on the parameter fitting. For example, the Zernike coefficients calculated based on the fitting can be used to determine one or more aberrations caused by the projection system. The phase component of the measurement data can be referred to as a wavefront aberration map, which represents the deformation of the wavefront of light approaching a point in the image plane of the projection system PS from a spherical wavefront (depending on the position in the pupil plane or, alternatively, the angle at which the radiation approaches the image plane of the projection system PS). The wavefront aberration map W(x,y) can be represented as a linear combination of Zernike polynomials:

[0077] W(x,y)=∑ n Z n ·z n (x,y) (1)

[0078] where x and y are coordinates in the pupil plane, z n (x,y) is the nth Zernike polynomial, and Z n are the Zernike coefficients with Knoll index n. The wavefront aberration map can then be given by the coefficient Z in this expansion n Different Zernike coefficients can provide information about different forms of aberrations caused by the projection system PS.

[0079] The first Zernike coefficient Z1 is related to the average value of the measured wavefront (which can be called translation). The first Zernike coefficient may be irrelevant to the performance of the projection system PS. The second Zernike coefficient Z2 is related to the tilt of the measured wavefront in the x-direction. The tilt of the wavefront in the x-direction is equivalent to the position of the projected image in the x-direction. The third Zernike coefficient Z3 is related to the tilt of the measured wavefront in the y-direction. The tilt of the wavefront in the y-direction is equivalent to the position of the projected image in the y-direction. The fourth Zernike coefficient Z4 is related to the defocus of the measured wavefront. The fourth Zernike coefficient is equivalent to the position of the projected image in the z-direction. Higher-order Zernike coefficients are related to other forms of aberrations caused by the projection system (such as astigmatism, coma, spherical aberration and other effects).

[0080] In this specification, the term "aberration" should be intended to include all forms of deviation of a wavefront from a perfectly spherical wavefront. That is, the term "aberration" can be associated with the position of the image (e.g., the second Zernike coefficient, the third Zernike coefficient, and the fourth Zernike coefficient), and / or can be associated with higher-order aberrations (such as aberrations associated with Zernike coefficients having a Knoll index of five or greater).

[0081] The present inventors have recognized that determining the optical properties of a projection system by fitting measured data in combination with estimated data provides a more accurate determination of the optical properties, compared to fitting measured data alone or fitting measured data based on an assumed (e.g., desired) illumination profile. Furthermore, fitting can be computationally less intensive, for example, because it can be based on some pre-calculated information, i.e., the estimated data. Consequently, fitting can take into account more coefficients and, therefore, higher-order effects. Alternatively, the process can be implemented faster and with lower processing requirements. A faster process with reduced hardware requirements can therefore be more easily implemented in real time.

[0082] The inventors have also realised that the process can be further improved by using selected components of the data, such as offset data, amplitude data or phase data. Specific components are particularly suitable for certain operations, so using separate components can significantly simplify the operation.

[0083] In the above example, where fitting is performed to determine aberrations caused by the projection system, the phase component of the estimated data and the phase component of the measured data can be used in the fitting process, for example because aberrations are well represented by the phase of the wavefront. The phase component of the estimated data can be fitted using Zernike coefficients to provide a set of estimated Zernike coefficients. This set of estimated Zernike coefficients can be used to fit the Zernike coefficients to the measured data. Because the set of estimated Zernike coefficients is provided as a starting point for the fitting process, fitting basis functions to the measured data is less computationally intensive. Consequently, a more accurate determination of the actual Zernike coefficients that fit the measured data can be obtained. Consequently, a more accurate determination of aberrations can be achieved. In other example embodiments, other optical properties (such as apodization and polarization) can also be determined based on the fitting.

[0084] Although the steps of the method for determining optical properties of a projection system are represented as a first step, a second step, a third step, etc., this does not imply a particular order. While some steps should be performed sequentially (e.g., the first step 310 of obtaining measurement data must be performed before the fourth step 340 of fitting to the measurement data), other steps can be performed in any order. In particular, obtaining measurement data 310 and obtaining an estimated illumination profile 320 can be performed in any order, including simultaneously.

[0085] Figure 4 A method for determining an estimated illumination profile for a projection system is shown. The estimated illumination profile may be, for example, Figure 3 The estimated illumination profile used in method 300 is described.

[0086] In a first step 410, measurement data is obtained. The acquisition of measurement data is described above with reference to Figure 2 and Figure 3 has been described in detail and will not be described further here.

[0087] In a second step 420, simulation data is obtained. The simulation data represents simulated radiation that would be output from the projection system given a specific input radiation. The simulation data includes multiple sets of simulation data. Each set can be based on input of radiation to the projection system having a predetermined illumination profile from a set of predetermined illumination profiles.

[0088] A predetermined illumination profile can be defined in terms of its illumination pupil, apodization and / or polarization. Any illumination profile can be represented or at least approximated by a combination of polynomial functions. For example, the spatial and / or angular intensity distribution defining the illumination pupil can be represented by a two-dimensional polynomial across the field of the radiation beam. The set of polynomial functions describing the illumination profile can be, for example, the set: 1, x, y, ..., x 3 ,x 2 y,xy 2 ,y 3 ,…. Any number of polynomial functions may be used, for example, two, three, or ten. A smaller number of orders may speed up the method, while an increased number may improve the accuracy of the determined estimated illumination profile. Three orders may provide a useful compromise between speed and accuracy. Each predetermined illumination profile is represented by one or a combination of a set of polynomial functions. The set may include predetermined illumination profiles corresponding to a desired illumination profile and / or include deviations from the desired illumination profile due to common aberrations.

[0089] The set of predetermined illumination profiles can also include any number of illumination profiles. Similar to the number of polynomial functions, increasing the number of predetermined illumination profiles can improve the accuracy of the estimated illumination profile, while a smaller number of predetermined illumination profiles can increase the speed of the calculation. A set of ten illumination profiles can provide a beneficial trade-off between speed and accuracy, but any number can be used, such as two, ten, fifteen, or twenty-one.

[0090] The propagation of radiation having each predetermined illumination profile through the projection system is simulated to generate simulation data. Such simulations can be performed using known optical principles that determine the propagation of radiation. The propagation can be based on a theoretical model of the projection system, for example, taking into account currently known optical properties of the projection system and its optical components. For example, the theoretical model may include known dimensions, focal lengths, and refractive indices of optical components in the projection system. Alternatively, the simulation data can be generated using a ray tracing process. The simulation data can be in the form of an analog signal output by a sensor, or can be data extracted therefrom (e.g., offset, amplitude, and / or phase data).

[0091] The simulation data can be generated in real time as part of the method of determining the estimated illumination pupil and / or profile 400. Alternatively, the simulation data can be pre-calculated and obtained when needed, for example from a storage device. The simulation data can be simulated for the specific projection system for which it is being determined, or for general projection systems of the same type, based on the estimated illumination pupil and / or profile.

[0092] In a third step 430, the measured data is fitted to the simulated data to generate a profile fit. The fit can include fitting a set of basis functions, such as described above with reference to Figure 3 The Zernike polynomials described in the fourth step 340 of the method 300 are shown in FIG.

[0093] In a fourth step 440, profile fitting is used to determine an estimated illumination profile. The estimated illumination profile is represented by a weighted combination of a set of predetermined illumination pupils and / or profiles. While in other approaches, the assumed illumination profile may be based solely on the expected illumination profile assumed to be provided by the illumination system, in this approach, a more accurate estimate of the illumination profile is provided. The estimated illumination profile is mathematically represented as a weighted sum of polynomials. Furthermore, based on the fitting in the third step 430, the estimated illumination profile has an associated Zernike component.

[0094] The fitting in the third step 430 can be performed using components other than phase in the measured and simulated data. For example, the measured and simulated data may include an offset component. Advantageously, the offset component provides a good estimate of the illumination profile, but is relatively unaffected by aberrations. Furthermore, the offset component is approximately linear in illumination and apodization. Therefore, fitting the offset component can provide an accurate estimate of the illumination pupil and / or profile with relatively low processing requirements, as there is no need to consider multiple components or nonlinear contributions. In alternative embodiments, an amplitude component can be used instead of or in addition to the offset component. The amplitude component is only weakly dependent on aberrations, but can provide a reliable method for estimating the illumination pupil and / or profile.

[0095] The method of determining the estimated illumination pupil and / or profile 400 can be performed separately or as part of the method described above for determining optical properties of the projection system 300. This combination is particularly beneficial because, when determining the estimated illumination pupil and / or profile, the fitting parameters generated during profile fitting can be used as a starting point for parameter fitting when determining the optical properties.

[0096] An example implementation of a combination of the two methods 300, 400 is as follows. After providing input radiation to a projection system, measuring the output radiation during phase stepping, and extracting offset and phase data therefrom, measurement data is obtained in the form of an offset map (referred to as a measured offset map) and a phase map (referred to as a measured phase map). Simulation data is obtained in the form of an offset map (referred to as a simulated offset map) by retrieving previously calculated simulation data from a storage device. The simulation data includes a plurality of offset maps, each associated with a predetermined irradiation profile from a set of predetermined irradiation profiles. Zernike polynomials are fitted to (the offset components of) the measurement data to calculate Zernike coefficients. The measured offset map can be fitted directly to the simulated offset map. Alternatively, the maps can be compressed by representing each map with a Zernike polynomial. In a compressed format, the fitting can then be performed by comparing the Zernike coefficients of the measured offset map with the Zernike coefficients of the simulated offset map. Using a compressed format has the benefit that storage space is reduced and processing speed is increased.

[0097] The calculated Zernike coefficients are then used to determine a weighted combination of simulated offset maps that, when fitted using Zernike polynomials, provides the same or similar Zernike coefficients. That is, the calculated Zernike coefficients are used to determine a weighted combination of simulated offset maps that provides a best estimate of the measured offset map. The weights associated with the weighted combination of simulated offset maps are then used to calculate an associated weighted combination of predetermined illumination profiles. Thus, the calculated weighted combination of predetermined illumination profiles represents an estimated illumination profile.

[0098] Using the estimated illumination profile, estimated data is generated. The estimated data is in the form of a phase map (referred to as an estimated phase map). The estimated phase map is then fitted with Zernike polynomials to generate estimated Zernike coefficients. These estimated Zernike coefficients are used as a starting point to fit Zernike polynomials to the measured phase map to generate measured Zernike coefficients. Based on the measured Zernike coefficients, the optical properties of the projection system are determined, such as aberrations caused by the projection system.

[0099] The steps of the methods described herein may be combined. In this case, the method (e.g., Figure 3 One or more steps of the method 300 may be combined with another method (e.g., Figure 4 One or more steps of the method 400) may be combined without all steps being used. That is, these method steps may be performed in isolation from other method steps. For example, in the combination Figure 3 The steps of method 300 and Figure 4 In an alternative to the steps of method 400, a process for estimating the illumination pupil and / or profile is determined (e.g., Figure 4The fourth step 440 of method 400 is removed.

[0100] In the first step, the measurement data are as shown in the reference Figure 2 and Figure 3 In particular, the measurement data may comprise a phase map.

[0101] In another step, simulation data is obtained. The simulation data represents simulated radiation that will be output from the projection system given a specific input radiation. The simulation data includes multiple sets of simulation data. In this example implementation, each set is based on the propagation of radiation through the projection system, where the propagation system causes specific aberrations. For example, the aberrations can be tilt, coma, etc., or a combination thereof. The aberrations can be described using Zernike polynomials, for example, each aberration being represented by a different Zernike order. Therefore, the simulation data can include phase maps, where each phase map represents a simulated phase of radiation that has been affected by a specific aberration (e.g., of a specific Zernike order).

[0102] In a further step, the measured data are fitted to the simulated data, e.g. as in reference Figure 4 The fitting can be performed as described in the third step 430 of method 400. The fitting can be performed by fitting the measured phase map to the simulated phase map. Alternatively, the phase maps can be compressed by representing each map using a Zernike polynomial. In the compressed format, the fitting can then be performed by comparing the Zernike coefficients of the measured offset map with the Zernike coefficients of the simulated offset map. Using a compressed format has the advantage of reducing storage space and increasing processing speed.

[0103] In a further step, a phase diagram offset and a phase diagram dependency for each Zernike coefficient are output. The phase diagram offset and the phase diagram dependency can be generated based on fitting the measured data to the simulated data. For example, they can represent a fit between the measured data and one of the simulated data in a set of simulated data. Thus, the phase diagram offset and the phase diagram dependency can represent a fit of the measured data to a specific Zernike order and, therefore, a specific aberration. In this way, fitting the measured data to the simulated data can be used to estimate the contribution of various aberrations caused by the projection system. The phase diagram dependency for each Zernike matrix represents the Jacobian matrix of the phase diagram relative to the Zernike matrix. The phase diagram dependency can show both linear and nonlinear dependencies.

[0104] The performance of the method described herein can be evaluated as follows: A wavefront aberration diagram represents the deformation of the wavefront of light approaching a point in the image plane of the projection system from a spherical wavefront and can be represented as a linear combination of Zernike polynomials:

[0105] W(x,y)=∑ n cn ·Z n (x,y) (2)

[0106] where x and y are coordinates in the pupil plane, z n (x,y) is the nth Zernike polynomial and c n is the coefficient, and n is the Knoll index. It is possible to convert a pure Zernike wavefront aberration map (e.g. Z n ) is input into the reconstruction algorithm and evaluated on how well the reconstruction algorithm reconstructs it as a linear combination of Zernike polynomials. Ideally, the reconstruction algorithm should output the Zernike coefficients c m The set of m=n, c m =1 and for m≠n, c m =0. c n Any variation from 1 can be called gain error. In addition, c m Any variation from 0 in the case of m≠n can be referred to as crosstalk error.

[0107] In general, if the projection system has a Zernike coefficient c actual The aberration map described by the vector is then the vector c of the Zernike coefficients reconstructed by the reconstruction algorithm reconstructed It can be given by:

[0108] c reconstructed =M·c actual (3)

[0109] Where M is a matrix containing the reconstructed gain error and crosstalk error. Specifically, the diagonal elements of the matrix M should ideally be 1, and the off-diagonal elements are the crosstalk errors (and ideally should be zero). Therefore, ideally, the matrix M should be the identity matrix, which will indicate perfect reconstruction. The error matrix E can be defined as:

[0110] E=MI (4)

[0111] Where I is the identity matrix. The diagonal elements of the matrix E are the gain errors (and ideally should be zero), and the off-diagonal elements are the crosstalk errors (and ideally should be zero). Therefore, the matrix E represents a good figure of merit for evaluating errors in aberration map reconstruction.

[0112] The error matrix E associated with another method of determining the optical properties of the projection system that does not use estimated data can exhibit error magnitudes in the range of greater than -250 to 200. On the other hand, the error matrix associated with the method described herein has significantly lower errors, with error magnitudes typically in the range of -10 to 40, demonstrating the improved performance of the method described herein that uses estimated data. Crosstalk errors are also improved when estimated data is used as described herein.

[0113] Figure 5 An alternative method 500 for determining optical properties of a projection system is shown. In a first step 510, a measured illumination profile is determined. The measured illumination profile is associated with the illumination profile of radiation output from the projection system. The measured illumination profile may include information about, for example, the illumination pupil, polarization, and / or apodization.

[0114] Measuring the irradiation profile can be done using Figure 2 A variant of the measurement system depicted in FIG is measured. In this variant, instead of providing a first measurement patterning device MA′ and a second measurement patterning device MA″, a pinhole is provided instead of the first measurement patterning device MA′. The pinhole is illuminated so that an image of the pinhole (or an interference pattern from the pinhole) is formed at the sensor 26. The positioning system PW scans the pinhole and the sensor 26 relative to each other and measures the radiation received at the sensor at each scan position. The measurement illumination profile can then be extracted from the signal output by the sensor 26 using known methods.

[0115] In a second step 520, the measured illumination profile is fitted to a set of predetermined illumination profiles. The set of predetermined illumination profiles may be similar to the one described above with reference to Figure 4 The set of predetermined irradiation profiles described is the same. Fitting may be performed in the same manner as described above, for example using Zernike basis functions. Fitting may provide a parametric fit, for example in the form of Zernike coefficients.

[0116] In a third step 530, the optical properties of the projection system are calculated. The optical properties can be determined directly from the parameter fitting determined in the previous step. Alternatively, measurement data can be obtained (using any of the methods described above) and fitted using the parameter fitting as a starting point. The fitting of the measurement data can then be used to calculate the optical properties.

[0117] The generation of measurement data described herein can be performed offline, i.e., not during the method for determining optical properties or estimating the illumination profile. Thus, measurement system 20 need not include sensors, measurement patterning devices, or positioning systems to perform the method for determining optical properties described herein. Instead, measurement data can be obtained, for example, by retrieval from a storage device, rather than generated on demand. Furthermore, while measurement system 20 is depicted as including a controller for applying adjustments to projection system PS or other components, the method for determining optical properties can be performed without a controller.

[0118] The data described herein may be in the form of an image, or may be in any other data format, such as a matrix, tensor, or other structured data format. Although the examples given herein illustrate the specific use of certain components (e.g., offset or phase), the methods may alternatively or additionally use other components. For example, the measured data, simulated data, and / or estimated data may each include one or more of offset, phase, and amplitude data.

[0119] The fitting described herein can be performed using images, for example, by fitting a measured camera image to a simulated camera image. Alternatively, a compression fitting method can be used. The compression method involves determining a simplified Zernike fit to the data (e.g., to a phase map) and storing the data in the form of compressed data (e.g., in the form of Zernike coefficients). When a subsequent fit is required, the entire set of measured data need not be fitted to, for example, the estimated data. Instead, the compressed data is fitted to the estimated data. Compression methods such as this one can reduce the required storage space and increase computational speed.

[0120] When fitting is performed for the purpose of determining the optical properties of the projection system, the output of the fitting may be referred to as a parameter fit. When fitting is performed for the purpose of determining the illumination profile, the output of the fitting may be referred to as a profile fit. The output of the fitting may be, for example, a set of Zernike coefficients.

[0121] Although specific reference may be made herein to embodiments of the present invention in the context of a lithographic apparatus, the methods and apparatus described herein may be used in other systems. The methods and apparatus described herein may be used in combination with a mask inspection apparatus, a metrology apparatus, or any apparatus for measuring or processing an object such as a wafer (or other substrate) or a mask (or other patterning device). These apparatuses may be generally referred to as lithographic tools. Such lithographic tools may use vacuum conditions or ambient (non-vacuum) conditions.

[0122] Where the context permits, the methods and systems described herein may be implemented in hardware, firmware, software, or any combination thereof. These methods may be implemented as instructions stored on a machine-readable medium that can be read and executed by one or more processors. A machine-readable medium may include any mechanism for storing or transmitting information in a form readable by a machine (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 propagated signal (e.g., a carrier wave, an infrared signal, a digital signal, etc.), and the like. In addition, firmware, software, routines, instructions may be described herein as performing certain actions. However, it should be understood that these descriptions are for convenience only, and that these actions are actually generated by a computing device, processor, controller, or other device that executes the firmware, software, routines, instructions, etc., and that when performing these actions, actuators or other devices may interact with the physical world.

[0123] Although specific embodiments of the present invention have been described above, it will be appreciated that the present invention may be practiced in other ways than as described. The foregoing description is intended to be illustrative and not limiting. Therefore, it will be appreciated by those skilled in the art that modifications may be made to the described invention without departing from the scope of the appended claims. Other aspects of the present invention are set forth in the following numbered clauses.

[0124] 1. A method for determining an optical property of a projection system, the method comprising:

[0125] obtaining measurement data representative of measurement radiation output from the projection system;

[0126] obtaining an estimated illumination profile of input radiation received by the projection system;

[0127] generating estimate data representing estimated radiation output from the projection system based on the estimated illumination profile;

[0128] fitting the estimated data to the measured data to generate a parameter fit; and

[0129] Optical properties of the projection system are calculated based on the parameter fitting.

[0130] 2. A method according to clause 1, wherein the measurement data represents at least one component of the measured output radiation, wherein the component is selected from the following set: a phase component, an amplitude component and an offset component; and the estimated data represents a corresponding at least one component of the estimated output radiation.

[0131] 3. A method according to clause 1 or 2, wherein the component of the measurement data and the corresponding component of the estimate data each comprise the phase component.

[0132] 4. The method of any preceding clause, wherein obtaining the estimated illumination profile comprises:

[0133] obtaining simulated data representing simulated radiation output from the projection system, wherein the simulated data comprises a plurality of sets of simulated data and each of the plurality of sets is based on input of radiation to the projection system having a predetermined illumination profile from a set of predetermined illumination profiles; and

[0134] fitting the measured data to the simulated data to generate a profile fit;

[0135] The estimated illumination profile is generated based on the profile fitting, wherein the estimated illumination profile comprises a weighted combination of the set of predetermined illumination profiles.

[0136] 5. The method of clause 4, wherein each of the predetermined illumination profiles is at least partially defined by the angular distribution, apodization and / or polarization of the input radiation.

[0137] 6. A method according to clause 4 or 5, wherein:

[0138] The measurement data represents at least one component of the output radiation measured, the at least one component being selected from the group consisting of: a phase component, an amplitude component, and an offset component; and

[0139] The simulation data represents the estimated corresponding at least one component of the output radiation.

[0140] 7. The method of clause 6, wherein the component of the measured data and the corresponding component of the simulated data each include the offset component.

[0141] 8. A method according to any preceding clause, wherein the measured data, the simulated data and / or the estimated data comprises an image.

[0142] 9. The method of any of clauses 4 to 8, wherein the simulation data is calculated by obtaining a theoretical model of the projection system and propagating each predetermined illumination profile in the set of predetermined illumination profiles using the theoretical model.

[0143] 10. A method according to any preceding clause, wherein fitting comprises fitting basis functions to the data.

[0144] 11. The method of clause 10, wherein the basis functions are Zernike polynomials.

[0145] 12. A method according to any preceding clause, wherein the optical properties include one or more aberrations caused by the projection system.

[0146] 13. The method of any of clauses 4 to 12, wherein each of the predetermined illumination profiles is represented using a polynomial.

[0147] 14. A method according to any preceding clause, further comprising: calculating an adjustment based on the determined optical property.

[0148] 15. The method of clause 14, wherein the adjusting comprises calibration of the projection system or a component external to the projection system.

[0149] 16. A method according to clause 14 or 15, wherein the adjusting comprises or also includes real-time control operations.

[0150] 17. The method of any of clauses 14 to 16, further comprising providing instructions to a component for adjusting the projection system or an external component to apply the adjustment.

[0151] 18. A method according to any preceding clause, further comprising providing an indication that the projection system or a component thereof requires replacement or cleaning.

[0152] 19. A method for determining an optical property of a projection system, the method comprising:

[0153] obtaining a measured illumination profile of input radiation received by the projection system;

[0154] fitting the measured illumination profile to a set of predetermined illumination profiles to generate a parametric fit; and

[0155] Optical properties of the projection system are calculated based on the parameter fitting.

[0156] 20. The method of clause 19, wherein obtaining a measured illumination profile comprises illuminating a pinhole in an object plane of the projection system and receiving radiation output from the projection system while scanning the illuminated pinhole within the object plane.

[0157] 21. The method of clause 19 or 20, wherein each of the predetermined illumination profiles is at least partially defined by the intensity, apodization and / or polarization of the input radiation.

[0158] 22. A method of determining an estimated illumination profile of a projection system, the method comprising:

[0159] obtaining measurement data representative of measurement radiation output from the projection system;

[0160] obtaining simulation data representing simulated radiation output from the projection system, wherein the simulation data comprises a plurality of sets of simulation data, and each set of the plurality of sets is based on input of radiation to the projection system having a predetermined illumination profile from a set of predetermined illumination profiles;

[0161] fitting the measured data to the simulated data to generate a profile fit; and

[0162] The estimated illumination profile is generated based on the profile fitting, wherein the estimated illumination profile comprises a weighted combination of the set of predetermined illumination profiles.

[0163] 23. A method for determining an optical property of a projection system, the method comprising:

[0164] obtaining measurement data representative of measurement radiation output from the projection system;

[0165] obtaining simulated data representing simulated radiation output from the projection system, wherein the simulated data comprises a plurality of sets of simulated data, and each set of the plurality of sets of simulated data is based on an aberration from a set of known aberrations; and

[0166] fitting the measured data to the simulated data to generate a parameter fit;

[0167] Optical properties of the projection system are calculated based on the parameter fitting.

[0168] 24. A computer-readable medium comprising instructions which, when executed by a computer, cause the computer to perform a method according to any preceding clause.

[0169] 25. A measurement system comprising a projection system and a processor configured to perform the method according to any of clauses 1 to 23.

[0170] 26. The measurement system according to clause 25, further comprising:

[0171] a first support configured to hold a first measurement patterning device in an object plane of the projection system;

[0172] a second support configured to hold a second measurement patterning device in an image plane of the projection system;

[0173] a positioning system configured to scan at least one of the first support and the second support relative to one of the first support and the second support; and

[0174] A sensor is configured to generate the measurement data.

[0175] 27. The measurement system of clause 25 or 26, further comprising a controller operable to:

[0176] applying adjustments to the projection system or components external to the projection system; and / or

[0177] An indication is provided that the projection system or a component thereof requires replacement or cleaning.

[0178] 28. A lithographic apparatus comprising a measurement system according to any of clauses 25 to 27.

[0179] 29. The lithographic apparatus of clause 28, further comprising a controller operable to apply adjustments to the lithographic apparatus.

[0180] 30. The lithographic apparatus of clause 28 or 29, further comprising a display screen configured to display the indication.

Claims

1. A method for determining an optical property of a projection system, the method comprising: obtaining measurement data representative of measurement radiation output from the projection system; obtaining an estimated illumination profile of input radiation received by the projection system; generating estimate data representing estimated radiation output from the projection system based on the estimated illumination profile; fitting the estimated data to the measured data to generate a parameter fit; as well as Optical properties of the projection system are calculated based on the parameter fitting.

2. The method of claim 1 , wherein the measurement data represents at least one component of the measured output radiation, wherein the component is selected from the following set: a phase component, an amplitude component, and an offset component; and the estimated data represents a corresponding at least one component of the estimated output radiation.

3. The method of claim 1 or 2, wherein the component of the measurement data and the corresponding component of the estimate data each comprise the phase component.

4. The method of any preceding claim, wherein obtaining the estimated illumination profile comprises: obtaining simulation data representing simulated radiation output from the projection system, wherein the simulation data comprises a plurality of sets of simulation data, and each set of the plurality of sets is based on input of radiation to the projection system having a predetermined illumination profile from a set of predetermined illumination profiles; as well as fitting the measured data to the simulated data to generate a profile fit; The estimated illumination profile is generated based on the profile fitting, wherein the estimated illumination profile comprises a weighted combination of the set of predetermined illumination profiles.

5. A method according to any preceding claim, wherein the measured data, the simulated data and / or the estimated data comprise images.

6. A method according to any preceding claim, wherein fitting comprises: Basis functions are fitted to the data.

7. A method according to any preceding claim, wherein the optical properties include one or more aberrations caused by the projection system.

8. The method according to any preceding claim, further comprising: An adjustment is calculated based on the determined optical properties.

9. The method according to any preceding claim, further comprising: An indication is provided that the projection system or a component of the projection system requires replacement or cleaning.

10. A method for determining an optical property of a projection system, the method comprising: obtaining a measured illumination profile of input radiation received by the projection system; fitting the measured illumination profile to a set of predetermined illumination profiles to generate a parametric fit; and Optical properties of the projection system are calculated based on the parameter fitting.

11. A method for determining an estimated illumination profile of a projection system, comprising: obtaining measurement data representative of measurement radiation output from the projection system; obtaining simulation data representing simulated radiation output from the projection system, wherein the simulation data comprises a plurality of sets of simulation data, and each set of the plurality of sets is based on input of radiation to the projection system having a predetermined illumination profile from a set of predetermined illumination profiles; fitting the measured data to the simulated data to generate a profile fit; and The estimated illumination profile is generated based on the profile fitting, wherein the estimated illumination profile comprises a weighted combination of the set of predetermined illumination profiles.

12. A method for determining an optical property of a projection system, the method comprising: obtaining measurement data representative of measurement radiation output from the projection system; obtaining simulated data representing simulated radiation output from the projection system, wherein the simulated data comprises a plurality of sets of simulated data, and each set of the plurality of sets of simulated data is based on an aberration from a set of known aberrations; as well as fitting the measured data to the simulated data to generate a parameter fit; Optical properties of the projection system are calculated based on the parameter fitting.

13. A computer-readable medium comprising instructions which, when executed by a computer, cause the computer to perform the method according to any preceding claim.

14. A measurement system comprising a projection system and a processor configured to perform the method according to any one of claims 1 to 12.

15. A lithographic apparatus comprising the measurement system according to claim 14.

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