Method and system for determining field dependent aberrations

Abstract

A method of determining field-dependent aberrations in an image field of an optical imaging system based on a measurement operation of determining aberration data for a plurality of field points in the image field, the method comprising the steps of:-defining a target grid comprising a plurality of target field points in the image field, where the target field points are the field points at which the aberration level is to be determined; defining a measurement grid comprising a first subset of the target field points, the first subset comprising all field points for which aberration levels are to be determined in a measurement operation; -measuring aberrations of all field points of the measurement grid to produce measured aberration data; defining an auxiliary grid comprising a second subset of the target field points, the second subset comprising selected target field points not included in the measurement grid, the aberration level of which is to be determined in an aberration data generation operation, wherein the aberration data generation operation is configured to generate aberration data for a target field point of the auxiliary grid based on (iii) knowledge of the optical imaging system, and (iv) potential system-specific aberration sources.

Description

Technical Field

[0001] This invention relates to a method for determining field-correlated aberrations in an optical imaging system. The optical imaging system can be configured as a projection lens for a microlithography projection exposure system. Background Technology

[0002] Microlithography projection exposure methods and systems are primarily used for producing semiconductor components and other finely patterned components. These methods involve using masks (photomasks, master masks) or other patterning devices that carry or form patterns of the structure to be imaged, such as the circuit patterns of layers in a semiconductor component. The pattern is positioned in the beam path between the illumination system and the projection lens in the projection exposure system, such that the pattern lies within the area of ​​the object plane of the projection lens. The projection lens is an optical imaging system. The substrate to be exposed, such as a semiconductor wafer coated with a radiation-sensitive layer (resist, photoresist), is held such that the radiation-sensitive surface of the substrate is configured within the area of ​​the image plane of the projection lens, which is optically conjugate to the object plane. During the exposure process, the pattern is illuminated by means of an illumination system that shapes the illumination radiation directed onto the pattern according to the radiation from a main radiation source. The illumination radiation is characterized by specific illumination parameters and illuminates the pattern within an illumination field that defines its shape and size. The pattern-modified radiation passes through the projection lens as projection radiation, which then projects or images the pattern onto the substrate to be exposed. An image is generated in the image field of the projection lens.

[0003] One of the purposes of developing projection lithography equipment is to create increasingly smaller structures on substrates using photolithography. Smaller structures lead to higher integration density, such as in semiconductor components, which typically has a beneficial impact on the performance of the manufactured microstructures.

[0004] The manufacturable structural dimensions depend primarily on the resolving power of the projection lens used. Projection lenses for microlithography typically include multiple optical elements to meet stringent requirements regarding imaging aberration correction. Refractive and catadioptric imaging systems operating in the DUV (deep ultraviolet) or VUV (vacuum ultraviolet) wavelength range are commonly used. These systems typically have ten or more transparent optical elements. In catadioptric systems, the transparent optical elements are combined with at least one imaging mirror (e.g., a concave mirror). Electromagnetic radiation from the extreme ultraviolet (EUV) range, particularly with operating wavelengths between 5 nm and 30 nm, cannot be focused or guided by refractive optical elements. Therefore, mirror systems (reflective systems) are used for EUV lithography and typically include, for example, four or six mirrors.

[0005] Due to its optical design and manufacturing, the projection lens inevitably exhibits inherent imaging aberrations. On the other hand, shipping to the customer site and assembly there, as well as environmental changes (such as temperature variations) and other effects that occur during operation throughout its lifespan (such as lens heating) can affect aberrations and require compensation.

[0006] The types and grades of aberrations that can be tolerated for a particular treatment may vary and are typically given in a set of aberration specifications that need to be met.

[0007] Optical systems (such as projection lenses for photolithography scanners) specify the image field used for expansion, on which sufficiently low aberration levels need to be ensured. Since every location on an integrated circuit is, or can be, filled by functional structures, aberrations at any field point need to be within common specifications.

[0008] Imaging aberration levels can vary between different points in the image field. So-called field-dependent aberrations are crucial, for example, regarding specifications related to overlap. To control overlap error levels, field-dependent aberrations must be understood and controlled. The term "overlap error" refers, for example, the accuracy of superposition between two consecutive lithographic planes. Overlap is a critical parameter in integrated circuit manufacturing because any type of alignment error can lead to manufacturing defects, such as short circuits or missing connections, thus limiting circuit functionality. Therefore, insufficient overlap significantly reduces the yield of qualified parts in the process, resulting in increased manufacturing costs per qualified part.

[0009] Typically, attempts are made to at least partially compensate for imaging aberrations that occur during the service life, especially those that occur during operation.

[0010] Compensation is typically performed by utilizing manipulators integrated into the optical system and / or by replacing individual selected optical elements, which can be individually shaped to optimize the optical quality of the system.

[0011] It is necessary to understand the field variations of aberrations with sufficient accuracy in order to successfully control the manipulator or provide the optimal shape for interchangeable elements, and to verify the success of these measures.

[0012] The highest resolution of many state-of-the-art photolithography systems depends on aberration measurements during production. These aberration measurements indicate changes in the optical performance of the projection lens, which may be caused by factors such as thermal effects.

[0013] Since imaging aberration levels may vary between different points in the image field, a preferred measurement system can measure at least one projected radiation characteristic related to image quality or aberration level by collecting measurement data at multiple spaced-apart measurement points distributed in the image field.

[0014] Measuring the aberrations at every location (point) in an image field is practically impossible. For practical reasons, precise measurements can only be taken at selected, spaced-apart field points. Potential measurement errors can be limited, for example, through self-calibration of the measuring equipment, where multiple measurements are performed at the same field point using different sensors fixed in relative positions. In this case, the metrological grid is defined by the sensor spacing and is thus given, for example, by a rectangular grid. Achieving finer resolution is at least time-consuming and typically requires significant additional effort on the measuring equipment.

[0015] Successful correction depends on sufficient information about the field-correlated aberration pattern to be corrected. However, generating this information through measurements is costly. Measurement operations should acquire data at multiple spaced-apart measurement points distributed throughout the image field.

[0016] Each measurement step performed at a measurement point takes time. If the measurement system can perform measurements in parallel at multiple measurement points, the number of field points that can be measured in parallel is usually limited. Summary of the Invention

[0017] The present invention aims to provide an economical method for determining field-correlated aberrations in the image field of an optical imaging system (e.g., a projection lens in a microlithography projection exposure system). This method should provide fine-scale aberration information with a moderate number of measurements as needed. Another objective is to provide a method capable of performing field-correlated aberration measurements with enhanced metrological robustness while maintaining high system throughput. Yet another objective is to provide a projection exposure apparatus capable of applying this method, and a method for manufacturing semiconductor devices using an optical imaging system configured by this method via optical lithography.

[0018] To address these and other problems, the present invention provides a method having the features of claim 1. Furthermore, the present invention provides a projection exposure apparatus including the features of claim 7, and a method for manufacturing a semiconductor device including the features of claim 8.

[0019] The advantageous developments are specified in the dependent claims. The wording of all claims is incorporated herein by reference.

[0020] According to one description, the present invention provides a method for determining field-correlated aberrations in the image field of an optical imaging system based on measurement operations that determine aberration data at multiple field points in the image field. In this application, the phrase "determine field-correlated aberrations" describes the steps of determining aberration data at multiple field points in the image field to quantify how aberration levels change in the image field. The method includes multiple method steps.

[0021] In one method step, a target mesh is defined containing multiple target field points in the image field. Target field points are the field points that determine the aberration levels. Generally, a large number of target field points need to be densely distributed across the image field to obtain a close approximation of the actual distribution of aberrations in the image field.

[0022] In another methodological step, a measurement grid is defined that includes a first subset of the target field points. This first subset includes all field points for which aberration levels will be determined during the measurement operation. Generally, the measurement grid contains fewer field points than the target grid, such that measurements are not performed on all target field points.

[0023] In the next method step, aberrations are measured at all field points of the measurement grid to generate measured aberration data representing wavefront aberrations. Once the measured aberration data is obtained, measurement information for all field points of the measurement grid is available; however, for those target field points that do not correspond to field points of the measurement grid, measured aberration data is not available.

[0024] In another methodological step, an auxiliary mesh is defined, comprising a second subset of the target field points, wherein this second subset includes selected target field points not included in the measurement mesh, for which aberration levels are determined in an aberration data generation operation (ADGO). The aberration data generation operation is configured to generate aberration data for the target field points of the auxiliary mesh. It is important to note that the aberration data generation operation does not include measurements used to determine the aberration levels for the target field points of the auxiliary mesh. Instead, this aberration data is generated based on calculations or simulations based on specific pre-existing knowledge of the optical imaging system and potential system-specific aberration sources (or causes).

[0025] This method combines two different approaches to obtaining aberration data. A measurement operation is performed to obtain actual measurement data defining the aberration levels of a first subset of the target field points. The potential aberration levels of other field points not belonging to the measurement grid are quantitatively determined in an aberration data generation operation (ADGO), which is not based on measurement. Essentially, this method is able to generate missing data on a fine grid (target grid) by utilizing pre-existing knowledge of the optical imaging system and the possible causes or sources of aberrations specific to the optical imaging system. In other words, the inventors propose a composite method that combines measurement data with data consistent with the measurement data, but the computationally obtained data is based on certain pre-existing knowledge about the optical imaging system.

[0026] By using this method, measurement errors of optical aberrations are typically reduced compared to other metrology schemes with equivalent effort. This method, combined with actuators, particularly rigid manipulators for mask masters (masks), optics, and substrates (e.g., wafers), and also with adaptive elements (e.g., rapid, fine-scale full-field aberration measurements), enables superior correction strategies to reduce optical aberrations, thereby meeting increasingly stringent specifications in future systems without sacrificing production speed.

[0027] In a preferred embodiment, the aberration data generation operation includes a reconstruction step and a forward calculation step. The reconstruction step includes reconstructing at least one (virtual) perturbation of at least one optical element in an optical imaging system consistent with an aberration fingerprint determined based on aberration data measured in a measurement grid. In the forward calculation step, forward calculation is performed based on the perturbation obtained in the reconstruction step to determine field aberration data for all field points in the target field.

[0028] In this paper, the term "perturbation" describes a deviation from reference conditions. For example, the optical surface of a mirror or lens in an optical imaging system has a nominal shape (surface shape) corresponding to the shape defined in the optical specification. In reality, due to manufacturing tolerances and other influences, the surface shape will differ from its nominal shape. This difference, i.e., the deviation of the actual shape of the optical surface from the nominal shape of the optical surface according to the specification, is expressed as "surface shape error" (described by the term "Passe" in German). Surface shape error may be the sole factor causing "perturbation." However, while an optical surface may have a perfect shape, the optical element as a whole may deviate slightly from the specification during installation, introducing deviations in attitude (position), such as tilt or eccentricity. In addition, installation stresses may occur, leading to perturbation. Generally, perturbation can be decomposed into several components, such as a tilt component, an eccentricity component, and a component describing deformation.

[0029] More specifically, the term "perturbation" is a general term used to describe deviations from an ideal optical design. Perturbations can include rigid body position errors of optical elements, such as eccentricity, rotation, or tilt. Additionally, surface shape errors can also cause perturbations. These errors may produce interfering effects only locally or at higher spatial frequencies. Generally, it is often difficult or impossible to strictly distinguish between perturbations originating from rigid body motion and those originating from surface shape errors. For example, if an optical surface has a small degree of misalignment, the effect may be similar to the effect of surface deformation that transforms the original surface shape into the surface shape at the misaligned location. Therefore, perturbations can be described by eccentricity and surface shape errors that have the same effect on aberrations.

[0030] This method can be performed in such a way that the measured aberration data are assumed to be "true," making the measured data treatable as fixed values. In another approach, the measured values ​​can vary during the process of finding the best-fitting aberration pattern. In many cases, the measured higher-order aberrations can be assumed to be true values, while lower-order aberrations, often associated with a higher degree of uncertainty (e.g., tilt or defocus), can be measured multiple times to obtain valid values, with the best possible approximation of the true aberration values ​​obtained by averaging and / or by adaptation based on multiple measurements. This method can be performed such that each aberration is measured only once. However, it is also possible to perform multiple measurements (two or more) on some or all aberrations. In this case, multiple measurements are usually accompanied by subsequent data processing to determine the average or adjustment.

[0031] An important aspect of the novel method described in this application can be described as enabling the determination from measurements potential sources of error compatible with optical elements present in a specific, real system. For example, if the optical system consists only of mirrors, and there is a vacuum between the mirrors, then aberrations are more likely to originate from defects or errors on the surfaces of the mirrors, rather than from the space between the mirror surfaces. This method takes into account the specific limitations of the particular system being examined to reduce the number of possible causes of error.

[0032] The reconstruction step involves reverse computation to identify the relationship between certain types of dummy perturbations and their impact on the aberration distribution in the image field. The term "aberration fingerprint" describes a specific pattern of field-related aberrations identified in the measurement step. It is important to note that the reconstruction step does not provide (confirmatory) evidence that a certain perturbation presumed to cause a certain aberration in the image field is the true cause of the aberration. Instead, the reconstruction step is set to find certain properties of the perturbations consistent with the measurement data. In other words, the measurement data can be interpreted by assuming that the dummy perturbations assumed in the reconstruction step are actually those present in the optical imaging system. Actual perturbations present in the measurement system may deviate from the dummy perturbations found in the reconstruction step to be consistent with the measured aberration fingerprint.

[0033] As described above, this method relies in part on pre-existing knowledge of certain characteristics of the optical imaging system. This significantly reduces the number of degrees of freedom in modeling how to interpret the specific aberration fingerprint determined by the measurement steps in terms of the actual structure of the optical imaging system. In a preferred embodiment, the knowledge of the optical system includes design data describing or representing the specifications of the nominal optical design in the optical imaging system. The design data includes surface pattern data describing each optical surface in the optical imaging system, and the nominal surface pattern according to the specifications. The surface pattern data may include coefficients describing the fundamental curvature (or radius of curvature) of the optical surface, coefficients describing potential deviations from a spherical shape, distance data describing the distance between the optical surface and adjacent optical surfaces, dimensional data describing the dimensions of the portion of the optical surface actually used when using the optical system (sometimes referred to as the "optical free diameter"), etc. More complex data may be needed to describe the shape of the freeform surface, which may deviate significantly from any rotationally symmetric spherical or aspherical surface shape. The design data also includes index data indicating the optical properties of the optical surfaces to distinguish between reflective surfaces (e.g., mirror surfaces) and refractive surfaces.

[0034] Design data describes an "ideal" optical system developed by optical designers to achieve certain performance specifications. Generally, this ideal configuration cannot be perfectly realized in actual optical systems due to manufacturing tolerances, environmental conditions, and other factors. Despite these deviations, design data still provides crucial information about which deviations from the ideal (perturbations) are typically more likely to occur than others, thus reducing the degrees of freedom in the analysis steps.

[0035] In a preferred embodiment, the knowledge of the optical system includes perturbation data, which includes sensitivity data. For each optical surface of the optical imaging system, the sensitivity data describes the relationship between surface shape error and the contribution of wavefront aberration caused by the surface shape error. Surface shape error (described by the German term "Passe") describes the deviation of the actual shape of the optical surface from the nominal shape in the optical surface according to specifications. The sensitivity data essentially describes the system behavior of the optical system based on the effect of the surface shape error on the wavefront of radiation emanating from the optical system toward the image field.

[0036] In a preferred embodiment, the reconstruction step includes setting the refractive index of the gap between the optical surfaces to a value of 1. This constraint greatly reduces the possible modes of aberration variation and allows reasonably correct aberrations to be found at non-measurement locations, even with reduced metrological information. This assumption leverages the fact that in the presence of a vacuum between optical elements (as is typical in EUV applications), it is clear that aberrations must originate from the optical elements or their surfaces themselves, rather than from elsewhere. This fact significantly reduces the number of potential sources of disturbance, making the model less complex and computationally more efficient.

[0037] However, this method is not limited to determining field-related aberrations in EUV optical imaging systems. Instead, it can also be used to obtain information needed for systems operating in the deep ultraviolet (DUV) range, where gaps between lenses and / or mirrors may be filled with gas rather than a vacuum. It has been found that this method still produces fairly accurate results when the potential effects of gaps on wavefront aberrations are neglected.

[0038] Several other considerations help reduce the number of possible degrees of freedom in the reconstruction step. In a preferred embodiment, the measurement grid width is set such that the distance between the target field points in the first subset is small enough that the sub-apertures associated with the target field points overlap and cover the entire useful area (or at least 80%, 90%, or 99%) on each optical surface of the optical imaging system. Adhering to this condition ensures that any perturbation on each optical surface will affect the measurement results because the measurement grid is fine enough that there are no gaps or blind spots on any optical surface. In other words, if this condition is not adhered to, there is a risk that perturbations actually present on a surface may not be reflected in the measurement data, making the measurement data not fully representative of the perturbation pattern on each surface.

[0039] The formula uses the term "sub-aperture," which is explained below. In an optical imaging system, a beam emanating from a specific point in the object field or converging towards a point in the image field has a certain aperture. Therefore, the beam intersects with an optical surface positioned at a certain distance from the field plane in an intersection region, the shape of which can be, for example, circular or elliptical, and is referred to as "sub-aperture" in this application. In the case of diverging beams, the sub-aperture diameter increases with increasing distance from the field. All sub-apertures overlap in the pupil surface, which has a Fourier transform relationship with the field plane. On the other hand, if the optical surface is optically close to the next field plane, the sub-apertures may not overlap at all. Regarding the grid size of the measurement grid, this means that if the optical system includes one or more optical surfaces close to the field plane, the measurement grid may need to be designed to be finer.

[0040] The present invention also relates to a projection exposure apparatus capable of applying this method and a method for producing semiconductor devices. Attached Figure Description

[0041] These and other features are apparent not only from the claims but also from the specification and drawings, wherein each feature may be implemented individually in each case, or as a combination of sub-forms in the embodiments of the invention and in other fields. Exemplary embodiments are shown in the figures and explained in more detail below.

[0042] Figure 1 Components of an EUV microlithography projection exposure device;

[0043] Figure 2 Show a comparison between the contributions of aberration paradigms measured on coarse and fine grids in the simulation to the wavefront aberration components Z2–Z5;

[0044] Figure 3 shows an example of coarse and fine measurement grids in an arc-shaped image field;

[0045] Figure 4 Demonstrates processing from coarse-grid metrology to fine-field aberration fingerprinting;

[0046] Figure 5 Displays the reconstructed results of surface shape deformation;

[0047] Figure 6 Display and Figure 5 The various aberrations related to the deformation of the surface shape are shown. Detailed Implementation

[0048] The concepts and aspects of the inventions and embodiments thereof disclosed in this application will now be described using an EUV microlithography projection exposure system as an example. Those skilled in the art will understand that these examples are not limiting; for example, these concepts may also be used in conjunction with systems operating in other wavelength ranges, such as DUV (deep ultraviolet) systems.

[0049] Figure 1 The diagram schematically illustrates components of an EUV microlithography projection exposure apparatus WSC, used to expose a radiation-sensitive substrate W arranged in an image plane IS of a projection lens PO using at least one image of a pattern PAT of a reflective mask M, the pattern being arranged in an area of ​​an object plane OS of the projection lens.

[0050] This projection exposure apparatus operates using radiation from the main radiation source RS. The illumination system ILL receives the radiation from the main radiation source and shapes the illumination radiation ILR directed onto the pattern. The projection lens PO is an optical imaging system configured to image the pattern structure onto the photosensitive substrate W.

[0051] The main radiation source RS can be a laser plasma source, a gas discharge source, or a synchrotron-based radiation source. This source produces radiation in the extreme ultraviolet (EUV) range, particularly radiation with wavelengths between 5 nm and 15 nm. To enable the illumination system and projection lens to operate within this wavelength range, they are constructed with components that reflect EUV radiation.

[0052] Radiation emitted from the radiation source RS is collected by a collector and directed to the illumination system ILL. This system shapes the radiation and uses the shaped illumination radiation ILR to illuminate the illumination field located in or near the object plane OS of the projection lens PO. In this case, the form and size of the illumination field determine the form and size of the object field OF effectively used in the object plane OS. The illumination field is typically trough-shaped, with a high aspect ratio between its width (along the x-direction) and height (along the y-direction).

[0053] Here, the projection lens PO has six mirrors M1 to M6, and images the mask pattern onto an image plane at a reduced scale, in which the substrate to be exposed, such as a semiconductor wafer, is arranged. The image field IF, conjugate with the object field optics, lies within the image plane. All mirrors are coated with a multilayer reflective coating that reflects EUV radiation and may contain Mo / Si layer pairs (double layers), etc.

[0054] The projected radiation PR from the mask M to the substrate is reflected sequentially by six mirrors (mirror M1 to mirror M6). All the rays that travel from the object field to the image field and contribute to image generation form the path of the projected beam.

[0055] The apparatus RST for holding and manipulating the mask M (mask master) is configured such that the pattern PAT disposed on the mask is located in the object plane OS of the projection lens PO, which is also designated herein as the mask master plane. The mask can be moved in this plane to perform scanner operation in the scanning direction (y-direction) perpendicular to the reference axis AX (z-direction) of the projection lens by means of a scan driver.

[0056] The substrate W to be exposed is held by a device WST containing a scanner driver so that it moves synchronously with the mask M in the scanning direction (y-direction) perpendicular to the reference axis AX. Depending on the design of the projection lens PO, these movements of the mask and substrate can be achieved in a manner that is parallel or antiparallel to each other.

[0057] The unit WST, also known as the "wafer stage," and the unit RST, also known as the "mask master stage," are part of a scanner unit controlled by a scan control unit. In the case of the scan control unit, this embodiment is integrated into the central control unit CU of the projection exposure system. A data storage device (not shown) is associated with the control unit.

[0058] In this embodiment, the object field OF and the corresponding image field IF have arcuate shapes (compare Figure 3). The size of the image field IF is smaller than the size of the object field, and the reduction ratio provided by the projection lens is related to the size of the object field OF.

[0059] All optical components of the WSC projection exposure system are housed in a vacuum-sealable housing. EUV projection exposure systems with similar basic structures are known, for example, from WO 2009 / 100856 A1, WO 2010 / 049020 A1 or WO 2015 / 049319 A1, the disclosures of which are incorporated herein by reference.

[0060] Other embodiments may have different layouts; for example, the projection lens may have more than six mirrors, such as eight or ten mirrors or more. The reduction ratio does not have to be isotropic (i.e., the same in all directions of the field). Instead, the projection lens may have a deformable design that results in different reduction ratios between the scanning direction and the cross-scanning direction.

[0061] The WSC projection exposure apparatus has an operation control system configured to perform near-instantaneous fine-tuning of the imaging-related properties of the projection exposure apparatus in response to environmental influences and other disturbances and / or based on stored control data. For this purpose, the operation control system has multiple manipulators that allow for targeted intervention in the projection behavior of the apparatus. One actively actuated manipulator includes one or more actuating elements or actuators whose current actuation value can be changed by executing defined actuation values, and thus by control signals from the operation control system.

[0062] The mask manipulator MM has an actuator that, depending on the drive, can cause the mask M to be displaced parallel to or perpendicular to the reference axis AX, and to tilt the mask as a whole. The mask manipulator can also be designed to, alternatively or additionally, perform mask deformation.

[0063] The substrate manipulator MSUB has an actuator that enables the position of the substrate relative to the projection lens to be changed by displacement parallel to or perpendicular to the reference axis and / or by tilting and / or deforming the substrate.

[0064] The first reflecting mirror M1, which directly follows the mask or the object plane in the direction of radiation transmission, can be laterally tilted and / or displaced and / or deformed relative to the direction of light propagation by means of the first reflecting mirror manipulator MM1.

[0065] It is also possible to provide corresponding mirror manipulators for one or more other mirrors. Specifically, in the current case, a third mirror manipulator MM3 is provided at the third mirror M3, which allows the third mirror as a whole to be shifted and / or tilted and / or deformed laterally or parallel to the direction of light propagation.

[0066] The controller can be controlled based on measurements.

[0067] This projection exposure system is equipped with a measurement system (MES), which in this embodiment is designed to perform measurements of the projected radiation wavefront, which passes through a mask in a projection lens onto the substrate to be exposed. Spatially resolving measurements of multiple field points at the image surface level are possible. For example, wavefront measurement systems of the type described in US 7,333,216 A1 or US 6,650,399 A1 are available, the disclosure of which is incorporated herein by reference.

[0068] The measurement system may include an integrated lens interferometer (ILIAS) at the scanner, an interferometric wavefront measurement system that enables static measurements of higher-order lens aberrations. It can be implemented as an integrated measurement system for system initialization and calibration, or it can be used for on-demand monitoring and recalibration.

[0069] All optical components of the WSC projection exposure equipment are housed within a vacuum-suppressible housing. The equipment operates under vacuum.

[0070] EUV projection exposure apparatus with a similar basic structure is known, for example, from WO 2009 / 100856 A1. Projection lenses with a similar basic construction are known, for example, from US 6,927,901 B2. In this regard, the disclosure of that document is incorporated herein by reference.

[0071] Since imaging aberration levels may vary between different points in the image field, the measurement system is configured to measure at least one projected radiation characteristic related to image quality or aberration level by collecting measurement data at multiple spaced-apart measurement points distributed in the image field.

[0072] To quantitatively characterize the spatial variation of field aberration levels under specific conditions, a "target grid" can be defined. The target grid includes multiple target field points in the image field, where the target field points are those for which the aberration levels are to be determined. Furthermore, a measurement grid can be defined, comprising a first subset of the target field points, which includes all field points for which the aberration levels are to be determined in a measurement operation. Additionally, an auxiliary grid can be defined, comprising a second subset of the target field points, which includes selected target field points not included in the measurement grid for which the aberration levels are to be determined without measurement at these points. In this embodiment, aberration information for the auxiliary grid field points is generated using an aberration data generation operation.

[0073] Measurable field points are distributed on the image field according to a two-dimensional measurement grid with a certain grid width. The spatial resolution of measurements in a selected direction is proportional to the grid width in the corresponding direction. The smaller the grid width (i.e., the distance between adjacent measurement field points), the smaller the spatial resolution. Figure 3 shows an example of a measurement grid in an arc-shaped image field. Coarse grid ( Figure 3A The reference identifier code TD01 includes 13*7=91 measurement points, while the fine grid ( Figure 3B The reference identifier (HD) includes 73*9=657 measurement points.

[0074] The inventors developed a method for obtaining aberration data that describes variations in imaging aberrations across the image field at a fine spatial scale, without requiring the measurement of every aberration component at all field points corresponding to that fine scale. This method is partly based on the understanding that some imaging aberration components are easier to measure than others. Some fundamental concepts are now described using an aberration description based on Zernike wavefront functions.

[0075] In geometrical optics, Zernike polynomials are commonly used to represent wavefronts and thus describe imaging aberrations in optical systems. In this paper, various imaging aberrations are described by the coefficients of the Zernike polynomials, i.e., the Zernike coefficients or their values ​​(in nm). In this chosen representation, Zernike coefficients Z2 and Z3 represent the tilt of the wavefront in the x and y directions, respectively, resulting in aberrations resembling distortion. Zernike coefficient Z4 describes the curvature of the wavefront, thus describing defocusing errors. Zernike coefficient Z5 describes the saddle-shaped deformation of the wavefront, thus describing the astigmatic component of the wavefront deformation. Zernike coefficients Z7 and Z8 represent coma, Zernike coefficient Z9 represents spherical aberration, and Zernike coefficients Z10 and Z11 represent cloverleaf aberrations.

[0076] This concept also uses system sensitivity to describe the behavior of the entire system. Within the scope of this application, sensitivity describes the functional relationship between a specific perturbation component and its effect on the wavefront. As an illustrative example, consider a mirror within an optical system. A tilted mirror typically shifts the image position, making the image position highly sensitive to this tilt. In contrast, system astigmatism also "senses" the tilt, but with significantly lower sensitivity. Therefore, a certain perturbation (here: the tilted mirror) is associated with a set of aberration components with different sensitivities.

[0077] Using an aberration description based on the Zernike wavefront function, it has been shown that measurements taken on a coarse grid (i.e., a grid of measurement points distributed across a field characterized by relatively low spatial frequencies) cannot reliably measure some aberrations with higher spatial frequencies in the field. Conversely, some form of undersampling may occur if there is an unfavorable mismatch between the spatial frequency of the aberration and the corresponding measurement grid.

[0078] In other words, when high-frequency features (i.e. features with high spatial frequencies in the field) cannot be resolved with sufficient accuracy on a coarse grid, relevant information will be lost if the sole source of information is a measurement of aberrations on the coarse grid.

[0079] To further illustrate this point, Figure 2 The contributions of Z2–Z5 to wavefront aberrations are depicted for aberration paradigms measured on the coarse-grid TD-01. Comparisons with the same aberrations given on the fine-grid HD show incompleteness. Each graph displays the field coordinates on the x-axis (field center at x=0 nm) and the wavefront aberration magnitudes corresponding to the Zernike coefficients on the y-axis.

[0080] Each chart shows exemplary aberrations (Z2 – Z5 contributions) on the coarse grid (TD01 grid) and the fine grid (HD grid). As shown in Figure 3, the coarse grid ( Figure 3A This includes 13 * 7 = 91 measurement points, while the fine grid ( Figure 3B This includes 73 * 9 = 657 measurement points.

[0081] The grid width of the measurement points on a finer grid (HD grid) is chosen to be small enough that the sub-apertures assigned to field points on the HD grid cover the entire surface of all optical elements relevant to the image building process. In contrast, the sub-apertures on a coarser grid leave gaps on some optical elements. In other words, measurements on a coarser grid may "miss" deformations in areas outside the covered sub-apertures, thus failing to obtain important information.

[0082] Although the overall shapes of spatial frequencies, number of peaks, and heights are quite similar for Z2 and Z5, significant undersampling was observed for Z3 and Z4. This indicates that measuring these aberrations on a coarse grid will result in information loss.

[0083] In practical examples, it has been shown that fine spatial resolution is difficult to achieve with Zernike Z2–Z4, while Zernike Z5 and Z100 can be measured on fine grids with only a certain amount of time and equipment complexity. The inventors believe the reasons for this observation can be described as follows: Some error sources that might strongly influence Z2–Z4 in isomorphic systems or Z2–Z5 in deformable systems appear to occur in more diverse ways and more frequently than other error sources that primarily influence other aberrations, such as Z5 or Z6. Within the scope of this application, Z2 describes the wavefront tilt in the x-direction, Z3 corresponds to the wavefront tilt in the y-direction (scanning direction), and contributions to Z4 can be easily generated by shifting optical elements in the radiation propagation direction. In deformable systems, misalignment of a mask (mask master) with a component perpendicular to the object surface can have a strong effect on Z5 due to the difference between the lateral and longitudinal imaging scales. Furthermore, compared to higher-order Zernike aberrations, some metrology systems that include movable sensors to generate measurements at different field points appear to have a greater impact on the measurement accuracy of Z2 to Z4 or Z5. Given these observations, it seems appropriate to distinguish between lower-order aberrations (e.g., Zernike Z2 to Zernike Z4) on the one hand, and higher-order aberrations (e.g., between Z5 and Z100) on the other.

[0084] The inventors developed a method to obtain fairly fine-scale information about Z2–Z5 by measuring these Zernike coefficients at a coarse scale, supplemented by information derived from measurements of higher-order Zernike coefficients with better resolution.

[0085] This allows for the discovery of aberration patterns on a finer grid based on measurements of at least some aberrations on a coarser grid. The method involves generating missing data on the finer grid by utilizing knowledge of the optical system and possible system-specific aberration origins (root causes).

[0086] The following description uses a projection lens for EUV lithography as an example to illustrate an embodiment. The exemplary projection lens has six mirrors M1 to M6 contained within a vacuum housing. Given the vacuum (refractive index = 1) between the optical elements, it is clear that aberrations are generated by the optical elements themselves (i.e., by the mirrors), and not elsewhere. This fact reduces the number of possible modes of aberration variation and helps to find the correct aberrations in non-measuring locations, even with reduced metrological information.

[0087] The method includes an aberration data generation operation (ADGO), which is set to generate aberration data for target field points of an auxiliary grid based on (i) knowledge of the optical imaging system and (ii) the underlying system-specific causes (root causes) of the aberrations.

[0088] The auxiliary grid is a grid that includes a second subset of target field points, which includes selected target field points not included in the measurement grid for which aberration levels are determined.

[0089] The aberration data generation operation includes a reconstruction step to reconstruct at least one (virtual) perturbation of at least one optical element in an optical imaging system consistent with an aberration fingerprint determined based on aberration data measured in a measurement grid, and a forward calculation of field aberration data for all field points in the target field based on the perturbation obtained in the reconstruction step.

[0090] In this embodiment, the reconstruction step includes setting the refractive index of the gap between the optical surfaces to a value of 1, thereby significantly reducing the complexity of the model.

[0091] The program is illustrated in... Figure 4 Inside, it displays a demonstration of processing from coarse-grid metrology to fine-field aberration fingerprinting.

[0092] Generally, measured aberrations can be traced back to perturbations in optical elements. In this case, the perturbation is the deformation of the mirror surface, which represents the fact that the actual surface shape of the mirror surface, or the surface shape, deviates from the nominal shape defined in the optical system specification.

[0093] In the MEAS-C measurement step, aberrations are measured on a coarse grid. The measurement results produce an "aberration fingerprint," which is the characteristic pattern of aberrations in the measured system. The RECON step represents the reconstruction of the perturbations of the optical elements that produce the observed aberration fingerprint. This step produces a set of deformations consistent with the measured aberrations. In this paper, the term "consistent" means that the deformations identified in the RECON step are consistent with the characteristics of the measurement results (and the aberration fingerprint), without contradiction. The reconstruction step does not necessarily produce true deformations, but the deformation patterns found in the reconstruction step are more likely than other deformation patterns that might lead to the measured aberration fingerprint.

[0094] In the next step, F-CALC, a forward calculation is performed to compute the aberration pattern on the finer grid based on the deformations obtained in the reconstruction step. The forward calculation computes the aberration pattern if the mirrors of the optical system under test actually suffer from the deformations found in the reconstruction step. The forward calculation step is expected to produce the correct (measured) aberrations at the field points observed in the measurement, as well as the consistent aberrations at the unmeasured field points, i.e., the aberrations on the field points of the finer grid (ABERR-F).

[0095] Adding information from higher Zernike wavefront coefficients to a finer mesh can fill in any gaps, as it will reconstruct a consistent combination of perturbations compatible with these higher Zernike wavefront coefficients, such as surface deformation. This reconstruction proves unique only when a sufficient amount of higher-order information is included.

[0096] Technically, reconstruction can be performed using known tomographic algorithms in the prior art, such as distributed backpropagation, where lost low-order Zernike information is simply ignored. Alternatively, or in combination, reconstruction can be performed using least-squares fitting of the sensitivity of optical element perturbations to the measurement data. Therefore, for a predefined set of degrees of freedom of the mirror surface deformation, which can be Zerniketically adapted to the mirror surface shape, spline function, or other functional basis known in the prior art, the effect on the measured wavefront properties can be calculated through optical simulation. Additional high-order Zernike information on a fine mesh can be obtained in the same manner.

[0097] In this embodiment, a Tikhonov-type algorithm is used to perform the process of reproducing the fundamental deformation from aberrations. As previously mentioned, the set of fundamental functions describing the aberrations that occur consists of adaptive Zernikes of the mirror surface shape that constitute the manipulator matrix 𝑀𝑀, where Z2–Z5 are resolved on a coarse TD01 grid, and higher-order Zernikes are resolved on a fine HD grid. Demonstration details are given below.

[0098] The optimized evaluation function is: , where M is the manipulator matrix, x is the target vector, and p is the perturbation. This equation can be formalized to obtain x: The various parts of the equation have the following meanings:

[0099] Disturbance p:

[0100] The wavefront of the disturbance is decomposed into wavefront Zernike coefficients:

[0101] An example of a coarse-field mesh, denoted as A, contains only one field point:

[0102]

[0103] An example of a fine-field mesh, called B, contains two field points:

[0104]

[0105]

[0106] in Z2 is the evaluation coefficient at field point A.

[0107] In the perturbation vector In the middle, the wavefront Zernike coefficients a of all Zernike and all field points Zi They are arranged one below the other, thus describing the wavefront effect of the disturbance.

[0108] Manipulator matrix M:

[0109] Manipulator Matrix This includes the set of all fundamental functions. These fundamental functions correspond to sensitivities, which can also be described as Zernike coefficients adapted to the mirror shape. Here, sensitivity is expressed similarly to perturbations of the wavefront Zernike coefficients. A single sensitivity, such as a 1 µm tilt in the x-direction of the mirror, will result in a certain wavefront effect in the lens output (i.e., in the image field). Therefore, similar to perturbations, the exponent *i* refers to the wavefront Zernike coefficients at all field points. The exponent *j* refers to the sensitivity (describing surface deformation), encompassing all optically active surfaces of the lens and all possible surface deformations, such as tilt.

[0110] Similar to the perturbation, the manipulator matrix M includes wavefront Zernike coefficients for a few measurement points of a coarse grid (the measurement grid, e.g., for Z2–Z5), and coefficients for many measurement points of a fine grid (e.g., > Z5).

[0111] Target vector x

[0112] Target vector This includes coefficients for surface sensitivity (Zenick coefficients adapted to the surface shape of the mirror). The product of the manipulator matrix M and the target vector x represents the wavefront effect of the target vector.

[0113] When the number of rows in M ​​is greater than the number of columns, the above formula... If M is injective, then there exists a unique solution x that precisely reproduces the wavefront. On the other hand, if M is not injective, then there exists a solution with... and The null space of the equation. If we are to solve for x in this equation, there is no unique solution, and therefore other solutions are possible. Therefore, sensitivity must be established accordingly so that there is enough information to find a unique solution.

[0114] Figure 5 and Figure 6 Display surface pattern deformation ( Figure 5 The reconstruction results of the input and its respective aberrations accurately reproduce the input. Figure 6 The model's optical system consists of six mirrors, M1 to M6. Only the third mirror, M3, exhibits surface deformation, causing the shape of its reflective surface to deviate from specifications. Figure 5 This algorithm demonstrates that it perfectly reproduces the surface graphic deformation of the reconstructed surface. Figure 6 Displaying deformation from surface graphics ( Figure 5 The reconstructed aberrations are completely consistent with the input data. The DIF line represents the difference between the input and reconstructed data. Additional information can only be obtained from higher-order Zernike aberrations. Therefore, this method has proven to be suitable for this specific case.

[0115] The inventors discovered that the spatial frequency of the perturbation plays a crucial role in reconstruction to determine which optical element is primarily responsible for the perturbation. Generally, it is difficult to draw accurate conclusions from the result (aberration) to the cause (e.g., errors on optical elements). In combination... Figure 5 and Figure 6 In the simulations provided, a relatively simple perturbation is assumed, which is expected to be reconstructed with sufficient accuracy using an appropriate algorithm. Mirror M3 was chosen as an example because it is located at a specific point in the radiation path that can influence the wavefront in a field-correlated manner. This specific location is advantageous for high-precision reconstruction. In this case, the inventors observed that the spatial frequency of the perturbation can play a significant role in identifying the most probable aberration source. The higher the spatial frequency, the easier it is to correlate the measured error with a specific originator. In this case, a perturbation with a high spatial frequency is assumed, which helps in identifying the correct source of the aberration.

[0116] Care must be taken when choosing the appropriate ratio of the wavefront Zernike and the fundamental function (the Zernike adapted to the mirror surface shape). As already mentioned, the unique reproduction of the injective manipulator matrix from this process can only be guaranteed under the necessary prerequisite that the number of rows exceeds the number of columns. In this case, zero modes that cannot be resolved and lead to ambiguity in the reconstruction can be excluded. In other words, use sufficient information to solve the problem between all degrees of freedom of interest.

[0117] As already mentioned, the perturbation 𝑝 can only be properly represented when it is somewhat consistent with the choice of the basic functions, or when there are a sufficiently large number of basic functions. However, the introduction of weighting factors and regularization factors can improve the reproduction results.

[0118] The set of degrees of freedom used needs to be adapted to real-world effects. Simulations of stress effects and graphical data from measurements often provide paradigms for suitable perturbation functions. For example, if considering the deformation of a mirror surface, a functional basis would be defined for a given set of measured and / or simulated deformation states. This basis might initially have a variable size, and residuals would be calculated for each sample state, which would be preserved after fitting, depending on the number of degrees of freedom. A good approach would be to keep the residuals below an acceptable level in all cases. However, increasing this number allows for unpredictable contributions, increases complexity, and requires more measurement information.

[0119] The choice of a fine mesh may stem from the requirement to obtain sufficient knowledge about the perturbation to ensure that the perturbation on each optical element reaches an acceptable level after correction. Ideally, the junction region of the sub-apertures at all field points in the fine mesh completely covers each optical element. Adjacent sub-apertures often overlap, which provides redundancy, resulting in lower sensitivity to measurement errors, the average of which depends on the number of sub-apertures covering a given location on the optical element. Figure 3 depicts two meshes with different spatial resolutions used for simulation measurements.

[0120] If all optical elements are controlled in this way, it can be automatically ensured that no unexpected situations occur even in areas not covered by the fine mesh. Sometimes, if, for example, the production process ensures that the unknown area has comparable quality to the area affecting the measurement, then reducing the 100% requirement to, for example, 90% is acceptable. Depending on the correction degrees of freedom considered, reducing perturbation information may also be sufficient. For example, if rigid body degrees of freedom are only available for correction, but there are no plans to change the individual surface shapes, then relatively few aberration patterns can be compensated for entirely. In these cases, very detailed knowledge of the surface patterns (which the correction scheme cannot obtain) is of little use and does not bring any improvement.

[0121] Some aspects of the present invention can be described as follows:

[0122] This invention relates to a method for providing performance information of an optical system on a fine-field grid. The method is characterized by measuring at least a portion of the performance information on a coarser grid, reconstructing root cause perturbations in the optical system compatible with the measured performance data, and generating performance data on a fine-field grid based on these reconstructed perturbations. This establishes indirect information transfer between different aberrations.

[0123] In a preferred embodiment, the number of performance features used for reconstruction is equal to or greater than the total number of degrees of freedom for reconstruction. In another preferred embodiment, the measurement locations are given by edge points on a rectangular grid of equal size.

[0124] One aspect can be described as a method in which the optical system is an EUV lithography projection optics device, and the root cause of the disturbance is the deformation of the mirror surface, which may be caused by installation stress, surface shape errors during the manufacturing process, or material degradation (such as densification) during the service life.

[0125] This document discloses a method for improving the optical performance of an optical system by first applying the method to generate aberration information on a fine mesh, and then generating and executing a compensation formula that can utilize manipulators and / or at least one replaceable optical element present in the optical system, which can be individually shaped to optimally influence the field-related aberration pattern on the fine mesh.

[0126] Preferably, the sub-aperture of the fine grid covers at least 80%, more preferably 90%, and even more preferably 99% of each optical element. This ensures that field positions outside the fine grid also exhibit sufficiently low aberration levels.

[0127] The present invention also relates to a method for producing semiconductor devices by optical lithography using an optical system configured with a deterministic field-correlated aberration method.

Claims

1. A method of determining field dependent aberrations in an image field of an optical imaging system based on a measurement operation determining aberration data for a plurality of field points in the image field, the method comprising the steps of: - defining a target grid comprising a plurality of target field points in the image field, wherein a target field point is a field point for which an aberration level is to be determined; - defining a measurement grid comprising a first subset of the target field points, the first subset comprising all field points for which an aberration level is to be determined in the measurement operation; - measuring aberrations for all field points of the measurement grid to produce measured aberration data; - defining an auxiliary grid comprising a second subset of the target field points, the second subset comprising selected target field points not comprised in the measurement grid for which an aberration level is to be determined in an aberration data producing operation, wherein the aberration data producing operation is arranged to produce aberration data for the target field points of the auxiliary grid based on: (i) knowledge of the optical imaging system; and (ii) potential system specific aberration sources.

2. The method according to claim 1, wherein the aberration data producing operation comprises the steps of: reconstructing at least one perturbation of at least one optical element of the optical imaging system consistent with an aberration fingerprint determined based on the measured aberration data in the measurement grid; performing the forward calculation based on the perturbation obtained in the reconstructing step to determine field aberration data for all field points in the target field.

3. The method according to claim 1 or 2, wherein the reconstructing step comprises setting the refractive index of the gap between said optical surfaces to a value of 1.

4. The method according to any of the preceding claims, wherein the knowledge of the optical system comprises design data representative of a nominal optical design specification of the optical imaging system, the design data comprising for each optical surface of the optical imaging system at least one of: surface shape data representative of a nominal surface shape according to a specification; distance data representative of a distance between the optical surface and an adjacent optical surface; dimension data representative of a dimension of a portion of the optical surface actually used when the optical system is in use; index data representative of an optical property of the optical surface to distinguish between a reflective surface and a refractive surface.

5. The method according to any of the preceding claims, wherein the knowledge of the optical system comprises perturbation data comprising sensitivity data representative of a relationship between surface shape errors representative of a deviation of an optical surface from a nominal optical surface according to a specification and a contribution to wavefront aberration caused by the surface shape errors for each optical surface of the optical imaging system.

6. The method according to any of the preceding claims, wherein a grid width of the measurement grid is set such that a distance between target field points of the first subset is sufficiently small such that sub-apertures associated with the target field points overlap and encompass an entire useful area on each optical surface of the optical imaging system.

7. A projection exposure apparatus comprising: an illumination system (ILL); a projection lens (PO); a measurement system (MES) arranged to measure a wavefront of projection radiation transferred in the projection lens from a mask to a substrate to be exposed in a spatially resolved measurement of a plurality of field points in an image field (IF) of the projection lens (PO); a system arranged to determine a field dependent aberration in the image field (IF) of the projection lens based on a measurement operation determining aberration data of a plurality of field points in the image field, wherein the system is arranged to determine the field dependent aberration according to the method of any of the preceding claims.

8. A method of manufacturing a semiconductor device by optical lithography using an optical imaging system established by the method of any of claims 1 to 6.

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