Method and apparatus for controlling lithographic apparatus, and lithographic apparatus

Abstract

A computer-implemented method of generating one or more control actions for controlling a lithographic apparatus. A lithographic apparatus includes an illumination system for illuminating a mask with a non-uniform beam of radiation. The illumination system is configured to receive a radiation beam from a radiation source and includes a beam shaping device configured to receive data specifying contour information and to shape a lateral contour of the radiation beam based on the contour information to form a non-uniform radiation beam. The method includes processing the profile information to generate an estimated diffraction pattern resulting from illuminating the mask with the non-uniform radiation beam, and processing the estimated diffraction pattern to generate one or more control actions for a control system of the lithographic apparatus.

Description

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS

[0002] This application claims priority to European application 22199967.5 filed on October 6, 2022, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present invention relates to a method and a device for controlling a lithography apparatus and a lithography apparatus. Background Art

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

[0005] To project a pattern on a substrate, a lithography apparatus may use electromagnetic radiation. The wavelength of this radiation determines the minimum size of features that can be formed on a 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-20nm (e.g., 6.7nm or 13.5nm) can be used to form smaller features on a substrate compared to a lithography apparatus using radiation with a wavelength of, for example, 193nm.

[0006] Low k1 lithography can be used to process features with dimensions smaller than the classical resolution limit of the lithographic apparatus. In such a process, the resolution formula can be expressed as CD=k1×λ / NA, where λ is the wavelength of radiation used, NA is the numerical aperture of the projection optics in the lithographic apparatus, CD is the "critical dimension" (usually the smallest feature size printed, but in this case it is the half pitch), and k1 is an empirical resolution factor. In general, the smaller the k1, the more difficult it is to reproduce on a substrate a pattern similar in shape and size to that planned by the circuit designer to achieve specific electrical functions and performance. To overcome these difficulties, complex fine-tuning steps can be applied to the lithographic projection apparatus and / or the design layout. These include, for example, but not limited to, optimization of NA, customized illumination schemes, use of phase-shifted patterning equipment, various optimizations of the design layout (such as optical proximity correction (OPC, sometimes also called "optical and process correction") in the design layout), or other methods generally defined as "resolution enhancement technology" (RET). Alternatively, a tight control loop for controlling the stability of the lithographic apparatus can be used to improve the reproduction of patterns at low k1.

[0007] It is often difficult to maintain a lithographic apparatus in optimal operating conditions. For example, electromagnetic radiation incident on optical surfaces (e.g., surfaces of mirrors or lenses) within the lithographic apparatus may cause thermal aberrations of these optical surfaces, thereby degrading the performance of the lithographic apparatus. Such thermal aberrations can be compensated by selective heating and / or cooling of the optical surfaces.

[0008] This can be achieved, for example, by using a mathematical model to first predict the wavefront error caused by thermal aberrations and then deriving control actions, such as heating and / or cooling the optical surface, to reduce the wavefront error. To accurately predict the wavefront error, the model takes as input the spatial distribution of electromagnetic radiation incident on the optical surface and considers the underlying physical properties of each component of the lithographic apparatus.

[0009] For example, the spatial distribution of electromagnetic radiation on a mirror that reflects an optical image from a mask is usually determined by the diffraction pattern of the mask. Traditionally, knowledge of the mask is required to derive the corresponding diffraction pattern and perform thermal compensation using the above mathematical model. However, the details of the mask and the corresponding diffraction pattern are usually user-specific and not accessible to the control system of the lithography apparatus.

[0010] It would therefore be desirable to provide an improved control system that can compensate for thermal aberrations or reduce thermal aberrations without requiring detailed knowledge of the mask. Summary of the invention

[0011] It is an object of the present invention to provide new and useful methods and systems for improved control of a lithographic apparatus.

[0012] A first aspect of the invention proposes a computer-implemented method for generating one or more control actions for controlling a lithographic apparatus. The lithographic apparatus comprises an illumination system for illuminating a mask with a non-uniform radiation beam. The illumination system is configured to receive a radiation beam from a radiation source and comprises a beam shaping device configured to receive data specifying profile information and to shape a profile of the radiation beam based on the profile information to form a non-uniform radiation beam. The method comprises processing the profile information to generate an estimated diffraction pattern produced by illuminating the mask with the non-uniform radiation beam, and processing the estimated diffraction pattern to generate one or more control actions for a control system of the lithographic apparatus.

[0013] This method enables more precise control of the lithographic apparatus, particularly when the computer generating the control actions does not have access to details of the mask, such as whether the mask is a line pattern or a hole pattern, etc. However, since the profile information is typically selected by an individual (or a computer system) based on knowledge of the mask, it is somewhat informative about the mask, and thus the diffraction pattern produced by the mask.

[0014] For example, the contour information may be generated by source mask optimization or source optimization only. Optionally, the method may include the step of generating the contour information by source mask optimization or source optimization only based on a mask pattern.

[0015] Optionally, processing the profile information to generate an estimated diffraction pattern generated by the illumination system may include: processing the profile information to generate a candidate mask pattern, processing the candidate mask pattern to generate a candidate diffraction pattern, and processing the candidate diffraction pattern and the profile information to generate an estimated diffraction pattern generated by the illumination system. For example, the estimated diffraction pattern may be generated by a computer as a diffraction pattern that a mask would generate if it were substantially the same as the candidate diffraction pattern.

[0016] Optionally, processing the contour information to generate the candidate mask pattern may include: processing the contour information using a clustering algorithm to generate clustering information, and processing the clustering information to generate the candidate mask pattern. The clustering information may include the total number of clusters identified by the clustering algorithm and shape information and position information of each identified cluster. This improves the method because it can reliably extract the main features included in the contour information while filtering out the secondary features that need to be considered to generate effective control actions.

[0017] Optionally, processing clustering information to generate a candidate mask pattern may include: processing the clustering information to determine whether the candidate mask pattern is a line pattern or a hole pattern as a determination result, processing shape information and position information of each identified cluster to determine a pitch of the candidate mask pattern, and processing the determination result and estimating the pitch of the mask to generate the candidate mask pattern.

[0018] When processing the profile information to generate an estimated diffraction pattern produced by the illumination system includes processing the candidate diffraction pattern and the profile information to generate the estimated diffraction pattern produced by the illumination system, processing the candidate diffraction pattern and the profile information may include performing a convolution of the candidate diffraction pattern and the profile information to generate the estimated diffraction pattern.

[0019] Alternatively, the beam shaping device may comprise a programmable mirror array.

[0020] When the beam shaping device comprises a programmable mirror array, the profile information may be a two-dimensional array specifying a configuration of the programmable mirror array.

[0021] Optionally, the control system can be configured to apply a thermal conditioning treatment (e.g., a heating treatment at (multiple) selected positions, and / or a cooling treatment at (multiple) selected positions, such as water cooling) to at least a portion of the lithography apparatus based on the control action.

[0022] When the control system is configured to apply a thermal conditioning treatment to at least a portion of the lithographic apparatus based on a control action, the control system may be configured to apply the thermal conditioning treatment to an optical element of the lithographic apparatus (such as a mirror surface of a reflector or a surface of a lens). The optical element may include an optical surface, which includes a plurality of regions, and one or more control actions control the control system to apply a corresponding selected thermal conditioning treatment to each region of the regions of the optical surface. In this case, the optical element may be a reflector. Therefore, the corresponding thermal conditioning treatment for each region of the regions of the optical surface may be individually selected (e.g., subject to any overall constraints on the set of selected thermal conditioning treatments) and may be different for different regions.

[0023] Note, however, that, as an alternative to or in addition to thermal conditioning, control actions can effectuate fine tuning of the mirror, for example using actuators controlled by a control system, such as applying a selected amount of force to an optical element of the lithography apparatus (e.g., at a selected location on the optical element) to cause it to bend.

[0024] A second aspect of the present invention provides a computer system comprising a processor and a data storage device, wherein the data storage device stores program instructions, which when executed by the processor cause the processor to perform the method according to the first aspect of the present invention.

[0025] A third aspect of the present invention provides a computer program product, the computer program product comprising instructions, which when executed by a computer causes the computer to perform the method according to the first aspect of the present invention. The computer program product may be a computer-readable storage medium (such as a tangible storage device) or software that can be downloaded via a data transmission system (such as the Internet).

[0026] A fourth aspect of the present invention provides a control device for a lithographic apparatus. The lithographic apparatus includes an illumination system for illuminating a mask with a non-uniform radiation beam. The illumination system is configured to receive a radiation beam from a radiation source and includes a beam shaping device configured to receive data specifying profile information and to shape a profile of the radiation beam based on the profile information to form a non-uniform radiation beam. The control device is configured to process the profile information to generate an estimated diffraction pattern produced by illuminating the mask with the non-uniform radiation beam, and to process the estimated diffraction pattern to generate one or more control actions for a control system of the lithographic apparatus.

[0027] Features of the control apparatus, the lithographic apparatus and the illumination system may be as explained above in relation to the first aspect of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Embodiments of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which:

[0029] - Figure 1 A schematic diagram of a photolithography apparatus is depicted;

[0030] - Figure 2 A schematic diagram of a lithography unit is depicted;

[0031] - Figure 3 A schematic diagram depicting overall lithography represents the collaboration between three key technologies to optimize semiconductor manufacturing;

[0033] - Figure 4 Six examples of contour information are depicted in the top row, and high-intensity point clusters identified in the corresponding contour information are depicted in the bottom row;

[0035] - Figure 5 is a flow chart of an example method of generating control actions for controlling a lithographic apparatus;

[0037] - Figure 6 yes Figure 5 A flowchart of an example method for processing contour information in the steps of the method;

[0039] - Figure 7 It is a graphic Figure 6 Schematic diagram of the method;

[0040] - Figure 8 Shown by using Figure 6 The experimental data obtained by the method, and

[0041] - Fig. 9 For 8 masks, the Figure 6 The estimated diffraction pattern generated by the method and the corresponding simulated diffraction pattern. DETAILED DESCRIPTION

[0042] 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 365nm, 248nm, 193nm, 157nm or 126nm) and EUV (extreme ultraviolet radiation, e.g., having a wavelength in the range of about 5nm-100nm).

[0043] The terms "reticle", "mask" or "patterning device" as used herein may be broadly interpreted as referring to a general patterning device that can be used to impart to an incident radiation beam a patterned cross-section corresponding to the pattern to be created in a target portion of a substrate. The term "light valve" may also be used in this context. In addition to classical masks (transmissive or reflective, binary, phase-shifting, hybrid, etc.), other examples of such patterning devices include programmable mirror arrays and programmable LCD arrays.

[0044] Figure 1A lithographic apparatus LA is schematically depicted. 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 stage) MT constructed to support a patterning device (e.g., a mask) MA and connected to a first positioner PM configured to precisely position the patterning device MA according to certain parameters, a substrate support (e.g., a wafer stage) WT constructed to hold a substrate (e.g., a resist-coated wafer) W and connected to a second positioner PW configured to precisely 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.

[0045] 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 directing, 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.

[0046] 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, depending on the exposure radiation used and / or other factors, such as the use of immersion liquid or the use of a vacuum. Any use of the term "projection lens" herein may be considered a synonym for the more general term "projection system" PS.

[0047] The lithographic apparatus LA may be of a type in which at least a portion of the substrate may be covered by a liquid having a relatively high refractive index (e.g. water) to fill the space between the projection system PS and the substrate W, which is also referred to as immersion lithography. More information on immersion technology is given in US6952253, which is incorporated herein by reference.

[0048] The lithographic apparatus LA may also be of a type having two or more substrate supports WT (also referred to as "dual stage"). In such a "multi-stage" machine, the substrate supports WT may be used in parallel, and / or preparatory steps for subsequent exposure of a 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 support WT, the lithographic apparatus LA may comprise a measuring table. The measuring table is arranged to accommodate sensors and / or cleaning equipment. The sensors may be arranged to measure characteristics of the projection system PS or characteristics of the radiation beam B. The measuring table may accommodate a plurality of sensors. The cleaning equipment may be arranged to clean a part of the lithographic apparatus, for example a part of the projection system PS or a part of a system for providing immersion liquid. The measuring table may be moved under the projection system PS when the substrate support WT is away from the projection system PS.

[0050] In operation, a radiation beam B is incident on a patterning device, such as a mask MA, which is held on a mask support MT, and the radiation beam B is patterned by a pattern (design layout) present on the patterning device MA. After passing 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 help of a second positioner PW and a position measurement system IF, the substrate support WT can be precisely moved, for example, to position different target portions C in the path of the radiation beam B in a focused and aligned position. Similarly, the first positioner PM and possibly another position sensor ( Figure 1 The patterning device MA (not explicitly shown) can be used to accurately position the patterning device MA relative to the path of the radiation beam B. The patterning device MA and the substrate W can be aligned using the mask alignment marks M1, M2 and the substrate alignment marks P1, P2. Although the substrate alignment marks P1, P2 as shown occupy dedicated target portions, they can be located in the space between target portions. When the substrate alignment marks P1, P2 are located between the target portions C, they are called scribing alignment marks.

[0051] like Figure 2 As shown, the lithography apparatus LA may form part of a lithography cell LC, sometimes also referred to as a lithography cell or (lithography) cluster, which typically also includes apparatus for performing pre-exposure and post-exposure processing on a substrate W. Conventionally, these apparatus include a spin coater SC for depositing a resist layer, a developer DE for developing the exposed resist, a cooling plate CH and a baking plate BK, for example for regulating the temperature of the substrate W, for example for regulating a solvent in the resist. A substrate handler or robot RO picks up substrates W from input / output ports I / O1, I / O2, moves them between different processing apparatuses, and transports the substrates W to a loading area LB of the lithography apparatus LA. The equipment in the lithography cell (also often collectively referred to as a track) is typically controlled by a track control unit TCU, which itself may be controlled by a monitoring system SCS, which may also control the lithography apparatus LA, for example via the lithography control unit LACU.

[0052] In order for the substrate W exposed by the lithography apparatus LA to be correctly and consistently exposed, the substrate needs to be inspected to measure characteristics of the patterned structure, such as overlay errors between subsequent layers, line thickness, critical dimensions (CD), etc. For this purpose, an inspection tool (not shown) may be included in the lithography cell LC. If an error is detected, for example, adjustments may be made to the exposure of subsequent substrates or other processing steps to be performed on the substrate W, particularly if the inspection is performed before other substrates W of the same batch or lot still need to be exposed or processed.

[0053] The inspection device (which may also be referred to as a metrology device) is used to determine properties of the substrate W, in particular to determine how properties vary from one substrate to another W, or how properties associated with different layers of the same substrate W vary from layer to layer. The inspection device may alternatively be configured to identify defects on the substrate W, and may for example be part of the lithography cell LC, or may be integrated into the lithography apparatus LA, or may even be a stand-alone device. The inspection device may measure properties on a latent image (the image in the resist layer after exposure), a semi-latent image (the image in the resist layer after a post-exposure bake step PEB), a developed resist image (where exposed or unexposed parts of the resist have been removed), or even an etched image (after a pattern transfer step such as etching).

[0054] Typically, the patterning process in the lithography apparatus LA is one of the most critical steps in the process, which requires high precision in determining the size and placement of structures on the substrate W. To ensure this high precision, three systems can be combined in a so-called "holistic" control environment, such as Figure 3 As shown. One of these systems is a lithography apparatus LA, which is (virtually) connected to a metrology tool MT (a second system) and a computer system CL (a third system). The key to this "holistic" environment is to optimize the cooperation between these three systems to enhance the overall process window, and to provide a tight control loop to ensure that the patterning performed by the lithography apparatus LA remains within the process window. The process window defines the range of process parameters (e.g., dose, focus, overlay) within which a particular manufacturing process produces a defined result (e.g., a functional semiconductor device), and process parameters in the lithography process or patterning process are usually allowed to vary within these parameter ranges.

[0055] The computer system CL can use (a portion of) the design layout to be patterned to predict which resolution enhancement technology to use, and perform computational lithography simulations and calculations to determine which mask layout and lithography apparatus settings achieve the maximum overall process window for the patterning process (e.g., Figure 3Typically, the resolution enhancement technique is arranged to match the patterning possibilities of the lithographic apparatus LA. The computer system CL may also be used to detect the current operating position of the lithographic apparatus LA within the process window (e.g. using input from the metrology tool MT) to predict whether there will be defects due to, for example, a suboptimal process (e.g. Figure 3 (as indicated by the arrow pointing to “0” in the second scale SC2).

[0056] The metrology tool MT may provide input to the computer system CL to enable accurate simulations and predictions, and may provide feedback to the lithographic apparatus LA to identify possible drifts, e.g. in the calibration state of the lithographic apparatus LA (e.g. Figure 3 (as shown by the multiple arrows in the third scale SC3).

[0057] The projection system PS of the lithographic apparatus LA may include one or more projection optics boxes (POBs) configured to transmit electromagnetic radiation between a patterning device and a target portion C of a substrate W.

[0058] Each projection optical box includes one or more mirrors. The mirrors reflect electromagnetic radiation onto a target of a lithographic apparatus, such as a semiconductor wafer. The reflected electromagnetic radiation causes deformation of the mirrors, resulting in aberrations of the mirrors, thereby reducing the accuracy of the processing performed by the lithographic apparatus. In order to compensate for the aberrations, each mirror is divided into a plurality of regions. The temperature of each region can be controlled by changing the power of an auxiliary heating device applied to each region. Alternatively or additionally, the temperature of each region of the mirror can be controlled by controlling the temperature of a coolant used to cool the region of the mirror. In one embodiment, water is used as a coolant, but in variations of this embodiment, other coolants can be implemented. If the heat generation distribution on the (multiple) mirrors is known, any aberrations of the mirrors caused by the reflected electromagnetic radiation can be compensated by controlling the temperature of each region of each mirror.

[0059] In addition to or instead of using mirrors, the projection system can be a refractive projection system that employs one or more lenses (typically multiple lenses). Lenses are also subject to heating-induced aberrations, and a heating and / or cooling system can be used to manage and reduce these aberrations by selectively heating and / or cooling different regions of the lens.

[0060] The illuminator IL of the lithographic apparatus LA may include a beam shaping device (not shown) configured to receive data specifying profile information and to condition the radiation beam B based on the profile information so that it has a desired spatial and angular intensity distribution in its cross-section at the plane of the patterning device MA. For this purpose, the illumination system IL may, for example, be arranged for the radiation beam to be reflected successively from a faceted field mirror device and a faceted pupil mirror device. The illumination system IL may include other mirrors or devices in addition to or instead of the faceted field mirror device 10 and / or the faceted pupil mirror device.

[0061] Typically, the beam shaping device is configured to shape a radiation beam B received by the illumination system IL from the radiation source SO to form a non-uniform radiation beam for illuminating the patterning device MA. The term "profile" (or "lateral profile") is used here to include the beam radiation intensity at any given point on the mask, but may also include the angular distribution in the direction of radiation propagation at each point of the mask, which angular distribution is not necessarily transverse to the mask. The radiation beam B is shaped based on profile information, which may be provided by a user of the lithographic apparatus or derived by a mathematical model or the like. The profile information may specify a configuration of the beam shaping device (i.e., the profile information may be control data of the beam shaping device (e.g., a faceted field mirror device and / or a faceted pupil mirror device) if these devices are included in the illuminator IL), which results in a desired spatial and angular intensity distribution of the radiation beam B at the plane of the patterning device MA. Typically, the profile information comprises an array of data, wherein each element of the array specifies a configuration of an adjustable degree of freedom of the beam shaping device.

[0062] It has been shown that the image fidelity of a pattern projected by the projection system PS onto a target portion C of the substrate W depends on the configuration of the radiation beam illuminating the patterning device MA. In particular, by illuminating the patterning device MA with a non-uniform radiation beam, the image fidelity may generally be improved. The improved image fidelity may include a reduction in image distortion and / or an improvement in image resolution. It has further been shown that in order to improve the image fidelity, the shape of the radiation beam, i.e. the spatial and angular intensity distribution, needs to be selected based on the patterning device MA, in particular based on the symmetry of the patterning device MA. Therefore, a user of a lithography apparatus knowing the patterning device MA may configure the radiation beam B in such a way that the profile information is selected so as to improve the image fidelity of a pattern projected by the projection system PS onto a target portion C of the substrate W.

[0063] In one embodiment, a user of the lithographic apparatus may select profile information from a plurality of sets of predetermined profile information provided by the lithographic apparatus, the profile information resulting in best image fidelity of a pattern projected onto a target portion C of a substrate W by the projection system PS.

[0064] In another embodiment, the profile information may be generated as an output of an optimization process configured to determine a configuration of a beam shaping device that optimizes the image fidelity of a pattern projected by the projection system PS onto a target portion C of the substrate W, as described in more detail below.

[0065] In another embodiment, the beam shaping device is an aperture placed within the illumination system IL in the beam path of the radiation beam B. In this case, the profile information may be indicative of the shape of the aperture.

[0066] Optionally, the beam shaping device may include a programmable mirror array (e.g., a faceted field mirror device and / or a faceted pupil mirror device), and the profile information is control data of the programmable mirror array. The programmable mirror array may include a plurality of individually controllable mirrors. In this embodiment, the radiation beam B may be configured to illuminate a plurality of mirrors. Each mirror may be controlled to be in an on state or a off state. A mirror in an on state may reflect a corresponding portion of the incident radiation beam B, thereby illuminating the patterning device MA. A mirror in an off state may prevent a corresponding portion of the incident radiation beam B from illuminating the patterning device MA. For example, a mirror in an off state may be arranged so that a corresponding portion of the incident radiation beam B is directed toward a beam block.

[0067] When the beam shaping device includes a programmable mirror array, the profile information may include a two-dimensional data array that specifies the configuration of the programmable mirror array. Each element of the two-dimensional data array may specify whether the corresponding mirror is arranged in an open state or a closed state. In other systems, the mirrors may be controlled using other more complex control options. For example, the control system may be configured so that each mirror can be rotated by a selected amount around either of two axes so as to redistribute radiation to another selected portion of the pupil plane rather than wasting radiation.

[0068] "Source mask optimization" (SMO) is a known computational method for improving the image fidelity of a lithography system. SMO aims to optimize the image fidelity of a projected pattern by jointly optimizing the degrees of freedom of the illumination source and the degrees of freedom of the mask. Various algorithms for SMO are known. Typically, a SMO algorithm receives as input a target pattern and an initial guess for the illumination source configuration and the mask. The source variables and the mask variables are then adjusted simultaneously to optimize the derived expected projection pattern. To derive the expected projection pattern, the SMO algorithm may also utilize other information, such as the optical properties of the lithography apparatus and the physical and chemical reactions in the resist. As output, optimized source and mask variables and the expected projection pattern are provided. Example SMO algorithms are described in Stephen Hsu et al., “An Innovative Source-Mask co-Optimization (SMO) Method for Extending Low k1 Imaging” (SPIE Asia, Vol. 7104 2008) and Stephen Hsu et al., “Source-mask co-optimization: optimize design for imaging and impact of source complexity on lithography performance” (Proc. SPIE 7520, 75200D (2009)).

[0069] "Source only optimization" refers to a computational method for optimizing the image fidelity of a projected pattern by optimizing illumination. It has been shown that source only optimization is an effective method for improving lithography imaging performance by adjusting the intensity distribution of the light source. Source only optimization algorithms typically receive an initial guess of the configuration of the target pattern, mask, and illumination source as input. The source variables are then adjusted to optimize the derived expected projection pattern. Compared to SMO, the mask is not optimized in terms of source only optimization. As output, optimized source variables and expected projection patterns are provided. In cases where it is no longer convenient to adjust the mask, for example because the mask has already been produced, source only optimization may be preferable to SMO. An example of a source only optimization algorithm is described in "Optimization of lithography source illumination arrays using diffractionsubspaces" (Optics Express Vol.26, Issue 4, pp.3738-3755 (2018)) by Xu Ma et al.

[0070] In one embodiment, the profile information is generated by source mask optimization based on the patterning device MA.

[0071] In another embodiment, the contour information is generated by source-only optimization based on the patterning device MA.

[0072] Whether SMO or source optimization alone is used to generate the profile information, or whether a user who knows the patterning device MA selects the profile information from a plurality of predetermined profile information sets, the profile information generated or selected depends on characteristics of the patterning device MA, such as its symmetry. Therefore, the characteristics of the patterning device MA, such as its symmetry, are encoded in the profile information. As described below, in this embodiment, the patterning information is used to control the operation of the lithographic apparatus LA, and generally no information about the patterning device MA is used.

[0073] Figure 4 Example profile information for six different patterning devices MA acquired by source-only optimization is shown in the top row (panels 10-20).

[0074] In this example, the beam shaping device comprises a programmable mirror array, and the profile information comprises a two-dimensional data array specifying a configuration of the programmable mirror array. Each element of the two-dimensional data array specifies whether the corresponding mirror is to be arranged in an open state or a closed state.

[0075] In the top row of panels 10-20, mirrors in the on state are shown in white and mirrors in the off state are shown in black. The lower row of panels 11, 13, 17, 19 and 21 show the results of a clustering algorithm applied to the arrays shown in the corresponding top panels, as described in detail below.

[0076] Figure 4 Panel 10 shows an optimized configuration of a programmable mirror array (illumination pupil) with a horizontal line pattern of 28 nm pitch.

[0077] Figure 4 Panel 12 shows an optimized configuration of a programmable mirror array with a horizontal line pattern of 30 nm pitch.

[0078] Figure 4 Panel 14 shows an optimized configuration of a programmable mirror array with a vertical line pattern of 30 nm pitch.

[0079] Figure 4 Panel 16 shows an optimized configuration of a programmable mirror array with a hole pattern arranged in a hexagonal lattice with a pitch of 37 nm.

[0080] Figure 4Panel 18 shows an optimized configuration of a programmable mirror array with a hole pattern arranged in a hexagonal lattice with a pitch of 43 nm.

[0081] Figure 4 Panel 20 shows an optimized configuration of a programmable mirror array with a hole pattern arranged as a square lattice with a pitch of 40 nm.

[0082] It is noteworthy that the optimized configurations of the programmable mirror arrays are quite different from each other, suggesting that the properties of the patterning device MA are encoded in the optimized configuration of the programmable mirror array.

[0083] As described above, by controlling the temperature of each region of each mirror of the projection system PS, any aberrations of the mirrors due to reflected electromagnetic radiation can be compensated. In principle, other methods can be used to reduce or compensate for thermal aberrations, such as fine-tuning the control data of the programmable mirror array(s). In order to accurately predict control actions to compensate for heating caused by electromagnetic radiation, such as applying heating or cooling to specific regions of the mirrors in the projection system PS, the spatial distribution of the radiation on the mirror surface is taken into account. This is because the spatial distribution of the electromagnetic radiation on the mirror surface corresponds to the spatial distribution of the thermal load experienced by the mirror.

[0084] If the spatial distribution of radiation on the mirror is known, a mathematical model can be used to first predict the wavefront error caused by thermal aberrations and then derive control actions to reduce the wavefront error. To accurately predict the wavefront error, the model takes into account the underlying physical properties of each component of the lithography setup.

[0085] The spatial distribution of the electromagnetic radiation on the mirrors in the projection system PS depends on the diffraction pattern produced by the patterning device MA under illumination by the radiation beam B. Conventionally, knowledge of the patterning device MA is required to derive the corresponding diffraction pattern and to derive appropriate control actions using the above-mentioned mathematical model. However, the details of the patterning device MA and the corresponding diffraction pattern are typically proprietary to the user of the lithographic apparatus and may not be available for generating control means for controlling control actions of the lithographic apparatus.

[0086] It would therefore be desirable to provide an improved control system that is able to compensate for thermal aberrations without requiring detailed knowledge of the patterning apparatus MA.

[0087] Figure 5 A flow chart of a method of generating one or more control actions for controlling a lithographic apparatus is shown.

[0088] In general, the method generates control actions to compensate for thermal aberrations without requiring detailed knowledge of the patterning device MA. To this end, the method first generates an estimate of the patterning device MA. This is possible because, as described above, the characteristics of the patterning device MA are encoded in the profile information. The estimated patterning device MA is then used to predict the diffraction pattern that will be produced when the non-uniform radiation beam B illuminates the estimated patterning device MA.

[0089] The estimated diffraction pattern of the patterning device MA is then used to predict the wavefront error caused by the diffraction pattern on the mirror surface, and appropriate control actions are generated. It is worth noting that the estimated patterning device MA may be different from the patterning device MA, because the profile information may not encode the details of the patterning device MA to a sufficiently high degree. However, the estimated patterning device MA does not need to be identical to the patterning device MA to be able to generate effective control actions for controlling the lithographic apparatus. This is because the minute details of the patterning device MA have little effect on the thermal load of the mirrors in the projection system PS.

[0090] In step S100 of the method, a control device of the lithographic apparatus (such as a computer (e.g., a microprocessor) provided in the lithographic apparatus or a separate computer such as a server system) processes profile information to generate an estimated diffraction pattern produced by illuminating the mask with a non-uniform radiation beam.

[0091] In step S200 of the method, a control apparatus for a lithographic apparatus processes the estimated diffraction pattern to generate one or more control actions for a control system of the lithographic apparatus.

[0092] In one embodiment, to generate one or more control actions for a control system of a lithographic apparatus, a mathematical model is used to first predict the wavefront error caused by the thermal load associated with the estimated diffraction pattern, and then derive control actions to reduce the wavefront error. To accurately predict the wavefront error, the model may take into account the underlying physical properties of each component of the lithographic apparatus. For example, such a physical mirror heating model is described in detail in WO 2022 / 012844 A1.

[0093] Figure 6 Shown is the method for executing Figure 5 The method shown is a flow chart of step S100 of the method.

[0094] Figure 7 yes Figure 6 Schematic diagram of an example of the method.

[0095] refer to Figure 6 and Figure 7In step S101 of the method, the contour information is processed using a clustering algorithm to generate clustering information. The clustering information may include the total number of clusters identified by the clustering algorithm and shape information and position information of each identified cluster.

[0096] In one embodiment, a clustering algorithm is a computational method that receives as input a data array included in the profile information and performs the task of grouping the elements of the input data array so that elements in the same group (called a cluster) are more similar than elements in other groups. In one example, the clustering algorithm performs grouping based on distances between elements.

[0097] In one embodiment, after performing the grouping, the clustering algorithm obtains the total number of clusters identified during the grouping. The clustering algorithm can also generate location information for each identified cluster, for example, information specifying the center location of each identified cluster using a data array. The clustering algorithm can also generate shape information for each identified cluster, for example, information specifying the outline of each identified cluster using a data array.

[0098] In one embodiment, the clustering algorithm provides as output clustering information including the total number of clusters identified by the clustering algorithm and shape information and location information for each identified cluster.

[0099] In one embodiment, the clustering algorithm is density-based spatial clustering of applications with noise (DBSCAN). DBSCAN is described in detail in Ester, M. et al., "A density-based algorithm for discovering clusters in large spatial databases with noise" (Proceedings of the Second International Conference on Knowledge Discovery in Databases and Data Mining, 226-231, Portland, OR; AAAI Press, 1996).

[0100] In broad terms, DBSCAN is an unsupervised clustering algorithm that can cluster elements of a two-dimensional array included in profile information based on a predetermined neighborhood search radius and a predetermined minimum number of elements to form a cluster. Thus, DBSCAN can be used to reliably identify the main features of the two-dimensional array included in the profile information while filtering out scattering points in the two-dimensional array that do not contribute significantly to the thermal load on the reflector in the projection system PS. Furthermore, DBCAN does not require knowledge of the total number of expected clusters and is able to identify nested clusters. Those skilled in the art will appreciate that other clustering algorithms may be suitable if they have all or some of the above-mentioned properties.

[0101] In one embodiment, when the beam shaping device comprises a programmable mirror array, and the profile information comprises a two-dimensional data array specifying a configuration of the programmable mirror array, the clustering algorithm may process the two-dimensional data array. Figure 4 The two-dimensional array shown in the top row is similar, Figure 7 In the example of , each element of the example data array 30 specifies whether the corresponding mirror is in an open state or an closed state, where the open mirror is represented by white and the closed mirror is represented by black.

[0102] Further references Figure 7 In the example shown, panel 31 shows the results of a clustering algorithm DBSCAN applied to an example data array 30. The clustering algorithm identifies two clusters 32, 33 of mirrors that are in an on state.

[0103] Comparing the example data array 30 and the clustering results shown in panel 31, the clustering algorithm identifies two main features of the example data array 30 as two clusters. It is worth noting that the clustering algorithm does not assign every on-state element of the example data array 30 to a cluster. In particular, the clustering algorithm does not assign on-state elements in low-density areas (i.e., on-state elements whose nearest neighbor distance is farther than a predetermined distance) to any cluster. The contribution of these elements to the thermal load experienced by the reflectors in the projection system PS is negligibly low. Therefore, it is beneficial not to assign on-state elements in low-density areas because this simplifies further processing of the clustering results without affecting the accuracy of the derived control actions.

[0104] refer to Figure 4 , Panels 11, 13, 17, 19, and 21 show the results of DBSCAN applied to the arrays shown in the corresponding top panels. Figure 7 The example shown is similar to, Figure 4 The clustering results in show a reliable grouping of elements in the main features, while elements in low-density areas are not assigned.

[0105] Reference again Figure 6In step S102 of the method, a control device of the lithography apparatus processes clustering information to determine whether the candidate mask pattern is a line pattern or a hole pattern as a determination result.

[0106] In one embodiment, determining whether the candidate mask pattern is a line pattern or a hole pattern is based on the symmetry of the identified clusters. For example, if the center positions of the clusters are substantially located on a straight line, the candidate mask pattern is determined to be a line pattern. For example, when only two clusters are identified (e.g., Figure 7 Examples shown) and Figure 4 This is the case for the clustering results 11, 13 and 15 shown. In another example, if more than two clusters are identified and the center positions of the clusters form a pattern that exhibits rotational symmetry, the candidate mask pattern is determined to be a hole pattern. Figure 4 This is the case for cluster results 17, 19 and 21 shown.

[0107] In step S103 of the method, a control device of the lithographic apparatus processes shape information and position information of each identified cluster to determine a pitch of a candidate mask pattern.

[0108] In one embodiment, the pitch is determined based on the distance between the center positions of the identified clusters. If the number of clusters is small (e.g., only two), the direction between their centers can be determined (usually horizontal or vertical), and a shift is applied to one cluster in that direction until the overlap of the two clusters is maximized. The amount of the shift determines the pitch.

[0109] More generally (e.g., if the number of clusters is greater than two), to determine the pitch, each identified cluster can be processed by applying a horizontal or vertical shift to its elements until the overlap of the two clusters is maximized. In this way, the overlap between all identified pairs of clusters can be found. The pitch p is then given by the vertical or horizontal distance d of the pair of clusters with the highest overlap,

[0110]

[0111] Where λ is the wavelength of the electromagnetic radiation and NA is the numerical aperture of the projection optics in the lithographic apparatus. In one example, the value of NA may be 0.13.

[0112] exist Figure 7 In the example of FIG. 4 , by applying a horizontal shift, the first cluster 32 may be shifted to overlap the second cluster 33 .

[0113] Figure 8 The pitches determined by performing S103 on 13 different patterning devices are shown, and these pitches have corresponding target values, which are numbered 1 to 13, and the corresponding numbers are Figure 8The first to sixth patterning devices have horizontal line space patterns, the seventh to tenth patterning devices have vertical line / space patterns, and the eleventh to thirteenth patterning devices use via / contact hole patterns. Figure 8 It is shown that the estimated pitch is close to the target value.

[0114] Reference again Figure 6 , in step S104 of the method, a control device of the lithography apparatus processes the determination result and estimates the pitch of the mask to generate a candidate mask pattern.

[0115] The generated candidate mask pattern may be a two-dimensional array representing a line or hole pattern according to the determination with a pitch p. The generated candidate mask pattern may be a binary array. In principle, practical masks are often binary, with a pattern of line / space or hole arrays, although sometimes other features may be present, but there is usually one feature dominating the diffraction pattern and having a pitch that can be evaluated by the present method.

[0116] exist Figure 7 In the example of , the generated candidate mask pattern 34 is a line pattern. Its spatial Fourier transform 36 is obtained using, for example, a Fast Fourier Transform (FFT) algorithm.

[0117] In step S105 of the method, the control device of the lithography apparatus processes the candidate mask pattern to generate a candidate diffraction pattern (e.g., Figure 7 The candidate diffraction pattern 36 is shown in FIG.

[0118] In one embodiment, the candidate diffraction patterns are generated based on applying a Fourier transform to the candidate mask patterns.

[0119] exist Figure 7 In the example of , the generated candidate diffraction pattern 36 is generated by applying Fourier transform to the candidate mask pattern 34.

[0120] In step S106 of the method, a control device of the lithographic apparatus processes the candidate diffraction pattern and the profile information to generate an estimated diffraction pattern produced by the illumination system.

[0121] In one embodiment, control means of the lithographic apparatus processes the candidate diffraction pattern and the profile information to generate an estimated diffraction pattern produced by the lithographic apparatus.

[0122] exist Figure 7 In the example of , the estimated diffraction pattern 38 is generated by performing a convolution of the candidate diffraction pattern 36 and the profile information 30. For example, this can be achieved by multiplying the spatial Fourier transform of the candidate diffraction pattern 36 (i.e., the candidate mask pattern 34) with the spatial Fourier transform of the data array 30 and then performing an inverse Fourier transform back to the spatial domain.

[0123] Fig. 9 In the lower panel 42, an example of performing the above steps for eight different profile information corresponding to eight different line / space patterning devices is shown. Figure 6 The estimated diffraction pattern generated by the method. Fig. 9 The top panel 40 shows the corresponding diffraction pattern generated by the optical simulation software taking into account the shape of the inhomogeneous radiation B and the patterning device. Fig. 9 A good agreement between the estimated and simulated diffraction patterns is shown.

[0124] Although the use of the lithography apparatus in IC manufacturing may be specifically mentioned herein, it should be understood that the lithography apparatus described herein may have other applications. Other possible applications include the manufacture of integrated optical systems, guidance and detection patterns of magnetic domain memories, flat panel displays, liquid crystal displays (LCDs), thin film magnetic heads, etc.

[0125] Although specific reference may be made herein to embodiments of the invention in the context of a lithographic apparatus, embodiments of the invention may also be used in other apparatuses. Embodiments of the invention may form part of a mask inspection apparatus, a metrology apparatus, or any apparatus that measures or processes an object, such as a wafer (or other substrate) or a mask (or other patterning device). These apparatuses may generally be referred to as lithographic tools. Such lithographic tools may use vacuum conditions or ambient (non-vacuum) conditions.

[0126] Although specific reference may be made above to the use of embodiments of the present invention in the context of optical lithography, it will be appreciated that the present invention is not limited to optical lithography and may also be used in other applications, such as imprint lithography, where the context permits.

[0127] Although specific embodiments of the present invention have been described above, it should be understood that the present invention may be practiced in a manner other than that described. The above description is intended to be illustrative rather than limiting. Therefore, it will be appreciated by those skilled in the art that modifications may be made to the present invention described without departing from the scope of the following claims.

[0128] Additional embodiments are disclosed in the subsequent numbered list of clauses:

[0129] 1. A computer-implemented method for generating one or more control actions for controlling a lithographic apparatus,

[0130] The lithographic apparatus comprises an illumination system for illuminating a mask with a non-uniform radiation beam,

[0131] The illumination system is configured to receive a radiation beam from a radiation source and includes a beam shaping device configured to receive data specifying profile information and to shape a profile of the radiation beam based on the profile information to form the non-uniform radiation beam;

[0132] The method comprises:

[0133] processing the profile information to generate an estimated diffraction pattern produced by illuminating the mask with the non-uniform radiation beam, and

[0134] The estimated diffraction pattern is processed to generate one or more control actions for a control system of the lithographic apparatus.

[0135] 2. The computer-implemented method of clause 1, wherein the contour information is generated by mask pattern based source mask optimization or source only optimization.

[0136] 3. A computer-implemented method according to clause 1 or 2, wherein processing the profile information to generate an estimated diffraction pattern produced by the illumination system comprises:

[0137] processing the contour information to generate a candidate mask pattern;

[0138] processing the candidate mask pattern to generate a candidate diffraction pattern, and

[0139] The candidate diffraction patterns and the profile information are processed to generate the estimated diffraction pattern produced by the illumination system.

[0140] 4. The computer-implemented method of clause 3, wherein processing the contour information to generate a candidate mask pattern comprises:

[0141] Processing the profile information using a clustering algorithm to generate clustering information, and

[0142] processing the clustering information to generate the candidate mask pattern,

[0143] The clustering information includes the total number of clusters identified by the clustering algorithm and shape information and location information of each identified cluster.

[0144] 5. The computer-implemented method of clause 4, wherein processing the clustering information to generate the candidate mask pattern comprises:

[0145] processing the clustering information to determine whether the candidate mask pattern is a line pattern or a hole pattern as a determination result,

[0146] processing the shape information and the position information of each identified cluster to determine a pitch of the candidate mask pattern, and

[0147] The determination result and the pitch of the estimated mask are processed to generate the candidate mask pattern.

[0148] 6. A computer-implemented method according to any one of clauses 3 to 5, wherein processing the candidate diffraction pattern and the profile information to generate the estimated diffraction pattern produced by the illumination system includes: performing a convolution of the candidate diffraction pattern and the profile information to generate the estimated diffraction pattern.

[0149] 7. A computer-implemented method according to any preceding clause, wherein the beam shaping device comprises a programmable mirror array.

[0150] 8. The computer-implemented method of clause 7, wherein the profile information is a two-dimensional array specifying a configuration of the programmable mirror array.

[0151] 9. A computer-implemented method according to any preceding clause, wherein the control system is configured to: apply a thermal conditioning process to at least a portion of the lithographic apparatus based on the control action.

[0152] 10. The computer-implemented method of clause 9, wherein the control system is configured to apply the thermal conditioning process to an optical element of the lithographic apparatus.

[0153] 11. A computer-implemented method according to clause 10, wherein the optical element includes an optical surface, the optical surface includes a plurality of regions, and the one or more control actions control the control system to apply a corresponding selected thermal conditioning treatment to each of the regions of the optical surface.

[0154] 12. The computer-implemented method of clause 11, wherein the optical element is a mirror or a lens.

[0155] 13. A computer-implemented method according to clause 11, wherein the step of processing the profile information and the step of processing the estimated diffraction pattern are performed by a processor of the lithographic apparatus.

[0156] 14. A computer system comprising a processor and a data storage device storing program instructions which, when executed by the processor, cause the processor to implement a method according to any preceding clause.

[0157] 15. A computer program product comprising instructions which, when executed by a computer, cause the computer to perform the method according to any one of clauses 1 to 12.

[0158] 16. A control device for a lithographic apparatus, the lithographic apparatus comprising an illumination system for illuminating a mask with a non-uniform radiation beam, the illumination system being configured to receive a radiation beam from a radiation source and comprising a beam shaping device, the beam shaping device being configured to receive data specifying profile information and to shape a profile of the radiation beam based on the profile information to form the non-uniform radiation beam;

[0159] The control device is configured to:

[0160] processing the profile information to generate an estimated diffraction pattern produced by illuminating the mask with the non-uniform radiation beam, and

[0161] The estimated diffraction pattern is processed to generate one or more control actions for a control system of the lithographic apparatus.

[0162] 17. The control device according to clause 15, further configured to generate the contour information by mask pattern based source mask optimization or source only optimization.

[0163] 18. A control device according to clause 16 or 17, the control device being configured to process the profile information to generate an estimated diffraction pattern produced by the illumination system by:

[0164] processing the contour information to generate a candidate mask pattern;

[0165] processing the candidate mask pattern to generate a candidate diffraction pattern, and

[0166] The candidate diffraction patterns and the profile information are processed to generate the estimated diffraction pattern produced by the illumination system.

[0167] 19. A control device according to clause 18, the control device being configured to process the contour information to generate a candidate mask pattern by:

[0168] Processing the profile information using a clustering algorithm to generate clustering information, and

[0169] processing the clustering information to generate the candidate mask pattern,

[0170] The clustering information includes the total number of clusters identified by the clustering algorithm and shape information and location information of each identified cluster.

[0171] 20. The control device according to clause 19, the control device being configured to process the clustering information to generate the candidate mask pattern by:

[0172] processing the clustering information to determine whether the candidate mask pattern is a line pattern or a hole pattern as a determination result,

[0173] processing the shape information and the position information of each identified cluster to determine a pitch of the candidate mask pattern, and

[0174] The determination result and the pitch of the estimated mask are processed to generate the candidate mask pattern.

[0175] 21. A control device according to any one of clauses 18 to 20, wherein the control device is configured to process the candidate diffraction pattern and the profile information to generate the estimated diffraction pattern produced by the illumination system in the following manner: performing a convolution of the candidate diffraction pattern and the profile information to generate the estimated diffraction pattern.

[0176] 22. A lithographic apparatus, comprising a control device and an illumination system according to any one of clauses 16 to 21, wherein the illumination system is used to illuminate a mask using a non-uniform radiation beam, the illumination system is configured to receive a radiation beam from a radiation source, and comprises a beam shaping device, the beam shaping device is configured to receive data specifying contour information, and to shape a lateral contour of the radiation beam based on the contour information to form the non-uniform radiation beam, the control device being configured to provide the control action to a control system of the lithographic apparatus.

[0177] 23. The lithographic apparatus of clause 22, wherein the beam shaping device comprises a programmable mirror array.

[0178] 24. The lithographic apparatus of clause 23, wherein the profile information is a two-dimensional array representing a configuration of the programmable mirror array.

[0179] 25. The lithographic apparatus of clause 23 or clause 24, wherein the control system is configured to apply a thermal conditioning process to at least a portion of the lithographic apparatus based on the control action.

[0180] 26. The lithographic apparatus of clause 25, wherein the control system is configured to apply the thermal conditioning process to an optical element of the lithographic apparatus.

[0181] 27. A lithographic apparatus according to clause 26, wherein the optical element comprises an optical surface, the optical surface comprising a plurality of regions, and the one or more control actions comprise applying a different thermal conditioning treatment to each of the regions of the optical surface.

[0182] 28. A lithographic apparatus according to clause 26 or 27, wherein the optical element is a mirror or a lens.

Claims

1. A computer-implemented method for generating one or more control actions for controlling a lithographic apparatus, The lithographic apparatus comprises an illumination system for illuminating a mask with a non-uniform radiation beam, The illumination system is configured to receive a radiation beam from a radiation source and includes a beam shaping device configured to receive data specifying profile information and to shape a profile of the radiation beam based on the profile information to form the non-uniform radiation beam; The method comprises: processing the profile information to generate an estimated diffraction pattern produced by illuminating the mask with the non-uniform radiation beam, and The estimated diffraction pattern is processed to generate one or more control actions for a control system of the lithographic apparatus. 2 . The computer-implemented method of claim 1 , wherein the contour information is generated by a mask pattern-based source mask optimization or a source-only optimization.

3. The computer-implemented method of claim 1 or 2, wherein processing the profile information to generate an estimated diffraction pattern produced by the illumination system comprises: processing the contour information to generate a candidate mask pattern; processing the candidate mask pattern to generate a candidate diffraction pattern, and The candidate diffraction patterns and the profile information are processed to generate the estimated diffraction pattern produced by the illumination system.

4. The computer-implemented method of claim 3 , wherein processing the contour information to generate a candidate mask pattern comprises: Processing the profile information using a clustering algorithm to generate clustering information, and processing the clustering information to generate the candidate mask pattern, The clustering information includes the total number of clusters identified by the clustering algorithm and shape information and location information of each identified cluster.

5. The computer-implemented method of claim 4, wherein processing the clustering information to generate the candidate mask pattern comprises: processing the clustering information to determine whether the candidate mask pattern is a line pattern or a hole pattern as a determination result, processing the shape information and the position information of each identified cluster to determine a pitch of the candidate mask pattern, and The determination result and the estimated pitch of the mask are processed to generate the candidate mask pattern.

6. The computer-implemented method of any one of claims 3 to 5, wherein processing the candidate diffraction pattern and the profile information to generate the estimated diffraction pattern produced by the illumination system comprises: A convolution of the candidate diffraction pattern and the profile information is performed to generate the estimated diffraction pattern.

7. A computer implemented method according to any preceding claim, wherein the beam shaping device comprises a programmable mirror array.

8. The computer implemented method of claim 7, wherein the profile information is a two-dimensional array specifying a configuration of the programmable mirror array.

9. A computer implemented method according to any preceding claim, wherein the control system is configured to apply a thermal conditioning process to at least a portion of the lithographic apparatus based on the control action.

10. The computer-implemented method of claim 9, wherein the control system is configured to apply the thermal conditioning process to an optical element of the lithographic apparatus.

11. The computer-implemented method of claim 10, wherein the optical element comprises an optical surface, the optical surface comprising a plurality of regions, and the one or more control actions control the control system to apply a corresponding selected thermal conditioning treatment to each of the regions of the optical surface.

12. The computer-implemented method of claim 11, wherein the optical element is a mirror or a lens.

13. The computer-implemented method of claim 11, wherein the steps of processing the profile information and processing the estimated diffraction pattern are performed by a processor of the lithographic apparatus.

14. A computer system comprising a processor and a data storage device storing program instructions which, when executed by the processor, cause the processor to implement a method according to any preceding claim.

15. A computer program product comprising instructions which, when executed by a computer, cause the computer to perform the method according to any one of claims 1 to 12.

16. A control device for a lithographic apparatus, the lithographic apparatus comprising an illumination system for illuminating a mask with a non-uniform radiation beam, the illumination system being configured to receive a radiation beam from a radiation source and comprising a beam shaping device, the beam shaping device being configured to receive data specifying profile information and to shape a profile of the radiation beam based on the profile information to form the non-uniform radiation beam; The control device is configured to: processing the profile information to generate an estimated diffraction pattern produced by illuminating the mask with the non-uniform radiation beam, and The estimated diffraction pattern is processed to generate one or more control actions for a control system of the lithographic apparatus.

17. A lithographic apparatus, comprising a control apparatus and an illumination system according to claim 16, wherein the illumination system is used to illuminate a mask using a non-uniform radiation beam, the illumination system is configured to receive a radiation beam from a radiation source, and comprises a beam shaping device, the beam shaping device is configured to receive data specifying profile information, and to shape a lateral profile of the radiation beam based on the profile information to form the non-uniform radiation beam, the control apparatus being configured to provide the control action to a control system of the lithographic apparatus.

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