Method of determination of imaging transfer function of charged-particle exposure apparatus, and exposure substrate

Abstract

To enable determination of an imaging transfer function in particular in electron beam lithography.SOLUTION: A method for determining parameters of an imaging transfer function (point spread function) is presented. With regard to a model that describes the imaging transfer function including a plurality of model parameters, a test substrate is exposed and developed using a test pattern (50) which comprises multiple sub-patterns (55) that are based on the same sub-pattern template but have varying control width of a feature in the template, such as the width of a line or a distance between lines. On the test substrate, isofocal dose measurement is performed using structures thus formed on the test substrate with varying control and imaging parameters. The isofocal dose thus determined are utilized to determine the model parameters of the imaging transfer function.SELECTED DRAWING: Figure 5D

Description

[Technical field]

[0001] This application claims the benefit of Paris Convention priority from European Patent Application No. 23180357.8, filed June 20, 2023, the entire contents of which are incorporated herein by reference.

[0002] The present invention relates to a pattern writing method for use in charged particle processing apparatus, and more particularly to determining an image transfer function - such as a point spread function - of a charged particle exposure apparatus during exposure of a target positioned in the target plane of the apparatus. [Background technology]

[0003] This kind of method and apparatus is used in reticle manufacturing or maskless direct write lithography. The applicant has described such methods and apparatus, for example, in US 9,520,268, US 6,768,125, US 8,222,621 and US 8,378,320. In particular, the applicant has already realized a 50 keV electron multi-beam writer for realizing a state-of-the-art composite photomask for 193 nm immersion lithography, of masks for EUV lithography and of templates (1× masks) for imprint lithography. The system is called eMET (electron Mask Exposure Tool) or MBMW (multi-beam mask writer) for exposure of 6″ mask blank substrates.

[0004] A typical embodiment of the invention uses a charged particle exposure apparatus as shown diagrammatically in FIG. 1 (not to scale). The apparatus includes a charged particle projection (illumination) system 11 that generates a charged particle beam 12, a projection optical system 13, and a beam shaping or aperture array device 14 that preferably modifies the shape of the beam or the pattern to be transferred to the substrate by shaping the beam into a number of parallel propagating sub-beams ("multi-beam" 19). The apparatus further includes an exposure chamber 10 that contains a target 15 to be exposed (e.g. a resist-coated quartz photomask or silicon wafer) mechanically fixed to a motion stage 17 by a clamp 16 (or other type of mount). The exposure apparatus is controlled by a processing system 18. Further details about charged particle exposure apparatus can be found in the published patent documents mentioned above.

[0005] The present invention is directed to certain improvements in the correction of proximity effects in electron beam lithography caused by the interaction of the electron beam used for the writing process with the resist and the substrate. In particular, the present invention is directed to a method for determining a point spread function suitable for use in proximity effect correction. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] US9,520,268 [Patent Document 2] US6,768,125 [Patent Document 3] US8,222,621 [Patent Document 4] US8,378,320 [Patent Document 5] US5,241,185 [Patent Document 6] US6,815,693 [Patent Document 7] US7,511,290 [Non-patent literature]

[0007] [Non-Patent Document 1] H. Tanabe et al. in Proc. SPIE Vol. 7748, Photomask and Next-Generation Lithography Mask Technology XVII, 774823; available at https: / / doi.org / 10.1117 / 12.862641 [Non-Patent Document 2] P. Hudek et al. in J. Micro / Nanopattern. Mats. Metro. 20(4) 041402; available at https: / / doi.org / 10.1117 / 1.JMM.20.4.041402 [Non-Patent Document 3] K. Keil et al. in Microelectronic Engineering, Volume 85, Issues 5-6, pp. 778-781; available at https: / / doi.org / 10.1016 / j.mee.2008.01.042 Summary of the Invention [Problem to be solved by the invention]

[0008] Proximity effect correction (PEC), which adjusts the pattern to be exposed or its exposure dose to take into account the additional dose from backscattered electrons, is a well-established technique in electron beam lithography, see for example US 5,241,185, US 6,815,693 or US 7,511,290.

[0009] For this purpose, it is known to model the electron-substrate interaction as an exposure intensity distribution function (or point spread function) that describes the image transfer function from a single element of the pattern definition device (which has minimal lateral extent and is ideally point-like) to the target surface; this exposure intensity distribution function is then convolved with the pattern to obtain the dose distribution on the target.

[0010] For Chrome on Glass (CoG) or Opaque MoSi on Glass (OMOG) photomasks used in 193 nm immersion lithography, one typical choice of point spread function is the two-component Multi-Gaussian. TIFF2025001656000002.tif10150, where: TIFF2025001656000003.tif6150 is the forward scattering component with range α (on the order of 20 nm) and weight normalized to 1, TIFF2025001656000004.tif6150 is the backscattered component with range β (on the order of 10 μm) and a weight or backscatter ratio η (with typical values ​​in the range 0.3 to 0.8), TIFF2025001656000005.tif11150 is a (rotationally symmetric) Gaussian distribution with integral normalized to 1.

[0011] In particular, for reticles used in extreme ultraviolet (EUV) lithography, the two-Gaussian model is usually not sufficient, since the backscattering effects generated by the thick Mo / Si multilayer structures found on EUV mask blanks are more complex (see H. Tanabe et al. in Proc. SPIE Vol. 7748, Photomask and Next-Generation Lithography Mask Technology XVII, 774823; available at https: / / doi.org / 10.1117 / 12.862641). Instead, models with more Gaussian components are suitable, e.g., the triple-Gaussian model. TIFF2025001656000006.tif10150 is used, where: TIFF2025001656000007.tif6150 is a mid-range scattering component with range γ (typically on the order of 400 nm) and corresponding weight ν (approximately 0.2).

[0012] One prior art approach determines the point spread function (PSF) by imposing and fitting an exposure model (which may include development and etching effects) to the critical dimension (CD) values ​​generated and measured for varying doses or patterns (see, for example, P. Hudek et al. in J. Micro / Nanopattern. Mats. Metro. 20(4) 041402; available at https: / / doi.org / 10.1117 / 1.JMM.20.4.041402).

[0013] Furthermore, the prior art has proposed the use of isofocal dose measurements to determine and compare process windows in electron beam lithography (see, for example, K. Keil et al. in Microelectronic Engineering, Volume 85, Issues 5-6, pp. 778-781; available at https: / / doi.org / 10.1016 / j.mee.2008.01.042); however, this approach is not suitable for determining the point spread function, especially with regard to proximity effect correction.

[0014] The aim of the method according to the invention described below is to determine the point spread function (or its parameters), and more generally the image transfer function, in particular for use in proximity effect correction in electron beam lithography. [Means for solving the problem]

[0015] According to a first aspect of the invention, there is provided a method for determining an image transfer function of a charged particle exposure tool during exposure of a target positioned in a target surface of the charged particle exposure tool, the image transfer function describing a distribution of dose or energy generated in the target surface from a single active element of a pattern definition device of the charged particle exposure tool resulting from the single active element being imaged onto a substrate in the charged particle exposure tool, The method includes the steps of: i. providing a model of the image transfer function, said model including at least one function parameter to be determined; ii. selecting a set of imaging characteristics, including at least one of beam blur and beam focus, that are adjustable by modifying predefinable imaging parameters of the charged particle exposure device other than a base exposure dose that describes an overall intensity of the image transfer function; iii. exposing a test substrate with a test pattern using said charged particle exposure device and developing said test substrate to form test structures on said at least one test substrate, the test pattern includes a plurality of sub-patterns, each sub-pattern being a copy of a sub-pattern template that is modified according to at least one control parameter, the at least one control parameter varying across the plurality of sub-patterns (varying for each sub-pattern of the plurality of sub-patterns) within a predetermined parameter range; and the test pattern is exposed onto the test substrate a number of times while the base exposure dose and at least one imaging parameter of the charged particle exposure tool are varied to form a number of test pattern copies on the substrate. the test structure so formed includes a plurality of substructures, each substructure being associated with imaging parameters, the base exposure dose, and particular values ​​of the at least one control parameter; iv. evaluating the plurality of substructures for at least one measurable quantity, including a critical dimension of a feature of the substructure; v. determining, for each value of the at least one control parameter, a change in the at least one measurable quantity between the plurality of substructures as a function of the imaging parameter, and determining from said change a respective value of an isofocal dose, wherein said change is a minimal change with respect to a change in the imaging parameter(s); vi. Calculating said at least one function parameter of said image transfer function as a function of said at least one control parameter using the isofocal dose value(s) determined in step v. According to a second aspect of the invention there is provided an exposed substrate comprising at least one test structure on a test substrate exposed in a charged particle exposure apparatus according to steps i-iii of the method of the invention. In the substrate, the test structure includes a plurality of substructures, the plurality of substructures being formed using copies of the same underlying subpattern template modified according to a control parameter that varies across the subpatterns. It is characterized by: DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0016] (Mode 1) See the first aspect of the present invention above. (Mode 2) In the method according to mode 1, The measurable quantity in steps iv and v includes a critical dimension of a feature of interest of the substructure(s). is preferred. (Form 3) In the method according to form 1 or 2, especially according to form 1, the image transfer function is modeled as a weighted sum of radially symmetric multi-Gaussian functions, where the weighted sum includes at least three Gaussian components as summands; In step vi, the weights and / or length scales of at least one of the summands are determined. is preferred. (Mode 4) In the method according to mode 3, the image transfer function includes a multi-Gaussian function including at least one mid-range component having weights and length scales as parameters determined in step vi, the length scales corresponding to widths limited to the range of 200 nm to 2 μm; is preferred. (Mode 5) In any one of modes 1 to 4, particularly in the method according to mode 1, The method further comprises the steps of: ii'. calculating, for the model provided in step i and its at least one functional parameter, a model calculation of said at least one measurable quantity as a function of said subset of said imaging and control parameters, and determining values ​​of said subset of parameters when said model calculation predicts that said at least one measurable quantity is invariant with respect to said parameter; containing, Step ii' is performed before step vi; Step vi includes performing a least squares fitting of said model calculation to a course of minimal variation to obtain final parameters of said image transfer function. is preferred. (Mode 6) In the method according to Mode 5, The fitting in step v[vi] is carried out by finding an optimum value of an evaluation function that includes a weighted sum of the squares of the differences between the values ​​of the parameters in the model calculation and the course of the minimum change. is preferred. (Mode 7) In the method according to mode 6, a regularization term is added to the evaluation function, the regularization term including the first and / or second radial derivatives of the image transfer function and / or its magnitude or the sum of the absolute values ​​of the vectors of the image transfer functions; is preferred. (Mode 8) In any one of modes 1 to 7, particularly in the method according to mode 1, A plurality of different values ​​of beam blur are generated by physically defocusing the beam by modulation of appropriate electrostatic voltages on lenses and / or multipole lens components of an imaging system of the charged particle exposure apparatus. is preferred. (Mode 9) In any one of modes 1 to 8, particularly in the method according to mode 1, By adjusting the pattern to emulate increased blur, multiple different values ​​of beam blur are generated. is preferred. (Mode 10) In any one of modes 1 to 9, particularly in the method according to mode 1, The subpattern template is: a single line, where the control parameter is the width of the line; a triple line structure including a central line bracketed by two outer lines, where the control parameter is the width of the other two lines; a triple line structure including a central line bracketed by two outer lines, where the control parameter is the distance of the other two lines from the central line; or a combination of these be selected from one of the following: The measurable quantity of the resulting substructure is the width of the single line or the central line. is preferred. (Mode 11) See the second aspect of the present invention above. (Mode 12) In the substrate according to Mode 11, The substrate further includes multiple sub-structures formed in the charged particle exposure tool by applying respective values ​​of imaging parameters, the values ​​being different among each of the multiple sub-structures. is preferred. (Mode 13) In the substrate according to mode 11 or 12, particularly mode 11, The underlying subpattern template is: a single line, where the control parameter is the width of the line; a triple line structure including a central line bracketed by two outer lines, where the control parameter is the width of the other two lines; a triple line structure including a central line bracketed by two outer lines, where the control parameter is the distance of the other two lines from the central line; or a combination thereof, Include one of the following: The measurable quantity of the resulting substructure is the width of the single line or the central line. is preferred.

[0017] The method approaches the problem in terms of a (mathematical or numerical) model describing the image transfer function by a number of model parameters, by exposing and developing a test substrate (which can also be a set of substrates, if preferred) with a test pattern including multiple sub-patterns based on the same sub-pattern template but with varying control widths of a feature of the template, such as line width or distance between lines. On this test substrate, a corresponding number of isofocal dose measurements are performed on the test structures thus formed, varying the control and imaging parameters (a feature of interest is of interest when the control width of a feature of the template is varied to affect the backscatter). The isofocal dose measurements are then used to determine the image transfer function (point spread function).

[0018] More specifically, the invention proposes a method for determining an image transfer function, in particular a point spread function, of a charged particle exposure apparatus during exposure of a target positioned in the target plane of the charged particle exposure apparatus, where the image transfer function describes the distribution of dose or energy generated in the target plane from a single active element (such as a single aperture opening or ideally a point-like opening) of a pattern definition device of the charged particle exposure apparatus when the single active element is imaged onto a substrate in the charged particle exposure apparatus, the method comprising the following steps: i. providing a model of an image transfer function, the model including at least one function parameter to be determined; ii. selecting a set of imaging characteristics (for the charged particle exposure device) that are adjustable by modifying predefined imaging parameters (of the charged particle exposure device); the imaging characteristics typically include beam blur and / or beam focus, but do not include a base exposure dose that describes the overall intensity (in the sense that it is the intensity integrated over the (entire) target surface) of the image transfer function; iii. exposing a test substrate (which may be a single substrate or a set of individual test substrates) to a test pattern using a charged particle exposure device and developing (and optionally further processing, e.g. etching) the test substrate to form a test structure on at least one of the test substrates, wherein the test pattern includes a plurality of sub-patterns, each sub-pattern being a copy of a sub-pattern template modified according to at least one control parameter that varies across sub-patterns of the plurality of sub-patterns within a predetermined parameter range; and the test pattern is exposed multiple times onto the test substrate while the values ​​of the base exposure dose and at least one imaging parameter of the charged particle (exposure) device are varied, thereby forming multiple test pattern copies on the substrate (so that each of the multiple test pattern copies may be associated with a respective / different instance of the imaging parameter(s)); the test structure so formed includes a plurality of substructures, each substructure being associated with imaging parameters, a base exposure dose, and particular values ​​of the at least one control parameter; iv. evaluating the plurality of substructures for at least one measurable quantity including a critical dimension of a feature(s) of the substructure; v. determining, for each value of at least one control parameter, a change in said at least one measurable quantity among a plurality of substructures as a function of imaging parameter(s) and determining from said change a respective value of an isofocal dose, said change being a minimal change with respect to a change in imaging parameter(s); vi. Calculating at least one functional parameter of an image transfer function as a function of the at least one control parameter using the isofocal dose value(s) determined in step v.

[0019] In particular, in the case of a point spread function (PSF), the imaging parameters include the global or maximum dose of the exposure and / or the blur of the PSF; measurable quantities are for example the line width of certain lines in the formed substructures. Furthermore, in many embodiments of the method according to the invention, additional parameters of the isofocal dose can also be determined. Examples of parameters of the PSF are parameters describing the "geometrical" shape and / or range of the PSF, such as the "range" parameters α, β, γ in the multi-Gaussian case above.

[0020] Compared to the above-mentioned conventional methods, the present method offers several advantages. First, the present method allows a certain degree of decoupling of electron-resist interactions (modeled by the point spread function) and process effects (such as development and etch bias or loading). This is because the isofocal dose measurements according to the present invention are performed by adjusting the optical parameters for a given pattern, so that a relatively narrow range of exposure CDs is obtained for each isofocal dose measurement, thus establishing a relatively constant etch and development regime. In contrast, known methods based on fitting a point spread function to line measurements typically use features (and pattern densities) with a wide range of feature sizes in a single fit, which necessarily incorporates process effects into the point spread function, thus detrimentally affecting the accuracy of the determined point spread function. Furthermore, for patterns that are sufficiently large compared to the forward scattering distance α, the isofocal dose (of the pattern) will depend only on the amount and distance of the backscattering, but not on the forward scattering distance. The inventors have realized that this allows the determination of the backscattering parameters alone, within the meaning of the present invention, and usually does not require the determination of the forward scattering distance. The critical dimension values ​​for non-isofocal doses and the change in CD under dose variation, on the other hand, strongly depend on the forward scattering distance α (depending on the dose and / or background), which is why known conventional methods generally require the determination of the complete variation range of the parameters of the point spread function. Thus, the present invention allows the determination of the isofocal dose and other PSF parameters faster and with reduced computational complexity.

[0021] In particular, in many embodiments of the invention, the image transfer function is a point spread function describing the distribution of absorbed energy in a resist layer of a resist-coated target positioned at the target surface in response to a particle beam generated by a single active element, and a model of the point spread function may be implemented to account for the scattering of charged particles in the target. In this case, it may be advantageous to expose the substructure(s) in step ii [iii] with different values ​​of maximum exposure dose and imaging blur. Furthermore, the measurable quantity in steps iv and v may include a critical dimension of a feature of interest in the substructure. Furthermore, many embodiments of the invention may include the determination of an isofocal dose or a parameter corresponding thereto, where the isofocal dose represents a dose value at which the measured critical dimension of the exposed pattern is invariant under changes in beam blur. In particular, the method typically includes the determination of an isofocal dose (or a parameter corresponding thereto), which may then be used in step vi for the calculation of the function parameter(s) of the image transfer function. It should be noted that the isofocal dose is usually a function of some of the control and imaging parameters, but in such cases the isofocal dose varies along a stationary parameter course; thus the calculation of the parameter(s) of the image transfer function may also include the dependence of the isofocal dose from certain parameters, such as the pattern density or the controlled width of the line spacing. Furthermore, as a simple but effective way to realize different values ​​of beam blur, these can be generated by physically defocusing the beam, by adjusting the appropriate electrostatic voltages of the lenses and / or multipole lens components of the imaging system of the charged particle exposure device, and / or by adjusting the pattern to emulate an increased blur. The adjustment of the pattern can be performed, for example, by convolution with a kernel, or by changing the vector pattern (for example in a VSB writer) along a (single) coordinate, which can be performed to obtain a gradual transition between the pattern and the surrounding area.

[0022] Furthermore, the method may advantageously comprise a fitting for the model calculation based on the mathematical expression. Thus, before step vi, an additional step may be provided: for the model provided in step i and its at least one function parameter, a model calculation (i.e. a mathematical expression) of said at least one measurable quantity as a function of said subset of imaging and control parameters, and determining the values ​​of said subset of parameters if said model calculation predicts that said at least one measurable quantity is stationary with respect to said parameters; in this case, step v[vi] comprises performing a least-squares fitting of said model calculation to the stationary parameter course in order to obtain the final parameters of the image transfer function. Preferably, this fitting may be performed by finding an optimum value of an evaluation function comprising a weighted sum of the squares of the differences between the values ​​of the parameters in the model calculation and the stationary parameter course. Furthermore, in order to improve the stability and convergence of the fitting method, it may be useful to supplement the evaluation function with a regularization term. The regularization term includes the first and / or second radial derivatives of the image transfer function and / or its magnitude (L2) or the sum of the absolute values ​​of the vectors of the image transfer function(s) (L1). The fitting may be performed by performing a least squares fitting to obtain the parameter(s) of the image transfer function. In exemplary embodiments of the invention, the image transfer function is modeled as a radially symmetric piecewise polynomial function; a radially symmetric multi-Gaussian; a weighted sum thereof; or a weighted combination thereof. For example, the image transfer function may include a multi-Gaussian including at least one mid-range component having a width between 200 nm and 2 μm.

[0023] A further aspect of the invention is directed to an exposed substrate comprising a test structure (developed or formed by the method of the invention in step iii based on the model / parameters provided in steps i and ii) on the test substrate, the test structure comprising a plurality of substructures exposed in a charged particle exposure apparatus as described above, the substructures being formed using copies of the same underlying subpattern template modified according to control parameters that vary across the subpatterns. Preferably, the substrate further comprises multiple substructures formed in the charged particle exposure apparatus by applying respective values ​​of the imaging parameters, the values ​​being different between each of the multiple substructures. Suitable examples of subpattern templates are e.g. A single line, where the control parameter is the line width; A triple line structure including a central line sandwiched between two outer lines, where the control parameter is the width of the two outer lines; A triple line structure including a central line flanked by two outer lines, where the control parameter is the distance of the two outer lines from the central line; or a combination of these It is.

[0024] In these cases, the width of the single line or the central line, respectively, may be advantageously used as a measurable quantity in the resulting substructure.

[0025] In the following, the invention will be explained in more detail by means of some embodiments with reference to the attached drawings, in which it is emphasized that the embodiments shown are illustrative and should not be understood as limiting the scope of the invention. [Brief description of the drawings]

[0026] [Figure 1] 1 is a schematic diagram of a longitudinal section of an example of a lithographic apparatus; [Figure 2A]Concept of isofocal dose for the example of a 50 nm line. The figure shows a continuous profile (graph). [Figure 2B] Concept of isofocal dose for the example 50 nm line. The pixel-based profile (graph) is shown in the figure. [Figure 3A] Procedure for determining the isofocal dose using Bossung plots. The figure shows an example with a continuous profile and a change in height of the beam focus ΔZ. [Figure 3B] Procedure for determining isofocal dose using Bossung plots. An example is shown in which pixel-based profiles are evaluated with varying pixel blur σ. [Figure 4] 1 is an example of a flowchart of method steps according to one embodiment of the present invention. [Figure 5A] An example of a test pattern that includes multiple sub-patterns, specifically a test pattern that includes multiple isolated lines with variable design widths. [Figure 5B] An example of a test pattern containing multiple sub-patterns, specifically a test pattern in which the sub-pattern templates have variable control widths of the two outer lines. [Figure 5C] An example of a test pattern that includes multiple sub-patterns, specifically a test pattern in which the sub-pattern templates have variable distances between the center line and the outer lines. [Figure 5D] 1 shows an example test pattern including an example array layout in response to varying imaging and control parameters. [Figure 6A] A set of cubic B-spline functions as basis functions for modeling the PSF behavior. [Figure 6B] An example of combining spline functions to fit an example function. [Figure 7]13 shows the effect of an example dose background on an example line edge profile. [Figure 8] Isofocal dose as a function of dose background b in units. [Figure 9] Some examples of the behavior of isofocal dose as a function of line width. [Figure 10] A test of the reproducibility of parameters determined from the fitting method according to the present invention. EXAMPLES

[0027] The detailed description (discussion) presented herein is intended to explain the present invention and its exemplary embodiments and further advantageous developments. It should be clear to one skilled in the art to freely combine some or all of the embodiments and aspects described herein as deemed appropriate for a particular application of the present invention. Throughout this disclosure, terms such as "advantageous", "exemplary" or "preferred" indicate elements or dimensions that are particularly appropriate (but not essential) for the present invention or an embodiment thereof, and can be modified as deemed appropriate by a person skilled in the art, unless expressly stated otherwise. It should be understood that the present invention is not limited to the exemplary embodiments described below, which are given for illustrative purposes and provide only preferred embodiments of the present invention.

[0028] In particular, the present invention is described in the exemplary context of an electron beam apparatus for lithographic mask manufacturing, although it can be used in conjunction with virtually any charged particle lithography apparatus. In particular, in the lithography apparatus of FIG. 1, the calculation and correction methods described below may be suitably implemented in the processing system 18 of the lithography apparatus and / or any other control system for data processing and control of the writing process on a substrate (the terms substrate and target are used interchangeably herein). Further details about multi-beam charged particle tools can be found in US 9,520,268, US 6,768,125, US 8,222,621 and US 8,378,320 and references cited therein, all of which are incorporated by reference as part of this disclosure.

[0029] The inventors propose a novel method for determining an image transfer function, described below for an example of a multi-component point spread function (PSF) in electron beam lithography, based on isofocal dose measurements for a test pattern containing various subpatterns, e.g., using the above-mentioned Multi-Gaussian PSF.

[0030] The flow chart of Fig. 4 illustrates a method according to one embodiment of the present invention. In a pre-step MDL, the method starts by defining or selecting an appropriate model of the PSF, which also determines the relevant parameters (and, if necessary, the ranges over which the parameters can vary). Typically, the model will be a mathematical description of the PSF, e.g. for a multi-Gaussian PSF the parameters are the ranges and relative weights. Alternatively, the model can be represented by a set of "knots" located in one-dimensional coordinates (such as a radius about the center of the PSF distribution) or at specific points on a two-dimensional spatial surface, and the PSF can then be interpolated between these knots, e.g. by linear interpolation or using splines. In step EXP, a test pattern including a number of sub-patterns (e.g. lines with variable widths) including several features of interest with different control dimensions corresponding to the control parameters of the claimed invention is exposed and developed by a charged particle exposure apparatus using a resist and a substrate with specific properties (not part of the invention) to produce a test substrate. In this document, "developing" a substrate is meant to include all processing steps required to obtain a substrate from which quantities of interest, such as critical dimensions on the substrate, can be measured. Varying imaging parameters during the exposure process, such as varying exposure dose and beam blur, are used for the various sub-patterns, thus forming a number of sub-structures. In the sub-structures, the respective features are reproduced with variations that depend on the respective imaging and control parameters. Then, in step MCD, the so-formed sub-structures are tested to measure one or more quantities, in particular the critical dimensions of the features of interest of the structures.Then, in a first post-processing step IFD, for each sub-pattern (or more precisely for features of interest in the sub-pattern) an isofocal dose is determined from the critical dimension measurements; more generally, this step IFD determines a stationary parameter set of imaging parameters. Finally, in a second post-processing step FIT, a PSF that models the interaction of the electron beam with the target is derived from the range of isofocal doses.

[0031] Test Pattern

[0032] This section describes some examples of test patterns, each containing a set of respective sub-patterns suitable for the present invention, with emphasis on lines with variable widths and distances; however, it should be noted that the concepts introduced by the inventors can be easily translated to other types of test patterns such as dots / contacts / rectangles, as well as more complex patterns.

[0033] FIG. 5A shows the subpatterns Variable design widths embodying TIFF2025001656000008.tif6150 (only three subpatterns are shown in FIG. 5A) 5A shows an example of a preferred embodiment of a test pattern 51 including a number of isolated lines 511, 512, 513 with TIFF2025001656000009.tif6150. In this example, each subpattern is a variant of an underlying subpattern template including a single line. Each subpattern will result in a respective substructure. For example, subpattern P1 may form a substructure shown superimposed as two contour lines 514 in FIG. 5A. Here, the linewidth of subpattern 514 (the difference between the design width and the exposed linewidth is shown exaggerated for clarity) is the critical dimension of interest (which serves as a metric for determining the backscatter generated by the line itself), while the design width of the lines is the critical dimension of interest (which serves as a metric for determining the backscatter generated by the line itself). TIFF2025001656000010.tif6150 represents a control width, which in this example can be interpreted as controlling the magnitude of backscattering.

[0034] FIG. 5B shows multiple subpatterns 5B shows an example of a test pattern 52 of another preferred embodiment that provides variants of a subpattern template including triple lines, reproduced as TIFF2025001656000011.tif6150 (only two of these subpatterns are shown in FIG. 5B). In each triplet, the central lines 521, 522 are configured with a constant line width W (preferably on the order of three forward scattering distances, e.g., 80 nm), and the outer two lines are configured with a variable control width W (preferably on the order of three forward scattering distances, e.g., 80 nm). TIFF2025001656000012.tif6150(i>2 width w i521, 522) are the features of interest, while the (two) outer lines serve as (backscattered) sources of dose background for each feature of interest. The pattern is preferably designed symmetrically to ensure equal dose background at the left and right edges (left and right sides) of the central line. The advantage of this approach is the uniformity of the field of view when measuring the central line by CD-SEM, which may facilitate more stable measurements.

[0035] 5C shows another example of a suitable test pattern 53 (again, only two of the subpatterns are shown). In this example, the base subpattern template includes triple lines of constant width, but variable distance. Thus, the test pattern includes subpatterns embodied as triple lines. TIFF2025001656000013.tif6150, in which the central lines 531, 532 of each sub-pattern are the feature of interest, i.e. the measured exposure critical dimension serves as a reference for determining the isofocal dose, and the two outer lines are background generators. In this variant, the width of the central line W (e.g. on the order of 3 forward scattering distances) and the width of the outer lines W0 (which are preferably at least 3 backscattering distances to ensure a fully saturated point spread function) are constant; the spacing between the central line and the (two) outer lines serving as background generators, to vary the magnitude of backscattering at the edges of the central line, is of variable width, constituting a control width in this pattern 53. This is embodied (achieved) by TIFF2025001656000014.tif6150.

[0036] In all variants, the length of the lines is preferably longer than 3 backscattering distances, which simplifies the model calculations and allows them to be performed one-dimensionally in this example. The variable width and spacing preferably correspond to the range of the point spread function to be determined, with a higher measurement density of the control width generally resulting in more accurate results. To determine the isofocal dose for each subpattern, it may be necessary to expose multiple copies of the subpattern with variable configurations of dose and blur. Furthermore, the accuracy may be increased to obtain several such measurements from the features of interest (e.g. at different positions along each feature of interest), which can be averaged to ensure low measurement noise or, in the case of a multi-beam exposure apparatus, to sample over the beam field (over which the blur may vary).

[0037] Also, subpatterns of several types (e.g., the types shown in Figures 5A, 5B, 5C and / or other figures) may be combined, for example, by fitting a point spread function to the combined data for the different subpattern types.

[0038] In all variants, the subpattern Advantageously, the distance between the TIFF2025001656000015.tif6150's may be chosen to be large enough to avoid mutual influence due to backscattering or other undesirable effects.

[0039] 5D shows an example of an example test pattern 50 including an example layout that allows exposure of multiple sub-patterns with varying exposure parameters. TIFF2025001656000016.tif6150, where each subpattern has a respective control width that varies across the subpatterns, for example, row 55. 5B or 5C, with TIFF2025001656000017.tif6150. The sub-patterns are preferably arranged according to an array, in which the sub-patterns TIFF2025001656000018.tif6150 forms columns 54 in which the sub-patterns all have the same control width, and within each column, the sub-patterns are imaged with different imaging parameters, in this case different dose values. TIFF2025001656000019.tif6150 (e.g. -10%, 0% and +10% relative to a predefined initial dose) and different blur values TIFF2025001656000020.tif6150 (e.g., −2 μm, 0 μm, and +2 μm beam focus relative to a reference focus, e.g., focus of the feature of interest). Preferably, these imaging parameters are assigned to the sub-patterns such that the parameters are constant within each of the rows 55 of the layout; the respective value sets for each column can be found in FIG. 5D. FIG. 5D shows a simplified embodiment, and in practice, one skilled in the art should appreciate that the layout may need to incorporate more values ​​of dose and blur to account for measurement noise and to ensure that the isofocal dose falls within the range of dose variation. The individual sub-patterns are separated (relative to each other) by a distance D. Preferably, this distance D will be at least three times the maximum backscattering distance (e.g. D=30 μm) so that interactions between sub-patterns are avoided (ideally, depending on the total pattern density, a value larger than one layer of D may be preferred to take into account long-range interactions such as fogging effects). In a preferred embodiment of the invention using the Applicant's MBMW described above for exposure, in order to ensure a uniform exposure blur, which may otherwise vary across the beam field, it will additionally be provided to ensure that the pattern to be measured (especially the central line) is exposed by the same part of the beam field in all sub-patterns. This can be provided, for example, by selecting the size and mutual distance of the sub-patterns to be an integer multiple of the size of the beam field.

[0040] It should be noted that, without loss of generality, in the embodiments of the invention described herein and below, the lines are defined as being oriented along the y direction ("vertically" in the plane of the drawing).

[0041] Isofocal Dose

[0042] The concept of isofocal dose is explained in this section with reference to FIG. 2A. The concept is based on the realization of binary patterns using a threshold model that models the relationship between the dose profile (i.e. the absorbed energy density in the resist) and the generated pattern shape. Thus, the parts of the exposure dose profile with a dose above the dose threshold will be retained after resist processing, while the other parts will be removed during resist processing (for positive resist; for negative resist the situation is reversed). For any pattern, the generated dose profile will generally depend on the blur of the beam used for exposure. With reference to FIG. 2A, for example, a 50 nm line, when exposed, would ideally have a dose profile 20, and the figure shows the emerging profiles for beam blurs with standard deviations of 4 nm (profile 21), 8 nm (profile 22) and 16 nm (profile 23), respectively. If the dose D1 assigned to the line is greater than the threshold dose D of the resist, then the resulting profile will be 0.01 μm. T If the number of D1 is twice as large as the number of D2, then D1 = 2D T In the case of , the exposure width is usually independent of beam blur - hence "isofocal", i.e., invariant to focal changes of the optical imaging system. Note that the value of the exposure dose D is normalized to D1 in the figure. For exposure, the dose would need to be adjusted for backscattering, which is neglected in FIG. 2A for simplicity. Note further that for feature sizes on the order of the standard deviation of the beam blur, such behavior is generally only possible for certain types of patterns (e.g. lines and spaces of equal width). Also, for physical resists with imperfect contrast curves, isofocality is only approximately possible, since the developed and etched features depend on the slope of the dose profile, which is usually blur-dependent.

[0043] In US 9,520,268 and US 9,373,482, in the context of a charged particle multi-beam mask writer, the applicant introduced a technique to emulate physical beam blur by adjusting the exposure pattern. Using this method, as shown in FIG. 2B, the ideal dose profile 20 is adjusted by convolution with a pixel-based kernel, thus obtaining a modified (corrected) exposure pattern 22 (steps are smoothed in profile 22 by a finite blur). Exposed with a physical blur of 4 nm standard deviation, the modified pattern produces a flatter dose profile 23 (corresponding to a larger blur) compared to the dose profile 21 produced by the original pattern. Note that when the pattern is exposed with an isofocal dose, the exposure line width is again invariant to the emulated blur (in particular, both exposure dose profiles 21 and 23 are below the dose threshold D T It should be noted that the two vertices intersect at

[0044] One suitable method (procedure) for experimentally determining the isofocal dose for a given pattern or subpattern (which will often also depend on the pattern density) uses a so-called "Bossung plot" that plots the change in CD (Critical Dimension) against the change in blur for several candidate dose values. This method is described with reference to FIG. 3A. Since a change in the beam focus height causes a corresponding change in beam blur, the pattern of interest is exposed and measured several times with dose levels varying between -30% and +30% with respect to a reference dose level while varying the beam focus height. The beam focus height is represented in FIG. 3A by a relative value ΔZ with respect to the Z position (or other standard position on the Z coordinate) of the target surface and is varied within a suitable range, for example ±8 μm. The resulting CD values, represented in FIG. 3A as relative values ​​ΔCD to an arbitrarily selected reference value of CD, are evaluated using a presentation as shown in plot 30 (different symbols indicate different dose levels); it is clear that the response to changes in beam blur depends on the dose level selected. Dose level D1 is represented in FIGS. 3A and 3B as a reference (standard) dose level D ref is expressed as a relative change to D ref A dose level equal to 0% corresponds to "+0%"; the reference (standard) dose level D ref is arbitrarily set to, for example, twice the estimated dose threshold, i.e., D ref =2D T (estim) , . Additionally, second order polynomials are fitted to the measured CD values ​​for each of the constant dose levels, as shown as the curves in plot 30. The curvatures of the polynomials of the curves in plot 30 (i.e., the coefficient a2 of the second order term, symbolically a2=d 2 (ΔC D ) / d(ΔZ) 2) is evaluated and the curvature value a2 is inserted into a plot 36 (as such) as a function of dose level D1. To determine the dose with the smallest variance under focus changes, a second regression curve is determined, as graphed in plot 36. At the location 32 of the change in sign of the regression curve, the curvature a2 is expected to be zero; this location can be referred to as the location of the "stationary parameters", and the dose at this location 32 is the isofocal dose (shown in this example at +3% relative to the reference dose, i.e. D isf =1.03D ref ).

[0045] The above method can be performed using an emulated pixel-based blur instead of a physical beam blur, as shown in FIG. 3B. As in the method described with reference to FIG. 3A, the pattern is exposed and measured with a dose that is varied between −30% and +30% for several levels of blur; however, the blur variation is generated by adjusting the pattern by convolution with a Gaussian kernel of increasing width (pixel blur with standard deviation σ). In plot 33, the data points are multiplied by regression lines to determine the value of the slope k1 (symbolically k1=d(ΔCD) / dσ). The slope a1[k1] is plotted against the assigned dose levels in plot 39, and a regression curve 34 of the slope values ​​is determined. To obtain the isofocal dose 35, the position of the sign change of the regression curve 34 is determined as the position of the “steady parameter” (also shown in this example at +3% relative to the reference).

[0046] It should be noted that in general there are further parameters that may affect the value of the isofocal dose, such as pattern density, which may be represented or simulated by appropriate control widths of the test pattern(s). Thus, the Bossung plots of Figures 3A and 3B will change slightly when such further parameters are changed, and the position of the steady-state parameters will change accordingly, as a function of the various parameters, as will the "steady-state parameter course".

[0047] The inventors have found that it is often advantageous to use a global dose modulation for the above, as this reduces complexity. Thus, a "global" isofocal dose is determined, i.e. the entire subpattern, including the background generating features, is exposed at a constant dose level (so that the dose background due to backscattering also corresponds to the selected dose level). Variations of the above method may also determine a "local" isofocal dose, where only the dose at the edge of the feature of interest is modulated; however, this variation needs to be taken into account in the post-processing steps, as explained further below.

[0048] Point Spread Function

[0049] In most embodiments, the present invention relies on the assumption that the image transfer function, such as the point spread function, to be determined by the present invention is rotationally symmetric and contains forward and backward scattering components, i.e. Starting point is TIFF2025001656000021.tif6150.

[0050] In many embodiments corresponding to a typical use case of the present invention, a multi-Gaussian PSF is determined, where the forward scattering distance α is taken along with the point spread function (symbol Weights are unknown parameters (collectively shown in TIFF2025001656000022.tif6150) TIFF2025001656000023.tif6150 and distance For Gaussian with TIFF2025001656000024.tif6150, TIFF2025001656000025.tif10150 TIFF2025001656000026.tif13150 TIFF2025001656000027.tif11150. The integral of the PSF over the target area is normalized to 1. Additionally, the forward scatter weight is fixed to 1, thus corresponding to the D50 dose (50% pattern density) for equal width lines and spaces, which is independent of blur, width and spacing. The D50 dose is usually determined separately and then used to normalize other dose values ​​after measurement to obtain relative doses. For example, the D50 dose can be determined by including equal width lines and spaces (or other suitable features of constant width) in a test pattern and performing the determination method for isofocal dose as described above based on the corresponding CD measurements.

[0051] The method of the present invention can also be used to determine a point spread function defined by a piecewise polynomial in radius, for example a cubic spline PSF. The use of this type of point spread function for proximity effect correction has already been proposed, for example in US 10,553,394. For least squares fitting, the use of B-splines (a set of basis functions for a given space of spline functions) is preferred. B-splines are easily constructed by routines in standard numerical libraries, such as scipy or PPPACK. Splines and B-splines can be used to model PSF functions more general than Gaussian or multi-Gaussian. TIFF2025001656000028.tif6 A spline basis in a polynomial degree M basis with 150 degrees of freedom First, radial grid points to define TIFF2025001656000029.tif6150 Determine a set R for TIFF2025001656000030.tif6150. Grid points are chosen at regular intervals (cardinal B-spline) and it is sufficient that their knots lie within the range of the point spread function of interest (0 outside). The B-spline function is a weighted sum It is combined with TIFF2025001656000031.tif13150, where the coefficient TIFF2025001656000032.tif6150 are the PSF parameters and form the PSF components.

[0052] Figure 6A shows an exemplary set of eight cardinal cubic B-splines 60 (i.e., K=8, L=12, M=3) with 12 grid points 61. Figure 6B shows an example illustrating how the spline functions 62 can be combined with a weighted sum to fit an arbitrary radial function 63 that decays outside of the interval defined by the grid points. This type of spline function can be used to model any PSF behavior.

[0053] To form a full PSF, multiple spline components of the above type with individual grids can be combined by normalizing summations and integrals to 1. For example, the forward scatter component (with weights normalized to 1) Fine grid for TIFF2025001656000033.tif8150 TIFF2025001656000034.tif6150 (and coefficient TIFF2025001656000035.tif6150) and the backscatter component (with arbitrary positive weights) Coarse grid for TIFF2025001656000036.tif6150 TIFF2025001656000037.tif6150 (and coefficient TIFF2025001656000038.tif6150) is The image can be given by TIFF2025001656000039.tif18150.

[0054] Where: TIFF2025001656000040.tif10150 shows the weights of the spline components, TIFF2025001656000041.tif6150 is a vector of combined PSF coefficients. It is also possible to form a composite point spread function by combining multi-Gaussian and spline PSFs, e.g., Gaussian components for forward and long-range backscattering (with weights of 1 and η) TIFF2025001656000042.tif6150 and spline components for mid-range backscattering in the range 200-2000 nm By using TIFF2025001656000043.tif6150, parameterization TIFF2025001656000044.tif6150 This can result in TIFF2025001656000045.tif12150.

[0055] In some embodiments of the invention, portions (or, equivalently, some parameters) of a certain type of point spread function may already be known (e.g., the backscattering distance β) or may prove not recoverable (independent) from the measured range of isofocal dose (e.g., within a very small control range). TIFF2025001656000046.tif6150) simply varies the isofocal dose. In such cases, it is generally a sufficient approach to insert values ​​that are known from experiment or literature, as one of skill in the art would recognize as appropriate, and proceed with the method with these inserted values.

[0056] Numerical isofocal dose

[0057] By using an exposure model, such as the threshold model described above, the isofocal dose can be determined for a given point spread function and subpattern, which can then be compared to the measured isofocal doses. For the threshold exposure model, the exposure dose profile TIFF2025001656000047.tif6150 is a subpattern The binary indicator function of TIFF2025001656000048.tif6150 (1 if in pattern, 0 if not) Convolution with the PSF represented by TIFF2025001656000049.tif6150 For the patterns shown above (see FIGS. 5A-5D), which use only vertical pattern lines, the integral above becomes: can be reduced to one dimension given by TIFF2025001656000051.tif14150, where (also called the marginal point spread function) TIFF2025001656000052.tif14150 and TIFF2025001656000053.tif6150 is a one-dimensional pattern in the x direction with a constant arbitrary value y0. For a multi-Gaussian PSF, the marginal point spread function is a one-dimensional multi-Gaussian; for a spline or composite PSF, the marginal PSF can be determined numerically (e.g., by numerical integration).

[0058] The continuous convolution of equation (6) is the function p and It can be adequately approximated by a discrete convolution of samples of TIFF2025001656000054.tif6150. The operation is preferably performed over at least three times the maximum range of the point spread function (for a multi-Gaussian) or over the support of a spline function.

[0059] Then, in the threshold model, the isofocal dose The dose at which the measured structure width changes least under blur variations can be determined by selecting the dose at which the measured structure width changes least under blur variations. TIFF2025001656000056.tif7150, where TIFF2025001656000057.tif6150 shows the marginal PSF with variable forward scattering distance (e.g., taken in a set of test blurs A and also experimentally applied to test patterns), and TIFF2025001656000058.tif6150 is the exposure dose A convolution pattern is used to determine the area or width of the exposed structural feature when TIFF2025001656000059.tif6150 is applied to the associated (significant) subpattern. This is the symbol for evaluating TIFF2025001656000060.tif6150. For example, for the threshold model, evaluation TIFF2025001656000061.tif6150 is the dose threshold of the exposed structure. This will result in the size (dimension) of the portion(s) at a dose exceeding 6150. The minimum value (dose of least change) can be determined for a set of candidate doses by either numerical minimization or direct calculation.

[0060] Analytical evaluation of isofocal dose

[0061] In some cases, a marginal PSF can be calculated without the need to compute multiple exposure dose profiles by (typically slow) convolution. Analytical (1-dimensional) subpattern from TIFF2025001656000063.tif6150 Isofocal dose for TIFF2025001656000064.tif6150 To do so, the first step is to calculate the line edge of the feature of interest (e.g. the width of the central line of an isoline 51 or a line triplet 52, 53). The dose background (per unit dose) in TIFF2025001656000066.tif6150 (which edge it is doesn't matter because the test pattern is symmetrical) is: Marginal point spread function, localized to the pattern edge, i.e., by TIFF2025001656000067.tif12150 Backscattered part of TIFF2025001656000068.tif6150 TIFF2025001656000069.tif14150 as pattern TIFF2025001656000070.tif6150. For a generic point spread function, this calculation can be conveniently performed on a computer by choosing a set of uniform grid points, summing the sampled function values ​​over the grid points of the pattern, and multiplying by the grid step (or by other types of numerical integration).

[0062] For some types of PSFs, the test pattern (9) can be evaluated using "standard" functions. For example, for a multi-Gaussian PSF (2) and isolines 51 as test patterns, TIFF2025001656000071.tif12150, where: TIFF2025001656000072.tif6150 is a Gaussian error function.

[0063] In the second step, the isofocal dose is determined from the dose background. TIFF2025001656000073.tif6150 (for example, 3α for multi-Gaussian PSF) <w) For lines, the line edges Isofocal dose in TIFF2025001656000074.tif6150 TIFF2025001656000075.tif6150 shows that in the threshold model shown in FIG. 7 for the 100 nm line 70, It is well known that the hologram is given by TIFF2025001656000076.tif6150 (see, for example, M. Yu et al., “Photomask and Next-Generation Lithography Mask Technology XII”, Proc. SPIE 5853, available at https: / / doi.org / 10.1117 / 12.617058), where: TIFF2025001656000077.tif6150 is a so-called iso-dose, i.e. an isofocal dose for isolated features (without a dose background), TIFF2025001656000078.tif6150 is the (absolute) dose background. Correction factor TIFF2025001656000079.tif6150 is the exposure dose profile 71 and the dose threshold The intersection with TIFF2025001656000080.tif6150 is chosen to remain at half the dose in the presence of background. Dose Background TIFF2025001656000081.tif6150 also corresponds to isofocal dose (assuming it is determined globally), so TIFF2025001656000082.tif7150, so isofocal dose TIFF2025001656000083.tif6150 is the unit dose background From TIFF2025001656000084.tif6150 This can be determined by TIFF2025001656000085.tif10150. See the graph in Figure 8 for TIFF2025001656000086.tif6150. The inverse is The image is given as TIFF2025001656000087.tif11150.

[0064] Inverse problem

[0065] The presence of an isofocal dose for a range of subpatterns with variable control width is a "signature" property of the point spread function that allows its determination by solving an inverse problem. For a multi-Gaussian PSF, for example, each parameter uniquely changes the shape of the isofocal dose trend curve. This is illustrated in Figure 9, which shows the results for isolated lines for linewidths ranging from 80-1500 nm. TIFF2025001656000088.tif6150 and parameters TIFF2025001656000089.tif6150 (long-range Gaussian weights and distance ranges) and TIFF2025001656000090.tif6150 (Triple Gaussian model with mid-range Gaussian weights and distance ranges) The values ​​determined for the four sets of parameters for TIFF2025001656000091.tif6150 are shown. In this example, the forward scatter distance α is not important since it does not affect the isofocal dose for the selected range of line widths.

[0066] The simulation approach of equation (8), or alternatively, a combination of equations (9) and (13), can be used to estimate the PSF for a given TIFF2025001656000092.tif6150 or its coefficients (multiple) TIFF2025001656000093.tif6150 (or a subset thereof, if they are partially known or not determinable from the measurement (distance) range), and (width (multiple) of Figures 5A to 5B) Subpattern control width (such as the one in TIFF2025001656000094.tif6150) TIFF2025001656000095.tif6150 as a function of isofocal dose Allows determination of TIFF2025001656000096.tif6150.

[0067] This forward measurement function has a control range(s) Measured isofocal dose corresponding to subpattern(s) with TIFF2025001656000097.tif6150 PSF coefficients (multiple) from TIFF2025001656000098.tif6150 To estimate TIFF2025001656000099.tif6150, the formula can be inverted (flipped). In a preferred embodiment of the present invention, a non-linear least squares fitting is used for this purpose, i.e. The file is TIFF2025001656000100.tif10150.

[0068] To increase the stability of the fitting method in the presence of noise (or insufficient measurements if many are available), it may be advantageous to supplement equation (16) with a suitable regularization term. For example, in the case of the L1 / L2 type, TIFF2025001656000101.tif10150. Here, for example, TIFF2025001656000102.tif6150 ("Lasso Regularization") or TIFF2025001656000103.tif6150 ("Tikhonov regularization"), TIFF2025001656000104.tif6150 is the regularization parameter that determines the amount of regularization, TIFF2025001656000105.tif6150 is a selection vector that selects the PSF coefficients (e.g., only the weights) to be regularized. If the PSF model has a large number of parameters, lasso regularization will usually be advantageous because the regularization term typically drives the least significant parameters to zero, so that unweighted terms can be removed from the model.

[0069] A different variant is the point spread function Penalize any changes or curvatures in TIFF2025001656000106.tif6150 Let TIFF2025001656000107.tif11150, where m=1 or 2. This variant approach can be useful to avoid overfitting to measurement noise.

[0070] The above minimization prescriptions (16), (17), (18) are easily implemented by prior art numerical packages such as the routines contained in scipy (using least squares routines or general objective minimization methods).

[0071] An example of the fitting method is shown in Figure 10. Parameters Starting from a hypothetical example of an initial PSF that is multi-Gaussian with TIFF2025001656000108.tif6150, we set the linewidths in the range 80-1500 nm. Isofocal dose trend curves 101 for 20 isolated lines of TIFF2025001656000109.tif6150 were generated, as shown by the dashed lines (indicated with GT for "ground truth"), and artificial noise was added to obtain a set of data points 102. Based on these data points 102, a fit 103 was made, which corresponds to the fitted trend curve 103, which is the reconstruction parameter(s) TIFF2025001656000110.tif6150 was generated. These reconstruction parameters (solid line) are within 10% of the initial PSF parameters, demonstrating the high ability of the present invention to reproduce the image transfer function parameters.

[0072] All or part of the above embodiments and examples can be described as the following supplementary notes, but are not limited thereto. [Appendix 1] A method for determining an image transfer function of a charged particle exposure system during exposure of a target positioned on a target surface of the system. the image transfer function describing a distribution of dose or energy generated at the target surface from a single active element of a pattern definition device of the charged particle exposure tool when the single active element is imaged onto a substrate in the charged particle exposure tool; The method includes the steps of: i. providing a model of said image transfer function, said model including at least one function parameter to be determined; ii. selecting a set of imaging characteristics, including at least one of beam blur and beam focus, that are adjustable by modifying predefinable imaging parameters of the charged particle exposure device other than a base exposure dose that describes an overall intensity of the image transfer function; iii. exposing a test substrate with a test pattern using said charged particle exposure device and developing said test substrate to form test structures on said at least one test substrate, the test pattern includes a plurality of sub-patterns, each sub-pattern being a copy of a sub-pattern template that is modified according to at least one control parameter, the at least one control parameter varying across the plurality of sub-patterns (varying for each sub-pattern of the plurality of sub-patterns) within a predetermined parameter range; and the test pattern is exposed onto the test substrate a number of times while the base exposure dose and at least one imaging parameter of the charged particle exposure tool are varied to form a number of test pattern copies on the substrate. The test structure so formed includes a plurality of substructures, each substructure being associated with imaging parameter(s), the base exposure dose and particular value(s) of the at least one control parameter; iv. evaluating the plurality of substructures for at least one measurable quantity including a critical dimension of a feature of the substructure; v. determining, for each value of the at least one control parameter, a change in the at least one measurable quantity between the plurality of substructures as a function of the imaging parameter, and determining from said change a respective value of an isofocal dose, wherein said change is a minimal change with respect to a change in the imaging parameter(s); vi. Calculating said at least one function parameter of said image transfer function as a function of said at least one control parameter using the isofocal dose value(s) determined in step v. [Appendix 2] In the method according to appendix 1, The measurable quantities in steps iv and v include critical dimensions of features of interest of the substructures. [Appendix 3] In the method according to appendix 1 or 2, the image transfer function is modeled as a weighted sum of radially symmetric multiple Gaussian functions, where the weighted sum includes at least three Gaussian components as summands; In step vi, the weights and / or length scales of at least one of the summands are determined. [Appendix 4] In the method according to Appendix 3, The image transfer function comprises a multi-Gaussian function including at least one mid-range component having weights and length scales as parameters determined in step vi, the length scales corresponding to widths constrained to the range of 200 nm to 2 μm. [Appendix 5] In the method according to any one of appendices 1 to 4, The method further comprises the steps of: ii'. for the model provided in step i and its at least one functional parameter, calculating a model calculation of said at least one measurable quantity as a function of said subset of said imaging and control parameters and determining values ​​of said subset of parameters where said model calculation predicts that said at least one measurable quantity is invariant with respect to said parameter; Contains; Step ii' is performed before step vi; Step vi involves performing a least squares fitting of said model calculation to the course of minimal variation to obtain the final parameters of said image transfer function. [Appendix 6] In the method according to Appendix 5, The fitting in step v[vi] is performed by finding the optimum value of a cost function that includes a weighted sum of the squares of the differences between the values ​​of the parameters in the model calculation and the course of the minimum change. [Appendix 7] In the method according to Appendix 6, The evaluation function is supplemented with a regularization term; the regularization term comprises the first and / or second radial derivatives of the image transfer function and / or its magnitude or the sum of the absolute values ​​of the vector of image transfer functions. [Appendix 8] In the method according to any one of appendices 1 to 7, By physically defocusing the beam through modulation of appropriate electrostatic voltages on lenses and / or multipole lens components of the imaging system of the charged particle exposure tool, different values ​​of beam blur are generated. [Appendix 9] In the method according to any one of appendices 1 to 8, By adjusting the pattern to emulate increased blur, several different values ​​of beam blur are generated. [Appendix 10] In the method according to any one of appendices 1 to 9, The subpattern template is: a single line, where the control parameter is the width of the line; a triple line structure including a central line flanked by two outer lines, wherein said control parameter is the width of said two outer lines; a triple line structure including a central line flanked by two outer lines, where the control parameter is the distance of the two outer lines from the central line; or a combination of these is selected from one of; A measurable quantity in the resulting substructure is the width of the single line or the central line. [Supplementary Note 11] An exposed substrate comprising at least one test structure on a test substrate exposed in a charged particle exposure apparatus according to steps i to iii of the method according to any one of Supplementary Notes 1 to 10. The test structure includes a plurality of substructures, the plurality of substructures being formed using copies of the same underlying subpattern template modified according to a control parameter that varies across the subpatterns. [Appendix 12] In the exposed substrate according to Appendix 11, The substrate further includes multiple sub-structures formed in the charged particle exposure tool by applying respective values ​​of imaging parameters, the values ​​differing among each of the multiple sub-structures. [Appendix 13] In the exposed substrate according to appendix 11 or 12, The underlying subpattern template is: a single line, where the control parameter is the width of the line; a triple line structure including a central line flanked by two outer lines, wherein said control parameter is the width of said two outer lines; a triple line structure including a central line flanked by two outer lines, where the control parameter is the distance of the two outer lines from the central line; or a combination thereof, Includes one of; A measurable quantity in the resulting substructure is the width of the single line or the central line.

[0073] Within the scope of the entire disclosure of the present invention (including the claims and drawings), modifications and adjustments of the embodiments are possible based on the basic technical ideas. Furthermore, within the scope of the entire disclosure of the present invention, various combinations or selections (including "non-selection") of various disclosed elements (including each element of each claim, each element of each embodiment, each element of each drawing, etc.) are possible. In other words, the present invention naturally includes various modifications and corrections that a person skilled in the art would be able to make in accordance with the entire disclosure including the claims and drawings and the technical ideas of the present invention. In particular, with regard to the numerical ranges described in this specification, any numerical value or subrange included in the range should be interpreted as being specifically described even if not otherwise specified.

[0074] Furthermore, the reference numerals in the drawings attached in the claims are intended solely to aid in the understanding of the invention, and are not intended to limit the invention to the embodiments and examples shown.

[0075] Furthermore, the entire contents of each of the above references are hereby incorporated by reference.

Claims

1. 1. A method for determining an image transfer function of a charged particle exposure system during exposure of a target positioned in a target surface of the charged particle exposure system, comprising: the image transfer function describing a distribution of dose or energy generated at the target surface from a single active element of a pattern definition device of the charged particle exposure tool when the single active element is imaged onto a substrate in the charged particle exposure tool; The method includes the steps of: i. providing a model of the image transfer function, said model including at least one function parameter to be determined; ii. selecting a set of imaging characteristics including at least one of beam blur and beam focus that are adjustable by modifying predefinable imaging parameters of the charged particle exposure device other than a base exposure dose that describes an overall intensity of the image transfer function; iii. exposing test substrates with a test pattern using the charged particle exposure device and developing the test substrates to form test structures on at least one test substrate, the test pattern includes a plurality of sub-patterns, each sub-pattern being a copy of a sub-pattern template that is modified according to at least one control parameter, the at least one control parameter varying across the plurality of sub-patterns within a predetermined parameter range; and the test pattern is exposed onto the test substrate a number of times while the base exposure dose and at least one imaging parameter of the charged particle exposure tool are varied to form a number of test pattern copies on the substrate. the test structure so formed includes a plurality of substructures, each substructure being associated with a particular value of an imaging parameter, the base exposure dose, and the at least one control parameter; iv. evaluating the plurality of substructures for at least one measurable quantity including a critical dimension of a feature of the substructure; v. determining, for each value of the at least one control parameter, a change in the at least one measurable quantity between the plurality of substructures as a function of the imaging parameter, and determining from said change a respective value of an isofocal dose, said change being a minimal change with respect to a change in the imaging parameter; vi. Calculating said at least one function parameter of said image transfer function as a function of said at least one control parameter using the value of isofocal dose determined in step v.

2. 10. The method of claim 1 , said measurable quantity in steps iv and v including a critical dimension of a feature of interest of said substructure; A method comprising:

3. 10. The method of claim 1 , the image transfer function is modeled as a weighted sum of radially symmetric multi-Gaussian functions, the weighted sum including at least three Gaussian components as summands; In step vi, the weights and / or the length scale of at least one of the summands are determined. A method comprising:

4. 4. The method of claim 3, the image transfer function includes a multi-Gaussian function including at least one mid-range component having weights and length scales as parameters determined in step vi, the length scales corresponding to widths limited to the range of 200 nm to 2 μm; A method comprising:

5. 10. The method of claim 1 , The method further comprises the steps of: ii'. For the model provided in step i and its at least one functional parameter, calculating a model calculation of said at least one measurable quantity as a function of said subset of imaging and control parameters, and determining values ​​of said subset of parameters when said model calculation predicts that said at least one measurable quantity is invariant with respect to said parameter; containing, step ii' is performed before step vi; Step vi includes performing a least squares fitting of the model calculation to a course of minimal variation to obtain final parameters of the image transfer function. A method comprising:

6. 6. The method of claim 5, The fitting in step v[vi] is carried out by finding the optimum value of an evaluation function that includes a weighted sum of the squares of the differences between the values ​​of the parameters in the model calculation and the course of the minimum change. A method comprising:

7. 7. The method of claim 6, A regularization term is added to the evaluation function, and the regularization term includes the first and / or second radial derivative (L2) of the image transfer function and / or its magnitude, or the sum of the absolute values ​​of the vector of the image transfer function (L1). A method comprising:

8. 10. The method of claim 1 , generating a plurality of different values ​​of beam blur by physically defocusing the beam through adjustment of appropriate electrostatic voltages on lenses and / or multipole lens components of an imaging system of said charged particle exposure apparatus; A method comprising:

9. 10. The method of claim 1 , By adjusting the pattern to emulate increased blur, multiple different values ​​of beam blur are generated. A method comprising:

10. 10. The method of claim 1 , The subpattern templates are: a single line, where the control parameter is the width of the line; a triple line structure including a central line flanked by two outer lines, wherein said control parameter is the width of said two outer lines; a triple line structure including a central line flanked by two outer lines, where the control parameter is the distance of the two outer lines from the central line; or a combination of these being selected from one of: The measurable quantity of the resulting substructure is the width of the single line or the central line. A method comprising:

11. An exposed substrate comprising at least one test structure on a test substrate exposed in a charged particle exposure apparatus according to steps i to iii of the method of any one of claims 1 to 10, the test structure includes a plurality of substructures, the plurality of substructures being formed using copies of the same base subpattern template modified according to a control parameter that varies across the subpattern; A substrate comprising:

12. The substrate according to claim 11, The substrate further includes multiple sub-structures formed in the charged particle exposure tool by applying respective values ​​of an imaging parameter, the values ​​being different among each of the multiple sub-structures. A substrate comprising:

13. The substrate according to claim 11, The base sub-pattern template may include: a single line, where the control parameter is the width of the line; a triple line structure including a central line flanked by two outer lines, wherein said control parameter is the width of said two outer lines; a triple line structure including a central line flanked by two outer lines, where the control parameter is the distance of the two outer lines from the central line; or a combination thereof, 1. The method of claim 1, The measurable quantity of the resulting substructure is the width of the single line or the central line. A substrate comprising:

Images