Method for assessing and compensating for positioning errors during combined rotational and translational positioning

Abstract

A method for providing data for the rotation-dependent position correction of a sample comprises rotating the sample about a rotation axis with respect to at least one rotation angle; recording at least one first planar recording of a first location of the sample for the at least one rotation angle; recording at least one second planar recording of a second location of the sample for the at least one rotation angle; and providing the data for the rotation-dependent position correction of the sample at least partially on the basis of the first and second planar recordings.

Description

[0001] December 17, 2025 Carl Zeiss SMT GmbH Z175478WO ANE / Sij

[0002] Method for assessing and compensating for positioning errors during combined rotational and translational positioning

[0003] The present Application for Patent claims priority to German Patent Application DE 10 2024139629.6, entitled “Verfahren zur Beurteilung und Kompensation von Position- ierungsfehlern bei kombinierter rotatorischer und translatorischer Positionierung”, filed on December 23, 2024, which is assigned to the assignee hereof and which is expressly incorporated by reference herein.

[0004] 1. Technical field

[0005] The invention relates to methods for providing data for the rotation-dependent position correction of a sample, methods for the rotation-dependent position correction of a sample, methods for processing a sample and also corresponding computer programs and devices for processing a sample.

[0006] 2. Prior art

[0007] Conventional devices for processing a sample can position samples relative to the tool chosen for processing typically by means of translational movements in such a way that the location to be processed is situated below the tool (along a z-direction). In addition, such devices can rotate the sample by means of rotational movements (relative to the tool). The main application for such rotations is to change the working angle. The working angle describes the orientation of a point of interest (POI) on the sample in the field of view (FOV) of an imaging unit, e.g. a light microscope or a scanning electron microscope (SEM). The rotational movement or rotation logically changes the angle of the sample. Ideally, these two movements would always allow the sample to be positioned relative to the tool as desired (in translation and rotation).

[0008] However, positioning errors play a role in all positioning tasks. Each axis is associated with a positioning accuracy that results, for example, from mechanical manufacturing errors, thermal changes and the control loop of the system. In many cases, the positioning errors of the different axes are independent. In view of the high requirements forpositional accuracy, such errors in conventional devices and methods result in losses in respect of quality, efficiency and time for processing the sample using corresponding devices and associated methods. Especially when processing samples with very small structures, such as photolithographic masks, for example, higher positioning accuracies are required.

[0009] The present invention is therefore based on the object of providing a method, a device and a computer program that enable the positioning of samples to be at least partially improved.

[0010] 3. Summary

[0011] This object is at least partly achieved by the aspects described herein.

[0012] A first aspect of the present invention relates to a method for providing data for the rotation-dependent position correction of a sample. The method comprises rotating the sample about a rotation axis with respect to at least one rotation angle; recording at least one first planar recording of a first location of the sample for the at least one rotation angle; recording at least one second planar recording of a second location of the sample for the at least one rotation angle; and providing the data for the rotation-dependent position correction of the sample at least partially on the basis of the first and second planar recordings.

[0013] Typically, a corresponding device can be equipped with a sample stage which, in addition to x-y-displacements (in translation), can also perform rotations by an angle 0, e.g. about an axis of rotation, which can be oriented approximately in the z-direction. If the centre of the FOV or POI is not situated exactly on the rotation axis (by extreme chance), the rotation entails a displacement of a point on the sample (in the x-y-plane) if said point is not situated exactly at the x,y-position of the axis of rotation. The inventors have recognized that inaccuracies in parameters related to rotation, e.g. the rotation angle 0 and the position of the centre of rotation (XR, YR), can therefore also influence the x-y-displacement.A corresponding exemplary positioning error is illustrated in Fig. 1. The outer square frames each show the FOV, for example of an SEM, in two situations: In both cases (left and right in Fig. i), a surface feature, in this example a corner, of a sample too, for example a photomask, is visible. In this example, the corner serves as a so-called reference marker. Before in-FOV rotation (left), the reference marker is situated in the centre of the FOV. In the example in Fig. 1, the FOV centre also represents the POI, but these may differ from one another in other examples. After in-FOV rotation by 0, the position of the reference marker deviates from the FOV centre (see on the right).

[0014] Specifically, the feature is displaced by AY in the y-direction and by AX in the x-direc-tion. In this example, the feature is still visible and the operator / algorithm of the device can reposition it as necessary. However, this positioning error becomes a problem if the feature, and thus the FOV, is smaller than the error. In this case, the feature may be lost from the FOV after an angle change, rendering some applications of the device unusable. Since in some examples small particles having sizes in the nanometre range and / or other structures having dimensions in the nanometre range can be repaired in the device, this case is of great practical relevance. The inventors have thus firstly recognized the relevance of various influencing factors and secondly found a solution to the problem identified:

[0015] The planar recordings described herein can make it possible to recognize exactly how the displacement of the sample takes place. By repeating the recording in the form of the at least one second planar recording of a second location of the sample for the at least one rotation angle (e.g. the same rotation angle(s) as for the first planar recording), the method can create a database that accurately tracks the rotation-induced displacements in the plane. On the basis of this, it is possible e.g. to calculate where a feature is displaced to on the sample (even in the case of unmeasured rotation angles which may occur e.g. in subsequent processing of the sample).

[0016] This tracking in the plane / area on the basis of the planar recordings in the x-y-plane is still unknown in the prior art, which hitherto has at most employed point measurement methods (such as e.g. height measurement methods along the trajectory of a height sensor on a rotating and / or moving sample), but those do not enable planar tracking -and thus also the advantages achieved by the present invention.The data for the rotation-dependent position correction of the sample can comprise e.g. the (first and / or second) planar recording and / or processed versions thereof.

[0017] The planar recording can image e.g. at least one location of the sample: For example, it can comprise a planar image recording or a planar image of the location of the sample, preferably the surface of the sample at the location; particularly preferably, the planar recording can comprise an SEM image. Essentially, the planar recording can comprise a property dependent on at least two coordinates (e.g. x-y-coordinates) which e.g. allow conclusions to be drawn about a planar position and / or rotation in the area / x-y-plane, such as e.g. an image of the part of the sample (e.g. an image of a marker on the sample). The property can comprise one or more items of information i(x,y) and / or be expressed thereby. The property of the sample can comprise, for example, a material property of the sample (e.g. a material, a material composition, a density, a thickness, an (electrostatic) charge and / or a coating of at least one part of the sample) and / or a topography property (e.g. a height perpendicular to the x-y-plane, a surface structure, an edge effect, etc.).

[0018] Planar recordings can be made accordingly for example using a scanning electron microscope (SEM), an atomic force microscope (AFM), an optical sensor or an optical microscope. In the example of an SEM, the planar recording can typically be an SEM image that can provide e.g. information about a two-dimensional area of the sample examined in the SEM. This can be an image which, as described herein, consists of a plurality of pixels that can be generated e.g. by raster-scanning of the sample or the surface thereof.

[0019] Planar can be understood substantially as in the x-y-plane, so that the planar recording extends in planar fashion over a finite area, e.g. in the x-y-plane. Such planar recordings can capture the distribution of surface features and / or of a property of the sample in the x-y-plane and / or can be present in the form (i(x,y), x, y). It is of course also possible to choose a different coordinate system, such as e.g. one based on polar coordinates, etc. The planar recordings can enable a detailed analysis of the position, structure and / or texture of the sample. For example, each x,y-value can represent a pixel. If the planar recording comprises an image, e.g. an SEM, AFM and / or other microscope recording, the information i(x,y) can comprise a pixel value, e.g. an intensity, at the re-spective x,y-position, such as for example in the example of a greyscale image (e.g. SEM greyscale image) as a planar recording. There, i(x,y) can correspond to the greyscale value of the respective pixel. In the example of multi-colour recordings, each x-y-posi-tion can be allocated a plurality of intensities (e.g. r(x,y), g(x,y) and b(x,y) for red, green and blue colour intensities). The planar recording can then comprise a plurality of (i(x,y), x, y) data. In one exemplary embodiment, the x,y-points can lie in a regular (e.g. square) grid. For example, it is possible that x e x0+Ax ■ a where a = 1, 2,..., n, so that the planar recording can comprise n+i different x- values. Equally, it is possible that for example y e y0+Ay ■ b where b = 1, 2, .... m, so that the planar recording can comprise m+i different y-values. The values n and m can be identical or different. Typically (e.g. for square pixels) n and m can represent the aspect ratio of the planar recording. For example, a planar recording can comprise information, e.g. an intensity, for a plurality of x-values and a plurality of y-values.

[0020] In contrast thereto, point recordings, such as those made by a height sensor, for example, only capture information from a single point on the surface of the sample. Line-byline recordings, which can likewise be made by a height sensor or similar devices, capture data along a line on the surface of the sample. This method affords a one-dimensional representation of the height profiles along this (straight or curved) line.

[0021] In summary, planar recordings can provide planar-resolved information, e.g. in the form i(x,y), of a sample, while point and line-by-line recordings can provide specific information about individual points or lines on the surface.

[0022] In the method according to the invention, the rotation axis can be known (e.g. in relation to the sample, the sample stage, and / or the imaging unit or the tool). The steps described herein of the methods mentioned can be based on this knowledge at least in part (e.g. in addition to the planar recording, the rotation angle and / or other parameters mentioned herein).

[0023] With the aid of the rotation axis, the displacement caused by a rotation at any point or at any location could be calculated in a simple manner in principle. However, in practice there are always deviations even with precise manufacture and control.For devices with high precision requirements, this calculation may therefore not be sufficient. In the example of an FOV with edge length in the nanometre to micrometre range, a sample with edge length of, for example, 5 to 7 inches (about 12.7 to 17.8 cm) and / or a rotation by a large angle, even deviations in the displacement in the range of (a few) nm / ° can lead to an element no longer lying in the FOV after rotation and calculated tracking.

[0024] In particular, the sample can comprise or be a mask, e.g. a photolithographic mask. The sample can have an aspect ratio of between 1:1 and 1:4, preferably between 1:1 and 1:2, particularly preferably of 1:1 or 1:2. The sample can have an almost rectangular shape. The sample can preferably have a length and width of 5 to 7 inches, particularly preferably a length and width of 6 inches. Alternatively, the sample can also have a length of 5 to 7 inches and a width of 10 to 14 inches, preferably a length of 6 inches and a width of 12 inches. The photolithographic mask can be a mask for photolithography in the UV spectral range (e.g. DUV, and / or EUV). This means the photolithographic mask maybe a mask for transmissive or reflective lithography. Furthermore, the mask may be of any type, as for example, binary or phase-shifting.

[0025] Therefore, the invention provides a solution that allows a calibration of the device which can take into account or determine such deviations and can also (optionally automatically) correct them. The resolution of the calibration or of the correction based thereon (as well as of the planar recording(s)) can be, for example, in the low nanometre range, e.g. below 10 nm, below 5 nm, below 2 nm or below 1 nm. Especially in the examples described herein in which the sample can comprise for example a mask, e.g. a photolithographic mask, particularly high requirements are made in respect of the accuracy of the methods described herein. The methods for processing such samples must be able to achieve processing steps with (sub-)nanometre accuracy in order to be able to ensure a sufficient sample quality after processing.

[0026] However, a sample is not restricted to a mask. Rather, a sample can comprise an object or an element for lithography. This means that apart from a mask, the object for lithography can, for example, comprise a template for nanoimprint lithography. The object for lithography can also comprise a lens for transmissive lithography and / or a mirror for reflective lithography. Furthermore, the object for lithography can comprise an ob-ject to be at least partially processed by lithography. In particular, a sample for an object for lithography may comprise a wafer (to be) processed by lithography. The wafer may be at any stage within its processing process. Further, a wafer may comprise a semiconductor wafer. The semiconductor wafer may comprise one single species of atoms (for example: silicon or germanium) or a compound of two or more semiconducting elements for example gallium arsenide, indium phosphide or indium gallium arsenic phosphide). The wafer maybe processed for fabricating, for example, an integrated circuit (IC), a micro-chip, a micro-electromechanical system (MEMS), nanoelectromechanical system (NEMS), a phonic integrated circuit (PIC), just to mention a few samples. During fabrication a microstructure may be generated on a wafer. The object for lithography may also comprise a (micro-)chip. The terms wafer and chip comprise any products or intermediate products during manufacture of integrated electrical or optical circuits, including chiplets or dies.

[0027] Processing an object or element for lithography can comprise manufacturing the object by using lithography and / or repairing the object for lithography during its manufacturing process and / or at the end of its manufacturing process.

[0028] In one exemplary embodiment, the at least one rotation angle can comprise a plurality of rotation angles, preferably substantially uniformly spaced rotation angles and / or rotation angles spanning an angle range of i8o° or more.

[0029] The inventors have recognized that a measurement of a plurality of rotation angles can lead to an accurate measurement of the planar behaviour in response to sample rotations. This enables the system to determine more accurately, so that the database thus obtained can allow a better, more accurate, more reliable and safer operation of the associated device.

[0030] The rotation angles spanning an angle range of i8o° or more can comprise e.g. a first and a second rotation angle, wherein the first and second rotation angles deviate from one another by i8o° or more.

[0031] The rotation angle can be defined herein as follows: A sample stage can rotate the sample by the angle A0. The rotation angle 0 can be defined as the angle resulting from therotation of the sample by the angle A0 starting from a starting position 0;defined by a starting angle (zero position): 0 = 0 i + A0. For example, the starting angle corresponds to the (rotational) position of the sample when the latter is in its so-called zero position. The latter can be defined for the method in any desired way (but globally). The mathematical treatment remains unaffected by that. For the sake of simplicity, 0;= o can be defined in order to obtain 0 = A0, which can reduce the computational complexity. This simplifying definition is adopted for the sake of simplicity in the examples described herein.

[0032] In one example, the at least one rotation angle can be the rotation angles n-io° where n = o, 1, 2, ... 35, so that in this example the entire angle range of from o° to 360° is covered in angular steps of io°. Smaller or larger angular steps, e.g. from the range of o.i° to 30°, are likewise possible.

[0033] The method can furthermore comprise for example correcting a planar position of the sample relative to a field of view at least partially on the basis of the rotating and / or the data (e.g. comprising the first and / or second planar recording). The correction can comprise a planar displacement of the sample relative to a field of view, especially also those that deviate from an ideal rotational behaviour.

[0034] For example, the correction can achieve an accuracy of the planar position of the sample of below 3 pm, below 1 pm, below too nm or below 10 nm. The accuracy can be limited by non- systematic inaccuracies of the device, in particular for example of a sample stage of the device which can be configured to receive the sample, position the sample in planar fashion, and / or rotate the sample about a rotation axis. The non-systematic inaccuracies can be based on bearing play, for example.

[0035] The correction can comprise e.g. planar displacements in the (sub-)nanometre range. After the rotating by an angle of at least io°, at least 30° or at least 6o°, with the aid of the calibration-based correction, e.g. (automatically), a specific point of the sample can become located at a location in the field of view which deviates from the location in the field of view before rotation within a radius of less than too nm, preferably less than 50 nm, particularly preferably less than 10 nm. In typical examples, the rotating can comprise rotation angles which can be expressed by 36o° / m (where m e N), such as for ex-ample io°, 30°, 450, 6o°, 90° and / or 180°. The direction of rotation can be chosen as desired. Consequently, an extremely high precision (e.g. in the range of the resolutions described herein) can be achieved which enables samples and in particular photolithographic masks or the small structures thereon to be processed quickly and precisely at different angles. For example, the processing can comprise a repair of the sample or of a structure on the sample.

[0036] The correcting can solve the problem recognized by the inventors insofar as the database obtained as described herein (e.g. comprising the rotation (comprising e.g. the at least one rotation angle) and / or the at least one planar recording) is used to compensate for the rotation-induced translation of a part of the sample, e.g. by virtue of the sample (at least partially during and / or at least partially after the rotation of the sample) being displaced in planar fashion such that the part of the sample which is of interest e.g. for processing the sample is displaced again to a predetermined position, e.g. the POI, in planar fashion. The correcting can thus comprise e.g. such tracking which can ensure that the planar recordings record a suitable sample region. The information about the correcting and / or tracking can be contained e.g. in the data provided by the method (and can be used e.g. for the position determinations described herein or the position determinations described herein can be at least partially based thereon).

[0037] In detail, a rotation of the sample as described herein can cause a planar x-displace-ment AX (as described e.g. with reference to Fig. 1) and / or a planar y-displacement AY (as described e.g. with reference to Fig. 1). The actual position of the corresponding part of the sample thus deviates from the target position (Xson, Yson) thereof. In this example, the actual position for the corresponding rotation angle is (Xson + AX, Yson + AY). In this example, the correction can comprise a planar displacement of the sample by the vector (-AX, - AY), so that the part of the sample can be returned to its target position (within the scope of conventional control errors). The concrete determination of the values AX and AY can take place for example as described herein. The latter in real devices, in addition to the simple displacement described by trigonometric functions, also comprise errors (for example, as described herein, a tilting of the sample from the planar plane, a rotation angle error, a runout deviation and / or a field of view displacement). The invention succeeds in allowing both the geometric (ideal) displacement and one or more errors ofthe device, to influence the correction described herein. This enables the correction to be carried out particularly accurately and completely.

[0038] In one example, the at least one first planar recording can comprise a first field of view and / or the at least one second planar recording can comprise a second field of view. The first field of view can be different from the second field of view. In this regard, e.g. the first field of view can at least partially overlap the second field of view, or the first and second fields of view can be disjoint (and thus e.g. image different parts of the sample).

[0039] The inventors have recognized that the choice of a plurality of (different) fields of view can result in a large number of advantages: In order to enable error correction for any desired positions or locations of the sample and / or rotation angles, this error assessment must be performed at more than one position or location of the sample. In order to be able to optimally recognize and compensate for positioning errors, it is preferable to select three measurement positions at a large distance from the rotation centre (in a manner comparable to the sample size - e.g. 0.2 times one edge length of the sample or more). The described method allows measurements (e.g. planar recordings) to be carried out at large distances from the rotation axis and over the entire rotation angle range. This enables the dominant positioning errors to be identified and modelled. Conventional methods, by contrast, are limited by the size of the FOV.

[0040] Preferably, recording the at least one first planar recording and / or recording the at least one second planar recording can comprise tracking the first and / or the second field of view at least partially during the rotating. Typically, methods for processing samples already comprise the observation of so-called markers on the sample. Fig. 2 shows a sample too with three exemplary markers 101, 102, 103. Since recordings of these are often made anyway and the sample is thus positioned accordingly so that the corresponding markers are situated (e.g. individually) in the FOV, the often readily recognizable markers can be used as parts of the sample that are recorded in the planar recordings. This entails further advantages: While the exact position with respect to the rotation centre R in Fig. 2 is not relevant, the markers are typically situated near the corners of the sample, which can lead to geometrically distantly spaced apart locations of the sample, which can make the method more robust and reliable. On account of thesufficiently large distances between the locations of the sample (i.e. the markers 101, 102, 103), it can moreover be ensured that at least one of them is sufficiently far away from the rotation axis R. The optimal / possible number of locations of the sample or positions can be determined depending on which errors are taken into account in the model and whether the error parameters are analytically determined or numerically estimated. This is described in detail herein. The first, second and / or further location on the sample as described herein can comprise substantially any feature of the sample whose position and / or orientation is recognizable in planar recordings.

[0041] The method can furthermore comprise providing the at least one first and / or second planar recording (and optionally further planar recordings, in each case e.g. per rotation angle). Specifically, a data set can be provided, for example, which comprises planar information I(x,y) per rotation angle and per position of the sample (where I is e.g. an intensity, e.g. of an SEM image). Alternatively or additionally, the data set could comprise further-processed information per rotation angle and per location of the sample, e.g. the determined actual position of the location (e.g. of a marker, as described herein).

[0042] By virtue of the planar recordings being provided, methods for further processing can subsequently access the database described herein, whereby the advantages described herein regarding the method for providing data for the rotation-dependent position correction of the sample can also spread into the methods based thereon.

[0043] For example, the at least one first and / or second planar recording (and optionally further planar recordings, each e.g. per rotation angle) can be provided to a unit or device which can carry out the methods according to one of the other described aspects (e.g. the second aspect) at least partially on the basis of the provided data.

[0044] Providing data can comprise at least one of the following:

[0045] capturing the data (e.g. comprising collecting raw data from various sources or sensors), processing the data (e.g. comprising performing calculations, analyses and / or transformations on the captured data), storing the data (e.g. comprising storing the data in databases, file systems and / or other storage media), transferring the data (e.g. comprising transmitting the data via networks or communication channels to othersystems or units), formatting the data (e.g. comprising converting the data into a specific format suitable for further processing), filtering the data (e.g. comprising removing irrelevant or erroneous data points in order to improve the quality of the data), aggregating the data (e.g. comprising combining data points to form larger data sets or statistical values), visualizing the data (e.g. comprising creating diagrams, graphics or other visual representations of the data), validating the data (e.g. checking the data for accuracy, consistency and / or completeness) and / or providing metadata (e.g. comprising adding descriptive information to the data, such as e.g. time stamps, source indications or processing logs). These activities can ensure that the data are provided in a form suitable for further processing by other units or systems.

[0046] The method can furthermore comprise for example recording at least one third planar recording of a third location of the sample for the at least one rotation angle.

[0047] The inventors have ascertained that the measurement of three positions or locations can achieve a particularly suitable compromise between the speed and efficiency of the method on the one hand and its achieved accuracy and reliability on the other.

[0048] In principle, the features and details concerning the present invention as described herein which are described with respect to the first and / or second planar recording are analogously applicable to third, fourth, fifth, and further planar recordings.

[0049] A second aspect of the present invention relates to a method for processing data for the rotation-dependent position correction of a sample. The method comprises obtaining at least one first planar recording of a first location of the sample for at least one rotation angle of the sample about a rotation axis; obtaining at least one second planar recording of a second location of the sample for the at least one rotation angle; determining at least one first planar position of the first location of the sample for at least one rotation angle at least partially on the basis of the first planar recording; and determining at least one second planar position of the second location of the sample for the at least one rotation angle at least partially on the basis of the second planar recording.Consequently, the database described herein (e.g. comprising at least the at least one first and second planar recordings) can be used to determine the actual positions after rotation of the sample.

[0050] Obtaining the at least one first planar recording of the first location of the sample for the at least one rotation angle of the sample about a rotation axis and obtaining the at least one second planar recording of the second location of the sample for the at least one rotation angle can also be understood as obtaining the data (e.g. provided by the method of the first aspect).

[0051] Processing data for the rotation-dependent position correction of a sample can comprise e.g. processing the data as described in relation to the second aspect in order to provide calibration data which can be used e.g. by the method for processing a sample (comprising correcting a (rotation-dependent) planar displacement of the sample) according to the third aspect.

[0052] Specifically, this can be implemented as follows: There maybe multiple contributions to the positioning error, such as the positioning accuracy of the individual linear axes (e.g. x-, y- and / or z-axes), the orthogonality error between x- and y-axes, and errors related to the rotational movement such as runout error, deviation between actual and target rotation angles 0, and concentricity error. The method according to the invention can measure the total error for the specific case of in-FOV rotation:

[0053] For example, a single rotation in the FOV can be performed (in a simple model) by means of two movements: specifically a rotation by A0 and a planar displacement in the x-y-plane, so that the actual position of the location of the sample is defined by

[0054] (xf\ (cos - sin dyfXi - XR\ , (XR\

[0055] z VsinA0 cosA0 / j — YR) \YR)

[0056] In this case, Xf, Yfdenote the end coordinates, Xi;Y, denote the initial coordinates, XR, YRdonate the coordinates of the centre of rotation and A0 denotes the angle A0 by which rotation is effected starting from the starting (angular) position 0;. In order to determine the dependence of the positioning error on 0 at a specific point in the x-y-plane, e.g. the following steps can be performed: Firstly, the sample stage can be positionedand rotated such that the location of the sample of interest is situated at the location (X; , Yi) and is in the starting (angular) position 0;.

[0057] Starting therefrom, the sample stage or the (location of the) sample can be rotated by A0 with respect to the rotation angle 0. After the rotation (and / or during the rotation), the actual position of the location of the sample (Xf;C, Yf;C) can be measured e.g. by means of one or more planar recordings. It is also possible to ascertain therefrom the displacement AX, AY between the calculated end pose Xf, Yf) and the actual end pose (Xf;C, Yf>c). These steps can be repeated, as described herein, for a desired A0 range, e.g. from o° to 3500in io° steps. In principle, the formula described cannot always lead to correct results or predictions, since the model mentioned does not address all possible errors, which is why it may be advantageous to include one or more corrections.

[0058] In one exemplary embodiment, the first and / or second planar position can comprise a first and / or second correction of a sample position. Accordingly, determining the first and / or second planar position can comprise determining the first and / or second correction.

[0059] The method according to the invention succeeds in ascertaining the position error depending on the rotation angle 0. For this purpose, a plurality of rotations with different angular steps A0 are carried out and the displacement error AX, AY between the target position and the actual position of the sample location of interest is measured. The positioning error not only depends on 0, but can also change with the point in the x-y-plane at which the rotation is started.

[0060] Specifically, the inventors have recognized that it can be assumed that the systematic inaccuracies of the translational x-, y- and z-axes are negligible or can be compensated for by a previous calibration.

[0061] The rotation of the sample about the axis of rotation can be influenced by a large number of different errors, e.g. owing to slight manufacturing defects and alignment errors. The frequently prevailing systematic errors are a runout deviation and a rotation angle error, which are illustrated in Fig. 3.The runout error leads to an x-y-displacement of the sample (left), while the rotation angle error results in an inaccurate rotation (middle). The linear combination of the two errors yields the actual position of the sample (right). As already indicated above, a sample may comprise an object or an element for lithography. For example, the object for lithography may comprise a wafer and / or a photomask.

[0062] Under these exemplary assumptions, for example, a system of equations can be established in which the correction of the sample position in the x- and y-directions can be determined as follows:

[0063] >

[0064]

[0065] In this case, dXRRand dYRRrepresent the runout error and d0(0)represents the rotation angle error. The system of equations thus comprises three unknowns (with a known rotation axis). Two or more planar recordings per rotation angle 0 already allow the system of equations to be solved. The final corrected coordinates XJ^corrand YJ^corron the left-hand side can be measured (e.g. ascertained from the planar recordings), and the initial coordinates X , Y and also the rotation centre XR, YRand the angle A0 on the right-hand side of the equation can be chosen by the user and / or (e.g. partially automatically) by the device. The index j indicates the location of the sample (for example, j = i corresponds to the first location and j = 2 to the second location).

[0066] For example, the first and / or second correction can comprise a first and / or second deviation between a first and / or second planar target position and a first and / or second planar actual position.

[0067] For example, the actual position for the corresponding rotation angle can be (Xson + AX, Ysoii + AY). The deviations AX and AY can correspond to the correction. The correction as described herein can also be carried out mechanically, so that a planar displacement of the sample is carried out, e.g. by the vector (-AX, -AY), so that the part of the sample can be returned to its target position.The first and / or second deviation can comprise for example a planar displacement of the sample relative to a field of view.

[0068] In one preferred embodiment, determining the correction can comprise analytically and / or numerically solving a geometric system of equations.

[0069] In one example, the geometric system of equations can comprise a tilting of the sample from the planar plane, a rotation angle error, a runout deviation and / or a field of view displacement, preferably a (e.g. undesired) beam deflection and / or a (e.g. desired) beam offset.

[0070] The (e.g. undesired) beam deflection or the resulting field of view displacement can occur for example if the planar recordings are recorded by particle beam-based imaging (using charged particles such as e.g. electrons). Owing to the influence of an electric and / or magnetic field of the sample stage on the particle beam or the resulting interaction between sample stage / sample and particle beam, it can happen that the FOV is displaced in planar fashion depending on the planar sample position and / or the rotation angle thereof (since the particle beam can be deflected). Specifically, the aforementioned electric and / or magnetic fields which are relevant in the context of the present invention can occur as a result of motor currents in one or more motors of the sample stage and can typically be static fields. Alternating fields can also occur and lead to certain complications (e.g. resolution reduction), but this typically has no significant influence on the correction presented here, but rather can be compensated for using other suitable measures, if necessary or desired. For example, these can have a deflecting effect on the electron beam of an SEM. Especially in the case of devices for processing (e.g. for repair) of samples (for example a mask as described herein), such motor currents and the resulting electric and / or magnetic fields can play a crucial role in view of the small structures on the sample and / or the high resolution of the particle beam by means of which the planar recordings can be recorded. Specifically, the deflection of the electron beam in relation to the resolution of the device can be so great that the quality of the processing without correction of this effect would be significantly reduced. The solution according to the invention can address such effects, too, without any problems.The inventors have recognized that, taking these sources of error into account, particularly robust and reliable results can be achieved. It is advantageous in particular that the mechanical origin of the errors does not matter, as long as the latter are taken into account computationally in the method e.g. as described herein.

[0071] The inventors have recognized that (e.g. in addition to the rotation angle error, runout deviation and / or field of view displacement described herein) the consideration of further systematic errors can be improved, such as for example the inclination error of the sample, i.e. the inclination angles px(0), Py(6) of the sample or its surface in relation to the x- and y-axis, respectively.

[0072] On the basis thereof, it is possible to establish this improved system of equations, for example, which can take into account the aforementioned inclination error:

[0073]

[0074] If an x-y-calibration with an initial 9 orientation was carried out previously, it may already contain the inclination error for this orientation. The inclination errors modelled here would then only reflect the tilt difference with respect to the initial 9 orientation of the x-y-calibration. An additional systematic error in rotatable positioning systems can be the precession of the axis of rotation. This error would be included in the combination of sample inclination and rotation angle error. Other systematic errors are either not relevant to the application of in-FOV rotation, such as e.g. an axial runout, or they are stochastic in nature and cannot be compensated for.

[0075] Analytically solving this exemplary system of equations can be effected for example as follows: All the aforementioned error parameters or sources of error can be expressed as functions of the rotation angle 0 and can be determined analytically. After the planar recordings described in relation to the first aspect have been made, a system of equations can be established from the data:At each measurement position, it is possible to carry out a series of measurements over the 0 range as described herein. Depending on which parameters are used in the model, a different number of measurement positions or locations on the sample are required. This can be recognized from the following examples: If the three errors described herein (e.g. rotation angle error, runout deviation and field of view displacement) are intended to be determined, three measurement positions are required, resulting in six equations for five (unknown) (error) parameters. If two of the errors described above are intended to be determined, two measurement positions are required, resulting in four equations for four (unknown) (error) parameters.

[0076] To simplify the analytical solution, it can be advantageous to choose measurement positions or locations with pairwise identical X- or Y-coordinates, i.e. positions aligned on a rectangle. This can be fulfilled for example by the use of the markers on a sample as described herein, since these typically have at least partially identical X- or Y-coordinates.

[0077] Depending on the number of measurement positions or locations of the sample, the system of equations can be overdetermined. In this case, it can be advantageous to solve it numerically. For example, a numerical solution could be based on formulating the situation as an optimization problem, so that the differences Xf- Xf>corrand Yf- Yf>corrare intended to be minimized, e.g. by using a least squares method to estimate the position error parameters.

[0078] A numerical solution can afford the advantage over the analytical solution that it allows the use of equations derived from the measurement data. This can increase the performance of the method and its robustness vis-a-vis outliers. In principle, any desired number of measurement positions can be chosen. The optimum number is a compromise between measurement outlay and calibration performance and can vary from system to system.

[0079] In addition to the inherent positioning errors (described herein) of the system, there is an often adjustable system parameter in scanning electron microscopes that influences the positioning: the so-called (e.g. desired) beam offset. This is a displacement of the electron beam in the x-y-plane that can be used to displace the FOV. In the example of an SEM, this displacement can be adjusted e.g. by means of voltages in the SEM col-umn. However, the solution presented here does not just concern imaging systems for charged particles such as SEM and FIB, but rather is independent of the imaging technology. In the case of a light microscope, a beam displacement can be generated for example by manipulation of the optical path in the microscope, e.g. by displacing at least one of the optical components (e.g. a lens and / or a mirror) of the microscope or even by an inclination of the optical axis relative to the sample.

[0080] A0 underlines the fact that what is relevant is the change in the sample angle or sample stage angle, and not the absolute rotational position. A beam displacement has the following effects on the system: In the case of a (e.g. desired or induced) beam offset, the effective coordinates, i.e. the sample and / or sample stage coordinates X-, T- in respect of which the POI is positioned in the centre of the FOV, can be changed by the absolute value of the beam displacement XBs, YBS:

[0081] X'i= Xi+ XBs

[0082] Y'i = Yi + YBS

[0083] In the case of exemplary devices described herein, the rotation plane can be the topmost plane of the sample stage. That can mean that the rotation axis is displaced during movement in the x-y-plane. If a beam offset is introduced and the effective coordinates of the sample stage or of the POI are thus displaced, the rotation axis or the rotation centre can thus be displaced as well. The rotation centre can be defined as the coordinates at which the rotation axis or the rotation centre lies in the centre of the FOV.

[0084] Consequently, the final coordinates, additionally taking into account a beam offset, can be expressed for example by the following system of equations:

[0085]

[0086] Correcting the planar position of the sample relative to the field of view in response to a corresponding beam offset by (XBs, YBS) can then be expressed e.g. by the following planar vector:&

[0087]

[0088] Consequently, the present method succeeds in compensating for such beam offsets and similar FOV adaptations. As a result, it is still possible to continue working with all functionalities of typical devices that users typically want to have recourse to.

[0089] In one exemplary embodiment, the method can furthermore comprise providing calibration data, wherein the calibration data can comprise the at least one first and / or second planar position and / or can be at least partially based on the at least one first and / or second planar position.

[0090] With the proposed combination of measurements at multiple locations of the sample, the described method makes it possible to create a calibration for the application of sample rotation (e.g. an in-FOV rotation) regardless of where on the sample the rotation is performed.

[0091] Essentially, the calibration data as described herein can comprise the solution of the system of equations (e.g. in the form of the error parameters and / or the determined positions per rotation angle) and / or information based thereon.

[0092] Essentially, the calibration data can comprise any information on the basis of which it is possible to determine the actual position of a location of the sample on the basis of the rotation angle and / or the planar position. The calibration data can thus be sufficient to correct a planar position of the sample relative to a field of view at least partially on the basis of calibration data (as further described herein). In one exemplary embodiment, the calibration data (and also any other information, e.g. which can be obtained by way of the solution of the systems of equations described herein, comprising e.g. also fit functions and the like) can be stored and / or provided as a look-up table, which can improve the efficiency of methods based thereon. In one exemplary look-up table, e.g. the vectors (0, d9, dXRR, dYRR, ftx, py) or vectors that do not comprise all of the parameters mentioned by way of example and / or additional parameters could be stored. For example, for each 6 value (e.g. of o°, io°, 20°, ... or of some other 6 se-quence), one or more of the parameters described herein can be stored in the look-up table. For example, a row or a column can be allocated to each of the parameters.

[0093] The sample may comprise an object for lithography. The object for lithography may comprise a photolithographic mask, a template for nanoimprint lithography, a wafer, an integrated circuit (IC), a micro-structured chip, a micro-electromechanical system (MEMS), a nano-electromechanical system (NEMS), and / or a photonic integrated circuit (PIC). The photolithographic mask may comprise a transmissive or a reflective mask. Furthermore, the wafer may comprise a microstructure on one of its surface at any stage of a manufacturing process.

[0094] A third aspect of the present invention relates to a method for processing a sample, wherein the method comprises: rotating the sample about a rotation axis with respect to at least one rotation angle; and correcting a planar position of the sample relative to a field of view at least partially on the basis of calibration data; wherein the correcting comprises a planar displacement of the sample relative to a field of view; and wherein the calibration data are at least partially based on a rotating of the sample.

[0095] The calibration data can have been provided e.g. by means of the method according to the second aspect and / or at least partially on the basis of the data (e.g. comprising planar recordings) provided by the method according to the first aspect.

[0096] In this case, the herein described planar displacement of the sample relative to the field of view in the context of the correcting can comprise displacing to the position (Xf, Yf) and / or with respect to the POL Herein, the field of view (FOV) can be the FOV of the planar recording and / or an FOV of a tool described herein for processing the sample. For example, the POI can be arranged substantially in the (geometric) centre of the FOV.

[0097] A fourth aspect of the present invention relates to a computer program comprising instructions for execution of the steps of at least one of the methods described herein.

[0098] A computer program can be written in any form of a programming language, including compiled or interpreted languages, and can be provided in any form, including as astandalone program or as a module, component, subroutine, or other entity suitable for use in a computer environment.

[0099] By way of example, the one or more computers can be configured to be suitable for the execution of a computer program, and they can comprise general and specialized microprocessors and any desired processors of any type of digital computer. In general, a processor receives instructions and data from a read-only memory or a random access memory, or both. Elements of a computer system comprise one or more processors for executing instructions and one or more storage devices for storing instructions and data. In general, a computer system also comprises, or is operatively coupled thereto, in order to receive data from one or more machine-readable storage media or to transmit data thereto, or both, such as e.g. hard disks, magnetic disks, solid-state drives, magneto-optical disks or optical disks. Machine-readable storage media suitable for embodying computer program instructions and data comprise various forms of nonvolatile memories, including for example semiconductor memory devices, e.g. EPROM, EEPROM, flash memory devices, and solid-state drives; magnetic disks, e.g. internal hard disks or removable disks; magneto-optical disks; and CD-ROM, DVD-ROM and / or Blu-ray Discs.

[0100] In some implementations, the processes described above can be executed with the aid of software executed on one or more mobile computing devices, one or more local computing devices and / or one or more remote computing devices (which can be, e.g. cloud computing devices). For example, the software methods form one or more computer programs that are executed on one or more programmed or programmable computer systems, either on the mobile computing devices, local computing devices or remote computing systems (which can comprise various architectures, such as distributed systems, client / server systems, grid systems or cloud systems), each comprising at least one processor, at least one data storage system (including volatile and non-volatile storage and / or storage elements), at least one wired or wireless input device or port, and at least one wired or wireless output device or port.

[0101] In some implementations, the software can be provided on a medium, such as e.g. CD-ROM, DVD-ROM, Blu-ray Disc, a solid-state drive or a hard disk, which can be read by a general or special programmable computer, or can be transmitted via a network (in amanner encoded in a propagated signal) to the computer where it is executed. The functions can be executed on a specific computer or with the aid of specific hardware, such as e.g. coprocessors. The software can be implemented in a distributed manner in which different parts of the calculations specified by the software are executed by different computers. Any such computer program is preferably stored or downloaded on a storage medium or a storage device (e.g. solid-state storage or storage media or magnetic or optical media), which can be read by a general or specific programmable computer in order to configure and operate the computer system upon reading by means of the computer system such that the methods described herein are executed. The system according to the invention can also be considered to be a computer-readable storage medium configured with a computer program, wherein the storage medium configured in this way causes the computer system to implement the functions described herein, in a specific and predefined manner.

[0102] For example, the computers, processors, etc. described herein can be comprised in the device described herein for processing the sample, for example in an associated control unit, and / or coupled thereto.

[0103] A fifth aspect relates to a device for processing a sample, comprising:

[0104] an imaging unit configured to record a planar recording of a location of the sample; a sample stage configured to receive the sample, position the sample in planar fashion, and rotate the sample about a rotation axis; and a control unit configured for automatically executing the steps of any of the methods described herein.

[0105] Automatic execution of the method steps described herein makes it possible not just to achieve the advantages described with regard thereto; time and resources can moreover be saved as a result of the automation.

[0106] In some implementations, the imaging unit for recording the planar recording(s) can comprise a light or particle beam source to generate light or (particle) radiation, an image sensor (e.g. CCD or CMOS sensor (complementary metal oxide semiconductor)) containing an array of individually addressable sensor elements for recording images of a sample, and optical units (e.g. one or more lenses, mirrors or reflective surfaces, filters and / or stops) to direct and / or focus the light or radiation from the light or radia-tion source to the sample and from the sample to the image sensor. In some implementations, the device can comprise a data processor and a storage medium. The data processor in the device can e.g. be configured to instruct the components of the device to at least partially execute the steps of the methods described herein. The storage medium can store the corresponding instructions, e.g. in the form of a computer program. In some implementations, the device can comprise one or more computers containing one or more data processors configured to execute one or more programs containing a plurality of instructions according to the principles described above. Each data processor can contain one or more processor cores, and each processor core can comprise logic circuits for data processing. By way of example, a data processor can comprise an arithmetic logic unit (ALU), a control unit and various registers. Each data processor can contain a cache memory. Each data processor can comprise a system-on-chip (SoC) containing a plurality of processor cores, a random access memory (RAM), graphics processors, one or more controllers, and one or more communication modules. Each data processor can contain millions or billions of transistors.

[0107] The data processing described in this document, such as obtaining the planar record-ing(s), determining planar position(s) of the location(s) of the sample for the at least one rotation angle, providing the calibration data, and / or other method steps described herein, can be carried out by one or more computers containing one or more data processors for data processing, one or more storage media for data storage and / or one or more computer programs comprising instructions which, when executed by the one or more computers, cause the processes to be carried out. The one or more computers can comprise one or more input devices, such as e.g. a keyboard, a mouse, a touchpad, and / or a voice command module, and one or more output devices, such as e.g. a display and / or a speaker.

[0108] In some implementations, the one or more computing devices can comprise digital electronic circuits, computer hardware, firmware, software, or a combination of the aforementioned elements. The features for data processing can be implemented in a computer program product that is materially embodied in an information carrier, e.g. in a machine-readable storage medium, for execution by a programmable processor; and method steps can be executed by a programmable processor that executes a program of instructions in order to fulfil the functions of the implementations described.Alternatively or additionally, the program instructions can be encoded in a propagated signal that is an artificially generated signal, e.g. a machine-generated electrical, optical or electromagnetic signal, which is generated in order to encode information for transmission to a suitable receiving device in order to be executed by a programmable processor.

[0109] The embodiments of the present invention described herein and the features and properties mentioned optionally in this respect should likewise be understood as disclosed in all combinations with one another. In particular, the description of a feature comprised by an embodiment - provided there are no explicit explanations to the contrary - should also not be construed in the present case as meaning that the feature is indispensable or essential to the function of the embodiment. In particular, the steps of the methods according to the first three aspects can be combined with one another, e.g. at least partially successively and / or on the basis of one another.

[0110] 4. Description of the figures

[0111] Fig. i illustrates the positioning error induced by a rotation of a sample.

[0112] Fig. 2 shows a sample, for example a photomask, with three exemplaiy markers.

[0113] Fig.3 illustrates a runout error and a rotation angle error and also their combination.

[0114] Fig.4 schematically shows a device for processing a sample.

[0115] 5. Detailed description of preferred embodiments

[0116] Fig.3 illustrates a runout error and a rotation angle error and also their combination. The runout error no leads to an x-y-displacement of the sample too (left), while the rotation angle error 120 results in an inaccurate rotation of the sample too (middle). The actual rotation angle of the sample too deviates by d0(0) from the set or desired rotation angle. The linear combination of the two errors yields the actual position of the sample too (right). In the three views in Fig. 3, the zero position of the sample too is represented in each case as a reference with a dotted border.As discussed above, the sample 100 may comprise an object or an element for lithography. For example, the object for lithography may comprise a photomask, a template for nanoimprint lithography or any kind of a wafer to be processed and / or to the repaired.

[0117] Fig. 4 schematically shows a device 200 for processing a sample 100. This device comprises a substantially horizontally (in the x-y-plane) oriented base plate 210, a sample stage 220 and an imaging means 230.

[0118] In the example in Fig. 4, the sample stage 220 comprises a movement platform 221, which can be configured to position and / or to move the sample 100 in planar fashion in the x-y-plane, e.g. along an axis in the x-direction 22ix and / or along a preferably orthogonal y-direction 22iy. In the example in Fig. 4, a rotating device 222 of the sample stage 220 is mounted on the movement platform 221, and can be configured to rotate or turn 222r the sample too mounted on a sample holder 223 in the x-y-plane in the clockwise or anticlockwise direction. The sample holder 223 can likewise be comprised by the sample stage 220.

[0119] The device 200 furthermore comprises an imaging means 230 (e.g. a camera and / or a microscope, preferably an SEM).

[0120] The skew poses and / or other errors, such as runout errors, rotation angle errors, etc., occurring in devices 200, as illustrated in Fig. 4, for example, can all be addressed and / or corrected or compensated for by means of the simple method according to the invention, without the need to determine the exact origin of all sources of error. Thus, the aspects according to the invention can provide a particularly simple solution.

Claims

December 17, 2025 Carl Zeiss SMT GmbH Z175478WO ANE / SijClaims1. Method for providing data for the rotation-dependent position correction of a sample, wherein the method comprises:rotating the sample about a rotation axis with respect to at least one rotation angle;recording at least one first planar recording of a first location of the sample for the at least one rotation angle;recording at least one second planar recording of a second location of the sample for the at least one rotation angle; andproviding the data for the rotation-dependent position correction of the sample at least partially on the basis of the first and second planar recordings.

2. Method according to Claim 1, wherein the at least one rotation angle comprises a plurality of rotation angles, preferably substantially uniformly spaced rotation angles and / or rotation angles spanning an angle range of 180° or more.

3. Method according to Claim 1 or 2, furthermore comprising correcting a planar position of the sample relative to a field of view at least partially on the basis of the rotating and / or the data;wherein the correction comprises a planar displacement of the sample relative to a field of view.

4. Method according to any of the preceding claims, wherein the at least one first planar recording comprises a first field of view and / or the at least one second planar recording comprises a second field of view;wherein preferably recording the at least one first planar recording and / or recording the at least one second planar recording comprises tracking the first and / or the second field of view at least partially during the rotating.

5. Method according to any of the preceding claims, furthermore comprising providing the at least one first and / or second planar recording.

6. Method according to any of the preceding claims, furthermore comprising: recording at least one third planar recording of a third location of the sample for the at least one rotation angle.

7. Method for processing data for the rotation-dependent position correction of a sample, wherein the method comprises:obtaining at least one first planar recording of a first location of the sample for at least one rotation angle of the sample about a rotation axis;obtaining at least one second planar recording of a second location of the sample for the at least one rotation angle;determining at least one first planar position of the first location of the sample for the at least one rotation angle at least partially on the basis of the first planar recording; anddetermining at least one second planar position of the second location of the sample for the at least one rotation angle at least partially on the basis of the second planar recording.

8. Method according to Claim 7, wherein the first and / or second planar position comprises a first and / or second correction of a sample position.

9. Method according to Claim 8, wherein the first and / or second correction comprises a first and / or second deviation between a first and / or second planar target position and a first and / or second planar actual position.

10. Method according to Claim 9, wherein the first and / or second deviation comprises a planar displacement of the sample relative to a field of view.

11. Method according to any of Claims 8-10, wherein determining the correction comprises analytically and / or numerically solving a geometric system of equations.

12. Method according to Claim 11, wherein the geometric system of equations comprises a tilting of the sample from the planar plane, a rotation angle error, arunout deviation and / or a field of view displacement, preferably a beam deflection and / or a beam offset.

13. Method according to any of Claims 7-12, furthermore comprising providing calibration data, wherein the calibration data comprise the at least one first and / or second planar position and / or are at least partially based on the at least one first and / or second planar position.

14. Method according to any of Claims 1-13, wherein the sample comprises an object for lithography.

15. Method according to Claim 14, wherein the object for lithography comprises a photolithographic mask, a template for nanoimprint lithography, a wafer, an integrated circuit (IC), a micro- structured chip, a micro-electromechanical system (MEMS), a nano-electromechanical system (NEMS), and / or a photonic integrated circuit (PIC).

16. Method according to Claim 15, wherein the photolithographic mask comprises a transmissive or a reflective mask.

17. Method according to Claim 15, wherein the wafer comprises a microstructure on one of its surface at any stage of a manufacturing process.

18. Method for processing a sample, wherein the method comprises:rotating the sample about a rotation axis with respect to at least one rotation angle; andcorrecting a planar position of the sample relative to a field of view, at least partially on the basis of calibration data;wherein the correcting comprises a planar displacement of the sample relative to a field of view; andwherein the calibration data are at least partially based on a rotating of the sample.19- Computer program comprising instructions causing a control unit of a device for processing a sample to automatically execute the steps of the method according to any of Claims 1-17.

20. Device for processing a sample, comprising:an imaging unit configured to record a planar recording of a location of the sample;a sample stage configured to receive the sample, position the sample in planar fashion, and rotate the sample about a rotation axis; anda control unit configured for automatically executing the steps of the method according to any of Claims 1-17.

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