WO2025125090A1 - Method for crosstalk modelling in a multi-mirror array having movable individual mirrors - Google Patents

Abstract

The invention relates to a method for crosstalk modelling in a multi-mirror array (31) having movable individual mirrors (32), the method comprising the following steps: providing a multi-mirror array (32), having N movable individual mirrors (32) and a control device (35) for positioning the individual mirrors (32); predefining an activation pattern (34) for positioning at least some of the individual mirrors (32*); positioning the individual mirrors (32*) by activating same by means of the activation pattern (34); detecting the actual positions of the individual mirrors (32*) actually resulting from the activation by the activation pattern (34); determining a coefficient matrix having coefficients for quantifying a crosstalk behaviour; adjusting the control device (35); wherein the activation pattern acts as a predictor of a training data set (33) for a neural network for predicting a relationship between an activation pattern (34) and the actual positions, resulting therefrom, of the individual mirrors (32); and wherein the coefficients of the determined coefficient matrix act as targets of the training data set.

Description

Method for crosstalk modeling in a multi-mirror arrangement with movable individual mirrors

This patent application claims priority from German patent application DE 10 2023 212 444.0, the contents of which are incorporated herein by reference.

The invention relates to a method for crosstalk modeling in a multi-mirror arrangement with movable individual mirrors. The invention further relates to a method for positioning the individual mirrors of a multi-mirror arrangement with movable individual mirrors. Furthermore, the invention relates to a facet mirror module for an illumination optics system of a projection exposure system, an illumination optics system with a corresponding facet mirror module, and an illumination system, an optical system, and a projection exposure system with such an illumination optics system. Finally, the invention relates to a method for producing a micro- or nanostructured component.

Projection exposure systems for microlithography can have multi-mirror grids with a multitude of movable individual mirrors. Crosstalk phenomena can occur during the positioning of the individual mirrors, where controlling a specific mirror affects the positioning of other mirrors. US 2022/0227621 A1 discloses a multi-mirror arrangement with improved crosstalk behavior. US 2022/0066196 A1 describes a method for modeling the crosstalk behavior. Due to the large number of individual mirrors, such a method can be very complex. Furthermore, applying a corresponding model to new mirror settings can be difficult.

It is therefore an object of the invention to improve a method for crosstalk modeling in a multi-mirror arrangement with displaceable individual mirrors.

This problem is solved by the features of claim 1.

A core of the invention is to use one or more control patterns for positioning at least a subset of the individual mirrors of a multi-mirror arrangement to To record interactions between the individual mirrors and to train a neural network with the recorded data. The neural network can be used, in particular, to predict a relationship between a control pattern and the resulting actual positions of the individual mirrors.

The control pattern(s) can serve as predictors of a training data set for the neural network. The coefficients of the determined coefficient matrix, which serve to quantify crosstalk behavior, can serve as targets of the training data set.

According to the invention, it was recognized that, due to the structural details of the multi-mirror arrangement, it may be possible to train a neural network from a relatively small number of control patterns and the corresponding interactions between the individual mirrors, by means of which neural network a prediction of a relationship between an essentially arbitrary control pattern and the resulting actual positions of the individual mirrors is possible. This can be advantageously exploited in particular if the multi-mirror arrangement has certain symmetries, in particular translation invariance. Edge effects can be particularly taken into account here. In particular in a multi-mirror arrangement with a very large number of individual mirrors, for example with more than 100,000 individual mirrors, in particular more than 300,000 individual mirrors, in particular more than 500,000 individual mirrors, the significance of edge effects increasingly decreases.

The individual mirrors of the multi-mirror arrangement can, in particular, be micromirrors, but this is not to be understood as a limitation. The micromirrors can, in particular, be formed by microelectromechanical systems (MEMS) or micro-optoelectromechanical systems (MOEMS). For details, please refer to US 2014/0055767 A1.

In particular, these can be mirrors for radiation in the DUV or EUV range. This is not intended to be limiting. Preferably, the individual mirrors of the multi-mirror array are arranged in a regular pattern, particularly one that is translationally invariant. This can be advantageously used when training a convolution kernel of a convolutional neural network (CNN).

In particular, it may be provided to determine the deviation of the actual positions of the individual mirrors from their target positions.

The coefficient matrix can contain as entries (coefficient) values or functions that characterize the influence of the control of neighboring mirrors on a specific individual mirror. These values can be expressed, for example, as a tilt angle (change) per control signal value (millirad/volt).

The coefficient matrix can reflect the geometry or topology of the arrangement of the individual mirrors in the multi-mirror array. For example, the coefficient matrix can have as many elements as a particular mirror has nearest neighbors. When considering higher-order interactions, a coefficient matrix can also be provided that has as many entries as a particular mirror has next-nearest neighbors and/or even more distant mirrors.

The coefficient matrix can also be represented one-dimensionally, i.e. as a coefficient vector.

Furthermore, it may be provided to determine several coefficient matrices corresponding to the interactions in different directions. In particular, it may be provided to determine one or more coefficient matrices for each of the degrees of freedom of displacement of the individual mirrors.

In addition, it is possible to determine the interactions of the control of certain individual mirrors in a first direction on the displacement position of other, in particular adjacent, individual mirrors in other directions, in particular a second direction oriented perpendicular to the first direction. In principle, the entries of the coefficient matrix can also be vector functions.

In the case of individual mirrors with two degrees of freedom of tilt, one, two, three, or more coefficient matrices can be determined for a specific individual mirror. In particular, interactions between the control of neighboring individual mirrors in the same displacement directions and interactions between the control of an individual mirror for positioning in a first direction and the deflection of another, particularly neighboring, individual mirror in a different direction, particularly perpendicular to it, can be taken into account.

The neural network can be integrated into the control device. It can also be part of an external computing device. In this case, the control device preferably has a memory in which the neural network can be stored for adapting the control device.

According to one aspect, in order to determine the coefficient matrix, one or more individual mirrors, in particular those which are not adjacent and/or not next but one adjacent, can be permanently controlled and/or one or more individual mirrors, in particular each adjacent to a fixedly controlled individual mirror, can be variably controlled, in particular with a variable actuation signal.

A fixed control is understood, in particular, to mean control with a predetermined, constant actuation signal. It can be identical for all control patterns, in particular using a . However, this is not absolutely necessary. It can also be different for different control patterns. The fixed control can also be zero, meaning that the corresponding individual mirror is not deflected.

The variable control can be discrete or continuous. Using the variable control, it is possible to determine functions for the interactions. This increases the flexibility for predicting interactions, especially for predicting say of mirror positions resulting from a specific control pattern.

To determine the coefficients of the coefficient matrix, a series expansion of a function that describes the influence of the variable control of an individual mirror on the positioning of another, in particular a neighboring, individual mirror can be used.

In the case of an interaction assumed to be linear, the first coefficient of the series expansion may suffice. To account for non-linear interactions, higher-order coefficients can be considered, particularly in additional coefficient matrices.

To determine second- and/or higher-order coefficient matrices, two or more control signals, particularly actuation signals of different strengths, can be provided for one and the same control pattern. This can apply separately to each displacement degree of freedom.

According to a further aspect, a plurality M of different control patterns can be used to determine the coefficient matrices, wherein the number M of control patterns used is smaller than the number N of individual mirrors in the multi-mirror arrangement. In particular, M : N < 0.1, in particular M : N < 0.01, in particular M : N < 0.001, can apply.

The number M of control patterns used to train the neural network can be, in particular, at most 10 ⁵ , in particular at most 3 * 10 ⁴ , in particular at most 10 ⁴ , in particular at most 5000, in particular at most 3000, in particular at most 2000, in particular at most 1000. One of the advantages of the present invention is that the effort for determining the crosstalk behavior can be significantly reduced. The number N of individual mirrors can be more than 100,000, in particular more than 200,000, in particular more than 300,000, in particular more than 500,000. It is in particular less than 10 ⁷ , in particular less than 10 ⁶ .

Especially when there is a relatively small number of control patterns for training the neural network, it can be advantageous to select them specifically.

Preferably, the individual mirrors activated by the control patterns can be distributed across substantially all subregions of the multi-mirror arrangement. For example, it is possible for the smallest convex envelope of the controlled individual mirrors to be at least 80%, in particular at least 90%, in particular at least 95%, of the total area of the smallest convex envelope of all individual mirrors in the multi-mirror arrangement.

It may be advantageous if the entire set of individual mirrors activated in the control pattern does not have large gaps. The largest gap may, in particular, be a maximum of ten individual mirrors, in particular a maximum of five individual mirrors, in particular a maximum of three individual mirrors. These values may each refer to the maximum or minimum diameter of a convex envelope of the gap.

The total number of individual mirrors activated by the control patterns can be evenly distributed across the multi-mirror array. It can also be unevenly distributed across the multi-mirror array.

The distribution of the activated individual mirrors can be modeled on a field or pupil facet mirror, depending on how they are used. Groups of adjacent individual mirrors can, in particular, each model a facet or a pupil facet mirror.

In a control pattern, the activated individual mirrors can be selected specifically or determined quasi-randomly. According to a further aspect, the entirety of the control patterns can comprise control patterns with different numbers of activated individual mirrors. The number of controlled individual mirrors can, in particular, be varied from 1 to N. The maximum number of controlled individual mirrors can, in particular, be at most N:2, in particular at most N:3, in particular at most N:5, in particular at most N:10.

In each pattern area, for example, 100000/600 individual mirrors can be controlled together to simulate 600 individual pupil facet mirrors.

According to a further aspect, a regressor can be determined to determine a coefficient matrix, in particular a coefficient vector, from a predetermined control pattern, in particular any control pattern. This can, in particular, be a random regressor.

The controlled individual mirrors can, in particular, be arranged as thinly distributed as possible. In particular, their arrangement can be selected such that their average spacing is greater than a lower limit. The lower limit can, in particular, be at least 50%, in particular at least 70%, in particular at least 90% of the maximum possible average spacing.

This is advantageous in order to be able to infer coefficient matrices for arbitrary control patterns based on a training data set of limited size.

The regressor can, in particular, be a multinomial regression. A favorable, fast embodiment of such a multinomial regressor is a random forest (tree) regressor. Alternatively, a gradient boost regressor can also be used. A neural network configured as a regressor, in particular a multilayer perceptron, can also be used as the regressor. Details of such regressors are known to those skilled in the art.

Regardless of the chosen embodiment, the regressor can be trained using the training data set, i.e., with predefined control patterns. it is possible to calculate the coefficient matrix for quantifying the crosstalk for a given driving pattern in a single calculation run.

The expected positioning errors, in particular the expected angular position errors, can then be determined by matrix multiplication of the control matrix with the coefficient matrix.

These errors can be used to correct the control signals.

A further object of the invention is to improve a method for positioning the individual mirrors of a multi-mirror arrangement with movable individual mirrors. This object is achieved by a method comprising the following steps:

Specification of a target control pattern for positioning at least a subset of the individual mirrors of the multi-mirror arrangement in target positions,

Prediction of the deviations of the actual positions from the target positions of the individual mirrors due to crosstalk effects using a neural network,

Adjustment of the target control pattern depending on the predicted deviations,

Positioning the individual mirrors by controlling them with the adapted control pattern.

The neural network for predicting the deviations of the actual positions from the target positions of the individual mirrors resulting from crosstalk effects is, in particular, a neural network that was trained according to the preceding description, in particular according to claim 1. It is, in particular, a neural network in which control patterns served as predictors for training, and the coefficients of the determined coefficient matrix served as targets.

The individual mirrors of the multi-mirror arrangement can in particular be the individual mirrors of the facet mirror module described below. The predicted deviations, especially positioning errors, especially angular position errors, can be obtained by matrix multiplication of a control matrix with the coefficient matrix. The coefficient matrix can be calculated using a regressor, as described above. A single calculation run may be sufficient for this.

A further object of the invention is to improve a facet mirror module for an illumination optics of a projection exposure system. This can be, in particular, a DUV projection exposure system or an EUV

Projection exposure system.

This object is achieved by a facet mirror module with a multi-mirror arrangement with displaceable individual mirrors and a control device for controlling the positioning of the individual mirrors, wherein the control device has a computing unit with a neural network for predicting the deviations of the actual positions of the individual mirrors from the target positions when controlling them with a given control pattern.

With the help of such a control device, deviations between the actual positions of the individual mirrors and the specified target positions, particularly due to crosstalk, can be reduced. In other words, the precision of the positioning of the individual mirrors can be improved.

The given control pattern can be essentially any control pattern. In particular, it can be a control pattern that was not used to train the neural network.

The neural network may in particular comprise at least one convolutional layer, in particular as a first layer.

The facet mirror module can also have a measuring system for detecting the actual positions of the individual mirrors. The measuring system for detecting the positions of the individual mirrors can, in particular, be connected to the control device in a signal-transmitting manner. This allows for feedback control of the positions of the individual mirrors. This can improve the precision and/or stability of the individual mirrors' positioning.

According to one aspect, the neural network can be integrated into the facet mirror module, in particular into the multi-mirror arrangement.

In particular, the neural network can be programmed into an application-specific integrated circuit (ASIC).

The neural network can also be programmed on a separate data carrier, in particular a separate storage medium. It can, in particular, be part of a computer program product. This improves the flexibility of the facet mirror module, in particular of its control device. The neural network can, in particular, be replaceable.

The multi-mirror arrangement of the facet mirror module can serve in particular as a field facet mirror, as a pupil facet mirror or as a speculative reflector.

Alternative applications in optical systems with structured illumination are also possible.

Further objects of the invention are to improve an illumination optics for a projection exposure apparatus, an illumination system for a projection exposure apparatus, an optical system for a projection exposure apparatus and a projection exposure apparatus.

These tasks are solved by appropriate optics or systems with a facet mirror module as described above. The advantages arise from those of the facet mirror module.

A further object of the invention is to improve a method for producing a micro- or nanostructured component, in particular a memory chip. This problem is solved by providing a projection exposure system with a facet mirror module as described above. The advantages are evident from those already described.

Further details and advantages of the invention will become apparent from the description of exemplary embodiments based on the figures. They show:

Fig. 1 schematically shows a projection exposure system for microlithography,

Fig. 2A to 2D schematically show different control patterns for determining coefficient matrices for modeling crosstalk behavior of a multi-mirror arrangement,

Fig. 3 shows a schematic representation to explain the structure of the training data set.

In the following, the basic structure of a projection exposure system 1 is first described by way of example with reference to Figure 1. This description is not to be understood as restrictive. The invention leads to advantages, in particular, regardless of the precise details of the projection exposure system 1. The invention is not limited to a projection exposure system, in particular not to an illumination optics system for a projection exposure system, in particular not to a facet mirror for such an illumination optics system. However, a facet mirror represents a concrete example of a component (a device) in which the advantages according to the invention come into play.

Fig. 1 shows a schematic meridional section of a projection exposure system 1 for microlithography. An illumination system 2 of the projection exposure system 1 has, in addition to a radiation source 3, an illumination optics 4 for exposing an object field 5 in an object plane 6. The object field 5 can be rectangular or arc-shaped with an x/y aspect ratio of, for example, 13/1. In this case, an object A reflective reticle (not shown in Fig. 1) arranged in the object field 5 carries a structure to be projected using the projection exposure system 1 for producing micro- or nanostructured semiconductor components. Projection optics 7 serve to image the object field 5 into an image field 8 in an image plane 9. The structure on the reticle is imaged onto a light-sensitive layer of a wafer arranged in the region of the image field 8 in the image plane 9, which wafer is not shown in the drawing.

The reticle, which is held by a reticle holder (not shown), and the wafer, which is held by a wafer holder (not shown), are scanned synchronously in the y-direction during operation of the projection exposure system 1. Depending on the image scale of the projection optics 7, the reticle can also be scanned in the opposite direction relative to the wafer.

With the aid of the projection exposure system 1, at least a portion of the reticle is imaged onto a region of a light-sensitive layer on the wafer for the lithographic production of a micro- or nanostructured component, in particular a semiconductor component, for example, a microchip. Depending on the design of the projection exposure system 1 as a scanner or as a stepper, the reticle and the wafer are moved in a temporally synchronized manner in the y-direction, continuously in scanner mode or stepwise in stepper mode.

Radiation source 3 is an EUV radiation source with an emitted useful radiation in the range between 5 nm and 30 nm. It can be a plasma source, for example, a GDPP (Gas Discharge Produced Plasma) or an LPP (Laser Produced Plasma) source. Other EUV radiation sources, such as those based on a synchrotron or a free electron laser (FEL), are also possible.

It can also be a DUV radiation source, in particular with emitted useful radiation at a wavelength of 193 nm. The radiation generated by the radiation source 3 is hereinafter also referred to as useful radiation 10, illumination light or imaging light.

Useful radiation 10 emanating from the radiation source 3 is focused by a collector 11. A corresponding collector is known, for example, from EP 1 225 481 A. After the collector 11, the useful radiation 10 propagates through an intermediate focal plane 12 before impinging on a field facet mirror 13 having a plurality of field facets 13a. The field facet mirror 13 is arranged in a plane of the illumination optics 4 that is optically conjugate to the object plane 6.

After the field facet mirror 13, the useful radiation 10 is reflected by a pupil facet mirror 14 having a plurality of pupil facets 14a. The pupil facet mirror 14 lies either in the entrance pupil plane of the illumination optics 7 or in a plane optically conjugate thereto. The field facet mirror 13 and the pupil facet mirror 14 are constructed from a plurality of individual mirrors, which are described in more detail below. The division of the field facet mirror 13 into individual mirrors can be such that each of the field facets 13a, which individually illuminate the entire object field 5, is represented by exactly one of the individual mirrors. Alternatively, it is possible to construct at least some or all of the field facets 13a from a plurality of such individual mirrors. The same applies to the design of the pupil facets 14a of the pupil facet mirror 14, which are respectively assigned to the field facets 13a and which can each be formed by a single individual mirror or by a plurality of such individual mirrors.

The useful radiation 10 strikes the two facet mirrors 13, 14 at an angle of incidence, measured normal to the mirror surface, that is less than or equal to 25°. The two facet mirrors 13, 14 are therefore exposed to the useful radiation 10 in the range of normal incidence operation. Exposure under grazing incidence is also possible. The pupil facet mirror 14 is arranged in a plane of the illumination optics 4, which represents a pupil plane of the projection optics 7 or is optically conjugate to a pupil plane of the projection optics 7. With the aid of the pupil facet mirror 14 and an imaging optical assembly in the form of a transmission optics 15 with mirrors 16, 17, and 18, designated in the order of the beam path for the useful radiation 10. The field facets of the field facet mirror 13 are imaged superimposed onto the object field 5. The last mirror 18 of the transmission optics 15 is a grazing incidence mirror. The transmission optics 15, together with the pupil facet mirror 14, are also referred to as the follow-up optics for transferring the useful radiation 10 from the field facet mirror 13 to the object field 5. The illumination light 10 is guided from the radiation source 3 to the object field 5 via a plurality of illumination channels. Each of these illumination channels is assigned a field facet 13a of the field facet mirror 13 and a pupil facet 14a of the pupil facet mirror 14 arranged downstream of this field facet. The individual mirrors of the field facet mirror 13 and the pupil facet mirror 14 can be tilted by actuators, allowing a change in the assignment of the pupil facets 14a to the field facets 13a and, accordingly, a modified configuration of the illumination channels. This results in different illumination settings that differ in the distribution of the illumination angles of the illumination light 10 across the object field 5.

The field facet mirror 13 can be designed in the form of a multi- or micro-mirror array (MMA). The multi- or micro-mirror array (MMA) serves below as a concrete example of a multi-mirror arrangement 31. The MMA can be designed, in particular, as a microelectromechanical system (MEMS). It can have a plurality of individual mirrors 32 arranged in a matrix-like array in rows and columns. The individual mirrors 32 can be designed to be tiltable by actuators. In total, the field facet mirror 13 can have over 100,000 individual mirrors 32. For details of the MMA, reference is made to DE 10 2011 006 100 A1.

Sensors that generate electrical or electromagnetic fields can be used to detect the positioning, in particular the tilt angle, of the individual mirrors 32. Eddy current sensors or capacitive sensors can be used as sensors, for example.

The fields of different sensors can influence each other. In particular, the fields of directly adjacent mirrors can lead to undesirable crosstalk, particularly causing a tilt angle error. When using the projection exposure system 1, the reticle 24 and the wafer 25, which bears a coating light-sensitive to the illumination light 10, are provided. Subsequently, at least a portion of the reticle 24 is projected onto the wafer 25 using the projection exposure system 1. During the projection of the reticle 24 onto the wafer 25, the reticle holder and/or the wafer holder can be displaced in a direction parallel to the object plane 6 or parallel to the image plane 9. The displacement of the reticle 24 and the wafer 25 can preferably occur synchronously with one another. Finally, the light-sensitive layer exposed to the illumination light 10 is developed on the wafer 25. In this way, a micro- or nanostructured component, in particular a semiconductor chip, is produced.

In a multi-mirror arrangement, undesirable crosstalk phenomena can occur when controlling the individual mirrors 32. In particular, it can happen that the control of a specific individual mirror 32 has an undesirable effect on the positioning of other, particularly neighboring, individual mirrors 32. Approaches to reducing such undesirable interactions are known, for example, from US 2022/0227621 A1 and US 2022/0066196 A1. In particular, the solutions known from US 2022/0066196 A1 are complex, particularly time-consuming, and allow only limited predictions of the effects in novel settings.

In the following, a method for crosstalk modeling in a multi-mirror arrangement 31 with displaceable individual mirrors 32 is described with reference to Figures 2A to 2D and Figure 3.

As shown by way of example in the figures, the multi-mirror arrangement 31 can be uniformly configured. In particular, it can be designed as a uniform mirror grid. It can exhibit translation invariance in one, two, or more directions. In particular, the arrangement of the individual mirrors 32 can correspond to the structure of a square, triangular, or hexagonal grid. The geometric centroids of the reflection surfaces of the individual mirrors 32 can, in particular, lie at the grid points of such a grid. In particular, in a multi-mirror arrangement 31 with a very large number of individual mirrors 32, edge effects for a large number of individual mirrors 32 can be neglected. The influence of the control of a neighboring individual mirror 32 on a given individual mirror 32* can be assumed to be small.

The interactions during the control of neighboring individual mirrors 32 can be summarized in an interaction matrix or an interaction vector. The interaction matrix or the interaction vector can be assumed to be translation-invariant.

To determine the interaction matrix or the interaction vector, a specific individual mirror 32* can be selected, and it can be determined how its positioning changes when a selection of the remaining individual mirrors 32 is controlled. The selection can comprise one or more of the individual mirrors 32. These can be controlled simultaneously or sequentially. In particular, they can be controlled variably, i.e., with actuation signals of varying strengths. A control device 35 is used to control, i.e., actuate, the individual mirrors 32. The control device 35 can be connected to the field facet mirror 13 and/or the pupil facet mirror 14 in a signal-transmitting manner.

In particular, it is possible, in a first part of a training data set, to permanently control a specific individual mirror 32* and to variably control other individual mirrors 32v, in particular its neighboring individual mirrors 32v, individually or in groups of several at the same time, and to track the change in the position of the selected individual mirror 32* using an external measuring system. The effects of controlling the other, in particular the neighboring individual mirrors 32v, can be entered into a target matrix. In this case, it is particularly possible to enter the coefficients of a series expansion of an interaction function into the target matrix. If only linear interactions are to be considered, it may be sufficient to enter only the first coefficient of the series expansion into the target matrix. In the non-linear case, further coefficients of the series expansion can also be taken into account. In addition to the nearest neighboring individual mirrors 32v, the next-nearest neighbors or, in principle, any other individual mirrors 32v can also be controlled. This can be easily accounted for in the dimension of the interaction matrix or the interaction vector.

Figures 2A and 2B illustrate how a specific individual mirror 32* is selected and the corresponding coefficient matrix is obtained by measuring the interaction. Each row corresponds to an observation, also referred to as a sample.

In another part of the training data set (see Figures 2C and 2D), several individual mirrors 32* are selected and the interaction coefficients for this selection are determined.

The selected individual mirrors 32* can be controlled permanently. The remaining individual mirrors 32v, especially adjacent individual mirrors 32v, can in turn be controlled variably.

Higher coefficients of the series expansion to account for nonlinear phenomena can also be stored in additional coefficient matrices or coefficient vectors.

The training dataset can then be used to train a neural network, specifically a convolution kernel of a convolutional neural network (CNN). The CNN trained in this way can be used to predict deviations of mirror settings from their target values.

The selection of the individual mirrors 32* is referred to as control pattern 34.

The control patterns 34 (shown on the left in Figures 2A to 2D) serve as predictors, the coefficient matrices as targets. Due to the translation invariance of the training data set 33, a similar coefficient matrix is obtained as a target around each controlled individual mirror 32*. Edge effects are also taken into account during training.

Due to the recurrence of similar patterns in the target dataset, it is easy to train the convolution kernel of a CNN. This trained convolution kernel results in a well-adapted neural network and good predictions of the coefficient matrix for newly specified control patterns. In other words: By repeatedly specifying a similar, but shifted, coefficient pattern in the training dataset, 33 it is possible to successfully train a local receptive field of a CNN.

When performing the calibration measurements, i.e., when training the neural network, it is not necessary to control each of the individual mirrors 32. It is sufficient to control a selection of the individual mirrors 32 and determine the corresponding coefficient matrices.

In principle, the number of controlled individual mirrors 32* should be denser the closer one gets to the edge of the multi-mirror arrangement 31.

The exact architecture of the neural network is relatively flexible.

Preferably, the neural network comprises a convolutional layer as the first layer.

The solution described above leads to the following advantages:

Due to the series expansion, in particular the Taylor series expansion, of the function describing an interaction, nonlinearities can be easily taken into account.

Calibration measurements are only required on a fraction of the total number of individual mirrors (32). This can significantly shorten the calibration measurement time. Once trained, the neural network can determine the coefficient matrix or coefficient matrices for newly specified control patterns in a single forward propagation step.

By carefully reducing the number of neurons in the layers of the neural network, a relatively smooth prediction function can be generated, and in particular, overshoots can be avoided.

The described task can be considered a regression problem. It can be solved using a so-called random forest regressor on the same training dataset.

The multiple mirror grid, i.e. the multi-mirror arrangement 31, can be used in particular for a field facet mirror 13 or for a pupil facet mirror 14.

The trained neural network can be programmed into the application-specific integrated circuit (ASIC). It can, in particular, be a permanently installed component of one of the facet mirror modules or the control device 35. It can also be integrated into a separate device, in particular an external computing unit.

Further details and variants of the crosstalk modeling according to the invention are described below.

For a selected control pattern 34, i.e., a selection of specific individual mirrors 32*, the coefficients quantifying the crosstalk are measured at all other individual mirrors 32 or a subset thereof, in particular the individual mirrors 32 arranged around the controlled individual mirror(s) 32*, i.e., adjacent to it, using at least one measuring arrangement. The individual mirrors 32v, which are variably controlled in particular to determine the interaction coefficients, are highlighted in the figures as examples and designated 32v. Where no crosstalk is expected, a measurement can be omitted. The corresponding coefficients can be set to zero.

In particular, the coefficient can be the quotient of the mirror tilt angle in a specific direction and the corresponding control signal value. The coefficients can, in particular, be in the unit rad/volt.

Different coefficient matrices can be determined for different directions. Alternatively, it is possible to use vectors or matrices as entries in the coefficient matrices themselves.

Here, it can be taken into account whether a tilt of the individual mirrors in a certain direction, for example the x-direction, leads to crosstalk in a linearly independent direction, for example in the y-direction, or not.

The selection of the individual mirrors 32* can be carried out according to a predetermined plan or randomly, in particular quasi-randomly.

Die Ansteuer-Muster 34, das heißt die Auswahl der Einzelspiegel 32* zur Definition der Ansteuervektoren, werden vorteilhafter Weise derart gewählt, dass über den Datensatz hinweg über alle Teilbereiche verteilt angesteuerte Einzelspiegel 32* vorliegen. An exemplary structure of a training dataset with M samples is summarized in the following table.

The control patterns 34, i.e. the selection of the individual mirrors 32* for defining the control vectors, are advantageously selected in such a way that controlled individual mirrors 32* are present distributed over all sub-areas across the data set.

The number S i (i = 1..M) of the controlled individual mirrors 32* can vary from 1 to the total number N of the individual mirrors 32 of the multi-mirror arrangement 31.

The entire training data set 33 is shown as an example in Figure 3.

The number of control patterns 34 can vary depending on the number S_i of the individual mirrors 32* controlled.

With binary control of the individual mirrors 32 and a total number N of them, 2 ^N control patterns 34 are in principle conceivable.

When using multi-mirror arrangements 31 for an illumination optics 4 of a projection exposure system 1, particularly as a component of a facet mirror, the multi-mirror arrangement 31 can have more than 1,000, particularly more than 10,000, and particularly more than 100,000 individual mirrors 32. If only the nearest adjacent mirrors are considered during crosstalk calibration, the number of control patterns 34 would still be very large for such a large number of individual mirrors 32. The required measurement time would be very long. An entire measurement sequence would require several hours, if not several days. This would result in significant production downtime.

A smaller number of samples is sufficient to train a neural network or a random forest regressor. The number of samples for training the neural network can, in particular, be in the range from 1,000 to 100,000. It can, in particular, be a maximum of 50,000, in particular a maximum of 30,000, in particular a maximum of 20,000, in particular a maximum of 10,000, in particular a maximum of 5,000, in particular a maximum of 3,000.

For effective calibration, the M control patterns 34 can preferably be distributed as evenly as possible over the surface of the multi-mirror arrangement 31. The different The control patterns 34 can, in particular, comprise different numbers of controlled mirrors 32*. They can, in particular, comprise at least 10, in particular at least 20, in particular at least 30, in particular at least 50, in particular at least 100 different numbers of controlled individual mirrors 32*. The ratio of the number of controlled individual mirrors 32* to the total number of individual mirrors 32 is also referred to as the fill level. The fill levels of any control pattern 34 can, in particular, be in the range from 10% to 60%.

According to a possible training data set design, the numbers of controlled individual mirrors 32* can be uniformly randomly distributed. For a selected number S_i of controlled individual mirrors 32* (1 < S_i < N), the controlled individual mirrors 32* are preferably distributed as evenly as possible across the multi-mirror arrangement 31. According to a variant, non-uniform distributions can also be selected. It can be particularly advantageous to distribute the centroids of the distributions of the individual mirrors 32* according to a distribution of the individual mirrors 32 used for specific lighting settings that typically occurs in practice. The centroids can, for example, also have a Gaussian distribution.

It may be provided to provide a separate training data set 33 for determining the crosstalk behavior of the individual mirrors 32 in a first direction, for example, an x-direction, which may be oriented parallel to a scanning direction. A further training data set 33 may be used to determine the coefficients for modeling the crosstalk behavior in a second direction, which is in particular perpendicular to the first direction, for example, a y-direction, which is perpendicular to the scanning direction.

In order to be able to infer the coefficient matrix for any control pattern 34 based on the training data set 33 or the training data sets 33, which have a limited scope, it can be provided to establish a regressor. This should infer the coefficient vector or the coefficient matrix from any given control pattern 34, preferably all elements thereof. The regressor can be a multinomial regressor. In particular, it can be a random forest tree regressor. Alternatively, a gradient Boost Regressor can be used. A neural network designed as a regressor, in particular a multilayer perceptron, can also be used as a regressor.

Regardless of the selected embodiment, the regressor can be trained using the training data set 33 or the training data sets 33. After training, the coefficient matrix for quantifying the crosstalk behavior can be calculated for a given control pattern 34 in a single calculation run.

The expected positioning errors, in particular the expected angular position errors, of the individual mirrors 32 are then determined by matrix multiplication of the control matrix by the coefficient matrix. These errors can be taken into account in the further process. They can be used, in particular, to correct the control signals.

As already mentioned, to account for nonlinearities, a second-order coefficient matrix or higher-order coefficient matrices can be measured in addition to the coefficient matrix. For this purpose, at least two or more control signals can be used with one and the same control pattern. The first- and second-order coefficient matrices, as well as higher-order ones if necessary, can be calculated from the measured angular positions. Separate matrices can be provided for different directions.

In addition to the first-order coefficient matrix, an additional regressor is selected for training each of the higher orders.

Claims

Patent claims 1. A method for crosstalk modeling in a multi-mirror arrangement (31) with displaceable individual mirrors (32), comprising the following steps: 1.1. Providing a multi-mirror arrangement (32) 1.1.1. with N movable individual mirrors (32) and 1.1.2. a control device (35) for positioning the individual mirrors (32), 1.2. Specification of a control pattern (34) for positioning at least a subset of the individual mirrors (32*), 1.3. Positioning the individual mirrors (32*) by controlling them with the control pattern (34), 1.4. Detecting the actual positions of the individual mirrors (32*) resulting from control with the control pattern (34), 1.5. Determination of a coefficient matrix with coefficients to quantify crosstalk behavior, 1.6. Adjustment of the control device (35), 1.6.1. wherein the control pattern serves as a predictor of a training data set (33) for a neural network for predicting a relationship between a control pattern (34) and the resulting actual positions of the individual mirrors (32), and 1.6.2.where the coefficients of the determined coefficient matrix serve as targets of the training data set. 2. Method according to claim 1, characterized in that, in order to determine the coefficient matrix, one or more individual mirrors (32*) are permanently controlled and/or one or more individual mirrors (32v) are variably controlled. 3. Method according to one of the preceding claims, characterized in that a series expansion of a function which describes the influence of the variable control of an individual mirror (32v) on the positioning of another individual mirror (32*) is used to determine the coefficients of the coefficient matrix. 4. Method according to one of the preceding claims, characterized in that a plurality M of different control patterns (34) are used to determine the coefficient matrices, wherein the number M of control patterns (34) used is smaller than the number N of individual mirrors (32) of the multi-mirror arrangement (31). 5. Method according to one of the preceding claims, characterized in that a regressor is determined to determine a coefficient vector from a predetermined control pattern (34). 6. Method for positioning the individual mirrors (32) of a multi-mirror arrangement (31) with displaceable individual mirrors (32), comprising the following steps: 6.1. Specification of a target control pattern for positioning at least a subset of the individual mirrors (32) of the multi-mirror arrangement (31) in target positions, 6.2. Prediction of the deviations of the actual positions from the target positions of the individual mirrors (32) resulting from crosstalk effects using a neural network, 6.3. Adjustment of the target control pattern depending on the predicted deviations, 6.4. Positioning the individual mirrors (32) by controlling them with the adapted control pattern. 7. Method according to claim 6, characterized in that the predicted deviations result from matrix multiplication of a control matrix with the coefficient matrix. 8. Facet mirror module (13, 14) for an illumination optics (4) of a projection exposure system (1) comprising 8.1. a multi-mirror arrangement (31) with movable individual mirrors (32) and 8.2. a control device (35) for controlling the positioning of the individual mirrors (32), 8.3. wherein the control device (35) comprises a computing unit with a neural network for predicting the deviations of the actual positions of the individual mirrors (32) from the target positions when controlling them with a given control pattern. 9. Facet mirror module (13, 14) according to claim 8, characterized in that the neural network is integrated into the facet mirror module (13, 14). 10. Facet mirror module (13, 14) according to one of claims 8 or 9, characterized in that the neural network is programmed into an application-specific integrated circuit (ASIC). 11. Illumination optics (4) for a projection exposure system (1) comprising a facet mirror module (13, 14) according to one of claims 8 to 10. 12. Illumination system (2) for a projection exposure apparatus (1) comprising an illumination optics (4) according to claim 11 and a radiation source (3). 13. Optical system for a projection exposure apparatus (1) comprising 13.1. an illumination optics (4) according to claim 11 and 13.2. a projection optics (7) for imaging a reticle (24) arranged in the object field (5) onto a wafer (25) arranged in an image plane (9). 14. Projection exposure system (1) with 14.1. an optical system according to claim 13 and 14.2. a radiation source (3). 15. A method for producing a nano- or microstructured component comprising the following steps: 15.1. Providing a projection exposure apparatus (1) according to claim 14, 15.2. Providing a reticle (24) with structures to be imaged, 15.3. Providing a wafer (25) on which a layer of a light-sensitive material is applied at least in some areas, Projecting at least a part of the reticle (24) onto a region of the light-sensitive layer on the wafer (25) with the aid of the projection exposure system (1).