DE102022201978A1 - Control for a manipulator of a projection lens - Google Patents

Abstract

The invention relates to a control device (14) for controlling at least one manipulator (M1-M4, 36) of a projection lens (16) for microlithography by generating a specification for a change to be made using the manipulator. The control device generates the specification from a state characterization (34) of the projection lens (16) comprising a plurality of state parameters (bj) by executing an optimization algorithm for optimizing a quality function. The merit function comprises at least one penalty term, which has a limit value (sj) of a target range (80) for one of the state parameters (bj) and a weighting factor (aj) for the limit value, the target range (80) being within a permissible value range of the state parameter (bj ) lies. Furthermore, after a first execution of the optimization algorithm, the control device determines the achieved value of the state parameter and compares it with the limit value (sj). If the determined value of the state parameter is outside the target range (80), the controller changes the weighting factor (aj) and executes the optimization algorithm again. Furthermore, the invention relates to an adjustment system and a control method.

Description

Background of the Invention

The invention relates to a control device and a method for controlling at least one manipulator for changing a parameter of a projection lens for microlithography by generating a specification for a travel variable, which defines a change in the parameter to be carried out by the manipulator along a travel. Furthermore, the invention relates to an adjustment system for adjusting a projection objective for microlithography by changing a parameter of the projection objective with such a control device.

A projection objective is used in microlithography for imaging structures of a mask onto a photosensitive layer of a substrate. With a semiconductor wafer as a substrate, the smallest structures for electronic semiconductor components, integrated circuits, nanoelectromechanical systems or other microstructured or nanostructured components can be produced in this way. The progressive miniaturization of the structures of semiconductor components and the need for faster manufacturing processes with shorter exposure times leads to ever increasing demands on the imaging properties of the projection lenses used. The pattern should be reproduced on the photosensitive layer over the entire service life with the smallest possible imaging errors or aberrations.

Before a projection lens is put into operation, an adjustment is therefore made to minimize image errors as a result of manufacturing and assembly tolerances. A large number of optical parameters of the projection lens are set in such a way that they are not larger or smaller than a respectively permissible range of values and thus correspond to the agreed delivery specifications. Imaging errors can also occur during operation, which are caused, for example, by aging effects or heat and make a new adjustment necessary.

Projection lenses therefore contain manipulators with which state changes can be carried out on individual or groups of optical elements in order to correct aberrations. Such state changes are, for example, a change in position in one or more of the six rigid body degrees of freedom of the relevant optical element, the application of heat or cold to the optical element, a deformation of the optical element or material processing, for example in the form of material removal. A post-processing device for material processing or material removal on an optical element is also understood in the context of this application as a manipulator of the projection lens in the general sense.

A change in a state variable of an optical element that takes place by means of a manipulator actuation for the purpose of changing its optical effect is referred to as “travel” or “travel”. Such a travel, defined by changing a state variable of the optical element, is specified via target change variables of the associated manipulator. The manipulation can take the form, for example, of a displacement or rotation of the optical element in a specific direction, the application of heat, cold, forces, moments, electromagnetic radiation of a specific wavelength or electrical currents, in particular locally or extensively, to the optical element, or an energy input into the optical element by bombardment with particles such as electrons. Furthermore, the manipulation can define a material processing or material removal to be carried out on an optical element by means of a post-processing device. For example, in the case of a displacement, the target change variable can define a path length to be covered or, in the case of a rotation, an angular range to be covered.

A reduction in imaging errors of a projection objective can be achieved by suitable manipulator changes. The calculation of manipulator changes to be carried out for the correction of an aberration characteristic of a projection objective usually takes place by means of a travel-generating optimization algorithm, which is also referred to as a “manipulator change model”. Such optimization algorithms are, for example, in the publications WO 2010/034674 A1 , DE 10 2015 206 448 A1 or DE 10 2019 200 218 B3 described.

Optimization algorithms known from the prior art can be used to calculate suitable travels x _i to solve the following optimization problem: $$\begin{array}{lll}min{\Vert Mx-b_{mess}\Vert }_2^2\hfill & \text{With}\hfill & f_i\left(x\right)\le s_j\hfill \end{array}$$

beschriebene Gütefunktion, auch Meritfunktion, Bewertungsfunktion oder Kostenfunktion genannt, mittels einer Bestimmung geeigneter Werte für x und unter Berücksichtigung der durch F_i(x) ≤ s_j beschriebenen Nebenbedingungen minimiert. Hierbei bezeichnet x einen Stellwegvektor mit Stellwegen x_i für die einzelnen Manipulatoren, bmess einen Zustandsvektor des Projektionsobjektivs, welcher eine gemessene Aberrationscharakteristik des Projektionsobjektivs beschreibt, M eine Sensitivitätsmatrix zur Beschreibung des Zusammenhangs zwischen Stellwegänderung und Veränderung des Zustandsvektors b, || ||₂ die Euklidische Norm, F_i(x) eine geeignete Funktion zur Beschreibung der Nebenbedingungen und s_j einen jeweiligen festen Grenzwert für Eigenschaften des Projektionsobjektivs, wie etwa für Parameter des Zustandsvektors b oder für einzelne Stellwege x_i. Grenzwerte für Parameter des Zustandsvektors b können insbesondere vorgegebene maximale Fehlerwerte sein, wie beispielsweise festgelegte Fertigungs- oder Lieferspezifikationen. Die Nebenbedingungen stellen somit harte Grenzen für die betreffenden Eigenschaften des Projektionsobjektiv dar und dürfen nicht überschritten werden.In such an optimization problem, the ${\Vert Mx-b_{mess}\Vert }_2^2$

described quality function, also called merit function, evaluation function or cost function, by determining suitable values for x and taking into account of the constraints described by F _i (x) ≤ s _j is minimized. Here, x designates a travel vector with travels x _i for the individual manipulators, bmess a state vector of the projection lens, which describes a measured aberration characteristic of the projection lens, M a sensitivity matrix for describing the relationship between the change in travel and the change in the state vector b, || || ₂ the Euclidean norm, F _i (x) a suitable function for describing the secondary conditions and s _j a respective fixed limit value for properties of the projection lens, such as for parameters of the state vector b or for individual adjustment paths x _i . In particular, limit values for parameters of the state vector b can be predetermined maximum error values, such as established production or delivery specifications. The secondary conditions thus represent hard limits for the relevant properties of the projection lens and must not be exceeded.

A major problem with this optimization method is the calculation time, which increases rapidly with the dimension of the travel vector. With a larger number of manipulator degrees of freedom, a time-efficient calculation of travel specifications is no longer achievable.

the DE 10 2015 206 448 A1 describes an optimization method to shorten the computing time, in which the limits defined by the secondary conditions are implicitly taken into account by means of a penalty function contained in the quality function. The closer a state value or image error value b _j of a selected travel vector x is to the specified limit value s _j , the greater the value of the penalty function. However, the penalty function based on a power with an (even-numbered) exponent cannot guarantee exact compliance with the secondary conditions in all cases. In the DE 10 2019 200 218 A1 the use of a quality function to be optimized with a penalty function is therefore disclosed, the function value of which runs towards infinity when a state value b _j approaches the corresponding limit s _j .

A disadvantage of the optimization method described, in addition to the problematic compliance with the secondary conditions, is the small influence on the ultimately determined travel vector as one of many possible solutions to the optimization problem. For example, the determined travel vector can lead to many state values or parameters that are close to the respective limit value, although valid travel vectors at other local minima result in parameters that are less close to the limit value and are therefore possibly more suitable.

Underlying Task

It is an object of the invention to provide a control device and a method with which the aforementioned problems are solved and in particular the quality of a travel specification generated therewith for reducing aberrations is improved. Advantageously, the quality of the control path specification generated in this way should be improved in such a way that state values can be specifically reduced within the permissible limit values.

Solution according to the invention

The aforementioned object can be achieved according to the invention, for example, with a control device for controlling at least one manipulator for changing a parameter of a projection lens for microlithography by generating a specification for a travel variable, which defines a change in the parameter to be carried out by the manipulator along a travel. The control device is configured to generate the specification from a state characterization of the projection lens comprising a plurality of state parameters by executing an optimization algorithm for optimizing a quality function at least once. The merit function includes at least one penalty term, which has a limit value of a target range for one of the state parameters and a weighting factor for the limit value, with the target range being within a permissible value range of the state parameter. The control device is also configured, after a first execution of the optimization algorithm, to determine the value of the state parameter achieved by means of the optimization result and to compare it with the limit value, and to change the weighting factor in the event that the determined value of the state parameter is outside the target range and re-run the optimization algorithm.

The at least one manipulator controlled by the control device serves in particular to change a parameter of one or more optical elements of the projection lens. Such parameters have already been described above and denote, for example, the position, orientation, temperature, deformation or material processing of the optical element. In addition, the manipulator can also be used to align a measurement mask or a sensor for adjusting the projection objective.

The quality function is also referred to as a merit function or cost function and describes, for example, a change in a measured but ration by means of an assumed specification for one or more travel variables. The optimization algorithm then searches for a specification in which the absolute value of the quality function and thus the aberration is minimal. The penalty term is to be understood as a term of the quality function which has the function of keeping a state parameter within the target range during the optimization or of counteracting the state parameter exceeding the limits of the target range. The penalty term is thus configured to consider the target range as an implicit constraint in the optimization. According to one embodiment, the quality function for different state parameters each includes an individual penalty term. Furthermore, the quality function for an upper and a lower limit of a target range can each contain an individual penalty term.

The target range is also called the target corridor in the following and represents an interval in which the status parameter should lie after optimization. The target range restricts a range for permissible values of the condition parameter, such as an assembly or delivery specification. Permissible values of state parameters can also be influenced by a maximum possible travel of a manipulator. From many possible adjustment travel specifications within the permissible value range as a possible result of an optimization, certain solutions are preferably determined by the target range.

For example, an upper or a lower limit of the target range is used as the limit value. The weighting factor for the limit is used to soften or strengthen the limit. For example, as the weighting factor increases or decreases, the penalty term increases. The larger the penalty term, the greater the cost of not complying with the limit during optimization and thus the less likely it is that the limit will be violated in the optimization result.

According to an embodiment of the invention, the penalty term includes a quotient whose denominator includes the limit of the target range for one of the state parameters and the weighting factor for the limit. In particular, one or more penalty terms with a quotient can be provided for several or all state parameters, individual limit values and weighting factors being contained in the denominator. The greater the magnitude of the numerator relative to that of the denominator, and thus relative to the limit and weighting factor, the greater the magnitude of the penalty term and vice versa.

According to a further embodiment of the invention, the quotient forms the basis of a power with an even exponent. In particular, the control device is configured to carry out a minimization of the quality function, with a negative limit value or state parameter being permitted in the quotient and the quotient being raised to the power of an even exponent. Thus the penalty term is always positive. In one embodiment, the exponent can be selectable from a predetermined range. The larger the exponent, the faster the penalty term grows for quotients greater than 1 or less than -1.

werden gemäß der Fringe-Sortierung mit Z_j bezeichnet. Die Fringe-Sortierung ist dem Fachmann zum Beispiel aus Tabelle 20-2 auf Seite 215 des „Handbook of Optical Systems“, Vol. 2 von H. Gross, 2005, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim bekannt.According to an embodiment of the control device according to the invention, the numerator of the quotient contains the state parameter in the form of an image error of the projection lens. In particular, the counter contains a difference between a measured image error and a change in the state parameter by means of an adjustment path to be undertaken. In an inventive embodiment, the numerator of the quotient includes a term containing the travel variable. In particular, the term represents a relationship between a travel and a change in the image error generated by the travel. The image error is denoted by Zernike coefficients b _j , for example. In the professional world, the Zernike coefficients bj are often also referred to as _Zj , ie with a normally set index, such as Z5 and Z6 for astigmatism. The Zernike polynomials or Zernike functions associated with the respective coefficients $Z_m^n$

are denoted by Z _j according to the fringe sorting. Fringe sorting is known to the person skilled in the art, for example, from Table 20-2 on page 215 of the “Handbook of Optical Systems”, Vol. 2 by H. Gross, 2005, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

According to one embodiment of the invention, the control device is configured to control a plurality of manipulators, the state parameters form a state vector and the numerator of the quotient includes a sensitivity matrix which defines a relationship between the travels of the manipulators and the state vector. In other words, the sensitivity matrix denotes the sensitivity of the manipulators in relation to their degrees of freedom of movement. In relation to a manipulator M _s , the sensitivity matrix defines how the state vector of the projection lens changes when the manipulator M _s is adjusted by a standard adjustment path. For example, the travels are combined as a travel vector. The multiplication of the travel vector by the sensitivity matrix results in the changes in the state vector of the projection lens resulting from the travels.

According to a further embodiment of the invention, the control device is configured to use the specification for the travel variable determined during the previous execution of the optimization algorithm as the starting value when the optimization algorithm is executed again. This constraint may be closer to a desired solution, which will allow the optimization to complete faster. Alternatively, the start value of the first execution of the optimization algorithm can be used as the start value for the travel variable. With this measure, the specification determined is discarded and a new optimization is carried out with different weighting factors. According to one embodiment, the control device is configured to carry out a selection for the starting value of a further execution of the optimization algorithm, taking into account the determined specification for the travel variable or a value of a state parameter determined therefrom. In particular, the selection can be made from the start value of the first execution or the determined specification for the control value from the previous execution.

In one embodiment, the control device is configured to repeat the optimization algorithm with a changed weighting factor until the determined value of the state parameter is within the target range. The determined value of the state parameter is determined using the determined specification for the travel variable. In particular, the optimization algorithm is also repeated when the determined value of the state parameter is within a permissible value range, such as within a manufacturing or delivery specification. The weighting factor is changed, for example, in such a way that the penalty term for determined values outside the target range becomes larger and these values are therefore less likely to result as a solution. In an alternative embodiment, the optimization algorithm is only repeated with a changed weighting factor until the determined value of the state parameter is within a permissible range of values, which includes the target range. In this way, the determined values are closer to the target range, but not necessarily within the target range.

According to an embodiment of the invention, a deviation of the determined value of the state parameter from the limit value is taken into account when changing the weighting factor. In particular, the weighting factor is changed in such a way that a greater penalty term results if there is a greater deviation from the limit value. In this way, in a subsequent optimization for a minimum image error, those travels with a larger deviation of the associated value of the state parameter from the limit value are actively avoided by the larger penalty term. For example, a weighting factor in the denominator of a quotient of the penalty term is set to be less than 1 for a value of the state parameter that is too large and closer to 0 with a larger deviation. Conversely, for example, a weighting factor greater than 1 is set for a value that is too small, with a larger weighting factor also being selected as the deviation increases. An individual weighting factor is preferably used and adapted for each state parameter. According to other embodiments, the weighting factor is changed or adapted only for state parameters with values outside the target range, and thus selective optimization.

According to a further embodiment of the invention, when changing the weighting factor, the limit of the target area closer to the determined value of the status parameter, the limit of the target area further away from the determined value of the status parameter or the mean value of the target area are taken into account. In particular, a limit value to be taken into account in the change is selected from the value of the closer limit, the value of the more distant limit or the mean value of the target area. This measure enables a further influencing of the optimization result. For example, the weighting factor is changed as a function of the distance between the value and the selected limit value in such a way that travels with values of the state parameter close to the selected limit value are preferred during optimization. In one embodiment with a mean value of the target range as a limit value, a very small target range around the mean value is defined in such a way that values determined for each state parameter are outside the target range and the weighting factor is therefore adjusted for all state parameters and forced optimization towards the mean value takes place. Alternatively, an adjustment of a weighting factor and an optimization can also be carried out for state parameters with values within the target range.

According to an embodiment of the invention, a target area is specified only for specific individual coordinate points of a state parameter. In particular, an individual maximum limit value and an individual minimum limit value of a target range for values of the state parameter at individual coordinate points are defined in each case. For example, for some field points as coordinate points, target ranges for the values of one, several or all Zernike coefficients b _j are fixed as state parameters placed. Different coordinate points, different target areas or both can also be defined for different status parameters.

In further embodiments according to the invention, individual target areas are specified for all coordinate points of a state parameter. For example, a coordinate-dependent target area with a maximum and a minimum limit value is assigned to all field points of a state parameter. In particular, the width of the target area can also vary from coordinate point to coordinate point. However, it is also possible to assign the same target area for all coordinate points of a state parameter. In turn, different target ranges can be specified for different state parameters, such as different Zernike coefficients b _j , for the same coordinate points.

According to an embodiment of the invention, the control device is configured to take into account an attenuation for the weighting factor when optimizing the merit function. For example, the damping takes place using a global additional factor, a limitation of the value range of a weighting factor, damping proportional to the rate of change of a weighting factor between two iterations of the optimization algorithm, or damping proportional to the rate of change of a state parameter between two iterations. Further embodiments include a combination of several of these attenuations. With such a damping, excessive changes in the weighting factor and the resulting build-up effects are prevented.

Furthermore, in an embodiment according to the invention, the control device is configured to subtract a lead from a state parameter before an optimization of the quality function and to add the lead again after the optimization. In particular, the mean value of a target range of the state parameter is subtracted before an optimization in the values of the state parameter and the limits of the target range. In this way, the mean value is shifted towards zero. The target area is centered around zero. This facilitates the optimization of the quality function. After an optimization, the derivative action is then added to the optimized values of the state parameter. According to an embodiment with an individual target area for each coordinate point of the state parameter, a coordinate-dependent subtraction of the respective mean values of the coordinate-dependent target areas takes place before an optimization and a corresponding addition after the optimization. In this way, an arbitrarily shaped, coordinate-dependent course of the target area is centered around zero for optimization.

Furthermore, an adjustment system for adjusting a projection objective for microlithography by changing a parameter of the projection objective by means of at least one manipulator is provided according to the invention. The adjustment system according to the invention comprises a measuring device for determining the state characterization of the projection lens and a control device according to one of the preceding embodiments or embodiment variants for generating a specification for a travel variable, which defines a change in the parameter to be carried out by means of the manipulator. According to one exemplary embodiment, the measuring device is configured as a wavefront measuring device. For example, the measuring device is designed as a shearing interferometer or point diffraction interferometer and for this purpose comprises a measuring mask with a periodic structure and a sensor element with an image grating. In particular, phase shifting methods known to those skilled in the art can be used to determine wavefront errors.

The aforementioned object can also be achieved, for example, with a method for controlling at least one manipulator for changing a parameter of a projection lens for microlithography. The method according to the invention comprises generating a specification for a travel variable, which defines a change in the parameter along a travel to be carried out by means of the manipulator, from a state characterization of the projection objective comprising several state parameters by executing an optimization algorithm at least once to optimize a quality function. The merit function includes at least one penalty term, which has a limit value of a target range for one of the state parameters and a weighting factor for the limit value, and the target range lies within a permissible value range of the state parameter. The method according to the invention also includes determining the value of the state parameter based on the optimization result after executing the optimization algorithm, comparing the determined value of the state parameter with the limit value and, if the determined value of the state parameter is outside the target range, changing the weighting factor and rerunning the optimization algorithm.

The features specified with regard to the above-mentioned embodiments, exemplary embodiments or embodiment variants, etc. of the control device according to the invention can be correspondingly transferred to the adjustment system according to the invention or the control method according to the invention and vice versa. These and other features of the embodiments according to the invention are explained in the description of the figures and the claims. The individual features can be realized either separately or in combination as embodiments of the invention. Furthermore, they can describe advantageous embodiments which are independently protectable and whose protection may only be claimed during or after the application is pending.

character list

• 1 ein Ausführungsbeispiel einer erfindungsgemäßen Justieranlage für ein Projektionsobjektiv sowie eine erfindungsgemäße Steuerungsvorrichtung zum Steuern von Manipulatoren eines Projektionsobjektivs in einer schematischen Veranschaulichung,
• 2 ein Ausführungsbeispiel eines erfindungsgemäßen Verfahrens zum Steuern von Manipulatoren eines Projektionsobjektivs in einem schematischen Diagramm,
• 3 eine Veranschaulichung des Ergebnisses vieler durchgeführter Justagen mit einer Berücksichtigung von Zielbereichen für Zustandsparameter,
• 4 eine Veranschaulichung des Ergebnisses vieler durchgeführter Justagen mit einer Berücksichtigung eines Zielwerts für Zustandsparameter,
• 5 eine Veranschaulichung von individuellen Zielbereichen für einzelne Koordinatenpunkte von Zustandsparametern für eine Optimierung,
• 6 eine Veranschaulichung von einem konstanten Zielbereich für alle Koordinatenpunkte von Zustandsparametern für eine Optimierung,
• 7 eine Veranschaulichung von individuellen Zielbereichen für alle Koordinatenpunkte von Zustandsparametern für eine Optimierung,
• 8 eine Veranschaulichung einer Optimierung mit einer Anpassung von Gewichtungsfaktoren nur bei Werten des Zustandsparameters außerhalb des Zielbereichs und unter Berücksichtigung des Abstands von der näheren Zielbereichsgrenze,
• 9 eine Veranschaulichung einer Optimierung mit einer Anpassung von Gewichtungsfaktoren nur bei Werten des Zustandsparameters außerhalb des Zielbereichs und unter Berücksichtigung des Abstands von der entfernteren Zielbereichsgrenze,
• 10 eine erste Veranschaulichung einer Optimierung mit einem zuvor von den Zustandsparametern abgezogenen Vorhalt, sowie
• 11 eine zweite Veranschaulichung einer Optimierung mit einem zuvor von den Zustandsparametern abgezogenen Vorhalt.

The above and other advantageous features of the invention are illustrated in the following detailed description of exemplary embodiments according to the invention with reference to the attached schematic drawings. It shows:

• 1 an exemplary embodiment of an adjustment system according to the invention for a projection lens and a control device according to the invention for controlling manipulators of a projection lens in a schematic illustration,
• 2 an embodiment of a method according to the invention for controlling manipulators of a projection lens in a schematic diagram,
• 3 an illustration of the result of many adjustments carried out with a consideration of target ranges for status parameters,
• 4 an illustration of the result of many adjustments carried out taking into account a target value for state parameters,
• 5 an illustration of individual target areas for individual coordinate points of state parameters for an optimization,
• 6 an illustration of a constant target range for all coordinate points of state parameters for an optimization,
• 7 an illustration of individual target areas for all coordinate points of state parameters for an optimization,
• 8th an illustration of an optimization with an adjustment of weighting factors only in the case of values of the state parameter outside the target range and taking into account the distance from the nearer target range limit,
• 9 an illustration of an optimization with an adjustment of weighting factors only in the case of values of the state parameter outside the target range and taking into account the distance from the more distant target range boundary,
• 10 a first illustration of an optimization with a lead previously subtracted from the state parameters, and
• 11 a second illustration of an optimization with a bias previously subtracted from the state parameters.

Detailed description of exemplary embodiments according to the invention

In the exemplary embodiments or embodiments or design variants described below, elements that are functionally or structurally similar to one another are provided with the same or similar reference symbols as far as possible. Therefore, for an understanding of the features of each element of a particular embodiment, reference should be made to the description of other embodiments or the general description of the invention.

To simplify the description, a Cartesian xyz coordinate system is indicated in some drawings, from which the respective positional relationship of the components shown in the figures results. In 1 the y-direction runs perpendicular to the plane of the drawing into it, the x-direction to the right and the z-direction upwards.

1 shows an adjustment system 10 for adjusting a projection lens 16 of a projection exposure system for microlithography in a schematic illustration. The individual components of the adjustment system 10 can be arranged separately from one another or integrated into a uniform system. The adjustment system 10 comprises a measuring device 12 for determining a state characterization 34 of the projection lens 16 and a control device 14 in the form of a so-called travel determiner for generating a travel command 38 from the state characterization 34.

The projection lens 16 is used to image mask structures from an object plane 24 into an image plane 28 and can be designed for exposure radiation of different wavelengths, such as 248 nm or 193 nm. In the present exemplary embodiment, the projection lens 16 is set to a wavelength in the extreme ultraviolet (EUV) wavelength range, eg 13.5 nm designed.

The measuring device 12 is configured to measure wavefront errors of the projection objective 16 and comprises an illumination device 18 and a measuring mask 22 on the input side of the projection objective 16 and a sensor element 26, a detector 30 and an evaluation device 32 on the output side of the projection objective 16. The measuring mask 22 is in 1 shown as an example as a transmission mask. In a preferred exemplary embodiment, however, the measurement mask 22 is operated in reflection. The illumination device 18 is configured to generate a measurement radiation 20 with the operating wavelength of the projection objective 16 to be tested, in the present case in the form of EUV radiation, and to radiate it onto the measurement mask 22, which is arranged in the object plane 24. In the context of this application, EUV radiation is to be understood as meaning electromagnetic radiation with a wavelength of less than 100 nm, in particular a wavelength of approximately 13.5 nm or approximately 6.7 nm. The measurement mask 22, often also referred to as a “coherence mask”, has a first periodic structure. The sensor element 26 is arranged in the image plane 28 in the form of an image grating which has a second periodic structure. Checkerboard structures in measurement mask 22 can also be combined with checkerboard structures in sensor element 26 . Other combinations of periodic structures known to those skilled in the art of shear interferometry or point diffraction interferometry can also be used. The sensor element 26 is 1 used in transmission. In particular, however, the sensor element 26 can also be operated in reflection.

A two-dimensionally resolving detector 30 in the form of a camera is arranged below the sensor element 26, specifically in a plane conjugate to the pupil plane of the projection lens 16. The sensor element 26 and the detector 30 together form a sensor module. The measurement mask 22 and the sensor module form a shearing interferometer or point diffraction interferometer known to those skilled in the art and are used to measure wavefront errors in the projection lens 16 . For this purpose, phase shift methods known to those skilled in the art are used in particular.

The evaluation device 32 determines the state characterization 34 of the projection objective 16 from the intensity patterns recorded by the detector 30. In this exemplary embodiment, the state characterization 34 includes a set of Zernike coefficients b _j characterizing the wavefront errors of the projection objective 16.

gemäß der sogenannten Fringe-Sortierung mit Z_j bezeichnet. Die b_j sind dann die den jeweiligen Zernike-Funktionen bzw. Zernike-Polynomen zugeordneten Zernike-Koeffizienten. Die Fringe-Sortierung ist beispielsweise in Tabelle 20-2 auf Seite 215 des „Handbook of Optical Systems“, Vol. 2 von H. Gross, 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim veranschaulicht. Eine Wellenfrontabweichung W(ρ,θ) an einem Punkt in der Bildebene des Projektionsobjektivs wird in Abhängigkeit von den Polarkoordinaten (ρ,θ) in der Pupillenebene wie folgt entwickelt: $$W\left(\rho ,\theta \right)={\displaystyle \sum {}_j{b}_j\cdot Z_j}\left(\rho ,\theta \right)$$

In the present application, as for example in paragraphs [0125] to [0129] of US2013/0188246A1 described, the Zernike functions known from, for example, Chapter 13.2.3 of the textbook "Optical Shop Testing", 2nd Edition (1992) by Daniel ^Malacara , ed. John Wiley & Sons, Inc $Z_m^n$

denoted by Z _j according to the so-called fringe sorting. The b _j are then the Zernike coefficients assigned to the respective Zernike functions or Zernike polynomials. The fringe sorting is illustrated, for example, in Table 20-2 on page 215 of the "Handbook of Optical Systems", Vol. 2 by H. Gross, 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. A wavefront deviation W(ρ,θ) at a point in the image plane of the projection lens is developed in terms of polar coordinates (ρ,θ) in the pupil plane as follows: $$W\left(\rho ,\theta \right)={\displaystyle \sum {}_j{b}_j\cdot Z_j}\left(\rho ,\theta \right)$$

While the Zernike polynomials are denoted by Zj, ie with a subscript j, the Zernike coefficients are denoted by b _j in the context of this application. At this point it should be noted that in the professional world the Zernike coefficients bj are often also referred to as _Zj , ie with a normally set index, such as Z5 and Z6 for astigmatism.

Die Stellwege x_i dienen der Steuerung von Manipulatoren M_s des Projektionsobjektivs 16, während die Stellwege ${\text{x}}_{\text{n}}^{\text{L}}$

der Steuerung einer Nachbearbeitungseinrichtung 36 zur mechanischen Nachbearbeitung von optischen Elementen des Projektionsobjektivs 16 dienen. Im Rahmen dieser Anmeldung werden sowohl die Manipulatoren M_s als auch die Nachbearbeitungseinrichtung 36 als Manipulatoren des Projektionsobjektivs 16 im allgemeinen Sinn verstanden. Allgemein gesprochen, umfasst der Stellwegbefehl 38 mit den Stellwegen x_i sowie den Stellwege ${\text{x}}_{\text{n}}^{\text{L}}$

Vorgaben für Stellwegvariablen, welche mittels Manipulatoren vorzunehmende Veränderungen eines jeweiligen Parameters eines oder mehrerer optischer Elemente des Projektionsobjektivs 16 definieren, wobei die zu verändernden Parameter der optischen Elemente insbesondere mittels der Manipulatoren M_s einstellbare Lageanordnungen der optischen Elemente oder mittels der Nachbearbeitungseinrichtung 36 vornehmbare Formzustände umfassen können.The state characterization 34 determined by the evaluation device 32 of the measuring device 12 is transferred to the control device 14, which uses it to generate a travel command 38 in the form of a travel variable x. In this exemplary embodiment, the travel variable is a vector and includes travels x _i and travels ${\text{x}}_{\text{n}}^{\text{L}}\text{.}$

The adjustment paths x _i are used to control manipulators M _s of the projection lens 16, while the adjustment paths ${\text{x}}_{\text{n}}^{\text{L}}$

serve to control a post-processing device 36 for mechanical post-processing of optical elements of the projection lens 16 . In the context of this application, both the manipulators M _s and the post-processing device 36 are understood as manipulators of the projection lens 16 in the general sense. Generally speaking, the travel command 38 includes the travels x _i and the travels ${\text{x}}_{\text{n}}^{\text{L}}$

Specifications for travel variables, which define changes to be made to a respective parameter of one or more optical elements of projection lens 16 by means of manipulators, wherein the parameters of the optical elements to be changed to be changed can include positional arrangements of the optical elements that can be adjusted by means of manipulators M _s or shape states that can be performed by means of post-processing device 36 .

The projection objective 16 has in the exemplary embodiment 1 only four optical elements E1 to E4. All optical elements are movably mounted. For this purpose, each of the optical elements E1 to E4 is assigned a manipulator M _s , specifically one of the manipulators M1 to M4. The manipulators M1, M2 and M3 each enable the associated optical elements E1, E2 and E3 to be displaced in the x and y direction and thus essentially parallel to the plane in which the reflecting surface of the respective optical elements lies.

The manipulator M4 is configured to tilt the optical element E4 by rotating it about a tilting axis 40 arranged parallel to the y-axis. This changes the angle of the reflecting surface of E4 with respect to the incident radiation. Further degrees of freedom for the manipulators are possible. For example, a displacement of a relevant optical element transverse to its optical surface or a rotation about a reference axis perpendicular to the reflecting surface can be provided.

Generally speaking, each of the manipulators M1 to M4 shown here is intended to bring about a displacement of the associated optical element E1 to E4 by executing a rigid-body movement along a predetermined adjustment path. Such an adjustment path can, for example, combine translations in different directions, tilting and/or rotations in any way. Alternatively or additionally, manipulators can also be provided, which are configured to undertake a different type of change in a state variable of the associated optical element by appropriate actuation of the manipulator. In this regard, an actuation can take place, for example, by subjecting the optical element to a specific temperature distribution or a specific force distribution. In this case, the travel can represent a change in the temperature distribution on the optical element or the application of a local stress on an optical element designed as a deformable lens or as a deformable mirror.

In the exemplary embodiment shown, the travels x _i covered by the travel command 38 contain the travels x ₁ , x ₂ , x ₃ and x ₄ , which specify changes to be made by the manipulators M1 to M4 of at least one parameter of one or more of the optical elements E1 to E4 and thus serve to control the manipulators M1 to M4 of the projection lens 16. The travels x ₁ to x ₄ determined are transmitted to the individual manipulators M1 to M4 via travel signals and specify correction travels to be carried out in each case. These define corresponding displacements of the associated optical elements E1 to E4 for correcting wavefront errors that have occurred in the projection lens 16. If a manipulator has multiple degrees of freedom, multiple adjustment paths x _i can also be transmitted to it.

enthalten in diesem Ausführungsbeispiel die Stellwege ${\text{x}}_{\text{n}}^1,{\text{x}}_{\text{n}}^2,{\text{x}}_{\text{n}}^3{\text{ und x}}_{\text{n}}^4$

zur Steuerung der Nachbearbeitungseinrichtung 36 für eine jeweilige mechanische Nachbearbeitung der optischen Elemente E1, E2, E3 oder E4 des Projektionsobjektivs 16 und damit ebenfalls der Veränderung mindestens eines Parameters eines oder mehrerer der optischen Elemente E1 bis E4. Die Stellwege ${\text{x}}_{\text{n}}^1$

bis ${\text{x}}_{\text{n}}^4$

dienen somit wie die Stellwege x₁ bis x₄ der Korrektur aufgetretener Wellenfrontfehler des Projektionsobjektivs 16.The travels further covered by the travel command 38 ${\text{x}}_{\text{n}}^{\text{L}}$

contain the adjustment paths in this exemplary embodiment ${\text{x}}_{\text{<figure-callout id="1" label="n" filenames="DE102022201978A1\_0024.png,DE102022201978A1\_0025.png" state="{{state}}">n</figure-callout>}}^1,{\text{x}}_{\text{n}}^2,{\text{<figure-callout id="3" label="x n" filenames="DE102022201978A1\_0026.png" state="{{state}}">x</figure-callout>}}_{\text{n}}^{}{\text{and x}}_{\text{n}}^4$

for controlling the post-processing device 36 for a respective mechanical post-processing of the optical elements E1, E2, E3 or E4 of the projection lens 16 and thus also the change of at least one parameter of one or more of the optical elements E1 to E4. The travel ways ${\text{x}}_{\text{<figure-callout id="1" label="n" filenames="DE102022201978A1\_0024.png,DE102022201978A1\_0025.png" state="{{state}}">n</figure-callout>}}^1$

until ${\text{x}}_{\text{n}}^4$

thus serve, like the adjustment paths x ₁ to x ₄ , to correct any wavefront errors that have occurred in the projection lens 16.

The post-processing device 36 of this exemplary embodiment is to be understood as a device for the mechanical removal of material on an optical surface of an optical element in the form of a lens or a mirror. This removal follows the production of the optical element and serves in particular to change the shape of a surface. The change to be made to the surface shape is aspherical and, moreover, does not have to be rotationally symmetrical. Therefore, the surface to be modified is called the correction asphere. In particular, an optical element already mounted in the projection lens 16 can be removed for post-processing and then reinstalled in the projection lens. In particular, a removal device typically used for the mechanical processing of correction aspheres can be used as the post-processing device 36 . The ablations are therefore also referred to below as "correction asphere ablations". An ion beam, for example, can be used for mechanical processing. Any desired correction profiles can thus be incorporated into an optical element to be post-processed. In order to post-process the surface shape of an EUV mirror that has already been coated, it is also possible, for example, to irradiate it using an electron beam. This can cause the material near the mirror surface to be compacted and thus change the surface shape.

für die Korrekturasphären-Nachbearbeitungseinrichtung 36 kann gemäß weiterer hier nicht im Detail veranschaulichter Ausführungsformen der Stellwegbefehl 38 auch weitere Stellwege umfassen. Diese Stellwege können Stellwege zur Verstellung weiterer ständig mittels der Steuerungsvorrichtung 14 ansteuerbarer Freiheitsgrade darstellen, wie beispielsweise zum Verstellen der Betriebswellenlänge oder der Position der Messmaske 22 oder des Sensorelements 26. Weiterhin können diese Stellwege manuell manipulierbarer Freiheitsgrade sowie Eingriffe in den mechanischen Aufbau des Projektionsobjektivs 16 definierende Stellwege umfassen. Derartige Eingriffe können eine Änderung von Abstimmringen oder Fassungspositionen betreffen, welche eine partielle Demontage und erneute Montage des Projektionsobjektivs und damit üblicherweise auch einen Ausbau des Projektionsobjektivs aus einer Justieranlage erfordern.In addition to the adjustment paths x _i described above for the manipulation, ie in the present exemplary embodiment the manipulators M1 to M4, which can be permanently or temporarily connected to the control device 14, as well as the travels ${\text{x}}_{\text{n}}^{\text{L}}$

for the correction asphere post-processing device 36, according to further specific embodiments not illustrated here in detail, the travel command 38 can also include further travels. These adjustment paths can represent adjustment paths for adjusting further degrees of freedom that can be constantly controlled by the control device 14, such as for adjusting the operating wavelength or the position of the measuring mask 22 or the sensor element 26. Furthermore, these adjustment paths can define manually manipulable degrees of freedom and interventions in the mechanical structure of the projection lens 16 Include travel. Interventions of this type can relate to a change in tuning rings or mount positions, which require partial disassembly and reassembly of the projection lens and thus usually also require the projection lens to be removed from an adjustment system.

In addition to receiving a measured state characterization 34 in the form of Zernike coefficients b _j as state parameters for describing image errors, the control device 14 is also configured to receive specified target areas in the form of limit values 42 for state parameters and weighting factors 44 for the limit values 42 and contains a appropriate, in 1 not shown interface.

Hierfür ist das Optimierungsmodul 46 zum Minimieren einer Gütefunktion mittels eines Optimierungsalgorithmus ausgebildet. In der Gütefunktion werden neben den gemessenen Bildfehlern als Zustandsparameter b_j und einem Einfluss von möglichen Stellwegen x_i bzw. ${\text{x}}_{\text{n}}^{\text{L}}$

auf diese Bildfehler in einem Bestrafungsterm auch die Grenzwerte 42 für Zielbereiche von Zustandsparametern berücksichtigt. Dafür berücksichtigt der Bestrafungsterm die Grenzwerte 42 und zugehörige Gewichtungsfaktoren 44 in der Art, dass eine Annäherung oder Überschreitung der Grenzen des Zielbereichs durch Zustandsparameter während einer Optimierung erschwert oder verhindert wird.Furthermore, the control device 14 includes an optimization module 46 for minimizing measured image errors of the projection lens 16 by means of a suitable selection of adjustment paths x _i or ${\text{x}}_{\text{n}}^{\text{L}}.$

For this purpose, the optimization module 46 is designed to minimize a quality function using an optimization algorithm. In the quality function, in addition to the measured image errors as state parameters b _j and an influence of possible adjustment paths x _i or ${\text{x}}_{\text{n}}^{\text{L}}$

the limit values 42 for target ranges of state parameters are also taken into account for these image errors in a penalty term. For this purpose, the penalty term takes into account the limit values 42 and associated weighting factors 44 in such a way that approaching or exceeding the limits of the target area is made more difficult or prevented by state parameters during an optimization.

After an optimization has been carried out, a value determination module 48 of the control device 14 determines the new state parameters of the projection lens 16 presumably caused by the determined travel vector x and transfers these to a comparison module 50. The comparison module 50 checks whether these state parameters lie within the specified target ranges. If this is the case, the determined travel vector x is transmitted as a travel command 38 from the control device 14 to the manipulators M _s . Otherwise, an adaptation module 52 of the control device 14 carries out a suitable change in the weighting factors 44 and transfers this to the optimization module 46 for renewed optimization. In the renewed optimization, the previously determined travel vector x can also be used as the starting value.

The more precise mode of operation of the control device 14 and its components is described below together with an exemplary embodiment of the method according to the invention for controlling manipulators of a projection lens for microlithography.

2 shows in a schematic diagram an embodiment of a method according to the invention for controlling at least one manipulator for changing parameters of a projection lens. Method 60 is executed by control device 14, for example. First, a measurement 62 takes place to determine the state characterization 34 of the projection lens 16. The measuring device 12 described above can be used for the measurement 62.

In this exemplary embodiment, the state characterization 34 takes place by means of a vector b with Zernike coefficients b _j as vector components. The Zernike coefficients b _j are also referred to as state parameters or parameters and describe image errors of the projection lens 16. The Zernike coefficients b _j can be used to specify wavefront deviations W(ρ,θ) for all field points in the image plane, as has already been explained above . For example, Z5 and Z6 describe an astigmatism of the projection lens 16. The state parameters are recorded in a measurement for a discrete coordinate grid or discrete field points and characterize aberrations not only by their magnitude but also by their sign.

According to further exemplary embodiments, the state vector b can also include parameters of aerial image variables, a direct two-dimensional wavefront representation, variables derived from the aforementioned variables, such as linear combinations, or any combination of these parameters in addition to Zernike coefficients or alternatively to these.

The measured values 64 as a measured state characterization and specified target ranges with weighting factors 66 are provided to the optimization module 46 of the control device 14 for an optimization of travels x _i . The target areas, also called target corridors, are defined in this exemplary embodiment by limits s ^min and s sj ^max fixed. An upper limit, a lower limit or both limits of a target range for a state parameter can be taken into account in the optimization. The target corridors lie within a permissible value range with limit values s _j for the parameters and thus specify preferred values for status parameters b _j . In the embodiment according to 3 the limit values are +S _j and -S _j and are therefore arranged symmetrically to the zero point. The permissible range of values is defined, for example, by manufacturing or delivery specifications, maximum possible adjustment paths, or the like. The weighting factors a _j are used during optimization to weight the target corridors. For example, limits s _j of a target corridor with a larger weighting factor are more likely to be adhered to during an optimization. Possible target ranges or limits s _j and weighting factors a _j are described in more detail below.

mit der vektoriellen Stellwegvariablen x, welche die Stellwege x_i der im Projektionsobjektiv 16 vorgesehenen Manipulatoren M1 bis M4 sowie die Stellwege ${\text{x}}_{\text{n}}^{\text{L}}$

zur Steuerung der Korrekturasphären-Nachbearbeitung umfasst.As the next step, an optimization 68 is carried out in the method 60 with the measured state parameters b _j , the target areas s _j and the weighting factors a _j . This is done with a travel-generating optimization algorithm to minimize a quality function Φ(x), which is also called a merit function or cost function. The optimization problem is thus $$\underset{x}{\text{at least}}\mathrm{\Phi }\left(x\right)$$

with the vectorial travel variable x, which represents the travels x _i of the manipulators M1 to M4 provided in the projection lens 16 and the travels ${\text{x}}_{\text{n}}^{\text{L}}$

for controlling correction aspheric post-processing.

The sensitivities of the manipulators, in this case the manipulators M1 to M4 and the post-processing device 36, in relation to their degrees of freedom in the event of a status change are described using a sensitivity matrix M in this exemplary embodiment. The sensitivity matrix M describes the relationship between an adjustment of a degree of freedom i of a manipulator by a standard adjustment path x _i ⁰ and a resulting change in the state vector b of the projection lens 16. The individual rows of the sensitivity matrix M, each relating to one of the Zernike coefficients b _j are denoted by M _j in the following.

The quality function Φ according to the exemplary embodiment explained here contains a penalty term for each target range of the state parameters b _j and is: $$\mathrm{\Phi }\left(x\right)=...+{\displaystyle \sum _j{\left(\frac{\left|M_{j}x-b_j\right|}{a_j\cdot s_j}\right)}^{2N}}+...$$

The penalty term contains a quotient, the numerator of which includes the distance between the measured state parameter b _j as an image error and the change in the state parameter b _j resulting from a selected travel vector x, described with the term Mx. Thus, the counter goes to zero when a selected travel vector corrects the artifact. The numerator therefore represents the amount of the resulting image error b̃ _j when using the travel vector x.

Je höher der Betrag des resultierenden Zustandsparameter b̃_j über dem Betrag der Grenze s_j liegt, desto größer wird der Quotient und somit der Bestrafungsterm. Stellwegvektoren mit solchen Bildfehlern b̃_j werden durch den Bestrafungsterm bei einer Minimierung unwahrscheinlicher als Ergebnis ermittelt.The denominator contains a limit s _j of the target area belonging to the state parameter b̃ _j and a weighting factor a _j . The limit s _j can be the upper limit s j ^max or the lower limit s _j ^min of the target range. In particular, in the case of a target area placed symmetrically around zero, only one limit is sufficient to describe the target area. In a further exemplary embodiment, a penalty term can be provided both for the upper and for the lower limit of a target range. The state parameter b̃ _j resulting from a travel vector x determined during optimization should be within the target range: $s_j^{min}\le {\tilde{\text{b}}}_{\text{j}}\le s_j^{max}.$

The higher the absolute value of the resulting state parameter b̃ _j is above the absolute value of the limit s _j , the greater the quotient and thus the penalty term. Travel vectors with such image errors b̃ _j are less likely to be determined as a result by the penalty term in the case of minimization.

The penalty system defines a "soft" limit for determined b _j , ie the limit s _j may be exceeded. The "hardness" of the limit can be set with the weighting factor a _j . The smaller the amount of the weighting factor in the denominator, the larger the penalty term and the less likely it is that the limit will be exceeded. Conversely, a large weight value leads to a small penalty term and thus to a greater probability of exceeding the limit s _j . Furthermore, the quotient is the basis of a power with the even-numbered exponent 2N. An even exponent always results in positive penalty values. The larger N, the more the penalty term increases when approaching or exceeding the limit s _j . According to one embodiment, in addition to changing the weighting factor, the exponent N is also or alternatively adjusted.

In addition to the penalty terms for target areas, the quality function Φ can also contain other penalty terms. In particular, the Quality function Φ according to an exemplary embodiment, penalty terms for the limit values S _j of permissible value ranges for the state parameters b _j , as specified, for example, by manufacturing or delivery specifications. Penalty terms for the maximum possible adjustment paths of manipulators can also be provided in the quality function Φ. If possible, these value ranges should not be exceeded and therefore require very “hard” limits. Such and other punishment terms are for example in the DE 10 2015 206 448 A1 described.

After an optimization 68 of the positioning paths x _i , the value determination module 50 of the control device 14 is used to determine 70 the image errors b _j resulting from the positioning paths x _i . This can be done using the sensitivity matrix M, for example. For example, the residual of the image errors can be determined via b̃ _j =Mx+b. A comparison 72 of all resulting image errors or state parameters b _j with the respective target areas is then carried out with the comparison module 50 . If all image errors b _j are within the respective target areas, all determined adjustment paths x _i are adjusted 74 on the manipulators M ₁ to M ₄ . For this purpose, a corresponding travel command 38 is transmitted to the manipulators. Alternatively, the determined travels x _i can also be used if only a few previously defined state parameters b _j or a predetermined number of state parameters b _j lie within the respective target ranges. According to a further exemplary embodiment, the travels x _i determined are already used when the state parameters b _j are only within the permissible value ranges for state parameters. In general, paths x _n ^L for ion beam processing can also be determined in this way.

oder $$a_j=\left|\frac{s_j^{max}}{M_{j}x-b_j}\right|$$

If the comparison 72 is negative, the adjustment module 52 carries out an adjustment 76 of the weighting factors a _j and then a renewed optimization 68 of the adjustment paths x _i takes place. A weighting factor a _j with 0<a _j <1 is selected for image errors that are too large, and a weighting factor a _j with a _j >1 for image errors that are too small. In particular, according to one embodiment, an adjustment 76 can take place as follows: $$a_j=\left|\frac{s_j^{min}}{M_{j}x-b_j}\right|$$

or $$a_j=\left|\frac{s_j^{max}}{M_{j}x-b_j}\right|$$

The adjusted weighting factors bring about better adherence to the target ranges for state parameters in the subsequent optimization 68. The optimization 68 with an optimization algorithm is carried out iteratively until the comparison 72 establishes a sufficient match between the resulting state parameters b̃ _j and the respective target ranges.

In 3 a result of many adjustments made is illustrated using a status parameter. A target range 80 is always in the permissible value range [-S _j , +S _j ]. -Sj and +S _j are also referred to as specification limits. Thus -S _j <s _j ^min ≦s j ^max <+S _j , where s _j ^min and s j ^max are the limits of the target area 80 . In the example of 3 it also holds that s _j ^min < s _j ^max . The lower limit s _j ^min can explicitly also be zero. Target ranges can be set for all state parameters b _j and other variables considered in the optimization. The state parameters b _j determined with an optimization are subject to a statistical distribution within the specification limits, ie a distribution of the state parameters b _j (population) results over many projection optics. The width of this distribution depends, among other things, on the flexibility of the system to assume different, equally valid values for state parameters during optimization. In 3 the scatter of a state parameter for many adjustments carried out in the case of an optimization without a target area is shown as an example as a solid curve 82 . In contrast, the scattering of state parameters in an optimization with a target area is shown as a dashed curve 84 . It can be clearly seen that the width of the statistical distribution is smaller for many adjustments with a target area than for adjustments without a target area. In other words, a target area reduces population spread.

4 shows an illustration of the result of many adjustments carried out using a status parameter with consideration of a target value. In this example, the limits of the target area are identical for the optimization, s _j ^min = s _j ^max . For example, the center of the target area is used as the target value. The target range thus transitions into a target value s _j . The solid curve 82 in turn represents the scatter of the values of a state parameter for many adjustments carried out in an optimization without a target range or target value. The maximum is identified by a solid line 86 . The scatter of the adjustment results, taking into account the target value s _j , is shown as a dashed curve 84 . When many adjustments are made with the target value s _j , there is a shift 88 in the population. The maximum of the scatter is now at that Target value s _j and becomes in 4 marked with a dashed line 90. By taking target ranges or target values into account, it is possible to influence the scattering of the values of state parameters when many adjustments are carried out. Target ranges and target values are therefore used for process and population control.

5 , 6 and 7 12 illustrate different target areas 80 for optimization. The values of the state parameters b ₁ , b ₂ , b _N-1 and b _N on the y-axis are shown graphically in coordinate systems as a function of the coordinate points or field points along the x-axis. According to 5 target ranges 80 are set only for values at single coordinate points. Target ranges 80 are set at two values each for b ₁ and b ₂ and at only one value for b _N-1 and b _N . In general, target ranges for one or more values can be specified individually for a status parameter. The same or different target areas 80 can be selected. The number and size of the target areas 80 for state values can be specified differently for different state parameters.

To 6 the same constant target range 80 is used for the values of state parameters at all coordinate points. As in 6 the same constant target range or target corridor can be defined for all values for all state parameters b ₁ to b _N . Alternatively, constant target ranges of different sizes can also be defined for different state parameters.

And finally, according to 7 individual target areas 80 defined for all coordinate points of a state parameter. The limits s _j ^min and sj ^max thus represent functions of the coordinate points. The limits can, for example, be step functions or other functions with jumps, functions with one or more break points, as for b ₁ , or smooth or differentiable functions, as for b ₂ , represent. The limits s _j ^min and s j ^max of these target areas, hereinafter also called target corridors, can run parallel or equidistant to one another, as for b ₁ , b ₂ and b _N-1 , or target areas of different widths can be used for different coordinate points, see the target corridor for b _N in 7 . Furthermore, such target corridors are set for only one, for several or for all status parameters. The target corridors are also individually defined differently for all status parameters, such as in 7 , or the same target corridors are used for several or all status parameters. Embodiments of the adjustment system 10, the control device 14 and the method 60 are configured to use one of the target areas described above or any combination of these target areas in an optimization.

In 5 , 6 and 7 Arrows 92 illustrate the adjustment 76 of the weighting factors a _j prior to a further optimization 68. In these exemplary embodiments, the adjustment takes into account the distance between the values of a state parameter and the center of the respective target area, which is shown as a dashed line 94. The center of the target area s For example, _j is taken as the arithmetic mean s _j = (s _j ^min + s _j ^max )/2. An adaptation 76 of the weighting factors a _j takes place before each iterative optimization 68, regardless of whether the values are in the target range 80 or not. Such a forced adjustment and optimization iteration for state parameters whose values are outside the respective target ranges, but also for state parameters whose values are within the respective target ranges, is 5 , 6 and 7 indicated by arrows 92 at the values for each coordinate point. In alternative exemplary embodiments, instead of the distance to the mean value, a distance to another value within the target range is taken into account when adjusting the weighting factors.

8th and 9 illustrate alternative adjustments of weighting factors a _j . Again, the values of the state parameters b ₁ , b ₂ , b _N−1 and b _N are shown graphically in coordinate systems as a function of the coordinate points or field points of the x-axis by way of example and schematically. According to 8th an adjustment of weighting factors a _j takes place only in the case of state parameters for which values lie outside the target range 80 . In 8th these are, for example, the state parameters b ₂ and b _N-1 , see arrows 92. The weighting factors a ₂ and a _N-1 are thus adjusted before an iterative optimization. According to the embodiment 8th the distance to the next limit s _j ^min or s j ^max is taken into account in an adjustment. As an example, fitting a ₂ scales with the deviation from sj ^max and fitting a _N-1 scales with the deviation from s _j ^min . The adjustment according to 9 corresponds to the selective adjustment after 8th except for the difference that the adjustment takes into account the distance to the more distant limit s _j ^min or s j ^max . For example, the adjustment of a ₂ now scales with the deviation from s _j ^min and the adjustment of a _N-1 with the deviation from s _j ^max , see arrows 92. In other exemplary embodiments, consideration of the distance from the center of the target area or from other values within the target range are selective for the state parameters whose values are outside the associated target range.

In all of the exemplary embodiments described here, damping for the weighting factor can also be provided when optimizing the quality function. With such a damping, excessive changes in the weighting factor and the resulting build-up effects are prevented. Damping is done, for example, by means of a global additional factor, a limitation of the value range of a weighting factor, damping proportional to the rate of change of a weighting factor between two iterations of optimization, damping proportional to the rate of change of a state parameter between two iterations of optimization, or any combination of these dampings.

10 shows an optimization with a lead for values of state parameters according to a further embodiment. To illustrate this, in 10 the values of a state parameter b _j and the associated target area are shown in coordinate systems at four consecutive points in time I to IV. Here, too, the coordinate points or field points are plotted on the x-axis. Coordinate system I shows the state values before optimization. The target range 80 is in the negative range and all values of the state parameter are outside the target range. From these values and the target range, for example, the respective mean value s _j of the target area, shown as dashed line 94, subtracted as a lead. The result is shown in coordinate system II. The mean of the target area 80 is now at zero and the values of the state parameter b _j are shifted upwards accordingly. The target area 80 centered around zero facilitates the optimization now carried out. The result of the optimization is shown in coordinate system III. All values of the state parameter are now within the target range. The end result shown in coordinate system IV results from the subsequent addition of the lead to the values and the target range.

In 11 another example of optimization with a lead is shown. In the coordinate system I, the values of a state parameter b _j are plotted over discrete field points or coordinate points. Some values are outside the target range 80 with non-constant limits s _j ^min and s _j ^max . As described above, these limits can take any shape. The arrows 92 indicate that an adjustment of the weighting factor a _j with the distance from the center s _j of the target area is to be scaled. To simplify the optimization, the center of the respective target area is subtracted beforehand s _j as an offset from the values of the state parameter and the target range 80. The result of this subtraction is shown in coordinate system II. The target range is now symmetrical around zero and the course of the values of the state parameter has changed accordingly. However, the respective distances, arrows 82, from the middle of the target area have remained the same. The adaptation of the weighting factor a _j is not changed by the derivative action. However, the optimization can be carried out much more easily and in less time. After the optimization, the derivative action is again added to the determined values of the state parameters.

The above description of exemplary embodiments, embodiments or embodiment variants is to be understood as an example. The disclosure thus made will enable those skilled in the art to understand the present invention and the advantages attendant thereto, while also encompassing variations and modifications to the described structures and methods that would become apparent to those skilled in the art. Therefore, all such alterations and modifications insofar as they come within the scope of the invention as defined in the appended claims, and equivalents, are intended to be covered by the protection of the claims.

reference list

10

adjustment system

12

measuring device

14

control device

16

projection lens

18

lighting device

20

measuring radiation

22

measurement mask

24

object level

26

sensor element

28

picture plane

30

detector

32

evaluation device

34

state characterization

36

post-processing facility

38

Travel command in the form of a travel variable

40

tilt axis

42

Limits target areas

44

weighting factors

46

optimization module

48

value determination module

50

comparison module

52

customization module

60

Method of controlling a manipulator

62

Measurement

64

Provision of measured values

66

Provision of target ranges and weighting factors

68

Run optimization

70

determining values of the state parameters

72

Compare to target areas

74

Adjust travel

76

Adjust weighting factors

80

target areas

82

Scatter of state parameter values without target range

84

Scatter of state parameter values with target range

86

Maximum with no target range

88

displacement maximum

90

Maximum with target range

92

Arrows weight change

94

center of target area

E1 - E4

optical elements

M1 - M4

manipulators

xi

Travel for manipulators

Travel for correction asphere post-processing device

bj

State parameters as image errors (Zernike coefficients)

sj

Target range limit

aj

weight factor

sjmax

upper limit of target range

sjmin

lower limit of target range

sj

center of target area

+Sj

upper limit of the permissible range of values for status parameters

-Sj

lower limit of the permissible range of values for status parameters

QUOTES INCLUDED IN DESCRIPTION

This list of the documents cited by the applicant was generated automatically and is included solely for the better information of the reader. The list is not part of the German patent or utility model application. The DPMA assumes no liability for any errors or omissions.

Patent Literature Cited

• WO 2010/034674 A1 [0006]
• DE 102015206448 A1 [0006, 0010, 0065]
• DE 102019200218 B3 [0006]
• DE 102019200218 A1 [0010]
• US 2013/0188246 A1 [0041]

Claims (15)

Control device (14) for controlling at least one manipulator (M1-M4, 36) for changing a parameter of a projection lens (16) for microlithography by generating a specification for a travel variable (38) which, by means of the manipulator (M1-M4, 36 ) defines the change to be made in the parameter along a travel (x _i ), the control device being configured to calculate the specification from a state characterization (34) of the projection lens (16) comprising a plurality of state parameters (b _j ) by at least once executing an optimization algorithm for optimizing a To generate a quality function, the quality function comprising at least one penalty term, which has a limit value (s _j ) of a target range (80) for one of the state parameters (b _j ) and a weighting factor (a _j ) for the limit value, the target range (80) is within a permissible value range of the state parameter (b _j ), and wherein the control device is further configured, after a first execution of the optimization algorithm, to determine the value of the state parameter achieved by means of the optimization result and to compare it with the limit value (s _j ), and in the event that the determined value of the state parameter is outside the target range (80) is to change the weighting factor (a _j ) and run the optimization algorithm again. control device claim 1 , in which the penalty term contains a quotient whose denominator has the limit value (s _j ) of the target area (80) for one of the state parameters (b _j ) and the weighting factor (a _j ) for the limit value. control device claim 2 , where the quotient is the base of a power with an even exponent. control device claim 2 or 3 , in which the numerator of the quotient contains the state parameter (b _j ) in the form of an image error of the projection lens (16). Control device according to one of claims 2 until 4 , which is configured to control a plurality of manipulators (M1-M4, 36), the state parameters (b _j ) form a state vector and the numerator of the quotient includes a sensitivity matrix which shows a relationship between the travels (x _i ) of the manipulators (M1-M4 , 36) and the state vector. Control device according to one of the preceding claims, wherein the control device is configured to use the specification for the travel variable (38) determined during the previous execution of the optimization algorithm as the starting value when the optimization algorithm is executed again. Control device according to one of the preceding claims, wherein the control device is configured to repeat the optimization algorithm with a changed weighting factor (a _j ) until the determined value of the state parameter is within the target range (80). Control device according to one of the preceding claims, wherein when changing the weighting factor (a _j ) a deviation of the determined value of the state parameter from the limit value (s _j ) is taken into account. Control device according to one of the preceding claims, wherein when the weighting factor (a _j ) changes, the limit of the target range (80) that is closer to the determined value of the state parameter, the limit of the target range (80) that is further away from the determined value of the state parameter, or the mean value of the target range ( 80) is taken into account. Control device according to one of the preceding claims, in which a target area (80) is specified only for specific individual coordinate points of a state parameter (b _j ). Control device according to one of the preceding claims, wherein individual target areas (80) are specified for all coordinate points of a state parameter (b _j ). Controller according to one of the preceding claims, wherein the controller is configured to take into account an attenuation for the weighting factor (a _j ) in the optimization of the merit function. Control device according to one of the preceding claims, wherein the control device is configured to subtract a lead from a state parameter (b _j ) before an optimization of the quality function and to add the lead again after the optimization. Adjustment system (10) for adjusting a projection objective (16) for microlithography by changing a parameter of the projection objective (16) using at least one manipulator (M1-M4, 36), the adjustment system comprising: - a measuring device (12) for determining the state characterization (34) of the projection lens (16), and - a control device (14) according to one of the preceding claims for generating a specification for a travel variable (x), which is a means of the manipulator (M1- M4, 36) defined change of the parameter to be carried out. Method (60) for controlling at least one manipulator (M1-M4, 36) for changing a parameter of a projection lens (16) for microlithography, with the steps: - generating a specification for a travel variable (x), which is set by means of the manipulator (M1 -M4, 36) defines the change to be made in the parameter along a travel (x _i ) from a state characterization (34) of the projection lens (16) comprising a plurality of state parameters by at least once executing (68) an optimization algorithm for optimizing a quality function, the quality function being at least comprises a penalty term which has a limit value (s _j ) of a target range (80) for one of the state parameters (b _j ) and a weighting factor (a _j ) for the limit value, and wherein the target range (80) is within an allowable value range of the state parameter ( b _j ) lies, - determining (70) the value of the state parameter based on the optimization result after executing the optimization algorithm, - comparing (72) the determined value of the state parameter with the limit value (s _j ), and - if the determined value of the state parameter is outside the target range (80), changing (76) the weighting factor (a _j ) and rerun (68) the optimization algorithm.

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