DE102020210567B3 - Control device and method for controlling manipulators for a projection lens, adjustment system, projection lens and projection exposure system - Google Patents

Abstract

A control device (14) for controlling manipulators (M1-M4, 36) for changing an optical behavior of a projection lens (16) for microlithography by generating respective specifications (38) for several travel variables, which manipulations to be carried out by means of the manipulators on at least one optical Element (E1-E4) of the projection lens for changing state parameters (34) of the projection lens is provided. The control device is configured to use a first optimization algorithm (74) to generate a respective approximation (38-1) of the specifications for the travel variables by optimizing a uniform scaling factor (86) which, in secondary conditions (82) of the first optimization algorithm, has a uniform scaling of defined limit values (84) for the individual state parameters, and in the event that an optimization result (87) determined by means of the first optimization algorithm for the uniform scaling factor does not exceed a predetermined threshold value (85), a respective end result (38) of the specifications for the To determine travel variables by means of at least one further optimization algorithm (76, 78).

Description

Background of the invention

The invention relates to a control device and a method for controlling manipulators for changing an optical behavior of a projection objective for microlithography. The invention also relates to an adjustment system for adjusting a projection lens for microlithography, a projection lens for a projection exposure system for microlithography with such a control device, and a projection exposure system for microlithography with such a projection lens.

A projection exposure system for microlithography is used in the production of semiconductor components to produce structures on a substrate in the form of a semiconductor wafer. For this purpose, the projection exposure system comprises a projection objective having a plurality of optical elements for imaging mask structures on the wafer during an exposure process.

To ensure that the mask structures are mapped onto the wafer as precisely as possible, a projection objective with the lowest possible wavefront aberrations is required. Projection objectives are therefore equipped with manipulators which make it possible to correct wavefront errors by changing the state of individual optical elements of the projection objective. Examples of such a change in state include: a change in position in one or more of the six rigid body degrees of freedom of the relevant optical element, an application of heat and / or cold to the optical element. Furthermore, one or more post-processing devices can also be provided for changing the shape of an optical element by removing material from an optical element by means of surface processing. Such a post-processing device can be part of the projection lens or also separate from it and is also referred to as a manipulator in the context of this text.

The calculation of manipulator changes to be carried out to correct an aberration characteristic of a projection lens is carried out by means of an optimization algorithm that generates travel, which is also referred to as the “manipulator change model”. Such optimization algorithms are for example in WO 2010/034674 A1 described.

mit $$NB:B_k\left(x\right)\le spe{c}_k^x$$

For example, optimization algorithms known from the prior art can be configured to solve the following optimization problem: $$\text{min}{\Vert \mathrm{M.}x-b_{mess}\Vert }_2^2$$

with $$N\mathrm{B.}:{\mathrm{B.}}_k\left(x\right)\le spe{c}_k^x$$

beschriebene Zielfunktion, auch Gütefunktion oder Meritfunktion bezeichnet, unter Berücksichtigung von durch $B_k\left(x\right)\le spe{c}_k^x$

beschriebenen Nebenbedingungen zu minimieren. Hierbei bezeichnet M eine Sensitivitätsmatrix, x einen Stellwegvektor mit Stellwegsvariablen X_k für die einzelnen Manipulatoren, bmess einen Zustandsvektor des Projektionsobjektivs, welcher die einzelnen Zustandsparameter einer gemessenen Aberrationscharakteristik des Projektionsobjektivs beschreibt, || ||₂ die Euklidische Norm und $spe{c}_k^x$

einen jeweiligen festen Grenzwert für einzelne Stellwegsvariablen x_k .Such an optimization problem is configured to be caused by ${\Vert \mathrm{M.}x-b_{mess}\Vert }_2^2$

target function described, also called quality function or merit function, taking into account by ${\mathrm{B.}}_k\left(x\right)\le spe{c}_k^x$

to minimize the constraints described. M denotes a sensitivity _{matrix, x a travel vector with travel variables X k} for the individual manipulators, bmess a state vector of the projection lens which describes the individual state parameters of a measured aberration characteristic of the projection lens, || || ₂ the Euclidean norm and $spe{c}_k^x$

a respective fixed limit value for individual travel variables x _k .

In order to ensure that limit values provided for the state parameters of the projection lens, in particular the image errors of the projection lens, are complied with, suitable penalty terms are conventionally included in the objective function. Such punishment terms essentially represent “soft” limit values or target values which, depending on the weighting and, if applicable, degree of severity of the punishment term in question, are adhered to or possibly exceeded to a certain extent.

_{Such penalty terms H b} contained in the objective function for limiting the state parameters of the projection lens are shown in DE10 2015 206 448 A1 shown as follows: $$H_b={{\displaystyle \sum _j\left(\frac{{\left(\mathrm{M.}x-b\right)}_j}{t_j^b\ast {\mathrm{S.}}_j^b}\right)}}^{2n_j^b}$$

jeweilige Zielwerte bzw. Spezifikationen für entsprechende Zustandsparameter des Projektionsobjektivs in Form von Zernike-Koeffizienten b_j . Weiterhin bezeichnen $t_j^b$

und $n_j^b$

vom Benutzer je nach Gewichtung und Härtegrad des betreffenden Bestrafungsterms frei wählbare Parameter.Designate here ${\mathrm{S.}}_j^b$

respective target values or specifications for corresponding state parameters of the projection lens in the form of Zernike coefficients b _j . Continue to denote $t_j^b$

and $n_j^b$

Parameters freely selectable by the user depending on the weighting and severity of the punishment term in question.

Further prior art can be found in the document DE10 2019 200 218 B3 .

To determine a so-called recipe for the manipulators of the projection lens, i.e. specifications for the travel variables of the manipulators, several iterations of the optimization algorithm are usually required, in which the weightings and, if necessary, the severity of the punishment terms are varied until the limit values for the condition parameters are maintained sufficiently well. This is a very time-consuming process, especially since, if a valid recipe is not found, one does not know whether one does not exist. In this context, a permissible recipe is understood to mean specifications for the travel variables of the manipulators. In the case of a permissible recipe, the specifications for the travel variables are selected in such a way that the specifications of the respective secondary conditions are complied with.

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, a recipe for the travel variables can be found in a comparatively short period of time.

Solution according to the invention

The aforementioned object can be achieved according to the invention, for example, with a control device for controlling manipulators for changing an optical behavior of a projection lens for microlithography by generating respective specifications for several travel variables, which manipulations to be carried out by means of the manipulators on at least one optical element of the projection lens for changing state parameters of the projection lens. The control device according to the invention is configured to use a first optimization algorithm to generate a respective approximation of the specifications for the travel variables by optimizing a uniform scaling factor which, in secondary conditions of the first optimization algorithm, defines a uniform scaling of limit values specified for the individual state parameters. Furthermore, the control device according to the invention is configured to determine a respective final result of the specifications for the travel variables using at least one further optimization algorithm in the event that an optimization result for the uniform scaling factor determined by means of the first optimization algorithm does not exceed a predetermined threshold value.

In other words, the respective final result of the specifications for the travel variable is determined by means of the at least one further optimization algorithm when the optimization result of the first optimization result for the uniform scaling factor is at most the specified control value. In this text, an “adjustment path” is understood to mean a change in a state parameter of one or more optical elements along the adjustment path by means of manipulator actuation for the purpose of changing the optical effect of the optical element or elements. The manipulation can consist, for example, of shifting the optical element in a special direction, but also, for example, in particular local or areal exposure of the optical element with heat, cold, forces, light of a certain wavelength or currents. Furthermore, the manipulation can define a material removal to be carried out on an optical element by means of a post-processing device.

The status parameters can in particular be image errors of the projection lens. The scaling factor can also be referred to as the target achievement variable. Such a target achievement variable describes a standardized distance between the limit values and the corresponding state parameters.
For example, the value 1 can be specified as the threshold value, ie the specified limit values are all adhered to. Furthermore, a higher value can be set as the threshold value. In this case it is at least known to what extent the limit values are exceeded.

The first optimization algorithm enables a reliable determination of whether a permissible recipe exists for a set of status parameters of the projection exposure system, i.e. whether the control device can determine specifications for the travel variables, whereby the limit values specified in the secondary conditions are adhered to. The first optimization algorithm and / or the second optimization algorithm are configured in particular to solve a non-linear optimization problem.

By generating a uniform scaling factor according to the invention by means of the first optimization algorithm, if the question whether the optimization result for the uniform scaling factor is at most the specified threshold value is answered positively, it can be safely assumed that a permissible recipe exists and thus the final result of the specifications for the travel variables can be found without adding several iterations of the further optimization algorithm with variation of Having to carry out weights. This means that the recipe for the travel variables can be found in a very time-efficient manner. In particular, it becomes possible to formulate the constraints as hard constraints that are reliably met, such as explicit constraints. Explicit secondary conditions are understood as secondary conditions which are not part of the relevant objective function, as is the case with the punishment terms used in the prior art.

According to a further embodiment, the control device is further configured to execute a state parameter optimization algorithm when executing the at least one further optimization algorithm, in which a weighted sum of individual scaling factors is optimized, taking into account the state parameter constraints relating to the state parameters, the individual scaling factors being included in the state parameters Secondary conditions define a respective scaling of the limit values specified for the individual status parameters.

In particular, the further secondary conditions, taking account of which the weighted sum of individual scaling factors is optimized, correspond to the previously mentioned explicit additional secondary conditions. In particular, when executing the at least one further optimization algorithm, the specifications for the travel variables are generated, taking into account the further secondary conditions, by optimizing the weighted sum of the individual scaling factors. In other words, the weighted sum of the individual scaling factors forms the objective function of the state parameter optimization algorithm. Scaling the specified limit values with respective individual scaling factors is to be understood as meaning that each of the limit values is assigned one of several individual scaling factors with which the respective limit value is then scaled. The status parameter secondary conditions in particular also include the limit values for the individual status parameters. The state parameter optimization algorithm is configured in particular to solve a non-linear optimization problem.

According to a further embodiment, the control device is further configured to execute a travel optimization algorithm when executing the at least one further optimization algorithm, in which a target function having the travel variables is optimized. In particular, the state parameter optimization algorithm is configured to solve a non-linear optimization problem.

According to a further embodiment, the control device is configured, when executing the at least one further optimization algorithm, to first execute the state parameter optimization algorithm and then the travel optimization algorithm, the travel optimization algorithm being configured to the target function taking into account the condition that further individual scaling factors to optimize the optimization results determined by the state parameter optimization algorithm for the corresponding first individual scaling factors by a maximum of 5%, in particular by a maximum of 1%. The condition mentioned is in particular part of travel optimization secondary conditions, which in particular continue to include the limit values for the individual status parameters. This relaxation for the further individual scaling factors gives the travel optimization algorithm leeway to find an optimized solution for the target function having the travel variables.

According to a further embodiment, the control device is also configured to base the travel optimization algorithm on further approximations of the specifications for the travel variables, which are determined when the state parameter optimization algorithm is executed.

According to a further embodiment, the state parameter constraints also include the condition that each of the first individual scaling factors may exceed the optimization result for the uniform scaling factor determined by the first optimization algorithm by a maximum of 5%, in particular by a maximum of 1%. This relaxation for the individual scaling factors gives the state parameter optimization algorithm leeway to find an optimized solution for the weighted sum of the individual scaling factors.

According to a further embodiment, the target function of the travel optimization algorithm contains the travel variables in at least quadratic form, i.e. in a power at which the exponent is at least two.

According to a further embodiment, the control device is further configured to base the at least one further optimization algorithm on the approximations of the specifications for the travel variables as starting values.

According to a further embodiment, the secondary conditions of the first optimization algorithm are formulated as explicit secondary conditions, which are not part of an objective function optimized during the execution of the first optimization algorithm. An explicit constraint is understood to be a constraint that is not part of the objective function, in contrast to this, an implicit constraint is part of the objective function. According to further embodiments, the status parameter secondary conditions and / or the secondary conditions on which the travel optimization algorithm is based are also formulated as explicit secondary conditions.

According to a further embodiment, the specifications determined for the travel variables define changes to be made in the state parameters of the projection lens by means of the manipulators. In particular, they define both changes to be made to status parameters of the projection lens and changes to be made to status parameters of the projection exposure system that do not relate to the projection lens, such as status parameters related to an illumination system of the projection exposure system.

Furthermore, an adjustment system for adjusting a projection objective for microlithography is provided according to the invention. The adjustment system comprises a measuring device for determining current values of state parameters of the projection lens and a control device according to one of the embodiments or design variants described above for generating the specifications for the travel variables from the current values of the state parameters.

Furthermore, according to the invention, a projection objective for a projection exposure system for microlithography is provided which comprises manipulators which are configured to change state parameters of the projection objective. Furthermore, the projection lens comprises a control device according to one of the embodiments or design variants described above for controlling the manipulators.

Furthermore, according to the invention, a projection exposure system for microlithography is provided which comprises the projection objective described above.

The aforementioned object can also be achieved, for example, with a method for controlling manipulators for changing an optical behavior of a projection objective for microlithography by generating respective specifications for several travel variables. The travel variables define manipulations to be carried out by means of the manipulators on at least one optical element of the projection objective in order to change state parameters. The method according to the invention comprises generating a respective approximation of the specifications for the travel variables by optimizing a uniform scaling factor by means of a first optimization algorithm, the uniform scaling factor defining a uniform scaling of limit values specified for the individual state parameters in secondary conditions of the first optimization algorithm, as well as for the case that an optimization result for the uniform scaling factor determined by means of the first optimization algorithm does not exceed a predetermined threshold value, a respective end result of the specifications for the travel variables is determined by means of at least one further optimization algorithm.

According to one embodiment of the method according to the invention, the respective final result of the specifications for the travel variables is determined by means of the at least one further optimization algorithm, taking into account explicit further secondary conditions for the state parameters of the projection lens, which are not part of a target function optimized when executing the at least one further optimization algorithm .

The features specified with regard to the above-mentioned embodiments, exemplary embodiments or design variants, etc. of the control device according to the invention can be transferred accordingly to the control method according to the invention. 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 that can be independently protected and whose protection may only be claimed during or after the application is pending.

Figure list

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

• 1 an adjustment system for adjusting a projection lens of a projection exposure system for microlithography with a control device for generating a travel command for manipulators,
• 2 a projection exposure system for microlithography with a control device for generating a travel command for manipulators, as well as
• 3 an illustration of the mode of operation of an embodiment of the aforementioned control device.

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, in order to understand the features of the individual elements of a particular exemplary embodiment, reference should be made to the description of other exemplary embodiments or the general description of the invention.

To facilitate the description, a Cartesian xyz coordinate system is indicated in the drawing, 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, the x-direction to the right and the z-direction upwards.

1 shows an adjustment system 10 for adjusting a projection lens 16 a projection exposure system for microlithography. The adjustment system 10 comprises a measuring device 12th to determine imaging errors of the projection lens 16 characterizing state parameters 34 of the projection lens 16 and a control device 14th in the form of a so-called steep path determiner for generating a travel command 38 with specifications 38n and 38p for travel variables x _k of manipulators from the state parameters 34 . The specifications 38n and 38p are also used in this text as a travel vector x denotes and defines manipulations to be carried out by means of manipulators on at least one optical element E1 to E4 of the projection objective 16 which are described in more detail below.

The projection lens 16 is used to map mask structures from an object plane 24 in an image plane 28 and can be designed for exposure radiation of different wavelengths, such as 248 nm or 193 nm. In the present embodiment, the projection lens is 16 designed for a wavelength in the EUV wavelength range of less than 100 nm, for example about 13.5 nm or about 6.8 nm.

The measuring device 12th is for measuring wavefront errors of the projection lens 16 configured and comprised on the input side of the projection lens 16 a lighting device 18th and a measurement mask 22nd as well as on the exit side of the projection lens 12th a sensor element 26th , a detector 30th as well as an evaluation device 32 . The lighting device 18th is configured to use a measuring radiation 20th with the operating wavelength of the projection lens to be tested 16 , in the present case in the form of EUV radiation, and to generate this on the measurement mask 22nd , which in the object level 24 is arranged to radiate. The measurement mask 22nd , often also called “coherence mask”, has a first periodic structure. In the image plane 28 is the sensor element 26th arranged in the form of an image grid which has a second periodic structure. Checkerboard structures can also be used in the measurement mask 22nd with checkerboard structures in the sensor element 26th be combined. Other combinations of periodic structures known to those skilled in the art from the field of shear interferometry or point diffraction interferometry can also be used.

Below the sensor element 26th , in one to the pupil plane of the projection lens 16 conjugate plane, is the two-dimensional resolving detector 30th arranged in the form of a camera. The sensor element 26th and the detector 30th together form a sensor module. The measurement mask 22nd , and the sensor module form a shear interferometer or point diffraction interferometer known to the person skilled in the art and serve to detect wavefront errors in the projection lens 16 to measure. For this purpose, phase shifting methods known to the person skilled in the art are used in particular.

The evaluation device 32 determined from the by the detector 30th recorded intensity patterns the state parameters 34 of the projection lens 16 . According to the present embodiment, the state parameters include 34 one the wavefront errors of the projection lens 16 characterizing set of Zernike coefficients b _j .

gemäß der sogenannten Fringe-Sortierung mit Z_j bezeichnet werden, wobei dann b_j die den jeweiligen Zernike-Polynomen (auch „Zernike-Funktionen“ bezeichnet) zugeordnete Zernike-Koeffizienten sind. 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,Φ) an einem Punkt in der Bildebene des Projektionsobjektivs wird in Abhängigkeit von den Polarkoordinaten (ρ, Φ) in der Pupillenebene wie folgt entwickelt: $$W\left(\rho ,\mathrm{\Phi }\right)={\displaystyle \sum _j{b}_j\cdot Z_j\left(\rho ,\mathrm{\Phi }\right)}$$

In the present application, as for example in sections [0125] to [0129] of US 2013 / 0188246A1 described consisting eg Chapter 13.2.3 of the textbook "Optical Shop Testing", ^2nd Edition (1992) by Daniel Malacara, Ed., John Wiley & Sons, Inc. known Zernike $Z_m^n$

_{are designated by Z j} according to the so-called fringe sorting, in which case b _j which are Zernike coefficients assigned to the respective Zernike polynomials (also referred to as “Zernike functions”). 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, Φ) at a point In the image plane of the projection lens, the following is developed as a function of the polar coordinates (ρ, Φ) in the pupil plane: $$\mathrm{W.}\left(\rho ,\mathrm{\Phi }\right)={\displaystyle \sum _j{b}_j\cdot Z_j\left(\rho ,\mathrm{\Phi }\right)}$$

While the Zernike polynomials _{are denoted by Z j} , ie with subscript j, in the context of this application the Zernike coefficients are denoted by b _j designated. At this point it should be noted that the Zernike coefficients b _j often also with Zj, ie with a normal index, such as Z5 and Z6 for astigmatism.

für Manipulatoren M1 bis M4 des Projektionsobjektivs 16, wobei L eine Zählvariable für mittels der Manipulatoren M1 bis M4 ansteuerbaren Stellwegsvariablen x_k ist. Die Vorgaben 38n umfassen Stellwegsvorgaben $x_n^L$

zur Steuerung einer Nachbearbeitungseinrichtung 36 zur mechanischen Nachbearbeitung von optischen Elementen E1 bis E4 des Projektionsobjektivs 16, wobei L eine Zählvariable für mittels der Nachbearbeitungseinrichtung 36 ansteuerbaren Stellwegsvariablen x_k ist.The from the evaluation device 32 the measuring device 12th Determined condition characterization 34 is sent to the control device 14th passed, which from it the travel command 38 generated. As already mentioned above, the travel command includes 38 in the present exemplary embodiment the specifications 38n and 38p . The specifications 38p include travel specifications $x_{\mathrm{P.}}^{\mathrm{L.}}$

for manipulators M1 until M4 of the projection lens 16 , where L is a counting variable for using the manipulators M1 until M4 controllable travel variables x _k is. The specifications 38n include travel specifications $x_n^{\mathrm{L.}}$

for controlling a post-processing device 36 for mechanical post-processing of optical elements E1 to E4 of the projection lens 16 , where L is a counting variable for means of the post-processing device 36 controllable travel variables x _k is.

In the context of this application, both the manipulators M1 until M4 of the projection lens 16 as well as the post-processing facility 36 as manipulators for changing the optical behavior of the projection lens 16 , more precisely for performing manipulations on at least one of the optical elements E1 to E4 of the projection lens 16 for changing state parameters 34 of the projection lens 16 Understood.

The projection lens 16 has in the embodiment according to 1 four optical elements E1 until E4 on. All optical elements are movably mounted. To do this is each of the optical elements E1 until E4 a respective manipulator MS, specifically one of the manipulators M1 until M4 , assigned. The manipulators M1 , M2 and M3 enable the associated optical elements to be shifted in each case E1 , E2 and E3 in the x and y directions and thus essentially parallel to the plane in which the respective reflective surface of the optical elements lies.

The manipulator M4 is configured to use the optical element E4 by rotating around a tilting axis arranged parallel to the y-axis 40 to tilt. This makes the angle of the reflective surface of E4 changed compared to the incident radiation. Further degrees of freedom for the manipulators are conceivable. For example, a relevant optical element can be displaced transversely to its optical surface or a rotation about a reference axis perpendicular to the reflective surface.

Generally speaking, any of the manipulators depicted here are M1 until M4 provided for a displacement of the associated optical element E1 until E4 while executing a rigid body movement along one by means of the specifications 38p to effect defined travel. Such a travel can, for example, combine translations in different directions, tilts and / or rotations in any way. Alternatively or in addition, manipulators can also be provided which are configured to carry out a different type of change in a state variable of the assigned optical element by appropriate actuation of the manipulator. In this regard, actuation can take place, for example, by applying a specific temperature distribution or a specific force distribution to the optical element. In this case, the travel can be a change in the temperature distribution on the optical element or the application of a local voltage to an optical element designed as a deformable lens or as a deformable mirror.

welche von den Manipulatoren M1 bis M4 auszuführende Veränderungen vorgeben und damit der Steuerung der Manipulatoren M1 bis M4 des Projektionsobjektivs 16 dienen. Die ermittelten Stellwege $x_P^1,x_P^2,x_P^3\text{ sowie }{x}_P^4$

werden den einzelnen Manipulatoren M1 bis M4 über Stellwegsignale übermittelt und geben diesen jeweilige auszuführende Korrekturstellwege vor. Diese definieren entsprechende Verlagerungen der zugeordneten optischen Elemente M1 bis M4 zur Korrektur aufgetretener Wellenfrontfehler des Projektionsobjektivs 16. Für den Fall, in dem ein Manipulator mehrere Freiheitsgrade aufweist, können diesem auch mehrere Stellwege $x_P^L$

übermittelt werden.The one from the travel command 38 covered travel ranges 38p contain the travel ranges in the case shown $x_{\mathrm{P.}}^1,x_{\mathrm{P.}}^2,x_{\mathrm{P.}}^3\text{as}{x}_{\mathrm{P.}}^{\mathrm{4th}},$

which of the manipulators M1 until M4 Specify the changes to be made and thus the control of the manipulators M1 until M4 of the projection lens 16 to serve. The determined travel ranges $x_{\mathrm{P.}}^1,x_{\mathrm{P.}}^2,x_{\mathrm{P.}}^3\text{as}{x}_{\mathrm{P.}}^{\mathrm{4th}}$

are the individual manipulators M1 until M4 transmitted via travel signals and specify the respective correction travel to be carried out. These define corresponding displacements of the assigned optical elements M1 until M4 to correct wavefront errors that have occurred in the projection lens 16 . In the event that a manipulator has several degrees of freedom, it can also have several travel ranges $x_{\mathrm{P.}}^{\mathrm{L.}}$

be transmitted.

für die Nachbearbeitungseinrichtung 36 enthalten im gezeigten Fall die Stellwege $x_n^1,x_n^2,x_n^3\text{ und }{x}_n^4,$

welcher der Steuerung der Nachbearbeitungseinrichtung 36 zur jeweiligen mechanischen Nachbearbeitung der optischen Elementen E1, E2, E3 bzw. E4 des Projektionsobjektivs 16 dienen. Die Stellwege $x_n^1\text{ bis }{x}_n^4$

dienen damit, wie die Stellwege $x_P^1$

bis $x_P^4,$

der Korrektur aufgetretener Wellenfrontfehler des Projektionsobjektivs 16.The continue from the travel command 38 included specifications 38n $\left(x_n^{\mathrm{L.}}\right)$

for the post-processing facility 36 contain the travel ranges in the case shown $x_n^1,x_n^2,x_n^3\text{and}{x}_n^{\mathrm{4th}},$

which of the control of the post-processing device 36 for the respective mechanical post-processing of the optical elements E1 , E2 , E3 respectively. E4 of the projection lens 16 to serve. The travel ranges ${\mathrm{<figure-callout\; id="1"\; label="x\; n"\; filenames="DE102020210567B3\_0080.png,DE102020210567B3\_0081.png"\; state="\{\{state\}\}">x</figure-callout>}}_n^{}\text{until}{x}_n^{\mathrm{4th}}$

thus serve as the travel ranges $x_{\mathrm{P.}}^1$

until $x_{\mathrm{P.}}^{\mathrm{4th}},$

the correction of wavefront errors that have occurred in the projection lens 16 .

Under the post-processing facility 36 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 takes place after the production of the optical element. A correspondingly reworked optical element is therefore also referred to as an intrinsically corrected asphere (ICA). As a post-processing facility 36 In particular, a removal device usually used for the mechanical processing of ICAs can be used. The erosions are therefore also referred to below as "ICA erosions". An ion beam, for example, can be used for mechanical processing. This allows any correction profiles to be incorporated into a post-processed optical element.

2 shows an embodiment according to the invention of a projection exposure apparatus 50 for microlithography. The present embodiment is designed for operation in the EUV wavelength range. Because of this operating wavelength, all optical elements are designed as mirrors. However, the invention is not limited to projection exposure systems in the EUV wavelength range. Further embodiments according to the invention are designed, for example, for operating wavelengths in the UV range, such as 365 nm, 248 nm or 193 nm, for example. In this case, at least some of the optical elements are configured as conventional transmission lenses.

The projection exposure system 50 according to 2 comprises an exposure radiation source 52 for generating exposure radiation 54 . In the present case, the exposure radiation source is 52 designed as an EUV source and can include, for example, a plasma radiation source. The exposure radiation 54 first goes through a lighting optic 56 and is put on a mask by this 58 steered. The lighting optics 56 is configured to have different angular distributions of the on the mask 58 incident exposure radiation 54 to create. The lighting optics are configured as a function of the lighting setting desired by the user, also known as the “lighting setting” 56 the angular distribution of the on the mask 58 incident exposure radiation 54 . Examples of lighting settings that can be selected include so-called dipole lighting, annular lighting and quadrupole lighting, and free-form lighting, ie an intensity distribution of the lighting profile that can be freely selected to a certain extent.

The mask 58 has mask structures for imaging on a substrate 64 in the form of a wafer and is on a mask shifting stage 60 movably mounted. The mask 58 can, as in 2 shown, designed as a reflection mask or alternatively, in particular for UV lithography, also be configured as a transmission mask. The exposure radiation 54 is in the embodiment according to 2 on the mask 58 reflects and then goes through this already with reference to the adjustment system 10 according to 1 projection lens described 16 . The projection lens 16 serves to the mask structures of the mask 58 on the substrate 64 map. The exposure radiation 54 is inside the projection lens 16 by means of a large number of optical elements E1 until E4 , in the present case in the form of mirrors. The substrate 64 is on a substrate transfer platform 66 movably mounted. The projection exposure system 50 can be designed as a so-called scanner or as a so-called stepper.

In the case of the implementation as a scanner, also referred to as a step and scan projection exposure system, the mask 58 on the substrate 64 , ie with each exposure of a field on the substrate 64 who have favourited the mask shifting platform 60 as well as the substrate transfer platform 66 moves in the opposite direction or in the same direction. As in 2 shown, moves the mask shifting stage, for example 60 in a left-facing scan direction 62 and the substrate shifting stage in a scanning direction pointing to the right 68 . So-called fading aberrations are due to the scanning movements during the field exposure of such a scanner and are explained in more detail below.

für die Manipulatoren M1 bis M4 umfasst. Die Zustandsparameter können mittels einer externen Wellenfrontmessvorrichtung, wie der in Bezug auf 1 beschriebenen Messvorrichtung 12, erhoben werden. Alternativ können die Zustandsparameter 34 aber auch von einer in der Substratverschiebebühne 66 integrierten Wellenfrontmesseinrichtung 70 gemessen werden. Die in der Projektionsbelichtungsanlage 50 enthaltene Steuerungsvorrichtung 14 kann gemäß einer weiteren Ausführungsform der Steuerungsvorrichtung 14 gemäß 1 entsprechen und einen Stellwegbefehl 38 generieren, der neben den Vorgaben 38p auch die Vorgaben 38n für die Nachbearbeitungseinrichtung 36 umfasst. In diesem Fall werden zunächst von der Nachbearbeitung betroffene optische Elemente E1 bis E4 aus dem Projektionsobjektiv 16 ausgebaut und anhand der Vorgaben 38n nachbearbeitet. Danach werden die optischen Elemente E1 bis E4 wieder in das Projektionsobjektiv 16 eingesetzt und der Vorgaben 38p mittels der Manipulatoren M1 bis M4 justiert.The projection exposure system 50 further comprises a control device 14th . In the illustrated embodiment, this differs only in this respect from the control device 14th according to 1 that the from the state parameters 34 generated travel command 38 only specifications 38p for the travel variables $x_{\mathrm{P.}}^{\mathrm{L.}}$

for the manipulators M1 until M4 includes. The state parameters can be determined by means of an external wavefront measuring device, such as that in relation to FIG 1 described measuring device 12th , be collected. Alternatively, the status parameters 34 but also from one in the substrate shifting platform 66 integrated wavefront measuring device 70 be measured. The one in the projection exposure system 50 included control device 14th can according to a further embodiment of the control device 14th according to 1 and a travel command 38 generate, in addition to the specifications 38p also the specifications 38n for the post-processing facility 36 includes. In this case, the optical elements affected by the post-processing are first of all affected E1 until E4 from the projection lens 16 expanded and based on the specifications 38n post-processed. After that the optical elements E1 until E4 back into the projection lens 16 used and the specifications 38p by means of the manipulators M1 until M4 adjusted.

The functioning of the control device 14th will be referred to below 3 exemplarily illustrated. This is for the execution of a travel-generating overall optimization algorithm 72 configured, the overall optimization algorithm 72 several individual optimization algorithms 74 , 76 and 78 includes.

The secondary conditions of the optimization problem include specification values or predetermined maximum values for the state parameters 34 of the projection lens 16 as well as specification values or maximum values for the travel variables x _k . The individual status parameters 34 are also shown below as ZPi, where i is a counting index.

The constraints related to the state parameters 34 of the projection lens 16 are generally represented as follows: $${\mathrm{B.}}_i\left(x\right)\le spe{c}_i^{Z\mathrm{P.}}$$

die Spezifikationswerte bzw. Grenzwerte für die mit dem Index i nummerierten Zustandsparameter ZPi des Projektionsobjektivs 16 und Bi(x) eine die jeweiligen Zustandsparameter des Projektionsobjektivs 16 umfassendes Funktional, ggf. in Abhängigkeit des Stellwegvektors x. Die Nebenbedingungen gemäß (2) umfassen gemäß einer Ausführungsform die folgenden Nebenbedingungsgruppen: $$\left|{\left(Mx-b\right)}_j\right|\le spe{c}_j^b$$

$$\delta f_i\le spe{c}_j^f$$

$$OV{L}_P\le spe{c}_p^{ovl},$$

sowie $$RM{S}^r\le spe{c}_r^{rms}$$

Here are $spe{c}_i^{Z\mathrm{P.}}$

the specification values or limit values for the state parameters ZPi of the projection lens numbered with the index i 16 and Bi ( x ) one of the respective state parameters of the projection lens 16 Comprehensive functionality, possibly depending on the travel vector x . According to one embodiment, the secondary conditions according to (2) include the following secondary condition groups: $$\left|{\left(\mathrm{M.}x-b\right)}_j\right|\le spe{c}_j^b$$

$$\delta f_i\le spe{c}_j^f$$

$$OV{\mathrm{L.}}_{\mathrm{P.}}\le spe{c}_p^{Ovl},$$

as $$\mathrm{R.}\mathrm{M.}{\mathrm{S.}}^r\le spe{c}_r^{rms}$$

die Spezifikation für den jeweiligen Zernike-Koeffizienten b_j , wobei der Index j von 1 bis $j_{max}^b$

läuft, d.h. die Zustandsparameter ZPi entsprechen in diesem Fall den Zernike-Koeffizienten b_j . Die Spezifikation $spe{c}_j^b$

entspricht den allgemeinen Spezifikationswerten $spe{c}_i^{ZP}$

aus Term (2) mit $\text{i}=1\text{ bis }{j}_{max}^b.$

M ist die bereits vorstehend erwähnte Sensitivitätsmatrix, welche den Zusammenhang zwischen einer Verstellung eines Freiheitsgrades k eines Manipulators um den Standard-Stellweg x_k ⁰ beschreibt.The secondary condition group in accordance with expression (3) relates to conditions for the individual Zernike coefficients b _j . Here is $spe{c}_j^b$

the specification for the respective Zernike coefficient b _j , where the index j is from 1 to $j_{max}^b$

running, ie the state parameters ZPi in this case correspond to the Zernike coefficients b _j . The specification $spe{c}_j^b$

corresponds to the general specification values $spe{c}_i^{Z\mathrm{P.}}$

from term (2) with $\text{i}=1\text{until}{j}_{max}^b.$

M is the previously mentioned sensitivity matrix, which describes the relationship between an adjustment of a degree of freedom k of a manipulator by the standard travel x _k ⁰ .

The expression δƒ _j from (4) reads: $$\delta f_i=\sqrt{{\displaystyle \sum _m{w}_m{\left({\mathrm{M.}}_f^{j}x-b_f^j\right)}_{\mathrm{<figure-callout\; id="2"\; label="m"\; filenames="DE102020210567B3\_0080.png,DE102020210567B3\_0082.png"\; state="\{\{state\}\}">m</figure-callout>}}^2}}$$

. Diese können aus den gemessenen Zernike-Aberrationen b_j berechnet werden. Weiterhin ist $spe{c}_j^f$

der Zielwert bzw. die vorgegebene Spezifikation für die Fading-Aberration $b_f^j,$

, wobei der Index j von 1 bis $j_{max}^f$

läuft. Das heißt, die Zustandsparameter ZPi entsprechen in diesem Fall den Fading-Aberration $b_f^j$

. Die Spezifikation $spe{c}_j^f$

entspricht den allgemeinen Spezifikationswerten $spe{c}_i^{ZP}$

aus Term (2) mit $\text{i}=j_{max}^b+1\text{ bis }{j}_{max}^b+j_{max}^f.$

Die Summe über den Index m geht über alle Feldpunkte entlang der Scan-Richtung der Projektionsbelichtungsanlage. Der Parameter w_m bezeichnet sogenannte Scan-Gewichte, d.h. Gewichtungen der Bildfehler, die auf die Scanbewegung zurückgehen. $M_f^j$

bezeichnet eine Sensitivitätsmatrix für die Fading-Aberrationen $b_f^j$

und definiert damit die Veränderung des Zustandsvektors b des Projektionsobjektivs aufgrund von Fading-Aberrationen bei Verstellung der Manipulatoren um einen Standardverstellweg x₀.The constraint group according to the expression (4) relates to conditions for so-called fading aberrations $b_f^j.$

. These can be obtained from the measured Zernike aberrations b _j be calculated. Furthermore is $spe{c}_j^f$

the target value or the specified specification for the fading aberration $b_f^j,$

, where the index j is from 1 to $j_{max}^f$

runs. That is to say, the state parameters ZPi correspond to the fading aberration in this case $b_f^j$

. The specification $spe{c}_j^f$

corresponds to the general specification values $spe{c}_i^{Z\mathrm{P.}}$

from term (2) with $\text{i}=j_{max}^b+1\text{until}{j}_{max}^b+j_{max}^f.$

The sum over the index m goes over all field points along the scan direction of the projection exposure system. The parameter w _m denotes so-called scan weights, ie weightings of the image errors that are due to the scanning movement. ${\mathrm{M.}}_f^j$

denotes a sensitivity matrix for the fading aberrations $b_f^j$

and thus defines the change in the state vector b of the projection lens due to fading aberrations when the manipulators are adjusted by a standard adjustment path x ₀ .

The constraint group according to expression (5) relates to conditions for overlay failure. Overlay errors are different for Structure types, such as isolated lines, lines arranged as grids, circular structures, etc. The different structure types are identified with the counter variable p. An overlay error depending on the structure type p and the field point m is described by the product (SZ ^p b) _m . S _Z ^p is a matrix which contains field point-dependent weights for the individual Zernike coefficients b _j includes. An overlay error (SZ ^p b) _m is thus caused by linear combinations of individual Zernike coefficients b _j educated.

The expression OVL _P from (5) is: $${\text{OVL}}_p={\text{Max}}_m\left({\left(\mathrm{S.}{Z}^p\mathrm{M.}x-\mathrm{S.}{Z}^{p}b\right)}_m\right)$$

der Zielwert bzw. die vorgegebene Spezifikation für den Overlay-Fehler des Strukturtyps p, wobei der Index p von 1 bis pmax läuft. Das heißt, die Zustandsparameter ZPi entsprechen in diesem Fall den Overlay-Fehlern (SZ^pb)_m . Die Spezifikation $spe{c}_p^{ovl}$

entspricht den allgemeinen Spezifikationswerten $spe{c}_i^{ZP}$

aus Term (2) mit $\text{i}=j_{max}^b+j_{max}^f+1\text{ bis }{j}_{max}^b+j_{max}^f+{\text{p}}_{\text{max}}.$

Die Matrix M ist die bereits vorstehend mit Bezug auf die Nebenbedingungsgruppe bezüglich der Bildfehler beschriebene Sensitivitätsmatrix. Die max-Funktion bestimmt das Maximum über alle Feldpunkte m.Furthermore is $spe{c}_p^{Ovl}$

the target value or the specified specification for the overlay error of the structure type p, with the index p running from 1 to pmax. This means that the state parameters ZPi in this case correspond to the overlay errors (SZ ^p b) _m . The specification $spe{c}_p^{Ovl}$

corresponds to the general specification values $spe{c}_i^{Z\mathrm{P.}}$

from term (2) with $\text{i}=j_{max}^b+j_{max}^f+1\text{until}{j}_{max}^b+j_{max}^f+{\text{p}}_{\text{Max}}.$

The matrix M is the sensitivity matrix already described above with reference to the secondary condition group with regard to the image defects. The max function determines the maximum over all field points m.

The constraint group according to expression (6) relates to conditions for grouped RMS values. RMS ^r is defined as follows: $${\text{RMS}}^r=\underset{m}{{\displaystyle \text{Max}}}\sqrt{{\displaystyle \sum _j\left({\alpha }_j^r{\left(\mathrm{M.}x-b\right)}_{j,m}^2\right)}}$$

sind die Gewichte der individuellen Zernike-Beiträge b_j zum RMS-Wert mit dem Index r und das Maximum wird über alle Feldpunkte m des Bildfeldes des Projektionsobjektivs 16 ermittelt. Die gruppierten RMS-Werte RMS^r umfassen gemäß unterschiedlichen Ausführungsformen jeweils eine Gruppe an Zernike-Koeffizienten Zj mit gleichzahliger azimutaler Welligkeit, typischerweise alle Zernike-Koeffizienten Zj mit der betreffenden azimutalen Welligkeit (z.B. 2-zählige oder 4-zählige azimutale Welligkeit) bis zu einer bestimmten radialen Welligkeit (d.h. radiale Welligkeit ≤ maximale radiale Welligkeit). Zum Beispiel umfasst der gruppierte-RMS Wert „RMS_AST_0“ die Zernike-Koeffizienten Zj mit j = 12, 21, 32, ... und der gruppierte RMS-Wert „RMS_Coma_x“ die Zernike-Koeffizienten Zj mit j = 7, 14, 23 sowie 34. In den im Ausdruck (6) angegebenen Bedingungen für die RMS-Werte RMS^r ist $spe{c}_r^{rms}$

die vorgegebene Spezifikation für den RMS-Wert mit dem Index r. Das heißt, die Zustandsparameter ZPi entsprechen in diesem Fall den RMS-Werten RMS^r.Here r is a counting variable of the grouped RMS value RMS ^r . The grouping takes place, for example, by classifying the corresponding Zernike coefficients b _j into the categories "spherical aberrations", "coma", "astigmatism", etc. The sum over j is a sum over the Zernike orders, ${\alpha }_j^r$

are the weights of the individual Zernike contributions b _j to the RMS value with the index r and the maximum is over all field points m of the image field of the projection lens 16 determined. According to different embodiments, the grouped RMS values RMS ^r each include a group of Zernike coefficients Zj with equal azimuthal ripple, typically all Zernike coefficients Zj with the relevant azimuthal ripple (eg 2-fold or 4-fold azimuthal ripple) up to one certain radial ripple (i.e. radial ripple ≤ maximum radial ripple). For example, the grouped RMS value “RMS_AST_0” includes the Zernike coefficients Zj with j = 12, 21, 32, ... and the grouped RMS value “RMS_Coma_x” includes the Zernike coefficients Zj with j = 7, 14, 23 and 34. In the conditions for the RMS values given in expression (6), RMS ^r is $spe{c}_r^{rms}$

the specified specification for the RMS value with the index r. This means that the status parameters ZPi in this case correspond to the RMS values RMS ^r .

unter den folgenden expliziten Nebenbedingungen: $$t_s\ge \mathrm{0,}$$

$$B_i\left(x\right)\le t_s\cdot spe{c}_i^{ZP},$$

sowie $$B_k\left(x\right)\le spe{c}_k^x$$

As mentioned above, comprised by the control device 14th executed overall optimization algorithm 72 several individual optimization algorithms. The first of these optimization algorithms, in 3 with the reference number 74 called, optimizes the following, in 3 with the reference number 80 designated objective function F, often also called quality function or merit function: $$\text{F.}\left(x,t_s\right)=t_s;\text{d}.\text{H}.\text{F.}\to \text{min}$$

under the following explicit constraints: $$t_s\ge \mathrm{0,}$$

$${\mathrm{B.}}_i\left(x\right)\le t_s\cdot spe{c}_i^{Z\mathrm{P.}},$$

as $${\mathrm{B.}}_k\left(x\right)\le spe{c}_k^x$$

jeweils ein einheitlicher Skalierungsfaktor t_s vorangestellt ist. Der in 3 mit dem Bezugszeichen 86 bezeichnete Skalierungsfaktor t_s ist für alle Spezifikationswerte $spe{c}_i^{ZP}$

gleich und dient der einheitlichen Skalierung der für die einzelnen Zustandsparameter ZPi des Projektionsobjektivs 14 vorgegebenen Spezifikationswerte bzw. Grenzwerte 84. Die unter (13) aufgeführten Nebenbedingungen schließlich geben Spezifikationen bzw. Grenzwerte $spe{c}_k^x$

für die einzelnen Stellwegsvariablen x_k vor und können je nach Ausführungsvariante auch weggelassen werden.The secondary condition listed under (11) specifies that t _{s must} not be negative. The secondary conditions listed under (12) in 3 with the reference number 82 referred to, relate to the state parameters ZP _{i of} the projection lens 16 and correspond to the secondary conditions listed under (2) with the exception that the in 3 with the reference number 84 designated limit values or specification values $spe{c}_i^{Z\mathrm{P.}}$

each is preceded by a uniform scaling factor t _s . The in 3 with the reference number 86 The designated scaling factor t _s is for all specification values $spe{c}_i^{Z\mathrm{P.}}$

the same and is used for the uniform scaling of the individual status parameters ZPi of the projection lens 14th specified specification values or limit values 84 . Finally, the secondary conditions listed under (13) give specifications and limit values $spe{c}_k^x$

for the individual travel variables x _k and can also be omitted depending on the design variant.

The optimization algorithm 74 is now configured to optimize the uniform scaling factor t _s by minimizing it. The result of this optimization is based on the measured state parameters 34 an approximated travel command 38-1 generated. This approximated travel command 38-1 includes approximations of the specifications 38p and possibly 38n for the travel variable x _k .

für den einheitlichen Skalierungsfaktor t_s einen vorgegebenen Schwellwert 85 nicht übersteigt, welcher vorzugsweise 1 ist, d.h. falls $t_s^{opt}\le \mathrm{1,}$

wird zum zweiten Optimierungsalgorithmus 76 übergegangen. In diesem Fall ist bereits sicher, dass ein zulässiges Rezept in Form von Vorgaben für die Stellwegsvariablen x_k für die Manipulatoren des Projektionsobjektivs 16 existiert, bei dem alle für die Zustandsparameter des Projektionsobjektivs vorgegebenen Grenzwerte 84 eingehalten werden. Ein zulässiges Rezept existiert also dann, wenn Vorgaben für die Stellwegsvariablen x_k existieren, für welche die Nebenbedingungen eingehalten werden. Falls $t_s^{opt}>1$

wird in der Regel die Optimierung abgebrochen, da kein derartiges zulässiges Rezept existiert. Allerdings kann es bei einer geringen Schwellwertüberschreitung durch t_s dennoch sinnvoll sein, mittels des zweiten und dritten Optimierungsalgorithmus 76 und 78 ein Rezept zu generieren, mit dem die Grenzwerte 84 wenigstens so gut wie möglich eingehalten werden.In the event that this is in 3 with the reference symbol 87 designated optimization result $t_s^{Opt}$

a predetermined threshold value for the uniform scaling factor t _s 85 does not exceed, which is preferably 1, ie if $t_s^{Opt}\le \mathrm{1,}$

becomes the second optimization algorithm 76 passed over. In this case it is already certain that a valid recipe in the form of specifications for the travel variables x _k for the manipulators of the projection lens 16 exists in which all limit values specified for the state parameters of the projection lens 84 be respected. A valid recipe exists if there are specifications for the travel variables x _k exist for which the constraints are met. If $t_s^{Opt}>1$

the optimization is usually aborted because there is no such permissible recipe. However, if the threshold value is exceeded slightly by t _{s, it can} still be useful to use the second and third optimization algorithms 76 and 78 Generate a recipe with which the limit values 84 at least as good as possible.

The second optimization algorithm 76 is used for the individual optimization of the status parameters 34 of the projection lens 16 and is therefore also referred to in this text as the state parameter optimization algorithm. For this purpose, each of the status parameters ZPi has a corresponding in 3 with the reference number 90 designated, individual scaling factor ti assigned.

In the 3 with the reference number 88 designated objective function F of the second optimization algorithm 76 is weighted by a sum 92 of the individual scaling factors ti, whereby the respective weighting factors are denoted by _{w i:} $$\mathrm{F.}\left(x,t_i\right)={\displaystyle \sum w_i\cdot t_i};$$

$$B_i\left(x\right)\le t_i\cdot spe{c}_i^{ZP},$$

sowie $$B_k\left(x\right)\le spe{c}_k^x$$

The optimization of the objective function F (ie F → min) shown in (14) takes place under the following explicit constraints: $$0\le t_i\le t_s^{Opt}\cdot \mathrm{1.01,}$$

$${\mathrm{B.}}_i\left(x\right)\le t_i\cdot spe{c}_i^{Z\mathrm{P.}},$$

as $${\mathrm{B.}}_k\left(x\right)\le spe{c}_k^x$$

für den einheitlichen Skalierungsfaktor t_s um höchstens 1% übersteigt. Gemäß weiterer Ausführungsformen kann die Nebenbedingung (15) auch so formuliert sein, dass ti das Optimierungsergebnis $t_s^{opt}$

um einen größeren Anteil, wie etwa um 5% übersteigen darf. Diese Lockerung für die Einzelskalierungsfaktoren 90 gibt dem zweiten Optimierungsalgorithmus 76 ausreichend Spielraum, eine optimierte Lösung für die gewichtete Summe 92 der Einzelskalierungsfaktoren 90 aufzufinden.The secondary conditions listed under (15) and (16) are also used in this text as state parameter secondary conditions 94 designated. The secondary condition listed under (15) specifies that the individual scaling factors ti must not be negative in each case, and that by means of the first optimization algorithm in each case 74 determined optimization result $t_s^{Opt}$

for the uniform scaling factor t _s by at most 1%. According to further embodiments, the secondary condition (15) can also be formulated in such a way that ti is the optimization result $t_s^{Opt}$

by a larger proportion, such as may exceed 5%. This relaxation for the individual scaling factors 90 gives the second optimization algorithm 76 sufficient margin, an optimized solution for the weighted sum 92 of the individual scaling factors 90 to find.

der einzelnen Zustandsparameter ZPi anstatt des einheitlichen Skalierungsfaktors t_s jeweils der betreffende Einzelskalierungsfaktor ti vorangestellt ist. Damit definieren die Einzelskalierungsfaktoren 90 eine jeweilige Skalierung der für die einzelnen Zustandsparameter ZPi vorgegebenen Grenzwerte 84. Die unter (17) aufgeführten Nebenbedingungen sind mit den Nebenbedingungen (13) des ersten Optimierungsalgorithmus 74 identisch und geben Spezifikationen bzw. Grenzwerte $spe{c}_k^x$

für die einzelnen Stellwegsvariablen x_k vor. Diese können analog zu den Nebenbedingungen (13) je nach Ausführungsvariante auch weggelassen werden.The condition of the status parameter secondary conditions listed under (16) 94 corresponds to the secondary condition ( 12th ) of the first optimization algorithm 74 except that the specification values $spe{c}_i^{Z\mathrm{P.}}$

the individual state parameter ZPi is preceded by the relevant individual scaling factor ti instead of the uniform scaling factor t _s. This defines the individual scaling factors 90 a respective scaling of the limit values specified for the individual status parameters ZPi 84 . The secondary conditions listed under (17) are identical to the secondary conditions (13) of the first optimization algorithm 74 identical and give specifications or limit values $spe{c}_k^x$

for the individual travel variables x _k before. These can also be omitted, analogous to the secondary conditions (13), depending on the design variant.

der Einzelskalierungsfaktoren ti. Der weitere genäherte Stellwegbefehl 38-2 umfasst weitere Näherungen der Vorgaben 38p und ggf. 38n für die Stellwegsvariablen x_k .The second optimization algorithm 76 the specifications that are in the first optimization algorithm 74 determined approximate travel command 38-1 are used as starting values. The result of the optimization by the second optimization algorithm 76 are another approximate travel command 38-2 as in 3 with the reference number 91 designated optimization results $t_i^{Opt}$

the individual scaling factors ti. The further approximated travel command 38-2 includes further approximations of the specifications 38p and possibly 38n for the travel variable x _k .

The third optimization algorithm 78 is used to optimize the manipulators of the projection lens 16 as well as the post-processing facility, if applicable 36 to be covered and by the travel command 38 specified travel ranges 38p respectively. 38n . As a rule, this is about minimizing these travel ranges. The third optimization algorithm 78 is therefore also referred to in this text as the travel optimization algorithm.

wobei $$H=M^t\cdot M\text{ und }f=b^t\cdot M$$

In the 3 with the reference number 96 designated objective function F of the third optimization algorithm 78 as follows: $$\mathrm{F.}\left(x,{\overline{t}}_i\right)=\frac{1}{2}\cdot x^t\cdot H\cdot x+f\cdot x$$

whereby $$H={\mathrm{M.}}^t\cdot \mathrm{M.}\text{and}f=b^t\cdot \mathrm{M.}$$

$$B_i\left(x\right)\le {\overline{t}}_i\cdot spe{c}_i^{ZP},$$

sowie $$B_k\left(x\right)\le spe{c}_k^x$$

Here, X ^t denotes the transposed travel vector x , M ^t the transposed sensitivity matrix M and b ^t the transposed vector from the Zernike coefficients b _j . Since the objective function F according to (18) with the travel vector x the travel variables x _k it becomes the third optimization algorithm 78 in this text also referred to as the travel optimization algorithm. Since the objective function F according to (18) contains x and x ^t as factors, the objective function F has the travel variables x _k in a square shape. The optimization of the objective function F (ie F → min) shown in (18) takes place under the following explicit constraints: $$0\le {\overline{t}}_i\le t_i^{Opt}\cdot \mathrm{1.01,}$$

$${\mathrm{B.}}_i\left(x\right)\le {\overline{t}}_i\cdot spe{c}_i^{Z\mathrm{P.}},$$

as $${\mathrm{B.}}_k\left(x\right)\le spe{c}_k^x$$

für den entsprechenden Einzelskalierungsfaktor ti um höchstens 1% übersteigt. Gemäß weiterer Ausführungsformen kann die Nebenbedingung (20) auch so formuliert sein, dass t _i das jeweilige Optimierungsergebnis $t_i^{opt}$

einen größeren Anteil, wie etwa um 5% übersteigen darf. Diese Lockerung für die weiteren Einzelskalierungsfaktoren 100 gibt dem dritten Optimierungsalgorithmus 78 ausreichend Spielraum, eine optimierte Lösung für die Stellwege 38p und ggf. 38n aufzufinden.The secondary conditions listed under (20) and (21) are also used in this text as travel optimization secondary conditions 98 designated. The secondary condition listed under (20) specifies that with the reference symbol 100 designated further individual scaling factors t _i may not be negative in each case, and that by means of the second optimization algorithm in each case 76 determined optimization result $t_i^{Opt}$

for the corresponding individual scaling factor ti by a maximum of 1%. According to further embodiments, the secondary condition ( 20th ) also be formulated in such a way that t _i the respective optimization result $t_i^{Opt}$

a larger proportion, such as may exceed by 5%. This relaxation for the other individual scaling factors 100 gives the third optimization algorithm 78 sufficient leeway, an optimized solution for the travel ranges 38p and find 38n if necessary.

für die einzelnen Stellwegsvariablen x_k vorgeben. Diese können analog zu den Nebenbedingungen (13) je nach Ausführungsvariante auch weggelassen werden.The condition of the secondary conditions listed under (21) 98 corresponds to the secondary condition ( 16 ) of the second optimization algorithm 76 with the exception that the individual scaling factors ti by the further individual scaling factors t _{i are} replaced. The secondary conditions listed under (22) are identical to the secondary conditions (13) of the first optimization algorithm 74 and the constraints (17) of the second optimization algorithm 76 identical which specifications or limit values $spe{c}_k^x$

for the individual travel variables x _k pretend. These can also be omitted, analogous to the secondary conditions (13), depending on the design variant.

The third optimization algorithm 78 the specifications that are in the second optimization algorithm 76 determined further approximate travel command 38-2 are included as starting values. The result of the optimization by the third optimization algorithm 78 is the travel command 38 . This includes the final results of the specifications 38p and possibly 38n for the travel variable x _k which thereupon, as already mentioned above with reference to the 1 and 2 described as control signals to the manipulators M1 until M4 of the projection lens 16 as well as the post-processing facility, if applicable 36 be passed on.

The above description of exemplary embodiments, embodiments or design variants is to be understood as exemplary. The disclosure thus made enables the person skilled in the art, on the one hand, to understand the present invention and the advantages associated therewith, and, on the other hand, also includes obvious changes and modifications of the structures and methods described in the understanding of the person skilled in the art. It is therefore intended to cover all such changes and modifications insofar as they come within the scope of the invention as defined in the appended claims, and equivalents of the scope of the claims.

List of reference symbols

10

Adjustment system

12th

Measuring device

14th

Control device

16

Projection lens

18th

Lighting device

20th

Measuring radiation

22nd

Measurement mask

24

Object level

26th

Sensor element

28

Image plane

30th

detector

32

Evaluation device

34

State parameters

36

Post-processing facility

38

Travel command

38-1

approximate travel command

38-2

further approximated travel command

38p

Specifications for manipulators of the projection lens

38n

Requirements for post-processing facility

40

Tilt axis

50

Projection exposure system

52

Exposure radiation source

54

Exposure radiation

56

Lighting optics

58

mask

60

Mask shifting platform

62

Scanning direction of the mask shifting stage

64

Substrate

66

Substrate transfer platform

68

Scanning direction of the substrate transfer platform

70

Wavefront measuring device

72

Overall optimization algorithm

74

first optimization algorithm

76

second optimization algorithm

78

third optimization algorithm

80

Objective function of the first optimization algorithm

82

Constraints of the first optimization algorithm

84

Limit values

85

Threshold

86

uniform scaling factor t _s

87

Optimization result of the uniform scaling factor t _s

88

Objective function of the second optimization algorithm

90

Individual scaling factors t _i

91

Optimization results of the individual scaling factors ti

92

weighted sum

94

State parameter constraints

96

Objective function of the third optimization algorithm

98

Travel optimization constraints

100

further individual scaling factors t _i

xi

Travel variables

bj

Image errors

xk

Travel variables

x

Travel vector

E1 - E4

optical elements

M1 - M4

Manipulators

Claims (15)

Control device (14) for controlling manipulators (M1-M4, 36) for changing an optical behavior of a projection lens (16) for microlithography by generating respective specifications (38) for several travel variables, which manipulations to be carried out on at least one optical element by means of the manipulators (E1-E4) of the projection lens for changing state parameters (34) of the projection lens, the control device being configured to: - Using a first optimization algorithm (74) to generate a respective approximation (38-1) of the specifications for the travel variables by optimizing a uniform scaling factor (86) which, in secondary conditions (82) of the first optimization algorithm, provides a uniform scaling for the individual state parameters Limits (84) defined, as well - in the event that an optimization result (87) for the uniform scaling factor determined by means of the first optimization algorithm does not exceed a predetermined threshold value (85), a respective final result (38) of the specifications for the travel variables by means of at least one further optimization algorithm (76, 78) to investigate. Control device according to Claim 1 , which is further configured to execute a state parameter optimization algorithm (76) when executing the at least one further optimization algorithm, in which a weighted sum (92) of individual scaling factors (90) is optimized, taking into account the state parameter secondary conditions (94) relating to the state parameters , the individual scaling factors (90) in the state parameter secondary conditions defining a respective scaling of the limit values (84) specified for the individual state parameters. Control device according to Claim 1 or 2 which is further configured to execute a travel optimization algorithm (78) when executing the at least one further optimization algorithm, in which a target function (96) having the travel variables is optimized. Control device according to Claim 2 as Claim 3 which is configured to first execute the state parameter optimization algorithm (76) and then the travel optimization algorithm (78) when executing the at least one further optimization algorithm, the travel optimization algorithm being configured to perform the target function (96) taking into account the Condition that further individual scaling factors (100) may respectively exceed optimization results (91) determined by the state parameter optimization algorithm (76) for the corresponding first individual scaling factors (90) by a maximum of 5%. Control device according to Claim 4 which is furthermore configured to base the travel optimization algorithm (78) on further approximations (38-2) of the specifications for the travel variables determined during the execution of the state parameter optimization algorithm (76). Control device according to Claim 2 , 4th or 5 , wherein the state parameter secondary conditions (94) furthermore include the condition that each of the first individual scaling factors (90) may exceed the optimization result for the uniform scaling factor determined by the first optimization algorithm (74) by at most 5%. Control device according to one of the Claims 3 until 6th , wherein the objective function (96) of the travel optimization algorithm (78) contains the travel variables in at least a quadratic form. Control device according to one of the preceding claims, which is also configured to base the at least one further optimization algorithm on the approximations (38-1) of the specifications for the travel variables as starting values. Control device according to one of the preceding claims, wherein the secondary conditions (82) of the first optimization algorithm (74) are formulated as explicit secondary conditions which are not part of an objective function (80) optimized during the execution of the first optimization algorithm. Control device according to one of the preceding claims, in which the determined specifications (38) for the travel variable by means of the manipulators (M1-M4, 36) define changes to be made to the state parameters of the projection lens. Adjustment system (10) for adjusting a projection lens (16) for microlithography with a measuring device (12) for determining current values of state parameters of the projection lens and a control device (14) according to one of the preceding claims for generating the specifications (38) for the travel variables from the current values of the status parameters. Projection objective (16) for a projection exposure system (50) for microlithography with manipulators (M1-M4) which are configured to change state parameters (34) of the projection objective, as well as a control device (14) according to one of the Claims 1 until 10 to control the manipulators. Projection exposure system (50) for microlithography with a projection objective (16) Claim 12 . Method for controlling manipulators (M1-M4, 36) for changing an optical behavior of a projection lens (16) for microlithography by generating respective specifications (38) for several travel variables, which manipulations to be carried out by means of the manipulators on at least one optical element (E1- E4) of the projection lens to change state parameters (34), with the following steps: - Generating a respective approximation (38-1) of the specifications for the travel variables by optimizing a uniform scaling factor (86) by means of a first optimization algorithm (74), wherein the uniform scaling factor in secondary conditions of the first optimization algorithm defines a uniform scaling of limit values (84) specified for the individual state parameters, and - in the event that an optimization result (87) for the uniform scaling factor determined by means of the first optimization algorithm does not exceed a predefined threshold value (85), determining a respective end result (38) of the specifications for the travel variables by means of at least one further optimization algorithm (76, 78) . Procedure according to Claim 14 , in which the determination of the respective end result (38) of the specifications for the travel variable by means of the at least one further optimization algorithm (76) takes place, taking into account explicit further secondary conditions (94) for the state parameters of the projection lens, which are not part of the execution of the at least target function (88) optimized for a further optimization algorithm.

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