DE102022211459A1 - Projection exposure system with a manipulator system - Google Patents

Abstract

A projection exposure system for microlithography comprises a mask holder (20) for holding a mask (18), a substrate holder (26) for holding a substrate (24) and a projection lens (22) with a plurality of optical elements (R1 - R4) for imaging mask structures of the mask onto the substrate, wherein the optical elements, the mask holder and the substrate holder are each a beam path element in an exposure beam path of the projection exposure system. The projection exposure system further comprises a manipulator system (M1 - M4) for setting at least one travel path (p1- p24) on at least one of the beam path elements (R1-R4, 20, 26) in at least one manipulator degree of freedom, at least one measuring device (E1 - E24) for measuring at least one measured variable (e1- e24), which serves to determine the at least one travel path setting (p1- p24) of the manipulator system, and a control device (44) which is configured to determine a control command (46) with at least one specification (e1* - e24*) for the at least one measured variable of the at least one measuring device in order to correct a specification (50) of a wavefront deviation of the projection lens using a model (64), wherein the model describes a relationship (58-1, 58-2) between the measured variables and the wavefront deviation and comprises at least one non-linear term (66).

Description

Background of the invention

The invention relates to a projection exposure system for microlithography with a projection lens, a method for operating such a projection exposure system and a calibration method for calibrating a control device for correcting a wavefront deviation of a projection lens. In this context, a control device is understood to mean both a device for feed-forward control and a device for control via a feedback control loop, which is usually referred to in the specialist world as control.

To ensure that mask structures are imaged onto a wafer as precisely as possible, a projection lens with the lowest possible wavefront aberrations is required. Projection lenses are therefore typically equipped with manipulators that make it possible to minimize wavefront errors through corrective measures in the form of changes in the state of individual optical elements of the projection lens. Examples of such changes in state include: applying heat and/or cold to the optical element, deforming the optical element and/or changing the position of the optical element in question in one or more of the six rigid body degrees of freedom.

Usually, the aberration characteristics of the projection lens are measured regularly and, if necessary, changes in the aberration characteristics between the individual measurements are determined by simulation. For example, lens or mirror heating effects can be taken into account mathematically. The calculation of the manipulator changes to be carried out to correct the aberration characteristics is carried out using a travel-generating optimization algorithm, which is also referred to as a “manipulator change model”. A correction command specifying the manipulator changes to be carried out is generated based on measured values from a wavefront sensor. Such an optimization algorithm is used, for example, in EN 10 2015 222 097 A1 described. Optimization algorithms of this type are based on an objective function that contains a sensitivity matrix that defines the respective linear relationships between an adjustment of manipulators by respective standard travel changes and the resulting changes in a state vector of the projection lens.

However, correction commands generated in a conventional manner are often very inaccurate and often no longer fully meet increasing requirements for the correction accuracy of the imaging behavior of the projection exposure system.

Underlying task

It is an object of the invention to provide a device and a method of the type mentioned at the outset, whereby the aforementioned problems are solved and, in particular, an improved correction accuracy of the imaging behavior of the projection exposure system can be achieved.

Inventive solution

The above-mentioned object can be achieved according to the invention, for example, with a projection exposure system for microlithography, which comprises: a mask holder for holding a mask, a substrate holder for holding a substrate and a projection lens with several optical elements for imaging mask structures of the mask onto the substrate, wherein the optical elements, the mask holder and the substrate holder are each a beam path element in an exposure beam path of the projection exposure system. The projection exposure system further comprises a manipulator system for setting at least one travel path on at least one of the beam path elements in at least one manipulator degree of freedom, in particular in several manipulator degrees of freedom. The projection exposure system further comprises at least one measuring device for measuring at least one measured variable, in particular several measuring devices for measuring different measured variables, which serves to determine the at least one travel path setting of the manipulator system. The projection exposure system further comprises a control device which is configured to determine a control command with at least one specification, in particular several specifications, for the at least one measured variable of the at least one measuring device in order to correct a specification of a wavefront deviation of the projection lens using a model. The model describes a relationship between the measured variables and the wavefront deviation and comprises at least one non-linear term. The non-linear term can comprise a power of a measured variable with the exponent of at least two, for example the square of the measured variable, and/or a product of at least two of the measured variables.

As already mentioned above, in this text a control device means both a feed-forward control device and also a device for controlling via a feedback control loop, which is commonly referred to as closed-loop control in the specialist world.

According to one embodiment, the measuring device serves to measure at least three, at least five or at least ten measured variables. So-called encoders can be used as measuring units.

The specification of a wavefront deviation of the projection lens is to be understood as a value of a wavefront deviation that is transmitted to the control device as a specification, which is advantageously determined by a device of the projection exposure system. This means that the value of the wavefront deviation can be measured, for example, by a measuring device of the projection exposure system and/or determined by a simulation device of the projection exposure system. Alternatively, the specification of the wavefront deviation can also be determined by an external device.

The model describes a relationship between the measured variables and the wavefront deviation, i.e. a wavefront deviation corresponding to the measured variables. The manipulator system can be part of the projection lens or be assigned to it. The same applies to the measuring devices.

The wavefront deviation of the projection lens refers to a deviation of the wavefront of the projection lens from a target wavefront. According to one embodiment, the target wavefront can be defined by spherical wavefronts present at the individual field points in the image plane of the projection lens. The wavefront deviation can be measured, for example, using a wavefront sensor integrated in the substrate displacement stage. The wavefront deviation can be specified by Zernike coefficients. Depending on the design, the Zernike coefficients Z2 to Z36 and possibly other Zernike coefficients can be used for this purpose. The wavefront deviation and thus the target correction can also be represented by a targeted selection of Zernike coefficients.

The measuring system comprising at least one measuring device can also be overdetermined. This means that the measuring system can be configured to measure more measured variables than the manipulator degrees of freedom provided.

According to one embodiment, the control device is configured to control the manipulator system during an exposure operation of the projection exposure system by providing the control command. The exposure operation of the projection exposure system is to be understood, for example, as the operation during the exposure of a wafer or a complete wafer set in the form of a wafer batch. The exposure of a wafer comprises the sequential exposure of all exposure fields (also referred to as "dies") on a wafer with dark periods in between, in which the correction of the wavefront error can advantageously take place ("inter-die corrections").

According to the invention, the correction of the predetermined wavefront deviation is carried out by generating a control command with at least one specification for the at least one measured variable of the at least one measuring device. This allows the travel paths of the manipulator system to be set on the basis of the specification of the at least one measured variable. According to the invention, a model is used to determine this control command, which describes a relationship between the measured variables and the wavefront deviation and includes at least one non-linear term. In comparison to an approach in which the specification of the measured variable is determined assuming a linear relationship between the travel paths of the manipulator system and the measured variables of the measuring devices and between the travel paths of the manipulator system and the resulting wavefront deviation, according to the invention, a more precise positioning of the optical surfaces and thus a smaller set wavefront error can be achieved due to the use of the non-linear term in non-iterative corrections of the wavefront errors without intermediate wavefront measurements. The generation of the specifications for the at least one measured variable according to the invention thus enables an improved correction accuracy of the imaging behavior of the projection exposure system. In particular, this means that close-meshed measurement of the imaging behavior can be largely dispensed with.

According to the invention, the correction of the predetermined wavefront deviation is not carried out by directly adjusting the travel of the manipulator system, i.e. not by generating a correction command with travel changes for the manipulator system, but by generating a control command with at least one specification for the at least one measured variable of the at least one measuring device. The travel of the manipulator system can thus be adjusted on the basis of the specification of the at least one measured variable. In comparison to the direct adjustment of the travel of the manipulator system, the indirect adjustment of the manipulator system on the basis of the at least one measured variable specification can avoid It can happen that due to setting inaccuracies or, for example, thermal drifts in the mechanics of the manipulator system, the actual setting of the manipulator system deviates from the setting specified by the correction command.

According to the invention, the use of the model comprising the non-linear term to determine the control command further ensures that non-linear effects in the relationship between the at least one measured variable and the wavefront deviation can be taken into account. For example, the response of an encoder used as a measuring device to a rotation or displacement of an optical element is generally a non-linear function in all degrees of freedom of the manipulator system. This is particularly true if the encoder is slightly misaligned. This means that these non-linear effects generated by the measuring devices can be taken into account accordingly using the model comprising the non-linear term. This in turn means that the correction accuracy of the imaging behavior of the projection exposure system achieved using the determined control command can be improved compared to the use of a linear model.

By combining, on the one hand, the inventive generation of specifications for the at least one manipulator setting and, on the other hand, the inventive use of a model comprising a non-linear term, a significantly improved correction accuracy of the imaging behavior of the projection exposure system between the individual measurements of the imaging behavior can be achieved. In particular, this means that a close-meshed measurement of the imaging behavior can be dispensed with. Instead, the imaging behavior of the projection exposure system can be measured at longer time intervals.

According to one embodiment, the at least one measuring device is configured to measure different measured variables, which serve to determine several travel settings of the manipulator system, and the non-linear term comprises a product of at least two of the measured variables. According to one embodiment, several measuring devices are provided for measuring the different measured variables.

According to a further embodiment, the nonlinear term comprises at least one bilinear coefficient which is associated with the product of the at least two of the measured variables.

According to a further embodiment, the non-linear term comprises a square or a higher power of one of the measured variables. A higher power is to be understood as a power with an exponent of at least three. Preferably, the non-linear term comprises a quadratic coefficient or a coefficient of a higher power, which is assigned to the square or the higher power of one of the measured variables. According to an embodiment variant, the non-linear term comprises at least one bilinear coefficient and a quadratic coefficient or a coefficient of a higher power.

According to one embodiment, the controller is configured to determine the control command by optimizing an objective function based on the model.

According to a further embodiment, the objective function comprises a linear sensitivity function with sensitivity coefficients determined by means of the model, which are each assigned to one of the measured variables and designate a local linear approximation of the relationship between the assigned measured variable and a corresponding deviation of the wavefront at the respective value of the measured variable present at the relevant operating time of the projection exposure system.

According to a further embodiment, the objective function comprises the relationship between the measured variables and the wavefront deviation described by the model. This means that the non-linear relationship described by the model is part of the objective function.

According to a further embodiment, the model comprises a plurality of non-linear terms, each of which comprises a product of at least two of the measured variables, wherein the products of different non-linear terms each comprise different combinations of the measured variables. In particular, the term comprises at least three, at least ten or at least one hundred products of different combinations of the measured variables. Each of the products of the different non-linear terms is advantageously assigned a bilinear coefficient.

According to a further embodiment, the model further comprises at least one linear term in which one of the measured variables is contained in the first power as well as a linear coefficient associated with this measured variable. In particular, the model comprises a linear term for each of the measured variables.

According to a further embodiment, the deviations in the wavefront described in the model are denoted by at least one Zernike coefficient.

According to a further embodiment, a plurality of the manipulator degrees of freedom can be set on just one of the optical elements of the projection lens by means of the manipulator system, and a plurality of the measured variables are used to determine the travel settings with respect to the manipulator degrees of freedom on the one optical element, wherein the relationship described by the model exists between the plurality of measured variables and the wavefront deviation. According to this embodiment, a plurality of the manipulation degrees of freedom can be set on just one of the optical elements of the projection lens. This means that this one optical element can be the only element of the projection lens on which manipulation degrees of freedom can be set. However, one or more other optical elements of the projection lens can also have manipulation degrees of freedom that can be set.

According to a further embodiment, the projection exposure system comprises a simulation device that is configured to determine a change in the wavefront that is caused by thermal heating of elements in the projection exposure system that occurs during exposure operation of the projection exposure system, and to determine the specification of the wavefront deviation on the basis of the calculated wavefront. The elements in the projection exposure system whose heating causes the change in the wavefront are in particular the optical elements of the projection lens and possibly other elements that lead to displacement/distortion of the optical elements or the reticle or the substrate. The change in the wavefront can be determined by calculation, for example based on a feed-forward model, or for example by reading from a "look-up table", i.e. a database with wavefront errors to be expected for the given boundary conditions. The starting point for determining the target correction can be a wavefront measurement, which is then adjusted based on the calculated wavefront change.

Furthermore, according to the invention, a method is provided for operating a projection exposure system for microlithography with a mask holder for holding a mask and a substrate holder for holding a substrate. The projection exposure system further comprises a projection lens with several optical elements for imaging mask structures of the mask onto the substrate, wherein the optical elements, the mask holder and the substrate holder are each a beam path element in an exposure beam path of the projection exposure system. Furthermore, the projection exposure system comprises a manipulator system for setting at least one adjustment path, in particular several adjustment paths, on at least one of the beam path elements, in particular on several of the beam input elements of the projection lens in several degrees of freedom and at least one measuring device for measuring at least one measured variable, in particular different measured variables, which serves to determine the at least one adjustment path setting of the manipulator system. The method according to the invention comprises the steps of: providing a specification of a wavefront deviation of the projection lens, determining at least one specification, in particular of several specifications, for the at least one measured variable of the at least one measuring device from the wavefront deviation using a model, wherein the model describes a relationship between the measured variables and the wavefront deviation and comprises at least one non-linear term, and correcting the wavefront deviation of the projection lens by adjusting the travel paths on the optical elements by means of the manipulator system in such a way that the at least one measured variable assumes the at least one determined specification.

Furthermore, according to the invention, a calibration method is provided for calibrating a control device for correcting a wavefront deviation of a projection lens of a projection exposure system for microlithography with a mask holder for holding a mask and a substrate holder for holding a substrate. The projection lens has several optical elements for imaging mask structures of the mask onto the substrate, wherein the optical elements, the mask holder and the substrate holder are each a beam path element in an exposure beam path of the projection exposure system. The calibration method comprises the steps of: setting travel paths on the beam path elements of the projection lens in various combinations by means of a manipulator system, measuring at least one measurement variable, in particular several measurement variables, on the beam path elements for the various travel path combinations, measuring the wavefront deviation of the projection lens for the various travel path combinations, and calibrating the control device based on an assignment of the measurement results of the at least one measured value for the respective measurement result of the wavefront deviation.

According to one embodiment of the calibration method according to the invention, the control device is configured to determine a control command with at least one specification for the at least one measured variable in the exposure mode of the projection exposure system in order to correct a wavefront deviation of the projection lens using a model that describes a relationship between the at least one measured variable and the wavefront deviation. Furthermore, by assigning the measurement results of the at least one measured variable to the respective measurement result of the wavefront deviation, at least one linear coefficient is determined, which is assigned to one of the measured variables in the model.

According to a further embodiment, the model is a non-linear model, in particular a quadratic model, which is determined from a linear parameterization at several travel combinations (setpoints). This can be advantageous because the linear calibration/parameterization is a standard process and by repeatedly executing a known process, the additional non-linear, for example quadratic, dependencies can be determined.

According to a further embodiment, at least one non-linear coefficient is determined by assigning the at least one measured variable to the respective measurement result of the wave front. The non-linear coefficient can be a bilinear coefficient, which in the model is assigned to the product of at least two of the measured variables, or a quadratic coefficient or a higher power coefficient, which in the model is assigned to the square or a higher power of a measured variable.

The features specified with regard to the above-mentioned embodiments, exemplary embodiments or design variants, etc. of the projection exposure system according to the invention can be transferred accordingly to the inventive method for operating a projection exposure system or the inventive calibration method and vice versa. The features of the inventive calibration method specified with regard to the above-mentioned embodiments can also be transferred to the projection exposure system 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 implemented either separately or in combination as embodiments of the invention. Furthermore, they can describe advantageous embodiments that are independently protectable and whose protection may only be claimed during or after the application has been filed.

Short description of the drawings

• 1 ein erfindungsgemäßes Ausführungsbeispiel einer Projektionsbelichtungsanlage für die Mikrolithographie mit einem Projektionsobjektiv sowie Manipulatoren zum Einstellen von Stellwegen an zugeordneten optischen Elementen des Projektionsobjektivs, Messeinrichtungen sowie einer Steuerungseinrichtung, welche dazu konfiguriert ist, zur Korrektur einer Vorgabe eine Wellenfrontabweichung des Projektionsobjektivs zu ermitteln, welche einen Algorithmus zum Ermitteln eines Stellwegsbefehls für die Manipulatoren umfasst,
• 2 ein Ausführungsbeispiel der Anordnung verschiedener Messeinrichtungen zur Vermessung der Position eines optischen Elements der Projektionsbelichtungsanlage gemäß 1 in sechs Starrkörperfreiheitsgraden,
• 3 ein erstes Ausführungsbeispiel der Steuerungseinrichtung gemäß 1,
• 4 ein zweites Ausführungsbeispiel der Steuerungseinrichtung gemäß 1, sowie
• 5 ein erfindungsgemäßes Ausführungsbeispiel einer Kalibrierung der Steuerungseinrichtung der Projektionsbelichtungsanlage gemäß 1.

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

• 1 an embodiment according to the invention of a projection exposure system for microlithography with a projection lens and manipulators for setting travel paths on associated optical elements of the projection lens, measuring devices and a control device which is configured to determine a wavefront deviation of the projection lens in order to correct a specification, which comprises an algorithm for determining a travel path command for the manipulators,
• 2 an embodiment of the arrangement of various measuring devices for measuring the position of an optical element of the projection exposure system according to 1 in six rigid body degrees of freedom,
• 3 a first embodiment of the control device according to 1 ,
• 4 a second embodiment of the control device according to 1 , as well as
• 5 an inventive embodiment of a calibration of the control device of the projection exposure system according to 1 .

Detailed description of embodiments according to the invention

In the embodiments or embodiments or variants described below, functionally or structurally similar elements are provided with the same or similar reference numerals as far as possible. Therefore, in order to understand the features of the individual elements of a specific embodiment, reference should be made to the description of other embodiments or the general description of the invention.

To facilitate the description, a Cartesian xyz coordinate system is shown in the drawing, from which the respective positional relationship of the components shown in the figures can be derived. In 1 The y-direction runs perpendicular to the drawing plane, the x-direction to the right and the z-direction upwards.

1 shows an inventive embodiment of a projection exposure system 10 for microlithography, which is configured to be operated by means of an embodiment of a method according to the invention. The present embodiment of the projection exposure system 10 is designed for operation in the EUV wavelength range, ie with electromagnetic radiation with a wavelength of less than 100 nm, in particular a wavelength of approximately 13.5 nm or approximately 6.8 nm. Due to this operating wavelength, all optical elements in the exposure beam path are designed as mirrors. In an alternative embodiment, the projection exposure exposure system 10 is designed for operation in the DUV wavelength range. In this case, the operating wavelength can be approximately 365 nm, approximately 248 nm or approximately 193 nm and at least some of the optical elements in the exposure beam path are designed as lens elements.

The projection exposure system 10 according to 1 comprises an exposure radiation source 12 for generating exposure radiation 14. In the present case, the exposure radiation source 12 is designed as an EUV source and can, for example, comprise a plasma radiation source. The exposure radiation 14 first passes through an illumination system 16 and is directed by it onto a mask 18.

The illumination system 16 is configured to generate different angular distributions of the exposure radiation 14 impinging on the mask 18. Depending on a lighting setting desired by the user, also called “lighting setting,” the illumination system 16 configures the angular distribution of the exposure radiation 14 impinging on the mask 18. Examples of selectable lighting settings include so-called dipole lighting, annular lighting, and quadrupole lighting.

The mask 18 has mask structures for imaging onto a substrate 24 in the form of a wafer and is displaceably mounted on a mask holder in the form of a mask displacement stage 20. The mask 18 can, as in 1 shown, can be designed as a reflection mask or alternatively can be configured as a transmission mask. The exposure radiation 14 is in the embodiment according to 1 reflected on the mask 18 and then passes through a projection lens 22, which is configured to image the mask structures onto the substrate 24. The exposure radiation 14 is guided within the projection lens 22 by means of a plurality of mirrors in an exposure beam path 23.

The substrate 24 is movably mounted on a substrate holder in the form of a substrate displacement stage 26. The projection exposure system 10 can be designed as a so-called scanner or as a so-called stepper. A wavefront sensor 48 for measuring a wavefront deviation 30 of the projection lens 22, designated Zi*, during exposure pauses is arranged on the substrate displacement stage 26. This wavefront deviation Zi* is also referred to in this text as a specification of a wavefront deviation for a control device 44, described in more detail below.

The projection lens 22 has in the embodiment according to 1 four optical elements in the form of mirrors R1 to R4 or reflective optical elements. As mentioned above, the projection lens 22 can also contain lenses as optical elements in another embodiment. The projection lens 22 can also have more or fewer optical elements in other embodiments. The projection lens 22 comprises a manipulator system with manipulator devices M1 to M4 for setting travel paths on the mirrors R1 to R4 in several manipulator degrees of freedom. The manipulator devices M1 to M4 are each assigned to one of the mirrors R1 to R4.

The mask displacement stage 20, the substrate displacement stage 26 and the mirrors R1 to R4 are also referred to as beam path elements because they are arranged along the beam path of the exposure radiation 14. As mentioned above, the mask displacement stage 20 and the substrate displacement stage 26 are configured to displace the mask 18 or the substrate 24. Furthermore, they can also tilt the mask 18 or the substrate. According to a further embodiment, the mask displacement stage 20 and the substrate displacement stage 26 also function as manipulator devices of the manipulator system, on which the translation and tilting positions of the mask 19 or the substrate 24 can be set as further adjustment paths of the manipulator system. In the present embodiment, each of the manipulator devices M1 to M4 is configured to move the respective mirror R1 to R4 in the six rigid body degrees of freedom, i.e. to carry out translation movements in three degrees of freedom and tilting movements in three degrees of freedom. The mirror R1, for example, can be moved in the x, y and z directions by means of the manipulator device M1 and by tilting axes aligned parallel to the x, y and z axes. The translational movements 32 of the mirrors R1 to R4 are in 1 Each is illustrated by way of example with a double arrow, which illustrates a shift in the plane of the drawing. The tilting movements 34 of the mirrors R1 to R4 are each illustrated by way of example with a curved double arrow, which illustrates a tilting with respect to a tilting axis aligned parallel to the y-axis.

In the embodiment shown, the manipulator system with the manipulator devices M1 to M4 thus comprises twenty-four degrees of freedom, which can be set using the travel specifications p ₁ * to p ₂₄ *. In alternative embodiments, the manipulator system can also have a different number of degrees of freedom; in particular, fewer than six degrees of freedom can be assigned to the individual optical element in the form of a mirror. In the embodiment shown, each of the manipulator devices M1 to M4 is assigned a manipulator control unit 36, which generates the respective travel path specifications, namely the manipulator control unit 36 of the manipulator device M1 the travel path specifications p ₁ * to p ₆ *, the manipulator control unit 36 of the manipulator device M2 the travel path specifications p ₇ * to p ₁₂ *, the manipulator control unit 36 of the manipulator device M3 the travel path specifications p ₁₃ * to p ₁₈ * and the manipulator control unit 36 of the manipulator device M4 the travel path specifications p ₁₉ * to p24 *.

Each of the mirrors R1 to R4 is assigned several measuring devices for determining the travel settings of the manipulator system, ie measuring devices for determining the settings actually made in the individual degrees of freedom of the manipulator system using the travel settings p ₁ * to p ₂₄ *. In the illustrated embodiment, the measuring devices are configured as encoders E1 to E24, with each mirror R1 to R4 being assigned six encoders, of which 1 To simplify the drawing, only one encoder is shown at a time (cf. encoder E1 with respect to mirror R1, encoder E7 with respect to mirror R2, encoder E13 with respect to mirror R3 and encoder E19 with respect to mirror R4).

2 illustrates the arrangement of the encoders E1 to E6 assigned to the mirror R1. The active mirror surface 38 of the mirror R1 for reflecting the exposure radiation 14 has in the illustration according to 2 upwards. Each of the encoders E1 to E6 generates a laser beam 40 which is directed at an associated measuring surface 42 on the mirror R1. The measuring surfaces 42 associated with the encoders E1, E5 and E6 are positioned at the edge region of the mirror R1, the surface of which is arranged transversely to the mirror surface 38. The measuring surfaces 42 associated with the encoders E2 to E4 are arranged on a rear side 39 of the mirror R1 opposite the mirror surface 38. In the illustrated embodiment, the measuring surfaces 42 each have a two-dimensional grid, a so-called target grid. The laser beams 40 each have an intensity distribution in cross-section which is adapted to the relevant target grid, so that the radiation reflected from the relevant measuring surface 42 to the relevant encoder has a modulation from which the exact point of impact of the laser beam 40 on the measuring surface 42 can be determined by the encoder.

The encoders E1 to E6 therefore measure the respective position of the relevant laser beam 40 on the relevant measuring surface 42 in orthogonal coordinates transverse to the laser beam 40, i.e., for example, the y and z coordinates of the position of the point of impact of the laser beam 40 on the measuring surface 42 assigned to the encoder E1. The position measurement data measured by the encoders E1 to E6 are transmitted as measured variables e ₁ to e ₆ to the manipulation control unit 36 of the manipulator M1, which can use this to determine the actual position of the mirror R1 in all six rigid body degrees of freedom. This measured actual position of the mirror R1 results in the actual settings of the travel paths p ₁ to p ₆ of the manipulator device M1, the values of which are specified by the travel path specifications p ₁ * to p ₆ *, but can deviate from these due to sources of error.

The configuration and arrangement of the encoders E7 to E24 in relation to the mirrors R2 to R4 is designed in the described embodiment analogously to the configuration and arrangement of the encoders E1 to E6 in relation to mirror R1 described above. However, the encoders can also be arranged in a different way and/or configured differently. For example, the encoders can be configured to carry out an interferometric distance measurement to the relevant measuring surfaces 42, which in this case do not have to have a grating. Instead of encoders, other measuring devices can also be used to determine the actual settings of the travel paths p ₁ to p ₂₄ .

As continued in 1 shown, the projection exposure system 10 comprises the control device 44, which is configured to determine a control command e _j * (reference number 46). The control command 46 comprises specifications e ₁ * to e ₂₄ * for the measured variables e ₁ to e ₂₄ of the Enco the E1 to E24. The specifications e ₁ * to e ₆ * are transmitted to the manipulator control unit 36 of the manipulator M1, the specifications e ₇ * to e ₁₂ * to the manipulator control unit 36 of the manipulator M2, the specifications e ₁₃ * to e ₁₈ * to the manipulator control unit 36 of the manipulator M3 and the specifications e ₁₉ * to e ₂₄ * to the manipulator control unit 36 of the manipulator M4.

The manipulator control units 36 then adjust the travel paths p ₁ to p ₂₄ of the manipulators M1 to M4 by correspondingly outputting travel path specifications p ₁ * to p ₂₄ * so that the measured variables e ₁ to e ₂₄ correspond to the specifications e ₁ * to e ₂₄ *. For example, the manipulator control unit 36 of the manipulator M1 adjusts the travel path settings x ₁ to x ₆ by correspondingly outputting the travel path specifications p ₁ * to p ₆ * so that the measured variables e ₁ to e ₆ correspond to the specifications e ₁ * to e ₆ *.

According to the above-mentioned embodiment, in which the mask displacement stage 20 and the substrate displacement stage 26 also serve as manipulator devices of the manipulator system, the control command 46 further comprises specifications for measurement variables from the encoders assigned to the mask displacement stage 20 and the substrate displacement stage 26. These encoders measure the translation coordinates and tilt positions of the mask 18 and the substrate 24.

The control device 44 is configured to determine the control command 46 for correcting the wavefront deviation Zi* of the projection lens 22. In other words, the control command 46 generated by the control device 44 is used to make a target correction to the wavefront of the projection lens 22 that is opposite to the wavefront deviation Zi*. The wavefront deviation Zi* of the projection lens 22 refers to a deviation of the wavefront of the projection lens 22 from a target wavefront. According to one embodiment, the target wavefront can be defined by spherical wavefronts present at the individual field points in the image plane of the projection lens 22.

The wavefront deviation Zi* is measured by means of a wavefront measuring device arranged on the substrate displacement stage 26 in the form of a wavefront sensor 48 during exposure pauses of the projection exposure system 10. The wavefront deviation Zi* measured by the wavefront sensor 48 is designated by the reference symbol 50. The wavefront deviation Zi* can be specified by Zernike coefficients. Depending on the design, the Zernike coefficients Z2 to Z36 and possibly other Zernike coefficients can be used for this purpose. The wavefront deviation 50 and thus a target correction can also be represented by a targeted selection of Zernike coefficients.

In the present application, as described for example in sections [0125] to [0129] of US2013/0188246A1 described, for example, in Chapter 13.2.3 of the textbook "Optical Shop Testing", 2nd Edition (1992) by Daniel Malacara, ed. John Wiley & Sons, Inc. known Zernike functions according to the so-called fringe sorting with Z _j , where b _j are the Zernike coefficients assigned to the respective Zernike polynomials (also called “Zernike functions”). The fringe sorting is, 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 illustrated. While the Zernike polynomials are designated with Z _j , ie with subscript j, in the context of this application the Zernike coefficients b _j are designated with Zj, ie with a normalized index, such as Z5 and Z6 for astigmatism. In the designation used for the wavefront deviation Zi*, the subscript i encodes both the Zernike coefficient and the field point.

The measurement of the wavefront deviation 50 can be carried out regularly after each exposure of a wafer or after exposure of a complete wafer set. Alternatively, instead of a measurement, a simulation or a combination of simulation and reduced measurement can be carried out. After the measurement, the wavefront deviation 50 can be transmitted directly to the control device 44 by means of the wavefront sensor 48 or, as further described in the 1 illustrated embodiment, to a state transmitter 91 for generating an updated wavefront deviation 50a.

In the embodiment shown, the measured wavefront deviation 50 is stored in a memory 92 of the state transmitter 91 and adapted by a simulation device 93 to the respective updated conditions during the exposure process. According to one embodiment variant, a current irradiation intensity 95 of the exposure radiation 14 radiated onto the mask 18 is regularly transmitted to the simulation device 93 by a central controller 90 of the projection exposure system 10.

The simulation device 93 calculates, on the basis of the respective lighting setting, changes in the aberration parameters caused by heating of optical elements, in this case mirror heating. parameters. Furthermore, the simulation device 93 continuously receives measured values from a pressure sensor 94 that monitors the ambient pressure of the projection exposure system 10. Effects of changes in the ambient pressure on the aberration parameters are taken into account by the simulation device 93. The status transmitter 91 transmits the updated wavefront deviation 50a determined by the simulation device 93 to the control device 44 either at predetermined time intervals or continuously in real time.

As mentioned above, the control device 44 serves to determine the control command 46 for correcting the wavefront deviation Zi* of the projection lens 22. In the exemplary embodiment shown here, the wavefront deviation Zi* is the updated wavefront deviation 50a. Alternatively, it can also be the wavefront deviation 50 coming directly from the wavefront sensor 48.

3 illustrates a first embodiment 44-1 of the control device 44. The control device 44-1 is configured to execute an optimization algorithm 52 and thereby determine the control command 46 by minimizing an objective function 54, also referred to as a quality function or merit function. According to one embodiment, the objective function 54 is as follows: $$D\left(\left\{Z_i-Z_i^{\text{target}}\right\}\right)$$

bezeichnet eine gewünschte Korrekturwellenfrontwirkung 56, diese wird auf den negativen Wert der vom Zustandsgeber 54 übermittelten Wellenfrontabweichung Zi* gesetzt. Zi bezeichnet eine mit dem Bezugszeichen 58-1 bezeichnete Sensitivitätsfunktion Z_i({e_j}), welche einen Zusammenhang zwischen den Messgrößen e_j, im vorliegenden Fall den Messgrößen e₁ bis e₂₄, und der zugehörigen Wellenfrontänderung Zi, d.h. der korrespondieren Wellenfrontabweichung des Projektionsobjektivs 22 darstellt. Die Zielfunktion kann darüber hinaus auch weitere Terme enthalten, beispielsweise Strafterme (etwa in Tikhonov-Formulierung) für Manipulatorverfahrwege, um einen möglichst keinen Verfahrweg zu gewährleisten.Here D is a metric, such as the square of the Euclidean norm || || ₂ . $Z_i^{\text{target}}$

denotes a desired correction wavefront effect 56, which is set to the negative value of the wavefront deviation Zi* transmitted by the status transmitter 54. Zi denotes a sensitivity function Z _i ({e _j }) denoted by the reference symbol 58-1, which represents a relationship between the measured variables e _j , in this case the measured variables e ₁ to e ₂₄ , and the associated wavefront change Zi, ie the corresponding wavefront deviation of the projection lens 22. The objective function can also contain further terms, for example penalty terms (for example in Tikhonov formulation) for manipulator travel paths, in order to ensure as little travel path as possible.

The resulting optimization problem has the form: $$\left\{e_j^{\text{opt}}\right\}=\underset{e_i}{{\displaystyle \text{min}}}D\left(\left\{Z_i-Z_i^{\text{target}}\right\}\right)$$

werden als die Werte e_j* des Steuerungsbefehls 46 ausgegeben. Darüber hinaus kann die Metrik erweitert werden, so dass nicht nur die angestrebte Korrekturwellenfrontwirkung möglichst genau erreicht wird, sondern auch die Verfahrwege für den Stepping/Scanning Prozess günstig gewählt werden. Dies kann sinnvoll sein, da große Verfahrwege in manchen Freiheitsgraden zu Schwingungen der optischen Komponenten (bspw. Spiegel) führen, die nicht rechtzeitig abklingen, um die Belichtung des folgenden Belichtungsfeldes nicht mehr zu beeinflussen. Als Resultat können für einen möglichst unverzögerten Belichtungsprozess kurze Verfahrwege in manchen Freiheitsgraden präferiert werden.The values determined $\left\{e_j^{\text{opt}}\right\}$

are output as the values e _j * of the control command 46. In addition, the metric can be extended so that not only the desired correction wavefront effect is achieved as precisely as possible, but also the travel paths for the stepping/scanning process are selected favorably. This can be useful because large travel paths in some degrees of freedom lead to vibrations of the optical components (e.g. mirrors) that do not decay in time to no longer influence the exposure of the following exposure field. As a result, short travel paths in some degrees of freedom can be preferred for an exposure process with as little delay as possible.

oder die erlaubten Verfahrwege sogenannte „neutrale Knobs“ berücksichtigen, das heißt Kombinationen von Verfahrwegen, die nur sehr geringe Wellenfrontwirkungen haben (d.h. „neutrale Knobs“) genutzt werden, um einen hinreichend guten Setpoint im Hinblick auf die Wellenfrontwirkung zu finden, der gleichzeitig nah an dem derzeitigen Setpoint der Maschine liegt.The metric can reflect this by either including a penalty term P({e _j }) for large travel distances, such that: $$\left\{e_j^{\text{opt}}\right\}=\underset{e_j}{\text{min}}D\left(\left\{Z_i-Z_i^{\text{target}}\right\}+P(\left\{e_j\right\}\right)$$

or the permitted travel paths take into account so-called "neutral knobs", i.e. combinations of travel paths that have only very low wavefront effects (ie "neutral knobs") are used to find a sufficiently good setpoint with regard to the wavefront effect, which at the same time is close to the current setpoint of the machine.

The sensitivity function 58-1 is a linear sensitivity function and in the present embodiment is as follows: $$Z_i\left(\left\{e_j\right\}\right)=Z_i^{base}+{\displaystyle \sum _{j=1}^{n_{enc}}{s}_{ij}\cdot e_j}$$

eine Ausgangswellenfront und s_ij lineare Sensitivitätskoeffizienten 60. Jeder Sensitivitätskoeffizient s_ij ist jeweils der betreffenden Messgröße e_j zugeordnet und bezeichnet eine lokale lineare Näherung des Zusammenhangs zwischen der zugeordneten Messgröße e_j und einer korrespondierenden Abweichung der Wellenfront, d.h. des Anteils der Wellenfrontabweichung Zi, der auf eine entsprechende Änderung der betreffenden Messgröße e_j zurückgeht. Diese lokale lineare Näherung des Zusammenhangs zwischen der zugeordneten Messgröße e_j und der korrespondierenden Abweichung der Wellenfront bezieht sich auf einen jeweiligen, zum betreffenden Betriebszeitpunkt der Projektionsbelichtungsanlage 10 vorliegenden Wert der Messgröße e_j. Die lokale lineare Näherung gilt auch für kleine Abweichungen, also in der lokalen Umgebung von e_j.Here, $Z_i^{base}$

an output wavefront and s _ij linear sensitivity coefficients 60. Each sensitivity coefficient s _ij is assigned to the respective measured variable e _j and denotes a local linear approximation of the relationship between the assigned measured variable e _j and a corresponding deviation of the wavefront, ie the portion of the wavefront deviation Zi that is due to a corresponding change in the respective measured variable e _j . This local linear approximation of the relationship between the assigned measured variable e _j and the corresponding deviation of the wavefront refers to a respective value of the measured variable e _j present at the respective operating time of the projection exposure system 10. The local linear approximation also applies to small deviations, i.e. in the local vicinity of e _j .

For this purpose, the linear sensitivity function 58-1 and thus also the sensitivity coefficients 60 are re-determined for each optimization of the target function 54 by means of a linearization module 62 when an updated wavefront deviation 50a is present. The linearization module 62 is part of the control device 44-1 and can physically be present as a separate module or simply be a functional unit of the control device 44-1.

To determine the linear sensitivity function 58-1, the linearization module 62 uses a predetermined non-linear model 64, which describes the relationship between the measured variables e _j , in the present case the measured variables e ₁ to e ₂₄ , and the corresponding wavefront deviation Z _i of the projection lens 22 and includes at least one non-linear term 66 for this purpose. To determine the linear sensitivity function 58, the linearization module 62 uses the measured variable settings e _j * (see reference numeral 46-0) that are current at that time. When determining the linear sensitivity function 58 for the first time, values measured by the encoders E1 to E24 can be used for this purpose. In subsequent determinations, the most current specifications from the control command 46 generated by the optimization algorithm 52 can be used. In one embodiment, the non-linear model 64 is as follows: $$Z_i=c_i+{\displaystyle \sum _{j=1}^{n_{\text{enc}}}{l}_{ij}\cdot e_j+{\displaystyle \sum _{j=1}^{n_{\text{enc}}}{\displaystyle \sum _{k=}^j{q}_{ijk}\cdot e_j\cdot e_k}}}$$

eine Vielzahl an mit dem Bezugszeichen 68 bezeichneten linearen Termen l_ij·e_j, und ${\displaystyle \sum _{j=1}^{n_{\text{enc}}}{\displaystyle \sum _{k=1}^j{q}_{ijk}\cdot e_j\cdot e_k}}$

eine Vielzahl der vorstehend erwähnten, mit dem Bezugszeichen 66 bezeichneten, nichtlinearen Terme q_ijk·e_j·e_k. In den linearen Termen 68 sind den verschiedenen Messgrößen e_j in erster Potenz für jeden Zernike Koeffizienten Z_i jeweils ein mit dem Bezugszeichen 70 bezeichneter linearer Koeffizient l_ij zugeordnet. In den nichtlinearen Termen 66 sind für jeden Zernike Koeffizienten Zi jeweils bilineare Koeffiezenten 72 bzw. quadratische Koeffizienten 74 enthalten. Dies sind die Koeffizienten q_ijk, wobei q_ijk für j≠k ein bilinearer Koeffizient 72 ist, welcher einem Produkt aus zwei unterschiedlichen Messgrößen zugeordnet ist, und für j=k ein quadratischer Koeffizient 74 ist, welche einem Quadrat eines der Messgrößen zugeordnet ist. Wie aus dem Term (5) ersichtlich ist, umfasst für n_enc ≥ 1 das nichtlineare Modell 64 eine Mehrzahl an nichtlinearen Termen q_ijk · e_j · e_k, die jeweils ein Produkt aus zwei der Messgrößen e_j umfassen, wobei die Produkte verschiedener nichtlinearer Terme jeweils unterschiedliche Kombinationen der Messgrößen e_j umfassen.Here c _i denotes constant coefficients 69, n _enc the number of encoders used, in this case twenty-four, ${\displaystyle \sum _{j=1}^{{\text{n}}_{\text{enc}}}{l}_{ij}\cdot e_j}$

a plurality of linear terms l _ij ·e _j designated by reference numeral 68, and ${\displaystyle \sum _{j=1}^{n_{\text{enc}}}{\displaystyle \sum _{k=1}^j{q}_{ijk}\cdot e_j\cdot e_k}}$

a plurality of the above-mentioned non-linear terms q _ijk ·e _j ·e _k , designated by the reference numeral 66. In the linear terms 68, the various measured variables e _j are each assigned a linear coefficient l _ij , designated by the reference numeral 70, to the first power for each Zernike coefficient Z _i . The non-linear terms 66 contain bilinear coefficients 72 and quadratic coefficients 74 for each Zernike coefficient Zi. These are the coefficients q _ijk , where q _ijk is a bilinear coefficient 72 for j≠k, which is assigned to a product of two different measured variables, and is a quadratic coefficient 74 for j=k, which is assigned to a square of one of the measured variables. As can be seen from term (5), for n _enc ≥ 1 the nonlinear model 64 comprises a plurality of nonlinear terms q _ijk · e _j · e _k , each comprising a product of two of the measured quantities e _j , where the products of different nonlinear terms each comprise different combinations of the measured quantities e _j .

In 4 a second embodiment 44-2 of the control device 44 according to 1 This embodiment 44-2 differs from the embodiment 44-1 in that in the objective function 54 minimized by the optimization algorithm 52, the sensitivity function Z _i ({e _j }) is not formed by the linear sensitivity function 58-1, but by the nonlinear sensitivity function Zi (reference number 58-2) defined by the nonlinear model 64.

Thus, the nonlinear model 64 and in particular the nonlinear relationship described by the model 64, in this embodiment 44-1, is part of the objective function 54.

The non-linear model 64 shown in (5) can be derived as follows. The encoder response in the form of the measured variable e _j of the encoder Ej j ∈ {1, 2, ... n _enc } to rotation or displacement of the degree of freedom in the form of the travel setting p _k ∈ {1, 2, ... n _dof } is generally a non-linear function e _j ({p _k }) in all degrees of freedom p _k , for example: $$e_j\left(\left\{p_k\right\}\right)=C_j+{\displaystyle \sum _{i=1}^{n_{\text{dof}}}{L}_{ji}\cdot p_i+{\displaystyle \sum _{i=1}^{n_{\text{dof}}}{\displaystyle \sum _{k=1}^{n_{\text{dof}}}{Q}_{jik}\cdot p_i\cdot p_k}}}$$

The coefficients Q _jik can be assumed to be zero for the degrees of freedom of different mirrors iA. Analogously, the wavefront effect at each field point, described by the Zernike coefficient Z _i , where the subscript i encodes both the coefficient and the field point, is in general a nonlinear function Z _i ({p _k }) in all degrees of freedom p _k , such as: $$Z_i\left(\left\{p_k\right\}\right)=C{\text{'}}_i+{\displaystyle \sum _{j=1}^{n_{\text{dof}}}L{\text{'}}_{ij}\cdot p_j+{\displaystyle \sum _{j=1}^{n_{\text{dof}}}{\displaystyle \sum _{k=1}^{n_{\text{dof}}}Q{\text{'}}_{ijk}}}}\cdot p_j\cdot p_k$$

Note that, in contrast to Q _jik, the coefficients Q' _jik for the degrees of freedom of different mirrors cannot generally be assumed to be zero. For a correction of the wavefront effect Z _i based on the encoder response e _j , the dependence Z _i ({e _j }) must be known and modeled with sufficient accuracy. It results from the above-mentioned dependencies of Z _i and e _j on the setpoint {p _k }.

beschreibt den realen Zusammenhang $Z_i^{\text{real}}\left(\left\{e_j\right\}\right)$

unzureichend genau, um die o.g. „blinden“ Korrekturen von Wellenfrontstörungen ausführen zu können. Unter dem Ausdruck „blinde Korrekturen“ sind Korrekturen ohne Messung der zu korrigierenden Wellenfrontstörung und ohne Überprüfung der eingestellten nachfolgenden Wellenfrontwirkung vor der folgenden Belichtung mittels eines Wellenfrontmesssystems zu verstehen.Conventionally, when describing the wavefront of projection lenses, the Relationship Z _i ({e _j }) is assumed to be linear in all e _j . The linear coefficients (also called sensitivities) are determined from simulations of the system design and are used for the correction of the system both virtually and physically. The resulting description $Z_i^{\text{lin}\text{, design}}\left(\left\{e_j\right\}\right)$

describes the real context $Z_i^{\text{real}}\left(\left\{e_j\right\}\right)$

insufficiently precise to be able to carry out the above-mentioned "blind" corrections of wavefront disturbances. The term "blind corrections" refers to corrections without measuring the wavefront disturbance to be corrected and without checking the set subsequent wavefront effect before the following exposure using a wavefront measuring system.

In order to obtain a better description of Z _i ({e _j }), a quadratic relationship is assumed in the nonlinear model 64 shown in (5). This functional relationship can be calibrated as explained in more detail below.

As in 5 As shown, according to one embodiment, the calibration of the functional relationship Z _i ({e _j }) of the non-linear model 64 is carried out by calibrating the control device 44 of the projection exposure system 10 according to 1 . Calibration is carried out in a calibration mode, which is usually carried out before commissioning of the projection exposure system 10 in the 1 illustrated exposure mode and then, if necessary, during exposure pauses. In the calibration mode, a setting transmitter 78 of a calibration device 77 generates a plurality of sets of travel path specifications p _j *, ie travel path specifications p ₁ * to p ₂₄ *, for setting the travel paths p ₁ to p ₂₄ of the manipulator devices M1 to M4. Each set of travel path specifications p _j * represents a different combination 80 of travel path settings, ie the travel paths p ₁ to p ₂₄ are set in different combinations 80 based on the different sets of travel path specifications p _j * by means of the manipulator system comprising the manipulator devices M1 to M4.

For each set of travel path specifications p _j *, ie for each travel path combination 80, the measured variables e ₁ to e ₂₄ are measured by means of the encoders E1 to E24 and transmitted to a calibration evaluation unit 84 of the calibration device 77 in the form of a measured variable data set e _j ^m designated with the reference symbol 82. Furthermore, the wavefront deviation 50 is measured for each travel path combination 80 and also transmitted to the calibration evaluation unit 84. The calibration evaluation unit 84 calibrates the control device 44 by assigning the relevant measurement variable data set 82 to the respective measurement result of the wavefront deviation 50. The result of the calibration is a determination of the following coefficients of the non-linear model 64: constant coefficients c _i (reference numeral 69), linear coefficients l _ij (reference numeral 70) and bilinear or quadratic coefficients q _ijk (reference numerals 72 and 74, respectively). The calibration device 77 can be part of the control device 44 or represent a separate unit.

quadratischen/bilinearen Koeffizient q_ijk für jeden Zernikekoeffizienten Zi durch parallele Messung von Wellenfront und Encoder an mehreren hinreichend voneinander entfernten, linear unabhängigen Stützstellen (Setpoints) bestimmt werden. Man beachte, dass lediglich $\frac{\left(n_{\text{enc}}+1\right)n_{\text{enc}}}{2},$

nicht $n_{enc}^2$

Koeffizienten benötigt werden, da aufgrund der Kommutivität q_ijk = q_ikj gilt.According to one embodiment, for the calibration of the non-linear model 64, the constant coefficients c _i , the n _enc linear coefficients l _ij and the $\frac{\left(n_{\text{enc}}+1\right)n_{\text{enc}}}{2}$

quadratic/bilinear coefficient q _ijk for each Zernike coefficient Zi by parallel measurement of wavefront and encoder at several sufficiently distant, linearly independent support points (setpoints). Note that only $\frac{\left(n_{\text{enc}}+1\right)n_{\text{enc}}}{2},$

not $n_{enc}^2$

Coefficients are needed because due to commutivity q _ijk = q _ikj .

Messungen von Encoder-Werten und Wellenfront erlauben das Gleichungssystem aus N_GLS Gleichungen für Z_i({e_j}) nach Koeffizienten für eine quadratische Beschreibung der realen Wellenfront des Systems zu ermitteln.This at least $N_{\text{GLS}}\ge 1+n_{enc}+\frac{\left(n_{enc}+1\right)n_{enc}}{2}$

Measurements of encoder values and wavefront allow to determine the system of equations from N _GLS equations for Z _i ({e _j }) in terms of coefficients for a quadratic description of the real wavefront of the system.

Such a calibration can be used to calibrate all effects that influence the relationship between encoder values and the determined wavefront effect, including but not limited to: installation tolerances, manufacturing errors, unknown setpoint, measurement errors of the wavefront sensor, measurement errors of the encoders, etc.

1. i) Es können mehr als die N_GLS Messungen gemacht werden, um die N_GLS Koeffizienten über einen Fit an die gemessenen Wellenfronten zu bestimmen. Dies erlaubt beispielsweise Messfehler zu reduzieren und so die Genauigkeit der Wellenfrontbeschreibung zu verbessern.
2. ii) Die Zahl der Messungen kann verringert werden, um weniger Zeit / Aufwand in die Kalibrierung zu stecken. Dies ist auf mehrere Weisen möglich:
   1. a) Nur die kritischsten Zernikekoeffizienten werden bestimmt (beispielsweise die Z2-Z4, die den größten Beitrag zur Wellenfrontveränderung und auch die größten Nicht-Linearitäten aufweisen). Alle weiteren Zernikekoeffizienten können als linear beschrieben werden.
   2. b) Ein Subset der Koeffizienten, beispielsweise die nichtlinearen Koeffizienten, werden über Simulationen bestimmt. Nur die verbleibenden (linearen) Koeffizienten müssen aus der Kalibrierung bestimmt werden. Dies ist möglich, da die höher als quadratischen Ordnungen in typischen Projektionssystemen kaum einen Beitrag zur Wellenfront leisten. Entsprechend sind die quadratischen Koeffizienten über große Verfahrwege hinweg konstant und müssen nicht immer wieder neu kalibriert werden. Nichtsdestotrotz können die quadratischen Koeffizienten von individuellen Systemeigenschaften, beispielsweise der genauen Position aller Encoder innerhalb der Einbautoleranzen, abhängen, was für die Bestimmung dieser Koeffizienten berücksichtigt werden muss.
   3. c) Ein Subset der Koeffizienten, beispielsweise die nichtlinearen Koeffizienten, werden nur einmal / seltener als andere Koeffizienten über die Kalibrierung bestimmt, so dass es unterschiedlich umfangreiche Kalibrierroutinen gibt, je nachdem, welcher Satz von Koeffizienten neu kalibriert werden muss.
   4. d) Einige Koeffizienten können a-priori als null (oder als konstant) angenommen werden und müssen entsprechend nicht kalibriert werden. Dies ist beispielsweise bei Freiheitsgraden unterschiedlicher Spiegel möglich, zwischen denen keine Korrelationen erwartet werden.
   5. e) Nicht der gesamte Raum möglicher Verfahrwege wird benötigt, sondern lediglich ein Unterraum, der durch Kombinationen unterschiedlicher Freiheitsgrade, sogenannte „Knobs“, aufgespannt wird. Dieser Unterraum kann niederdimensionaler als der Raum aller Freiheitsgrade sein. Falls die Korrekturen sich auf diesen Unterraum beschränken, ist es möglich nur die jeweiligen Knobs zu kalibrieren, was aufgrund der kleineren Zahl von Freiheitsgraden auch zu einer kleineren Zahl benötigter Messungen führt.
3. iii) Die Zahl der Messungen kann variiert werden, um Fehler durch die Nichtlinearität des Messsystems bei großen Wellenfrontänderungen zu reduzieren:
   1. a) Daher sind Kalibrierstellungen entlang von „Neutral Knobs“ und deren Kombinationen zu bevorzugen, so dass die eingestellten Wellenfrontänderungen beherrschbar bleiben.
   2. b) Alternativ ermittelt man die linearen Sensitivitäten, d.h. die lineare Änderung der Wellenfront bei Veränderung eines Encoder-Signals, an mehreren, weit auseinanderliegenden Kalibrier-Setpoints. Die so ermittelten punktweisen Gradienten werden schließlich rechnerisch zu einem quadratischen Verlauf zusammengestückelt. Durch die Bestimmung einer nichtlinearen Beschreibung der Wellenfront wird eine nichtlineare Korrektur/Optimierung der Wellenfront möglich, wie nachfolgend exemplarisch erläutert.

The number of measurements N _GLS can also be increased or decreased for various reasons:

1. i) More than N _GLS measurements can be made to determine the N _GLS coefficients by fitting them to the measured wavefronts. This allows, for example, to reduce measurement errors and thus improve the accuracy of the wavefront description.
2. ii) The number of measurements can be reduced to reduce the time/effort required for calibration. This can be done in several ways:
   1. a) Only the most critical Zernike coefficients are determined (for example the Z2-Z4, which make the largest contribution to the wavefront change and also exhibit the largest nonlinearities). All other Zernike coefficients can be described as linear.
   2. b) A subset of the coefficients, for example the non-linear coefficients, are determined via simulations. Only the remaining (linear) coefficients have to be determined from the calibration. This is possible because the higher than square orders in typical projection systems hardly contribute to the wavefront. Accordingly, the square coefficients are constant over large travel distances and do not have to be recalibrated again and again. Nevertheless, the square coefficients can depend on individual system properties, for example the exact position of all encoders within the installation tolerances, which must be taken into account when determining these coefficients.
   3. c) A subset of the coefficients, for example the nonlinear coefficients, are determined only once / less frequently than other coefficients via calibration, so that there are calibration routines of varying extent depending on which set of coefficients needs to be recalibrated.
   4. d) Some coefficients can be assumed a priori to be zero (or constant) and therefore do not need to be calibrated. This is possible, for example, for degrees of freedom of different mirrors between which no correlations are expected.
   5. e) Not the entire space of possible travel paths is required, but only a subspace that is spanned by combinations of different degrees of freedom, so-called "knobs". This subspace can be lower-dimensional than the space of all degrees of freedom. If the corrections are limited to this subspace, it is possible to calibrate only the respective knobs, which also leads to a smaller number of measurements required due to the smaller number of degrees of freedom.
3. iii) The number of measurements can be varied to reduce errors due to the nonlinearity of the measuring system at large wavefront changes:
   1. a) Therefore, calibration positions along “Neutral Knobs” and their combinations are to be preferred so that the adjusted wavefront changes remain manageable.
   2. b) Alternatively, the linear sensitivities, ie the linear change in the wavefront when an encoder signal changes, are determined at several widely spaced calibration setpoints. The point-by-point gradients determined in this way are then mathematically pieced together to form a quadratic curve. By determining a non-linear description of the wavefront, a non-linear correction/optimization of the wavefront is possible, as explained below using an example.

For the four movable mirrors R1 to R4 according to 1 with six degrees of freedom each, 24 linear and 300 quadratic/bilinear coefficients result. Together with the reference/output wavefront, 325 scalar quantities are determined for each Zernike coefficient at each field point according to the embodiment. If all Zernike coefficients and field points are measured in parallel, such a calibration requires 325 wavefront measurements to calibrate the system if all coefficients of the above model are to be determined via measurements.

By successively moving individual degrees of freedom and pairs of degrees of freedom by ±50µm or ±50µrad (or by encoder values that "approximately" correspond to these travel paths), a set of measurements can be generated that sample the quadratic relationship Z _i ({e _j }) described above with sufficient accuracy. The resulting linear system of 325 equations can be solved (for example by a "least-square fit" based on the summed, quadratic deviations in the Zernike coefficients) to determine the 325 unknown coefficients for each Zernike coefficient and field point.

The step size of ±50µm or ±50µrad results from a balance between several effects: Firstly, the step size should be large enough to observe non-linear effects. Secondly, the linear effects in the step size should not become so large that the measuring system can no longer observe the quadratic effects above them. Thirdly, the step size should be in a range in which quadratic and linear effects dominate, i.e. where higher order contributions are negligible.

One of the challenges of such an encoder wavefront description using the non-linear model 64 is the temporally stable validity of the calibration. Due to drift effects (e.g. encoder drifts), it is possible that the setpoint of the system changes differently than would be expected based on the changes in the encoder values. In order to check that such a calibration is still valid after a certain time (days, weeks, months, ...), so-called "control chart setpoints" could be used. At each of these setpoints, It must be checked whether the wavefront prediction based on the calibrated quadratic model continues to agree with the wavefront measurement. These control chart setpoints should cover the range of travels allowed by the calibration sufficiently well and thus allow the validity of the calibration to be checked at regular intervals over its entire travel range.

The above description of exemplary embodiments, embodiments or variants is to be understood as exemplary. The disclosure made thereby enables the person skilled in the art to understand the present invention and the associated advantages, and on the other hand also includes obvious changes and modifications to the structures and methods described in the understanding of the person skilled in the art. Therefore, all such changes and modifications, insofar as they fall within the scope of the invention as defined in the appended claims, as well as equivalents, are intended to be covered by the protection of the claims.

List of reference symbols

10

Projection exposure system

12

Exposure radiation source

14

Exposure radiation

16

Lighting system

18

mask

20

Mask transfer platform

22

Projection lens

23

Exposure beam path

24

Substrat

26

Substrate transfer stage

28

Wavefront sensor

30

Wavefront deviation

32

Translational movement

34

Tilting movement

36

Manipulator control unit

38

active mirror surface

39

back

40

laser beam

42

Measuring area

44

Control device

44-1

first embodiment of the control device

44-2

second embodiment of the control device

46

Control command

48

Wavefront sensor

50

Wavefront deviation

50a

updated wavefront deviation

52

Optimization algorithm

54

Objective function

56

desired correction wavefront effect

58-1

linear sensitivity function

58-2

nonlinear sensitivity function

60

Sensitivity coefficient

62

Linearization module

64

nonlinear model

66

nonlinear term

68

linear term

69

constant coefficient

70

linear coefficient

72

bilinear coefficient

74

quadratic coefficient

76

Product of two measurements

77

Calibration device

78

Setting provider

80

Travel combination

82

Measurement data set

84

Calibration evaluation unit

90

central control

91

Status transmitter

92

Storage

93

Simulation facility

94

Pressure sensor

95

current irradiation intensity

p1* to p24*

Travel specifications

p1 to p24

Travel range

e1 to e24, ej

Measurands

e1* to e24*

Specifications for the measured variables

R1 to R4

Mirror

M1 to M4

Manipulator devices

E1 to E24

Encoders

QUOTES INCLUDED IN THE DESCRIPTION

This list of documents listed 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 accepts no liability for any errors or omissions.

Cited patent literature

• DE 102015222097 A1 [0003]
• US 20130188246 A1 [0055]

Cited non-patent literature

• "Optical Shop Testing", 2nd Edition (1992) by Daniel Malacara, ed. John Wiley & Sons, Inc. [0055]
• 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 [0055]

Claims (16)

Projection exposure system (10) for microlithography with: - a mask holder (20) for holding a mask (18), a substrate holder (26) for holding a substrate (24) and a projection lens (22) with several optical elements (R1 - R4) for imaging mask structures of the mask onto the substrate, wherein the optical elements, the mask holder and the substrate holder are each a beam path element in an exposure beam path of the projection exposure system, - a manipulator system (M1 - M4) for setting at least one travel path (p ₁ - p ₂₄ ) on at least one of the beam path elements (R1-R4, 20, 26) in at least one manipulator degree of freedom, - at least one measuring device (E1 - E24) for measuring at least one measured variable (e ₁ - e ₂₄ ), which serves to determine the at least one travel path setting (p ₁ - p ₂₄ ) of the manipulator system, and - a control device (44) which is configured to determine a control command (46) with at least one specification (e ₁ * - e ₂₄ *) for the at least one measured variable of the at least one measuring device in order to correct a specification (50) of a wavefront deviation of the projection lens using a model (64), wherein the model describes a relationship (58-1, 58-2) between the measured variables and the wavefront deviation and comprises at least one non-linear term (66). Projection exposure system according to Claim 1 , in which the at least one measuring device (E1 - E24) is configured to measure different measured variables (e ₁ - e ₂₄ ), which serve to determine several travel settings (p ₁ - p ₂₄ ) of the manipulator system, and the non-linear term (66) comprises a product (76) of at least two of the measured variables. Projection exposure system Claim 2 , wherein the nonlinear term (68) comprises at least one bilinear coefficient (72) which is associated with the product (76) of the at least two of the measured variables (e _j ). Projection exposure system according to one of the preceding claims, wherein the non-linear term (66) comprises a square or a higher power of one of the measured quantities. Projection exposure apparatus according to one of the preceding claims, wherein the control device is configured to determine the control command by optimizing an objective function (54) which is based on the model. Projection exposure system according to Claim 5 , wherein the objective function comprises a linear sensitivity function (58-1) with sensitivity coefficients (60) determined by means of the model, which are each assigned to one of the measured variables and denote a local linear approximation of the relationship between the assigned measured variable (e _j ) and a corresponding deviation of the wavefront at the respective value (e _j *) of the measured variable present at the relevant operating time of the projection exposure system. Projection exposure system according to Claim 5 , wherein the objective function (54) comprises the relationship between the measured variables (e _j ) and the wavefront deviation (Zi) described by the model (64). Projection exposure system according to one of the preceding claims, wherein the model (64) comprises a plurality of non-linear terms (66), each comprising a product (76) of at least two of the measured variables, wherein the products of different non-linear terms each comprise different combinations of the measured variables. Projection exposure system according to one of the preceding claims, wherein the model (64) further comprises at least one linear term (68) in which one of the measured variables (e _j ) is contained in the first power and a linear coefficient (70) associated with this measured variable. Projection exposure system according to one of the preceding claims, wherein the deviations in the wavefront described in the model (64) are designated by at least one Zernike coefficient. Projection exposure system according to one of the preceding claims, wherein a plurality of the manipulator degrees of freedom can be adjusted on only one of the optical elements of the projection lens by means of the manipulator system (M1 - M4) and a plurality of the measured variables (e ₁ - e ₂₄ ) serve to determine the travel settings (p ₁ - p ₂₄ ) with regard to the manipulator degrees of freedom on the one optical element, and wherein the relationship described by the model exists between the plurality of measured variables and the wavefront deviation. Projection exposure apparatus according to one of the preceding claims, which comprises a simulation device (93) which is configured to simulate a change in the wavefront which is caused by a thermal heating of elements in the projection exposure area occurring during the exposure operation of the projection exposure apparatus (10). system and to determine the specification (50) of the wavefront deviation on the basis of the calculated wavefront. Method for operating a projection exposure system (10) for microlithography with a mask holder (20) for holding a mask (18), a substrate holder (26) for holding a substrate (24) and a projection lens (22) with several optical elements (R1-R4) for imaging mask structures of the mask onto the substrate, wherein the optical elements, the mask holder and the substrate holder are each a beam path element in an exposure beam path of the projection exposure system, a manipulator system (M1 - M4) for setting at least one travel path (p ₁ - p ₂₄ ) on at least one of the beam path elements (R1 - R4, 20, 26)) of the projection lens in several degrees of freedom and at least one measuring device (E1 - E24) for measuring at least one measured variable (e ₁ - e ₂₄ ), which serves to determine the at least one travel path setting (p ₁ - p ₂₄ ) of the manipulator system, with the Steps: - providing a specification (50) of a wavefront deviation of the projection lens, - determining at least one specification (e ₁ * - e ₂₄ *) for the at least one measured variable of the at least one measuring device from the wavefront deviation using a model (64), wherein the model describes a relationship (58-1, 58-2) between the measured variables and the wavefront deviation and comprises at least one non-linear term (66), and - correcting the wavefront deviation of the projection lens by adjusting the travel paths on the optical elements by means of the manipulator system in such a way that the at least one measured variable assumes the at least one determined specification. Calibration method for calibrating a control device (44) for correcting a wavefront deviation of a projection lens (22) of a projection exposure system (10) for microlithography with a mask holder (20) for holding a mask (18) and a substrate holder (26) for holding a substrate (24), wherein the projection lens has a plurality of optical elements (R1-R4) for imaging mask structures of the mask onto the substrate and wherein the optical elements, the mask holder and the substrate holder are each a beam path element in an exposure beam path of the projection exposure system, with the steps: - setting adjustment paths (p ₁ - p ₂₄ ) on the beam path elements of the projection lens in different combinations (80) by means of a manipulator system (M1 - M4), - measuring at least one measurement variable (e ₁ - e ₂₄ ) on the beam path elements for the different adjustment path combinations, - measuring the wavefront deviation of the projection lens for the different Travel range combinations, and - calibrating the control device based on an assignment of the measurement results (82) of the at least one measured variable to the respective measurement result of the wavefront deviation (50). Calibration procedure according to Claim 14 , in which the control device (44) is configured to determine a control command (46) with at least one specification (e ₁ * - e ₂₄ *) for the at least one measured variable in the exposure mode of the projection exposure system ( ₁₀ ) in order to correct a wavefront deviation (50) of the projection lens using a model (64) which describes a relationship between the at least one measured variable (e j ) and the wavefront deviation, and in which by assigning the measurement results (82) of the at least one measured variable to the respective measurement result of the wavefront deviation (50) at least one linear coefficient (70) is determined which is assigned to one of the measured variables (e _j ) in the model (64). Calibration procedure according to Claim 15 , in which at least one non-linear coefficient (72) is further determined by assigning the at least one measured variable to the respective measurement result of the wavefront.

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