WO2022038163A1

WO2022038163A1 - Control device for controlling manipulators for a projection lens

Info

Publication number: WO2022038163A1
Application number: PCT/EP2021/072876
Authority: WO
Inventors: Maximilian Schlemmer; Stefan Rist
Original assignee: Carl Zeiss Smt Gmbh
Priority date: 2020-08-20
Filing date: 2021-08-18
Publication date: 2022-02-24
Also published as: TWI785747B; TW202221422A; DE102020210567B3

Abstract

ZE7150WO – 2020P00299WO 33 Abstract Control device for controlling manipulators for a projection lens A control device (14) for controlling manipulators (M1-M4, 36) for changing an op-5 tical behaviour of a microlithographic projection lens (16) by generating respective stipulations (38) for a plurality of travel variables which define manipulations, to be undertaken by means of the manipulators, of at least one optical element (E1-E4) of the projection lens for the purposes of changing state parameters (34) of the projection lens is provided. The control device is configured to generate a respec-10 tive approximation (38-1) of the stipulations for the travel variables by optimizing a uniform scaling factor (86) using a first optimization algorithm (74), said scaling factor, in constraints (82) of the first optimization algorithm, defining a uniform scaling of limits (84) specified for the individual state parameters, and to ascertain a respective final result (38) of the stipulations for the travel variables by means of 15 at least one further optimization algorithm (76, 78) in the case where an optimiza- tion result (87) for the uniform scaling factor, as ascertained by means of the first optimization algorithm, does not exceed a specified threshold (85). (Fig. 3) 20 25

Description

Control device for controlling manipulators for a projection lens

This application claims priority to the German Patent Application No. 10 2020 210 567.7 filed on August 20, 2020. The entire disclosure of this patent application is incorporated into the present application by reference.

Background of the invention

The invention relates to a control device and a method for controlling manipulators for changing an optical behaviour of a microlithographic projection lens. Furthermore, the invention relates to an adjustment apparatus for adjusting a microlithographic projection lens, a projection lens for a microlithographic projection exposure apparatus having such a control device, and a microlithographic projection exposure apparatus having such a projection lens.

A microlithographic projection exposure apparatus serves for the generation of structures on a substrate in the form of a semiconductor wafer during the production of semiconductor components. To this end, the projection exposure apparatus comprises a projection lens having a plurality of optical elements, for imaging mask structures on the wafer during an exposure process.

A projection lens with wavefront aberrations that are as small as possible is required to guarantee imaging of the mask structures on the wafer as precisely as possible. Therefore, projection lenses are equipped with manipulators, which render it possible to correct wavefront errors by changing the state of individual optical elements of the projection lens. Examples of such a change in state include: a change of relative position in one or more of the six rigid-body degrees of freedom of the relevant optical element, application of heat and/or cold to the optical element. Furthermore, one or more post-processing units can also be provided for changing the shape of an optical element by ablating material from an optical element by means of surface processing. Such a post-processing unit can be part of the projection lens, or else be separate therefrom, and is likewise referred to as a manipulator within the scope of this document.

Manipulator modifications to be carried out in order to correct an aberration characteristic of a projection lens are calculated by means of a travel-generating optimization algorithm, which is also referred to as "manipulator modification model". By way of example, such optimization algorithms are described in WO 2010/034674 A1.

Thus, optimization algorithms known from the prior art may be configured to solve the following optimization problem:

Such an optimization problem is configured to minimize the target function, also referred to as merit function or as figure-of-merit function, described by

, t_aki_ng into account constraints described by B_k(x < spec_k .

Here, M denotes a sensitivity matrix, x denotes a travel vector with travel variables x/ or the individual manipulators, b_mess denotes a state vector of the projection lens which describes the individual state parameters of a measured aberration characteristic of the projection lens, I ^HI I ^lI^l2 denotes the Euclidean norm and spec_k denotes a respective fixed limit for individual travel variables Xk.

To ensure that envisaged limits are observed even for the state parameters of the projection lens, in particular the aberrations of the projection lens, suitable penalty terms are conventionally incorporated into the target function. Such penalty terms substantially represent "soft" limits or targets which, depending on the weighting and optionally the strictness of the relevant penalty term, are observed or optionally exceeded to a certain extent. Such penalty terms Hb or restricting the state parameters of the projection lens contained in the target function are represented in DE10 2015 206 448 A1 as follows:

Here, denote respective target values or specifications for corresponding state parameters of the projection lens in the form of Zernike coefficients bj. Fur- n^h thermore, and J denote parameters that are freely selectable by the user depending on the weighting and strictness of the relevant penalty term.

To determine a so-called recipe for the manipulators of the projection lens, i.e., stipulations for the travel variables of the manipulators, a plurality of iterations of the optimization algorithm are conventionally required as a rule, within the scope of which the weightings and optionally the strictness of the penalty terms are varied until the limits for the state parameters are observed sufficiently well. This is a very time-consuming process, in particular since it is unknown whether a reliable recipe does in fact exist if none can be found. In this context, a reliable recipe is understood to mean stipulations for the travel variables of the manipulators. In the case of a reliable recipe, the stipulations for the travel variables are chosen in such a way that constraints of respective specifications are observed.

Underlying object

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

By way of example, according to the invention, the aforementioned object can be achieved by a control device for controlling manipulators for changing an optical behaviour of a microlithographic projection lens by generating respective stipulations for a plurality of travel variables which define manipulations, to be undertaken by means of the manipulators, of at least one optical element of the projection lens for the purposes of changing state parameters of the projection lens. The control device according to the invention is configured to generate a respective approximation of the stipulations for the travel variables by optimizing a uniform scaling factor using a first optimization algorithm, said scaling factor, in constraints of the first optimization algorithm, defining a uniform scaling of limits specified for the individual state parameters. Furthermore, the control device according to the invention is configured to ascertain a respective final result of the stipulations for the travel variables by means of at least one further optimization algorithm in the case where an optimization result for the uniform scaling factor, as ascertained by means of the first optimization algorithm, does not exceed a specified threshold.

Expressed differently, the respective final result of the stipulations for the travel variables is ascertained by means of the at least one further optimization algorithm if the optimization result of the first optimization result for the uniform scaling factor is no more than the specified travel. In this document, a "travel" is understood to mean a change in state parameter of one or more optical elements along the travel, implemented by means of the manipulator actuation, for the purposes of changing the optical power of the optical element or elements. By way of example, the manipulation can consist of the displacement of the optical element in a specific direction, but it can also consist of e.g. an impingement, in particular a local or two-dimensional impingement, of the optical element with heat, coldness, forces, light with a specific wavelength or currents. Furthermore, the manipulation can define material ablation at an optical element, which is to be carried out by means of a post-processing unit. In particular, the state parameters can be aberrations of the projection lens. The scaling factor can also be referred to as target reaching variable. Such a target reaching variable describes a normalized distance between the limits and the corresponding state parameters. By way of example, the value 1 can be specified as a threshold, i.e., the specified limits are all observed. Furthermore, a higher value can be set as threshold. What is known at least in this case is the extent to which the limits are exceeded.

The first optimization algorithm facilitates a reliable determination whether an admissible recipe exists for a set of state parameters of the projection exposure apparatus, i.e., whether the control device can ascertain stipulations for the travel variables by means of which the limits specified in the constraints are observed. In particular, the first optimization algorithm and/or the second optimization algorithm are configured to solve a nonlinear optimization problem.

By way of the inventive generation of a uniform scaling factor by means of the first optimization algorithm, it is possible to reliably assume that there is a reliable recipe and hence that the final result of the stipulations for the travel variables is found without having to carry out a plurality of iterations of the further optimization algorithm with variations of the weightings in this case should there be a positive response to the question as to whether the optimization result for the uniform scaling factor is no more than the specified threshold. Hence, the recipe for the travel variables can be found in a very time-efficient manner. In particular, it is possible to formulate the constraints as hard constraints which are reliably observed, for instance as explicit constraints. Explicit constraints are understood to be constraints which are not part of the relevant target function, as is the case for the penalty terms used in the prior art.

According to a further embodiment, the control device is furthermore configured to carry out a state parameter optimization algorithm when carrying out the at least one further optimization algorithm, a weighted sum of individual scaling factors being optimized in said state parameter optimization algorithm with state parameter constraints relating to the state parameters being taken into account, wherein the individual scaling factors in the state parameter constraints define a respective scaling of the limits specified for the individual state parameters.

In particular, the further constraints, under the consideration of which the weighted sum of individual scaling factors is optimized, correspond to the aforementioned explicit further constraints. In particular, when carrying out the at least one further optimization algorithm, the stipulations for the travel variables are generated taking account of the further constraints by optimizing the weighted sum of the individual scaling factors. Expressed differently, the weighted sum of the individual scaling factors forms the target function of the state parameter optimization algorithm. Scaling the specified limits with respective individual scaling factors should be understood to mean that one of a plurality of individual scaling factors is assigned to each of the limits, the respective limit then being scaled with the respective scaling factor. In particular, the state parameter constraints furthermore comprise the limits for the individual state parameters. In particular, the state parameter optimization algorithm is configured to solve a nonlinear optimization problem.

According to a further embodiment, the control device is furthermore configured to carry out a travel optimization algorithm, in which a target function containing the travel variables is optimized, when carrying out the at least one further optimization algorithm. In particular, the state parameter optimization algorithm is configured to solve a nonlinear optimization problem.

According to a further embodiment, the control device is configured, when carrying out the at least one further optimization algorithm, to initially carry out the state parameter optimization algorithm and subsequently carry out the travel optimization algorithm, wherein the travel optimization algorithm is configured to optimize the target function taking account of the condition that further individual scaling factors may each exceed optimization results for the corresponding first individual scaling factors, as ascertained by the state parameter optimization algorithm, by no more than 5%, in particular by no more than 1 %. In particular, the specified condition is a part of travel optimization constraints which, in particular, furthermore comprise the limits for the individual state parameters. This loosening for the further individual scaling factors provides the travel optimization algorithm with sufficient play to find an optimized solution for the target function containing the travel variables.

According to a further embodiment, the control device is furthermore configured to base the travel optimization algorithm on further approximations of the stipulations for the travel variables, which are ascertained when carrying out the state parameter optimization algorithm.

According to a further embodiment, the state parameter constraints furthermore comprise the condition that each of the first individual scaling factors may exceed the optimization result for the uniform scaling factor, as ascertained by the first optimization algorithm, by no more than 5%, in particular by no more than 1 %. This loosening for the individual scaling factors provides the state parameter optimization algorithm with play 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 where the exponent is at least two.

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

According to a further embodiment, the constraints of the first optimization algorithm are formulated as explicit constraints, which are not part of a target function optimized when carrying out the first optimization algorithm. Thus, an explicit constraint is understood to be a constraint that is not part of the target function; in contrast to this, an implicit constraint is part of the target function. According to further embodiments, the state parameter constraints and/or the constraints underlying the travel optimization algorithm are likewise formulated as explicit constraints.

According to a further embodiment, the ascertained stipulations for the travel variables define changes in the state parameters of the projection lens to be undertaken by means of the manipulators. In particular, they define both changes to be undertaken in state parameters of the projection lens and changes to be undertaken in state parameters of the projection exposure apparatus not relating to the projection lens, for instance state parameters relating to an illumination system of the projection exposure apparatus.

Furthermore, an adjustment apparatus for adjusting a microlithographic projection lens is provided according to the invention. The adjustment apparatus comprises a measuring device for ascertaining current values of state parameters of the projection lens and a control device according to any one of the embodiments or embodiment variants described above for generating the stipulations for the travel variables from the current values of the state parameters.

Furthermore, a projection lens for a microlithographic projection exposure apparatus is provided according to the invention, said projection lens comprising manipulators that are configured to alter state parameters of the projection lens. Furthermore, the projection lens comprises a control device according to any one of the above-described embodiments or embodiment variants for controlling the manipulators.

Furthermore, a microlithographic projection exposure apparatus is provided according to the invention, said microlithographic projection exposure apparatus comprising the above-described projection lens. Furthermore, the aforementioned object can be achieved, for example, by means of a method for controlling manipulators for changing an optical behaviour of a mi- crolithographic projection lens by generating respective stipulations for a plurality of travel variables. The travel variables define manipulations, to be undertaken by means of the manipulators, on at least one optical element of the projection lens for changing the state parameters. The method according to the invention comprises a generation of a respective approximation of the stipulations for the travel variables by optimizing a uniform scaling factor using a first optimization algorithm, wherein the uniform scaling factor, in constraints of the first optimization algorithm, defines a uniform scaling of limits specified for the individual state parameters, and an ascertainment of a respective final result of the stipulations for the travel variables by means of at least one further optimization algorithm in the case where an optimization result for the uniform scaling factor, as ascertained by means of the first optimization algorithm, does not exceed a specified threshold.

According to one embodiment of the method according to the invention, the respective final result of the stipulations for the travel variables is ascertained using the at least one further optimization algorithm taking into account explicit further constraints for the state parameters of the projection lens, which are not part of a target function optimized when carrying out the at least one further optimization algorithm.

The features specified in respect of the embodiments, exemplary embodiments and embodiment variants etc., of the control device according to the invention, listed above, can be accordingly transferred 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 in the claims. The individual features can be implemented, either separately or in combination, as embodiments of the invention. Furthermore, they can describe advantageous embodiments which are independently protectable and protection for which is claimed if appropriate only during or after pendency of the application. Brief description of the drawings

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. In the drawings:

Fig. 1 shows an adjustment apparatus for adjusting a projection lens of a micro- lithographic projection exposure apparatus comprising a control device for generating a travel command for manipulators,

Fig. 2 shows a microlithographic projection exposure apparatus comprising a control device for generating a travel command for manipulators, and

Fig. 3 shows a visualization of the functionality of an embodiment of the aforementioned control device.

Detailed description of exemplary embodiments according to the invention

In the exemplary embodiments or embodiments or embodiment variants described below, elements which are functionally or structurally similar to one another are provided with the same or similar reference signs as far as possible. Therefore, for understanding the features of the individual elements of a specific exemplary embodiment, reference should be made to the description of other exemplary embodiments or the general description of the invention.

In order to facilitate the description, a Cartesian xyz-coordinate system is indicated in the drawing, from which system the respective positional relationship of the components illustrated in the figures is evident. In Figure 1 , the y-direction extends perpendicularly to the plane of the drawing into said plane, the x-direction extends toward the right, and the z-direction extends upward.

Figure 1 shows an adjustment apparatus 10 for adjusting a projection lens 16 of a microlithographic projection exposure apparatus. The adjustment apparatus 10 comprises a measuring device 12 for ascertaining the state parameters 34 of the projection lens 16 which characterize aberrations of the projection lens 16 and a control device 14 in the form of a so-called travel ascertaining device for generating a travel command 38 with stipulations 38n and 38p for travel variables Xk of manipulators from the state parameters 34. In this document, the stipulations 38n and 38p are also referred to as travel vectors x and define manipulations to be undertaken on at least one optical element E1 to E4 of the projection lens 16, described in more detail below, by means of manipulators.

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

The measuring device 12 is configured to measure wavefront errors of the projection lens 16 and comprises an illumination unit 18 and a measurement mask 22 on the entrance side of the projection lens 16 and a sensor element 26, a detector 30 and an evaluation unit 32 on the exit side of the projection lens 16. The illumination unit 18 is configured to generate measurement radiation 20 at the operating wavelength of the projection lens 16 to be tested, in the present case in the form of EUV radiation, and to radiate said radiation onto the measurement mask 22, which is arranged in the object plane 24. The measurement mask 22, which is often also referred to as a "coherence mask", has a first periodic structure. The sensor element 26 in the form of an image grating, which has a second periodic structure, is arranged in the image plane 28. It is also possible to combine chequerboard structures in the measurement mask 22 with chequerboard structures in the sensor element 26. It is also possible to use other combinations of periodic structures known to a person skilled in the art from the field of shearing interferometry or point diffraction interferometry.

The detector 30 in the form of a camera, which resolves in two dimensions, is arranged below the sensor element 26, to be precise in a plane conjugate to the pupil plane of the projection lens 16. Together, the sensor element 26 and the detector 30 form a sensor module. The measurement mask 22 and the sensor module form a shearing interferometer or point diffraction interferometer, known to a person skilled in the art, and serve to measure wavefront errors of the projection lens 16. To this end, phase shifting methods, which are known to a person skilled in the art, are applied in particular.

The evaluation unit 32 ascertains the state parameters 34 of the projection lens 16 from the intensity patterns recorded by the detector 30. According to the present embodiment, the state parameters 34 comprises a set of Zernike coefficients characterizing the wavefront errors of the projection lens 16.

Z”

In the present application, the Zernike functions ^m , as known from, e.g., Chapter 13.2.3 in the textbook "Optical Shop Testing", 2nd Edition (1992) by Daniel Malacara, pub. John Wiley & Sons, Inc., are denoted by Zj in accordance with the so-called fringe sorting, as described in, e.g., paragraphs [0125]-[0129] in US 2013/0188246A1 , with bj then being the Zernike coefficients assigned to the respective Zernike polynomials (also referred to as "Zernike functions"). Fringe sorting is illustrated for example in Table 20-2 on page 215 of “Handbook of Optical Systems”, Vol. 2 by H. Gross, 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. A wavefront deviation W(p,<l>) at a point in the object plane of the projection lens is then series-expanded as follows in a manner dependent on the polar coordinates (p, ) of the pupil plane:

While the Zernike polynomials are denoted by Zj, i.e., with the subscript index j, the Zernike coefficients are denoted by bj within the scope of this application. It should be noted here that the Zernike coefficients bj are often also denoted by Zj, i.e. with a normally written index, in the specialist world, such as, e.g., Z5 and Z6 representing astigmatism.

The state characterization 34 established by the evaluation unit 32 of the measuring device 12 is transferred to the control device 14, which generates the travel command 38 therefrom. As already mentioned above, the travel command 38 in the present exemplary embodiment comprises the stipulations 38n and 38p. The stipulations 38p comprise travel stipulations Xp for manipulators M1 to M4 of the projection lens 16, where L is a counter for travel variables Xk controllable by means of the manipulators M1 to M4. The stipulations 38n comprise travel stipula- x tions ^nL for controlling a post-processing unit 36 for mechanical post-processing of optical elements E1 to E4 of the projection lens 16, where L is a counter for travel variables Xk controllable by means of the post-processing unit 36.

Within the scope of this application, both the manipulators M1 to M4 of the projection lens 16 and the post-processing unit 36 are understood to be manipulators for changing the optical behaviour of the projection lens 16, more precisely for undertaking manipulations on at least one of the optical elements E1 to E4 of the projection lens 16 for the purposes of changing state parameters 34 of the projection lens 16.

The projection lens 16 has four optical elements E1 to E4 in the embodiment as per Figure 1 . All optical elements are mounted in a movable manner. To this end, a respective manipulator MS, in particular respectively one of the manipulators M1 to M4, is assigned to each one of the optical elements E1 to E4. The manipulators M1 , M2 and M3 each enable a displacement of the assigned optical elements E1 , E2 and E3 in the x- and y-direction and therefore substantially parallel to the plane in which the respective reflecting surface of the optical elements lies.

The manipulator M4 is configured to tilt the optical element E4 by rotation about a tilt axis 40 arranged parallel to the y-axis. As a result, the angle of the reflecting surface of E4 is modified in relation to the incident radiation. Further degrees of freedom for the manipulators are conceivable. Thus, for example, provision can be made for a displacement of a relevant optical element across the optical surface thereof or for a rotation about a reference axis perpendicular to the reflecting surface.

In general terms, each one of the manipulators M1 to M4 illustrated here is provided to bring about a displacement of the associated optical element E1 to E4 while performing a rigid body movement along a travel defined by means of the stipulations 38p. By way of example, such a travel can combine translations in different directions, tilts and/or rotations in any manner. As an alternative or in addition thereto, it is also possible to provide manipulators which are configured to undertake a different mannered change of a state variable of the associated optical element by an appropriate actuation of the manipulator. In this respect, an actuation can be carried out by, e.g., applying a specific temperature distribution or a specific force distribution to the optical element. In this case, the travel can be as a result of a change in the temperature distribution on the optical element or the application of a local tension to an optical element embodied as a deformable lens or as a deformable mirror.

In the shown case, the travels 38p comprised by the travel command 38 contain the travels Xp, Xp, Xp and Xp, which predetermine changes to be carried out by the manipulators M1 to M4 and which therefore serve to control the manipulators M1 to M4 of the projection lens 16. The ascertained travels Xp, Xp, Xp and Xp are communicated to the individual manipulators M1 to M4 by means of travel signals and predefine for them respective correction travels to be implemented. These define corresponding displacements of the assigned optical elements M1 to M4 for correcting wavefront errors of the projection lens 16 that occurred. In the case where a manipulator has a plurality of degrees of freedom, it is also possible to communicate a plurality of travels Xp thereto. x

The stipulations 38n ( ^nL ) for the post-processing unit 36 furthermore comprised

1 2 3 4

X X X X by the travel command 38 contain the travels ⁿ , ⁿ , ⁿ and ⁿ in the shown case, which travels serve to control the post-processing unit 36 for the respective mechanical post-processing of the optical elements E1 , E2, E3 and E4 of the pro- x on lens 16. Therefore, like the travels Xp to Xp, the travels ⁿ¹ x jecti to ⁿ⁴ serve to correct wavefront errors of the projection lens 16 that occurred.

The post-processing unit 36 should be understood to mean a unit for mechanical ablation of material at an optical surface of an optical element in the form of a lens or a mirror. This ablation follows the production of the optical element. Therefore, a correspondingly post-processed optical element is also referred to as an intrinsically corrected asphere (ICA). In particular, an ablation unit usually used for the mechanical processing of ICAs can be used as a post-processing unit 36. Therefore, the ablations are also referred to as "ICA ablations" below. By way of example, an ion beam can be used for mechanical processing. Using this, it is possible to work any correction profile into a post-processed optical element.

Figure 2 shows an embodiment according to the invention of a microlithographic projection exposure apparatus 50. The present embodiment is designed for operation in the EUV wavelength range. All optical elements are embodied as mirrors as a result of this operating wavelength. However, the invention is not restricted to projection exposure apparatuses in the EUV wavelength range. Further embodiments according to the invention are designed, for example, for operating wavelengths in the UV range, such as e.g. 365 nm, 248 nm or 193 nm. In this case, at least some of the optical elements are configured as conventional transmission lens elements. The projection exposure apparatus 50 in accordance with Figure 2 comprises an exposure radiation source 52 for generating exposure radiation 54. In the present case, the exposure radiation source 52 is embodied as an EUV source and it can comprise, for example, a plasma radiation source. The exposure radiation 54 initially passes through an illumination optical unit 56 and it is deflected onto a mask 58 thereby. The illumination optical unit 56 is configured to generate different angle distributions of the exposure radiation 54 incident on the mask 58. Depending on an illumination setting desired by the user, the illumination optical unit 56 configures the angle distribution of the exposure radiation 54 incident on the mask 58. Examples for selectable illumination settings comprise a so-called dipole illumination, annular illumination and quadrupole illumination, and also a free-form illumination, i.e., an intensity distribution of the illumination profile that is freely selectable up to a point.

The mask 58 has mask structures to be imaged on a substrate 64 in the form of a wafer and it is displaceably mounted on a mask displacement stage 60. As depicted in Figure 2, the mask 58 can be embodied as a reflection mask or, alternatively, it can also be configured as a transmission mask, in particular for UV lithography. In the embodiment in accordance with Figure 2, the exposure radiation 54 is reflected at the mask 58 and it thereupon passes through the projection lens 16, which was already described with reference to the adjustment apparatus 10 in accordance with Figure 1 . The projection lens 16 serves to image the mask structures of the mask 58 on the substrate 64. The exposure radiation 54 is guided within the projection lens 16 by means of a multiplicity of optical elements E1 to E4, presently in the form of mirrors. The substrate 64 is displaceably mounted on a substrate displacement stage 66. The projection exposure apparatus 50 can be designed as a so-called scanner or a so-called stepper.

In the case of an embodiment as a scanner, which is also referred to as a step- and scan projection exposure apparatus, the mask displacement stage 60 and the substrate displacement stage 66 are moved in opposite directions or in the same direction during each instance of imaging the mask 58 on the substrate 64, i.e., each instance of exposing a field on the substrate 64. As shown in Figure 2, in this case, for example, the mask displacement stage 60 moves in a scanning direction 62 pointing to the left and the substrate displacement stage moves in a scanning direction 68 pointing to the right. So-called fading aberrations can be traced back to the scanning movements during the field exposure of such a scanner and are explained in more detail below.

The projection exposure apparatus 50 furthermore comprises a control device 14. In the visualized embodiment, said control device only differs from the control device 14 as per Figure 1 in that the travel command 38 generated from the state parameters 34 only comprises stipulations 38p for the travel variables Xp for the manipulators M1 to M4. The state parameters can be gathered by means of an external wavefront measuring device, such as the measuring device 12 described with reference to Figure 1 . Alternatively, however, the state parameters 34 can also be measured by a wavefront measuring unit 70 integrated in the substrate displacing stage 66. The control device 14 contained in the projection exposure apparatus 50 can correspond to the control device 14 as per Figure 1 in accordance with a further embodiment and can generate a travel command 38 which, in addition to the stipulations 38p, also comprises the stipulations 38n for the postprocessing unit 36. In this case, the optical elements E1 to E4 affected by the post-processing are firstly removed from the projection lens 16 and post-pro- cessed on the basis of the stipulations 38n. Then, the optical elements E1 to E4 are reinserted into the projection lens 16 and adjusted in accordance with the stipulations 38p by means of the manipulators M1 to M4.

The functionality of the control device 14 is elucidated below in an exemplary manner, with reference being made to Figure 3. It is configured to carry out a travel-generating overall optimization algorithm 72, with the overall optimization algorithm 72 comprising a plurality of individual optimization algorithms 74, 76 and 78. The constraints of the optimization problem comprise specification values or stipulated maximum values for the state parameters 34 of the projection lens 16 and specification values or maximum values for the travel variables Xk. The individual state parameters 34 are also represented as ZPi below, where i is a counter.

The constraints in respect of the state parameters 34 of the projection lens 16 are represented in general as set forth below:

5j(x) < spec ^p (2)

Here, spec ¹³ are the specification values or limits for the state parameters ZPi of the projection lens 16 numbered by the index i and Bi(x) is a functional comprising the respective state parameters of the projection lens 16, possibly as a function of the travel factor x. The constraints as per (2) comprise the following constraint groups according to one embodiment:

8fj < spec (4)

OVLp < speCp^Vl , and (5)

RMS^r < spec^^ms (6)

Here, the constraint group as per expression (3) relates to conditions for the individual Zernike coefficients bj. Here, spec¹- is the specification for the respective

Zernike coefficients bj, where the index j runs from 1 to jmax^ '-^e-> the state parameters ZPi in this case correspond to the Zernike coefficients bj. The specification spec¹- corresponds to the general specification values spec ^p from term (2) with i = 1 t° jmax- M is a sensitivity matrix already mentioned above, which describes the relationship between an adjustment of a degree of freedom k of a manipulator by the standard travel Xk°.

The expression 8fj from (4) is:

The constraint group as per expression (4) relates to conditions for so-called fad- ing aberrations J . These can be calculated from the measured Zernike aberra- f tions bj. Furthermore, spec'- is the target value or the specified specification for

A, .f the fading aberration J , where the index j runs from 1 to J^ax- ^{That is t0 sa}y, ^the state parameters ZPi correspond to the fading aberration

in this case. The specification spec'- corresponds to the general specification values spec from term (2) with i = jmax+^ ^t0 jmax + jmax- The ^{SLjm over} the index m runs over all field points along the scanning direction of the projection exposure apparatus. The parameter w_m denotes so-called scan weightings, i.e., weightings of the image ab- errations traced back to the scan movements.

denotes a sensitivity matrix for the fading aberrations / and hence defines the change in the state vector b of the projection lens on account of fading aberrations when adjusting the manipulators by a standard travel xo.

The constraint group as per expression (5) relates to conditions for overlay error. Overlay errors are determined for different structure types, such as e.g. isolated lines, lines arranged in a grid, circular structures, etc. The different structure types are denoted by the index p. An overlay error as a function of the structure type p (SZ^pb) and the field point m is denoted by the product ^{v Jm} . Here, SZP is a matrix which comprises field point-dependent weightings for the individual Zernike coeffi- (SZ^pb) cients bj. An overlay error ^{v Jm} is therefore formed by linear combinations of individual Zernike coefficients bj.

The expression OVLp from (5) is:

Furthermore, spec™¹ is the target value or the specified specification for the overlay error of the structure type p, where the index p runs from 1 to pmax. That is (SZ^pb) to say, the state parameters ZPi correspond to the overlay errors ^{v Jm} in this case. The specification spec™¹ corresponds to the general specification values spec ^p from term

trix M is the sensitivity matrix already described above in relation to the constraint group in respect of the aberrations. The max function determines the maximum over all field points m.

The constraint group as per expression (6) relates to conditions for grouped RMS values. Here, RMS^r is defined as follows:

Here, r is an index of the grouped RMS value RMS^r. By way of example, the grouping is carried out by classifying the corresponding Zernike coefficients bj into the categories "spherical aberrations", "coma", "astigmatism", etc. The sum over j I • is a sum over Zernike orders, J are the weightings of the individual Zernike contributions bj to the RMS value with the index r and the maximum is established over all field points m of the image field of the projection lens 16. The grouped RMS values RMS^r each comprise a group of Zernike coefficients Zj with equal azimuthal waviness according to various embodiments, typically all Zernike coefficients Zj with the relevant azimuthal waviness (e.g., 2-fold or 4-fold azimuthal waviness) up to a certain radial waviness (i.e., radial waviness < maximum radial waviness). By way of example, the grouped RMS value "RMS_AST_0" comprises the Zernike coefficients Zj with j = 12, 21 , 32, ... and the grouped RMS value "RMS_Coma_x" comprises the Zernike coefficients Zj with j = 7, 14, 23 and 34. In the conditions specified in expression (6) for the RMS values RMS^r, spec ⁵ is the specified specification for the RMS value with the index r. That is to say, the state parameters ZPi correspond to the RMS values RMS^r in this case.

As mentioned above, the overall optimization algorithm 72 carried out by the control device 14 comprises a plurality of individual optimization algorithms. The first of these optimization algorithms, denoted by reference sign 74 in Figure 3, optimizes the following target function F, often also referred to as merit function or as figure-of-merit function, which is denoted by reference sign 80 in Figure 3:

F(x, t_s) = t_s ; i.e., F — > min (10) with the following explicit constraints: t_s > 0 , (1 1 )

5j(x) < t_s ■ spec ^p , and (12)

F_k(x) < spec (13) The constraint cited in (1 1 ) specifies that ts must not be negative. The constraints cited in (12), denoted by reference 82 in Figure 3, relate to the state parameters ZPi of the projection lens 12 and correspond to the constraints cited in (2) with the exception that the limits or specification values spec ¹³ denoted by reference sign 84 in Figure 3 are each preceded by a uniform scaling factor ts. The scaling factor t_s denoted by reference sign 86 in Figure 3 is the same for all specification values spec ^p and serves to uniformly scale the specification values or limits 84 specified for the individual state parameters ZPi of the projection lens 14. The constraints cited in (13) finally specify specifications or limits spec for the individual travel variables Xk and can also be omitted depending on the embodiment variant.

The optimization algorithm 74 is now configured to optimize the uniform scaling factor t_s by minimization. As a result of this optimization, an approximated travel command 38-1 is generated on the basis of the measured state parameters 34. This approximated travel command 38-1 comprises approximations of the stipulations 38p and optionally 38n for the travel variables Xk.

In the case where the optimization result t°^pt for the uniform scaling factor ts, denoted by reference sign 87 in Figure 3, does not exceed a specified threshold 85, which is preferably 1 , i.e., if t°^pt < 1 , there is a transition to the second optimization algorithm 76. In this case, it is already certain that an admissible recipe exists in the form of stipulations for the travel variables Xk for the manipulators of the projection lens 16, in which all limits 84 specified for the state parameters of the projection lens are observed. Thus, an admissible recipe exists if stipulations for the travel variables Xk for which the constraints are observed exist. If t°^pt> 1 , the optimization is generally terminated since no such admissible recipe exists. However, if t_s just exceeds the threshold it may nevertheless be advantageous to generate a recipe by means of the second and third optimization algorithm 76 and 78, by means of which recipe the limits 84 are observed at least to the best possible extent. The second optimization algorithm 76 serves for the individual optimization of the state parameters 34 of the projection lens 16 and is therefore also referred to as state parameter optimization algorithm in this document. To this end, each of the state parameters ZPi is assigned a corresponding individual scaling factor ti denoted by reference sign 90 in Figure 3.

The target function F of the second optimization algorithm 76, denoted by reference sign 88 in Figure 3, is formed by a weighted sum 92 of the individual scaling factors ti, where the respective weighting factors are denoted by wi:

The optimization of the target function F illustrated in (14) (i.e., F — min) is implemented under the following explicit constraints:

1.01 , (15)

5j(x) < ti ■ speCi ^P , and (16)

B_k(x) < spec (17)

The constraints cited in (15) and (16) are also referred to as state parameter constraints 94 in this document. The constraint cited in (15) specifies that the individual scaling factors ti in each case cannot be negative and in each case exceed the optimization result t°^pt ascertained by means of the first optimization algorithm 74 for the uniform scaling factor t_s by no more than 1 %. According to further embodiments, the constraint (15) can also be formulated in such a way that ti may exceed the optimization result

by a greater percentage, such as for instance by 5%. This loosening for the individual scaling factors 90 provides the second optimization algorithm 76 with sufficient play to find an optimized solution for the weighted sum 92 of the individual scaling factors 90. The condition of the state parameter constraints 94 cited in (16) corresponds to constraint (12) of the first optimization algorithm 74, with the exception that the specification values spec ¹³ of the individual state parameters ZPi are each preceded by the relevant individual scaling factor ti instead of the uniform scaling factor t_s. Hence, the individual scaling factors 90 define a respective scaling of the limits 84 specified for the individual state parameters ZPi. The constraints cited in (17) are identical to the constraints (13) of the first optimization algorithm 74 and specify specifications or limits spec for the individual travel variables Xk. Depending on the embodiment variant, these can also be omitted in a manner analogous to the constraints (13).

The stipulations which are contained in the approximated travel command 38-1 ascertained by the first optimization algorithm 74 are taken as a basis for the second optimization algorithm 76 as start values. The optimization by the second optimization algorithm 76 results in a further approximated travel command 38-2 and optimization results t°^pt for the individual scaling factors ti denoted by reference sign 91 in Figure 3. The further approximated travel command 38-2 comprises further approximations of the stipulations 38p and optionally 38n for the travel variables Xk.

The third optimization algorithm 78 serves to optimize the travels 38p and 38n which are to be carried out by the manipulators of the projection lens 16 and, optionally, by the post-processing unit 36 and which are specified by the travel command 38. As a rule, the object here is to minimize these travels. Therefore, the third optimization algorithm 78 is also referred to as travel optimization algorithm in this document.

The target function F of the third optimization algorithm 78, denoted by reference 96 in Figure 3, is as follows:

Here, x^f denotes the transposed travel vector x, M ^f denotes the transposed sensitivity matrix /W and

denotes the transposed vector of the Zernike coefficients bj. Since the target function F as per (18) contains the travel variables Xk by way of the travel vector x, the third optimization algorithm 78 is also referred to as travel optimization algorithm in this document. Since the target function F as per (18) contains x and x^f as factors, the target function F contains the travel variables Xk in quadratic form. The optimization of the target function F illustrated in (18) (i.e., F — min) is implemented under the following explicit constraints:

F_k(x) < spec (22)

The constraints cited in (20) and (21 ) are also referred to as travel optimization constraints 98 in this document. The constraint cited in (20) specifies that the further individual scaling factors

denoted by reference sign 100, in each case cannot be negative and in each case exceed the optimization result t°^pt ascertained by means of the second optimization algorithm 76 for the corresponding individual scaling factor ti by no more than 1 %. According to further embodiments, the constraint (20) can also be formulated in such a way that

may exceed the respective optimization result t°^pt by a greater percentage, such as for instance by 5%. This loosening for the further individual scaling factors 100 provides the third optimization algorithm 78 with sufficient play to find an optimized solution for the travels 38p and optionally 38n.

The condition of the constraint 98 cited in (21 ) corresponds to the constraint (16) of the second optimization algorithm 76, with the exception that the individual scaling factors ti are replaced by the further individual scaling factors

The constraints cited in (22) are identical to the constraints (13) of the first optimization algorithm 74 and the constraints (17) of the second optimization algorithm 76, which specify specifications or limits spec for the individual travel variables Xk. Depending on the embodiment variant, these can also be omitted in a manner analogous to the constraints (13).

The stipulations which are contained in the further approximated travel command 38-2 ascertained by the second optimization algorithm 76 are taken as a basis for the third optimization algorithm 78 as start values. The result of optimization by the third optimization algorithm 78 is the travel command 38. The latter comprises the final results of the stipulations 38p and optionally 38n for the travel variables Xk, which thereupon are transmitted as control signals to the manipulators M1 to M4 of the projection lens 16 and optionally to the post-processing unit 36, as described above with reference to Figures 1 and 2.

The above description of exemplary embodiments, embodiments or embodiment variants is to be understood to be by way of example. The disclosure effected thereby firstly enables the person skilled in the art to understand the present invention and the advantages associated therewith, and secondly encompasses alterations and modifications of the described structures and methods that are also obvious in the understanding of the person skilled in the art. Therefore, all such alterations and modifications, in so far as they fall within the scope of the invention in accordance with the definition in the accompanying claims, and equivalents are intended to be covered by the protection of the claims. List of reference signs

10 Adjustment apparatus

12 Measuring device

14 Control device

16 Projection lens

18 Illumination unit

20 Measurement radiation

22 Measurement mask

24 Object plane

26 Sensor element

28 Image plane

30 Detector

32 Evaluation unit

34 State parameter

36 Post-processing unit

38 Travel command

38-1 Approximated travel command

38-2 Further approximated travel command

38p Stipulations for manipulators of the projection lens

38n Stipulations for the post-processing unit

40 Tilt axis

50 Projection exposure apparatus

52 Exposure radiation source

54 Exposure radiation

56 Illumination optical unit

58 Mask

60 Mask displacement stage

62 Scanning direction of the mask displacement stage

64 Substrate

66 Substrate displacement stage

68 Scanning direction of the substrate displacement stage 70 Wavefront measuring unit

72 Overall optimization algorithm

74 First optimization algorithm

76 Second optimization algorithm

78 Third optimization algorithm

80 Target function of the first optimization algorithm

82 Constraints of the first optimization algorithm

84 Limits

85 Threshold

86 Uniform scaling factor ts

87 Optimization result of the uniform scaling factor ts

88 Target function of the second optimization algorithm

90 Individual scaling factors ti

91 Optimization results of the individual scaling factors ti

92 Weighted sum

94 State parameter constraints

96 Target function of the third optimization algorithm

98 Travel optimization constraints - I

100 Further individual scaling factors ¹

Xi Travel variables bj Aberrations

Xk Travel variables x Travel vector

E1 - E4 Optical elements

M1 - M4 Manipulators

Claims

29 Claims

1 . A control device for controlling manipulators for changing an optical behaviour of a microlithographic projection lens by generating respective stipulations for a plurality of travel variables which define manipulations, to be undertaken by means of the manipulators, of at least one optical element of the projection lens for the purposes of changing state parameters of the projection lens, wherein the control device is configured:

- to generate a respective approximation of the stipulations for the travel variables by optimizing a uniform scaling factor using a first optimization algorithm, said scaling factor, in constraints of the first optimization algorithm, defining a uniform scaling of limits specified for the individual state parameters, and

- to ascertain a respective final result of the stipulations for the travel variables by means of at least one further optimization algorithm in the case where an optimization result for the uniform scaling factor, as ascertained by means of the first optimization algorithm, does not exceed a specified threshold.

2. The control device according to Claim 1 , which is furthermore configured to carry out a state parameter optimization algorithm when carrying out the at least one further optimization algorithm, a weighted sum of individual scaling factors being optimized in said state parameter optimization algorithm with state parameter constraints relating to the state parameters being taken into account, wherein the individual scaling factors in the state parameter constraints define a respective scaling of the limits specified for the individual state parameters.

3. The control device according to Claim 1 or 2, which is furthermore configured to carry out a travel optimization algorithm, in which a target function containing the travel variables is optimized, when carrying out the at least one further optimization algorithm.

4. The control device according to Claim 2 and Claim 3, 30 which is configured, when carrying out the at least one further optimization algorithm, to initially carry out the state parameter optimization algorithm and subsequently carry out the travel optimization algorithm, wherein the travel optimization algorithm is configured to optimize the target function taking account of the condition that further individual scaling factors may each exceed optimization results for the corresponding first individual scaling factors, as ascertained by the state parameter optimization algorithm, by no more than 5%.

5. The control device according to Claim 4, which is furthermore configured to base the travel optimization algorithm on further approximations of the stipulations for the travel variables, as ascertained when carrying out the state parameter optimization algorithm.

6. The control device according to Claim 2, 4 or 5, wherein the state parameter constraints furthermore comprise the condition that each of the first individual scaling factors may exceed the optimization result for the uniform scaling factor, as ascertained by the first optimization algorithm, by no more than 5%.

7. The control device according to any one of Claims 3 to 6, wherein the target function of the travel optimization algorithm contains the travel variables in at least quadratic form.

8. The control device according to any one of the preceding claims, which is furthermore configured to base the at least one further optimization algorithm on the approximations of the stipulations for the travel variables as start values.

9. The control device according to any one of the preceding claims, wherein the constraints of the first optimization algorithm are formulated as explicit constraints which are not part of a target function optimized when carrying out the first optimization algorithm.

10. The control device according to any one of the preceding claims, wherein the ascertained stipulations for the travel variables define changes in the state parameters of the projection lens which are to be carried out by means of the manipulators.

11 . An adjustment apparatus for adjusting a microlithographic projection lens, comprising a measuring device for ascertaining current values of state parameters of the projection lens and a control device according to any one of the preceding claims for generating the stipulations for the travel variables from the current values of the state parameters.

12. A projection lens for a microlithographic projection exposure apparatus, comprising manipulators which are configured to change state parameters of the projection lens, and a control device according to any one of Claims 1 to 10 for controlling the manipulators.

13. A microlithographic projection exposure apparatus, comprising a projection lens according to Claim 12.

14. A method for controlling manipulators for changing an optical behaviour of a microlithographic projection lens by generating respective stipulations for a plurality of travel variables which define manipulations, to be undertaken by means of the manipulators, of at least one optical element of the projection lens for the purposes of changing state parameters, including the following steps:

- generating a respective approximation of the stipulations for the travel variables by optimizing a uniform scaling factor using a first optimization algorithm, wherein the uniform scaling factor, in constraints of the first optimization algorithm, defines a uniform scaling of limits specified for the individual state parameters, and - ascertaining a respective final result of the stipulations for the travel variables by means of at least one further optimization algorithm in the case where an optimization result for the uniform scaling factor, as ascertained by means of the first optimization algorithm, does not exceed a specified threshold.

15. The method according to Claim 14, wherein the respective final result of the stipulations for the travel variables is ascertained using the at least one further optimization algorithm taking into account explicit further constraints for the state parameters of the projection lens, which are not part of a target function optimized when carrying out the at least one further optimization algorithm.