DE102021202502B4 - Device and method for changing a shape of a surface of an object - Google Patents

Abstract

Device (10) for changing a shape of a surface (12) of an object (14) with: - a shape manipulation device (16), which is configured to generate a surface change on the object as a function of a control variable (32), and Control device (30), which is configured to determine a specification (32E) for the control variable of the shape manipulation device from a specified desired change (28) in the surface shape of the object by means of a two-stage optimization (34, 50), with a first stage (34) the optimization is configured to determine an approximation (32N) of the specification for the control variable by minimizing a deviation (40) of a prediction (36) of the surface change that can be generated using the control variable from the target change, with a second stage (50) of the optimization for this is configured, a final result (32E) of the target for the control variable by minimizing a total time (54) leading to ore augmentation of the surface change is required by means of the shape manipulation device, and the final result of the specification (32E) for the control variable is determined under a secondary condition (60) limiting the deviation (40) of the surface change from the target change.

Description

Background of the Invention

The invention relates to a device and a method for changing the shape of a surface of an object.

Out DE102012212199A1 such a device is known, for example. This includes a shape manipulation device for surface structuring of micro- or nanostructured components made of glass or ceramics by means of electron beams. For this purpose, a particle beam, such as an electron beam, with a diameter in the range of the smallest structures to be produced can be directed onto selected partial areas of the surface in order to achieve local densification and thus local lowering of the surface in accordance with the desired surface structuring. Furthermore, processing of an optical element of a projection exposure system for microlithography with an electron beam is described. Imaging errors of the projection exposure system caused by the production process can be compensated for by a suitably implemented compression and an associated change in the shape of the optical surface of an optical element. In addition to the densification of material described, particle beams can also be used for direct material removal on the surface of the irradiated optical element.

In this case, the actual shape of the surface of the optical element is usually first measured and its deviation from a predetermined desired shape is determined. In order to adapt the surface shape to the target shape, a specification for a control variable of the shape manipulation device to be introduced into the optical element by the irradiation, such as in the form of an energy dose distribution of an electron beam, is conventionally first determined, which is suitable for a desired correction of the surface shape of the optical element effect.

Conventionally, the specification for the control variable of the shape manipulation device is determined while minimizing the surface deviation from the target change. The result determined in this way generally achieves the goal of a small surface deviation, but its implementation using the shape manipulation device is often very time-consuming.

From the DE4108404A1 For example, a method for controlling the ion irradiation of solid surfaces is known, which is used in particular for surface correction in the final processing of optical functional surfaces.

Out DE102017130797A1 a method and a device for generating a desired surface profile by applying material to and/or removing material from a workpiece are known.

A device and a method for changing a surface of an optical element by means of electron beams are known DE102016203591A1 known.

A method for controlling the local etch or deposition rate when modifying surfaces with pulsed ion beams is out DE102005017632A1 known.

Underlying Task

It is an object of the invention to provide a device and a method with which the aforementioned problems are solved, and in particular a specification for the control variable of the shape manipulation device can be determined, with which the shape manipulation device can bring about a small surface deviation from a specified target shape in a time-efficient manner.

The aforementioned object can be achieved according to the invention, for example, with a device for changing a shape of a surface of an object, which includes a shape manipulation device that is configured to produce a surface change on the object as a function of a control variable. Furthermore, the device according to the invention comprises a control device which is configured to determine a specification for the control variable of the shape manipulation device from a specified desired change in the surface shape of the object by means of a two-stage optimization. In this case, a first stage of the optimization is configured to determine an approximation of the specification for the control variable by minimizing a deviation of a prediction of the surface change that can be generated using the control variable from the target change. A second stage of the optimization is configured to determine an end result of the target control variable by minimizing a total time required to generate the surface modification using the shape manipulation device. Furthermore, the final result of the specification for the control variable is determined under a secondary condition that limits the deviation of the surface change from the target change.

In other words, the first stage of the optimization is configured to optimize a quality function that contains a difference between a prediction of the surface change that can be generated by the control variable and the target change. This means that the approximation of the specification for the control variable determined by means of the first stage of the optimization is selected in such a way that the surface change that could thus be generated by the shape manipulation device deviates as little as possible from the target change.

In other words, the second stage of the optimization is configured to optimize another merit function containing a variable indicative of the total time to produce the surface change. This means that the end result of the specification for the control variable determined using the second stage of optimization is selected in such a way that the time required to generate the defined surface change is as short as possible, with the deviation of the surface change from the target change being limited is, for example, the mean of the deviation or the square of the deviation must not exceed a fixed limit.

The surface change of the object can take place, for example, as a result of material removal from the object or as a result of local material compression, so-called compaction, in the object.

The two-stage optimization according to the invention makes it possible to determine a specification for the control variable, with which the shape of the surface can be adapted to a target shape in a time-efficient manner with a high degree of accuracy by means of the shape manipulation device. The high level of accuracy in adapting the shape of the surface to the target shape is achieved by the first stage of optimization and by the constraint in the second stage of optimization, which limits the deviation of the surface change from the target change. By minimizing the overall time that is required to produce the surface change by means of the shape manipulation device, the specification determined is implemented by the shape manipulation device with a high level of time efficiency.

According to one specific embodiment, the control device is configured to start with the optimization of the second stage based on the approximation of the specification for the control variable determined in the first stage. In other words, the approximation is used as a starting point, i.e. as a starting value or starting values, for the optimization taking place in the second stage.

According to a further embodiment, the surface of the object comprises a usable area which has a curved edge boundary and/or holes in a top view, and the control device is configured to limit the minimization taking place in the first and/or second stage of the optimization to the usable area. To put it more precisely, the minimization of the deviation of the surface change from the target change, which takes place in the first optimization stage, is limited to the usable area. In the case of the curved edge delimitation, the usable area in plan view, also referred to below as plan view area, is not a rectangle, rather it can in particular be a circle or an ellipse. Due to the limitation to the projection area, the deviation of the surface change is not minimized with regard to a rectangular area, but with regard to the top view area with the curved edge boundary and, if applicable, disk-shaped topography. This solution differs from the conventional solution of an FFT-based deconvolution task, in which a rectangular region is calculated in a plan view of the surface. Even in the case of a usable area with a general shape, in particular also a rectangular shape, which has holes, the solution differs from the conventional solution mentioned for an FFT-based unfolding task.

According to a further embodiment, the limitation to the usable area in the first stage is carried out by means of a weighting function, which is multiplied by the deviation in a quality function, which is minimized in the first stage, the weighting function being adapted to a form which defines the usable area in the Has top view, is adjusted. The deviation is to be understood as meaning the deviation of the surface change that can be generated by means of the control variable from the target change. The adjustment of the weighting function to the shape of the plan view area is carried out in particular by the weighting within the plan view area being selected to be greater than outside of the plan view area. For example, a weighting of 1 can be provided within the top view area and a weighting of 0 outside the top view area.

According to a further embodiment, the weighting function specifies a continuous variation between 0 and 1. The continuous weighting can serve to reduce the influence of unreliable measured values in the removal specification 28 .

According to a further embodiment, the object is an optical element for an optical arrangement and the usable area is a surface section on the optical element, which at an appropriate use of the optical element in the optical arrangement is arranged in a useful beam path of the optical arrangement. The optical arrangement can be, for example, illumination optics or projection optics, also called projection objective, of a projection exposure system for microlithography. If the optical element is, for example, a mirror or a lens for a lithography projection exposure system, for example for a projection optics of the same, the usable area is that surface section of the optical element which is irradiated by an illumination radiation or projection radiation during operation of the lithography projection exposure system.

According to a further embodiment, the device is configured to adapt a shape of a surface of an optical element of a projection exposure system for microlithography to a target shape. This can be an optical element of projection optics or an illumination system of the projection exposure system. The optical element can be a mirror or a lens. The projection exposure system can have EUV radiation or DUV radiation as the exposure radiation.

According to a further embodiment, the constraint, which limits the deviation of the surface change from the target change, defines a limit value for a mean value of the deviation calculated over the area to which the target change relates. The mean can be, for example, an arithmetic or a root mean square or some other relationship used to quantify the surface roughness.

According to a further embodiment, the optimization takes place in at least one of the two stages under a further secondary condition, which defines a minimum dwell time of a processing agent used to produce the surface change at individual locations on the surface. In particular, a minimum value for the dwell time of the processing agent for all locations in a useful area of the surface is specified by the further secondary condition. The processing means can include, for example, particles blasted onto the surface or a mechanical tool with which material is removed from the surface by means of friction.

According to a further embodiment, the specification for the control variable is determined as a function dependent on the location on the surface of the object, and a respective quality function minimized in at least one of the two stages of optimization includes a respective penalty term, with which a local gradient of the control variable is kept low. In other words, the quality function on which the first stage of optimization is based can include such a penalty term and/or the quality function on which the second stage of optimization is based can include such a penalty term. A penalty term serves as a so-called “implicit constraint”. Its function is to counteract an increase in the location gradient during the optimization, in particular to counteract the location gradient approaching an upper limit or the location gradient exceeding the upper limit. The penalty term causes a smoothing of the optimization solution, i.e. the specification determined has a location-dependent course that is as smooth as possible.

According to a further embodiment, the shape manipulation device comprises a particle irradiation device or a mechanical removal device, which is configured to bring about local changes in the surface of the object by means of a spatially resolved effect distribution as a function of the control variable. According to one embodiment variant, the particle irradiation device is configured to irradiate particles onto the surface of the object with a spatially resolved effect distribution in order to produce local surface changes, depending on the control variable. The particles used can be ions or electrons, for example, i.e. the device can be configured as an ion beam processing system or as an electron beam processing system. Alternatively, the shape manipulation device may comprise a polishing tool for mechanically removing material on the surface by direct contact of the polishing tool with the surface.

The aforementioned object can also be achieved, for example, with a method for changing a shape of a surface of an object, in which a specification for a control variable of a shape manipulation device is determined from a specified desired change using a two-stage optimization. In a first stage of the optimization, an approximation of the specification for the control variable is determined by minimizing a deviation of a surface change that can be generated by means of the control variable from the target change. Furthermore, in a second stage of the optimization, an end result of the specification for the control variable is determined by minimizing a total time required to produce the surface change using the shape manipulation device. Furthermore, the final result is determined under a secondary condition that limits the deviation of the surface change from the desired change. Based on The end result of the specification for the control variable is that the shape of the surface is adapted to the target shape by means of the shape manipulation device.

According to a further embodiment, the optimization of the second stage is based on the approximation determined in the first stage.

According to a further embodiment, the surface of the object comprises a usable area which has a curved edge boundary and/or holes in a plan view and to which the minimization taking place in the first and/or second stage of the optimization is limited.

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

character list

• 1 ein Ausführungsbeispiel einer Vorrichtung zum Verändern einer Form einer Oberfläche eines Objekts mit einer Formmanipulationseinrichtung sowie einer Steuerungseinrichtung zur Ermittlung einer Vorgabe für eine Steuerungsgröße der Formmanipulationseinrichtung,
• 2 eine Darstellung der Oberfläche des Objekts in Draufsicht,
• 3 die Darstellung der Oberfläche des Objekts in Draufsicht gemäß 2 mit zusätzlich eingezeichneten Bearbeitungstrajektorien der Formmanipulationseinrichtung, sowie
• 4 schematisch im Meridionalschnitt eine Projektionsbelichtungsanlage für die EUV-Projektionslithografie.

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

• 1 an embodiment of a device for changing a shape of a surface of an object with a shape manipulation device and a control device for determining a specification for a control variable of the shape manipulation device,
• 2 a representation of the surface of the object in plan view,
• 3 the representation of the surface of the object in plan view according to 2 with additional processing trajectories of the shape manipulation device, as well as
• 4 a schematic meridional section of a projection exposure system for EUV projection lithography.

Detailed description of exemplary embodiments according to the invention

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

To facilitate the description, in 1 specified a coordinate system from which the respective positional relationship of the components shown in the figures results. The x ₁ direction runs to the right, the x ₂ direction into the plane of the drawing and the z direction upwards. in the in 1 and the formulas given below, x designates a two-dimensional position vector with the coordinates (x ₁ , x ₂ ).

In 1 an exemplary embodiment of a device 10 for changing a shape of a surface 12 of an object 14 in the form of an optical element by means of electron beam irradiation is shown schematically. A mirror for the EUV wavelength range, ie for electromagnetic radiation with a wavelength of less than 100 nm, in particular a wavelength of approximately 13.5 nm or approximately 6.8 nm, is shown as an example of the optical element. This can be an optical element for an illumination system or projection optics of a projection exposure system for EUV microlithography or DUV microlithography. Such a projection exposure system 101 for EUV microlithography is described below with reference to FIG 4 described. The optical element that can be modified by means of device 10 can be a deflection mirror 119, facets 121 or 123 of a first or a second facet mirror 120 or 122 of illumination optics 104, or a mirror M1 to M6 of projection optics 110 of projection exposure system 101 4 act.

However, the device 10 is also suitable for the high-precision production of surface shapes or surface shape changes for other optical elements, such as mirrors for other wavelength ranges, lenses or optical elements with diffractive structures, or also for objects that do not form an optical element.

The apparatus 10 includes a shape manipulation device 16 in the form of a particle irradiation device for generating an on off selectable locations of the surface 12 directed and bundled particle beam 18. Alternatively, the shape manipulation device 16 can also be configured as a polishing system, which includes a polishing tool for mechanical removal of material on the surface 12 by direct contact of the polishing tool with the surface 12.

in the in 1 In the illustrated embodiment of a particle irradiation device, the particle beam 18 is formed by electrons, so the particle irradiation device is an electron irradiation device. In other design variants, ions, for example in systems for IBF surface treatment, or uncharged particles can also be used. When ions are used, they are typically neutralized after acceleration in the electric field before hitting the surface. The particle beam 18 is particularly energetically designed such that, depending on the energy dose, a more or less pronounced local ablation or a more or less pronounced local compaction of the material of the object 14 on the surface 12 is brought about. The absorbed dose is the energy per area that is introduced into the object 14 by the particle beam 18 . The energy dose is thus dependent in particular on the dwell time of the electron beam at the selected location and on its intensity.

Both a material removal and a local compaction cause a local lowering of the surface 12 on the object 14, such as an optical element. Compaction occurs particularly in amorphous materials through a redistribution of electron bonds. The local compaction takes place in all spatial directions, i.e. there is not only a local surface lowering in the area of a surface element in the negative z-direction, but also a compaction parallel to the surface 12. In the process, forces acting parallel to the surface 12 arise, as a result of which stresses are induced in the object 14 . These stresses can cause deformation of a surface section that is significantly larger than that affected by the local compaction. The surface section can include part of the surface 12 or also the entire surface 12 .

In order to generate the particle beam 18 in the form of an electron beam, the shape manipulation device 16 designed as a particle irradiation device contains according to FIG 1 an electron source 20 and an acceleration unit 22. A hot cathode, a crystal cathode or a field emission cathode can be used as the electron source 20, for example. The acceleration unit 22 accelerates and focuses the electrons emitted by the electron source 20 . For this purpose, the acceleration unit 22 can have an anode with a high positive electrostatic potential compared to the electron source 20 and a small exit opening for the accelerated electrons. In order to focus and adjust the intensity of the particle beam 18, the acceleration unit 22 also contains a control electrode, for example a Wehnelt cylinder. The intensity or the beam current indicates the number of electrons which pass through an imaginary surface perpendicular to the electron beam per unit of time.

In order to focus the particle beam 18 coming from the acceleration unit 22, the particle irradiation device also includes a focusing unit 24 with suitably designed electrical or magnetic components.

auf die Oberfläche 12 des optischen Elements 14 auf. Ein derartiger Ort $x_i=\left(x_1{}^{\text{i}},x_2{}^{\text{i}}\right)$

ist in 1 mit dem Bezugszeichen 33 bezeichnet.The particle beam 18 can be deflected in both the x ₁ and x ₂ directions with a deflection unit 26 of the particle irradiation device 16 . For this purpose, the deflection unit 26 also contains suitably designed electrical or magnetic components. Depending on the setting of the deflection unit 26, the particle beam 18 strikes at a specific location $x_i=\left(x_1{}^{\text{i}},x_2{}^{\text{i}}\right)$

onto the surface 12 of the optical element 14 . Such a place $x_i=\left(x_1{}^{\text{i}},x_2{}^{\text{i}}\right)$

is in 1 denoted by the reference numeral 33.

In this way, a large number of different locations 33 on the surface 12 can be irradiated one after the other and thus a spatially resolved effect distribution in the form of an energy dose distribution over the surface 12 can be achieved. The spatially resolved energy dose distribution is to be understood here as a distribution of the energy introduced per area as a function of the spatial coordinate x=(x ₁ , x ₂ ) of the surface 12 of the optical element 14 . The irradiation can, for example, take place in a grid pattern or also continuously over the entire surface. An irregular or regular arrangement of different locations to be irradiated, for example in lines, circles, ellipses or the like, is also possible.

To prevent the electrons of particle beam 18 from being absorbed by air, shape manipulation device 16 also has a vacuum chamber in which electron source 20, acceleration unit 22, focusing unit 24, deflection unit 26, and object 14 or at least surface 12 of object 14 are arranged.

The device 10 also contains a control device 30 for controlling the particle irradiation device 16. The control device 30 is designed to generate a predetermined desired change h(x) for the shape of the surface 12 of the optical element 14, which is denoted by the reference numeral 28, and denoted by the reference numeral 32E Specification τ _E (x) for a control variable 32 of the particle irradiation device 16 for the irradiation of the surface 12 with the particle beam 18, with which the desired change 28 in the shape of the surface 12 is achieved very precisely. The specification 32E of the control variable 32 causes the above-described distribution of effects to be generated in the form of the absorbed dose distribution in a suitable form. The target change 28 is usually determined by measuring the actual surface shape and comparing the measured shape with a target shape, ie the target change 28 is that change in surface shape that is required to give the surface 12 the target shape.

If surfaces 12 are processed using the shape manipulation device 16, the surface change, which can be represented by a function of the spatial coordinates, depends linearly on the residence time of the processing tool, in the present case the particle beam 18, over the respective position x of the surface 12. The location coordinate x is also denoted below with a slightly different font (x).

As already mentioned above, the target change 28 in the surface shape is denoted by h(x) in the present case. The control variable 32 is described by a residence time τ(x) of the particle beam 18 or, in general, of a polishing tool as a function of the position x ∈ ℝ ² on the surface 12 to be machined. The effect of the tool in the form of the particle beam 18 is characterized by a so-called tool function k(y), y ∈ ℝ ² , denoted by reference numeral 35 .

A surface change prediction g(x), also denoted by reference numeral 36, also denoted removal prediction, then results as follows: $$G\left(x\right)={\displaystyle \int {}_{\Omega \text{'}}\tau \left(y\right)k\left(x-y\right)\mathrm{i.e}y}$$

In other words, g(x) is described by the convolution 9 = τ ⊗ k on the two-dimensional domain Ω' ⊂ ℝ ² . The region Ω′ here describes a processing area 68 on the surface 12 of the object 14, ie a processing area accessible to the particle beam 18 or the processing tool. The area Ω' is in the 2 and 3 shown in a plan view. In this view, the area Ω' is circular, ie it has a curved border 70 . Furthermore, in the 2 and 3 a square frame 72 of the area Ω' is shown, which represents the area that is defined by an area integral over a function in the area Ω' that is defined as a function of the two-dimensional spatial coordinate x = (x ₁ , x ₂ ), as defined below as expression (4 ) designated integral, is recorded at least.

The inner area of the working surface Ω' contains a useful surface 64, which is denoted by Ω'. The usable area Ω' is for the case in which the object 14 is an optical element for a lithography projection exposure system 101 of the following with reference to 4 described type, a surface section on the optical element, which is arranged in a useful beam path 124 when installed in the projection exposure system 101 . In other words, the useful area Ω′ is or contains the area section actually used in later operation of the optical element. The usable area Ω' is also in the in the 2 and 3 The top view shown is circular and thus also has a curved edge boundary 66 . In 3 processing trajectories 74 are also drawn in in the form of parallel lines, only some of these processing trajectories being denoted by reference numeral 74 . The processing trajectories 74 indicate the path of the particle beam 18 or a processing tool on the surface 12 when the device 10 is in operation.

The control device 30 is configured to carry out a two-stage optimization in order to determine the specification 32E from the specified setpoint change 28 . In a first stage 34 of the optimization, an approximation τ _N (x), denoted by the reference symbol 32N, of the specification for the control variable 32 is determined by minimizing a quality function 38: $${\text{argmin}}_{\tau }{\displaystyle \int {\Vert w_{\Omega }\left(x\right)\odot \left(G-H\right)\left(x\right)\Vert }_2^2+\mathrm{\lambda }{\Vert \nabla \mathrm{\tau }\Vert }_2^2\mathrm{i.e}x}$$

The minimization of the quality function 38 takes place under a secondary condition 44: $$\text{NB:}\tau \left(x_i\right)\ge {\tau }_{min}$$

A standard method for convex optimization can be used as the optimization method for minimizing the merit function 38 . For example, the (linearized) ADMM algorithm (see Neal Parikh & Stephen Boyd, "Proximal algorithms, Foundations and Trends in Optimization, 1 (3): 127-239, 2014) or the Chambolle-Pock algorithm (see Antonin Chambolle and Thomas Pock, "A first-order primal-dual algorithm for convex problems with applications to imaging, Journal of Mathematical Imaging and Vision, 40(1): 120-145, May 2011) are used if standards other than the 2 standards are to be used. In the concrete form (2) with quadratic norms, the conjugate gradient method is preferably used. In this case, the secondary condition is realized by subsequent shifting of control variable 32. In the case of small problem sizes, for example if the erosion prediction is represented in a basis, a direct solution of the resulting system of linear equations can also be used.

umfasst ein Integral über die zweidimensionale Ortskoordinate x = (x₁, x₂) und damit über die Fläche der in den 2 und 3 dargestellten rechteckigen bzw. quadratischen Einrahmung 72. Die Gütefunktion 38 ist im vorliegenden Fall ein Funktional. Der Integrand umfasst zwei Terme in Form von zwei Summanden. Der erste Term wird durch das Quadrat der Euklidischen Norm in elementweiser Multiplikation (angezeigt durch die Notation ⊙) einer mit dem Bezugszeichen 42 bezeichneten Gewichtungsfunktion w_Ω(x) und einer Abweichung 40 der Oberflächenveränderungsvorhersage g(x) von der Solländerung h(x) gebildet. Dabei wird die Oberflächenveränderungsvorhersage g(x) analog zur vorstehenden Darstellung in Ausdruck (1) durch die folgende Faltung beschrieben: $$g=k\otimes \left(w_{\Omega \text{'}}\odot \tau \right)$$

The quality function 38 in the form shown under (2). $${\displaystyle \int {\Vert w_{\Omega }\left(x\right)\odot \left(G-H\right)\left(x\right)\Vert }_2^2+\mathrm{\lambda }{\Vert \nabla \mathrm{\tau }\Vert }_2^2\mathrm{i.e}x}$$

includes an integral over the two-dimensional spatial coordinate x = (x ₁ , x ₂ ) and thus over the area in the 2 and 3 illustrated rectangular or square frame 72. The quality function 38 is a functional in the present case. The integrand includes two terms in the form of two summands. The first term is formed by the square of the Euclidean norm in element-wise multiplication (indicated by the notation ⊙) of a weighting function w _Ω (x) denoted by reference numeral 42 and a deviation 40 of the surface change prediction g(x) from the target change h(x). . The surface change prediction g(x) is described analogously to the above representation in expression (1) by the following convolution: $$G=k\otimes \left(w_{\Omega \text{'}}\odot \tau \right)$$

In this case, w _Ω′ is a weighting function which provides a non-zero weighting, eg “1”, for coordinates within the working area Ω′ and a considerably lower weighting, in particular the weighting “0”, for coordinates outside the working area Ω′.

The weighting function 42 (w _Ω (x)) serves to limit the minimization taking place in the first stage 34 of the optimization to the effective area Ω′. For this purpose, the weighting function w _Ω (x) provides a non-zero weighting, eg "1", for coordinates within the effective area Ω, and a considerably lower weighting, in particular the weighting "0", for coordinates outside the effective area Ω. Based on the first term of the quality function 38, the approximation 32N is determined in the first stage 34 of the optimization by minimizing the deviation 40.

The second term of the integrand of the quality function 38 serves as a penalty term 56, with which a local gradient 58 of the control variable 32 (ie the length of stay τ) is kept low. In other words, the second term serves to enforce smoothness of the solution τ _N (x) of expression (2). The second term includes the square of the Euclidean norm of the spatial gradient ∇τ and a scalar factor λ to regulate the smoothness of the solution. Higher derivatives than the gradient can be used similarly.

The secondary condition 48 according to expression (3) defines a minimum dwell time τ _min of the particle beam 18, denoted by reference numeral 48, at the individual locations 33 (x _i ) on the surface 12. That is, for the respective individual dwell time τ(x _i ) 46 at location x _i a lower limit is defined with τ _min . The local expansion of the particle beam cross section can be taken into account when formulating the secondary condition 48, so that it is ensured that a minimum radiation dose acts on the object 14 at all relevant locations 33 on the surface 12, in particular at all locations 33 of the useful area Ω. The effect of a minimum radiation dose at all locations 33 of the usable area Ω causes the surface to be smoothed at all locations 33 in the area of the usable area Ω.

In a second stage 50 of the optimization, the specification 32E, ie an end result of the specification for the control variable 32, is determined by minimizing a further quality function 52: $${\text{argmin}}_{\tau }{\displaystyle \int \left|\tau \left(x\right)\right|+\mathrm{\lambda }{\Vert \nabla \mathrm{\tau }\Vert }_2^2\mathrm{i.e}x}$$

wobei ρ eine Mittelwertsfunktion bildet, sowie einer zweiten Nebenbedingung 44: $$\text{NB}2\text{:}\tau \left(x_i\right)\ge {\tau }_{min}$$

The minimization of the quality function 52 takes place under a first secondary condition 60: $$\text{NB}1:\rho \left(w_{\Omega }\left(x\right)\odot \left(G-H\right)\left(x\right)\right)<{\text{RMS}}_{\text{spec}}$$

where ρ forms an averaging function, and a second constraint 44: $$\text{NB}2\text{:}\tau \left(x_i\right)\ge {\tau }_{min}$$

The optimization of the second stage 50 is based on a starting specification for the control variable τ(x), also referred to as the starting value or starting point. According to the 1 In the embodiment illustrated, in the optimization of the second stage 50, the approximation 32N of the specification for the control variable determined in the first stage is used as the starting point for the control variable T(x). This means that the optimization of the second stage 50 is based on the value distribution of the approximation τ _N (x) determined in the first stage for the length of stay T(x).

A standard method designed as an interior point method can also be used here as an optimization method for minimizing the quality function 52 can be used for convex optimization, ie a feasible island solution that satisfies constraints 60 and 44 is required. This can be ensured, for example, by solving the problem according to expression (2) with a realizable user specification. Then the condition according to expression (7) can be realized by means of a logarithmic barrier and, for example, with the help of the generalized forward-backward splitting method (cf. Hugo Raguet, Jalal Fadili, and Gabriel Peyre, "A generalized forward-backward splitting", SIAM Journal on Imaging Sciences, 6(3): 1199-1226, 2013).

umfasst ein Integral über die zweidimensionale Ortskoordinate x = (x₁, x₂) und damit über die Fläche der in den 2 und 3 dargestellten rechteckigen bzw. quadratischen Einrahmung 72. Die Gütefunktion 52 ist wie auch die Gütefunktion 38 ein Funktional. Der Integrand der Gütefunktion 52 umfasst zwei Terme in Form von zwei Summanden.The quality function 52 in the form shown under (6). $${\displaystyle \int \left|\tau \left(x\right)\right|+\mathrm{\lambda }{\Vert \nabla \mathrm{\tau }\Vert }_2^2\mathrm{i.e}x}$$

includes an integral over the two-dimensional spatial coordinate x = (x ₁ , x ₂ ) and thus over the area in the 2 and 3 illustrated rectangular or square frame 72. The quality function 52, like the quality function 38, is a functional. The integrand of the quality function 52 includes two terms in the form of two summands.

The first term is formed by the cumulative norm of the control variable in the form of the length of stay τ(x). The integral over this term corresponds to the total time 54 that is required to generate the surface change defined with the specification 32E using the shape manipulation device 16 . Based on the first term of the quality function 52, the end result 32E of the specification for the control variable 32 is determined in the second stage 50 of the optimization by minimizing the total time 54.

The second term of the integrand of the quality function 52 corresponds to the penalty term 56 already contained in the quality function 38 of the first stage 34, with which a local gradient 58 of the control variable 32 (i.e. the length of stay τ) is kept low.

The first secondary condition 60 limits the deviation 40 of the surface change generated by means of the shape manipulation device 16, i.e. the prediction 36 of the surface change, from the target change 28. For this purpose, a limit value RMS _spec denoted by the reference symbol 62 is used for a value over the effective surface Ω on which the Target change 28 refers, calculated mean value of the deviation 40 defined. This mean value is formed in the first secondary condition 60 by means of the mean value function ρ denoted by the reference symbol 43 . The mean value function ρ can, as in in 1 case shown, a root mean square or even an arithmetic mean of their argument or other measures of surface roughness. The argument used _{is the expression ρ(w Ω (} x ) ⊙ (g - h)(x)) is used.

The second constraint 44 corresponds to the constraint according to expression (3) already explained above with reference to the first stage 34 of the optimization, with which the minimum dwell time τ _min of the particle beam 18 at the individual locations 33 (x _i ) on the surface 12 is specified.

The following are referring to 4 the essential components of the above-mentioned projection exposure system 101 for microlithography are described by way of example, in which an optical element processed by means of the device 10 described above can be used. The description of the basic structure of the projection exposure system 101 and its components should not be understood as limiting here. The projection exposure apparatus 101 described here is an embodiment for EUV lithography. Analogously to this, an optical element processed by means of the device 10 can also be used in a projection exposure system for DUV lithography. Furthermore, an optical element processed by means of the device 10 can be used for any optical applications with free-form surfaces, eg progressive lenses etc.

In addition to a radiation source 103, an illumination system 102 of the projection exposure system 101 includes the aforementioned illumination optics 104 for illuminating an object field 105 in an object plane 106. A reticle 107 arranged in the object field 105 is exposed. The reticle 107 is held by a reticle holder 108. The reticle holder 108 can be displaced in particular in a scanning direction via a reticle displacement drive 109 .

In 4 a Cartesian xyz coordinate system is drawn in for explanation. The x-direction runs perpendicularly into the plane of the drawing. The y-direction is horizontal and the z-direction is vertical. The scanning direction is in the 4 along the y-direction. The z-direction runs perpendicular to the object plane 106.

The projection exposure system 101 also includes the projection optics 110 already mentioned above. The projection optics 110 are used to image the object field 105 in an image field 111 in an image plane 112. The image plane 112 runs parallel to the object plane 106. Alternatively, an angle different from 0° between the object plane 106 and the image plane 112 is also possible.

A structure on the reticle 107 is imaged onto a light-sensitive layer of a wafer 113 arranged in the region of the image field 111 in the image plane 112. The wafer 113 is held by a wafer holder 114. The wafer holder 114 can be displaced via a wafer displacement drive 115, in particular along the y-direction. The displacement of the reticle 107 via the reticle displacement drive 109 on the one hand and the wafer 113 on the other hand via the wafer displacement drive 115 can be synchronized with one another.

The radiation source 103 is an EUV radiation source. The radiation source 103 emits illumination radiation 116, in particular in the form of EUV radiation, which is also referred to below as useful radiation. In particular, the useful radiation has a wavelength in the range between 5 nm and 30 nm, in particular a wavelength of approximately 13.5 nm or approximately 6.8 nm. The radiation source 103 can be a plasma source, for example an LPP (laser Produced Plasma (laser generated plasma) source or a DPP (Gas Discharged Produced Plasma) source. It can also be a synchrotron-based radiation source. The radiation source 103 can also be a free-electron laser (FEL).

The illumination radiation 116 emanating from the radiation source 103 is bundled by a collector 117 . The collector 117 can be a collector with one or more ellipsoidal and/or hyperboloidal reflection surfaces. The at least one reflection surface of the collector 117 can be exposed to the illumination radiation 116 in grazing incidence (Grazing Incidence, GI), i.e. with angles of incidence greater than 45°, or in normal incidence (Normal Incidence, NI), i.e. with angles of incidence less than 45° will. The collector 117 can be structured and/or coated on the one hand to optimize its reflectivity for the useful radiation and on the other hand to suppress stray light.

After the collector 117, the illumination radiation 116 propagates through an intermediate focus in an intermediate focal plane 118. The intermediate focal plane 118 can represent a separation between a radiation source module, comprising the radiation source 103 and the collector 117, and the illumination optics 104. The course of the illumination radiation 116 through the illumination optics 104 and the projection optics 110 is referred to below as the useful beam path 124 .

The illumination optics 104 includes the above-mentioned deflection mirror 119 and the first facet mirror 120 downstream of this in the beam path. Alternatively or additionally, the mirror 119 can be designed as a spectral filter, which separates a useful light wavelength of the illumination radiation 116 from stray light of a different wavelength. If the first facet mirror 120 is arranged in a plane of the illumination optics 104 which is optically conjugate to the object plane 106 as a field plane, it is also referred to as a field facet mirror. The first facet mirror 120 includes a multiplicity of individual first facets 121, which are also referred to below as field facets. Of these facets 121 are in 4 only a few shown as examples.

The first facets 121 can be embodied as macroscopic facets, in particular as rectangular facets or as facets with an arcuate or part-circular edge contour. The first facets 121 can be embodied as planar facets or alternatively as convexly or concavely curved facets.

Such as from DE 10 2008 009 600 A1 is known, the first facets 121 themselves can each also be composed of a multiplicity of individual mirrors, in particular a multiplicity of micromirrors. The first facet mirror 120 can be embodied in particular as a microelectromechanical system (MEMS system). For details go to DE 10 2008 009 600 A1 referred.

The illumination radiation 116 runs horizontally between the collector 117 and the deflection mirror 119, ie along the y-direction.

In the useful beam path of the illumination optics 104 , the first facet mirror 120 is followed by the second facet mirror 122 already mentioned above. If the second facet mirror 122 is arranged in a pupil plane of the illumination optics 104, it is also referred to as a pupil facet mirror. The second facet mirror 122 can also be arranged at a distance from a pupil plane of the illumination optics 104 . In this case, the combination of the first facet mirror 120 and the second facet mirror 122 is also referred to as a specular reflector. Specular reflectors are off US2006/0132747 A1 , EP 1 614 008 B1 and U.S. 6,573,978 B1 known.

The second facet mirror 122 includes a plurality of second facets 123. In the case of a pupil facet mirror, the second facets 123 are also referred to as pupil facets.

The second facets 123 can also be macroscopic facets, which can have round, rectangular or hexagonal borders, for example, or alternatively facets composed of micromirrors. In this regard, also on DE 10 2008 009 600 A1 referred.

The second facets 123 can have plane or alternatively convexly or concavely curved reflection surfaces.

The illumination optics 104 thus forms a double-faceted system. This basic principle is also known as the Fly's Eye Integrator.

It can be advantageous not to arrange the second facet mirror 122 exactly in a plane which is optically conjugate to a pupil plane of the projection optics 119 .

The individual first facets 121 are imaged in the object field 105 with the aid of the second facet mirror 122 . The second facet mirror 122 is the last beam-forming mirror or actually the last mirror for the illumination radiation 116 in the useful beam path in front of the object field 105.

In a further embodiment of the illumination optics 104 (not shown), transmission optics can be arranged in the useful beam path between the second facet mirror 122 and the object field 105, which contributes in particular to the imaging of the first facets 121 in the object field 105. The transmission optics can have exactly one mirror, but alternatively also two or more mirrors, which are arranged one behind the other in the useful beam path of the illumination optics 104 . The transmission optics can in particular comprise one or two mirrors for normal incidence (NI mirror, normal incidence mirror) and/or one or two mirrors for grazing incidence (GI mirror, gracing incidence mirror).

In the embodiment shown in FIG 4 shown, exactly three mirrors after the collector 117, namely the deflection mirror 119, the field facet mirror 120 and the pupil facet mirror 122.

In a further embodiment of the illumination optics 104, the deflection mirror 119 can also be omitted, so that the illumination optics 104 can then have exactly two mirrors downstream of the collector 117, namely the first facet mirror 120 and the second facet mirror 122.

The imaging of the first facets 121 by means of the second facets 123 or with the second facets 123 and transmission optics in the object plane 106 is generally only an approximate imaging.

The projection optics 110 includes a plurality of mirrors Mi, which are numbered consecutively according to their arrangement in the useful beam path of the projection exposure system 101 .

At the in 4 illustrated example, the projection optics 110 includes six mirrors M1 to M6. Alternatives with four, eight, ten, twelve or another number of mirrors Mi are also possible. The penultimate mirror M5 and the last mirror M6 each have a passage opening for the illumination radiation 116. The projection optics 110 are doubly obscured optics. The projection optics 110 has an image-side numerical aperture which is greater than 0.5 and which can also be greater than 0.6 and which can be 0.7 or 0.75, for example.

Reflection surfaces of the mirrors Mi can be designed as free-form surfaces without an axis of rotational symmetry. Alternatively, the reflection surfaces of the mirrors Mi can be designed as aspherical surfaces with exactly one axis of rotational symmetry of the reflection surface shape. Just like the mirrors of the illumination optics 4, the mirrors Mi can have highly reflective coatings for the illumination radiation 16. These coatings can be designed as multilayer coatings, in particular with alternating layers of molybdenum and silicon.

The projection optics 110 has a large object-image offset in the y-direction between a y-coordinate of a center of the object field 105 and a y-coordinate of the center of the image field 111. This object-image offset in the y-direction can be something like this be as large as a z-distance between the object plane 106 and the image plane 112.

The projection optics 110 can in particular be anamorphic. In particular, it has different imaging scales β _x , β _y in the x and y directions. The two image scales β _x , β _y of the projection optics 110 are preferably at (β _x , β _y )=(+/−0.25, /+−0.125). A positive image scale β means an image without image reversal. A negative sign for the Image scale β means an image with image reversal.

The projection optics 110 thus leads to a reduction in the ratio 4:1 in the x-direction, that is to say in the direction perpendicular to the scanning direction. The projection optics 110 lead to a reduction of 8:1 in the y-direction, ie in the scanning direction. Other imaging scales are also possible. Image scales with the same sign and absolutely the same in the x and y directions, for example with absolute values of 0.125 or 0.25, are also possible.

The number of intermediate image planes in the x-direction and in the y-direction in the useful beam path between the object field 105 and the image field 111 can be the same or, depending on the design of the projection optics 110, can be different. Examples of projection optics with different numbers of such intermediate images in the x and y directions are known from U.S. 2018/0074303 A1 known.

In each case one of the pupil facets 123 is assigned to precisely one of the field facets 121 in order to form a respective illumination channel for illuminating the object field 105 . In this way, in particular, lighting can result according to Köhler's principle. The far field is broken down into a large number of object fields 5 with the aid of the field facets 121 . The field facets 121 generate a plurality of images of the intermediate focus on the pupil facets 123 assigned to them.

The field facets 121 are each imaged onto the reticle 107 by an assigned pupil facet 123 in a superimposed manner in order to illuminate the object field 105 . In particular, the illumination of the object field 105 is as homogeneous as possible. It preferably has a uniformity error of less than 2%. Field uniformity can be achieved by superimposing different illumination channels.

The illumination of the entrance pupil of the projection optics 110 can be geometrically defined by an arrangement of the pupil facets. The intensity distribution in the entrance pupil of the projection optics 110 can be set by selecting the illumination channels, in particular the subset of the pupil facets that guide light. This intensity distribution is also referred to as an illumination setting.

A likewise preferred pupil uniformity in the area of defined illuminated sections of an illumination pupil of the illumination optics 104 can be achieved by redistributing the illumination channels.

Further aspects and details of the illumination of the object field 105 and in particular the entrance pupil of the projection optics 110 are described below.

The projection optics 110 can in particular have a homocentric entrance pupil. This can be accessible. It can also be inaccessible.

The entrance pupil of the projection optics 110 cannot regularly be illuminated exactly with the pupil facet mirror 122 . When imaging the projection optics 110, which telecentrically images the center of the pupil facet mirror 122 onto the wafer 113, the aperture rays often do not intersect at a single point. However, a surface can be found in which the distance between the aperture rays, which is determined in pairs, is minimal. This surface represents the entrance pupil or a surface conjugate to it in position space. In particular, this surface shows a finite curvature.

The projection optics 110 may have different positions of the entrance pupil for the tangential and for the sagittal beam path. In this case, an imaging element, in particular an optical component of the transmission optics, should be provided between the second facet mirror 122 and the reticle 107 . With the help of this optical element, the different positions of the tangential entrance pupil and the sagittal entrance pupil can be taken into account.

At the in 4 In the arrangement of the components of the illumination optics 104 shown, the pupil facet mirror 122 is arranged in a surface conjugate to the entrance pupil of the projection optics 110 . The field facet mirror 120 is arranged tilted to the object plane 105 . The first facet mirror 120 is tilted relative to an arrangement plane that is defined by the deflection mirror 119 .

The first facet mirror 120 is arranged tilted to an arrangement plane that is defined by the second facet mirror 122 .

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

Reference List

10

Device for changing the shape of a surface

12

surface

14

object

16

shape manipulation device

18

particle beam

20

electron source

22

acceleration unit

24

focusing unit

26

distraction unit

28

predetermined target change

30

control device

32

control variable

32N

Approximation of the specification for the control variable

32E

Final result of the specification for the control variable

33

location on the surface

34

first stage of optimization

35

tool function

36

surface change prediction

38

Merit function of the first stage of optimization

40

Deviation of a prediction of the surface change from the target change

42

weight function

43

averaging function

44

constraint

46

Individual residence time at location x _i

48

minimum residence time

50

second stage of optimization

52

Quality function of the second stage of optimization

54

total time

56

punishment term

58

Spatial gradient of the control variable

60

constraint

62

limit

64

floor space

66

Boundary delimitation of the usable area

68

processing area

70

Boundary delimitation of the processing area

72

square border

74

machining trajectory

101

Projection exposure system for microlithography

102

lighting system

103

radiation source

104

lighting optics

105

object field

106

object level

107

reticle

108

reticle holder

109

reticle displacement drive

110

projection optics

111

image field

112

picture plane

113

wafers

114

wafer holder

115

Wafer displacement drive

116

illumination radiation

117

collector

118

intermediate focal plane

119

deflection mirror

120

first facet mirror

121

facets

122

second facet mirror

123

facets

124

useful beam path

M1-M6

mirror

Claims (14)

Device (10) for changing a shape of a surface (12) of an object (14) with: - a shape manipulation device (16) which is configured to produce a surface change on the object as a function of a control variable (32), and - A control device (30), which is configured to determine a specification (32E) for the control variable of the shape manipulation device from a specified desired change (28) in the surface shape of the object by means of a two-stage optimization (34, 50), a first stage ( 34) the optimization is configured to determine an approximation (32N) of the specification for the control variable by minimizing a deviation (40) of a prediction (36) of the surface change that can be generated using the control variable from the target change, with a second stage (50) of the Optimization is configured to determine a final result (32E) of the target for the control variable by minimizing a total time (54) required to generate the surface change using the shape manipulation device, and wherein the determination of the final result of the target (32E) for the Control variable under one the deviation (40) of the surface change from the target area tion limiting constraint (60) takes place. device after claim 1 , in which the control device (30) is configured to proceed from the approximation (32N) of the specification for the control variable determined in the first stage in the optimization of the second stage (50). device after claim 1 or 2 , in which the surface (12) of the object comprises a working area (64) which in a plan view has a curved edge boundary (66) and/or holes and in which the control device (30) is configured to, in the first and/or or second stage of the optimization to limit the minimization to the usable area. device after claim 3 , in which the limitation to the usable area (64), which takes place in the first stage, is carried out by means of a weighting function (42), which is multiplied by the deviation (40) in a quality function (38) minimized in the first stage, the weighting function being connected to a Shape, which has the usable area in plan view, is adapted. device after claim 4 , where the weighting function specifies a continuous variation between 0 and 1. Device according to one of claims 3 until 5 , wherein the object (14) is an optical element (119; 121; 123; M1-M6) for an optical arrangement (104; 110) and wherein the usable surface (64) is a surface section on the optical element, which with an appropriate Use of the optical element in the optical arrangement is arranged in a useful beam path (124) of the optical arrangement. Device according to one of the preceding claims, which is configured to adapt a shape of a surface of an optical element (119; 121; 123; M1-M6) of a projection exposure tool (101) for microlithography to a desired shape. Device according to one of the preceding claims, in which the constraint (60) which limits the deviation of the surface change from the target change, a limit value (62) for a calculated mean value of the deviation (40) over the area to which the target change relates Are defined. Device according to one of the preceding claims, in which the optimization (34, 50) takes place in at least one of the two stages under a further secondary condition (44), which requires a minimum dwell time (48) of a processing means (18) used to produce the surface change at individual locations the surface defined. Device according to one of the preceding claims, in which the specification (32E) for the control variable is determined as a function dependent on the location on the surface of the object and a respective quality function (52) minimized in at least one of the two stages of the optimization has a respective penalty term ( 56) with which a local gradient (58) of the control variable is kept small. Device according to one of the preceding claims, in which the shape manipulation device (16) comprises a particle irradiation device or a mechanical removal device which is configured to bring about local changes in the surface of the object by means of a spatially resolved effect distribution as a function of the control variable (32). Method for changing a shape of a surface (12) of an object (14), in which: a specification for a control variable (32) of a shape manipulation device (16) is determined from a specified desired change (28) by means of a two-stage optimization (34, 50), in a first stage (34) of the optimization, an approximation (32N) of the specification for the control variable is determined by minimizing a deviation of a surface change that can be generated by means of the control variable from the target change, with a final result (32E) of the specification in a second stage of the optimization for the control variable by minimizing a total time (54), which is required to produce the surface change by means of the shape manipulation device, is determined, the determination of the final result taking place under a secondary condition that limits the deviation of the surface change from the target change, and the shape being determined on the basis of the final result of the specification (32E) for the control variable by means of the shape manipulation device the surface is adapted to a target shape. procedure after claim 12 , in which the optimization of the second stage (50) is based on the approximation (32N) determined in the first stage. Procedure according to one of Claims 12 until 13 , in which the surface of the object comprises a usable area (64) which, in a plan view, has a curved edge boundary (66) and/or holes and to which the minimization taking place in the first and/or second stage of optimization is limited.

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