DE102022212136A1 - Process for determining image errors in high-resolution imaging systems using wavefront measurement - Google Patents

Abstract

The invention relates to a method for determining image errors in high-resolution imaging systems using wavefront measurements and a corresponding computer program product. According to the invention, a design matrix is used to determine image errors of an imaging system, which in addition to diffractions of the zeroth and first order also takes into account diffractions of the second and/or other higher orders. On the basis of images of the imaging system of known, doubly diffracted illumination beams recorded by an interferogram sensor, imaging errors can then be precisely determined.

Description

The invention relates to a method for determining image errors in high-resolution imaging systems using wavefront measurement and a corresponding computer program product.

In applications such as microlithography, particularly high-resolution imaging systems are used in order to transfer the structure of a mask (also known as a reticle) in a reduced manner onto a substrate coated with a light-sensitive layer. The imaging system is also referred to as a projection system which, together with an illumination system which illuminates the mask, forms a projection exposure system such as is used in particular for microlithography in the production of semiconductor components.

The optical elements involved in the imaging system, such as mirrors or lenses, must be manufactured with high precision so that the structures of a mask, which are usually already very fine, are properly imaged by the imaging system, if necessary reduced. Despite the high-precision production of the individual optical elements, it has been shown that when they interact in an imaging system, there are still small deviations in the image, which are extremely relevant, for example in the manufacture of semiconductors, and are also referred to as image errors.

Methods are known from the prior art with which the imaging quality of an imaging system can be determined or possible image errors in the imaging system can be detected in a spatially resolved manner. Using this information, individual optical elements of the imaging system can then be identified and post-processed in such a way that after reinsertion into the imaging system, the image fields have been reduced in such a way that the imaging quality of the imaging system can be increased to a desired level.

A method for determining possible image errors is the wavefront detection of multiple grating-diffracted illumination beams. Illumination beams are transmitted from known positions in the object-side pupil plane of the imaging system to a first diffraction grating arranged in the object-side field plane through the imaging system to a second diffraction grating arranged in the image-side field plane, so that an interferometric image of the illumination rays results in the image-side pupil plane, which a suitable sensor can be detected.

If the process is repeated with different positions from which the illumination beam emanates and/or with the planned displacement of one of the two diffraction gratings in the field plane on the image side, a large number of interferometric images result, from which the imaging quality of the imaging system can then be determined locally, e.g .using a matrix that is fitted to the measurement results in the form of the interferometric images. It is then possible to identify those optical elements in the imaging system in which image errors of the imaging system can be reduced or whose imaging quality can be increased by suitable post-processing measures.

Even if measures for correcting the optical elements of a high-resolution imaging system resulting from a matrix determined according to the state of the art can regularly achieve good and often also sufficient results in increasing the imaging quality, it is particularly important with regard to ever-increasing demands on the imaging quality, as they occur, for example, in EUV technology - i.e. exposure to a wavelength of 5 nm to 30 nm - and the particularly small structures that are possible to be projected, are not always certain that the determination of known from the prior art Image errors can also ensure adequate imaging quality in such systems.

It is therefore the object of the present invention to provide a method and a computer program product for determining image errors in high-resolution imaging systems in which the possible disadvantages of the prior art do not occur or occur only to a reduced extent.

The invention is achieved by a method according to the main claim and a computer program product according to the independent claim. Advantageous developments are the subject of the dependent claims.

• - Beleuchten des ersten Beugungsgitters mit durch die Beleuchtungsquelle erzeugten Beleuchtungsstrahlen ausgehend von bekannten Positionen in der objektseitigen Pupillenebene;
• - Erfassen des sich durch die Beugungsgitter und das Abbildungssystem ergebenden Abbildes des Beleuchtungsstrahls auf dem Interferogramm-Sensor auch umfassend Beugungen 2ter und größerer Ordnungen;
• - Wiederholen der vorstehenden Schritte bei vorgegebener Verschiebung des verschiebbaren Beugungsgitters in der zugehörigen Feldebene;
• - Berechnen einer die idealen optischen Eigenschaften des Abbildungssystems wiedergebenden Designmatrix, wobei die Designmatrix wenigstens Beugungen nullter, erster, zweiter Ordnung umfasst; und
• - Ermitteln von Bildfehlern des Abbildungssystems auf Basis der durch den Interferogramm-Sensor erfassten Abbildungen und einer die idealen optischen Eigenschaften des Abbildungssystems wiedergebenden Designmatrix, wobei die Designmatrix wenigstens Beugungen nullter, erster, zweiter Ordnung umfasst.

Accordingly, the invention relates to a method for determining image errors in high-resolution imaging systems by wavefront measurement, with in an object-side pupil plane of the imaging system an illumination source, a first diffraction grating in an object-side field plane lying between illumination source and imaging system, an interferogram sensor in an image-side pupil plane and a second diffraction grating in an image-side field plane lying between imaging system and interferogram sensor, with one of the two diffraction gratings in the field plane in which it is arranged, can be displaced, comprising the steps:

• - Illuminating the first diffraction grating with illumination beams generated by the illumination source, starting from known positions in the object-side pupil plane;
• - Detecting the image of the illumination beam produced by the diffraction grating and the imaging system on the interferogram sensor, also including diffractions of the 2nd and larger orders;
• - repeating the above steps with a predetermined displacement of the displaceable diffraction grating in the associated field plane;
• - calculating a design matrix which represents the ideal optical properties of the imaging system, the design matrix comprising at least zeroth, first and second order diffractions; and
• - Determination of image errors of the imaging system on the basis of the images recorded by the interferogram sensor and a design matrix reflecting the ideal optical properties of the imaging system, the design matrix comprising at least zeroth, first, second order diffractions.

Furthermore, the invention relates to a computer program product or a set of computer program products, comprising program parts which, when loaded into a computer or into interconnected computers for calculation, reflect the ideal optical properties of the imaging system, the design matrix comprising at least diffractions of the zeroth, first, second order , and are designed to determine values reflecting the image errors of the imaging system on the basis of the images recorded by the interferogram sensor and the design matrix.

First, some terms used in connection with the invention are explained:

“Object-side pupil plane” and “object-side field plane” designate planes that lie on the side of the imaging system on which the object to be imaged is usually to be expected. The illumination can, for example, be arranged in an object-side pupil plane, while a field plane on the object-side can be, for example, the reticle plane.

“Image-side pupil plane” and “image-side field plane” designate planes that lie on the side of the imaging system on which imaging of an object is usually to be expected. A camera, for example, can be arranged in an image-side pupil plane. An image-side field plane can be the wafer plane, for example.

The invention is based on the finding that the assumption, widespread in the prior art, that to determine the imaging quality of an imaging system by wavefront measurement, it is sufficient to only consider the zeroth and first order diffraction - which is why the known algorithms for determining a design matrix of a Imaging system are finally limited to these orders - do not result in sufficient accuracy for all applications. As a result, post-processing measures determined on the basis of such a design matrix cannot ensure an ultimately sufficient imaging quality of the imaging system examined for all applications.

The core of the invention is to map the imaging properties of an imaging system as precisely as possible in a design matrix, so that a comparison with recorded interferometric images of exposure beams results in more precise information on possible imaging errors, from which post-processing measures suitable for increasing the imaging quality can be derived more reliably.

It was recognized that the limitation to zeroth and first-order diffractions, which is considered sufficient in the prior art and has proven to be sufficient for a large number of applications, ultimately limits the realism of the design matrix and thus the possible increase in imaging quality through suitable post-processing measures on the basis of the design matrix and must be canceled so that higher-order diffractions can also be taken into account. Even if Although at first glance these higher-order diffractions may only have a small effect on the imaging quality and/or the accuracy of the design matrix, it has been shown that when the requirements for imaging quality are particularly high, they cannot be neglected. However, since the algorithms known from the prior art for determining a design matrix based on interferometric images can only take into account zeroth and first order diffractions, part of the present invention is a new algorithm with which a significantly more realistic design matrix can be created than in the prior art the technology possible.

It has also been shown that - provided no higher accuracy in the design matrix is required compared to the methods known from the prior art - in the method according to the invention a reduced number of interferometric measurements compared to the prior art is sufficient to obtain comparably reliable statements to be able to meet imaging errors. In such cases, the method according to the invention can therefore be faster than that known from the prior art.

A preferred possibility of determining image errors in high-resolution imaging systems by wavefront measurement, in which diffractions of the second and/or higher orders can also be taken into account, is explained below.

The actual determination of interferometric images takes place in a manner comparable to the known prior art: starting from an illumination source arranged in an object-side pupil plane of the imaging system, defined—i.e. H. illuminating rays are emitted into the imaging system - known in position on and orientation relative to the pupillary plane. As a rule, it is advantageous if the illumination beam has the same or a comparable wavelength as the illumination provided when the imaging system is later used. If the imaging system is therefore a projection exposure system for microlithography, the illumination beam preferably has a wavelength comparable to that which is provided for exposure in the course of microlithography. In the case of an imaging system provided for EUV microlithography, the wavelength for the illumination beam is therefore in the range from 5 nm to 30 nm, for example.

The illumination source can be arranged directly in the pupil plane; however, it is also possible for the element actually generating the light to be arranged outside of said pupil plane, with optical elements deflecting the light generated away from the pupil plane into the pupil plane in such a way that it can be assumed for further viewing that the illumination beams emanating from the pupil plane would be generated by an illumination source placed on the pupil plane. In this case one can also speak of a "virtual illumination source" on the pupil level.

Before the illuminating beam enters the imaging system, it has to traverse a first diffraction grating arranged in the appropriate object-side field plane of the imaging system. The first diffraction grating can be designed according to the state of the art and in particular can have a pattern that has been tried and tested there. In the first diffraction grating, the incident illumination beam is "fanned out" into the various diffractions of the zeroth, first, second and higher orders, whereby the individual diffractions can be viewed as separate beams according to their order, starting from the first diffraction grating, which at least for the most part into the Enter imaging system and be mapped by this.

If the imaging system is a projection system for microlithography, the first diffraction grating can be arranged, for example, in the plane in which the mask (also called reticle) to be projected is usually arranged. The first diffraction grating can also be referred to below as a reticle diffraction grating.

A second diffraction grating is arranged in an image-side field plane of the imaging system, which is also designed as known from the prior art. With the help of this second diffraction grating, the beam paths of the individual diffractions transmitted through the imaging system are diffracted again.

At least one of the two diffraction gratings can be displaced in the field plane in which it is arranged, in order to generate other diffraction patterns, depending on the position.

If the imaging system is a projection system for microlithography, the second diffraction grating can be arranged, for example, in the plane in which the semiconductor wafer is usually arranged, onto which the image of the mask or reticle is to be projected . Within the scope of the present invention, the second diffraction grating is also referred to as a sensor diffraction grating.

For the imaging system located between the two field planes mentioned, a single pupil plane can be assumed in a model consideration, regardless of its design and e.g. the actual number of intermediate pupil or field planes, in which, for example, the numerical aperture of the imaging system is also located can be defined.

The rays diffracted by the second diffraction grating impinge on an interferogram sensor arranged in a subsequent image-side pupil plane of the imaging system and are recorded there. Due to the fanning out of the illumination beam by the first diffraction grating and depending on the position of the second diffraction pattern, different images of the illumination beam result on the interferogram sensor, namely interference or wavefront images, which, through suitable analysis, allow conclusions to be drawn about signals that may not have been optimally transmitted or transmitted by the imaging system .allow diffractions shown.

In this context, it is known to determine the imaging errors of the optical system by comparing the recorded interference images or wavefront images with a design matrix of the imaging system. With a suitable configuration of the design matrix, parameters of a Zernike polynomial can be determined, for example by appropriate fitting methods for the detected wavefront images, with any deviation from ideal values (such as zero) providing an indication of an imaging error. The parameters determined in this way can be used together with the design matrix and knowledge of the actual structure of the imaging system in order to identify post-processing measures for the imaging system or individual elements thereof with which the imaging errors can be reduced. Methods for determining necessary or advantageous post-processing measures for an imaging system, for example the projection system of a microlithography system, starting from a design matrix, are known in the prior art.

It was previously considered sufficient to only take into account the zeroth and first-order diffractions of an illumination beam when determining aberrations, and to improve the accuracy of determining the aberrations, various approaches were pursued to avoid the imaging of higher-order diffractions by the imaging system , the present invention goes the opposite way: by not only allowing higher-order diffractions, but also taking them into account when determining the design matrix and thus the imaging quality, the design matrix becomes more realistic. The increased realism of the design matrix in turn enables a more precise identification of aberrations. As a result, a more precise post-processing of the imaging system is possible, at the end of which there is an increased imaging quality of the imaging system, which cannot be reliably achieved with the methods known from the prior art. Because measures to suppress higher-order diffractions in the actual measurement can be completely dispensed with, the measurement process can often be accelerated. Flexibility in selecting the grid design is also increased.

To determine the design matrix, a representation of the beam paths at the pupil planes scaled to the refraction angle in Cartesian coordinates is used, i. That is, an integer coordinate step in the Cartesian system of a pupil plane corresponds to a step by the diffraction angle between two adjacent diffractions, and the zero point in the Cartesian coordinate system coincides with a diffracted ray. The coordinates for the object-side pupil plane, in which the illumination source is arranged, and the objective pupil plane describing the imaging system are scaled to the refraction angle of the first diffraction grating, while the coordinates for the image-side pupil plane, in which the interferogram sensor is arranged, the scaling of the Coordinates based on the angle of refraction of the second diffraction grating. The angle of refraction of the second diffraction grating is usually a multiple of the angle of refraction of the first diffraction grating, corresponding to the magnification factor of the imaging system.

• Objektseitige Pupillenebene: $\left(x{i}_i,y{i}_i\right)$
  
• Objektivpupillenebene: $\left(x_k,y_k\right)$
  
• Bildseitige Pupillenebene: $\left(x{c}_j,y{c}_j\right)$
  

For the following considerations, the scaled coordinates are defined as follows:

• Object-side pupil plane: $\left(x{i}_i,y{i}_i\right)$
  
• Lens Pupil Level: $\left(x_k,y_k\right)$
  
• Image-side pupil plane: $\left(x{c}_j,y{c}_j\right)$
  

The design matrix, which initially reflects the wavefronts in the objective pupil plane from the images recorded by the interferogram sensor, which in turn can then be used to identify aberrations in the imaging system or individual components on it and to provide suitable post-processing measures to reduce the aberrations.

mit $$S_{ik}^{x,h1}=\frac{\partial {\mathrm{\Phi }}_{x,h1}\left(x{c}_i,y{c}_i\right)}{\partial z_k}|{}_{z_1\dots z_N=0}$$

$$S_{jk}^{y,h1}=\frac{\partial {\mathrm{\Phi }}_{y,h1}\left(x{c}_j,y{c}_j\right)}{\partial z_k}|{}_{z_1\dots z_N=0}$$

wobei diese Ableitungen um den Punkt, an dem die Zernike-Faktoren z₁..z_N gleich null sind, linearisiert werden.In general, the design matrix can be formulated as $$s=\left(\begin{array}{c}{S}_{iK}^{x,H1}\\ S_{jK}^{y,H1}\end{array}\right)$$

with $$S_{ik}^{x,H1}=\frac{\partial {\mathrm{\Phi }}_{x,H1}\left(x{c}_i,y{c}_i\right)}{\partial {\mathrm{e.g}}_k}|{}_{{\mathrm{e.g}}_1...{\mathrm{e.g}}_N=0}$$

$$S_{jk}^{y,H1}=\frac{\partial {\mathrm{\Phi }}_{y,H1}\left(x{c}_j,y{c}_j\right)}{\partial {\mathrm{e.g}}_k}|{}_{{\mathrm{e.g}}_1...{\mathrm{e.g}}_N=0}$$

where these derivatives are linearized around the point where the Zernike factors z ₁ ..z _N equal zero.

mit $$\begin{array}{l}{A}_{x,12}=g_{x,sen}^{*}\left(n{x}_1,n{y}_1\right)g_{x,sen}\left(n{x}_1+1,n{y}_1\right)g_{x,ret}^{*}\left(o_x-n{x}_1,o_y-n{y}_1\right)g_{x,ret}(o_x\\ -n{x}_1-1,o_y-n{y}_2)\end{array}$$

$$x_{1j}=x{c}_j-n{x}_1$$

$$y_{1j}=y{c}_j-n{y}_1$$

$$y_{2j}=y{c}_j-n{y}_2$$

und den Randbedingungen $$x_{1j}^2+y_{1k}^2\le NA$$

$$x_{2j}^2+y_{2j}^2={\left(x_{1j}+1\right)}^2+y_{2j}^2\le NA$$

$$x{i}_i^2+y{i}_i^2\le N{A}_{illu}$$

On the one hand, $$\begin{array}{l}{\mathrm{\Phi }}_{x,H1}\left(x{c}_{j}y{c}_j\right)\hfill \\ =a\mathrm{right}G\left({\displaystyle \sum _{O_x=O{x}_{min}}^{O{x}_{max}}{\displaystyle \sum _{O_y=O{y}_{min}}^{O{y}_{max}}{\displaystyle \sum _{n{x}_1=n{x}_{max}}^{n{x}_{max}-1}{\displaystyle \sum _{n{y}_2=n{y}_{min}}^{n{y}_{max}}{\displaystyle \sum _{n{y}_1=n{y}_{min}}^{n{y}_2}{A}_{x,12}\text{ex}(i(\varphi (x_{1j}+1,y_{2j}}}}}}\right)\hfill \\ -\varphi \left(x_{1j},y_{1j}\right))))\hfill \end{array}$$

with $$\begin{array}{l}{A}_{x,12}=G_{x,sen}^{*}\left(n{x}_1,n{y}_1\right)G_{x,sen}\left(n{x}_1+1,n{y}_1\right)G_{x,\mathrm{right}et}^{*}\left(O_x-n{x}_1,O_y-n{y}_1\right)G_{x,\mathrm{right}et}(O_x\\ -n{x}_1-1,O_y-n{y}_2)\end{array}$$

$$x_{1j}=x{c}_j-n{x}_1$$

$$y_{1j}=y{c}_j-n{y}_1$$

$$y_{2j}=y{c}_j-n{y}_2$$

and the boundary conditions $$x_{1j}^2+y_{1k}^2\le NA$$

$$x_{2j}^2+y_{2j}^2={\left(x_{1j}+1\right)}^2+y_{2j}^2\le NA$$

$$x{i}_i^2+y{i}_i^2\le N{A}_{ill\mathrm{and}}$$

mit $$\begin{array}{l}{A}_{y\mathrm{,12}}=g_{y,sen}^{*}\left(n{x}_1,n{y}_1\right)g_{y,sen}\left(n{x}_2,n{y}_1+1\right)g_{y,ret}^{*}\left(o_x-n{x}_1,o_y-n{y}_1\right)g_{y,ret}(o_x\\ -n{x}_2,o_y-n{y}_1-1)\end{array}$$

$$x_{1j}=x{c}_j-n{x}_1$$

$$y_{1j}=y{c}_j-n{y}_1$$

$$x_{2j}=x{c}_j-n{x}_2$$

und den Randbedingungen $$x_{1j}^2+y_{1k}^2\le NA$$

$$x_{2j}^2+y_{2k}^2=x_{2j}^2+{\left(y_{1j}+1\right)}^2\le NA$$

$$x{i}_i^2+y{i}_i^2\le N{A}_{illu}$$

On the other hand $$\begin{array}{l}{\mathrm{\Phi }}_{y,H1}\left(x{c}_{j}y{c}_j\right)\hfill \\ =a\mathrm{right}G\left({\displaystyle \sum _{O_x=O{x}_{min}}^{O{x}_{max}}{\displaystyle \sum _{O_y=O{y}_{min}}^{O{y}_{max}}{\displaystyle \sum _{n{x}_2=n{x}_{min}}^{n{x}_{max}}{\displaystyle \sum _{n{x}_1=n{x}_{min}}^{n{x}_2}{\displaystyle \sum _{n{y}_1=n{y}_{min}}^{n{y}_{max}-1}{A}_{x,12}\text{ex}(i(\varphi (x_{2j},y_{1j}+1}}}}}\right)\hfill \\ -\varphi \left(x_{1j},y_{1j}\right))))\hfill \end{array}$$

with $$\begin{array}{l}{A}_{y\mathrm{,12}}=G_{y,sen}^{*}\left(n{x}_1,n{y}_1\right)G_{y,sen}\left(n{x}_2,n{y}_1+1\right)G_{y,\mathrm{right}et}^{*}\left(O_x-n{x}_1,O_y-n{y}_1\right)G_{y,\mathrm{right}et}(O_x\\ -n{x}_2,O_y-n{y}_1-1)\end{array}$$

$$x_{1j}=x{c}_j-n{x}_1$$

$$y_{1j}=y{c}_j-n{y}_1$$

$$x_{2j}=x{c}_j-n{x}_2$$

and the boundary conditions $$x_{1j}^2+y_{1k}^2\le NA$$

$$x_{2j}^2+y_{2k}^2=x_{2j}^2+{\left(y_{1j}+1\right)}^2\le NA$$

$$x{i}_i^2+y{i}_i^2\le N{A}_{ill\mathrm{and}}$$

The indices "x" and "y" used in the above formulas make it clear that the algorithm presented here can fundamentally take into account different diffraction properties in the x and y direction, which can be considered separately, for example, in two consecutive measurement sequences. In this case, the displaceable diffraction grating can first be displaced in the x-direction in the first measurement sequence and in the y-direction in a subsequent measurement sequence.

wobei $$p_n\left(x_j,y_j\right)$$

das n-te, für den Punkt (x_j,y_j) ausgewertete Zernike-Polynom ist und sich die Phase am fraglichen Punkt - nach Ermittlung der Zernike-Parameter - aus der Summe der Zernike-Polynome ergibt.The following generally applies to all the above formulas $$\varphi \left({\text{x}}_{\text{j}}{\text{y}}_{\text{j}}\right)={\displaystyle \sum _{n=1}^N{\mathrm{e.g}}_n{p}_n\left(x_j,y_j\right)}$$

in which $$p_n\left(x_j,y_j\right)$$

is the nth Zernike polynomial evaluated for the point (x _j ,y _j ) and the phase at the point in question results - after determining the Zernike parameters - from the sum of the Zernike polynomials.

The complex conjugable functions g _ret (nx,ny) and g _sen (nx,ny) are the complex diffraction spectra of the first or reticle diffraction grating and the second or sensor diffraction grating for the respective diffraction orders in the x and y-direction, whereby the two functions can in turn be set up separately for the x- and y-direction (cf. indices when used in the above formulas).

NA denotes the numerical aperture of the imaging system. NA _illu denotes the aperture of the illumination.

$$y{i}_i=y{c}_j-o_y$$

sowie $$o_x=n{x}_{ret,1}+n{x}_{sen,1}=n{x}_{ret,2}+n{x}_{sen,2}$$

$$o_y=n{y}_{ret,1}+n{y}_{sen,1}=n{y}_{ret,2}+n{y}_{sen,2}$$

Furthermore, the general rule applies $$x{i}_i=x{c}_j-O_x$$

$$y{i}_i=y{c}_j-O_y$$

such as $$O_x=n{x}_{\mathrm{right}et,1}+n{x}_{sen,1}=n{x}_{\mathrm{right}et,2}+n{x}_{sen,2}$$

$$O_y=n{y}_{\mathrm{right}et,1}+n{y}_{sen,1}=n{y}_{\mathrm{right}et,2}+n{y}_{sen,2}$$

The latter formula also introduces the restriction into the algorithm that only diffractions that result from a common illumination direction can actually interfere with one another at the interferogram sensor. At the same time, the summation of the variables o _x and o _y ensures that those contributions from the radiation impinging on the interferogram sensor can also be taken into account, the angle of which emanates from the second diffraction grating does not correspond to the angle of incidence of the original illumination beam at the first diffraction grating.

Here, nx and ny represent the diffraction order at the - depending on the index - the first or reticle diffraction grating or the second or sensor diffraction grating in the x or y direction.

bzw. $S_{jk}^{y,h1}$

der Designmatrix vereinfacht darstellen lassen als $$\begin{array}{l}{S}_{jk}=\frac{\partial }{\partial z_k}(arg({\displaystyle \sum _{l,m}{A}_{l,m}exp(i({\displaystyle \sum _{n=1}^N{z}_n(p_n\left(x_{jl},y_{jl}\right)-p_n\left(x_{jm},y_{jm}\right))))))}}|{}_{z_1\dots z_N=0}\\ =\frac{1}{2}(\frac{{\displaystyle {\sum }_{l,m}{A}_{l,m}\left(p_k\left(x_{jl},y_{jl}\right)-p_n\left(x_{jm},y_{jm}\right)\right)}}{{\displaystyle {\sum }_{l,m}{A}_{l,m}}}\\ +\frac{{\displaystyle {\sum }_{l,m}{A}_{l,m}^{*}\left(p_k\left(x_{jl},y_{jl}\right)-p_k\left(x_{jm},y_{jm}\right)\right)}}{{\displaystyle {\sum }_{l,m}{A}_{l,m}^{*}}})\end{array}$$

From the above considerations it has been shown that the components $S_{jk}^{x,H1}$

or. $S_{jk}^{y,H1}$

of the design matrix can be represented in a simplified way as $$\begin{array}{l}{S}_{jk}=\frac{\partial }{\partial {\mathrm{e.g}}_k}(a\mathrm{right}G({\displaystyle \sum _{l,m}{A}_{l,m}exp(i({\displaystyle \sum _{n=1}^N{\mathrm{e.g}}_n(p_n\left(x_{jl},y_{jl}\right)-p_n\left(x_{jm},y_{jm}\right))))))}}|{}_{{\mathrm{e.g}}_1...{\mathrm{e.g}}_N=0}\\ =\frac{1}{2}(\frac{{\displaystyle {\sum }_{l,m}{A}_{l,m}\left(p_k\left(x_{jl},y_{jl}\right)-p_n\left(x_{jm},y_{jm}\right)\right)}}{{\displaystyle {\sum }_{l,m}{A}_{l,m}}}\\ +\frac{{\displaystyle {\sum }_{l,m}{A}_{l,m}^{*}\left(p_k\left(x_{jl},y_{jl}\right)-p_k\left(x_{jm},y_{jm}\right)\right)}}{{\displaystyle {\sum }_{l,m}{A}_{l,m}^{*}}})\end{array}$$

wandeln: $$A_{l,m}=A_{x,12}$$

$$x_{jl}=x_{j1}$$

$$y_{jl}=y_{j1}$$

$$x_{jm}=x_{j2}$$

$$y_{jm}=y_{j2}$$

$${\displaystyle \sum _{l,m}={\displaystyle \sum _{o_x}{\displaystyle \sum _{o_y}{\displaystyle \sum _{n{y}_{sen\mathrm{,1}}}{\displaystyle \sum _{n{y}_{sen\mathrm{,2}}}{\displaystyle \sum _{n{x}_{sen\mathrm{,1}}=n{x}_{sen,min}}^{n{x}_{sen,max}-1}}}}}}}$$

For example, the above general formula for S _jk can be replaced by the following $S_{jk}^{x,H1}$

walk: $$A_{l,m}=A_{x,12}$$

$$x_{jl}=x_{j1}$$

$$y_{jl}=y_{j1}$$

$$x_{jm}=x_{j2}$$

$$y_{jm}=y_{j2}$$

$${\displaystyle \sum _{l,m}={\displaystyle \sum _{O_x}{\displaystyle \sum _{O_y}{\displaystyle \sum _{n{y}_{sen\mathrm{,1}}}{\displaystyle \sum _{n{y}_{sen\mathrm{,2}}}{\displaystyle \sum _{n{x}_{sen\mathrm{,1}}=n{x}_{sen,min}}^{n{x}_{sen,max}-1}}}}}}}$$

möglich.This is also the same for $S_{jk}^{y,H1}$

possible.

bzw. $$\left(\begin{array}{c}{\widehat{z}}_1\\ {\widehat{z}}_2\\ ⋮\\ {\widehat{z}}_K\end{array}\right)=\left(\begin{array}{c}\left(\begin{array}{cccc}{S}_{11}^{x,h1}& S_{12}^{x,h1}& \dots & S_{1K}^{x,h1}\\ S_{21}^{x,h1}& S_{22}^{x,h1}& \dots & S_{2K}^{x,h1}\\ ⋮& ⋮& \ddots & ⋮\\ S_{I1}^{x,h1}& S_{I2}^{x,h1}& \dots & S_{IK}^{x,h1}\end{array}\right)\\ \left(\begin{array}{cccc}{S}_{11}^{y,h1}& S_{12}^{y,h1}& \dots & S_{1K}^{y,h1}\\ S_{21}^{y,h1}& S_{22}^{y,h1}& \dots & S_{2K}^{y,h1}\\ ⋮& ⋮& \ddots & ⋮\\ S_{J1}^{y,h1}& S_{J2}^{y,h1}& \dots & S_{JK}^{y,h1}\end{array}\right)\end{array}\right)\text{/}\left(\begin{array}{c}\left(\begin{array}{c}{\Phi }_{meas}^{x,h1}\left(x{c}_1,y{c}_1\right)\\ {\Phi }_{meas}^{x,h1}\left(x{c}_2,y{c}_2\right)\\ ⋮\\ {\Phi }_{meas}^{x,h1}\left(x{c}_I,y{c}_I\right)\end{array}\right)\\ \left(\begin{array}{c}{\Phi }_{meas}^{y,h1}\left(x{c}_1,y{c}_1\right)\\ {\Phi }_{meas}^{y,h1}\left(x{c}_2,y{c}_2\right)\\ ⋮\\ {\Phi }_{meas}^{y,h1}\left(x{c}_J,y{c}_J\right)\end{array}\right)\end{array}\right)$$

wobei Φ_meas die am jeweiligen Punkt in der objektseitigen Pupillenebene aus dem Interferogramm ergebende Phase ist.Using the design matrix that can be determined in this way, a vector of the Zernike parameters can be determined based on measured interferogram images with suitable x and y phase steps for each measuring point of the interferogram sensor and - for example - the method of the (possibly weighted) least squares: $${\widehat{\mathrm{e.g}}}_k=\left(\begin{array}{c}{S}_{ik}^{x,H1}\\ S_{jk}^{y,H1}\end{array}\right)\text{}\left(\begin{array}{c}{\Phi }_{meas}^{x,H1}\left(x{c}_i,y{c}_i\right)\\ {\Phi }_{meas}^{y,H1}\left(x{c}_j,y{c}_j\right)\end{array}\right)$$

or. $$\left(\begin{array}{c}{\widehat{\mathrm{e.g}}}_1\\ {\widehat{\mathrm{e.g}}}_2\\ ⋮\\ {\widehat{\mathrm{e.g}}}_K\end{array}\right)=\left(\begin{array}{c}\left(\begin{array}{cccc}{S}_{11}^{x,H1}& S_{12}^{x,H1}& ...& S_{1K}^{x,H1}\\ S_{21}^{x,H1}& S_{22}^{x,H1}& ...& S_{2K}^{x,H1}\\ ⋮& ⋮& \ddots & ⋮\\ S_{I1}^{x,H1}& S_{I2}^{x,H1}& ...& S_{IK}^{x,H1}\end{array}\right)\\ \left(\begin{array}{cccc}{S}_{11}^{y,H1}& S_{12}^{y,H1}& ...& S_{1K}^{y,H1}\\ S_{21}^{y,H1}& S_{22}^{y,H1}& ...& S_{2K}^{y,H1}\\ ⋮& ⋮& \ddots & ⋮\\ S_{J1}^{y,H1}& S_{J2}^{y,H1}& ...& S_{JK}^{y,H1}\end{array}\right)\end{array}\right)\text{/}\left(\begin{array}{c}\left(\begin{array}{c}{\Phi }_{meas}^{x,H1}\left(x{c}_1,y{c}_1\right)\\ {\Phi }_{meas}^{x,H1}\left(x{c}_2,y{c}_2\right)\\ ⋮\\ {\Phi }_{meas}^{x,H1}\left(x{c}_I,y{c}_I\right)\end{array}\right)\\ \left(\begin{array}{c}{\Phi }_{meas}^{y,H1}\left(x{c}_1,y{c}_1\right)\\ {\Phi }_{meas}^{y,H1}\left(x{c}_2,y{c}_2\right)\\ ⋮\\ {\Phi }_{meas}^{y,H1}\left(x{c}_J,y{c}_J\right)\end{array}\right)\end{array}\right)$$

where Φ _meas is the phase resulting from the interferogram at the respective point in the object-side pupil plane.

If, e.g. with the help of the above formulas, when calculating the design matrix, diffractions of up to the sixth order, which represents a preferred minimum, are taken into account, comparison calculations with known algorithms that only take into account the zeroth and first diffraction orders can significantly improve the realism of the design matrix be achieved, as a rule by a factor of at least 2. As already explained, this in turn enables a more precise determination of imaging errors and enables a more precise post-processing of the imaging system in order to achieve a very high imaging quality as a result.

$$o_y=0$$

$$n{y}_{sen\mathrm{,1}}=0$$

$$n{y}_{sen\mathrm{,1}}=0$$

$$n{x}_{sen,min}=-1$$

$$n{x}_{sen,max}=1$$

und für die y-Phasenverschiebung $$o_x=0$$

$$o_y=0$$

$$n{x}_{sen\mathrm{,1}}=0$$

$$n{x}_{sen\mathrm{,1}}=0$$

$$n{y}_{sen,min}=-1$$

$$n{y}_{sen,max}=1$$

zu verwenden. Zusammen mit der Annahme symmetrischer Beugungsspektren, womit gilt $$g_{sen}^x\left(-\mathrm{1,0}\right)=g_{sen}^x\left(\mathrm{1,0}\right)$$

$$g_{ret}^x\left(-\mathrm{1,0}\right)=g_{ret}^x\left(\mathrm{1,0}\right)$$

$$g_{sen}^y\left(-\mathrm{1,0}\right)=g_{sen}^y\left(\mathrm{1,0}\right)$$

$$g_{ret}^y\left(-\mathrm{1,0}\right)=g_{ret}^y\left(\mathrm{1,0}\right)$$

ergibt sich für die Komponenten der Designmatrix $$S_{jk}^{x,h1}\approx \frac{1}{2}\left(p_n\left(c{x}_i-\mathrm{1,}c{y}_i\right)-p_n\left(c{x}_i+\mathrm{1,}c{y}_i\right)\right)$$

$$S_{jk}^{y,h1}\approx \frac{1}{2}\left(p_n\left(c{x}_i,c{y}_i-1\right)-p_n\left(c{x}_i,c{y}_i+1\right)\right)$$

As also already mentioned, the algorithm according to the invention can also be limited to the diffractions of the zeroth and first order, so that results comparable to the prior art are then achieved. The parameters for the x-phase shift are for the reduction to an algorithm that only takes into account the zeroth and first diffraction orders $$O_x=0$$

$$O_y=0$$

$$n{y}_{sen\mathrm{,1}}=0$$

$$n{y}_{sen\mathrm{,1}}=0$$

$$n{x}_{sen,min}=-1$$

$$n{x}_{sen,max}=1$$

and for the y phase shift $$O_x=0$$

$$O_y=0$$

$$n{x}_{sen\mathrm{,1}}=0$$

$$n{x}_{sen\mathrm{,1}}=0$$

$$n{y}_{sen,min}=-1$$

$$n{y}_{sen,max}=1$$

to use. Together with the assumption of symmetrical diffraction spectra, with which holds $$G_{sen}^x\left(-1.0\right)=G_{sen}^x\left(1.0\right)$$

$$G_{\mathrm{right}et}^x\left(-1.0\right)=G_{\mathrm{right}et}^x\left(1.0\right)$$

$$G_{sen}^y\left(-1.0\right)=G_{sen}^y\left(1.0\right)$$

$$G_{\mathrm{right}et}^y\left(-1.0\right)=G_{\mathrm{right}et}^y\left(1.0\right)$$

results for the components of the design matrix $$S_{jk}^{x,H1}\approx \frac{1}{2}\left(p_n\left(c{x}_i-\mathrm{1,}c{y}_i\right)-p_n\left(c{x}_i+\mathrm{1,}c{y}_i\right)\right)$$

$$S_{jk}^{y,H1}\approx \frac{1}{2}\left(p_n\left(c{x}_i,c{y}_i-1\right)-p_n\left(c{x}_i,c{y}_i+1\right)\right)$$

bzw. $S_{jk}^{y,h1}$

der Designmatrix kann näherungsweise weiter vereinfacht werden zu: $$S_{jk}\approx arg\left({\displaystyle \sum _{l,m}{A}_{l,m}}\text{exp}\left(-i\left(p_j\left(x_l,y_l\right)-p_j\left(x_m,y_m\right)\right)\right)\right)$$

oder $$S_{jk}\approx arg\left({\displaystyle \sum _{l,m}{A}_{l,m}}\text{exp}\left(-i\left(p_j\left(x_l,y_l\right)-p_j\left(x_m,y_m\right)\right)\right)\right)$$

The simplified representation of the components shown above $S_{jk}^{x,H1}$

or. $S_{jk}^{y,H1}$

the design matrix can be further simplified to: $$S_{jk}\approx a\mathrm{right}G\left({\displaystyle \sum _{l,m}{A}_{l,m}}\text{ex}\left(-i\left(p_j\left(x_l,y_l\right)-p_j\left(x_m,y_m\right)\right)\right)\right)$$

or $$S_{jk}\approx a\mathrm{right}G\left({\displaystyle \sum _{l,m}{A}_{l,m}}\text{ex}\left(-i\left(p_j\left(x_l,y_l\right)-p_j\left(x_m,y_m\right)\right)\right)\right)$$

mit $$D_{ik}^{x,h1}={\frac{\partial {\Phi }_{x,h1}\left(x{c}_i,y{c}_i\right)}{\partial \varphi \left(x_k,y_k\right)}|}_{\varphi =0}$$

$$D_{ik}^{y,h1}={\frac{\partial {\Phi }_{y,h1}\left(x{c}_j,y{c}_j\right)}{\partial \varphi \left(x_k,y_k\right)}|}_{\varphi =0}$$

As an alternative to determining the design matrix, from which the phase in the objective pupil plane can then be calculated, it is alternatively also possible, essentially analogously to the above considerations, directly to determine the location-dependent phase Φ(x _j ,y _j ) and without explicit calculation of Zernike determine coefficients, namely by resorting to the derivative of the model function at the desired point: $$D=\left(\begin{array}{c}{D}_{ik}^{x,H1}\\ D_{jk}^{y,H1}\end{array}\right)$$

with $$D_{ik}^{x,H1}={\frac{\partial {\Phi }_{x,H1}\left(x{c}_i,y{c}_i\right)}{\partial \varphi \left(x_k,y_k\right)}|}_{\varphi =0}$$

$$D_{ik}^{y,H1}={\frac{\partial {\Phi }_{y,H1}\left(x{c}_j,y{c}_j\right)}{\partial \varphi \left(x_k,y_k\right)}|}_{\varphi =0}$$

In this case in particular, the phase in the objective pupil plane can also be represented by polynomials other than the Zernike polynomials, for example the Tatian polynomials.

The interferogram sensor can be, for example, a two-dimensional CCD array sensor or an active pixel sensor.

• 1: eine schematische Darstellung einer Projektionsbelichtungsanlage für die Mikrolithografie mit einem Projektionssystem als Abbildungssystem;
• 2: modellhafte Darstellung des Abbildungssystems aus 1 zur Ermittlung von Bildfehlern, wie sie der Erfindung zugrunde liegt; und
• 3: schematische Darstellung der Verbesserung in der Genauigkeit einer erfindungsgemäß ermittelten Designmatrix gegenüber dem Stand der Technik.

The invention will now be further illustrated with reference to the accompanying drawings. Show it:

• 1 : a schematic representation of a projection exposure system for microlithography with a projection system as an imaging system;
• 2 : model representation of the imaging system 1 for determining image errors, as is the basis of the invention; and
• 3 : schematic representation of the improvement in the accuracy of a design matrix determined according to the invention compared to the prior art.

In 1 a projection exposure system 1 for microlithography is shown in a schematic meridional section. The projection exposure system 1 comprises an illumination system 10 and a projection system 20.

An object field 11 in an object plane or reticle plane 12 is illuminated with the aid of the illumination system 10 . For this purpose, the illumination system 10 comprises an exposure radiation source 13 which, in the illustrated exemplary embodiment, emits illumination radiation at least comprising useful light in the EUV range, ie in particular with a wavelength between 5 nm and 30 nm. The exposure radiation source 13 can be a plasma source, for example an LPP (Laser Produced Plasma) source or a DPP (Gas Discharged Produced Plasma) source. It can also be a synchrotron-based radiation source. The exposure radiation source 13 can also be a free-electron laser (free-electron laser, FEL).

The illumination radiation emanating from the exposure radiation source 13 is initially bundled in a collector 14 . The collector 14 can be a collector with one or more ellipsoidal and/or hyperboloidal reflection surfaces. The at least one reflection surface of the collector 14 can be exposed to the illumination radiation in 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° . The collector 14 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 14, the illumination radiation propagates through an intermediate focus in an intermediate focal plane 15. If the illumination system 10 is constructed in a modular design, the intermediate focal plane 15 can in principle be used for the - also structural - separation of the illumination system 10 into a radiation source module, comprising the exposure radiation source 13 and the Collector 14, and the illumination optics 16 described below are used. With a corresponding separation, the radiation source module and the illumination optics 16 then together form a modular illumination system 10.

The illumination optics 16 include a deflection mirror 17. The deflection mirror 17 can be a planar deflection mirror or alternatively a mirror with an effect that influences the beam beyond the pure deflection effect. Alternatively or additionally, the deflection mirror 15 can be designed as a spectral filter, which separates a useful light wavelength of the illumination radiation from stray light of a different wavelength.

The radiation originating from the exposure radiation source 13 is deflected onto a first facet mirror 18 by the deflection mirror 17 . If the first facet mirror 18 is arranged—as in the present case—in a plane of the illumination optics 16 that is optically conjugated to the reticle plane 12 as a field plane, it is also referred to as a field facet mirror.

The first facet mirror 18 comprises a multiplicity of micromirrors (not shown in more detail) which can be pivoted individually about two axes running perpendicular to one another, for the controllable formation of facets. The first facet mirror 18 is therefore a microelectromechanical system (MEMS system), as is also the case, for example, in FIG DE 10 2008 009 600 A1 is described.

In the beam path of the illumination optics 16, a second facet mirror 19 is arranged after the first facet mirror 18, resulting in a double-faceted system whose basic principle is also referred to as a honeycomb condenser (fly's eye integrator). If the second facet mirror 19--as in the exemplary embodiment shown--is arranged in a pupil plane of the illumination optics 16, it is also referred to as a pupil facet mirror. The second facet mirror 19 can also be arranged at a distance from a pupil plane of the illumination optics 4, which means that the combination of the first th and the second facet mirror 18, 19 results in a specular reflector, as for example US 2006/0132747 A1 , the EP 1 614 008 B1 and the U.S. 6,573,978 is described.

The second facet mirror 19 also comprises a multiplicity of micromirrors which can each be pivoted individually about two axes running perpendicular to one another. For further explanation, refer to the DE 10 2008 009 600 A1 referred.

With the help of the second facet mirror 19, the individual facets of the first facet mirror 18 are imaged in the object field 11, which is usually only an approximate image. The second facet mirror 19 is the last beam-forming mirror or actually the last mirror for the illumination radiation in the beam path in front of the object field 11.

In each case one of the facets of the second facet mirror 19 is assigned to exactly one of the facets of the first facet mirror 18 to form an illumination channel for illuminating the object field 11 . In this way, in particular, lighting can result according to the Kohler principle.

The facets of the first facet mirror 18 are each imaged superimposed by an associated facet of the second facet mirror 19 in order to illuminate the object field 5 . The illumination of the object field 11 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 intensity distribution in the entrance pupil of the projection system 20 described below can also be adjusted by selecting the illumination channels that are ultimately used, which is easily possible by suitably adjusting the micromirrors of the first facet mirror 18 . This intensity distribution is also referred to as an illumination setting. Moreover, it can be advantageous if the second facet mirror 19 is not to be arranged exactly in a plane which is optically conjugate to a pupil plane of the projection system 20 . In particular, the pupil facet mirror 19 can be arranged tilted relative to a pupil plane of the projection system 20, as is the case, for example, in FIG DE 10 2017 220 586 A1 is described.

At the in the 1 However, the arrangement of the components of the illumination optics 16 shown in the illustration, the second facet mirror 19 is arranged in a surface conjugate to the entrance pupil of the projection system 20 . Deflection mirror 17 and the two facet mirrors 18, 19 are each arranged tilted relative to the object plane 12 and each other.

In an alternative embodiment of the illumination optics 16 (not shown), transmission optics comprising one or more mirrors can also be provided in the beam path between the second facet mirror 19 and the object field 11 . 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 particular, different positions of the entrance pupil for the tangential and for the sagittal beam path of the projection system 20 described below can be taken into account with additional transmission optics.

Alternatively, it is possible that the in 1 deflection mirror 17 shown is dispensed with, for which purpose the facet mirrors 18, 19 are to be arranged in a suitable manner opposite the radiation source 13 and the collector 14.

The object field 11 in the reticle plane 12 is transferred to the image field 21 in the image plane 22 with the aid of the projection system 20 .

For this purpose, the projection system 20 comprises a plurality of mirrors 25, M _i , which are numbered consecutively according to their arrangement in the beam path of the projection exposure system 1 .

At the in the 1 illustrated example, the projection system 20 comprises six mirrors 25, M ₁ to M ₆ . Alternatives with four, eight, ten, twelve or another number of mirrors 25, M ₁ are also possible. The penultimate mirror 25, M ₅ and the last mirror 25, M ₆ each have a passage opening for the illumination radiation, which means that the projection system 20 shown is a double obs cured optics. The projection system 20 has an image-side numerical aperture which is greater than 0.3 and which can also be greater than 0.6 and which can be, for example, 0.7 or 0.75.

The reflection surfaces of the mirrors 25, M _i can be designed as free-form surfaces without an axis of rotational symmetry. Alternatively, the reflection surfaces of the mirrors 25, M _i can also be designed as aspherical surfaces with exactly one axis of rotational symmetry of the reflection surface shape. Like the mirrors of the illumination optics 16, the mirrors 25, M _i can have highly reflective coatings for the illumination radiation. These coatings can be designed as multilayer coatings, in particular with alternating layers of molybdenum and silicon.

The projection system 20 has a large object-image offset in the y-direction between a y-coordinate of a center of the object field 11 and a y-coordinate of the center of the image field 21. This object-image offset in the y-direction can approximately as large as a z-distance between the object plane 12 and the image plane 22.

The projection system 20 can in particular be anamorphic, ie it has in particular different image scales β _x , β _y in the x and y directions. The two image scales β _x , β _y of the projection system 20 are preferably at (β _x , β _y )=(+/−0.25, /+−0.125). A magnification β of 0.25 corresponds to a reduction in the ratio 4:1, while a magnification β of 0.125 results in a reduction in the ratio 8:1. A positive sign for the imaging scale β means imaging without image reversal, a negative sign imaging with image reversal.

Other imaging scales are also possible. Image scales β _x , β _y with the same sign and absolutely the same in the x and y directions are also possible.

The number of intermediate image planes in the x-direction and in the y-direction in the beam path between the object field 11 and the image field 21 can be the same or different, depending on the design of the projection system 20. Examples of projection systems 20 with different numbers of such intermediate images in the x and y directions are known from FIG U.S. 2018/0074303 A1 .

In particular, the projection system 20 can have a homocentric entrance pupil. This can be accessible. But it can also be inaccessible.

A reticle 30 (also called a mask) arranged in the object field 11 is exposed by the illumination system 10 and transferred to the image plane 21 by the projection system 20 . The reticle 30 is held by a reticle holder 31 . The reticle holder 31 can be displaced in particular in a scanning direction via a reticle displacement drive 32 . In the exemplary embodiment shown, the scanning direction runs in the x-direction.

A structure on the reticle 30 is imaged onto a light-sensitive layer of a wafer 35 arranged in the region of the image field 21 in the image plane 22. The wafer 35 is held by a wafer holder 36. The wafer holder 36 can be displaced in particular along the x-direction via a wafer displacement drive 37 . The displacement of the reticle 30 on the one hand via the reticle displacement drive 32 and on the other hand the wafer 35 via the wafer displacement drive 37 can be synchronized with one another.

In the 1 The projection exposure system 1 shown according to the above description essentially represents the known state of the art.

In order to ensure a high quality of the semiconductors to be produced with the aid of the projection exposure system 1, it is necessary for the projection system 20, which represents an extremely high-resolution imaging system 20, to have little or no image errors. For this purpose, it is known in the prior art to determine the imaging quality of the imaging system 20 by means of a wave front measurement and, if necessary, to carry out post-processing on the imaging system 20 or its various optical elements, namely the mirrors M ₁ to M ₆ , until the desired imaging quality is achieved . For this purpose, it is known from the prior art to determine the wave front or a design matrix of the imaging system 20 from interferogram images generated using diffraction gratings, on the basis of which post-processing measures suitable for increasing the imaging quality can then be determined and implemented. In contrast to the prior art, in which only diffractions of the zeroth and first order can be taken into account, it is provided according to the invention that second-order diffraction and/or even further higher orders are also taken into account.

For this purpose, as in 2a shown schematically and in the form of the model consideration used in the invention, a determination of interferometric images known in principle from the prior art is carried out, in which, however, diffractions of the second or higher orders are also imaged.

The determination of interferometric images proceeds from an illumination source arranged in an object-side pupil plane 100 of the imaging system 20 with which defined illumination beams 101 - ie known in position on and alignment with respect to the pupil plane 100 - are emitted into the imaging system 20 . For reasons of clarity, in 2a only a single illumination beam 101 is shown. The illumination beam 101 is a beam of the same wavelength as that in the projection exposure system 1 according to FIG 1 utilized. With a corresponding configuration, the exposure system 10 of the projection exposure system 1 can even be used as a source for the illumination beam 101 and form a virtual illumination source: if the facet mirror 19 (cf. 1 ) are arranged in the pupil plane 101 of the imaging system 20, by suitably controlling the facet mirrors 18, 19 of the illumination system 10, suitable illumination beams 101 can be introduced into the imaging system, which can be viewed as emanating from the pupil plane 101, even if the actual exposure radiation source 13 is at a distance from it is arranged. Due to the identity of the exposure radiation source 13, an illumination beam 101 generated in this way then also has the same wavelength directly as is used later in the exposure of semiconductor wafers and thus in the actually intended use of the imaging system.

Before the illumination beam 101 actually enters the imaging system 20, it has to traverse a first diffraction grating 103 arranged in the appropriate object-side field plane 102 of the imaging system. In the first diffraction grating 103, the incident illumination beam 101 is "fanned out" into the various diffractions of the zeroth, first, second and higher orders, whereby the individual diffractions can be viewed as separate beams 104 depending on their order, starting from the first diffraction grating 103, which at least for the most part predominantly enter into the imaging system 20 and are imaged by it. The first diffraction grating 103 can in particular be a reflective diffraction grating, as is known from the prior art, which can be arranged, for example, in the reticle plane 12 of the projection exposure system 1 . It is essential that the first diffraction grating 103 is arranged in an image-side field plane of the imaging system 20 .

A second diffraction grating 106 is arranged in an image-side field plane 105 of the imaging system 20, with which the beam paths of the individual diffractions 104 transmitted through the imaging system 20 are diffracted again. The second diffraction grating 106 can be displaced in the field plane 105 . In the embodiment according to 1 For example, the second diffraction grating 105 can be arranged in the image plane 22 in particular, it being possible for the wafer holder 36 with the wafer displacement drive 37 to be used to displace the second diffraction grating 106 .

For the imaging system 20 located between the two mentioned field planes 12, 102, 22, 105, in the mathematical model according to 2a regardless of its configuration and, for example, the actual number of intermediate pupil or field planes, assume a single pupil plane 107 in which the numerical aperture 108 of the imaging system 20 can also be defined.

The rays diffracted by the second diffraction grating 106 impinge on an interferogram sensor 110 arranged in a subsequent image-side pupil plane 109 of the imaging system 20 and are detected there. The interferogram sensor 110 is a two-dimensional CCD array sensor.

With a according to the schematic diagram 2a As is known from the prior art, the measuring device constructed can be used to determine various images of the wave fronts of defined illumination beams 101 .

As explained in detail in the general part of the description, a design matrix can be determined algorithmically for the imaging system 20 . In order to avoid detailed repetitions in this regard, reference is made to the part of the description mentioned for an explanation of the creation of the design matrix.

The design matrix can then be used to determine image errors of the imaging system together with the images captured by the interferogram sensor. Can connect targeted one Individual optical elements of the imaging system 20 are reworked in order to further increase the imaging quality.

In 3 shows an example of the improvements in the accuracy of the design matrix that can be achieved by the method according to the invention compared to the prior art: the Zernike coefficients (filled columns) determined by the method according to the invention reflect the aberrations much more precisely than those according to the prior art determined Zernike coefficients (line). Correspondingly, required post-processing can also be defined more precisely, which results in a higher imaging quality overall.

QUOTES INCLUDED IN DESCRIPTION

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

Patent Literature Cited

• DE 102008009600 A1 [0061, 0063]
• US20060132747A1[0062]
• EP 1614008 B1 [0062]
• US6573978 [0062]
• DE 102017220586 A1 [0067]
• US 20180074303 A1 [0078]

Claims (7)

A method for determining image errors in high-resolution imaging systems using wavefront measurement, with an illumination source in an object-side pupil plane of the imaging system, a first diffraction grating in an object-side field plane between the illumination source and the imaging system, an interferogram sensor in an image-side pupil plane, and an interferogram sensor in an image-side pupil plane between the imaging system and A second diffraction grating is arranged in the field plane lying on the interferogram sensor, at least one of the diffraction gratings being displaceable in the field plane in which it is arranged, comprising the steps: - Illuminating the first diffraction grating with illumination beams generated by the illumination source, starting from known positions in the object-side pupil plane; - detecting the image of the illumination beams resulting from the diffraction grating and the imaging system on the interferogram sensor, also including diffractions of the 2nd and larger orders; - repeating the above steps with a predetermined displacement of the second diffraction grating in the field plane; and - Determination of image errors of the imaging system on the basis of the images recorded by the interferogram sensor and a design matrix reflecting the ideal optical properties of the imaging system, the design matrix comprising at least zeroth, first, second order diffractions. procedure after claim 1 , characterized in that when calculating the design matrix, diffractions are taken into account at least up to the sixth order. Method according to one of the preceding claims, characterized in that the design matrix is formed as $$S=\left(\begin{array}{c}{S}_{ik}^{x,H1}\\ S_{jk}^{y,H1}\end{array}\right)$$

with $$S_{ik}^{x,H1}={\frac{\partial {\Phi }_{x,H1}\left(x{c}_i,y{c}_i\right)}{\partial {\mathrm{e.g}}_k}|}_{{\mathrm{e.g}}_1...{\mathrm{e.g}}_N=0}$$

$$S_{jk}^{y,H1}={\frac{\partial {\Phi }_{y,H1}\left(x{c}_j,y{c}_j\right)}{\partial {\mathrm{e.g}}_k}|}_{{\mathrm{e.g}}_1...{\mathrm{e.g}}_N=0}$$

Method according to one of the preceding claims, characterized in that the illumination beam has a wavelength comparable or identical to the wavelength of the illumination to be expected when using the imaging system. Method according to one of the preceding claims, characterized in that the determined design matrix is used to determine necessary post-processing of the imaging system, and the post-processing thus determined is carried out on the imaging system. Computer program product or set of computer program products, comprising program parts which, when loaded into a computer or into interconnected computers, are used to calculate a design matrix reflecting the image errors of an imaging system on the basis of the images of the imaging system of known, doubly diffracted illumination beams recorded by an interferogram sensor, comprising at least diffractions zeroth, first, second order are formed. Computer program product or set of computer program products as claimed in claim 1, characterized in that when calculating the design matrix, diffractions are taken into account at least up to the sixth order.

Images