DE102021214363A1 - Method for areal, spatially resolved determination of at least one structural parameter - Google Patents

Abstract

The invention relates to a method for the areal, spatially resolved determination of at least one structural parameter of a geometric and/or optical structural model of a computer-generated hologram, CGH (1), using at least one optical measuring method (7), - using the at least one optical measuring method (7) CGH (1) or the wafer are measured and at least one measured value (10) characterizing the at least one structural parameter is determined in a spatially resolved manner, - a simulation calculation assigning a probability distribution (12) of the measured values to the at least one structural parameter, - the at least one structural parameter being is determined in such a way that at least one most probable simulated measured value assigned to the at least one structure parameter corresponds at least approximately to the at least one determined measured value (10), and wherein- the probability distribution (12) of the measured values or the structure turparameter is described by stochastic fields on the CGH (1) or wafer, which have correlations (14) between at least two different locations.

Description

• - wobei mittels des wenigstens einen optischen Messverfahrens das CGH oder der Wafer vermessen und ortsaufgelöst wenigstens ein den wenigstens einen Strukturparameter charakterisierender Messwert ermittelt wird,
• - wobei eine Simulationsrechnung dem wenigstens einen Strukturparameter eine Wahrscheinlichkeitsverteilung der Messwerte zuordnet,
• - wobei in einer Ausgleichsrechnung der wenigstens eine Strukturparameter derart bestimmt wird, dass wenigstens ein dem wenigstens einen Strukturparameter zugeordneter wahrscheinlichster simulierter Messwert dem wenigstens einen ermittelten Messwert wenigstens annähernd entspricht.

The invention relates to a method for the areal, spatially resolved determination of at least one structural parameter of a geometric and/or optical structural model of a computer-generated hologram, CGH, or wafer using at least one optical measuring method,

• - the CGH or the wafer being measured by means of the at least one optical measuring method and at least one measured value characterizing the at least one structural parameter being determined in a spatially resolved manner,
• - wherein a simulation calculation assigns a probability distribution of the measured values to the at least one structure parameter,
• - the at least one structure parameter being determined in a fitting calculation in such a way that at least one most probable simulated measured value assigned to the at least one structure parameter corresponds at least approximately to the at least one determined measured value.

In a known manner, CGHe can be used to shape wavefronts of light rays interacting with them.

CGHs are therefore also used, for example, in lithography systems, in particular in projection exposure systems.

Lithography systems, in particular projection exposure systems, have a large number of optical elements. Especially when using the optical elements with a microlithographic DUV (Deep Ultra Violet) projection exposure system and especially when using a microlithographic EUV projection exposure system, a particularly precise surface treatment is necessary because the optical elements, for example EUV mirrors , modulated light on the one hand has a very small wavelength and the resulting wavefronts are thus disturbed by even the slightest processing error on the optical element. On the other hand, the structures shown on the projection surface are very small and therefore also susceptible to the slightest processing error on the optical element. Therefore, the accuracy requirements for the optical element can amount to fractions of a nanometer. Test light waves, which emanate from the CGH, are used to check the quality of the optical elements.

In order to shape the wavefronts correctly, the optical properties of the CGH must be precisely designed according to a given design.

Profile parameters or structure parameters of the surface, such as an etching depth, position of the structure edges and/or a trench radius, usually define the optical properties of the CGH.

It is advantageous and known in the prior art to check the CGH after production for a configuration of the structural parameters that is appropriate to the design, in order to ensure that correctly formed wave fronts emanate from the CGH when used, for example, in a projection exposure system. In particular, a spatially resolved check of the structural parameters should be aimed for, since even local deviations of a structural parameter from the specified design can cause disturbances in the wave fronts.

In other words, it should be determined which value a specific structural parameter assumes at a specific location on the surface of the CGH.

As a result, it can be determined, for example, within the framework of a manufacturing quality check, in which areas of the surface a CGH has the values of a structure parameter provided within the specifications. The determination of the values of the structure parameters should ideally be carried out over the entire surface in order to minimize the time required for the determination.

In order to obtain information that is as decorrelated as possible, it is provided in the prior art that the CGH or the wafer is measured using at least one optical measuring method and several measured values characterizing the at least one structure parameter are determined in a spatially resolved manner. The value of the structure parameter can be determined more precisely by collecting many measured values using measurement methods which are as decorrelated as possible and which characterize the same structure parameter.

In the DE 10 2018 200 568 A1 a characterization of a CGH with regard to manufacturing defects is described using a so-called diffraction measuring device.

The measurement is simulated with the aid of a computer using a method that is known from the prior art and can also be referred to as forward calculation. Typically, the forward calculation is based on Maxwell solvers, common algorithms are e.g. B. the Fourier-based Rigorous Coupled Wave Analysis or FEM (Finite Element Method)-based solvers. This results in a distribution of simulated, predicted measured values for the at least one examined structure parameter that has a value at a location on the CGH, which is weighted with the probabilities of observing the measured values. The forward calculation enables an analysis of the influence of different possible values of a structural parameter on the predicted measurement values, which favors the identification of suitable measurement methods.

In a further method step, a value of a structure parameter is usually determined as the most credible value within the framework of the measurement method, which predicts such a probability distribution of measured values in the forward calculation that most likely corresponds to the actually determined measured value.

A disadvantage of the prior art is that different structural parameters can have strongly correlated measurement signals. As a result, the measurement methods used are no longer orthogonal, as is ideally desired. As a result, the reconstruction is error-prone, in particular structure parameters with correlated measurement signals have high error bars in the reconstruction.

Such a lack of accuracy in the measurement and reconstruction of structural parameters on CGHs that are used to generate a test wave for measuring aspherical free-form surfaces, such as mirrors, is particularly problematic, because incorrect mapping of the structural parameters on the CGH leads to an incorrectly calibrated test wave.

The present invention is therefore based on the issue of creating a method of the type mentioned at the outset, which avoids the disadvantages of the prior art, and in particular enables a high level of accuracy when determining structural parameters of a CGH or wafer.

According to the invention, this object is achieved by a method having the features specified in claim 1.

The method according to the invention for the areal, preferably full-surface, spatially resolved determination of at least one structural parameter of a geometric and/or optical structural model of a computer-generated hologram, CGH, or wafer using at least one optical measuring method provides that the CGH or the wafer is measured using the at least one optical measuring method and at least one measured value characterizing the at least one structure parameter is determined in a spatially resolved manner, with a simulation calculation assigning a probability distribution of the measured values to the at least one structure parameter, the at least one structure parameter being determined in a compensation calculation in such a way that at least one most probable simulated measured value assigned to the at least one structure parameter corresponds to the corresponds at least approximately to at least one determined measured value. Furthermore, the method according to the invention provides that the probability distribution of the measured values or the structure parameters is described by stochastic fields on the CGH or wafer, which have correlations between at least two different locations.

The description according to the invention of a probability distribution of a structure parameter by stochastic fields on the CGH or wafer, which have correlations between at least two different locations, can limit the set of values that the structure parameter can assume at the at least two different locations and thus stabilize the reconstruction will.

According to the invention, all structure parameters are described as a vector-valued stochastic field.

Within the scope of the invention, it has been shown that a structural parameter, for example an etching depth, may not be able to assume any values at any locations. In a simple form, the implementation of site-to-site correlations introduces a continuity condition for the mapping of the structure parameter, since abrupt changes in the values of the structure parameter between closely spaced sites of similar CGH patterning can be considered unlikely. The consideration of site-to-site correlations according to the invention thus represents an inclusion of additional information in the determination method for the value of a structure parameter at a site on the CGH or wafer, which can in particular break up dependencies between signals of different structure parameter variations at this site. Among other possible functions, a function with an exponential dependence on the Euclidean distance has been shown to be suitable for the approximate description of the place-to-place correlations.

In an advantageous development of the invention, it can be provided that the at least one optical measuring method comprises scatterometry and/or interferometry. Both methods are based on the fact that the light scattered into a solid angle range by the CGH at a scattering angle depends on the structural parameters of the CGH. In a local lattice approximation, the scattering angles are in particular discrete directions of diffraction k, so that the light scattered in direction k at location x of the CGH is described by a field strength vector E _k (x).

und den Interferenzkontrast bestimmen.Scatterometric methods essentially measure an intensity |E _k (x)| ² at least one diffraction direction k, while interferometric methods measure the intensity of a coherent superposition |E _k (x)+E _ref | ² with at least one, but preferably several, phase-shifted reference wave Eref and from this in particular the interference phase $$\text{bad}〈E_k\left(x\right)|E_{\mathrm{right}ef}〉$$

and determine the interference contrast.

The use of interferometry can advantageously result in a higher measurement precision than is the case with scatterometry. In particular, a calibration of a CGH test wave adapted to a mirror is all the more accurate the more the measurement signals of a mirror and CGH measurement are correlated. It is therefore particularly advantageous to use the same interferometer with different illumination polarizations and test or calibration mirrors.

A combination of scatterometry and interferometry can result in an overall increased measurement precision and, in particular, make the method more robust against inadequacies in the structure parameter model.

In an advantageous development of the invention, it can be provided that the measured values are brightness or intensity values or interference phases.

By using brightness or intensity values as a measured variable in both scatterometry and interferometry, it is possible to use light-sensitive detector devices, such as CCD or CMOS sensors, for direct acquisition of the measured values.

Conceivable detection devices for areal detection of the light are CCD, EMCCD, CMOS or SCMOS cameras with a corresponding camera chip.

In an advantageous development of the invention, it can be provided that in the at least one optical measuring method, a diffraction measuring stand is used, by means of which brightness or intensity values of a transmission or reflection of the CGH or wafer with a full-area illumination with several different wavelengths and polarizations, in particular in the zeroth diffraction order.

Depending on the geometry and nature of the optical element to be measured, positioning the optical element in the beam path in a reflection or transmission configuration can prove to be advantageous. By capturing measured values with full-area illumination of the CGH or wafer, the time required for the measurement and the radiation energy introduced by the illumination onto the CGH or wafer are minimized compared to a grid method with small-area illumination. The measurement of brightness or intensity values in such a diffraction measuring system can advantageously be carried out using different wavelengths and polarizations of a test light beam. If the influence of the structure parameter on the measured values determined is dependent on the wavelength and/or the direction of polarization, then a measurement using different wavelengths and different directions of polarization enables the determination of the structure parameter to be made more precise. Becomes If, particularly advantageously, the zeroth diffraction order is detected in a local lattice approximation, the optical elements belonging to the diffraction measuring station can be arranged in accordance with geometric optics. In addition, better signal-to-noise ratios for the measured values to be recorded can be achieved by detecting the zeroth diffraction order due to the brightnesses or intensities prevailing there, which are higher in comparison to higher diffraction orders. A measurement in a reflection configuration can advantageously contribute to simplifying the structure of the measuring device or can also be advantageous in the case of a low general optical transparency of the CGH, depending on the material from which the CGH is made. Furthermore, several measured values characterizing a structural parameter can be collected by measuring the CGH or wafer under different wavelengths and different polarizations without having to transfer the CGH or the wafer to another measuring device and readjust it there.

In an advantageous development of the invention, it can be provided that in the at least one optical measuring method, an interferometer is used, by means of which at least one full-surface interference phase of two mutually coherent light waves can be determined as measured values for at least one output wavelength and polarization, with at least one of the light waves being either at which CGH was reflected or at least once passes through the CGH in transmission.

In an advantageous development of the invention, it can be provided that at least one transmitted diffracted light wave is reflected in itself after the first pass through a calibration mirror and passes through the CGH a second time in the opposite direction.

In this way, in particular the effect of local position drifts of the CGH on the interference phase to be measured can be at least partially decoupled from the effect of other local structural parameters of the CGH, such as polarization effects.

In general, the number of reconstructable structure parameters advantageously increases a priori with the number of independent measurement channels, but not necessarily the accuracy of their reconstruction as a result of signal correlations.

This correlation problem is solved by considering site-to-site correlations as described below.

In an advantageous development of the invention, it can be provided that a local etching depth or web height, a local trench radius, a local edge offset and/or a local flank angle are used as structure parameters or parameters of a production model of a CGH structuring process are used as structure parameters.

In an advantageous development of the invention, provision can be made to use structure parameters that result from modeling a CGH production process, for example a description of edge offsets with the aid of parameterizable convolution kernels, such as are used in diffusion models of a resist mask.

In an advantageous development of the invention, it can be provided that linear combinations of Fourier coefficients of the in particular periodically continued local CGH lattice structures are used as structure parameters, such as are used in RCWA Maxwell solvers, for example.

The structure parameters can be described as a vector-valued stochastic field.

In an advantageous development of the invention, it can be provided that a Gaussian process or a combination of several Gaussian sub-processes is used as the stochastic field.

Compared to other stochastic fields, Gaussian processes are characterized by the fact that they allow fast analytical methods and can be described by comparatively few hyperparameters of a large covariance matrix. The use of several Gaussian sub-processes also enables the advantageous consideration of site-to-site correlations of several different structure parameters and the consideration of further supplementary information and can be efficiently implemented numerically. Furthermore, it has been shown that in many situations the scattering of parameter values around a certain expected value can be approximated by Gaussian processes, which can be of a temporal or spatial nature. can be described. In a first approximation, such a situation can also be assumed for the distribution of values of a structural parameter on the surface of a CGH.

In a simple embodiment, an a priori covariance matrix K given by the formula (1) can be determined to take into account a possible place-to-place correlation of the Gaussian process or at least one of the Gaussian sub-processes. $$K=cOv{\left(I,I\text{'};x\right)}^{-\frac{1}{2}}cO\mathrm{right}\mathrm{right}{\left(x,x\text{'},L\right)}^{-1}cOv{\left(I,I\text{'};x\right)}^{-\frac{1}{2}}$$

In formula (1), corr(x, x', L) describes the correlation between two locations x and x' on the CGH and L a set of typically few hyperparameters, for example correlation lengths in correlations that decrease exponentially with a distance, in equation (16 ) given form. In principle, any correlations between the value of a structure parameter at the locations x and x' are possible for implementation in corr(x, x', L) and may be advantageous. For the specific calculation, it can be provided that a function of the form specified in formula (2), which is the logarithmized likelihood function m of the Gaussian process, is subjected to a compensation calculation to be carried out to determine a parameter value at a location x: $$m\left[p\left(x\right)\right]=-\frac{1}{2}<\mathrm{\Delta }I\left(x,p\right)\left|K\right|\mathrm{\Delta }I\left(x\text{'},p\text{'}\right)>+cOnst.$$

Formula (3) applies by definition. $$\mathrm{\Delta }I\left(x,p\right):=I_{mess}\left(x\right)-I\left(x,p\left(x\right)\right)$$

In this case, I _meas (x) represents the measured value (e.g. a light or radiation intensity) determined for the location x. The predicted measured value I(x, p(x)), on the other hand, is calculated from a possibly non-linear forward calculation p( x) → I(x,p(x)) determined from the CGH geometry model. In a particularly advantageous embodiment, the optimization process can be accelerated by using a polynomial fit of a database to carry out the forward calculation.

In another possible embodiment of the Gaussian process as a combination of Gaussian sub-processes, different hyperparameters can be considered for determining different structure parameters. For this purpose, the several Gaussian sub-processes are defined and then superimposed as a linear combination to form a target function Z. Based on the function given in formula (2), the function given according to formula (4) is provided as the first portion A. $$A=<\mathrm{\Delta }I\left(x,p\right)\left|K\right|\mathrm{\Delta }I\left(x\text{'},p\text{'}\right)>$$

Here, the deviation of the measured values predicted from the forward calculation from the determined measured values is minimized. For example, K can have vanishing site-to-site correlations, ie corr(x,x';L)=δ(x-x').

A consideration of the correlations between different parameters as well as a smoothing is provided as the second part B′ in the target function Z. This results in the form given in formula (5) for B'. $$B\text{'}=〈p\left(x\right)-p_{ip}\left(x\right)\left|cO{\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="DE102021214363A1\_0031.png,DE102021214363A1\_0032.png"\; state="\{\{state\}\}">v</figure-callout>}}_2^{-\frac{1}{2}}\left(p,p\text{'},x\text{'}\right)CO\mathrm{right}\mathrm{right}\left(x,x\text{'};L\right)\mathrm{<figure-callout\; id="2"\; label="c\; O\; v"\; filenames="DE102021214363A1\_0031.png,DE102021214363A1\_0032.png"\; state="\{\{state\}\}">c</figure-callout>}O{v}_{}^{}{}_2^{-\frac{1}{2}}\left(p,p\text{'},x\text{'}\right)\right|p\text{'}\left(x\text{'}\right)-p_{ip}\left(x\right)〉$$

entsprechen. Für Interpolationen zwischen sehr nahen Orten kann dann als eine untere Näherung die Formel (6) verstanden werden. Dies ergibt sich aus der Tatsache, dass in unterster Näherung in Pixelgröße / L corr_BB proportional zur Einheitsmatrix ist, also für translationsinvariante Kovarianzmatrizen näherungsweise gilt: $$C_x^{\text{'}}\approx cov\left(1-cor{r}_{xB}cor{r}_{BB}^{-1}cor{r}_{Bx}\right)=:cov\cdot ƒ\left(L\right)$$

In this case, p _ip (x) represents an interpolation value over the set of all pixels complementary to x. A covariance between different parameters cov ₂ (p, p', x) is used, which can be determined approximately by analyzing the covariance of the combination of the processes used in formula (4) and formula (5). The covariance cov ₂ (p, p′, x) used can be determined here by using a continuity argument. Thus, the covariance M of a Gaussian process combined from the parts A and B at a location x must be at least approximately the covariance to be calculated from the part A by, for example, Kriging interpolation at the location x $C_x^{\text{'}}$

correspond to. For interpolations between very close locations, formula (6) can then be understood as a lower approximation. This follows from the facts that in the lowest approximation in pixel size / L corr _BB is proportional to the identity matrix, i.e. for translation-invariant covariance matrices it approximately applies: $$C_x^{\text{'}}\approx cOv\left(1-cO\mathrm{right}{\mathrm{right}}_{xB}cO\mathrm{right}{\mathrm{right}}_{BB}^{-1}cO\mathrm{right}{\mathrm{right}}_{Bx}\right)=:cOv\cdot ƒ\left(L\right)$$

On the other hand, formula (7) must hold. $$C_x^{\text{'}}={{\left(cO{v}^{-1}+\mathrm{<figure-callout\; id="2"\; label="c\; O\; v"\; filenames="DE102021214363A1\_0031.png,DE102021214363A1\_0032.png"\; state="\{\{state\}\}">c</figure-callout>}O{v}_{}^{}{}_2^{-1}\right)}^{-1}|}_{xx}=:M$$

Formula (8) is obtained by solving. $$\mathrm{<figure-callout\; id="2"\; label="c\; O\; v"\; filenames="DE102021214363A1\_0031.png,DE102021214363A1\_0032.png"\; state="\{\{state\}\}">c</figure-callout>}O{v}_{}{}_2={\left(ƒ{\left(L\right)}^{-1}+1\right)}^{-1}cOv\approx \frac{cOv}{\beta L^2}\left(1+O\left(L\right)\right)$$

This applies to small lengths L with β ≈ 0.0025/pixel ² . In the case of strongly inhomogeneous covariance matrices, the weighted mean can be used to determine the covariance cov.

Kriging interpolation can also be used to more directly determine the values of p _ip and cov ₂ . This is especially true for Gaussian correlation kernels, which ensure smooth interpolation.

It is also possible to determine cov ₂ empirically, for example by means of AFM spot measurements. In particular, in typical etching processes, etching depth and trench radius are strongly correlated at a location x of the CGH, which can flow into cov ₂ as empirical a priori knowledge.

As the third portion D of the combined Gaussian process, markers attached to the CGH and their properties can be included in the calculation for better precision. The proportion is defined here by the expression given in formula (9): $$D={\displaystyle \sum _i\frac{{\left|\mathrm{\Delta }p\left(x_i\right)\right|}^2}{{\mathrm{<figure-callout\; id="2"\; label="\sigma \; p"\; filenames="DE102021214363A1\_0031.png,DE102021214363A1\_0032.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_p^{}}}$$

an.Δp(x _i ) gives the difference between the values of the parameter p calculated by the method according to the invention at the locations of the marker x _i with i=1, . . . , m and the values and determined for these locations and the parameter by external measurement standard deviation ${\sigma }_p^{}$${}_2^{}$

on.

gemäß Spezifikationen als vierter Term E in Formel (10) angegeben werden. $$E={\displaystyle \sum _i\frac{{\left|\mathrm{\Delta }p\left(x_i\right)\right|}^2}{{\sigma }_p^2}}$$

Alternatively, the difference between the values of the parameter p calculated by the method according to the invention at the locations of the marker x _i with i=1, . . . , m from the values and standard deviation determined for these locations and the parameter by the nominal design ${\sigma }_p^{}$${}_2^{}$

according to specifications can be given as the fourth term E in formula (10). $$E={\displaystyle \sum _i\frac{{\left|\mathrm{\Delta }p\left(x_i\right)\right|}^2}{{\mathrm{<figure-callout\; id="2"\; label="\sigma \; p"\; filenames="DE102021214363A1\_0031.png,DE102021214363A1\_0032.png"\; state="\{\{state\}\}">\sigma </figure-callout>}}_p^{}}}$$

In particular, an advantageous further development of the method can provide for components D and E to be combined. This can be done in the form of two independent log-likelihood summands in the target function Z, for example.

The parts B' and C can be interpreted as a Bayesian update of the residual term. Specifically, this update is part of a nonlinear optimization and effectively combines the three Gaussian processes into a single a posteriori process.

It is also conceivable to use the data for a Bayesian update of the optimization results or to interpolate the data using a kriging method with subsequent addition as a Tykhonov term to the target function Z.

In an advantageous development of the invention, it can be provided that for at least one Gaussian sub-process an expected value and/or a variance at a location of the CGH comes from an interpolation, in particular via a weighted average or kriging of the structural parameters of its surroundings.

As an advantageous embodiment, it can be provided that if one does not have access to a value of a structure parameter at a specific location, such a value can be determined via an interpolation, if necessary. For the exemplary calculation of a value p _kriged (x) determined by kriging of a parameter at location x on the CGH, the following formula (11) can be used after the kriging interpolation for the prior: $$p_{k\mathrm{right}iGe\mathrm{i.e}}\left(x\right)=CO\mathrm{right}{\mathrm{right}}_{xB}CO\mathrm{right}{\mathrm{right}}_{BB}^{-1}p\left(B\right)$$

die inverse Korrelationsmatrix zwischen allen Elementen der Menge B bezogen auf die Ausprägung des Parameters p, p(B) die Ausprägung des Werts des Strukturparameters auf der Menge B und Corr_xB die Korrelationsmatrix zwischen den Elementen der Menge B und dem Ort x in Bezug auf die Ausprägung des Strukturparameters p. In Anlehnung an die Formel (11) kann beispielweise ein Interpolationswert p_ip(x) berechnet werden durch die Formel (12) $$p_{ip}\left(x\right)={\alpha }_{x}Cor{r}_{xB}p\left(B\right)$$

Here, B describes the set of all locations complementary to x, or in the case of a camera recording all pixels complementary to x, $CO\mathrm{right}{\mathrm{right}}_{BB}^{-1}$

the inverse correlation matrix between all elements of the set B related to the expression of the parameter p, p(B) the expression of the value of the structure parameter on the set B and Corr _xB the correlation matrix between the elements of the set B and the location x in relation to the Expression of the structure parameter p. Based on the formula (11), for example, an interpolation value p _ip (x) can be calculated using the formula (12) $$p_{ip}\left(x\right)=a_{x}CO\mathrm{right}{\mathrm{right}}_{xB}p\left(B\right)$$

und ist damit gegeben durch die Summe aller Korrelations- bzw. Einflussterme der Bezugsmenge B mit dem Ort x. Insbesondere ist eine Wahl der Menge B aus der räumlich angrenzenden Umgebung des Ortes x von Vorteil, da hierdurch eine möglicherweise beobachtete Stetigkeit eines Strukturparameters im Verfahren berücksichtigt werden kann.Here, the linear factor α _x is defined by the formula (13). $$a_x^{-1}:={\displaystyle \sum _{y\in B}CO\mathrm{right}{\mathrm{right}}_{xy}}$$

and is therefore given by the sum of all correlation or influence terms of the reference set B with the location x. In particular, selecting the set B from the spatially adjacent surroundings of the location x is advantageous, since this allows any observed continuity of a structure parameter in the method to be taken into account.

ausgegangen werden, bei der die Formel (14) gilt. $$C_x^{\text{'}}\approx cov\left(1-cor{r}_{xB}cor{r}_{BB}^{-1}cor{r}_{Bx}\right)$$

An estimate of the covariance can also be obtained by kriging interpolation of the covariance values in the B neighborhood. Here, in the direct vicinity of location x, an approximate description of the covariance to be found in location x can be obtained $C_x^{\text{'}}$

be assumed, in which the formula (14) applies. $$C_x^{\text{'}}\approx cOv\left(1-cO\mathrm{right}{\mathrm{right}}_{xB}cO\mathrm{right}{\mathrm{right}}_{BB}^{-1}cO\mathrm{right}{\mathrm{right}}_{Bx}\right)$$

In this case, the intrinsic covariance cov at the location x is multiplied by a factor f(L), which in turn depends on the correlations Corr _xB , Corr _BB and Corr _Bx between the reference set B and the location x. By definition, this results in formula (15). $$C_x^{\text{'}}\approx cOv\left(1-cO\mathrm{right}{\mathrm{right}}_{xB}cO\mathrm{right}{\mathrm{right}}_{BB}^{-1}cO\mathrm{right}{\mathrm{right}}_{Bx}\right)=:cOv\cdot ƒ\left(L\right)$$

Here L is given by the distance between the location x and the elements of the reference set B.

In an advantageous development of the invention, it can be provided that the variance of at least one Gaussian sub-process at a location of the CGH is determined from a priori specifications of the CGH production or a measuring device, empirical random sample measurements and/or maximum likelihood estimators.

An a priori determinable covariance cov(I, I′, x) of the measured values of different measurement methods determined at a location x can result from contributions from independent error sources. According to the contributions, the a priori determinable covariance can be influenced by systematic error contributions of the CGH, in particular by a line edge roughness (LER) of the CGH structure edges, a structure-dependent etch depth variation, which can be caused by a delay of a reactive ion etching, an unmodeled error of the edge placement (EPE) and other errors that may be caused by material properties.

Furthermore, systematic sources of error can be taken into account through the acquisition of measured values by means of a measuring device, for example a diffraction measuring stand, referred to below as BMS, or an interferometer.

In the case of a BMS, for example, a wavelength bandwidth and an absorption of the tunable color filter used, a rotation of the polarization and an absorption of the rotatable polarizer and a non-linearity of the detection device used, in particular a camera, may be mentioned.

Alternatively, systematic error parameters can be part of the optimization by using adjusted measurement signals instead of ΔI(x′,p′) in formula (4), which are defined in formula (41) by a linear combination with real error amplitudes Δα _i to be optimized. $$\mathrm{\Delta }I\left(x\text{'},p\text{'}\right)+\frac{\partial I\left(x\text{'},p\text{'}\right)}{\partial a_i}\mathrm{\Delta }{a}_i$$

In contrast to the CGH structure parameters, additional adjustment parameters Δα _i do not depend on the CGH and can usually be assumed to be independent and normally distributed.

In addition, a measurement of brightness or intensity values can have shot noise and random camera effects, for example due to manufacturing variations in the quality of the camera pixels, as well as defective pixels as error sources. The contributions mentioned can, at least by assumption, be regarded as independent and normally distributed. For example, empirical observations, empirical random sample measurements or simulations on a nominal design of the CGH can be used to determine the contributions.

The covariance cov(I, I', x) that can be determined a priori from the above-mentioned contributions therefore relates to an uncertainty of the measured values, which in turn can be taken into account when determining the uncertainty of the determined values of the structure parameter.

The covariance of the structure parameter results from Gaussian error propagation according to formula (16) $$cOv\left(p,p\text{'},x\right):=\frac{\partial p}{\partial I}cOv\left(I,I\text{'},x\right)\frac{\partial p{\text{'}}^t}{\partial I}$$

Formula (17) for defining the derivation or Jacobian matrix also applies here. $$\frac{\partial p}{\partial I}:={\left(\mathrm{i.e}{I}^t\cdot \mathrm{i.e}I\right)}^{-1}\mathrm{i.e}{I}^t$$

des Strukturparameters ergänzt. Dies kann wie in Formel (18) gezeigt vorgenommen werden und verhindert insbesondere singuläre Kovarianzmatrizen in Formel (16). $$cov{\left(p,p\text{'};x\right)}^{-1}\mapsto cov{\left(p,p\text{'};x\right)}^{-1}+diag\left({\sigma }_{spec}^{-2}\left(p_1\right),\dots ,{\sigma }_{spec}^{-2}\left(p_m\right)\right)$$

In order to take into account previously known information about a scattering of values, the covariance of the values of a structure parameter p _i is variances corresponding to a specification ${\sigma }_{spec}^{-2}\left(p_i\right)$

of the structure parameter added. This can be done as shown in formula (18) and in particular prevents singular covariance matrices in formula (16). $$cOv{\left(p,p\text{'};x\right)}^{-1}\mapsto cOv{\left(p,p\text{'};x\right)}^{-1}+\mathrm{i.e}iaG\left({\sigma }_{spec}^{-2}\left(p_1\right),...,{\sigma }_{spec}^{-2}\left(p_m\right)\right)$$

Furthermore, a possible contribution of an a priori or empirical site-to-site correlation can be taken into account.

In an advantageous development of the invention, it can be provided that location-to-location correlations of the Gaussian process or at least one of the Gaussian sub-processes for at least one structure parameter are functions of the distance between CGH locations or wafer locations, which are preferably few depend on hyperparameters.

However, in a simple—since stationary—form, the correlations can be decisively given by the preferably Euclidean distance between points x and x′. The formula (19) with a correlation length L then results as an expression for the correlation between the locations x and x'. $$cO\mathrm{right}\mathrm{right}\left(x,x\text{'};L\right)=\text{ex}\left(-\frac{\left|x-x\text{'}\right|}{L}\right)$$

When formula (2) and formula (5) are used, the correlation length L is advantageously included as the only hyperparameter in the covariance of the Gaussian process. Choosing more complex correlations can therefore also increase the number of hyperparameters. Since the correlation given in formula (19) depends only on the spatial difference, the matrix-vector multiplication required for formula (2) can be achieved quickly and in a memory-saving manner by so-called cyclic embedding and Fourier transformation, which diagonalizes a cyclically expanded covariance matrix.

In an advantageous development of the invention, it can be provided that the hyperparameters are determined based on a priori knowledge about the production of the CGH or wafer, empirical random sample measurements and/or maximum likelihood estimators.

For example, the expression of the correlation length of the etch depth given in formula (19) is based on a random sample measurement. A determination of the hyperparameter based on knowledge about the manufacturing process of the CGH is also conceivable. It is thus conceivable that the correlation length is determined unambiguously by material properties of the CGH, which result, for example, from an alloy composition and is therefore known a priori.

In an advantageous development of the invention, it can be provided that the probability distribution or a density of the probability distribution of a structure parameter distribution is maximized together with further parameters or hyperparameters of the stochastic field.

In particular, it can be provided that the at least one hyperparameter is subjected to an optimization process. This makes it possible to implement a correlation between different locations in the method according to the invention even without a priori knowledge of the hyperparameter, for example the correlation length L. In particular, the type of place-to-place correlation can be qualitatively defined by the suitable choice of a correlation model, a process kernel, for example an exponential kernel.

In this context, it has proven to be particularly favorable if variables characterizing the at least one structure parameter are taken into account in the stochastic field, in particular variables determined randomly using other measurement methods. Taking markers into account is particularly advantageous. The latter can contain calibration structures, for example, which can be reconstructed more precisely as a result of more strongly decorrelated signals, or which can also be randomly measured using other methods.

According to formula (9), such markers can be included in the target function Z such as the log-likelihood of an a posteriori Gaussian field, whereby either only the locations of the markers themselves or their kriging interpolation over the entire CGH can be used.

In particular, adding such terms to the objective function Z can make the reconstruction results more reliable can be advantageous. Sample measurements, for example using atomic force microscopy (AFM), using electron microscopy (EM) or using X-ray spectroscopy (RS), can be considered as possible methods that are independent of scatterometry and/or interferometry.

In an advantageous development of the invention, it can be provided that a density of the probability distribution or a strictly monotonic function thereof is described by a non-degenerate quadratic form, in particular, for example, the logarithm of a Gaussian density.

The description of the probability density or a function calculated from it by concatenation with a strictly monotonic function, such as the logarithm of a Gaussian probability density function, by a non-degenerate quadratic form offers the possibility of accelerating the adjustment calculation by a quadratic approximation.

In particular, the method of least squares can be used in the adjustment calculation.

Using the method explained, it is also possible to specify an error calculation for a wavefront obtained from the reconstruction.

Covariances cov ^post the mapping p(x) of the structural parameters of the CGH result from formula (16) and formula (17), as well as a modification by the method steps used of the Bayesian update and the kriging interpolation of the markers. Hyperparameters to be optimized, for example the correlation lengths, can then be determined empirically, for example by an autocorrelation of the mapping. With higher-dimensional Gaussian error propagation, a covariance determined in this way can be translated into a covariance of the wavefront or its approximation by orthonormal polynomials.

In addition, it should be noted that terms such as "comprising", "having" or "with" do not exclude any other features or steps. Furthermore, terms such as "a" or "that" which indicate a singular number of steps or features do not exclude a plurality of features or steps - and vice versa.

The figures each show preferred exemplary embodiments in which individual features of the present invention are shown in combination with one another. Features of an exemplary embodiment can also be implemented separately from the other features of the same exemplary embodiment and can accordingly easily be connected by a person skilled in the art to further meaningful combinations and sub-combinations with features of other exemplary embodiments.

If the description refers to the measurement of a CGH, then this of course also includes the fact that the method according to the invention for measuring structure parameters can be used on surfaces of any kind. In particular, the measurement of wafers should be mentioned, which, because they are produced in significantly larger quantities, require a significantly higher number of inspection measurements.

Elements with the same function are provided with the same reference symbols in the figures.

• 1 eine EUV-Projektionsbelichtungsanlage;
• 2 eine DUV-Projektionsbelichtungsanlage;
• 3 eine immersionslithographische Projektionsbelichtungsanlage;
• 4 einen Querschnitt durch eine Oberfläche eines CGH;
• 5 eine Draufsicht auf die Oberfläche des CGH;
• 6 eine prinzipmäßige Darstellung des erfindungsgemäßen Bestimmungsverfahrens;
• 7 ein Diagramm der empirischen Korrelationslängen der Ätztiefe auf einem CGH;
• 8 eine vereinfachte Darstellung einer möglichen Messanordnung zur Durchführung des erfindungsgemäßen Verfahrens in Transmissionskonfiguration;
• 9 eine vereinfachte Darstellung einer möglichen Messanordnung zur Durchführung des erfindungsgemäßen Verfahrens in Reflexionskonfiguration;
• 10 eine Blockdiagramm einer Bestimmung einer Kovarianz;
• 11 ein Diagramm eines numerisch ermittelten Skalierungsfaktors; und
• 12 eine bildliche Darstellung eines Vergleichs zwischen einem mittels des Standes der Technik und einem mittels des erfindungsgemäßen Verfahrens bestimmten ortsaufgelösten Kartierung des Strukturparameters auf einer Oberfläche eines CGH.

They show schematically:

• 1 an EUV projection exposure system;
• 2 a DUV projection exposure system;
• 3 an immersion lithographic projection exposure system;
• 4 a cross section through a surface of a CGH;
• 5 a plan view of the surface of the CGH;
• 6 a basic representation of the determination method according to the invention;
• 7 a plot of empirical correlation lengths of etch depth on a CGH;
• 8th a simplified representation of a possible measurement arrangement for carrying out the method according to the invention in transmission configuration;
• 9 a simplified representation of a possible measurement arrangement for carrying out the method according to the invention in a reflection configuration;
• 10 Figure 12 is a block diagram of a determination of a covariance;
• 11 a diagram of a numerically determined scaling factor; and
• 12 a pictorial representation of a comparison between a spatially resolved mapping of the structural parameter on a surface of a CGH determined by means of the prior art and one determined by means of the method according to the invention.

1 shows an example of the basic structure of an EUV projection exposure system 400 for semiconductor lithography, for which the invention can be used. In particular, the invention can be applied through the installation of an optical element polished by means of the device according to the invention or the method according to the invention. In addition to a radiation source 402 , an illumination system 401 of the projection exposure system 400 has optics 403 for illuminating an object field 404 in an object plane 405 . A reticle 406 arranged in the object field 404 is illuminated a reticle holder 407 shown schematically. Projection optics 408, shown only schematically, are used to image the object field 404 in an image field 409 in an image plane 410. A structure on the reticle 406 is imaged on a light-sensitive layer of a wafer 411 arranged in the area of the image field 409 in the image plane 410, which is wafer holder 412, also shown in part, is held.

The radiation source 402 can emit EUV radiation 413, in particular in the range between 5 nanometers and 30 nanometers, in particular 13.5 nm. To control the radiation path of the EUV radiation 413, optically differently designed and mechanically adjustable optical elements are used. The optical elements of the in 1 The EUV projection exposure system 400 shown is configured as an adjustable mirror in suitable embodiments that are mentioned below only by way of example.

The EUV radiation 413 generated with the radiation source 402 is aligned by means of a collector integrated in the radiation source 402 in such a way that the EUV radiation 413 passes through an intermediate focus in the region of an intermediate focal plane 414 before the EUV radiation 413 impinges on a field facet mirror 415. Downstream of the field facet mirror 415, the EUV radiation 413 is reflected by a pupil facet mirror 416. Field facets of the field facet mirror 415 are imaged in the object field 404 with the aid of the pupil facet mirror 416 and an optical assembly 417 with mirrors 418, 419, 420.

In 2 an exemplary DUV projection exposure system 100 is shown. The projection exposure system 100 has an illumination system 103, a device known as a reticle stage 104 for receiving and precisely positioning a reticle 105, by means of which the later structures on a wafer 102 are determined, a wafer holder 106 for holding, moving and precisely positioning the wafer 102, and an imaging device , namely a projection lens 107, with a plurality of optical elements 108 which are held in a lens housing 140 of the projection lens 107 by means of sockets 109.

The optical elements 108 as individual refractive, diffractive and / or reflective optical elements 108 such. B. lenses, mirrors, prisms, end plates and the like, be formed.

The basic functional principle of the projection exposure system 100 provides that the structures introduced into the reticle 105 are imaged onto the wafer 102 .

The illumination system 103 provides a projection beam 111 in the form of electromagnetic radiation that is required for imaging the reticle 105 onto the wafer 102 . A laser, a plasma source or the like can be used as the source for this radiation. The radiation is shaped in the illumination system 103 via optical elements in such a way that the projection beam 111 has the desired properties in terms of diameter, polarization, shape of the wave front and the like when it strikes the reticle 105 .

An image of the reticle 105 is generated by means of the projection beam 111 and transmitted to the wafer 102 by the projection lens 107 in a correspondingly reduced size. The reticle 105 and the wafer 102 can be moved synchronously, so that areas of the reticle 105 are imaged onto corresponding areas of the wafer 102 practically continuously during a so-called scanning process.

In 3 a third projection exposure system 200 in the form of an immersion lithographic DUV projection exposure system is shown as an example. For further background of such a projection exposure system 200, reference is made, for example, to WO 2005/069055 A2 referenced, the content of which is incorporated by reference into the present description; the exact mode of operation is therefore not discussed in detail at this point.

It can be seen that it is comparable to the DUV projection exposure system 100 according to FIG 2 , a reticle stage 104, by which the later structures on the wafer 102, which is arranged on the wafer holder 106 or wafer table, are determined. The projection exposure system 200 of 3 also has a number of optical elements, in particular lenses 108 and mirrors 201, for this purpose.

The method according to the invention is not limited to CGHe for checking optical elements of projection exposure systems 100, 200, 400, in particular not to optical elements of projects tion exposure systems 100, 200, 400 with the structure described. However, the invention is particularly suitable for optical elements of projection exposure systems, in particular for CGHe for testing mirrors of EUV projection exposure systems.

Although the invention is described in the exemplary embodiments using CGHs for testing optical elements of projection exposure systems, the disclosure is to be understood such that the method according to the invention can be used for any CGHs and also other structured surfaces, in particular of wafers.

The following figures represent the invention only by way of example and in a highly schematic manner.

4 shows an exemplary cross section through a surface of a CGH 1 to be measured with the method according to the invention with a groove 4 etched by an etching depth 2 below an outer surface 3, which has a trench radius 5 in a lower area and a flank angle 6 in an upper area.

The local etching depth 2 or web height, the local trench radius 5, the local edge offset and/or the local flank angle 6 or parameters of a production model of a CGH structuring process are preferably used as structure parameters to be determined by the method according to the invention. The local etching depth 2 or web height, the local trench radius 5, the local edge offset and/or the local flank angle 6 result from a manufacturing process of the CGH. Parameters of a manufacturing model of a CGH structuring process are alternative and a priori preferred structure parameters and thus effective parameters of a model of this manufacturing process. For example, the scaling of fold cores, which describes diffusion processes in a resist mask for structuring the CGH and can lead to locally varying edge offsets during the subsequent etching of the structure, should be mentioned. The particular advantage of such manufacturing parameters is that CGH structuring errors can be described with just a few parameters.

5 shows an exemplary plan view of a surface of a CGH 1 to be measured with the method according to the invention, which has grooves 4 and smaller holes 4a, which, as in FIG 4 described can be characterized by structural parameters.

In the exemplary embodiment, linear combinations of Fourier coefficients of the periodically continued local CGH lattice structures can be used as structure parameters.

In 6 a basic representation of the determination method according to the invention is shown.

The aim of the method according to the invention is to enable an areal, spatially resolved determination of at least one structural parameter of a geometric and/or optical structural model of a CGH 1, with at least one optical measuring method 7 being used.

For this purpose, an assignment of a model value 8 (p(x), p(x')) of the at least one structure parameter to a location x or x' (see also 5 ) provided at which the structure parameter assumes this value. In this case, this value should come as close as possible to a real value 9 (p _real (x), p _real (x′)) of the structure parameter that is assumed or actually exists.

Using the at least one optical measuring method (indicated by an arrow 7), the CGH 1 is measured and several measured values 10 (I _mess (x), I _mess (x')) characterizing the at least one structural parameter are spatially resolved at the locations x, x' erm means.

A simulation calculation (indicated by an arrow 11) or a forward calculation assigns a probability distribution 12 (I(x,p(x)),I(x′,p(x′))) of the measured values to the at least one structure parameter.

In order to determine a model value of a structure parameter 10 at a location x or x' on the CGH 1, it is provided that in a compensation calculation 13 indicated by an arrow 13, the model value 8 of the at least one structure parameter is determined in such a way that at least one corresponds to the model value 8 of the at least one structure parameter associated most probable simulated measured value of the at least corresponds at least approximately to a determined measured value 10 . For example, the method of least squares can be used in the least squares calculation.

It is also provided that the probability distribution (12) of the measured values or the structure parameters is described by stochastic fields on the CGH 1, which have correlations 14 between at least two different locations x and x', which in the exemplary embodiment are a scalar correlation function corr(x ,x';L) are formed. This takes into account that there can be dependencies between different locations x, x′ in the expression of the real values 9 of a structure parameter.

7 shows an example of an empirical observation of the site-to-site correlations 14 provided for the implementation of the method according to the invention using an etching depth at a transition between two structuring specifications.

8th shows a schematic representation of a possible measurement arrangement for carrying out the method according to the invention in a transmission configuration.

9 shows a schematic representation of a possible measurement arrangement for carrying out the method according to the invention in a reflection configuration.

While it can be provided for the method according to the invention that the at least one optical measuring method comprises scatterometry and/or interferometry, the exemplary embodiment only shows a schematic representation of a measuring arrangement suitable for scatterometry, in particular a scatterometer 15 . In this case, starting from a polychromatic plasma source 16, light is thrown onto the CGH 1 through illumination optics 17, a rotatable polarizer 18 and a tunable color filter 19. Light transmitted through the CGH 1 or light reflected by the CGH 1 is projected onto a camera 22 by imaging optics 20 having a diaphragm 21 with a small numerical aperture. The light beam impinging on the camera 22 thus corresponds to the zeroth diffraction order of the light radiated onto the CGH 1 in a local grating approximation. A form of implementation of the method in which an interferometry is carried out by means of an interferometer is not shown, but is also possible.

This in 8th The scatterometer 15 shown is preferably designed in such a way that the measured values 10 recorded by it are brightness or intensity values or interference phases.

By means of the scatterometer 15 shown, also referred to as a diffraction measuring stand, brightness or intensity values of a transmission or reflection are preferably measured as values 10 (see 9 ) of the CGH 1 in the case of full-area illumination with a plurality of different wavelengths, which are to be set using the color filter 19, and polarizations, which are to be set using the polarizer 18, in particular in the zeroth diffraction order.

A possible embodiment of the method is not shown, according to which an interferometer is used in the at least one optical measuring method, by means of which at least one full-surface interference phase of two mutually coherent light waves is determined as measured values 10 for at least one output wavelength and polarization, with at least one of the light waves being either at which CGH 1 was reflected or passes through CGH 1 at least once in transmission.

A method is not shown, but is possible, according to which at least one transmitted diffracted light wave is reflected in itself after the first pass through a calibration mirror and passes through the CGH 1 a second time in the opposite direction.

In 10 a simplified block diagram of a determination of a covariance is shown.

Block 23 of a group of independent covariances 24 contains systematic errors or model parameters of the CGH 1 that cannot be adjusted. These include, for example, a line edge roughness (LER) of the CGH structure edges, a structure-dependent etching depth variation that is not mapped by structure parameters, which can be caused by a delay in reactive ion etching , errors in the description of the edge placement (EPE) that are not represented by structural parameters, and other errors that can be caused by material properties.

Block 25 of the group of independent covariances 24 contains systematic error sources due to the measured value acquisition using the measuring arrangement, in particular the diffraction measuring system (BMS) and/or the interferometer. In the case of the BMS, these include, for example, a bandwidth of wavelengths and an absorption of the tunable color filter 19 used, a rotation of the polarization and an absorption of the rotatable polarizer 18 and a non-linearity of the detection device used, in particular the camera 22. In the case of an interferometer, this also includes Deviations from a desired input polarization at the CGH 1, and/or an undetected diattenuation, ie an undetected polarization-dependent transmission, in a propagation between CGH 1 and camera 22, and/or uncertainties in a reference wavefront, for example due to errors in a pass measurement or an adjustment of a reference mirror, as well as adjustment errors in the entire interferometer. As described in the adjusted measurement values according to formula (41), parts of these parameters or effective parameters that effectively capture their error propagation can also be part of the optimization parameters of the reconstruction.

Block 26 of the set of independent covariances 24 contains noise from the diffraction gauge measurement. This includes shot noise and random camera effects.

Block 27 of a set of Bayesian updates of covariance 28 contains a priori specified specification limits.

Block 29 of the set of Bayesian updates of covariance 28 contains measurements on markers made by AFM or other methods.

Block 30 of the set of Bayesian covariance updates 28 contains a priori and/or empirically determined cross-correlations between pixels.

Block 31 of the set of Bayesian updates of covariance 28 contains residuals.

Block 32 contains a covariance determined from blocks 23, 25, 26, 27, 29, 30 and 31 of groups 24 and 28.

Here, the stochastic field is preferably implemented as a Gaussian process or a combination of several Gaussian sub-processes, and for at least one Gaussian sub-process, an expected value and/or a variance at a location of the CGH or wafer preferably comes from an interpolation, in particular via a weighted Means or kriging the structural parameters of its surroundings.

Preferably, simple site-to-site correlations 14 are used, which for at least one structural parameter are functions of the distance from CGH sites or wafer sites, which depend on preferably few hyperparameters, in the exemplary embodiment the correlation length L.

A scaling factor f(L) required for this between the covariances of the individual Gaussian processes is in 11 plotted as a function of the correlation length L

Not shown in the exemplary embodiment, but it is possible for the covariance to be determined using maximum likelihood estimators in addition to the methods mentioned in groups 24 and 28 .

The probability distribution or a density of the probability distribution of a structure parameter distribution can be maximized together with further parameters or hyperparameters of the stochastic field.

Further orthogonally determined variables can be taken into account in the covariance and/or a mean value of the stochastic field.

In the case of the stochastic field, variables characterizing the at least one structure parameter can be taken into account, in particular variables determined randomly using other measurement methods.

A density of the probability distribution or a strictly monotonic function thereof can be described by a non-degenerate quadratic form, in particular, for example, the logarithm of a Gaussian density.

12 shows a comparison between mappings on a CGH of the structural parameters flank angle 6 (upper half of the image), and trench radius 5 (lower half of the image). Mappings of the structural parameters according to the prior art are shown in the left-hand column, while mappings according to the method according to the invention are shown on the right-hand side. Map 33 therefore shows a trench radius 5 determined according to the prior art. Map 34 shows a trench radius 5 determined according to the method according to the invention. Map 35 shows a flank angle 6 determined according to the prior art. Map 36 shows a flank angle 6 determined according to the method according to the invention It can be seen from the illustrations that the method according to the invention provides significantly smoother results.

reference list

1

CGH

2

etching depth

3

outer surface

4

groove

4a

Hole

5

trench radius

6

flank angle

7

measurement method

8th

model value

9

real value

10

reading

11

simulation calculation

12

Probability distribution of the measured values

13

balancing calculation

14

correlation

15

scatterometer

16

plasma source

17

lighting optics

18

polarizer

19

color filter

20

imaging optics

21

cover

22

camera

23

Error of the CGH

24

Independent covariances

25

Scatterometer error

26

Measurement process error

27

specification limits

28

covariance updates

29

marker measurement

30

cross correlations

31

residuals

32

covariance

33

Trench radius conventional

34

Trench radius according to the invention

35

Flank angle conventional

36

Flank angle according to the invention

100

projection exposure system

102

wafers

103

lighting system

104

reticle stage

105

reticle

106

wafer holder

107

projection lens

108

optical element

109

version

111

projection beam

140

lens body

200

projection exposure system

201

mirror

400

projection exposure system

401

lighting system

402

radiation source

403

optics

404

object field

405

object level

406

reticle

407

reticle holder

408

projection optics

409

image field

410

picture plane

411

wafers

412

wafer holder

413

EUV radiation

414

intermediate focal plane

415

field facet mirror

416

pupil facet mirror

417

optical assembly

418

mirror

419

mirror

420

mirror

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 102018200568 A1 [0011]
• WO 2005/069055 A2 [0108]

Claims (17)

Method for the areal, spatially resolved determination of at least one structural parameter of a geometric and/or optical structural model of a computer-generated hologram, CGH (1), or wafer by means of at least one optical measuring method (7), - wherein by means of the at least one optical measuring method (7) the CGH ( 1) or the wafer is measured and at least one measured value (10) characterizing the at least one structure parameter is determined in a spatially resolved manner, - a simulation calculation assigning a probability distribution (12) of the measured values to the at least one structure parameter, - the at least one structure parameter being determined in this way in a fitting calculation is that at least one of the at least one structure parameter associated most probable simulated measured value corresponds at least approximately to the at least one determined measured value (10), characterized in that the probability distribution (12) of the measured values or the Structural parameters are described by stochastic fields on the CGH (1) or wafer, which have correlations (14) between at least two different locations. procedure after claim 1 , wherein the at least one optical measuring method (7) comprises scatterometry and/or interferometry. procedure after claim 1 or 2 , the measured values (10) being brightness or intensity values or interference phases. procedure after claim 1 , 2 or 3 , wherein in the at least one optical measuring method (7) a diffraction measuring stand is used, by means of which the measured values (10) are brightness or intensity values of a transmission or reflection of the CGH (1) or wafer with a full-area illumination with several different wavelengths and polarizations, in particular in the zeroth diffraction order. procedure after claim 1 , 2 or 3 , wherein in the at least one optical measuring method (7) an interferometer is used, by means of which at least one full-area interference phase of two mutually coherent light waves is determined as measured values (10) for at least one output wavelength and polarization, with at least one of the light waves either at the CGH (1) or wafer was reflected or the CGH (1) passes at least once in transmission. procedure after claim 5 , wherein at least one transmitted diffracted light wave is reflected in itself after the first pass through a calibration mirror and passes through the CGH (1) a second time in the opposite direction. Procedure according to one of Claims 1 until 6 , wherein a local etching depth (2) or web height, a local trench radius (5), a local edge offset and/or a local flank angle (6) are used as structure parameters or parameters of a manufacturing model of a CGH structuring process are used as structure parameters. Procedure according to one of Claims 1 until 6 , where linear combinations of Fourier coefficients of the in particular periodically continued local CGH lattice structures are used as structure parameters. Procedure according to one of Claims 1 until 8th , where a Gaussian process or a combination of several Gaussian sub-processes is used as the stochastic field. procedure after claim 9 , wherein for at least one Gaussian sub-process an expected value and/or a variance at a location of the CGH (1) or wafer comes from an interpolation, in particular via a weighted average or kriging of the structural parameters of its surroundings. Procedure according to one of claims 9 or 10 , wherein the variance of at least one Gaussian sub-process at a location of the CGH (1) or wafer is determined from a priori specifications of the CGH production or a measuring device, empirical random sample measurements and/or maximum likelihood estimators. Procedure according to one of claims 9 or 10 , wherein location-to-location correlations (14) of the Gaussian process or at least one of the Gaussian sub-processes are functions of the distance from CGH locations or wafer locations for at least one structure parameter, which depend on preferably few hyperparameters. procedure after claim 12 , wherein the hyperparameters are determined based on a priori knowledge of the manufacture of the CGH (1) or wafer, empirical random sample measurements and/or maximum likelihood estimators. Procedure according to one of Claims 1 until 13 wherein the probability distribution or a density of the probability distribution of a structure parameter distribution is maximized together with further parameters or hyperparameters of the stochastic field. Procedure according to one of Claims 1 until 14 , wherein in the stochastic field, variables that characterize the at least one structure parameter, in particular variables determined randomly using other measurement methods, are taken into account. Procedure according to one of Claims 1 until 15 , where a density of the probability distribution or a strictly monotonic function thereof is described by a non-degenerate quadratic form, in particular, for example, the logarithm of a Gaussian density. Procedure according to one of Claims 1 until 16 , where the least squares method is used for the adjustment calculation.

Images