TWI889030B - Method for three-dimensional determination of an aerial image of a measurement object with the aid of a metrology system and metrology system for carrying out the determination method - Google Patents

Abstract

For the three-dimensional determination of an aerial image of a measurement object with the aid of a metrology system, a 3D aerial image of the measurement object is measured as a measurement intensity result in an image field in a plurality of measurement operating situations (35), each of which corresponds to a defocus value of an imaging optical unit of the metrology system. Furthermore, a model intensity result of the 3D aerial image in the image field in corresponding model operating situations is specified (36). A complex-valued diffraction spectrum of the measurement object, calculated in a pupil plane of the imaging optical unit on the basis of a measurement object location function, of an object field illumination angle distribution and of a complex-valued imaging optical unit transfer function, are included in the specified model intensity result. A deviation of the measurement intensity result from the model intensity result is minimized (37) by adapting the model intensity result via a variation of the complex-valued diffraction spectrum. The location function of the measurement object is calculated back (38) from the diffraction spectrum for which the deviation is minimized, which is then output (39). The result is an aerial image determination method in which a noise level of an aerial image result is reduced during the measurement.

Description

Method for three-dimensional determination of a spatial image of a measurement object by means of a metrology system and a metrology system for implementing the determination method [Cross-reference]

This patent application claims priority from German patent application DE 10 2022 212 750.1, the content of which is incorporated herein by reference.

The present invention relates to a method for three-dimensionally determining a spatial image of a measurement object using a metrology system. The present invention also relates to a metrology system for executing such a determination method.

Such methods and metrology systems for this purpose are known from WO 2016/012 426 A1 and WO 2020/225 411 A. A method for determining the optical phase difference of measurement light of a measurement light wavelength on the surface of a structured object is known from WO 2021/073 994 A1. A method for characterizing a lithography mask is known from DE 10 2020 123 615 B9. DE 10 2019 215 800 A1 discloses a method for determining the optical phase difference of measurement light of a measurement light wavelength across the surface of a structured object. DE 10 2021 205 541 A1 discloses a method for determining the imaging quality of an optical system when illuminating light into an entrance pupil to be measured. DE 10 2022 200 372 A1 discloses a method for simulating the illumination and imaging properties of an optical generation system during illumination and imaging of an object via an optical measurement system.

One object of the present invention is to further develop a method for determining a spatial image of a measurement object using a metrology system so that the noise level of the spatial image result in the image field is reduced during the measurement of the spatial image.

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

According to the invention, it is understood that during the measurement of a spatial image as part of a determination method, the measured intensity result can be fitted via a specified model intensity result, i.e. the deviation between the results can be minimized. This reduces the result noise in the spatial image to be determined, since in particular intensity anomalies are detected in the measured intensity result. In particular, different measured intensity results for various defocus values of the imaging optical unit can be used for deviation minimization. The reproducibility of the results of the determination method, i.e. the position function of the measurement object, is improved. The measurement throughput can be increased.

The measurement object may be a lithography mask or a photomask. In particular, by using EUV light in the wavelength range between 5 nm and 30 nm as illumination light for the metrology system, a very high spatial resolution can be achieved in the position function of the measurement object to be determined, in particular better than 50 nm.

Model intensity results can be assigned to the same defocus values as measured intensity results. Alternatively or in addition, model intensity results can also be assigned to other defocus values (i.e. defocus values that have not been measured).

Minimization according to claim 2 is suitable for the imaging ratio within the metering system.

The ratio of the number of fitted parameters to the number of measurement points according to claim 3 ensures that the actual deviation is minimized when executing the determination method. The model strength results will not be overdetermined due to an excessive number of fitted parameters. This ratio of the number of fitted parameters to the number of measurement points may be no greater than 0.1, no greater than 0.05, or even smaller. This ratio is usually greater than 0.001.

The Hopkins approximation according to claim 4 leads to an advantageously small number of fitting parameters.

The determination of the complex-valued diffraction spectrum according to claim 5 is exact. Even after the determination, the number of fitting parameters can be kept within ideal limits.

Determining the focus position according to claim 6 eliminates the need for non-ideal pre-calibration of the focus position when measuring the intensity measurement result. This can save measurement time.

In the determination method according to claim 7, the complete spatial image is advantageously also determined in the defocus dimension.

The advantages of the metering system according to claim 8 correspond to those explained above with reference to the determination method.

The metrology system may have a light source for illumination light. Such a light source may be designed as an EUV light source. The EUV wavelength range of the light source may be between 5nm and 30nm. It may also be a light source in the DUV wavelength range (e.g., in the 193nm range).

The metering system may be implemented to perform the determined method as described above.

1: illumination light

2: Measuring system

3: Material field

4: Object plane

5: Test structure

6: Absorption line

7:Multilayer lines

8: EUV light source

9: Lighting optical unit

10: pupil and light gate

11: Illumination optical unit pupil plane

13: Image plane

15: Lighting beam path

16: Displacement drive

17: Object holder

18: Object displacement driver

19: Field distribution

20: Projection optical unit

21: Diffraction spectrum

22: Pupil plane

23: Aperture aperture

24: Incident light aperture

25: Displacement drive

26: Outgoing light gate

27: Spatial analysis detection device/camera

28: Complex field distribution

29: Image plane

30: Image field

31:Intensity distribution

32: Hidden Lines

33: bright line

35: Measurement steps

36:Specify steps

37: Minimization step

38: Back calculation step

39: Output step

40:Measurement image

41: Measurement point

42: Sample field

43: Sample pixels

dx: pixel width

I _meas (x,y,z _i ): 3D spatial image

Exemplary embodiments of the invention will be explained in more detail below with reference to the accompanying drawings, in which: FIG. 1 highly schematically shows a side view of a metrology system for determining a spatial image of a measurement object (e.g. a lithography spectrum), wherein the metrology system has an illumination optical unit and an imaging optical unit, each of which is shown highly schematically; FIG. 2 shows a top view of a binary periodic test structure arranged at II in the metrology system according to FIG. 1; FIG. 3 similarly shows a top view of the field distribution of the electromagnetic field of the illumination light in the illumination beam path at III in FIG. 1 after exposure of the test structure according to FIG. 2.

FIG. 4 again shows the diffraction spectrum of the test structure in the illumination beam path at IV in FIG. 1 in a top view according to FIG. 2 ; FIG. 5 shows the diffraction spectrum cut along the periphery due to the aperture diaphragm at V in FIG. 1 of the metrology system in a diagram similar to FIG. 4 ; and FIG. 6 shows the diffraction spectrum in a diagram similar to FIG. 5 , which includes the wavefront effect indicated as a contour line by the imaging optical unit of the metrology system as an output of the imaging optical unit at VI in FIG. 1 FIG. 7 shows the measurement spectrum in the projection pupil region in a top view similar to FIG. 3 , showing the complex field distribution of the illumination light during the exposure of the spatially resolved detection device of the metrology system in the imaging beam path at position VII in FIG. 1 ; FIG. 8 shows the illumination light intensity measured by the detection device at the position of the detection device VIII in FIG. 1 in a diagram similar to FIG. 7 ; FIG. 9 shows a flow chart of a method for three-dimensionally determining the spatial image of a measurement object using a metrology system.

FIG. 10 shows the juxtaposition of the pixel resolution at the location of the detection device and the propagation direction resolution corresponding to the Fourier transform at the location of the measured spectrum; FIG. 11 shows in a diagram the dependence of the spatial image contrast of the determined spatial image on the defocus value, which can be used to determine the focus position of the modeled 3D spatial image.

The Cartesian xyz coordinate system is used below to facilitate the description of the posture relationship. The x-axis in Figure 1 extends perpendicular to the drawing plane and to the drawing plane. The y-axis in Figure 1 extends to the left. The z-axis in Figure 1 is vertically upward.

FIG. 1 shows, in a view corresponding to a meridional section, the beam path of EUV illumination or imaging light 1 in a metrology system 2 for three-dimensional determination of a spatial image of a measurement object, in particular a lithography mask. At the same time, the metrology system 2 is used to reproduce the illumination and imaging properties of the optical production system during illumination and imaging of the object by the optical metrology system of the metrology system 2. In this case, a test structure 5 is shown, which is also referred to as a measurement object and is arranged in an object plane 4 in the object field 3.

An example of a test structure 5 is shown in the top view of FIG2 . The test structure 5 is periodic in one dimension, specifically, for example, along the y-coordinate. The test structure 5 is designed as a binary test structure having absorber lines 6 and alternating multilayer lines 7, which are reflective for the illumination light 1. Lines 6, 7 are vertical structures, for example, extending in the y-direction.

The metrology system 2 serves to analyze a three-dimensional (3D) spatial image (spatial image metrology system). One application is the reconstruction of a spatial image of a lithography mask, as would also be seen in an optical production system (e.g. in a scanner) for producing a projection exposure system. For this purpose, in particular, the imaging quality of the metrology system 2 itself can be measured and, if necessary, adjusted. The analysis of the spatial image can thus be used to determine the imaging quality of a projection optical unit of the metrology system 2 or, in particular, within a projection exposure apparatus. Metering systems are known from WO 2016/012 426 A1, US 2013/0063716 A1 (see FIG. 3), DE 102 20 815 A1 (see FIG. 9), DE 102 20 816 A1 (see FIG. 2) and US 2013/001.

The illumination light 1 is reflected and diffracted at the test structure 5. The incident plane of the illumination light 1 is parallel to the yz plane under the central initial illumination. The field distribution of the electromagnetic field of the illumination light 1 after the test structure 5 is exposed is shown in the top view according to FIG. 3.

EUV illumination light 1 is generated by an EUV light source 8. Light source 8 can be a laser produced plasma (LPP) source or a discharge produced plasma (DPP) source. In principle, a synchrotron-based light source, such as a free electron laser (FEL), can also be used. The wavelength range of the EUV light source can be between 5nm and 30nm. The light wavelength of EUV can be 13.5nm. Instead of light source 8, in principle, the light source used in the variant of the metrology system 2 can also be a light source of a different light wavelength, for example a light source with a wavelength of 193nm.

An illumination optical unit 9 of the metrology system 2 is arranged between the light source 8 and the test structure 5. The illumination optical unit 9 is used to illuminate the test structure 5 to be inspected with a defined illumination intensity distribution on the object field 3 and at the same time with a defined illumination angle distribution, and the field points of the object field 3 are illuminated by the illumination angle distribution. This illumination angle distribution is also called an illumination setting. Those skilled in the art can find examples of this illumination setting in WO 2012/028 303 A1, etc. The illumination optical unit 9 and the light source 8 together form a partially coherent illumination system of the metrology system 2.

The various illumination angle distributions of the diffracted light 1 are specified by a pupil diaphragm 10 arranged in a pupil plane 11 of the illumination optical unit. The pupil diaphragm 10 is also called a sigma diaphragm.

The pupil diaphragm 10 of the illumination optical unit 9 is implemented as a driven displaceable diaphragm in the illumination beam path 15 of the illumination light 1 upstream of the object plane 4. The drive unit for the driven displacement of the pupil diaphragm 10 is referenced 16 in FIG. 1 .

The selected pupil aperture 10 can be displaced along at least one pupil coordinate in the pupil plane 11 by using a displacement driver 16.

The displacement drive 16 may also include an aperture exchange unit, through which a specific pupil aperture 10 can be exchanged for another specific pupil aperture 10. For this purpose, the aperture exchange unit can remove the corresponding selected pupil aperture from the aperture box and return the exchanged aperture to the aperture box.

The test structure 5 is supported by the object support 17 of the metrology system 2. The object support 17 cooperates with the object displacement driver 18 to move the test structure 5, especially along the z coordinate.

The distribution 19 of the electromagnetic field of the illumination light 1 after reflection at the test structure 5 corresponds to FIG. 2 and is shown in FIG. 3 in a top view. In the field distribution 19, the amplitude and phase values correspond to the absorber lines 6 and the multilayer lines 7 of the test structure 5.

The illumination light 1 reflected by the test structure 5 enters the imaging optical unit or projection optical unit 20 of the measurement system 2.

In the pupil plane of the projection optical unit 20, a diffraction spectrum 21 is obtained due to the periodicity of the test structure 5 (see Figure 4).

The zero-order diffraction of the test structure 5 is located at the center of the diffraction spectrum 21. In addition, FIG4 also shows the positive and negative first-order diffraction and the positive and negative order diffraction 21 of the diffraction spectrum.

The diffraction order of the diffraction spectrum 21 shown in FIG4 appears in this form in the pupil plane of the optical system of the metrology system 2, for example, in the incident pupil plane 22 of the projection optical unit 20. In this incident pupil plane 22, an aperture diaphragm 23 of the projection optical unit 20 is configured, and its periphery defines the incident pupil 24 of the projection optical unit 20. The aperture diaphragm 23 is also called the imaging pupil diaphragm of the metrology system 2.

The imaging pupil aperture 23 actively contacts the displacement actuator 25, and the function of the displacement actuator 25 corresponds to the function of the displacement actuator 16 of the sigma aperture 10.

FIG5 shows the entrance pupil 24 of the diffraction spectrum 21 and three diffraction orders located in the entrance pupil 24 in the initial illumination angle distribution, namely the zeroth order and positive and negative first order diffraction.

FIG6 shows the intensity distribution of the illumination/imaging light 1 in the exit pupil plane of the projection optical unit 20. The exit pupil 26 shown in FIG6 produces an image as the entrance pupil 24.

Pupil 24 (see FIG. 5 ) and pupil 26 (see FIG. 6 ) are elliptical. With alternative specifications for the corresponding aperture diaphragm 21 , pupils 22, 24 can also be another shape deviating from a circular shape, wherein the pupil is at least approximately circular. The pupil radius can be calculated as an average radius. For example, such an alternative pupil can be designed as an ellipse, the aspect ratio between its semi-axes being in the range of, for example, 1 and 3. In an embodiment not shown in the figure, pupils 24 and 26 can also be circular.

The images of the negative 1, 0 and positive 1 order diffraction and the imaging contribution of the optical system (to be precise the projection optical unit 20) contribute to the intensity distribution in the exit pupil 26. This imaging contribution, shown in FIG6 by a dashed outline, can be described by the transfer function of the optical system as will be explained below. The unavoidable imaging errors of the optical system result in a measurable intensity of the illumination/imaging light 1 also being present in the region around the diffraction orders in the exit pupil 26.

The projection optical unit 20 images the test structure 5 toward the spatial resolution detection device 27 of the measurement system 2. The spatial resolution detection device 27 is designed as a camera, in particular a CCD camera or a CMOS camera.

The projection optical unit 20 is designed as a magnification optical unit. The magnification factor of the projection optical unit 20 can be greater than 10, greater than 50, greater than 100, and greater. Usually, the magnification is less than 1000.

FIG. 7 corresponds to FIG. 4 and shows a complex field distribution 28 of the illumination/imaging light 1 in the region of the image plane 29, in which a spatially resolved detection device 27 is arranged.

FIG8 shows the intensity distribution 31 of the illumination/imaging light 1 measured by the camera 27 in the image field 30 in the image plane 29. In the intensity distribution 31, the image of the absorber line 6 is represented as a substantially dark line 32 of low brightness, and the image of the multilayer line 7 is represented as a bright line 33 of greater intensity.

In order to determine the spatial image of the measurement object 5 in three dimensions by means of the metrology system 2, the 3D spatial image I _meas (x, y, z _i ) of the measurement object 5 is measured in a measurement step 35 (see FIG. 9 ) in the image field 30 as a measurement intensity result 2 in a plurality of measurement operation scenarios of the metrology system. These measurement operation scenarios all correspond to the defocus values z _i of the projection optical unit 20.

In a specification step 36 of the determination method, a model intensity result I _fit of the 3D spatial image in the image field 30 is specified again in a plurality of model operations, which each correspond to a defocus value z _i of the projection optical unit 20 .

The fitting model used here is the result of electromagnetic wave propagation through the optical system of measurement system 2.

)來描述計量系統2的部分同調照明系統，再現由照明光闌10透射的照明方向

。這裡假設照明光學單元9的照明設定不會過度照射投影光學單元20的物側數值孔徑，即最大照明角度小於物側數值孔徑(|

|<)。 You can use the function (

) is used to describe the partially coherent illumination system of the metering system 2, reproducing the illumination direction transmitted by the illumination aperture 10

Here, it is assumed that the illumination setting of the illumination optical unit 9 will not over-illuminate the object side numerical aperture of the projection optical unit 20, that is, the maximum illumination angle is smaller than the object side numerical aperture (|

|<).

產生一個平面波，在物件平面4中平面波的場分佈為

。光罩下游的場分佈(見圖3)為

。 Each lighting direction

Generates a plane wave. The field distribution of the plane wave in object plane 4 is

The field distribution downstream of the mask (see Figure 3) is

.

)是複值光罩函數，其描述測量物件5的位置相關的複反射率。隨後將場E的恆定振幅設為零。 m(

) is a complex-valued mask function which describes the position-dependent complex reflectivity of the measurement object 5. The constant amplitude of the field E is then set to zero.

In the entrance pupil 24 of the imaging optical unit 20, the field distribution interferes with the equally complex-valued diffraction spectrum 21.

This diffraction spectrum 21 can be described as:

)的傅立葉變換。λ是計量系統2所使用的光波長。因此，來自

方向的照明僅導致該模型中繞射光譜的偏移(霍普金斯近似)。

是各電磁波在成像光學單元20中的傳播方向。 In this case, _M0 is the spectral function ₀ (

). λ is the wavelength of light used by the measurement system 2. Therefore,

Directional illumination only causes a shift in the diffraction spectrum in the model (Hopkins approximation).

It is the propagation direction of each electromagnetic wave in the imaging optical unit 20.

Electromagnetic wave propagation using the projection optical unit 20 can be modeled by multiplying with the known complex-valued transfer function of the optical unit:

是由成像光學單元20的數值孔徑造成的切割，且

是由散焦z所引起的波前誤差。 Here,

is the cut caused by the numerical aperture of the imaging optical unit 20, and

is the wavefront error caused by defocus z.

The propagated spectrum now interferes with the field distribution in the image plane 29. The camera 27 measures the intensity of the field distribution integrated in all illumination directions of the illumination system (see Figure 8).

The spatial image measured in each case by the camera 27 in the image field 30 with the corresponding defocus z can be modeled as follows:

,)。這是在最小化步驟37中完成的(參見圖9)，其中將測量強度結果I_meas與模型強度結果I_fit的偏差進行最小化，透過測量物件5的複值繞射光譜M的變化來調整模型強度結果I_fit。擬合參數是描述光罩光譜M₀(

)的參數。 FT stands for Fourier transform. Using this spatial image model, we can now fit the measured aerial image I _meas (

,). This is done in a minimization step 37 (see FIG. 9 ), in which the deviation between the measured intensity result I _meas and the model intensity result I _fit is minimized by adjusting the model intensity result I _fit by measuring the change in the complex diffraction spectrum M of the object 5. The fitting parameters are the parameters describing the mask spectrum M ₀ (

) parameters.

)，其中模擬(I_fit)和測量(I_meas)空間圖像之間的RMS(平方平均數)差異F被最小化。解決了以下最佳化問題：

In the minimization step 37, a nonlinear optimization method is used to search for the mask spectrum M ₀ (

), where the RMS (squared mean) difference F between the simulated (I _fit ) and measured (I _meas ) spatial images is minimized. The following optimization problem is solved:

|<2NA對圖像有貢獻。自由擬合參數只是在光罩光譜中滿足此條件的部分。測得的雜訊強度I _meas (

,z _n )現在被擬合的雜訊強度I _fit (

,z _n )而取代。 The numerical aperture of the imaging optical unit 20 cuts the diffraction spectrum 21 (see FIGS. 5 and 6 ). Due to the oblique illumination of the object field 3, the diffraction spectrum 21 also shifts the value of the numerical aperture to the greatest extent. Therefore, only the spatial frequency |

|<2 NA contributes to the image. The free fitting parameters are only those parts of the mask spectrum that satisfy this condition. The measured noise intensity I _meas (

, z _n ) is now fitted with the noise intensity I _fit (

, z _n ) and replaced.

z

z _max 上執行。這樣，也確定了該z值範圍的位置函數，結果是測量物件的三維空間影像。這種利用模型強度結果I_fit所進行的確定方法可以理解為過濾雜訊測量數據I_meas。 Based on the modeled complex-valued diffraction spectrum M obtained in the minimization step 37, the position function m of the measurement object 5 is then back-calculated in an inversion step 38, in particular by means of a Fourier transformation. This position function m is then output in an output step 39 of the method. The method operates within a known range of defocus values z _min

z

z _max . In this way, the position function of the z value range is also determined, and the result is a three-dimensional spatial image of the measured object. This determination method using the model intensity result I _fit can be understood as filtering the noise measurement data I _meas .

In order to ensure reliable noise suppression by this filtering, the number of simulated parameters should be significantly smaller than the number of measurement points. This can be ensured by a corresponding choice of parameters (see Figure 10 for this approach as well).

In particular, the measurement image 40 may occupy the entire image field 30 and may be composed of NxN measurement pixels 41 having a pixel width dx. 3 to 15 focal planes z _i are measured. N may range from 100 to 5,000. dx may range from 10 nm to 50 nm. The numerical aperture of the projection optical unit 20 may be 0.1.

This number of focal planes is also referred to as Nz. Therefore, the number of measured values is N*N*Nz. If the Fourier transform I _fit in the above equation is calculated by means of FFT, the mask spectrum must be sampled on the same grid, i.e. also has NxN pixels. An example of a sample field 42 of a mask spectrum 21 is shown on the right side of FIG. 10 in pupil coordinates. The sample domain 42 is divided into sample pixels 43. Each sample pixel 43 corresponds to a propagation direction in the imaging optical unit 20. The total range of this spectral sample field 42 is 1/Res. Therefore, at the NxN sample pixels 43 of the spectral sample field 42, the range of the corresponding sample pixel 43 is 1/NRes.

The maximum spatial frequency of FFT is 1/dx. Only the points of the mask spectrum 21 with a spatial frequency less than 2* NA/λ are required as free fitting parameters. Therefore, the ratio of the number of fitting parameters to the number of measurement points is:

倍。 For the example numbers above (Nz=7), the obtained ratio N _fit / N _meas has a value of 0.039. As shown in the example, each fitting parameter is assigned about 25 measurement points, which leads to a reduction in noise.

times.

的依賴性，可以對測試結構5的角度相關光譜M採用以下方法：

In the case where the above Hopkins approximation is insufficient, some additional parameters can be used to describe the illumination angle dependence of the diffraction spectrum, which can also be determined in the reconstruction (fitting) of the mask spectrum.

The following method can be used for the angle-dependent spectrum M of the test structure 5:

)是與照明方向無關的光譜，類似於霍普金斯近似。C(

,

,

)是重建先前定義的任何複值函數，C(

,

,

)模擬了振幅和相位對照明方向的依賴性。α_1..N是作為最佳化的一部分而確定出的自由參數。 In this case, M ₀ (

) is a spectrum that is independent of the illumination direction, similar to the Hopkins approximation. C(

,

,

) is to reconstruct any complex-valued function previously defined, C(

,

,

) models the dependence of amplitude and phase on the illumination direction. _{α 1..N} are free parameters determined as part of the optimization.

,

,α ₁,α ₂,...,α _N )作為範例：

You can use the following function C (

,

, α ₁ , α ₂ ,..., α _N ) as an example:

)建模為獨立於照明方向的光譜和校正函數(C(

,

,α ₁,α ₂,...,α _N ))。 In the reconstruction of the complex mask transfer function M, the mask spectrum M (

) is modeled as a spectrum independent of the illumination direction and a correction function ( C (

,

, α ₁ , α ₂ ,..., α _N )).

)和參數α_1..N，進而將測量空間圖像和模擬空間圖像之間的差異最小化。此最佳化問題已被解決：

Now search for mask spectrum M ₀ (

) and parameters α _1..N , thereby minimizing the difference between the measured and simulated spatial images. This optimization problem has been solved:

Therefore, the number of free parameters increases only by N compared to the Hopkins approximation, where N is usually small.

Using the reconstructed, now direction-dependent spectrum, the modeled spatial image I _fit can be computed for the target illumination setting σ _target and the target defocus z _target :

This equation can then be used to compare the simulated spatial image I _sim with the separately measured spatial image I _meas , which can be used to reconstruct the mask spectrum M and the corresponding complex mask transfer function.

From this equation, the 3D spatial image can be calculated using the reconstructed mask transfer function M and the illumination settings σ _target of the optical production system. In this way, for example, it is possible to determine what the spatial image of the test structure 5 would look like if it were imaged by the optical production system.

Therefore, the number of fitting parameters increases only slightly. In practice, three to five parameters α _i of the correction function C defined as in equation (7) above are usually sufficient. For NxN pixels, this is practically negligible. Therefore, the filtering effect remains unchanged.

Based on the evaluation of the model intensity result I _fit , the focus position of the model intensity result I _fit can be determined as a function of the defocus dimension z as a result of the minimization 37 of the determination method at different defocus values z _i . The calibration of the corresponding focus position during the measurement step 35 can then be omitted.

Therefore, the diffraction spectrum determined when fitting the measurement image can additionally be used to subsequently focus the image "digitally". This eliminates the need for focusing before the actual measurement, which results in higher throughput. In addition, the focusing accuracy and the reproducibility of the focusing can be improved. The sequence for digital focusing is as follows:

)計算M個支撐點z ₁...z _M 處的合成焦點堆疊。例如，在瑞利長度上使用七個焦點平面：

1. Use the following formula to fit the spectrum M ₀ (

) computes the resultant focus stack at M support points z ₁ ... z _M. For example, using seven focus planes on the Rayleigh length:

2. Determine any contrast criteria for each focal plane, such as the standard deviation of image brightness:

3. Plot the contrast K ( z _m ) versus the focal position z _m . Determine the location of the maximum z ₀ contrast, for example by fitting a parabola. This is shown in FIG. 11 .

4. Now calculate the new focused synthetic aerial image I _synth , whose maximum contrast is at z=0:

These images now not only have less noise, but also have maximum contrast at the z=0 position, which is the sharpest image.

35: Measurement steps

36:Specify steps

37: Minimization step

38: Back calculation step

39: Output step

Claims (8)

A method for three-dimensionally determining a spatial image of a measurement object (5) by means of a metrology system (2), the metrology system (2) having an illumination optical unit (9) for illuminating an object field (3), wherein the part of the measurement object (5) to be measured is arrangable, and an imaging optical unit (20) for imaging the object field (3) as an image field (30), wherein a spatially resolved detection device (27) is arrangable, the method comprising the following steps: measuring (35) a 3D spatial image of the measurement object (5) as a measurement intensity result in the image field (30) in a plurality of measurement operation situations, wherein each of the plurality of measurement operation situations corresponds to a defocus value (z _i ) of the imaging optical unit (20), Specifying (36) model intensity results (I _fit ) of a 3D spatial image in an image field (30) under a plurality of model operation conditions, each model intensity result corresponding to the defocus value (z _i ) of the imaging optical unit (20), wherein the specified model intensity results (I _fit ) include: a complex-valued diffraction spectrum (M) of the measurement object (5), a position function (m( )), the illumination angle distribution (σ( )), and the complex transfer function (P( )), adjusting the model intensity result (I _fit ) by changing the complex diffraction spectrum (M) of the measurement object (5), minimizing the deviation between the measurement intensity result (I _meas ) and the model intensity result (I _fit ) (37), and back-calculating (38) the position function (m( )), output (39) the position function (m( )). The method as claimed in claim 1 is characterized in that in the minimization (37) only the light propagation direction ( ), for which the following conditions apply: Wherein NA is the object side numerical aperture of the imaging optical unit (20). The method as claimed in claim 1 or 2, characterized in that the variation of the number N _fit of the fitting parameters of the complex diffraction spectrum (M) in the minimization (37) relative to the number N _meas of the measurement points (41) of the spatially resolved detection device (27) in the image field (30) is expressed in the minimization (37) as follows: . The method of claim 1, wherein, for the complex-valued diffraction spectrum (M) specified in (36), the model strength result (I _fit ) comprises a Hopkins approximation. The method as claimed in claim 1 is characterized in that, in the model intensity result (I _fit ) used for the specified (36), the complex diffraction spectrum (M) includes the amplitude and phase of the illumination light (1) of the measurement system (2) and the illumination direction ( ) The method of claim 1, characterized in that, as a result of performing the minimization (37) at different defocus values (z _i ), based on an evaluation of the model intensity result (I _fit ), a focal position (z ₀ ) of the model intensity result (I _fit ) of the spatial image is determined as a function of the defocus size (z). A method as claimed in claim 1, wherein the measured intensity result (I _meas ) is determined in three dimensions at an absolute defocus value (z _i ) which deviates from an ideal focus position (i.e., an image plane (13) where the image field (30) is located) by more than one Rayleigh length. A metrology system (2) for performing a determination method as described in any one of claims 1 to 7, the system: comprising an illumination system having an illumination optical unit (9) for illuminating a measurement object (5) to be inspected, comprising an imaging optical unit (20) for imaging a portion of the measurement object (5) into an image field (30) in an image plane (29), and having a spatial resolution detection device (27) arranged in the image plane (29).