**METHOD FOR DETERMINING AN OPTICAL PHASE DIFFERENCE OF MEASUREMENT LIGHT OF A MEASUREMENT LIGHT WAVELENGTH OVER A SURFACE OF A STRUCTURED OBJECT**

HELLWEG DIRK (DE)

HUSEMANN CHRISTOPH (DE)

CAPELLI RENZO (DE)

GEHRKE RALF (DE)

KERSTEEN GRIZELDA (DE)

*;*

**G03F1/84***;*

**G01N21/956**

**G03F7/20**WO2017207297A1 | 2017-12-07 |

US20170132782A1 | 2017-05-11 | |||

US20070032896A1 | 2007-02-08 | |||

US20170352144A1 | 2017-12-07 | |||

CN110297401A | 2019-10-01 | |||

DE102019215800A | 2019-10-15 |

S. PERLITZ ET AL.: "Phame™: a novel phase metrology tool of Carl Zeiss for in-die phase measurements under scanner relevant optical settings", PROCEEDINGS OF SPIE, March 2007 (2007-03-01)

SHERWIN ET AL.: "Measuring the Phase of EUV Photomasks", PROC. OF SPIE, vol. 11147 111471F-l to 1114721F-11

ERDMANN ET AL.: "Attenuated phase shift mask for extreme ultraviolet: can they mitigate three-dimensional mask effects?", J. MICRO/NANOLITH. MEMS MOEMS, vol. 18, no. 1, 2018, pages 011005

CON-STANCIAS ET AL., PROC. SPIE 6151, EMERGING LITHOGRAPHIC TECHNOLOGIES X, 61511W, 23 March 2006 (2006-03-23)

ROSENBLUTH ET AL., PROC. SPIE 4346, OPTICAL MICROLITHOGRAPHY XIV, 14 September 2001 (2001-09-14)

LIU ET AL., PROC. SPIE 9048, EXTREME ULTRAVIOLET (EUV) LITHOGRAPHY V, 90480Q, 17 April 2014 (2014-04-17)

Patent Claims 1. Method for determining an optical phase difference ( Δφ) of measure- ment light (1) of a measurement light wavelength (λ) over a surface of a structured object (8; 20; 25; 27; 30), wherein the phase difference ( Δφ) between - a top structure phase ( φ - a bottom reflector structure phase (φ (8; 20; 25; 27; 30), is determined as a characteristic that is applicable overall over an ob- ject structure to be measured, comprising the following steps: - measuring (16) a series of 2D images of the object (8; 20; 25; 27; 30) in each case in different focal planes for recording a 3D aerial image of the object (8) using a projection optical unit (5), - reconstructing (17) an image-side field distribution (f — on an object period (p) of the object (8; 20; 25; 27; 30) and/or — on a critical dimension (CD) of the object (8; 20; 25; 27; 30) and/or — on a complex reflectivity (r — on a complex reflectivity (r 22), — wherein the image-side field distribution (f (5), - comparing the computed image-side field distribution (f - computing the phase difference (Δφ) from the model parameters, resulting in the minimization, for the complex reflectivities (r 3. Method according to Claim 2, characterized in that, in the computa- tion of the image-side field distribution (f 4. Method according to Claim 2 or 3, characterized by an iterative fitting method. 5. Method according to one of Claims 2 to 4, characterized in that a real part (f 6. Method according to one of Claims 2 to 5, characterized by at least one Fourier transform as a constituent part of the fitting method. 7. Method according to one of Claims 1 to 6, characterized in that, dur- ing the measurement (16), at least two orders of diffraction (j) of meas- urement light (1) diffracted by the object (8; 20; 25; 27; 30) are guided by the projection optical unit (5) to an image side. 8. Metrology system (2) having an optical measurement system for carry- ing out the method according to one of Claims 1 to 7, - having an illumination optical unit (4) for illuminating the object (8; 20; 25; 27; 30) to be examined with a specified illumination setting, - having an imaging optical unit (5) for imaging a portion of the ob- ject (8; 20; 25; 27; 30) into a measurement plane (12), and - having a spatially resolving detection device (14), arranged in the measurement plane (12). 9. Metrology system according to Claim 8, characterized by a design of the imaging optical unit (5) such that, during the measurement (16), at least two orders of diffraction (j) of measurement light (1) diffracted by the object (8) are guided by the imaging optical unit (5) to an image side of the imaging optical unit (5). 10. Metrology system according to Claim 8 or 9, characterized by an EUV light source (3). |

The invention relates to a method for determining an optical phase differ- ence of measurement light of a measurement light wavelength over a sur- face of a structured object.

Phase measurement systems and measurement methods that can be per- formed therewith are known from the papers “Phase-shift/Transmittance measurements in micro pattern using MPM193EX” by H. Nozawa et al., Photomask and Next-Generation Lithography Mask Technology XVI, pro- ceedings of SPIE Vol. 7379, 737925 and “Phame™: a novel phase metrol- ogy tool of Carl Zeiss for in-die phase measurements under scanner rele- vant optical settings” by S. Perlitz et ah, proceedings of SPIE, March 2007, Art. No. 65184 R.

Regarding the measuring of the phase of EUV photomasks, it is further re- ferred to a paper “Measuring the Phase of EUV Photomasks” of Sherwin et ah, Proc. of SPIE Vol. 11147 111471F- 1 to 1114721F- 11 which was pub- lished after the priority date of this application.

The theoretical determination of the ideal phase and reflectivity of a spe- cific absorbing material is known from the paper “Attenuated phase shift mask for extreme ultraviolet: can they mitigate three-dimensional mask ef- fects?” of Erdmann et ah, J. Micro/Nanolith. MEMS MOEMS 18 (1), 011005 (2018).

Phase-shift masks for EUV lithography are discussed in a paper of Con- stancias et ah, Proc. SPIE 6151, Emerging Lithographic Technologies X, 61511W (23 March 2006).

Optimum masks and source patterns to print a given shape are discussed in Rosenbluth et ah, Proc. SPIE 4346, Optical Microlithography XIV, (14 September 2001).

EUV source-mask optimization for 7 nm node and beyond is discussed in Liu et ah, Proc. SPIE 9048, Extreme Ultraviolet (EUV) Lithography V, 90480Q (17 April 2014).

It is an object of the present invention to provide a phase difference deter- mination method that yields highly usable values during the optimization of an image contrast when using the structured object as a reflection lithog- raphy mask.

This object is achieved according to the invention by a determination method having the features specified in Claim 1.

It has been found according to the invention that a phase difference deter- mination from a reconstructed field distribution in which both amplitude and phase of an electric field are included produces meaningful results as compared to phase determination methods of the prior art, which regularly consider only the phase values but not associated amplitude values, be- cause in particular phase values in the case of small amplitudes can be weighted less. The resulting phase difference is a parameter that can be used overall for the image contrast qualification of the measured structured object. It is thus possible to optimize a design of object structures based on the respectively measured phase differences, resulting in as strong an im- age contrast as possible. The determination method according to the inven- tion does not depend on a communication of a phase value over a possibly arbitrarily determined surface area of the object structure. This, too, in- creases the reliability and reproducibility of the determined optical phase difference.

The phase calibration can be converted into a computing algorithm, which means that the phase calibration can be effected automatically.

Object structures for which the phase difference can be determined are line structures, contact-hole or contact-pin structures and general structure forms that extend in two dimensions, in particular periodic structure forms. An object with such object structures may be used as a lithography mask.

The top structures of the object may be embodied as absorber structures of an absorber material which e.g. was coated on the bottom reflector struc- tures. Alternatively or in addition, the top structures of the object may be embodied as top reflector structures. In that case, the top reflector struc- tures on the one hand and the bottom reflector structures on the other can be produced by etching a respective reflector structure, in particular a mul- tilayer reflector structure. The structured object may be a lithographic mask, in particular suited for EUV lithography. In particular, the structured object may be embodied as a phase mask, in particular as a phase-shift mask (PSM), e.g. as a hard PSM. Such phase mask may require an optical phase difference of 180° between etched bottom structures and non-etched top structures.

Such phase masks may include an etch stop layer (ESL) between the etched bottom structures and the non-etched top structures. A phase differ- ence between the etched and the non-etched areas of such phase mask de- pends on the etching depth and on the thickness of the ESL. The depend- ency of the optical phase shift induced by the ESL on the ESL thickness is non-linear and thus needs to be carefully determined.

The optical phase difference determination method may be used as a prepa- ration method during the production of phase masks. During such method, a raw phase mask having calibration structures is produced. These calibra- tion structures include top structures above the ESL having a required height, i.e. producing a desired optical phase difference of e.g. 180°. Fur- ther, such raw phase mask includes an ESL having a given thickness.

After production of such raw phase mask, the optical phase difference de- termination is carried out to determine the optical phase difference between the top structures and the bottom structures of the phase mask. After that, the thickness of the ESL and/or an etching depth of the top (calibration) structures is varied to ensure that the desired optical phase difference is present between the top structure phase on the one hand and the bottom re- flector structure phase on the other. In case the structured object whose phase difference is to be determined is used as a lithography mask, such structured object is imaged to produce a 3D image of the mask structure in or near an image plane of the projection exposure apparatus used in the lithography production process. 3D imaging effects in such projection exposure apparatus may result in a contrast re- duction, i.e. may result in lower image quality. Contributions to such lower image quality may be a displacement of a focal plane, effects which affect the imaging tele centricity and further effects which affect a lateral dis- placement of the structure in the image plane. These contributions all can be seen as 3D effects, i.e. are at least partly generated by the structures on the mask to be imaged during the lithography production process. These 3D effects are to be minimized to obtain a desired imaging quality.

From the above-mentioned reference Erdmann et al. it is known to deter- mine an ideal absorber phase and an absorber reflectivity for a given ab- sorber material that minimize such 3D effects. After that, a phase metrol- ogy using the optical phase difference determining method according to the invention is used to determine the complex reflectivity in particular of the absorber material. After that, the thickness of the absorber structures of the structured object is varied in order to adjust the desired phase and reflectiv- ity of the absorber material to obtain minimized 3D effects.

The method for determining an optical phase difference may be used as part of a method to repair defects. During such calibration method, the op- tical phase difference determination method according to the invention, in particular including phase metrology, is used to determine the complex re- flectivity of repair absorber material depending on the thickness and on the composition of the repair absorber material. Using such optical phase dif- ference determination method, in particular including phase metrology, also the complex reflectivity of the absorber material of the absorber struc- tures of the mask to be repaired is determined. After determination of the complex reflectivities of the repair absorber material on the one hand and of the absorber material of the mask to be repaired on the other, the respec- tive absorber material composition and absorber material thickness is cho- sen for a repair step such that the complex reflectivity of the repair material matches to the complex reflectivity of the absorber material of the mask to be repaired.

Further, the method for determining an optical phase difference according to the invention may be used as part of an optimization process to ensure generation of a desired structure on a wafer with a given mask layout on the one hand and using a given illumination setting, in particular a partially coherent illumination distribution on the other, desirably ensuring a process window as large as possible. With respect to such source mask optimiza- tion (SMO) it is referred to Rosenbluth et al. and to Liu et al. cited above.

The source mask optimization requires as input parameter the complex re- flectivity of the absorber material of the absorber structures on the mask. Results of the SMO depend on such complex reflectivity. Using the method for determining an optical phase difference according to the inven- tion may be part of a calibration process to optimize parameters of a litho- graphic mask for source mask optimization. In such calibration process, the method for determining an optical phase difference, in particular including phase metrology is used to determine the complex reflectivity of a given absorber material which is used for the absorber structures of the lithogra- phy mask to be calibrated. The complex reflectivity determined by such de- termination method then is used as input parameter for the source mask op- timization to determine the mask layout and also to determine the illumina- tion setting.

During the fitting method, output functions that were initially non-linear can be linearized.

Modelling according to Claim 3 permits the use of different modelling pa- rameters for the real part and also for the imaginary part of the image-side field distribution. This can increase the stability of the computing method.

With the aid of an iterative fitting method according to Claim 4, it becomes possible to track non-linear functional dependencies through linear fittings in each iteration step.

An independent fitting of real and imaginary parts of the image- side field distribution according to Claim 5 can increase an accuracy of the fitting method.

A Fourier transform according to Claim 6 can simplify the fitting method.

A measurement according to Claim 7 permits an accurate determination of the phase difference. Even a greater number than two orders of diffraction can be guided by the projection optical unit from the object to the image side, for example three, four or even more orders of diffraction.

The advantages of a metrology system according to Claim 8 or 9 corre- spond to those that have already been explained above with reference to the determination method according to the invention. A metrology system according to Claim 10 permits a measurement with a very high resolution. A measurement light wavelength provided by the EUV light source may lie in a wavelength range between 5 nm and 30 nm. The measurement light wavelength is thus adapted to typical illumination wavelengths of projection exposure apparatuses, in which the structured objects to be measured in the form of lithography masks can be used in semiconductor chip production. An exemplary embodiment of the invention is explained in greater detail below with reference to the drawing. In said drawing:

Figure 1 schematically illustrates a metrology system for ascertaining an aerial image of an object to be measured in the form of a lithography mask, having an illumination system, an imaging optical unit and a spatially resolving detection device, wherein, additionally, plan views of the object to be measured and also of a 2D image, produced by way of example, of the object as a partial data set of a 3D aerial image are illustrated;

Figure 2 strongly enlarged compared to Figure 1, shows a cross sec- tion of a portion of the object to be measured including an ab- sorber surface top structure portion and a reflector surface bottom structure portion of the object, wherein two illumina- tion or measurement light rays that are reflected, for one, by layers of the absorber surface portion and, for another, by lay- ers of the reflector surface portion are illustrated by way of example; Figure 3 shows a diagram of a dependence of a phase difference Δφ between an absorber structure phase of the illumination or measurement light that is reflected by the absorber surface portions of the object and a reflector structure phase of the measurement light that is reflected by the reflector surface portions of the object on a thickness or height extent h _{abs } of an absorber structure of the absorber surface portions, wherein this dependence is illustrated for two different ab- sorber material compositions AM1 and AM2;

Figure 4 shows a flow chart for determining the optical phase differ- ence Δφ and for optimizing object structures of the structured object to be measured such that an image contrast is opti- mized when the structured object is used in projection lithog- raphy;

Figure 5 shows phase values of the absorber surface phase and the re- flector surface phase as a result of a reconstruction of an im- age-side field distribution as part of the method as per Figure 4 using the example of an object as per Figure 1 with a line structure;

Figure 6 shows an illustration of a computation of an image-side field distribution with the aid of a model based on a determined object distribution that is dependent on an object period, on a critical dimension of the object, on a complex reflectivity of the absorber surface portions and on a complex reflectivity of the reflector surface portions; Figure 7 in a cross section similar to Figure 2, a further embodiment of the object to be measured, the object being embodied as a EUV phase shift mask including a reflector surface top struc- ture portion and a reflector surface bottom structure portion;

Figure 8 in a depiction according to Figure 7 another embodiment of a structured object embodied as a phase shift mask with an etch stop layer located between reflector surface top structure por- tions and reflector surface bottom structure portions, wherein the etch stop layer covers the reflector surface bottom struc- tures;

Figure 9 in a depiction similar to Figure 8 an embodiment of the struc- tured object again embodied as a phase shift mask, wherein the etch stop layer is removed from the reflector surface bot- tom structure portions; and

Figure 10 in a depiction similar to that of Figures 2 and 7 to 9 a further embodiment of the object to be measured including absorber surface top structure portions and reflector surface bottom structure portions, wherein one of the absorber surface top structure portions is supplemented by a defect repair struc- ture. Figure 1 shows, in a sectional view corresponding to a meridional section, a beam path of EUV illumination light or EUV imaging light 1 in a metrol- ogy system 2. The illumination light 1 is produced by an EUV light source 3. In order to facilitate the representation of positional relationships, a Carte- sian xyz-coordinate system is used hereinafter. The x-axis in Figure 1 ex- tends perpendicular to the plane of the drawing and out of the latter. The y- axis in Figure 1 extends toward the right. The z-axis in Figure 1 extends upwardly.

The light source 3 can be a laser plasma source (LPP; laser produced plasma) or a discharge source (DPP; discharge produced plasma). In princi- ple, a synchrotron-based light source can also be used, for example a free electron laser (FEL). A used wavelength of the illumination light 1 can lie in the range of between 5 nm and 30 nm. In principle, in the case of a vari- ant of the projection exposure apparatus 2, it is also possible to use a light source for another used light wavelength, for example for a used wave- length of 193 nm.

The illumination light 1 is conditioned in an illumination optical unit 4 of an illumination system of the metrology system 2 such that a specific illu- mination setting of the illumination is provided, that is to say a specific il- lumination angle distribution. A specific intensity distribution of the illumi- nation light 1 in an illumination pupil of the illumination optical unit 4 cor- responds to said illumination setting. To specify the illumination setting, the illumination optical unit 4 can have a setting stop, which is not illus- trated in the drawing.

Together with an imaging optical unit or projection optical unit 8, the illu- mination optical unit 4 constitutes an optical measurement system of the metrology system 2. With the illumination setting that is respectively set, the illumination light 1 illuminates an object field 6 in an object plane 7 of the metrology system 2. A lithography mask 8, also referred to as a reticle, is arranged as a re- flective object in the object plane 7. The reticle 8 is an example of a struc- tured object whose optical phase difference is to be determined by a method which shall be described therein after. The object plane 7 extends parallel to the x-y-plane.

The object 8 has a line structure with line-type absorber top structures 9 that extend parallel to one another and parallel to the x-direction. A reflec- tor bottom structure 10 is situated between in each case two adjacent ab- sorber structures 9.

For illustrative purposes, Figure 1 shows, above the object plane 7, a plan view of a reticle 8 to be measured that is tilted about the y-axis by 90° into the plan-view position shown compared to the reticle 8 in the measurement position. The absorber structures 9 and the reflector structures 10, which in each case lie between the absorber structures, can be seen in this plan view as line structures that extend parallel to the z-direction.

As compared to the reflector structures 10, the absorber structures 9 have a height extent h _{abs } in the z-direction (cf. Figure 2). The absorber structures 9 can each have a multilayer construction with comparatively few individual layers 9 _{1 }, 9 _{2 }.

The reflector structures 10 are designed to be highly reflective multilayer structures with a multiplicity of individual layers 10i. The absorber struc- tures 9 for their part are located on said multilayer structure. Figure 1 additionally shows an illustration in accordance with a formula for the electric field of the illumination light 1 in the object field 6:

E _{ret } here denotes the electric field strength of the illumination light and (φ _{ret } denotes the phase of the electric field of the illumination light 1.

For two rays 1 _{i }, 1 _{j } of the illumination light 1, Figure 2 illustrates the effect of the respective layer construction of the absorber structures 9 and of the reflector structures 10 on a respectively reflected proportion of the light ray 1 _{i }, 1 _{j } . In this case, the light ray 1 _{i } is incident on the absorber structure 9, il- lustrated in Figure 2, and the light ray 1 _{j } is incident on the reflector struc- ture 10. In accordance with the formula, Figure 2 depicts the reflectivities r _{abs } for the absorber structure 9 and r _{ML } for the reflector structure 10. The following holds true: φ _{abs } and φ _{ML } here denote the phases of the reflected light rays 1 _{i }, 1 _{j }. A ph _{a }se difference will also be referred to as Δφ below. Figure 3 shows a function of the phase difference Δφ on the height h _{abs } of the absorber structure 9 using the example of two absorber material vari- ants, denoted AM1 and AM2. As the height h _{abs } of the absorber structure 9 increases, the phase difference Δφ also increases. This growth is not mono- tonic and is periodic. In addition, different absorber material variants lead to different slopes of said growth of the phase difference Δφ as a function of the height h _{abs } of the absorber structure 9.

The phase difference Δφ should lie in the region of 180° so that good im- age contrast is obtained during the imaging of the structures of the object 8 using the projection optical unit 5. Absorber structure heights h _{abs } that have such a phase difference Δφ in the region of 180° are marked each with a star in Figure 3. It can be seen that these structure heights h _{abs } for the ab- sorber structure 9 depend strongly on the respective absorber material vari- ant. For this reason it is necessary to precisely determine the phase differ- ence Δφ using the metrology system 2, wherein said phase difference value Δφ is to be independent of a structure extension of the absorber structures 9 in the object plane 7, that is to say in particular independent of a pitch, that is to say of a periodicity of the absorber structures 9 over the object field 6. This determination method is illustrated in more detail below.

The illumination light 1 is reflected by the lithography mask 8, as illus- trated schematically in Figure 1, and enters an entrance pupil of the imag- ing optical unit 5 in an entrance pupil plane. The used entrance pupil of the imaging optical unit 5 can have a circular or an elliptic boundary.

Within the imaging optical unit 5, the illumination or imaging light 1 prop- agates between the entrance pupil plane and an exit pupil plane. A circular exit pupil of the imaging optical unit 5 lies in the exit pupil plane.

The imaging optical unit 5 images the object field 6 into an image field 11 in an image plane 12 of the metrology system 2. The image plane 12 is also referred to as measurement plane. An imaging scale during the imaging us- ing the projection optical unit 5 is greater than 500. Depending on the em- bodiment of the projection optical unit 5, the magnifying imaging scale can be greater than 100, can be greater than 200, can be greater than 250, can be greater than 300, can be greater than 400 and can also be significantly greater than 500. The imaging scale of the projection optical unit 8 is regu- larly less than 2000.

The projection optical unit 5 serves for imaging a portion of the object 8 into the image plane 12.

Similarly to the illustration of the plan view of the object 8 in Figure 1, a plan view of an aerial image 13 of the imaging of the object 8 is illustrated there below the image plane 12, which is perpendicular to the plane of the drawing. This aerial image 13 is a partial data set of an entire 3D aerial im- age, the measurement of which will be explained below.

The electric field of the illumination light 1 in the image field 11 can be de- scribed as:

During the transfer of the electric field of the illumination light 1 from the object field 6 into the image field 11, aberrations and a defocus of the pro- jection optical unit 5 affect the form of the electric field. A spatially resolving detection device 14 of the metrology system 2 is ar- ranged in the image plane 12. This detection device may be a CCD camera. The detection device 14 is used to measure an intensity I, for which:

The detection device 14 is displaceable in the z-direction and is illustrated in Figure 1 in a recessed position at a distance from the image plane 12. During the measurement operation, the detection device 14 is arranged in or near the image plane 12. A detection plane 15 of the detection device 14 can thus coincide with the image plane 12 or have a defined distance there- from.

The metrology system 2 is used for performing a method for determining the optical phase difference Δφ as a characteristic that is applicable overall over an object structure to be measured. This characteristic can then be used to qualify the object 8 with respect to its contrast properties during imaging of the object 8 by way of a projection exposure apparatus. Main steps of the determination method will be explained additionally with respect to Figure 4 ff.

In a measurement step 16, a series of two-dimensional images I(x,y) of the object 8 are measured in each case in different focal planes for recording a three-dimensional aerial image of the object 8 using the projection optical unit 5. After each 2D image measurement, during which 2D image inten- sity values I(x,y) are recorded, the detection device 14 is displaced by a specified increment Δz with the aid of a detection displacement device (not illustrated). For example five, seven, nine, eleven or thirteen such 2D im- ages I(x,y) are recorded at different z-values for the complete measurement of the 3D aerial image. During this measurement, at least two orders of dif- fraction of the illumination light or measurement light 1 diffracted by the object 8 are guided by the projection optical unit 5 to the image field 11, that is to say to the image side of the metrology system 2.

In a subsequent reconstruction step 17, an image-side electric field distribu- tion f _{rec }(x,y) including an amplitude and a phase of the electric field E of the 3D aerial image is reconstructed.

Figure 5 shows by way of example a phase distribution over the image field 11 as the result of the reconstruction step 17 for the object 8 with the line structure. The absorber structures 9 have a different absolute phase φ in the region of 30° than the reflector structures 10 with an absolute phase in the region of 210°.

The reconstruction step 17 can be worked through with the aid of a method known from WO 2017/207297 A1.

Next, the phase difference is determined from the reconstructed field distri- bution f _{rec } with the aid of a phase calibration step 18. During the phase cali- bration, an image-side field distribution f _{im } is computed by introducing a model based on an object field distribution that is dependent on an object period or a pitch p of the object 8, on a critical dimension CD of the object 8, on a complex reflectivity r _{abs } of the absorber structures 9 and on a com- plex reflectivity r _{ML } of the reflector structures 10. The image-side field dis- tribution f _{im } is the result of a convolution of the object field distribution with a coherent point spread function PSF of the projection optical unit 5. The coherent point spread function is the Fourier transform of the coherent optical transfer function.

This is illustrated in Figure 6. Figure 6 shows, on the left, the object field distribution f _{obj }, which is dependent on the spatial coordinate x, on the re- flectivity r _{ML } of the reflector structures 10, on the reflectivity r _{abs } of the ab- sorber structures 9, on a duty cycle d and on a period (pitch) p. For the duty cycle d: d = CD/p.

Based on this object structure f _{obj }, which is divided into a real part (index r) and an imaginary part (index i), the influence of the projection optical unit 5 in the generation of the imaging of the object field distribution is now taken into account by convolution with the point spread function PSF _{coh }of the projection optical unit 5. This is shown at the centre of Figure 6, wherein the real part and the imaginary part are specified in each case for the different parameters r, d. The result of the convolution of the object field distribution with the point spread function PSF is a real part F ^{r } _{im } and an imaginary part F ^{i } _{im } of the image-side field distribution f _{im }, which is shown schematically on the right in Figure 6. This image-side field distri- bution f _{im } in turn is dependent on the spatial coordinate x, on the reflectivi- ties r _{ML }, r _{abs } of the reflector structures 10 and of the absorber structures 9, on the imaginary part d _{i } and on the real part d _{r } of the duty cycle and on the pitch p.

Subsequently, the image-side field distribution f _{im } that has thus been com- puted in the manner of a model is compared to the reconstructed image- side field distribution f _{rec }. For this purpose, a difference between said field distributions is minimized with the aid of a fitting method by variation of at least one of the model parameters object period (pitch p), critical dimen- sion CD and complex reflectivities rM _{L }, r _{abs }. This is done with the aid of a merit function, which is considered integrated over the x-y field extent and minimized. This merit function M can be written as follows: For minimizing this merit function, which is realized in accordance with the above equation (6) independently for the real part and for the imaginary part, the reconstructed image-side field distribution f _{rec } and also the com- puted image-side field distribution f _{im } are Fourier transformed. These Fou- rier transforms F _{rec }, F _{im } are then dependent on the spatial frequencies v _{x }, v _{y }.

With the aid of said Fourier transforms F _{rec }, F _{im }, which in turn are split into real and imaginary parts, the merit function M can be written as follows:

The integration in the frequency domain can be replaced for periodic struc- tures by a summation over those frequencies in which the respective argu- ments deviate from 0, wherein the considered line structure of the object 8 is the frequencies v _{x } = j/p for j = -j _{max... }j _{max. } j _{max } is in this case the maximum order of diffraction transmitted by the pro- jection optical unit 5.

In order that the projection optical unit 5 meets the condition , the following must hold true for the pitch p of the object 8: p ≥ 2λ/NA. λ is here the wavelength of the illumination light 1 and NA is the object- side numerical aperture of the projection optical unit 5. This summation for the real part and the imaginary part of the merit func- tion is linearly dependent on the real and imaginary parts of the reflectivi- ties r _{ML }, r _{abs }.

The coefficients of this linear notation are additionally non-linearly de- pendent on the real and imaginary parts d _{r }, d _{i } of the duty cycle d. These non-linear duty cycle output functions can be linearized as described be- low.

The optimization of the real part and of the imaginary part d _{r }, d _{i } of the duty cycle and of the reflectivities r _{ML } and r _{abs } for minimizing the merit function can then be effected by way of an iterative fitting method, wherein initially starting values d ^{0 } _{r,i } for the real and imaginary parts of the duty cycle d are taken and then corresponding starting values r ^{r,i } _{ML,0 } and r ^{r,i } _{abs,0 } for the re- flectivities are computed. To this end, the merit function can be written in the initial iteration step as follows: Here, Ŝ denotes the coefficients for the reflectivities r, which are in turn de- pendent on the real and imaginary parts of the duty cycle d. Ŝ is in this case a matrix having j _{max } rows and, due to the effect of the matrix on the two re- flectivities r _{M1 }, r _{abs }, two columns. The starting values of the reflectivities r ^{r,i } _{ML,0 } and r ^{r,i } _{abs,0 } are determined based on a starting value of the duty cycles d ^{0 } _{r,i } by linear optimization.

The individual matrix elements of Ŝ can now be expanded around the start- ing value of the duty cycles in a Taylor series. The second term of this Tay- lor series is linear in a value Δd ^{0 } _{r,i }, that is to say a correction value of the real and imaginary parts for the starting value of the duty cycle d. Said cor- rection value is the one by which the starting value must be changed for the next step of the iteration method.

Inserting the Taylor expansion up to the order Δd into the equation (8) re- sults in a linear dependence on the reflectivities and on the correction value for the duty cycles. The modified matrix Ŝ _{2 } is dependent only on the known starting values for the duty cycles and the already computed starting values of the reflectivi- ties. Δd ^{0 } _{r,i } can now be determined again by linear optimization, with the result that, based on the starting value, the next value d ^{1 } _{r,i } for the iteration can then be determined as per the following formula:

The matrix Ŝ in the above formula (9) is now updated with the new values for the duty cycle, and a new linear optimization of the reflectivities is per- formed. This iteration method is repeated until, in an iteration step m, the repeated correction Δd ^{m } _{r,i } lies below a specified threshold.

After the convergence of this iterative fitting method, the reflectivity values for r _{ML }, r _{abs } for which the merit function M is minimized will be known.

The desired value for the phase difference Df is then obtained from the re- flectivity values r _{ML }, r _{abs } obtained in accordance with the following for- mula: It is thus possible to compute a phase difference value for a specific mask structure on the basis of modelling the object structure such that it is possi- ble to check whether a specific structure design gives a phase difference that is optimum with respect to the image contrast.

Figure 7 shows another example of an object 20 whose optical phase dif- ference is to be determined using the method embodiments described above. Such object 20 may be used instead of the object 8 discussed above in particular with respect to Figure 2.

The object 20 is a hard phase shift mask (PSM) having top structures 21 and etched bottom structures 22 carried by a common base layer 23. The top structures 21 are embodied as reflector surface top structure portions having a reflectivity R1. The bottom structures 22 are embodied as reflec- tor surface bottom structures which are etched from the multilayer which sets up both top and bottom structures. The bottom structures 22 have a re- flectivity R2. For the reflectivities R1, R2, the following alternative rela- tions may hold: R1 > R2, R1 = R2.

The top/bottom structures 21, 22 generate an optical phase difference Δφ on the measurement light 1 which is reflected by the top structures 21 on the one hand and by the bottom structure 22 on the other. An etching depth of the bottom structures 22 with respect to the top structures 21 is shown at h in Figure 7.

The phase difference Δφ of the measurement light 1 over the surface of the object 20 between the top structure phase of the measurement light 1 re- flected by the top structures 21 and the bottom reflector structure phase of the measurement light 1 reflected by the bottom structures 22 can be deter- mined according to the method embodiments discussed above.

Different to the object 8, in the object 20, the top structures 21 also are made of the multilayer material. In particular, the object 20 is produced by etching a multilayer substrate.

Figure 8 shows another embodiment of an object 25 which may be used in place of the objects 8 or 20 described above. Components and functions which are discussed above with respect in particular to Figures 2 and 7 are given the same terms and reference numerals and are not described in de- tail again.

The object 25 has in between the top structures 21 and the bottom struc- tures 22 an etch stop layer 26 being of a material which is different from the layer materials of the multilayer composition of the top and bottom structures 21, 22. Such etch stop layer is used to differentiate in the etch production process of the object 25 between top structure portions and bot- tom structure portions as etching is done until the etch stop layer 26 is reached.

Of course, the reflectivity, the material and the thickness of the etch stop layer 26 of the object 25 affects the optical phase difference of the meas- urement light 1 between the top structure phase on the one hand and the bottom reflector structure phase on the other. This can be used in an opti- mization process to produce hard phase shift masks. During such calibra- tion process, a calibration raw phase shift mask according to the object 25 is produced. Then, the optical phase difference Δφ between the top struc- ture phase and the bottom reflector structure phase of such raw calibration mask is determined. After that, the thickness of the etch stop layer 26 and/or the etching depth h is varied to achieve a desired phase difference Δφ, e.g. a phase difference of 180° (=π).

Figure 9 shows another embodiment of an object 27 which also can be used as a phase shift mask and may replace objects 8, 20 and 25 described above. Components and functions which are discussed above with respect in particular to Figures 2 and 8 are given the same terms and reference nu- merals and are not described in detail again.

The object 27 also includes the etch stop layer 26. Different to the layout of object 25, the etch stop layer 26 of object 27 is removed at the bottom structure portions of the bottom structures 22.

Figure 10 shows another embodiment of an object 30 which may be used instead of objects 8, 20, 25 and 27 described above. Components and func- tions which are discussed above with respect in particular to Figures 2 and

9 are given the same terms and reference numerals and are not described in detail again.

The object 30 includes top absorber structures 9 and bottom reflector struc- tures 10 according to those described above with respect in particular to Figure 2.

As example, one of such absorber structures 9 which is denoted in figure

10 by 9 _{D } includes a defect. Such defect is present by a reduced extension of the absorber structure 9 _{D } in the x-direction. As a repair of such defect, the object 30 carries a structure supplement 31 which is made of a repair absorber material. Such repair absorber material in general is different from the absorber material of the original absorber structures 9 of the object 30. As compared to the height h of the nominal absorber structures 9, the repair structure supplement 31 has a height h _{D } which in general is different of h.

During a repair process, at least one embodiment of the phase metrology of the determining method discussed above is used to determine the complex reflectivity depending on the repair absorber material to be used for the structure supplement is determined. Also, as mentioned above, the complex reflectivity of the absorber material of the object 30 to be repaired is deter- mined. After having determined the complex reflectivities of the repair ab- sorber material on the one hand and on the absorber material of the object to be repaired on the other, the repair absorber material and also its height ho is chosen such that the complex reflectivity of the repair absorber mate- rial matches to the complex reflectivity of the absorber material of the mask to be repaired.

The optical phase difference determining method and in particular the phase metrology may further be used to optimize the phase difference Δφ to minimize object 3D effects on the imaging in a production projection ex- posure apparatus. Further, such determining method in particular the phase metrology may be used to calibrate object parameters and in particular the lithography mask parameters for source mask optimization, e.g. for simul- taneous optimization of a mask layout on the one hand and of a illumina- tion setting of a production projection exposure apparatus on the other. In particular, it has been recognized that the arrangement of the top struc- tures of the respective object has an influence on the phase difference Δφ and therefore may affect the imaging result in a production projection ex- posure apparatus.

Such top structure effects may be measured using the above-mentioned embodiments of methods for determining the optical phase difference Δφ and may be stored for different top structure arrangements in a phase dif- ference library for later use regarding optimization of lithography masks.

Regarding the optical phase difference Df, the thicknesses and the complex refractive indices, i.e. in particular absorbing influences of the refractive in- dex, of each of the layers of a multilayer structure are influencing parame- ters.

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