This application claims the benefit of the U.S. patent US 9 658 527 B2, entitled“Correc- tion of errors of a photolithographic mask using a joint optimization process” which is expressly incorporated by reference herein in its entirety.

1. Field of the invention

The present invention relates to the field of determining an effect of one or more pixels to be introduced into a substrate of a photolithographic mask. In particular, the present invention refers to a method and an apparatus for determining a calibration routine for the correction of errors of a photolithographic mask.

2. Background of the invention

As a result of the constantly increasing integration density in the semiconductor indus- try, photolithographic masks must project smaller and smaller structures onto a photo- sensitive layer, i.e. a photoresist on wafers. In order to fulfil this demand, the exposure wavelength of photolithographic masks has been shifted from the near ultraviolet across the mean ultraviolet into the far ultraviolet region of the electromagnetic spec- trum. Presently, a wavelength of 193 nm is typically used for the exposure of the photo- resist on wafers. In future, photolithographic masks will use significantly smaller wave- lengths in the extreme ultraviolet (EUV) wavelength range of the electromagnetic spec- trum (approximately 10 nm to 15 nm).

Consequently, the manufacturing of photolithographic masks which fulfil the increas- ing resolution requirements is becoming more and more complex, and thus more and more expensive as well. It is not unusual that photolithographic masks, photomasks or simply masks have defects at the end of their manufacturing process. Due to the time- consuming mask fabrication process, defects of photomasks should be repaired when- ever possible. Photolithographic masks can have several kinds or types of errors. An important type of defect of photolithographic masks is mask image placement errors or registration er- rors. This type of error or defect occurs if one or more pattern elements of a pattern arranged on a photolithographic mask are not precisely at their positions which are predetermined by the layout data of the mask.

WO 2013 / 123 973 describes a method for compensating polarization defects of optical elements in an optical system caused by a birefringence of the material of the optical component by introducing one or more arrangements of pixels into the optical element, preferably in an optically not relevant part of the optical element.

A further type of errors is an inhomogeneity of the optical transmission across the area of the photolithographic mask which leads to a respective variation of the optical inten- sity dose or simply dose applied to the photoresist on the wafer when illuminating a wafer by means of a mask. The variation of the locally applied optical intensity dose or simply dose results in a fluctuation or a variation of the structure dimension of a pat- tern element in the developed photoresist. The uniformity of the imaging of a pattern element across the area of the photolithographic mask is called critical dimension uni- formity (CDU).

Further, another important type of defect is overlay defects or an On Product Overlay (OPO). This error type is linked to a shift of a feature element on a wafer which is im- aged by two or more subsequent illumination steps using two or more different photo- masks. Moreover, a bending of the substrate of a photomask is a further type of errors.

The applicant has disclosed methods for correcting these and other errors of photolith- ographic masks by introducing or writing pixels into a substrate of a photomask. For example, some of these methods are described in the U.S. patent US 9 658 527 B2 of the applicant. Further, the applicant has constructed several tools (RegC®, ForTune®) which are already routinely used for reliably correcting several error types of photo- masks. Nevertheless, there is room for a further improvement of these defect correction processes. It is therefore one objective of the present invention to provide a method and an appa- ratus for improving the above-mentioned methods of correcting defects of a photolith- ographic mask.

3. Summary of the invention

According to an aspect of the invention, a method according to patent claim 1 is provid- ed. In an embodiment, a method for determining an effect of one or more of pixels to be introduced into a substrate of a photolithographic mask, wherein the photolithographic mask has one or more pattern elements, and wherein the one or more pixels serve to at least partly correct one or more errors of the photolithographic mask, comprises: de- termining the effect of the one or more introduced pixels by determining a change in birefringence of the substrate of the photolithographic mask having the one or more pattern elements.

Pixels which are introduced into a substrate of a photolithographic mask to correct var- ious types of errors or defects of a photolithographic mask can locally modify the opti- cal transmission of the mask substrate. In the following, the benefit of the inventive method is illustrated for the example of correcting registration errors of a mask. How- ever, the inventive method is not restricted to the correction of registration errors of photolithographic masks.

Pixels introduced or written into a mask substrate to correct for example registration errors, generate small scattering centers for the optical radiation transmitting the mask substrate. For example, pixels which correct one or more registration defects may in- troduce local inhomogeneities in the optical transmission of the mask when a repaired mask having pixels in its substrate is operated in a photolithographic illumination sys- tem. Thus, the introduction of pixels correcting registration errors would result in a critical dimension (CD) variation across the photomask or a critical dimension uni- formity (CDU) problem of the photolithographic mask.

To avoid a CDU problem when correcting registration errors, a distribution of a second type of pixel may simultaneously be determined with the determination of the first type of pixel correcting the registration errors. The second type of pixel predominantly local - ly scatters the optical radiation impacting on the pixel(s) in a defined manner. The sec- ond type of pixels does essentially not locally change the density of the substrate. Typi- cally, the second type of pixel is introduced into a mask substrate together with the first type of pixel which corrects for example the registration error(s) of the photolitho- graphic mask.

Typically, both, the first type of pixel and the second type of pixel are not homogene- ously distributed in the substrate of a photolithographic mask to be corrected. The cor- recting effect of the one or more pixels depends on the details of the pixel writing pro- cess. Thus, the laser beam parameters of the laser system introducing the pixel(s) must precisely be controlled. Further, there exists a maximum of the allowed optical trans- mission variation which can be corrected by a scanner or a stepper which uses the cor- rected mask in a lithography process to project the pattern elements of the mask onto a photoresist arranged on a wafer. Consequently, the pixel writing process has to be cali- brated to ensure the allowed optical transmission variation is not surpassed at a posi- tion of the mask.

Presently, the optical transmission variation of the photolithographic at the actinic wavelength is used to calibrate the pixel writing process and to determine the maxi- mum amount of allowed optical transmission variation caused by an error correction process by introducing the one or more pixels into the substrate of the photolithograph- ic mask.

This approach has two drawbacks: (a) The primaiy parameter which is linked to a change of the mask substrate caused by the introduction of the one or more pixel(s) into substrate is not the optical transmission, but the stress generated by the error cor- recting pixel(s). This means that the present calibration process uses an indirect quan- tity for describing the effect of the one or more pixels and for determining the maxi- mum tolerable optical transmission variation (b) Further, and even more important, future EUV masks will be reflective optical elements. The actinic wavelength can no longer be used in transmission for calibrating an error correction process based on the introduction of pixel(s) into the substrate of a photolithographic mask. Thus, using the presently established calibration process also for EUV masks would result in a change of the workflow of the defect correction, since the optical transmission calibration would have to be done on an uncoated EUV mask substrate.

The inventive method considers a change in birefringence caused by the stress in the mask substrate due to the writing of one or more pixels which correct the mask defect. By using the primary effect of the error correcting pixels, namely the stress birefrin- gence for calibrating the defect correction process, both drawbacks of the present cali- bration process can be avoided.

Determining the change in birefringence may comprise measuring a birefringence of the substrate prior to introducing the one or more pixels and after introducing the one or more pixels into the substrate.

Typically, optically isotropic materials are used for substrates of photomasks, as for example quartz substrates or LTE (Low Temperature Expansion) materials. For these materials, the induced birefringence is directly proportional to the stress optical coeffi- cient K (unit: [mm ² /N]). It can be measured as the difference in the optical path length or retardation D between two incident plain waves oriented parallel and perpendicular to the main axis of stress which transmit the sample at a measurement position.

The one or more errors may comprise at least one of: a registration error, an optical transmission variation across the substrate, an overlay defect, and a bending of the substrate of the photolithographic mask.

This list of correctable defects is not complete. For example, polarization defects of photolithographic masks may also be corrected by introducing pixel(s) into the sub- strate of the photolithographic mask.

In this application, the term“photolithographic mask” also includes templates for the nanoimprint technology.

The one or more introduced pixels may not have an effect on the polarization of an op- tical radiation which has been modified by the one or more pattern elements of the photolithographic mask. This is correct for EUV masks; the EUV photons do not pass the layer where the pixels are arranged. Determining the effect of the one or more introduced pixels may comprise: determining the change in the birefringence as a function of at least one laser beam parameter of a laser system used for introducing the one or more pixels into the substrate of the pho- tolithographic mask.

The inventive method may further comprise the step of controlling the at least one laser beam parameter of the laser system based on the determined change in birefringence when writing the one or more of pixels into the substrate of the photolithographic mask in order to correct the one or more errors of the photolithographic mask

By determining a change or a variation of the birefringence caused by the stress of in- troducing one or more pixels into the substrate depending on one or more laser beam parameters allows the determination of a calibration curve which can be used for con- trolling the pixel writing process.

Determining a birefringence variation can comprise using a transmissive optical bire- fringence measurement system using a wavelength which is larger than the actinic wavelength of the photolithographic mask. Further, determining the birefringence var- iation can comprise using a reflective optical birefringence measurement system using a wavelength which is larger than the actinic wavelength of the photolithographic mask.

Using the stress birefringence as the quantity to determine the stress induced by the writing of error correcting pixel(s) into a mask substrate allows a de-coupling of the determination of the pixel effects from the actinic wavelength. Thus, the wavelength for measuring the stress birefringence can be selected independently of the actinic wave- length. Rather, the wavelength for measuring the stress birefringence can be adapted to the optical properties of the mask substrate so that the stress birefringence can be de- termined with high precision.

The wavelength of the transmissive optical birefringence measurement system can be in the visible wavelength range. Substrates of EUV masks do not transmit EUV photons, but are typically at least par- tially transmissive in the visible wavelength range. Therefore, the inventive method can be used to directly determine the stress birefringence caused by the defect correction process by writing one or more pixels for both, conventional transmissive photolitho- graphic masks irrespective of their actinic wavelength and future EUV masks also inde- pendent of their specific actinic wavelengths.

The at least one laser beam parameter can comprise at least one of: a power of the laser beam, a pulse length, a pulse density, a focus width, a focus depth, a wavelength, a wave front, and a polarization of the laser beam.

The wave front describes a shape of the wave front of the electromagnetic radiation which generates the one or more pixels in the substrate of a photolithographic mask.

The defined method can further comprise the step of: linking the change in birefrin- gence with a stress model of one or more pixels to be introduced into the substrate of the photolithographic mask.

The method defined above may comprise: determining an optical transmission varia- tion of the substrate as a function of the at least one laser beam parameter.

This step allows connecting the conventional calibration process with the new calibra- tion process explained in this application. This step is also necessary for linking the stress birefringence with the optical transmission variation.

The pulse length, the pulse density, the focus width, the focus depth, the wave front, and the polarization of the laser beam may be fixed and the power of the laser beam may be varied as a parameter.

The defined method may further comprise the step of: linking the change in birefrin- gence with the optical transmission variation caused by the one or more pixels to be introduced into the substrate, wherein the at least one laser beam parameter is a pa- rameter. It is possible to establish a relation between a stress birefringence and an induced opti- cal transmission variation for each type of substrate of a photolithographic mask. This means that the optical transmission variation of the mask substrate can be deduced to the amount of stress introduced into the substrate during a pixel writing process.

Controlling the at least one laser beam parameter may comprise limiting a numerical value of the at least one laser beam parameter so that introducing the one or more pix- els into the substrate does locally not exceed a predetermined threshold of the variation of the optical transmission of the substrate of the photolithographic mask.

Based on a calibration process, wherein the stress birefringence is determined as a function of the optical transmission variation with the at least one laser beam parame- ter as a parameter, it can be secured that the error correction process by the writing pixel(s) into the mask substrate effectively corrects the defects of a photolithographic mask without introducing one or more new errors which cannot be corrected by writing further pixels into the substrate in a second error correction process.

The defined method may further comprise the step of determining an optical transmis- sion variation of the substrate at the wavelength used by the laser system for introduc- ing the one or more pixels into the substrate. The substrate may comprise a substrate for a photolithographic mask for an extreme ultraviolet (EUV) wavelength range.

As already described above, the stress introduced into a mask substrate by introducing one or more pixels into the substrate depends on at least one laser beam parameter.

The at least one laser beam parameter may be the power of the laser beam, if the other above-mentioned laser beam parameters have been fixed. A substrate, in particular a substrate of an EUV mask may have an optical absorption which cannot be neglected at the wavelength at which the laser system generating the pixels operates when deter- mining at least one laser beam parameter. In particular, the optical absorption of pho- tomasks may vary from batch to batch. If this effect is not considered, the at least one actual laser beam parameter may deviate from the determined laser beam parameter at the position where the pixel is generated. Thus, the error correction process is not op- timal or may even fail completely. Determining the optical transmission variation of the substrate may comprise deter- mining a variation of the optical transmission as a function of a lateral position of the substrate of the photolithographic mask.

Typically, the optical transmission may vary across an EUV mask substrate. Therefore, it is necessary to take into account the variation of the optical attenuation of the sub- strate at the pixel writing wavelength for a precise defect correction by pixel writing.

A lateral position of a mask is a position in the plane of the photolithographic mask (x- direction and y-direction). The z-direction is perpendicular to the mask plane.

The defined method may further comprise the step of determining an optical transmis- sion variation as a function of a depth and a lateral position of the substrate where the one or more pixels are to be introduced into the substrate.

Depending on the type of error to be corrected of a photolithographic mask, the one or more pixels may be introduced in various depths of the mask substrate. Thus, the at- tenuation of the laser beam within the substrate may be dependent on the type of error to be corrected. For optimizing the defect correction process, it is favourable to consid- er the depth into which the parameters are introduced.

The substrate may have a coating on a rear surface of the substrate, wherein the coating is electrically conductive and at least partially optically transmissive at the wavelength at which the one or more pixels are to be introduced into the substrate when determin- ing the at least one laser beam parameter.

The substrates of EUV masks may have a coating on their rear surface. The coating is typically electrically conductive so that the EUV mask may be fixed to an electronic chuck. To correct defects of EUV masks pixel(s) are typically introduced via the rear side of the mask substrate. Typically, a multi-layer structure acting as a reflective ele- ment for EUV radiation is arranged on a front side of the mask substrate. Thus, the front side of an EUV mask is normally not accessible for introducing pixel(s) into the mask substrate. It is therefore necessary that the electrically conductive rear side coat- ing is at least partially optically transparent at the wavelength the pixel(s) are intro- duced into the substrate of the EUV mask.

The coating may comprise at least one material of: indium tin oxide (ITO), fluorine tin oxide (FTO), and antimony tin oxide (ATO). The thickness of the coating may comprise a range of l nm - 200 nm, preferably 2 nm - 100 nm, more preferred 3 nm - 50 nm, and most preferred 4 nm - 30 nm. Alternatively, the electrically conductive coating may comprise two layers. A first layer may comprise chromium nitride (CrN) having a thickness of 2 nm— 50 nm, preferably 4 nm - 30 nm, more preferred 6 nm - 20 nm, and most preferred 8 nm - 12 nm. A second layer may comprise a metal oxide layer, as for example a tantalum oxynitride layer, having a thickness of 50 nm - 1000 nm, pref- erably 100 nm - 800 nm, and preferred 200 nm - 600 nm.

The method defined above may further comprise the step of determining the optical transmission variation of the substrate and/or the coating at the wavelength used by the laser system for introducing the plurality of pixels into the substrate.

The coating is often based on a trade-off between a low electrical resistance and a high optical transmission. The rear side coating of the substrate may have an optical absorp- tion in the range of a few percent to a few tens of percent, depending on the material composition and the thickness of the coating. Therefore, it is highly beneficial to con- sider the optical attenuation of the coating when determining the at least one laser beam parameter used for writing the pixel(s).

Determining the optical transmission variation of the substrate and/or the coating may comprise determining a variation of the optical transmission as a function of a lateral position of the substrate of the photolithographic mask. Similar to the substrate, the optical transmission of the coating may fluctuate across the mask substrate. This may occur due to a location variation of the depth of the coating, and/ or a local variation of the material composition, and/or a local variation of a doping of the coating.

Determining the optical transmission variation of the substrate may comprise deter- mining an optical reflection of the substrate and determining an optical transmission of the substrate. Further, determining the optical transmission variation of the substrate and the coating may comprise determining an optical reflection of the substrate and the coating and determining an optical transmission of the coating and the substrate. The three quantities: reflection, absorption and transmission substantially characterize a dielectric material. By measuring two of these quantities the third one can be deduced.

The method defined above may further comprise the step of determining the optical transmission variation of the substrate and/or the coating as a function of the depth and the lateral position of the substrate where the one or more pixels are to be intro- duced into the substrate.

The error correction process can be optimized by adapting the pixel writing process to the optical properties of the mask substrate and the mask coating on the one hand and the depth into which the pixel(s) are introduced on the other hand.

The one or more pixels may comprise a first writing map having a first type of pixels for correcting the one or more errors, wherein the first writing map describes a distribu- tion of the one or more pixels to be introduced in the substrate of the photolithographic mask.

The defined method may further comprise the step of determining a second writing map having a second type of pixels for correcting the optical transmission variation of the substrate based on the determined change in birefringence and/or the determined optical transmission variation of the substrate and/ or the coating at the wavelength the one or more pixels are to be introduced into the substrate.

A computer program may comprise instructions for causing a computer system to per- form the steps of the inventive method and of any of the aspects described above.

According to another aspect of the invention, an apparatus according to patent claim 16 is provided. In an embodiment, an apparatus for determining an effect of one or more pixels to be introduced into a substrate of a photolithographic mask, wherein the pho- tolithographic mask has one or more pattern elements, and wherein the one or more pixels serve to at least partly correct one or more errors of the photolithographic mask, comprises: means for determining the effect of the one or more introduced pixels by determining a change in birefringence of the substrate of the photolithographic mask having the one or more pattern elements.

The means for determining the change in birefringence may comprise at least one of: a polarimeter, an ellipsometer, and a birefringence imaging system.

The means for determining the effect of the one or more introduced pixels may corn- prise means for determining a stress distribution on a surface of the photolithographic mask. The means for determining the stress distribution may comprise an apparatus for determining surface plasmon resonances. When precisely modelling the photomask response to internal stress, it is possible to use information on surface stress on either side of the mask to determine the pixel effect.

Directly determining a stress distribution on a mask surface is an alternative to the de- termination of the effect of pixels written into a mask substrate.

The inventive apparatus may further comprise an optical measurement system adapted to determine an optical reflection and/ or an optical transmission of the substrate and/ or a coating arranged on the substrate.

The apparatus may further comprise a pixel writing system used for correcting the one or more errors.

The means for determining the change in birefringence, the optical measurement sys tem, and the laser system used for correcting the one or more errors may be combined in a single apparatus.

Finally, the apparatus may be adapted to execute the step of the inventive method and the steps of any of the aspects described above.

4. Description of the drawings

In order to better understand the present invention and to appreciate its practical ap- plications, the following Figures are provided and referenced hereafter. It should be noted that the Figures are given as examples only and in no way limit the scope of the invention.

Fig. l shows in cross-section of a schematic view of a transmissive photolitho- graphic mask;

Fig. 2 schematically depicts a cross-sectional view of a template used in the

nanoimprint lithography;

Fig. 3 schematically shows a cross-section of a of a reflective extreme ultraviolet

(EUV) mask;

Fig. 4 schematically presents a block diagram of some components of an appa- ratus which can be used to determine a stress birefringence;

Fig. 5 shows some components of an optical measurement system that allows to measure the optical reflection and the optical transmission of a sample;

Fig. 6 the upper image presents a variation of the transmission of a mask sub- strate of an EUV mask across the substrate and the lower image depicts a variation of the reflection of a coating on the rear of a substrate of a reflec- tive mask, both images are determined with the optical measurement sys- tem of Fig. 5;

Fig. 7 schematically shows a cross-section of some components of a pixel writing system;

Fig. 8 schematically represents a cross-section of an apparatus combining the apparatus of Fig. 4, the optical measurement system of Fig. 5, and pixel writing system of Fig. 7;

Fig. 9 presents the optical transmission variation at the actinic wavelength caused by the introduction of pixels into a substrate of a photolithographic mask as a function of the laser power of the laser system used for writing the pixels into the substrate;

Fig. 10 depicts the optical transmission variation at the actinic wavelength and the stress birefringence caused by the introduction of pixels into a substrate of a photolithographic mask as a function of the laser power of the laser sys- tem used for writing the pixels into the substrate;

Fig. 11 shows a representation of the stress birefringence (ordinate) across the op- tical transmission variation (abscissa) for various laser powers used for the introduction of pixels into a mask substrate; and

Fig. 12 presents a flow chart of the inventive method of the present application.

5. Detailed description of preferred embodiments

In the following, the present invention will be more fully described hereinafter with reference to the accompanying figures, in which exemplary embodiments of the inven- tion are illustrated. However, the present invention may be embodied in different forms and should not be construed as limited to the embodiments set forth herein. Ra- ther, these embodiments are provided so that this disclosure will be thorough and will convey the scope of the invention to persons skilled in the art.

In particular, the inventive method is described in the context of photolithographic masks. However, the person skilled in the art will appreciate that the defined method is not restricted to the application of correcting defective photolithographic masks. The inventive method can also be used for correcting defective templates 200 to be used in the nanoimprint lithography. In general, the inventive method can be applied to all transmissive optical elements which can be corrected by the introduction of one or more stress causing pixels. It is beneficially used for optical elements for which optical transmission uniformity is not a critical parameter.

Fig. l represents a schematic cross-section view of a transmissive photolithographic mask too. The mask too comprises a substrate no having a first or front surface 150 and a second or rear surface 160. The substrate no must be transparent for the wave- length used for the illumination of the photoresist on a wafer. This wavelength is called actinic wavelength. The exposure wavelength 180 may be in the deep ultraviolet (DUV) spectral range of the electromagnetic spectrum, in particular around 193 nm. Typically, the substrate material comprises quartz. The substrate 110 typically has lateral dimen- sions of 152 mm x 152 mm and a depth or height of essentially 6.35 mm. The substrate no of the photolithographic mask 100 has on its front surface 150 pattern elements 120 of a pattern 130 often fabricated from chromium which images pattern elements 120 predetermined by the layout data in a photoresist arranged on a wafer.

In the example depicted in Fig. 1, the mask 100 has an error 190 in form of a registra- tion error, i.e. the distance of two or more pattern elements 120 deviates from the posi- tion predetermined by the layout data. It is also possible that the error 190 may be a planarity error of the mask substrate 110, an overlay error, or an inhomogeneity of the optical transmission across the mask substrate 110 (not depicted in Fig. 1).

The portion of the substrate 110 of the photolithographic mask 100 carrying pattern elements 120 is called active area 170 of the mask 100, whereas the boundary portion which does not have pattern elements 120 is called non-active area 175. A laser beam having the actinic exposure or illumination wavelength illuminates the substrate no of the mask 100 through the second or rear surface 160 of the substrate 110.

The term“essentially” means in the context of this application the designation of a measured variable within its error margin when using state of the art metrology tools to measure the variable.

Fig. 2 schematically illustrates a template 200 used in the nanoimprint lithography to transfer pattern elements on a wafer. The template 200 comprises a material 210 which is transparent in the UV and DUV spectral range, often fused silica is used as a template material. The exemplary template 200 of Fig. 2 has an error 290. The pattern elements on the front template side 220 are fabricated in a process which is very similar to the fabrication of the pattern elements 120 of the photolithographic mask 100 of Fig. 1. Thus, the inventive principle can also be applied to correct various kinds of errors of a template 200 used in the nanoimprint lithography. The template 200 is illuminated by electromagnetic radiation 280 through the template rear side 230.

Fig. 3 shows a schematic cross-sectional view of a photolithographic mask 300 for an exposure wavelength of 13.5 nm. Different from the photolithographic mask of Fig. 1, the EUV mask 300 is a reflective optical element based on a multilayer structure 305. The multilayer structure 305 acts as a mirror which selectively reflects incident EUV photons 350. The multilayer structure 305 of the EUV mask 300 is deposited on a front substrate surface 315 of a suitable substrate 310, such as fused silica substrate. Other transparent dielectrics, glass materials or semiconducting materials may also be ap- plied as substrates for photolithographic masks as for example ZERODUR®, ULE® or CLEARCERAM®. It is advantageous that the material of the substrate 310 has a very low thermal expansion (LTE) coefficient.

The multilayer film or multilayer structure 305 comprises 20 to 60 pairs of alternating molybdenum (Mo) 320 and silicon (Si) layers 325. The thickness of each Mo layer 220 is 4.15 nm and that of the Si layer 225 amounts to 2.80 nm. To protect the multilayer structure 305, a capping layer 330 of silicon with a native oxide of 7 nm depth is ar- ranged on top of the multilayer structure 305. Other materials can also be used for forming a capping layer 330 as for example ruthenium.

In the multilayer 305, the Mo layers 320 act as scattering layers, whereas the silicon layers 325 function as separation layers. Instead of Mo, other elements with a high Z number may utilized for the scattering layers, such as cobalt (Co), nickel (Ni), tungsten (W), rhenium (Re) and iridium (Ir).

As already mentioned, the multilayer structure 305 on the substrate 310 of the EUV mask 300 acts as a mirror for EUV electromagnetic radiation. To become an EUV mask 300, a buffer structure 335 and an absorbing pattern structure 340 are additionally deposited on the capping layer 330. The buffer layer 335 may be deposited to protect the multilayer structure 305 during processing, for example during etching and/or re- pairing of the absorbing pattern structure 340. Possible buffer structure materials are for example fused silica (Si0 ₂ ), silicon-oxygen-nitride (SiON), ruthenium (Ru), chro- mium (Cr), and/or chromium nitride (CrN). The absorbing structure 340 comprises a material having a large absorption constant for photons in the EUV wavelength range. Examples of these materials are chromium (Cr), titanium nitride (TiN) and/or tanta- lum nitride (TaN).

An anti-reflective (AR) layer 345 can additionally be arranged on the absorbing pattern structure 340 to secure that no photons are reflected by the surface of the absorber pat- tern 340. Tantalum oxynitride (TaON) may be used for fabricating an AR layer. A thickness of about 50 nm is sufficient to essentially absorb all EUV photons 350 inci- dent on the absorbing structure 340. In contrast, the majority of the photons 350 inci- dent on the capping layer 330 is reflected as photons 355.

In the example of Fig. 3, the pattern element 360 has an error 390 in form of a registra- tion error. The portion of the pattern element 360 indicated by the dotted line 395 should be free of absorbing material.

Similar to transmissive photomasks 110, the substrate 310 of the EUV mask 300 has normally lateral dimensions of 152 mm x 152 mm and a thickness or height of essential- ly 6.35 mm. The rear surface 370 of the substrate 310 or the rear substrate surface 370 has a thin coating 375. The coating 375 should be electrically conductive so that the EUV mask 300 maybe fixed by electrostatic forces, i.e. it may electronically be chucked on a sample stage of a lithographic illumination system. Further, the coating should be at least partially optically transparent around the wavelength which the laser system uses to introduce the pixel(s) into the substrate 310. Materials which fulfil both re- quirements are for example indium tin oxide (ITO), fluorine tin oxide (FTO), and/or antimony tin oxide (ATO). The coating 375 may have a thickness of 10 nm to 50 nm. Alternatively, the coating may comprise a chromium nitride (CrN) layer having a thick- ness of 10 nm to 20 nm. Further, it is also possible that the alternative coating compris- es a CrN layer and a metal oxide layer having a thickness in a range of up to 600 nm.

In a further alternative, very thin metal layers maybe used for the coating 375. For ex- ample, the coating 375 may comprise at least one metal of the group of: nickel (Ni), chromium (Cr), aluminum (Al), gold (Au), silver (Ag), copper (Cu), titanium (Ti), wolf- ram (W), indium (In), platinum (Pt), molybdenum (Mo), rhodium (Rh), and/or zinc (Zn) and/or mixtures of at least two of these metals. The thickness of the metal layer is typically smaller than 30 nm.

Fig. 4 presents a cross-section of an apparatus 400 which can be used to determine a stress birefringence induced by introducing pixel(s) in a substrate 110, 310 of a photo- lithographic mask 100, 300. The apparatus 400 comprises a light source 420, which may be a laser source 420. The light source may emit light in the visible range of the electromagnetic spectrum. For example, in Fig. 4 a HeNe (Helium Neon) laser is used as a light source. The light beam 430 generated by the light source 420 passes through a photo-elastic modulator (PEM) 440. The PEM 440 comprises a polarizer at its en- trance (not shown in Fig. 4) and typically a piezo-electric transducer which periodically compresses and expands an optical medium which is often a quartz glass plate. Nor- mally, the modulation frequency is 50 kHz. Thus, the photo-elastic modulator 440 modulates a polarization of the light beam leaving the polarizer.

The modulated light beam 450 transmits a sample 410. The sample 410 may be a mask substrate 110, 310 of a photolithographic mask 100, 300 or maybe a template 200 ap- plied to the nanoimprint lithography. As discussed in the context of Figures 1 and 3, the substrate of a photolithographic mask is typically an optically isotropic material. But, stress may be induced into mask substrate 110, 310 by the mask fabrication process, i.e. by the fabrication of the pattern 130 for a transmissive mask 100 or by the fabrication of the pattern elements 360 on the front side 315 and/or the coating 375 on the rear surface 370 for a reflective mask 300. Thus, a substrate 110, 310 which is free of defects may have an induced stress after a photolithographic mask 100, 300 is fabricated based on the substrate 110, 310. Consequently, a photolithographic mask 100, 300 may show a stress birefringence. To eliminate this stress birefringence contribution, the meas- urements of the stress birefringence are difference measurements, i.e. the stress bire- fringence is measured prior to and after the introduction of the pixel(s) into the mask substrate 110, 310.

Further, for example, stress can temporarily be applied to a photolithographic mask 100, 300 by an inappropriate fixing of the mask 100, 300. This temporal stress caused by an inappropriate handling of a photomask 100, 300 is not considered in the present application. The introduction of pixel(s) into the substrate 100, 310 of a mask 100, 300 induces a local permanent stress into the mask substrate 100, 300 in a defined manner. It is known that an induced stress causes or induces a change in the impermeability Ab _ϋ which linearly depends on the stress induced in the material of the mask substrate 100, 300, wherein the impermeability b and the permittivity e are linked by:

This dependence can be expressed with the aid of the components of the stress optic matrix:

wherein q is the stress optical coefficient matrix, and s is the stress tensor. Therefore, the stress induced in the material of the mask substrate 110, 310 by introducing or writ- ing pixel(s) into the substrate 110, 310 is directly linked to the retardation D of an opti- cal beam in the material of the substrate 110, 310 and is given by the equation:

where d is the thickness of the mask substrate 110, 310, n ₀ is the refractive index of the isotropic material of the substrate 110, 310 and b _ϋ are the components of the imper- meability matrix of the substrate material of the photomask 100, 300. Equation 3 de- scribes the retardation in a two-dimensional deformation model in the plane of a pho- tolithographic mask 100, 300.

The retardation D caused by the stress birefringence resulting from the introduction of pixel(s) into a mask substrate 110, 310 is connected in a simple manner to precisely measurable quantities. The retardation D of a photolithographic mask 100, 300 having a material birefringence is determined by the thickness d of the substrate 110, 310 of the mask 100, 300 and the refractive indices of its fast n _F and slow axis n _s of the sub- strate 110, 310 according to the equation:

D = d - n _{s -} n _F ) = d An = d d (4) where d is called birefringence. The dimension of the retardation is meter; typically, it is indicated in nanometer. The retardation D caused by the material birefringence of the mask substrate no, 310 results in a variation of the polarization of the laser beam 460 leaving the sample 410 with respect to the polarization of the incident laser beam 450.

The light beam 460 leaving the sample 410 enters a detection system 470. The detec- tion system 470 may contain a beam splitting mirror which separates the modulated light beam 460 in two beams having essentially the same optical intensity. Each partial beam passes a combination of an analyser and a filter and is then detected by a photo- detector. The components inside the detection system 470 are not indicated in Fig. 4.

The lateral resolution of the apparatus 400 is determined by the focal width of the modulated laser beam 450 in the sample 410. Presently, the lateral resolution for the determination of the stress birefringence is in the range of 4 pm.

A computing unit (not shown in Fig. 4) may convert the measuring signals of the two photodetectors into parameters from which the birefringence of the sample 410 can be determined. The apparatus 400 or the computing unit provides as output signals the retardation D and the fast axis angle. Typically, the resolution limit of the apparatus 400 is in the range of some picometer. A resolution down to 1 pm is possible, typically the repeatability in about ±10 pm.

The light source 420, the PEM 440, and the detection system 470 of the apparatus 400 may have interfaces 480. The apparatus 400 may output the data of the computing unit via the interface 480. It is also possible that the apparatus 400 may externally be con- trolled via the interface 480 and transmits its measured data to an external computer system by means of the interface 480.

The apparatus 400 of Fig. 4 determines a stress birefringence induced by introducing pixel(s) in a substrate 110, 310 of a photolithographic mask 100, 300 by transmitting light through the substrate 110, 310. But, it is also possible determining a stress bire- fringence by using an apparatus which exclusively operates on the basis of light reflect- ed from the substrate 110, 310 (not shown in Fig. 4). Thus, an apparatus can be used for analysing stress birefringence of EUV masks 300. Fig. 5 schematically presents some components of an optical measurement system 500 which can be used to determine the optical absorption of a mask substrate 100, 300, in particular the substrate 310 of the EUV mask 300. The optical measurement system 500 comprises a light source 520 which may be a laser system. The wavelength of the light source 520 may be adapted to the wavelength of the laser system which is used to introduce the pixel(s) into the mask substrate 110, 310. In the examples of Fig. 5, the light source is a light emitting diode (LED). By means of the cable 515 the light source 520 is connected to a controlling unit (not depicted in Fig. 5). The light generated by the light source 520 is connected via the optical fiber 525 to a projection system 530 which directs the light beam 535 onto a sample 510. The sample 510 maybe a photo- lithographic mask 100, 300 or maybe a template 200.

A first typically small portion of the incident light beam 535 is reflected at the front side of the sample 510. For example, the front side 575 of the sample 510 may be the rear side 160 of the substrate 110 of the transmissive mask 100 or may be the surface of the front side of the coating 375 of the substrate 310 of the photolithographic mask 300. A second portion of the light beam 535 is reflected from the rear side 580 of the sample 510. The rear side 580 of the sample 510 may be the front side 190 of the substrate 110 of the transmissive mask 100 or may be the front side 315 of the substrate 310 of the EUV mask 300.

The first reflected portion 555 and the second reflected portion 565 maybe separated by an aperture 550, for example by a pinhole 550. Further, the beam transmitting the aperture 550 is filtered by a filter 560 and is then measured by the photodetector 570. Thus, the first reflected portion 555 and the second reflected portion 565 can be meas- ured sequentially by the photodetector 570. It is also possible to use two different pho- todetectors 570 to simultaneously detecting the first 555 and the second 565 reflected portion.

A second photodetector 540 is arranged behind the sample 510 which detects the por- tion 545 of the incident light 535 that transmits the sample 510 and is not reflected at the rear side 580 of the sample 510. The photodetector 540, 570 can comprise a photo- diode, for example a PIN diode or an avalanche diode. Alternatively, a photomultiplier may be used as a photodetector 540, 570. The lateral resolution of the detection of the reflected 555, 565 and the transmitted ra- diation depends on the focal width of the incident light beam 535 which is determined by the projection system 530 and the apertures 550 of the photodetectors 540 and 570. The lateral resolution of the optical measurement system 500 is in the range of too pm to 1 mm. A higher lateral resolution can be obtained at expense of the signal-to-noise ratio of the signals of the photodetectors 540, 570 when using apertures 550 having smaller openings.

Based on the measurements of the photodetectors 540 and 570, the reflected portion 555, 565 and the transmitted portion 545 of the light beam 535 incident on the sample 510 can be determined. Based on these measurements, the absorption or the attenua- tion of the substrate 110, 310 can be calculated. Further, the data measured by the pho- todetectors 540, 570 also enables to determine absorption of the coating layer 375 of the EUV mask 300. Moreover, the photodetectors 540, 570 may measure the reflected 555, 565 and the transmitted portion 545 of the incident light beam 535 as a function of a lateral position of the mask substrate 110, 310. Therefore, the measurement system 500 allows determining the absorption or the attenuation of both the substrate 110, 310 and/ or the coating 375 with a high spatial resolution.

The upper image 600 of Fig. 6 presents the variation of the transmitted portion 545 of the incident light beam 535 across the photolithographic mask 300 as a function of the lateral position. The light source 520 has a wavelength of 532 nm. As can be taken from image 600, the absolute transmission variation is approximately 3% across the photo- mask 300.

The lower image 650 of Fig. 6 depicts the variation of the first reflected portion 555 of the incident light beam 535 across the coating 375 of the substrate 300 of the EUV mask 300 again for a wavelength of the incident light beam 535 of 532 nm. The maxi- mum absolute variation amounts to about 0.7%.

The person skilled in the art will recognize that the images 600 and 650 show absolute numerical values of the light beams transmitted 545 and reflected 555 across the sub- strate 310 of the EUV mask 330. This means that the substrate 310 and the coating 375 of the EUV mask 300 transmit approximately 20% of the incident light beam 535 in the example presented in Fig. 6. The light 555 reflected in the first order from the front side 575 of the sample 510 amounts approximately 29% in the example of Fig. 6. Thus, ac- cording to A = \ - R - T , about 50% of the incident light 535 is absorbed in the sub- strate 310 and the coating 375 of the EUV mask 300 in the example of Fig. 6. Typical first order reflection values are in a range of 30% to 60%. Further, typically 15% to 25% of the incident light 535 are transmitted through the substrate 310 and the coating 375 of an EUV mask 300. Therefore, in the example of Fig. 6, the absorption of the sub- strate 310 and the coating 375 of EUV masks comprise a range of 15% to 55%. However, as already mentioned, this is just an example. There are other coatings and substrates which may have no significant absorption, or which may have higher or lower optical transmissions or may have higher and lower numerical reflectivity values than indicat- ed in the example of Fig. 6.

Fig. 7 depicts a schematic block diagram of an exemplary pixel writing apparatus 700 which can be used to correct errors of the photolithographic masks 100, 300 of Figures 1 and 3 as well as the templates 200 of Fig. 2. The pixel writing apparatus 700 compris- es a chuck 820 which may be movable in three dimensions. The sample 710 maybe fixed to the chuck 720 by using various techniques as for example clamping. The sam- ple 710 is mounted upside down to the chuck 720 so that its rear substrate surface is directed towards the objective 740. The sample 710 may be the photolithographic mask 100, 300, or may be the template 200.

The pixel writing apparatus 700 includes a pulse laser source 730 which produces a beam or a light beam 735 of pulses or light pulses. The laser source 730 generates light pulses of variable duration. The pulse duration may be as low as 10 fs (femtosecond) but may also be continuously increased up to 100 ps (picosecond). The pulse energy of the light pulses generated by the pulsed laser source 730 can also be adjusted across a huge range reaching from 0.01 pJ per pulse up to 10 mJ per pulse. Further, the repeti- tion rate of the light pulses comprises the range from 1 Hz to 100 MHz. For example, the light pulses may be generated by a Ti: Sapphire laser operating at a wavelength of 800 nm. However, the error correction method by introducing of pixel(s) into a mask substrate 110, 310 is not limited to this laser type, principally all laser types may be used having a photon energy which is smaller than the band gap to the substrate 110, 310 of the photolithographic mask 100, 300 or the template 200 and which are able to generate pulses with durations in the femtosecond range. Therefore, for example, Nd- YAG laser or dye laser systems may also be applied (not shown in Fig. 7).

The steering mirror 790 directs the pulsed laser beam 735 into the focusing objective 740. The objective 740 focuses the pulsed laser beam 735 through the rear substrate surface 160, 370 into the substrate 110, 310 of the photolithographic mask 100 300.

The NA (numerical aperture) of the applied objectives 740 depends on the predeter- mined spot size of the focal point and the position of the focal point within the sub- strate 110, 310 of the photolithographic mask 100, 300 relative to the rear substrate surface 160, 370. The NA of the objective 840 may be up to 0.9 which results in a focal point spot diameter of essentially 1 pm and a maximum intensity of essentially 10 ²⁰ W/cm ² .

The pixel writing apparatus 700 also includes a controller 780 and a computer system 760 which manage the translations of the two-axis positioning stage of the sample holder 720 in the plane of the sample 710 (x- and y-directions). The controller 780 and the computer system 760 also control the translation of the objective 740 perpendicular to the plane of the chuck 720 (z-direction) via the one-axis positioning stage 750 to which the objective 740 is fixed. It should be noted that in other embodiments of the pixel writing apparatus 700, the chuck 720 may be equipped with a three-axis position- ing system to move the sample 710 to the target location and the objective 740 may be fixed, or the chuck 520 may be fixed and the objective 540 may be moveable in three dimensions.

The computer system 760 may be a microprocessor, a general-purpose processor, a special purpose processor, a CPU (central processing unit), or the like. It may be ar- ranged in the controller 780, or may be a separate unit such as a PC (personal comput- er), a workstation, a mainframe, etc. The computer system 760 may further comprise an interface which connects the computer system 760 to the apparatus 400 of Fig. 4 via the connection 755. Further, the computer system 760 may control the laser source 520 via the connection 515 and the photodetectors 540 and 570 of the optical measurement system 500 of Fig. 5 by means of the connection 795. Further, the pixel writing apparatus 700 may also provide a viewing system including a CCD (charge-coupled device) camera 865 which receives light from an illumination source arranged in the chuck 720 via the dichroic mirror 745. The viewing system facili tates navigation of the sample 710 to the target position. Further, the viewing system may also be used to observe the formation of a modified area on the rear substrate sur- face of the sample 710 by the pulse laser beam 735 of the light source 730.

The computer system 760 may comprise a processing unit which determines the laser beam parameters of the laser beam 735 from error data and measurement data ob- tained from the apparatus 400 via the interface 480 and the measurement system 500 by means of the interface 515. By considering the experimental data of both the appa- ratus 400 and the measurement system 500, the one of more errors of the photolitho- graphic masks 100, 300 can effectively be corrected without having the risk that the error correction process causes a new defect of the photomask 100, 300. Further details of a pixel writing process are described in the US 9 658 527 B2.

Fig, 8 schematically depicts a cross-section of a combined apparatus 800 which corn- bines the apparatus 400 of Fig. 4, the optical measurement system 500 of Fig. 5 and the pixel writing apparatus 700 of Fig. 7 in a single device. A control and processing unit 850 controls the apparatus 400 via the connection 810, the measurement system 500 by means of the connection 820, and the pixel writing apparatus by means of the con- nection 830. Further, the control and processing unit 850 is connected to an external interface 860 via the connection 840.

The control and processing unit 850 controls the measurement of the stress birefrin- gence by the apparatus 400 and obtains the experimental data from the apparatus 400 via the connection 810. Furthermore, the control and processing unit controls the measurement of the optical reflection and the optical transmission of the substrate 310 and/or the coating 375 and receives the measured data. For example, based on these data, the control and processing unit 850 may determine the power of a laser beam 735 incident on the coating 375 of the mask substrate 110, 310 as a function of the depth within the substrate 310. As the correcting effect of a pixel strongly depends on the lo- cal energy density at the location where a pixel is generated, the error correction pro- cess of the pixel writing apparatus can precisely be controlled by the pixel writing appa- ratus 700.

The control and processing unit 850 may receive error data of the mask too, 300 from a defect metrology system via the interface 860 and the connection 840. Based on the obtained error data, the determined stress birefringence of the substrate 110, 310 and the determined reflection and transmission characteristics of the substrate 110, 310, the control and processing unit can determine the laser beam parameters of the pixel writ- ing apparatus 700. The control and processing unit 850 may be implemented in hard- ware, software, firmware, and a combination thereof. The control and processing unit 850 may comprise an algorithm that calculates the parameters of the laser beam 735 of the laser system 730 of the pixel writing apparatus 700 from the measured data re- ceived from the apparatus 400 and the optical measurement system 500.

The diagram 900 of Fig. 9 presents a measurement of the optical transmission varia- tion of the substrate 110 of the photolithographic mask too into which a plurality of pixel arrangements has been introduced. In Fig. 9 and the follow Fig. 10, the pixels within each of the plurality of pixel arrangements have a constant density. In the exam- ple of Fig. 9, the lateral dimensions of the pixel arrangements are 3 mm x 3 mm and the pixels have a pitch of about 4 pm in both directions. All pixel arrangements have been written in the center of the substrate 110, i.e. in a depth of 3.175 mm. The various pixel arrangements have been introduced into the substrate 110 with different power levels of the laser system 730 of the pixel writing apparatus 700. The laser beam parameters used for introducing the pixel arrangements into the mask substrate 110 are indicated in the following table.

Table 1: Numerical values of selected laser beam parameters

For obtaining the measurement points indicated in Fig. 9, the substrate 110 having the pixel arrangements has been illuminated in CW (Continuous Wave) mode with a DUV (Deep Ultraviolet) lamp. The radiation of the DUV has been filtered with a narrowband filter. Alternatively, the measurement data of Fig. 9 can also be measured at the actinic wavelength of the mask 100, i.e. at 193 nm. Thus, the light source of a photolithograph- ic illumination system can be used for this measurement. Typically, the light source of the photolithographic illumination system radiates the substrate 110 in CW mode or quasi CW mode.

As can be seen from the diagram 900, the attenuation of the optical radiation in the deep ultraviolet (DUV) wavelength range almost linearly increases as a function of the laser power used in the pixel writing process. The details of the curve 910 fitted to the measurement points 920 are indicated in Fig. 9. Based on the curve 910, a look-up ta- ble can be established which can be used for the determination of second pixel ar- rangements containing a second type of pixel which compensates the variation of the optical transmission or the DUV attenuation across the substrate 110 of the photomask too. Based on the look-up table, the laser beam parameters of the laser system 730 can be hxed for writing the second type of pixel arrangements having at least one second type of pixel for compensating the variation of the optical transmission of the photo- lithographic mask 100.

In the example depicted in Fig. 9, there is a maximum for the tolerable optical attenua- tion of the mask substrate 110 of 3%. This amount of optical attenuation of the sub- strate 110 can be compensated by a scanner or a stepper which uses the corrected pho- tolithographic mask 100 to project the pattern 130 of the mask 100 onto a photoresist arranged on a wafer. Thus, the maximum of tolerable optical attenuation fixes the max- imum power of the laser beam 735 during a pixel writing process which corrects, for example, the error 190 of the photolithographic mask 100. The dash-dotted curve 930 illustrates this relation.

Fig. 9 describes the conventional calibration process for a defect correction process or a RegC process which introduces pixel(s) into a substrate 110 of a photolithographic mask loo. As already explained above, this calibration procedure can no longer be used for EUV masks 300. The substrate 310 of EUV masks 300 is not transparent for the actinic wavelength. Further, the conventional calibration process indirectly deduces the effect of the pixels introduced into the mask substrate 110 from the induced variation of the optical transmission of the substrate 110. Moreover, the optical transmission is not a relevant parameter for an EUV mask 300. It does not have to be maintained at a con- stant level, but can be chosen freely.

Fig. 10 shows again the optical transmission variation or the optical attenuation of pixel arrangements which are written into the mask substrate 110 with different power levels of the laser beam 735 of the pixel writing system 700. In Fig. 10 the pixel arrangements are written in a bare mask substrate 110. The measurement points 1020 are indicated by rotated squares. For the measurement points 1020 the ordinate is given on the right side of the diagram 1000. The fitted curve 1010 is given by the equation 1050.

Fig. 10 also presents stress birefringence measurements for the same pixel arrange- ments in the bare mask substrate 110. The measurement points 1040 are depicted by squares in Fig. 10. The results of the fitted curve 1030 are given by 1060 in the diagram 1000. The stress birefringence measurements presented in Fig. 10 are difference meas- urements. This means, the stress birefringence of the substrate 110 has been measured prior to the introduction the pixel arrangements into the mask substrate 110. Thus, the effect of a stress birefringence which may already exist in the substrate 110 prior the introduction of pixel arrangements is excluded from the data presented in Fig. 10.

The diagram 1000 clearly shows that pixel arrangements induce a stress birefringence. Further, Fig. 10 also reveals that the stress birefringence varies as a function of the laser power with which the pixels arrangements have been introduced into the substrate 110. Moreover, the measurement points 1120 and 1040 as well as the calculated curves 1010 and 1030 show that there is a correlation between the stress birefringence variation and the attenuation of the optical radiation in the DUV wavelength range.

Fig. 11 presents a representation in which the optical attenuation data of Fig. 10 is rep- resented on the abscissa and the stress birefringence data of Fig. 10 is presented on the ordinate for various levels of the laser power used for writing the pixel arrangements into the substrate no. As can be clearly seen from the curve mo, there is a linear rela- tion between the optical attenuation and the stress birefringence caused by pixel ar- rangements which have been written with laser beams 835 having different power lev- els.

Thus, the diagram 1100 of Fig. 11 verifies that a stress birefringence measurement can be used for the calibration of RegC processes for transmissive photolithographic masks 100. The determination of stress birefringence can be used in addition to the conven- tional calibration process. However, a RegC calibration process based a stress birefrin- gence determination can also replace the present calibration approach based on the measurement of the optical attenuation caused by the pixels written into the substrate 110.

Even more important, as indicated in Fig. 4, the apparatus 400 uses a HeNe laser source as light source 420 so that the stress birefringence is measured at a wavelength of 632 nm. Therefore, the measurement of the stress birefringence can also be per- formed for the substrate 310 of the EUV mask 300 that is typically optically transparent in the visible wavelength range. By de-coupling the RegC calibration from the actinic wavelength, the method described in the present application can be used for both, transmissive 100 and reflective photolithographic masks 300.

Finally, Fig. 12 shows a flow chart 1200 of the inventive method. The method begins at 1210. At step 1220 the effect of the one or more introduced pixels is determined by de- termining a change in birefringence of the substrate 110, 310 of a photolithographic mask 100, 300 having one or more pattern elements 120, 360. This step may be per- formed by an apparatus 400 which is designed for executing stress birefringence meas- urements.

At step 1230 at least one laser beam parameter is determined based on the determined effect of the one or more introduced pixels. Step 1230 is an optional step of the in- ventive method. This is indicated by a dotted frame in the flow chart 1200. The method ends at step 1340.