Patent Publication Number: US-2023152685-A1

Title: Method and apparatus for repairing a defect of a lithographic mask

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of and claims priority under 35 U.S.C. § 120 from PCT Application No. PCT/EP2021/069641, filed on Jul. 14, 2021, which claims priority from German patent application DE 10 2020 208 980.9, filed on Jul. 17, 2020, and entitled “Verfahren and Vorrichtung zum Reparieren eines Defekts einer lithographischen Maske.” The entire contents of each of the above priority applications are incorporated herein by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a method and an apparatus for repairing at least one defect of a lithographic mask. Furthermore, the present invention relates to a method and an apparatus for repairing at least one pattern element of a lithographic mask. 
     BACKGROUND 
     As a consequence of the growing integration density in the semiconductor industry, lithographic masks have to image increasingly smaller structures on wafers. One possibility for taking account of this trend is to use lithographic or photolithographic masks whose actinic wavelength is shifted to ever shorter wavelengths. Currently, ArF (argon fluoride) excimer lasers that emit at a wavelength of approximately 193 nm are frequently used as light sources in photolithography. The use of masks for double or multiple exposures makes it possible to produce in a photoresist structures having dimensional sizes that cannot be achieved with a single exposure step. 
     Photolithography systems are presently being developed that use electromagnetic radiation in the EUV (extreme ultraviolet) wavelength range (preferably in the range of 10 nm to 15 nm). These EUV photolithography systems are based on a completely new beam guiding concept which uses reflective optical elements, since no materials are currently available that are optically transparent in the stated EUV range. The technological challenges in developing EUV systems are enormous, and tremendous development efforts are necessary to bring said systems to a level where they are ready for industrial application. 
     A crucial contribution to the imaging of ever smaller structures in the photoresist arranged on a wafer is accorded to lithographic masks, photolithographic masks, exposure masks, photomasks or just masks. With every further increase in integration density, it becomes increasingly more important to reduce the minimum structure size that exposure masks can image. In order that the structures of a mask that are becoming smaller can be reliably imaged in a photoresist applied to a wafer, resolution enhancement techniques (RETs) such as, for instance, optical proximity correction (OPC) techniques are being used to an increasing extent. The following exemplary documents describe various aspects of RET or OPC techniques: W.-M. Gan et al.: “Placement of sub-resolution assist features based on a generic algorithm”, DOI 10.1109/ACCESS.2019.2926102, IEEE ACCESS, P. Gupta et al.: “Manufacturing-aware design methodology for assist feature correctness”, Design and Process Integration for Microelectronic Manufacturing III, Proc. of SPIE Vol. 4756, Bellingham, Wash., 2005, doi: 10.1117/12.604872, US 2006/0046160 A1, U.S. Pat. No. 8,739,080 B1, U.S. Pat. No. 8,498,469 B2, US 2008/0077907 A1, US 2009/0258302 A1 and U.S. Pat. No. 10,318,697 B2. 
     Owing to the combination of structure elements or pattern elements that are becoming smaller and the use of RET techniques, the process for producing photolithographic masks is becoming increasingly more complex and thus more time-consuming and ultimately also more expensive. 
     On account of the tiny structure sizes of the pattern elements, ever smaller deviations of the pattern elements produced on a wafer from the design specifications during mask production are manifested in visible or “printable” errors. These must be repaired—whenever possible. Owing to the small dimensional sizes of the defects visible on a wafer, which attain values in the low double-digit nanometers range, for example, the outlay required to detect said defects is becoming very high. Furthermore, the repair of increasingly smaller defects is becoming more and more difficult. Firstly, the positioning of a repair tool relative to an identified defect is possible only with very complex metrology and, secondly, setting the repair tool to a specific small defect requires a high expenditure of time. 
     The present invention therefore addresses the problem of specifying methods and apparatuses that improve the repair of, in particular, small defects of lithographic masks. 
     SUMMARY 
     In accordance with one exemplary embodiment of the present invention, this problem is solved by use of a method according to claim  1  and an apparatus according to claim  22 . In a further exemplary embodiment, this problem is solved by use of a method according to claim  18  and an apparatus according to claim  23 . 
     In one embodiment, the method for repairing at least one defect of a lithographic mask comprises the step of: ascertaining parameters of at least one repair shape for the at least one defect, wherein ascertaining parameters comprises: allocating at least one numerical value to a parameter, wherein the numerical value deviates from the numerical value predefined by the at least one defect for said parameter. In particular, this may be advantageous for small defects, i.e. defects having at least one dimensional size which is smaller than ten times the resolution limit of the mask, smaller than five times the resolution limit, smaller than three times the resolution limit, or smaller than the resolution limit. It may be particularly advantageous if small defects have at least one-dimensional size within a range of 2% to 50% of the resolution limit. 
     A defect to be repaired typically defines the parameters of the repair shape which are used for repairing the defect. Through comprehensive analyses the inventor has discovered that the compensation or repair of, in particular, very small defects that hitherto had been able to be eliminated only with extreme difficulty can be significantly simplified if at least one of the parameters of the repair shape is allocated a different numerical value from what is actually required by the repair of the defect. In particular, this may be advantageous for small defects, i.e. defects having at least one-dimensional size which is within a range of 2% to 50% of the resolution limit of the mask. 
     A repair shape, whose parameters exclusively have numerical values which were ascertained on the basis of measured values is also referred to hereinafter as nominal repair shape. A nominal repair shape is typically formed from the difference between a measured mask segment having a defect and a measured equivalent defect-free mask segment. Alternatively and/or additionally, it is also possible to produce a nominal repair shape by the design data of a measured, defective mask segment being subtracted from the latter. A repair shape used in a method according to the invention differs from a nominal repair shape in that in the first-mentioned repair shape at least one parameter has a numerical value which deviates from the numerical value ascertained from measurement results. 
     Put simply, it may be advantageous to effect a repair (e.g. of an edge error) not exclusively on the basis of parameters whose numerical values are predefined by the respective defect (e.g. in the case of an edge error by the difference between the erroneous edge position and the target edge position predefined by the mask design). This is because, particularly if the numerical value of a parameter is in the region of the resolution limit or even below that (e.g. the edge position is only very slightly erroneous), a very precise repair is necessary in order to correct this (small) defect. Small errors during the repair may have the effect here that the repair does not entail a significant improvement. However, if a targeted departure is made from a numerical value predefined by the respective defect for the corresponding parameter, what can be achieved is that errors during the repair have a significantly less pronounced effect, however, and so the requirements made of the repair process can be relaxed, if appropriate. 
     The method according to the invention is explained below on the basis of the example of an edge placement error of a pattern element. A deviation dx of an edge of a pattern element from the specifications of the mask design is transformed by the mask, during an exposure process, into an edge placement error EPE, given by the product of the deviation dx, a possible mask enhancement factor MEEF (Mask Error Enhancement Factor) for the defect or the deviation and the magnification or reduction of the projection lens disposed downstream of the mask. A projection lens of a photolithographic exposure system often has a magnification M=¼ or M=⅕. 
     However, if the deviation dx of an edge of a pattern element becomes smaller than the resolution limit of the photolithographic mask, the latter translates the deviation dx to a greatly reduced extent during an exposure process into a reduced edge placement error. This is caused by the actinic radiation of a photomask being averaged over structures whose dimensional sizes are smaller than the resolution capability of the mask. The details of this averaging process depend on the structures considered and the details of the exposure process used for imaging these structure elements. The present application makes use of this substantive matter in order to facilitate the repair of defects whose dimensional sizes are below the resolution limit of the lithographic mask. 
     In this regard, during an edge repair of a pattern element, for example, the parameters of which repair (or the parameters of the corresponding nominal repair shape) actually (predefined numerically by the defect) require deposition of material from the measured edge as far as the target edge, material can deliberately be deposited at a distance from the measured edge, wherein the material is optionally deposited over a smaller length. An error in the exact positioning of the deposited material can thus (e.g. on account of diffraction effects) have a significantly lesser effect on the quality of the repaired mask. This analogously also applies to the case of an error that requires etching of material, in which in the case of an edge error, for example, material can be etched at a distance from the measured edge. 
     A repair shape combines the sum of the instructions that are carried out by a repair tool in order to eliminate a defect of a photomask. For the example of a defect of excess material, the repair shape describes a local etching process that can be used to remove the excess material from the mask. A repair shape typically has a basic area scanned by a particle beam in the manner defined in the repair shape. This means that the repair shape defines the energy of the particles of the particle beam, the spot width at the focus of the particle beam, the residence duration thereof on a location, the distance between adjacent points of incidence of the particle beam on the mask or the defect, and the time period until the particle beam reaches the starting point again. The area scanned by the particle beam and also the numerical values of the parameters indicated above may change in the course of implementing the repair shape. In the case of a local etching process, the repair shape furthermore specifies the temporal progression of the provision of the etching gas(es), i.e. the repair shape controls the gas volumetric flow of the etching gas(es) during the processing of the at least one defect. 
     In this application, the term lithographic mask encompasses a photolithographic mask. 
     The at least one parameter can comprise at least one element from the group: at least one lateral dimensional size of the at least one repair shape, a height dimensional size of the at least one repair shape, a distance between the at least one repair shape and the at least one defect, a material composition of the at least one defect, a geometric shape of the at least one repair shape, and surroundings of the at least one defect on the lithographic mask. The material composition of the at least one defect predominantly determines the complex refractive index thereof. 
     The facilitation or improvement of the repair or compensation of small defects can be brought about by various measures. In one respect, the defect need not be repaired 1:1, as predefined by the parameters of a nominal repair shape. In this regard, the basic area of the repair shape can be smaller than the basic area of the defect. In another respect, the height of the repair shape can be smaller than the height of the defect. The method defined above thus enables a defect correction in which a material removal from the mask or a material build-up on the mask can be smaller than the volume of the defect. This circumstance has a favorable effect on the defect processing time. 
     In another aspect, the above-explained averaging of the actinic radiation over structures that are smaller than the resolution capability enables the repair shape to be placed somewhat away from the position of the original defect. As a result, the very stringent requirements made of the positional accuracy during the placement of the repair shape for a defect are distinctly relaxed, without the quality of the defect repair or defect compensation being significantly disadvantageously influenced. 
     Furthermore, the geometric shape of the repair shape can deviate from the actual defect shape. This allows the defect repair to be distinctly simplified since the shape of the repair shape can be chosen at least partly independently of the defect shape and thus with a geometric shape that can be produced significantly more simply. 
     The at least one parameter can deviate by a predetermined absolute value from the numerical value predefined by the at least one defect for said parameter. 
     The deviation of the numerical value of the at least one lateral parameter can be selected from a range whose lower limit is greater than zero and whose upper limit is less than a resolution limit (of a defect-free region) of the lithographic mask. 
     The resolution limit of a lithographic mask can be determined by an actinic wavelength of the lithographic mask, a numerical aperture (NA), and an exposure setting suitable for projecting a pattern of the lithographic mask into a photoresist arranged on a wafer. 
     The numerical aperture can comprise the NA of a projection lens of an exposure system suitable for projecting the pattern of the lithographic mask into the photoresist. The NA of the projection lens can comprise a mask-side numerical aperture (NA M ). 
     Typically, a lithographic mask is designed for operation in a specific exposure system. This means that lithographic masks are specifically designed for an actinic wavelength, a numerical aperture of the projection lens (NA M ) of the exposure system as well as the exposure setting specifically used by the exposure system for projecting the pattern of the lithographic mask into a photoresist. In this sense, the design of a lithographic mask determines or fixes its resolution limit. 
     The resolution limit of the lithographic mask can comprise a mask-side resolution limit of an exposure system suitable for exposing a wafer using the lithographic mask. 
     The mask-side resolution limit (R M ) can be determined by 
     
       
         
           
             
               
                 R 
                 M 
               
               = 
               
                 
                   0.5 
                   · 
                   λ 
                 
                 
                   
                     NA 
                     M 
                   
                   · 
                   
                     ( 
                     
                       1 
                       + 
                       σ 
                     
                     ) 
                   
                 
               
             
             , 
           
         
       
     
     wherein λ is the actinic wavelength of the lithographic mask, NA M  is the mask-side numerical aperture of the projection lens of the exposure system, and σ is an exposure setting of the exposure system exposing the lithographic mask 
     The mask-side resolution limit R M  is proportional to the actinic wavelength λ and inversely proportional to the mask-side numerical aperture NA M . The NA M  can have numerical values in the range of approximately 0.1 to 0.5. Furthermore, the resolution limit of the lithographic mask is dependent on the exposure setting σ of the exposure system that exposes a wafer by using the lithographic mask. The numerical values of σ range from 0 (for central illumination) to 1 (for maximally oblique illumination). Oblique exposure is also referred to as off-axis exposure in the technical field. 
     Depending on the numerical aperture NA M  and the exposure setting σ, the resolution limit for photomasks that are exposed with the deep ultraviolet (DUV) wavelength λ=193 nm is between 150 nm≤R M ≤300 nm. For EUV masks with an actinic wavelength of λ=13.5 nm, the resolution limit is currently in a range of 50 nm≤R M ≤100 nm. This means that the range within which one numerical value of one parameter or the numerical values of a plurality of parameters of the repair shape can be chosen shrinks as the actinic wavelength of the photolithographic mask decreases. To put it another way, the method defined above opens up a larger range of new degrees of freedom in the DUV wavelength range than in the EUV range. 
     The deviation of the numerical value of the at least one parameter can comprise a range of 2% to 80%, preferably 2% to 50%, and most preferably 2% to 30%, of a resolution limit of the lithographic mask. 
     A dimensional size of at least one dimension of the at least one repair shape can comprise a range of 10% to 90%, preferably 20% to 80%, more preferably 30% to 70%, and most preferably 40% to 60%, of a dimensional size of the corresponding dimension of the at least one defect. 
     The dimensional size of the at least one dimension of the at least one repair shape can comprise at least one lateral dimension and/or a height of the at least one repair shape. 
     A distance between the at least one repair shape and the at least one defect can comprise a range of 2% to 80%, preferably 2% to 50%, more preferably 2% to 30%, and most preferably 2% to 10%, of a resolution limit of a defect-free region of the lithographic mask. 
     The repair shape can have a lateral displacement in relation to the nominal repair shape, the repair shape can have lateral deviations of its dimensional sizes in relation to the nominal repair shape, and the repair shape can have a deviation of its height in relation to the nominal repair shape, such that the repair shape and the nominal repair shape produce substantially the same optical intensity distribution in a photoresist. This means that the lateral dimensional size(s) and the height of a repair shape can be coupled or correlated. By way of example, a small height of a repair shape can be compensated for by increasing one or both lateral dimensional sizes, and vice versa. Furthermore, a correlation between the height or the lateral dimensional size(s) of a repair shape and a lateral displacement of the repair shape in relation to a defect is also possible. The details depend on the repair shape, the surroundings of the mask in which the repair shape is produced, and the exposure process. 
     The at least one defect can comprise at least one element from the group: an edge placement error of a pattern element, an interrupted and/or a bridged connection of a pattern element, an outlier of an edge roughness of a pattern element, a particle adhering on the lithographic mask, a lateral defect having only low printability, a defect residue of a defect repair carried out, a sidewall angle error of a pattern element, and a center of gravity error of a pattern element and/or of a distance range between two pattern elements. 
     Ascertaining the parameters for the at least one repair shape can comprise: recording at least one aerial image of the at least one defect. An aerial image can be measured with the aid of a mask inspection apparatus. A mask inspection apparatus can comprise an optical inspection apparatus and/or an inspection apparatus that scans the mask surface. An optical mask inspection apparatus can comprise a laser interferometer, for example, and a mask inspection apparatus that scans the mask surface can comprise an atomic force microscope, for example. An optical mask inspection apparatus can be designed to record an aerial image and/or an aerial image focus stack of a photomask. 
     Recording the at least one aerial image can comprise: recording the at least one aerial image of the at least one defect at an actinic wavelength of the lithographic mask, and/or recording an aerial image focus stack of the at least one defect. Recording the aerial image at the actinic wavelength shows in the aerial image the details which are imaged during later exposure of the photomask in the photoresist. Recording an aerial image at the actinic wavelength of said mask is therefore advantageous. It is even more expedient to determine the imaging behavior of a defective region of a photolithographic mask during tuning through the focus of said mask. 
     Ascertaining the parameters for the at least one repair shape can comprise: scanning the at least one defect by use of a scanning particle microscope and/or a scanning probe microscope. Furthermore, ascertaining the parameters for the at least one repair shape can comprise: recording at least one aerial image of the at least one defect and scanning the at least one defect by use of a scanning particle microscope and/or a scanning probe microscope. 
     A scanning particle microscope can comprise at least one element from the group: a scanning electron microscope (SEM), a scanning ion microscope (FIB, Focused Ion Beam), and a scanning electron microscope with polarization analysis (SEMPA). 
     A scanning probe microscope can comprise at least one element from the group: a scanning tunneling microscope (STM), an atomic force microscope (AFM), a magnetic force microscope (MFM), a scanning near-field optical microscope (SNOM) and a scanning near-field acoustic microscope (SNAM). 
     Ascertaining the parameters of the at least one repair shape can additionally be based on at least one element from the group: an exposure setting with which the lithographic mask is exposed during operation, design data of the lithographic mask, refractive index data of a deposited material for repairing a defect of missing material, and RET techniques of resolution enhancement for the lithographic mask. 
     Ascertaining the parameters of the at least one repair shape can comprise: applying at least one algorithm to measurement data of the at least one defect and design data of the lithographic mask. 
     The at least one algorithm can be realized using hardware, software, firmware or a combination thereof. Furthermore, the at least one algorithm can be stored in a non-volatile memory. In particular, the at least one algorithm can be stored in a solid state memory (SSD, Solid State Drive). 
     Allocating the numerical value can comprise: applying a trained machine learning model for determining the deviation of the numerical value of the at least one parameter from the numerical value predefined by the at least one defect for said parameter. 
     The machine learning model can comprise a transformation model having at least two transformation blocks, wherein the at least two transformation blocks at least each comprise a generically learnable function that converts inputs into outputs that are used as inputs for a subsequent transformation block. The machine learning model can comprise at least one element from the group: a parametric mapping, an artificial neural network, a deep neural network, a time-delayed neural network, a convolutional neural network, a recurrent neural network, a long short-term memory network, a generative model, a kernel density estimator, a statistical model, a decision tree, a linear model, and a time-invariant model. 
     The machine learning model can comprise: (a) at least one encoder block for determining information-carrying features of an image of the at least one defect and the design data assigned to the image of the at least one defect; and (b) at least one decoder block for producing at least one effect of the at least one defect from the determined information-carrying features, wherein the at least one effect of the at least one defect shows what a superimposition of the image of the at least one defect with the corresponding design data looks like. 
     Ascertaining the parameters of the at least one repair shape can comprise: applying a trained machine learning model for ascertaining the parameters of the at least one repair shape. 
     A trained machine learning model can be used in at least two embodiments of a method described above. Firstly, a correspondingly trained machine learning model can be used to allocate to one or more parameters of a repair shape a numerical value or numerical values that deviate(s) from that or those as a result of the at least one defect. However, it is also possible—and this is the currently preferred embodiment—for a correspondingly trained machine learning model to ascertain all parameters of the at least one repair shape for repairing the at least one defect on the basis of measurement data, for example one or more aerial images of the defect, design data of the mask and optionally structures of one or more RET techniques. 
     The method according to the invention can furthermore comprise the step of: producing at least one repair element on the lithographic mask by use of the ascertained repair shape. Implementing the repair shape produces on the photomask a repair element that is designed as far as possible to eliminate, i.e. to repair or to compensate for, the at least one defect. 
     The at least one repair element may not be imaged during the exposure of the photolithographic mask. The at least one repair element may change an imaging behavior of the at least one defect during the exposure of the lithographic mask. 
     A produced repair element typically has deviations in relation to a nominal repair shape that are below the resolution limit of the photolithographic mask, and for this reason may not be imaged in a photoresist, and thus in the wafer situated underneath, during the exposure of the mask with the actinic wavelength. However, the repair element generated on the mask is designed such that it changes the imaging behavior of the defective region of the photomask, such that the defective region in combination with the repair element brings about an imaging behavior that is very similar to a defect-free region with an identical pattern arrangement. As a result, during an exposure process, the repaired mask produces substantially the same edge position as a defect-free mask. The effect of the at least one repair element is based at least partly on diffraction effects of the actinic exposure radiation at the repair element. 
     Producing the at least one repair element can comprise: carrying out at least one local etching process and/or carrying out at least one local deposition process by use of at least one focused particle beam and at least one precursor gas. 
     The at least one focused particle beam can comprise at least one element from the group: a photon beam, an electron beam, an ion beam, an atomic beam and a molecular beam. 
     The at least one precursor gas can comprise at least one element from the group: an etching gas, a deposition gas and an additive gas. 
     The etching gas can comprise at least one element from the group: a halogen (F 2 , Cl 2 , Br 2 , J 2 ), oxygen (O 2 ), ozone (O 3 ), hydrochloric acid (HCl), hydrogen fluoride (HF), xenon difluoride (XeF 2 ), xenon tetrafluoride (XeF 4 ), xenon hexafluoride (XeF 6 ), xenon chloride (XeCl), argon fluoride (ArF), krypton fluoride (KrF), sulfur difluoride (SF 2 ), sulfur tetrafluoride (SF 4 ), sulfur hexafluoride (SF 6 ), nitrosyl chloride (NOCl), phosphorus trichloride (PCl 3 ), phosphorus pentachloride (PCl 5 ), phosphorus trifluoride (PF 3 ), nitrogen trifluoride (NF 3 ), water vapor (H 2 O), hydrogen peroxide (H 2 O 2 ), nitrous oxide (N 2 O), nitrogen oxide (NO), nitrogen dioxide (NO 2 ) and nitric acid (HNO 3 ). 
     The at least one deposition gas can comprise at least one element from the group: a metal alkyl, a transition element alkyl, a main group alkyl, a metal carbonyl, a transition element carbonyl, a main group carbonyl, a metal alkoxide, a transition element alkoxide, a main group alkoxide, a metal complex, a transition element complex, a main group complex and an organic compound. 
     The metal alkyl, the transition element alkyl and the main group alkyl can comprise at least one element from the group: cyclopentadienyl (Cp) trimethyl platinum (CpPtMe 3 ), methylcyclopentadienyl (MeCp) trimethyl platinum (MeCpPtMe 3 ), tetramethyltin (SnMe 4 ), trimethylgallium (GaMe 3 ), ferrocene (Co 2 Fe) and bisarylchromium (Ar 2 Cr). 
     The metal carbonyl, the transition element carbonyl and the main group carbonyl can comprise at least one element from the group: chromium hexacarbonyl (Cr(CO) 6 ), molybdenum hexacarbonyl (Mo(CO) 6 ), tungsten hexacarbonyl (W(CO) 6 ), dicobalt octacarbonyl (Co 2 (CO) 8 ), triruthenium dodecacarbonyl (Ru 3 (CO) 12 ) and iron pentacarbonyl (Fe(CO) 5 ). 
     The metal alkoxide, the transition element alkoxide and the main group alkoxide can comprise at least one element from the group: tetraethyl orthosilicate (TEOS, Si(OC 2 H 5 ) 4 ) and tetraisopropoxytitanium (Ti(OC 3 H 7 ) 4 ). The metal halide, the transition element halide and the main group halide can comprise at least one element from the group: tungsten hexafluoride (WF 6 ), tungsten hexachloride (WCl 6 ), titanium hexachloride (TiCl 6 ), boron trichloride (BCl 3 ) and silicon tetrachloride (SiCl 4 ). 
     The metal complex, the transition element complex and the main group complex can comprise at least one element from the group: copper bis(hexafluoroacetylacetonate) (Cu(C 5 F 6 HO 2 ) 2 ) and dimethylgold trifluoroacetylacetonate (Me 2 Au(C 5 F 3 H 4 O 2 )). 
     The organic compound can comprise at least one element from the group: carbon monoxide (CO), carbon dioxide (CO 2 ), an aliphatic hydrocarbon, an aromatic hydrocarbon, a constituent of vacuum pump oils and a volatile organic compound. An aromatic hydrocarbon can comprise styrene. 
     The at least one additive gas can comprise at least one element from the group: an oxidizing agent, a halide and a reducing agent. 
     The oxidizing agent can comprise at least one element from the group: oxygen (O 2 ), ozone (O 3 ), water vapor (H 2 O), hydrogen peroxide (H 2 O 2 ), nitrous oxide (N 2 O), nitrogen oxide (NO), nitrogen dioxide (NO 2 ) and nitric acid (HNO 3 ). The halide can comprise at least one element from the group: chlorine (Cl 2 ), hydrochloric acid (HCl), xenon difluoride (XeF 2 ), hydrogen fluoride (HF), iodine (I 2 ), hydrogen iodide (HI), bromine (Br 2 ), hydrogen bromide (HBr), nitrosyl chloride (NOCl), phosphorus trichloride (PCl 3 ), phosphorus pentachloride (PCl 5 ) and phosphorus trifluoride (PF 3 ). The reducing agent can comprise at least one element from the group: hydrogen (H 2 ), ammonia (NH 3 ) and methane (CH 4 ). 
     The at least one repair element produced can at least partly overlap the at least one defect. A deposited repair element can comprise a material of the lithographic mask. The deposited repair element can comprise: a metal, for instance chromium (Cr), a metal compound, for instance tantalum nitride (TaN), silicon (Si), silicon dioxide (SiO 2 ) and molybdenum silicon oxynitride (Mo x SiO y N z ), wherein 0&lt;x≤0.5, 0≤y≤2 and 0≤z≤4/3. An etched repair element can etch a material of the photolithographic mask. The etched repair element can comprise the mask materials mentioned above. 
     The method defined above can comprise the steps of: (a) producing at least one repair element by use of at least one repair shape for which the parameters are defined by the at least one defect; and (b) ascertaining parameters of a repair shape for a remaining defect residue, wherein ascertaining parameters for the repair shape for the remaining defect residue comprises: allocating at least one numerical value to a parameter which deviates from the numerical value predefined by the remaining defect residue for said parameter. 
     The method defined above can be used as a second stage of a general defect repair process. In this case, in a first stage, a large defect, i.e. a defect that is large vis-à-vis the resolution limit of the photomask, can be repaired by implementing a repair shape in the form of a local etching process or in the form of a local deposition process or by producing the corresponding repair element. The repaired mask is then inspected. If it is established during the inspection of the mask that a repaired location still does not always fulfil the specification, a repair shape is determined for the residual defect residue, the parameters of which repair shape are determined in accordance with the method according to the invention. It is assumed here that the residual defect residue constitutes a small defect, i.e. a defect having at least one dimensional size in at least one dimension which is smaller than the resolution capability or the resolution limit of the photolithographic mask. The residual defect residue can subsequently be repaired or compensated for by producing the corresponding repair element on the basis of the repair shape ascertained in the second step. 
     In a second embodiment, the method for repairing at least one defective pattern element of a lithographic mask comprises the steps of: (a) determining at least one repair element of the lithographic mask which does not image the lithographic mask during the exposure thereof, wherein the at least one repair element is configured to change an imaging behavior of the at least one defective pattern element; and (b) producing the at least one repair element on the lithographic mask by use of at least one focused particle beam and at least one precursor gas. 
     The at least one repair element produced can have in at least one dimension a dimensional size which is smaller than the resolution limit R of the photomask. As already explained above, the averaging of the actinic radiation over structures with dimensional sizes below the resolution capability of the mask results in a reduced effect of a placement error of a repair element. This circumstance significantly facilitates the positioning of the repair element(s) in relation to the position of a defect to be repaired. Furthermore, by virtue of the non-imaging of the repair element(s), the geometric shape(s) thereof can deviate from the shape of the defect in a significant way, without the compensation of the defect being adversely influenced in an appreciable way. This fact considerably simplifies the repair or the compensation of small defects. 
     However, the repair element(s) produced on the mask locally change(s) the diffraction behavior of the mask at the actinic wavelength. The repair element(s) is (are) designed, then, such that said repair element(s) in combination with the defective pattern element substantially realize the imaging behavior of a corresponding defect-free region of the photolithographic mask. 
     The at least one repair element can have at least one dimensional size which comprises a range of 10% to 90%, preferably 20% to 80%, more preferably 30% to 70%, and most preferably 40% to 60%, of a resolution limit of the lithographic mask. 
     A distance between the at least one repair element and the at least one defective pattern element can comprise a range of 2% to 80%, preferably 2% to 50%, more preferably 2% to 30%, and most preferably 2% to 10%, of the resolution limit of the lithographic mask. 
     At least one-dimensional size of the at least one repair element can comprise a range of 10% to 90%, preferably 20% to 80%, more preferably 30% to 70%, and most preferably 40% to 60%, of the resolution limit of the lithographic mask. 
     Further aspects of a repair element have been described above in connection with the first embodiment. 
     A computer program can comprise instructions which, when the latter are executed by a computer system, cause the computer system to carry out the method steps of one of the aspects indicated above. 
     In one embodiment, the apparatus for repairing at least one defect of a lithographic mask comprises means for ascertaining parameters of at least one repair shape for the at least one defect, wherein the means for ascertaining parameters comprises: means for allocating a numerical value to at least one parameter which deviates from the numerical value predefined by the at least one defect for said parameter. 
     The apparatus can furthermore comprise means for producing the at least one repair element on the lithographic mask by use of the ascertained repair shape. 
     The means for ascertaining parameters of the at least one repair shape can comprise at least one coprocessor configured to determine the parameters of the at least one repair shape from measurement data of the at least one defect and design data of the lithographic mask. Furthermore, the at least one coprocessor can be configured to allocate to the at least one corresponding parameter at least one numerical value which deviates from the numerical value predefined by the at least one defect. Allocating the deviating numerical value of the at least one corresponding parameter can be effected on the basis of the resolution limit of the lithographic mask and the resolution limit when producing the at least one repair element. 
     The resolution limit when producing the at least one repair element is essentially influenced by two parameters. The first parameter is the minimum spot diameter to which a particle beam for producing a repair element can be focused. In the case of a photon beam, the achievable spot diameter is determined by the wavelength of the photons. In order to produce a repair element on a mask for the DUV wavelength range with the aid of a photon beam, photons from the EUV wavelength range are necessary. EUV photon sources are still very expensive at the present time. It is therefore advantageous, for the purpose of generating a repair element, to use a particle beam having mass, for example an electron beam, the resolution limit of which is given by the de Broglie wavelength. Electron beams can currently be focused to a spot diameter in the range of a few nanometers. The positioning accuracy of an electron beam is significantly higher and extends into the sub-nanometer range. 
     The second parameter that determines the resolution limit when producing a repair element is the interaction region or the scattering cone of the secondary electrons generated by a particle beam having mass. The diameter of said interaction region on the mask surface determines the extent of the local chemical reaction initiated by the particle beam and the at least one precursor gas. The size of the interaction region depends on the energy of the particles incident on the photomask. Furthermore, the local material composition of the photomask at the interaction site has a significant influence on the size of the interaction region. Currently, local chemical reactions may be restricted to lateral dimensions of approximately 5 nm. 
     The means for ascertaining parameters of the at least one repair shape can comprise at least one algorithm embodied as an application specific integrated circuit (ASIC), as a complex programmable logic circuit (CPLD, Complex Programmable Logic Device) and/or as a field programmable gate array (FPGA). 
     The means for ascertaining parameters of the at least one repair shape can comprise at least one trained machine learning model. Furthermore, the means for allocating to at least one corresponding parameter a numerical value that deviates from the numerical value predefined by the at least one defect can comprise a trained machine learning model. 
     The means for ascertaining parameters of the at least one repair shape can comprise at least one element from the group: a mask inspection apparatus, an interferometer, a confocal microscope, a scanning particle microscope and a scanning probe microscope. An element from said group can record measurement data from the at least one defect. 
     The means for producing the at least one repair element can comprise: at least one focused particle beam and at least one precursor gas, which are configured to carry out a local chemical reaction. 
     In a second embodiment, the apparatus for repairing at least one defective pattern element of a lithographic mask comprises: (a) means for determining at least one repair element of the lithographic mask which does not image the lithographic mask during the exposure thereof, wherein the repair element is configured to change an imaging behavior of the at least one defective pattern element; and (b) means for providing a focused particle beam and at least one precursor gas which are configured to produce the at least one repair element on the lithographic mask. 
     The means for determining at least one repair element can comprise at least one coprocessor configured to determine the at least one repair element from measurement data of the at least one defect and design data of the lithographic mask. Determining the at least one repair element can be effected on the basis of the resolution limit of the lithographic mask and a minimum spot size of the focused particle beam at the focus thereof. 
     The means for determining the at least one repair element of the lithographic mask can comprise at least one algorithm embodied as an application specific integrated circuit (ASIC), as a complex programmable logic circuit (CPLD, Complex Programmable Logic Device) and/or as a field programmable gate array (FPGA). 
     The means for determining the at least one repair element can comprise at least one trained machine learning model. 
     The means for determining the at least one repair element can comprise at least one element from the group: a mask inspection apparatus, an interferometer, a confocal microscope, a scanning particle microscope and a scanning probe microscope. 
     A further embodiment comprises a lithographic mask which is repaired according to any of the methods described above. The repaired lithographic mask can be used in an exposure system. Further, the repaired lithographic mask may be repaired based on at least one repair shape determined according to any of the aspects described above. Moreover, the repaired lithographic mask can contain at least one repair element generated by using the determined at least one repair shape. The lithographic mask can be repaired by performing a particle beam induced local deposition process and/or a local etching process. 
     In another embodiment an exposure system uses a lithographic mask repaired according to any of the above described method steps. 
     An exposure system may be a photolithographic exposure system. In particular, the exposure system may be a microlithographic projection exposure system. The exposure system may be any type of exposure system, as for example, an exposure system suitable for using transmissive lithographic masks and an exposure system suitable for using reflective lithographic masks. 
     A resolution limit of the exposure system can be determined by: a wavelength of a light source of the exposure system, a numerical aperture of a projection lens of the exposure system, and an exposure setting of the exposure system. 
     At least two resolution limits may be defined for an exposure system which refer to the two ends of the projection lens or the projection objective of the exposure system. 
     The resolution limit of the exposure system may be a wafer-side resolution limit of the projection lens of the exposure system. 
     The wafer-side resolution limit may be determined by 
     
       
         
           
             
               
                 R 
                 W 
               
               = 
               
                 
                   0.5 
                   · 
                   λ 
                 
                 
                   
                     NA 
                     W 
                   
                   · 
                   
                     ( 
                     
                       1 
                       + 
                       σ 
                     
                     ) 
                   
                 
               
             
             , 
           
         
       
     
     wherein λ is the actinic wavelength of the lithographic mask, NA W  is the wafer-side numerical aperture of the projection lens of the exposure system, and σ is an exposure setting of the exposure system suitable for exposing the lithographic mask for projecting a pattern of the lithographic mask in a photoresist arranged on a wafer. 
     The NA on the wafer side of the projection lens, i.e. NA W , is usually selected as large as possible in order to obtain a wafer-side resolution limit as low as possible. When using an immersion liquid, NA W  can be larger than 1, for example 1.3. 
     A mask-side resolution limit of the projection lens of the exposure system can be determined by 
     
       
         
           
             
               
                 R 
                 M 
               
               = 
               
                 
                   0.5 
                   · 
                   λ 
                 
                 
                   
                     NA 
                     M 
                   
                   · 
                   
                     ( 
                     
                       1 
                       + 
                       σ 
                     
                     ) 
                   
                 
               
             
             , 
           
         
       
     
     wherein λ is me actinic wavelength of the lithographic mask, NA M  is the mask-side numerical aperture of the projection lens of the exposure system, and σ is an exposure setting of the exposure system suitable for exposing the lithographic mask for projecting a pattern of the lithographic mask in a photoresist arranged on a wafer. 
     The ratio of the mask-side (NA M ) and the wafer-side numerical aperture (NA W ) defines the magnification M of the projection lens: 
     
       
         
           
             M 
             = 
             
               
                 
                   NA 
                   M 
                 
                 
                   NA 
                   W 
                 
               
               . 
             
           
         
       
     
     For transmissive lithographic masks the magnification typically has numerical values of M=¼ or ⅕ for 4× and 5× reduction projection lenses. This means for an immersion projection lens having NA W =1.2 and M=4, the mask-side numerical aperture NA M  is 0.30. For reflective lithographic masks, the magnification may depend on the direction an exposure beam is scanned across a wafer. For example, M may be ⅛ in the scan direction and M may be ¼ in a direction perpendicular to the scan direction. 
    
    
     
       DESCRIPTION OF DRAWINGS 
       The detailed description that follows describes currently preferred exemplary embodiments of the invention with reference to the drawings, wherein: 
         FIG.  1    in the upper partial image illustrates a schematic section through a pattern element of a photolithographic mask, said pattern element having an edge at the position predefined by the design, and in the lower partial image schematically represents an effective dose distribution of the optical intensity around the mask segment presented in the upper partial image in a photoresist during the exposure of the photomask; 
         FIG.  2    in the upper partial image exhibits a schematic section through a mask with a defective pattern element, and in the lower partial image illustrates the effect of the defective pattern element on the effective dose distribution applied in a photoresist; 
         FIG.  3    in the upper partial image shows a repair of the defective pattern element of the photolithographic mask from  FIG.  2    according to the prior art, and in the lower partial image illustrates the effect of the defect repair on the optical intensity distribution of the repaired mask segment from the upper partial image; 
         FIG.  4    in the upper partial image presents an ideal repair of the defective pattern element of the photolithographic mask from  FIG.  2    on the basis of a method according to the invention, and in the lower partial image shows the optical intensity distribution generated by the optimally repaired photomask in the photoresist of a wafer; 
         FIG.  5    in the upper partial image presents a real repair of the defective pattern element of the mask from  FIG.  2    on the basis of a method according to the invention, and in the lower partial image illustrates the effect of the repaired photomask on the optical intensity distribution generated in a photoresist; 
         FIG.  6    schematically illustrates an alternative exemplary embodiment of a repair element for compensating for the defect from  FIG.  2   ; 
         FIG.  7    in the upper partial image  715  schematically presents a perfectly placed edge of a pattern element, in the partial image  735  represents a pattern element having a defect of excess absorber material, in the partial image  755  represents the repairing of the defect from the partial image  735  in accordance with the prior art, in the partial image  775  illustrates the compensation of the defect from the partial image  735  by production of a repair element described in this application, and in the partial image  795  illustrates a second exemplary embodiment of a repair element according to the invention; 
         FIG.  8    in the upper partial image  805  represents a pattern element of a photolithographic mask, the edge of which pattern element is positioned exactly at the location provided by the design, in the central partial image  835  illustrates the repair of a defect of missing absorber material by production of a repair element according to the invention, and in the lower partial image  855  presents the repair of a defect of excess absorber material by generation of a repair element according to the invention; 
         FIG.  9    in the upper partial image presents a schematic plan view of a strip structure with a defect, and in the lower partial image represents the strip structure after the repair of the defect in accordance with the prior art; 
         FIG.  10    in the upper partial image reproduces the upper partial image from  FIG.  9   , in the central partial image illustrates an exemplary repair of the defect from the upper partial image in accordance with one of the methods described in this application, and in the lower partial image illustrates the averaging of the complex amplitude of the actinic radiation on a length scale of the optical resolution; 
         FIG.  11    in the upper partial image  1105  schematically illustrates a plan view of an absorbing, angular pattern element, in the partial image  1125  represents a pattern element having a defect of excess absorber material, in the partial image  1145  represents the repair of the defect from the partial image  1125  in accordance with the prior art, in the partial image  1165  illustrates the compensation of the defect from the partial image  1125  by production of a repair element described in this application, and in the partial image  1185  illustrates the generation of a second example of a repair element according to the invention; 
         FIG.  12    represents the repair of a defect of missing absorber material according to the scheme presented in  FIG.  11   ; 
         FIG.  13    in the upper partial image  1305  represents a strip structure of a mask arranged on a substrate, wherein a pattern element has a defect of missing absorber material, the central partial image  1335  illustrates a rigorous simulation of the defective mask segment, and the lower partial image  1365  shows the optical intensity distribution of the defective mask segment; 
         FIG.  14    illustrates the mask segment from  FIG.  13    after an optimum repair of the defect by a method according to the invention; 
         FIG.  15    represents the mask segment from  FIG.  13    after a repair of the defect from  FIG.  13    with a repair element which was not optimally positioned; 
         FIG.  16    in the top left partial image  1605  illustrates a mask segment having a defect, said mask segment being measured by a scanning electron microscope, in the top right partial image  1635  represents a repair element in the mask segment from the top left partial image, which repair element compensates for the defect, and in the bottom left partial image  1665  presents the repaired mask segment from the top left partial image  1605 ; 
         FIG.  17    in the upper partial image  1705  represents the normalized CD variation within the defective mask segment from the top left partial image in  FIG.  16   , and in the lower partial image  1755  illustrates the normalized CD variation of the repaired mask segment from the bottom left partial image  1665  in  FIG.  16   ; 
         FIG.  18    in the upper partial image  1805  represents a schematic section through a strip structure with a defect, in the partial image  1825  illustrates the mask segment from the partial image  1805  around the repaired defect, in the partial image  1835  illustrates the CD variation caused by the defect from the upper partial image, and in the lower partial image  1865  presents the CD variation that still remains after the defect repair; 
         FIG.  19    indicates a flowchart of a first embodiment of the method for repairing at least one defect of a lithographic mask; 
         FIG.  20    represents a flow diagram of a second embodiment of the method for repairing at least one defect of a lithographic mask; 
         FIG.  21    presents a schematic section through an apparatus for repairing one or more defects of a lithographic mask; 
         FIG.  22    illustrates a schematic section through an optical mask inspection apparatus and a comparison with a scanner of a photolithographic exposure system; 
         FIG.  23    presents a schematic section through an apparatus for repairing at least one defective pattern element of a lithographic mask; and 
         FIG.  24    illustrates a schematic section through an apparatus that realizes a particle beam source and a gas providing system from  FIG.  23   . 
     
    
    
     DETAILED DESCRIPTION 
     Currently preferred embodiments of a method according to the invention and of an apparatus according to the invention for repairing one or more defects of a lithographic mask are explained in more detail below. Furthermore, exemplary embodiments of a method according to the invention and of an apparatus according to the invention for repairing a defective pattern element of a lithographic mask are explained in detail below. The methods according to the invention are described on the basis of the example of a binary photomask for the deep ultraviolet (DUV) wavelength range. However, they are not restricted to improving the repair of defective DUV masks. Furthermore, the methods according to the invention are principally explained on the basis of edge placement errors of pattern elements. However, these methods are not limited to repairing this type of errors. Rather, they can be used to facilitate the repair of, in particular, small defects of any type and for the various types of photolithographic masks. The masks can comprise transmissive and reflective photomasks. Furthermore, small defects of binary and/or phase shifting masks can be repaired just like small defects of masks for multiple exposure. Hereinafter, the term mask or photomask is also intended to encompass a template for nanoimprint lithography. 
     Furthermore, the apparatuses according to the invention for repairing one or more defects of lithographic masks are explained on the basis of the example of a modified scanning electron microscope. However, the apparatuses according to the invention can be realized not only on the basis of a scanning electron microscope. Rather, apparatuses according to the invention can be based on any scanning particle microscope, that is to say that an apparatus defined in this application can use any type of particle, preferably a type of particle having mass, for examining and/or for producing one or more repair elements of a photomask. 
     The upper partial image  105  in  FIG.  1    shows a schematic section through a one-dimensional (1D) segment of a photolithographic mask  100 . The mask  100  can be a transmissive or a reflective mask  100 . In the example in  FIG.  1   , the photomask  100  comprises a binary transmissive mask  100 . The photolithographic mask  100  comprises a substrate  110  having a surface  115 . A pattern element  120  or a structure element  120  having a surface  125  is arranged on the surface  115  of the substrate  110 . The substrate  110  can comprise a quartz substrate and/or a material with a low coefficient of thermal expansion (LTE (low thermal expansion) substrate). In the case of a transmissive photomask  100 , the substrate  110  thereof is substantially optically transparent to electromagnetic radiation at the actinic wavelength. The pattern element  120  can be a structure element  120  of a binary photomask  100 . In this case, the pattern element  120  can comprise an element of an absorber structure  120  and can comprise chromium, for example. An absorbing pattern element  120  absorbs substantially the entire electromagnetic radiation at the actinic wavelength that is incident on the pattern element  120 . For DUV masks, the thickness of a pattern element  120  is in the range of 60 nm to 200 nm. Absorbing pattern elements of EUV masks currently have a layer thickness in the range of 50 nm to 70 nm (not illustrated in  FIG.  1   ). 
     Here and elsewhere in this description, the expression “substantially” denotes an indication of a measurement variable within the conventional measurement errors if measuring instruments in accordance with the prior art are used to determine the measurement variable. 
     Furthermore, it is possible for the pattern element  120  to comprise a structure element  120  which both shifts the phase of the actinic radiation relative to the radiation incident on the substrate  110  and absorbs part of the light at the actinic wavelength that is incident on the pattern element  120 . Examples of such masks are AttPSM (Attenuated Phase Shifting Mask) based on molybdenum silicide or based on silicon nitride. Such masks usually transmit in the dark region 6% to 20% of the incident optical intensity with a phase shift by 180° in comparison with a transparent region of the photomask. 
     However, the pattern element  120  can also be a structure element  120  of a purely phase shifting photomask  100 . A purely phase shifting mask  100  can be produced for example by etching a corresponding pattern into the substrate  110  of the mask  100 , which substrate substantially comprises quartz (SiO 2 ) in this case. This type of mask is called a CPL (Chromeless Phase Shifting) mask. A further example of a type of purely phase shifting mask is AltPSM (Alternating Phase Shifting Mask) masks. 
     The upper partial image  105  in  FIG.  1    shows an ideal edge  130  predefined by the design, said edge having a sidewall angle  135  of substantially 90°. Furthermore, the edge  130  is placed exactly at the location predefined by the design. 
     The lower partial image  155  in  FIG.  1    schematically presents an effective dose distribution of the optical intensity  160  during the exposure of the pattern element  120  of the photomask  100 . The pattern element  120  absorbs the radiation incident on the mask  100  from above, such that at some distance from the edge  130  below the pattern element  120  substantially no optical intensity is to be found in the photoresist of a wafer. In the transparent substrate region  110  of the mask  100 , said substrate region being at a distance from the edge  130  of the pattern element  120 , a photoresist applied to a wafer is exposed with the maximum optical intensity. The edge  130  of a pattern element  120  is typically defined as the location at which the optical intensity in the photoresist reaches 50% of the maximum optical intensity or of the maximum effective dose. In the lower partial image  155  in  FIG.  1   , this is illustrated by the point of intersection of the dashed vertical straight line  170  and the horizontal straight line  180 . 
     In the upper partial image  205  in  FIG.  2   , the edge  230  of the pattern element  220  is not placed at the position predefined by the design. Rather, the edge  230  is at a distance dx, illustrated by the horizontal double-headed arrow  240 . The distance dx from the target position of the edge  230  as predefined by the design can arise as a result of an erroneous placement of the pattern element  220 , the dimensional sizes of which have the values predefined by the design. In this case, the pattern element  220  can be corrected by ascertaining two repair shapes and producing two repair elements with the aid of said repair shapes. On the one hand, a first repair element defines the deposition of missing absorber material in the region identified by the double-headed arrow  240  in  FIG.  2   . On the other hand, a second repair shape specifies the removal of the excess absorber material, or absorber material positioned at the incorrect location, of the pattern element  220  (not illustrated in  FIG.  2   ). 
     It is assumed hereinafter that that edge of the pattern element  220  which is not reproduced in the 1D illustration in  FIG.  2    is positioned correctly, and that the pattern element  220  has to be corrected by the deposition of missing absorber material only in the region of the edge  230 . Furthermore, it is assumed below that the defect  240  is a small defect. This means that the dimensional size dx of the one-dimensional defect  240  is smaller than the resolution limit of the photolithographic mask  200  at the actinic wavelength thereof. The positioning or placement accuracy of an edge  130 ,  230  of a pattern element  120 ,  220  is of crucial importance in particular on account of the overlay problem for lithography systems which perform a plurality of exposure steps in order to fix a pattern element in a photoresist. 
     The lower partial image  255  in  FIG.  2    shows the optical intensity distribution  260  or the effective dose distribution  260  produced by the erroneous placement or positioning of the edge  230  of the pattern element  220  in a photoresist arranged on a wafer during the exposure of the photolithographic mask  200  with actinic electromagnetic radiation. During the exposure of a wafer, the position error of the edge  230  of the pattern element  220 , said error being described by dx in the one-dimensional example in  FIG.  2   , is translated by the mask  200  into an edge placement error EPE, illustrated schematically by the double-headed arrow  280  in the lower partial image  255  in  FIG.  2   . The relationship between the EPE  280  on the wafer and the mask defect  240  is described by the following relationship: EPE=mask error·MEEF·M. In this case, in the example represented in  FIG.  2   , the mask defect  240  or the mask error  240  denotes the fact that the edge  230  of the pattern element  220  is positioned erroneously by dx. The mask enhancement factor MEEF (Mask Error Enhancement Factor) stands for a magnification or enhancement of the mask defect  240  that is possibly caused by the mask  200 . For reasons of simplicity, it is assumed hereinafter that the following holds true: MEEF=1. The factor M denotes the magnification or the reduction with which a projection lens of an exposure system images the pattern element  220  of the mask  200  onto a wafer. For currently used projection lenses, it holds true that: M=¼ or M=⅕.  FIG.  2    and likewise the subsequent figures do not illustrate the relationship between a mask defect  240  and an EPE  280  in a manner true to scale. 
     An ideal repair of the mask defect  240  by perfect implementation of a perfect repair shape would place a repair element at the defective edge  230  of the pattern element  220 , such that the defective pattern element  220  would look like the pattern element  120  illustrated in  FIG.  1   . However, this would require ideal positioning of a repair tool in relation to the edge  230  of the defective pattern element  220 . Moreover, perfect repair of the defect  240  would presuppose that the resolution limit of the repair tool would be very small, ideally zero. 
     The upper partial image  305  in  FIG.  3    illustrates a real repair of the defect  240  from  FIG.  2    in accordance with the prior art. On account of the finite positioning accuracy of the repair tool, the latter cannot be aligned perfectly with the edge  230  of the defective pattern element  220 . Therefore, the repair element  310  produced by the repair shape does not correspond ideally to the 1D dimensional size dx of the defect  240 . Rather, on account of the limited positioning accuracy of the repair tool, the repair shape of the defect  240  produces a small part  320  of the repair element  310  on the surface  125  of the defective pattern element  220 . For this reason, the edge  330  of the repair element  310  deviates from the position predefined by the design. The remaining defect  340  has a dimensional size dx′. 
     The lower partial image  355  in  FIG.  3    illustrates the change in the optical intensity distribution  360  or of the EPE in a photoresist during the exposure of the repaired mask segment  300  from the upper partial image in  FIG.  3   . Compared with the exposure of the unrepaired mask  200 , the repaired mask  300  comes significantly closer to the pattern geometry predefined by the design from  FIG.  1   . However, there still remains a discrepancy or an EPE  380 , illustrated by the double-headed arrow  380 , which brings about a CD (Critical Dimension) deviation of the repaired pattern element  220  that lies outside the permissible error budget of the mask  300 . The defect  340  that remains after the repair in accordance with the prior art can be repaired or compensated for, as explained below. However, it is more advantageous to repair the defect  240  directly, i.e. in a single step, as described below with reference to  FIG.  4   . 
       FIG.  4    illustrates in the upper partial image  405  the best possible repair of the defective pattern element  220  from  FIG.  2    according to one of the methods described in this application. The repair shape for correcting the defective pattern element  200  from  FIG.  2    is designed such that implementing the repair shape generates a repair element  410  that is at a distance  420  from the edge  230  of the defective pattern element  220 . The ideal distance  420  between the edge  230  of the defective pattern element  220  and the repair element  410  is approximately dx/2, i.e. half of the distance between the edge  230  and the vertical line  170  or the edge error  240  of the defective pattern element  220 . For a height  430  of the repair element  410  that corresponds substantially identically to the height of the pattern element  220 , the repair element  410  and thus the repair shape underlying the repair element  410  has a dimensional size corresponding to approximately 80% of the distance  240  between the edge  230  of the pattern element  220  and the vertical line  170 . As already explained above, the mask-side resolution limit of DUV masks is in the range of 150 nm to approximately 300 nm, and that of EUV masks is in a range of approximately 50 nm to 100 nm. 
     The lower partial image  455  in  FIG.  4    presents the optical intensity distribution  460  of the repaired photomask  400  having the repair element  410  arranged at a distance  420  from the edge  230  of the defective pattern element  220  of the photomask  200 . A comparison of  FIGS.  1  and  4    makes it clear that the optical intensity distribution  460  brought about by the combined effect of the defective pattern element  220  with the repair element  410  generates in a photoresist a pattern element that precisely realizes the edge  130  predefined by the design. The repair element  410  brings about the ideal production of a pattern element predefined by the design in a photoresist and thus on a wafer, even though the repair element  410  does not adjoin the edge  230 , nor does the extent of the defect  240  correspond to the one-dimensional dimensional size  435  of the repair element  410 . 
     The repair element  410  can be produced by a repair tool, which is explained below in the context of  FIGS.  21  to  24   , on the basis of a corresponding repair shape on the photomask  400 . For this purpose, the repair tool can carry out a local chemical deposition reaction by use of a particle beam and at least one precursor gas. The material composition of the repair element  410  can correspond to the material composition of the pattern element  220 . However, the material composition of the repair element  410  can also deviate from the material of the pattern element  220  as long as the material of the repair element  410  substantially completely absorbs the actinic wavelength of the photolithographic mask  420 . 
       FIG.  4    represents perfect compensation of the defective pattern element  220  by the production of the repair element  410  at a distance  420  from the edge  230  of the defective pattern element  220 . The upper partial image  505  in  FIG.  5    represents a repair of the defective pattern element  220  that is able to be carried out in reality. On account of the finite positioning accuracy of a repair tool, the ascertained repair shape cannot position the repair element  510  exactly at the location provided for an optimum compensation of the defective pattern element. In the example illustrated in  FIG.  5   , the distance  520  of the edge  230  of the defective pattern element  220  is smaller than in the optimum repair of the defective pattern element  220  as illustrated in  FIG.  4   . As is evident from the lower partial image  555  in  FIG.  5   , the placement error  540  of the repair element  510  results in a scarcely perceptible deviation of the optical intensity distribution  560  compared with the ideal optical intensity distribution  460  in  FIG.  4    in a photoresist applied to a wafer. This means that the EPE of the mask  500 , illustrated by the arrow  580  in  FIG.  5   , is negligibly small after the repair of said mask by the production of the repair element  510 . 
     This is caused by a stepped-down reduction of the placement error  540  of the repair element  510  during transfer into a photoresist, by approximately the factor 1/R M , wherein R M  denotes the resolution limit of the photolithographic mask. This is one of the major advantages of the methods described here for repairing small defects of photolithographic masks. The sensitivity of the placement of a repair element  410 ,  510  to the EPE  580  is significantly reduced when the methods according to the invention are carried out. This reduction of the placement sensitivity of one or more repair elements  410 ,  510  is described by the resolution limit R M  of the photolithographic mask  400 ,  500 . The repair element  410 ,  510  can be placed at a distance of approximately 1% to 30% of the resolution limit R M  of the photolithographic mask  400 ,  500 , without the EPE  580 , i.e. the repair or compensation of the pattern element  220 , deviating by more than 10% from the best possible optical intensity distribution  460  in  FIG.  4   . 
       FIG.  6    illustrates a second example of a repair element  610  that can be used for repairing or compensating for the defective pattern element  220  from  FIG.  2   . Unlike the height  530  of the repair element  510  in  FIG.  5   , the height  630  of the repair element  610  in the upper partial image  605  in  FIG.  6    is smaller than the height or thickness of the pattern element  220  of the mask  600 . In order to compensate for the smaller height  630  of the repair element  610 , the repair element  610  has a larger 1D dimensional size  635  than the repair element  510  from  FIG.  5   . As can be gathered from the lower partial image  655  in  FIG.  6   , the changed repair element  610  substantially does not lead to a change in the optical intensity distribution  660  in a photoresist. The EPE  680 —in a manner similar to that in  FIG.  5   —is negligibly small. 
     Besides the reduced placement sensitivity of the repair elements  410 ,  510 ,  610 , by implementing an ascertained repair shape it is possible to produce a repair element  410 ,  510 ,  610  whose lateral dimensional size  435 ,  535 ,  635  deviates significantly from the 1D dimensional size dx of the defect  240 . The defect repair methods presented in this application have thus significantly reduced the sensitivity with which a parametrized repair shape transfers one or more lateral dimensional sizes of a defect  240  into a repair element  410 ,  510 ,  610 . Besides the relaxed placement sensitivity, this is the second significant advantage of the methods for repairing small defects of photolithographic masks as described in this application. In particular, the repair element  410 ,  510 ,  610  can be significantly smaller than a defect  240  to be repaired. This circumstance has a favorable effect on the time required for the defect repair, i.e. the production of the repair element  410 ,  510 ,  610 . 
     The application of the methods presented in this application for repairing a defect of missing absorber material, i.e. a clear defect, is explained in  FIGS.  1  to  6   .  FIG.  7    explains how these methods can be used for repairing a defect of excess material, i.e. a so-called dark defect. The upper partial image  705  in  FIG.  7    presents a pattern element  720  arranged on the surface  715  of a substrate  710  of the mask  700 . The edge  730  of the pattern element  720  is positioned exactly at the location provided by the design, said location being identified by the dashed vertical line  170 . 
     In the partial image  735  second from the top, the pattern element  740  has a defect  750  of excess material. The defect  750  has a 1D dimensional size  725  extending beyond the edge  730  of the defect-free pattern element  720 . The defect  750  can be caused by an erroneous placement of a pattern element  720  whose dimensional sizes have precisely the magnitude provided by the design. As already discussed in the context of  FIG.  2   , however, it is also possible that too little absorber material was removed in the region of the edge  730  during the patterning of the mask  700 . 
     The partial image  755  represents the repair of the defect  750  in accordance with the prior art. If ideal production of the repair element  760  is accomplished, the defect  750  can be repaired perfectly, as indicated in the partial image  755 . The challenges associated with a repair of, in particular, small defects  750  in accordance with the prior art have already been explained in the discussion of  FIG.  3   . 
     The repair of the defect  750  of excess material by the production of a repair element  770  according to the invention is illustrated in the partial image  775 . The repair element  770  is not designed for removing the excess material of the defect  750  by carrying out a local etching process. Rather, the production of the repair element  770  eliminates a part of the defect  750  and a small part of the defective pattern element  740 . After the production of the repair element  770 , the remaining defect residue  780  in combination with the repaired pattern element  740  influences the imaging behavior of the repaired mask  700  in the region of the repaired pattern element, such that this has an imaging behavior like the pattern element  720 . 
     Finally, the bottommost partial image  795  in  FIG.  7    presents a second repair element  790 , which can be produced as an alternative to the repair element  770 . The generation of the repair element  790  removes a part of the material of the defective pattern element  740  in the region of the edge  730  of the error-free pattern element  720 . The 1D dimensional size of the repair element  790  is larger than the repair element  770 . The larger 1D dimensional size of the repair element  790  is compensated for by virtue of the fact that the implementation of the repair shape underlying the repair element  790  does not etch the pattern element  740  down to the surface  715  of the substrate  710  of the mask  700 . 
     The implementation of the repair elements  770 ,  790  for repairing the defect  740  opens up the additional degrees of freedom that were explained above in the context of  FIGS.  5  and  6   . 
       FIG.  8    presents in the upper partial image  805  an absorbing pattern element  720  having a surface  725 , which pattern element is arranged on the surface  715  of a substrate  710  that is optically transparent to the actinic wavelength of the photolithographic mask  800 . The edge  730  of the pattern element  720  is positioned precisely at the location provided by the design. Said location is marked by the dashed vertical line  170  in  FIG.  8   . 
     The central partial image  835  in  FIG.  8    represents a defective pattern element  840 . The edge  830  of the pattern element  840  is not positioned at the location provided by the design of the mask. As a result, the pattern element  840  forms a clear defect or a defect of missing absorber material. In the partial image  835 , the defect is compensated for by implementing a corresponding repair shape for producing a repair element  850 . In the example in  FIG.  8   , the repair element  850  is adjacent to the edge  830  of the defective pattern element  840 . The repair element  850  comprises deposited absorber material whose 1D dimensional size extends beyond the limit of missing absorber material. The height of the exemplary repair element  850  is approximately half the height of the pattern element  820 ,  840 . 
     The lower partial image  855  in  FIG.  8    presents a pattern element  860  having a defect of excess absorber material. The defect of excess material is repaired by removing an upper part of the excess absorber material by producing the repair shape  870 . The edge  880  of the repaired pattern element  860  does not correspond to the position predefined by the design, said position being indicated by the dashed line  170  in  FIG.  8   . Nevertheless, the repair element  870  eliminates the effect of the defect of excess material apart from a negligibly small portion. 
     On account of the reduced placement requirements made of the repair tool, the production of the repair elements  850 ,  870  can be carried out with less outlay compared with the production of the repair elements  310 ,  760  in accordance with the prior art. 
       FIG.  9    presents in the upper partial image  905  a schematic plan view of a mask segment  900  having a strip structure (“lines and space pattern”) having two absorbing strips  920  and  930  arranged on an optically transparent substrate  910 . In the example illustrated in  FIG.  9   , the left pattern element  920  has a two-dimensional (2D) defect  940  of excess absorbing material. 
     The lower partial image  955  in  FIG.  9    illustrates the repair of the defect  940  by carrying out a local etching process with the aid of a particle beam and an etching gas. In the example of a repair process represented in the lower partial image  955  in  FIG.  9   , the defect  940  has been almost perfectly eliminated apart from a negligible defect residue  950 . In general, the laterally extended defect  940  cannot be removed in as exact a manner as represented in the lower partial image  955  in  FIG.  9   . As already explained above, the precision with which a repair tool or the repair shape of the defect  940  can be positioned in relation to the defect  940  or relative to the pattern element  920  is finite. Moreover, both the photomask  900  and the repair shape are subject to drift, for instance thermal drift, during the production of a repair element. The repaired pattern element  920  therefore often has along the processed right edge an edge roughness that is outside a predefined error interval (not represented in  FIG.  9   ). The production of a corresponding repair shape for removing the defect  940  extending along the pattern element  930  is therefore a very complex and time-consuming process. 
       FIG.  10    illustrates the repair of the 2D defect  940  from  FIG.  9    with the aid of one of the methods presented in this application. The upper partial image  1005  in  FIG.  10    reproduces again the upper partial image  905  from  FIG.  9   . The central partial image  1035  in  FIG.  10    illustrates the compensation of the defect  940  of excess material by the generation of the repair elements  1010 . The repair elements  1010  produced local etched structures in the defect  940 , partly in the substrate  910  of the mask  900  and partly also in the pattern element  920 . The various repair elements  1010  can be produced on the basis of a single repair shape produced at various positions along the defect extending at the right edge of the pattern element. However, it is also possible to ascertain a single repair shape, which produces the various repair elements  1010 , as illustrated in the central partial image  1035  in  FIG.  10   . 
     The great advantage of the repair of the defect  940  as represented in the partial image  1035  is the significantly reduced sensitivity of the placement or the positioning of the repair elements  1010  in relation to the defect  940 . The lower partial image  1065  in  FIG.  10    schematically illustrates the reduced sensitivity during placement of the repair elements  1010 . The dashed ellipses  1050  illustrate the area region of a photolithographic mask  900  or the length scale over which the mask  900  subjects the complex amplitude of the actinic electromagnetic radiation to averaging. If on a photomask there are structures present whose dimensional sizes in one or two dimensions are smaller than the resolution limit of the photomask, the actinic radiation averages across the details of said structures. This means that the microroughness of pattern elements does not influence, or scarcely influences, the imaging behavior of the photolithographic mask, whereas the complex amplitude of the electromagnetic actinic radiation averaged over a dimensional size in the region of the resolution limit influences the imaging behavior of the photomask. 
     The dashed ellipses  1050  show the regions of a mask which contribute optical intensity portions to a point of an imaging of the mask in a photoresist. The scale of this averaging region is determined—as already explained above—by the resolution limit R M  of the photolithographic mask. As long as the dimensional sizes of the repair elements  1010  are small relative to the resolution limit R M , the size and placement thereof are less sensitive by up to the factor 1/R M  compared with both the size and the positioning of repair elements from the prior art. This means that a very large range of different repair elements  1010  leads to the same or a very similar result with regard to the imaging behavior of a photolithographic mask. The methods described in this application make use of this circumstance in order to improve the repair of small defects that hitherto had been particularly difficult to repair. 
     The resolution limits of present-day DUV and EUV masks are indicated above. 
       FIGS.  11  and  12    explain the repair of a defect of excess absorber material and missing absorber material, wherein the repair element can have a different geometric shape from the defect to be repaired. The partial image  1105  shows a mask segment  1100  with an angular pattern element  1120 , which is arranged on a mask substrate  1110 , and the shape of which fulfils the design specifications. In the partial image  1125  in  FIG.  11   , the pattern element  1130  has a defect  1140  of excess absorber material, this defect being located at the inner side of the angular region of the pattern element  1130 . 
     The partial image  1145  in  FIG.  11    presents the repair of the defect by the implementation of a repair shape assigned to the defect in accordance with the prior art, which repair shape produces the repair element  1150  in the region of the defect  1140 . The problem associated with this has already been thoroughly explained above in the context of  FIGS.  3  and  9   . 
     The partial image  1165  in  FIG.  11    illustrates a first example of the production of a repair element  1170 , which compensates for the defect  1140 , and which is much less sensitive than the repair element  1150  from the partial image  1145  both with regard to firstly the placement of the repair element  1170  relative to the defect  1140  and with regard to secondly the lateral dimensional sizes of the repair element  1170  in relation to the dimensional sizes of the defect  1140 . Finally, the partial image  1185  represents a repair element  1190 , the geometric shape of which is distinctly different from the shape of the defect to be repaired. A circular or circle-like repair element  1190  is able to be generated significantly more simply than a rectangular or square repair element  1170 . The repair element  1190  in the partial image  1185  nevertheless brings about a compensation of the defect  1140  that is in no way inferior to the compensation of the repair element  1170 . The reasons for this have been explained in the discussion of  FIG.  10   . 
     The repair of a defect of missing absorber material will now be described with reference to  FIG.  12   . The partial image  1205  in  FIG.  12    shows a square pattern element  1220  placed on an optically transparent substrate  1210  of a photolithographic mask  1200 . In the pattern element  1230  in the partial image  1225 , a part  1240  of the pattern element  1230  is missing. This means that the latter has a clear defect  1240  or a defect  1240  of missing absorbing material. 
     The partial image  1245  in  FIG.  12    illustrates the repair of the defect  1240  of missing material by applying a corresponding repair element  1250  over the defect  1240  by implementing the repair shape ascertained for the defect. The repair element  1250  is implemented in accordance with the prior art. 
     The partial image  1265  in  FIG.  12    shows a first example of a repair element  1270 , which was produced in accordance with one of the methods described in this application, and which avoids the sensitivity of the repair method in the partial image  1245 . Furthermore, the repair element  1290  illustrates a second exemplary embodiment of a repair element  1290 , which only partly reproduces the complicated contour of the defect  1240 , and is therefore able to be produced even more simply than the repair element  1270 . 
       FIG.  13    presents in the upper partial image  1305  a plan view of a mask segment  1300  having a strip structure with absorbing strip-shaped pattern elements  1320  applied on a substrate  1310  of the photomask  1300 . The second pattern element  1320  from the left has a defect  1330  of missing material. The width of the defect  1330  was chosen as 15% of the half-pitch of the strip structure. The central partial image  1335  in  FIG.  13    presents a rigorous simulation of the imaging behavior of the mask segment  1300  from the upper partial image  1305 . The defect  1330  is clearly visible as defect  1340  in the central partial image  1335 . 
     The lower partial image  1365  in  FIG.  13    represents the optical intensity distribution of the defective mask segment  1300 . The dashed horizontal line  1360  indicates the maximum of the optical intensity distribution or the effective dose distribution of an error-free mask segment. The points of intersection between the intensity distribution and the dashed horizontal line  1370  describe the points at which a photoresist is deemed to be exposed. Said points of intersection thus represent the width of the strip-shaped pattern element produced on a wafer by the mask segment  1300 . The defect  1330  is mirrored in a wider central pattern element produced on a wafer. A variation of the width of the pattern element imaged in a photoresist by the mask segment  1300  results in a variation of the CD (Critical Dimension) along the imaged pattern structure. 
       FIG.  14    represents in the upper partial image  1405  the defective mask segment  1300  for the repair of the defect  1330  by the production of a repair element  1440 . In the example illustrated in  FIG.  14   , the repair element  1440  was not placed on the defect  1330 , as usual in the prior art, but rather was positioned directly next to the defect  1330  of missing absorber material. As can be gathered from the central partial image  1435 , the repaired defect  1330  is no longer visible in the imaging simulation. In addition, it is clearly evident from the lower partial image  1465  that the repair element  1440  repairs the defect  1330  perfectly, and so there is no variation of the optical intensity over the length of the pattern elements  1320 . 
       FIG.  15    illustrates in the upper partial image  1505  a repair of the defect  1330  from  FIG.  13   , during which repair the repair element  1540  was placed at a distance of 15% of the half-pitch from the pattern element  1320 . No deviation from a defect-free mask structure is discernible in the imaging simulation illustrated in the central partial image  1535  in  FIG.  15   . A slight reduction of the maximum of the optical intensity distribution is visible in the lower partial image  1565  in  FIG.  15   , and results in a smaller width of the central pattern element in a wafer. However, the deviation of the width is still within the error budget predefined for the mask  1300 . 
     The top left partial image in  FIG.  16    shows a mask segment  1600  recorded by a scanning electron microscope, said mask segment having a strip pattern (lines &amp; space pattern) with a half-pitch of 152 nm on the mask  1600 . As indicated by the dashed vertical line  1625  having a bend, a pattern element  1620  of the mask segment  1600  has a defect  1630  of missing absorbing material. The exemplary defect  1630  in  FIG.  16    has an extent in the region of 10 nm perpendicular to the pattern element  1620 . This extent is significantly smaller than the resolution limit R M  of the photolithographic mask  1600 . 
     The repair element  1640  is depicted schematically in the top right partial image  1635 , said repair element being designed such that in combination with the adjacent pattern elements  1620  it compensates for the defect  1630 . The bottom left partial image  1665  in  FIG.  16    represents the repaired mask segment from the top left partial image  1605  as a difference image with respect to the top right partial image  1635 . As indicated by the straight vertical line  1645 , the defect  1630  is no longer visible in the recording of the mask segment  1600 . 
     The upper partial image  1705  in  FIG.  17    shows the variation of the CD for the various pattern elements from the top left partial image  1605  in  FIG.  16    along the pattern elements. The dashed line  1710  specifies the CD—predefined by the design—of a pattern element produced on a wafer by use of the mask  1600 ; in the example illustrated in  FIG.  17   , said CD is: CD=37.68 nm. The dashed horizontal lines  1720  and  1730  represent the lower limit and upper limit, respectively, of the permissible CD variation (ΔCD). The CD variation range ΔCD is ±2.5% in the example in  FIG.  17   . The curves in the upper partial image  1705  reveal that the curve  1750  touches the upper limit of the CD tolerance interval and the CD curve  1760  progresses far outside the CD tolerance interval of ±2.5% over the majority of its profile. The maximum of the normalized CD variation for the curve  1760  is: ΔCD/CD=8.6%. 
     The lower partial image  1755  in  FIG.  17    presents the CD variation for the various pattern elements  1620  of the repaired mask segment from the bottom left partial image  1665  in  FIG.  16   . All the CD curve profiles lie within the permissible tolerance interval, that is to say that all the CD curves satisfy the requirement: ΔCD/CD&lt;±2.5%. This means that the repair element  1640  completely compensates for the defect  1630 . 
     The upper partial image  1805  in  FIG.  18    shows a 1D section through a mask segment  1800  with eight pattern elements  1820  in the form of a strip structure, which are arranged on an optically transparent substrate  1810  of the mask  1800 . The eight pattern elements  1820  generate seven optically transparent strips, numbered consecutively from 0 to 6 in the partial image  1805 . The half-pitch of the strip structure on the mask  1800  is 152 nm or 38 nm on a wafer. In the upper partial image  1805 , the second pattern element  1820  from the left has at its right edge a defect  1840  of excess, absorbing and phase shifting molybdenum silicide (MoSi) material. In order to analyze the effect of the defect  1840 , the strip structure of the defective mask segment  1800  represented in the partial image  1805  is simulated. The simulation parameters are: NA=1.35, λ=193 nm, outer σ value: 1.0, inner σ value: 0.88, exposure setting: Disar, polarization: y-direction, pattern: L&amp;S (lines &amp; space) MoSi with 6% absorption at the actinic wavelength. The electromagnetic radiation incident on the mask  1800  is assumed to be coherent. 
     The central partial image  1835  in  FIG.  18    presents the variation of the CD for the seven optically transparent strips  0  to  6  along the strip direction, i.e. perpendicular to the plane of the drawing, in a simulation. In addition, the shift of the center of gravity (CoG) of the optical intensity distribution is ascertained with the aid of the simulation. The dashed horizontal line  1870  represents the target CD predefined for the mask  1800 . The curves in the central partial image  1835  describe the variation of the critical dimension, i.e. ΔCD, along the pattern elements  1820 . The table in the central partial image  1835  summarizes the ΔCD and ΔCoG for the optically transparent strips  0 ,  1  and  2 . The table shows that the variation of the CD for the zeroth strip is 3.1 nm, and is thus significantly greater than the error budget of the mask  1800  of 2.5%. The effect of the defect  1840  on the second optically transparent strip is a consequence of the exposure of the mask  1800  with coherent radiation. The simulation was carried out by use of the rigorous optical imaging program Dr. Litho from the Fraunhofer Institute for Integrated Device Technology (IISB) Erlangen. 
     The enlarged segment  1825  shows the pattern elements  1820  around the defective transparent strip  1  after the repair of the defect  1840  by implementing the corresponding repair shape ascertained for the defect. When implementing the repair shape for local etching of the defect  1840  it is assumed that the local etching process produces a sidewall angle  1850  with a negative angle of −20°. The negative sidewall angle  1860  causes an amplitude defect in an aerial image or during the exposure of a wafer. It is taken into account by a magnification factor MEEF=1.4. The negative sidewall angle  1850  is compensated for by a (positive) shift of the base point  1860  of the edge  1830 , such that the breadth or width of the strip  1  corresponds approximately to half the magnitude of the nominal width of the optically transparent strip. Errors of the sidewall angle, for an angular range of approximately ±20°, can be substantially completely compensated for by use of a corresponding shift of the base point of the edge  1830  of the repaired pattern element  1820 . The lateral shift required for this is in a range of approximately ±3.3 nm for λ=193 nm. 
     The lower partial image  1865  indicates the simulated variation of the CD for the optically transparent strips  0  to  6  along the strip direction. Furthermore, the CoG shift of the optical intensity distribution is determined with the aid of the simulation. The dashed horizontal line  1870  describes the target value of the CD on a wafer. It is immediately evident from a comparison of the sets of curves in the partial images  1835  and  1865  that the repair of the defect  1840  drastically reduces the CD variation. The table in the lower partial image  1865 —in a similar manner to the table in the central partial image  1865 —summarizes the ΔCD and ΔCoG for the optically transparent strips  0 ,  1  and  2 . In comparison with the table in the central partial image  1835 , the repair of the defect  1840  has reduced the CD variation by more than one order of magnitude. 
     The repair of a defect  1840  of excess material has been discussed in association with  FIG.  18   , said defect adjoining the edge  1830  of a pattern element  1820  without completely covering the transparent strip. It goes without saying that it is also possible to repair a defect of excess material that completely bridges two pattern elements. Furthermore, the method explained in the context of  FIG.  18    can also be used for repairing defects of missing material. 
     The flow diagram  1900  in  FIG.  19    describes a first exemplary embodiment of the method discussed in this application for repairing at least one defect  240 ,  750 ,  940 ,  1140 ,  1240 ,  1330 ,  1630 ,  1840  of a lithographic mask  200 ,  400 ,  500 ,  600 ,  700 ,  800 ,  900 ,  1100 ,  1200 ,  1300 ,  1600 ,  1800 . The method begins in step  1910 . In the next step  1920 , parameters of at least one repair shape for the at least one defect  240 ,  750 ,  940 ,  1140 ,  1240 ,  1330 ,  1630 ,  1840  are ascertained, wherein ascertaining parameters comprises: allocating to at least one corresponding parameter a numerical value that deviates from the numerical value predefined by the at least one defect  240 ,  750 ,  940 ,  1140 ,  1240 ,  1330 ,  1630 ,  1840 . The method ends in step  1930 . 
     Furthermore, the flowchart  2000  in  FIG.  20    presents the steps of a second exemplary embodiment of the method for repairing at least one defective pattern element  220 ,  740 ,  840 ,  860 ,  920 ,  1130 ,  1230 ,  1320 ,  1620 ,  1820  of a lithographic mask  200 ,  400 ,  500 ,  600 ,  700 ,  800 ,  900 ,  1000 ,  1100 ,  1200 ,  1300 ,  1600 ,  1800 . The method begins in step  2010 . In the next step  2020 , at least one repair element  410 ,  510 ,  610 ,  770 ,  790 ,  850 ,  870 ,  1010 ,  1170 ,  1190 ,  1270 ,  1290 ,  1440 ,  1540 ,  1640  of the lithographic mask which does not image the lithographic mask during the exposure thereof is determined, wherein the repair element changes an imaging behavior of the at least one defective pattern element. 
     Then, in step  2030 , at least one repair element is produced on the lithographic mask by use of a focused particle beam and at least one precursor gas. The method ends in step  2040 . 
       FIG.  21    schematically shows a section through an apparatus  2100  designed for ascertaining parameters for a repair shape for at least one defect  240 . For this purpose, the apparatus  2100  comprises an optical mask inspection apparatus  2110 .  FIG.  22    illustrates the principle of an optical mask inspection apparatus designed for recording an aerial image of a transmissive mask  200 . Some components of a scanner are illustrated schematically in the left partial image  2205  in  FIG.  22   . An exposure system focuses electromagnetic radiation of the actinic wavelength onto a photolithographic mask. A projection optical unit or a projection lens images the radiation passing through the photomask with reduction (typically 1:4 or 1:5) on a wafer or on a photoresist distributed on the wafer with a large numerical aperture (NA W ). 
     The right partial image  2255  in  FIG.  22    shows some components of an optical mask inspection apparatus  2110  designed for the actinic wavelength of the scanner from the left partial image  2205 . The exposure system of the scanner and of an optical mask inspection apparatus  2110  are substantially identical. This means that the image generation is substantially the same for both systems. The optical mask inspection apparatus  2110  thus images a segment of the optical intensity distribution of a mask such as is incident on a photoresist arranged on the wafer. Unlike in the case of a scanner, however, in the case of an optical mask inspection apparatus  2110  a lens images a small segment of the optical intensity distribution of a photomask with great magnification on a CCD (Charge-Coupled Device) camera. As a result, it becomes possible to represent defects which a photomask has at the actinic wavelength in its aerial image and to detect said defects with the aid of a CCD sensor or a CCD camera. 
     The optical mask inspection apparatus  2110  of the apparatus  2100  can provide the measurement data of one or more aerial images to a computer system  2130  of the apparatus  2100  via the connection  2120 . The computer system  2130  of the apparatus  2100  can ascertain the parameters of a repair shape assigned to the defect of the aerial image from the measurement data of the aerial image(s). For this purpose, the computer system  2130  can comprise a coprocessor  2140  specifically designed to efficiently execute an algorithm that determines the parameters of a repair shape assigned to the defect from the aerial image(s) of the optical mask inspection apparatus. Furthermore, the computer system  2130  of the apparatus  2100  can have a second algorithm designed to allocate to one or more parameters of the repair shape a value or a numerical value that deviates from the numerical value predefined by the defect. The second algorithm can likewise be executed by the coprocessor  2140 . 
     However, it is also possible for the computer system  2130  to have a dedicated hardware component  2150  that executes one or both of the algorithms described above. The hardware component  2150  of the computer system can be implemented in the form of an ASIC (Application Specific Integrated Circuit), a complex programmable logic circuit (CPLD, Complex Programmable Logic Device) and/or a field programmable gate array (FPGA). 
     Additionally or alternatively, the computer system  2130  can comprise a dedicated graphics processor  2160  designed to implement a trained machine learning model. A machine learning model can be trained in at least two ways, or the graphics processor can implement two different trained machine learning models designed for the respective problem formulated. Firstly, a machine learning model can be trained to ascertain from the measurement data of the optical mask inspection apparatus  2110 , from design data of the lithographic mask  200 , settings of the exposure system and optionally of RET structures produced on the mask  200  the parameters of one or more repair shapes implemented in order to repair or to compensate for the defect(s), i.e. in order to generate one or more repair elements  410 ,  510 ,  610 . 
     Alternatively or additionally, a machine learning model, for a repair shape that has already been parametrized, can allocate a different numerical value to one or more parameters for the purpose of ascertaining the above-described repair elements  410 ,  510 ,  610  according to the invention. The currently preferred embodiment, however, is that, from the input data indicated above, a machine learning model directly predicts the parameters of a repair shape for the purpose of forming one of the repair elements  410 ,  510 ,  610  described in this application. The process of training a machine learning model will not be discussed in this application. 
     Furthermore, the computer system  2130  can comprise a non-volatile memory  2170 , in which the algorithm(s), the machine learning model(s), and/or the trained machine learning model(s) are/is stored. The non-volatile memory  2170  can comprise a solid state memory (SSD, Solid State Drive). 
     Furthermore, the computer system  2130  can comprise a control device  2180  designed for controlling the optical mask inspection apparatus  2110 . 
     Furthermore, the apparatus  2100  can comprise a scanning particle microscope, a scanning probe microscope, and/or a confocal microscope, which are designed to scan a defect  240  of a photolithographic mask  200  and to generate a pictorial representation of the measurement data. If the apparatus  2100  comprises one or more of these measuring instruments, the control device  2180  can likewise control these measuring devices. 
       FIG.  23    schematically presents a section through an apparatus  2300  that can repair at least one defective pattern element  220 . For this purpose, the apparatus  2300  comprises an optical mask inspection apparatus  2310 . This type of measuring instruments has already been described above in the context of the discussion of  FIG.  22   . 
     The optical mask inspection apparatus  2310  of the apparatus  2300  can provide the measurement data of one or more aerial images or of an aerial image stack to a computer system  2330  of the apparatus  2300  via the connection  2320 . The computer system  2330  of the apparatus  2300  can be similar to the computer system  2130  of the apparatus  2100  from  FIG.  21   . In order to avoid long drawn-out passages, a description of the computer system  2330  will be dispensed with. Rather, reference is made to the discussion of  FIG.  21   . 
     The apparatus  2300  furthermore comprises a particle beam source  2350 , which can provide a focused particle beam. The focused particle beam of the particle beam source  2350  can be used firstly for analyzing a defect  240  of a photolithographic mask  200 . On the basis of the measurement data of the focused particle beam and/or the measurement data of the optical mask inspection apparatus  2310 , a repair shape for the defect can be determined with the aid of one or more algorithms or one or more machine learning models. Secondly, the focused particle beam of the particle beam source  2350  in combination with the gas providing system  2390  of the apparatus  2300  can be used for repairing the analyzed defect  240 . Both the particle beam source  2350  and the gas providing system  2390  can exchange data with the computer system  2330  via the connections  2340  and  2360 . Furthermore, the control unit  2180  of the computer system  2330  can control the optical mask inspection apparatus  2310 , the particle beam source  2350  and the gas providing system  2390 . 
       FIG.  24    shows a schematic section through an apparatus  2400  that combines a particle beam source  2350  and a gas providing system  2390  of the apparatus  2300 . A repair element  410 ,  510 ,  610  for repairing the defect  240  can be produced by the apparatus  2400 . The exemplary apparatus  2400  in  FIG.  24    comprises a modified scanning particle microscope  2410  in the form of a scanning electron microscope (SEM)  2410 . The apparatus  2400  comprises a particle beam source  2350  in the form of an electron beam source  2405 , which generates an electron beam  2415  as a particle beam having mass  2415 . An electron beam  2415  can be focused to a spot that is significantly smaller than the focus diameter of a photon beam. On account of the small de Broglie wavelength of electrons, the electron beam  2415  can be focused to a spot diameter in the range of a few nanometers. As an analysis or measurement tool, an electron beam  2415  thus has a very great lateral resolution capability. 
     Furthermore, an electron beam  2415 —compared with an ion beam—has the advantage that the electrons incident on the sample  2425 , for example the photolithographic mask  200 , substantially cannot damage the sample  2425  or the photomask  200 . However, it is also possible to use an ion beam, an atomic beam or a molecular beam (not illustrated in  FIG.  24   ) in the apparatus  2400  for the purposes of processing the sample  2425 . 
     The scanning particle microscope  2410  is composed of an electron beam source  2405  and a column  2420 , in which is arranged the beam optical unit  2413  for instance in the form of an electron optical unit of the SEM  2410 . In the SEM  2410  in  FIG.  24   , the electron beam source  2405  generates an electron beam  2415 , which is directed as a focused electron beam  2415  onto the sample  2425 , which can comprise the photolithographic mask  200 , at the location  2422  by the imaging elements arranged in the column  2420 , said imaging elements not being illustrated in  FIG.  24   . The beam optical unit  2413  thus forms the imaging system  2413  of the electron beam source  2405  of the apparatus  2400 . 
     Further, the imaging elements of the column  2420  of the SEM  2410  can scan the electron beam  2415  over the sample  2425 . The sample  2425  can be examined using the electron beam  2415  of the apparatus  2400 . In general, the electron beam  2415  is incident on the sample  2425  perpendicularly. 
     The backscattered electrons and secondary electrons generated in an interaction region or a scattering cone of the sample  2425  by the electron beam  2415  are registered by the detector  2417 . The detector  2417  that is arranged in the electron column  2420  is referred to as an “in lens detector.” The detector  2417  can be installed in the column  2420  in various embodiments. The detector  2417  converts the secondary electrons generated by the electron beam  2415  at the measurement point  2422  and/or the electrons backscattered from the sample  2425  into an electrical measurement signal and transmits the latter to an evaluation unit  2480  of the apparatus  2400 . The evaluation unit  2480  analyzes the measurement signals from the detectors  2417  and  2419  and generates an image of the sample  2425  therefrom, said image being displayed on the display  2495  of the evaluation unit  2480 . The detector  2417  can additionally contain a filter or a filter system in order to discriminate the electrons in terms of energy and/or solid angle (not represented in  FIG.  24   ). 
     The exemplary apparatus  2400  can include a second detector  2419 . The second detector  2419  can be designed to detect electromagnetic radiation, in particular in the X-ray range. As a result, the detector  2419  makes it possible to analyze a material composition of the radiation generated by the sample  2425  during the examination thereof. The detectors  2417  and  2419  can be controlled by the control unit  2180  of the computer system  2330 . In an alternative embodiment, the apparatus  2400  comprises a dedicated control unit (not illustrated in  FIG.  24   ). 
     Further, the apparatus  2400  can comprise a third detector (not illustrated in  FIG.  24   ). The third detector can be embodied in the form of an Everhart-Thornley detector and is typically arranged outside the column  2420 . In general, it is used to detect secondary electrons. 
     The apparatus  2400  can comprise an ion source that provides ions with low kinetic energy in the region of the sample  2425  (not represented in  FIG.  24   ). The ions with low kinetic energy can compensate for charging of the sample  2425 . 
     The sample  2425  is arranged on a sample stage  2430  or a sample holder  2430  for examination purposes. A sample stage  2430  is also known as a “stage” in the art. As symbolized by the arrows in  FIG.  24   , the sample stage  2430  can be moved in three spatial directions relative to the column  2415  of the SEM  2410 , for example by way of micro-manipulators that are not illustrated in  FIG.  24   . 
     Besides the translational movement, the sample stage  2430  can be rotated at least about an axis oriented parallel to the beam direction of the particle beam source  2405 . It is furthermore possible for the sample stage  2430  to be embodied such that it is rotatable about one or two further axes, this axis or these axes being arranged in the plane of the sample stage  2430 . The two or three axes of rotation preferably form a rectangular coordinate system. 
     The sample  2425  to be examined can be any arbitrary microstructured component or device that requires analysis and, if appropriate, subsequent processing, for example the repair of a local defect  240  of a pattern element  220  of a photolithographic mask  200 . 
     Further, the apparatus  2400  in  FIG.  24    can comprise one or more scanning probe microscopes, for example in the form of an atomic force microscope (AFM) (not shown in  FIG.  24   ), which can be used to analyze and/or process the sample  2425 . 
     The scanning electron microscope  2410  illustrated by way of example in  FIG.  24    is operated in a vacuum chamber  2470 . In order to generate and maintain a reduced pressure required in the vacuum chamber  2470 , the SEM  2410  in  FIG.  24    has a pump system  2472 . 
     The gas providing system  2390  realized by the apparatus  2400  is discussed below. As already explained above, the sample  2425  is arranged on a sample stage  2430 . The imaging elements of the column  2420  of the SEM  2410  can focus the electron beam  2415  and scan the latter over the sample  2525 . The electron beam  2415  of the SEM  2410  can be used to induce a particle beam-induced deposition process (EBID, electron beam induced deposition) and/or a particle beam-induced etching process (EBIE, electron beam induced etching). The exemplary apparatus  2400  in  FIG.  24    has three different supply containers  2440 ,  2450  and  2460 , for storing various precursor gases, for the purposes of carrying out these processes. 
     The first supply container  2440  stores a precursor gas, for example a metal carbonyl, for instance chromium hexacarbonyl (Cr(CO) 6 ), or a main group metal alkoxide, such as TEOS, for instance. With the aid of the precursor gas stored in the first supply container  2440 , material missing from the photolithographic mask  200  can be deposited thereon within the scope of a local chemical deposition reaction, for example. Missing material of a mask  200  can comprise missing absorber material, for example chromium, missing substrate material  210 , for instance quartz, missing material of an OMOG mask, for instance molybdenum silicide, or missing material of a multilayer structure of a reflective photomask, for instance molybdenum and/or silicon. 
     The electron beam  2415  of the SEM  2410  acts as an energy supplier for splitting the precursor gas, which is stored in the first supply container  2440 , at the site where material is intended to be deposited on the sample  2425 . This means that the combined provision of an electron beam  2415  and a precursor gas leads to an EBID process being carried out for local deposition of missing material, for example material missing from the photomask  200 . The modified SEM  2410  of the apparatus  2400  in combination with the precursor gas stored in the first supply container  2440  can comprise an apparatus for producing a repair element  410 ,  510 ,  610  on a photolithographic mask. 
     As already explained above, an electron beam  2415  can be focused to a spot diameter in the range of a few nanometers. The interaction region or the scattering cone in which an electron beam  2415  generates secondary electrons depends firstly on the energy of the electron beam  2415  and secondly on the material composition on which the electron beam  2415  impinges. The diameters of interaction regions attain values in the low single-digit nanometer range. The diameter of a scattering cone of an electron beam  2415  thus limits the achievable resolution limit during the generation of a repair element  410 ,  510 ,  610  by implementing the corresponding repair shape. Said resolution limit at the present time is in the single-digit nanometer range. 
     In the apparatus  2400  illustrated in  FIG.  24   , the second supply container  2450  stores an etching gas, which allows a local electron beam-induced etching (EBIE) process to be carried out. With the aid of an electron beam-induced etching process, excess material can be removed from the sample  2425 , for instance the excess material of the pattern element  860  can be removed from the photolithographic mask  800 . By way of example, an etching gas can comprise xenon difluoride (XeF 2 ), a halogen or nitrosyl chloride (NOCl). The particle beam source  2350  in combination with the gas providing system  2390  thus forms an apparatus  2400  for producing a repair element  410 ,  510 ,  610 . 
     An additive or additional gas can be stored in the third supply container  2460 , said gas, where necessary, being able to be added to the etching gas kept available in the second supply container  2450  or to the precursor gas stored in the first supply container  2440 . Alternatively, the third supply container  2460  can store a second precursor gas or a second etching gas. 
     In the apparatus  2400  illustrated in  FIG.  24   , each of the supply containers  2440 ,  2450  and  2460  has its own control valve  2442 ,  2452  and  2462  in order to monitor or control the amount of the corresponding gas that is provided per unit time, i.e., the gas volumetric flow at the site  2422  of the incidence of the electron beam  2415  on the sample  2425 . The control valves  2442 ,  2452  and  2462  can be controlled and supervised by the control unit  2180  of the computer system  2330 . It is thus possible to set the partial pressure ratios of the gas or gases provided at the processing location  2422  for carrying out an EBID and/or EBIE process in a wide range. 
     Furthermore, in the exemplary apparatus  2400  in  FIG.  24   , each supply container  2440 ,  2450  and  2460  has its own gas feedline system  2445 ,  2455  and  2465 , which ends with a nozzle  2447 ,  2457  and  2467  in the vicinity of the point of incidence  2422  of the electron beam  2415  on the sample  2425 . 
     The supply containers  2440 ,  2450  and  2460  can have their own temperature setting element and/or control element, which allows both cooling and heating of the corresponding supply containers  2440 ,  2450  and  2460 . This makes it possible to store and in particular provide the precursor gas at the respectively optimum temperature (not shown in  FIG.  24   ). The control unit  2180  can control the temperature setting elements and the temperature control elements of the supply containers  2440 ,  2450 ,  2460 . During the EBID and the EBIE processing processes, the temperature setting elements of the supply containers  2440 ,  2450  and  2460  can further be used to set the vapor pressure of the precursor gases stored therein by way of the selection of an appropriate temperature. 
     The apparatus  2400  can comprise more than one supply container  2440  in order to store two or more precursor gases. Further, the apparatus  2400  can comprise more than one supply container  2450  in order to store two or more etching gases (not shown in  FIG.  24   ).