Patent Publication Number: US-2023152089-A1

Title: Method and device for determining an alignment of a photomask on a sample stage which is displaceable along at least one axis and rotatable about at least one axis

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/EP2021/071439, filed on Jul. 30, 2021, which claims priority from German patent application DE 10 2020 209 638.4, entitled “Verfahren und Vorrichtung zum Bestimmen einer Ausrichtung einer Fotomaske auf einem Probentisch, der entlang zumindest einer Achse verschiebbar und zumindest um eine Achse drehbar ist,” filed on Jul. 30, 2020. 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 a device for determining an alignment of a photomask on a sample stage which is displaceable along at least one axis and rotatable about at least one axis. In particular, the present invention relates to a method and a device for determining an alignment of a photomask on a sample stage which is displaceable along at least one axis that is parallel to a chuck surface, and is rotatable about at least one axis that is perpendicular to the chuck surface of the sample stage. 
     BACKGROUND 
     As a consequence of the growing integration density in the semiconductor industry, photolithography masks have to image increasingly smaller structures on wafers. Producing the small structure dimensions imaged onto the wafer requires photolithographic masks or templates for nanoimprint lithography with ever smaller structures or pattern elements. The process for producing photolithographic masks and templates for nanoimprint lithography is therefore 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 of photolithographic masks or templates, faults during mask or template production cannot be ruled out. These must be repaired—whenever possible. 
     Faults or defects of photolithographic masks, photomasks, exposure masks, or just masks, are often repaired by providing one or more process or precursor gases at the repair location and scanning the defect with an electron beam, for example. The electron beam usually induces a local chemical reaction which, depending on the precursor gas used, results in a local etching process that can be used to remove locally excess material from the photomasks or a template for nanoimprint lithography. Alternatively, in the presence of a corresponding precursor gas, the electron beam induces a local chemical deposition reaction that deposits material locally on the photomask and thus replaces locally missing material of the mask. 
     A further cause of defects of photolithographic masks is particles that arise for instance as a result of the handling of the mask and deposit on the mask. These particles that disturb the imaging of the mask must likewise be removed from the mask. Disturbing particles can be removed from the photomask firstly with the aid of a local particle beam-induced etching process. Furthermore, it is possible to use a micromanipulator, for example in the form of a scanning probe microscope, in order to remove excess material, for instance particles present on the mask, from the photomask by use of mechanical processing of the particle. 
     On account of the increasingly smaller structures of photomasks and the decreasing actinic wavelength with which masks are exposed, ever smaller defects and/or ever smaller particles are having a disturbing effect on the imaging behavior of photomasks. In this regard, in the case of masks for the extreme ultraviolet (EUV) wavelength range, for instance, the actinic wavelength is in a range of approximately 10 nm to 15 nm. This means that ever better tools for processing defects of photolithographic masks are required. Furthermore, this development has the consequence that the requirements in respect of the precision with which identified defects must be able to be approached for repair purposes are likewise increasing. 
     Owing firstly to the increasing requirements in respect of precision and secondly to extended possibilities for movement of the sample stage, the exact alignment or calibration of a mask in relation to the sample stage or the mask plate is becoming increasingly more complex and more costly. As a result, the alignment or the calibration of a mask to be repaired on a sample stage is increasingly influencing the repair times of defective masks. As a result, said repair times are becoming longer or the throughput of masks to be repaired is becoming lower. 
     Therefore, the problem addressed by the present invention is that of specifying a method and a device which improve the determining of an alignment of a photomask. 
     SUMMARY 
     In accordance with one exemplary embodiment of the present invention, this problem is at least partly solved by means of the subjects of the independent claims of the present application. Exemplary embodiments are described in the dependent claims. 
     A first embodiment relates to a method for determining an alignment of a photomask on a sample stage which is displaceable along at least one axis that is parallel to a chuck surface of the sample stage, and is rotatable about at least one axis that is perpendicular to the chuck surface. The method comprises the following step: rotating the sample stage by a predefined angle and measuring a height change of the photomask during rotation at a predetermined, non-vanishing distance with respect to the rotation axis for the purpose of determining the alignment of the photomask on the sample stage. 
     A sample stage for a photomask typically has three translation axes that are perpendicular to one another. A sample stage which carries a photomask to be repaired, and which is not just displaceable in three directions, but rather is additionally rotatable about an axis perpendicular to the surface of the sample stage, extends the possibilities of defect repair by virtue of the fact that a defect can be imaged and/or processed from different sides. Moreover, defects having specific contours can be tracked to a processing location by use of a combined rotational and translational movement in a simpler form, compared with movements composed of two mutually perpendicular displacements. 
     The inventors have discovered, however, that a rotation of the sample stage about the z-axis perpendicular to the chuck surface can result in a height change at a processing location situated outside the rotation axis. The height change of the photomask is caused by a rotation axis that is not aligned perpendicular to the surface of the mask. A rotation axis that is not perpendicular to the mask results in a wobble movement of the photomask during the rotation thereof. As a result, the tool processing a defect can be positioned incorrectly in the z-direction, i.e. perpendicular to the chuck surface. In the worst case, as a result, during a rotational movement of the sample stage, a repair tool may damage a non-defective mask location as a result of unintended mechanical contact. 
     The method according to the invention determines the height change caused by a rotation of the sample stage at a defect processing location on the photomask. The defect processing location can be localized at any desired position on the mask. As a result, the method according to the invention fully exploits the improved defect repair possibilities resulting from the rotatable sample stage. Moreover, the method according to the invention avoids unintended damage to a photomask during a rotation process. 
     The sample stage can be rotated by an angle that is greater than or equal to: 60°, preferably 90°, more preferably 180°, and most preferably 360°. 
     As the rotation angle increases, there is an increase in the accuracy with which it is possible to determine the height change or a height profile of the photomask during rotation. It is therefore advantageous to choose the rotation angle to be as large as possible, i.e. approximately 360°. Rotations with an even greater rotation angle merely improve the data recording statistics. 
     A photomask can comprise a transmissive photomask or a reflective photomask. A transmissive mask can comprise an arbitrary conventional photomask, such as, for instance, a binary mask, a phase shifting mask or a mask for multiple exposure. A reflective photomask can comprise a mask for the extreme ultraviolet (EUV) wavelength range, in particular a binary mask or a phase shifting mask. However, a photomask can also comprise a template for nanoimprint lithography. 
     The sample stage can be the sample stage of a repair tool. In particular, the repair tool can induce a local etching and/or deposition process. Furthermore, the repair tool can comprise one or more scanning probe microscopes that can be used as manipulators or micromanipulators for processing a defect. 
     The height change can be measured by at least one height sensor. 
     The method according to the invention can comprise the additional step of predetermining the non-vanishing distance with respect to the rotation axis. Furthermore, the method according to the invention can comprise the additional step of determining coordinates of the rotation axis on a surface of the photomask. 
     Determining the coordinates of the rotation axis can comprise: (a) Measuring a first set of coordinates for at least two markings of the photomask by use of a particle beam of at least one particle beam source, without rotating the photomask; (b) Rotating the photomask by an angle 0°&lt;0&lt;180° or 180°&lt;0&lt;360°; and (c) Measuring a second set of coordinates for the at least two markings of the rotated photomask by use of the particle beam of the particle beam source. 
     A photomask usually has a number of markings that are typically applied at regular intervals on that side of the mask which is structured by the pattern. Each of the markings generally has a reference point. The mask coordinates (u, v), which are typically specified by the mask manufacturer, refer to said point. The coordinates (u D , v D ) of a defect of the mask are also referred to these reference points. In order to maximize the measurement accuracy when measuring the two reference points of the markings, it is advantageous to use markings which are at the greatest possible distance from one another on the photomask. 
     On the basis of the two measured coordinate sets of two markings, wherein the photomask is rotated before the second set is measured, the coordinates of the rotation axis of the photomask can be ascertained. 
     Furthermore, determining the coordinates of the rotation axis can comprise: lowering the sample stage before approaching the at least two markings for the purpose of measuring the first and/or the second set of coordinates, and/or before rotating the sample stage. 
     This measure prevents the particle beam source and/or the one or more scanning probe microscopes or the micromanipulators thereof from being able to make contact unintentionally with the surface of the photomask during the movement of the photomask. 
     Determining the coordinates of the rotation axis can comprise: determining the coordinates of the rotation axis from the first and second sets of measured coordinates of the at least two markings. 
     Choosing a rotation angle in the region of 90° optimizes the accuracy when determining the rotation axis or when determining the coordinates of the rotation axis. It is therefore advantageous to choose an angle in the region of 90° for the rotation of the photomask. 
     Measuring the at least two markings can be effected by use of the at least one particle beam source configured to generate at least one focused particle beam from the following group: a photon beam, an electron beam, an ion beam, an atomic beam and a molecular beam. 
     The electron beam of a scanning electron microscope (SEM) or of a modified SEM is often used for measuring the markings, or for the reference points thereof. An electron beam can be focused to a very small spot (Ds&lt;1 nm). This enables a very high lateral resolution when determining the reference points of the markings. Moreover, imaging the markings with an electron beam causes no or only very little damage to the markings and thus to the photomask overall. The markings can be imaged manually and/or in an automated form. By way of example, this can be done by centering a specific structure of the marking, for instance the reference point thereof, in the SEM image. After centering the electron beam in relation to the marking, the measuring transducers of the sample stage indicate the coordinate values sought. 
     Predetermining the non-vanishing distance with respect to the rotation axis can comprise: determining coordinates of a point of incidence of the particle beam of the at least one height sensor on the photomask. The particle beam of the at least one height sensor can comprise a massless particle beam, for example a photon beam or a light beam, and/or a particle beam having mass, for example an electron beam. 
     For accurately ascertaining the height change of the photomask during the rotation of the sample stage, it is necessary to know the distance between the coordinates of the rotation axis and the coordinates of the point of incidence of the particle beam of the height sensor on the photomask. Measuring this distance makes it possible to determine the radius of the circle or of the circle segment of the point of incidence of the particle beam of the height sensor on the photomask during the rotation of the sample stage and thus of the photomask during the measurement of the height change. 
     Determining the coordinates of the point of incidence of the particle beam of the at least one height sensor can comprise: scanning the sample stage for the purpose of centering the at least one height sensor over the at least one of the at least two markings. 
     Scanning the sample stage can comprise a scan path adapted to one of the at least two markings. 
     Scanning the sample stage can comprise displacing the sample stage, without rotating the sample stage. Scanning the sample stage can comprise: (a) first scanning of the sample stage in a diagonal direction with respect to a marking to be scanned; (b) displacing the scan path for a second scan by a predefined distance perpendicular to the first scan path; and (c) repeating step (b) until the repeated scan meets a reference point of the scanned marking. 
     Furthermore, scanning the sample stage can comprise: rotating the sample stage, such that a scanned circle segment covers at least one part of at least one of the at least two markings. 
     Furthermore, scanning the sample stage can comprise: Carrying out the scanning so that a scan time for centering the at least one height sensor attains a minimum value. 
     Identifying a reference point of a marking is a complicated process. In contrast to the particle beam of the particle beam source, the particle beam of the height sensor cannot be scanned over the photomask. Rather, a large portion of the sample stage carrying the mask, including the photomask itself, has to be moved in order to determine the position at which the reference point of the marking of the photomask becomes located under the point of incidence of the particle beam of the height sensor. It is therefore very advantageous to choose the scanning of the sample stage so as to minimize the length of the required scan path and thus the time required for scanning. 
     Measuring the height change can comprise: displacing the rotation axis under a point of incidence of the particle beam of the at least one particle beam source on the photomask. 
     Measuring the height change can comprise: displacing the coordinates of the rotation axis under a point of incidence of the particle beam on the photomask. 
     By means of determining the coordinates of the rotation axis on the photomask, it is possible to ascertain the distance between the height sensor and the rotation axis, as explained above, and the radius of the circle or of the circle segment on which the point of incidence of the particle beam of the height sensor runs around the rotation axis during the measurement of the height change is thus known. 
     The method according to the invention can furthermore comprise the following step: interpolating and/or extrapolating the measured height change of the photomask for a value deviating from the predetermined, non-vanishing distance. Interpolating and/or extrapolating the measured height change can comprise: fitting the measured height change to a mathematical model. Fitting the measured height change to the mathematical model can comprise a fit to function curves. 
     The method can additionally comprise the following step: interpolating and/or extrapolating the measured height change of the photomask for a distance that does not correspond to the distance between the points of incidence of the at least one particle beam of the particle beam source and the particle beam of the at least one height sensor, for the purpose of determining a height change of an arbitrary position on the photomask. Interpolating and/or extrapolating can comprise linear interpolating and/or linear extrapolating. 
     Measuring the height change can furthermore comprise: determining an orientation of the rotation axis in relation to a perpendicular to the mask of the sample stage and/or determining a maximum height change during the rotation of the sample stage. 
     The perpendicular to the chuck surface of the sample stage corresponds to the z-axis of the coordinate system of the sample stage. A deviation of the orientation of the rotation axis with respect to the perpendicular to the chuck surface or a tilting of the rotation axis relative to the z-axis does not per se result in a height change measured by the at least one height sensor during the rotation of the photomask as a result of rotation of the sample stage. Rather, a height change of the photomask when a rotation of the sample stage is carried out is caused only if the rotation axis of the sample stage is not aligned perpendicularly to the surface of the photomask, i.e. if the rotation axis has a tilting relative to the normal to the mask. 
     Moreover, measuring the height change can comprise: setting the at least one height sensor to a central position of its measurement region before the rotation of the sample stage. This ensures that the height sensor can detect the entirety of the height change during the rotation of the sample stage. 
     The method according to the invention can furthermore comprise the following step: measuring a z-coordinate of the photomask on the rotation axis. Moreover, the method according to the invention can comprise the following step: measuring a z-coordinate of the photomask at the coordinates of the rotation axis. 
     The sample stage can be displaceable along at least two axes that are parallel to the chuck surface, and the method according to the invention can furthermore comprise the following steps: (a) Measuring coordinates of at least two markings by use of a particle beam of at least one particle beam source, without rotating the photomask with the sample stage; and (b) Determining an affine transformation between a coordinate system of the photomask and a coordinate system of the sample stage. The coordinate system associated with the sample stage can be the coordinate system related to the chuck surface. 
     The method for determining an alignment of a photomask can be divided into at least two steps. The sequence of the two steps can be chosen as desired. It is assumed hereinafter that the two steps do not mutually influence one another. In one step, the mask coordinates u, v assigned to the mask design, said mask coordinates typically being made available by the mask manufacturer and thus forming the coordinate system assigned to the photomask, are put into a one-to-one relationship with a coordinate system (x, y) associated with the sample stage. This is preferably the coordinate system related to the chuck surface of the sample stage. A further step involves—as explained above—ascertaining the effect of a rotation axis that is not oriented perpendicularly to the surface of the mask. For this purpose, the photomask is rotated by a predefined angle by the sample stage and the height change that occurs in the process is measured. From the measurement data, it is possible to ascertain a height change of the mask during the rotation thereof and/or the displacement thereof. 
     After the method according to the invention has been carried out, the coordinates of a defect u D , v D , which are typically specified in mask coordinates, can be converted into the coordinate system of the sample stage x D , y D , z D  as a function of the rotation angle θ. In particular, it is possible to ascertain a height position of the mask or of the defect at the repair position thereof. The sample stage can bring the photomask positioned thereon to an envisaged repair location of the defect. Furthermore, the repair tool can be positioned with great precision for processing the defect. 
     The method according to the invention can furthermore comprise the following step: determining an affine transformation between a coordinate system of the photomask and a coordinate system of the sample stage from the first set of coordinates of the at least two markings of the photomask. 
     For reasons of economy in the method, it is expedient for the first measured coordinate set of the two markings, which were measured for determining the coordinates of the rotation axis, to be used again for determining the affine transformation. However, it is also possible to choose two new markings of the photomask and to measure them with the particle beam of the at least one particle beam source. 
     Determining the affine transformation can comprise: determining the parameters of a translation, a scaling and a rotation of the coordinate systems of the photomask and of the sample stage with respect to one another on the basis of the measured coordinates of the at least two markings. 
     On the basis of two measured reference points x 1 , y 1  and x 2 , y 2  of two markings and two reference points u 1 , v 1  and u 2 , v 2  that are predefined by the mask manufacturer in the mask coordinate system, it is possible to determine four parameters: two parameters (a, b) of a displacement, one parameter of a rotation (α) and one parameter of a scaling (s). 
     Determining the affine transformation can comprise: measuring coordinates of at least three markings of the photomask and determining the parameters of a translation, a scaling, a rotation, a shear and a parallel stretching of the coordinate systems of the photomask and of the sample stage. Arbitrary combinations of the affine transformations listed can be described with the aid of a 2×3 matrix. Determining the six matrix coefficients requires six equations that can be ascertained by the measurements of at least three markings. 
     Six parameters can be determined with the aid of six equations. Besides the four parameters already determined above, these are the parameters of a shear and a parallel stretching. 
     The at least one height sensor and/or the at least one particle beam source can be in a known relationship with the coordinate system of the sample stage. 
     The sample stage can be displaceable along at least two axes that are parallel to a chuck surface of the sample stage, and the method according to the invention can furthermore comprise the following step: measuring a height difference of at least three points on the photomask that do not lie on a straight line by use of the at least one height sensor, without rotating the sample stage. 
     The method according to the invention can furthermore comprise the following step: interpolating and/or extrapolating the height difference at a position of the photomask that deviates from the three measured points from the measured height difference. Interpolating and/or extrapolating can comprise linear interpolating and/or linear extrapolating. 
     The interpolating and/or extrapolating step makes it possible to calculate the height of each point of the photomask on account of a skew position or an oblique position of the mask from the measurement data of the three measured points. 
     The method of determining an alignment of a photomask can thus be divided into three parts. The order in which the individual parts of the method are carried out can be chosen as desired. It is expedient, however, for the part mentioned last to be carried out first. On the basis of the measured height difference, it is possible—as already described above—to ascertain an oblique or skewed position of the photomask on the sample stage. 
     This position can be taken into account when carrying out the measurements for the further parts of the method. It is thus possible reliably to prevent damage to the mask when carrying out translational movements of the mask that are carried out in order to bring said mask to the positions required for the measurements. 
     After the method according to the invention has been carried out, the coordinates of a defect (u D , v D ), which are typically specified in mask coordinates, can be converted into the coordinate system of the sample stage (x D , y D , z D ). In particular, it is possible to ascertain a height position of the mask or of the defect at the repair position thereof. The sample stage can bring the photomask positioned thereon to an envisaged repair location of the defect. Furthermore, the repair tool can be positioned with great precision for processing the defect. 
     The z-coordinate or the height of a point on the front side of the mask, i.e. the side that carries a pattern, is composed of three contributions: (a) the height of the photomask at the position of the rotation axis, (b) a height change of the point under consideration in relation to the rotation axis on account of an oblique position of the mask, and (c) a height change of the point under consideration in relation to a rotation on account of a rotation axis not directed perpendicularly to the surface of the mask. The actual z-coordinate of the point under consideration results from addition of these three contributions. The three contributions are additive and are dependent on the rotation angle θ. 
     In a first embodiment, a device for determining an alignment of a photomask on a sample stage which is displaceable along at least one axis that is parallel to a chuck surface of the sample stage, and is rotatable about at least one axis that is perpendicular to the chuck surface, comprises: at least one height sensor configured for measuring a height change during rotation of the sample stage by a predefined angle, wherein the at least one height sensor is at a predetermined, non-vanishing distance with respect to the rotation axis, for the purpose of determining the alignment of the photomask on the sample stage. 
     The height sensor can comprise a chromatic confocal sensor. The height sensor can furthermore comprise at least one element from the group: an optical microscope, a capacitive distance sensor, an interferometer and a scanning probe microscope. A scanning probe microscope can comprise an atomic force microscope (AFM), a scanning tunneling microscope (STM), a magnetic force microscope, a scanning near-field optical microscope and a scanning near-field acoustic microscope. Furthermore, the height sensor can comprise a scanning electron microscope (SEM). 
     The device can be configured to carry out the steps of the method according to the invention. The device can be configured to carry out the method according to the invention in an automated form. In particular, the device can be configured to automatically carry out different aspects of the method according to the invention by themselves or in combination with other aspects. 
     Finally, a computer program can comprise instructions which, when they are executed by a computer system, cause the computer system to carry out the method steps of the method described above. 
    
    
     
       DESCRIPTION OF DRAWINGS 
       The detailed description that follows describes currently preferred exemplary embodiments of the invention with reference to the drawings, wherein: 
         FIG.  1    illustrates a schematic view of an exemplary sample stage having three translation axes and one rotation axis; 
         FIG.  2    presents a schematic section through the exemplary sample stage from  FIG.  1   ; 
         FIG.  3    represents the various coordinates of the coordinate systems within an exemplary sample stage and the coordinate system associated with a photomask; 
         FIG.  4    elucidates a skew position of the photomask on the sample stage from  FIG.  1   , and schematically illustrates a particle beam source for scanning markings of the photomask and a height sensor for measuring a z-coordinate of the photomask; 
         FIG.  5    schematically illustrates the measurement of the z-coordinate by use of the height sensor for various mask patterns; 
         FIG.  6    illustrates a plan view of one type of a marking with the associated reference point thereof; 
         FIG.  7    shows a plan view of an exemplary photomask having three markings; 
         FIG.  8    illustrates a first example of the scanning of a height sensor within the marking from  FIG.  6   ; 
         FIG.  9 A  illustrates the first part of the flow diagram of the scanning of the height sensor in accordance with the first example from  FIG.  8   ; 
         FIG.  9 B  reproduces the second part of the flow diagram of the scanning of the height sensor in accordance with the first example from  FIG.  8   ; 
         FIG.  10    elucidates a second example of the scanning of a height sensor within the marking from  FIG.  6   ; 
         FIG.  11    shows a plan view of the photomask from  FIG.  7    in a state rotated by 90°; 
         FIG.  12    presents a plan view of the photomask from  FIG.  7    after a rotation with an arbitrary rotation angle; 
         FIG.  13    schematically elucidates a translation induced by a rotation; 
         FIG.  14    illustrates a skew position of a photomask on the sample stage and represents a rotation axis that is not oriented perpendicularly to the mask, and therefore results in a wobble movement of the photomask during the rotation thereof; 
         FIG.  15    shows in the upper partial image a plan view of the mask from  FIG.  7   , in which at a distance do from the rotation axis the height change and the height profile during the rotation of the mask are measured, and illustrates in the lower partial image a deviation of the orientation of the rotation axis from the perpendicular to the photomask; 
         FIG.  16    shows one example of a height profile as a function of the rotation angle for a rotation axis that is not aligned perpendicularly to the mask; 
         FIG.  17    represents a flow diagram of the method according to the invention for determining an alignment of a photomask on a sample stage; 
         FIG.  18 A  shows the first part of the flow diagram from  FIG.  17    with details being specified to a greater degree; and 
         FIG.  18 B  illustrates the second part of the flow diagram from  FIG.  17    with details being specified to a greater degree. 
     
    
    
     DETAILED DESCRIPTION 
     Currently preferred embodiments of the method according to the invention and of the device according to the invention are explained below. The method according to the invention will be explained in detail on the basis of determining an alignment of a photomask on a sample stage which, besides three translation axes, additionally has one rotation axis. For applying the method described here, it is not necessary for a sample stage to have three translation axes; one displacement axis parallel to a sample receiving surface and one rotation axis aligned perpendicularly to the sample receiving surface are sufficient for this. Furthermore, the method according to the invention and the device according to the invention are not limited to the alignment of a photomask on a sample stage. Rather, they can be used not only for aligning templates for nanoimprint lithography but also for aligning arbitrary components in microsystems technology if said components have markings. 
       FIG.  1    shows a schematic view of an exemplary sample stage  100  having three translation axes and one rotation axis. The translation axes are substantially mutually perpendicular to one another and thus form an orthogonal coordinate system. The sample stage  100  hereinafter is also called mask stage  100  or stage  100 . The baseplate  110  of the sample stage  100  has rails  120  for displacing the chuck surface of the sample stage  100  in the y-direction. The slide  130  of the sample stage  100  can be moved on the rails  120  along the y-axis. On its top side, the slide  130  carries rails  140  enabling a second slide  150  of the sample stage  100  to be displaced along the x-direction. The second slide  150  forms the baseplate  160  for the displacing unit  170  in the z-direction. The rotation axis  180  is arranged on the displacing unit  170  of the sample stage  100  for the z-direction, said rotation axis being oriented or aligned parallel to the z-direction. The rotation axis  180  carries the chuck  190 , the mask holder  190  or the mask plate  190 . Hereinafter the chuck surface  195  of the chuck  190  denotes the sum of the points on which a photomask, on its underside, which has no pattern, bears on the chuck  190 . 
     Here—and also elsewhere in the description—the expression “substantially” denotes a measurement variable within the margin of error thereof if measuring devices in accordance with the prior art are used for measuring the variable. 
     The diagram  200  in  FIG.  2    presents a schematic section through the sample stage  100  from  FIG.  1   . The coordinate systems of the sample stage  100  are additionally indicated on the left-hand side. The coordinate system x b , y b , z b  relates to the baseplate  205  of the sample stage  100  from  FIG.  1   . 
     The baseplate  205  carries the rails  210  for displacing the slide  215  in the y-direction, oriented perpendicularly to the plane of the drawing. The slide  215  has on its top side the rails  220  for moving the second slide  225  in the x-direction. The second slide  225  forms the baseplate for the displacing unit  235  in the z-direction. The displacing unit  235  is fixed on the second slide  225  with the aid of the securing pins  230 . By displacing the wedges  237 , the upper plate  245  can be moved in the z-direction. 
     On the upper plate  245  bearing on the displacing unit  235 , the rotation axis  250  is in turn fixed with the aid of the pins  255 . The coordinate system associated with the top side of the upper plate  245  is abbreviated hereinafter with x w , y w , z w . The rotation axis  250  of the sample stage  100  from  FIG.  1    is oriented in the z-direction. As already explained above, the rotation axis  250  carries the chuck  260  or the chuck surface  265 . The chuck  260  can comprise a three-point mounting. However, it is also possible for the chuck  260  to fix a photomask  270  on the chuck  260  with the aid of electrostatic forces (electrostatic chuck) or by generating a vacuum (vacuum chuck). The coordinates associated with the top side of the chuck  260  are designated hereinafter as x ch , y ch , z ch . 
     The chuck  260  or the mask plate  260  carries the photomask  270 . The mask  270  can be a transmissive mask or a reflective mask. A photomask  270  typically comprises at least a substrate  275  and a pattern  280 . The substrate  275  can comprise a quartz substrate and/or a material with a low coefficient of thermal expansion (LTE (low thermal expansion) substrate). The pattern  280  can be the pattern of a binary photomask  270 . In this case, the pattern  280  can comprise an absorber structure and can comprise chromium, for example. However, the pattern  280  can also comprise the pattern  280  of a phase shifting photomask  270 . A phase shifting mask  270  can be produced for example by etching a corresponding pattern  280  into the substrate  275  of the mask  270 . Furthermore, it is possible for the pattern  280  to comprise structure elements which both shift the phase of the actinic radiation relative to the radiation incident on the substrate  275  and absorb part of the light at the actinic wavelength that is incident on the pattern  280 . Examples thereof are OMOG (opaque MoSi (Molybdenum Silicide) On Glass) masks. 
     Reflective masks  270  comprise photomasks for the extreme ultraviolet (EUV) wavelength range, having an actinic wavelength that is typically in the range of 10 nm to 15 nm. EUV masks can be embodied as binary masks and/or as phase shifting masks. 
     The arrow u directed towards the right describes the u-coordinate of the mask coordinate system in  FIG.  2   . The coordinates x c h and y c h can be measured by use of the particle beam  285  of the particle beam source  290  and can be put into a relationship with the coordinate system x b , y b , z b  of the baseplate  110 ,  205 . The particle beam source  290  is in a known relationship with the baseplate  110 ,  205  of the sample stage  100 . This relationship is symbolized by the double-headed arrow  277  in  FIG.  2   . 
     The diagram  300  in  FIG.  3    represents schematically again the various intermediate stages of the coordinate systems within the sample stage  100  as far as the coordinate system of the photomask  270 . As indicated in block  310 , the coordinate system related to the baseplate  205  of the sample stage  100  is designated by x b , y b , z b , wherein the letter b stands for “base.” The double-headed arrow  320  in  FIG.  3    symbolizes the transition from the baseplate  205  of the sample stage  100  to the top side of the upper plate  245 , to which the rotation axis  250  is fitted. As indicated in block  330 , the associated coordinate system is abbreviated to x w , y w , z w , wherein the index w stands for “wedge.” Relative to the coordinate system of the baseplate  110 ,  205 , the coordinate system x w , y w , z w  can have translations in all three spatial directions. 
     The double-headed arrow  340  elucidates the transition from the coordinate system associated with the upper plate  245  to the coordinate system of the chuck  260 . This coordinate system has—relative to the coordinate system of the baseplate—besides three translation coordinates a rotation angle θ describing the rotation of the sample stage  100  and thus of the photomask  270  about the rotation axis  250  of the sample stage  100 : x ch , y ch , z ch , θ. The index “ch” stands for the chuck  260 : “chuck”. This coordinate system is indicated in the block  350  in  FIG.  3   . The coordinate system associated with the chuck  260  can have a rotation θ about the rotation axis  250  relative to the coordinate system coupled to the upper plate  245 . 
     Finally, the double-headed arrow  360  symbolizes the transition from the coordinate system of the sample receptacle or the chuck  190 ,  260  to the coordinate system associated with the photomask  270 : u, v, w, θ. As explained above, the associations of the various coordinate systems within the sample stage  100  are known. This means that the position of the particle beam  285  of the particle beam source  290  is in a known relationship with the coordinate system of the baseplate  110 ,  205  of the sample stage  100 . 
     The reference point of the focused electron beam  285  of the SEM  290  can be chosen such that the following holds true: u=0, v=0, w=0, θ=0. After a corresponding adjustment the electron beam  285  of the SEM  290  is typically circular and thus rotationally invariant. If a rotation about the rotation axis  250  does not occur, the coordinate systems of the mask  270  and of the mask holder  260  are reduced to u, v, w and x ch , y ch , z ch . For describing the structure elements of a pattern, as well as defects possibly present, only the lateral coordinates u, v of the mask coordinate system u, v, w are of importance. Therefore, a mask manufacturer specifies for the reference points of markings typically only the u- and v-coordinates thereof. 
     The diagram  400  in  FIG.  4    elucidates the determination of an oblique position or a skew position of the photomask  410  on the chuck  190 ,  260 . An oblique position of the mask  410  can be caused by a skewing of the chuck  190 ,  260 . It is also possible for the chuck  190 ,  260  and/or an underside  420  of the photomask  310  to have one or more particles that result in a skew position of the mask  410  (not illustrated in  FIG.  4   ). It goes without saying that a combination of skewing of the chuck  190 ,  260  and one or more particles between the chuck surface  195 ,  265  and the underside of the photomask  410  can also result in an oblique position of the mask  410 . 
       FIG.  4    represents a device  400  comprising a modified scanning electron microscope (SEM, Scanning Electron Microscope)  440  as an example of a particle beam source  440 . Hereinafter, the particle beam source  440  is always realized as a modified SEM. From the output of the column  445  of the SEM  440 , an electron beam  450  can be scanned over the top side  430  or front side  430  of the photomask  410 . As already explained above, an electron beam  450  can be focused to a very small spot, such that the latter has a very small lateral extent during the scanning of the mask  410 . For this reason, a focused electron beam  450 , in the presence of a suitable precursor gas, can induce (not illustrated in  FIG.  4   ), a laterally delimited chemical etching reaction (EBIE, Electron Beam Induced Etching) or a locally delimited chemical deposition reaction (EBID, Electron Beam Induced Deposition). 
     It is also possible, as an alternative or in addition to the electron beam  450 , to use an ion beam, for instance a beam of gallium ions, for scanning the photomask  270 ,  410  or for scanning a marking of the mask  270 ,  410 . Atomic and/or molecular beams, for example a helium beam, can likewise be used for this purpose. Finally, photon beams can also be used for scanning photomasks  270 ,  410  or the markings thereof. When photons are used, it is expedient to use any particle beam source having the shortest possible wavelength, for example a particle beam source for the EUV wavelength range. As the wavelength of the photon beam used decreases, the resolution capability of the photo beam source increases. In an alternative exemplary embodiment, a digital camera can be used for imaging a marking of the mask  270 ,  410 . 
     The resolution capability of a focused electron beam  450  in the beam direction is limited, however, on account of the profile of said beam in the beam direction. For this reason, the device  400  comprises a height sensor  460 , which can be used for detecting a height or the z-coordinate of the photomask  410 ,  460 . The height sensor  460  directs a particle beam in the form of a light beam  470  onto the top or front side  430  of the photomask  410  and determines the distance between the height sensor  460  and the top side  430  of the photomask  410  on the basis of the radiation reflected from the front side  430 , said radiation not being represented in  FIG.  4   . The height sensor  460  can thus be used to bring the photomask  410 ,  460  to the working distance of the electron beam  450 . 
     The height sensor  460  can be embodied in the form of an interferometer, for example as a Fabry-Perot interferometer or as a white light interferometer. However, the height sensor  460  can also be realized as a confocal point sensor, as a chromatic confocal sensor or as a confocal laser scanning microscope. The height sensor  460  typically has a resolution capability in the submicron range. In order to extend the resolution range of the height sensor  460 , the height sensor  460  can comprise two or more sensors having different measurement ranges and resolution capabilities. It thus becomes possible to measure the distance between the top side  430  of the mask  410  and the height sensor(s)  460  with coarse resolution in a first step and then with increasingly higher resolution in one or more subsequent steps. 
     The height sensor  460  ascertains the distance between the height sensor  460  and the top side  430  of the photomask  410  for at least three points of the surface of the mask that do not lie on a straight line. For this purpose, the sample stage  100  displaces the photomask  410  along the x-direction and the y-direction. In order to minimize the measurement error when determining the height difference from the three measured points, it is advantageous to choose the measurement points such that they are at the greatest possible distance from one another. A large distance between the at least three measurement points of the height sensor  460  can be D&gt;5 cm, for example. Furthermore, in order to minimize the measurement error when measuring the height difference it is expedient if the three measurement points span a rectangular coordinate system. 
     Furthermore, the device  400  comprises the exemplary sample stage  100 , which is not represented in  FIG.  4   . Furthermore, the coordinate system x b , y b , z b  assigned to the baseplate  110 ,  205  of the sample stage  100  and the coordinate system u, v associated with the photomask  410  are indicated in  FIG.  4   . Finally, the coordinate z w  represents the height change of the photomask  410  on account of the oblique or skewed position thereof. 
     The upper partial image  500  in  FIG.  5    elucidates the measurement data for ascertaining an oblique position of a mask from the height difference of at least three measurement points, wherein the mask  410  has only a sparse pattern  520 . The data measured by the height sensor  460  represents a superimposition of an oblique position of the mask  410  and the pattern geometry. This relationship is illustrated in the diagram  530  arranged under the mask  410 . The diagram  540  presents the variation of the optical intensity detected by the height sensor  460  if the height sensor  460  is scanned over a pattern element  520 , the substrate  510  and then over a second pattern element  520 . The height or the thickness of a pattern element  520  is in the range of 70 nm to 100 nm for a binary mask, for example. This means that, in the example indicated in  FIG.  5   , the resolution of the height sensor  460  is approximately 10 nm. 
     The lower partial image  550  in  FIG.  5    illustrates the scanning of the height sensor  460  over a mask  410  having a dense pattern  570 . The diagrams  580  and  590  represent the measured height profile and the intensity profile detected by the height sensor  460  during the scanning of the height sensor  460  over the dense pattern  570 . The height measured over the dense pattern  570  is a combination of the height of the substrate  510  and the height or the distance of the top side of the pattern  570  from the height sensor  460 . 
     In order to avoid a deterioration in the resolution when measuring the height difference of at least three points distributed over the mask  410 , measurement points which lie within a dense pattern  570  should be disregarded, whenever possible, when determining a height difference of the at least three measurement points. In this case, the measured intensity profile  540 ,  590  of the height sensor  460  can be used to establish whether or not a measurement point lies in a dense pattern  570 . If it is established that a measurement point of the height sensor  460  lies in the region of a dense pattern  570 , this measurement point should be discarded and replaced by a measurement point that becomes located either on a large-area pattern element  520  or on the substrate  510  of the photomask  410 . 
     From the height difference of at least three measurement points that is measured by the height sensor, it is possible to determine the plane which is spanned by the at least three measurement points and in which the top side  430  of the photomask  410  is embedded. An oblique position of the mask  410  can be determined as a result. A variation of the height of the top side  430  of the photomask for an arbitrary point of the mask can be determined by ascertaining this point on the surface of the mask. It is also possible, of course, to determine the height or the z-coordinate of an arbitrary point on the surface of the mask by interpolating and/or extrapolating the height difference of the at least three points measured by the height sensor. 
     As soon as the oblique position of the photomask  410  is known, this can be taken into account when translational movements are carried out by the sample stage  100 . As a result, it is possible reliably to prevent translational movements of the sample stage  100  from resulting in unintended damage to a skew mounted photomask  410  and/or the SEM  440 . Besides an SEM  440 , a device for identifying and for repairing a photomask  410  can comprise one or more scanning probe microscopes, not illustrated in  FIG.  4   . Said scanning probe microscopes are often fitted at a certain distance from the SEM  440  in the vicinity of the top side  430  of the photomask  410 . In the case of a skew mounted mask, it can easily happen that carrying out translational movements for large distances results in a probe and/or a micromanipulator of a scanning probe microscope unintentionally making contact with the photomask  410 . After ascertaining the oblique position of the photomask  410 , this problem can be avoided. 
       FIG.  6    presents an example of a marking  600  or of a reference sign  600 . Markings  600  are applied by the mask manufacturer typically at regular or irregular intervals on a photomask  270 ,  410 . The exemplary marking  600  has a square shape having an edge length  640  of 350 μm. The marking  600  is divided into four quadrants by two crosspieces  610  and  620 . In the top right quadrant  630 , the marking  600  has a small square  660 . The top right corner of the square  660  defines the reference point  650  of the marking  600 . 
     The white or transparent part of the top right quadrant  630  of the marking  600  can be the substrate  275 ,  510  of the photomask  270 ,  410 . The crosspieces  610 ,  620  and the small black square  660  can comprise absorber material, for example of a binary photomask  270 , such as chromium for instance. 
     The marking  600  can be scanned by use of the electron beam  450  of the SEM  440  and the reference point  650  of the reference sign  600  can be ascertained from the scan data. 
       FIG.  7    shows a schematic plan view of a photomask  700 . The exemplary photomask  700  has three markings  710 ,  730 ,  750  in the form of right angles at three corners. The reference points  720 ,  740  and  760  of the exemplary markings  710 ,  730  and  750  form the points of intersection of the interior of the right angles. The coordinate system u, v associated with the photomask  700  is indicated on the mask  700 . The reference points u 1 , v 1 , u 2 , v 2  and u 3 , v 3  in the mask coordinate system u, v are provided to the user of the mask  700  by the mask manufacturer. The markings  710 ,  730  and  750  often have the form of the marking  600  from  FIG.  6   . 
     By use of the electron beam  450  of the SEM  440 , at least two of the three markings  710 ,  730 ,  750  are scanned in order to determine at least two reference points  720 ,  740 ,  760  of the three markings  710 ,  730 ,  750 . In order to position the markings  710 ,  730 ,  750  under the electron beam  450  of the SEM  440 , the sample stage  100  carries out exclusively translational movements of the chuck  190 ,  260  in the x-direction and y-direction. A rotational movement of the sample stage  100  for determining the reference points  720 ,  740 ,  760  is not carried out. As soon as one of the markings  710 ,  730 ,  750  is positioned under the electron beam  450 , the electron beam  450  scans the marking  710 ,  730 ,  750  in order to ascertain the reference point  720 ,  740 ,  760  thereof. 
     After the scanning of two markings, for example the markings  710 ,  730 , the reference points  720 ,  740  thereof in the coordinate system x, y of the sample stage  110  are known: x 1 , y 1  and x 2 , y 2 . With the aid of the two measured reference points x 1 , y 1  and x 2 , y 2  and also the reference points u 1 , v 1  and u 2 , v 2  provided by the mask manufacturer, it is possible to determine a displacement, a rotation and a scaling of the two coordinate systems with respect to one another. An affine transformation combines the measured reference points x 1 , y 1  and x 2 , y 2  with the reference points u 1 , v 1  and u 2 , v 2  provided by the mask manufacturer. If only two markings are used, then a general affine transformation is underdetermined. Such an embodiment restricts an affine transformation to a displacement (offset), a scaling and a rotation. 
     The established description of affine coordinates is given in a matrix representation using homogeneous coordinates: 
     
       
         
           
             
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     In the case of the alignment of the two coordinate systems with respect to one another on the basis of two reference points, for example the reference points  720  and  740 , the general vector equation above is reduced: 
     
       
         
           
             
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     In this case, the parameters denote: a, b a displacement or an offset, s a scaling; and α a rotation angle of the two coordinate systems with respect to one another. 
     Inserting the measured and the predefined reference points  720 ,  740  results in a system of equations that can be solved using methods of linear algebra. If, for the photomask  700 , the reference points  720 ,  740 ,  760  of the three markings  710 ,  730 ,  750  are measured and inserted into the general vector equation, the parameters of a shear m and a rotation stretching can additionally be determined besides a displacement a, b, a scaling s, a rotation α. 
     The coordinates of an identified defect u D , v D  are typically indicated in coordinates of the coordinate system u, v linked with the photomask  270 ,  410 ,  700 . After the parameters of the affine transformation have been ascertained, these coordinates can be converted into coordinates of the sample stage  100 . As already explained above, the SEM  440  operates with coordinates of the sample stage  100 . 
     A description will now be given below of how to determine a height change of a photomask  270 ,  410 ,  700  as a consequence of a wobble movement of the mask  270 ,  410 ,  700  caused by a rotation axis not oriented perpendicularly to the mask  410  or to the top side  430  of the mask  410 . The step described first of determining a distance  490  between the SEM  440  and the height sensor  460  or the points of incidence of the particle beam  450  of the SEM  440  and the particle beam  470  of the height sensor  460  on the photomask  270 ,  410 ,  700  is necessary only if this distance is not already known. This is the case, for example, after service work that has altered this distance has been carried out on the device  400 . 
     The distance  490  is ascertained in two substeps. In the first substep, the height sensor  460  is positioned under a reference point  720 ,  740 ,  760  of the markings  710 ,  730 ,  750  that had already been measured by use of the electron beam  440  of the SEM  450 . If only the two markings  710  and  730  had been measured by use of the electron beam  440  of the SEM  450 , one of the markings  710  or  730  is selected for this purpose. 
     This process may be very time-consuming if the sample stage  100  scans the marking in a manner similar to the electron beam  450  of the SEM  440 . In contrast to the electron beam  450  of the SEM  440 , the particle beam  470  of the height sensor is stationary. Therefore—in contrast to the case during the scanning of the electron beam  450 —in order to position the particle beam  470  of the height sensor  460  under a reference point  720 ,  740 ,  760  of one of the markings  710 ,  730 ,  750 , the photomask  270 ,  410 ,  700  has to be moved under the particle beam  470  of the height sensor  460 . This necessitates moving the mass of the photomask  270 ,  410 ,  700  and a large portion of the mass of the sample stage  100 . For this reason, centering the particle beam  470  of the height sensor  460  under one of the reference points is a time-consuming process. Simply scanning the photomask  270 ,  410 ,  700  by carrying out translational movements of the sample stage  100  is therefore not effective in practice. Rather, it is very advantageous to choose the scan path of the sample stage such that the reference point  720 ,  740 ,  760  of one of the markings  710 ,  730 ,  750  becomes located under the particle beam  470  of the height sensor  460  after the shortest possible scan time, i.e. after the fewest possible translational movements of the sample stage  100 . The scan path for which this is applicable depends on the type of marking  500 ,  710  present on the photomask  270 ,  410 ,  700 . 
       FIG.  8    schematically presents for the exemplary marking  600  from  FIG.  6    an expedient scan path that makes it possible to position or to center the reference point  650  of the marking  600  under the particle beam  470  of the height sensor  460  after a short scan time. The flow diagram  900  in  FIGS.  9 A and  9 B  indicates the various steps for centering the particle beam  470  of the height sensor  460  under the reference point  650 . The method begins at  900 . Step  905  involves scanning the sample stage  100  within the marking  600  in a diagonal direction in relation to the crosspieces  610  and  620 . This first scan is symbolized by the straight line  810  in the partial image on the left in  FIG.  8   . The length of the first scan  810  is chosen such that the particle beam  470  of the height sensor  460  “sees” or images the crosspieces  610  and  620  of the marking  600 . The intensity signal detected by the height sensor  460  during the first scan  810  is illustrated in the top right partial image in  FIG.  8   . At the positions of the crosspieces  610  and  620 , the absorber material thereof has the effect that the intensity signal reflected from the marking dips, or vanishes. 
     After the first scan  810 , in step  915  the signal detected by the height sensor  460  is analyzed and the distance d 1  between the two crosspieces  610  and  620  is determined. Then, in step  920 , the sample stage  100  is displaced perpendicularly to the diagonal scan direction by a predefined distance. The next step  925  involves carrying out a second scan  820 , as indicated in  FIG.  8   . Afterwards, in step  930 , the distance d 2  between the two crosspieces  610  and  620  of the marking  600  is ascertained for the second scan  820 . This is elucidated schematically in the middle left partial image in  FIG.  8   . The wider range of vanishing signal indicates that the second scan  820  leads partly through the square  660  of the marking  600 . 
     Decision block  935  then involves deciding whether the distance d 1  is greater than d 2 . If this is applicable, the displacement of the sample stage  100  between the first scan  810  and the second scan  820  has been effected in the correct direction, i.e. in the direction of the reference point  650  of the marking  600 . As indicated in block  945 , this is the direction towards the bottom right. Step  950  then involves ascertaining the offset or the displacement of the sample stage  100  that is necessary in order to lead the third scan  830  diagonally through the square  660  and thus the reference point  650  of the marking  600 . In step  955 , the sample stage  100  is displaced perpendicularly to the second scan  820  by the offset ascertained. 
     In step  960 , the third scan  830  is carried out with the aid of the sample stage  100 . The third scan  830  is effected, as illustrated in  FIG.  8   , along the diagonal of the square  660 . Afterward, in step  965 , the third scan  830  is analyzed and the reference point  650  of the marking  600  is determined from the third scan  830 . This is indicated schematically in the bottom left partial image in  FIG.  8   . The sought reference point  650  of the marking  600  is the point in the top right corner of the square  660  of the marking  600  at the right-hand edge of the region of the third scan  830  with vanishing detected signal. Finally, the method ends in step  970 . 
     If, in decision block  935 , it is established that the distance d 2  is greater than d 1 , the direction of the displacement of the sample stage  100  for the next scan is reversed with respect to the displacement carried out between the first scan  810  and the second scan  820 . This is implemented in block  940  in  FIG.  9   . Step  950  involves ascertaining the offset that is necessary in order to lead the third scan  830  through the diagonal of the square  660  and thus the reference point  650  of the marking  600 . The further steps are then carried out as already explained in the preceding section. 
       FIG.  10    schematically shows an alternative method for centering a reference point  720 ,  740 ,  760  of a marking  710 ,  730 ,  750  of a photomask  270 ,  410 ,  700  under the particle beam  470  of the height sensor  460 . Instead of the translational movements of the sample stage  100  explained above, it is also possible, with the aid of a rotation of the sample stage  100  about a defined rotation axis or a pivot point within one of the markings  710 ,  730 ,  750 , to position the particle beam  470  of the height sensor  460  under the reference point  720 ,  740 ,  760  thereof. 
       FIG.  10    represents a first scan  1010  within the marking  600 . The top right partial image in  FIG.  10    illustrates the intensity profile detected by the height sensor  460  during the rotation of the sample stage  100 . The two dips in the detected optical intensity of the first scan  1010  represent the scanning of the particle beam  470  of the height sensor  460  under the crosspieces  610  and  620 . The wider range of vanishing reflected optical intensity represents the scanning of the particle beam  470  of the height sensor  460  over a part of the square  660  of the marking  600 . 
     After displacing the pivot point of the rotation axis within the marking  600 , a second scan  1020  is carried out by rotating the rotation axis  250  of the sample stage  100 . The result of that is illustrated in the middle right partial image in  FIG.  10   . This shows once again the scanning of the particle beam  470  of the height sensor  460  over the two crosspieces  610  and  620  and the square  660  of the marking  600 . From the two scans  1010  and  1020 , the displacement—effected between the two scans—of the rotation axis within the marking  600  and also the change in the radius of the circular rotational movement, the pivot point and the radius of the circular scan which leads the third scan  1030  through the reference point  650  of the marking  600  are ascertained. The bottom right partial image represents the intensity profile detected by the height sensor  460  during the circular scan. The sought reference point  650  of the marking  600  can be determined from the scans  1010 ,  1020  and  1030  as the top right corner  650  of the square  660  of the marking  600 . Determining the reference point  650  of the marking  600  by use of the circular or crescent-shaped scans  1010 ,  1020  and  1030  is more complicated compared with the linear scans  810 ,  820 ,  830  explained with reference to  FIG.  8   . 
     After the centering of the particle beam  470  of the height sensor  460 , the coordinates thereof in the coordinate system of the sample stage  100  are known. As explained above, the marking  710 ,  730  or  750  selected for the centering of the particle beam  470  of the height sensor  460  had already been scanned by use of the electron beam  450  of the SEM  440 . The sought distance  490  between the particle beam  450  of the SEM  440  and the particle beam  470  of the height sensor  460  is given by the difference between the coordinates of the reference point  650  of the marking  710 ,  730  or  750  that are measured by the SEM  440  and the coordinates of the reference point  710 ,  730 ,  750  of the marking  710 ,  730  or  750  that are measured by the height sensor  460 . 
     The three steps described below serve for determining the position of the rotation axis on the photomask  270 ,  410 ,  700 . These calibration steps have to be carried out once for a new or a modified device  400 . Furthermore, these calibration steps need to be carried out if the coordinates of the electron beam  450  of the SEM  440  in relation to the coordinate system of the sample stage  100  have been lost. 
     In the first substep for ascertaining the position of the rotation axis, the photomask  270 ,  410 ,  700  with the sample stage  100  is rotated by 90°.  FIG.  11    presents the photomask  700  from  FIG.  7    rotated about the z-axis of the coordinate system of the sample stage  100  by 90° in the anticlockwise direction. A rotation of the photomask  270 ,  410 ,  700  by a rotation angle of 90° is advantageous since the choice of this angle makes it possible to determine the position of the rotation axis in relation to the photomask  270 ,  410 ,  700  with minimal error. However, it is also possible to choose a rotation angle within the range 0&lt;θ&lt;180°. 
     Since, at the time of the rotation of the photomask  700 , a possible wobble movement owing to the rotation is not yet known, it is advantageous, before carrying out the rotation, to increase the distance between the output of the column  445  of the SEM  440  and, if present, between the probe(s) or micromanipulator(s) of one or more scanning probe microscope(s), in order to prevent damage to the photomask  700 , the SEM  440  or the scanning probe microscope(s) and/or a gas injection system. This can be done for example by lowering the chuck  260  of the sample stage  100 . A gas injection system, not illustrated in  FIG.  4   , can be used for example for providing one or more corresponding precursor gases at the location where an EBIE process or an EBID process is carried out. 
     In the next step, the reference points  720 ,  740 ,  760  of at least two of the three markings  710 ,  730 ,  750  of the rotated photomask  700  are measured again by use of the electron beam  450  of the SEM  440 . The implementation of these measurements has been explained above in the context of the discussion of  FIGS.  6  and  7   . As likewise already explained above, during the determination of the reference points  720 ,  740 ,  760  of at least two of the three markings  710 ,  730 ,  750 , no rotation through the rotation axis  250  of the sample stage  100  is permitted to be carried out. Furthermore, care should be taken to ensure that, between carrying out the rotational movement by use of the sample stage  100  and measuring the reference points  720 ,  740 ,  760  of the rotated photomask  700  by use of the electron beam  450  of the SEM  440 , the device  400  does not carry out any tasks that may alter firstly the position of the sample stage  100  and secondly the position of the electron beam  450  of the SEM  400 . 
     If a photomask  270 ,  410 ,  700  is arranged on the chuck  190 ,  260  such that its center point lies exactly over the rotation axis  250  of the sample stage  100 , a rotation of the photomask  270 ,  410 ,  700  through the rotation axis  250  of the sample stage  100  has the effect that the markings  710 ,  730 ,  750 , just like the reference points  720 ,  740 ,  760  thereof, circulate on a known circular path around the rotation axis  250  of the sample stage  100 . Generally, a photomask  270 ,  410 ,  700  fixed by the mask holder does not satisfy this condition, however, since in the general case the position of the rotation axis  250  and therefore the center point of the circular path of the reference points  720 ,  740 ,  760  are not known. 
     As already explained above, a combined translational and rotational movement can be described by an affine transformation.  FIG.  12    schematically elucidates a rotation of the photomask  700  with a rotation axis that is perpendicular to the surface of said photomask, by an arbitrary angle θ. The coordinates of the reference points  720 ,  740  of the markings  710 ,  730  before carrying out the rotation are: x 1i , y 1i  and x 2i , y 2i , wherein the index “i” stands for the original coordinates of the reference points  720 ,  740  of the markings  710 ,  730 . After the rotation, the reference points  720 ,  740  have the coordinates x 1r , y 1r  and x 2r , y 2r ; in this case, the index “r” denotes the coordinates of the reference points  720 ,  740  of the markings  710 ,  730  after the rotation. As can be gathered from  FIG.  12   , the changes in the coordinates of the reference points  720 ,  740  can be expressed: Δx i =x 2i −x 1i , Δ yi =y 2i −y 1i , Δx r =x 2r −x 1r  and Δy r =y 2r −y 1r . The following relationships additionally hold true: tan(θ i )=Δy i /Δx i , tan(θ r )=Δy r /Δx r  and θ=θ r −θ i . Accordingly, the rotation angle θ can be determined from the measured reference points  720 ,  740  of the markings  710 ,  730 . 
     The parameters t x  and t y  stand for a translation or displacement of the markings  710  and  730  that is induced by the rotation. The following thus results for the affine transformation describing the rotation: 
     
       
         
           
             
               [ 
               
                 
                   
                     
                       x 
                       r 
                     
                   
                 
                 
                   
                     
                       y 
                       r 
                     
                   
                 
                 
                   
                     1 
                   
                 
               
               ] 
             
             = 
             
               
                 [ 
                 
                   
                     
                       
                         
                           s 
                           · 
                           cos 
                         
                         ⁢ 
                         θ 
                       
                     
                     
                       
                         
                           
                             - 
                             s 
                           
                           · 
                           sin 
                         
                         ⁢ 
                         θ 
                       
                     
                     
                       
                         t 
                         x 
                       
                     
                   
                   
                     
                       
                         
                           s 
                           · 
                           sin 
                         
                         ⁢ 
                         θ 
                       
                     
                     
                       
                         
                           s 
                           · 
                           cos 
                         
                         ⁢ 
                         θ 
                       
                     
                     
                       
                         t 
                         y 
                       
                     
                   
                   
                     
                       0 
                     
                     
                       0 
                     
                     
                       1 
                     
                   
                 
                 ] 
               
               [ 
               
                 
                   
                     
                       x 
                       i 
                     
                   
                 
                 
                   
                     
                       y 
                       i 
                     
                   
                 
                 
                   
                     1 
                   
                 
               
               ] 
             
           
         
       
     
     A rotation of the photomask by an angle θ should not bring about any scaling of the mask  700 . The following can therefore be assumed for the parameter s to a good approximation: s=1. A deviation when determining s that is greater than the error when ascertaining the other parameters therefore gives an indication of an error when determining the position of the rotation axis. For the translation parameters t x  and t y  the following results from the matrix equation above: 
         t   x   =x   r −cos θ· x   i +sin θ y   i  
 
         t   y   =y   r −sin θ· x   i −cos θ y   i  
 
     The aim then, is to find the coordinates x c , y c  of the rotation axis for which the following holds true: 
     
       
      
       x 
       r 
       =x 
       i  
      
     
     
       
      
       y 
       r 
       =y 
       i  
      
     
     The coordinates of the rotation axis are described by x c , y c , where “c” stands for center. The markings  710 ,  730 ,  750  and respectively their reference points  720 ,  740 ,  760  move on a circular path around the rotation axis  250 . If the sample stage  110  is then moved in the x- and y-directions such that the coordinates x c , y c  of the rotation axis  250  correspond to the coordinates of the point of incidence of the electron beam  450  of the SEM  440 , then an image recorded by the SEM  440  rotates around the center point thereof, i.e. the points of the SEM image have a pure rotational movement. 
     Apart from this special case, i.e. if the rotation axis  250  does not correspond to the axis of the electron beam  450 , all points viewed by the SEM  440  during a rotation of the mask  700  experience a combined rotational and translational movement. If, for example, a defect with the coordinates x D , y D  lies within the region scanned by the electron beam  450  of the SEM  440 , said defect normally migrates out of the scanned region or the field of view of the SEM during a rotation of the photomask  700  about the rotation axis  250 . By use of a compensating translational movement of the sample stage  110  in the x- and y-directions, the defect x D , y D  can be displaced into the field of view or the scanned region of the SEM  440  again after the end of the rotation of the mask  700 . The combination of a rotation of the sample stage  110  about the rotation axis  250  and a compensating translational movement of the sample stage  110  results in a rotation of the sample stage  110  around a defect x D , y D . 
     The origin of the coordinate system x c , y c , z c  of the chuck surface  265  of the chuck  190 ,  260  is typically chosen such that the electron beam  450  of the SEM  440  lies at the coordinate origin. 
     After some conversions and using the conditions specified above for x i , x r  and y i , y r , it is possible to express the coordinates of the central rotation axis x c , y c  as a function of the translations t x  and t y  and of the rotation angle θ: 
     
       
         
           
             
               x 
               c 
             
             = 
             
               
                 - 
                 
                   
                     
                       t 
                       y 
                     
                     ( 
                     
                       1 
                       + 
                       
                         cos 
                         ⁢ 
                         θ 
                       
                     
                     ) 
                   
                   
                     
                       2 
                       · 
                       sin 
                     
                     ⁢ 
                     θ 
                   
                 
               
               + 
               
                 1 
                 / 
                 2 
                 ⁢ 
                 
                   t 
                   x 
                 
               
             
           
         
       
       
         
           
             
               y 
               c 
             
             = 
             
               
                 
                   
                     t 
                     x 
                   
                   ⁢ 
                   sin 
                   ⁢ 
                   θ 
                 
                 
                   2 
                   - 
                   
                     
                       2 
                       · 
                       cos 
                     
                     ⁢ 
                     θ 
                   
                 
               
               + 
               
                 1 
                 / 
                 2 
                 ⁢ 
                 
                   t 
                   y 
                 
               
             
           
         
       
     
     In this case, the translation parameters t x  and t y  are determined from the equations specified above, wherein the measured coordinates of the reference points  720 ,  740 ,  760  of the markings  710 ,  730 ,  750  before and after the rotation are to be inserted into said equations. 
     If, after the parameters t x , t y  and θ have been determined, the sample stage  100  is displaced such that the rotation axis has the coordinates x c , y c , a rotation of the chuck  190 ,  260  does not result in a displacement of the scan region of the electron beam  450  of the SEM  440 . 
       FIG.  13    illustrates a translation of a point x i , y i  by carrying out a rotation AO wherein the coordinates of the rotation axis do not correspond to the coordinates of the point of incidence of the electron beam  440  on the photomask  270 ,  410 ,  700 . Therefore, as explained above, the rotation by AO additionally results in a displacement of the point x i , y i . This induced translation is identified by the indices “it.” It can be expressed as a function of the original coordinates of the point x i , y i  and the rotation angle Δθ: 
         x   it =( x   i   −x   c )·cos Δθ−( y   i   −y   c )·sin Δθ+ x   c   −x   i  
 
         y   it =( x   i   −x   c )·sin Δθ+( y   i   −y   c )·cos Δθ+ y   c   −y   i  
 
     In order to compensate for the translation caused by the rotation in relation to a scan region of the electron beam  450  of the SEM  440 , the sample stage  100  has to be displaced in the opposite direction by the magnitude specified above. 
     The diagram  1400  in  FIG.  14    elucidates various possibly occurring deficiencies or defects of diverse components of the sample stage  100 . As illustrated in  FIG.  14   , the second slide  225  of the sample stage  100 , which moves the mask plate  190 ,  260  along the x-direction, can be tilted by an angle α relative to the baseplate  205  of the sample stage  100 . Furthermore, the second slide  225  of the sample stage  100  can be rotated by an angle θ relative to the chuck  190 ,  260  or the mask plate  190 ,  260 . These two inadequacies of the sample stage  100  result in an oblique or skew position of the photomask  270 . A detailed explanation has already been given above of how a skew position of the photomask  270  can be ascertained and can be taken into account when carrying out translational movements of the sample stage  100 . 
     However, an oblique position of the photomask  270  does not result in a wobble movement of the mask  270  as long as the rotation axis  1450  of the sample stage  100  is aligned perpendicularly to the mask  270 ,  410 ,  700  or to the top side  430  thereof. By contrast, an orientation of the rotation axis  1450  that deviates from the perpendicular to the photomask  270 ,  410 ,  700  results in a height change during the rotation of the mask  270 ,  410 ,  700  by the sample stage  100 . A height change of the photomask  270 ,  410 ,  700  during the rotation is referred to hereinafter as a wobble movement of the mask  270 ,  410 ,  700 . 
       FIG.  14    schematically shows that the rotation axis  1450  has an angle δ relative to the z-axis of the baseplate  205  of the sample stage  100 . However, the angle deviation δ does not result in a wobble movement of the photomask  270 ,  410 ,  700  during the rotation thereof as long as the rotation axis  1450  is oriented perpendicularly with respect to the mask  270 ,  410 ,  700 , i.e. γ=90° holds true. In the exemplary diagram  1400 , the angle γ measuring the angle between the surface  430  of the mask and the orientation of the rotation axis  1450  has a numerical value that deviates from 90°. The angle γ≠90° results, however, in a height change during the rotation of the mask  270 ,  410 ,  700  about the rotation axis  1450 , which height change is detected by the particle beam  470  of the height sensor  460 . 
     The diagram  1500  in  FIG.  15    presents a plan view of the mask  700  in the upper partial image. The sample stage  100  has displaced the photomask  700  such that the coordinates  1510  of the rotation axis  1450  on the photomask  700  correspond to the coordinates of the point of incidence x c , y c  of the electron beam  450  of the SEM  440 . The point of incidence of the particle beam  470  of the height sensor  460  is at a distance  490  or do from the point of incidence of the electron beam  450  of the SEM  440 . What is sought is the height change, the height profile or the wobble movement of the point  1520  if the rotation axis—as illustrated in the lower partial image in  FIG.  15   —is not oriented perpendicularly to the photomask  700 . 
     It is then assumed that, for the rotation angle indicated in  FIG.  15   , the height sensor  460  detects the maximum height change during the rotation of the photomask  700  about the rotation axis  1450 . This rotation angle is therefore designated as θ max . For θ max =±90°, it then holds true that γ=90° and the height change as a result of the wobble movement vanishes. For θ max ±180°, the height change of the photomask  700  detected by the height sensor  460  reverses its sign. 
     From the lower partial image in  FIG.  15   , the following can be determined for the maximum height change, the height change Δh max    1570  detected by the height sensor  460 : 
       Δ h   max   =d   0 ·tan(δ+γ−90°)
 
     For the height profile h(θ, d 0 ) measured as a function of the rotation angle θ by the height sensor  460  during the rotation of the photomask  700  about the rotation axis  1450 , the following therefore results: 
         h (θ, d   0 )=cos(θ−θ max )· d   0 ·tan(δ+γ−90°)+ h   off  
 
       or: 
         h (θ, d   0 )=Δ h   max ·cos(θ−θ max )+ h   off  
 
     wherein the parameters θ max , Δh max  and h off  are initially unknown. 
     The diagram  1600  in  FIG.  16    shows an example of the measured height profile h(θ, d 0 ) as a function of the rotation angle θ indicated in radian measure. The height change or the height profile is represented in micrometers. The points  1610  in  FIG.  16    represent measurement points of the height sensor  460  during a rotation process. The solid curve  1620  represents a function fitted to the measurement points  1610 . Numerical optimization algorithms, such as the Levenberg-Marquardt algorithm, for example, can be used for fitting the measurement points  1610 . The parameters θ max , Δh max  and h off  are determined as a result of fitting the measurement data  1610  to the function indicated above. 
     The height change at an arbitrary point of the photomask  700 , for instance at the point  1520 , can be ascertained by use of a linear interpolation and/or a linear extrapolation of the height profile h(θ, d 0 ): 
     
       
         
           
             
               h 
               ⁡ 
               ( 
               
                 θ 
                 , 
                 d 
               
               ) 
             
             = 
             
               
                 h 
                 ⁡ 
                 ( 
                 
                   θ 
                   , 
                   
                     d 
                     0 
                   
                 
                 ) 
               
               · 
               
                 d 
                 
                   d 
                   0 
                 
               
             
           
         
       
     
     wherein h(θ, d) describes the height profile of the photomask  700  as a function of the rotation angle θ and the distance d from the rotation axis. 
     The flow diagram  1700  in  FIG.  17    presents once again exemplary steps of the process of determining an alignment of a photomask  270 ,  410 ,  700  on a sample stage  100  which is displaceable along at least one axis that is parallel to a chuck surface  195 ,  265  of the sample stage  100 , and is rotatable about at least one axis  250 ,  1450  that is perpendicular to the chuck surface  195 ,  265 . The method begins in step  1710 . 
     The next step  1720  involves determining an oblique position of the photomask  270 ,  410 ,  700 . For this purpose, a height sensor  460  measures the z-coordinate of at least three points on the mask, wherein the three measurement points do not lie on a straight line. 
     Step  1730  involves determining the parameters of an affine transformation that combines the coordinate system of the sample stage  100  with the coordinate system of the photomask  270 ,  410 ,  700 . For this purpose, the coordinates of at least two markings  710 ,  730 ,  750  of the photomask  270 ,  410 ,  700  are measured by use of a particle beam  450  of a particle beam source  440 . 
     Both steps  1720  and  1730  are optional steps and are therefore represented with dashed boxes around them in  FIG.  17   . 
     In step  1740 , the sample stage  100  is rotated by a predefined angle and the height change of the photomask  270 ,  410 ,  700  is measured during rotation at a non-vanishing distance with respect to the rotation axis  250 ,  1450  for the purpose of determining the alignment of the photomask  270 ,  410 ,  700 . 
     The method ends in step  1750 . 
     Finally, the flow diagram  1800  in  FIGS.  18 A and  18 B  reproduces the method explained in  FIG.  17    in greater detail. The method begins in step  1805 . 
     In the next step  1810 , at least one height sensor  460  measures a height difference of at least three points on a photomask  270 ,  410 ,  700  which do not lie on a straight line. In step  1815 , an oblique position of the photomask  270 ,  410 ,  700  is determined from the measured height difference. 
     Then, in step  1820 , a first set of coordinates of at least two markings  710 ,  730 ,  750  of the photomask  270 ,  410 ,  700  are determined by use of a particle beam  450  of at least one particle beam source  440 . 
     In step  1825 , the parameters of an affine transformation that combines the coordinate system of the photomask  270 ,  410 ,  700  with the coordinate system of the sample stage  100  are determined on the basis of the first set of measured coordinates and the coordinates of the at least two markings  710 ,  730 ,  750  that are supplied by the mask manufacturer. 
     The four steps  1810  to  1825  are optional steps and are therefore illustrated with dashed boxes around them in  FIG.  18   . 
     In step  1830 , the height sensor  460  is centered over one of the at least two markings  710 ,  730 ,  750  measured by use of the particle beam  450  of the at least one particle beam source  440 . After that, in step  1835 , the distance  490  between the point of incidence of the particle beam  450  of the at least one particle beam source  440  and the point of incidence of the particle beam  470  of the height sensor  460  is determined. 
     Steps  1830  and  1835  have to be carried out for example only if the distance  490  is not already known. This circumstance is illustrated by use of dotted boxes around the two optional steps. 
     In step  1840 , the photomask  270 ,  410 ,  700  is rotated by an angle 0°&lt;α&lt;180°. The rotation effected is preferably by an angle of 90°. 
     Then, in step  1845 , a second set of coordinates of the at least two markings  710 ,  730 ,  750  of the photomask  270 ,  410 ,  700  is measured by use of the particle beam  450  of the at least one particle beam source  440 . Afterwards, in step  1850 , the coordinates of the rotation axis  1450  on the photomask  270 ,  410 ,  700  are determined. 
     Steps  1840  to  1850  are optional steps and are therefore illustrated with dotted boxes around them in  FIG.  18   . They may be carried out for example only if the position of the rotation axis  1450  on the photomask  270 ,  410 ,  700  is not known. This is the case for example if the coordinates of the particle beam  450  of the at least one particle beam source  440  in the coordinate system of the sample stage  100  are lost. 
     In step  1855 , the rotation axis  1450  is optionally displaced with the aid of the sample stage  100  such that its coordinates correspond to the coordinates of the point of incidence of the particle beam  450  of the at least one particle beam source  440 . 
     In the next step  1860 , the sample stage  100  is rotated by a predefined angle and the height change h(θ, d 0 ) of the photomask  270 ,  410 ,  700  is measured during rotation. Afterward, in step  1865 , a wobble movement of the photomask can be determined from the measured height change h(θ, d 0 ). The method finally ends at  1870 .